{-# LANGUAGE BangPatterns #-}
{-# LANGUAGE EmptyCase #-}
{-# LANGUAGE EmptyDataDecls #-}
{-# LANGUAGE ExistentialQuantification #-}
{-# LANGUAGE NoMonomorphismRestriction #-}
{-# LANGUAGE OverloadedStrings #-}
{-# LANGUAGE PatternSynonyms #-}
{-# LANGUAGE RankNTypes #-}
{-# LANGUAGE ScopedTypeVariables #-}

{-# OPTIONS_GHC -Wno-overlapping-patterns #-}

module MAlonzo.Code.Algebra.Bundles where

import MAlonzo.RTE (coe, erased, AgdaAny, addInt, subInt, mulInt,
                    quotInt, remInt, geqInt, ltInt, eqInt, add64, sub64, mul64, quot64,
                    rem64, lt64, eq64, word64FromNat, word64ToNat)
import qualified MAlonzo.RTE
import qualified Data.Text
import qualified MAlonzo.Code.Agda.Builtin.Equality
import qualified MAlonzo.Code.Agda.Builtin.Sigma
import qualified MAlonzo.Code.Agda.Primitive
import qualified MAlonzo.Code.Algebra.Bundles.Raw
import qualified MAlonzo.Code.Algebra.Structures
import qualified MAlonzo.Code.Data.Irrelevant
import qualified MAlonzo.Code.Data.Sum.Base
import qualified MAlonzo.Code.Relation.Binary.Bundles
import qualified MAlonzo.Code.Relation.Binary.Structures

-- Algebra.Bundles.SuccessorSet
d_SuccessorSet_8 :: p -> p -> ()
d_SuccessorSet_8 p
a0 p
a1 = ()
data T_SuccessorSet_8
  = C_SuccessorSet'46'constructor_227 (AgdaAny -> AgdaAny) AgdaAny
                                      MAlonzo.Code.Algebra.Structures.T_IsSuccessorSet_146
-- Algebra.Bundles.SuccessorSet.Carrier
d_Carrier_24 :: T_SuccessorSet_8 -> ()
d_Carrier_24 :: T_SuccessorSet_8 -> ()
d_Carrier_24 = T_SuccessorSet_8 -> ()
forall a. a
erased
-- Algebra.Bundles.SuccessorSet._≈_
d__'8776'__26 :: T_SuccessorSet_8 -> AgdaAny -> AgdaAny -> ()
d__'8776'__26 :: T_SuccessorSet_8 -> AgdaAny -> AgdaAny -> ()
d__'8776'__26 = T_SuccessorSet_8 -> AgdaAny -> AgdaAny -> ()
forall a. a
erased
-- Algebra.Bundles.SuccessorSet.suc#
d_suc'35'_28 :: T_SuccessorSet_8 -> AgdaAny -> AgdaAny
d_suc'35'_28 :: T_SuccessorSet_8 -> AgdaAny -> AgdaAny
d_suc'35'_28 T_SuccessorSet_8
v0
  = case T_SuccessorSet_8 -> T_SuccessorSet_8
forall a b. a -> b
coe T_SuccessorSet_8
v0 of
      C_SuccessorSet'46'constructor_227 AgdaAny -> AgdaAny
v3 AgdaAny
v4 T_IsSuccessorSet_146
v5 -> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v3
      T_SuccessorSet_8
_ -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.SuccessorSet.zero#
d_zero'35'_30 :: T_SuccessorSet_8 -> AgdaAny
d_zero'35'_30 :: T_SuccessorSet_8 -> AgdaAny
d_zero'35'_30 T_SuccessorSet_8
v0
  = case T_SuccessorSet_8 -> T_SuccessorSet_8
forall a b. a -> b
coe T_SuccessorSet_8
v0 of
      C_SuccessorSet'46'constructor_227 AgdaAny -> AgdaAny
v3 AgdaAny
v4 T_IsSuccessorSet_146
v5 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v4
      T_SuccessorSet_8
_ -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.SuccessorSet.isSuccessorSet
d_isSuccessorSet_32 ::
  T_SuccessorSet_8 ->
  MAlonzo.Code.Algebra.Structures.T_IsSuccessorSet_146
d_isSuccessorSet_32 :: T_SuccessorSet_8 -> T_IsSuccessorSet_146
d_isSuccessorSet_32 T_SuccessorSet_8
v0
  = case T_SuccessorSet_8 -> T_SuccessorSet_8
forall a b. a -> b
coe T_SuccessorSet_8
v0 of
      C_SuccessorSet'46'constructor_227 AgdaAny -> AgdaAny
v3 AgdaAny
v4 T_IsSuccessorSet_146
v5 -> T_IsSuccessorSet_146 -> T_IsSuccessorSet_146
forall a b. a -> b
coe T_IsSuccessorSet_146
v5
      T_SuccessorSet_8
_ -> T_IsSuccessorSet_146
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.SuccessorSet._.isEquivalence
d_isEquivalence_36 ::
  T_SuccessorSet_8 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_36 :: T_SuccessorSet_8 -> T_IsEquivalence_26
d_isEquivalence_36 T_SuccessorSet_8
v0
  = (T_IsSuccessorSet_146 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      T_IsSuccessorSet_146 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_156
      ((T_SuccessorSet_8 -> T_IsSuccessorSet_146) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SuccessorSet_8 -> T_IsSuccessorSet_146
d_isSuccessorSet_32 (T_SuccessorSet_8 -> AgdaAny
forall a b. a -> b
coe T_SuccessorSet_8
v0))
-- Algebra.Bundles.SuccessorSet._.isPartialEquivalence
d_isPartialEquivalence_38 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SuccessorSet_8 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_38 :: () -> () -> T_SuccessorSet_8 -> T_IsPartialEquivalence_16
d_isPartialEquivalence_38 ~()
v0 ~()
v1 T_SuccessorSet_8
v2
  = T_SuccessorSet_8 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_38 T_SuccessorSet_8
v2
du_isPartialEquivalence_38 ::
  T_SuccessorSet_8 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_38 :: T_SuccessorSet_8 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_38 T_SuccessorSet_8
v0
  = let v1 :: T_IsSuccessorSet_146
v1 = T_SuccessorSet_8 -> T_IsSuccessorSet_146
d_isSuccessorSet_32 (T_SuccessorSet_8 -> T_SuccessorSet_8
forall a b. a -> b
coe T_SuccessorSet_8
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      ((T_IsEquivalence_26 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsEquivalence_26 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
         ((T_IsSuccessorSet_146 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSuccessorSet_146 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_156 (T_IsSuccessorSet_146 -> AgdaAny
forall a b. a -> b
coe T_IsSuccessorSet_146
v1)))
-- Algebra.Bundles.SuccessorSet._.refl
d_refl_40 :: T_SuccessorSet_8 -> AgdaAny -> AgdaAny
d_refl_40 :: T_SuccessorSet_8 -> AgdaAny -> AgdaAny
d_refl_40 T_SuccessorSet_8
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_34
      ((T_IsSuccessorSet_146 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSuccessorSet_146 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_156
         ((T_SuccessorSet_8 -> T_IsSuccessorSet_146) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SuccessorSet_8 -> T_IsSuccessorSet_146
d_isSuccessorSet_32 (T_SuccessorSet_8 -> AgdaAny
forall a b. a -> b
coe T_SuccessorSet_8
v0)))
-- Algebra.Bundles.SuccessorSet._.reflexive
d_reflexive_42 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SuccessorSet_8 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_42 :: ()
-> ()
-> T_SuccessorSet_8
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_42 ~()
v0 ~()
v1 T_SuccessorSet_8
v2 = T_SuccessorSet_8 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_42 T_SuccessorSet_8
v2
du_reflexive_42 ::
  T_SuccessorSet_8 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_42 :: T_SuccessorSet_8 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_42 T_SuccessorSet_8
v0
  = let v1 :: T_IsSuccessorSet_146
v1 = T_SuccessorSet_8 -> T_IsSuccessorSet_146
d_isSuccessorSet_32 (T_SuccessorSet_8 -> T_SuccessorSet_8
forall a b. a -> b
coe T_SuccessorSet_8
v0) in
    (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (\ AgdaAny
v2 AgdaAny
v3 AgdaAny
v4 ->
         (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
           T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
           ((T_IsSuccessorSet_146 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSuccessorSet_146 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_156 (T_IsSuccessorSet_146 -> AgdaAny
forall a b. a -> b
coe T_IsSuccessorSet_146
v1))
           AgdaAny
v2)
-- Algebra.Bundles.SuccessorSet._.setoid
d_setoid_44 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SuccessorSet_8 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_44 :: () -> () -> T_SuccessorSet_8 -> T_Setoid_44
d_setoid_44 ~()
v0 ~()
v1 T_SuccessorSet_8
v2 = T_SuccessorSet_8 -> T_Setoid_44
du_setoid_44 T_SuccessorSet_8
v2
du_setoid_44 ::
  T_SuccessorSet_8 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_44 :: T_SuccessorSet_8 -> T_Setoid_44
du_setoid_44 T_SuccessorSet_8
v0
  = (T_IsSuccessorSet_146 -> T_Setoid_44) -> AgdaAny -> T_Setoid_44
forall a b. a -> b
coe
      T_IsSuccessorSet_146 -> T_Setoid_44
MAlonzo.Code.Algebra.Structures.du_setoid_172
      ((T_SuccessorSet_8 -> T_IsSuccessorSet_146) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SuccessorSet_8 -> T_IsSuccessorSet_146
d_isSuccessorSet_32 (T_SuccessorSet_8 -> AgdaAny
forall a b. a -> b
coe T_SuccessorSet_8
v0))
-- Algebra.Bundles.SuccessorSet._.suc#-cong
d_suc'35''45'cong_46 ::
  T_SuccessorSet_8 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_suc'35''45'cong_46 :: T_SuccessorSet_8 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_suc'35''45'cong_46 T_SuccessorSet_8
v0
  = (T_IsSuccessorSet_146 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsSuccessorSet_146 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_suc'35''45'cong_158
      ((T_SuccessorSet_8 -> T_IsSuccessorSet_146) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SuccessorSet_8 -> T_IsSuccessorSet_146
d_isSuccessorSet_32 (T_SuccessorSet_8 -> AgdaAny
forall a b. a -> b
coe T_SuccessorSet_8
v0))
-- Algebra.Bundles.SuccessorSet._.sym
d_sym_48 ::
  T_SuccessorSet_8 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_48 :: T_SuccessorSet_8 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_48 T_SuccessorSet_8
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_36
      ((T_IsSuccessorSet_146 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSuccessorSet_146 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_156
         ((T_SuccessorSet_8 -> T_IsSuccessorSet_146) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SuccessorSet_8 -> T_IsSuccessorSet_146
d_isSuccessorSet_32 (T_SuccessorSet_8 -> AgdaAny
forall a b. a -> b
coe T_SuccessorSet_8
v0)))
-- Algebra.Bundles.SuccessorSet._.trans
d_trans_50 ::
  T_SuccessorSet_8 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_50 :: T_SuccessorSet_8
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_50 T_SuccessorSet_8
v0
  = (T_IsEquivalence_26
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_38
      ((T_IsSuccessorSet_146 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSuccessorSet_146 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_156
         ((T_SuccessorSet_8 -> T_IsSuccessorSet_146) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SuccessorSet_8 -> T_IsSuccessorSet_146
d_isSuccessorSet_32 (T_SuccessorSet_8 -> AgdaAny
forall a b. a -> b
coe T_SuccessorSet_8
v0)))
-- Algebra.Bundles.SuccessorSet.rawSuccessorSet
d_rawSuccessorSet_52 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SuccessorSet_8 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawSuccessorSet_10
d_rawSuccessorSet_52 :: () -> () -> T_SuccessorSet_8 -> T_RawSuccessorSet_10
d_rawSuccessorSet_52 ~()
v0 ~()
v1 T_SuccessorSet_8
v2 = T_SuccessorSet_8 -> T_RawSuccessorSet_10
du_rawSuccessorSet_52 T_SuccessorSet_8
v2
du_rawSuccessorSet_52 ::
  T_SuccessorSet_8 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawSuccessorSet_10
du_rawSuccessorSet_52 :: T_SuccessorSet_8 -> T_RawSuccessorSet_10
du_rawSuccessorSet_52 T_SuccessorSet_8
v0
  = ((AgdaAny -> AgdaAny) -> AgdaAny -> T_RawSuccessorSet_10)
-> (AgdaAny -> AgdaAny) -> AgdaAny -> T_RawSuccessorSet_10
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny) -> AgdaAny -> T_RawSuccessorSet_10
MAlonzo.Code.Algebra.Bundles.Raw.C_RawSuccessorSet'46'constructor_89
      (T_SuccessorSet_8 -> AgdaAny -> AgdaAny
d_suc'35'_28 (T_SuccessorSet_8 -> T_SuccessorSet_8
forall a b. a -> b
coe T_SuccessorSet_8
v0)) (T_SuccessorSet_8 -> AgdaAny
d_zero'35'_30 (T_SuccessorSet_8 -> T_SuccessorSet_8
forall a b. a -> b
coe T_SuccessorSet_8
v0))
-- Algebra.Bundles.SuccessorSet._._≈_
d__'8776'__56 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SuccessorSet_8 -> AgdaAny -> AgdaAny -> ()
d__'8776'__56 :: () -> () -> T_SuccessorSet_8 -> AgdaAny -> AgdaAny -> ()
d__'8776'__56 = () -> () -> T_SuccessorSet_8 -> AgdaAny -> AgdaAny -> ()
forall a. a
erased
-- Algebra.Bundles.SuccessorSet._.Carrier
d_Carrier_58 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 -> T_SuccessorSet_8 -> ()
d_Carrier_58 :: () -> () -> T_SuccessorSet_8 -> ()
d_Carrier_58 = () -> () -> T_SuccessorSet_8 -> ()
forall a. a
erased
-- Algebra.Bundles.SuccessorSet._.suc#
d_suc'35'_60 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SuccessorSet_8 -> AgdaAny -> AgdaAny
d_suc'35'_60 :: () -> () -> T_SuccessorSet_8 -> AgdaAny -> AgdaAny
d_suc'35'_60 ~()
v0 ~()
v1 T_SuccessorSet_8
v2 = T_SuccessorSet_8 -> AgdaAny -> AgdaAny
du_suc'35'_60 T_SuccessorSet_8
v2
du_suc'35'_60 :: T_SuccessorSet_8 -> AgdaAny -> AgdaAny
du_suc'35'_60 :: T_SuccessorSet_8 -> AgdaAny -> AgdaAny
du_suc'35'_60 T_SuccessorSet_8
v0 = (T_SuccessorSet_8 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SuccessorSet_8 -> AgdaAny -> AgdaAny
d_suc'35'_28 (T_SuccessorSet_8 -> AgdaAny
forall a b. a -> b
coe T_SuccessorSet_8
v0)
-- Algebra.Bundles.SuccessorSet._.zero#
d_zero'35'_62 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SuccessorSet_8 -> AgdaAny
d_zero'35'_62 :: () -> () -> T_SuccessorSet_8 -> AgdaAny
d_zero'35'_62 ~()
v0 ~()
v1 T_SuccessorSet_8
v2 = T_SuccessorSet_8 -> AgdaAny
du_zero'35'_62 T_SuccessorSet_8
v2
du_zero'35'_62 :: T_SuccessorSet_8 -> AgdaAny
du_zero'35'_62 :: T_SuccessorSet_8 -> AgdaAny
du_zero'35'_62 T_SuccessorSet_8
v0 = (T_SuccessorSet_8 -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SuccessorSet_8 -> AgdaAny
d_zero'35'_30 (T_SuccessorSet_8 -> AgdaAny
forall a b. a -> b
coe T_SuccessorSet_8
v0)
-- Algebra.Bundles.Magma
d_Magma_68 :: p -> p -> ()
d_Magma_68 p
a0 p
a1 = ()
data T_Magma_68
  = C_Magma'46'constructor_1279 (AgdaAny -> AgdaAny -> AgdaAny)
                                MAlonzo.Code.Algebra.Structures.T_IsMagma_176
-- Algebra.Bundles.Magma.Carrier
d_Carrier_82 :: T_Magma_68 -> ()
d_Carrier_82 :: T_Magma_68 -> ()
d_Carrier_82 = T_Magma_68 -> ()
forall a. a
erased
-- Algebra.Bundles.Magma._≈_
d__'8776'__84 :: T_Magma_68 -> AgdaAny -> AgdaAny -> ()
d__'8776'__84 :: T_Magma_68 -> AgdaAny -> AgdaAny -> ()
d__'8776'__84 = T_Magma_68 -> AgdaAny -> AgdaAny -> ()
forall a. a
erased
-- Algebra.Bundles.Magma._∙_
d__'8729'__86 :: T_Magma_68 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__86 :: T_Magma_68 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__86 T_Magma_68
v0
  = case T_Magma_68 -> T_Magma_68
forall a b. a -> b
coe T_Magma_68
v0 of
      C_Magma'46'constructor_1279 AgdaAny -> AgdaAny -> AgdaAny
v3 T_IsMagma_176
v4 -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v3
      T_Magma_68
_ -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.Magma.isMagma
d_isMagma_88 ::
  T_Magma_68 -> MAlonzo.Code.Algebra.Structures.T_IsMagma_176
d_isMagma_88 :: T_Magma_68 -> T_IsMagma_176
d_isMagma_88 T_Magma_68
v0
  = case T_Magma_68 -> T_Magma_68
forall a b. a -> b
coe T_Magma_68
v0 of
      C_Magma'46'constructor_1279 AgdaAny -> AgdaAny -> AgdaAny
v3 T_IsMagma_176
v4 -> T_IsMagma_176 -> T_IsMagma_176
forall a b. a -> b
coe T_IsMagma_176
v4
      T_Magma_68
_ -> T_IsMagma_176
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.Magma._.isEquivalence
d_isEquivalence_92 ::
  T_Magma_68 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_92 :: T_Magma_68 -> T_IsEquivalence_26
d_isEquivalence_92 T_Magma_68
v0
  = (T_IsMagma_176 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
      ((T_Magma_68 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Magma_68 -> T_IsMagma_176
d_isMagma_88 (T_Magma_68 -> AgdaAny
forall a b. a -> b
coe T_Magma_68
v0))
-- Algebra.Bundles.Magma._.isPartialEquivalence
d_isPartialEquivalence_94 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Magma_68 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_94 :: () -> () -> T_Magma_68 -> T_IsPartialEquivalence_16
d_isPartialEquivalence_94 ~()
v0 ~()
v1 T_Magma_68
v2
  = T_Magma_68 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_94 T_Magma_68
v2
du_isPartialEquivalence_94 ::
  T_Magma_68 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_94 :: T_Magma_68 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_94 T_Magma_68
v0
  = let v1 :: T_IsMagma_176
v1 = T_Magma_68 -> T_IsMagma_176
d_isMagma_88 (T_Magma_68 -> T_Magma_68
forall a b. a -> b
coe T_Magma_68
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      ((T_IsEquivalence_26 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsEquivalence_26 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
         ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v1)))
-- Algebra.Bundles.Magma._.refl
d_refl_96 :: T_Magma_68 -> AgdaAny -> AgdaAny
d_refl_96 :: T_Magma_68 -> AgdaAny -> AgdaAny
d_refl_96 T_Magma_68
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_34
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
         ((T_Magma_68 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Magma_68 -> T_IsMagma_176
d_isMagma_88 (T_Magma_68 -> AgdaAny
forall a b. a -> b
coe T_Magma_68
v0)))
-- Algebra.Bundles.Magma._.reflexive
d_reflexive_98 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Magma_68 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_98 :: ()
-> ()
-> T_Magma_68
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_98 ~()
v0 ~()
v1 T_Magma_68
v2 = T_Magma_68 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_98 T_Magma_68
v2
du_reflexive_98 ::
  T_Magma_68 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_98 :: T_Magma_68 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_98 T_Magma_68
v0
  = let v1 :: T_IsMagma_176
v1 = T_Magma_68 -> T_IsMagma_176
d_isMagma_88 (T_Magma_68 -> T_Magma_68
forall a b. a -> b
coe T_Magma_68
v0) in
    (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (\ AgdaAny
v2 AgdaAny
v3 AgdaAny
v4 ->
         (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
           T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
           ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v1))
           AgdaAny
v2)
-- Algebra.Bundles.Magma._.setoid
d_setoid_100 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Magma_68 -> MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_100 :: () -> () -> T_Magma_68 -> T_Setoid_44
d_setoid_100 ~()
v0 ~()
v1 T_Magma_68
v2 = T_Magma_68 -> T_Setoid_44
du_setoid_100 T_Magma_68
v2
du_setoid_100 ::
  T_Magma_68 -> MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_100 :: T_Magma_68 -> T_Setoid_44
du_setoid_100 T_Magma_68
v0
  = (T_IsMagma_176 -> T_Setoid_44) -> AgdaAny -> T_Setoid_44
forall a b. a -> b
coe
      T_IsMagma_176 -> T_Setoid_44
MAlonzo.Code.Algebra.Structures.du_setoid_200
      ((T_Magma_68 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Magma_68 -> T_IsMagma_176
d_isMagma_88 (T_Magma_68 -> AgdaAny
forall a b. a -> b
coe T_Magma_68
v0))
-- Algebra.Bundles.Magma._.sym
d_sym_102 :: T_Magma_68 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_102 :: T_Magma_68 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_102 T_Magma_68
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_36
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
         ((T_Magma_68 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Magma_68 -> T_IsMagma_176
d_isMagma_88 (T_Magma_68 -> AgdaAny
forall a b. a -> b
coe T_Magma_68
v0)))
-- Algebra.Bundles.Magma._.trans
d_trans_104 ::
  T_Magma_68 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_104 :: T_Magma_68
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_104 T_Magma_68
v0
  = (T_IsEquivalence_26
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_38
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
         ((T_Magma_68 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Magma_68 -> T_IsMagma_176
d_isMagma_88 (T_Magma_68 -> AgdaAny
forall a b. a -> b
coe T_Magma_68
v0)))
-- Algebra.Bundles.Magma._.∙-cong
d_'8729''45'cong_106 ::
  T_Magma_68 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_106 :: T_Magma_68
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_106 T_Magma_68
v0
  = (T_IsMagma_176
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsMagma_176
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_186
      ((T_Magma_68 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Magma_68 -> T_IsMagma_176
d_isMagma_88 (T_Magma_68 -> AgdaAny
forall a b. a -> b
coe T_Magma_68
v0))
-- Algebra.Bundles.Magma._.∙-congʳ
d_'8729''45'cong'691'_108 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Magma_68 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_108 :: ()
-> ()
-> T_Magma_68
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_108 ~()
v0 ~()
v1 T_Magma_68
v2
  = T_Magma_68 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_108 T_Magma_68
v2
du_'8729''45'cong'691'_108 ::
  T_Magma_68 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_108 :: T_Magma_68 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_108 T_Magma_68
v0
  = (T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'691'_206
      ((T_Magma_68 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Magma_68 -> T_IsMagma_176
d_isMagma_88 (T_Magma_68 -> AgdaAny
forall a b. a -> b
coe T_Magma_68
v0))
-- Algebra.Bundles.Magma._.∙-congˡ
d_'8729''45'cong'737'_110 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Magma_68 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_110 :: ()
-> ()
-> T_Magma_68
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_110 ~()
v0 ~()
v1 T_Magma_68
v2
  = T_Magma_68 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_110 T_Magma_68
v2
du_'8729''45'cong'737'_110 ::
  T_Magma_68 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_110 :: T_Magma_68 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_110 T_Magma_68
v0
  = (T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'737'_202
      ((T_Magma_68 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Magma_68 -> T_IsMagma_176
d_isMagma_88 (T_Magma_68 -> AgdaAny
forall a b. a -> b
coe T_Magma_68
v0))
-- Algebra.Bundles.Magma.rawMagma
d_rawMagma_112 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Magma_68 -> MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
d_rawMagma_112 :: () -> () -> T_Magma_68 -> T_RawMagma_36
d_rawMagma_112 ~()
v0 ~()
v1 T_Magma_68
v2 = T_Magma_68 -> T_RawMagma_36
du_rawMagma_112 T_Magma_68
v2
du_rawMagma_112 ::
  T_Magma_68 -> MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
du_rawMagma_112 :: T_Magma_68 -> T_RawMagma_36
du_rawMagma_112 T_Magma_68
v0
  = ((AgdaAny -> AgdaAny -> AgdaAny) -> T_RawMagma_36)
-> (AgdaAny -> AgdaAny -> AgdaAny) -> T_RawMagma_36
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny) -> T_RawMagma_36
MAlonzo.Code.Algebra.Bundles.Raw.C_RawMagma'46'constructor_341
      (T_Magma_68 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__86 (T_Magma_68 -> T_Magma_68
forall a b. a -> b
coe T_Magma_68
v0))
-- Algebra.Bundles.Magma._._≉_
d__'8777'__116 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Magma_68 -> AgdaAny -> AgdaAny -> ()
d__'8777'__116 :: () -> () -> T_Magma_68 -> AgdaAny -> AgdaAny -> ()
d__'8777'__116 = () -> () -> T_Magma_68 -> AgdaAny -> AgdaAny -> ()
forall a. a
erased
-- Algebra.Bundles.SelectiveMagma
d_SelectiveMagma_122 :: p -> p -> ()
d_SelectiveMagma_122 p
a0 p
a1 = ()
data T_SelectiveMagma_122
  = C_SelectiveMagma'46'constructor_2287 (AgdaAny ->
                                          AgdaAny -> AgdaAny)
                                         MAlonzo.Code.Algebra.Structures.T_IsSelectiveMagma_436
-- Algebra.Bundles.SelectiveMagma.Carrier
d_Carrier_136 :: T_SelectiveMagma_122 -> ()
d_Carrier_136 :: T_SelectiveMagma_122 -> ()
d_Carrier_136 = T_SelectiveMagma_122 -> ()
forall a. a
erased
-- Algebra.Bundles.SelectiveMagma._≈_
d__'8776'__138 :: T_SelectiveMagma_122 -> AgdaAny -> AgdaAny -> ()
d__'8776'__138 :: T_SelectiveMagma_122 -> AgdaAny -> AgdaAny -> ()
d__'8776'__138 = T_SelectiveMagma_122 -> AgdaAny -> AgdaAny -> ()
forall a. a
erased
-- Algebra.Bundles.SelectiveMagma._∙_
d__'8729'__140 ::
  T_SelectiveMagma_122 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__140 :: T_SelectiveMagma_122 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__140 T_SelectiveMagma_122
v0
  = case T_SelectiveMagma_122 -> T_SelectiveMagma_122
forall a b. a -> b
coe T_SelectiveMagma_122
v0 of
      C_SelectiveMagma'46'constructor_2287 AgdaAny -> AgdaAny -> AgdaAny
v3 T_IsSelectiveMagma_436
v4 -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v3
      T_SelectiveMagma_122
_ -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.SelectiveMagma.isSelectiveMagma
d_isSelectiveMagma_142 ::
  T_SelectiveMagma_122 ->
  MAlonzo.Code.Algebra.Structures.T_IsSelectiveMagma_436
d_isSelectiveMagma_142 :: T_SelectiveMagma_122 -> T_IsSelectiveMagma_436
d_isSelectiveMagma_142 T_SelectiveMagma_122
v0
  = case T_SelectiveMagma_122 -> T_SelectiveMagma_122
forall a b. a -> b
coe T_SelectiveMagma_122
v0 of
      C_SelectiveMagma'46'constructor_2287 AgdaAny -> AgdaAny -> AgdaAny
v3 T_IsSelectiveMagma_436
v4 -> T_IsSelectiveMagma_436 -> T_IsSelectiveMagma_436
forall a b. a -> b
coe T_IsSelectiveMagma_436
v4
      T_SelectiveMagma_122
_ -> T_IsSelectiveMagma_436
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.SelectiveMagma._.isEquivalence
d_isEquivalence_146 ::
  T_SelectiveMagma_122 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_146 :: T_SelectiveMagma_122 -> T_IsEquivalence_26
d_isEquivalence_146 T_SelectiveMagma_122
v0
  = (T_IsMagma_176 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
      ((T_IsSelectiveMagma_436 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSelectiveMagma_436 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_444
         ((T_SelectiveMagma_122 -> T_IsSelectiveMagma_436)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SelectiveMagma_122 -> T_IsSelectiveMagma_436
d_isSelectiveMagma_142 (T_SelectiveMagma_122 -> AgdaAny
forall a b. a -> b
coe T_SelectiveMagma_122
v0)))
-- Algebra.Bundles.SelectiveMagma._.isMagma
d_isMagma_148 ::
  T_SelectiveMagma_122 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_176
d_isMagma_148 :: T_SelectiveMagma_122 -> T_IsMagma_176
d_isMagma_148 T_SelectiveMagma_122
v0
  = (T_IsSelectiveMagma_436 -> T_IsMagma_176)
-> AgdaAny -> T_IsMagma_176
forall a b. a -> b
coe
      T_IsSelectiveMagma_436 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_444
      ((T_SelectiveMagma_122 -> T_IsSelectiveMagma_436)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SelectiveMagma_122 -> T_IsSelectiveMagma_436
d_isSelectiveMagma_142 (T_SelectiveMagma_122 -> AgdaAny
forall a b. a -> b
coe T_SelectiveMagma_122
v0))
-- Algebra.Bundles.SelectiveMagma._.isPartialEquivalence
d_isPartialEquivalence_150 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SelectiveMagma_122 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_150 :: () -> () -> T_SelectiveMagma_122 -> T_IsPartialEquivalence_16
d_isPartialEquivalence_150 ~()
v0 ~()
v1 T_SelectiveMagma_122
v2
  = T_SelectiveMagma_122 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_150 T_SelectiveMagma_122
v2
du_isPartialEquivalence_150 ::
  T_SelectiveMagma_122 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_150 :: T_SelectiveMagma_122 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_150 T_SelectiveMagma_122
v0
  = let v1 :: T_IsSelectiveMagma_436
v1 = T_SelectiveMagma_122 -> T_IsSelectiveMagma_436
d_isSelectiveMagma_142 (T_SelectiveMagma_122 -> T_SelectiveMagma_122
forall a b. a -> b
coe T_SelectiveMagma_122
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsMagma_176
v2 = T_IsSelectiveMagma_436 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_444 (T_IsSelectiveMagma_436 -> T_IsSelectiveMagma_436
forall a b. a -> b
coe T_IsSelectiveMagma_436
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsEquivalence_26 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsEquivalence_26 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
            ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v2))))
-- Algebra.Bundles.SelectiveMagma._.refl
d_refl_152 :: T_SelectiveMagma_122 -> AgdaAny -> AgdaAny
d_refl_152 :: T_SelectiveMagma_122 -> AgdaAny -> AgdaAny
d_refl_152 T_SelectiveMagma_122
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_34
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
         ((T_IsSelectiveMagma_436 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSelectiveMagma_436 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_444
            ((T_SelectiveMagma_122 -> T_IsSelectiveMagma_436)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SelectiveMagma_122 -> T_IsSelectiveMagma_436
d_isSelectiveMagma_142 (T_SelectiveMagma_122 -> AgdaAny
forall a b. a -> b
coe T_SelectiveMagma_122
v0))))
-- Algebra.Bundles.SelectiveMagma._.reflexive
d_reflexive_154 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SelectiveMagma_122 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_154 :: ()
-> ()
-> T_SelectiveMagma_122
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_154 ~()
v0 ~()
v1 T_SelectiveMagma_122
v2 = T_SelectiveMagma_122
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_154 T_SelectiveMagma_122
v2
du_reflexive_154 ::
  T_SelectiveMagma_122 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_154 :: T_SelectiveMagma_122
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_154 T_SelectiveMagma_122
v0
  = let v1 :: T_IsSelectiveMagma_436
v1 = T_SelectiveMagma_122 -> T_IsSelectiveMagma_436
d_isSelectiveMagma_142 (T_SelectiveMagma_122 -> T_SelectiveMagma_122
forall a b. a -> b
coe T_SelectiveMagma_122
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsMagma_176
v2 = T_IsSelectiveMagma_436 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_444 (T_IsSelectiveMagma_436 -> T_IsSelectiveMagma_436
forall a b. a -> b
coe T_IsSelectiveMagma_436
v1) in
       (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
         (\ AgdaAny
v3 AgdaAny
v4 AgdaAny
v5 ->
            (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
              T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
              ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v2))
              AgdaAny
v3))
-- Algebra.Bundles.SelectiveMagma._.sel
d_sel_156 ::
  T_SelectiveMagma_122 ->
  AgdaAny -> AgdaAny -> MAlonzo.Code.Data.Sum.Base.T__'8846'__30
d_sel_156 :: T_SelectiveMagma_122 -> AgdaAny -> AgdaAny -> T__'8846'__30
d_sel_156 T_SelectiveMagma_122
v0
  = (T_IsSelectiveMagma_436 -> AgdaAny -> AgdaAny -> T__'8846'__30)
-> AgdaAny -> AgdaAny -> AgdaAny -> T__'8846'__30
forall a b. a -> b
coe
      T_IsSelectiveMagma_436 -> AgdaAny -> AgdaAny -> T__'8846'__30
MAlonzo.Code.Algebra.Structures.d_sel_446
      ((T_SelectiveMagma_122 -> T_IsSelectiveMagma_436)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SelectiveMagma_122 -> T_IsSelectiveMagma_436
d_isSelectiveMagma_142 (T_SelectiveMagma_122 -> AgdaAny
forall a b. a -> b
coe T_SelectiveMagma_122
v0))
-- Algebra.Bundles.SelectiveMagma._.setoid
d_setoid_158 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SelectiveMagma_122 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_158 :: () -> () -> T_SelectiveMagma_122 -> T_Setoid_44
d_setoid_158 ~()
v0 ~()
v1 T_SelectiveMagma_122
v2 = T_SelectiveMagma_122 -> T_Setoid_44
du_setoid_158 T_SelectiveMagma_122
v2
du_setoid_158 ::
  T_SelectiveMagma_122 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_158 :: T_SelectiveMagma_122 -> T_Setoid_44
du_setoid_158 T_SelectiveMagma_122
v0
  = let v1 :: T_IsSelectiveMagma_436
v1 = T_SelectiveMagma_122 -> T_IsSelectiveMagma_436
d_isSelectiveMagma_142 (T_SelectiveMagma_122 -> T_SelectiveMagma_122
forall a b. a -> b
coe T_SelectiveMagma_122
v0) in
    AgdaAny -> T_Setoid_44
forall a b. a -> b
coe
      ((T_IsMagma_176 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_Setoid_44
MAlonzo.Code.Algebra.Structures.du_setoid_200
         ((T_IsSelectiveMagma_436 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSelectiveMagma_436 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_444 (T_IsSelectiveMagma_436 -> AgdaAny
forall a b. a -> b
coe T_IsSelectiveMagma_436
v1)))
-- Algebra.Bundles.SelectiveMagma._.sym
d_sym_160 ::
  T_SelectiveMagma_122 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_160 :: T_SelectiveMagma_122 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_160 T_SelectiveMagma_122
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_36
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
         ((T_IsSelectiveMagma_436 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSelectiveMagma_436 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_444
            ((T_SelectiveMagma_122 -> T_IsSelectiveMagma_436)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SelectiveMagma_122 -> T_IsSelectiveMagma_436
d_isSelectiveMagma_142 (T_SelectiveMagma_122 -> AgdaAny
forall a b. a -> b
coe T_SelectiveMagma_122
v0))))
-- Algebra.Bundles.SelectiveMagma._.trans
d_trans_162 ::
  T_SelectiveMagma_122 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_162 :: T_SelectiveMagma_122
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_162 T_SelectiveMagma_122
v0
  = (T_IsEquivalence_26
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_38
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
         ((T_IsSelectiveMagma_436 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSelectiveMagma_436 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_444
            ((T_SelectiveMagma_122 -> T_IsSelectiveMagma_436)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SelectiveMagma_122 -> T_IsSelectiveMagma_436
d_isSelectiveMagma_142 (T_SelectiveMagma_122 -> AgdaAny
forall a b. a -> b
coe T_SelectiveMagma_122
v0))))
-- Algebra.Bundles.SelectiveMagma._.∙-cong
d_'8729''45'cong_164 ::
  T_SelectiveMagma_122 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_164 :: T_SelectiveMagma_122
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_164 T_SelectiveMagma_122
v0
  = (T_IsMagma_176
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsMagma_176
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_186
      ((T_IsSelectiveMagma_436 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSelectiveMagma_436 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_444
         ((T_SelectiveMagma_122 -> T_IsSelectiveMagma_436)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SelectiveMagma_122 -> T_IsSelectiveMagma_436
d_isSelectiveMagma_142 (T_SelectiveMagma_122 -> AgdaAny
forall a b. a -> b
coe T_SelectiveMagma_122
v0)))
-- Algebra.Bundles.SelectiveMagma._.∙-congʳ
d_'8729''45'cong'691'_166 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SelectiveMagma_122 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_166 :: ()
-> ()
-> T_SelectiveMagma_122
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_166 ~()
v0 ~()
v1 T_SelectiveMagma_122
v2
  = T_SelectiveMagma_122
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_166 T_SelectiveMagma_122
v2
du_'8729''45'cong'691'_166 ::
  T_SelectiveMagma_122 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_166 :: T_SelectiveMagma_122
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_166 T_SelectiveMagma_122
v0
  = let v1 :: T_IsSelectiveMagma_436
v1 = T_SelectiveMagma_122 -> T_IsSelectiveMagma_436
d_isSelectiveMagma_142 (T_SelectiveMagma_122 -> T_SelectiveMagma_122
forall a b. a -> b
coe T_SelectiveMagma_122
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'691'_206
         ((T_IsSelectiveMagma_436 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSelectiveMagma_436 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_444 (T_IsSelectiveMagma_436 -> AgdaAny
forall a b. a -> b
coe T_IsSelectiveMagma_436
v1)))
-- Algebra.Bundles.SelectiveMagma._.∙-congˡ
d_'8729''45'cong'737'_168 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SelectiveMagma_122 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_168 :: ()
-> ()
-> T_SelectiveMagma_122
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_168 ~()
v0 ~()
v1 T_SelectiveMagma_122
v2
  = T_SelectiveMagma_122
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_168 T_SelectiveMagma_122
v2
du_'8729''45'cong'737'_168 ::
  T_SelectiveMagma_122 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_168 :: T_SelectiveMagma_122
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_168 T_SelectiveMagma_122
v0
  = let v1 :: T_IsSelectiveMagma_436
v1 = T_SelectiveMagma_122 -> T_IsSelectiveMagma_436
d_isSelectiveMagma_142 (T_SelectiveMagma_122 -> T_SelectiveMagma_122
forall a b. a -> b
coe T_SelectiveMagma_122
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'737'_202
         ((T_IsSelectiveMagma_436 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSelectiveMagma_436 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_444 (T_IsSelectiveMagma_436 -> AgdaAny
forall a b. a -> b
coe T_IsSelectiveMagma_436
v1)))
-- Algebra.Bundles.SelectiveMagma.magma
d_magma_170 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SelectiveMagma_122 -> T_Magma_68
d_magma_170 :: () -> () -> T_SelectiveMagma_122 -> T_Magma_68
d_magma_170 ~()
v0 ~()
v1 T_SelectiveMagma_122
v2 = T_SelectiveMagma_122 -> T_Magma_68
du_magma_170 T_SelectiveMagma_122
v2
du_magma_170 :: T_SelectiveMagma_122 -> T_Magma_68
du_magma_170 :: T_SelectiveMagma_122 -> T_Magma_68
du_magma_170 T_SelectiveMagma_122
v0
  = ((AgdaAny -> AgdaAny -> AgdaAny) -> T_IsMagma_176 -> T_Magma_68)
-> (AgdaAny -> AgdaAny -> AgdaAny) -> T_IsMagma_176 -> T_Magma_68
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny) -> T_IsMagma_176 -> T_Magma_68
C_Magma'46'constructor_1279 (T_SelectiveMagma_122 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__140 (T_SelectiveMagma_122 -> T_SelectiveMagma_122
forall a b. a -> b
coe T_SelectiveMagma_122
v0))
      (T_IsSelectiveMagma_436 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_444
         ((T_SelectiveMagma_122 -> T_IsSelectiveMagma_436)
-> AgdaAny -> T_IsSelectiveMagma_436
forall a b. a -> b
coe T_SelectiveMagma_122 -> T_IsSelectiveMagma_436
d_isSelectiveMagma_142 (T_SelectiveMagma_122 -> AgdaAny
forall a b. a -> b
coe T_SelectiveMagma_122
v0)))
-- Algebra.Bundles.SelectiveMagma._.rawMagma
d_rawMagma_174 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SelectiveMagma_122 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
d_rawMagma_174 :: () -> () -> T_SelectiveMagma_122 -> T_RawMagma_36
d_rawMagma_174 ~()
v0 ~()
v1 T_SelectiveMagma_122
v2 = T_SelectiveMagma_122 -> T_RawMagma_36
du_rawMagma_174 T_SelectiveMagma_122
v2
du_rawMagma_174 ::
  T_SelectiveMagma_122 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
du_rawMagma_174 :: T_SelectiveMagma_122 -> T_RawMagma_36
du_rawMagma_174 T_SelectiveMagma_122
v0
  = (T_Magma_68 -> T_RawMagma_36) -> AgdaAny -> T_RawMagma_36
forall a b. a -> b
coe T_Magma_68 -> T_RawMagma_36
du_rawMagma_112 ((T_SelectiveMagma_122 -> T_Magma_68) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SelectiveMagma_122 -> T_Magma_68
du_magma_170 (T_SelectiveMagma_122 -> AgdaAny
forall a b. a -> b
coe T_SelectiveMagma_122
v0))
-- Algebra.Bundles.CommutativeMagma
d_CommutativeMagma_180 :: p -> p -> ()
d_CommutativeMagma_180 p
a0 p
a1 = ()
data T_CommutativeMagma_180
  = C_CommutativeMagma'46'constructor_3345 (AgdaAny ->
                                            AgdaAny -> AgdaAny)
                                           MAlonzo.Code.Algebra.Structures.T_IsCommutativeMagma_212
-- Algebra.Bundles.CommutativeMagma.Carrier
d_Carrier_194 :: T_CommutativeMagma_180 -> ()
d_Carrier_194 :: T_CommutativeMagma_180 -> ()
d_Carrier_194 = T_CommutativeMagma_180 -> ()
forall a. a
erased
-- Algebra.Bundles.CommutativeMagma._≈_
d__'8776'__196 ::
  T_CommutativeMagma_180 -> AgdaAny -> AgdaAny -> ()
d__'8776'__196 :: T_CommutativeMagma_180 -> AgdaAny -> AgdaAny -> ()
d__'8776'__196 = T_CommutativeMagma_180 -> AgdaAny -> AgdaAny -> ()
forall a. a
erased
-- Algebra.Bundles.CommutativeMagma._∙_
d__'8729'__198 ::
  T_CommutativeMagma_180 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__198 :: T_CommutativeMagma_180 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__198 T_CommutativeMagma_180
v0
  = case T_CommutativeMagma_180 -> T_CommutativeMagma_180
forall a b. a -> b
coe T_CommutativeMagma_180
v0 of
      C_CommutativeMagma'46'constructor_3345 AgdaAny -> AgdaAny -> AgdaAny
v3 T_IsCommutativeMagma_212
v4 -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v3
      T_CommutativeMagma_180
_ -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.CommutativeMagma.isCommutativeMagma
d_isCommutativeMagma_200 ::
  T_CommutativeMagma_180 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMagma_212
d_isCommutativeMagma_200 :: T_CommutativeMagma_180 -> T_IsCommutativeMagma_212
d_isCommutativeMagma_200 T_CommutativeMagma_180
v0
  = case T_CommutativeMagma_180 -> T_CommutativeMagma_180
forall a b. a -> b
coe T_CommutativeMagma_180
v0 of
      C_CommutativeMagma'46'constructor_3345 AgdaAny -> AgdaAny -> AgdaAny
v3 T_IsCommutativeMagma_212
v4 -> T_IsCommutativeMagma_212 -> T_IsCommutativeMagma_212
forall a b. a -> b
coe T_IsCommutativeMagma_212
v4
      T_CommutativeMagma_180
_ -> T_IsCommutativeMagma_212
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.CommutativeMagma._.comm
d_comm_204 ::
  T_CommutativeMagma_180 -> AgdaAny -> AgdaAny -> AgdaAny
d_comm_204 :: T_CommutativeMagma_180 -> AgdaAny -> AgdaAny -> AgdaAny
d_comm_204 T_CommutativeMagma_180
v0
  = (T_IsCommutativeMagma_212 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsCommutativeMagma_212 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_comm_222
      ((T_CommutativeMagma_180 -> T_IsCommutativeMagma_212)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeMagma_180 -> T_IsCommutativeMagma_212
d_isCommutativeMagma_200 (T_CommutativeMagma_180 -> AgdaAny
forall a b. a -> b
coe T_CommutativeMagma_180
v0))
-- Algebra.Bundles.CommutativeMagma._.isEquivalence
d_isEquivalence_206 ::
  T_CommutativeMagma_180 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_206 :: T_CommutativeMagma_180 -> T_IsEquivalence_26
d_isEquivalence_206 T_CommutativeMagma_180
v0
  = (T_IsMagma_176 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
      ((T_IsCommutativeMagma_212 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCommutativeMagma_212 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_220
         ((T_CommutativeMagma_180 -> T_IsCommutativeMagma_212)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeMagma_180 -> T_IsCommutativeMagma_212
d_isCommutativeMagma_200 (T_CommutativeMagma_180 -> AgdaAny
forall a b. a -> b
coe T_CommutativeMagma_180
v0)))
-- Algebra.Bundles.CommutativeMagma._.isMagma
d_isMagma_208 ::
  T_CommutativeMagma_180 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_176
d_isMagma_208 :: T_CommutativeMagma_180 -> T_IsMagma_176
d_isMagma_208 T_CommutativeMagma_180
v0
  = (T_IsCommutativeMagma_212 -> T_IsMagma_176)
-> AgdaAny -> T_IsMagma_176
forall a b. a -> b
coe
      T_IsCommutativeMagma_212 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_220
      ((T_CommutativeMagma_180 -> T_IsCommutativeMagma_212)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeMagma_180 -> T_IsCommutativeMagma_212
d_isCommutativeMagma_200 (T_CommutativeMagma_180 -> AgdaAny
forall a b. a -> b
coe T_CommutativeMagma_180
v0))
-- Algebra.Bundles.CommutativeMagma._.isPartialEquivalence
d_isPartialEquivalence_210 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeMagma_180 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_210 :: () -> () -> T_CommutativeMagma_180 -> T_IsPartialEquivalence_16
d_isPartialEquivalence_210 ~()
v0 ~()
v1 T_CommutativeMagma_180
v2
  = T_CommutativeMagma_180 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_210 T_CommutativeMagma_180
v2
du_isPartialEquivalence_210 ::
  T_CommutativeMagma_180 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_210 :: T_CommutativeMagma_180 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_210 T_CommutativeMagma_180
v0
  = let v1 :: T_IsCommutativeMagma_212
v1 = T_CommutativeMagma_180 -> T_IsCommutativeMagma_212
d_isCommutativeMagma_200 (T_CommutativeMagma_180 -> T_CommutativeMagma_180
forall a b. a -> b
coe T_CommutativeMagma_180
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsMagma_176
v2 = T_IsCommutativeMagma_212 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_220 (T_IsCommutativeMagma_212 -> T_IsCommutativeMagma_212
forall a b. a -> b
coe T_IsCommutativeMagma_212
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsEquivalence_26 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsEquivalence_26 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
            ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v2))))
-- Algebra.Bundles.CommutativeMagma._.refl
d_refl_212 :: T_CommutativeMagma_180 -> AgdaAny -> AgdaAny
d_refl_212 :: T_CommutativeMagma_180 -> AgdaAny -> AgdaAny
d_refl_212 T_CommutativeMagma_180
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_34
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
         ((T_IsCommutativeMagma_212 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCommutativeMagma_212 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_220
            ((T_CommutativeMagma_180 -> T_IsCommutativeMagma_212)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeMagma_180 -> T_IsCommutativeMagma_212
d_isCommutativeMagma_200 (T_CommutativeMagma_180 -> AgdaAny
forall a b. a -> b
coe T_CommutativeMagma_180
v0))))
-- Algebra.Bundles.CommutativeMagma._.reflexive
d_reflexive_214 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeMagma_180 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_214 :: ()
-> ()
-> T_CommutativeMagma_180
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_214 ~()
v0 ~()
v1 T_CommutativeMagma_180
v2 = T_CommutativeMagma_180
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_214 T_CommutativeMagma_180
v2
du_reflexive_214 ::
  T_CommutativeMagma_180 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_214 :: T_CommutativeMagma_180
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_214 T_CommutativeMagma_180
v0
  = let v1 :: T_IsCommutativeMagma_212
v1 = T_CommutativeMagma_180 -> T_IsCommutativeMagma_212
d_isCommutativeMagma_200 (T_CommutativeMagma_180 -> T_CommutativeMagma_180
forall a b. a -> b
coe T_CommutativeMagma_180
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsMagma_176
v2 = T_IsCommutativeMagma_212 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_220 (T_IsCommutativeMagma_212 -> T_IsCommutativeMagma_212
forall a b. a -> b
coe T_IsCommutativeMagma_212
v1) in
       (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
         (\ AgdaAny
v3 AgdaAny
v4 AgdaAny
v5 ->
            (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
              T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
              ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v2))
              AgdaAny
v3))
-- Algebra.Bundles.CommutativeMagma._.setoid
d_setoid_216 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeMagma_180 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_216 :: () -> () -> T_CommutativeMagma_180 -> T_Setoid_44
d_setoid_216 ~()
v0 ~()
v1 T_CommutativeMagma_180
v2 = T_CommutativeMagma_180 -> T_Setoid_44
du_setoid_216 T_CommutativeMagma_180
v2
du_setoid_216 ::
  T_CommutativeMagma_180 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_216 :: T_CommutativeMagma_180 -> T_Setoid_44
du_setoid_216 T_CommutativeMagma_180
v0
  = let v1 :: T_IsCommutativeMagma_212
v1 = T_CommutativeMagma_180 -> T_IsCommutativeMagma_212
d_isCommutativeMagma_200 (T_CommutativeMagma_180 -> T_CommutativeMagma_180
forall a b. a -> b
coe T_CommutativeMagma_180
v0) in
    AgdaAny -> T_Setoid_44
forall a b. a -> b
coe
      ((T_IsMagma_176 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_Setoid_44
MAlonzo.Code.Algebra.Structures.du_setoid_200
         ((T_IsCommutativeMagma_212 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMagma_212 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_220 (T_IsCommutativeMagma_212 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMagma_212
v1)))
-- Algebra.Bundles.CommutativeMagma._.sym
d_sym_218 ::
  T_CommutativeMagma_180 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_218 :: T_CommutativeMagma_180 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_218 T_CommutativeMagma_180
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_36
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
         ((T_IsCommutativeMagma_212 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCommutativeMagma_212 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_220
            ((T_CommutativeMagma_180 -> T_IsCommutativeMagma_212)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeMagma_180 -> T_IsCommutativeMagma_212
d_isCommutativeMagma_200 (T_CommutativeMagma_180 -> AgdaAny
forall a b. a -> b
coe T_CommutativeMagma_180
v0))))
-- Algebra.Bundles.CommutativeMagma._.trans
d_trans_220 ::
  T_CommutativeMagma_180 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_220 :: T_CommutativeMagma_180
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_220 T_CommutativeMagma_180
v0
  = (T_IsEquivalence_26
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_38
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
         ((T_IsCommutativeMagma_212 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCommutativeMagma_212 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_220
            ((T_CommutativeMagma_180 -> T_IsCommutativeMagma_212)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeMagma_180 -> T_IsCommutativeMagma_212
d_isCommutativeMagma_200 (T_CommutativeMagma_180 -> AgdaAny
forall a b. a -> b
coe T_CommutativeMagma_180
v0))))
-- Algebra.Bundles.CommutativeMagma._.∙-cong
d_'8729''45'cong_222 ::
  T_CommutativeMagma_180 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_222 :: T_CommutativeMagma_180
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_222 T_CommutativeMagma_180
v0
  = (T_IsMagma_176
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsMagma_176
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_186
      ((T_IsCommutativeMagma_212 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCommutativeMagma_212 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_220
         ((T_CommutativeMagma_180 -> T_IsCommutativeMagma_212)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeMagma_180 -> T_IsCommutativeMagma_212
d_isCommutativeMagma_200 (T_CommutativeMagma_180 -> AgdaAny
forall a b. a -> b
coe T_CommutativeMagma_180
v0)))
-- Algebra.Bundles.CommutativeMagma._.∙-congʳ
d_'8729''45'cong'691'_224 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeMagma_180 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_224 :: ()
-> ()
-> T_CommutativeMagma_180
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_224 ~()
v0 ~()
v1 T_CommutativeMagma_180
v2
  = T_CommutativeMagma_180
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_224 T_CommutativeMagma_180
v2
du_'8729''45'cong'691'_224 ::
  T_CommutativeMagma_180 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_224 :: T_CommutativeMagma_180
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_224 T_CommutativeMagma_180
v0
  = let v1 :: T_IsCommutativeMagma_212
v1 = T_CommutativeMagma_180 -> T_IsCommutativeMagma_212
d_isCommutativeMagma_200 (T_CommutativeMagma_180 -> T_CommutativeMagma_180
forall a b. a -> b
coe T_CommutativeMagma_180
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'691'_206
         ((T_IsCommutativeMagma_212 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMagma_212 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_220 (T_IsCommutativeMagma_212 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMagma_212
v1)))
-- Algebra.Bundles.CommutativeMagma._.∙-congˡ
d_'8729''45'cong'737'_226 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeMagma_180 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_226 :: ()
-> ()
-> T_CommutativeMagma_180
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_226 ~()
v0 ~()
v1 T_CommutativeMagma_180
v2
  = T_CommutativeMagma_180
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_226 T_CommutativeMagma_180
v2
du_'8729''45'cong'737'_226 ::
  T_CommutativeMagma_180 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_226 :: T_CommutativeMagma_180
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_226 T_CommutativeMagma_180
v0
  = let v1 :: T_IsCommutativeMagma_212
v1 = T_CommutativeMagma_180 -> T_IsCommutativeMagma_212
d_isCommutativeMagma_200 (T_CommutativeMagma_180 -> T_CommutativeMagma_180
forall a b. a -> b
coe T_CommutativeMagma_180
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'737'_202
         ((T_IsCommutativeMagma_212 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMagma_212 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_220 (T_IsCommutativeMagma_212 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMagma_212
v1)))
-- Algebra.Bundles.CommutativeMagma.magma
d_magma_228 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeMagma_180 -> T_Magma_68
d_magma_228 :: () -> () -> T_CommutativeMagma_180 -> T_Magma_68
d_magma_228 ~()
v0 ~()
v1 T_CommutativeMagma_180
v2 = T_CommutativeMagma_180 -> T_Magma_68
du_magma_228 T_CommutativeMagma_180
v2
du_magma_228 :: T_CommutativeMagma_180 -> T_Magma_68
du_magma_228 :: T_CommutativeMagma_180 -> T_Magma_68
du_magma_228 T_CommutativeMagma_180
v0
  = ((AgdaAny -> AgdaAny -> AgdaAny) -> T_IsMagma_176 -> T_Magma_68)
-> (AgdaAny -> AgdaAny -> AgdaAny) -> T_IsMagma_176 -> T_Magma_68
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny) -> T_IsMagma_176 -> T_Magma_68
C_Magma'46'constructor_1279 (T_CommutativeMagma_180 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__198 (T_CommutativeMagma_180 -> T_CommutativeMagma_180
forall a b. a -> b
coe T_CommutativeMagma_180
v0))
      (T_IsCommutativeMagma_212 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_220
         ((T_CommutativeMagma_180 -> T_IsCommutativeMagma_212)
-> AgdaAny -> T_IsCommutativeMagma_212
forall a b. a -> b
coe T_CommutativeMagma_180 -> T_IsCommutativeMagma_212
d_isCommutativeMagma_200 (T_CommutativeMagma_180 -> AgdaAny
forall a b. a -> b
coe T_CommutativeMagma_180
v0)))
-- Algebra.Bundles.CommutativeMagma._.rawMagma
d_rawMagma_232 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeMagma_180 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
d_rawMagma_232 :: () -> () -> T_CommutativeMagma_180 -> T_RawMagma_36
d_rawMagma_232 ~()
v0 ~()
v1 T_CommutativeMagma_180
v2 = T_CommutativeMagma_180 -> T_RawMagma_36
du_rawMagma_232 T_CommutativeMagma_180
v2
du_rawMagma_232 ::
  T_CommutativeMagma_180 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
du_rawMagma_232 :: T_CommutativeMagma_180 -> T_RawMagma_36
du_rawMagma_232 T_CommutativeMagma_180
v0
  = (T_Magma_68 -> T_RawMagma_36) -> AgdaAny -> T_RawMagma_36
forall a b. a -> b
coe T_Magma_68 -> T_RawMagma_36
du_rawMagma_112 ((T_CommutativeMagma_180 -> T_Magma_68) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeMagma_180 -> T_Magma_68
du_magma_228 (T_CommutativeMagma_180 -> AgdaAny
forall a b. a -> b
coe T_CommutativeMagma_180
v0))
-- Algebra.Bundles.IdempotentMagma
d_IdempotentMagma_238 :: p -> p -> ()
d_IdempotentMagma_238 p
a0 p
a1 = ()
data T_IdempotentMagma_238
  = C_IdempotentMagma'46'constructor_4403 (AgdaAny ->
                                           AgdaAny -> AgdaAny)
                                          MAlonzo.Code.Algebra.Structures.T_IsIdempotentMagma_248
-- Algebra.Bundles.IdempotentMagma.Carrier
d_Carrier_252 :: T_IdempotentMagma_238 -> ()
d_Carrier_252 :: T_IdempotentMagma_238 -> ()
d_Carrier_252 = T_IdempotentMagma_238 -> ()
forall a. a
erased
-- Algebra.Bundles.IdempotentMagma._≈_
d__'8776'__254 :: T_IdempotentMagma_238 -> AgdaAny -> AgdaAny -> ()
d__'8776'__254 :: T_IdempotentMagma_238 -> AgdaAny -> AgdaAny -> ()
d__'8776'__254 = T_IdempotentMagma_238 -> AgdaAny -> AgdaAny -> ()
forall a. a
erased
-- Algebra.Bundles.IdempotentMagma._∙_
d__'8729'__256 ::
  T_IdempotentMagma_238 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__256 :: T_IdempotentMagma_238 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__256 T_IdempotentMagma_238
v0
  = case T_IdempotentMagma_238 -> T_IdempotentMagma_238
forall a b. a -> b
coe T_IdempotentMagma_238
v0 of
      C_IdempotentMagma'46'constructor_4403 AgdaAny -> AgdaAny -> AgdaAny
v3 T_IsIdempotentMagma_248
v4 -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v3
      T_IdempotentMagma_238
_ -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.IdempotentMagma.isIdempotentMagma
d_isIdempotentMagma_258 ::
  T_IdempotentMagma_238 ->
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentMagma_248
d_isIdempotentMagma_258 :: T_IdempotentMagma_238 -> T_IsIdempotentMagma_248
d_isIdempotentMagma_258 T_IdempotentMagma_238
v0
  = case T_IdempotentMagma_238 -> T_IdempotentMagma_238
forall a b. a -> b
coe T_IdempotentMagma_238
v0 of
      C_IdempotentMagma'46'constructor_4403 AgdaAny -> AgdaAny -> AgdaAny
v3 T_IsIdempotentMagma_248
v4 -> T_IsIdempotentMagma_248 -> T_IsIdempotentMagma_248
forall a b. a -> b
coe T_IsIdempotentMagma_248
v4
      T_IdempotentMagma_238
_ -> T_IsIdempotentMagma_248
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.IdempotentMagma._.idem
d_idem_262 :: T_IdempotentMagma_238 -> AgdaAny -> AgdaAny
d_idem_262 :: T_IdempotentMagma_238 -> AgdaAny -> AgdaAny
d_idem_262 T_IdempotentMagma_238
v0
  = (T_IsIdempotentMagma_248 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsIdempotentMagma_248 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_idem_258
      ((T_IdempotentMagma_238 -> T_IsIdempotentMagma_248)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IdempotentMagma_238 -> T_IsIdempotentMagma_248
d_isIdempotentMagma_258 (T_IdempotentMagma_238 -> AgdaAny
forall a b. a -> b
coe T_IdempotentMagma_238
v0))
-- Algebra.Bundles.IdempotentMagma._.isEquivalence
d_isEquivalence_264 ::
  T_IdempotentMagma_238 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_264 :: T_IdempotentMagma_238 -> T_IsEquivalence_26
d_isEquivalence_264 T_IdempotentMagma_238
v0
  = (T_IsMagma_176 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
      ((T_IsIdempotentMagma_248 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsIdempotentMagma_248 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_256
         ((T_IdempotentMagma_238 -> T_IsIdempotentMagma_248)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IdempotentMagma_238 -> T_IsIdempotentMagma_248
d_isIdempotentMagma_258 (T_IdempotentMagma_238 -> AgdaAny
forall a b. a -> b
coe T_IdempotentMagma_238
v0)))
-- Algebra.Bundles.IdempotentMagma._.isMagma
d_isMagma_266 ::
  T_IdempotentMagma_238 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_176
d_isMagma_266 :: T_IdempotentMagma_238 -> T_IsMagma_176
d_isMagma_266 T_IdempotentMagma_238
v0
  = (T_IsIdempotentMagma_248 -> T_IsMagma_176)
-> AgdaAny -> T_IsMagma_176
forall a b. a -> b
coe
      T_IsIdempotentMagma_248 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_256
      ((T_IdempotentMagma_238 -> T_IsIdempotentMagma_248)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IdempotentMagma_238 -> T_IsIdempotentMagma_248
d_isIdempotentMagma_258 (T_IdempotentMagma_238 -> AgdaAny
forall a b. a -> b
coe T_IdempotentMagma_238
v0))
-- Algebra.Bundles.IdempotentMagma._.isPartialEquivalence
d_isPartialEquivalence_268 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentMagma_238 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_268 :: () -> () -> T_IdempotentMagma_238 -> T_IsPartialEquivalence_16
d_isPartialEquivalence_268 ~()
v0 ~()
v1 T_IdempotentMagma_238
v2
  = T_IdempotentMagma_238 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_268 T_IdempotentMagma_238
v2
du_isPartialEquivalence_268 ::
  T_IdempotentMagma_238 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_268 :: T_IdempotentMagma_238 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_268 T_IdempotentMagma_238
v0
  = let v1 :: T_IsIdempotentMagma_248
v1 = T_IdempotentMagma_238 -> T_IsIdempotentMagma_248
d_isIdempotentMagma_258 (T_IdempotentMagma_238 -> T_IdempotentMagma_238
forall a b. a -> b
coe T_IdempotentMagma_238
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsMagma_176
v2 = T_IsIdempotentMagma_248 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_256 (T_IsIdempotentMagma_248 -> T_IsIdempotentMagma_248
forall a b. a -> b
coe T_IsIdempotentMagma_248
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsEquivalence_26 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsEquivalence_26 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
            ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v2))))
-- Algebra.Bundles.IdempotentMagma._.refl
d_refl_270 :: T_IdempotentMagma_238 -> AgdaAny -> AgdaAny
d_refl_270 :: T_IdempotentMagma_238 -> AgdaAny -> AgdaAny
d_refl_270 T_IdempotentMagma_238
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_34
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
         ((T_IsIdempotentMagma_248 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsIdempotentMagma_248 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_256
            ((T_IdempotentMagma_238 -> T_IsIdempotentMagma_248)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IdempotentMagma_238 -> T_IsIdempotentMagma_248
d_isIdempotentMagma_258 (T_IdempotentMagma_238 -> AgdaAny
forall a b. a -> b
coe T_IdempotentMagma_238
v0))))
-- Algebra.Bundles.IdempotentMagma._.reflexive
d_reflexive_272 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentMagma_238 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_272 :: ()
-> ()
-> T_IdempotentMagma_238
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_272 ~()
v0 ~()
v1 T_IdempotentMagma_238
v2 = T_IdempotentMagma_238
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_272 T_IdempotentMagma_238
v2
du_reflexive_272 ::
  T_IdempotentMagma_238 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_272 :: T_IdempotentMagma_238
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_272 T_IdempotentMagma_238
v0
  = let v1 :: T_IsIdempotentMagma_248
v1 = T_IdempotentMagma_238 -> T_IsIdempotentMagma_248
d_isIdempotentMagma_258 (T_IdempotentMagma_238 -> T_IdempotentMagma_238
forall a b. a -> b
coe T_IdempotentMagma_238
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsMagma_176
v2 = T_IsIdempotentMagma_248 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_256 (T_IsIdempotentMagma_248 -> T_IsIdempotentMagma_248
forall a b. a -> b
coe T_IsIdempotentMagma_248
v1) in
       (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
         (\ AgdaAny
v3 AgdaAny
v4 AgdaAny
v5 ->
            (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
              T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
              ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v2))
              AgdaAny
v3))
-- Algebra.Bundles.IdempotentMagma._.setoid
d_setoid_274 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentMagma_238 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_274 :: () -> () -> T_IdempotentMagma_238 -> T_Setoid_44
d_setoid_274 ~()
v0 ~()
v1 T_IdempotentMagma_238
v2 = T_IdempotentMagma_238 -> T_Setoid_44
du_setoid_274 T_IdempotentMagma_238
v2
du_setoid_274 ::
  T_IdempotentMagma_238 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_274 :: T_IdempotentMagma_238 -> T_Setoid_44
du_setoid_274 T_IdempotentMagma_238
v0
  = let v1 :: T_IsIdempotentMagma_248
v1 = T_IdempotentMagma_238 -> T_IsIdempotentMagma_248
d_isIdempotentMagma_258 (T_IdempotentMagma_238 -> T_IdempotentMagma_238
forall a b. a -> b
coe T_IdempotentMagma_238
v0) in
    AgdaAny -> T_Setoid_44
forall a b. a -> b
coe
      ((T_IsMagma_176 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_Setoid_44
MAlonzo.Code.Algebra.Structures.du_setoid_200
         ((T_IsIdempotentMagma_248 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentMagma_248 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_256 (T_IsIdempotentMagma_248 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentMagma_248
v1)))
-- Algebra.Bundles.IdempotentMagma._.sym
d_sym_276 ::
  T_IdempotentMagma_238 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_276 :: T_IdempotentMagma_238 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_276 T_IdempotentMagma_238
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_36
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
         ((T_IsIdempotentMagma_248 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsIdempotentMagma_248 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_256
            ((T_IdempotentMagma_238 -> T_IsIdempotentMagma_248)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IdempotentMagma_238 -> T_IsIdempotentMagma_248
d_isIdempotentMagma_258 (T_IdempotentMagma_238 -> AgdaAny
forall a b. a -> b
coe T_IdempotentMagma_238
v0))))
-- Algebra.Bundles.IdempotentMagma._.trans
d_trans_278 ::
  T_IdempotentMagma_238 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_278 :: T_IdempotentMagma_238
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_278 T_IdempotentMagma_238
v0
  = (T_IsEquivalence_26
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_38
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
         ((T_IsIdempotentMagma_248 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsIdempotentMagma_248 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_256
            ((T_IdempotentMagma_238 -> T_IsIdempotentMagma_248)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IdempotentMagma_238 -> T_IsIdempotentMagma_248
d_isIdempotentMagma_258 (T_IdempotentMagma_238 -> AgdaAny
forall a b. a -> b
coe T_IdempotentMagma_238
v0))))
-- Algebra.Bundles.IdempotentMagma._.∙-cong
d_'8729''45'cong_280 ::
  T_IdempotentMagma_238 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_280 :: T_IdempotentMagma_238
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_280 T_IdempotentMagma_238
v0
  = (T_IsMagma_176
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsMagma_176
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_186
      ((T_IsIdempotentMagma_248 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsIdempotentMagma_248 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_256
         ((T_IdempotentMagma_238 -> T_IsIdempotentMagma_248)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IdempotentMagma_238 -> T_IsIdempotentMagma_248
d_isIdempotentMagma_258 (T_IdempotentMagma_238 -> AgdaAny
forall a b. a -> b
coe T_IdempotentMagma_238
v0)))
-- Algebra.Bundles.IdempotentMagma._.∙-congʳ
d_'8729''45'cong'691'_282 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentMagma_238 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_282 :: ()
-> ()
-> T_IdempotentMagma_238
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_282 ~()
v0 ~()
v1 T_IdempotentMagma_238
v2
  = T_IdempotentMagma_238
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_282 T_IdempotentMagma_238
v2
du_'8729''45'cong'691'_282 ::
  T_IdempotentMagma_238 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_282 :: T_IdempotentMagma_238
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_282 T_IdempotentMagma_238
v0
  = let v1 :: T_IsIdempotentMagma_248
v1 = T_IdempotentMagma_238 -> T_IsIdempotentMagma_248
d_isIdempotentMagma_258 (T_IdempotentMagma_238 -> T_IdempotentMagma_238
forall a b. a -> b
coe T_IdempotentMagma_238
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'691'_206
         ((T_IsIdempotentMagma_248 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentMagma_248 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_256 (T_IsIdempotentMagma_248 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentMagma_248
v1)))
-- Algebra.Bundles.IdempotentMagma._.∙-congˡ
d_'8729''45'cong'737'_284 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentMagma_238 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_284 :: ()
-> ()
-> T_IdempotentMagma_238
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_284 ~()
v0 ~()
v1 T_IdempotentMagma_238
v2
  = T_IdempotentMagma_238
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_284 T_IdempotentMagma_238
v2
du_'8729''45'cong'737'_284 ::
  T_IdempotentMagma_238 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_284 :: T_IdempotentMagma_238
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_284 T_IdempotentMagma_238
v0
  = let v1 :: T_IsIdempotentMagma_248
v1 = T_IdempotentMagma_238 -> T_IsIdempotentMagma_248
d_isIdempotentMagma_258 (T_IdempotentMagma_238 -> T_IdempotentMagma_238
forall a b. a -> b
coe T_IdempotentMagma_238
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'737'_202
         ((T_IsIdempotentMagma_248 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentMagma_248 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_256 (T_IsIdempotentMagma_248 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentMagma_248
v1)))
-- Algebra.Bundles.IdempotentMagma.magma
d_magma_286 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentMagma_238 -> T_Magma_68
d_magma_286 :: () -> () -> T_IdempotentMagma_238 -> T_Magma_68
d_magma_286 ~()
v0 ~()
v1 T_IdempotentMagma_238
v2 = T_IdempotentMagma_238 -> T_Magma_68
du_magma_286 T_IdempotentMagma_238
v2
du_magma_286 :: T_IdempotentMagma_238 -> T_Magma_68
du_magma_286 :: T_IdempotentMagma_238 -> T_Magma_68
du_magma_286 T_IdempotentMagma_238
v0
  = ((AgdaAny -> AgdaAny -> AgdaAny) -> T_IsMagma_176 -> T_Magma_68)
-> (AgdaAny -> AgdaAny -> AgdaAny) -> T_IsMagma_176 -> T_Magma_68
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny) -> T_IsMagma_176 -> T_Magma_68
C_Magma'46'constructor_1279 (T_IdempotentMagma_238 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__256 (T_IdempotentMagma_238 -> T_IdempotentMagma_238
forall a b. a -> b
coe T_IdempotentMagma_238
v0))
      (T_IsIdempotentMagma_248 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_256
         ((T_IdempotentMagma_238 -> T_IsIdempotentMagma_248)
-> AgdaAny -> T_IsIdempotentMagma_248
forall a b. a -> b
coe T_IdempotentMagma_238 -> T_IsIdempotentMagma_248
d_isIdempotentMagma_258 (T_IdempotentMagma_238 -> AgdaAny
forall a b. a -> b
coe T_IdempotentMagma_238
v0)))
-- Algebra.Bundles.IdempotentMagma._.rawMagma
d_rawMagma_290 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentMagma_238 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
d_rawMagma_290 :: () -> () -> T_IdempotentMagma_238 -> T_RawMagma_36
d_rawMagma_290 ~()
v0 ~()
v1 T_IdempotentMagma_238
v2 = T_IdempotentMagma_238 -> T_RawMagma_36
du_rawMagma_290 T_IdempotentMagma_238
v2
du_rawMagma_290 ::
  T_IdempotentMagma_238 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
du_rawMagma_290 :: T_IdempotentMagma_238 -> T_RawMagma_36
du_rawMagma_290 T_IdempotentMagma_238
v0
  = (T_Magma_68 -> T_RawMagma_36) -> AgdaAny -> T_RawMagma_36
forall a b. a -> b
coe T_Magma_68 -> T_RawMagma_36
du_rawMagma_112 ((T_IdempotentMagma_238 -> T_Magma_68) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IdempotentMagma_238 -> T_Magma_68
du_magma_286 (T_IdempotentMagma_238 -> AgdaAny
forall a b. a -> b
coe T_IdempotentMagma_238
v0))
-- Algebra.Bundles.AlternativeMagma
d_AlternativeMagma_296 :: p -> p -> ()
d_AlternativeMagma_296 p
a0 p
a1 = ()
data T_AlternativeMagma_296
  = C_AlternativeMagma'46'constructor_5457 (AgdaAny ->
                                            AgdaAny -> AgdaAny)
                                           MAlonzo.Code.Algebra.Structures.T_IsAlternativeMagma_284
-- Algebra.Bundles.AlternativeMagma.Carrier
d_Carrier_310 :: T_AlternativeMagma_296 -> ()
d_Carrier_310 :: T_AlternativeMagma_296 -> ()
d_Carrier_310 = T_AlternativeMagma_296 -> ()
forall a. a
erased
-- Algebra.Bundles.AlternativeMagma._≈_
d__'8776'__312 ::
  T_AlternativeMagma_296 -> AgdaAny -> AgdaAny -> ()
d__'8776'__312 :: T_AlternativeMagma_296 -> AgdaAny -> AgdaAny -> ()
d__'8776'__312 = T_AlternativeMagma_296 -> AgdaAny -> AgdaAny -> ()
forall a. a
erased
-- Algebra.Bundles.AlternativeMagma._∙_
d__'8729'__314 ::
  T_AlternativeMagma_296 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__314 :: T_AlternativeMagma_296 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__314 T_AlternativeMagma_296
v0
  = case T_AlternativeMagma_296 -> T_AlternativeMagma_296
forall a b. a -> b
coe T_AlternativeMagma_296
v0 of
      C_AlternativeMagma'46'constructor_5457 AgdaAny -> AgdaAny -> AgdaAny
v3 T_IsAlternativeMagma_284
v4 -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v3
      T_AlternativeMagma_296
_ -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.AlternativeMagma.isAlternativeMagma
d_isAlternativeMagma_316 ::
  T_AlternativeMagma_296 ->
  MAlonzo.Code.Algebra.Structures.T_IsAlternativeMagma_284
d_isAlternativeMagma_316 :: T_AlternativeMagma_296 -> T_IsAlternativeMagma_284
d_isAlternativeMagma_316 T_AlternativeMagma_296
v0
  = case T_AlternativeMagma_296 -> T_AlternativeMagma_296
forall a b. a -> b
coe T_AlternativeMagma_296
v0 of
      C_AlternativeMagma'46'constructor_5457 AgdaAny -> AgdaAny -> AgdaAny
v3 T_IsAlternativeMagma_284
v4 -> T_IsAlternativeMagma_284 -> T_IsAlternativeMagma_284
forall a b. a -> b
coe T_IsAlternativeMagma_284
v4
      T_AlternativeMagma_296
_ -> T_IsAlternativeMagma_284
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.AlternativeMagma._.alter
d_alter_320 ::
  T_AlternativeMagma_296 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_alter_320 :: T_AlternativeMagma_296 -> T_Σ_14
d_alter_320 T_AlternativeMagma_296
v0
  = (T_IsAlternativeMagma_284 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsAlternativeMagma_284 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_alter_294
      ((T_AlternativeMagma_296 -> T_IsAlternativeMagma_284)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_AlternativeMagma_296 -> T_IsAlternativeMagma_284
d_isAlternativeMagma_316 (T_AlternativeMagma_296 -> AgdaAny
forall a b. a -> b
coe T_AlternativeMagma_296
v0))
-- Algebra.Bundles.AlternativeMagma._.alternativeʳ
d_alternative'691'_322 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_AlternativeMagma_296 -> AgdaAny -> AgdaAny -> AgdaAny
d_alternative'691'_322 :: () -> () -> T_AlternativeMagma_296 -> AgdaAny -> AgdaAny -> AgdaAny
d_alternative'691'_322 ~()
v0 ~()
v1 T_AlternativeMagma_296
v2 = T_AlternativeMagma_296 -> AgdaAny -> AgdaAny -> AgdaAny
du_alternative'691'_322 T_AlternativeMagma_296
v2
du_alternative'691'_322 ::
  T_AlternativeMagma_296 -> AgdaAny -> AgdaAny -> AgdaAny
du_alternative'691'_322 :: T_AlternativeMagma_296 -> AgdaAny -> AgdaAny -> AgdaAny
du_alternative'691'_322 T_AlternativeMagma_296
v0
  = (T_IsAlternativeMagma_284 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsAlternativeMagma_284 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_alternative'691'_320
      ((T_AlternativeMagma_296 -> T_IsAlternativeMagma_284)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_AlternativeMagma_296 -> T_IsAlternativeMagma_284
d_isAlternativeMagma_316 (T_AlternativeMagma_296 -> AgdaAny
forall a b. a -> b
coe T_AlternativeMagma_296
v0))
-- Algebra.Bundles.AlternativeMagma._.alternativeˡ
d_alternative'737'_324 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_AlternativeMagma_296 -> AgdaAny -> AgdaAny -> AgdaAny
d_alternative'737'_324 :: () -> () -> T_AlternativeMagma_296 -> AgdaAny -> AgdaAny -> AgdaAny
d_alternative'737'_324 ~()
v0 ~()
v1 T_AlternativeMagma_296
v2 = T_AlternativeMagma_296 -> AgdaAny -> AgdaAny -> AgdaAny
du_alternative'737'_324 T_AlternativeMagma_296
v2
du_alternative'737'_324 ::
  T_AlternativeMagma_296 -> AgdaAny -> AgdaAny -> AgdaAny
du_alternative'737'_324 :: T_AlternativeMagma_296 -> AgdaAny -> AgdaAny -> AgdaAny
du_alternative'737'_324 T_AlternativeMagma_296
v0
  = (T_IsAlternativeMagma_284 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsAlternativeMagma_284 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_alternative'737'_318
      ((T_AlternativeMagma_296 -> T_IsAlternativeMagma_284)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_AlternativeMagma_296 -> T_IsAlternativeMagma_284
d_isAlternativeMagma_316 (T_AlternativeMagma_296 -> AgdaAny
forall a b. a -> b
coe T_AlternativeMagma_296
v0))
-- Algebra.Bundles.AlternativeMagma._.isEquivalence
d_isEquivalence_326 ::
  T_AlternativeMagma_296 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_326 :: T_AlternativeMagma_296 -> T_IsEquivalence_26
d_isEquivalence_326 T_AlternativeMagma_296
v0
  = (T_IsMagma_176 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
      ((T_IsAlternativeMagma_284 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsAlternativeMagma_284 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_292
         ((T_AlternativeMagma_296 -> T_IsAlternativeMagma_284)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_AlternativeMagma_296 -> T_IsAlternativeMagma_284
d_isAlternativeMagma_316 (T_AlternativeMagma_296 -> AgdaAny
forall a b. a -> b
coe T_AlternativeMagma_296
v0)))
-- Algebra.Bundles.AlternativeMagma._.isMagma
d_isMagma_328 ::
  T_AlternativeMagma_296 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_176
d_isMagma_328 :: T_AlternativeMagma_296 -> T_IsMagma_176
d_isMagma_328 T_AlternativeMagma_296
v0
  = (T_IsAlternativeMagma_284 -> T_IsMagma_176)
-> AgdaAny -> T_IsMagma_176
forall a b. a -> b
coe
      T_IsAlternativeMagma_284 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_292
      ((T_AlternativeMagma_296 -> T_IsAlternativeMagma_284)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_AlternativeMagma_296 -> T_IsAlternativeMagma_284
d_isAlternativeMagma_316 (T_AlternativeMagma_296 -> AgdaAny
forall a b. a -> b
coe T_AlternativeMagma_296
v0))
-- Algebra.Bundles.AlternativeMagma._.isPartialEquivalence
d_isPartialEquivalence_330 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_AlternativeMagma_296 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_330 :: () -> () -> T_AlternativeMagma_296 -> T_IsPartialEquivalence_16
d_isPartialEquivalence_330 ~()
v0 ~()
v1 T_AlternativeMagma_296
v2
  = T_AlternativeMagma_296 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_330 T_AlternativeMagma_296
v2
du_isPartialEquivalence_330 ::
  T_AlternativeMagma_296 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_330 :: T_AlternativeMagma_296 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_330 T_AlternativeMagma_296
v0
  = let v1 :: T_IsAlternativeMagma_284
v1 = T_AlternativeMagma_296 -> T_IsAlternativeMagma_284
d_isAlternativeMagma_316 (T_AlternativeMagma_296 -> T_AlternativeMagma_296
forall a b. a -> b
coe T_AlternativeMagma_296
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsMagma_176
v2 = T_IsAlternativeMagma_284 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_292 (T_IsAlternativeMagma_284 -> T_IsAlternativeMagma_284
forall a b. a -> b
coe T_IsAlternativeMagma_284
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsEquivalence_26 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsEquivalence_26 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
            ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v2))))
-- Algebra.Bundles.AlternativeMagma._.refl
d_refl_332 :: T_AlternativeMagma_296 -> AgdaAny -> AgdaAny
d_refl_332 :: T_AlternativeMagma_296 -> AgdaAny -> AgdaAny
d_refl_332 T_AlternativeMagma_296
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_34
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
         ((T_IsAlternativeMagma_284 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsAlternativeMagma_284 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_292
            ((T_AlternativeMagma_296 -> T_IsAlternativeMagma_284)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_AlternativeMagma_296 -> T_IsAlternativeMagma_284
d_isAlternativeMagma_316 (T_AlternativeMagma_296 -> AgdaAny
forall a b. a -> b
coe T_AlternativeMagma_296
v0))))
-- Algebra.Bundles.AlternativeMagma._.reflexive
d_reflexive_334 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_AlternativeMagma_296 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_334 :: ()
-> ()
-> T_AlternativeMagma_296
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_334 ~()
v0 ~()
v1 T_AlternativeMagma_296
v2 = T_AlternativeMagma_296
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_334 T_AlternativeMagma_296
v2
du_reflexive_334 ::
  T_AlternativeMagma_296 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_334 :: T_AlternativeMagma_296
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_334 T_AlternativeMagma_296
v0
  = let v1 :: T_IsAlternativeMagma_284
v1 = T_AlternativeMagma_296 -> T_IsAlternativeMagma_284
d_isAlternativeMagma_316 (T_AlternativeMagma_296 -> T_AlternativeMagma_296
forall a b. a -> b
coe T_AlternativeMagma_296
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsMagma_176
v2 = T_IsAlternativeMagma_284 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_292 (T_IsAlternativeMagma_284 -> T_IsAlternativeMagma_284
forall a b. a -> b
coe T_IsAlternativeMagma_284
v1) in
       (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
         (\ AgdaAny
v3 AgdaAny
v4 AgdaAny
v5 ->
            (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
              T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
              ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v2))
              AgdaAny
v3))
-- Algebra.Bundles.AlternativeMagma._.setoid
d_setoid_336 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_AlternativeMagma_296 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_336 :: () -> () -> T_AlternativeMagma_296 -> T_Setoid_44
d_setoid_336 ~()
v0 ~()
v1 T_AlternativeMagma_296
v2 = T_AlternativeMagma_296 -> T_Setoid_44
du_setoid_336 T_AlternativeMagma_296
v2
du_setoid_336 ::
  T_AlternativeMagma_296 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_336 :: T_AlternativeMagma_296 -> T_Setoid_44
du_setoid_336 T_AlternativeMagma_296
v0
  = let v1 :: T_IsAlternativeMagma_284
v1 = T_AlternativeMagma_296 -> T_IsAlternativeMagma_284
d_isAlternativeMagma_316 (T_AlternativeMagma_296 -> T_AlternativeMagma_296
forall a b. a -> b
coe T_AlternativeMagma_296
v0) in
    AgdaAny -> T_Setoid_44
forall a b. a -> b
coe
      ((T_IsMagma_176 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_Setoid_44
MAlonzo.Code.Algebra.Structures.du_setoid_200
         ((T_IsAlternativeMagma_284 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAlternativeMagma_284 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_292 (T_IsAlternativeMagma_284 -> AgdaAny
forall a b. a -> b
coe T_IsAlternativeMagma_284
v1)))
-- Algebra.Bundles.AlternativeMagma._.sym
d_sym_338 ::
  T_AlternativeMagma_296 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_338 :: T_AlternativeMagma_296 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_338 T_AlternativeMagma_296
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_36
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
         ((T_IsAlternativeMagma_284 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsAlternativeMagma_284 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_292
            ((T_AlternativeMagma_296 -> T_IsAlternativeMagma_284)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_AlternativeMagma_296 -> T_IsAlternativeMagma_284
d_isAlternativeMagma_316 (T_AlternativeMagma_296 -> AgdaAny
forall a b. a -> b
coe T_AlternativeMagma_296
v0))))
-- Algebra.Bundles.AlternativeMagma._.trans
d_trans_340 ::
  T_AlternativeMagma_296 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_340 :: T_AlternativeMagma_296
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_340 T_AlternativeMagma_296
v0
  = (T_IsEquivalence_26
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_38
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
         ((T_IsAlternativeMagma_284 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsAlternativeMagma_284 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_292
            ((T_AlternativeMagma_296 -> T_IsAlternativeMagma_284)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_AlternativeMagma_296 -> T_IsAlternativeMagma_284
d_isAlternativeMagma_316 (T_AlternativeMagma_296 -> AgdaAny
forall a b. a -> b
coe T_AlternativeMagma_296
v0))))
-- Algebra.Bundles.AlternativeMagma._.∙-cong
d_'8729''45'cong_342 ::
  T_AlternativeMagma_296 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_342 :: T_AlternativeMagma_296
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_342 T_AlternativeMagma_296
v0
  = (T_IsMagma_176
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsMagma_176
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_186
      ((T_IsAlternativeMagma_284 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsAlternativeMagma_284 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_292
         ((T_AlternativeMagma_296 -> T_IsAlternativeMagma_284)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_AlternativeMagma_296 -> T_IsAlternativeMagma_284
d_isAlternativeMagma_316 (T_AlternativeMagma_296 -> AgdaAny
forall a b. a -> b
coe T_AlternativeMagma_296
v0)))
-- Algebra.Bundles.AlternativeMagma._.∙-congʳ
d_'8729''45'cong'691'_344 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_AlternativeMagma_296 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_344 :: ()
-> ()
-> T_AlternativeMagma_296
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_344 ~()
v0 ~()
v1 T_AlternativeMagma_296
v2
  = T_AlternativeMagma_296
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_344 T_AlternativeMagma_296
v2
du_'8729''45'cong'691'_344 ::
  T_AlternativeMagma_296 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_344 :: T_AlternativeMagma_296
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_344 T_AlternativeMagma_296
v0
  = let v1 :: T_IsAlternativeMagma_284
v1 = T_AlternativeMagma_296 -> T_IsAlternativeMagma_284
d_isAlternativeMagma_316 (T_AlternativeMagma_296 -> T_AlternativeMagma_296
forall a b. a -> b
coe T_AlternativeMagma_296
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'691'_206
         ((T_IsAlternativeMagma_284 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAlternativeMagma_284 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_292 (T_IsAlternativeMagma_284 -> AgdaAny
forall a b. a -> b
coe T_IsAlternativeMagma_284
v1)))
-- Algebra.Bundles.AlternativeMagma._.∙-congˡ
d_'8729''45'cong'737'_346 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_AlternativeMagma_296 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_346 :: ()
-> ()
-> T_AlternativeMagma_296
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_346 ~()
v0 ~()
v1 T_AlternativeMagma_296
v2
  = T_AlternativeMagma_296
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_346 T_AlternativeMagma_296
v2
du_'8729''45'cong'737'_346 ::
  T_AlternativeMagma_296 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_346 :: T_AlternativeMagma_296
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_346 T_AlternativeMagma_296
v0
  = let v1 :: T_IsAlternativeMagma_284
v1 = T_AlternativeMagma_296 -> T_IsAlternativeMagma_284
d_isAlternativeMagma_316 (T_AlternativeMagma_296 -> T_AlternativeMagma_296
forall a b. a -> b
coe T_AlternativeMagma_296
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'737'_202
         ((T_IsAlternativeMagma_284 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAlternativeMagma_284 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_292 (T_IsAlternativeMagma_284 -> AgdaAny
forall a b. a -> b
coe T_IsAlternativeMagma_284
v1)))
-- Algebra.Bundles.AlternativeMagma.magma
d_magma_348 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_AlternativeMagma_296 -> T_Magma_68
d_magma_348 :: () -> () -> T_AlternativeMagma_296 -> T_Magma_68
d_magma_348 ~()
v0 ~()
v1 T_AlternativeMagma_296
v2 = T_AlternativeMagma_296 -> T_Magma_68
du_magma_348 T_AlternativeMagma_296
v2
du_magma_348 :: T_AlternativeMagma_296 -> T_Magma_68
du_magma_348 :: T_AlternativeMagma_296 -> T_Magma_68
du_magma_348 T_AlternativeMagma_296
v0
  = ((AgdaAny -> AgdaAny -> AgdaAny) -> T_IsMagma_176 -> T_Magma_68)
-> (AgdaAny -> AgdaAny -> AgdaAny) -> T_IsMagma_176 -> T_Magma_68
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny) -> T_IsMagma_176 -> T_Magma_68
C_Magma'46'constructor_1279 (T_AlternativeMagma_296 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__314 (T_AlternativeMagma_296 -> T_AlternativeMagma_296
forall a b. a -> b
coe T_AlternativeMagma_296
v0))
      (T_IsAlternativeMagma_284 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_292
         ((T_AlternativeMagma_296 -> T_IsAlternativeMagma_284)
-> AgdaAny -> T_IsAlternativeMagma_284
forall a b. a -> b
coe T_AlternativeMagma_296 -> T_IsAlternativeMagma_284
d_isAlternativeMagma_316 (T_AlternativeMagma_296 -> AgdaAny
forall a b. a -> b
coe T_AlternativeMagma_296
v0)))
-- Algebra.Bundles.AlternativeMagma._.rawMagma
d_rawMagma_352 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_AlternativeMagma_296 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
d_rawMagma_352 :: () -> () -> T_AlternativeMagma_296 -> T_RawMagma_36
d_rawMagma_352 ~()
v0 ~()
v1 T_AlternativeMagma_296
v2 = T_AlternativeMagma_296 -> T_RawMagma_36
du_rawMagma_352 T_AlternativeMagma_296
v2
du_rawMagma_352 ::
  T_AlternativeMagma_296 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
du_rawMagma_352 :: T_AlternativeMagma_296 -> T_RawMagma_36
du_rawMagma_352 T_AlternativeMagma_296
v0
  = (T_Magma_68 -> T_RawMagma_36) -> AgdaAny -> T_RawMagma_36
forall a b. a -> b
coe T_Magma_68 -> T_RawMagma_36
du_rawMagma_112 ((T_AlternativeMagma_296 -> T_Magma_68) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_AlternativeMagma_296 -> T_Magma_68
du_magma_348 (T_AlternativeMagma_296 -> AgdaAny
forall a b. a -> b
coe T_AlternativeMagma_296
v0))
-- Algebra.Bundles.FlexibleMagma
d_FlexibleMagma_358 :: p -> p -> ()
d_FlexibleMagma_358 p
a0 p
a1 = ()
data T_FlexibleMagma_358
  = C_FlexibleMagma'46'constructor_6559 (AgdaAny ->
                                         AgdaAny -> AgdaAny)
                                        MAlonzo.Code.Algebra.Structures.T_IsFlexibleMagma_324
-- Algebra.Bundles.FlexibleMagma.Carrier
d_Carrier_372 :: T_FlexibleMagma_358 -> ()
d_Carrier_372 :: T_FlexibleMagma_358 -> ()
d_Carrier_372 = T_FlexibleMagma_358 -> ()
forall a. a
erased
-- Algebra.Bundles.FlexibleMagma._≈_
d__'8776'__374 :: T_FlexibleMagma_358 -> AgdaAny -> AgdaAny -> ()
d__'8776'__374 :: T_FlexibleMagma_358 -> AgdaAny -> AgdaAny -> ()
d__'8776'__374 = T_FlexibleMagma_358 -> AgdaAny -> AgdaAny -> ()
forall a. a
erased
-- Algebra.Bundles.FlexibleMagma._∙_
d__'8729'__376 ::
  T_FlexibleMagma_358 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__376 :: T_FlexibleMagma_358 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__376 T_FlexibleMagma_358
v0
  = case T_FlexibleMagma_358 -> T_FlexibleMagma_358
forall a b. a -> b
coe T_FlexibleMagma_358
v0 of
      C_FlexibleMagma'46'constructor_6559 AgdaAny -> AgdaAny -> AgdaAny
v3 T_IsFlexibleMagma_324
v4 -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v3
      T_FlexibleMagma_358
_ -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.FlexibleMagma.isFlexibleMagma
d_isFlexibleMagma_378 ::
  T_FlexibleMagma_358 ->
  MAlonzo.Code.Algebra.Structures.T_IsFlexibleMagma_324
d_isFlexibleMagma_378 :: T_FlexibleMagma_358 -> T_IsFlexibleMagma_324
d_isFlexibleMagma_378 T_FlexibleMagma_358
v0
  = case T_FlexibleMagma_358 -> T_FlexibleMagma_358
forall a b. a -> b
coe T_FlexibleMagma_358
v0 of
      C_FlexibleMagma'46'constructor_6559 AgdaAny -> AgdaAny -> AgdaAny
v3 T_IsFlexibleMagma_324
v4 -> T_IsFlexibleMagma_324 -> T_IsFlexibleMagma_324
forall a b. a -> b
coe T_IsFlexibleMagma_324
v4
      T_FlexibleMagma_358
_ -> T_IsFlexibleMagma_324
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.FlexibleMagma._.flex
d_flex_382 :: T_FlexibleMagma_358 -> AgdaAny -> AgdaAny -> AgdaAny
d_flex_382 :: T_FlexibleMagma_358 -> AgdaAny -> AgdaAny -> AgdaAny
d_flex_382 T_FlexibleMagma_358
v0
  = (T_IsFlexibleMagma_324 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsFlexibleMagma_324 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_flex_334
      ((T_FlexibleMagma_358 -> T_IsFlexibleMagma_324)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_FlexibleMagma_358 -> T_IsFlexibleMagma_324
d_isFlexibleMagma_378 (T_FlexibleMagma_358 -> AgdaAny
forall a b. a -> b
coe T_FlexibleMagma_358
v0))
-- Algebra.Bundles.FlexibleMagma._.isEquivalence
d_isEquivalence_384 ::
  T_FlexibleMagma_358 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_384 :: T_FlexibleMagma_358 -> T_IsEquivalence_26
d_isEquivalence_384 T_FlexibleMagma_358
v0
  = (T_IsMagma_176 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
      ((T_IsFlexibleMagma_324 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsFlexibleMagma_324 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_332
         ((T_FlexibleMagma_358 -> T_IsFlexibleMagma_324)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_FlexibleMagma_358 -> T_IsFlexibleMagma_324
d_isFlexibleMagma_378 (T_FlexibleMagma_358 -> AgdaAny
forall a b. a -> b
coe T_FlexibleMagma_358
v0)))
-- Algebra.Bundles.FlexibleMagma._.isMagma
d_isMagma_386 ::
  T_FlexibleMagma_358 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_176
d_isMagma_386 :: T_FlexibleMagma_358 -> T_IsMagma_176
d_isMagma_386 T_FlexibleMagma_358
v0
  = (T_IsFlexibleMagma_324 -> T_IsMagma_176)
-> AgdaAny -> T_IsMagma_176
forall a b. a -> b
coe
      T_IsFlexibleMagma_324 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_332
      ((T_FlexibleMagma_358 -> T_IsFlexibleMagma_324)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_FlexibleMagma_358 -> T_IsFlexibleMagma_324
d_isFlexibleMagma_378 (T_FlexibleMagma_358 -> AgdaAny
forall a b. a -> b
coe T_FlexibleMagma_358
v0))
-- Algebra.Bundles.FlexibleMagma._.isPartialEquivalence
d_isPartialEquivalence_388 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_FlexibleMagma_358 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_388 :: () -> () -> T_FlexibleMagma_358 -> T_IsPartialEquivalence_16
d_isPartialEquivalence_388 ~()
v0 ~()
v1 T_FlexibleMagma_358
v2
  = T_FlexibleMagma_358 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_388 T_FlexibleMagma_358
v2
du_isPartialEquivalence_388 ::
  T_FlexibleMagma_358 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_388 :: T_FlexibleMagma_358 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_388 T_FlexibleMagma_358
v0
  = let v1 :: T_IsFlexibleMagma_324
v1 = T_FlexibleMagma_358 -> T_IsFlexibleMagma_324
d_isFlexibleMagma_378 (T_FlexibleMagma_358 -> T_FlexibleMagma_358
forall a b. a -> b
coe T_FlexibleMagma_358
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsMagma_176
v2 = T_IsFlexibleMagma_324 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_332 (T_IsFlexibleMagma_324 -> T_IsFlexibleMagma_324
forall a b. a -> b
coe T_IsFlexibleMagma_324
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsEquivalence_26 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsEquivalence_26 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
            ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v2))))
-- Algebra.Bundles.FlexibleMagma._.refl
d_refl_390 :: T_FlexibleMagma_358 -> AgdaAny -> AgdaAny
d_refl_390 :: T_FlexibleMagma_358 -> AgdaAny -> AgdaAny
d_refl_390 T_FlexibleMagma_358
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_34
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
         ((T_IsFlexibleMagma_324 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsFlexibleMagma_324 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_332
            ((T_FlexibleMagma_358 -> T_IsFlexibleMagma_324)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_FlexibleMagma_358 -> T_IsFlexibleMagma_324
d_isFlexibleMagma_378 (T_FlexibleMagma_358 -> AgdaAny
forall a b. a -> b
coe T_FlexibleMagma_358
v0))))
-- Algebra.Bundles.FlexibleMagma._.reflexive
d_reflexive_392 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_FlexibleMagma_358 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_392 :: ()
-> ()
-> T_FlexibleMagma_358
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_392 ~()
v0 ~()
v1 T_FlexibleMagma_358
v2 = T_FlexibleMagma_358
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_392 T_FlexibleMagma_358
v2
du_reflexive_392 ::
  T_FlexibleMagma_358 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_392 :: T_FlexibleMagma_358
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_392 T_FlexibleMagma_358
v0
  = let v1 :: T_IsFlexibleMagma_324
v1 = T_FlexibleMagma_358 -> T_IsFlexibleMagma_324
d_isFlexibleMagma_378 (T_FlexibleMagma_358 -> T_FlexibleMagma_358
forall a b. a -> b
coe T_FlexibleMagma_358
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsMagma_176
v2 = T_IsFlexibleMagma_324 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_332 (T_IsFlexibleMagma_324 -> T_IsFlexibleMagma_324
forall a b. a -> b
coe T_IsFlexibleMagma_324
v1) in
       (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
         (\ AgdaAny
v3 AgdaAny
v4 AgdaAny
v5 ->
            (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
              T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
              ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v2))
              AgdaAny
v3))
-- Algebra.Bundles.FlexibleMagma._.setoid
d_setoid_394 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_FlexibleMagma_358 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_394 :: () -> () -> T_FlexibleMagma_358 -> T_Setoid_44
d_setoid_394 ~()
v0 ~()
v1 T_FlexibleMagma_358
v2 = T_FlexibleMagma_358 -> T_Setoid_44
du_setoid_394 T_FlexibleMagma_358
v2
du_setoid_394 ::
  T_FlexibleMagma_358 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_394 :: T_FlexibleMagma_358 -> T_Setoid_44
du_setoid_394 T_FlexibleMagma_358
v0
  = let v1 :: T_IsFlexibleMagma_324
v1 = T_FlexibleMagma_358 -> T_IsFlexibleMagma_324
d_isFlexibleMagma_378 (T_FlexibleMagma_358 -> T_FlexibleMagma_358
forall a b. a -> b
coe T_FlexibleMagma_358
v0) in
    AgdaAny -> T_Setoid_44
forall a b. a -> b
coe
      ((T_IsMagma_176 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_Setoid_44
MAlonzo.Code.Algebra.Structures.du_setoid_200
         ((T_IsFlexibleMagma_324 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsFlexibleMagma_324 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_332 (T_IsFlexibleMagma_324 -> AgdaAny
forall a b. a -> b
coe T_IsFlexibleMagma_324
v1)))
-- Algebra.Bundles.FlexibleMagma._.sym
d_sym_396 ::
  T_FlexibleMagma_358 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_396 :: T_FlexibleMagma_358 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_396 T_FlexibleMagma_358
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_36
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
         ((T_IsFlexibleMagma_324 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsFlexibleMagma_324 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_332
            ((T_FlexibleMagma_358 -> T_IsFlexibleMagma_324)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_FlexibleMagma_358 -> T_IsFlexibleMagma_324
d_isFlexibleMagma_378 (T_FlexibleMagma_358 -> AgdaAny
forall a b. a -> b
coe T_FlexibleMagma_358
v0))))
-- Algebra.Bundles.FlexibleMagma._.trans
d_trans_398 ::
  T_FlexibleMagma_358 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_398 :: T_FlexibleMagma_358
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_398 T_FlexibleMagma_358
v0
  = (T_IsEquivalence_26
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_38
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
         ((T_IsFlexibleMagma_324 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsFlexibleMagma_324 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_332
            ((T_FlexibleMagma_358 -> T_IsFlexibleMagma_324)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_FlexibleMagma_358 -> T_IsFlexibleMagma_324
d_isFlexibleMagma_378 (T_FlexibleMagma_358 -> AgdaAny
forall a b. a -> b
coe T_FlexibleMagma_358
v0))))
-- Algebra.Bundles.FlexibleMagma._.∙-cong
d_'8729''45'cong_400 ::
  T_FlexibleMagma_358 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_400 :: T_FlexibleMagma_358
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_400 T_FlexibleMagma_358
v0
  = (T_IsMagma_176
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsMagma_176
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_186
      ((T_IsFlexibleMagma_324 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsFlexibleMagma_324 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_332
         ((T_FlexibleMagma_358 -> T_IsFlexibleMagma_324)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_FlexibleMagma_358 -> T_IsFlexibleMagma_324
d_isFlexibleMagma_378 (T_FlexibleMagma_358 -> AgdaAny
forall a b. a -> b
coe T_FlexibleMagma_358
v0)))
-- Algebra.Bundles.FlexibleMagma._.∙-congʳ
d_'8729''45'cong'691'_402 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_FlexibleMagma_358 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_402 :: ()
-> ()
-> T_FlexibleMagma_358
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_402 ~()
v0 ~()
v1 T_FlexibleMagma_358
v2
  = T_FlexibleMagma_358
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_402 T_FlexibleMagma_358
v2
du_'8729''45'cong'691'_402 ::
  T_FlexibleMagma_358 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_402 :: T_FlexibleMagma_358
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_402 T_FlexibleMagma_358
v0
  = let v1 :: T_IsFlexibleMagma_324
v1 = T_FlexibleMagma_358 -> T_IsFlexibleMagma_324
d_isFlexibleMagma_378 (T_FlexibleMagma_358 -> T_FlexibleMagma_358
forall a b. a -> b
coe T_FlexibleMagma_358
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'691'_206
         ((T_IsFlexibleMagma_324 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsFlexibleMagma_324 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_332 (T_IsFlexibleMagma_324 -> AgdaAny
forall a b. a -> b
coe T_IsFlexibleMagma_324
v1)))
-- Algebra.Bundles.FlexibleMagma._.∙-congˡ
d_'8729''45'cong'737'_404 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_FlexibleMagma_358 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_404 :: ()
-> ()
-> T_FlexibleMagma_358
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_404 ~()
v0 ~()
v1 T_FlexibleMagma_358
v2
  = T_FlexibleMagma_358
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_404 T_FlexibleMagma_358
v2
du_'8729''45'cong'737'_404 ::
  T_FlexibleMagma_358 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_404 :: T_FlexibleMagma_358
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_404 T_FlexibleMagma_358
v0
  = let v1 :: T_IsFlexibleMagma_324
v1 = T_FlexibleMagma_358 -> T_IsFlexibleMagma_324
d_isFlexibleMagma_378 (T_FlexibleMagma_358 -> T_FlexibleMagma_358
forall a b. a -> b
coe T_FlexibleMagma_358
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'737'_202
         ((T_IsFlexibleMagma_324 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsFlexibleMagma_324 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_332 (T_IsFlexibleMagma_324 -> AgdaAny
forall a b. a -> b
coe T_IsFlexibleMagma_324
v1)))
-- Algebra.Bundles.FlexibleMagma.magma
d_magma_406 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_FlexibleMagma_358 -> T_Magma_68
d_magma_406 :: () -> () -> T_FlexibleMagma_358 -> T_Magma_68
d_magma_406 ~()
v0 ~()
v1 T_FlexibleMagma_358
v2 = T_FlexibleMagma_358 -> T_Magma_68
du_magma_406 T_FlexibleMagma_358
v2
du_magma_406 :: T_FlexibleMagma_358 -> T_Magma_68
du_magma_406 :: T_FlexibleMagma_358 -> T_Magma_68
du_magma_406 T_FlexibleMagma_358
v0
  = ((AgdaAny -> AgdaAny -> AgdaAny) -> T_IsMagma_176 -> T_Magma_68)
-> (AgdaAny -> AgdaAny -> AgdaAny) -> T_IsMagma_176 -> T_Magma_68
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny) -> T_IsMagma_176 -> T_Magma_68
C_Magma'46'constructor_1279 (T_FlexibleMagma_358 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__376 (T_FlexibleMagma_358 -> T_FlexibleMagma_358
forall a b. a -> b
coe T_FlexibleMagma_358
v0))
      (T_IsFlexibleMagma_324 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_332
         ((T_FlexibleMagma_358 -> T_IsFlexibleMagma_324)
-> AgdaAny -> T_IsFlexibleMagma_324
forall a b. a -> b
coe T_FlexibleMagma_358 -> T_IsFlexibleMagma_324
d_isFlexibleMagma_378 (T_FlexibleMagma_358 -> AgdaAny
forall a b. a -> b
coe T_FlexibleMagma_358
v0)))
-- Algebra.Bundles.FlexibleMagma._.rawMagma
d_rawMagma_410 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_FlexibleMagma_358 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
d_rawMagma_410 :: () -> () -> T_FlexibleMagma_358 -> T_RawMagma_36
d_rawMagma_410 ~()
v0 ~()
v1 T_FlexibleMagma_358
v2 = T_FlexibleMagma_358 -> T_RawMagma_36
du_rawMagma_410 T_FlexibleMagma_358
v2
du_rawMagma_410 ::
  T_FlexibleMagma_358 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
du_rawMagma_410 :: T_FlexibleMagma_358 -> T_RawMagma_36
du_rawMagma_410 T_FlexibleMagma_358
v0
  = (T_Magma_68 -> T_RawMagma_36) -> AgdaAny -> T_RawMagma_36
forall a b. a -> b
coe T_Magma_68 -> T_RawMagma_36
du_rawMagma_112 ((T_FlexibleMagma_358 -> T_Magma_68) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_FlexibleMagma_358 -> T_Magma_68
du_magma_406 (T_FlexibleMagma_358 -> AgdaAny
forall a b. a -> b
coe T_FlexibleMagma_358
v0))
-- Algebra.Bundles.MedialMagma
d_MedialMagma_416 :: p -> p -> ()
d_MedialMagma_416 p
a0 p
a1 = ()
data T_MedialMagma_416
  = C_MedialMagma'46'constructor_7617 (AgdaAny -> AgdaAny -> AgdaAny)
                                      MAlonzo.Code.Algebra.Structures.T_IsMedialMagma_360
-- Algebra.Bundles.MedialMagma.Carrier
d_Carrier_430 :: T_MedialMagma_416 -> ()
d_Carrier_430 :: T_MedialMagma_416 -> ()
d_Carrier_430 = T_MedialMagma_416 -> ()
forall a. a
erased
-- Algebra.Bundles.MedialMagma._≈_
d__'8776'__432 :: T_MedialMagma_416 -> AgdaAny -> AgdaAny -> ()
d__'8776'__432 :: T_MedialMagma_416 -> AgdaAny -> AgdaAny -> ()
d__'8776'__432 = T_MedialMagma_416 -> AgdaAny -> AgdaAny -> ()
forall a. a
erased
-- Algebra.Bundles.MedialMagma._∙_
d__'8729'__434 ::
  T_MedialMagma_416 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__434 :: T_MedialMagma_416 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__434 T_MedialMagma_416
v0
  = case T_MedialMagma_416 -> T_MedialMagma_416
forall a b. a -> b
coe T_MedialMagma_416
v0 of
      C_MedialMagma'46'constructor_7617 AgdaAny -> AgdaAny -> AgdaAny
v3 T_IsMedialMagma_360
v4 -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v3
      T_MedialMagma_416
_ -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.MedialMagma.isMedialMagma
d_isMedialMagma_436 ::
  T_MedialMagma_416 ->
  MAlonzo.Code.Algebra.Structures.T_IsMedialMagma_360
d_isMedialMagma_436 :: T_MedialMagma_416 -> T_IsMedialMagma_360
d_isMedialMagma_436 T_MedialMagma_416
v0
  = case T_MedialMagma_416 -> T_MedialMagma_416
forall a b. a -> b
coe T_MedialMagma_416
v0 of
      C_MedialMagma'46'constructor_7617 AgdaAny -> AgdaAny -> AgdaAny
v3 T_IsMedialMagma_360
v4 -> T_IsMedialMagma_360 -> T_IsMedialMagma_360
forall a b. a -> b
coe T_IsMedialMagma_360
v4
      T_MedialMagma_416
_ -> T_IsMedialMagma_360
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.MedialMagma._.isEquivalence
d_isEquivalence_440 ::
  T_MedialMagma_416 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_440 :: T_MedialMagma_416 -> T_IsEquivalence_26
d_isEquivalence_440 T_MedialMagma_416
v0
  = (T_IsMagma_176 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
      ((T_IsMedialMagma_360 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMedialMagma_360 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_368
         ((T_MedialMagma_416 -> T_IsMedialMagma_360) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_MedialMagma_416 -> T_IsMedialMagma_360
d_isMedialMagma_436 (T_MedialMagma_416 -> AgdaAny
forall a b. a -> b
coe T_MedialMagma_416
v0)))
-- Algebra.Bundles.MedialMagma._.isMagma
d_isMagma_442 ::
  T_MedialMagma_416 -> MAlonzo.Code.Algebra.Structures.T_IsMagma_176
d_isMagma_442 :: T_MedialMagma_416 -> T_IsMagma_176
d_isMagma_442 T_MedialMagma_416
v0
  = (T_IsMedialMagma_360 -> T_IsMagma_176) -> AgdaAny -> T_IsMagma_176
forall a b. a -> b
coe
      T_IsMedialMagma_360 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_368
      ((T_MedialMagma_416 -> T_IsMedialMagma_360) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_MedialMagma_416 -> T_IsMedialMagma_360
d_isMedialMagma_436 (T_MedialMagma_416 -> AgdaAny
forall a b. a -> b
coe T_MedialMagma_416
v0))
-- Algebra.Bundles.MedialMagma._.isPartialEquivalence
d_isPartialEquivalence_444 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_MedialMagma_416 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_444 :: () -> () -> T_MedialMagma_416 -> T_IsPartialEquivalence_16
d_isPartialEquivalence_444 ~()
v0 ~()
v1 T_MedialMagma_416
v2
  = T_MedialMagma_416 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_444 T_MedialMagma_416
v2
du_isPartialEquivalence_444 ::
  T_MedialMagma_416 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_444 :: T_MedialMagma_416 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_444 T_MedialMagma_416
v0
  = let v1 :: T_IsMedialMagma_360
v1 = T_MedialMagma_416 -> T_IsMedialMagma_360
d_isMedialMagma_436 (T_MedialMagma_416 -> T_MedialMagma_416
forall a b. a -> b
coe T_MedialMagma_416
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsMagma_176
v2 = T_IsMedialMagma_360 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_368 (T_IsMedialMagma_360 -> T_IsMedialMagma_360
forall a b. a -> b
coe T_IsMedialMagma_360
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsEquivalence_26 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsEquivalence_26 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
            ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v2))))
-- Algebra.Bundles.MedialMagma._.medial
d_medial_446 ::
  T_MedialMagma_416 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_medial_446 :: T_MedialMagma_416
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_medial_446 T_MedialMagma_416
v0
  = (T_IsMedialMagma_360
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsMedialMagma_360
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_medial_370
      ((T_MedialMagma_416 -> T_IsMedialMagma_360) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_MedialMagma_416 -> T_IsMedialMagma_360
d_isMedialMagma_436 (T_MedialMagma_416 -> AgdaAny
forall a b. a -> b
coe T_MedialMagma_416
v0))
-- Algebra.Bundles.MedialMagma._.refl
d_refl_448 :: T_MedialMagma_416 -> AgdaAny -> AgdaAny
d_refl_448 :: T_MedialMagma_416 -> AgdaAny -> AgdaAny
d_refl_448 T_MedialMagma_416
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_34
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
         ((T_IsMedialMagma_360 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMedialMagma_360 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_368
            ((T_MedialMagma_416 -> T_IsMedialMagma_360) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_MedialMagma_416 -> T_IsMedialMagma_360
d_isMedialMagma_436 (T_MedialMagma_416 -> AgdaAny
forall a b. a -> b
coe T_MedialMagma_416
v0))))
-- Algebra.Bundles.MedialMagma._.reflexive
d_reflexive_450 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_MedialMagma_416 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_450 :: ()
-> ()
-> T_MedialMagma_416
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_450 ~()
v0 ~()
v1 T_MedialMagma_416
v2 = T_MedialMagma_416 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_450 T_MedialMagma_416
v2
du_reflexive_450 ::
  T_MedialMagma_416 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_450 :: T_MedialMagma_416 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_450 T_MedialMagma_416
v0
  = let v1 :: T_IsMedialMagma_360
v1 = T_MedialMagma_416 -> T_IsMedialMagma_360
d_isMedialMagma_436 (T_MedialMagma_416 -> T_MedialMagma_416
forall a b. a -> b
coe T_MedialMagma_416
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsMagma_176
v2 = T_IsMedialMagma_360 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_368 (T_IsMedialMagma_360 -> T_IsMedialMagma_360
forall a b. a -> b
coe T_IsMedialMagma_360
v1) in
       (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
         (\ AgdaAny
v3 AgdaAny
v4 AgdaAny
v5 ->
            (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
              T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
              ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v2))
              AgdaAny
v3))
-- Algebra.Bundles.MedialMagma._.setoid
d_setoid_452 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_MedialMagma_416 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_452 :: () -> () -> T_MedialMagma_416 -> T_Setoid_44
d_setoid_452 ~()
v0 ~()
v1 T_MedialMagma_416
v2 = T_MedialMagma_416 -> T_Setoid_44
du_setoid_452 T_MedialMagma_416
v2
du_setoid_452 ::
  T_MedialMagma_416 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_452 :: T_MedialMagma_416 -> T_Setoid_44
du_setoid_452 T_MedialMagma_416
v0
  = let v1 :: T_IsMedialMagma_360
v1 = T_MedialMagma_416 -> T_IsMedialMagma_360
d_isMedialMagma_436 (T_MedialMagma_416 -> T_MedialMagma_416
forall a b. a -> b
coe T_MedialMagma_416
v0) in
    AgdaAny -> T_Setoid_44
forall a b. a -> b
coe
      ((T_IsMagma_176 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_Setoid_44
MAlonzo.Code.Algebra.Structures.du_setoid_200
         ((T_IsMedialMagma_360 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMedialMagma_360 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_368 (T_IsMedialMagma_360 -> AgdaAny
forall a b. a -> b
coe T_IsMedialMagma_360
v1)))
-- Algebra.Bundles.MedialMagma._.sym
d_sym_454 ::
  T_MedialMagma_416 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_454 :: T_MedialMagma_416 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_454 T_MedialMagma_416
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_36
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
         ((T_IsMedialMagma_360 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMedialMagma_360 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_368
            ((T_MedialMagma_416 -> T_IsMedialMagma_360) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_MedialMagma_416 -> T_IsMedialMagma_360
d_isMedialMagma_436 (T_MedialMagma_416 -> AgdaAny
forall a b. a -> b
coe T_MedialMagma_416
v0))))
-- Algebra.Bundles.MedialMagma._.trans
d_trans_456 ::
  T_MedialMagma_416 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_456 :: T_MedialMagma_416
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_456 T_MedialMagma_416
v0
  = (T_IsEquivalence_26
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_38
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
         ((T_IsMedialMagma_360 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMedialMagma_360 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_368
            ((T_MedialMagma_416 -> T_IsMedialMagma_360) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_MedialMagma_416 -> T_IsMedialMagma_360
d_isMedialMagma_436 (T_MedialMagma_416 -> AgdaAny
forall a b. a -> b
coe T_MedialMagma_416
v0))))
-- Algebra.Bundles.MedialMagma._.∙-cong
d_'8729''45'cong_458 ::
  T_MedialMagma_416 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_458 :: T_MedialMagma_416
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_458 T_MedialMagma_416
v0
  = (T_IsMagma_176
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsMagma_176
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_186
      ((T_IsMedialMagma_360 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMedialMagma_360 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_368
         ((T_MedialMagma_416 -> T_IsMedialMagma_360) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_MedialMagma_416 -> T_IsMedialMagma_360
d_isMedialMagma_436 (T_MedialMagma_416 -> AgdaAny
forall a b. a -> b
coe T_MedialMagma_416
v0)))
-- Algebra.Bundles.MedialMagma._.∙-congʳ
d_'8729''45'cong'691'_460 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_MedialMagma_416 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_460 :: ()
-> ()
-> T_MedialMagma_416
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_460 ~()
v0 ~()
v1 T_MedialMagma_416
v2
  = T_MedialMagma_416
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_460 T_MedialMagma_416
v2
du_'8729''45'cong'691'_460 ::
  T_MedialMagma_416 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_460 :: T_MedialMagma_416
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_460 T_MedialMagma_416
v0
  = let v1 :: T_IsMedialMagma_360
v1 = T_MedialMagma_416 -> T_IsMedialMagma_360
d_isMedialMagma_436 (T_MedialMagma_416 -> T_MedialMagma_416
forall a b. a -> b
coe T_MedialMagma_416
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'691'_206
         ((T_IsMedialMagma_360 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMedialMagma_360 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_368 (T_IsMedialMagma_360 -> AgdaAny
forall a b. a -> b
coe T_IsMedialMagma_360
v1)))
-- Algebra.Bundles.MedialMagma._.∙-congˡ
d_'8729''45'cong'737'_462 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_MedialMagma_416 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_462 :: ()
-> ()
-> T_MedialMagma_416
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_462 ~()
v0 ~()
v1 T_MedialMagma_416
v2
  = T_MedialMagma_416
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_462 T_MedialMagma_416
v2
du_'8729''45'cong'737'_462 ::
  T_MedialMagma_416 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_462 :: T_MedialMagma_416
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_462 T_MedialMagma_416
v0
  = let v1 :: T_IsMedialMagma_360
v1 = T_MedialMagma_416 -> T_IsMedialMagma_360
d_isMedialMagma_436 (T_MedialMagma_416 -> T_MedialMagma_416
forall a b. a -> b
coe T_MedialMagma_416
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'737'_202
         ((T_IsMedialMagma_360 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMedialMagma_360 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_368 (T_IsMedialMagma_360 -> AgdaAny
forall a b. a -> b
coe T_IsMedialMagma_360
v1)))
-- Algebra.Bundles.MedialMagma.magma
d_magma_464 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_MedialMagma_416 -> T_Magma_68
d_magma_464 :: () -> () -> T_MedialMagma_416 -> T_Magma_68
d_magma_464 ~()
v0 ~()
v1 T_MedialMagma_416
v2 = T_MedialMagma_416 -> T_Magma_68
du_magma_464 T_MedialMagma_416
v2
du_magma_464 :: T_MedialMagma_416 -> T_Magma_68
du_magma_464 :: T_MedialMagma_416 -> T_Magma_68
du_magma_464 T_MedialMagma_416
v0
  = ((AgdaAny -> AgdaAny -> AgdaAny) -> T_IsMagma_176 -> T_Magma_68)
-> (AgdaAny -> AgdaAny -> AgdaAny) -> T_IsMagma_176 -> T_Magma_68
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny) -> T_IsMagma_176 -> T_Magma_68
C_Magma'46'constructor_1279 (T_MedialMagma_416 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__434 (T_MedialMagma_416 -> T_MedialMagma_416
forall a b. a -> b
coe T_MedialMagma_416
v0))
      (T_IsMedialMagma_360 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_368
         ((T_MedialMagma_416 -> T_IsMedialMagma_360)
-> AgdaAny -> T_IsMedialMagma_360
forall a b. a -> b
coe T_MedialMagma_416 -> T_IsMedialMagma_360
d_isMedialMagma_436 (T_MedialMagma_416 -> AgdaAny
forall a b. a -> b
coe T_MedialMagma_416
v0)))
-- Algebra.Bundles.MedialMagma._.rawMagma
d_rawMagma_468 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_MedialMagma_416 -> MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
d_rawMagma_468 :: () -> () -> T_MedialMagma_416 -> T_RawMagma_36
d_rawMagma_468 ~()
v0 ~()
v1 T_MedialMagma_416
v2 = T_MedialMagma_416 -> T_RawMagma_36
du_rawMagma_468 T_MedialMagma_416
v2
du_rawMagma_468 ::
  T_MedialMagma_416 -> MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
du_rawMagma_468 :: T_MedialMagma_416 -> T_RawMagma_36
du_rawMagma_468 T_MedialMagma_416
v0
  = (T_Magma_68 -> T_RawMagma_36) -> AgdaAny -> T_RawMagma_36
forall a b. a -> b
coe T_Magma_68 -> T_RawMagma_36
du_rawMagma_112 ((T_MedialMagma_416 -> T_Magma_68) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_MedialMagma_416 -> T_Magma_68
du_magma_464 (T_MedialMagma_416 -> AgdaAny
forall a b. a -> b
coe T_MedialMagma_416
v0))
-- Algebra.Bundles.SemimedialMagma
d_SemimedialMagma_474 :: p -> p -> ()
d_SemimedialMagma_474 p
a0 p
a1 = ()
data T_SemimedialMagma_474
  = C_SemimedialMagma'46'constructor_8683 (AgdaAny ->
                                           AgdaAny -> AgdaAny)
                                          MAlonzo.Code.Algebra.Structures.T_IsSemimedialMagma_396
-- Algebra.Bundles.SemimedialMagma.Carrier
d_Carrier_488 :: T_SemimedialMagma_474 -> ()
d_Carrier_488 :: T_SemimedialMagma_474 -> ()
d_Carrier_488 = T_SemimedialMagma_474 -> ()
forall a. a
erased
-- Algebra.Bundles.SemimedialMagma._≈_
d__'8776'__490 :: T_SemimedialMagma_474 -> AgdaAny -> AgdaAny -> ()
d__'8776'__490 :: T_SemimedialMagma_474 -> AgdaAny -> AgdaAny -> ()
d__'8776'__490 = T_SemimedialMagma_474 -> AgdaAny -> AgdaAny -> ()
forall a. a
erased
-- Algebra.Bundles.SemimedialMagma._∙_
d__'8729'__492 ::
  T_SemimedialMagma_474 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__492 :: T_SemimedialMagma_474 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__492 T_SemimedialMagma_474
v0
  = case T_SemimedialMagma_474 -> T_SemimedialMagma_474
forall a b. a -> b
coe T_SemimedialMagma_474
v0 of
      C_SemimedialMagma'46'constructor_8683 AgdaAny -> AgdaAny -> AgdaAny
v3 T_IsSemimedialMagma_396
v4 -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v3
      T_SemimedialMagma_474
_ -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.SemimedialMagma.isSemimedialMagma
d_isSemimedialMagma_494 ::
  T_SemimedialMagma_474 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemimedialMagma_396
d_isSemimedialMagma_494 :: T_SemimedialMagma_474 -> T_IsSemimedialMagma_396
d_isSemimedialMagma_494 T_SemimedialMagma_474
v0
  = case T_SemimedialMagma_474 -> T_SemimedialMagma_474
forall a b. a -> b
coe T_SemimedialMagma_474
v0 of
      C_SemimedialMagma'46'constructor_8683 AgdaAny -> AgdaAny -> AgdaAny
v3 T_IsSemimedialMagma_396
v4 -> T_IsSemimedialMagma_396 -> T_IsSemimedialMagma_396
forall a b. a -> b
coe T_IsSemimedialMagma_396
v4
      T_SemimedialMagma_474
_ -> T_IsSemimedialMagma_396
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.SemimedialMagma._.isEquivalence
d_isEquivalence_498 ::
  T_SemimedialMagma_474 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_498 :: T_SemimedialMagma_474 -> T_IsEquivalence_26
d_isEquivalence_498 T_SemimedialMagma_474
v0
  = (T_IsMagma_176 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
      ((T_IsSemimedialMagma_396 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemimedialMagma_396 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_404
         ((T_SemimedialMagma_474 -> T_IsSemimedialMagma_396)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SemimedialMagma_474 -> T_IsSemimedialMagma_396
d_isSemimedialMagma_494 (T_SemimedialMagma_474 -> AgdaAny
forall a b. a -> b
coe T_SemimedialMagma_474
v0)))
-- Algebra.Bundles.SemimedialMagma._.isMagma
d_isMagma_500 ::
  T_SemimedialMagma_474 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_176
d_isMagma_500 :: T_SemimedialMagma_474 -> T_IsMagma_176
d_isMagma_500 T_SemimedialMagma_474
v0
  = (T_IsSemimedialMagma_396 -> T_IsMagma_176)
-> AgdaAny -> T_IsMagma_176
forall a b. a -> b
coe
      T_IsSemimedialMagma_396 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_404
      ((T_SemimedialMagma_474 -> T_IsSemimedialMagma_396)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SemimedialMagma_474 -> T_IsSemimedialMagma_396
d_isSemimedialMagma_494 (T_SemimedialMagma_474 -> AgdaAny
forall a b. a -> b
coe T_SemimedialMagma_474
v0))
-- Algebra.Bundles.SemimedialMagma._.isPartialEquivalence
d_isPartialEquivalence_502 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SemimedialMagma_474 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_502 :: () -> () -> T_SemimedialMagma_474 -> T_IsPartialEquivalence_16
d_isPartialEquivalence_502 ~()
v0 ~()
v1 T_SemimedialMagma_474
v2
  = T_SemimedialMagma_474 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_502 T_SemimedialMagma_474
v2
du_isPartialEquivalence_502 ::
  T_SemimedialMagma_474 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_502 :: T_SemimedialMagma_474 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_502 T_SemimedialMagma_474
v0
  = let v1 :: T_IsSemimedialMagma_396
v1 = T_SemimedialMagma_474 -> T_IsSemimedialMagma_396
d_isSemimedialMagma_494 (T_SemimedialMagma_474 -> T_SemimedialMagma_474
forall a b. a -> b
coe T_SemimedialMagma_474
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsMagma_176
v2 = T_IsSemimedialMagma_396 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_404 (T_IsSemimedialMagma_396 -> T_IsSemimedialMagma_396
forall a b. a -> b
coe T_IsSemimedialMagma_396
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsEquivalence_26 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsEquivalence_26 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
            ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v2))))
-- Algebra.Bundles.SemimedialMagma._.refl
d_refl_504 :: T_SemimedialMagma_474 -> AgdaAny -> AgdaAny
d_refl_504 :: T_SemimedialMagma_474 -> AgdaAny -> AgdaAny
d_refl_504 T_SemimedialMagma_474
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_34
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
         ((T_IsSemimedialMagma_396 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemimedialMagma_396 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_404
            ((T_SemimedialMagma_474 -> T_IsSemimedialMagma_396)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SemimedialMagma_474 -> T_IsSemimedialMagma_396
d_isSemimedialMagma_494 (T_SemimedialMagma_474 -> AgdaAny
forall a b. a -> b
coe T_SemimedialMagma_474
v0))))
-- Algebra.Bundles.SemimedialMagma._.reflexive
d_reflexive_506 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SemimedialMagma_474 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_506 :: ()
-> ()
-> T_SemimedialMagma_474
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_506 ~()
v0 ~()
v1 T_SemimedialMagma_474
v2 = T_SemimedialMagma_474
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_506 T_SemimedialMagma_474
v2
du_reflexive_506 ::
  T_SemimedialMagma_474 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_506 :: T_SemimedialMagma_474
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_506 T_SemimedialMagma_474
v0
  = let v1 :: T_IsSemimedialMagma_396
v1 = T_SemimedialMagma_474 -> T_IsSemimedialMagma_396
d_isSemimedialMagma_494 (T_SemimedialMagma_474 -> T_SemimedialMagma_474
forall a b. a -> b
coe T_SemimedialMagma_474
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsMagma_176
v2 = T_IsSemimedialMagma_396 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_404 (T_IsSemimedialMagma_396 -> T_IsSemimedialMagma_396
forall a b. a -> b
coe T_IsSemimedialMagma_396
v1) in
       (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
         (\ AgdaAny
v3 AgdaAny
v4 AgdaAny
v5 ->
            (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
              T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
              ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v2))
              AgdaAny
v3))
-- Algebra.Bundles.SemimedialMagma._.semiMedial
d_semiMedial_508 ::
  T_SemimedialMagma_474 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_semiMedial_508 :: T_SemimedialMagma_474 -> T_Σ_14
d_semiMedial_508 T_SemimedialMagma_474
v0
  = (T_IsSemimedialMagma_396 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsSemimedialMagma_396 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_semiMedial_406
      ((T_SemimedialMagma_474 -> T_IsSemimedialMagma_396)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SemimedialMagma_474 -> T_IsSemimedialMagma_396
d_isSemimedialMagma_494 (T_SemimedialMagma_474 -> AgdaAny
forall a b. a -> b
coe T_SemimedialMagma_474
v0))
-- Algebra.Bundles.SemimedialMagma._.semimedialʳ
d_semimedial'691'_510 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SemimedialMagma_474 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_semimedial'691'_510 :: ()
-> ()
-> T_SemimedialMagma_474
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_semimedial'691'_510 ~()
v0 ~()
v1 T_SemimedialMagma_474
v2 = T_SemimedialMagma_474 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_semimedial'691'_510 T_SemimedialMagma_474
v2
du_semimedial'691'_510 ::
  T_SemimedialMagma_474 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_semimedial'691'_510 :: T_SemimedialMagma_474 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_semimedial'691'_510 T_SemimedialMagma_474
v0
  = (T_IsSemimedialMagma_396
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsSemimedialMagma_396 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_semimedial'691'_432
      ((T_SemimedialMagma_474 -> T_IsSemimedialMagma_396)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SemimedialMagma_474 -> T_IsSemimedialMagma_396
d_isSemimedialMagma_494 (T_SemimedialMagma_474 -> AgdaAny
forall a b. a -> b
coe T_SemimedialMagma_474
v0))
-- Algebra.Bundles.SemimedialMagma._.semimedialˡ
d_semimedial'737'_512 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SemimedialMagma_474 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_semimedial'737'_512 :: ()
-> ()
-> T_SemimedialMagma_474
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_semimedial'737'_512 ~()
v0 ~()
v1 T_SemimedialMagma_474
v2 = T_SemimedialMagma_474 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_semimedial'737'_512 T_SemimedialMagma_474
v2
du_semimedial'737'_512 ::
  T_SemimedialMagma_474 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_semimedial'737'_512 :: T_SemimedialMagma_474 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_semimedial'737'_512 T_SemimedialMagma_474
v0
  = (T_IsSemimedialMagma_396
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsSemimedialMagma_396 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_semimedial'737'_430
      ((T_SemimedialMagma_474 -> T_IsSemimedialMagma_396)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SemimedialMagma_474 -> T_IsSemimedialMagma_396
d_isSemimedialMagma_494 (T_SemimedialMagma_474 -> AgdaAny
forall a b. a -> b
coe T_SemimedialMagma_474
v0))
-- Algebra.Bundles.SemimedialMagma._.setoid
d_setoid_514 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SemimedialMagma_474 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_514 :: () -> () -> T_SemimedialMagma_474 -> T_Setoid_44
d_setoid_514 ~()
v0 ~()
v1 T_SemimedialMagma_474
v2 = T_SemimedialMagma_474 -> T_Setoid_44
du_setoid_514 T_SemimedialMagma_474
v2
du_setoid_514 ::
  T_SemimedialMagma_474 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_514 :: T_SemimedialMagma_474 -> T_Setoid_44
du_setoid_514 T_SemimedialMagma_474
v0
  = let v1 :: T_IsSemimedialMagma_396
v1 = T_SemimedialMagma_474 -> T_IsSemimedialMagma_396
d_isSemimedialMagma_494 (T_SemimedialMagma_474 -> T_SemimedialMagma_474
forall a b. a -> b
coe T_SemimedialMagma_474
v0) in
    AgdaAny -> T_Setoid_44
forall a b. a -> b
coe
      ((T_IsMagma_176 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_Setoid_44
MAlonzo.Code.Algebra.Structures.du_setoid_200
         ((T_IsSemimedialMagma_396 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemimedialMagma_396 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_404 (T_IsSemimedialMagma_396 -> AgdaAny
forall a b. a -> b
coe T_IsSemimedialMagma_396
v1)))
-- Algebra.Bundles.SemimedialMagma._.sym
d_sym_516 ::
  T_SemimedialMagma_474 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_516 :: T_SemimedialMagma_474 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_516 T_SemimedialMagma_474
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_36
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
         ((T_IsSemimedialMagma_396 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemimedialMagma_396 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_404
            ((T_SemimedialMagma_474 -> T_IsSemimedialMagma_396)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SemimedialMagma_474 -> T_IsSemimedialMagma_396
d_isSemimedialMagma_494 (T_SemimedialMagma_474 -> AgdaAny
forall a b. a -> b
coe T_SemimedialMagma_474
v0))))
-- Algebra.Bundles.SemimedialMagma._.trans
d_trans_518 ::
  T_SemimedialMagma_474 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_518 :: T_SemimedialMagma_474
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_518 T_SemimedialMagma_474
v0
  = (T_IsEquivalence_26
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_38
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
         ((T_IsSemimedialMagma_396 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemimedialMagma_396 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_404
            ((T_SemimedialMagma_474 -> T_IsSemimedialMagma_396)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SemimedialMagma_474 -> T_IsSemimedialMagma_396
d_isSemimedialMagma_494 (T_SemimedialMagma_474 -> AgdaAny
forall a b. a -> b
coe T_SemimedialMagma_474
v0))))
-- Algebra.Bundles.SemimedialMagma._.∙-cong
d_'8729''45'cong_520 ::
  T_SemimedialMagma_474 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_520 :: T_SemimedialMagma_474
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_520 T_SemimedialMagma_474
v0
  = (T_IsMagma_176
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsMagma_176
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_186
      ((T_IsSemimedialMagma_396 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemimedialMagma_396 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_404
         ((T_SemimedialMagma_474 -> T_IsSemimedialMagma_396)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SemimedialMagma_474 -> T_IsSemimedialMagma_396
d_isSemimedialMagma_494 (T_SemimedialMagma_474 -> AgdaAny
forall a b. a -> b
coe T_SemimedialMagma_474
v0)))
-- Algebra.Bundles.SemimedialMagma._.∙-congʳ
d_'8729''45'cong'691'_522 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SemimedialMagma_474 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_522 :: ()
-> ()
-> T_SemimedialMagma_474
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_522 ~()
v0 ~()
v1 T_SemimedialMagma_474
v2
  = T_SemimedialMagma_474
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_522 T_SemimedialMagma_474
v2
du_'8729''45'cong'691'_522 ::
  T_SemimedialMagma_474 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_522 :: T_SemimedialMagma_474
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_522 T_SemimedialMagma_474
v0
  = let v1 :: T_IsSemimedialMagma_396
v1 = T_SemimedialMagma_474 -> T_IsSemimedialMagma_396
d_isSemimedialMagma_494 (T_SemimedialMagma_474 -> T_SemimedialMagma_474
forall a b. a -> b
coe T_SemimedialMagma_474
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'691'_206
         ((T_IsSemimedialMagma_396 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemimedialMagma_396 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_404 (T_IsSemimedialMagma_396 -> AgdaAny
forall a b. a -> b
coe T_IsSemimedialMagma_396
v1)))
-- Algebra.Bundles.SemimedialMagma._.∙-congˡ
d_'8729''45'cong'737'_524 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SemimedialMagma_474 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_524 :: ()
-> ()
-> T_SemimedialMagma_474
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_524 ~()
v0 ~()
v1 T_SemimedialMagma_474
v2
  = T_SemimedialMagma_474
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_524 T_SemimedialMagma_474
v2
du_'8729''45'cong'737'_524 ::
  T_SemimedialMagma_474 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_524 :: T_SemimedialMagma_474
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_524 T_SemimedialMagma_474
v0
  = let v1 :: T_IsSemimedialMagma_396
v1 = T_SemimedialMagma_474 -> T_IsSemimedialMagma_396
d_isSemimedialMagma_494 (T_SemimedialMagma_474 -> T_SemimedialMagma_474
forall a b. a -> b
coe T_SemimedialMagma_474
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'737'_202
         ((T_IsSemimedialMagma_396 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemimedialMagma_396 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_404 (T_IsSemimedialMagma_396 -> AgdaAny
forall a b. a -> b
coe T_IsSemimedialMagma_396
v1)))
-- Algebra.Bundles.SemimedialMagma.magma
d_magma_526 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SemimedialMagma_474 -> T_Magma_68
d_magma_526 :: () -> () -> T_SemimedialMagma_474 -> T_Magma_68
d_magma_526 ~()
v0 ~()
v1 T_SemimedialMagma_474
v2 = T_SemimedialMagma_474 -> T_Magma_68
du_magma_526 T_SemimedialMagma_474
v2
du_magma_526 :: T_SemimedialMagma_474 -> T_Magma_68
du_magma_526 :: T_SemimedialMagma_474 -> T_Magma_68
du_magma_526 T_SemimedialMagma_474
v0
  = ((AgdaAny -> AgdaAny -> AgdaAny) -> T_IsMagma_176 -> T_Magma_68)
-> (AgdaAny -> AgdaAny -> AgdaAny) -> T_IsMagma_176 -> T_Magma_68
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny) -> T_IsMagma_176 -> T_Magma_68
C_Magma'46'constructor_1279 (T_SemimedialMagma_474 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__492 (T_SemimedialMagma_474 -> T_SemimedialMagma_474
forall a b. a -> b
coe T_SemimedialMagma_474
v0))
      (T_IsSemimedialMagma_396 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_404
         ((T_SemimedialMagma_474 -> T_IsSemimedialMagma_396)
-> AgdaAny -> T_IsSemimedialMagma_396
forall a b. a -> b
coe T_SemimedialMagma_474 -> T_IsSemimedialMagma_396
d_isSemimedialMagma_494 (T_SemimedialMagma_474 -> AgdaAny
forall a b. a -> b
coe T_SemimedialMagma_474
v0)))
-- Algebra.Bundles.SemimedialMagma._.rawMagma
d_rawMagma_530 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SemimedialMagma_474 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
d_rawMagma_530 :: () -> () -> T_SemimedialMagma_474 -> T_RawMagma_36
d_rawMagma_530 ~()
v0 ~()
v1 T_SemimedialMagma_474
v2 = T_SemimedialMagma_474 -> T_RawMagma_36
du_rawMagma_530 T_SemimedialMagma_474
v2
du_rawMagma_530 ::
  T_SemimedialMagma_474 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
du_rawMagma_530 :: T_SemimedialMagma_474 -> T_RawMagma_36
du_rawMagma_530 T_SemimedialMagma_474
v0
  = (T_Magma_68 -> T_RawMagma_36) -> AgdaAny -> T_RawMagma_36
forall a b. a -> b
coe T_Magma_68 -> T_RawMagma_36
du_rawMagma_112 ((T_SemimedialMagma_474 -> T_Magma_68) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SemimedialMagma_474 -> T_Magma_68
du_magma_526 (T_SemimedialMagma_474 -> AgdaAny
forall a b. a -> b
coe T_SemimedialMagma_474
v0))
-- Algebra.Bundles.Semigroup
d_Semigroup_536 :: p -> p -> ()
d_Semigroup_536 p
a0 p
a1 = ()
data T_Semigroup_536
  = C_Semigroup'46'constructor_9793 (AgdaAny -> AgdaAny -> AgdaAny)
                                    MAlonzo.Code.Algebra.Structures.T_IsSemigroup_472
-- Algebra.Bundles.Semigroup.Carrier
d_Carrier_550 :: T_Semigroup_536 -> ()
d_Carrier_550 :: T_Semigroup_536 -> ()
d_Carrier_550 = T_Semigroup_536 -> ()
forall a. a
erased
-- Algebra.Bundles.Semigroup._≈_
d__'8776'__552 :: T_Semigroup_536 -> AgdaAny -> AgdaAny -> ()
d__'8776'__552 :: T_Semigroup_536 -> AgdaAny -> AgdaAny -> ()
d__'8776'__552 = T_Semigroup_536 -> AgdaAny -> AgdaAny -> ()
forall a. a
erased
-- Algebra.Bundles.Semigroup._∙_
d__'8729'__554 :: T_Semigroup_536 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__554 :: T_Semigroup_536 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__554 T_Semigroup_536
v0
  = case T_Semigroup_536 -> T_Semigroup_536
forall a b. a -> b
coe T_Semigroup_536
v0 of
      C_Semigroup'46'constructor_9793 AgdaAny -> AgdaAny -> AgdaAny
v3 T_IsSemigroup_472
v4 -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v3
      T_Semigroup_536
_ -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.Semigroup.isSemigroup
d_isSemigroup_556 ::
  T_Semigroup_536 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_472
d_isSemigroup_556 :: T_Semigroup_536 -> T_IsSemigroup_472
d_isSemigroup_556 T_Semigroup_536
v0
  = case T_Semigroup_536 -> T_Semigroup_536
forall a b. a -> b
coe T_Semigroup_536
v0 of
      C_Semigroup'46'constructor_9793 AgdaAny -> AgdaAny -> AgdaAny
v3 T_IsSemigroup_472
v4 -> T_IsSemigroup_472 -> T_IsSemigroup_472
forall a b. a -> b
coe T_IsSemigroup_472
v4
      T_Semigroup_536
_ -> T_IsSemigroup_472
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.Semigroup._.assoc
d_assoc_560 ::
  T_Semigroup_536 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_560 :: T_Semigroup_536 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_560 T_Semigroup_536
v0
  = (T_IsSemigroup_472 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsSemigroup_472 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_assoc_482
      ((T_Semigroup_536 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semigroup_536 -> T_IsSemigroup_472
d_isSemigroup_556 (T_Semigroup_536 -> AgdaAny
forall a b. a -> b
coe T_Semigroup_536
v0))
-- Algebra.Bundles.Semigroup._.isEquivalence
d_isEquivalence_562 ::
  T_Semigroup_536 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_562 :: T_Semigroup_536 -> T_IsEquivalence_26
d_isEquivalence_562 T_Semigroup_536
v0
  = (T_IsMagma_176 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
      ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480
         ((T_Semigroup_536 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semigroup_536 -> T_IsSemigroup_472
d_isSemigroup_556 (T_Semigroup_536 -> AgdaAny
forall a b. a -> b
coe T_Semigroup_536
v0)))
-- Algebra.Bundles.Semigroup._.isMagma
d_isMagma_564 ::
  T_Semigroup_536 -> MAlonzo.Code.Algebra.Structures.T_IsMagma_176
d_isMagma_564 :: T_Semigroup_536 -> T_IsMagma_176
d_isMagma_564 T_Semigroup_536
v0
  = (T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> T_IsMagma_176
forall a b. a -> b
coe
      T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480
      ((T_Semigroup_536 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semigroup_536 -> T_IsSemigroup_472
d_isSemigroup_556 (T_Semigroup_536 -> AgdaAny
forall a b. a -> b
coe T_Semigroup_536
v0))
-- Algebra.Bundles.Semigroup._.isPartialEquivalence
d_isPartialEquivalence_566 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Semigroup_536 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_566 :: () -> () -> T_Semigroup_536 -> T_IsPartialEquivalence_16
d_isPartialEquivalence_566 ~()
v0 ~()
v1 T_Semigroup_536
v2
  = T_Semigroup_536 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_566 T_Semigroup_536
v2
du_isPartialEquivalence_566 ::
  T_Semigroup_536 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_566 :: T_Semigroup_536 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_566 T_Semigroup_536
v0
  = let v1 :: T_IsSemigroup_472
v1 = T_Semigroup_536 -> T_IsSemigroup_472
d_isSemigroup_556 (T_Semigroup_536 -> T_Semigroup_536
forall a b. a -> b
coe T_Semigroup_536
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsMagma_176
v2 = T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (T_IsSemigroup_472 -> T_IsSemigroup_472
forall a b. a -> b
coe T_IsSemigroup_472
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsEquivalence_26 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsEquivalence_26 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
            ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v2))))
-- Algebra.Bundles.Semigroup._.refl
d_refl_568 :: T_Semigroup_536 -> AgdaAny -> AgdaAny
d_refl_568 :: T_Semigroup_536 -> AgdaAny -> AgdaAny
d_refl_568 T_Semigroup_536
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_34
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
         ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480
            ((T_Semigroup_536 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semigroup_536 -> T_IsSemigroup_472
d_isSemigroup_556 (T_Semigroup_536 -> AgdaAny
forall a b. a -> b
coe T_Semigroup_536
v0))))
-- Algebra.Bundles.Semigroup._.reflexive
d_reflexive_570 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Semigroup_536 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_570 :: ()
-> ()
-> T_Semigroup_536
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_570 ~()
v0 ~()
v1 T_Semigroup_536
v2 = T_Semigroup_536 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_570 T_Semigroup_536
v2
du_reflexive_570 ::
  T_Semigroup_536 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_570 :: T_Semigroup_536 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_570 T_Semigroup_536
v0
  = let v1 :: T_IsSemigroup_472
v1 = T_Semigroup_536 -> T_IsSemigroup_472
d_isSemigroup_556 (T_Semigroup_536 -> T_Semigroup_536
forall a b. a -> b
coe T_Semigroup_536
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsMagma_176
v2 = T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (T_IsSemigroup_472 -> T_IsSemigroup_472
forall a b. a -> b
coe T_IsSemigroup_472
v1) in
       (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
         (\ AgdaAny
v3 AgdaAny
v4 AgdaAny
v5 ->
            (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
              T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
              ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v2))
              AgdaAny
v3))
-- Algebra.Bundles.Semigroup._.setoid
d_setoid_572 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Semigroup_536 -> MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_572 :: () -> () -> T_Semigroup_536 -> T_Setoid_44
d_setoid_572 ~()
v0 ~()
v1 T_Semigroup_536
v2 = T_Semigroup_536 -> T_Setoid_44
du_setoid_572 T_Semigroup_536
v2
du_setoid_572 ::
  T_Semigroup_536 -> MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_572 :: T_Semigroup_536 -> T_Setoid_44
du_setoid_572 T_Semigroup_536
v0
  = let v1 :: T_IsSemigroup_472
v1 = T_Semigroup_536 -> T_IsSemigroup_472
d_isSemigroup_556 (T_Semigroup_536 -> T_Semigroup_536
forall a b. a -> b
coe T_Semigroup_536
v0) in
    AgdaAny -> T_Setoid_44
forall a b. a -> b
coe
      ((T_IsMagma_176 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_Setoid_44
MAlonzo.Code.Algebra.Structures.du_setoid_200
         ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v1)))
-- Algebra.Bundles.Semigroup._.sym
d_sym_574 ::
  T_Semigroup_536 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_574 :: T_Semigroup_536 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_574 T_Semigroup_536
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_36
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
         ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480
            ((T_Semigroup_536 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semigroup_536 -> T_IsSemigroup_472
d_isSemigroup_556 (T_Semigroup_536 -> AgdaAny
forall a b. a -> b
coe T_Semigroup_536
v0))))
-- Algebra.Bundles.Semigroup._.trans
d_trans_576 ::
  T_Semigroup_536 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_576 :: T_Semigroup_536
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_576 T_Semigroup_536
v0
  = (T_IsEquivalence_26
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_38
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
         ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480
            ((T_Semigroup_536 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semigroup_536 -> T_IsSemigroup_472
d_isSemigroup_556 (T_Semigroup_536 -> AgdaAny
forall a b. a -> b
coe T_Semigroup_536
v0))))
-- Algebra.Bundles.Semigroup._.∙-cong
d_'8729''45'cong_578 ::
  T_Semigroup_536 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_578 :: T_Semigroup_536
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_578 T_Semigroup_536
v0
  = (T_IsMagma_176
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsMagma_176
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_186
      ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480
         ((T_Semigroup_536 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semigroup_536 -> T_IsSemigroup_472
d_isSemigroup_556 (T_Semigroup_536 -> AgdaAny
forall a b. a -> b
coe T_Semigroup_536
v0)))
-- Algebra.Bundles.Semigroup._.∙-congʳ
d_'8729''45'cong'691'_580 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Semigroup_536 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_580 :: ()
-> ()
-> T_Semigroup_536
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_580 ~()
v0 ~()
v1 T_Semigroup_536
v2
  = T_Semigroup_536
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_580 T_Semigroup_536
v2
du_'8729''45'cong'691'_580 ::
  T_Semigroup_536 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_580 :: T_Semigroup_536
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_580 T_Semigroup_536
v0
  = let v1 :: T_IsSemigroup_472
v1 = T_Semigroup_536 -> T_IsSemigroup_472
d_isSemigroup_556 (T_Semigroup_536 -> T_Semigroup_536
forall a b. a -> b
coe T_Semigroup_536
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'691'_206
         ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v1)))
-- Algebra.Bundles.Semigroup._.∙-congˡ
d_'8729''45'cong'737'_582 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Semigroup_536 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_582 :: ()
-> ()
-> T_Semigroup_536
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_582 ~()
v0 ~()
v1 T_Semigroup_536
v2
  = T_Semigroup_536
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_582 T_Semigroup_536
v2
du_'8729''45'cong'737'_582 ::
  T_Semigroup_536 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_582 :: T_Semigroup_536
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_582 T_Semigroup_536
v0
  = let v1 :: T_IsSemigroup_472
v1 = T_Semigroup_536 -> T_IsSemigroup_472
d_isSemigroup_556 (T_Semigroup_536 -> T_Semigroup_536
forall a b. a -> b
coe T_Semigroup_536
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'737'_202
         ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v1)))
-- Algebra.Bundles.Semigroup.magma
d_magma_584 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Semigroup_536 -> T_Magma_68
d_magma_584 :: () -> () -> T_Semigroup_536 -> T_Magma_68
d_magma_584 ~()
v0 ~()
v1 T_Semigroup_536
v2 = T_Semigroup_536 -> T_Magma_68
du_magma_584 T_Semigroup_536
v2
du_magma_584 :: T_Semigroup_536 -> T_Magma_68
du_magma_584 :: T_Semigroup_536 -> T_Magma_68
du_magma_584 T_Semigroup_536
v0
  = ((AgdaAny -> AgdaAny -> AgdaAny) -> T_IsMagma_176 -> T_Magma_68)
-> (AgdaAny -> AgdaAny -> AgdaAny) -> T_IsMagma_176 -> T_Magma_68
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny) -> T_IsMagma_176 -> T_Magma_68
C_Magma'46'constructor_1279 (T_Semigroup_536 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__554 (T_Semigroup_536 -> T_Semigroup_536
forall a b. a -> b
coe T_Semigroup_536
v0))
      (T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480
         ((T_Semigroup_536 -> T_IsSemigroup_472)
-> AgdaAny -> T_IsSemigroup_472
forall a b. a -> b
coe T_Semigroup_536 -> T_IsSemigroup_472
d_isSemigroup_556 (T_Semigroup_536 -> AgdaAny
forall a b. a -> b
coe T_Semigroup_536
v0)))
-- Algebra.Bundles.Semigroup._._≉_
d__'8777'__588 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Semigroup_536 -> AgdaAny -> AgdaAny -> ()
d__'8777'__588 :: () -> () -> T_Semigroup_536 -> AgdaAny -> AgdaAny -> ()
d__'8777'__588 = () -> () -> T_Semigroup_536 -> AgdaAny -> AgdaAny -> ()
forall a. a
erased
-- Algebra.Bundles.Semigroup._.rawMagma
d_rawMagma_590 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Semigroup_536 -> MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
d_rawMagma_590 :: () -> () -> T_Semigroup_536 -> T_RawMagma_36
d_rawMagma_590 ~()
v0 ~()
v1 T_Semigroup_536
v2 = T_Semigroup_536 -> T_RawMagma_36
du_rawMagma_590 T_Semigroup_536
v2
du_rawMagma_590 ::
  T_Semigroup_536 -> MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
du_rawMagma_590 :: T_Semigroup_536 -> T_RawMagma_36
du_rawMagma_590 T_Semigroup_536
v0
  = (T_Magma_68 -> T_RawMagma_36) -> AgdaAny -> T_RawMagma_36
forall a b. a -> b
coe T_Magma_68 -> T_RawMagma_36
du_rawMagma_112 ((T_Semigroup_536 -> T_Magma_68) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semigroup_536 -> T_Magma_68
du_magma_584 (T_Semigroup_536 -> AgdaAny
forall a b. a -> b
coe T_Semigroup_536
v0))
-- Algebra.Bundles.Band
d_Band_596 :: p -> p -> ()
d_Band_596 p
a0 p
a1 = ()
data T_Band_596
  = C_Band'46'constructor_10881 (AgdaAny -> AgdaAny -> AgdaAny)
                                MAlonzo.Code.Algebra.Structures.T_IsBand_508
-- Algebra.Bundles.Band.Carrier
d_Carrier_610 :: T_Band_596 -> ()
d_Carrier_610 :: T_Band_596 -> ()
d_Carrier_610 = T_Band_596 -> ()
forall a. a
erased
-- Algebra.Bundles.Band._≈_
d__'8776'__612 :: T_Band_596 -> AgdaAny -> AgdaAny -> ()
d__'8776'__612 :: T_Band_596 -> AgdaAny -> AgdaAny -> ()
d__'8776'__612 = T_Band_596 -> AgdaAny -> AgdaAny -> ()
forall a. a
erased
-- Algebra.Bundles.Band._∙_
d__'8729'__614 :: T_Band_596 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__614 :: T_Band_596 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__614 T_Band_596
v0
  = case T_Band_596 -> T_Band_596
forall a b. a -> b
coe T_Band_596
v0 of
      C_Band'46'constructor_10881 AgdaAny -> AgdaAny -> AgdaAny
v3 T_IsBand_508
v4 -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v3
      T_Band_596
_ -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.Band.isBand
d_isBand_616 ::
  T_Band_596 -> MAlonzo.Code.Algebra.Structures.T_IsBand_508
d_isBand_616 :: T_Band_596 -> T_IsBand_508
d_isBand_616 T_Band_596
v0
  = case T_Band_596 -> T_Band_596
forall a b. a -> b
coe T_Band_596
v0 of
      C_Band'46'constructor_10881 AgdaAny -> AgdaAny -> AgdaAny
v3 T_IsBand_508
v4 -> T_IsBand_508 -> T_IsBand_508
forall a b. a -> b
coe T_IsBand_508
v4
      T_Band_596
_ -> T_IsBand_508
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.Band._.assoc
d_assoc_620 ::
  T_Band_596 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_620 :: T_Band_596 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_620 T_Band_596
v0
  = (T_IsSemigroup_472 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsSemigroup_472 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_assoc_482
      ((T_IsBand_508 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsBand_508 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_516
         ((T_Band_596 -> T_IsBand_508) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Band_596 -> T_IsBand_508
d_isBand_616 (T_Band_596 -> AgdaAny
forall a b. a -> b
coe T_Band_596
v0)))
-- Algebra.Bundles.Band._.idem
d_idem_622 :: T_Band_596 -> AgdaAny -> AgdaAny
d_idem_622 :: T_Band_596 -> AgdaAny -> AgdaAny
d_idem_622 T_Band_596
v0
  = (T_IsBand_508 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsBand_508 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_idem_518
      ((T_Band_596 -> T_IsBand_508) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Band_596 -> T_IsBand_508
d_isBand_616 (T_Band_596 -> AgdaAny
forall a b. a -> b
coe T_Band_596
v0))
-- Algebra.Bundles.Band._.isEquivalence
d_isEquivalence_624 ::
  T_Band_596 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_624 :: T_Band_596 -> T_IsEquivalence_26
d_isEquivalence_624 T_Band_596
v0
  = (T_IsMagma_176 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
      ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480
         ((T_IsBand_508 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsBand_508 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_516
            ((T_Band_596 -> T_IsBand_508) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Band_596 -> T_IsBand_508
d_isBand_616 (T_Band_596 -> AgdaAny
forall a b. a -> b
coe T_Band_596
v0))))
-- Algebra.Bundles.Band._.isMagma
d_isMagma_626 ::
  T_Band_596 -> MAlonzo.Code.Algebra.Structures.T_IsMagma_176
d_isMagma_626 :: T_Band_596 -> T_IsMagma_176
d_isMagma_626 T_Band_596
v0
  = (T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> T_IsMagma_176
forall a b. a -> b
coe
      T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480
      ((T_IsBand_508 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsBand_508 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_516
         ((T_Band_596 -> T_IsBand_508) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Band_596 -> T_IsBand_508
d_isBand_616 (T_Band_596 -> AgdaAny
forall a b. a -> b
coe T_Band_596
v0)))
-- Algebra.Bundles.Band._.isPartialEquivalence
d_isPartialEquivalence_628 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Band_596 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_628 :: () -> () -> T_Band_596 -> T_IsPartialEquivalence_16
d_isPartialEquivalence_628 ~()
v0 ~()
v1 T_Band_596
v2
  = T_Band_596 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_628 T_Band_596
v2
du_isPartialEquivalence_628 ::
  T_Band_596 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_628 :: T_Band_596 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_628 T_Band_596
v0
  = let v1 :: T_IsBand_508
v1 = T_Band_596 -> T_IsBand_508
d_isBand_616 (T_Band_596 -> T_Band_596
forall a b. a -> b
coe T_Band_596
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsSemigroup_472
v2
             = T_IsBand_508 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_516 (T_IsBand_508 -> T_IsBand_508
forall a b. a -> b
coe T_IsBand_508
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsMagma_176
v3 = T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (T_IsSemigroup_472 -> T_IsSemigroup_472
forall a b. a -> b
coe T_IsSemigroup_472
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsEquivalence_26 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsEquivalence_26 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
               ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v3)))))
-- Algebra.Bundles.Band._.isSemigroup
d_isSemigroup_630 ::
  T_Band_596 -> MAlonzo.Code.Algebra.Structures.T_IsSemigroup_472
d_isSemigroup_630 :: T_Band_596 -> T_IsSemigroup_472
d_isSemigroup_630 T_Band_596
v0
  = (T_IsBand_508 -> T_IsSemigroup_472) -> AgdaAny -> T_IsSemigroup_472
forall a b. a -> b
coe
      T_IsBand_508 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_516
      ((T_Band_596 -> T_IsBand_508) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Band_596 -> T_IsBand_508
d_isBand_616 (T_Band_596 -> AgdaAny
forall a b. a -> b
coe T_Band_596
v0))
-- Algebra.Bundles.Band._.refl
d_refl_632 :: T_Band_596 -> AgdaAny -> AgdaAny
d_refl_632 :: T_Band_596 -> AgdaAny -> AgdaAny
d_refl_632 T_Band_596
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_34
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
         ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480
            ((T_IsBand_508 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsBand_508 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_516
               ((T_Band_596 -> T_IsBand_508) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Band_596 -> T_IsBand_508
d_isBand_616 (T_Band_596 -> AgdaAny
forall a b. a -> b
coe T_Band_596
v0)))))
-- Algebra.Bundles.Band._.reflexive
d_reflexive_634 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Band_596 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_634 :: ()
-> ()
-> T_Band_596
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_634 ~()
v0 ~()
v1 T_Band_596
v2 = T_Band_596 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_634 T_Band_596
v2
du_reflexive_634 ::
  T_Band_596 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_634 :: T_Band_596 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_634 T_Band_596
v0
  = let v1 :: T_IsBand_508
v1 = T_Band_596 -> T_IsBand_508
d_isBand_616 (T_Band_596 -> T_Band_596
forall a b. a -> b
coe T_Band_596
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemigroup_472
v2
             = T_IsBand_508 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_516 (T_IsBand_508 -> T_IsBand_508
forall a b. a -> b
coe T_IsBand_508
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsMagma_176
v3 = T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (T_IsSemigroup_472 -> T_IsSemigroup_472
forall a b. a -> b
coe T_IsSemigroup_472
v2) in
          (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
            (\ AgdaAny
v4 AgdaAny
v5 AgdaAny
v6 ->
               (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                 T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
                 ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v3))
                 AgdaAny
v4)))
-- Algebra.Bundles.Band._.setoid
d_setoid_636 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Band_596 -> MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_636 :: () -> () -> T_Band_596 -> T_Setoid_44
d_setoid_636 ~()
v0 ~()
v1 T_Band_596
v2 = T_Band_596 -> T_Setoid_44
du_setoid_636 T_Band_596
v2
du_setoid_636 ::
  T_Band_596 -> MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_636 :: T_Band_596 -> T_Setoid_44
du_setoid_636 T_Band_596
v0
  = let v1 :: T_IsBand_508
v1 = T_Band_596 -> T_IsBand_508
d_isBand_616 (T_Band_596 -> T_Band_596
forall a b. a -> b
coe T_Band_596
v0) in
    AgdaAny -> T_Setoid_44
forall a b. a -> b
coe
      (let v2 :: T_IsSemigroup_472
v2
             = T_IsBand_508 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_516 (T_IsBand_508 -> T_IsBand_508
forall a b. a -> b
coe T_IsBand_508
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsMagma_176 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMagma_176 -> T_Setoid_44
MAlonzo.Code.Algebra.Structures.du_setoid_200
            ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v2))))
-- Algebra.Bundles.Band._.sym
d_sym_638 :: T_Band_596 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_638 :: T_Band_596 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_638 T_Band_596
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_36
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
         ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480
            ((T_IsBand_508 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsBand_508 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_516
               ((T_Band_596 -> T_IsBand_508) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Band_596 -> T_IsBand_508
d_isBand_616 (T_Band_596 -> AgdaAny
forall a b. a -> b
coe T_Band_596
v0)))))
-- Algebra.Bundles.Band._.trans
d_trans_640 ::
  T_Band_596 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_640 :: T_Band_596
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_640 T_Band_596
v0
  = (T_IsEquivalence_26
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_38
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
         ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480
            ((T_IsBand_508 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsBand_508 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_516
               ((T_Band_596 -> T_IsBand_508) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Band_596 -> T_IsBand_508
d_isBand_616 (T_Band_596 -> AgdaAny
forall a b. a -> b
coe T_Band_596
v0)))))
-- Algebra.Bundles.Band._.∙-cong
d_'8729''45'cong_642 ::
  T_Band_596 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_642 :: T_Band_596
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_642 T_Band_596
v0
  = (T_IsMagma_176
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsMagma_176
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_186
      ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480
         ((T_IsBand_508 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsBand_508 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_516
            ((T_Band_596 -> T_IsBand_508) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Band_596 -> T_IsBand_508
d_isBand_616 (T_Band_596 -> AgdaAny
forall a b. a -> b
coe T_Band_596
v0))))
-- Algebra.Bundles.Band._.∙-congʳ
d_'8729''45'cong'691'_644 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Band_596 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_644 :: ()
-> ()
-> T_Band_596
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_644 ~()
v0 ~()
v1 T_Band_596
v2
  = T_Band_596 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_644 T_Band_596
v2
du_'8729''45'cong'691'_644 ::
  T_Band_596 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_644 :: T_Band_596 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_644 T_Band_596
v0
  = let v1 :: T_IsBand_508
v1 = T_Band_596 -> T_IsBand_508
d_isBand_616 (T_Band_596 -> T_Band_596
forall a b. a -> b
coe T_Band_596
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemigroup_472
v2
             = T_IsBand_508 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_516 (T_IsBand_508 -> T_IsBand_508
forall a b. a -> b
coe T_IsBand_508
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'691'_206
            ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v2))))
-- Algebra.Bundles.Band._.∙-congˡ
d_'8729''45'cong'737'_646 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Band_596 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_646 :: ()
-> ()
-> T_Band_596
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_646 ~()
v0 ~()
v1 T_Band_596
v2
  = T_Band_596 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_646 T_Band_596
v2
du_'8729''45'cong'737'_646 ::
  T_Band_596 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_646 :: T_Band_596 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_646 T_Band_596
v0
  = let v1 :: T_IsBand_508
v1 = T_Band_596 -> T_IsBand_508
d_isBand_616 (T_Band_596 -> T_Band_596
forall a b. a -> b
coe T_Band_596
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemigroup_472
v2
             = T_IsBand_508 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_516 (T_IsBand_508 -> T_IsBand_508
forall a b. a -> b
coe T_IsBand_508
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'737'_202
            ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v2))))
-- Algebra.Bundles.Band.semigroup
d_semigroup_648 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Band_596 -> T_Semigroup_536
d_semigroup_648 :: () -> () -> T_Band_596 -> T_Semigroup_536
d_semigroup_648 ~()
v0 ~()
v1 T_Band_596
v2 = T_Band_596 -> T_Semigroup_536
du_semigroup_648 T_Band_596
v2
du_semigroup_648 :: T_Band_596 -> T_Semigroup_536
du_semigroup_648 :: T_Band_596 -> T_Semigroup_536
du_semigroup_648 T_Band_596
v0
  = ((AgdaAny -> AgdaAny -> AgdaAny)
 -> T_IsSemigroup_472 -> T_Semigroup_536)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsSemigroup_472
-> T_Semigroup_536
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsSemigroup_472 -> T_Semigroup_536
C_Semigroup'46'constructor_9793 (T_Band_596 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__614 (T_Band_596 -> T_Band_596
forall a b. a -> b
coe T_Band_596
v0))
      (T_IsBand_508 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_516
         ((T_Band_596 -> T_IsBand_508) -> AgdaAny -> T_IsBand_508
forall a b. a -> b
coe T_Band_596 -> T_IsBand_508
d_isBand_616 (T_Band_596 -> AgdaAny
forall a b. a -> b
coe T_Band_596
v0)))
-- Algebra.Bundles.Band._._≉_
d__'8777'__652 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Band_596 -> AgdaAny -> AgdaAny -> ()
d__'8777'__652 :: () -> () -> T_Band_596 -> AgdaAny -> AgdaAny -> ()
d__'8777'__652 = () -> () -> T_Band_596 -> AgdaAny -> AgdaAny -> ()
forall a. a
erased
-- Algebra.Bundles.Band._.magma
d_magma_654 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 -> T_Band_596 -> T_Magma_68
d_magma_654 :: () -> () -> T_Band_596 -> T_Magma_68
d_magma_654 ~()
v0 ~()
v1 T_Band_596
v2 = T_Band_596 -> T_Magma_68
du_magma_654 T_Band_596
v2
du_magma_654 :: T_Band_596 -> T_Magma_68
du_magma_654 :: T_Band_596 -> T_Magma_68
du_magma_654 T_Band_596
v0 = (T_Semigroup_536 -> T_Magma_68) -> AgdaAny -> T_Magma_68
forall a b. a -> b
coe T_Semigroup_536 -> T_Magma_68
du_magma_584 ((T_Band_596 -> T_Semigroup_536) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Band_596 -> T_Semigroup_536
du_semigroup_648 (T_Band_596 -> AgdaAny
forall a b. a -> b
coe T_Band_596
v0))
-- Algebra.Bundles.Band._.rawMagma
d_rawMagma_656 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Band_596 -> MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
d_rawMagma_656 :: () -> () -> T_Band_596 -> T_RawMagma_36
d_rawMagma_656 ~()
v0 ~()
v1 T_Band_596
v2 = T_Band_596 -> T_RawMagma_36
du_rawMagma_656 T_Band_596
v2
du_rawMagma_656 ::
  T_Band_596 -> MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
du_rawMagma_656 :: T_Band_596 -> T_RawMagma_36
du_rawMagma_656 T_Band_596
v0
  = let v1 :: t
v1 = (T_Band_596 -> T_Semigroup_536) -> AgdaAny -> t
forall a b. a -> b
coe T_Band_596 -> T_Semigroup_536
du_semigroup_648 (T_Band_596 -> AgdaAny
forall a b. a -> b
coe T_Band_596
v0) in
    AgdaAny -> T_RawMagma_36
forall a b. a -> b
coe ((T_Magma_68 -> T_RawMagma_36) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Magma_68 -> T_RawMagma_36
du_rawMagma_112 ((T_Semigroup_536 -> T_Magma_68) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semigroup_536 -> T_Magma_68
du_magma_584 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1)))
-- Algebra.Bundles.CommutativeSemigroup
d_CommutativeSemigroup_662 :: p -> p -> ()
d_CommutativeSemigroup_662 p
a0 p
a1 = ()
data T_CommutativeSemigroup_662
  = C_CommutativeSemigroup'46'constructor_12035 (AgdaAny ->
                                                 AgdaAny -> AgdaAny)
                                                MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_548
-- Algebra.Bundles.CommutativeSemigroup.Carrier
d_Carrier_676 :: T_CommutativeSemigroup_662 -> ()
d_Carrier_676 :: T_CommutativeSemigroup_662 -> ()
d_Carrier_676 = T_CommutativeSemigroup_662 -> ()
forall a. a
erased
-- Algebra.Bundles.CommutativeSemigroup._≈_
d__'8776'__678 ::
  T_CommutativeSemigroup_662 -> AgdaAny -> AgdaAny -> ()
d__'8776'__678 :: T_CommutativeSemigroup_662 -> AgdaAny -> AgdaAny -> ()
d__'8776'__678 = T_CommutativeSemigroup_662 -> AgdaAny -> AgdaAny -> ()
forall a. a
erased
-- Algebra.Bundles.CommutativeSemigroup._∙_
d__'8729'__680 ::
  T_CommutativeSemigroup_662 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__680 :: T_CommutativeSemigroup_662 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__680 T_CommutativeSemigroup_662
v0
  = case T_CommutativeSemigroup_662 -> T_CommutativeSemigroup_662
forall a b. a -> b
coe T_CommutativeSemigroup_662
v0 of
      C_CommutativeSemigroup'46'constructor_12035 AgdaAny -> AgdaAny -> AgdaAny
v3 T_IsCommutativeSemigroup_548
v4 -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v3
      T_CommutativeSemigroup_662
_ -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.CommutativeSemigroup.isCommutativeSemigroup
d_isCommutativeSemigroup_682 ::
  T_CommutativeSemigroup_662 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_548
d_isCommutativeSemigroup_682 :: T_CommutativeSemigroup_662 -> T_IsCommutativeSemigroup_548
d_isCommutativeSemigroup_682 T_CommutativeSemigroup_662
v0
  = case T_CommutativeSemigroup_662 -> T_CommutativeSemigroup_662
forall a b. a -> b
coe T_CommutativeSemigroup_662
v0 of
      C_CommutativeSemigroup'46'constructor_12035 AgdaAny -> AgdaAny -> AgdaAny
v3 T_IsCommutativeSemigroup_548
v4 -> T_IsCommutativeSemigroup_548 -> T_IsCommutativeSemigroup_548
forall a b. a -> b
coe T_IsCommutativeSemigroup_548
v4
      T_CommutativeSemigroup_662
_ -> T_IsCommutativeSemigroup_548
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.CommutativeSemigroup._.assoc
d_assoc_686 ::
  T_CommutativeSemigroup_662 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_686 :: T_CommutativeSemigroup_662
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_686 T_CommutativeSemigroup_662
v0
  = (T_IsSemigroup_472 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsSemigroup_472 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_assoc_482
      ((T_IsCommutativeSemigroup_548 -> T_IsSemigroup_472)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCommutativeSemigroup_548 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_556
         ((T_CommutativeSemigroup_662 -> T_IsCommutativeSemigroup_548)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemigroup_662 -> T_IsCommutativeSemigroup_548
d_isCommutativeSemigroup_682 (T_CommutativeSemigroup_662 -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemigroup_662
v0)))
-- Algebra.Bundles.CommutativeSemigroup._.comm
d_comm_688 ::
  T_CommutativeSemigroup_662 -> AgdaAny -> AgdaAny -> AgdaAny
d_comm_688 :: T_CommutativeSemigroup_662 -> AgdaAny -> AgdaAny -> AgdaAny
d_comm_688 T_CommutativeSemigroup_662
v0
  = (T_IsCommutativeSemigroup_548 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsCommutativeSemigroup_548 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_comm_558
      ((T_CommutativeSemigroup_662 -> T_IsCommutativeSemigroup_548)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemigroup_662 -> T_IsCommutativeSemigroup_548
d_isCommutativeSemigroup_682 (T_CommutativeSemigroup_662 -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemigroup_662
v0))
-- Algebra.Bundles.CommutativeSemigroup._.isCommutativeMagma
d_isCommutativeMagma_690 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeSemigroup_662 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMagma_212
d_isCommutativeMagma_690 :: () -> () -> T_CommutativeSemigroup_662 -> T_IsCommutativeMagma_212
d_isCommutativeMagma_690 ~()
v0 ~()
v1 T_CommutativeSemigroup_662
v2 = T_CommutativeSemigroup_662 -> T_IsCommutativeMagma_212
du_isCommutativeMagma_690 T_CommutativeSemigroup_662
v2
du_isCommutativeMagma_690 ::
  T_CommutativeSemigroup_662 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMagma_212
du_isCommutativeMagma_690 :: T_CommutativeSemigroup_662 -> T_IsCommutativeMagma_212
du_isCommutativeMagma_690 T_CommutativeSemigroup_662
v0
  = (T_IsCommutativeSemigroup_548 -> T_IsCommutativeMagma_212)
-> AgdaAny -> T_IsCommutativeMagma_212
forall a b. a -> b
coe
      T_IsCommutativeSemigroup_548 -> T_IsCommutativeMagma_212
MAlonzo.Code.Algebra.Structures.du_isCommutativeMagma_586
      ((T_CommutativeSemigroup_662 -> T_IsCommutativeSemigroup_548)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemigroup_662 -> T_IsCommutativeSemigroup_548
d_isCommutativeSemigroup_682 (T_CommutativeSemigroup_662 -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemigroup_662
v0))
-- Algebra.Bundles.CommutativeSemigroup._.isEquivalence
d_isEquivalence_692 ::
  T_CommutativeSemigroup_662 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_692 :: T_CommutativeSemigroup_662 -> T_IsEquivalence_26
d_isEquivalence_692 T_CommutativeSemigroup_662
v0
  = (T_IsMagma_176 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
      ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480
         ((T_IsCommutativeSemigroup_548 -> T_IsSemigroup_472)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCommutativeSemigroup_548 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_556
            ((T_CommutativeSemigroup_662 -> T_IsCommutativeSemigroup_548)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemigroup_662 -> T_IsCommutativeSemigroup_548
d_isCommutativeSemigroup_682 (T_CommutativeSemigroup_662 -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemigroup_662
v0))))
-- Algebra.Bundles.CommutativeSemigroup._.isMagma
d_isMagma_694 ::
  T_CommutativeSemigroup_662 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_176
d_isMagma_694 :: T_CommutativeSemigroup_662 -> T_IsMagma_176
d_isMagma_694 T_CommutativeSemigroup_662
v0
  = (T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> T_IsMagma_176
forall a b. a -> b
coe
      T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480
      ((T_IsCommutativeSemigroup_548 -> T_IsSemigroup_472)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCommutativeSemigroup_548 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_556
         ((T_CommutativeSemigroup_662 -> T_IsCommutativeSemigroup_548)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemigroup_662 -> T_IsCommutativeSemigroup_548
d_isCommutativeSemigroup_682 (T_CommutativeSemigroup_662 -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemigroup_662
v0)))
-- Algebra.Bundles.CommutativeSemigroup._.isPartialEquivalence
d_isPartialEquivalence_696 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeSemigroup_662 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_696 :: () -> () -> T_CommutativeSemigroup_662 -> T_IsPartialEquivalence_16
d_isPartialEquivalence_696 ~()
v0 ~()
v1 T_CommutativeSemigroup_662
v2
  = T_CommutativeSemigroup_662 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_696 T_CommutativeSemigroup_662
v2
du_isPartialEquivalence_696 ::
  T_CommutativeSemigroup_662 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_696 :: T_CommutativeSemigroup_662 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_696 T_CommutativeSemigroup_662
v0
  = let v1 :: T_IsCommutativeSemigroup_548
v1 = T_CommutativeSemigroup_662 -> T_IsCommutativeSemigroup_548
d_isCommutativeSemigroup_682 (T_CommutativeSemigroup_662 -> T_CommutativeSemigroup_662
forall a b. a -> b
coe T_CommutativeSemigroup_662
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsSemigroup_472
v2
             = T_IsCommutativeSemigroup_548 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_556 (T_IsCommutativeSemigroup_548 -> T_IsCommutativeSemigroup_548
forall a b. a -> b
coe T_IsCommutativeSemigroup_548
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsMagma_176
v3 = T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (T_IsSemigroup_472 -> T_IsSemigroup_472
forall a b. a -> b
coe T_IsSemigroup_472
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsEquivalence_26 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsEquivalence_26 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
               ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v3)))))
-- Algebra.Bundles.CommutativeSemigroup._.isSemigroup
d_isSemigroup_698 ::
  T_CommutativeSemigroup_662 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_472
d_isSemigroup_698 :: T_CommutativeSemigroup_662 -> T_IsSemigroup_472
d_isSemigroup_698 T_CommutativeSemigroup_662
v0
  = (T_IsCommutativeSemigroup_548 -> T_IsSemigroup_472)
-> AgdaAny -> T_IsSemigroup_472
forall a b. a -> b
coe
      T_IsCommutativeSemigroup_548 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_556
      ((T_CommutativeSemigroup_662 -> T_IsCommutativeSemigroup_548)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemigroup_662 -> T_IsCommutativeSemigroup_548
d_isCommutativeSemigroup_682 (T_CommutativeSemigroup_662 -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemigroup_662
v0))
-- Algebra.Bundles.CommutativeSemigroup._.refl
d_refl_700 :: T_CommutativeSemigroup_662 -> AgdaAny -> AgdaAny
d_refl_700 :: T_CommutativeSemigroup_662 -> AgdaAny -> AgdaAny
d_refl_700 T_CommutativeSemigroup_662
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_34
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
         ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480
            ((T_IsCommutativeSemigroup_548 -> T_IsSemigroup_472)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsCommutativeSemigroup_548 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_556
               ((T_CommutativeSemigroup_662 -> T_IsCommutativeSemigroup_548)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemigroup_662 -> T_IsCommutativeSemigroup_548
d_isCommutativeSemigroup_682 (T_CommutativeSemigroup_662 -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemigroup_662
v0)))))
-- Algebra.Bundles.CommutativeSemigroup._.reflexive
d_reflexive_702 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeSemigroup_662 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_702 :: ()
-> ()
-> T_CommutativeSemigroup_662
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_702 ~()
v0 ~()
v1 T_CommutativeSemigroup_662
v2 = T_CommutativeSemigroup_662
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_702 T_CommutativeSemigroup_662
v2
du_reflexive_702 ::
  T_CommutativeSemigroup_662 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_702 :: T_CommutativeSemigroup_662
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_702 T_CommutativeSemigroup_662
v0
  = let v1 :: T_IsCommutativeSemigroup_548
v1 = T_CommutativeSemigroup_662 -> T_IsCommutativeSemigroup_548
d_isCommutativeSemigroup_682 (T_CommutativeSemigroup_662 -> T_CommutativeSemigroup_662
forall a b. a -> b
coe T_CommutativeSemigroup_662
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemigroup_472
v2
             = T_IsCommutativeSemigroup_548 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_556 (T_IsCommutativeSemigroup_548 -> T_IsCommutativeSemigroup_548
forall a b. a -> b
coe T_IsCommutativeSemigroup_548
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsMagma_176
v3 = T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (T_IsSemigroup_472 -> T_IsSemigroup_472
forall a b. a -> b
coe T_IsSemigroup_472
v2) in
          (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
            (\ AgdaAny
v4 AgdaAny
v5 AgdaAny
v6 ->
               (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                 T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
                 ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v3))
                 AgdaAny
v4)))
-- Algebra.Bundles.CommutativeSemigroup._.setoid
d_setoid_704 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeSemigroup_662 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_704 :: () -> () -> T_CommutativeSemigroup_662 -> T_Setoid_44
d_setoid_704 ~()
v0 ~()
v1 T_CommutativeSemigroup_662
v2 = T_CommutativeSemigroup_662 -> T_Setoid_44
du_setoid_704 T_CommutativeSemigroup_662
v2
du_setoid_704 ::
  T_CommutativeSemigroup_662 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_704 :: T_CommutativeSemigroup_662 -> T_Setoid_44
du_setoid_704 T_CommutativeSemigroup_662
v0
  = let v1 :: T_IsCommutativeSemigroup_548
v1 = T_CommutativeSemigroup_662 -> T_IsCommutativeSemigroup_548
d_isCommutativeSemigroup_682 (T_CommutativeSemigroup_662 -> T_CommutativeSemigroup_662
forall a b. a -> b
coe T_CommutativeSemigroup_662
v0) in
    AgdaAny -> T_Setoid_44
forall a b. a -> b
coe
      (let v2 :: T_IsSemigroup_472
v2
             = T_IsCommutativeSemigroup_548 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_556 (T_IsCommutativeSemigroup_548 -> T_IsCommutativeSemigroup_548
forall a b. a -> b
coe T_IsCommutativeSemigroup_548
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsMagma_176 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMagma_176 -> T_Setoid_44
MAlonzo.Code.Algebra.Structures.du_setoid_200
            ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v2))))
-- Algebra.Bundles.CommutativeSemigroup._.sym
d_sym_706 ::
  T_CommutativeSemigroup_662 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_706 :: T_CommutativeSemigroup_662
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_706 T_CommutativeSemigroup_662
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_36
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
         ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480
            ((T_IsCommutativeSemigroup_548 -> T_IsSemigroup_472)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsCommutativeSemigroup_548 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_556
               ((T_CommutativeSemigroup_662 -> T_IsCommutativeSemigroup_548)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemigroup_662 -> T_IsCommutativeSemigroup_548
d_isCommutativeSemigroup_682 (T_CommutativeSemigroup_662 -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemigroup_662
v0)))))
-- Algebra.Bundles.CommutativeSemigroup._.trans
d_trans_708 ::
  T_CommutativeSemigroup_662 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_708 :: T_CommutativeSemigroup_662
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_708 T_CommutativeSemigroup_662
v0
  = (T_IsEquivalence_26
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_38
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
         ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480
            ((T_IsCommutativeSemigroup_548 -> T_IsSemigroup_472)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsCommutativeSemigroup_548 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_556
               ((T_CommutativeSemigroup_662 -> T_IsCommutativeSemigroup_548)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemigroup_662 -> T_IsCommutativeSemigroup_548
d_isCommutativeSemigroup_682 (T_CommutativeSemigroup_662 -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemigroup_662
v0)))))
-- Algebra.Bundles.CommutativeSemigroup._.∙-cong
d_'8729''45'cong_710 ::
  T_CommutativeSemigroup_662 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_710 :: T_CommutativeSemigroup_662
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_710 T_CommutativeSemigroup_662
v0
  = (T_IsMagma_176
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsMagma_176
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_186
      ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480
         ((T_IsCommutativeSemigroup_548 -> T_IsSemigroup_472)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCommutativeSemigroup_548 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_556
            ((T_CommutativeSemigroup_662 -> T_IsCommutativeSemigroup_548)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemigroup_662 -> T_IsCommutativeSemigroup_548
d_isCommutativeSemigroup_682 (T_CommutativeSemigroup_662 -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemigroup_662
v0))))
-- Algebra.Bundles.CommutativeSemigroup._.∙-congʳ
d_'8729''45'cong'691'_712 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeSemigroup_662 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_712 :: ()
-> ()
-> T_CommutativeSemigroup_662
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_712 ~()
v0 ~()
v1 T_CommutativeSemigroup_662
v2
  = T_CommutativeSemigroup_662
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_712 T_CommutativeSemigroup_662
v2
du_'8729''45'cong'691'_712 ::
  T_CommutativeSemigroup_662 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_712 :: T_CommutativeSemigroup_662
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_712 T_CommutativeSemigroup_662
v0
  = let v1 :: T_IsCommutativeSemigroup_548
v1 = T_CommutativeSemigroup_662 -> T_IsCommutativeSemigroup_548
d_isCommutativeSemigroup_682 (T_CommutativeSemigroup_662 -> T_CommutativeSemigroup_662
forall a b. a -> b
coe T_CommutativeSemigroup_662
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemigroup_472
v2
             = T_IsCommutativeSemigroup_548 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_556 (T_IsCommutativeSemigroup_548 -> T_IsCommutativeSemigroup_548
forall a b. a -> b
coe T_IsCommutativeSemigroup_548
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'691'_206
            ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v2))))
-- Algebra.Bundles.CommutativeSemigroup._.∙-congˡ
d_'8729''45'cong'737'_714 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeSemigroup_662 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_714 :: ()
-> ()
-> T_CommutativeSemigroup_662
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_714 ~()
v0 ~()
v1 T_CommutativeSemigroup_662
v2
  = T_CommutativeSemigroup_662
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_714 T_CommutativeSemigroup_662
v2
du_'8729''45'cong'737'_714 ::
  T_CommutativeSemigroup_662 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_714 :: T_CommutativeSemigroup_662
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_714 T_CommutativeSemigroup_662
v0
  = let v1 :: T_IsCommutativeSemigroup_548
v1 = T_CommutativeSemigroup_662 -> T_IsCommutativeSemigroup_548
d_isCommutativeSemigroup_682 (T_CommutativeSemigroup_662 -> T_CommutativeSemigroup_662
forall a b. a -> b
coe T_CommutativeSemigroup_662
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemigroup_472
v2
             = T_IsCommutativeSemigroup_548 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_556 (T_IsCommutativeSemigroup_548 -> T_IsCommutativeSemigroup_548
forall a b. a -> b
coe T_IsCommutativeSemigroup_548
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'737'_202
            ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v2))))
-- Algebra.Bundles.CommutativeSemigroup.semigroup
d_semigroup_716 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeSemigroup_662 -> T_Semigroup_536
d_semigroup_716 :: () -> () -> T_CommutativeSemigroup_662 -> T_Semigroup_536
d_semigroup_716 ~()
v0 ~()
v1 T_CommutativeSemigroup_662
v2 = T_CommutativeSemigroup_662 -> T_Semigroup_536
du_semigroup_716 T_CommutativeSemigroup_662
v2
du_semigroup_716 :: T_CommutativeSemigroup_662 -> T_Semigroup_536
du_semigroup_716 :: T_CommutativeSemigroup_662 -> T_Semigroup_536
du_semigroup_716 T_CommutativeSemigroup_662
v0
  = ((AgdaAny -> AgdaAny -> AgdaAny)
 -> T_IsSemigroup_472 -> T_Semigroup_536)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsSemigroup_472
-> T_Semigroup_536
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsSemigroup_472 -> T_Semigroup_536
C_Semigroup'46'constructor_9793 (T_CommutativeSemigroup_662 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__680 (T_CommutativeSemigroup_662 -> T_CommutativeSemigroup_662
forall a b. a -> b
coe T_CommutativeSemigroup_662
v0))
      (T_IsCommutativeSemigroup_548 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_556
         ((T_CommutativeSemigroup_662 -> T_IsCommutativeSemigroup_548)
-> AgdaAny -> T_IsCommutativeSemigroup_548
forall a b. a -> b
coe T_CommutativeSemigroup_662 -> T_IsCommutativeSemigroup_548
d_isCommutativeSemigroup_682 (T_CommutativeSemigroup_662 -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemigroup_662
v0)))
-- Algebra.Bundles.CommutativeSemigroup._._≉_
d__'8777'__720 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeSemigroup_662 -> AgdaAny -> AgdaAny -> ()
d__'8777'__720 :: () -> () -> T_CommutativeSemigroup_662 -> AgdaAny -> AgdaAny -> ()
d__'8777'__720 = () -> () -> T_CommutativeSemigroup_662 -> AgdaAny -> AgdaAny -> ()
forall a. a
erased
-- Algebra.Bundles.CommutativeSemigroup._.magma
d_magma_722 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeSemigroup_662 -> T_Magma_68
d_magma_722 :: () -> () -> T_CommutativeSemigroup_662 -> T_Magma_68
d_magma_722 ~()
v0 ~()
v1 T_CommutativeSemigroup_662
v2 = T_CommutativeSemigroup_662 -> T_Magma_68
du_magma_722 T_CommutativeSemigroup_662
v2
du_magma_722 :: T_CommutativeSemigroup_662 -> T_Magma_68
du_magma_722 :: T_CommutativeSemigroup_662 -> T_Magma_68
du_magma_722 T_CommutativeSemigroup_662
v0 = (T_Semigroup_536 -> T_Magma_68) -> AgdaAny -> T_Magma_68
forall a b. a -> b
coe T_Semigroup_536 -> T_Magma_68
du_magma_584 ((T_CommutativeSemigroup_662 -> T_Semigroup_536)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemigroup_662 -> T_Semigroup_536
du_semigroup_716 (T_CommutativeSemigroup_662 -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemigroup_662
v0))
-- Algebra.Bundles.CommutativeSemigroup._.rawMagma
d_rawMagma_724 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeSemigroup_662 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
d_rawMagma_724 :: () -> () -> T_CommutativeSemigroup_662 -> T_RawMagma_36
d_rawMagma_724 ~()
v0 ~()
v1 T_CommutativeSemigroup_662
v2 = T_CommutativeSemigroup_662 -> T_RawMagma_36
du_rawMagma_724 T_CommutativeSemigroup_662
v2
du_rawMagma_724 ::
  T_CommutativeSemigroup_662 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
du_rawMagma_724 :: T_CommutativeSemigroup_662 -> T_RawMagma_36
du_rawMagma_724 T_CommutativeSemigroup_662
v0
  = let v1 :: t
v1 = (T_CommutativeSemigroup_662 -> T_Semigroup_536) -> AgdaAny -> t
forall a b. a -> b
coe T_CommutativeSemigroup_662 -> T_Semigroup_536
du_semigroup_716 (T_CommutativeSemigroup_662 -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemigroup_662
v0) in
    AgdaAny -> T_RawMagma_36
forall a b. a -> b
coe ((T_Magma_68 -> T_RawMagma_36) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Magma_68 -> T_RawMagma_36
du_rawMagma_112 ((T_Semigroup_536 -> T_Magma_68) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semigroup_536 -> T_Magma_68
du_magma_584 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1)))
-- Algebra.Bundles.CommutativeSemigroup.commutativeMagma
d_commutativeMagma_726 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeSemigroup_662 -> T_CommutativeMagma_180
d_commutativeMagma_726 :: () -> () -> T_CommutativeSemigroup_662 -> T_CommutativeMagma_180
d_commutativeMagma_726 ~()
v0 ~()
v1 T_CommutativeSemigroup_662
v2 = T_CommutativeSemigroup_662 -> T_CommutativeMagma_180
du_commutativeMagma_726 T_CommutativeSemigroup_662
v2
du_commutativeMagma_726 ::
  T_CommutativeSemigroup_662 -> T_CommutativeMagma_180
du_commutativeMagma_726 :: T_CommutativeSemigroup_662 -> T_CommutativeMagma_180
du_commutativeMagma_726 T_CommutativeSemigroup_662
v0
  = ((AgdaAny -> AgdaAny -> AgdaAny)
 -> T_IsCommutativeMagma_212 -> T_CommutativeMagma_180)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_CommutativeMagma_180
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsCommutativeMagma_212 -> T_CommutativeMagma_180
C_CommutativeMagma'46'constructor_3345 (T_CommutativeSemigroup_662 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__680 (T_CommutativeSemigroup_662 -> T_CommutativeSemigroup_662
forall a b. a -> b
coe T_CommutativeSemigroup_662
v0))
      ((T_IsCommutativeSemigroup_548 -> T_IsCommutativeMagma_212)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCommutativeSemigroup_548 -> T_IsCommutativeMagma_212
MAlonzo.Code.Algebra.Structures.du_isCommutativeMagma_586
         ((T_CommutativeSemigroup_662 -> T_IsCommutativeSemigroup_548)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemigroup_662 -> T_IsCommutativeSemigroup_548
d_isCommutativeSemigroup_682 (T_CommutativeSemigroup_662 -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemigroup_662
v0)))
-- Algebra.Bundles.CommutativeBand
d_CommutativeBand_732 :: p -> p -> ()
d_CommutativeBand_732 p
a0 p
a1 = ()
data T_CommutativeBand_732
  = C_CommutativeBand'46'constructor_13365 (AgdaAny ->
                                            AgdaAny -> AgdaAny)
                                           MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_590
-- Algebra.Bundles.CommutativeBand.Carrier
d_Carrier_746 :: T_CommutativeBand_732 -> ()
d_Carrier_746 :: T_CommutativeBand_732 -> ()
d_Carrier_746 = T_CommutativeBand_732 -> ()
forall a. a
erased
-- Algebra.Bundles.CommutativeBand._≈_
d__'8776'__748 :: T_CommutativeBand_732 -> AgdaAny -> AgdaAny -> ()
d__'8776'__748 :: T_CommutativeBand_732 -> AgdaAny -> AgdaAny -> ()
d__'8776'__748 = T_CommutativeBand_732 -> AgdaAny -> AgdaAny -> ()
forall a. a
erased
-- Algebra.Bundles.CommutativeBand._∙_
d__'8729'__750 ::
  T_CommutativeBand_732 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__750 :: T_CommutativeBand_732 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__750 T_CommutativeBand_732
v0
  = case T_CommutativeBand_732 -> T_CommutativeBand_732
forall a b. a -> b
coe T_CommutativeBand_732
v0 of
      C_CommutativeBand'46'constructor_13365 AgdaAny -> AgdaAny -> AgdaAny
v3 T_IsCommutativeBand_590
v4 -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v3
      T_CommutativeBand_732
_ -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.CommutativeBand.isCommutativeBand
d_isCommutativeBand_752 ::
  T_CommutativeBand_732 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_590
d_isCommutativeBand_752 :: T_CommutativeBand_732 -> T_IsCommutativeBand_590
d_isCommutativeBand_752 T_CommutativeBand_732
v0
  = case T_CommutativeBand_732 -> T_CommutativeBand_732
forall a b. a -> b
coe T_CommutativeBand_732
v0 of
      C_CommutativeBand'46'constructor_13365 AgdaAny -> AgdaAny -> AgdaAny
v3 T_IsCommutativeBand_590
v4 -> T_IsCommutativeBand_590 -> T_IsCommutativeBand_590
forall a b. a -> b
coe T_IsCommutativeBand_590
v4
      T_CommutativeBand_732
_ -> T_IsCommutativeBand_590
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.CommutativeBand._.assoc
d_assoc_756 ::
  T_CommutativeBand_732 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_756 :: T_CommutativeBand_732 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_756 T_CommutativeBand_732
v0
  = (T_IsSemigroup_472 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsSemigroup_472 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_assoc_482
      ((T_IsBand_508 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsBand_508 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_516
         ((T_IsCommutativeBand_590 -> T_IsBand_508) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCommutativeBand_590 -> T_IsBand_508
MAlonzo.Code.Algebra.Structures.d_isBand_598
            ((T_CommutativeBand_732 -> T_IsCommutativeBand_590)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeBand_732 -> T_IsCommutativeBand_590
d_isCommutativeBand_752 (T_CommutativeBand_732 -> AgdaAny
forall a b. a -> b
coe T_CommutativeBand_732
v0))))
-- Algebra.Bundles.CommutativeBand._.comm
d_comm_758 ::
  T_CommutativeBand_732 -> AgdaAny -> AgdaAny -> AgdaAny
d_comm_758 :: T_CommutativeBand_732 -> AgdaAny -> AgdaAny -> AgdaAny
d_comm_758 T_CommutativeBand_732
v0
  = (T_IsCommutativeBand_590 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsCommutativeBand_590 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_comm_600
      ((T_CommutativeBand_732 -> T_IsCommutativeBand_590)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeBand_732 -> T_IsCommutativeBand_590
d_isCommutativeBand_752 (T_CommutativeBand_732 -> AgdaAny
forall a b. a -> b
coe T_CommutativeBand_732
v0))
-- Algebra.Bundles.CommutativeBand._.idem
d_idem_760 :: T_CommutativeBand_732 -> AgdaAny -> AgdaAny
d_idem_760 :: T_CommutativeBand_732 -> AgdaAny -> AgdaAny
d_idem_760 T_CommutativeBand_732
v0
  = (T_IsBand_508 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsBand_508 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_idem_518
      ((T_IsCommutativeBand_590 -> T_IsBand_508) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCommutativeBand_590 -> T_IsBand_508
MAlonzo.Code.Algebra.Structures.d_isBand_598
         ((T_CommutativeBand_732 -> T_IsCommutativeBand_590)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeBand_732 -> T_IsCommutativeBand_590
d_isCommutativeBand_752 (T_CommutativeBand_732 -> AgdaAny
forall a b. a -> b
coe T_CommutativeBand_732
v0)))
-- Algebra.Bundles.CommutativeBand._.isBand
d_isBand_762 ::
  T_CommutativeBand_732 ->
  MAlonzo.Code.Algebra.Structures.T_IsBand_508
d_isBand_762 :: T_CommutativeBand_732 -> T_IsBand_508
d_isBand_762 T_CommutativeBand_732
v0
  = (T_IsCommutativeBand_590 -> T_IsBand_508)
-> AgdaAny -> T_IsBand_508
forall a b. a -> b
coe
      T_IsCommutativeBand_590 -> T_IsBand_508
MAlonzo.Code.Algebra.Structures.d_isBand_598
      ((T_CommutativeBand_732 -> T_IsCommutativeBand_590)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeBand_732 -> T_IsCommutativeBand_590
d_isCommutativeBand_752 (T_CommutativeBand_732 -> AgdaAny
forall a b. a -> b
coe T_CommutativeBand_732
v0))
-- Algebra.Bundles.CommutativeBand._.isCommutativeMagma
d_isCommutativeMagma_764 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeBand_732 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMagma_212
d_isCommutativeMagma_764 :: () -> () -> T_CommutativeBand_732 -> T_IsCommutativeMagma_212
d_isCommutativeMagma_764 ~()
v0 ~()
v1 T_CommutativeBand_732
v2 = T_CommutativeBand_732 -> T_IsCommutativeMagma_212
du_isCommutativeMagma_764 T_CommutativeBand_732
v2
du_isCommutativeMagma_764 ::
  T_CommutativeBand_732 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMagma_212
du_isCommutativeMagma_764 :: T_CommutativeBand_732 -> T_IsCommutativeMagma_212
du_isCommutativeMagma_764 T_CommutativeBand_732
v0
  = let v1 :: T_IsCommutativeBand_590
v1 = T_CommutativeBand_732 -> T_IsCommutativeBand_590
d_isCommutativeBand_752 (T_CommutativeBand_732 -> T_CommutativeBand_732
forall a b. a -> b
coe T_CommutativeBand_732
v0) in
    AgdaAny -> T_IsCommutativeMagma_212
forall a b. a -> b
coe
      ((T_IsCommutativeSemigroup_548 -> T_IsCommutativeMagma_212)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCommutativeSemigroup_548 -> T_IsCommutativeMagma_212
MAlonzo.Code.Algebra.Structures.du_isCommutativeMagma_586
         ((T_IsCommutativeBand_590 -> T_IsCommutativeSemigroup_548)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCommutativeBand_590 -> T_IsCommutativeSemigroup_548
MAlonzo.Code.Algebra.Structures.du_isCommutativeSemigroup_632
            (T_IsCommutativeBand_590 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590
v1)))
-- Algebra.Bundles.CommutativeBand._.isCommutativeSemigroup
d_isCommutativeSemigroup_766 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeBand_732 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_548
d_isCommutativeSemigroup_766 :: () -> () -> T_CommutativeBand_732 -> T_IsCommutativeSemigroup_548
d_isCommutativeSemigroup_766 ~()
v0 ~()
v1 T_CommutativeBand_732
v2
  = T_CommutativeBand_732 -> T_IsCommutativeSemigroup_548
du_isCommutativeSemigroup_766 T_CommutativeBand_732
v2
du_isCommutativeSemigroup_766 ::
  T_CommutativeBand_732 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_548
du_isCommutativeSemigroup_766 :: T_CommutativeBand_732 -> T_IsCommutativeSemigroup_548
du_isCommutativeSemigroup_766 T_CommutativeBand_732
v0
  = (T_IsCommutativeBand_590 -> T_IsCommutativeSemigroup_548)
-> AgdaAny -> T_IsCommutativeSemigroup_548
forall a b. a -> b
coe
      T_IsCommutativeBand_590 -> T_IsCommutativeSemigroup_548
MAlonzo.Code.Algebra.Structures.du_isCommutativeSemigroup_632
      ((T_CommutativeBand_732 -> T_IsCommutativeBand_590)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeBand_732 -> T_IsCommutativeBand_590
d_isCommutativeBand_752 (T_CommutativeBand_732 -> AgdaAny
forall a b. a -> b
coe T_CommutativeBand_732
v0))
-- Algebra.Bundles.CommutativeBand._.isEquivalence
d_isEquivalence_768 ::
  T_CommutativeBand_732 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_768 :: T_CommutativeBand_732 -> T_IsEquivalence_26
d_isEquivalence_768 T_CommutativeBand_732
v0
  = (T_IsMagma_176 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
      ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480
         ((T_IsBand_508 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsBand_508 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_516
            ((T_IsCommutativeBand_590 -> T_IsBand_508) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsCommutativeBand_590 -> T_IsBand_508
MAlonzo.Code.Algebra.Structures.d_isBand_598
               ((T_CommutativeBand_732 -> T_IsCommutativeBand_590)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeBand_732 -> T_IsCommutativeBand_590
d_isCommutativeBand_752 (T_CommutativeBand_732 -> AgdaAny
forall a b. a -> b
coe T_CommutativeBand_732
v0)))))
-- Algebra.Bundles.CommutativeBand._.isMagma
d_isMagma_770 ::
  T_CommutativeBand_732 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_176
d_isMagma_770 :: T_CommutativeBand_732 -> T_IsMagma_176
d_isMagma_770 T_CommutativeBand_732
v0
  = (T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> T_IsMagma_176
forall a b. a -> b
coe
      T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480
      ((T_IsBand_508 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsBand_508 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_516
         ((T_IsCommutativeBand_590 -> T_IsBand_508) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCommutativeBand_590 -> T_IsBand_508
MAlonzo.Code.Algebra.Structures.d_isBand_598
            ((T_CommutativeBand_732 -> T_IsCommutativeBand_590)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeBand_732 -> T_IsCommutativeBand_590
d_isCommutativeBand_752 (T_CommutativeBand_732 -> AgdaAny
forall a b. a -> b
coe T_CommutativeBand_732
v0))))
-- Algebra.Bundles.CommutativeBand._.isPartialEquivalence
d_isPartialEquivalence_772 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeBand_732 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_772 :: () -> () -> T_CommutativeBand_732 -> T_IsPartialEquivalence_16
d_isPartialEquivalence_772 ~()
v0 ~()
v1 T_CommutativeBand_732
v2
  = T_CommutativeBand_732 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_772 T_CommutativeBand_732
v2
du_isPartialEquivalence_772 ::
  T_CommutativeBand_732 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_772 :: T_CommutativeBand_732 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_772 T_CommutativeBand_732
v0
  = let v1 :: T_IsCommutativeBand_590
v1 = T_CommutativeBand_732 -> T_IsCommutativeBand_590
d_isCommutativeBand_752 (T_CommutativeBand_732 -> T_CommutativeBand_732
forall a b. a -> b
coe T_CommutativeBand_732
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsBand_508
v2 = T_IsCommutativeBand_590 -> T_IsBand_508
MAlonzo.Code.Algebra.Structures.d_isBand_598 (T_IsCommutativeBand_590 -> T_IsCommutativeBand_590
forall a b. a -> b
coe T_IsCommutativeBand_590
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_472
v3
                = T_IsBand_508 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_516 (T_IsBand_508 -> T_IsBand_508
forall a b. a -> b
coe T_IsBand_508
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsMagma_176
v4 = T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (T_IsSemigroup_472 -> T_IsSemigroup_472
forall a b. a -> b
coe T_IsSemigroup_472
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               ((T_IsEquivalence_26 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsEquivalence_26 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
                  ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v4))))))
-- Algebra.Bundles.CommutativeBand._.isSemigroup
d_isSemigroup_774 ::
  T_CommutativeBand_732 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_472
d_isSemigroup_774 :: T_CommutativeBand_732 -> T_IsSemigroup_472
d_isSemigroup_774 T_CommutativeBand_732
v0
  = (T_IsBand_508 -> T_IsSemigroup_472) -> AgdaAny -> T_IsSemigroup_472
forall a b. a -> b
coe
      T_IsBand_508 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_516
      ((T_IsCommutativeBand_590 -> T_IsBand_508) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCommutativeBand_590 -> T_IsBand_508
MAlonzo.Code.Algebra.Structures.d_isBand_598
         ((T_CommutativeBand_732 -> T_IsCommutativeBand_590)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeBand_732 -> T_IsCommutativeBand_590
d_isCommutativeBand_752 (T_CommutativeBand_732 -> AgdaAny
forall a b. a -> b
coe T_CommutativeBand_732
v0)))
-- Algebra.Bundles.CommutativeBand._.refl
d_refl_776 :: T_CommutativeBand_732 -> AgdaAny -> AgdaAny
d_refl_776 :: T_CommutativeBand_732 -> AgdaAny -> AgdaAny
d_refl_776 T_CommutativeBand_732
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_34
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
         ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480
            ((T_IsBand_508 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsBand_508 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_516
               ((T_IsCommutativeBand_590 -> T_IsBand_508) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsCommutativeBand_590 -> T_IsBand_508
MAlonzo.Code.Algebra.Structures.d_isBand_598
                  ((T_CommutativeBand_732 -> T_IsCommutativeBand_590)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeBand_732 -> T_IsCommutativeBand_590
d_isCommutativeBand_752 (T_CommutativeBand_732 -> AgdaAny
forall a b. a -> b
coe T_CommutativeBand_732
v0))))))
-- Algebra.Bundles.CommutativeBand._.reflexive
d_reflexive_778 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeBand_732 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_778 :: ()
-> ()
-> T_CommutativeBand_732
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_778 ~()
v0 ~()
v1 T_CommutativeBand_732
v2 = T_CommutativeBand_732
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_778 T_CommutativeBand_732
v2
du_reflexive_778 ::
  T_CommutativeBand_732 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_778 :: T_CommutativeBand_732
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_778 T_CommutativeBand_732
v0
  = let v1 :: T_IsCommutativeBand_590
v1 = T_CommutativeBand_732 -> T_IsCommutativeBand_590
d_isCommutativeBand_752 (T_CommutativeBand_732 -> T_CommutativeBand_732
forall a b. a -> b
coe T_CommutativeBand_732
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsBand_508
v2 = T_IsCommutativeBand_590 -> T_IsBand_508
MAlonzo.Code.Algebra.Structures.d_isBand_598 (T_IsCommutativeBand_590 -> T_IsCommutativeBand_590
forall a b. a -> b
coe T_IsCommutativeBand_590
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_472
v3
                = T_IsBand_508 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_516 (T_IsBand_508 -> T_IsBand_508
forall a b. a -> b
coe T_IsBand_508
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsMagma_176
v4 = T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (T_IsSemigroup_472 -> T_IsSemigroup_472
forall a b. a -> b
coe T_IsSemigroup_472
v3) in
             (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
               (\ AgdaAny
v5 AgdaAny
v6 AgdaAny
v7 ->
                  (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                    T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
                    ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v4))
                    AgdaAny
v5))))
-- Algebra.Bundles.CommutativeBand._.setoid
d_setoid_780 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeBand_732 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_780 :: () -> () -> T_CommutativeBand_732 -> T_Setoid_44
d_setoid_780 ~()
v0 ~()
v1 T_CommutativeBand_732
v2 = T_CommutativeBand_732 -> T_Setoid_44
du_setoid_780 T_CommutativeBand_732
v2
du_setoid_780 ::
  T_CommutativeBand_732 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_780 :: T_CommutativeBand_732 -> T_Setoid_44
du_setoid_780 T_CommutativeBand_732
v0
  = let v1 :: T_IsCommutativeBand_590
v1 = T_CommutativeBand_732 -> T_IsCommutativeBand_590
d_isCommutativeBand_752 (T_CommutativeBand_732 -> T_CommutativeBand_732
forall a b. a -> b
coe T_CommutativeBand_732
v0) in
    AgdaAny -> T_Setoid_44
forall a b. a -> b
coe
      (let v2 :: T_IsBand_508
v2 = T_IsCommutativeBand_590 -> T_IsBand_508
MAlonzo.Code.Algebra.Structures.d_isBand_598 (T_IsCommutativeBand_590 -> T_IsCommutativeBand_590
forall a b. a -> b
coe T_IsCommutativeBand_590
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_472
v3
                = T_IsBand_508 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_516 (T_IsBand_508 -> T_IsBand_508
forall a b. a -> b
coe T_IsBand_508
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsMagma_176 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMagma_176 -> T_Setoid_44
MAlonzo.Code.Algebra.Structures.du_setoid_200
               ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v3)))))
-- Algebra.Bundles.CommutativeBand._.sym
d_sym_782 ::
  T_CommutativeBand_732 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_782 :: T_CommutativeBand_732 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_782 T_CommutativeBand_732
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_36
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
         ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480
            ((T_IsBand_508 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsBand_508 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_516
               ((T_IsCommutativeBand_590 -> T_IsBand_508) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsCommutativeBand_590 -> T_IsBand_508
MAlonzo.Code.Algebra.Structures.d_isBand_598
                  ((T_CommutativeBand_732 -> T_IsCommutativeBand_590)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeBand_732 -> T_IsCommutativeBand_590
d_isCommutativeBand_752 (T_CommutativeBand_732 -> AgdaAny
forall a b. a -> b
coe T_CommutativeBand_732
v0))))))
-- Algebra.Bundles.CommutativeBand._.trans
d_trans_784 ::
  T_CommutativeBand_732 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_784 :: T_CommutativeBand_732
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_784 T_CommutativeBand_732
v0
  = (T_IsEquivalence_26
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_38
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
         ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480
            ((T_IsBand_508 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsBand_508 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_516
               ((T_IsCommutativeBand_590 -> T_IsBand_508) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsCommutativeBand_590 -> T_IsBand_508
MAlonzo.Code.Algebra.Structures.d_isBand_598
                  ((T_CommutativeBand_732 -> T_IsCommutativeBand_590)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeBand_732 -> T_IsCommutativeBand_590
d_isCommutativeBand_752 (T_CommutativeBand_732 -> AgdaAny
forall a b. a -> b
coe T_CommutativeBand_732
v0))))))
-- Algebra.Bundles.CommutativeBand._.∙-cong
d_'8729''45'cong_786 ::
  T_CommutativeBand_732 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_786 :: T_CommutativeBand_732
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_786 T_CommutativeBand_732
v0
  = (T_IsMagma_176
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsMagma_176
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_186
      ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480
         ((T_IsBand_508 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsBand_508 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_516
            ((T_IsCommutativeBand_590 -> T_IsBand_508) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsCommutativeBand_590 -> T_IsBand_508
MAlonzo.Code.Algebra.Structures.d_isBand_598
               ((T_CommutativeBand_732 -> T_IsCommutativeBand_590)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeBand_732 -> T_IsCommutativeBand_590
d_isCommutativeBand_752 (T_CommutativeBand_732 -> AgdaAny
forall a b. a -> b
coe T_CommutativeBand_732
v0)))))
-- Algebra.Bundles.CommutativeBand._.∙-congʳ
d_'8729''45'cong'691'_788 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeBand_732 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_788 :: ()
-> ()
-> T_CommutativeBand_732
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_788 ~()
v0 ~()
v1 T_CommutativeBand_732
v2
  = T_CommutativeBand_732
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_788 T_CommutativeBand_732
v2
du_'8729''45'cong'691'_788 ::
  T_CommutativeBand_732 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_788 :: T_CommutativeBand_732
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_788 T_CommutativeBand_732
v0
  = let v1 :: T_IsCommutativeBand_590
v1 = T_CommutativeBand_732 -> T_IsCommutativeBand_590
d_isCommutativeBand_752 (T_CommutativeBand_732 -> T_CommutativeBand_732
forall a b. a -> b
coe T_CommutativeBand_732
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsBand_508
v2 = T_IsCommutativeBand_590 -> T_IsBand_508
MAlonzo.Code.Algebra.Structures.d_isBand_598 (T_IsCommutativeBand_590 -> T_IsCommutativeBand_590
forall a b. a -> b
coe T_IsCommutativeBand_590
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_472
v3
                = T_IsBand_508 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_516 (T_IsBand_508 -> T_IsBand_508
forall a b. a -> b
coe T_IsBand_508
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'691'_206
               ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v3)))))
-- Algebra.Bundles.CommutativeBand._.∙-congˡ
d_'8729''45'cong'737'_790 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeBand_732 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_790 :: ()
-> ()
-> T_CommutativeBand_732
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_790 ~()
v0 ~()
v1 T_CommutativeBand_732
v2
  = T_CommutativeBand_732
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_790 T_CommutativeBand_732
v2
du_'8729''45'cong'737'_790 ::
  T_CommutativeBand_732 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_790 :: T_CommutativeBand_732
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_790 T_CommutativeBand_732
v0
  = let v1 :: T_IsCommutativeBand_590
v1 = T_CommutativeBand_732 -> T_IsCommutativeBand_590
d_isCommutativeBand_752 (T_CommutativeBand_732 -> T_CommutativeBand_732
forall a b. a -> b
coe T_CommutativeBand_732
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsBand_508
v2 = T_IsCommutativeBand_590 -> T_IsBand_508
MAlonzo.Code.Algebra.Structures.d_isBand_598 (T_IsCommutativeBand_590 -> T_IsCommutativeBand_590
forall a b. a -> b
coe T_IsCommutativeBand_590
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_472
v3
                = T_IsBand_508 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_516 (T_IsBand_508 -> T_IsBand_508
forall a b. a -> b
coe T_IsBand_508
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'737'_202
               ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v3)))))
-- Algebra.Bundles.CommutativeBand.band
d_band_792 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeBand_732 -> T_Band_596
d_band_792 :: () -> () -> T_CommutativeBand_732 -> T_Band_596
d_band_792 ~()
v0 ~()
v1 T_CommutativeBand_732
v2 = T_CommutativeBand_732 -> T_Band_596
du_band_792 T_CommutativeBand_732
v2
du_band_792 :: T_CommutativeBand_732 -> T_Band_596
du_band_792 :: T_CommutativeBand_732 -> T_Band_596
du_band_792 T_CommutativeBand_732
v0
  = ((AgdaAny -> AgdaAny -> AgdaAny) -> T_IsBand_508 -> T_Band_596)
-> (AgdaAny -> AgdaAny -> AgdaAny) -> T_IsBand_508 -> T_Band_596
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny) -> T_IsBand_508 -> T_Band_596
C_Band'46'constructor_10881 (T_CommutativeBand_732 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__750 (T_CommutativeBand_732 -> T_CommutativeBand_732
forall a b. a -> b
coe T_CommutativeBand_732
v0))
      (T_IsCommutativeBand_590 -> T_IsBand_508
MAlonzo.Code.Algebra.Structures.d_isBand_598
         ((T_CommutativeBand_732 -> T_IsCommutativeBand_590)
-> AgdaAny -> T_IsCommutativeBand_590
forall a b. a -> b
coe T_CommutativeBand_732 -> T_IsCommutativeBand_590
d_isCommutativeBand_752 (T_CommutativeBand_732 -> AgdaAny
forall a b. a -> b
coe T_CommutativeBand_732
v0)))
-- Algebra.Bundles.CommutativeBand._._≉_
d__'8777'__796 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeBand_732 -> AgdaAny -> AgdaAny -> ()
d__'8777'__796 :: () -> () -> T_CommutativeBand_732 -> AgdaAny -> AgdaAny -> ()
d__'8777'__796 = () -> () -> T_CommutativeBand_732 -> AgdaAny -> AgdaAny -> ()
forall a. a
erased
-- Algebra.Bundles.CommutativeBand._.magma
d_magma_798 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeBand_732 -> T_Magma_68
d_magma_798 :: () -> () -> T_CommutativeBand_732 -> T_Magma_68
d_magma_798 ~()
v0 ~()
v1 T_CommutativeBand_732
v2 = T_CommutativeBand_732 -> T_Magma_68
du_magma_798 T_CommutativeBand_732
v2
du_magma_798 :: T_CommutativeBand_732 -> T_Magma_68
du_magma_798 :: T_CommutativeBand_732 -> T_Magma_68
du_magma_798 T_CommutativeBand_732
v0
  = let v1 :: t
v1 = (T_CommutativeBand_732 -> T_Band_596) -> AgdaAny -> t
forall a b. a -> b
coe T_CommutativeBand_732 -> T_Band_596
du_band_792 (T_CommutativeBand_732 -> AgdaAny
forall a b. a -> b
coe T_CommutativeBand_732
v0) in
    AgdaAny -> T_Magma_68
forall a b. a -> b
coe ((T_Semigroup_536 -> T_Magma_68) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semigroup_536 -> T_Magma_68
du_magma_584 ((T_Band_596 -> T_Semigroup_536) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Band_596 -> T_Semigroup_536
du_semigroup_648 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1)))
-- Algebra.Bundles.CommutativeBand._.rawMagma
d_rawMagma_800 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeBand_732 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
d_rawMagma_800 :: () -> () -> T_CommutativeBand_732 -> T_RawMagma_36
d_rawMagma_800 ~()
v0 ~()
v1 T_CommutativeBand_732
v2 = T_CommutativeBand_732 -> T_RawMagma_36
du_rawMagma_800 T_CommutativeBand_732
v2
du_rawMagma_800 ::
  T_CommutativeBand_732 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
du_rawMagma_800 :: T_CommutativeBand_732 -> T_RawMagma_36
du_rawMagma_800 T_CommutativeBand_732
v0
  = let v1 :: t
v1 = (T_CommutativeBand_732 -> T_Band_596) -> AgdaAny -> t
forall a b. a -> b
coe T_CommutativeBand_732 -> T_Band_596
du_band_792 (T_CommutativeBand_732 -> AgdaAny
forall a b. a -> b
coe T_CommutativeBand_732
v0) in
    AgdaAny -> T_RawMagma_36
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_Band_596 -> T_Semigroup_536) -> AgdaAny -> t
forall a b. a -> b
coe T_Band_596 -> T_Semigroup_536
du_semigroup_648 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_Magma_68 -> T_RawMagma_36) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Magma_68 -> T_RawMagma_36
du_rawMagma_112 ((T_Semigroup_536 -> T_Magma_68) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semigroup_536 -> T_Magma_68
du_magma_584 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2))))
-- Algebra.Bundles.CommutativeBand._.semigroup
d_semigroup_802 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeBand_732 -> T_Semigroup_536
d_semigroup_802 :: () -> () -> T_CommutativeBand_732 -> T_Semigroup_536
d_semigroup_802 ~()
v0 ~()
v1 T_CommutativeBand_732
v2 = T_CommutativeBand_732 -> T_Semigroup_536
du_semigroup_802 T_CommutativeBand_732
v2
du_semigroup_802 :: T_CommutativeBand_732 -> T_Semigroup_536
du_semigroup_802 :: T_CommutativeBand_732 -> T_Semigroup_536
du_semigroup_802 T_CommutativeBand_732
v0
  = (T_Band_596 -> T_Semigroup_536) -> AgdaAny -> T_Semigroup_536
forall a b. a -> b
coe T_Band_596 -> T_Semigroup_536
du_semigroup_648 ((T_CommutativeBand_732 -> T_Band_596) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeBand_732 -> T_Band_596
du_band_792 (T_CommutativeBand_732 -> AgdaAny
forall a b. a -> b
coe T_CommutativeBand_732
v0))
-- Algebra.Bundles.CommutativeBand.commutativeSemigroup
d_commutativeSemigroup_804 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeBand_732 -> T_CommutativeSemigroup_662
d_commutativeSemigroup_804 :: () -> () -> T_CommutativeBand_732 -> T_CommutativeSemigroup_662
d_commutativeSemigroup_804 ~()
v0 ~()
v1 T_CommutativeBand_732
v2
  = T_CommutativeBand_732 -> T_CommutativeSemigroup_662
du_commutativeSemigroup_804 T_CommutativeBand_732
v2
du_commutativeSemigroup_804 ::
  T_CommutativeBand_732 -> T_CommutativeSemigroup_662
du_commutativeSemigroup_804 :: T_CommutativeBand_732 -> T_CommutativeSemigroup_662
du_commutativeSemigroup_804 T_CommutativeBand_732
v0
  = ((AgdaAny -> AgdaAny -> AgdaAny)
 -> T_IsCommutativeSemigroup_548 -> T_CommutativeSemigroup_662)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_CommutativeSemigroup_662
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsCommutativeSemigroup_548 -> T_CommutativeSemigroup_662
C_CommutativeSemigroup'46'constructor_12035
      (T_CommutativeBand_732 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__750 (T_CommutativeBand_732 -> T_CommutativeBand_732
forall a b. a -> b
coe T_CommutativeBand_732
v0))
      ((T_IsCommutativeBand_590 -> T_IsCommutativeSemigroup_548)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCommutativeBand_590 -> T_IsCommutativeSemigroup_548
MAlonzo.Code.Algebra.Structures.du_isCommutativeSemigroup_632
         ((T_CommutativeBand_732 -> T_IsCommutativeBand_590)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeBand_732 -> T_IsCommutativeBand_590
d_isCommutativeBand_752 (T_CommutativeBand_732 -> AgdaAny
forall a b. a -> b
coe T_CommutativeBand_732
v0)))
-- Algebra.Bundles.CommutativeBand._.commutativeMagma
d_commutativeMagma_808 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeBand_732 -> T_CommutativeMagma_180
d_commutativeMagma_808 :: () -> () -> T_CommutativeBand_732 -> T_CommutativeMagma_180
d_commutativeMagma_808 ~()
v0 ~()
v1 T_CommutativeBand_732
v2 = T_CommutativeBand_732 -> T_CommutativeMagma_180
du_commutativeMagma_808 T_CommutativeBand_732
v2
du_commutativeMagma_808 ::
  T_CommutativeBand_732 -> T_CommutativeMagma_180
du_commutativeMagma_808 :: T_CommutativeBand_732 -> T_CommutativeMagma_180
du_commutativeMagma_808 T_CommutativeBand_732
v0
  = (T_CommutativeSemigroup_662 -> T_CommutativeMagma_180)
-> AgdaAny -> T_CommutativeMagma_180
forall a b. a -> b
coe
      T_CommutativeSemigroup_662 -> T_CommutativeMagma_180
du_commutativeMagma_726 ((T_CommutativeBand_732 -> T_CommutativeSemigroup_662)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeBand_732 -> T_CommutativeSemigroup_662
du_commutativeSemigroup_804 (T_CommutativeBand_732 -> AgdaAny
forall a b. a -> b
coe T_CommutativeBand_732
v0))
-- Algebra.Bundles.UnitalMagma
d_UnitalMagma_814 :: p -> p -> ()
d_UnitalMagma_814 p
a0 p
a1 = ()
data T_UnitalMagma_814
  = C_UnitalMagma'46'constructor_14927 (AgdaAny ->
                                        AgdaAny -> AgdaAny)
                                       AgdaAny MAlonzo.Code.Algebra.Structures.T_IsUnitalMagma_642
-- Algebra.Bundles.UnitalMagma.Carrier
d_Carrier_830 :: T_UnitalMagma_814 -> ()
d_Carrier_830 :: T_UnitalMagma_814 -> ()
d_Carrier_830 = T_UnitalMagma_814 -> ()
forall a. a
erased
-- Algebra.Bundles.UnitalMagma._≈_
d__'8776'__832 :: T_UnitalMagma_814 -> AgdaAny -> AgdaAny -> ()
d__'8776'__832 :: T_UnitalMagma_814 -> AgdaAny -> AgdaAny -> ()
d__'8776'__832 = T_UnitalMagma_814 -> AgdaAny -> AgdaAny -> ()
forall a. a
erased
-- Algebra.Bundles.UnitalMagma._∙_
d__'8729'__834 ::
  T_UnitalMagma_814 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__834 :: T_UnitalMagma_814 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__834 T_UnitalMagma_814
v0
  = case T_UnitalMagma_814 -> T_UnitalMagma_814
forall a b. a -> b
coe T_UnitalMagma_814
v0 of
      C_UnitalMagma'46'constructor_14927 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny
v4 T_IsUnitalMagma_642
v5 -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v3
      T_UnitalMagma_814
_ -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.UnitalMagma.ε
d_ε_836 :: T_UnitalMagma_814 -> AgdaAny
d_ε_836 :: T_UnitalMagma_814 -> AgdaAny
d_ε_836 T_UnitalMagma_814
v0
  = case T_UnitalMagma_814 -> T_UnitalMagma_814
forall a b. a -> b
coe T_UnitalMagma_814
v0 of
      C_UnitalMagma'46'constructor_14927 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny
v4 T_IsUnitalMagma_642
v5 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v4
      T_UnitalMagma_814
_ -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.UnitalMagma.isUnitalMagma
d_isUnitalMagma_838 ::
  T_UnitalMagma_814 ->
  MAlonzo.Code.Algebra.Structures.T_IsUnitalMagma_642
d_isUnitalMagma_838 :: T_UnitalMagma_814 -> T_IsUnitalMagma_642
d_isUnitalMagma_838 T_UnitalMagma_814
v0
  = case T_UnitalMagma_814 -> T_UnitalMagma_814
forall a b. a -> b
coe T_UnitalMagma_814
v0 of
      C_UnitalMagma'46'constructor_14927 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny
v4 T_IsUnitalMagma_642
v5 -> T_IsUnitalMagma_642 -> T_IsUnitalMagma_642
forall a b. a -> b
coe T_IsUnitalMagma_642
v5
      T_UnitalMagma_814
_ -> T_IsUnitalMagma_642
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.UnitalMagma._.identity
d_identity_842 ::
  T_UnitalMagma_814 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_identity_842 :: T_UnitalMagma_814 -> T_Σ_14
d_identity_842 T_UnitalMagma_814
v0
  = (T_IsUnitalMagma_642 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsUnitalMagma_642 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_identity_654
      ((T_UnitalMagma_814 -> T_IsUnitalMagma_642) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_UnitalMagma_814 -> T_IsUnitalMagma_642
d_isUnitalMagma_838 (T_UnitalMagma_814 -> AgdaAny
forall a b. a -> b
coe T_UnitalMagma_814
v0))
-- Algebra.Bundles.UnitalMagma._.identityʳ
d_identity'691'_844 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_UnitalMagma_814 -> AgdaAny -> AgdaAny
d_identity'691'_844 :: () -> () -> T_UnitalMagma_814 -> AgdaAny -> AgdaAny
d_identity'691'_844 ~()
v0 ~()
v1 T_UnitalMagma_814
v2 = T_UnitalMagma_814 -> AgdaAny -> AgdaAny
du_identity'691'_844 T_UnitalMagma_814
v2
du_identity'691'_844 :: T_UnitalMagma_814 -> AgdaAny -> AgdaAny
du_identity'691'_844 :: T_UnitalMagma_814 -> AgdaAny -> AgdaAny
du_identity'691'_844 T_UnitalMagma_814
v0
  = (T_IsUnitalMagma_642 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsUnitalMagma_642 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_identity'691'_680
      ((T_UnitalMagma_814 -> T_IsUnitalMagma_642) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_UnitalMagma_814 -> T_IsUnitalMagma_642
d_isUnitalMagma_838 (T_UnitalMagma_814 -> AgdaAny
forall a b. a -> b
coe T_UnitalMagma_814
v0))
-- Algebra.Bundles.UnitalMagma._.identityˡ
d_identity'737'_846 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_UnitalMagma_814 -> AgdaAny -> AgdaAny
d_identity'737'_846 :: () -> () -> T_UnitalMagma_814 -> AgdaAny -> AgdaAny
d_identity'737'_846 ~()
v0 ~()
v1 T_UnitalMagma_814
v2 = T_UnitalMagma_814 -> AgdaAny -> AgdaAny
du_identity'737'_846 T_UnitalMagma_814
v2
du_identity'737'_846 :: T_UnitalMagma_814 -> AgdaAny -> AgdaAny
du_identity'737'_846 :: T_UnitalMagma_814 -> AgdaAny -> AgdaAny
du_identity'737'_846 T_UnitalMagma_814
v0
  = (T_IsUnitalMagma_642 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsUnitalMagma_642 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_identity'737'_678
      ((T_UnitalMagma_814 -> T_IsUnitalMagma_642) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_UnitalMagma_814 -> T_IsUnitalMagma_642
d_isUnitalMagma_838 (T_UnitalMagma_814 -> AgdaAny
forall a b. a -> b
coe T_UnitalMagma_814
v0))
-- Algebra.Bundles.UnitalMagma._.isEquivalence
d_isEquivalence_848 ::
  T_UnitalMagma_814 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_848 :: T_UnitalMagma_814 -> T_IsEquivalence_26
d_isEquivalence_848 T_UnitalMagma_814
v0
  = (T_IsMagma_176 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
      ((T_IsUnitalMagma_642 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsUnitalMagma_642 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_652
         ((T_UnitalMagma_814 -> T_IsUnitalMagma_642) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_UnitalMagma_814 -> T_IsUnitalMagma_642
d_isUnitalMagma_838 (T_UnitalMagma_814 -> AgdaAny
forall a b. a -> b
coe T_UnitalMagma_814
v0)))
-- Algebra.Bundles.UnitalMagma._.isMagma
d_isMagma_850 ::
  T_UnitalMagma_814 -> MAlonzo.Code.Algebra.Structures.T_IsMagma_176
d_isMagma_850 :: T_UnitalMagma_814 -> T_IsMagma_176
d_isMagma_850 T_UnitalMagma_814
v0
  = (T_IsUnitalMagma_642 -> T_IsMagma_176) -> AgdaAny -> T_IsMagma_176
forall a b. a -> b
coe
      T_IsUnitalMagma_642 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_652
      ((T_UnitalMagma_814 -> T_IsUnitalMagma_642) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_UnitalMagma_814 -> T_IsUnitalMagma_642
d_isUnitalMagma_838 (T_UnitalMagma_814 -> AgdaAny
forall a b. a -> b
coe T_UnitalMagma_814
v0))
-- Algebra.Bundles.UnitalMagma._.isPartialEquivalence
d_isPartialEquivalence_852 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_UnitalMagma_814 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_852 :: () -> () -> T_UnitalMagma_814 -> T_IsPartialEquivalence_16
d_isPartialEquivalence_852 ~()
v0 ~()
v1 T_UnitalMagma_814
v2
  = T_UnitalMagma_814 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_852 T_UnitalMagma_814
v2
du_isPartialEquivalence_852 ::
  T_UnitalMagma_814 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_852 :: T_UnitalMagma_814 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_852 T_UnitalMagma_814
v0
  = let v1 :: T_IsUnitalMagma_642
v1 = T_UnitalMagma_814 -> T_IsUnitalMagma_642
d_isUnitalMagma_838 (T_UnitalMagma_814 -> T_UnitalMagma_814
forall a b. a -> b
coe T_UnitalMagma_814
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsMagma_176
v2 = T_IsUnitalMagma_642 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_652 (T_IsUnitalMagma_642 -> T_IsUnitalMagma_642
forall a b. a -> b
coe T_IsUnitalMagma_642
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsEquivalence_26 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsEquivalence_26 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
            ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v2))))
-- Algebra.Bundles.UnitalMagma._.refl
d_refl_854 :: T_UnitalMagma_814 -> AgdaAny -> AgdaAny
d_refl_854 :: T_UnitalMagma_814 -> AgdaAny -> AgdaAny
d_refl_854 T_UnitalMagma_814
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_34
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
         ((T_IsUnitalMagma_642 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsUnitalMagma_642 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_652
            ((T_UnitalMagma_814 -> T_IsUnitalMagma_642) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_UnitalMagma_814 -> T_IsUnitalMagma_642
d_isUnitalMagma_838 (T_UnitalMagma_814 -> AgdaAny
forall a b. a -> b
coe T_UnitalMagma_814
v0))))
-- Algebra.Bundles.UnitalMagma._.reflexive
d_reflexive_856 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_UnitalMagma_814 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_856 :: ()
-> ()
-> T_UnitalMagma_814
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_856 ~()
v0 ~()
v1 T_UnitalMagma_814
v2 = T_UnitalMagma_814 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_856 T_UnitalMagma_814
v2
du_reflexive_856 ::
  T_UnitalMagma_814 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_856 :: T_UnitalMagma_814 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_856 T_UnitalMagma_814
v0
  = let v1 :: T_IsUnitalMagma_642
v1 = T_UnitalMagma_814 -> T_IsUnitalMagma_642
d_isUnitalMagma_838 (T_UnitalMagma_814 -> T_UnitalMagma_814
forall a b. a -> b
coe T_UnitalMagma_814
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsMagma_176
v2 = T_IsUnitalMagma_642 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_652 (T_IsUnitalMagma_642 -> T_IsUnitalMagma_642
forall a b. a -> b
coe T_IsUnitalMagma_642
v1) in
       (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
         (\ AgdaAny
v3 AgdaAny
v4 AgdaAny
v5 ->
            (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
              T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
              ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v2))
              AgdaAny
v3))
-- Algebra.Bundles.UnitalMagma._.setoid
d_setoid_858 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_UnitalMagma_814 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_858 :: () -> () -> T_UnitalMagma_814 -> T_Setoid_44
d_setoid_858 ~()
v0 ~()
v1 T_UnitalMagma_814
v2 = T_UnitalMagma_814 -> T_Setoid_44
du_setoid_858 T_UnitalMagma_814
v2
du_setoid_858 ::
  T_UnitalMagma_814 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_858 :: T_UnitalMagma_814 -> T_Setoid_44
du_setoid_858 T_UnitalMagma_814
v0
  = let v1 :: T_IsUnitalMagma_642
v1 = T_UnitalMagma_814 -> T_IsUnitalMagma_642
d_isUnitalMagma_838 (T_UnitalMagma_814 -> T_UnitalMagma_814
forall a b. a -> b
coe T_UnitalMagma_814
v0) in
    AgdaAny -> T_Setoid_44
forall a b. a -> b
coe
      ((T_IsMagma_176 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_Setoid_44
MAlonzo.Code.Algebra.Structures.du_setoid_200
         ((T_IsUnitalMagma_642 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsUnitalMagma_642 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_652 (T_IsUnitalMagma_642 -> AgdaAny
forall a b. a -> b
coe T_IsUnitalMagma_642
v1)))
-- Algebra.Bundles.UnitalMagma._.sym
d_sym_860 ::
  T_UnitalMagma_814 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_860 :: T_UnitalMagma_814 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_860 T_UnitalMagma_814
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_36
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
         ((T_IsUnitalMagma_642 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsUnitalMagma_642 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_652
            ((T_UnitalMagma_814 -> T_IsUnitalMagma_642) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_UnitalMagma_814 -> T_IsUnitalMagma_642
d_isUnitalMagma_838 (T_UnitalMagma_814 -> AgdaAny
forall a b. a -> b
coe T_UnitalMagma_814
v0))))
-- Algebra.Bundles.UnitalMagma._.trans
d_trans_862 ::
  T_UnitalMagma_814 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_862 :: T_UnitalMagma_814
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_862 T_UnitalMagma_814
v0
  = (T_IsEquivalence_26
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_38
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
         ((T_IsUnitalMagma_642 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsUnitalMagma_642 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_652
            ((T_UnitalMagma_814 -> T_IsUnitalMagma_642) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_UnitalMagma_814 -> T_IsUnitalMagma_642
d_isUnitalMagma_838 (T_UnitalMagma_814 -> AgdaAny
forall a b. a -> b
coe T_UnitalMagma_814
v0))))
-- Algebra.Bundles.UnitalMagma._.∙-cong
d_'8729''45'cong_864 ::
  T_UnitalMagma_814 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_864 :: T_UnitalMagma_814
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_864 T_UnitalMagma_814
v0
  = (T_IsMagma_176
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsMagma_176
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_186
      ((T_IsUnitalMagma_642 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsUnitalMagma_642 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_652
         ((T_UnitalMagma_814 -> T_IsUnitalMagma_642) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_UnitalMagma_814 -> T_IsUnitalMagma_642
d_isUnitalMagma_838 (T_UnitalMagma_814 -> AgdaAny
forall a b. a -> b
coe T_UnitalMagma_814
v0)))
-- Algebra.Bundles.UnitalMagma._.∙-congʳ
d_'8729''45'cong'691'_866 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_UnitalMagma_814 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_866 :: ()
-> ()
-> T_UnitalMagma_814
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_866 ~()
v0 ~()
v1 T_UnitalMagma_814
v2
  = T_UnitalMagma_814
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_866 T_UnitalMagma_814
v2
du_'8729''45'cong'691'_866 ::
  T_UnitalMagma_814 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_866 :: T_UnitalMagma_814
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_866 T_UnitalMagma_814
v0
  = let v1 :: T_IsUnitalMagma_642
v1 = T_UnitalMagma_814 -> T_IsUnitalMagma_642
d_isUnitalMagma_838 (T_UnitalMagma_814 -> T_UnitalMagma_814
forall a b. a -> b
coe T_UnitalMagma_814
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'691'_206
         ((T_IsUnitalMagma_642 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsUnitalMagma_642 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_652 (T_IsUnitalMagma_642 -> AgdaAny
forall a b. a -> b
coe T_IsUnitalMagma_642
v1)))
-- Algebra.Bundles.UnitalMagma._.∙-congˡ
d_'8729''45'cong'737'_868 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_UnitalMagma_814 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_868 :: ()
-> ()
-> T_UnitalMagma_814
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_868 ~()
v0 ~()
v1 T_UnitalMagma_814
v2
  = T_UnitalMagma_814
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_868 T_UnitalMagma_814
v2
du_'8729''45'cong'737'_868 ::
  T_UnitalMagma_814 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_868 :: T_UnitalMagma_814
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_868 T_UnitalMagma_814
v0
  = let v1 :: T_IsUnitalMagma_642
v1 = T_UnitalMagma_814 -> T_IsUnitalMagma_642
d_isUnitalMagma_838 (T_UnitalMagma_814 -> T_UnitalMagma_814
forall a b. a -> b
coe T_UnitalMagma_814
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'737'_202
         ((T_IsUnitalMagma_642 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsUnitalMagma_642 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_652 (T_IsUnitalMagma_642 -> AgdaAny
forall a b. a -> b
coe T_IsUnitalMagma_642
v1)))
-- Algebra.Bundles.UnitalMagma.magma
d_magma_870 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_UnitalMagma_814 -> T_Magma_68
d_magma_870 :: () -> () -> T_UnitalMagma_814 -> T_Magma_68
d_magma_870 ~()
v0 ~()
v1 T_UnitalMagma_814
v2 = T_UnitalMagma_814 -> T_Magma_68
du_magma_870 T_UnitalMagma_814
v2
du_magma_870 :: T_UnitalMagma_814 -> T_Magma_68
du_magma_870 :: T_UnitalMagma_814 -> T_Magma_68
du_magma_870 T_UnitalMagma_814
v0
  = ((AgdaAny -> AgdaAny -> AgdaAny) -> T_IsMagma_176 -> T_Magma_68)
-> (AgdaAny -> AgdaAny -> AgdaAny) -> T_IsMagma_176 -> T_Magma_68
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny) -> T_IsMagma_176 -> T_Magma_68
C_Magma'46'constructor_1279 (T_UnitalMagma_814 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__834 (T_UnitalMagma_814 -> T_UnitalMagma_814
forall a b. a -> b
coe T_UnitalMagma_814
v0))
      (T_IsUnitalMagma_642 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_652
         ((T_UnitalMagma_814 -> T_IsUnitalMagma_642)
-> AgdaAny -> T_IsUnitalMagma_642
forall a b. a -> b
coe T_UnitalMagma_814 -> T_IsUnitalMagma_642
d_isUnitalMagma_838 (T_UnitalMagma_814 -> AgdaAny
forall a b. a -> b
coe T_UnitalMagma_814
v0)))
-- Algebra.Bundles.UnitalMagma._._≉_
d__'8777'__874 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_UnitalMagma_814 -> AgdaAny -> AgdaAny -> ()
d__'8777'__874 :: () -> () -> T_UnitalMagma_814 -> AgdaAny -> AgdaAny -> ()
d__'8777'__874 = () -> () -> T_UnitalMagma_814 -> AgdaAny -> AgdaAny -> ()
forall a. a
erased
-- Algebra.Bundles.UnitalMagma._.rawMagma
d_rawMagma_876 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_UnitalMagma_814 -> MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
d_rawMagma_876 :: () -> () -> T_UnitalMagma_814 -> T_RawMagma_36
d_rawMagma_876 ~()
v0 ~()
v1 T_UnitalMagma_814
v2 = T_UnitalMagma_814 -> T_RawMagma_36
du_rawMagma_876 T_UnitalMagma_814
v2
du_rawMagma_876 ::
  T_UnitalMagma_814 -> MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
du_rawMagma_876 :: T_UnitalMagma_814 -> T_RawMagma_36
du_rawMagma_876 T_UnitalMagma_814
v0
  = (T_Magma_68 -> T_RawMagma_36) -> AgdaAny -> T_RawMagma_36
forall a b. a -> b
coe T_Magma_68 -> T_RawMagma_36
du_rawMagma_112 ((T_UnitalMagma_814 -> T_Magma_68) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_UnitalMagma_814 -> T_Magma_68
du_magma_870 (T_UnitalMagma_814 -> AgdaAny
forall a b. a -> b
coe T_UnitalMagma_814
v0))
-- Algebra.Bundles.Monoid
d_Monoid_882 :: p -> p -> ()
d_Monoid_882 p
a0 p
a1 = ()
data T_Monoid_882
  = C_Monoid'46'constructor_16157 (AgdaAny -> AgdaAny -> AgdaAny)
                                  AgdaAny MAlonzo.Code.Algebra.Structures.T_IsMonoid_686
-- Algebra.Bundles.Monoid.Carrier
d_Carrier_898 :: T_Monoid_882 -> ()
d_Carrier_898 :: T_Monoid_882 -> ()
d_Carrier_898 = T_Monoid_882 -> ()
forall a. a
erased
-- Algebra.Bundles.Monoid._≈_
d__'8776'__900 :: T_Monoid_882 -> AgdaAny -> AgdaAny -> ()
d__'8776'__900 :: T_Monoid_882 -> AgdaAny -> AgdaAny -> ()
d__'8776'__900 = T_Monoid_882 -> AgdaAny -> AgdaAny -> ()
forall a. a
erased
-- Algebra.Bundles.Monoid._∙_
d__'8729'__902 :: T_Monoid_882 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__902 :: T_Monoid_882 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__902 T_Monoid_882
v0
  = case T_Monoid_882 -> T_Monoid_882
forall a b. a -> b
coe T_Monoid_882
v0 of
      C_Monoid'46'constructor_16157 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny
v4 T_IsMonoid_686
v5 -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v3
      T_Monoid_882
_ -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.Monoid.ε
d_ε_904 :: T_Monoid_882 -> AgdaAny
d_ε_904 :: T_Monoid_882 -> AgdaAny
d_ε_904 T_Monoid_882
v0
  = case T_Monoid_882 -> T_Monoid_882
forall a b. a -> b
coe T_Monoid_882
v0 of
      C_Monoid'46'constructor_16157 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny
v4 T_IsMonoid_686
v5 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v4
      T_Monoid_882
_ -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.Monoid.isMonoid
d_isMonoid_906 ::
  T_Monoid_882 -> MAlonzo.Code.Algebra.Structures.T_IsMonoid_686
d_isMonoid_906 :: T_Monoid_882 -> T_IsMonoid_686
d_isMonoid_906 T_Monoid_882
v0
  = case T_Monoid_882 -> T_Monoid_882
forall a b. a -> b
coe T_Monoid_882
v0 of
      C_Monoid'46'constructor_16157 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny
v4 T_IsMonoid_686
v5 -> T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v5
      T_Monoid_882
_ -> T_IsMonoid_686
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.Monoid._.assoc
d_assoc_910 ::
  T_Monoid_882 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_910 :: T_Monoid_882 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_910 T_Monoid_882
v0
  = (T_IsSemigroup_472 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsSemigroup_472 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_assoc_482
      ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
         ((T_Monoid_882 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Monoid_882 -> T_IsMonoid_686
d_isMonoid_906 (T_Monoid_882 -> AgdaAny
forall a b. a -> b
coe T_Monoid_882
v0)))
-- Algebra.Bundles.Monoid._.identity
d_identity_912 ::
  T_Monoid_882 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_identity_912 :: T_Monoid_882 -> T_Σ_14
d_identity_912 T_Monoid_882
v0
  = (T_IsMonoid_686 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsMonoid_686 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_identity_698
      ((T_Monoid_882 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Monoid_882 -> T_IsMonoid_686
d_isMonoid_906 (T_Monoid_882 -> AgdaAny
forall a b. a -> b
coe T_Monoid_882
v0))
-- Algebra.Bundles.Monoid._.identityʳ
d_identity'691'_914 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Monoid_882 -> AgdaAny -> AgdaAny
d_identity'691'_914 :: () -> () -> T_Monoid_882 -> AgdaAny -> AgdaAny
d_identity'691'_914 ~()
v0 ~()
v1 T_Monoid_882
v2 = T_Monoid_882 -> AgdaAny -> AgdaAny
du_identity'691'_914 T_Monoid_882
v2
du_identity'691'_914 :: T_Monoid_882 -> AgdaAny -> AgdaAny
du_identity'691'_914 :: T_Monoid_882 -> AgdaAny -> AgdaAny
du_identity'691'_914 T_Monoid_882
v0
  = (T_IsMonoid_686 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsMonoid_686 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_identity'691'_728
      ((T_Monoid_882 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Monoid_882 -> T_IsMonoid_686
d_isMonoid_906 (T_Monoid_882 -> AgdaAny
forall a b. a -> b
coe T_Monoid_882
v0))
-- Algebra.Bundles.Monoid._.identityˡ
d_identity'737'_916 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Monoid_882 -> AgdaAny -> AgdaAny
d_identity'737'_916 :: () -> () -> T_Monoid_882 -> AgdaAny -> AgdaAny
d_identity'737'_916 ~()
v0 ~()
v1 T_Monoid_882
v2 = T_Monoid_882 -> AgdaAny -> AgdaAny
du_identity'737'_916 T_Monoid_882
v2
du_identity'737'_916 :: T_Monoid_882 -> AgdaAny -> AgdaAny
du_identity'737'_916 :: T_Monoid_882 -> AgdaAny -> AgdaAny
du_identity'737'_916 T_Monoid_882
v0
  = (T_IsMonoid_686 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsMonoid_686 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_identity'737'_726
      ((T_Monoid_882 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Monoid_882 -> T_IsMonoid_686
d_isMonoid_906 (T_Monoid_882 -> AgdaAny
forall a b. a -> b
coe T_Monoid_882
v0))
-- Algebra.Bundles.Monoid._.isEquivalence
d_isEquivalence_918 ::
  T_Monoid_882 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_918 :: T_Monoid_882 -> T_IsEquivalence_26
d_isEquivalence_918 T_Monoid_882
v0
  = (T_IsMagma_176 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
      ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480
         ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
            ((T_Monoid_882 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Monoid_882 -> T_IsMonoid_686
d_isMonoid_906 (T_Monoid_882 -> AgdaAny
forall a b. a -> b
coe T_Monoid_882
v0))))
-- Algebra.Bundles.Monoid._.isMagma
d_isMagma_920 ::
  T_Monoid_882 -> MAlonzo.Code.Algebra.Structures.T_IsMagma_176
d_isMagma_920 :: T_Monoid_882 -> T_IsMagma_176
d_isMagma_920 T_Monoid_882
v0
  = (T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> T_IsMagma_176
forall a b. a -> b
coe
      T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480
      ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
         ((T_Monoid_882 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Monoid_882 -> T_IsMonoid_686
d_isMonoid_906 (T_Monoid_882 -> AgdaAny
forall a b. a -> b
coe T_Monoid_882
v0)))
-- Algebra.Bundles.Monoid._.isPartialEquivalence
d_isPartialEquivalence_922 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Monoid_882 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_922 :: () -> () -> T_Monoid_882 -> T_IsPartialEquivalence_16
d_isPartialEquivalence_922 ~()
v0 ~()
v1 T_Monoid_882
v2
  = T_Monoid_882 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_922 T_Monoid_882
v2
du_isPartialEquivalence_922 ::
  T_Monoid_882 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_922 :: T_Monoid_882 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_922 T_Monoid_882
v0
  = let v1 :: T_IsMonoid_686
v1 = T_Monoid_882 -> T_IsMonoid_686
d_isMonoid_906 (T_Monoid_882 -> T_Monoid_882
forall a b. a -> b
coe T_Monoid_882
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsSemigroup_472
v2
             = T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsMagma_176
v3 = T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (T_IsSemigroup_472 -> T_IsSemigroup_472
forall a b. a -> b
coe T_IsSemigroup_472
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsEquivalence_26 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsEquivalence_26 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
               ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v3)))))
-- Algebra.Bundles.Monoid._.isSemigroup
d_isSemigroup_924 ::
  T_Monoid_882 -> MAlonzo.Code.Algebra.Structures.T_IsSemigroup_472
d_isSemigroup_924 :: T_Monoid_882 -> T_IsSemigroup_472
d_isSemigroup_924 T_Monoid_882
v0
  = (T_IsMonoid_686 -> T_IsSemigroup_472)
-> AgdaAny -> T_IsSemigroup_472
forall a b. a -> b
coe
      T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
      ((T_Monoid_882 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Monoid_882 -> T_IsMonoid_686
d_isMonoid_906 (T_Monoid_882 -> AgdaAny
forall a b. a -> b
coe T_Monoid_882
v0))
-- Algebra.Bundles.Monoid._.isUnitalMagma
d_isUnitalMagma_926 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Monoid_882 -> MAlonzo.Code.Algebra.Structures.T_IsUnitalMagma_642
d_isUnitalMagma_926 :: () -> () -> T_Monoid_882 -> T_IsUnitalMagma_642
d_isUnitalMagma_926 ~()
v0 ~()
v1 T_Monoid_882
v2 = T_Monoid_882 -> T_IsUnitalMagma_642
du_isUnitalMagma_926 T_Monoid_882
v2
du_isUnitalMagma_926 ::
  T_Monoid_882 -> MAlonzo.Code.Algebra.Structures.T_IsUnitalMagma_642
du_isUnitalMagma_926 :: T_Monoid_882 -> T_IsUnitalMagma_642
du_isUnitalMagma_926 T_Monoid_882
v0
  = (T_IsMonoid_686 -> T_IsUnitalMagma_642)
-> AgdaAny -> T_IsUnitalMagma_642
forall a b. a -> b
coe
      T_IsMonoid_686 -> T_IsUnitalMagma_642
MAlonzo.Code.Algebra.Structures.du_isUnitalMagma_730
      ((T_Monoid_882 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Monoid_882 -> T_IsMonoid_686
d_isMonoid_906 (T_Monoid_882 -> AgdaAny
forall a b. a -> b
coe T_Monoid_882
v0))
-- Algebra.Bundles.Monoid._.refl
d_refl_928 :: T_Monoid_882 -> AgdaAny -> AgdaAny
d_refl_928 :: T_Monoid_882 -> AgdaAny -> AgdaAny
d_refl_928 T_Monoid_882
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_34
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
         ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480
            ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
               ((T_Monoid_882 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Monoid_882 -> T_IsMonoid_686
d_isMonoid_906 (T_Monoid_882 -> AgdaAny
forall a b. a -> b
coe T_Monoid_882
v0)))))
-- Algebra.Bundles.Monoid._.reflexive
d_reflexive_930 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Monoid_882 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_930 :: ()
-> ()
-> T_Monoid_882
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_930 ~()
v0 ~()
v1 T_Monoid_882
v2 = T_Monoid_882 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_930 T_Monoid_882
v2
du_reflexive_930 ::
  T_Monoid_882 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_930 :: T_Monoid_882 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_930 T_Monoid_882
v0
  = let v1 :: T_IsMonoid_686
v1 = T_Monoid_882 -> T_IsMonoid_686
d_isMonoid_906 (T_Monoid_882 -> T_Monoid_882
forall a b. a -> b
coe T_Monoid_882
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemigroup_472
v2
             = T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsMagma_176
v3 = T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (T_IsSemigroup_472 -> T_IsSemigroup_472
forall a b. a -> b
coe T_IsSemigroup_472
v2) in
          (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
            (\ AgdaAny
v4 AgdaAny
v5 AgdaAny
v6 ->
               (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                 T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
                 ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v3))
                 AgdaAny
v4)))
-- Algebra.Bundles.Monoid._.setoid
d_setoid_932 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Monoid_882 -> MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_932 :: () -> () -> T_Monoid_882 -> T_Setoid_44
d_setoid_932 ~()
v0 ~()
v1 T_Monoid_882
v2 = T_Monoid_882 -> T_Setoid_44
du_setoid_932 T_Monoid_882
v2
du_setoid_932 ::
  T_Monoid_882 -> MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_932 :: T_Monoid_882 -> T_Setoid_44
du_setoid_932 T_Monoid_882
v0
  = let v1 :: T_IsMonoid_686
v1 = T_Monoid_882 -> T_IsMonoid_686
d_isMonoid_906 (T_Monoid_882 -> T_Monoid_882
forall a b. a -> b
coe T_Monoid_882
v0) in
    AgdaAny -> T_Setoid_44
forall a b. a -> b
coe
      (let v2 :: T_IsSemigroup_472
v2
             = T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsMagma_176 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMagma_176 -> T_Setoid_44
MAlonzo.Code.Algebra.Structures.du_setoid_200
            ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v2))))
-- Algebra.Bundles.Monoid._.sym
d_sym_934 ::
  T_Monoid_882 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_934 :: T_Monoid_882 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_934 T_Monoid_882
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_36
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
         ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480
            ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
               ((T_Monoid_882 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Monoid_882 -> T_IsMonoid_686
d_isMonoid_906 (T_Monoid_882 -> AgdaAny
forall a b. a -> b
coe T_Monoid_882
v0)))))
-- Algebra.Bundles.Monoid._.trans
d_trans_936 ::
  T_Monoid_882 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_936 :: T_Monoid_882
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_936 T_Monoid_882
v0
  = (T_IsEquivalence_26
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_38
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
         ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480
            ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
               ((T_Monoid_882 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Monoid_882 -> T_IsMonoid_686
d_isMonoid_906 (T_Monoid_882 -> AgdaAny
forall a b. a -> b
coe T_Monoid_882
v0)))))
-- Algebra.Bundles.Monoid._.∙-cong
d_'8729''45'cong_938 ::
  T_Monoid_882 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_938 :: T_Monoid_882
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_938 T_Monoid_882
v0
  = (T_IsMagma_176
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsMagma_176
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_186
      ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480
         ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
            ((T_Monoid_882 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Monoid_882 -> T_IsMonoid_686
d_isMonoid_906 (T_Monoid_882 -> AgdaAny
forall a b. a -> b
coe T_Monoid_882
v0))))
-- Algebra.Bundles.Monoid._.∙-congʳ
d_'8729''45'cong'691'_940 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Monoid_882 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_940 :: ()
-> ()
-> T_Monoid_882
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_940 ~()
v0 ~()
v1 T_Monoid_882
v2
  = T_Monoid_882 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_940 T_Monoid_882
v2
du_'8729''45'cong'691'_940 ::
  T_Monoid_882 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_940 :: T_Monoid_882 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_940 T_Monoid_882
v0
  = let v1 :: T_IsMonoid_686
v1 = T_Monoid_882 -> T_IsMonoid_686
d_isMonoid_906 (T_Monoid_882 -> T_Monoid_882
forall a b. a -> b
coe T_Monoid_882
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemigroup_472
v2
             = T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'691'_206
            ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v2))))
-- Algebra.Bundles.Monoid._.∙-congˡ
d_'8729''45'cong'737'_942 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Monoid_882 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_942 :: ()
-> ()
-> T_Monoid_882
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_942 ~()
v0 ~()
v1 T_Monoid_882
v2
  = T_Monoid_882 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_942 T_Monoid_882
v2
du_'8729''45'cong'737'_942 ::
  T_Monoid_882 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_942 :: T_Monoid_882 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_942 T_Monoid_882
v0
  = let v1 :: T_IsMonoid_686
v1 = T_Monoid_882 -> T_IsMonoid_686
d_isMonoid_906 (T_Monoid_882 -> T_Monoid_882
forall a b. a -> b
coe T_Monoid_882
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemigroup_472
v2
             = T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'737'_202
            ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v2))))
-- Algebra.Bundles.Monoid.semigroup
d_semigroup_944 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Monoid_882 -> T_Semigroup_536
d_semigroup_944 :: () -> () -> T_Monoid_882 -> T_Semigroup_536
d_semigroup_944 ~()
v0 ~()
v1 T_Monoid_882
v2 = T_Monoid_882 -> T_Semigroup_536
du_semigroup_944 T_Monoid_882
v2
du_semigroup_944 :: T_Monoid_882 -> T_Semigroup_536
du_semigroup_944 :: T_Monoid_882 -> T_Semigroup_536
du_semigroup_944 T_Monoid_882
v0
  = ((AgdaAny -> AgdaAny -> AgdaAny)
 -> T_IsSemigroup_472 -> T_Semigroup_536)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsSemigroup_472
-> T_Semigroup_536
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsSemigroup_472 -> T_Semigroup_536
C_Semigroup'46'constructor_9793 (T_Monoid_882 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__902 (T_Monoid_882 -> T_Monoid_882
forall a b. a -> b
coe T_Monoid_882
v0))
      (T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
         ((T_Monoid_882 -> T_IsMonoid_686) -> AgdaAny -> T_IsMonoid_686
forall a b. a -> b
coe T_Monoid_882 -> T_IsMonoid_686
d_isMonoid_906 (T_Monoid_882 -> AgdaAny
forall a b. a -> b
coe T_Monoid_882
v0)))
-- Algebra.Bundles.Monoid._._≉_
d__'8777'__948 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Monoid_882 -> AgdaAny -> AgdaAny -> ()
d__'8777'__948 :: () -> () -> T_Monoid_882 -> AgdaAny -> AgdaAny -> ()
d__'8777'__948 = () -> () -> T_Monoid_882 -> AgdaAny -> AgdaAny -> ()
forall a. a
erased
-- Algebra.Bundles.Monoid._.magma
d_magma_950 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Monoid_882 -> T_Magma_68
d_magma_950 :: () -> () -> T_Monoid_882 -> T_Magma_68
d_magma_950 ~()
v0 ~()
v1 T_Monoid_882
v2 = T_Monoid_882 -> T_Magma_68
du_magma_950 T_Monoid_882
v2
du_magma_950 :: T_Monoid_882 -> T_Magma_68
du_magma_950 :: T_Monoid_882 -> T_Magma_68
du_magma_950 T_Monoid_882
v0 = (T_Semigroup_536 -> T_Magma_68) -> AgdaAny -> T_Magma_68
forall a b. a -> b
coe T_Semigroup_536 -> T_Magma_68
du_magma_584 ((T_Monoid_882 -> T_Semigroup_536) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Monoid_882 -> T_Semigroup_536
du_semigroup_944 (T_Monoid_882 -> AgdaAny
forall a b. a -> b
coe T_Monoid_882
v0))
-- Algebra.Bundles.Monoid._.rawMagma
d_rawMagma_952 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Monoid_882 -> MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
d_rawMagma_952 :: () -> () -> T_Monoid_882 -> T_RawMagma_36
d_rawMagma_952 ~()
v0 ~()
v1 T_Monoid_882
v2 = T_Monoid_882 -> T_RawMagma_36
du_rawMagma_952 T_Monoid_882
v2
du_rawMagma_952 ::
  T_Monoid_882 -> MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
du_rawMagma_952 :: T_Monoid_882 -> T_RawMagma_36
du_rawMagma_952 T_Monoid_882
v0
  = let v1 :: t
v1 = (T_Monoid_882 -> T_Semigroup_536) -> AgdaAny -> t
forall a b. a -> b
coe T_Monoid_882 -> T_Semigroup_536
du_semigroup_944 (T_Monoid_882 -> AgdaAny
forall a b. a -> b
coe T_Monoid_882
v0) in
    AgdaAny -> T_RawMagma_36
forall a b. a -> b
coe ((T_Magma_68 -> T_RawMagma_36) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Magma_68 -> T_RawMagma_36
du_rawMagma_112 ((T_Semigroup_536 -> T_Magma_68) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semigroup_536 -> T_Magma_68
du_magma_584 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1)))
-- Algebra.Bundles.Monoid.rawMonoid
d_rawMonoid_954 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Monoid_882 -> MAlonzo.Code.Algebra.Bundles.Raw.T_RawMonoid_64
d_rawMonoid_954 :: () -> () -> T_Monoid_882 -> T_RawMonoid_64
d_rawMonoid_954 ~()
v0 ~()
v1 T_Monoid_882
v2 = T_Monoid_882 -> T_RawMonoid_64
du_rawMonoid_954 T_Monoid_882
v2
du_rawMonoid_954 ::
  T_Monoid_882 -> MAlonzo.Code.Algebra.Bundles.Raw.T_RawMonoid_64
du_rawMonoid_954 :: T_Monoid_882 -> T_RawMonoid_64
du_rawMonoid_954 T_Monoid_882
v0
  = ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> T_RawMonoid_64)
-> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> T_RawMonoid_64
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> T_RawMonoid_64
MAlonzo.Code.Algebra.Bundles.Raw.C_RawMonoid'46'constructor_745
      (T_Monoid_882 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__902 (T_Monoid_882 -> T_Monoid_882
forall a b. a -> b
coe T_Monoid_882
v0)) (T_Monoid_882 -> AgdaAny
d_ε_904 (T_Monoid_882 -> T_Monoid_882
forall a b. a -> b
coe T_Monoid_882
v0))
-- Algebra.Bundles.Monoid.unitalMagma
d_unitalMagma_956 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Monoid_882 -> T_UnitalMagma_814
d_unitalMagma_956 :: () -> () -> T_Monoid_882 -> T_UnitalMagma_814
d_unitalMagma_956 ~()
v0 ~()
v1 T_Monoid_882
v2 = T_Monoid_882 -> T_UnitalMagma_814
du_unitalMagma_956 T_Monoid_882
v2
du_unitalMagma_956 :: T_Monoid_882 -> T_UnitalMagma_814
du_unitalMagma_956 :: T_Monoid_882 -> T_UnitalMagma_814
du_unitalMagma_956 T_Monoid_882
v0
  = ((AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny -> T_IsUnitalMagma_642 -> T_UnitalMagma_814)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_UnitalMagma_814
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> T_IsUnitalMagma_642 -> T_UnitalMagma_814
C_UnitalMagma'46'constructor_14927 (T_Monoid_882 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__902 (T_Monoid_882 -> T_Monoid_882
forall a b. a -> b
coe T_Monoid_882
v0))
      (T_Monoid_882 -> AgdaAny
d_ε_904 (T_Monoid_882 -> T_Monoid_882
forall a b. a -> b
coe T_Monoid_882
v0))
      ((T_IsMonoid_686 -> T_IsUnitalMagma_642) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoid_686 -> T_IsUnitalMagma_642
MAlonzo.Code.Algebra.Structures.du_isUnitalMagma_730
         ((T_Monoid_882 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Monoid_882 -> T_IsMonoid_686
d_isMonoid_906 (T_Monoid_882 -> AgdaAny
forall a b. a -> b
coe T_Monoid_882
v0)))
-- Algebra.Bundles.CommutativeMonoid
d_CommutativeMonoid_962 :: p -> p -> ()
d_CommutativeMonoid_962 p
a0 p
a1 = ()
data T_CommutativeMonoid_962
  = C_CommutativeMonoid'46'constructor_17931 (AgdaAny ->
                                              AgdaAny -> AgdaAny)
                                             AgdaAny
                                             MAlonzo.Code.Algebra.Structures.T_IsCommutativeMonoid_736
-- Algebra.Bundles.CommutativeMonoid.Carrier
d_Carrier_978 :: T_CommutativeMonoid_962 -> ()
d_Carrier_978 :: T_CommutativeMonoid_962 -> ()
d_Carrier_978 = T_CommutativeMonoid_962 -> ()
forall a. a
erased
-- Algebra.Bundles.CommutativeMonoid._≈_
d__'8776'__980 ::
  T_CommutativeMonoid_962 -> AgdaAny -> AgdaAny -> ()
d__'8776'__980 :: T_CommutativeMonoid_962 -> AgdaAny -> AgdaAny -> ()
d__'8776'__980 = T_CommutativeMonoid_962 -> AgdaAny -> AgdaAny -> ()
forall a. a
erased
-- Algebra.Bundles.CommutativeMonoid._∙_
d__'8729'__982 ::
  T_CommutativeMonoid_962 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__982 :: T_CommutativeMonoid_962 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__982 T_CommutativeMonoid_962
v0
  = case T_CommutativeMonoid_962 -> T_CommutativeMonoid_962
forall a b. a -> b
coe T_CommutativeMonoid_962
v0 of
      C_CommutativeMonoid'46'constructor_17931 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny
v4 T_IsCommutativeMonoid_736
v5 -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v3
      T_CommutativeMonoid_962
_ -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.CommutativeMonoid.ε
d_ε_984 :: T_CommutativeMonoid_962 -> AgdaAny
d_ε_984 :: T_CommutativeMonoid_962 -> AgdaAny
d_ε_984 T_CommutativeMonoid_962
v0
  = case T_CommutativeMonoid_962 -> T_CommutativeMonoid_962
forall a b. a -> b
coe T_CommutativeMonoid_962
v0 of
      C_CommutativeMonoid'46'constructor_17931 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny
v4 T_IsCommutativeMonoid_736
v5 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v4
      T_CommutativeMonoid_962
_ -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.CommutativeMonoid.isCommutativeMonoid
d_isCommutativeMonoid_986 ::
  T_CommutativeMonoid_962 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMonoid_736
d_isCommutativeMonoid_986 :: T_CommutativeMonoid_962 -> T_IsCommutativeMonoid_736
d_isCommutativeMonoid_986 T_CommutativeMonoid_962
v0
  = case T_CommutativeMonoid_962 -> T_CommutativeMonoid_962
forall a b. a -> b
coe T_CommutativeMonoid_962
v0 of
      C_CommutativeMonoid'46'constructor_17931 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny
v4 T_IsCommutativeMonoid_736
v5 -> T_IsCommutativeMonoid_736 -> T_IsCommutativeMonoid_736
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v5
      T_CommutativeMonoid_962
_ -> T_IsCommutativeMonoid_736
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.CommutativeMonoid._.assoc
d_assoc_990 ::
  T_CommutativeMonoid_962 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_990 :: T_CommutativeMonoid_962 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_990 T_CommutativeMonoid_962
v0
  = (T_IsSemigroup_472 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsSemigroup_472 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_assoc_482
      ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
         ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746
            ((T_CommutativeMonoid_962 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeMonoid_962 -> T_IsCommutativeMonoid_736
d_isCommutativeMonoid_986 (T_CommutativeMonoid_962 -> AgdaAny
forall a b. a -> b
coe T_CommutativeMonoid_962
v0))))
-- Algebra.Bundles.CommutativeMonoid._.comm
d_comm_992 ::
  T_CommutativeMonoid_962 -> AgdaAny -> AgdaAny -> AgdaAny
d_comm_992 :: T_CommutativeMonoid_962 -> AgdaAny -> AgdaAny -> AgdaAny
d_comm_992 T_CommutativeMonoid_962
v0
  = (T_IsCommutativeMonoid_736 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsCommutativeMonoid_736 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_comm_748
      ((T_CommutativeMonoid_962 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeMonoid_962 -> T_IsCommutativeMonoid_736
d_isCommutativeMonoid_986 (T_CommutativeMonoid_962 -> AgdaAny
forall a b. a -> b
coe T_CommutativeMonoid_962
v0))
-- Algebra.Bundles.CommutativeMonoid._.identity
d_identity_994 ::
  T_CommutativeMonoid_962 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_identity_994 :: T_CommutativeMonoid_962 -> T_Σ_14
d_identity_994 T_CommutativeMonoid_962
v0
  = (T_IsMonoid_686 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsMonoid_686 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_identity_698
      ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746
         ((T_CommutativeMonoid_962 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeMonoid_962 -> T_IsCommutativeMonoid_736
d_isCommutativeMonoid_986 (T_CommutativeMonoid_962 -> AgdaAny
forall a b. a -> b
coe T_CommutativeMonoid_962
v0)))
-- Algebra.Bundles.CommutativeMonoid._.identityʳ
d_identity'691'_996 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeMonoid_962 -> AgdaAny -> AgdaAny
d_identity'691'_996 :: () -> () -> T_CommutativeMonoid_962 -> AgdaAny -> AgdaAny
d_identity'691'_996 ~()
v0 ~()
v1 T_CommutativeMonoid_962
v2 = T_CommutativeMonoid_962 -> AgdaAny -> AgdaAny
du_identity'691'_996 T_CommutativeMonoid_962
v2
du_identity'691'_996 ::
  T_CommutativeMonoid_962 -> AgdaAny -> AgdaAny
du_identity'691'_996 :: T_CommutativeMonoid_962 -> AgdaAny -> AgdaAny
du_identity'691'_996 T_CommutativeMonoid_962
v0
  = let v1 :: T_IsCommutativeMonoid_736
v1 = T_CommutativeMonoid_962 -> T_IsCommutativeMonoid_736
d_isCommutativeMonoid_986 (T_CommutativeMonoid_962 -> T_CommutativeMonoid_962
forall a b. a -> b
coe T_CommutativeMonoid_962
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsMonoid_686 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoid_686 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_identity'691'_728
         ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746 (T_IsCommutativeMonoid_736 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v1)))
-- Algebra.Bundles.CommutativeMonoid._.identityˡ
d_identity'737'_998 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeMonoid_962 -> AgdaAny -> AgdaAny
d_identity'737'_998 :: () -> () -> T_CommutativeMonoid_962 -> AgdaAny -> AgdaAny
d_identity'737'_998 ~()
v0 ~()
v1 T_CommutativeMonoid_962
v2 = T_CommutativeMonoid_962 -> AgdaAny -> AgdaAny
du_identity'737'_998 T_CommutativeMonoid_962
v2
du_identity'737'_998 ::
  T_CommutativeMonoid_962 -> AgdaAny -> AgdaAny
du_identity'737'_998 :: T_CommutativeMonoid_962 -> AgdaAny -> AgdaAny
du_identity'737'_998 T_CommutativeMonoid_962
v0
  = let v1 :: T_IsCommutativeMonoid_736
v1 = T_CommutativeMonoid_962 -> T_IsCommutativeMonoid_736
d_isCommutativeMonoid_986 (T_CommutativeMonoid_962 -> T_CommutativeMonoid_962
forall a b. a -> b
coe T_CommutativeMonoid_962
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsMonoid_686 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoid_686 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_identity'737'_726
         ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746 (T_IsCommutativeMonoid_736 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v1)))
-- Algebra.Bundles.CommutativeMonoid._.isCommutativeMagma
d_isCommutativeMagma_1000 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeMonoid_962 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMagma_212
d_isCommutativeMagma_1000 :: () -> () -> T_CommutativeMonoid_962 -> T_IsCommutativeMagma_212
d_isCommutativeMagma_1000 ~()
v0 ~()
v1 T_CommutativeMonoid_962
v2
  = T_CommutativeMonoid_962 -> T_IsCommutativeMagma_212
du_isCommutativeMagma_1000 T_CommutativeMonoid_962
v2
du_isCommutativeMagma_1000 ::
  T_CommutativeMonoid_962 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMagma_212
du_isCommutativeMagma_1000 :: T_CommutativeMonoid_962 -> T_IsCommutativeMagma_212
du_isCommutativeMagma_1000 T_CommutativeMonoid_962
v0
  = let v1 :: T_IsCommutativeMonoid_736
v1 = T_CommutativeMonoid_962 -> T_IsCommutativeMonoid_736
d_isCommutativeMonoid_986 (T_CommutativeMonoid_962 -> T_CommutativeMonoid_962
forall a b. a -> b
coe T_CommutativeMonoid_962
v0) in
    AgdaAny -> T_IsCommutativeMagma_212
forall a b. a -> b
coe
      ((T_IsCommutativeSemigroup_548 -> T_IsCommutativeMagma_212)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCommutativeSemigroup_548 -> T_IsCommutativeMagma_212
MAlonzo.Code.Algebra.Structures.du_isCommutativeMagma_586
         ((T_IsCommutativeMonoid_736 -> T_IsCommutativeSemigroup_548)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCommutativeMonoid_736 -> T_IsCommutativeSemigroup_548
MAlonzo.Code.Algebra.Structures.du_isCommutativeSemigroup_786
            (T_IsCommutativeMonoid_736 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v1)))
-- Algebra.Bundles.CommutativeMonoid._.isCommutativeSemigroup
d_isCommutativeSemigroup_1002 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeMonoid_962 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_548
d_isCommutativeSemigroup_1002 :: () -> () -> T_CommutativeMonoid_962 -> T_IsCommutativeSemigroup_548
d_isCommutativeSemigroup_1002 ~()
v0 ~()
v1 T_CommutativeMonoid_962
v2
  = T_CommutativeMonoid_962 -> T_IsCommutativeSemigroup_548
du_isCommutativeSemigroup_1002 T_CommutativeMonoid_962
v2
du_isCommutativeSemigroup_1002 ::
  T_CommutativeMonoid_962 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_548
du_isCommutativeSemigroup_1002 :: T_CommutativeMonoid_962 -> T_IsCommutativeSemigroup_548
du_isCommutativeSemigroup_1002 T_CommutativeMonoid_962
v0
  = (T_IsCommutativeMonoid_736 -> T_IsCommutativeSemigroup_548)
-> AgdaAny -> T_IsCommutativeSemigroup_548
forall a b. a -> b
coe
      T_IsCommutativeMonoid_736 -> T_IsCommutativeSemigroup_548
MAlonzo.Code.Algebra.Structures.du_isCommutativeSemigroup_786
      ((T_CommutativeMonoid_962 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeMonoid_962 -> T_IsCommutativeMonoid_736
d_isCommutativeMonoid_986 (T_CommutativeMonoid_962 -> AgdaAny
forall a b. a -> b
coe T_CommutativeMonoid_962
v0))
-- Algebra.Bundles.CommutativeMonoid._.isEquivalence
d_isEquivalence_1004 ::
  T_CommutativeMonoid_962 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_1004 :: T_CommutativeMonoid_962 -> T_IsEquivalence_26
d_isEquivalence_1004 T_CommutativeMonoid_962
v0
  = (T_IsMagma_176 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
      ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480
         ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
            ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746
               ((T_CommutativeMonoid_962 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeMonoid_962 -> T_IsCommutativeMonoid_736
d_isCommutativeMonoid_986 (T_CommutativeMonoid_962 -> AgdaAny
forall a b. a -> b
coe T_CommutativeMonoid_962
v0)))))
-- Algebra.Bundles.CommutativeMonoid._.isMagma
d_isMagma_1006 ::
  T_CommutativeMonoid_962 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_176
d_isMagma_1006 :: T_CommutativeMonoid_962 -> T_IsMagma_176
d_isMagma_1006 T_CommutativeMonoid_962
v0
  = (T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> T_IsMagma_176
forall a b. a -> b
coe
      T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480
      ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
         ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746
            ((T_CommutativeMonoid_962 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeMonoid_962 -> T_IsCommutativeMonoid_736
d_isCommutativeMonoid_986 (T_CommutativeMonoid_962 -> AgdaAny
forall a b. a -> b
coe T_CommutativeMonoid_962
v0))))
-- Algebra.Bundles.CommutativeMonoid._.isMonoid
d_isMonoid_1008 ::
  T_CommutativeMonoid_962 ->
  MAlonzo.Code.Algebra.Structures.T_IsMonoid_686
d_isMonoid_1008 :: T_CommutativeMonoid_962 -> T_IsMonoid_686
d_isMonoid_1008 T_CommutativeMonoid_962
v0
  = (T_IsCommutativeMonoid_736 -> T_IsMonoid_686)
-> AgdaAny -> T_IsMonoid_686
forall a b. a -> b
coe
      T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746
      ((T_CommutativeMonoid_962 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeMonoid_962 -> T_IsCommutativeMonoid_736
d_isCommutativeMonoid_986 (T_CommutativeMonoid_962 -> AgdaAny
forall a b. a -> b
coe T_CommutativeMonoid_962
v0))
-- Algebra.Bundles.CommutativeMonoid._.isPartialEquivalence
d_isPartialEquivalence_1010 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeMonoid_962 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_1010 :: () -> () -> T_CommutativeMonoid_962 -> T_IsPartialEquivalence_16
d_isPartialEquivalence_1010 ~()
v0 ~()
v1 T_CommutativeMonoid_962
v2
  = T_CommutativeMonoid_962 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_1010 T_CommutativeMonoid_962
v2
du_isPartialEquivalence_1010 ::
  T_CommutativeMonoid_962 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_1010 :: T_CommutativeMonoid_962 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_1010 T_CommutativeMonoid_962
v0
  = let v1 :: T_IsCommutativeMonoid_736
v1 = T_CommutativeMonoid_962 -> T_IsCommutativeMonoid_736
d_isCommutativeMonoid_986 (T_CommutativeMonoid_962 -> T_CommutativeMonoid_962
forall a b. a -> b
coe T_CommutativeMonoid_962
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsMonoid_686
v2
             = T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746 (T_IsCommutativeMonoid_736 -> T_IsCommutativeMonoid_736
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_472
v3
                = T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsMagma_176
v4 = T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (T_IsSemigroup_472 -> T_IsSemigroup_472
forall a b. a -> b
coe T_IsSemigroup_472
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               ((T_IsEquivalence_26 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsEquivalence_26 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
                  ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v4))))))
-- Algebra.Bundles.CommutativeMonoid._.isSemigroup
d_isSemigroup_1012 ::
  T_CommutativeMonoid_962 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_472
d_isSemigroup_1012 :: T_CommutativeMonoid_962 -> T_IsSemigroup_472
d_isSemigroup_1012 T_CommutativeMonoid_962
v0
  = (T_IsMonoid_686 -> T_IsSemigroup_472)
-> AgdaAny -> T_IsSemigroup_472
forall a b. a -> b
coe
      T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
      ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746
         ((T_CommutativeMonoid_962 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeMonoid_962 -> T_IsCommutativeMonoid_736
d_isCommutativeMonoid_986 (T_CommutativeMonoid_962 -> AgdaAny
forall a b. a -> b
coe T_CommutativeMonoid_962
v0)))
-- Algebra.Bundles.CommutativeMonoid._.isUnitalMagma
d_isUnitalMagma_1014 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeMonoid_962 ->
  MAlonzo.Code.Algebra.Structures.T_IsUnitalMagma_642
d_isUnitalMagma_1014 :: () -> () -> T_CommutativeMonoid_962 -> T_IsUnitalMagma_642
d_isUnitalMagma_1014 ~()
v0 ~()
v1 T_CommutativeMonoid_962
v2 = T_CommutativeMonoid_962 -> T_IsUnitalMagma_642
du_isUnitalMagma_1014 T_CommutativeMonoid_962
v2
du_isUnitalMagma_1014 ::
  T_CommutativeMonoid_962 ->
  MAlonzo.Code.Algebra.Structures.T_IsUnitalMagma_642
du_isUnitalMagma_1014 :: T_CommutativeMonoid_962 -> T_IsUnitalMagma_642
du_isUnitalMagma_1014 T_CommutativeMonoid_962
v0
  = let v1 :: T_IsCommutativeMonoid_736
v1 = T_CommutativeMonoid_962 -> T_IsCommutativeMonoid_736
d_isCommutativeMonoid_986 (T_CommutativeMonoid_962 -> T_CommutativeMonoid_962
forall a b. a -> b
coe T_CommutativeMonoid_962
v0) in
    AgdaAny -> T_IsUnitalMagma_642
forall a b. a -> b
coe
      ((T_IsMonoid_686 -> T_IsUnitalMagma_642) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoid_686 -> T_IsUnitalMagma_642
MAlonzo.Code.Algebra.Structures.du_isUnitalMagma_730
         ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746 (T_IsCommutativeMonoid_736 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v1)))
-- Algebra.Bundles.CommutativeMonoid._.refl
d_refl_1016 :: T_CommutativeMonoid_962 -> AgdaAny -> AgdaAny
d_refl_1016 :: T_CommutativeMonoid_962 -> AgdaAny -> AgdaAny
d_refl_1016 T_CommutativeMonoid_962
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_34
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
         ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480
            ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
               ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746
                  ((T_CommutativeMonoid_962 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeMonoid_962 -> T_IsCommutativeMonoid_736
d_isCommutativeMonoid_986 (T_CommutativeMonoid_962 -> AgdaAny
forall a b. a -> b
coe T_CommutativeMonoid_962
v0))))))
-- Algebra.Bundles.CommutativeMonoid._.reflexive
d_reflexive_1018 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeMonoid_962 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_1018 :: ()
-> ()
-> T_CommutativeMonoid_962
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_1018 ~()
v0 ~()
v1 T_CommutativeMonoid_962
v2 = T_CommutativeMonoid_962
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_1018 T_CommutativeMonoid_962
v2
du_reflexive_1018 ::
  T_CommutativeMonoid_962 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_1018 :: T_CommutativeMonoid_962
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_1018 T_CommutativeMonoid_962
v0
  = let v1 :: T_IsCommutativeMonoid_736
v1 = T_CommutativeMonoid_962 -> T_IsCommutativeMonoid_736
d_isCommutativeMonoid_986 (T_CommutativeMonoid_962 -> T_CommutativeMonoid_962
forall a b. a -> b
coe T_CommutativeMonoid_962
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsMonoid_686
v2
             = T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746 (T_IsCommutativeMonoid_736 -> T_IsCommutativeMonoid_736
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_472
v3
                = T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsMagma_176
v4 = T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (T_IsSemigroup_472 -> T_IsSemigroup_472
forall a b. a -> b
coe T_IsSemigroup_472
v3) in
             (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
               (\ AgdaAny
v5 AgdaAny
v6 AgdaAny
v7 ->
                  (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                    T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
                    ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v4))
                    AgdaAny
v5))))
-- Algebra.Bundles.CommutativeMonoid._.setoid
d_setoid_1020 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeMonoid_962 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_1020 :: () -> () -> T_CommutativeMonoid_962 -> T_Setoid_44
d_setoid_1020 ~()
v0 ~()
v1 T_CommutativeMonoid_962
v2 = T_CommutativeMonoid_962 -> T_Setoid_44
du_setoid_1020 T_CommutativeMonoid_962
v2
du_setoid_1020 ::
  T_CommutativeMonoid_962 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_1020 :: T_CommutativeMonoid_962 -> T_Setoid_44
du_setoid_1020 T_CommutativeMonoid_962
v0
  = let v1 :: T_IsCommutativeMonoid_736
v1 = T_CommutativeMonoid_962 -> T_IsCommutativeMonoid_736
d_isCommutativeMonoid_986 (T_CommutativeMonoid_962 -> T_CommutativeMonoid_962
forall a b. a -> b
coe T_CommutativeMonoid_962
v0) in
    AgdaAny -> T_Setoid_44
forall a b. a -> b
coe
      (let v2 :: T_IsMonoid_686
v2
             = T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746 (T_IsCommutativeMonoid_736 -> T_IsCommutativeMonoid_736
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_472
v3
                = T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsMagma_176 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMagma_176 -> T_Setoid_44
MAlonzo.Code.Algebra.Structures.du_setoid_200
               ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v3)))))
-- Algebra.Bundles.CommutativeMonoid._.sym
d_sym_1022 ::
  T_CommutativeMonoid_962 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_1022 :: T_CommutativeMonoid_962 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_1022 T_CommutativeMonoid_962
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_36
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
         ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480
            ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
               ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746
                  ((T_CommutativeMonoid_962 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeMonoid_962 -> T_IsCommutativeMonoid_736
d_isCommutativeMonoid_986 (T_CommutativeMonoid_962 -> AgdaAny
forall a b. a -> b
coe T_CommutativeMonoid_962
v0))))))
-- Algebra.Bundles.CommutativeMonoid._.trans
d_trans_1024 ::
  T_CommutativeMonoid_962 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_1024 :: T_CommutativeMonoid_962
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_1024 T_CommutativeMonoid_962
v0
  = (T_IsEquivalence_26
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_38
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
         ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480
            ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
               ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746
                  ((T_CommutativeMonoid_962 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeMonoid_962 -> T_IsCommutativeMonoid_736
d_isCommutativeMonoid_986 (T_CommutativeMonoid_962 -> AgdaAny
forall a b. a -> b
coe T_CommutativeMonoid_962
v0))))))
-- Algebra.Bundles.CommutativeMonoid._.∙-cong
d_'8729''45'cong_1026 ::
  T_CommutativeMonoid_962 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_1026 :: T_CommutativeMonoid_962
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_1026 T_CommutativeMonoid_962
v0
  = (T_IsMagma_176
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsMagma_176
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_186
      ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480
         ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
            ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746
               ((T_CommutativeMonoid_962 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeMonoid_962 -> T_IsCommutativeMonoid_736
d_isCommutativeMonoid_986 (T_CommutativeMonoid_962 -> AgdaAny
forall a b. a -> b
coe T_CommutativeMonoid_962
v0)))))
-- Algebra.Bundles.CommutativeMonoid._.∙-congʳ
d_'8729''45'cong'691'_1028 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeMonoid_962 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_1028 :: ()
-> ()
-> T_CommutativeMonoid_962
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_1028 ~()
v0 ~()
v1 T_CommutativeMonoid_962
v2
  = T_CommutativeMonoid_962
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1028 T_CommutativeMonoid_962
v2
du_'8729''45'cong'691'_1028 ::
  T_CommutativeMonoid_962 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1028 :: T_CommutativeMonoid_962
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1028 T_CommutativeMonoid_962
v0
  = let v1 :: T_IsCommutativeMonoid_736
v1 = T_CommutativeMonoid_962 -> T_IsCommutativeMonoid_736
d_isCommutativeMonoid_986 (T_CommutativeMonoid_962 -> T_CommutativeMonoid_962
forall a b. a -> b
coe T_CommutativeMonoid_962
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsMonoid_686
v2
             = T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746 (T_IsCommutativeMonoid_736 -> T_IsCommutativeMonoid_736
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_472
v3
                = T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'691'_206
               ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v3)))))
-- Algebra.Bundles.CommutativeMonoid._.∙-congˡ
d_'8729''45'cong'737'_1030 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeMonoid_962 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_1030 :: ()
-> ()
-> T_CommutativeMonoid_962
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_1030 ~()
v0 ~()
v1 T_CommutativeMonoid_962
v2
  = T_CommutativeMonoid_962
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1030 T_CommutativeMonoid_962
v2
du_'8729''45'cong'737'_1030 ::
  T_CommutativeMonoid_962 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1030 :: T_CommutativeMonoid_962
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1030 T_CommutativeMonoid_962
v0
  = let v1 :: T_IsCommutativeMonoid_736
v1 = T_CommutativeMonoid_962 -> T_IsCommutativeMonoid_736
d_isCommutativeMonoid_986 (T_CommutativeMonoid_962 -> T_CommutativeMonoid_962
forall a b. a -> b
coe T_CommutativeMonoid_962
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsMonoid_686
v2
             = T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746 (T_IsCommutativeMonoid_736 -> T_IsCommutativeMonoid_736
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_472
v3
                = T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'737'_202
               ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v3)))))
-- Algebra.Bundles.CommutativeMonoid.monoid
d_monoid_1032 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeMonoid_962 -> T_Monoid_882
d_monoid_1032 :: () -> () -> T_CommutativeMonoid_962 -> T_Monoid_882
d_monoid_1032 ~()
v0 ~()
v1 T_CommutativeMonoid_962
v2 = T_CommutativeMonoid_962 -> T_Monoid_882
du_monoid_1032 T_CommutativeMonoid_962
v2
du_monoid_1032 :: T_CommutativeMonoid_962 -> T_Monoid_882
du_monoid_1032 :: T_CommutativeMonoid_962 -> T_Monoid_882
du_monoid_1032 T_CommutativeMonoid_962
v0
  = ((AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny -> T_IsMonoid_686 -> T_Monoid_882)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsMonoid_686
-> T_Monoid_882
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> T_IsMonoid_686 -> T_Monoid_882
C_Monoid'46'constructor_16157 (T_CommutativeMonoid_962 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__982 (T_CommutativeMonoid_962 -> T_CommutativeMonoid_962
forall a b. a -> b
coe T_CommutativeMonoid_962
v0))
      (T_CommutativeMonoid_962 -> AgdaAny
d_ε_984 (T_CommutativeMonoid_962 -> T_CommutativeMonoid_962
forall a b. a -> b
coe T_CommutativeMonoid_962
v0))
      (T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746
         ((T_CommutativeMonoid_962 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> T_IsCommutativeMonoid_736
forall a b. a -> b
coe T_CommutativeMonoid_962 -> T_IsCommutativeMonoid_736
d_isCommutativeMonoid_986 (T_CommutativeMonoid_962 -> AgdaAny
forall a b. a -> b
coe T_CommutativeMonoid_962
v0)))
-- Algebra.Bundles.CommutativeMonoid._._≉_
d__'8777'__1036 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeMonoid_962 -> AgdaAny -> AgdaAny -> ()
d__'8777'__1036 :: () -> () -> T_CommutativeMonoid_962 -> AgdaAny -> AgdaAny -> ()
d__'8777'__1036 = () -> () -> T_CommutativeMonoid_962 -> AgdaAny -> AgdaAny -> ()
forall a. a
erased
-- Algebra.Bundles.CommutativeMonoid._.magma
d_magma_1038 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeMonoid_962 -> T_Magma_68
d_magma_1038 :: () -> () -> T_CommutativeMonoid_962 -> T_Magma_68
d_magma_1038 ~()
v0 ~()
v1 T_CommutativeMonoid_962
v2 = T_CommutativeMonoid_962 -> T_Magma_68
du_magma_1038 T_CommutativeMonoid_962
v2
du_magma_1038 :: T_CommutativeMonoid_962 -> T_Magma_68
du_magma_1038 :: T_CommutativeMonoid_962 -> T_Magma_68
du_magma_1038 T_CommutativeMonoid_962
v0
  = let v1 :: t
v1 = (T_CommutativeMonoid_962 -> T_Monoid_882) -> AgdaAny -> t
forall a b. a -> b
coe T_CommutativeMonoid_962 -> T_Monoid_882
du_monoid_1032 (T_CommutativeMonoid_962 -> AgdaAny
forall a b. a -> b
coe T_CommutativeMonoid_962
v0) in
    AgdaAny -> T_Magma_68
forall a b. a -> b
coe ((T_Semigroup_536 -> T_Magma_68) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semigroup_536 -> T_Magma_68
du_magma_584 ((T_Monoid_882 -> T_Semigroup_536) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Monoid_882 -> T_Semigroup_536
du_semigroup_944 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1)))
-- Algebra.Bundles.CommutativeMonoid._.rawMagma
d_rawMagma_1040 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeMonoid_962 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
d_rawMagma_1040 :: () -> () -> T_CommutativeMonoid_962 -> T_RawMagma_36
d_rawMagma_1040 ~()
v0 ~()
v1 T_CommutativeMonoid_962
v2 = T_CommutativeMonoid_962 -> T_RawMagma_36
du_rawMagma_1040 T_CommutativeMonoid_962
v2
du_rawMagma_1040 ::
  T_CommutativeMonoid_962 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
du_rawMagma_1040 :: T_CommutativeMonoid_962 -> T_RawMagma_36
du_rawMagma_1040 T_CommutativeMonoid_962
v0
  = let v1 :: t
v1 = (T_CommutativeMonoid_962 -> T_Monoid_882) -> AgdaAny -> t
forall a b. a -> b
coe T_CommutativeMonoid_962 -> T_Monoid_882
du_monoid_1032 (T_CommutativeMonoid_962 -> AgdaAny
forall a b. a -> b
coe T_CommutativeMonoid_962
v0) in
    AgdaAny -> T_RawMagma_36
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_Monoid_882 -> T_Semigroup_536) -> AgdaAny -> t
forall a b. a -> b
coe T_Monoid_882 -> T_Semigroup_536
du_semigroup_944 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_Magma_68 -> T_RawMagma_36) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Magma_68 -> T_RawMagma_36
du_rawMagma_112 ((T_Semigroup_536 -> T_Magma_68) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semigroup_536 -> T_Magma_68
du_magma_584 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2))))
-- Algebra.Bundles.CommutativeMonoid._.rawMonoid
d_rawMonoid_1042 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeMonoid_962 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMonoid_64
d_rawMonoid_1042 :: () -> () -> T_CommutativeMonoid_962 -> T_RawMonoid_64
d_rawMonoid_1042 ~()
v0 ~()
v1 T_CommutativeMonoid_962
v2 = T_CommutativeMonoid_962 -> T_RawMonoid_64
du_rawMonoid_1042 T_CommutativeMonoid_962
v2
du_rawMonoid_1042 ::
  T_CommutativeMonoid_962 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMonoid_64
du_rawMonoid_1042 :: T_CommutativeMonoid_962 -> T_RawMonoid_64
du_rawMonoid_1042 T_CommutativeMonoid_962
v0
  = (T_Monoid_882 -> T_RawMonoid_64) -> AgdaAny -> T_RawMonoid_64
forall a b. a -> b
coe T_Monoid_882 -> T_RawMonoid_64
du_rawMonoid_954 ((T_CommutativeMonoid_962 -> T_Monoid_882) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeMonoid_962 -> T_Monoid_882
du_monoid_1032 (T_CommutativeMonoid_962 -> AgdaAny
forall a b. a -> b
coe T_CommutativeMonoid_962
v0))
-- Algebra.Bundles.CommutativeMonoid._.semigroup
d_semigroup_1044 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeMonoid_962 -> T_Semigroup_536
d_semigroup_1044 :: () -> () -> T_CommutativeMonoid_962 -> T_Semigroup_536
d_semigroup_1044 ~()
v0 ~()
v1 T_CommutativeMonoid_962
v2 = T_CommutativeMonoid_962 -> T_Semigroup_536
du_semigroup_1044 T_CommutativeMonoid_962
v2
du_semigroup_1044 :: T_CommutativeMonoid_962 -> T_Semigroup_536
du_semigroup_1044 :: T_CommutativeMonoid_962 -> T_Semigroup_536
du_semigroup_1044 T_CommutativeMonoid_962
v0
  = (T_Monoid_882 -> T_Semigroup_536) -> AgdaAny -> T_Semigroup_536
forall a b. a -> b
coe T_Monoid_882 -> T_Semigroup_536
du_semigroup_944 ((T_CommutativeMonoid_962 -> T_Monoid_882) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeMonoid_962 -> T_Monoid_882
du_monoid_1032 (T_CommutativeMonoid_962 -> AgdaAny
forall a b. a -> b
coe T_CommutativeMonoid_962
v0))
-- Algebra.Bundles.CommutativeMonoid._.unitalMagma
d_unitalMagma_1046 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeMonoid_962 -> T_UnitalMagma_814
d_unitalMagma_1046 :: () -> () -> T_CommutativeMonoid_962 -> T_UnitalMagma_814
d_unitalMagma_1046 ~()
v0 ~()
v1 T_CommutativeMonoid_962
v2 = T_CommutativeMonoid_962 -> T_UnitalMagma_814
du_unitalMagma_1046 T_CommutativeMonoid_962
v2
du_unitalMagma_1046 :: T_CommutativeMonoid_962 -> T_UnitalMagma_814
du_unitalMagma_1046 :: T_CommutativeMonoid_962 -> T_UnitalMagma_814
du_unitalMagma_1046 T_CommutativeMonoid_962
v0
  = (T_Monoid_882 -> T_UnitalMagma_814) -> AgdaAny -> T_UnitalMagma_814
forall a b. a -> b
coe T_Monoid_882 -> T_UnitalMagma_814
du_unitalMagma_956 ((T_CommutativeMonoid_962 -> T_Monoid_882) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeMonoid_962 -> T_Monoid_882
du_monoid_1032 (T_CommutativeMonoid_962 -> AgdaAny
forall a b. a -> b
coe T_CommutativeMonoid_962
v0))
-- Algebra.Bundles.CommutativeMonoid.commutativeSemigroup
d_commutativeSemigroup_1048 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeMonoid_962 -> T_CommutativeSemigroup_662
d_commutativeSemigroup_1048 :: () -> () -> T_CommutativeMonoid_962 -> T_CommutativeSemigroup_662
d_commutativeSemigroup_1048 ~()
v0 ~()
v1 T_CommutativeMonoid_962
v2
  = T_CommutativeMonoid_962 -> T_CommutativeSemigroup_662
du_commutativeSemigroup_1048 T_CommutativeMonoid_962
v2
du_commutativeSemigroup_1048 ::
  T_CommutativeMonoid_962 -> T_CommutativeSemigroup_662
du_commutativeSemigroup_1048 :: T_CommutativeMonoid_962 -> T_CommutativeSemigroup_662
du_commutativeSemigroup_1048 T_CommutativeMonoid_962
v0
  = ((AgdaAny -> AgdaAny -> AgdaAny)
 -> T_IsCommutativeSemigroup_548 -> T_CommutativeSemigroup_662)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_CommutativeSemigroup_662
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsCommutativeSemigroup_548 -> T_CommutativeSemigroup_662
C_CommutativeSemigroup'46'constructor_12035
      (T_CommutativeMonoid_962 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__982 (T_CommutativeMonoid_962 -> T_CommutativeMonoid_962
forall a b. a -> b
coe T_CommutativeMonoid_962
v0))
      ((T_IsCommutativeMonoid_736 -> T_IsCommutativeSemigroup_548)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCommutativeMonoid_736 -> T_IsCommutativeSemigroup_548
MAlonzo.Code.Algebra.Structures.du_isCommutativeSemigroup_786
         ((T_CommutativeMonoid_962 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeMonoid_962 -> T_IsCommutativeMonoid_736
d_isCommutativeMonoid_986 (T_CommutativeMonoid_962 -> AgdaAny
forall a b. a -> b
coe T_CommutativeMonoid_962
v0)))
-- Algebra.Bundles.CommutativeMonoid._.commutativeMagma
d_commutativeMagma_1052 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeMonoid_962 -> T_CommutativeMagma_180
d_commutativeMagma_1052 :: () -> () -> T_CommutativeMonoid_962 -> T_CommutativeMagma_180
d_commutativeMagma_1052 ~()
v0 ~()
v1 T_CommutativeMonoid_962
v2 = T_CommutativeMonoid_962 -> T_CommutativeMagma_180
du_commutativeMagma_1052 T_CommutativeMonoid_962
v2
du_commutativeMagma_1052 ::
  T_CommutativeMonoid_962 -> T_CommutativeMagma_180
du_commutativeMagma_1052 :: T_CommutativeMonoid_962 -> T_CommutativeMagma_180
du_commutativeMagma_1052 T_CommutativeMonoid_962
v0
  = (T_CommutativeSemigroup_662 -> T_CommutativeMagma_180)
-> AgdaAny -> T_CommutativeMagma_180
forall a b. a -> b
coe
      T_CommutativeSemigroup_662 -> T_CommutativeMagma_180
du_commutativeMagma_726 ((T_CommutativeMonoid_962 -> T_CommutativeSemigroup_662)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeMonoid_962 -> T_CommutativeSemigroup_662
du_commutativeSemigroup_1048 (T_CommutativeMonoid_962 -> AgdaAny
forall a b. a -> b
coe T_CommutativeMonoid_962
v0))
-- Algebra.Bundles.IdempotentMonoid
d_IdempotentMonoid_1058 :: p -> p -> ()
d_IdempotentMonoid_1058 p
a0 p
a1 = ()
data T_IdempotentMonoid_1058
  = C_IdempotentMonoid'46'constructor_19753 (AgdaAny ->
                                             AgdaAny -> AgdaAny)
                                            AgdaAny
                                            MAlonzo.Code.Algebra.Structures.T_IsIdempotentMonoid_796
-- Algebra.Bundles.IdempotentMonoid.Carrier
d_Carrier_1074 :: T_IdempotentMonoid_1058 -> ()
d_Carrier_1074 :: T_IdempotentMonoid_1058 -> ()
d_Carrier_1074 = T_IdempotentMonoid_1058 -> ()
forall a. a
erased
-- Algebra.Bundles.IdempotentMonoid._≈_
d__'8776'__1076 ::
  T_IdempotentMonoid_1058 -> AgdaAny -> AgdaAny -> ()
d__'8776'__1076 :: T_IdempotentMonoid_1058 -> AgdaAny -> AgdaAny -> ()
d__'8776'__1076 = T_IdempotentMonoid_1058 -> AgdaAny -> AgdaAny -> ()
forall a. a
erased
-- Algebra.Bundles.IdempotentMonoid._∙_
d__'8729'__1078 ::
  T_IdempotentMonoid_1058 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__1078 :: T_IdempotentMonoid_1058 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__1078 T_IdempotentMonoid_1058
v0
  = case T_IdempotentMonoid_1058 -> T_IdempotentMonoid_1058
forall a b. a -> b
coe T_IdempotentMonoid_1058
v0 of
      C_IdempotentMonoid'46'constructor_19753 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny
v4 T_IsIdempotentMonoid_796
v5 -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v3
      T_IdempotentMonoid_1058
_ -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.IdempotentMonoid.ε
d_ε_1080 :: T_IdempotentMonoid_1058 -> AgdaAny
d_ε_1080 :: T_IdempotentMonoid_1058 -> AgdaAny
d_ε_1080 T_IdempotentMonoid_1058
v0
  = case T_IdempotentMonoid_1058 -> T_IdempotentMonoid_1058
forall a b. a -> b
coe T_IdempotentMonoid_1058
v0 of
      C_IdempotentMonoid'46'constructor_19753 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny
v4 T_IsIdempotentMonoid_796
v5 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v4
      T_IdempotentMonoid_1058
_ -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.IdempotentMonoid.isIdempotentMonoid
d_isIdempotentMonoid_1082 ::
  T_IdempotentMonoid_1058 ->
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentMonoid_796
d_isIdempotentMonoid_1082 :: T_IdempotentMonoid_1058 -> T_IsIdempotentMonoid_796
d_isIdempotentMonoid_1082 T_IdempotentMonoid_1058
v0
  = case T_IdempotentMonoid_1058 -> T_IdempotentMonoid_1058
forall a b. a -> b
coe T_IdempotentMonoid_1058
v0 of
      C_IdempotentMonoid'46'constructor_19753 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny
v4 T_IsIdempotentMonoid_796
v5 -> T_IsIdempotentMonoid_796 -> T_IsIdempotentMonoid_796
forall a b. a -> b
coe T_IsIdempotentMonoid_796
v5
      T_IdempotentMonoid_1058
_ -> T_IsIdempotentMonoid_796
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.IdempotentMonoid._.assoc
d_assoc_1086 ::
  T_IdempotentMonoid_1058 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_1086 :: T_IdempotentMonoid_1058 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_1086 T_IdempotentMonoid_1058
v0
  = (T_IsSemigroup_472 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsSemigroup_472 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_assoc_482
      ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
         ((T_IsIdempotentMonoid_796 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsIdempotentMonoid_796 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_806
            ((T_IdempotentMonoid_1058 -> T_IsIdempotentMonoid_796)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IdempotentMonoid_1058 -> T_IsIdempotentMonoid_796
d_isIdempotentMonoid_1082 (T_IdempotentMonoid_1058 -> AgdaAny
forall a b. a -> b
coe T_IdempotentMonoid_1058
v0))))
-- Algebra.Bundles.IdempotentMonoid._.idem
d_idem_1088 :: T_IdempotentMonoid_1058 -> AgdaAny -> AgdaAny
d_idem_1088 :: T_IdempotentMonoid_1058 -> AgdaAny -> AgdaAny
d_idem_1088 T_IdempotentMonoid_1058
v0
  = (T_IsIdempotentMonoid_796 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsIdempotentMonoid_796 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_idem_808
      ((T_IdempotentMonoid_1058 -> T_IsIdempotentMonoid_796)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IdempotentMonoid_1058 -> T_IsIdempotentMonoid_796
d_isIdempotentMonoid_1082 (T_IdempotentMonoid_1058 -> AgdaAny
forall a b. a -> b
coe T_IdempotentMonoid_1058
v0))
-- Algebra.Bundles.IdempotentMonoid._.identity
d_identity_1090 ::
  T_IdempotentMonoid_1058 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_identity_1090 :: T_IdempotentMonoid_1058 -> T_Σ_14
d_identity_1090 T_IdempotentMonoid_1058
v0
  = (T_IsMonoid_686 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsMonoid_686 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_identity_698
      ((T_IsIdempotentMonoid_796 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsIdempotentMonoid_796 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_806
         ((T_IdempotentMonoid_1058 -> T_IsIdempotentMonoid_796)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IdempotentMonoid_1058 -> T_IsIdempotentMonoid_796
d_isIdempotentMonoid_1082 (T_IdempotentMonoid_1058 -> AgdaAny
forall a b. a -> b
coe T_IdempotentMonoid_1058
v0)))
-- Algebra.Bundles.IdempotentMonoid._.identityʳ
d_identity'691'_1092 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentMonoid_1058 -> AgdaAny -> AgdaAny
d_identity'691'_1092 :: () -> () -> T_IdempotentMonoid_1058 -> AgdaAny -> AgdaAny
d_identity'691'_1092 ~()
v0 ~()
v1 T_IdempotentMonoid_1058
v2 = T_IdempotentMonoid_1058 -> AgdaAny -> AgdaAny
du_identity'691'_1092 T_IdempotentMonoid_1058
v2
du_identity'691'_1092 ::
  T_IdempotentMonoid_1058 -> AgdaAny -> AgdaAny
du_identity'691'_1092 :: T_IdempotentMonoid_1058 -> AgdaAny -> AgdaAny
du_identity'691'_1092 T_IdempotentMonoid_1058
v0
  = let v1 :: T_IsIdempotentMonoid_796
v1 = T_IdempotentMonoid_1058 -> T_IsIdempotentMonoid_796
d_isIdempotentMonoid_1082 (T_IdempotentMonoid_1058 -> T_IdempotentMonoid_1058
forall a b. a -> b
coe T_IdempotentMonoid_1058
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsMonoid_686 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoid_686 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_identity'691'_728
         ((T_IsIdempotentMonoid_796 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentMonoid_796 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_806 (T_IsIdempotentMonoid_796 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentMonoid_796
v1)))
-- Algebra.Bundles.IdempotentMonoid._.identityˡ
d_identity'737'_1094 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentMonoid_1058 -> AgdaAny -> AgdaAny
d_identity'737'_1094 :: () -> () -> T_IdempotentMonoid_1058 -> AgdaAny -> AgdaAny
d_identity'737'_1094 ~()
v0 ~()
v1 T_IdempotentMonoid_1058
v2 = T_IdempotentMonoid_1058 -> AgdaAny -> AgdaAny
du_identity'737'_1094 T_IdempotentMonoid_1058
v2
du_identity'737'_1094 ::
  T_IdempotentMonoid_1058 -> AgdaAny -> AgdaAny
du_identity'737'_1094 :: T_IdempotentMonoid_1058 -> AgdaAny -> AgdaAny
du_identity'737'_1094 T_IdempotentMonoid_1058
v0
  = let v1 :: T_IsIdempotentMonoid_796
v1 = T_IdempotentMonoid_1058 -> T_IsIdempotentMonoid_796
d_isIdempotentMonoid_1082 (T_IdempotentMonoid_1058 -> T_IdempotentMonoid_1058
forall a b. a -> b
coe T_IdempotentMonoid_1058
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsMonoid_686 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoid_686 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_identity'737'_726
         ((T_IsIdempotentMonoid_796 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentMonoid_796 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_806 (T_IsIdempotentMonoid_796 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentMonoid_796
v1)))
-- Algebra.Bundles.IdempotentMonoid._.isBand
d_isBand_1096 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentMonoid_1058 ->
  MAlonzo.Code.Algebra.Structures.T_IsBand_508
d_isBand_1096 :: () -> () -> T_IdempotentMonoid_1058 -> T_IsBand_508
d_isBand_1096 ~()
v0 ~()
v1 T_IdempotentMonoid_1058
v2 = T_IdempotentMonoid_1058 -> T_IsBand_508
du_isBand_1096 T_IdempotentMonoid_1058
v2
du_isBand_1096 ::
  T_IdempotentMonoid_1058 ->
  MAlonzo.Code.Algebra.Structures.T_IsBand_508
du_isBand_1096 :: T_IdempotentMonoid_1058 -> T_IsBand_508
du_isBand_1096 T_IdempotentMonoid_1058
v0
  = (T_IsIdempotentMonoid_796 -> T_IsBand_508)
-> AgdaAny -> T_IsBand_508
forall a b. a -> b
coe
      T_IsIdempotentMonoid_796 -> T_IsBand_508
MAlonzo.Code.Algebra.Structures.du_isBand_846
      ((T_IdempotentMonoid_1058 -> T_IsIdempotentMonoid_796)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IdempotentMonoid_1058 -> T_IsIdempotentMonoid_796
d_isIdempotentMonoid_1082 (T_IdempotentMonoid_1058 -> AgdaAny
forall a b. a -> b
coe T_IdempotentMonoid_1058
v0))
-- Algebra.Bundles.IdempotentMonoid._.isEquivalence
d_isEquivalence_1098 ::
  T_IdempotentMonoid_1058 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_1098 :: T_IdempotentMonoid_1058 -> T_IsEquivalence_26
d_isEquivalence_1098 T_IdempotentMonoid_1058
v0
  = (T_IsMagma_176 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
      ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480
         ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
            ((T_IsIdempotentMonoid_796 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsIdempotentMonoid_796 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_806
               ((T_IdempotentMonoid_1058 -> T_IsIdempotentMonoid_796)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IdempotentMonoid_1058 -> T_IsIdempotentMonoid_796
d_isIdempotentMonoid_1082 (T_IdempotentMonoid_1058 -> AgdaAny
forall a b. a -> b
coe T_IdempotentMonoid_1058
v0)))))
-- Algebra.Bundles.IdempotentMonoid._.isMagma
d_isMagma_1100 ::
  T_IdempotentMonoid_1058 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_176
d_isMagma_1100 :: T_IdempotentMonoid_1058 -> T_IsMagma_176
d_isMagma_1100 T_IdempotentMonoid_1058
v0
  = (T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> T_IsMagma_176
forall a b. a -> b
coe
      T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480
      ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
         ((T_IsIdempotentMonoid_796 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsIdempotentMonoid_796 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_806
            ((T_IdempotentMonoid_1058 -> T_IsIdempotentMonoid_796)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IdempotentMonoid_1058 -> T_IsIdempotentMonoid_796
d_isIdempotentMonoid_1082 (T_IdempotentMonoid_1058 -> AgdaAny
forall a b. a -> b
coe T_IdempotentMonoid_1058
v0))))
-- Algebra.Bundles.IdempotentMonoid._.isMonoid
d_isMonoid_1102 ::
  T_IdempotentMonoid_1058 ->
  MAlonzo.Code.Algebra.Structures.T_IsMonoid_686
d_isMonoid_1102 :: T_IdempotentMonoid_1058 -> T_IsMonoid_686
d_isMonoid_1102 T_IdempotentMonoid_1058
v0
  = (T_IsIdempotentMonoid_796 -> T_IsMonoid_686)
-> AgdaAny -> T_IsMonoid_686
forall a b. a -> b
coe
      T_IsIdempotentMonoid_796 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_806
      ((T_IdempotentMonoid_1058 -> T_IsIdempotentMonoid_796)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IdempotentMonoid_1058 -> T_IsIdempotentMonoid_796
d_isIdempotentMonoid_1082 (T_IdempotentMonoid_1058 -> AgdaAny
forall a b. a -> b
coe T_IdempotentMonoid_1058
v0))
-- Algebra.Bundles.IdempotentMonoid._.isPartialEquivalence
d_isPartialEquivalence_1104 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentMonoid_1058 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_1104 :: () -> () -> T_IdempotentMonoid_1058 -> T_IsPartialEquivalence_16
d_isPartialEquivalence_1104 ~()
v0 ~()
v1 T_IdempotentMonoid_1058
v2
  = T_IdempotentMonoid_1058 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_1104 T_IdempotentMonoid_1058
v2
du_isPartialEquivalence_1104 ::
  T_IdempotentMonoid_1058 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_1104 :: T_IdempotentMonoid_1058 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_1104 T_IdempotentMonoid_1058
v0
  = let v1 :: T_IsIdempotentMonoid_796
v1 = T_IdempotentMonoid_1058 -> T_IsIdempotentMonoid_796
d_isIdempotentMonoid_1082 (T_IdempotentMonoid_1058 -> T_IdempotentMonoid_1058
forall a b. a -> b
coe T_IdempotentMonoid_1058
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsMonoid_686
v2
             = T_IsIdempotentMonoid_796 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_806 (T_IsIdempotentMonoid_796 -> T_IsIdempotentMonoid_796
forall a b. a -> b
coe T_IsIdempotentMonoid_796
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_472
v3
                = T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsMagma_176
v4 = T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (T_IsSemigroup_472 -> T_IsSemigroup_472
forall a b. a -> b
coe T_IsSemigroup_472
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               ((T_IsEquivalence_26 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsEquivalence_26 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
                  ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v4))))))
-- Algebra.Bundles.IdempotentMonoid._.isSemigroup
d_isSemigroup_1106 ::
  T_IdempotentMonoid_1058 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_472
d_isSemigroup_1106 :: T_IdempotentMonoid_1058 -> T_IsSemigroup_472
d_isSemigroup_1106 T_IdempotentMonoid_1058
v0
  = (T_IsMonoid_686 -> T_IsSemigroup_472)
-> AgdaAny -> T_IsSemigroup_472
forall a b. a -> b
coe
      T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
      ((T_IsIdempotentMonoid_796 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsIdempotentMonoid_796 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_806
         ((T_IdempotentMonoid_1058 -> T_IsIdempotentMonoid_796)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IdempotentMonoid_1058 -> T_IsIdempotentMonoid_796
d_isIdempotentMonoid_1082 (T_IdempotentMonoid_1058 -> AgdaAny
forall a b. a -> b
coe T_IdempotentMonoid_1058
v0)))
-- Algebra.Bundles.IdempotentMonoid._.isUnitalMagma
d_isUnitalMagma_1108 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentMonoid_1058 ->
  MAlonzo.Code.Algebra.Structures.T_IsUnitalMagma_642
d_isUnitalMagma_1108 :: () -> () -> T_IdempotentMonoid_1058 -> T_IsUnitalMagma_642
d_isUnitalMagma_1108 ~()
v0 ~()
v1 T_IdempotentMonoid_1058
v2 = T_IdempotentMonoid_1058 -> T_IsUnitalMagma_642
du_isUnitalMagma_1108 T_IdempotentMonoid_1058
v2
du_isUnitalMagma_1108 ::
  T_IdempotentMonoid_1058 ->
  MAlonzo.Code.Algebra.Structures.T_IsUnitalMagma_642
du_isUnitalMagma_1108 :: T_IdempotentMonoid_1058 -> T_IsUnitalMagma_642
du_isUnitalMagma_1108 T_IdempotentMonoid_1058
v0
  = let v1 :: T_IsIdempotentMonoid_796
v1 = T_IdempotentMonoid_1058 -> T_IsIdempotentMonoid_796
d_isIdempotentMonoid_1082 (T_IdempotentMonoid_1058 -> T_IdempotentMonoid_1058
forall a b. a -> b
coe T_IdempotentMonoid_1058
v0) in
    AgdaAny -> T_IsUnitalMagma_642
forall a b. a -> b
coe
      ((T_IsMonoid_686 -> T_IsUnitalMagma_642) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoid_686 -> T_IsUnitalMagma_642
MAlonzo.Code.Algebra.Structures.du_isUnitalMagma_730
         ((T_IsIdempotentMonoid_796 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentMonoid_796 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_806 (T_IsIdempotentMonoid_796 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentMonoid_796
v1)))
-- Algebra.Bundles.IdempotentMonoid._.refl
d_refl_1110 :: T_IdempotentMonoid_1058 -> AgdaAny -> AgdaAny
d_refl_1110 :: T_IdempotentMonoid_1058 -> AgdaAny -> AgdaAny
d_refl_1110 T_IdempotentMonoid_1058
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_34
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
         ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480
            ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
               ((T_IsIdempotentMonoid_796 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsIdempotentMonoid_796 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_806
                  ((T_IdempotentMonoid_1058 -> T_IsIdempotentMonoid_796)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IdempotentMonoid_1058 -> T_IsIdempotentMonoid_796
d_isIdempotentMonoid_1082 (T_IdempotentMonoid_1058 -> AgdaAny
forall a b. a -> b
coe T_IdempotentMonoid_1058
v0))))))
-- Algebra.Bundles.IdempotentMonoid._.reflexive
d_reflexive_1112 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentMonoid_1058 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_1112 :: ()
-> ()
-> T_IdempotentMonoid_1058
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_1112 ~()
v0 ~()
v1 T_IdempotentMonoid_1058
v2 = T_IdempotentMonoid_1058
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_1112 T_IdempotentMonoid_1058
v2
du_reflexive_1112 ::
  T_IdempotentMonoid_1058 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_1112 :: T_IdempotentMonoid_1058
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_1112 T_IdempotentMonoid_1058
v0
  = let v1 :: T_IsIdempotentMonoid_796
v1 = T_IdempotentMonoid_1058 -> T_IsIdempotentMonoid_796
d_isIdempotentMonoid_1082 (T_IdempotentMonoid_1058 -> T_IdempotentMonoid_1058
forall a b. a -> b
coe T_IdempotentMonoid_1058
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsMonoid_686
v2
             = T_IsIdempotentMonoid_796 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_806 (T_IsIdempotentMonoid_796 -> T_IsIdempotentMonoid_796
forall a b. a -> b
coe T_IsIdempotentMonoid_796
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_472
v3
                = T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsMagma_176
v4 = T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (T_IsSemigroup_472 -> T_IsSemigroup_472
forall a b. a -> b
coe T_IsSemigroup_472
v3) in
             (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
               (\ AgdaAny
v5 AgdaAny
v6 AgdaAny
v7 ->
                  (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                    T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
                    ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v4))
                    AgdaAny
v5))))
-- Algebra.Bundles.IdempotentMonoid._.setoid
d_setoid_1114 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentMonoid_1058 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_1114 :: () -> () -> T_IdempotentMonoid_1058 -> T_Setoid_44
d_setoid_1114 ~()
v0 ~()
v1 T_IdempotentMonoid_1058
v2 = T_IdempotentMonoid_1058 -> T_Setoid_44
du_setoid_1114 T_IdempotentMonoid_1058
v2
du_setoid_1114 ::
  T_IdempotentMonoid_1058 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_1114 :: T_IdempotentMonoid_1058 -> T_Setoid_44
du_setoid_1114 T_IdempotentMonoid_1058
v0
  = let v1 :: T_IsIdempotentMonoid_796
v1 = T_IdempotentMonoid_1058 -> T_IsIdempotentMonoid_796
d_isIdempotentMonoid_1082 (T_IdempotentMonoid_1058 -> T_IdempotentMonoid_1058
forall a b. a -> b
coe T_IdempotentMonoid_1058
v0) in
    AgdaAny -> T_Setoid_44
forall a b. a -> b
coe
      (let v2 :: T_IsMonoid_686
v2
             = T_IsIdempotentMonoid_796 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_806 (T_IsIdempotentMonoid_796 -> T_IsIdempotentMonoid_796
forall a b. a -> b
coe T_IsIdempotentMonoid_796
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_472
v3
                = T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsMagma_176 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMagma_176 -> T_Setoid_44
MAlonzo.Code.Algebra.Structures.du_setoid_200
               ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v3)))))
-- Algebra.Bundles.IdempotentMonoid._.sym
d_sym_1116 ::
  T_IdempotentMonoid_1058 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_1116 :: T_IdempotentMonoid_1058 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_1116 T_IdempotentMonoid_1058
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_36
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
         ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480
            ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
               ((T_IsIdempotentMonoid_796 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsIdempotentMonoid_796 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_806
                  ((T_IdempotentMonoid_1058 -> T_IsIdempotentMonoid_796)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IdempotentMonoid_1058 -> T_IsIdempotentMonoid_796
d_isIdempotentMonoid_1082 (T_IdempotentMonoid_1058 -> AgdaAny
forall a b. a -> b
coe T_IdempotentMonoid_1058
v0))))))
-- Algebra.Bundles.IdempotentMonoid._.trans
d_trans_1118 ::
  T_IdempotentMonoid_1058 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_1118 :: T_IdempotentMonoid_1058
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_1118 T_IdempotentMonoid_1058
v0
  = (T_IsEquivalence_26
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_38
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
         ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480
            ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
               ((T_IsIdempotentMonoid_796 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsIdempotentMonoid_796 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_806
                  ((T_IdempotentMonoid_1058 -> T_IsIdempotentMonoid_796)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IdempotentMonoid_1058 -> T_IsIdempotentMonoid_796
d_isIdempotentMonoid_1082 (T_IdempotentMonoid_1058 -> AgdaAny
forall a b. a -> b
coe T_IdempotentMonoid_1058
v0))))))
-- Algebra.Bundles.IdempotentMonoid._.∙-cong
d_'8729''45'cong_1120 ::
  T_IdempotentMonoid_1058 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_1120 :: T_IdempotentMonoid_1058
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_1120 T_IdempotentMonoid_1058
v0
  = (T_IsMagma_176
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsMagma_176
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_186
      ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480
         ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
            ((T_IsIdempotentMonoid_796 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsIdempotentMonoid_796 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_806
               ((T_IdempotentMonoid_1058 -> T_IsIdempotentMonoid_796)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IdempotentMonoid_1058 -> T_IsIdempotentMonoid_796
d_isIdempotentMonoid_1082 (T_IdempotentMonoid_1058 -> AgdaAny
forall a b. a -> b
coe T_IdempotentMonoid_1058
v0)))))
-- Algebra.Bundles.IdempotentMonoid._.∙-congʳ
d_'8729''45'cong'691'_1122 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentMonoid_1058 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_1122 :: ()
-> ()
-> T_IdempotentMonoid_1058
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_1122 ~()
v0 ~()
v1 T_IdempotentMonoid_1058
v2
  = T_IdempotentMonoid_1058
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1122 T_IdempotentMonoid_1058
v2
du_'8729''45'cong'691'_1122 ::
  T_IdempotentMonoid_1058 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1122 :: T_IdempotentMonoid_1058
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1122 T_IdempotentMonoid_1058
v0
  = let v1 :: T_IsIdempotentMonoid_796
v1 = T_IdempotentMonoid_1058 -> T_IsIdempotentMonoid_796
d_isIdempotentMonoid_1082 (T_IdempotentMonoid_1058 -> T_IdempotentMonoid_1058
forall a b. a -> b
coe T_IdempotentMonoid_1058
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsMonoid_686
v2
             = T_IsIdempotentMonoid_796 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_806 (T_IsIdempotentMonoid_796 -> T_IsIdempotentMonoid_796
forall a b. a -> b
coe T_IsIdempotentMonoid_796
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_472
v3
                = T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'691'_206
               ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v3)))))
-- Algebra.Bundles.IdempotentMonoid._.∙-congˡ
d_'8729''45'cong'737'_1124 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentMonoid_1058 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_1124 :: ()
-> ()
-> T_IdempotentMonoid_1058
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_1124 ~()
v0 ~()
v1 T_IdempotentMonoid_1058
v2
  = T_IdempotentMonoid_1058
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1124 T_IdempotentMonoid_1058
v2
du_'8729''45'cong'737'_1124 ::
  T_IdempotentMonoid_1058 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1124 :: T_IdempotentMonoid_1058
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1124 T_IdempotentMonoid_1058
v0
  = let v1 :: T_IsIdempotentMonoid_796
v1 = T_IdempotentMonoid_1058 -> T_IsIdempotentMonoid_796
d_isIdempotentMonoid_1082 (T_IdempotentMonoid_1058 -> T_IdempotentMonoid_1058
forall a b. a -> b
coe T_IdempotentMonoid_1058
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsMonoid_686
v2
             = T_IsIdempotentMonoid_796 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_806 (T_IsIdempotentMonoid_796 -> T_IsIdempotentMonoid_796
forall a b. a -> b
coe T_IsIdempotentMonoid_796
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_472
v3
                = T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'737'_202
               ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v3)))))
-- Algebra.Bundles.IdempotentMonoid.monoid
d_monoid_1126 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentMonoid_1058 -> T_Monoid_882
d_monoid_1126 :: () -> () -> T_IdempotentMonoid_1058 -> T_Monoid_882
d_monoid_1126 ~()
v0 ~()
v1 T_IdempotentMonoid_1058
v2 = T_IdempotentMonoid_1058 -> T_Monoid_882
du_monoid_1126 T_IdempotentMonoid_1058
v2
du_monoid_1126 :: T_IdempotentMonoid_1058 -> T_Monoid_882
du_monoid_1126 :: T_IdempotentMonoid_1058 -> T_Monoid_882
du_monoid_1126 T_IdempotentMonoid_1058
v0
  = ((AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny -> T_IsMonoid_686 -> T_Monoid_882)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsMonoid_686
-> T_Monoid_882
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> T_IsMonoid_686 -> T_Monoid_882
C_Monoid'46'constructor_16157 (T_IdempotentMonoid_1058 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__1078 (T_IdempotentMonoid_1058 -> T_IdempotentMonoid_1058
forall a b. a -> b
coe T_IdempotentMonoid_1058
v0))
      (T_IdempotentMonoid_1058 -> AgdaAny
d_ε_1080 (T_IdempotentMonoid_1058 -> T_IdempotentMonoid_1058
forall a b. a -> b
coe T_IdempotentMonoid_1058
v0))
      (T_IsIdempotentMonoid_796 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_806
         ((T_IdempotentMonoid_1058 -> T_IsIdempotentMonoid_796)
-> AgdaAny -> T_IsIdempotentMonoid_796
forall a b. a -> b
coe T_IdempotentMonoid_1058 -> T_IsIdempotentMonoid_796
d_isIdempotentMonoid_1082 (T_IdempotentMonoid_1058 -> AgdaAny
forall a b. a -> b
coe T_IdempotentMonoid_1058
v0)))
-- Algebra.Bundles.IdempotentMonoid._._≉_
d__'8777'__1130 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentMonoid_1058 -> AgdaAny -> AgdaAny -> ()
d__'8777'__1130 :: () -> () -> T_IdempotentMonoid_1058 -> AgdaAny -> AgdaAny -> ()
d__'8777'__1130 = () -> () -> T_IdempotentMonoid_1058 -> AgdaAny -> AgdaAny -> ()
forall a. a
erased
-- Algebra.Bundles.IdempotentMonoid._.magma
d_magma_1132 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentMonoid_1058 -> T_Magma_68
d_magma_1132 :: () -> () -> T_IdempotentMonoid_1058 -> T_Magma_68
d_magma_1132 ~()
v0 ~()
v1 T_IdempotentMonoid_1058
v2 = T_IdempotentMonoid_1058 -> T_Magma_68
du_magma_1132 T_IdempotentMonoid_1058
v2
du_magma_1132 :: T_IdempotentMonoid_1058 -> T_Magma_68
du_magma_1132 :: T_IdempotentMonoid_1058 -> T_Magma_68
du_magma_1132 T_IdempotentMonoid_1058
v0
  = let v1 :: t
v1 = (T_IdempotentMonoid_1058 -> T_Monoid_882) -> AgdaAny -> t
forall a b. a -> b
coe T_IdempotentMonoid_1058 -> T_Monoid_882
du_monoid_1126 (T_IdempotentMonoid_1058 -> AgdaAny
forall a b. a -> b
coe T_IdempotentMonoid_1058
v0) in
    AgdaAny -> T_Magma_68
forall a b. a -> b
coe ((T_Semigroup_536 -> T_Magma_68) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semigroup_536 -> T_Magma_68
du_magma_584 ((T_Monoid_882 -> T_Semigroup_536) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Monoid_882 -> T_Semigroup_536
du_semigroup_944 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1)))
-- Algebra.Bundles.IdempotentMonoid._.rawMagma
d_rawMagma_1134 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentMonoid_1058 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
d_rawMagma_1134 :: () -> () -> T_IdempotentMonoid_1058 -> T_RawMagma_36
d_rawMagma_1134 ~()
v0 ~()
v1 T_IdempotentMonoid_1058
v2 = T_IdempotentMonoid_1058 -> T_RawMagma_36
du_rawMagma_1134 T_IdempotentMonoid_1058
v2
du_rawMagma_1134 ::
  T_IdempotentMonoid_1058 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
du_rawMagma_1134 :: T_IdempotentMonoid_1058 -> T_RawMagma_36
du_rawMagma_1134 T_IdempotentMonoid_1058
v0
  = let v1 :: t
v1 = (T_IdempotentMonoid_1058 -> T_Monoid_882) -> AgdaAny -> t
forall a b. a -> b
coe T_IdempotentMonoid_1058 -> T_Monoid_882
du_monoid_1126 (T_IdempotentMonoid_1058 -> AgdaAny
forall a b. a -> b
coe T_IdempotentMonoid_1058
v0) in
    AgdaAny -> T_RawMagma_36
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_Monoid_882 -> T_Semigroup_536) -> AgdaAny -> t
forall a b. a -> b
coe T_Monoid_882 -> T_Semigroup_536
du_semigroup_944 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_Magma_68 -> T_RawMagma_36) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Magma_68 -> T_RawMagma_36
du_rawMagma_112 ((T_Semigroup_536 -> T_Magma_68) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semigroup_536 -> T_Magma_68
du_magma_584 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2))))
-- Algebra.Bundles.IdempotentMonoid._.rawMonoid
d_rawMonoid_1136 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentMonoid_1058 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMonoid_64
d_rawMonoid_1136 :: () -> () -> T_IdempotentMonoid_1058 -> T_RawMonoid_64
d_rawMonoid_1136 ~()
v0 ~()
v1 T_IdempotentMonoid_1058
v2 = T_IdempotentMonoid_1058 -> T_RawMonoid_64
du_rawMonoid_1136 T_IdempotentMonoid_1058
v2
du_rawMonoid_1136 ::
  T_IdempotentMonoid_1058 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMonoid_64
du_rawMonoid_1136 :: T_IdempotentMonoid_1058 -> T_RawMonoid_64
du_rawMonoid_1136 T_IdempotentMonoid_1058
v0
  = (T_Monoid_882 -> T_RawMonoid_64) -> AgdaAny -> T_RawMonoid_64
forall a b. a -> b
coe T_Monoid_882 -> T_RawMonoid_64
du_rawMonoid_954 ((T_IdempotentMonoid_1058 -> T_Monoid_882) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IdempotentMonoid_1058 -> T_Monoid_882
du_monoid_1126 (T_IdempotentMonoid_1058 -> AgdaAny
forall a b. a -> b
coe T_IdempotentMonoid_1058
v0))
-- Algebra.Bundles.IdempotentMonoid._.semigroup
d_semigroup_1138 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentMonoid_1058 -> T_Semigroup_536
d_semigroup_1138 :: () -> () -> T_IdempotentMonoid_1058 -> T_Semigroup_536
d_semigroup_1138 ~()
v0 ~()
v1 T_IdempotentMonoid_1058
v2 = T_IdempotentMonoid_1058 -> T_Semigroup_536
du_semigroup_1138 T_IdempotentMonoid_1058
v2
du_semigroup_1138 :: T_IdempotentMonoid_1058 -> T_Semigroup_536
du_semigroup_1138 :: T_IdempotentMonoid_1058 -> T_Semigroup_536
du_semigroup_1138 T_IdempotentMonoid_1058
v0
  = (T_Monoid_882 -> T_Semigroup_536) -> AgdaAny -> T_Semigroup_536
forall a b. a -> b
coe T_Monoid_882 -> T_Semigroup_536
du_semigroup_944 ((T_IdempotentMonoid_1058 -> T_Monoid_882) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IdempotentMonoid_1058 -> T_Monoid_882
du_monoid_1126 (T_IdempotentMonoid_1058 -> AgdaAny
forall a b. a -> b
coe T_IdempotentMonoid_1058
v0))
-- Algebra.Bundles.IdempotentMonoid._.unitalMagma
d_unitalMagma_1140 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentMonoid_1058 -> T_UnitalMagma_814
d_unitalMagma_1140 :: () -> () -> T_IdempotentMonoid_1058 -> T_UnitalMagma_814
d_unitalMagma_1140 ~()
v0 ~()
v1 T_IdempotentMonoid_1058
v2 = T_IdempotentMonoid_1058 -> T_UnitalMagma_814
du_unitalMagma_1140 T_IdempotentMonoid_1058
v2
du_unitalMagma_1140 :: T_IdempotentMonoid_1058 -> T_UnitalMagma_814
du_unitalMagma_1140 :: T_IdempotentMonoid_1058 -> T_UnitalMagma_814
du_unitalMagma_1140 T_IdempotentMonoid_1058
v0
  = (T_Monoid_882 -> T_UnitalMagma_814) -> AgdaAny -> T_UnitalMagma_814
forall a b. a -> b
coe T_Monoid_882 -> T_UnitalMagma_814
du_unitalMagma_956 ((T_IdempotentMonoid_1058 -> T_Monoid_882) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IdempotentMonoid_1058 -> T_Monoid_882
du_monoid_1126 (T_IdempotentMonoid_1058 -> AgdaAny
forall a b. a -> b
coe T_IdempotentMonoid_1058
v0))
-- Algebra.Bundles.IdempotentMonoid.band
d_band_1142 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentMonoid_1058 -> T_Band_596
d_band_1142 :: () -> () -> T_IdempotentMonoid_1058 -> T_Band_596
d_band_1142 ~()
v0 ~()
v1 T_IdempotentMonoid_1058
v2 = T_IdempotentMonoid_1058 -> T_Band_596
du_band_1142 T_IdempotentMonoid_1058
v2
du_band_1142 :: T_IdempotentMonoid_1058 -> T_Band_596
du_band_1142 :: T_IdempotentMonoid_1058 -> T_Band_596
du_band_1142 T_IdempotentMonoid_1058
v0
  = ((AgdaAny -> AgdaAny -> AgdaAny) -> T_IsBand_508 -> T_Band_596)
-> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> T_Band_596
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny) -> T_IsBand_508 -> T_Band_596
C_Band'46'constructor_10881 (T_IdempotentMonoid_1058 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__1078 (T_IdempotentMonoid_1058 -> T_IdempotentMonoid_1058
forall a b. a -> b
coe T_IdempotentMonoid_1058
v0))
      ((T_IsIdempotentMonoid_796 -> T_IsBand_508) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsIdempotentMonoid_796 -> T_IsBand_508
MAlonzo.Code.Algebra.Structures.du_isBand_846
         ((T_IdempotentMonoid_1058 -> T_IsIdempotentMonoid_796)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IdempotentMonoid_1058 -> T_IsIdempotentMonoid_796
d_isIdempotentMonoid_1082 (T_IdempotentMonoid_1058 -> AgdaAny
forall a b. a -> b
coe T_IdempotentMonoid_1058
v0)))
-- Algebra.Bundles.IdempotentCommutativeMonoid
d_IdempotentCommutativeMonoid_1148 :: p -> p -> ()
d_IdempotentCommutativeMonoid_1148 p
a0 p
a1 = ()
data T_IdempotentCommutativeMonoid_1148
  = C_IdempotentCommutativeMonoid'46'constructor_21499 (AgdaAny ->
                                                        AgdaAny -> AgdaAny)
                                                       AgdaAny
                                                       MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_852
-- Algebra.Bundles.IdempotentCommutativeMonoid.Carrier
d_Carrier_1164 :: T_IdempotentCommutativeMonoid_1148 -> ()
d_Carrier_1164 :: T_IdempotentCommutativeMonoid_1148 -> ()
d_Carrier_1164 = T_IdempotentCommutativeMonoid_1148 -> ()
forall a. a
erased
-- Algebra.Bundles.IdempotentCommutativeMonoid._≈_
d__'8776'__1166 ::
  T_IdempotentCommutativeMonoid_1148 -> AgdaAny -> AgdaAny -> ()
d__'8776'__1166 :: T_IdempotentCommutativeMonoid_1148 -> AgdaAny -> AgdaAny -> ()
d__'8776'__1166 = T_IdempotentCommutativeMonoid_1148 -> AgdaAny -> AgdaAny -> ()
forall a. a
erased
-- Algebra.Bundles.IdempotentCommutativeMonoid._∙_
d__'8729'__1168 ::
  T_IdempotentCommutativeMonoid_1148 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__1168 :: T_IdempotentCommutativeMonoid_1148 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__1168 T_IdempotentCommutativeMonoid_1148
v0
  = case T_IdempotentCommutativeMonoid_1148
-> T_IdempotentCommutativeMonoid_1148
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1148
v0 of
      C_IdempotentCommutativeMonoid'46'constructor_21499 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny
v4 T_IsIdempotentCommutativeMonoid_852
v5
        -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v3
      T_IdempotentCommutativeMonoid_1148
_ -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.IdempotentCommutativeMonoid.ε
d_ε_1170 :: T_IdempotentCommutativeMonoid_1148 -> AgdaAny
d_ε_1170 :: T_IdempotentCommutativeMonoid_1148 -> AgdaAny
d_ε_1170 T_IdempotentCommutativeMonoid_1148
v0
  = case T_IdempotentCommutativeMonoid_1148
-> T_IdempotentCommutativeMonoid_1148
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1148
v0 of
      C_IdempotentCommutativeMonoid'46'constructor_21499 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny
v4 T_IsIdempotentCommutativeMonoid_852
v5
        -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v4
      T_IdempotentCommutativeMonoid_1148
_ -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.IdempotentCommutativeMonoid.isIdempotentCommutativeMonoid
d_isIdempotentCommutativeMonoid_1172 ::
  T_IdempotentCommutativeMonoid_1148 ->
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_852
d_isIdempotentCommutativeMonoid_1172 :: T_IdempotentCommutativeMonoid_1148
-> T_IsIdempotentCommutativeMonoid_852
d_isIdempotentCommutativeMonoid_1172 T_IdempotentCommutativeMonoid_1148
v0
  = case T_IdempotentCommutativeMonoid_1148
-> T_IdempotentCommutativeMonoid_1148
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1148
v0 of
      C_IdempotentCommutativeMonoid'46'constructor_21499 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny
v4 T_IsIdempotentCommutativeMonoid_852
v5
        -> T_IsIdempotentCommutativeMonoid_852
-> T_IsIdempotentCommutativeMonoid_852
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852
v5
      T_IdempotentCommutativeMonoid_1148
_ -> T_IsIdempotentCommutativeMonoid_852
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.IdempotentCommutativeMonoid._.assoc
d_assoc_1176 ::
  T_IdempotentCommutativeMonoid_1148 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_1176 :: T_IdempotentCommutativeMonoid_1148
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_1176 T_IdempotentCommutativeMonoid_1148
v0
  = (T_IsSemigroup_472 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsSemigroup_472 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_assoc_482
      ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
         ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746
            ((T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_862
               ((T_IdempotentCommutativeMonoid_1148
 -> T_IsIdempotentCommutativeMonoid_852)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1148
-> T_IsIdempotentCommutativeMonoid_852
d_isIdempotentCommutativeMonoid_1172 (T_IdempotentCommutativeMonoid_1148 -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1148
v0)))))
-- Algebra.Bundles.IdempotentCommutativeMonoid._.comm
d_comm_1178 ::
  T_IdempotentCommutativeMonoid_1148 -> AgdaAny -> AgdaAny -> AgdaAny
d_comm_1178 :: T_IdempotentCommutativeMonoid_1148 -> AgdaAny -> AgdaAny -> AgdaAny
d_comm_1178 T_IdempotentCommutativeMonoid_1148
v0
  = (T_IsCommutativeMonoid_736 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsCommutativeMonoid_736 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_comm_748
      ((T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_862
         ((T_IdempotentCommutativeMonoid_1148
 -> T_IsIdempotentCommutativeMonoid_852)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1148
-> T_IsIdempotentCommutativeMonoid_852
d_isIdempotentCommutativeMonoid_1172 (T_IdempotentCommutativeMonoid_1148 -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1148
v0)))
-- Algebra.Bundles.IdempotentCommutativeMonoid._.idem
d_idem_1180 ::
  T_IdempotentCommutativeMonoid_1148 -> AgdaAny -> AgdaAny
d_idem_1180 :: T_IdempotentCommutativeMonoid_1148 -> AgdaAny -> AgdaAny
d_idem_1180 T_IdempotentCommutativeMonoid_1148
v0
  = (T_IsIdempotentCommutativeMonoid_852 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsIdempotentCommutativeMonoid_852 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_idem_864
      ((T_IdempotentCommutativeMonoid_1148
 -> T_IsIdempotentCommutativeMonoid_852)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1148
-> T_IsIdempotentCommutativeMonoid_852
d_isIdempotentCommutativeMonoid_1172 (T_IdempotentCommutativeMonoid_1148 -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1148
v0))
-- Algebra.Bundles.IdempotentCommutativeMonoid._.identity
d_identity_1182 ::
  T_IdempotentCommutativeMonoid_1148 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_identity_1182 :: T_IdempotentCommutativeMonoid_1148 -> T_Σ_14
d_identity_1182 T_IdempotentCommutativeMonoid_1148
v0
  = (T_IsMonoid_686 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsMonoid_686 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_identity_698
      ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746
         ((T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_862
            ((T_IdempotentCommutativeMonoid_1148
 -> T_IsIdempotentCommutativeMonoid_852)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1148
-> T_IsIdempotentCommutativeMonoid_852
d_isIdempotentCommutativeMonoid_1172 (T_IdempotentCommutativeMonoid_1148 -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1148
v0))))
-- Algebra.Bundles.IdempotentCommutativeMonoid._.identityʳ
d_identity'691'_1184 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentCommutativeMonoid_1148 -> AgdaAny -> AgdaAny
d_identity'691'_1184 :: ()
-> () -> T_IdempotentCommutativeMonoid_1148 -> AgdaAny -> AgdaAny
d_identity'691'_1184 ~()
v0 ~()
v1 T_IdempotentCommutativeMonoid_1148
v2 = T_IdempotentCommutativeMonoid_1148 -> AgdaAny -> AgdaAny
du_identity'691'_1184 T_IdempotentCommutativeMonoid_1148
v2
du_identity'691'_1184 ::
  T_IdempotentCommutativeMonoid_1148 -> AgdaAny -> AgdaAny
du_identity'691'_1184 :: T_IdempotentCommutativeMonoid_1148 -> AgdaAny -> AgdaAny
du_identity'691'_1184 T_IdempotentCommutativeMonoid_1148
v0
  = let v1 :: T_IsIdempotentCommutativeMonoid_852
v1 = T_IdempotentCommutativeMonoid_1148
-> T_IsIdempotentCommutativeMonoid_852
d_isIdempotentCommutativeMonoid_1172 (T_IdempotentCommutativeMonoid_1148
-> T_IdempotentCommutativeMonoid_1148
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1148
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsCommutativeMonoid_736
v2
             = T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_862
                 (T_IsIdempotentCommutativeMonoid_852
-> T_IsIdempotentCommutativeMonoid_852
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsMonoid_686 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoid_686 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_identity'691'_728
            ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746 (T_IsCommutativeMonoid_736 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v2))))
-- Algebra.Bundles.IdempotentCommutativeMonoid._.identityˡ
d_identity'737'_1186 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentCommutativeMonoid_1148 -> AgdaAny -> AgdaAny
d_identity'737'_1186 :: ()
-> () -> T_IdempotentCommutativeMonoid_1148 -> AgdaAny -> AgdaAny
d_identity'737'_1186 ~()
v0 ~()
v1 T_IdempotentCommutativeMonoid_1148
v2 = T_IdempotentCommutativeMonoid_1148 -> AgdaAny -> AgdaAny
du_identity'737'_1186 T_IdempotentCommutativeMonoid_1148
v2
du_identity'737'_1186 ::
  T_IdempotentCommutativeMonoid_1148 -> AgdaAny -> AgdaAny
du_identity'737'_1186 :: T_IdempotentCommutativeMonoid_1148 -> AgdaAny -> AgdaAny
du_identity'737'_1186 T_IdempotentCommutativeMonoid_1148
v0
  = let v1 :: T_IsIdempotentCommutativeMonoid_852
v1 = T_IdempotentCommutativeMonoid_1148
-> T_IsIdempotentCommutativeMonoid_852
d_isIdempotentCommutativeMonoid_1172 (T_IdempotentCommutativeMonoid_1148
-> T_IdempotentCommutativeMonoid_1148
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1148
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsCommutativeMonoid_736
v2
             = T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_862
                 (T_IsIdempotentCommutativeMonoid_852
-> T_IsIdempotentCommutativeMonoid_852
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsMonoid_686 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoid_686 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_identity'737'_726
            ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746 (T_IsCommutativeMonoid_736 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v2))))
-- Algebra.Bundles.IdempotentCommutativeMonoid._.isBand
d_isBand_1188 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentCommutativeMonoid_1148 ->
  MAlonzo.Code.Algebra.Structures.T_IsBand_508
d_isBand_1188 :: () -> () -> T_IdempotentCommutativeMonoid_1148 -> T_IsBand_508
d_isBand_1188 ~()
v0 ~()
v1 T_IdempotentCommutativeMonoid_1148
v2 = T_IdempotentCommutativeMonoid_1148 -> T_IsBand_508
du_isBand_1188 T_IdempotentCommutativeMonoid_1148
v2
du_isBand_1188 ::
  T_IdempotentCommutativeMonoid_1148 ->
  MAlonzo.Code.Algebra.Structures.T_IsBand_508
du_isBand_1188 :: T_IdempotentCommutativeMonoid_1148 -> T_IsBand_508
du_isBand_1188 T_IdempotentCommutativeMonoid_1148
v0
  = let v1 :: T_IsIdempotentCommutativeMonoid_852
v1 = T_IdempotentCommutativeMonoid_1148
-> T_IsIdempotentCommutativeMonoid_852
d_isIdempotentCommutativeMonoid_1172 (T_IdempotentCommutativeMonoid_1148
-> T_IdempotentCommutativeMonoid_1148
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1148
v0) in
    AgdaAny -> T_IsBand_508
forall a b. a -> b
coe
      ((T_IsIdempotentMonoid_796 -> T_IsBand_508) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsIdempotentMonoid_796 -> T_IsBand_508
MAlonzo.Code.Algebra.Structures.du_isBand_846
         ((T_IsIdempotentCommutativeMonoid_852 -> T_IsIdempotentMonoid_796)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsIdempotentCommutativeMonoid_852 -> T_IsIdempotentMonoid_796
MAlonzo.Code.Algebra.Structures.du_isIdempotentMonoid_910
            (T_IsIdempotentCommutativeMonoid_852 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852
v1)))
-- Algebra.Bundles.IdempotentCommutativeMonoid._.isCommutativeBand
d_isCommutativeBand_1190 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentCommutativeMonoid_1148 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_590
d_isCommutativeBand_1190 :: ()
-> ()
-> T_IdempotentCommutativeMonoid_1148
-> T_IsCommutativeBand_590
d_isCommutativeBand_1190 ~()
v0 ~()
v1 T_IdempotentCommutativeMonoid_1148
v2 = T_IdempotentCommutativeMonoid_1148 -> T_IsCommutativeBand_590
du_isCommutativeBand_1190 T_IdempotentCommutativeMonoid_1148
v2
du_isCommutativeBand_1190 ::
  T_IdempotentCommutativeMonoid_1148 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_590
du_isCommutativeBand_1190 :: T_IdempotentCommutativeMonoid_1148 -> T_IsCommutativeBand_590
du_isCommutativeBand_1190 T_IdempotentCommutativeMonoid_1148
v0
  = (T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeBand_590)
-> AgdaAny -> T_IsCommutativeBand_590
forall a b. a -> b
coe
      T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeBand_590
MAlonzo.Code.Algebra.Structures.du_isCommutativeBand_916
      ((T_IdempotentCommutativeMonoid_1148
 -> T_IsIdempotentCommutativeMonoid_852)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1148
-> T_IsIdempotentCommutativeMonoid_852
d_isIdempotentCommutativeMonoid_1172 (T_IdempotentCommutativeMonoid_1148 -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1148
v0))
-- Algebra.Bundles.IdempotentCommutativeMonoid._.isCommutativeMagma
d_isCommutativeMagma_1192 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentCommutativeMonoid_1148 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMagma_212
d_isCommutativeMagma_1192 :: ()
-> ()
-> T_IdempotentCommutativeMonoid_1148
-> T_IsCommutativeMagma_212
d_isCommutativeMagma_1192 ~()
v0 ~()
v1 T_IdempotentCommutativeMonoid_1148
v2
  = T_IdempotentCommutativeMonoid_1148 -> T_IsCommutativeMagma_212
du_isCommutativeMagma_1192 T_IdempotentCommutativeMonoid_1148
v2
du_isCommutativeMagma_1192 ::
  T_IdempotentCommutativeMonoid_1148 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMagma_212
du_isCommutativeMagma_1192 :: T_IdempotentCommutativeMonoid_1148 -> T_IsCommutativeMagma_212
du_isCommutativeMagma_1192 T_IdempotentCommutativeMonoid_1148
v0
  = let v1 :: T_IsIdempotentCommutativeMonoid_852
v1 = T_IdempotentCommutativeMonoid_1148
-> T_IsIdempotentCommutativeMonoid_852
d_isIdempotentCommutativeMonoid_1172 (T_IdempotentCommutativeMonoid_1148
-> T_IdempotentCommutativeMonoid_1148
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1148
v0) in
    AgdaAny -> T_IsCommutativeMagma_212
forall a b. a -> b
coe
      (let v2 :: T_IsCommutativeMonoid_736
v2
             = T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_862
                 (T_IsIdempotentCommutativeMonoid_852
-> T_IsIdempotentCommutativeMonoid_852
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsCommutativeSemigroup_548 -> T_IsCommutativeMagma_212)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCommutativeSemigroup_548 -> T_IsCommutativeMagma_212
MAlonzo.Code.Algebra.Structures.du_isCommutativeMagma_586
            ((T_IsCommutativeMonoid_736 -> T_IsCommutativeSemigroup_548)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsCommutativeMonoid_736 -> T_IsCommutativeSemigroup_548
MAlonzo.Code.Algebra.Structures.du_isCommutativeSemigroup_786
               (T_IsCommutativeMonoid_736 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v2))))
-- Algebra.Bundles.IdempotentCommutativeMonoid._.isCommutativeMonoid
d_isCommutativeMonoid_1194 ::
  T_IdempotentCommutativeMonoid_1148 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMonoid_736
d_isCommutativeMonoid_1194 :: T_IdempotentCommutativeMonoid_1148 -> T_IsCommutativeMonoid_736
d_isCommutativeMonoid_1194 T_IdempotentCommutativeMonoid_1148
v0
  = (T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> T_IsCommutativeMonoid_736
forall a b. a -> b
coe
      T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_862
      ((T_IdempotentCommutativeMonoid_1148
 -> T_IsIdempotentCommutativeMonoid_852)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1148
-> T_IsIdempotentCommutativeMonoid_852
d_isIdempotentCommutativeMonoid_1172 (T_IdempotentCommutativeMonoid_1148 -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1148
v0))
-- Algebra.Bundles.IdempotentCommutativeMonoid._.isCommutativeSemigroup
d_isCommutativeSemigroup_1196 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentCommutativeMonoid_1148 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_548
d_isCommutativeSemigroup_1196 :: ()
-> ()
-> T_IdempotentCommutativeMonoid_1148
-> T_IsCommutativeSemigroup_548
d_isCommutativeSemigroup_1196 ~()
v0 ~()
v1 T_IdempotentCommutativeMonoid_1148
v2
  = T_IdempotentCommutativeMonoid_1148 -> T_IsCommutativeSemigroup_548
du_isCommutativeSemigroup_1196 T_IdempotentCommutativeMonoid_1148
v2
du_isCommutativeSemigroup_1196 ::
  T_IdempotentCommutativeMonoid_1148 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_548
du_isCommutativeSemigroup_1196 :: T_IdempotentCommutativeMonoid_1148 -> T_IsCommutativeSemigroup_548
du_isCommutativeSemigroup_1196 T_IdempotentCommutativeMonoid_1148
v0
  = let v1 :: T_IsIdempotentCommutativeMonoid_852
v1 = T_IdempotentCommutativeMonoid_1148
-> T_IsIdempotentCommutativeMonoid_852
d_isIdempotentCommutativeMonoid_1172 (T_IdempotentCommutativeMonoid_1148
-> T_IdempotentCommutativeMonoid_1148
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1148
v0) in
    AgdaAny -> T_IsCommutativeSemigroup_548
forall a b. a -> b
coe
      ((T_IsCommutativeMonoid_736 -> T_IsCommutativeSemigroup_548)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCommutativeMonoid_736 -> T_IsCommutativeSemigroup_548
MAlonzo.Code.Algebra.Structures.du_isCommutativeSemigroup_786
         ((T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_862
            (T_IsIdempotentCommutativeMonoid_852 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852
v1)))
-- Algebra.Bundles.IdempotentCommutativeMonoid._.isEquivalence
d_isEquivalence_1198 ::
  T_IdempotentCommutativeMonoid_1148 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_1198 :: T_IdempotentCommutativeMonoid_1148 -> T_IsEquivalence_26
d_isEquivalence_1198 T_IdempotentCommutativeMonoid_1148
v0
  = (T_IsMagma_176 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
      ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480
         ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
            ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746
               ((T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_862
                  ((T_IdempotentCommutativeMonoid_1148
 -> T_IsIdempotentCommutativeMonoid_852)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1148
-> T_IsIdempotentCommutativeMonoid_852
d_isIdempotentCommutativeMonoid_1172 (T_IdempotentCommutativeMonoid_1148 -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1148
v0))))))
-- Algebra.Bundles.IdempotentCommutativeMonoid._.isIdempotentMonoid
d_isIdempotentMonoid_1200 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentCommutativeMonoid_1148 ->
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentMonoid_796
d_isIdempotentMonoid_1200 :: ()
-> ()
-> T_IdempotentCommutativeMonoid_1148
-> T_IsIdempotentMonoid_796
d_isIdempotentMonoid_1200 ~()
v0 ~()
v1 T_IdempotentCommutativeMonoid_1148
v2
  = T_IdempotentCommutativeMonoid_1148 -> T_IsIdempotentMonoid_796
du_isIdempotentMonoid_1200 T_IdempotentCommutativeMonoid_1148
v2
du_isIdempotentMonoid_1200 ::
  T_IdempotentCommutativeMonoid_1148 ->
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentMonoid_796
du_isIdempotentMonoid_1200 :: T_IdempotentCommutativeMonoid_1148 -> T_IsIdempotentMonoid_796
du_isIdempotentMonoid_1200 T_IdempotentCommutativeMonoid_1148
v0
  = (T_IsIdempotentCommutativeMonoid_852 -> T_IsIdempotentMonoid_796)
-> AgdaAny -> T_IsIdempotentMonoid_796
forall a b. a -> b
coe
      T_IsIdempotentCommutativeMonoid_852 -> T_IsIdempotentMonoid_796
MAlonzo.Code.Algebra.Structures.du_isIdempotentMonoid_910
      ((T_IdempotentCommutativeMonoid_1148
 -> T_IsIdempotentCommutativeMonoid_852)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1148
-> T_IsIdempotentCommutativeMonoid_852
d_isIdempotentCommutativeMonoid_1172 (T_IdempotentCommutativeMonoid_1148 -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1148
v0))
-- Algebra.Bundles.IdempotentCommutativeMonoid._.isMagma
d_isMagma_1202 ::
  T_IdempotentCommutativeMonoid_1148 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_176
d_isMagma_1202 :: T_IdempotentCommutativeMonoid_1148 -> T_IsMagma_176
d_isMagma_1202 T_IdempotentCommutativeMonoid_1148
v0
  = (T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> T_IsMagma_176
forall a b. a -> b
coe
      T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480
      ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
         ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746
            ((T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_862
               ((T_IdempotentCommutativeMonoid_1148
 -> T_IsIdempotentCommutativeMonoid_852)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1148
-> T_IsIdempotentCommutativeMonoid_852
d_isIdempotentCommutativeMonoid_1172 (T_IdempotentCommutativeMonoid_1148 -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1148
v0)))))
-- Algebra.Bundles.IdempotentCommutativeMonoid._.isMonoid
d_isMonoid_1204 ::
  T_IdempotentCommutativeMonoid_1148 ->
  MAlonzo.Code.Algebra.Structures.T_IsMonoid_686
d_isMonoid_1204 :: T_IdempotentCommutativeMonoid_1148 -> T_IsMonoid_686
d_isMonoid_1204 T_IdempotentCommutativeMonoid_1148
v0
  = (T_IsCommutativeMonoid_736 -> T_IsMonoid_686)
-> AgdaAny -> T_IsMonoid_686
forall a b. a -> b
coe
      T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746
      ((T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_862
         ((T_IdempotentCommutativeMonoid_1148
 -> T_IsIdempotentCommutativeMonoid_852)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1148
-> T_IsIdempotentCommutativeMonoid_852
d_isIdempotentCommutativeMonoid_1172 (T_IdempotentCommutativeMonoid_1148 -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1148
v0)))
-- Algebra.Bundles.IdempotentCommutativeMonoid._.isPartialEquivalence
d_isPartialEquivalence_1206 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentCommutativeMonoid_1148 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_1206 :: ()
-> ()
-> T_IdempotentCommutativeMonoid_1148
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_1206 ~()
v0 ~()
v1 T_IdempotentCommutativeMonoid_1148
v2
  = T_IdempotentCommutativeMonoid_1148 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_1206 T_IdempotentCommutativeMonoid_1148
v2
du_isPartialEquivalence_1206 ::
  T_IdempotentCommutativeMonoid_1148 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_1206 :: T_IdempotentCommutativeMonoid_1148 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_1206 T_IdempotentCommutativeMonoid_1148
v0
  = let v1 :: T_IsIdempotentCommutativeMonoid_852
v1 = T_IdempotentCommutativeMonoid_1148
-> T_IsIdempotentCommutativeMonoid_852
d_isIdempotentCommutativeMonoid_1172 (T_IdempotentCommutativeMonoid_1148
-> T_IdempotentCommutativeMonoid_1148
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1148
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsCommutativeMonoid_736
v2
             = T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_862
                 (T_IsIdempotentCommutativeMonoid_852
-> T_IsIdempotentCommutativeMonoid_852
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsMonoid_686
v3
                = T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746 (T_IsCommutativeMonoid_736 -> T_IsCommutativeMonoid_736
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsSemigroup_472
v4
                   = T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsMagma_176
v5 = T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (T_IsSemigroup_472 -> T_IsSemigroup_472
forall a b. a -> b
coe T_IsSemigroup_472
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  ((T_IsEquivalence_26 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsEquivalence_26 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
                     ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v5)))))))
-- Algebra.Bundles.IdempotentCommutativeMonoid._.isSemigroup
d_isSemigroup_1208 ::
  T_IdempotentCommutativeMonoid_1148 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_472
d_isSemigroup_1208 :: T_IdempotentCommutativeMonoid_1148 -> T_IsSemigroup_472
d_isSemigroup_1208 T_IdempotentCommutativeMonoid_1148
v0
  = (T_IsMonoid_686 -> T_IsSemigroup_472)
-> AgdaAny -> T_IsSemigroup_472
forall a b. a -> b
coe
      T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
      ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746
         ((T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_862
            ((T_IdempotentCommutativeMonoid_1148
 -> T_IsIdempotentCommutativeMonoid_852)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1148
-> T_IsIdempotentCommutativeMonoid_852
d_isIdempotentCommutativeMonoid_1172 (T_IdempotentCommutativeMonoid_1148 -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1148
v0))))
-- Algebra.Bundles.IdempotentCommutativeMonoid._.isUnitalMagma
d_isUnitalMagma_1210 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentCommutativeMonoid_1148 ->
  MAlonzo.Code.Algebra.Structures.T_IsUnitalMagma_642
d_isUnitalMagma_1210 :: ()
-> () -> T_IdempotentCommutativeMonoid_1148 -> T_IsUnitalMagma_642
d_isUnitalMagma_1210 ~()
v0 ~()
v1 T_IdempotentCommutativeMonoid_1148
v2 = T_IdempotentCommutativeMonoid_1148 -> T_IsUnitalMagma_642
du_isUnitalMagma_1210 T_IdempotentCommutativeMonoid_1148
v2
du_isUnitalMagma_1210 ::
  T_IdempotentCommutativeMonoid_1148 ->
  MAlonzo.Code.Algebra.Structures.T_IsUnitalMagma_642
du_isUnitalMagma_1210 :: T_IdempotentCommutativeMonoid_1148 -> T_IsUnitalMagma_642
du_isUnitalMagma_1210 T_IdempotentCommutativeMonoid_1148
v0
  = let v1 :: T_IsIdempotentCommutativeMonoid_852
v1 = T_IdempotentCommutativeMonoid_1148
-> T_IsIdempotentCommutativeMonoid_852
d_isIdempotentCommutativeMonoid_1172 (T_IdempotentCommutativeMonoid_1148
-> T_IdempotentCommutativeMonoid_1148
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1148
v0) in
    AgdaAny -> T_IsUnitalMagma_642
forall a b. a -> b
coe
      (let v2 :: T_IsCommutativeMonoid_736
v2
             = T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_862
                 (T_IsIdempotentCommutativeMonoid_852
-> T_IsIdempotentCommutativeMonoid_852
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsMonoid_686 -> T_IsUnitalMagma_642) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoid_686 -> T_IsUnitalMagma_642
MAlonzo.Code.Algebra.Structures.du_isUnitalMagma_730
            ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746 (T_IsCommutativeMonoid_736 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v2))))
-- Algebra.Bundles.IdempotentCommutativeMonoid._.refl
d_refl_1212 ::
  T_IdempotentCommutativeMonoid_1148 -> AgdaAny -> AgdaAny
d_refl_1212 :: T_IdempotentCommutativeMonoid_1148 -> AgdaAny -> AgdaAny
d_refl_1212 T_IdempotentCommutativeMonoid_1148
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_34
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
         ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480
            ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
               ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746
                  ((T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_862
                     ((T_IdempotentCommutativeMonoid_1148
 -> T_IsIdempotentCommutativeMonoid_852)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1148
-> T_IsIdempotentCommutativeMonoid_852
d_isIdempotentCommutativeMonoid_1172 (T_IdempotentCommutativeMonoid_1148 -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1148
v0)))))))
-- Algebra.Bundles.IdempotentCommutativeMonoid._.reflexive
d_reflexive_1214 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentCommutativeMonoid_1148 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_1214 :: ()
-> ()
-> T_IdempotentCommutativeMonoid_1148
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_1214 ~()
v0 ~()
v1 T_IdempotentCommutativeMonoid_1148
v2 = T_IdempotentCommutativeMonoid_1148
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_1214 T_IdempotentCommutativeMonoid_1148
v2
du_reflexive_1214 ::
  T_IdempotentCommutativeMonoid_1148 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_1214 :: T_IdempotentCommutativeMonoid_1148
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_1214 T_IdempotentCommutativeMonoid_1148
v0
  = let v1 :: T_IsIdempotentCommutativeMonoid_852
v1 = T_IdempotentCommutativeMonoid_1148
-> T_IsIdempotentCommutativeMonoid_852
d_isIdempotentCommutativeMonoid_1172 (T_IdempotentCommutativeMonoid_1148
-> T_IdempotentCommutativeMonoid_1148
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1148
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsCommutativeMonoid_736
v2
             = T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_862
                 (T_IsIdempotentCommutativeMonoid_852
-> T_IsIdempotentCommutativeMonoid_852
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsMonoid_686
v3
                = T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746 (T_IsCommutativeMonoid_736 -> T_IsCommutativeMonoid_736
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsSemigroup_472
v4
                   = T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsMagma_176
v5 = T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (T_IsSemigroup_472 -> T_IsSemigroup_472
forall a b. a -> b
coe T_IsSemigroup_472
v4) in
                (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
                  (\ AgdaAny
v6 AgdaAny
v7 AgdaAny
v8 ->
                     (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                       T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
                       ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v5))
                       AgdaAny
v6)))))
-- Algebra.Bundles.IdempotentCommutativeMonoid._.setoid
d_setoid_1216 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentCommutativeMonoid_1148 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_1216 :: () -> () -> T_IdempotentCommutativeMonoid_1148 -> T_Setoid_44
d_setoid_1216 ~()
v0 ~()
v1 T_IdempotentCommutativeMonoid_1148
v2 = T_IdempotentCommutativeMonoid_1148 -> T_Setoid_44
du_setoid_1216 T_IdempotentCommutativeMonoid_1148
v2
du_setoid_1216 ::
  T_IdempotentCommutativeMonoid_1148 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_1216 :: T_IdempotentCommutativeMonoid_1148 -> T_Setoid_44
du_setoid_1216 T_IdempotentCommutativeMonoid_1148
v0
  = let v1 :: T_IsIdempotentCommutativeMonoid_852
v1 = T_IdempotentCommutativeMonoid_1148
-> T_IsIdempotentCommutativeMonoid_852
d_isIdempotentCommutativeMonoid_1172 (T_IdempotentCommutativeMonoid_1148
-> T_IdempotentCommutativeMonoid_1148
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1148
v0) in
    AgdaAny -> T_Setoid_44
forall a b. a -> b
coe
      (let v2 :: T_IsCommutativeMonoid_736
v2
             = T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_862
                 (T_IsIdempotentCommutativeMonoid_852
-> T_IsIdempotentCommutativeMonoid_852
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsMonoid_686
v3
                = T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746 (T_IsCommutativeMonoid_736 -> T_IsCommutativeMonoid_736
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsSemigroup_472
v4
                   = T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               ((T_IsMagma_176 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsMagma_176 -> T_Setoid_44
MAlonzo.Code.Algebra.Structures.du_setoid_200
                  ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v4))))))
-- Algebra.Bundles.IdempotentCommutativeMonoid._.sym
d_sym_1218 ::
  T_IdempotentCommutativeMonoid_1148 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_1218 :: T_IdempotentCommutativeMonoid_1148
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_1218 T_IdempotentCommutativeMonoid_1148
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_36
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
         ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480
            ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
               ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746
                  ((T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_862
                     ((T_IdempotentCommutativeMonoid_1148
 -> T_IsIdempotentCommutativeMonoid_852)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1148
-> T_IsIdempotentCommutativeMonoid_852
d_isIdempotentCommutativeMonoid_1172 (T_IdempotentCommutativeMonoid_1148 -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1148
v0)))))))
-- Algebra.Bundles.IdempotentCommutativeMonoid._.trans
d_trans_1220 ::
  T_IdempotentCommutativeMonoid_1148 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_1220 :: T_IdempotentCommutativeMonoid_1148
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_1220 T_IdempotentCommutativeMonoid_1148
v0
  = (T_IsEquivalence_26
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_38
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
         ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480
            ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
               ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746
                  ((T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_862
                     ((T_IdempotentCommutativeMonoid_1148
 -> T_IsIdempotentCommutativeMonoid_852)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1148
-> T_IsIdempotentCommutativeMonoid_852
d_isIdempotentCommutativeMonoid_1172 (T_IdempotentCommutativeMonoid_1148 -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1148
v0)))))))
-- Algebra.Bundles.IdempotentCommutativeMonoid._.∙-cong
d_'8729''45'cong_1222 ::
  T_IdempotentCommutativeMonoid_1148 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_1222 :: T_IdempotentCommutativeMonoid_1148
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_1222 T_IdempotentCommutativeMonoid_1148
v0
  = (T_IsMagma_176
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsMagma_176
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_186
      ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480
         ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
            ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746
               ((T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_862
                  ((T_IdempotentCommutativeMonoid_1148
 -> T_IsIdempotentCommutativeMonoid_852)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1148
-> T_IsIdempotentCommutativeMonoid_852
d_isIdempotentCommutativeMonoid_1172 (T_IdempotentCommutativeMonoid_1148 -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1148
v0))))))
-- Algebra.Bundles.IdempotentCommutativeMonoid._.∙-congʳ
d_'8729''45'cong'691'_1224 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentCommutativeMonoid_1148 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_1224 :: ()
-> ()
-> T_IdempotentCommutativeMonoid_1148
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_1224 ~()
v0 ~()
v1 T_IdempotentCommutativeMonoid_1148
v2
  = T_IdempotentCommutativeMonoid_1148
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1224 T_IdempotentCommutativeMonoid_1148
v2
du_'8729''45'cong'691'_1224 ::
  T_IdempotentCommutativeMonoid_1148 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1224 :: T_IdempotentCommutativeMonoid_1148
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1224 T_IdempotentCommutativeMonoid_1148
v0
  = let v1 :: T_IsIdempotentCommutativeMonoid_852
v1 = T_IdempotentCommutativeMonoid_1148
-> T_IsIdempotentCommutativeMonoid_852
d_isIdempotentCommutativeMonoid_1172 (T_IdempotentCommutativeMonoid_1148
-> T_IdempotentCommutativeMonoid_1148
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1148
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsCommutativeMonoid_736
v2
             = T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_862
                 (T_IsIdempotentCommutativeMonoid_852
-> T_IsIdempotentCommutativeMonoid_852
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsMonoid_686
v3
                = T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746 (T_IsCommutativeMonoid_736 -> T_IsCommutativeMonoid_736
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsSemigroup_472
v4
                   = T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'691'_206
                  ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v4))))))
-- Algebra.Bundles.IdempotentCommutativeMonoid._.∙-congˡ
d_'8729''45'cong'737'_1226 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentCommutativeMonoid_1148 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_1226 :: ()
-> ()
-> T_IdempotentCommutativeMonoid_1148
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_1226 ~()
v0 ~()
v1 T_IdempotentCommutativeMonoid_1148
v2
  = T_IdempotentCommutativeMonoid_1148
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1226 T_IdempotentCommutativeMonoid_1148
v2
du_'8729''45'cong'737'_1226 ::
  T_IdempotentCommutativeMonoid_1148 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1226 :: T_IdempotentCommutativeMonoid_1148
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1226 T_IdempotentCommutativeMonoid_1148
v0
  = let v1 :: T_IsIdempotentCommutativeMonoid_852
v1 = T_IdempotentCommutativeMonoid_1148
-> T_IsIdempotentCommutativeMonoid_852
d_isIdempotentCommutativeMonoid_1172 (T_IdempotentCommutativeMonoid_1148
-> T_IdempotentCommutativeMonoid_1148
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1148
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsCommutativeMonoid_736
v2
             = T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_862
                 (T_IsIdempotentCommutativeMonoid_852
-> T_IsIdempotentCommutativeMonoid_852
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsMonoid_686
v3
                = T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746 (T_IsCommutativeMonoid_736 -> T_IsCommutativeMonoid_736
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsSemigroup_472
v4
                   = T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'737'_202
                  ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v4))))))
-- Algebra.Bundles.IdempotentCommutativeMonoid.commutativeMonoid
d_commutativeMonoid_1228 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentCommutativeMonoid_1148 -> T_CommutativeMonoid_962
d_commutativeMonoid_1228 :: ()
-> ()
-> T_IdempotentCommutativeMonoid_1148
-> T_CommutativeMonoid_962
d_commutativeMonoid_1228 ~()
v0 ~()
v1 T_IdempotentCommutativeMonoid_1148
v2 = T_IdempotentCommutativeMonoid_1148 -> T_CommutativeMonoid_962
du_commutativeMonoid_1228 T_IdempotentCommutativeMonoid_1148
v2
du_commutativeMonoid_1228 ::
  T_IdempotentCommutativeMonoid_1148 -> T_CommutativeMonoid_962
du_commutativeMonoid_1228 :: T_IdempotentCommutativeMonoid_1148 -> T_CommutativeMonoid_962
du_commutativeMonoid_1228 T_IdempotentCommutativeMonoid_1148
v0
  = ((AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny -> T_IsCommutativeMonoid_736 -> T_CommutativeMonoid_962)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsCommutativeMonoid_736
-> T_CommutativeMonoid_962
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> T_IsCommutativeMonoid_736 -> T_CommutativeMonoid_962
C_CommutativeMonoid'46'constructor_17931 (T_IdempotentCommutativeMonoid_1148 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__1168 (T_IdempotentCommutativeMonoid_1148
-> T_IdempotentCommutativeMonoid_1148
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1148
v0))
      (T_IdempotentCommutativeMonoid_1148 -> AgdaAny
d_ε_1170 (T_IdempotentCommutativeMonoid_1148
-> T_IdempotentCommutativeMonoid_1148
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1148
v0))
      (T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_862
         ((T_IdempotentCommutativeMonoid_1148
 -> T_IsIdempotentCommutativeMonoid_852)
-> AgdaAny -> T_IsIdempotentCommutativeMonoid_852
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1148
-> T_IsIdempotentCommutativeMonoid_852
d_isIdempotentCommutativeMonoid_1172 (T_IdempotentCommutativeMonoid_1148 -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1148
v0)))
-- Algebra.Bundles.IdempotentCommutativeMonoid.idempotentMonoid
d_idempotentMonoid_1230 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentCommutativeMonoid_1148 -> T_IdempotentMonoid_1058
d_idempotentMonoid_1230 :: ()
-> ()
-> T_IdempotentCommutativeMonoid_1148
-> T_IdempotentMonoid_1058
d_idempotentMonoid_1230 ~()
v0 ~()
v1 T_IdempotentCommutativeMonoid_1148
v2 = T_IdempotentCommutativeMonoid_1148 -> T_IdempotentMonoid_1058
du_idempotentMonoid_1230 T_IdempotentCommutativeMonoid_1148
v2
du_idempotentMonoid_1230 ::
  T_IdempotentCommutativeMonoid_1148 -> T_IdempotentMonoid_1058
du_idempotentMonoid_1230 :: T_IdempotentCommutativeMonoid_1148 -> T_IdempotentMonoid_1058
du_idempotentMonoid_1230 T_IdempotentCommutativeMonoid_1148
v0
  = ((AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny -> T_IsIdempotentMonoid_796 -> T_IdempotentMonoid_1058)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IdempotentMonoid_1058
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> T_IsIdempotentMonoid_796 -> T_IdempotentMonoid_1058
C_IdempotentMonoid'46'constructor_19753 (T_IdempotentCommutativeMonoid_1148 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__1168 (T_IdempotentCommutativeMonoid_1148
-> T_IdempotentCommutativeMonoid_1148
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1148
v0))
      (T_IdempotentCommutativeMonoid_1148 -> AgdaAny
d_ε_1170 (T_IdempotentCommutativeMonoid_1148
-> T_IdempotentCommutativeMonoid_1148
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1148
v0))
      ((T_IsIdempotentCommutativeMonoid_852 -> T_IsIdempotentMonoid_796)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsIdempotentCommutativeMonoid_852 -> T_IsIdempotentMonoid_796
MAlonzo.Code.Algebra.Structures.du_isIdempotentMonoid_910
         ((T_IdempotentCommutativeMonoid_1148
 -> T_IsIdempotentCommutativeMonoid_852)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1148
-> T_IsIdempotentCommutativeMonoid_852
d_isIdempotentCommutativeMonoid_1172 (T_IdempotentCommutativeMonoid_1148 -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1148
v0)))
-- Algebra.Bundles.IdempotentCommutativeMonoid.commutativeBand
d_commutativeBand_1232 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentCommutativeMonoid_1148 -> T_CommutativeBand_732
d_commutativeBand_1232 :: ()
-> ()
-> T_IdempotentCommutativeMonoid_1148
-> T_CommutativeBand_732
d_commutativeBand_1232 ~()
v0 ~()
v1 T_IdempotentCommutativeMonoid_1148
v2 = T_IdempotentCommutativeMonoid_1148 -> T_CommutativeBand_732
du_commutativeBand_1232 T_IdempotentCommutativeMonoid_1148
v2
du_commutativeBand_1232 ::
  T_IdempotentCommutativeMonoid_1148 -> T_CommutativeBand_732
du_commutativeBand_1232 :: T_IdempotentCommutativeMonoid_1148 -> T_CommutativeBand_732
du_commutativeBand_1232 T_IdempotentCommutativeMonoid_1148
v0
  = ((AgdaAny -> AgdaAny -> AgdaAny)
 -> T_IsCommutativeBand_590 -> T_CommutativeBand_732)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_CommutativeBand_732
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsCommutativeBand_590 -> T_CommutativeBand_732
C_CommutativeBand'46'constructor_13365 (T_IdempotentCommutativeMonoid_1148 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__1168 (T_IdempotentCommutativeMonoid_1148
-> T_IdempotentCommutativeMonoid_1148
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1148
v0))
      ((T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeBand_590)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeBand_590
MAlonzo.Code.Algebra.Structures.du_isCommutativeBand_916
         ((T_IdempotentCommutativeMonoid_1148
 -> T_IsIdempotentCommutativeMonoid_852)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1148
-> T_IsIdempotentCommutativeMonoid_852
d_isIdempotentCommutativeMonoid_1172 (T_IdempotentCommutativeMonoid_1148 -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1148
v0)))
-- Algebra.Bundles.IdempotentCommutativeMonoid._._≉_
d__'8777'__1236 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentCommutativeMonoid_1148 -> AgdaAny -> AgdaAny -> ()
d__'8777'__1236 :: ()
-> ()
-> T_IdempotentCommutativeMonoid_1148
-> AgdaAny
-> AgdaAny
-> ()
d__'8777'__1236 = ()
-> ()
-> T_IdempotentCommutativeMonoid_1148
-> AgdaAny
-> AgdaAny
-> ()
forall a. a
erased
-- Algebra.Bundles.IdempotentCommutativeMonoid._.commutativeMagma
d_commutativeMagma_1238 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentCommutativeMonoid_1148 -> T_CommutativeMagma_180
d_commutativeMagma_1238 :: ()
-> ()
-> T_IdempotentCommutativeMonoid_1148
-> T_CommutativeMagma_180
d_commutativeMagma_1238 ~()
v0 ~()
v1 T_IdempotentCommutativeMonoid_1148
v2 = T_IdempotentCommutativeMonoid_1148 -> T_CommutativeMagma_180
du_commutativeMagma_1238 T_IdempotentCommutativeMonoid_1148
v2
du_commutativeMagma_1238 ::
  T_IdempotentCommutativeMonoid_1148 -> T_CommutativeMagma_180
du_commutativeMagma_1238 :: T_IdempotentCommutativeMonoid_1148 -> T_CommutativeMagma_180
du_commutativeMagma_1238 T_IdempotentCommutativeMonoid_1148
v0
  = let v1 :: t
v1 = (T_IdempotentCommutativeMonoid_1148 -> T_CommutativeMonoid_962)
-> AgdaAny -> t
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1148 -> T_CommutativeMonoid_962
du_commutativeMonoid_1228 (T_IdempotentCommutativeMonoid_1148 -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1148
v0) in
    AgdaAny -> T_CommutativeMagma_180
forall a b. a -> b
coe
      ((T_CommutativeSemigroup_662 -> T_CommutativeMagma_180)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_CommutativeSemigroup_662 -> T_CommutativeMagma_180
du_commutativeMagma_726
         ((T_CommutativeMonoid_962 -> T_CommutativeSemigroup_662)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeMonoid_962 -> T_CommutativeSemigroup_662
du_commutativeSemigroup_1048 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1)))
-- Algebra.Bundles.IdempotentCommutativeMonoid._.commutativeSemigroup
d_commutativeSemigroup_1240 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentCommutativeMonoid_1148 -> T_CommutativeSemigroup_662
d_commutativeSemigroup_1240 :: ()
-> ()
-> T_IdempotentCommutativeMonoid_1148
-> T_CommutativeSemigroup_662
d_commutativeSemigroup_1240 ~()
v0 ~()
v1 T_IdempotentCommutativeMonoid_1148
v2
  = T_IdempotentCommutativeMonoid_1148 -> T_CommutativeSemigroup_662
du_commutativeSemigroup_1240 T_IdempotentCommutativeMonoid_1148
v2
du_commutativeSemigroup_1240 ::
  T_IdempotentCommutativeMonoid_1148 -> T_CommutativeSemigroup_662
du_commutativeSemigroup_1240 :: T_IdempotentCommutativeMonoid_1148 -> T_CommutativeSemigroup_662
du_commutativeSemigroup_1240 T_IdempotentCommutativeMonoid_1148
v0
  = (T_CommutativeMonoid_962 -> T_CommutativeSemigroup_662)
-> AgdaAny -> T_CommutativeSemigroup_662
forall a b. a -> b
coe
      T_CommutativeMonoid_962 -> T_CommutativeSemigroup_662
du_commutativeSemigroup_1048
      ((T_IdempotentCommutativeMonoid_1148 -> T_CommutativeMonoid_962)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1148 -> T_CommutativeMonoid_962
du_commutativeMonoid_1228 (T_IdempotentCommutativeMonoid_1148 -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1148
v0))
-- Algebra.Bundles.IdempotentCommutativeMonoid._.magma
d_magma_1242 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentCommutativeMonoid_1148 -> T_Magma_68
d_magma_1242 :: () -> () -> T_IdempotentCommutativeMonoid_1148 -> T_Magma_68
d_magma_1242 ~()
v0 ~()
v1 T_IdempotentCommutativeMonoid_1148
v2 = T_IdempotentCommutativeMonoid_1148 -> T_Magma_68
du_magma_1242 T_IdempotentCommutativeMonoid_1148
v2
du_magma_1242 :: T_IdempotentCommutativeMonoid_1148 -> T_Magma_68
du_magma_1242 :: T_IdempotentCommutativeMonoid_1148 -> T_Magma_68
du_magma_1242 T_IdempotentCommutativeMonoid_1148
v0
  = let v1 :: t
v1 = (T_IdempotentCommutativeMonoid_1148 -> T_CommutativeMonoid_962)
-> AgdaAny -> t
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1148 -> T_CommutativeMonoid_962
du_commutativeMonoid_1228 (T_IdempotentCommutativeMonoid_1148 -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1148
v0) in
    AgdaAny -> T_Magma_68
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_CommutativeMonoid_962 -> T_Monoid_882) -> AgdaAny -> t
forall a b. a -> b
coe T_CommutativeMonoid_962 -> T_Monoid_882
du_monoid_1032 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_Semigroup_536 -> T_Magma_68) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semigroup_536 -> T_Magma_68
du_magma_584 ((T_Monoid_882 -> T_Semigroup_536) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Monoid_882 -> T_Semigroup_536
du_semigroup_944 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2))))
-- Algebra.Bundles.IdempotentCommutativeMonoid._.monoid
d_monoid_1244 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentCommutativeMonoid_1148 -> T_Monoid_882
d_monoid_1244 :: () -> () -> T_IdempotentCommutativeMonoid_1148 -> T_Monoid_882
d_monoid_1244 ~()
v0 ~()
v1 T_IdempotentCommutativeMonoid_1148
v2 = T_IdempotentCommutativeMonoid_1148 -> T_Monoid_882
du_monoid_1244 T_IdempotentCommutativeMonoid_1148
v2
du_monoid_1244 ::
  T_IdempotentCommutativeMonoid_1148 -> T_Monoid_882
du_monoid_1244 :: T_IdempotentCommutativeMonoid_1148 -> T_Monoid_882
du_monoid_1244 T_IdempotentCommutativeMonoid_1148
v0
  = (T_CommutativeMonoid_962 -> T_Monoid_882)
-> AgdaAny -> T_Monoid_882
forall a b. a -> b
coe T_CommutativeMonoid_962 -> T_Monoid_882
du_monoid_1032 ((T_IdempotentCommutativeMonoid_1148 -> T_CommutativeMonoid_962)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1148 -> T_CommutativeMonoid_962
du_commutativeMonoid_1228 (T_IdempotentCommutativeMonoid_1148 -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1148
v0))
-- Algebra.Bundles.IdempotentCommutativeMonoid._.rawMagma
d_rawMagma_1246 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentCommutativeMonoid_1148 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
d_rawMagma_1246 :: () -> () -> T_IdempotentCommutativeMonoid_1148 -> T_RawMagma_36
d_rawMagma_1246 ~()
v0 ~()
v1 T_IdempotentCommutativeMonoid_1148
v2 = T_IdempotentCommutativeMonoid_1148 -> T_RawMagma_36
du_rawMagma_1246 T_IdempotentCommutativeMonoid_1148
v2
du_rawMagma_1246 ::
  T_IdempotentCommutativeMonoid_1148 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
du_rawMagma_1246 :: T_IdempotentCommutativeMonoid_1148 -> T_RawMagma_36
du_rawMagma_1246 T_IdempotentCommutativeMonoid_1148
v0
  = let v1 :: t
v1 = (T_IdempotentCommutativeMonoid_1148 -> T_CommutativeMonoid_962)
-> AgdaAny -> t
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1148 -> T_CommutativeMonoid_962
du_commutativeMonoid_1228 (T_IdempotentCommutativeMonoid_1148 -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1148
v0) in
    AgdaAny -> T_RawMagma_36
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_CommutativeMonoid_962 -> T_Monoid_882) -> AgdaAny -> t
forall a b. a -> b
coe T_CommutativeMonoid_962 -> T_Monoid_882
du_monoid_1032 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: t
v3 = (T_Monoid_882 -> T_Semigroup_536) -> AgdaAny -> t
forall a b. a -> b
coe T_Monoid_882 -> T_Semigroup_536
du_semigroup_944 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_Magma_68 -> T_RawMagma_36) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Magma_68 -> T_RawMagma_36
du_rawMagma_112 ((T_Semigroup_536 -> T_Magma_68) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semigroup_536 -> T_Magma_68
du_magma_584 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3)))))
-- Algebra.Bundles.IdempotentCommutativeMonoid._.rawMonoid
d_rawMonoid_1248 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentCommutativeMonoid_1148 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMonoid_64
d_rawMonoid_1248 :: () -> () -> T_IdempotentCommutativeMonoid_1148 -> T_RawMonoid_64
d_rawMonoid_1248 ~()
v0 ~()
v1 T_IdempotentCommutativeMonoid_1148
v2 = T_IdempotentCommutativeMonoid_1148 -> T_RawMonoid_64
du_rawMonoid_1248 T_IdempotentCommutativeMonoid_1148
v2
du_rawMonoid_1248 ::
  T_IdempotentCommutativeMonoid_1148 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMonoid_64
du_rawMonoid_1248 :: T_IdempotentCommutativeMonoid_1148 -> T_RawMonoid_64
du_rawMonoid_1248 T_IdempotentCommutativeMonoid_1148
v0
  = let v1 :: t
v1 = (T_IdempotentCommutativeMonoid_1148 -> T_CommutativeMonoid_962)
-> AgdaAny -> t
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1148 -> T_CommutativeMonoid_962
du_commutativeMonoid_1228 (T_IdempotentCommutativeMonoid_1148 -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1148
v0) in
    AgdaAny -> T_RawMonoid_64
forall a b. a -> b
coe ((T_Monoid_882 -> T_RawMonoid_64) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Monoid_882 -> T_RawMonoid_64
du_rawMonoid_954 ((T_CommutativeMonoid_962 -> T_Monoid_882) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeMonoid_962 -> T_Monoid_882
du_monoid_1032 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1)))
-- Algebra.Bundles.IdempotentCommutativeMonoid._.semigroup
d_semigroup_1250 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentCommutativeMonoid_1148 -> T_Semigroup_536
d_semigroup_1250 :: () -> () -> T_IdempotentCommutativeMonoid_1148 -> T_Semigroup_536
d_semigroup_1250 ~()
v0 ~()
v1 T_IdempotentCommutativeMonoid_1148
v2 = T_IdempotentCommutativeMonoid_1148 -> T_Semigroup_536
du_semigroup_1250 T_IdempotentCommutativeMonoid_1148
v2
du_semigroup_1250 ::
  T_IdempotentCommutativeMonoid_1148 -> T_Semigroup_536
du_semigroup_1250 :: T_IdempotentCommutativeMonoid_1148 -> T_Semigroup_536
du_semigroup_1250 T_IdempotentCommutativeMonoid_1148
v0
  = let v1 :: t
v1 = (T_IdempotentCommutativeMonoid_1148 -> T_CommutativeMonoid_962)
-> AgdaAny -> t
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1148 -> T_CommutativeMonoid_962
du_commutativeMonoid_1228 (T_IdempotentCommutativeMonoid_1148 -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1148
v0) in
    AgdaAny -> T_Semigroup_536
forall a b. a -> b
coe ((T_Monoid_882 -> T_Semigroup_536) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Monoid_882 -> T_Semigroup_536
du_semigroup_944 ((T_CommutativeMonoid_962 -> T_Monoid_882) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeMonoid_962 -> T_Monoid_882
du_monoid_1032 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1)))
-- Algebra.Bundles.IdempotentCommutativeMonoid._.unitalMagma
d_unitalMagma_1252 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentCommutativeMonoid_1148 -> T_UnitalMagma_814
d_unitalMagma_1252 :: () -> () -> T_IdempotentCommutativeMonoid_1148 -> T_UnitalMagma_814
d_unitalMagma_1252 ~()
v0 ~()
v1 T_IdempotentCommutativeMonoid_1148
v2 = T_IdempotentCommutativeMonoid_1148 -> T_UnitalMagma_814
du_unitalMagma_1252 T_IdempotentCommutativeMonoid_1148
v2
du_unitalMagma_1252 ::
  T_IdempotentCommutativeMonoid_1148 -> T_UnitalMagma_814
du_unitalMagma_1252 :: T_IdempotentCommutativeMonoid_1148 -> T_UnitalMagma_814
du_unitalMagma_1252 T_IdempotentCommutativeMonoid_1148
v0
  = let v1 :: t
v1 = (T_IdempotentCommutativeMonoid_1148 -> T_CommutativeMonoid_962)
-> AgdaAny -> t
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1148 -> T_CommutativeMonoid_962
du_commutativeMonoid_1228 (T_IdempotentCommutativeMonoid_1148 -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1148
v0) in
    AgdaAny -> T_UnitalMagma_814
forall a b. a -> b
coe ((T_Monoid_882 -> T_UnitalMagma_814) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Monoid_882 -> T_UnitalMagma_814
du_unitalMagma_956 ((T_CommutativeMonoid_962 -> T_Monoid_882) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeMonoid_962 -> T_Monoid_882
du_monoid_1032 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1)))
-- Algebra.Bundles.IdempotentCommutativeMonoid._.band
d_band_1256 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentCommutativeMonoid_1148 -> T_Band_596
d_band_1256 :: () -> () -> T_IdempotentCommutativeMonoid_1148 -> T_Band_596
d_band_1256 ~()
v0 ~()
v1 T_IdempotentCommutativeMonoid_1148
v2 = T_IdempotentCommutativeMonoid_1148 -> T_Band_596
du_band_1256 T_IdempotentCommutativeMonoid_1148
v2
du_band_1256 :: T_IdempotentCommutativeMonoid_1148 -> T_Band_596
du_band_1256 :: T_IdempotentCommutativeMonoid_1148 -> T_Band_596
du_band_1256 T_IdempotentCommutativeMonoid_1148
v0
  = (T_CommutativeBand_732 -> T_Band_596) -> AgdaAny -> T_Band_596
forall a b. a -> b
coe T_CommutativeBand_732 -> T_Band_596
du_band_792 ((T_IdempotentCommutativeMonoid_1148 -> T_CommutativeBand_732)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1148 -> T_CommutativeBand_732
du_commutativeBand_1232 (T_IdempotentCommutativeMonoid_1148 -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1148
v0))
-- Algebra.Bundles.BoundedLattice
d_BoundedLattice_1258 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 -> ()
d_BoundedLattice_1258 :: () -> () -> ()
d_BoundedLattice_1258 = () -> () -> ()
forall a. a
erased
-- Algebra.Bundles.BoundedLattice._∙_
d__'8729'__1268 ::
  T_IdempotentCommutativeMonoid_1148 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__1268 :: T_IdempotentCommutativeMonoid_1148 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__1268 T_IdempotentCommutativeMonoid_1148
v0 = (T_IdempotentCommutativeMonoid_1148
 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1148 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__1168 (T_IdempotentCommutativeMonoid_1148 -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1148
v0)
-- Algebra.Bundles.BoundedLattice._≈_
d__'8776'__1270 ::
  T_IdempotentCommutativeMonoid_1148 -> AgdaAny -> AgdaAny -> ()
d__'8776'__1270 :: T_IdempotentCommutativeMonoid_1148 -> AgdaAny -> AgdaAny -> ()
d__'8776'__1270 = T_IdempotentCommutativeMonoid_1148 -> AgdaAny -> AgdaAny -> ()
forall a. a
erased
-- Algebra.Bundles.BoundedLattice._≉_
d__'8777'__1272 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentCommutativeMonoid_1148 -> AgdaAny -> AgdaAny -> ()
d__'8777'__1272 :: ()
-> ()
-> T_IdempotentCommutativeMonoid_1148
-> AgdaAny
-> AgdaAny
-> ()
d__'8777'__1272 = ()
-> ()
-> T_IdempotentCommutativeMonoid_1148
-> AgdaAny
-> AgdaAny
-> ()
forall a. a
erased
-- Algebra.Bundles.BoundedLattice.Carrier
d_Carrier_1274 :: T_IdempotentCommutativeMonoid_1148 -> ()
d_Carrier_1274 :: T_IdempotentCommutativeMonoid_1148 -> ()
d_Carrier_1274 = T_IdempotentCommutativeMonoid_1148 -> ()
forall a. a
erased
-- Algebra.Bundles.BoundedLattice.assoc
d_assoc_1276 ::
  T_IdempotentCommutativeMonoid_1148 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_1276 :: T_IdempotentCommutativeMonoid_1148
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_1276 T_IdempotentCommutativeMonoid_1148
v0
  = (T_IsSemigroup_472 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsSemigroup_472 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_assoc_482
      ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
         ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746
            ((T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_862
               ((T_IdempotentCommutativeMonoid_1148
 -> T_IsIdempotentCommutativeMonoid_852)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1148
-> T_IsIdempotentCommutativeMonoid_852
d_isIdempotentCommutativeMonoid_1172 (T_IdempotentCommutativeMonoid_1148 -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1148
v0)))))
-- Algebra.Bundles.BoundedLattice.band
d_band_1278 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentCommutativeMonoid_1148 -> T_Band_596
d_band_1278 :: () -> () -> T_IdempotentCommutativeMonoid_1148 -> T_Band_596
d_band_1278 ~()
v0 ~()
v1 T_IdempotentCommutativeMonoid_1148
v2 = T_IdempotentCommutativeMonoid_1148 -> T_Band_596
du_band_1278 T_IdempotentCommutativeMonoid_1148
v2
du_band_1278 :: T_IdempotentCommutativeMonoid_1148 -> T_Band_596
du_band_1278 :: T_IdempotentCommutativeMonoid_1148 -> T_Band_596
du_band_1278 T_IdempotentCommutativeMonoid_1148
v0
  = (T_CommutativeBand_732 -> T_Band_596) -> AgdaAny -> T_Band_596
forall a b. a -> b
coe T_CommutativeBand_732 -> T_Band_596
du_band_792 ((T_IdempotentCommutativeMonoid_1148 -> T_CommutativeBand_732)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1148 -> T_CommutativeBand_732
du_commutativeBand_1232 (T_IdempotentCommutativeMonoid_1148 -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1148
v0))
-- Algebra.Bundles.BoundedLattice.comm
d_comm_1280 ::
  T_IdempotentCommutativeMonoid_1148 -> AgdaAny -> AgdaAny -> AgdaAny
d_comm_1280 :: T_IdempotentCommutativeMonoid_1148 -> AgdaAny -> AgdaAny -> AgdaAny
d_comm_1280 T_IdempotentCommutativeMonoid_1148
v0
  = (T_IsCommutativeMonoid_736 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsCommutativeMonoid_736 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_comm_748
      ((T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_862
         ((T_IdempotentCommutativeMonoid_1148
 -> T_IsIdempotentCommutativeMonoid_852)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1148
-> T_IsIdempotentCommutativeMonoid_852
d_isIdempotentCommutativeMonoid_1172 (T_IdempotentCommutativeMonoid_1148 -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1148
v0)))
-- Algebra.Bundles.BoundedLattice.commutativeBand
d_commutativeBand_1282 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentCommutativeMonoid_1148 -> T_CommutativeBand_732
d_commutativeBand_1282 :: ()
-> ()
-> T_IdempotentCommutativeMonoid_1148
-> T_CommutativeBand_732
d_commutativeBand_1282 ~()
v0 ~()
v1 T_IdempotentCommutativeMonoid_1148
v2 = T_IdempotentCommutativeMonoid_1148 -> T_CommutativeBand_732
du_commutativeBand_1282 T_IdempotentCommutativeMonoid_1148
v2
du_commutativeBand_1282 ::
  T_IdempotentCommutativeMonoid_1148 -> T_CommutativeBand_732
du_commutativeBand_1282 :: T_IdempotentCommutativeMonoid_1148 -> T_CommutativeBand_732
du_commutativeBand_1282 T_IdempotentCommutativeMonoid_1148
v0 = (T_IdempotentCommutativeMonoid_1148 -> T_CommutativeBand_732)
-> AgdaAny -> T_CommutativeBand_732
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1148 -> T_CommutativeBand_732
du_commutativeBand_1232 (T_IdempotentCommutativeMonoid_1148 -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1148
v0)
-- Algebra.Bundles.BoundedLattice.commutativeMagma
d_commutativeMagma_1284 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentCommutativeMonoid_1148 -> T_CommutativeMagma_180
d_commutativeMagma_1284 :: ()
-> ()
-> T_IdempotentCommutativeMonoid_1148
-> T_CommutativeMagma_180
d_commutativeMagma_1284 ~()
v0 ~()
v1 T_IdempotentCommutativeMonoid_1148
v2 = T_IdempotentCommutativeMonoid_1148 -> T_CommutativeMagma_180
du_commutativeMagma_1284 T_IdempotentCommutativeMonoid_1148
v2
du_commutativeMagma_1284 ::
  T_IdempotentCommutativeMonoid_1148 -> T_CommutativeMagma_180
du_commutativeMagma_1284 :: T_IdempotentCommutativeMonoid_1148 -> T_CommutativeMagma_180
du_commutativeMagma_1284 T_IdempotentCommutativeMonoid_1148
v0
  = let v1 :: t
v1 = (T_IdempotentCommutativeMonoid_1148 -> T_CommutativeMonoid_962)
-> AgdaAny -> t
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1148 -> T_CommutativeMonoid_962
du_commutativeMonoid_1228 (T_IdempotentCommutativeMonoid_1148 -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1148
v0) in
    AgdaAny -> T_CommutativeMagma_180
forall a b. a -> b
coe
      ((T_CommutativeSemigroup_662 -> T_CommutativeMagma_180)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_CommutativeSemigroup_662 -> T_CommutativeMagma_180
du_commutativeMagma_726
         ((T_CommutativeMonoid_962 -> T_CommutativeSemigroup_662)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeMonoid_962 -> T_CommutativeSemigroup_662
du_commutativeSemigroup_1048 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1)))
-- Algebra.Bundles.BoundedLattice.commutativeMonoid
d_commutativeMonoid_1286 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentCommutativeMonoid_1148 -> T_CommutativeMonoid_962
d_commutativeMonoid_1286 :: ()
-> ()
-> T_IdempotentCommutativeMonoid_1148
-> T_CommutativeMonoid_962
d_commutativeMonoid_1286 ~()
v0 ~()
v1 T_IdempotentCommutativeMonoid_1148
v2 = T_IdempotentCommutativeMonoid_1148 -> T_CommutativeMonoid_962
du_commutativeMonoid_1286 T_IdempotentCommutativeMonoid_1148
v2
du_commutativeMonoid_1286 ::
  T_IdempotentCommutativeMonoid_1148 -> T_CommutativeMonoid_962
du_commutativeMonoid_1286 :: T_IdempotentCommutativeMonoid_1148 -> T_CommutativeMonoid_962
du_commutativeMonoid_1286 T_IdempotentCommutativeMonoid_1148
v0
  = (T_IdempotentCommutativeMonoid_1148 -> T_CommutativeMonoid_962)
-> AgdaAny -> T_CommutativeMonoid_962
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1148 -> T_CommutativeMonoid_962
du_commutativeMonoid_1228 (T_IdempotentCommutativeMonoid_1148 -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1148
v0)
-- Algebra.Bundles.BoundedLattice.commutativeSemigroup
d_commutativeSemigroup_1288 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentCommutativeMonoid_1148 -> T_CommutativeSemigroup_662
d_commutativeSemigroup_1288 :: ()
-> ()
-> T_IdempotentCommutativeMonoid_1148
-> T_CommutativeSemigroup_662
d_commutativeSemigroup_1288 ~()
v0 ~()
v1 T_IdempotentCommutativeMonoid_1148
v2
  = T_IdempotentCommutativeMonoid_1148 -> T_CommutativeSemigroup_662
du_commutativeSemigroup_1288 T_IdempotentCommutativeMonoid_1148
v2
du_commutativeSemigroup_1288 ::
  T_IdempotentCommutativeMonoid_1148 -> T_CommutativeSemigroup_662
du_commutativeSemigroup_1288 :: T_IdempotentCommutativeMonoid_1148 -> T_CommutativeSemigroup_662
du_commutativeSemigroup_1288 T_IdempotentCommutativeMonoid_1148
v0
  = (T_CommutativeMonoid_962 -> T_CommutativeSemigroup_662)
-> AgdaAny -> T_CommutativeSemigroup_662
forall a b. a -> b
coe
      T_CommutativeMonoid_962 -> T_CommutativeSemigroup_662
du_commutativeSemigroup_1048
      ((T_IdempotentCommutativeMonoid_1148 -> T_CommutativeMonoid_962)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1148 -> T_CommutativeMonoid_962
du_commutativeMonoid_1228 (T_IdempotentCommutativeMonoid_1148 -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1148
v0))
-- Algebra.Bundles.BoundedLattice.idem
d_idem_1290 ::
  T_IdempotentCommutativeMonoid_1148 -> AgdaAny -> AgdaAny
d_idem_1290 :: T_IdempotentCommutativeMonoid_1148 -> AgdaAny -> AgdaAny
d_idem_1290 T_IdempotentCommutativeMonoid_1148
v0
  = (T_IsIdempotentCommutativeMonoid_852 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsIdempotentCommutativeMonoid_852 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_idem_864
      ((T_IdempotentCommutativeMonoid_1148
 -> T_IsIdempotentCommutativeMonoid_852)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1148
-> T_IsIdempotentCommutativeMonoid_852
d_isIdempotentCommutativeMonoid_1172 (T_IdempotentCommutativeMonoid_1148 -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1148
v0))
-- Algebra.Bundles.BoundedLattice.idempotentMonoid
d_idempotentMonoid_1292 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentCommutativeMonoid_1148 -> T_IdempotentMonoid_1058
d_idempotentMonoid_1292 :: ()
-> ()
-> T_IdempotentCommutativeMonoid_1148
-> T_IdempotentMonoid_1058
d_idempotentMonoid_1292 ~()
v0 ~()
v1 T_IdempotentCommutativeMonoid_1148
v2 = T_IdempotentCommutativeMonoid_1148 -> T_IdempotentMonoid_1058
du_idempotentMonoid_1292 T_IdempotentCommutativeMonoid_1148
v2
du_idempotentMonoid_1292 ::
  T_IdempotentCommutativeMonoid_1148 -> T_IdempotentMonoid_1058
du_idempotentMonoid_1292 :: T_IdempotentCommutativeMonoid_1148 -> T_IdempotentMonoid_1058
du_idempotentMonoid_1292 T_IdempotentCommutativeMonoid_1148
v0 = (T_IdempotentCommutativeMonoid_1148 -> T_IdempotentMonoid_1058)
-> AgdaAny -> T_IdempotentMonoid_1058
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1148 -> T_IdempotentMonoid_1058
du_idempotentMonoid_1230 (T_IdempotentCommutativeMonoid_1148 -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1148
v0)
-- Algebra.Bundles.BoundedLattice.identity
d_identity_1294 ::
  T_IdempotentCommutativeMonoid_1148 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_identity_1294 :: T_IdempotentCommutativeMonoid_1148 -> T_Σ_14
d_identity_1294 T_IdempotentCommutativeMonoid_1148
v0
  = (T_IsMonoid_686 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsMonoid_686 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_identity_698
      ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746
         ((T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_862
            ((T_IdempotentCommutativeMonoid_1148
 -> T_IsIdempotentCommutativeMonoid_852)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1148
-> T_IsIdempotentCommutativeMonoid_852
d_isIdempotentCommutativeMonoid_1172 (T_IdempotentCommutativeMonoid_1148 -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1148
v0))))
-- Algebra.Bundles.BoundedLattice.identityʳ
d_identity'691'_1296 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentCommutativeMonoid_1148 -> AgdaAny -> AgdaAny
d_identity'691'_1296 :: ()
-> () -> T_IdempotentCommutativeMonoid_1148 -> AgdaAny -> AgdaAny
d_identity'691'_1296 ~()
v0 ~()
v1 T_IdempotentCommutativeMonoid_1148
v2 = T_IdempotentCommutativeMonoid_1148 -> AgdaAny -> AgdaAny
du_identity'691'_1296 T_IdempotentCommutativeMonoid_1148
v2
du_identity'691'_1296 ::
  T_IdempotentCommutativeMonoid_1148 -> AgdaAny -> AgdaAny
du_identity'691'_1296 :: T_IdempotentCommutativeMonoid_1148 -> AgdaAny -> AgdaAny
du_identity'691'_1296 T_IdempotentCommutativeMonoid_1148
v0
  = let v1 :: T_IsIdempotentCommutativeMonoid_852
v1 = T_IdempotentCommutativeMonoid_1148
-> T_IsIdempotentCommutativeMonoid_852
d_isIdempotentCommutativeMonoid_1172 (T_IdempotentCommutativeMonoid_1148
-> T_IdempotentCommutativeMonoid_1148
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1148
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsCommutativeMonoid_736
v2
             = T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_862
                 (T_IsIdempotentCommutativeMonoid_852
-> T_IsIdempotentCommutativeMonoid_852
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsMonoid_686 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoid_686 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_identity'691'_728
            ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746 (T_IsCommutativeMonoid_736 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v2))))
-- Algebra.Bundles.BoundedLattice.identityˡ
d_identity'737'_1298 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentCommutativeMonoid_1148 -> AgdaAny -> AgdaAny
d_identity'737'_1298 :: ()
-> () -> T_IdempotentCommutativeMonoid_1148 -> AgdaAny -> AgdaAny
d_identity'737'_1298 ~()
v0 ~()
v1 T_IdempotentCommutativeMonoid_1148
v2 = T_IdempotentCommutativeMonoid_1148 -> AgdaAny -> AgdaAny
du_identity'737'_1298 T_IdempotentCommutativeMonoid_1148
v2
du_identity'737'_1298 ::
  T_IdempotentCommutativeMonoid_1148 -> AgdaAny -> AgdaAny
du_identity'737'_1298 :: T_IdempotentCommutativeMonoid_1148 -> AgdaAny -> AgdaAny
du_identity'737'_1298 T_IdempotentCommutativeMonoid_1148
v0
  = let v1 :: T_IsIdempotentCommutativeMonoid_852
v1 = T_IdempotentCommutativeMonoid_1148
-> T_IsIdempotentCommutativeMonoid_852
d_isIdempotentCommutativeMonoid_1172 (T_IdempotentCommutativeMonoid_1148
-> T_IdempotentCommutativeMonoid_1148
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1148
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsCommutativeMonoid_736
v2
             = T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_862
                 (T_IsIdempotentCommutativeMonoid_852
-> T_IsIdempotentCommutativeMonoid_852
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsMonoid_686 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoid_686 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_identity'737'_726
            ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746 (T_IsCommutativeMonoid_736 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v2))))
-- Algebra.Bundles.BoundedLattice.isBand
d_isBand_1300 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentCommutativeMonoid_1148 ->
  MAlonzo.Code.Algebra.Structures.T_IsBand_508
d_isBand_1300 :: () -> () -> T_IdempotentCommutativeMonoid_1148 -> T_IsBand_508
d_isBand_1300 ~()
v0 ~()
v1 T_IdempotentCommutativeMonoid_1148
v2 = T_IdempotentCommutativeMonoid_1148 -> T_IsBand_508
du_isBand_1300 T_IdempotentCommutativeMonoid_1148
v2
du_isBand_1300 ::
  T_IdempotentCommutativeMonoid_1148 ->
  MAlonzo.Code.Algebra.Structures.T_IsBand_508
du_isBand_1300 :: T_IdempotentCommutativeMonoid_1148 -> T_IsBand_508
du_isBand_1300 T_IdempotentCommutativeMonoid_1148
v0
  = let v1 :: T_IsIdempotentCommutativeMonoid_852
v1 = T_IdempotentCommutativeMonoid_1148
-> T_IsIdempotentCommutativeMonoid_852
d_isIdempotentCommutativeMonoid_1172 (T_IdempotentCommutativeMonoid_1148
-> T_IdempotentCommutativeMonoid_1148
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1148
v0) in
    AgdaAny -> T_IsBand_508
forall a b. a -> b
coe
      ((T_IsIdempotentMonoid_796 -> T_IsBand_508) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsIdempotentMonoid_796 -> T_IsBand_508
MAlonzo.Code.Algebra.Structures.du_isBand_846
         ((T_IsIdempotentCommutativeMonoid_852 -> T_IsIdempotentMonoid_796)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsIdempotentCommutativeMonoid_852 -> T_IsIdempotentMonoid_796
MAlonzo.Code.Algebra.Structures.du_isIdempotentMonoid_910
            (T_IsIdempotentCommutativeMonoid_852 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852
v1)))
-- Algebra.Bundles.BoundedLattice.isCommutativeBand
d_isCommutativeBand_1302 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentCommutativeMonoid_1148 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_590
d_isCommutativeBand_1302 :: ()
-> ()
-> T_IdempotentCommutativeMonoid_1148
-> T_IsCommutativeBand_590
d_isCommutativeBand_1302 ~()
v0 ~()
v1 T_IdempotentCommutativeMonoid_1148
v2 = T_IdempotentCommutativeMonoid_1148 -> T_IsCommutativeBand_590
du_isCommutativeBand_1302 T_IdempotentCommutativeMonoid_1148
v2
du_isCommutativeBand_1302 ::
  T_IdempotentCommutativeMonoid_1148 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_590
du_isCommutativeBand_1302 :: T_IdempotentCommutativeMonoid_1148 -> T_IsCommutativeBand_590
du_isCommutativeBand_1302 T_IdempotentCommutativeMonoid_1148
v0
  = (T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeBand_590)
-> AgdaAny -> T_IsCommutativeBand_590
forall a b. a -> b
coe
      T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeBand_590
MAlonzo.Code.Algebra.Structures.du_isCommutativeBand_916
      ((T_IdempotentCommutativeMonoid_1148
 -> T_IsIdempotentCommutativeMonoid_852)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1148
-> T_IsIdempotentCommutativeMonoid_852
d_isIdempotentCommutativeMonoid_1172 (T_IdempotentCommutativeMonoid_1148 -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1148
v0))
-- Algebra.Bundles.BoundedLattice.isCommutativeMagma
d_isCommutativeMagma_1304 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentCommutativeMonoid_1148 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMagma_212
d_isCommutativeMagma_1304 :: ()
-> ()
-> T_IdempotentCommutativeMonoid_1148
-> T_IsCommutativeMagma_212
d_isCommutativeMagma_1304 ~()
v0 ~()
v1 T_IdempotentCommutativeMonoid_1148
v2
  = T_IdempotentCommutativeMonoid_1148 -> T_IsCommutativeMagma_212
du_isCommutativeMagma_1304 T_IdempotentCommutativeMonoid_1148
v2
du_isCommutativeMagma_1304 ::
  T_IdempotentCommutativeMonoid_1148 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMagma_212
du_isCommutativeMagma_1304 :: T_IdempotentCommutativeMonoid_1148 -> T_IsCommutativeMagma_212
du_isCommutativeMagma_1304 T_IdempotentCommutativeMonoid_1148
v0
  = let v1 :: T_IsIdempotentCommutativeMonoid_852
v1 = T_IdempotentCommutativeMonoid_1148
-> T_IsIdempotentCommutativeMonoid_852
d_isIdempotentCommutativeMonoid_1172 (T_IdempotentCommutativeMonoid_1148
-> T_IdempotentCommutativeMonoid_1148
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1148
v0) in
    AgdaAny -> T_IsCommutativeMagma_212
forall a b. a -> b
coe
      (let v2 :: T_IsCommutativeMonoid_736
v2
             = T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_862
                 (T_IsIdempotentCommutativeMonoid_852
-> T_IsIdempotentCommutativeMonoid_852
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsCommutativeSemigroup_548 -> T_IsCommutativeMagma_212)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCommutativeSemigroup_548 -> T_IsCommutativeMagma_212
MAlonzo.Code.Algebra.Structures.du_isCommutativeMagma_586
            ((T_IsCommutativeMonoid_736 -> T_IsCommutativeSemigroup_548)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsCommutativeMonoid_736 -> T_IsCommutativeSemigroup_548
MAlonzo.Code.Algebra.Structures.du_isCommutativeSemigroup_786
               (T_IsCommutativeMonoid_736 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v2))))
-- Algebra.Bundles.BoundedLattice.isCommutativeMonoid
d_isCommutativeMonoid_1306 ::
  T_IdempotentCommutativeMonoid_1148 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMonoid_736
d_isCommutativeMonoid_1306 :: T_IdempotentCommutativeMonoid_1148 -> T_IsCommutativeMonoid_736
d_isCommutativeMonoid_1306 T_IdempotentCommutativeMonoid_1148
v0
  = (T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> T_IsCommutativeMonoid_736
forall a b. a -> b
coe
      T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_862
      ((T_IdempotentCommutativeMonoid_1148
 -> T_IsIdempotentCommutativeMonoid_852)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1148
-> T_IsIdempotentCommutativeMonoid_852
d_isIdempotentCommutativeMonoid_1172 (T_IdempotentCommutativeMonoid_1148 -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1148
v0))
-- Algebra.Bundles.BoundedLattice.isCommutativeSemigroup
d_isCommutativeSemigroup_1308 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentCommutativeMonoid_1148 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_548
d_isCommutativeSemigroup_1308 :: ()
-> ()
-> T_IdempotentCommutativeMonoid_1148
-> T_IsCommutativeSemigroup_548
d_isCommutativeSemigroup_1308 ~()
v0 ~()
v1 T_IdempotentCommutativeMonoid_1148
v2
  = T_IdempotentCommutativeMonoid_1148 -> T_IsCommutativeSemigroup_548
du_isCommutativeSemigroup_1308 T_IdempotentCommutativeMonoid_1148
v2
du_isCommutativeSemigroup_1308 ::
  T_IdempotentCommutativeMonoid_1148 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_548
du_isCommutativeSemigroup_1308 :: T_IdempotentCommutativeMonoid_1148 -> T_IsCommutativeSemigroup_548
du_isCommutativeSemigroup_1308 T_IdempotentCommutativeMonoid_1148
v0
  = let v1 :: T_IsIdempotentCommutativeMonoid_852
v1 = T_IdempotentCommutativeMonoid_1148
-> T_IsIdempotentCommutativeMonoid_852
d_isIdempotentCommutativeMonoid_1172 (T_IdempotentCommutativeMonoid_1148
-> T_IdempotentCommutativeMonoid_1148
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1148
v0) in
    AgdaAny -> T_IsCommutativeSemigroup_548
forall a b. a -> b
coe
      ((T_IsCommutativeMonoid_736 -> T_IsCommutativeSemigroup_548)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCommutativeMonoid_736 -> T_IsCommutativeSemigroup_548
MAlonzo.Code.Algebra.Structures.du_isCommutativeSemigroup_786
         ((T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_862
            (T_IsIdempotentCommutativeMonoid_852 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852
v1)))
-- Algebra.Bundles.BoundedLattice.isEquivalence
d_isEquivalence_1310 ::
  T_IdempotentCommutativeMonoid_1148 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_1310 :: T_IdempotentCommutativeMonoid_1148 -> T_IsEquivalence_26
d_isEquivalence_1310 T_IdempotentCommutativeMonoid_1148
v0
  = (T_IsMagma_176 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
      ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480
         ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
            ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746
               ((T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_862
                  ((T_IdempotentCommutativeMonoid_1148
 -> T_IsIdempotentCommutativeMonoid_852)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1148
-> T_IsIdempotentCommutativeMonoid_852
d_isIdempotentCommutativeMonoid_1172 (T_IdempotentCommutativeMonoid_1148 -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1148
v0))))))
-- Algebra.Bundles.BoundedLattice.isIdempotentCommutativeMonoid
d_isIdempotentCommutativeMonoid_1312 ::
  T_IdempotentCommutativeMonoid_1148 ->
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_852
d_isIdempotentCommutativeMonoid_1312 :: T_IdempotentCommutativeMonoid_1148
-> T_IsIdempotentCommutativeMonoid_852
d_isIdempotentCommutativeMonoid_1312 T_IdempotentCommutativeMonoid_1148
v0
  = (T_IdempotentCommutativeMonoid_1148
 -> T_IsIdempotentCommutativeMonoid_852)
-> AgdaAny -> T_IsIdempotentCommutativeMonoid_852
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1148
-> T_IsIdempotentCommutativeMonoid_852
d_isIdempotentCommutativeMonoid_1172 (T_IdempotentCommutativeMonoid_1148 -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1148
v0)
-- Algebra.Bundles.BoundedLattice.isIdempotentMonoid
d_isIdempotentMonoid_1314 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentCommutativeMonoid_1148 ->
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentMonoid_796
d_isIdempotentMonoid_1314 :: ()
-> ()
-> T_IdempotentCommutativeMonoid_1148
-> T_IsIdempotentMonoid_796
d_isIdempotentMonoid_1314 ~()
v0 ~()
v1 T_IdempotentCommutativeMonoid_1148
v2
  = T_IdempotentCommutativeMonoid_1148 -> T_IsIdempotentMonoid_796
du_isIdempotentMonoid_1314 T_IdempotentCommutativeMonoid_1148
v2
du_isIdempotentMonoid_1314 ::
  T_IdempotentCommutativeMonoid_1148 ->
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentMonoid_796
du_isIdempotentMonoid_1314 :: T_IdempotentCommutativeMonoid_1148 -> T_IsIdempotentMonoid_796
du_isIdempotentMonoid_1314 T_IdempotentCommutativeMonoid_1148
v0
  = (T_IsIdempotentCommutativeMonoid_852 -> T_IsIdempotentMonoid_796)
-> AgdaAny -> T_IsIdempotentMonoid_796
forall a b. a -> b
coe
      T_IsIdempotentCommutativeMonoid_852 -> T_IsIdempotentMonoid_796
MAlonzo.Code.Algebra.Structures.du_isIdempotentMonoid_910
      ((T_IdempotentCommutativeMonoid_1148
 -> T_IsIdempotentCommutativeMonoid_852)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1148
-> T_IsIdempotentCommutativeMonoid_852
d_isIdempotentCommutativeMonoid_1172 (T_IdempotentCommutativeMonoid_1148 -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1148
v0))
-- Algebra.Bundles.BoundedLattice.isMagma
d_isMagma_1316 ::
  T_IdempotentCommutativeMonoid_1148 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_176
d_isMagma_1316 :: T_IdempotentCommutativeMonoid_1148 -> T_IsMagma_176
d_isMagma_1316 T_IdempotentCommutativeMonoid_1148
v0
  = (T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> T_IsMagma_176
forall a b. a -> b
coe
      T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480
      ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
         ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746
            ((T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_862
               ((T_IdempotentCommutativeMonoid_1148
 -> T_IsIdempotentCommutativeMonoid_852)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1148
-> T_IsIdempotentCommutativeMonoid_852
d_isIdempotentCommutativeMonoid_1172 (T_IdempotentCommutativeMonoid_1148 -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1148
v0)))))
-- Algebra.Bundles.BoundedLattice.isMonoid
d_isMonoid_1318 ::
  T_IdempotentCommutativeMonoid_1148 ->
  MAlonzo.Code.Algebra.Structures.T_IsMonoid_686
d_isMonoid_1318 :: T_IdempotentCommutativeMonoid_1148 -> T_IsMonoid_686
d_isMonoid_1318 T_IdempotentCommutativeMonoid_1148
v0
  = (T_IsCommutativeMonoid_736 -> T_IsMonoid_686)
-> AgdaAny -> T_IsMonoid_686
forall a b. a -> b
coe
      T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746
      ((T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_862
         ((T_IdempotentCommutativeMonoid_1148
 -> T_IsIdempotentCommutativeMonoid_852)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1148
-> T_IsIdempotentCommutativeMonoid_852
d_isIdempotentCommutativeMonoid_1172 (T_IdempotentCommutativeMonoid_1148 -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1148
v0)))
-- Algebra.Bundles.BoundedLattice.isPartialEquivalence
d_isPartialEquivalence_1320 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentCommutativeMonoid_1148 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_1320 :: ()
-> ()
-> T_IdempotentCommutativeMonoid_1148
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_1320 ~()
v0 ~()
v1 T_IdempotentCommutativeMonoid_1148
v2
  = T_IdempotentCommutativeMonoid_1148 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_1320 T_IdempotentCommutativeMonoid_1148
v2
du_isPartialEquivalence_1320 ::
  T_IdempotentCommutativeMonoid_1148 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_1320 :: T_IdempotentCommutativeMonoid_1148 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_1320 T_IdempotentCommutativeMonoid_1148
v0
  = let v1 :: T_IsIdempotentCommutativeMonoid_852
v1 = T_IdempotentCommutativeMonoid_1148
-> T_IsIdempotentCommutativeMonoid_852
d_isIdempotentCommutativeMonoid_1172 (T_IdempotentCommutativeMonoid_1148
-> T_IdempotentCommutativeMonoid_1148
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1148
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsCommutativeMonoid_736
v2
             = T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_862
                 (T_IsIdempotentCommutativeMonoid_852
-> T_IsIdempotentCommutativeMonoid_852
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsMonoid_686
v3
                = T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746 (T_IsCommutativeMonoid_736 -> T_IsCommutativeMonoid_736
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsSemigroup_472
v4
                   = T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsMagma_176
v5 = T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (T_IsSemigroup_472 -> T_IsSemigroup_472
forall a b. a -> b
coe T_IsSemigroup_472
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  ((T_IsEquivalence_26 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsEquivalence_26 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
                     ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v5)))))))
-- Algebra.Bundles.BoundedLattice.isSemigroup
d_isSemigroup_1322 ::
  T_IdempotentCommutativeMonoid_1148 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_472
d_isSemigroup_1322 :: T_IdempotentCommutativeMonoid_1148 -> T_IsSemigroup_472
d_isSemigroup_1322 T_IdempotentCommutativeMonoid_1148
v0
  = (T_IsMonoid_686 -> T_IsSemigroup_472)
-> AgdaAny -> T_IsSemigroup_472
forall a b. a -> b
coe
      T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
      ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746
         ((T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_862
            ((T_IdempotentCommutativeMonoid_1148
 -> T_IsIdempotentCommutativeMonoid_852)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1148
-> T_IsIdempotentCommutativeMonoid_852
d_isIdempotentCommutativeMonoid_1172 (T_IdempotentCommutativeMonoid_1148 -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1148
v0))))
-- Algebra.Bundles.BoundedLattice.isUnitalMagma
d_isUnitalMagma_1324 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentCommutativeMonoid_1148 ->
  MAlonzo.Code.Algebra.Structures.T_IsUnitalMagma_642
d_isUnitalMagma_1324 :: ()
-> () -> T_IdempotentCommutativeMonoid_1148 -> T_IsUnitalMagma_642
d_isUnitalMagma_1324 ~()
v0 ~()
v1 T_IdempotentCommutativeMonoid_1148
v2 = T_IdempotentCommutativeMonoid_1148 -> T_IsUnitalMagma_642
du_isUnitalMagma_1324 T_IdempotentCommutativeMonoid_1148
v2
du_isUnitalMagma_1324 ::
  T_IdempotentCommutativeMonoid_1148 ->
  MAlonzo.Code.Algebra.Structures.T_IsUnitalMagma_642
du_isUnitalMagma_1324 :: T_IdempotentCommutativeMonoid_1148 -> T_IsUnitalMagma_642
du_isUnitalMagma_1324 T_IdempotentCommutativeMonoid_1148
v0
  = let v1 :: T_IsIdempotentCommutativeMonoid_852
v1 = T_IdempotentCommutativeMonoid_1148
-> T_IsIdempotentCommutativeMonoid_852
d_isIdempotentCommutativeMonoid_1172 (T_IdempotentCommutativeMonoid_1148
-> T_IdempotentCommutativeMonoid_1148
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1148
v0) in
    AgdaAny -> T_IsUnitalMagma_642
forall a b. a -> b
coe
      (let v2 :: T_IsCommutativeMonoid_736
v2
             = T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_862
                 (T_IsIdempotentCommutativeMonoid_852
-> T_IsIdempotentCommutativeMonoid_852
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsMonoid_686 -> T_IsUnitalMagma_642) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoid_686 -> T_IsUnitalMagma_642
MAlonzo.Code.Algebra.Structures.du_isUnitalMagma_730
            ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746 (T_IsCommutativeMonoid_736 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v2))))
-- Algebra.Bundles.BoundedLattice.magma
d_magma_1326 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentCommutativeMonoid_1148 -> T_Magma_68
d_magma_1326 :: () -> () -> T_IdempotentCommutativeMonoid_1148 -> T_Magma_68
d_magma_1326 ~()
v0 ~()
v1 T_IdempotentCommutativeMonoid_1148
v2 = T_IdempotentCommutativeMonoid_1148 -> T_Magma_68
du_magma_1326 T_IdempotentCommutativeMonoid_1148
v2
du_magma_1326 :: T_IdempotentCommutativeMonoid_1148 -> T_Magma_68
du_magma_1326 :: T_IdempotentCommutativeMonoid_1148 -> T_Magma_68
du_magma_1326 T_IdempotentCommutativeMonoid_1148
v0
  = let v1 :: t
v1 = (T_IdempotentCommutativeMonoid_1148 -> T_CommutativeMonoid_962)
-> AgdaAny -> t
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1148 -> T_CommutativeMonoid_962
du_commutativeMonoid_1228 (T_IdempotentCommutativeMonoid_1148 -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1148
v0) in
    AgdaAny -> T_Magma_68
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_CommutativeMonoid_962 -> T_Monoid_882) -> AgdaAny -> t
forall a b. a -> b
coe T_CommutativeMonoid_962 -> T_Monoid_882
du_monoid_1032 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_Semigroup_536 -> T_Magma_68) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semigroup_536 -> T_Magma_68
du_magma_584 ((T_Monoid_882 -> T_Semigroup_536) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Monoid_882 -> T_Semigroup_536
du_semigroup_944 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2))))
-- Algebra.Bundles.BoundedLattice.monoid
d_monoid_1328 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentCommutativeMonoid_1148 -> T_Monoid_882
d_monoid_1328 :: () -> () -> T_IdempotentCommutativeMonoid_1148 -> T_Monoid_882
d_monoid_1328 ~()
v0 ~()
v1 T_IdempotentCommutativeMonoid_1148
v2 = T_IdempotentCommutativeMonoid_1148 -> T_Monoid_882
du_monoid_1328 T_IdempotentCommutativeMonoid_1148
v2
du_monoid_1328 ::
  T_IdempotentCommutativeMonoid_1148 -> T_Monoid_882
du_monoid_1328 :: T_IdempotentCommutativeMonoid_1148 -> T_Monoid_882
du_monoid_1328 T_IdempotentCommutativeMonoid_1148
v0
  = (T_CommutativeMonoid_962 -> T_Monoid_882)
-> AgdaAny -> T_Monoid_882
forall a b. a -> b
coe T_CommutativeMonoid_962 -> T_Monoid_882
du_monoid_1032 ((T_IdempotentCommutativeMonoid_1148 -> T_CommutativeMonoid_962)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1148 -> T_CommutativeMonoid_962
du_commutativeMonoid_1228 (T_IdempotentCommutativeMonoid_1148 -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1148
v0))
-- Algebra.Bundles.BoundedLattice.rawMagma
d_rawMagma_1330 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentCommutativeMonoid_1148 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
d_rawMagma_1330 :: () -> () -> T_IdempotentCommutativeMonoid_1148 -> T_RawMagma_36
d_rawMagma_1330 ~()
v0 ~()
v1 T_IdempotentCommutativeMonoid_1148
v2 = T_IdempotentCommutativeMonoid_1148 -> T_RawMagma_36
du_rawMagma_1330 T_IdempotentCommutativeMonoid_1148
v2
du_rawMagma_1330 ::
  T_IdempotentCommutativeMonoid_1148 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
du_rawMagma_1330 :: T_IdempotentCommutativeMonoid_1148 -> T_RawMagma_36
du_rawMagma_1330 T_IdempotentCommutativeMonoid_1148
v0
  = let v1 :: t
v1 = (T_IdempotentCommutativeMonoid_1148 -> T_CommutativeMonoid_962)
-> AgdaAny -> t
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1148 -> T_CommutativeMonoid_962
du_commutativeMonoid_1228 (T_IdempotentCommutativeMonoid_1148 -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1148
v0) in
    AgdaAny -> T_RawMagma_36
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_CommutativeMonoid_962 -> T_Monoid_882) -> AgdaAny -> t
forall a b. a -> b
coe T_CommutativeMonoid_962 -> T_Monoid_882
du_monoid_1032 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: t
v3 = (T_Monoid_882 -> T_Semigroup_536) -> AgdaAny -> t
forall a b. a -> b
coe T_Monoid_882 -> T_Semigroup_536
du_semigroup_944 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_Magma_68 -> T_RawMagma_36) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Magma_68 -> T_RawMagma_36
du_rawMagma_112 ((T_Semigroup_536 -> T_Magma_68) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semigroup_536 -> T_Magma_68
du_magma_584 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3)))))
-- Algebra.Bundles.BoundedLattice.rawMonoid
d_rawMonoid_1332 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentCommutativeMonoid_1148 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMonoid_64
d_rawMonoid_1332 :: () -> () -> T_IdempotentCommutativeMonoid_1148 -> T_RawMonoid_64
d_rawMonoid_1332 ~()
v0 ~()
v1 T_IdempotentCommutativeMonoid_1148
v2 = T_IdempotentCommutativeMonoid_1148 -> T_RawMonoid_64
du_rawMonoid_1332 T_IdempotentCommutativeMonoid_1148
v2
du_rawMonoid_1332 ::
  T_IdempotentCommutativeMonoid_1148 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMonoid_64
du_rawMonoid_1332 :: T_IdempotentCommutativeMonoid_1148 -> T_RawMonoid_64
du_rawMonoid_1332 T_IdempotentCommutativeMonoid_1148
v0
  = let v1 :: t
v1 = (T_IdempotentCommutativeMonoid_1148 -> T_CommutativeMonoid_962)
-> AgdaAny -> t
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1148 -> T_CommutativeMonoid_962
du_commutativeMonoid_1228 (T_IdempotentCommutativeMonoid_1148 -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1148
v0) in
    AgdaAny -> T_RawMonoid_64
forall a b. a -> b
coe ((T_Monoid_882 -> T_RawMonoid_64) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Monoid_882 -> T_RawMonoid_64
du_rawMonoid_954 ((T_CommutativeMonoid_962 -> T_Monoid_882) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeMonoid_962 -> T_Monoid_882
du_monoid_1032 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1)))
-- Algebra.Bundles.BoundedLattice.refl
d_refl_1334 ::
  T_IdempotentCommutativeMonoid_1148 -> AgdaAny -> AgdaAny
d_refl_1334 :: T_IdempotentCommutativeMonoid_1148 -> AgdaAny -> AgdaAny
d_refl_1334 T_IdempotentCommutativeMonoid_1148
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_34
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
         ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480
            ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
               ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746
                  ((T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_862
                     ((T_IdempotentCommutativeMonoid_1148
 -> T_IsIdempotentCommutativeMonoid_852)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1148
-> T_IsIdempotentCommutativeMonoid_852
d_isIdempotentCommutativeMonoid_1172 (T_IdempotentCommutativeMonoid_1148 -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1148
v0)))))))
-- Algebra.Bundles.BoundedLattice.reflexive
d_reflexive_1336 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentCommutativeMonoid_1148 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_1336 :: ()
-> ()
-> T_IdempotentCommutativeMonoid_1148
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_1336 ~()
v0 ~()
v1 T_IdempotentCommutativeMonoid_1148
v2 = T_IdempotentCommutativeMonoid_1148
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_1336 T_IdempotentCommutativeMonoid_1148
v2
du_reflexive_1336 ::
  T_IdempotentCommutativeMonoid_1148 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_1336 :: T_IdempotentCommutativeMonoid_1148
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_1336 T_IdempotentCommutativeMonoid_1148
v0
  = let v1 :: T_IsIdempotentCommutativeMonoid_852
v1 = T_IdempotentCommutativeMonoid_1148
-> T_IsIdempotentCommutativeMonoid_852
d_isIdempotentCommutativeMonoid_1172 (T_IdempotentCommutativeMonoid_1148
-> T_IdempotentCommutativeMonoid_1148
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1148
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsCommutativeMonoid_736
v2
             = T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_862
                 (T_IsIdempotentCommutativeMonoid_852
-> T_IsIdempotentCommutativeMonoid_852
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsMonoid_686
v3
                = T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746 (T_IsCommutativeMonoid_736 -> T_IsCommutativeMonoid_736
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsSemigroup_472
v4
                   = T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsMagma_176
v5 = T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (T_IsSemigroup_472 -> T_IsSemigroup_472
forall a b. a -> b
coe T_IsSemigroup_472
v4) in
                (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
                  (\ AgdaAny
v6 AgdaAny
v7 AgdaAny
v8 ->
                     (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                       T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
                       ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v5))
                       AgdaAny
v6)))))
-- Algebra.Bundles.BoundedLattice.semigroup
d_semigroup_1338 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentCommutativeMonoid_1148 -> T_Semigroup_536
d_semigroup_1338 :: () -> () -> T_IdempotentCommutativeMonoid_1148 -> T_Semigroup_536
d_semigroup_1338 ~()
v0 ~()
v1 T_IdempotentCommutativeMonoid_1148
v2 = T_IdempotentCommutativeMonoid_1148 -> T_Semigroup_536
du_semigroup_1338 T_IdempotentCommutativeMonoid_1148
v2
du_semigroup_1338 ::
  T_IdempotentCommutativeMonoid_1148 -> T_Semigroup_536
du_semigroup_1338 :: T_IdempotentCommutativeMonoid_1148 -> T_Semigroup_536
du_semigroup_1338 T_IdempotentCommutativeMonoid_1148
v0
  = let v1 :: t
v1 = (T_IdempotentCommutativeMonoid_1148 -> T_CommutativeMonoid_962)
-> AgdaAny -> t
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1148 -> T_CommutativeMonoid_962
du_commutativeMonoid_1228 (T_IdempotentCommutativeMonoid_1148 -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1148
v0) in
    AgdaAny -> T_Semigroup_536
forall a b. a -> b
coe ((T_Monoid_882 -> T_Semigroup_536) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Monoid_882 -> T_Semigroup_536
du_semigroup_944 ((T_CommutativeMonoid_962 -> T_Monoid_882) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeMonoid_962 -> T_Monoid_882
du_monoid_1032 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1)))
-- Algebra.Bundles.BoundedLattice.setoid
d_setoid_1340 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentCommutativeMonoid_1148 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_1340 :: () -> () -> T_IdempotentCommutativeMonoid_1148 -> T_Setoid_44
d_setoid_1340 ~()
v0 ~()
v1 T_IdempotentCommutativeMonoid_1148
v2 = T_IdempotentCommutativeMonoid_1148 -> T_Setoid_44
du_setoid_1340 T_IdempotentCommutativeMonoid_1148
v2
du_setoid_1340 ::
  T_IdempotentCommutativeMonoid_1148 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_1340 :: T_IdempotentCommutativeMonoid_1148 -> T_Setoid_44
du_setoid_1340 T_IdempotentCommutativeMonoid_1148
v0
  = let v1 :: T_IsIdempotentCommutativeMonoid_852
v1 = T_IdempotentCommutativeMonoid_1148
-> T_IsIdempotentCommutativeMonoid_852
d_isIdempotentCommutativeMonoid_1172 (T_IdempotentCommutativeMonoid_1148
-> T_IdempotentCommutativeMonoid_1148
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1148
v0) in
    AgdaAny -> T_Setoid_44
forall a b. a -> b
coe
      (let v2 :: T_IsCommutativeMonoid_736
v2
             = T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_862
                 (T_IsIdempotentCommutativeMonoid_852
-> T_IsIdempotentCommutativeMonoid_852
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsMonoid_686
v3
                = T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746 (T_IsCommutativeMonoid_736 -> T_IsCommutativeMonoid_736
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsSemigroup_472
v4
                   = T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               ((T_IsMagma_176 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsMagma_176 -> T_Setoid_44
MAlonzo.Code.Algebra.Structures.du_setoid_200
                  ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v4))))))
-- Algebra.Bundles.BoundedLattice.sym
d_sym_1342 ::
  T_IdempotentCommutativeMonoid_1148 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_1342 :: T_IdempotentCommutativeMonoid_1148
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_1342 T_IdempotentCommutativeMonoid_1148
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_36
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
         ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480
            ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
               ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746
                  ((T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_862
                     ((T_IdempotentCommutativeMonoid_1148
 -> T_IsIdempotentCommutativeMonoid_852)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1148
-> T_IsIdempotentCommutativeMonoid_852
d_isIdempotentCommutativeMonoid_1172 (T_IdempotentCommutativeMonoid_1148 -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1148
v0)))))))
-- Algebra.Bundles.BoundedLattice.trans
d_trans_1344 ::
  T_IdempotentCommutativeMonoid_1148 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_1344 :: T_IdempotentCommutativeMonoid_1148
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_1344 T_IdempotentCommutativeMonoid_1148
v0
  = (T_IsEquivalence_26
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_38
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
         ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480
            ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
               ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746
                  ((T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_862
                     ((T_IdempotentCommutativeMonoid_1148
 -> T_IsIdempotentCommutativeMonoid_852)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1148
-> T_IsIdempotentCommutativeMonoid_852
d_isIdempotentCommutativeMonoid_1172 (T_IdempotentCommutativeMonoid_1148 -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1148
v0)))))))
-- Algebra.Bundles.BoundedLattice.unitalMagma
d_unitalMagma_1346 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentCommutativeMonoid_1148 -> T_UnitalMagma_814
d_unitalMagma_1346 :: () -> () -> T_IdempotentCommutativeMonoid_1148 -> T_UnitalMagma_814
d_unitalMagma_1346 ~()
v0 ~()
v1 T_IdempotentCommutativeMonoid_1148
v2 = T_IdempotentCommutativeMonoid_1148 -> T_UnitalMagma_814
du_unitalMagma_1346 T_IdempotentCommutativeMonoid_1148
v2
du_unitalMagma_1346 ::
  T_IdempotentCommutativeMonoid_1148 -> T_UnitalMagma_814
du_unitalMagma_1346 :: T_IdempotentCommutativeMonoid_1148 -> T_UnitalMagma_814
du_unitalMagma_1346 T_IdempotentCommutativeMonoid_1148
v0
  = let v1 :: t
v1 = (T_IdempotentCommutativeMonoid_1148 -> T_CommutativeMonoid_962)
-> AgdaAny -> t
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1148 -> T_CommutativeMonoid_962
du_commutativeMonoid_1228 (T_IdempotentCommutativeMonoid_1148 -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1148
v0) in
    AgdaAny -> T_UnitalMagma_814
forall a b. a -> b
coe ((T_Monoid_882 -> T_UnitalMagma_814) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Monoid_882 -> T_UnitalMagma_814
du_unitalMagma_956 ((T_CommutativeMonoid_962 -> T_Monoid_882) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeMonoid_962 -> T_Monoid_882
du_monoid_1032 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1)))
-- Algebra.Bundles.BoundedLattice.ε
d_ε_1348 :: T_IdempotentCommutativeMonoid_1148 -> AgdaAny
d_ε_1348 :: T_IdempotentCommutativeMonoid_1148 -> AgdaAny
d_ε_1348 T_IdempotentCommutativeMonoid_1148
v0 = (T_IdempotentCommutativeMonoid_1148 -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1148 -> AgdaAny
d_ε_1170 (T_IdempotentCommutativeMonoid_1148 -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1148
v0)
-- Algebra.Bundles.BoundedLattice.∙-cong
d_'8729''45'cong_1350 ::
  T_IdempotentCommutativeMonoid_1148 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_1350 :: T_IdempotentCommutativeMonoid_1148
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_1350 T_IdempotentCommutativeMonoid_1148
v0
  = (T_IsMagma_176
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsMagma_176
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_186
      ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480
         ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
            ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746
               ((T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_862
                  ((T_IdempotentCommutativeMonoid_1148
 -> T_IsIdempotentCommutativeMonoid_852)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1148
-> T_IsIdempotentCommutativeMonoid_852
d_isIdempotentCommutativeMonoid_1172 (T_IdempotentCommutativeMonoid_1148 -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1148
v0))))))
-- Algebra.Bundles.BoundedLattice.∙-congʳ
d_'8729''45'cong'691'_1352 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentCommutativeMonoid_1148 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_1352 :: ()
-> ()
-> T_IdempotentCommutativeMonoid_1148
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_1352 ~()
v0 ~()
v1 T_IdempotentCommutativeMonoid_1148
v2
  = T_IdempotentCommutativeMonoid_1148
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1352 T_IdempotentCommutativeMonoid_1148
v2
du_'8729''45'cong'691'_1352 ::
  T_IdempotentCommutativeMonoid_1148 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1352 :: T_IdempotentCommutativeMonoid_1148
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1352 T_IdempotentCommutativeMonoid_1148
v0
  = let v1 :: T_IsIdempotentCommutativeMonoid_852
v1 = T_IdempotentCommutativeMonoid_1148
-> T_IsIdempotentCommutativeMonoid_852
d_isIdempotentCommutativeMonoid_1172 (T_IdempotentCommutativeMonoid_1148
-> T_IdempotentCommutativeMonoid_1148
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1148
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsCommutativeMonoid_736
v2
             = T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_862
                 (T_IsIdempotentCommutativeMonoid_852
-> T_IsIdempotentCommutativeMonoid_852
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsMonoid_686
v3
                = T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746 (T_IsCommutativeMonoid_736 -> T_IsCommutativeMonoid_736
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsSemigroup_472
v4
                   = T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'691'_206
                  ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v4))))))
-- Algebra.Bundles.BoundedLattice.∙-congˡ
d_'8729''45'cong'737'_1354 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentCommutativeMonoid_1148 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_1354 :: ()
-> ()
-> T_IdempotentCommutativeMonoid_1148
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_1354 ~()
v0 ~()
v1 T_IdempotentCommutativeMonoid_1148
v2
  = T_IdempotentCommutativeMonoid_1148
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1354 T_IdempotentCommutativeMonoid_1148
v2
du_'8729''45'cong'737'_1354 ::
  T_IdempotentCommutativeMonoid_1148 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1354 :: T_IdempotentCommutativeMonoid_1148
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1354 T_IdempotentCommutativeMonoid_1148
v0
  = let v1 :: T_IsIdempotentCommutativeMonoid_852
v1 = T_IdempotentCommutativeMonoid_1148
-> T_IsIdempotentCommutativeMonoid_852
d_isIdempotentCommutativeMonoid_1172 (T_IdempotentCommutativeMonoid_1148
-> T_IdempotentCommutativeMonoid_1148
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1148
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsCommutativeMonoid_736
v2
             = T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_862
                 (T_IsIdempotentCommutativeMonoid_852
-> T_IsIdempotentCommutativeMonoid_852
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_852
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsMonoid_686
v3
                = T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746 (T_IsCommutativeMonoid_736 -> T_IsCommutativeMonoid_736
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsSemigroup_472
v4
                   = T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'737'_202
                  ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v4))))))
-- Algebra.Bundles.InvertibleMagma
d_InvertibleMagma_1360 :: p -> p -> ()
d_InvertibleMagma_1360 p
a0 p
a1 = ()
data T_InvertibleMagma_1360
  = C_InvertibleMagma'46'constructor_24127 (AgdaAny ->
                                            AgdaAny -> AgdaAny)
                                           AgdaAny (AgdaAny -> AgdaAny)
                                           MAlonzo.Code.Algebra.Structures.T_IsInvertibleMagma_924
-- Algebra.Bundles.InvertibleMagma.Carrier
d_Carrier_1378 :: T_InvertibleMagma_1360 -> ()
d_Carrier_1378 :: T_InvertibleMagma_1360 -> ()
d_Carrier_1378 = T_InvertibleMagma_1360 -> ()
forall a. a
erased
-- Algebra.Bundles.InvertibleMagma._≈_
d__'8776'__1380 ::
  T_InvertibleMagma_1360 -> AgdaAny -> AgdaAny -> ()
d__'8776'__1380 :: T_InvertibleMagma_1360 -> AgdaAny -> AgdaAny -> ()
d__'8776'__1380 = T_InvertibleMagma_1360 -> AgdaAny -> AgdaAny -> ()
forall a. a
erased
-- Algebra.Bundles.InvertibleMagma._∙_
d__'8729'__1382 ::
  T_InvertibleMagma_1360 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__1382 :: T_InvertibleMagma_1360 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__1382 T_InvertibleMagma_1360
v0
  = case T_InvertibleMagma_1360 -> T_InvertibleMagma_1360
forall a b. a -> b
coe T_InvertibleMagma_1360
v0 of
      C_InvertibleMagma'46'constructor_24127 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny
v4 AgdaAny -> AgdaAny
v5 T_IsInvertibleMagma_924
v6 -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v3
      T_InvertibleMagma_1360
_ -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.InvertibleMagma.ε
d_ε_1384 :: T_InvertibleMagma_1360 -> AgdaAny
d_ε_1384 :: T_InvertibleMagma_1360 -> AgdaAny
d_ε_1384 T_InvertibleMagma_1360
v0
  = case T_InvertibleMagma_1360 -> T_InvertibleMagma_1360
forall a b. a -> b
coe T_InvertibleMagma_1360
v0 of
      C_InvertibleMagma'46'constructor_24127 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny
v4 AgdaAny -> AgdaAny
v5 T_IsInvertibleMagma_924
v6 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v4
      T_InvertibleMagma_1360
_ -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.InvertibleMagma._⁻¹
d__'8315''185'_1386 :: T_InvertibleMagma_1360 -> AgdaAny -> AgdaAny
d__'8315''185'_1386 :: T_InvertibleMagma_1360 -> AgdaAny -> AgdaAny
d__'8315''185'_1386 T_InvertibleMagma_1360
v0
  = case T_InvertibleMagma_1360 -> T_InvertibleMagma_1360
forall a b. a -> b
coe T_InvertibleMagma_1360
v0 of
      C_InvertibleMagma'46'constructor_24127 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny
v4 AgdaAny -> AgdaAny
v5 T_IsInvertibleMagma_924
v6 -> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v5
      T_InvertibleMagma_1360
_ -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.InvertibleMagma.isInvertibleMagma
d_isInvertibleMagma_1388 ::
  T_InvertibleMagma_1360 ->
  MAlonzo.Code.Algebra.Structures.T_IsInvertibleMagma_924
d_isInvertibleMagma_1388 :: T_InvertibleMagma_1360 -> T_IsInvertibleMagma_924
d_isInvertibleMagma_1388 T_InvertibleMagma_1360
v0
  = case T_InvertibleMagma_1360 -> T_InvertibleMagma_1360
forall a b. a -> b
coe T_InvertibleMagma_1360
v0 of
      C_InvertibleMagma'46'constructor_24127 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny
v4 AgdaAny -> AgdaAny
v5 T_IsInvertibleMagma_924
v6 -> T_IsInvertibleMagma_924 -> T_IsInvertibleMagma_924
forall a b. a -> b
coe T_IsInvertibleMagma_924
v6
      T_InvertibleMagma_1360
_ -> T_IsInvertibleMagma_924
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.InvertibleMagma._.inverse
d_inverse_1392 ::
  T_InvertibleMagma_1360 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_inverse_1392 :: T_InvertibleMagma_1360 -> T_Σ_14
d_inverse_1392 T_InvertibleMagma_1360
v0
  = (T_IsInvertibleMagma_924 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsInvertibleMagma_924 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_inverse_940
      ((T_InvertibleMagma_1360 -> T_IsInvertibleMagma_924)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_InvertibleMagma_1360 -> T_IsInvertibleMagma_924
d_isInvertibleMagma_1388 (T_InvertibleMagma_1360 -> AgdaAny
forall a b. a -> b
coe T_InvertibleMagma_1360
v0))
-- Algebra.Bundles.InvertibleMagma._.inverseʳ
d_inverse'691'_1394 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_InvertibleMagma_1360 -> AgdaAny -> AgdaAny
d_inverse'691'_1394 :: () -> () -> T_InvertibleMagma_1360 -> AgdaAny -> AgdaAny
d_inverse'691'_1394 ~()
v0 ~()
v1 T_InvertibleMagma_1360
v2 = T_InvertibleMagma_1360 -> AgdaAny -> AgdaAny
du_inverse'691'_1394 T_InvertibleMagma_1360
v2
du_inverse'691'_1394 ::
  T_InvertibleMagma_1360 -> AgdaAny -> AgdaAny
du_inverse'691'_1394 :: T_InvertibleMagma_1360 -> AgdaAny -> AgdaAny
du_inverse'691'_1394 T_InvertibleMagma_1360
v0
  = (T_IsInvertibleMagma_924 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsInvertibleMagma_924 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_inverse'691'_968
      ((T_InvertibleMagma_1360 -> T_IsInvertibleMagma_924)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_InvertibleMagma_1360 -> T_IsInvertibleMagma_924
d_isInvertibleMagma_1388 (T_InvertibleMagma_1360 -> AgdaAny
forall a b. a -> b
coe T_InvertibleMagma_1360
v0))
-- Algebra.Bundles.InvertibleMagma._.inverseˡ
d_inverse'737'_1396 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_InvertibleMagma_1360 -> AgdaAny -> AgdaAny
d_inverse'737'_1396 :: () -> () -> T_InvertibleMagma_1360 -> AgdaAny -> AgdaAny
d_inverse'737'_1396 ~()
v0 ~()
v1 T_InvertibleMagma_1360
v2 = T_InvertibleMagma_1360 -> AgdaAny -> AgdaAny
du_inverse'737'_1396 T_InvertibleMagma_1360
v2
du_inverse'737'_1396 ::
  T_InvertibleMagma_1360 -> AgdaAny -> AgdaAny
du_inverse'737'_1396 :: T_InvertibleMagma_1360 -> AgdaAny -> AgdaAny
du_inverse'737'_1396 T_InvertibleMagma_1360
v0
  = (T_IsInvertibleMagma_924 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsInvertibleMagma_924 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_inverse'737'_966
      ((T_InvertibleMagma_1360 -> T_IsInvertibleMagma_924)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_InvertibleMagma_1360 -> T_IsInvertibleMagma_924
d_isInvertibleMagma_1388 (T_InvertibleMagma_1360 -> AgdaAny
forall a b. a -> b
coe T_InvertibleMagma_1360
v0))
-- Algebra.Bundles.InvertibleMagma._.isEquivalence
d_isEquivalence_1398 ::
  T_InvertibleMagma_1360 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_1398 :: T_InvertibleMagma_1360 -> T_IsEquivalence_26
d_isEquivalence_1398 T_InvertibleMagma_1360
v0
  = (T_IsMagma_176 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
      ((T_IsInvertibleMagma_924 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsInvertibleMagma_924 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_938
         ((T_InvertibleMagma_1360 -> T_IsInvertibleMagma_924)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_InvertibleMagma_1360 -> T_IsInvertibleMagma_924
d_isInvertibleMagma_1388 (T_InvertibleMagma_1360 -> AgdaAny
forall a b. a -> b
coe T_InvertibleMagma_1360
v0)))
-- Algebra.Bundles.InvertibleMagma._.isMagma
d_isMagma_1400 ::
  T_InvertibleMagma_1360 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_176
d_isMagma_1400 :: T_InvertibleMagma_1360 -> T_IsMagma_176
d_isMagma_1400 T_InvertibleMagma_1360
v0
  = (T_IsInvertibleMagma_924 -> T_IsMagma_176)
-> AgdaAny -> T_IsMagma_176
forall a b. a -> b
coe
      T_IsInvertibleMagma_924 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_938
      ((T_InvertibleMagma_1360 -> T_IsInvertibleMagma_924)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_InvertibleMagma_1360 -> T_IsInvertibleMagma_924
d_isInvertibleMagma_1388 (T_InvertibleMagma_1360 -> AgdaAny
forall a b. a -> b
coe T_InvertibleMagma_1360
v0))
-- Algebra.Bundles.InvertibleMagma._.isPartialEquivalence
d_isPartialEquivalence_1402 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_InvertibleMagma_1360 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_1402 :: () -> () -> T_InvertibleMagma_1360 -> T_IsPartialEquivalence_16
d_isPartialEquivalence_1402 ~()
v0 ~()
v1 T_InvertibleMagma_1360
v2
  = T_InvertibleMagma_1360 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_1402 T_InvertibleMagma_1360
v2
du_isPartialEquivalence_1402 ::
  T_InvertibleMagma_1360 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_1402 :: T_InvertibleMagma_1360 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_1402 T_InvertibleMagma_1360
v0
  = let v1 :: T_IsInvertibleMagma_924
v1 = T_InvertibleMagma_1360 -> T_IsInvertibleMagma_924
d_isInvertibleMagma_1388 (T_InvertibleMagma_1360 -> T_InvertibleMagma_1360
forall a b. a -> b
coe T_InvertibleMagma_1360
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsMagma_176
v2 = T_IsInvertibleMagma_924 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_938 (T_IsInvertibleMagma_924 -> T_IsInvertibleMagma_924
forall a b. a -> b
coe T_IsInvertibleMagma_924
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsEquivalence_26 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsEquivalence_26 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
            ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v2))))
-- Algebra.Bundles.InvertibleMagma._.refl
d_refl_1404 :: T_InvertibleMagma_1360 -> AgdaAny -> AgdaAny
d_refl_1404 :: T_InvertibleMagma_1360 -> AgdaAny -> AgdaAny
d_refl_1404 T_InvertibleMagma_1360
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_34
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
         ((T_IsInvertibleMagma_924 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsInvertibleMagma_924 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_938
            ((T_InvertibleMagma_1360 -> T_IsInvertibleMagma_924)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_InvertibleMagma_1360 -> T_IsInvertibleMagma_924
d_isInvertibleMagma_1388 (T_InvertibleMagma_1360 -> AgdaAny
forall a b. a -> b
coe T_InvertibleMagma_1360
v0))))
-- Algebra.Bundles.InvertibleMagma._.reflexive
d_reflexive_1406 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_InvertibleMagma_1360 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_1406 :: ()
-> ()
-> T_InvertibleMagma_1360
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_1406 ~()
v0 ~()
v1 T_InvertibleMagma_1360
v2 = T_InvertibleMagma_1360
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_1406 T_InvertibleMagma_1360
v2
du_reflexive_1406 ::
  T_InvertibleMagma_1360 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_1406 :: T_InvertibleMagma_1360
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_1406 T_InvertibleMagma_1360
v0
  = let v1 :: T_IsInvertibleMagma_924
v1 = T_InvertibleMagma_1360 -> T_IsInvertibleMagma_924
d_isInvertibleMagma_1388 (T_InvertibleMagma_1360 -> T_InvertibleMagma_1360
forall a b. a -> b
coe T_InvertibleMagma_1360
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsMagma_176
v2 = T_IsInvertibleMagma_924 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_938 (T_IsInvertibleMagma_924 -> T_IsInvertibleMagma_924
forall a b. a -> b
coe T_IsInvertibleMagma_924
v1) in
       (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
         (\ AgdaAny
v3 AgdaAny
v4 AgdaAny
v5 ->
            (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
              T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
              ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v2))
              AgdaAny
v3))
-- Algebra.Bundles.InvertibleMagma._.setoid
d_setoid_1408 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_InvertibleMagma_1360 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_1408 :: () -> () -> T_InvertibleMagma_1360 -> T_Setoid_44
d_setoid_1408 ~()
v0 ~()
v1 T_InvertibleMagma_1360
v2 = T_InvertibleMagma_1360 -> T_Setoid_44
du_setoid_1408 T_InvertibleMagma_1360
v2
du_setoid_1408 ::
  T_InvertibleMagma_1360 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_1408 :: T_InvertibleMagma_1360 -> T_Setoid_44
du_setoid_1408 T_InvertibleMagma_1360
v0
  = let v1 :: T_IsInvertibleMagma_924
v1 = T_InvertibleMagma_1360 -> T_IsInvertibleMagma_924
d_isInvertibleMagma_1388 (T_InvertibleMagma_1360 -> T_InvertibleMagma_1360
forall a b. a -> b
coe T_InvertibleMagma_1360
v0) in
    AgdaAny -> T_Setoid_44
forall a b. a -> b
coe
      ((T_IsMagma_176 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_Setoid_44
MAlonzo.Code.Algebra.Structures.du_setoid_200
         ((T_IsInvertibleMagma_924 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsInvertibleMagma_924 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_938 (T_IsInvertibleMagma_924 -> AgdaAny
forall a b. a -> b
coe T_IsInvertibleMagma_924
v1)))
-- Algebra.Bundles.InvertibleMagma._.sym
d_sym_1410 ::
  T_InvertibleMagma_1360 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_1410 :: T_InvertibleMagma_1360 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_1410 T_InvertibleMagma_1360
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_36
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
         ((T_IsInvertibleMagma_924 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsInvertibleMagma_924 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_938
            ((T_InvertibleMagma_1360 -> T_IsInvertibleMagma_924)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_InvertibleMagma_1360 -> T_IsInvertibleMagma_924
d_isInvertibleMagma_1388 (T_InvertibleMagma_1360 -> AgdaAny
forall a b. a -> b
coe T_InvertibleMagma_1360
v0))))
-- Algebra.Bundles.InvertibleMagma._.trans
d_trans_1412 ::
  T_InvertibleMagma_1360 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_1412 :: T_InvertibleMagma_1360
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_1412 T_InvertibleMagma_1360
v0
  = (T_IsEquivalence_26
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_38
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
         ((T_IsInvertibleMagma_924 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsInvertibleMagma_924 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_938
            ((T_InvertibleMagma_1360 -> T_IsInvertibleMagma_924)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_InvertibleMagma_1360 -> T_IsInvertibleMagma_924
d_isInvertibleMagma_1388 (T_InvertibleMagma_1360 -> AgdaAny
forall a b. a -> b
coe T_InvertibleMagma_1360
v0))))
-- Algebra.Bundles.InvertibleMagma._.⁻¹-cong
d_'8315''185''45'cong_1414 ::
  T_InvertibleMagma_1360 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8315''185''45'cong_1414 :: T_InvertibleMagma_1360 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8315''185''45'cong_1414 T_InvertibleMagma_1360
v0
  = (T_IsInvertibleMagma_924
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsInvertibleMagma_924 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8315''185''45'cong_942
      ((T_InvertibleMagma_1360 -> T_IsInvertibleMagma_924)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_InvertibleMagma_1360 -> T_IsInvertibleMagma_924
d_isInvertibleMagma_1388 (T_InvertibleMagma_1360 -> AgdaAny
forall a b. a -> b
coe T_InvertibleMagma_1360
v0))
-- Algebra.Bundles.InvertibleMagma._.∙-cong
d_'8729''45'cong_1416 ::
  T_InvertibleMagma_1360 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_1416 :: T_InvertibleMagma_1360
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_1416 T_InvertibleMagma_1360
v0
  = (T_IsMagma_176
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsMagma_176
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_186
      ((T_IsInvertibleMagma_924 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsInvertibleMagma_924 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_938
         ((T_InvertibleMagma_1360 -> T_IsInvertibleMagma_924)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_InvertibleMagma_1360 -> T_IsInvertibleMagma_924
d_isInvertibleMagma_1388 (T_InvertibleMagma_1360 -> AgdaAny
forall a b. a -> b
coe T_InvertibleMagma_1360
v0)))
-- Algebra.Bundles.InvertibleMagma._.∙-congʳ
d_'8729''45'cong'691'_1418 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_InvertibleMagma_1360 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_1418 :: ()
-> ()
-> T_InvertibleMagma_1360
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_1418 ~()
v0 ~()
v1 T_InvertibleMagma_1360
v2
  = T_InvertibleMagma_1360
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1418 T_InvertibleMagma_1360
v2
du_'8729''45'cong'691'_1418 ::
  T_InvertibleMagma_1360 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1418 :: T_InvertibleMagma_1360
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1418 T_InvertibleMagma_1360
v0
  = let v1 :: T_IsInvertibleMagma_924
v1 = T_InvertibleMagma_1360 -> T_IsInvertibleMagma_924
d_isInvertibleMagma_1388 (T_InvertibleMagma_1360 -> T_InvertibleMagma_1360
forall a b. a -> b
coe T_InvertibleMagma_1360
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'691'_206
         ((T_IsInvertibleMagma_924 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsInvertibleMagma_924 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_938 (T_IsInvertibleMagma_924 -> AgdaAny
forall a b. a -> b
coe T_IsInvertibleMagma_924
v1)))
-- Algebra.Bundles.InvertibleMagma._.∙-congˡ
d_'8729''45'cong'737'_1420 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_InvertibleMagma_1360 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_1420 :: ()
-> ()
-> T_InvertibleMagma_1360
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_1420 ~()
v0 ~()
v1 T_InvertibleMagma_1360
v2
  = T_InvertibleMagma_1360
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1420 T_InvertibleMagma_1360
v2
du_'8729''45'cong'737'_1420 ::
  T_InvertibleMagma_1360 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1420 :: T_InvertibleMagma_1360
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1420 T_InvertibleMagma_1360
v0
  = let v1 :: T_IsInvertibleMagma_924
v1 = T_InvertibleMagma_1360 -> T_IsInvertibleMagma_924
d_isInvertibleMagma_1388 (T_InvertibleMagma_1360 -> T_InvertibleMagma_1360
forall a b. a -> b
coe T_InvertibleMagma_1360
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'737'_202
         ((T_IsInvertibleMagma_924 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsInvertibleMagma_924 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_938 (T_IsInvertibleMagma_924 -> AgdaAny
forall a b. a -> b
coe T_IsInvertibleMagma_924
v1)))
-- Algebra.Bundles.InvertibleMagma.magma
d_magma_1422 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_InvertibleMagma_1360 -> T_Magma_68
d_magma_1422 :: () -> () -> T_InvertibleMagma_1360 -> T_Magma_68
d_magma_1422 ~()
v0 ~()
v1 T_InvertibleMagma_1360
v2 = T_InvertibleMagma_1360 -> T_Magma_68
du_magma_1422 T_InvertibleMagma_1360
v2
du_magma_1422 :: T_InvertibleMagma_1360 -> T_Magma_68
du_magma_1422 :: T_InvertibleMagma_1360 -> T_Magma_68
du_magma_1422 T_InvertibleMagma_1360
v0
  = ((AgdaAny -> AgdaAny -> AgdaAny) -> T_IsMagma_176 -> T_Magma_68)
-> (AgdaAny -> AgdaAny -> AgdaAny) -> T_IsMagma_176 -> T_Magma_68
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny) -> T_IsMagma_176 -> T_Magma_68
C_Magma'46'constructor_1279 (T_InvertibleMagma_1360 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__1382 (T_InvertibleMagma_1360 -> T_InvertibleMagma_1360
forall a b. a -> b
coe T_InvertibleMagma_1360
v0))
      (T_IsInvertibleMagma_924 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_938
         ((T_InvertibleMagma_1360 -> T_IsInvertibleMagma_924)
-> AgdaAny -> T_IsInvertibleMagma_924
forall a b. a -> b
coe T_InvertibleMagma_1360 -> T_IsInvertibleMagma_924
d_isInvertibleMagma_1388 (T_InvertibleMagma_1360 -> AgdaAny
forall a b. a -> b
coe T_InvertibleMagma_1360
v0)))
-- Algebra.Bundles.InvertibleMagma._._≉_
d__'8777'__1426 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_InvertibleMagma_1360 -> AgdaAny -> AgdaAny -> ()
d__'8777'__1426 :: () -> () -> T_InvertibleMagma_1360 -> AgdaAny -> AgdaAny -> ()
d__'8777'__1426 = () -> () -> T_InvertibleMagma_1360 -> AgdaAny -> AgdaAny -> ()
forall a. a
erased
-- Algebra.Bundles.InvertibleMagma._.rawMagma
d_rawMagma_1428 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_InvertibleMagma_1360 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
d_rawMagma_1428 :: () -> () -> T_InvertibleMagma_1360 -> T_RawMagma_36
d_rawMagma_1428 ~()
v0 ~()
v1 T_InvertibleMagma_1360
v2 = T_InvertibleMagma_1360 -> T_RawMagma_36
du_rawMagma_1428 T_InvertibleMagma_1360
v2
du_rawMagma_1428 ::
  T_InvertibleMagma_1360 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
du_rawMagma_1428 :: T_InvertibleMagma_1360 -> T_RawMagma_36
du_rawMagma_1428 T_InvertibleMagma_1360
v0
  = (T_Magma_68 -> T_RawMagma_36) -> AgdaAny -> T_RawMagma_36
forall a b. a -> b
coe T_Magma_68 -> T_RawMagma_36
du_rawMagma_112 ((T_InvertibleMagma_1360 -> T_Magma_68) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_InvertibleMagma_1360 -> T_Magma_68
du_magma_1422 (T_InvertibleMagma_1360 -> AgdaAny
forall a b. a -> b
coe T_InvertibleMagma_1360
v0))
-- Algebra.Bundles.InvertibleUnitalMagma
d_InvertibleUnitalMagma_1434 :: p -> p -> ()
d_InvertibleUnitalMagma_1434 p
a0 p
a1 = ()
data T_InvertibleUnitalMagma_1434
  = C_InvertibleUnitalMagma'46'constructor_25619 (AgdaAny ->
                                                  AgdaAny -> AgdaAny)
                                                 AgdaAny (AgdaAny -> AgdaAny)
                                                 MAlonzo.Code.Algebra.Structures.T_IsInvertibleUnitalMagma_976
-- Algebra.Bundles.InvertibleUnitalMagma.Carrier
d_Carrier_1452 :: T_InvertibleUnitalMagma_1434 -> ()
d_Carrier_1452 :: T_InvertibleUnitalMagma_1434 -> ()
d_Carrier_1452 = T_InvertibleUnitalMagma_1434 -> ()
forall a. a
erased
-- Algebra.Bundles.InvertibleUnitalMagma._≈_
d__'8776'__1454 ::
  T_InvertibleUnitalMagma_1434 -> AgdaAny -> AgdaAny -> ()
d__'8776'__1454 :: T_InvertibleUnitalMagma_1434 -> AgdaAny -> AgdaAny -> ()
d__'8776'__1454 = T_InvertibleUnitalMagma_1434 -> AgdaAny -> AgdaAny -> ()
forall a. a
erased
-- Algebra.Bundles.InvertibleUnitalMagma._∙_
d__'8729'__1456 ::
  T_InvertibleUnitalMagma_1434 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__1456 :: T_InvertibleUnitalMagma_1434 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__1456 T_InvertibleUnitalMagma_1434
v0
  = case T_InvertibleUnitalMagma_1434 -> T_InvertibleUnitalMagma_1434
forall a b. a -> b
coe T_InvertibleUnitalMagma_1434
v0 of
      C_InvertibleUnitalMagma'46'constructor_25619 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny
v4 AgdaAny -> AgdaAny
v5 T_IsInvertibleUnitalMagma_976
v6 -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v3
      T_InvertibleUnitalMagma_1434
_ -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.InvertibleUnitalMagma.ε
d_ε_1458 :: T_InvertibleUnitalMagma_1434 -> AgdaAny
d_ε_1458 :: T_InvertibleUnitalMagma_1434 -> AgdaAny
d_ε_1458 T_InvertibleUnitalMagma_1434
v0
  = case T_InvertibleUnitalMagma_1434 -> T_InvertibleUnitalMagma_1434
forall a b. a -> b
coe T_InvertibleUnitalMagma_1434
v0 of
      C_InvertibleUnitalMagma'46'constructor_25619 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny
v4 AgdaAny -> AgdaAny
v5 T_IsInvertibleUnitalMagma_976
v6 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v4
      T_InvertibleUnitalMagma_1434
_ -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.InvertibleUnitalMagma._⁻¹
d__'8315''185'_1460 ::
  T_InvertibleUnitalMagma_1434 -> AgdaAny -> AgdaAny
d__'8315''185'_1460 :: T_InvertibleUnitalMagma_1434 -> AgdaAny -> AgdaAny
d__'8315''185'_1460 T_InvertibleUnitalMagma_1434
v0
  = case T_InvertibleUnitalMagma_1434 -> T_InvertibleUnitalMagma_1434
forall a b. a -> b
coe T_InvertibleUnitalMagma_1434
v0 of
      C_InvertibleUnitalMagma'46'constructor_25619 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny
v4 AgdaAny -> AgdaAny
v5 T_IsInvertibleUnitalMagma_976
v6 -> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v5
      T_InvertibleUnitalMagma_1434
_ -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.InvertibleUnitalMagma.isInvertibleUnitalMagma
d_isInvertibleUnitalMagma_1462 ::
  T_InvertibleUnitalMagma_1434 ->
  MAlonzo.Code.Algebra.Structures.T_IsInvertibleUnitalMagma_976
d_isInvertibleUnitalMagma_1462 :: T_InvertibleUnitalMagma_1434 -> T_IsInvertibleUnitalMagma_976
d_isInvertibleUnitalMagma_1462 T_InvertibleUnitalMagma_1434
v0
  = case T_InvertibleUnitalMagma_1434 -> T_InvertibleUnitalMagma_1434
forall a b. a -> b
coe T_InvertibleUnitalMagma_1434
v0 of
      C_InvertibleUnitalMagma'46'constructor_25619 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny
v4 AgdaAny -> AgdaAny
v5 T_IsInvertibleUnitalMagma_976
v6 -> T_IsInvertibleUnitalMagma_976 -> T_IsInvertibleUnitalMagma_976
forall a b. a -> b
coe T_IsInvertibleUnitalMagma_976
v6
      T_InvertibleUnitalMagma_1434
_ -> T_IsInvertibleUnitalMagma_976
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.InvertibleUnitalMagma._.identity
d_identity_1466 ::
  T_InvertibleUnitalMagma_1434 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_identity_1466 :: T_InvertibleUnitalMagma_1434 -> T_Σ_14
d_identity_1466 T_InvertibleUnitalMagma_1434
v0
  = (T_IsInvertibleUnitalMagma_976 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsInvertibleUnitalMagma_976 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_identity_990
      ((T_InvertibleUnitalMagma_1434 -> T_IsInvertibleUnitalMagma_976)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_InvertibleUnitalMagma_1434 -> T_IsInvertibleUnitalMagma_976
d_isInvertibleUnitalMagma_1462 (T_InvertibleUnitalMagma_1434 -> AgdaAny
forall a b. a -> b
coe T_InvertibleUnitalMagma_1434
v0))
-- Algebra.Bundles.InvertibleUnitalMagma._.identityʳ
d_identity'691'_1468 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_InvertibleUnitalMagma_1434 -> AgdaAny -> AgdaAny
d_identity'691'_1468 :: () -> () -> T_InvertibleUnitalMagma_1434 -> AgdaAny -> AgdaAny
d_identity'691'_1468 ~()
v0 ~()
v1 T_InvertibleUnitalMagma_1434
v2 = T_InvertibleUnitalMagma_1434 -> AgdaAny -> AgdaAny
du_identity'691'_1468 T_InvertibleUnitalMagma_1434
v2
du_identity'691'_1468 ::
  T_InvertibleUnitalMagma_1434 -> AgdaAny -> AgdaAny
du_identity'691'_1468 :: T_InvertibleUnitalMagma_1434 -> AgdaAny -> AgdaAny
du_identity'691'_1468 T_InvertibleUnitalMagma_1434
v0
  = (T_IsInvertibleUnitalMagma_976 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsInvertibleUnitalMagma_976 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_identity'691'_1026
      ((T_InvertibleUnitalMagma_1434 -> T_IsInvertibleUnitalMagma_976)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_InvertibleUnitalMagma_1434 -> T_IsInvertibleUnitalMagma_976
d_isInvertibleUnitalMagma_1462 (T_InvertibleUnitalMagma_1434 -> AgdaAny
forall a b. a -> b
coe T_InvertibleUnitalMagma_1434
v0))
-- Algebra.Bundles.InvertibleUnitalMagma._.identityˡ
d_identity'737'_1470 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_InvertibleUnitalMagma_1434 -> AgdaAny -> AgdaAny
d_identity'737'_1470 :: () -> () -> T_InvertibleUnitalMagma_1434 -> AgdaAny -> AgdaAny
d_identity'737'_1470 ~()
v0 ~()
v1 T_InvertibleUnitalMagma_1434
v2 = T_InvertibleUnitalMagma_1434 -> AgdaAny -> AgdaAny
du_identity'737'_1470 T_InvertibleUnitalMagma_1434
v2
du_identity'737'_1470 ::
  T_InvertibleUnitalMagma_1434 -> AgdaAny -> AgdaAny
du_identity'737'_1470 :: T_InvertibleUnitalMagma_1434 -> AgdaAny -> AgdaAny
du_identity'737'_1470 T_InvertibleUnitalMagma_1434
v0
  = (T_IsInvertibleUnitalMagma_976 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsInvertibleUnitalMagma_976 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_identity'737'_1024
      ((T_InvertibleUnitalMagma_1434 -> T_IsInvertibleUnitalMagma_976)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_InvertibleUnitalMagma_1434 -> T_IsInvertibleUnitalMagma_976
d_isInvertibleUnitalMagma_1462 (T_InvertibleUnitalMagma_1434 -> AgdaAny
forall a b. a -> b
coe T_InvertibleUnitalMagma_1434
v0))
-- Algebra.Bundles.InvertibleUnitalMagma._.inverse
d_inverse_1472 ::
  T_InvertibleUnitalMagma_1434 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_inverse_1472 :: T_InvertibleUnitalMagma_1434 -> T_Σ_14
d_inverse_1472 T_InvertibleUnitalMagma_1434
v0
  = (T_IsInvertibleMagma_924 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsInvertibleMagma_924 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_inverse_940
      ((T_IsInvertibleUnitalMagma_976 -> T_IsInvertibleMagma_924)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsInvertibleUnitalMagma_976 -> T_IsInvertibleMagma_924
MAlonzo.Code.Algebra.Structures.d_isInvertibleMagma_988
         ((T_InvertibleUnitalMagma_1434 -> T_IsInvertibleUnitalMagma_976)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_InvertibleUnitalMagma_1434 -> T_IsInvertibleUnitalMagma_976
d_isInvertibleUnitalMagma_1462 (T_InvertibleUnitalMagma_1434 -> AgdaAny
forall a b. a -> b
coe T_InvertibleUnitalMagma_1434
v0)))
-- Algebra.Bundles.InvertibleUnitalMagma._.inverseʳ
d_inverse'691'_1474 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_InvertibleUnitalMagma_1434 -> AgdaAny -> AgdaAny
d_inverse'691'_1474 :: () -> () -> T_InvertibleUnitalMagma_1434 -> AgdaAny -> AgdaAny
d_inverse'691'_1474 ~()
v0 ~()
v1 T_InvertibleUnitalMagma_1434
v2 = T_InvertibleUnitalMagma_1434 -> AgdaAny -> AgdaAny
du_inverse'691'_1474 T_InvertibleUnitalMagma_1434
v2
du_inverse'691'_1474 ::
  T_InvertibleUnitalMagma_1434 -> AgdaAny -> AgdaAny
du_inverse'691'_1474 :: T_InvertibleUnitalMagma_1434 -> AgdaAny -> AgdaAny
du_inverse'691'_1474 T_InvertibleUnitalMagma_1434
v0
  = let v1 :: T_IsInvertibleUnitalMagma_976
v1 = T_InvertibleUnitalMagma_1434 -> T_IsInvertibleUnitalMagma_976
d_isInvertibleUnitalMagma_1462 (T_InvertibleUnitalMagma_1434 -> T_InvertibleUnitalMagma_1434
forall a b. a -> b
coe T_InvertibleUnitalMagma_1434
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsInvertibleMagma_924 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsInvertibleMagma_924 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_inverse'691'_968
         ((T_IsInvertibleUnitalMagma_976 -> T_IsInvertibleMagma_924)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsInvertibleUnitalMagma_976 -> T_IsInvertibleMagma_924
MAlonzo.Code.Algebra.Structures.d_isInvertibleMagma_988 (T_IsInvertibleUnitalMagma_976 -> AgdaAny
forall a b. a -> b
coe T_IsInvertibleUnitalMagma_976
v1)))
-- Algebra.Bundles.InvertibleUnitalMagma._.inverseˡ
d_inverse'737'_1476 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_InvertibleUnitalMagma_1434 -> AgdaAny -> AgdaAny
d_inverse'737'_1476 :: () -> () -> T_InvertibleUnitalMagma_1434 -> AgdaAny -> AgdaAny
d_inverse'737'_1476 ~()
v0 ~()
v1 T_InvertibleUnitalMagma_1434
v2 = T_InvertibleUnitalMagma_1434 -> AgdaAny -> AgdaAny
du_inverse'737'_1476 T_InvertibleUnitalMagma_1434
v2
du_inverse'737'_1476 ::
  T_InvertibleUnitalMagma_1434 -> AgdaAny -> AgdaAny
du_inverse'737'_1476 :: T_InvertibleUnitalMagma_1434 -> AgdaAny -> AgdaAny
du_inverse'737'_1476 T_InvertibleUnitalMagma_1434
v0
  = let v1 :: T_IsInvertibleUnitalMagma_976
v1 = T_InvertibleUnitalMagma_1434 -> T_IsInvertibleUnitalMagma_976
d_isInvertibleUnitalMagma_1462 (T_InvertibleUnitalMagma_1434 -> T_InvertibleUnitalMagma_1434
forall a b. a -> b
coe T_InvertibleUnitalMagma_1434
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsInvertibleMagma_924 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsInvertibleMagma_924 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_inverse'737'_966
         ((T_IsInvertibleUnitalMagma_976 -> T_IsInvertibleMagma_924)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsInvertibleUnitalMagma_976 -> T_IsInvertibleMagma_924
MAlonzo.Code.Algebra.Structures.d_isInvertibleMagma_988 (T_IsInvertibleUnitalMagma_976 -> AgdaAny
forall a b. a -> b
coe T_IsInvertibleUnitalMagma_976
v1)))
-- Algebra.Bundles.InvertibleUnitalMagma._.isEquivalence
d_isEquivalence_1478 ::
  T_InvertibleUnitalMagma_1434 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_1478 :: T_InvertibleUnitalMagma_1434 -> T_IsEquivalence_26
d_isEquivalence_1478 T_InvertibleUnitalMagma_1434
v0
  = (T_IsMagma_176 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
      ((T_IsInvertibleMagma_924 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsInvertibleMagma_924 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_938
         ((T_IsInvertibleUnitalMagma_976 -> T_IsInvertibleMagma_924)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsInvertibleUnitalMagma_976 -> T_IsInvertibleMagma_924
MAlonzo.Code.Algebra.Structures.d_isInvertibleMagma_988
            ((T_InvertibleUnitalMagma_1434 -> T_IsInvertibleUnitalMagma_976)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_InvertibleUnitalMagma_1434 -> T_IsInvertibleUnitalMagma_976
d_isInvertibleUnitalMagma_1462 (T_InvertibleUnitalMagma_1434 -> AgdaAny
forall a b. a -> b
coe T_InvertibleUnitalMagma_1434
v0))))
-- Algebra.Bundles.InvertibleUnitalMagma._.isInvertibleMagma
d_isInvertibleMagma_1480 ::
  T_InvertibleUnitalMagma_1434 ->
  MAlonzo.Code.Algebra.Structures.T_IsInvertibleMagma_924
d_isInvertibleMagma_1480 :: T_InvertibleUnitalMagma_1434 -> T_IsInvertibleMagma_924
d_isInvertibleMagma_1480 T_InvertibleUnitalMagma_1434
v0
  = (T_IsInvertibleUnitalMagma_976 -> T_IsInvertibleMagma_924)
-> AgdaAny -> T_IsInvertibleMagma_924
forall a b. a -> b
coe
      T_IsInvertibleUnitalMagma_976 -> T_IsInvertibleMagma_924
MAlonzo.Code.Algebra.Structures.d_isInvertibleMagma_988
      ((T_InvertibleUnitalMagma_1434 -> T_IsInvertibleUnitalMagma_976)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_InvertibleUnitalMagma_1434 -> T_IsInvertibleUnitalMagma_976
d_isInvertibleUnitalMagma_1462 (T_InvertibleUnitalMagma_1434 -> AgdaAny
forall a b. a -> b
coe T_InvertibleUnitalMagma_1434
v0))
-- Algebra.Bundles.InvertibleUnitalMagma._.isMagma
d_isMagma_1482 ::
  T_InvertibleUnitalMagma_1434 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_176
d_isMagma_1482 :: T_InvertibleUnitalMagma_1434 -> T_IsMagma_176
d_isMagma_1482 T_InvertibleUnitalMagma_1434
v0
  = (T_IsInvertibleMagma_924 -> T_IsMagma_176)
-> AgdaAny -> T_IsMagma_176
forall a b. a -> b
coe
      T_IsInvertibleMagma_924 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_938
      ((T_IsInvertibleUnitalMagma_976 -> T_IsInvertibleMagma_924)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsInvertibleUnitalMagma_976 -> T_IsInvertibleMagma_924
MAlonzo.Code.Algebra.Structures.d_isInvertibleMagma_988
         ((T_InvertibleUnitalMagma_1434 -> T_IsInvertibleUnitalMagma_976)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_InvertibleUnitalMagma_1434 -> T_IsInvertibleUnitalMagma_976
d_isInvertibleUnitalMagma_1462 (T_InvertibleUnitalMagma_1434 -> AgdaAny
forall a b. a -> b
coe T_InvertibleUnitalMagma_1434
v0)))
-- Algebra.Bundles.InvertibleUnitalMagma._.isPartialEquivalence
d_isPartialEquivalence_1484 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_InvertibleUnitalMagma_1434 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_1484 :: ()
-> () -> T_InvertibleUnitalMagma_1434 -> T_IsPartialEquivalence_16
d_isPartialEquivalence_1484 ~()
v0 ~()
v1 T_InvertibleUnitalMagma_1434
v2
  = T_InvertibleUnitalMagma_1434 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_1484 T_InvertibleUnitalMagma_1434
v2
du_isPartialEquivalence_1484 ::
  T_InvertibleUnitalMagma_1434 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_1484 :: T_InvertibleUnitalMagma_1434 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_1484 T_InvertibleUnitalMagma_1434
v0
  = let v1 :: T_IsInvertibleUnitalMagma_976
v1 = T_InvertibleUnitalMagma_1434 -> T_IsInvertibleUnitalMagma_976
d_isInvertibleUnitalMagma_1462 (T_InvertibleUnitalMagma_1434 -> T_InvertibleUnitalMagma_1434
forall a b. a -> b
coe T_InvertibleUnitalMagma_1434
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsInvertibleMagma_924
v2
             = T_IsInvertibleUnitalMagma_976 -> T_IsInvertibleMagma_924
MAlonzo.Code.Algebra.Structures.d_isInvertibleMagma_988
                 (T_IsInvertibleUnitalMagma_976 -> T_IsInvertibleUnitalMagma_976
forall a b. a -> b
coe T_IsInvertibleUnitalMagma_976
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsMagma_176
v3 = T_IsInvertibleMagma_924 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_938 (T_IsInvertibleMagma_924 -> T_IsInvertibleMagma_924
forall a b. a -> b
coe T_IsInvertibleMagma_924
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsEquivalence_26 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsEquivalence_26 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
               ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v3)))))
-- Algebra.Bundles.InvertibleUnitalMagma._.isUnitalMagma
d_isUnitalMagma_1486 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_InvertibleUnitalMagma_1434 ->
  MAlonzo.Code.Algebra.Structures.T_IsUnitalMagma_642
d_isUnitalMagma_1486 :: () -> () -> T_InvertibleUnitalMagma_1434 -> T_IsUnitalMagma_642
d_isUnitalMagma_1486 ~()
v0 ~()
v1 T_InvertibleUnitalMagma_1434
v2 = T_InvertibleUnitalMagma_1434 -> T_IsUnitalMagma_642
du_isUnitalMagma_1486 T_InvertibleUnitalMagma_1434
v2
du_isUnitalMagma_1486 ::
  T_InvertibleUnitalMagma_1434 ->
  MAlonzo.Code.Algebra.Structures.T_IsUnitalMagma_642
du_isUnitalMagma_1486 :: T_InvertibleUnitalMagma_1434 -> T_IsUnitalMagma_642
du_isUnitalMagma_1486 T_InvertibleUnitalMagma_1434
v0
  = (T_IsInvertibleUnitalMagma_976 -> T_IsUnitalMagma_642)
-> AgdaAny -> T_IsUnitalMagma_642
forall a b. a -> b
coe
      T_IsInvertibleUnitalMagma_976 -> T_IsUnitalMagma_642
MAlonzo.Code.Algebra.Structures.du_isUnitalMagma_1028
      ((T_InvertibleUnitalMagma_1434 -> T_IsInvertibleUnitalMagma_976)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_InvertibleUnitalMagma_1434 -> T_IsInvertibleUnitalMagma_976
d_isInvertibleUnitalMagma_1462 (T_InvertibleUnitalMagma_1434 -> AgdaAny
forall a b. a -> b
coe T_InvertibleUnitalMagma_1434
v0))
-- Algebra.Bundles.InvertibleUnitalMagma._.refl
d_refl_1488 :: T_InvertibleUnitalMagma_1434 -> AgdaAny -> AgdaAny
d_refl_1488 :: T_InvertibleUnitalMagma_1434 -> AgdaAny -> AgdaAny
d_refl_1488 T_InvertibleUnitalMagma_1434
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_34
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
         ((T_IsInvertibleMagma_924 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsInvertibleMagma_924 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_938
            ((T_IsInvertibleUnitalMagma_976 -> T_IsInvertibleMagma_924)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsInvertibleUnitalMagma_976 -> T_IsInvertibleMagma_924
MAlonzo.Code.Algebra.Structures.d_isInvertibleMagma_988
               ((T_InvertibleUnitalMagma_1434 -> T_IsInvertibleUnitalMagma_976)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_InvertibleUnitalMagma_1434 -> T_IsInvertibleUnitalMagma_976
d_isInvertibleUnitalMagma_1462 (T_InvertibleUnitalMagma_1434 -> AgdaAny
forall a b. a -> b
coe T_InvertibleUnitalMagma_1434
v0)))))
-- Algebra.Bundles.InvertibleUnitalMagma._.reflexive
d_reflexive_1490 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_InvertibleUnitalMagma_1434 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_1490 :: ()
-> ()
-> T_InvertibleUnitalMagma_1434
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_1490 ~()
v0 ~()
v1 T_InvertibleUnitalMagma_1434
v2 = T_InvertibleUnitalMagma_1434
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_1490 T_InvertibleUnitalMagma_1434
v2
du_reflexive_1490 ::
  T_InvertibleUnitalMagma_1434 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_1490 :: T_InvertibleUnitalMagma_1434
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_1490 T_InvertibleUnitalMagma_1434
v0
  = let v1 :: T_IsInvertibleUnitalMagma_976
v1 = T_InvertibleUnitalMagma_1434 -> T_IsInvertibleUnitalMagma_976
d_isInvertibleUnitalMagma_1462 (T_InvertibleUnitalMagma_1434 -> T_InvertibleUnitalMagma_1434
forall a b. a -> b
coe T_InvertibleUnitalMagma_1434
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsInvertibleMagma_924
v2
             = T_IsInvertibleUnitalMagma_976 -> T_IsInvertibleMagma_924
MAlonzo.Code.Algebra.Structures.d_isInvertibleMagma_988
                 (T_IsInvertibleUnitalMagma_976 -> T_IsInvertibleUnitalMagma_976
forall a b. a -> b
coe T_IsInvertibleUnitalMagma_976
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsMagma_176
v3 = T_IsInvertibleMagma_924 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_938 (T_IsInvertibleMagma_924 -> T_IsInvertibleMagma_924
forall a b. a -> b
coe T_IsInvertibleMagma_924
v2) in
          (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
            (\ AgdaAny
v4 AgdaAny
v5 AgdaAny
v6 ->
               (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                 T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
                 ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v3))
                 AgdaAny
v4)))
-- Algebra.Bundles.InvertibleUnitalMagma._.setoid
d_setoid_1492 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_InvertibleUnitalMagma_1434 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_1492 :: () -> () -> T_InvertibleUnitalMagma_1434 -> T_Setoid_44
d_setoid_1492 ~()
v0 ~()
v1 T_InvertibleUnitalMagma_1434
v2 = T_InvertibleUnitalMagma_1434 -> T_Setoid_44
du_setoid_1492 T_InvertibleUnitalMagma_1434
v2
du_setoid_1492 ::
  T_InvertibleUnitalMagma_1434 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_1492 :: T_InvertibleUnitalMagma_1434 -> T_Setoid_44
du_setoid_1492 T_InvertibleUnitalMagma_1434
v0
  = let v1 :: T_IsInvertibleUnitalMagma_976
v1 = T_InvertibleUnitalMagma_1434 -> T_IsInvertibleUnitalMagma_976
d_isInvertibleUnitalMagma_1462 (T_InvertibleUnitalMagma_1434 -> T_InvertibleUnitalMagma_1434
forall a b. a -> b
coe T_InvertibleUnitalMagma_1434
v0) in
    AgdaAny -> T_Setoid_44
forall a b. a -> b
coe
      (let v2 :: T_IsInvertibleMagma_924
v2
             = T_IsInvertibleUnitalMagma_976 -> T_IsInvertibleMagma_924
MAlonzo.Code.Algebra.Structures.d_isInvertibleMagma_988
                 (T_IsInvertibleUnitalMagma_976 -> T_IsInvertibleUnitalMagma_976
forall a b. a -> b
coe T_IsInvertibleUnitalMagma_976
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsMagma_176 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMagma_176 -> T_Setoid_44
MAlonzo.Code.Algebra.Structures.du_setoid_200
            ((T_IsInvertibleMagma_924 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsInvertibleMagma_924 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_938 (T_IsInvertibleMagma_924 -> AgdaAny
forall a b. a -> b
coe T_IsInvertibleMagma_924
v2))))
-- Algebra.Bundles.InvertibleUnitalMagma._.sym
d_sym_1494 ::
  T_InvertibleUnitalMagma_1434 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_1494 :: T_InvertibleUnitalMagma_1434
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_1494 T_InvertibleUnitalMagma_1434
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_36
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
         ((T_IsInvertibleMagma_924 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsInvertibleMagma_924 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_938
            ((T_IsInvertibleUnitalMagma_976 -> T_IsInvertibleMagma_924)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsInvertibleUnitalMagma_976 -> T_IsInvertibleMagma_924
MAlonzo.Code.Algebra.Structures.d_isInvertibleMagma_988
               ((T_InvertibleUnitalMagma_1434 -> T_IsInvertibleUnitalMagma_976)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_InvertibleUnitalMagma_1434 -> T_IsInvertibleUnitalMagma_976
d_isInvertibleUnitalMagma_1462 (T_InvertibleUnitalMagma_1434 -> AgdaAny
forall a b. a -> b
coe T_InvertibleUnitalMagma_1434
v0)))))
-- Algebra.Bundles.InvertibleUnitalMagma._.trans
d_trans_1496 ::
  T_InvertibleUnitalMagma_1434 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_1496 :: T_InvertibleUnitalMagma_1434
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_1496 T_InvertibleUnitalMagma_1434
v0
  = (T_IsEquivalence_26
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_38
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
         ((T_IsInvertibleMagma_924 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsInvertibleMagma_924 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_938
            ((T_IsInvertibleUnitalMagma_976 -> T_IsInvertibleMagma_924)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsInvertibleUnitalMagma_976 -> T_IsInvertibleMagma_924
MAlonzo.Code.Algebra.Structures.d_isInvertibleMagma_988
               ((T_InvertibleUnitalMagma_1434 -> T_IsInvertibleUnitalMagma_976)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_InvertibleUnitalMagma_1434 -> T_IsInvertibleUnitalMagma_976
d_isInvertibleUnitalMagma_1462 (T_InvertibleUnitalMagma_1434 -> AgdaAny
forall a b. a -> b
coe T_InvertibleUnitalMagma_1434
v0)))))
-- Algebra.Bundles.InvertibleUnitalMagma._.⁻¹-cong
d_'8315''185''45'cong_1498 ::
  T_InvertibleUnitalMagma_1434 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8315''185''45'cong_1498 :: T_InvertibleUnitalMagma_1434
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8315''185''45'cong_1498 T_InvertibleUnitalMagma_1434
v0
  = (T_IsInvertibleMagma_924
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsInvertibleMagma_924 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8315''185''45'cong_942
      ((T_IsInvertibleUnitalMagma_976 -> T_IsInvertibleMagma_924)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsInvertibleUnitalMagma_976 -> T_IsInvertibleMagma_924
MAlonzo.Code.Algebra.Structures.d_isInvertibleMagma_988
         ((T_InvertibleUnitalMagma_1434 -> T_IsInvertibleUnitalMagma_976)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_InvertibleUnitalMagma_1434 -> T_IsInvertibleUnitalMagma_976
d_isInvertibleUnitalMagma_1462 (T_InvertibleUnitalMagma_1434 -> AgdaAny
forall a b. a -> b
coe T_InvertibleUnitalMagma_1434
v0)))
-- Algebra.Bundles.InvertibleUnitalMagma._.∙-cong
d_'8729''45'cong_1500 ::
  T_InvertibleUnitalMagma_1434 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_1500 :: T_InvertibleUnitalMagma_1434
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_1500 T_InvertibleUnitalMagma_1434
v0
  = (T_IsMagma_176
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsMagma_176
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_186
      ((T_IsInvertibleMagma_924 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsInvertibleMagma_924 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_938
         ((T_IsInvertibleUnitalMagma_976 -> T_IsInvertibleMagma_924)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsInvertibleUnitalMagma_976 -> T_IsInvertibleMagma_924
MAlonzo.Code.Algebra.Structures.d_isInvertibleMagma_988
            ((T_InvertibleUnitalMagma_1434 -> T_IsInvertibleUnitalMagma_976)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_InvertibleUnitalMagma_1434 -> T_IsInvertibleUnitalMagma_976
d_isInvertibleUnitalMagma_1462 (T_InvertibleUnitalMagma_1434 -> AgdaAny
forall a b. a -> b
coe T_InvertibleUnitalMagma_1434
v0))))
-- Algebra.Bundles.InvertibleUnitalMagma._.∙-congʳ
d_'8729''45'cong'691'_1502 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_InvertibleUnitalMagma_1434 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_1502 :: ()
-> ()
-> T_InvertibleUnitalMagma_1434
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_1502 ~()
v0 ~()
v1 T_InvertibleUnitalMagma_1434
v2
  = T_InvertibleUnitalMagma_1434
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1502 T_InvertibleUnitalMagma_1434
v2
du_'8729''45'cong'691'_1502 ::
  T_InvertibleUnitalMagma_1434 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1502 :: T_InvertibleUnitalMagma_1434
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1502 T_InvertibleUnitalMagma_1434
v0
  = let v1 :: T_IsInvertibleUnitalMagma_976
v1 = T_InvertibleUnitalMagma_1434 -> T_IsInvertibleUnitalMagma_976
d_isInvertibleUnitalMagma_1462 (T_InvertibleUnitalMagma_1434 -> T_InvertibleUnitalMagma_1434
forall a b. a -> b
coe T_InvertibleUnitalMagma_1434
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsInvertibleMagma_924
v2
             = T_IsInvertibleUnitalMagma_976 -> T_IsInvertibleMagma_924
MAlonzo.Code.Algebra.Structures.d_isInvertibleMagma_988
                 (T_IsInvertibleUnitalMagma_976 -> T_IsInvertibleUnitalMagma_976
forall a b. a -> b
coe T_IsInvertibleUnitalMagma_976
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'691'_206
            ((T_IsInvertibleMagma_924 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsInvertibleMagma_924 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_938 (T_IsInvertibleMagma_924 -> AgdaAny
forall a b. a -> b
coe T_IsInvertibleMagma_924
v2))))
-- Algebra.Bundles.InvertibleUnitalMagma._.∙-congˡ
d_'8729''45'cong'737'_1504 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_InvertibleUnitalMagma_1434 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_1504 :: ()
-> ()
-> T_InvertibleUnitalMagma_1434
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_1504 ~()
v0 ~()
v1 T_InvertibleUnitalMagma_1434
v2
  = T_InvertibleUnitalMagma_1434
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1504 T_InvertibleUnitalMagma_1434
v2
du_'8729''45'cong'737'_1504 ::
  T_InvertibleUnitalMagma_1434 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1504 :: T_InvertibleUnitalMagma_1434
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1504 T_InvertibleUnitalMagma_1434
v0
  = let v1 :: T_IsInvertibleUnitalMagma_976
v1 = T_InvertibleUnitalMagma_1434 -> T_IsInvertibleUnitalMagma_976
d_isInvertibleUnitalMagma_1462 (T_InvertibleUnitalMagma_1434 -> T_InvertibleUnitalMagma_1434
forall a b. a -> b
coe T_InvertibleUnitalMagma_1434
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsInvertibleMagma_924
v2
             = T_IsInvertibleUnitalMagma_976 -> T_IsInvertibleMagma_924
MAlonzo.Code.Algebra.Structures.d_isInvertibleMagma_988
                 (T_IsInvertibleUnitalMagma_976 -> T_IsInvertibleUnitalMagma_976
forall a b. a -> b
coe T_IsInvertibleUnitalMagma_976
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'737'_202
            ((T_IsInvertibleMagma_924 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsInvertibleMagma_924 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_938 (T_IsInvertibleMagma_924 -> AgdaAny
forall a b. a -> b
coe T_IsInvertibleMagma_924
v2))))
-- Algebra.Bundles.InvertibleUnitalMagma.invertibleMagma
d_invertibleMagma_1506 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_InvertibleUnitalMagma_1434 -> T_InvertibleMagma_1360
d_invertibleMagma_1506 :: () -> () -> T_InvertibleUnitalMagma_1434 -> T_InvertibleMagma_1360
d_invertibleMagma_1506 ~()
v0 ~()
v1 T_InvertibleUnitalMagma_1434
v2 = T_InvertibleUnitalMagma_1434 -> T_InvertibleMagma_1360
du_invertibleMagma_1506 T_InvertibleUnitalMagma_1434
v2
du_invertibleMagma_1506 ::
  T_InvertibleUnitalMagma_1434 -> T_InvertibleMagma_1360
du_invertibleMagma_1506 :: T_InvertibleUnitalMagma_1434 -> T_InvertibleMagma_1360
du_invertibleMagma_1506 T_InvertibleUnitalMagma_1434
v0
  = ((AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> (AgdaAny -> AgdaAny)
 -> T_IsInvertibleMagma_924
 -> T_InvertibleMagma_1360)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsInvertibleMagma_924
-> T_InvertibleMagma_1360
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsInvertibleMagma_924
-> T_InvertibleMagma_1360
C_InvertibleMagma'46'constructor_24127 (T_InvertibleUnitalMagma_1434 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__1456 (T_InvertibleUnitalMagma_1434 -> T_InvertibleUnitalMagma_1434
forall a b. a -> b
coe T_InvertibleUnitalMagma_1434
v0))
      (T_InvertibleUnitalMagma_1434 -> AgdaAny
d_ε_1458 (T_InvertibleUnitalMagma_1434 -> T_InvertibleUnitalMagma_1434
forall a b. a -> b
coe T_InvertibleUnitalMagma_1434
v0)) (T_InvertibleUnitalMagma_1434 -> AgdaAny -> AgdaAny
d__'8315''185'_1460 (T_InvertibleUnitalMagma_1434 -> T_InvertibleUnitalMagma_1434
forall a b. a -> b
coe T_InvertibleUnitalMagma_1434
v0))
      (T_IsInvertibleUnitalMagma_976 -> T_IsInvertibleMagma_924
MAlonzo.Code.Algebra.Structures.d_isInvertibleMagma_988
         ((T_InvertibleUnitalMagma_1434 -> T_IsInvertibleUnitalMagma_976)
-> AgdaAny -> T_IsInvertibleUnitalMagma_976
forall a b. a -> b
coe T_InvertibleUnitalMagma_1434 -> T_IsInvertibleUnitalMagma_976
d_isInvertibleUnitalMagma_1462 (T_InvertibleUnitalMagma_1434 -> AgdaAny
forall a b. a -> b
coe T_InvertibleUnitalMagma_1434
v0)))
-- Algebra.Bundles.InvertibleUnitalMagma._._≉_
d__'8777'__1510 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_InvertibleUnitalMagma_1434 -> AgdaAny -> AgdaAny -> ()
d__'8777'__1510 :: ()
-> () -> T_InvertibleUnitalMagma_1434 -> AgdaAny -> AgdaAny -> ()
d__'8777'__1510 = ()
-> () -> T_InvertibleUnitalMagma_1434 -> AgdaAny -> AgdaAny -> ()
forall a. a
erased
-- Algebra.Bundles.InvertibleUnitalMagma._.magma
d_magma_1512 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_InvertibleUnitalMagma_1434 -> T_Magma_68
d_magma_1512 :: () -> () -> T_InvertibleUnitalMagma_1434 -> T_Magma_68
d_magma_1512 ~()
v0 ~()
v1 T_InvertibleUnitalMagma_1434
v2 = T_InvertibleUnitalMagma_1434 -> T_Magma_68
du_magma_1512 T_InvertibleUnitalMagma_1434
v2
du_magma_1512 :: T_InvertibleUnitalMagma_1434 -> T_Magma_68
du_magma_1512 :: T_InvertibleUnitalMagma_1434 -> T_Magma_68
du_magma_1512 T_InvertibleUnitalMagma_1434
v0
  = (T_InvertibleMagma_1360 -> T_Magma_68) -> AgdaAny -> T_Magma_68
forall a b. a -> b
coe T_InvertibleMagma_1360 -> T_Magma_68
du_magma_1422 ((T_InvertibleUnitalMagma_1434 -> T_InvertibleMagma_1360)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_InvertibleUnitalMagma_1434 -> T_InvertibleMagma_1360
du_invertibleMagma_1506 (T_InvertibleUnitalMagma_1434 -> AgdaAny
forall a b. a -> b
coe T_InvertibleUnitalMagma_1434
v0))
-- Algebra.Bundles.InvertibleUnitalMagma._.rawMagma
d_rawMagma_1514 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_InvertibleUnitalMagma_1434 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
d_rawMagma_1514 :: () -> () -> T_InvertibleUnitalMagma_1434 -> T_RawMagma_36
d_rawMagma_1514 ~()
v0 ~()
v1 T_InvertibleUnitalMagma_1434
v2 = T_InvertibleUnitalMagma_1434 -> T_RawMagma_36
du_rawMagma_1514 T_InvertibleUnitalMagma_1434
v2
du_rawMagma_1514 ::
  T_InvertibleUnitalMagma_1434 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
du_rawMagma_1514 :: T_InvertibleUnitalMagma_1434 -> T_RawMagma_36
du_rawMagma_1514 T_InvertibleUnitalMagma_1434
v0
  = let v1 :: t
v1 = (T_InvertibleUnitalMagma_1434 -> T_InvertibleMagma_1360)
-> AgdaAny -> t
forall a b. a -> b
coe T_InvertibleUnitalMagma_1434 -> T_InvertibleMagma_1360
du_invertibleMagma_1506 (T_InvertibleUnitalMagma_1434 -> AgdaAny
forall a b. a -> b
coe T_InvertibleUnitalMagma_1434
v0) in
    AgdaAny -> T_RawMagma_36
forall a b. a -> b
coe ((T_Magma_68 -> T_RawMagma_36) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Magma_68 -> T_RawMagma_36
du_rawMagma_112 ((T_InvertibleMagma_1360 -> T_Magma_68) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_InvertibleMagma_1360 -> T_Magma_68
du_magma_1422 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1)))
-- Algebra.Bundles.Group
d_Group_1520 :: p -> p -> ()
d_Group_1520 p
a0 p
a1 = ()
data T_Group_1520
  = C_Group'46'constructor_27303 (AgdaAny -> AgdaAny -> AgdaAny)
                                 AgdaAny (AgdaAny -> AgdaAny)
                                 MAlonzo.Code.Algebra.Structures.T_IsGroup_1036
-- Algebra.Bundles.Group.Carrier
d_Carrier_1538 :: T_Group_1520 -> ()
d_Carrier_1538 :: T_Group_1520 -> ()
d_Carrier_1538 = T_Group_1520 -> ()
forall a. a
erased
-- Algebra.Bundles.Group._≈_
d__'8776'__1540 :: T_Group_1520 -> AgdaAny -> AgdaAny -> ()
d__'8776'__1540 :: T_Group_1520 -> AgdaAny -> AgdaAny -> ()
d__'8776'__1540 = T_Group_1520 -> AgdaAny -> AgdaAny -> ()
forall a. a
erased
-- Algebra.Bundles.Group._∙_
d__'8729'__1542 :: T_Group_1520 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__1542 :: T_Group_1520 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__1542 T_Group_1520
v0
  = case T_Group_1520 -> T_Group_1520
forall a b. a -> b
coe T_Group_1520
v0 of
      C_Group'46'constructor_27303 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny
v4 AgdaAny -> AgdaAny
v5 T_IsGroup_1036
v6 -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v3
      T_Group_1520
_ -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.Group.ε
d_ε_1544 :: T_Group_1520 -> AgdaAny
d_ε_1544 :: T_Group_1520 -> AgdaAny
d_ε_1544 T_Group_1520
v0
  = case T_Group_1520 -> T_Group_1520
forall a b. a -> b
coe T_Group_1520
v0 of
      C_Group'46'constructor_27303 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny
v4 AgdaAny -> AgdaAny
v5 T_IsGroup_1036
v6 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v4
      T_Group_1520
_ -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.Group._⁻¹
d__'8315''185'_1546 :: T_Group_1520 -> AgdaAny -> AgdaAny
d__'8315''185'_1546 :: T_Group_1520 -> AgdaAny -> AgdaAny
d__'8315''185'_1546 T_Group_1520
v0
  = case T_Group_1520 -> T_Group_1520
forall a b. a -> b
coe T_Group_1520
v0 of
      C_Group'46'constructor_27303 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny
v4 AgdaAny -> AgdaAny
v5 T_IsGroup_1036
v6 -> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v5
      T_Group_1520
_ -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.Group.isGroup
d_isGroup_1548 ::
  T_Group_1520 -> MAlonzo.Code.Algebra.Structures.T_IsGroup_1036
d_isGroup_1548 :: T_Group_1520 -> T_IsGroup_1036
d_isGroup_1548 T_Group_1520
v0
  = case T_Group_1520 -> T_Group_1520
forall a b. a -> b
coe T_Group_1520
v0 of
      C_Group'46'constructor_27303 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny
v4 AgdaAny -> AgdaAny
v5 T_IsGroup_1036
v6 -> T_IsGroup_1036 -> T_IsGroup_1036
forall a b. a -> b
coe T_IsGroup_1036
v6
      T_Group_1520
_ -> T_IsGroup_1036
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.Group._._-_
d__'45'__1552 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Group_1520 -> AgdaAny -> AgdaAny -> AgdaAny
d__'45'__1552 :: () -> () -> T_Group_1520 -> AgdaAny -> AgdaAny -> AgdaAny
d__'45'__1552 ~()
v0 ~()
v1 T_Group_1520
v2 = T_Group_1520 -> AgdaAny -> AgdaAny -> AgdaAny
du__'45'__1552 T_Group_1520
v2
du__'45'__1552 :: T_Group_1520 -> AgdaAny -> AgdaAny -> AgdaAny
du__'45'__1552 :: T_Group_1520 -> AgdaAny -> AgdaAny -> AgdaAny
du__'45'__1552 T_Group_1520
v0
  = ((AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du__'45'__1104
      ((T_Group_1520 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Group_1520 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__1542 (T_Group_1520 -> AgdaAny
forall a b. a -> b
coe T_Group_1520
v0)) ((T_Group_1520 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Group_1520 -> AgdaAny -> AgdaAny
d__'8315''185'_1546 (T_Group_1520 -> AgdaAny
forall a b. a -> b
coe T_Group_1520
v0))
-- Algebra.Bundles.Group._._//_
d__'47''47'__1554 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Group_1520 -> AgdaAny -> AgdaAny -> AgdaAny
d__'47''47'__1554 :: () -> () -> T_Group_1520 -> AgdaAny -> AgdaAny -> AgdaAny
d__'47''47'__1554 ~()
v0 ~()
v1 T_Group_1520
v2 = T_Group_1520 -> AgdaAny -> AgdaAny -> AgdaAny
du__'47''47'__1554 T_Group_1520
v2
du__'47''47'__1554 :: T_Group_1520 -> AgdaAny -> AgdaAny -> AgdaAny
du__'47''47'__1554 :: T_Group_1520 -> AgdaAny -> AgdaAny -> AgdaAny
du__'47''47'__1554 T_Group_1520
v0
  = ((AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du__'47''47'__1098
      ((T_Group_1520 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Group_1520 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__1542 (T_Group_1520 -> AgdaAny
forall a b. a -> b
coe T_Group_1520
v0)) ((T_Group_1520 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Group_1520 -> AgdaAny -> AgdaAny
d__'8315''185'_1546 (T_Group_1520 -> AgdaAny
forall a b. a -> b
coe T_Group_1520
v0))
-- Algebra.Bundles.Group._._\\_
d__'92''92'__1556 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Group_1520 -> AgdaAny -> AgdaAny -> AgdaAny
d__'92''92'__1556 :: () -> () -> T_Group_1520 -> AgdaAny -> AgdaAny -> AgdaAny
d__'92''92'__1556 ~()
v0 ~()
v1 T_Group_1520
v2 = T_Group_1520 -> AgdaAny -> AgdaAny -> AgdaAny
du__'92''92'__1556 T_Group_1520
v2
du__'92''92'__1556 :: T_Group_1520 -> AgdaAny -> AgdaAny -> AgdaAny
du__'92''92'__1556 :: T_Group_1520 -> AgdaAny -> AgdaAny -> AgdaAny
du__'92''92'__1556 T_Group_1520
v0
  = ((AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du__'92''92'__1092
      ((T_Group_1520 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Group_1520 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__1542 (T_Group_1520 -> AgdaAny
forall a b. a -> b
coe T_Group_1520
v0)) ((T_Group_1520 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Group_1520 -> AgdaAny -> AgdaAny
d__'8315''185'_1546 (T_Group_1520 -> AgdaAny
forall a b. a -> b
coe T_Group_1520
v0))
-- Algebra.Bundles.Group._.assoc
d_assoc_1558 ::
  T_Group_1520 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_1558 :: T_Group_1520 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_1558 T_Group_1520
v0
  = (T_IsSemigroup_472 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsSemigroup_472 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_assoc_482
      ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
         ((T_IsGroup_1036 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsGroup_1036 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_1050
            ((T_Group_1520 -> T_IsGroup_1036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Group_1520 -> T_IsGroup_1036
d_isGroup_1548 (T_Group_1520 -> AgdaAny
forall a b. a -> b
coe T_Group_1520
v0))))
-- Algebra.Bundles.Group._.identity
d_identity_1560 ::
  T_Group_1520 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_identity_1560 :: T_Group_1520 -> T_Σ_14
d_identity_1560 T_Group_1520
v0
  = (T_IsMonoid_686 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsMonoid_686 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_identity_698
      ((T_IsGroup_1036 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsGroup_1036 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_1050
         ((T_Group_1520 -> T_IsGroup_1036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Group_1520 -> T_IsGroup_1036
d_isGroup_1548 (T_Group_1520 -> AgdaAny
forall a b. a -> b
coe T_Group_1520
v0)))
-- Algebra.Bundles.Group._.identityʳ
d_identity'691'_1562 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Group_1520 -> AgdaAny -> AgdaAny
d_identity'691'_1562 :: () -> () -> T_Group_1520 -> AgdaAny -> AgdaAny
d_identity'691'_1562 ~()
v0 ~()
v1 T_Group_1520
v2 = T_Group_1520 -> AgdaAny -> AgdaAny
du_identity'691'_1562 T_Group_1520
v2
du_identity'691'_1562 :: T_Group_1520 -> AgdaAny -> AgdaAny
du_identity'691'_1562 :: T_Group_1520 -> AgdaAny -> AgdaAny
du_identity'691'_1562 T_Group_1520
v0
  = let v1 :: T_IsGroup_1036
v1 = T_Group_1520 -> T_IsGroup_1036
d_isGroup_1548 (T_Group_1520 -> T_Group_1520
forall a b. a -> b
coe T_Group_1520
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsMonoid_686 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoid_686 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_identity'691'_728
         ((T_IsGroup_1036 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1036 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_1050 (T_IsGroup_1036 -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1036
v1)))
-- Algebra.Bundles.Group._.identityˡ
d_identity'737'_1564 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Group_1520 -> AgdaAny -> AgdaAny
d_identity'737'_1564 :: () -> () -> T_Group_1520 -> AgdaAny -> AgdaAny
d_identity'737'_1564 ~()
v0 ~()
v1 T_Group_1520
v2 = T_Group_1520 -> AgdaAny -> AgdaAny
du_identity'737'_1564 T_Group_1520
v2
du_identity'737'_1564 :: T_Group_1520 -> AgdaAny -> AgdaAny
du_identity'737'_1564 :: T_Group_1520 -> AgdaAny -> AgdaAny
du_identity'737'_1564 T_Group_1520
v0
  = let v1 :: T_IsGroup_1036
v1 = T_Group_1520 -> T_IsGroup_1036
d_isGroup_1548 (T_Group_1520 -> T_Group_1520
forall a b. a -> b
coe T_Group_1520
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsMonoid_686 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoid_686 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_identity'737'_726
         ((T_IsGroup_1036 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1036 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_1050 (T_IsGroup_1036 -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1036
v1)))
-- Algebra.Bundles.Group._.inverse
d_inverse_1566 ::
  T_Group_1520 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_inverse_1566 :: T_Group_1520 -> T_Σ_14
d_inverse_1566 T_Group_1520
v0
  = (T_IsGroup_1036 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsGroup_1036 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_inverse_1052
      ((T_Group_1520 -> T_IsGroup_1036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Group_1520 -> T_IsGroup_1036
d_isGroup_1548 (T_Group_1520 -> AgdaAny
forall a b. a -> b
coe T_Group_1520
v0))
-- Algebra.Bundles.Group._.inverseʳ
d_inverse'691'_1568 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Group_1520 -> AgdaAny -> AgdaAny
d_inverse'691'_1568 :: () -> () -> T_Group_1520 -> AgdaAny -> AgdaAny
d_inverse'691'_1568 ~()
v0 ~()
v1 T_Group_1520
v2 = T_Group_1520 -> AgdaAny -> AgdaAny
du_inverse'691'_1568 T_Group_1520
v2
du_inverse'691'_1568 :: T_Group_1520 -> AgdaAny -> AgdaAny
du_inverse'691'_1568 :: T_Group_1520 -> AgdaAny -> AgdaAny
du_inverse'691'_1568 T_Group_1520
v0
  = (T_IsGroup_1036 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsGroup_1036 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_inverse'691'_1108
      ((T_Group_1520 -> T_IsGroup_1036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Group_1520 -> T_IsGroup_1036
d_isGroup_1548 (T_Group_1520 -> AgdaAny
forall a b. a -> b
coe T_Group_1520
v0))
-- Algebra.Bundles.Group._.inverseˡ
d_inverse'737'_1570 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Group_1520 -> AgdaAny -> AgdaAny
d_inverse'737'_1570 :: () -> () -> T_Group_1520 -> AgdaAny -> AgdaAny
d_inverse'737'_1570 ~()
v0 ~()
v1 T_Group_1520
v2 = T_Group_1520 -> AgdaAny -> AgdaAny
du_inverse'737'_1570 T_Group_1520
v2
du_inverse'737'_1570 :: T_Group_1520 -> AgdaAny -> AgdaAny
du_inverse'737'_1570 :: T_Group_1520 -> AgdaAny -> AgdaAny
du_inverse'737'_1570 T_Group_1520
v0
  = (T_IsGroup_1036 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsGroup_1036 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_inverse'737'_1106
      ((T_Group_1520 -> T_IsGroup_1036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Group_1520 -> T_IsGroup_1036
d_isGroup_1548 (T_Group_1520 -> AgdaAny
forall a b. a -> b
coe T_Group_1520
v0))
-- Algebra.Bundles.Group._.isEquivalence
d_isEquivalence_1572 ::
  T_Group_1520 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_1572 :: T_Group_1520 -> T_IsEquivalence_26
d_isEquivalence_1572 T_Group_1520
v0
  = (T_IsMagma_176 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
      ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480
         ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
            ((T_IsGroup_1036 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsGroup_1036 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_1050
               ((T_Group_1520 -> T_IsGroup_1036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Group_1520 -> T_IsGroup_1036
d_isGroup_1548 (T_Group_1520 -> AgdaAny
forall a b. a -> b
coe T_Group_1520
v0)))))
-- Algebra.Bundles.Group._.isInvertibleMagma
d_isInvertibleMagma_1574 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Group_1520 ->
  MAlonzo.Code.Algebra.Structures.T_IsInvertibleMagma_924
d_isInvertibleMagma_1574 :: () -> () -> T_Group_1520 -> T_IsInvertibleMagma_924
d_isInvertibleMagma_1574 ~()
v0 ~()
v1 T_Group_1520
v2 = T_Group_1520 -> T_IsInvertibleMagma_924
du_isInvertibleMagma_1574 T_Group_1520
v2
du_isInvertibleMagma_1574 ::
  T_Group_1520 ->
  MAlonzo.Code.Algebra.Structures.T_IsInvertibleMagma_924
du_isInvertibleMagma_1574 :: T_Group_1520 -> T_IsInvertibleMagma_924
du_isInvertibleMagma_1574 T_Group_1520
v0
  = (T_IsGroup_1036 -> T_IsInvertibleMagma_924)
-> AgdaAny -> T_IsInvertibleMagma_924
forall a b. a -> b
coe
      T_IsGroup_1036 -> T_IsInvertibleMagma_924
MAlonzo.Code.Algebra.Structures.du_isInvertibleMagma_1122
      ((T_Group_1520 -> T_IsGroup_1036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Group_1520 -> T_IsGroup_1036
d_isGroup_1548 (T_Group_1520 -> AgdaAny
forall a b. a -> b
coe T_Group_1520
v0))
-- Algebra.Bundles.Group._.isInvertibleUnitalMagma
d_isInvertibleUnitalMagma_1576 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Group_1520 ->
  MAlonzo.Code.Algebra.Structures.T_IsInvertibleUnitalMagma_976
d_isInvertibleUnitalMagma_1576 :: () -> () -> T_Group_1520 -> T_IsInvertibleUnitalMagma_976
d_isInvertibleUnitalMagma_1576 ~()
v0 ~()
v1 T_Group_1520
v2
  = T_Group_1520 -> T_IsInvertibleUnitalMagma_976
du_isInvertibleUnitalMagma_1576 T_Group_1520
v2
du_isInvertibleUnitalMagma_1576 ::
  T_Group_1520 ->
  MAlonzo.Code.Algebra.Structures.T_IsInvertibleUnitalMagma_976
du_isInvertibleUnitalMagma_1576 :: T_Group_1520 -> T_IsInvertibleUnitalMagma_976
du_isInvertibleUnitalMagma_1576 T_Group_1520
v0
  = (T_IsGroup_1036 -> T_IsInvertibleUnitalMagma_976)
-> AgdaAny -> T_IsInvertibleUnitalMagma_976
forall a b. a -> b
coe
      T_IsGroup_1036 -> T_IsInvertibleUnitalMagma_976
MAlonzo.Code.Algebra.Structures.du_isInvertibleUnitalMagma_1124
      ((T_Group_1520 -> T_IsGroup_1036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Group_1520 -> T_IsGroup_1036
d_isGroup_1548 (T_Group_1520 -> AgdaAny
forall a b. a -> b
coe T_Group_1520
v0))
-- Algebra.Bundles.Group._.isMagma
d_isMagma_1578 ::
  T_Group_1520 -> MAlonzo.Code.Algebra.Structures.T_IsMagma_176
d_isMagma_1578 :: T_Group_1520 -> T_IsMagma_176
d_isMagma_1578 T_Group_1520
v0
  = (T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> T_IsMagma_176
forall a b. a -> b
coe
      T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480
      ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
         ((T_IsGroup_1036 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsGroup_1036 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_1050
            ((T_Group_1520 -> T_IsGroup_1036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Group_1520 -> T_IsGroup_1036
d_isGroup_1548 (T_Group_1520 -> AgdaAny
forall a b. a -> b
coe T_Group_1520
v0))))
-- Algebra.Bundles.Group._.isMonoid
d_isMonoid_1580 ::
  T_Group_1520 -> MAlonzo.Code.Algebra.Structures.T_IsMonoid_686
d_isMonoid_1580 :: T_Group_1520 -> T_IsMonoid_686
d_isMonoid_1580 T_Group_1520
v0
  = (T_IsGroup_1036 -> T_IsMonoid_686) -> AgdaAny -> T_IsMonoid_686
forall a b. a -> b
coe
      T_IsGroup_1036 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_1050
      ((T_Group_1520 -> T_IsGroup_1036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Group_1520 -> T_IsGroup_1036
d_isGroup_1548 (T_Group_1520 -> AgdaAny
forall a b. a -> b
coe T_Group_1520
v0))
-- Algebra.Bundles.Group._.isPartialEquivalence
d_isPartialEquivalence_1582 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Group_1520 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_1582 :: () -> () -> T_Group_1520 -> T_IsPartialEquivalence_16
d_isPartialEquivalence_1582 ~()
v0 ~()
v1 T_Group_1520
v2
  = T_Group_1520 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_1582 T_Group_1520
v2
du_isPartialEquivalence_1582 ::
  T_Group_1520 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_1582 :: T_Group_1520 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_1582 T_Group_1520
v0
  = let v1 :: T_IsGroup_1036
v1 = T_Group_1520 -> T_IsGroup_1036
d_isGroup_1548 (T_Group_1520 -> T_Group_1520
forall a b. a -> b
coe T_Group_1520
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsMonoid_686
v2
             = T_IsGroup_1036 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_1050 (T_IsGroup_1036 -> T_IsGroup_1036
forall a b. a -> b
coe T_IsGroup_1036
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_472
v3
                = T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsMagma_176
v4 = T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (T_IsSemigroup_472 -> T_IsSemigroup_472
forall a b. a -> b
coe T_IsSemigroup_472
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               ((T_IsEquivalence_26 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsEquivalence_26 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
                  ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v4))))))
-- Algebra.Bundles.Group._.isSemigroup
d_isSemigroup_1584 ::
  T_Group_1520 -> MAlonzo.Code.Algebra.Structures.T_IsSemigroup_472
d_isSemigroup_1584 :: T_Group_1520 -> T_IsSemigroup_472
d_isSemigroup_1584 T_Group_1520
v0
  = (T_IsMonoid_686 -> T_IsSemigroup_472)
-> AgdaAny -> T_IsSemigroup_472
forall a b. a -> b
coe
      T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
      ((T_IsGroup_1036 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsGroup_1036 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_1050
         ((T_Group_1520 -> T_IsGroup_1036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Group_1520 -> T_IsGroup_1036
d_isGroup_1548 (T_Group_1520 -> AgdaAny
forall a b. a -> b
coe T_Group_1520
v0)))
-- Algebra.Bundles.Group._.isUnitalMagma
d_isUnitalMagma_1586 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Group_1520 -> MAlonzo.Code.Algebra.Structures.T_IsUnitalMagma_642
d_isUnitalMagma_1586 :: () -> () -> T_Group_1520 -> T_IsUnitalMagma_642
d_isUnitalMagma_1586 ~()
v0 ~()
v1 T_Group_1520
v2 = T_Group_1520 -> T_IsUnitalMagma_642
du_isUnitalMagma_1586 T_Group_1520
v2
du_isUnitalMagma_1586 ::
  T_Group_1520 -> MAlonzo.Code.Algebra.Structures.T_IsUnitalMagma_642
du_isUnitalMagma_1586 :: T_Group_1520 -> T_IsUnitalMagma_642
du_isUnitalMagma_1586 T_Group_1520
v0
  = let v1 :: T_IsGroup_1036
v1 = T_Group_1520 -> T_IsGroup_1036
d_isGroup_1548 (T_Group_1520 -> T_Group_1520
forall a b. a -> b
coe T_Group_1520
v0) in
    AgdaAny -> T_IsUnitalMagma_642
forall a b. a -> b
coe
      ((T_IsMonoid_686 -> T_IsUnitalMagma_642) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoid_686 -> T_IsUnitalMagma_642
MAlonzo.Code.Algebra.Structures.du_isUnitalMagma_730
         ((T_IsGroup_1036 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1036 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_1050 (T_IsGroup_1036 -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1036
v1)))
-- Algebra.Bundles.Group._.refl
d_refl_1588 :: T_Group_1520 -> AgdaAny -> AgdaAny
d_refl_1588 :: T_Group_1520 -> AgdaAny -> AgdaAny
d_refl_1588 T_Group_1520
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_34
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
         ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480
            ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
               ((T_IsGroup_1036 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsGroup_1036 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_1050
                  ((T_Group_1520 -> T_IsGroup_1036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Group_1520 -> T_IsGroup_1036
d_isGroup_1548 (T_Group_1520 -> AgdaAny
forall a b. a -> b
coe T_Group_1520
v0))))))
-- Algebra.Bundles.Group._.reflexive
d_reflexive_1590 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Group_1520 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_1590 :: ()
-> ()
-> T_Group_1520
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_1590 ~()
v0 ~()
v1 T_Group_1520
v2 = T_Group_1520 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_1590 T_Group_1520
v2
du_reflexive_1590 ::
  T_Group_1520 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_1590 :: T_Group_1520 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_1590 T_Group_1520
v0
  = let v1 :: T_IsGroup_1036
v1 = T_Group_1520 -> T_IsGroup_1036
d_isGroup_1548 (T_Group_1520 -> T_Group_1520
forall a b. a -> b
coe T_Group_1520
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsMonoid_686
v2
             = T_IsGroup_1036 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_1050 (T_IsGroup_1036 -> T_IsGroup_1036
forall a b. a -> b
coe T_IsGroup_1036
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_472
v3
                = T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsMagma_176
v4 = T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (T_IsSemigroup_472 -> T_IsSemigroup_472
forall a b. a -> b
coe T_IsSemigroup_472
v3) in
             (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
               (\ AgdaAny
v5 AgdaAny
v6 AgdaAny
v7 ->
                  (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                    T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
                    ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v4))
                    AgdaAny
v5))))
-- Algebra.Bundles.Group._.setoid
d_setoid_1592 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Group_1520 -> MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_1592 :: () -> () -> T_Group_1520 -> T_Setoid_44
d_setoid_1592 ~()
v0 ~()
v1 T_Group_1520
v2 = T_Group_1520 -> T_Setoid_44
du_setoid_1592 T_Group_1520
v2
du_setoid_1592 ::
  T_Group_1520 -> MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_1592 :: T_Group_1520 -> T_Setoid_44
du_setoid_1592 T_Group_1520
v0
  = let v1 :: T_IsGroup_1036
v1 = T_Group_1520 -> T_IsGroup_1036
d_isGroup_1548 (T_Group_1520 -> T_Group_1520
forall a b. a -> b
coe T_Group_1520
v0) in
    AgdaAny -> T_Setoid_44
forall a b. a -> b
coe
      (let v2 :: T_IsMonoid_686
v2
             = T_IsGroup_1036 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_1050 (T_IsGroup_1036 -> T_IsGroup_1036
forall a b. a -> b
coe T_IsGroup_1036
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_472
v3
                = T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsMagma_176 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMagma_176 -> T_Setoid_44
MAlonzo.Code.Algebra.Structures.du_setoid_200
               ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v3)))))
-- Algebra.Bundles.Group._.sym
d_sym_1594 ::
  T_Group_1520 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_1594 :: T_Group_1520 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_1594 T_Group_1520
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_36
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
         ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480
            ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
               ((T_IsGroup_1036 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsGroup_1036 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_1050
                  ((T_Group_1520 -> T_IsGroup_1036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Group_1520 -> T_IsGroup_1036
d_isGroup_1548 (T_Group_1520 -> AgdaAny
forall a b. a -> b
coe T_Group_1520
v0))))))
-- Algebra.Bundles.Group._.trans
d_trans_1596 ::
  T_Group_1520 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_1596 :: T_Group_1520
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_1596 T_Group_1520
v0
  = (T_IsEquivalence_26
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_38
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
         ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480
            ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
               ((T_IsGroup_1036 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsGroup_1036 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_1050
                  ((T_Group_1520 -> T_IsGroup_1036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Group_1520 -> T_IsGroup_1036
d_isGroup_1548 (T_Group_1520 -> AgdaAny
forall a b. a -> b
coe T_Group_1520
v0))))))
-- Algebra.Bundles.Group._.uniqueʳ-⁻¹
d_unique'691''45''8315''185'_1598 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Group_1520 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_unique'691''45''8315''185'_1598 :: ()
-> () -> T_Group_1520 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_unique'691''45''8315''185'_1598 ~()
v0 ~()
v1 T_Group_1520
v2
  = T_Group_1520 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_unique'691''45''8315''185'_1598 T_Group_1520
v2
du_unique'691''45''8315''185'_1598 ::
  T_Group_1520 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_unique'691''45''8315''185'_1598 :: T_Group_1520 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_unique'691''45''8315''185'_1598 T_Group_1520
v0
  = ((AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> (AgdaAny -> AgdaAny)
 -> T_IsGroup_1036
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsGroup_1036
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.du_unique'691''45''8315''185'_1120
      ((T_Group_1520 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Group_1520 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__1542 (T_Group_1520 -> AgdaAny
forall a b. a -> b
coe T_Group_1520
v0)) ((T_Group_1520 -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Group_1520 -> AgdaAny
d_ε_1544 (T_Group_1520 -> AgdaAny
forall a b. a -> b
coe T_Group_1520
v0))
      ((T_Group_1520 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Group_1520 -> AgdaAny -> AgdaAny
d__'8315''185'_1546 (T_Group_1520 -> AgdaAny
forall a b. a -> b
coe T_Group_1520
v0)) ((T_Group_1520 -> T_IsGroup_1036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Group_1520 -> T_IsGroup_1036
d_isGroup_1548 (T_Group_1520 -> AgdaAny
forall a b. a -> b
coe T_Group_1520
v0))
-- Algebra.Bundles.Group._.uniqueˡ-⁻¹
d_unique'737''45''8315''185'_1600 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Group_1520 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_unique'737''45''8315''185'_1600 :: ()
-> () -> T_Group_1520 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_unique'737''45''8315''185'_1600 ~()
v0 ~()
v1 T_Group_1520
v2
  = T_Group_1520 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_unique'737''45''8315''185'_1600 T_Group_1520
v2
du_unique'737''45''8315''185'_1600 ::
  T_Group_1520 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_unique'737''45''8315''185'_1600 :: T_Group_1520 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_unique'737''45''8315''185'_1600 T_Group_1520
v0
  = ((AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> (AgdaAny -> AgdaAny)
 -> T_IsGroup_1036
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsGroup_1036
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.du_unique'737''45''8315''185'_1114
      ((T_Group_1520 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Group_1520 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__1542 (T_Group_1520 -> AgdaAny
forall a b. a -> b
coe T_Group_1520
v0)) ((T_Group_1520 -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Group_1520 -> AgdaAny
d_ε_1544 (T_Group_1520 -> AgdaAny
forall a b. a -> b
coe T_Group_1520
v0))
      ((T_Group_1520 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Group_1520 -> AgdaAny -> AgdaAny
d__'8315''185'_1546 (T_Group_1520 -> AgdaAny
forall a b. a -> b
coe T_Group_1520
v0)) ((T_Group_1520 -> T_IsGroup_1036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Group_1520 -> T_IsGroup_1036
d_isGroup_1548 (T_Group_1520 -> AgdaAny
forall a b. a -> b
coe T_Group_1520
v0))
-- Algebra.Bundles.Group._.⁻¹-cong
d_'8315''185''45'cong_1602 ::
  T_Group_1520 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8315''185''45'cong_1602 :: T_Group_1520 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8315''185''45'cong_1602 T_Group_1520
v0
  = (T_IsGroup_1036 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsGroup_1036 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8315''185''45'cong_1054
      ((T_Group_1520 -> T_IsGroup_1036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Group_1520 -> T_IsGroup_1036
d_isGroup_1548 (T_Group_1520 -> AgdaAny
forall a b. a -> b
coe T_Group_1520
v0))
-- Algebra.Bundles.Group._.∙-cong
d_'8729''45'cong_1604 ::
  T_Group_1520 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_1604 :: T_Group_1520
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_1604 T_Group_1520
v0
  = (T_IsMagma_176
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsMagma_176
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_186
      ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480
         ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
            ((T_IsGroup_1036 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsGroup_1036 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_1050
               ((T_Group_1520 -> T_IsGroup_1036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Group_1520 -> T_IsGroup_1036
d_isGroup_1548 (T_Group_1520 -> AgdaAny
forall a b. a -> b
coe T_Group_1520
v0)))))
-- Algebra.Bundles.Group._.∙-congʳ
d_'8729''45'cong'691'_1606 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Group_1520 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_1606 :: ()
-> ()
-> T_Group_1520
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_1606 ~()
v0 ~()
v1 T_Group_1520
v2
  = T_Group_1520 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1606 T_Group_1520
v2
du_'8729''45'cong'691'_1606 ::
  T_Group_1520 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1606 :: T_Group_1520 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1606 T_Group_1520
v0
  = let v1 :: T_IsGroup_1036
v1 = T_Group_1520 -> T_IsGroup_1036
d_isGroup_1548 (T_Group_1520 -> T_Group_1520
forall a b. a -> b
coe T_Group_1520
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsMonoid_686
v2
             = T_IsGroup_1036 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_1050 (T_IsGroup_1036 -> T_IsGroup_1036
forall a b. a -> b
coe T_IsGroup_1036
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_472
v3
                = T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'691'_206
               ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v3)))))
-- Algebra.Bundles.Group._.∙-congˡ
d_'8729''45'cong'737'_1608 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Group_1520 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_1608 :: ()
-> ()
-> T_Group_1520
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_1608 ~()
v0 ~()
v1 T_Group_1520
v2
  = T_Group_1520 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1608 T_Group_1520
v2
du_'8729''45'cong'737'_1608 ::
  T_Group_1520 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1608 :: T_Group_1520 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1608 T_Group_1520
v0
  = let v1 :: T_IsGroup_1036
v1 = T_Group_1520 -> T_IsGroup_1036
d_isGroup_1548 (T_Group_1520 -> T_Group_1520
forall a b. a -> b
coe T_Group_1520
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsMonoid_686
v2
             = T_IsGroup_1036 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_1050 (T_IsGroup_1036 -> T_IsGroup_1036
forall a b. a -> b
coe T_IsGroup_1036
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_472
v3
                = T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'737'_202
               ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v3)))))
-- Algebra.Bundles.Group.rawGroup
d_rawGroup_1610 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Group_1520 -> MAlonzo.Code.Algebra.Bundles.Raw.T_RawGroup_96
d_rawGroup_1610 :: () -> () -> T_Group_1520 -> T_RawGroup_96
d_rawGroup_1610 ~()
v0 ~()
v1 T_Group_1520
v2 = T_Group_1520 -> T_RawGroup_96
du_rawGroup_1610 T_Group_1520
v2
du_rawGroup_1610 ::
  T_Group_1520 -> MAlonzo.Code.Algebra.Bundles.Raw.T_RawGroup_96
du_rawGroup_1610 :: T_Group_1520 -> T_RawGroup_96
du_rawGroup_1610 T_Group_1520
v0
  = ((AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny -> (AgdaAny -> AgdaAny) -> T_RawGroup_96)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_RawGroup_96
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> (AgdaAny -> AgdaAny) -> T_RawGroup_96
MAlonzo.Code.Algebra.Bundles.Raw.C_RawGroup'46'constructor_1207
      (T_Group_1520 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__1542 (T_Group_1520 -> T_Group_1520
forall a b. a -> b
coe T_Group_1520
v0)) (T_Group_1520 -> AgdaAny
d_ε_1544 (T_Group_1520 -> T_Group_1520
forall a b. a -> b
coe T_Group_1520
v0))
      (T_Group_1520 -> AgdaAny -> AgdaAny
d__'8315''185'_1546 (T_Group_1520 -> T_Group_1520
forall a b. a -> b
coe T_Group_1520
v0))
-- Algebra.Bundles.Group.monoid
d_monoid_1612 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Group_1520 -> T_Monoid_882
d_monoid_1612 :: () -> () -> T_Group_1520 -> T_Monoid_882
d_monoid_1612 ~()
v0 ~()
v1 T_Group_1520
v2 = T_Group_1520 -> T_Monoid_882
du_monoid_1612 T_Group_1520
v2
du_monoid_1612 :: T_Group_1520 -> T_Monoid_882
du_monoid_1612 :: T_Group_1520 -> T_Monoid_882
du_monoid_1612 T_Group_1520
v0
  = ((AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny -> T_IsMonoid_686 -> T_Monoid_882)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsMonoid_686
-> T_Monoid_882
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> T_IsMonoid_686 -> T_Monoid_882
C_Monoid'46'constructor_16157 (T_Group_1520 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__1542 (T_Group_1520 -> T_Group_1520
forall a b. a -> b
coe T_Group_1520
v0))
      (T_Group_1520 -> AgdaAny
d_ε_1544 (T_Group_1520 -> T_Group_1520
forall a b. a -> b
coe T_Group_1520
v0))
      (T_IsGroup_1036 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_1050
         ((T_Group_1520 -> T_IsGroup_1036) -> AgdaAny -> T_IsGroup_1036
forall a b. a -> b
coe T_Group_1520 -> T_IsGroup_1036
d_isGroup_1548 (T_Group_1520 -> AgdaAny
forall a b. a -> b
coe T_Group_1520
v0)))
-- Algebra.Bundles.Group._._≉_
d__'8777'__1616 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Group_1520 -> AgdaAny -> AgdaAny -> ()
d__'8777'__1616 :: () -> () -> T_Group_1520 -> AgdaAny -> AgdaAny -> ()
d__'8777'__1616 = () -> () -> T_Group_1520 -> AgdaAny -> AgdaAny -> ()
forall a. a
erased
-- Algebra.Bundles.Group._.magma
d_magma_1618 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Group_1520 -> T_Magma_68
d_magma_1618 :: () -> () -> T_Group_1520 -> T_Magma_68
d_magma_1618 ~()
v0 ~()
v1 T_Group_1520
v2 = T_Group_1520 -> T_Magma_68
du_magma_1618 T_Group_1520
v2
du_magma_1618 :: T_Group_1520 -> T_Magma_68
du_magma_1618 :: T_Group_1520 -> T_Magma_68
du_magma_1618 T_Group_1520
v0
  = let v1 :: t
v1 = (T_Group_1520 -> T_Monoid_882) -> AgdaAny -> t
forall a b. a -> b
coe T_Group_1520 -> T_Monoid_882
du_monoid_1612 (T_Group_1520 -> AgdaAny
forall a b. a -> b
coe T_Group_1520
v0) in
    AgdaAny -> T_Magma_68
forall a b. a -> b
coe ((T_Semigroup_536 -> T_Magma_68) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semigroup_536 -> T_Magma_68
du_magma_584 ((T_Monoid_882 -> T_Semigroup_536) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Monoid_882 -> T_Semigroup_536
du_semigroup_944 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1)))
-- Algebra.Bundles.Group._.rawMagma
d_rawMagma_1620 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Group_1520 -> MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
d_rawMagma_1620 :: () -> () -> T_Group_1520 -> T_RawMagma_36
d_rawMagma_1620 ~()
v0 ~()
v1 T_Group_1520
v2 = T_Group_1520 -> T_RawMagma_36
du_rawMagma_1620 T_Group_1520
v2
du_rawMagma_1620 ::
  T_Group_1520 -> MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
du_rawMagma_1620 :: T_Group_1520 -> T_RawMagma_36
du_rawMagma_1620 T_Group_1520
v0
  = let v1 :: t
v1 = (T_Group_1520 -> T_Monoid_882) -> AgdaAny -> t
forall a b. a -> b
coe T_Group_1520 -> T_Monoid_882
du_monoid_1612 (T_Group_1520 -> AgdaAny
forall a b. a -> b
coe T_Group_1520
v0) in
    AgdaAny -> T_RawMagma_36
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_Monoid_882 -> T_Semigroup_536) -> AgdaAny -> t
forall a b. a -> b
coe T_Monoid_882 -> T_Semigroup_536
du_semigroup_944 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_Magma_68 -> T_RawMagma_36) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Magma_68 -> T_RawMagma_36
du_rawMagma_112 ((T_Semigroup_536 -> T_Magma_68) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semigroup_536 -> T_Magma_68
du_magma_584 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2))))
-- Algebra.Bundles.Group._.rawMonoid
d_rawMonoid_1622 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Group_1520 -> MAlonzo.Code.Algebra.Bundles.Raw.T_RawMonoid_64
d_rawMonoid_1622 :: () -> () -> T_Group_1520 -> T_RawMonoid_64
d_rawMonoid_1622 ~()
v0 ~()
v1 T_Group_1520
v2 = T_Group_1520 -> T_RawMonoid_64
du_rawMonoid_1622 T_Group_1520
v2
du_rawMonoid_1622 ::
  T_Group_1520 -> MAlonzo.Code.Algebra.Bundles.Raw.T_RawMonoid_64
du_rawMonoid_1622 :: T_Group_1520 -> T_RawMonoid_64
du_rawMonoid_1622 T_Group_1520
v0
  = (T_Monoid_882 -> T_RawMonoid_64) -> AgdaAny -> T_RawMonoid_64
forall a b. a -> b
coe T_Monoid_882 -> T_RawMonoid_64
du_rawMonoid_954 ((T_Group_1520 -> T_Monoid_882) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Group_1520 -> T_Monoid_882
du_monoid_1612 (T_Group_1520 -> AgdaAny
forall a b. a -> b
coe T_Group_1520
v0))
-- Algebra.Bundles.Group._.semigroup
d_semigroup_1624 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Group_1520 -> T_Semigroup_536
d_semigroup_1624 :: () -> () -> T_Group_1520 -> T_Semigroup_536
d_semigroup_1624 ~()
v0 ~()
v1 T_Group_1520
v2 = T_Group_1520 -> T_Semigroup_536
du_semigroup_1624 T_Group_1520
v2
du_semigroup_1624 :: T_Group_1520 -> T_Semigroup_536
du_semigroup_1624 :: T_Group_1520 -> T_Semigroup_536
du_semigroup_1624 T_Group_1520
v0
  = (T_Monoid_882 -> T_Semigroup_536) -> AgdaAny -> T_Semigroup_536
forall a b. a -> b
coe T_Monoid_882 -> T_Semigroup_536
du_semigroup_944 ((T_Group_1520 -> T_Monoid_882) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Group_1520 -> T_Monoid_882
du_monoid_1612 (T_Group_1520 -> AgdaAny
forall a b. a -> b
coe T_Group_1520
v0))
-- Algebra.Bundles.Group._.unitalMagma
d_unitalMagma_1626 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Group_1520 -> T_UnitalMagma_814
d_unitalMagma_1626 :: () -> () -> T_Group_1520 -> T_UnitalMagma_814
d_unitalMagma_1626 ~()
v0 ~()
v1 T_Group_1520
v2 = T_Group_1520 -> T_UnitalMagma_814
du_unitalMagma_1626 T_Group_1520
v2
du_unitalMagma_1626 :: T_Group_1520 -> T_UnitalMagma_814
du_unitalMagma_1626 :: T_Group_1520 -> T_UnitalMagma_814
du_unitalMagma_1626 T_Group_1520
v0
  = (T_Monoid_882 -> T_UnitalMagma_814) -> AgdaAny -> T_UnitalMagma_814
forall a b. a -> b
coe T_Monoid_882 -> T_UnitalMagma_814
du_unitalMagma_956 ((T_Group_1520 -> T_Monoid_882) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Group_1520 -> T_Monoid_882
du_monoid_1612 (T_Group_1520 -> AgdaAny
forall a b. a -> b
coe T_Group_1520
v0))
-- Algebra.Bundles.Group.invertibleMagma
d_invertibleMagma_1628 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Group_1520 -> T_InvertibleMagma_1360
d_invertibleMagma_1628 :: () -> () -> T_Group_1520 -> T_InvertibleMagma_1360
d_invertibleMagma_1628 ~()
v0 ~()
v1 T_Group_1520
v2 = T_Group_1520 -> T_InvertibleMagma_1360
du_invertibleMagma_1628 T_Group_1520
v2
du_invertibleMagma_1628 :: T_Group_1520 -> T_InvertibleMagma_1360
du_invertibleMagma_1628 :: T_Group_1520 -> T_InvertibleMagma_1360
du_invertibleMagma_1628 T_Group_1520
v0
  = ((AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> (AgdaAny -> AgdaAny)
 -> T_IsInvertibleMagma_924
 -> T_InvertibleMagma_1360)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> T_InvertibleMagma_1360
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsInvertibleMagma_924
-> T_InvertibleMagma_1360
C_InvertibleMagma'46'constructor_24127 (T_Group_1520 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__1542 (T_Group_1520 -> T_Group_1520
forall a b. a -> b
coe T_Group_1520
v0))
      (T_Group_1520 -> AgdaAny
d_ε_1544 (T_Group_1520 -> T_Group_1520
forall a b. a -> b
coe T_Group_1520
v0)) (T_Group_1520 -> AgdaAny -> AgdaAny
d__'8315''185'_1546 (T_Group_1520 -> T_Group_1520
forall a b. a -> b
coe T_Group_1520
v0))
      ((T_IsGroup_1036 -> T_IsInvertibleMagma_924) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsGroup_1036 -> T_IsInvertibleMagma_924
MAlonzo.Code.Algebra.Structures.du_isInvertibleMagma_1122
         ((T_Group_1520 -> T_IsGroup_1036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Group_1520 -> T_IsGroup_1036
d_isGroup_1548 (T_Group_1520 -> AgdaAny
forall a b. a -> b
coe T_Group_1520
v0)))
-- Algebra.Bundles.Group.invertibleUnitalMagma
d_invertibleUnitalMagma_1630 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Group_1520 -> T_InvertibleUnitalMagma_1434
d_invertibleUnitalMagma_1630 :: () -> () -> T_Group_1520 -> T_InvertibleUnitalMagma_1434
d_invertibleUnitalMagma_1630 ~()
v0 ~()
v1 T_Group_1520
v2
  = T_Group_1520 -> T_InvertibleUnitalMagma_1434
du_invertibleUnitalMagma_1630 T_Group_1520
v2
du_invertibleUnitalMagma_1630 ::
  T_Group_1520 -> T_InvertibleUnitalMagma_1434
du_invertibleUnitalMagma_1630 :: T_Group_1520 -> T_InvertibleUnitalMagma_1434
du_invertibleUnitalMagma_1630 T_Group_1520
v0
  = ((AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> (AgdaAny -> AgdaAny)
 -> T_IsInvertibleUnitalMagma_976
 -> T_InvertibleUnitalMagma_1434)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> T_InvertibleUnitalMagma_1434
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsInvertibleUnitalMagma_976
-> T_InvertibleUnitalMagma_1434
C_InvertibleUnitalMagma'46'constructor_25619
      (T_Group_1520 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__1542 (T_Group_1520 -> T_Group_1520
forall a b. a -> b
coe T_Group_1520
v0)) (T_Group_1520 -> AgdaAny
d_ε_1544 (T_Group_1520 -> T_Group_1520
forall a b. a -> b
coe T_Group_1520
v0))
      (T_Group_1520 -> AgdaAny -> AgdaAny
d__'8315''185'_1546 (T_Group_1520 -> T_Group_1520
forall a b. a -> b
coe T_Group_1520
v0))
      ((T_IsGroup_1036 -> T_IsInvertibleUnitalMagma_976)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsGroup_1036 -> T_IsInvertibleUnitalMagma_976
MAlonzo.Code.Algebra.Structures.du_isInvertibleUnitalMagma_1124
         ((T_Group_1520 -> T_IsGroup_1036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Group_1520 -> T_IsGroup_1036
d_isGroup_1548 (T_Group_1520 -> AgdaAny
forall a b. a -> b
coe T_Group_1520
v0)))
-- Algebra.Bundles.AbelianGroup
d_AbelianGroup_1636 :: p -> p -> ()
d_AbelianGroup_1636 p
a0 p
a1 = ()
data T_AbelianGroup_1636
  = C_AbelianGroup'46'constructor_29855 (AgdaAny ->
                                         AgdaAny -> AgdaAny)
                                        AgdaAny (AgdaAny -> AgdaAny)
                                        MAlonzo.Code.Algebra.Structures.T_IsAbelianGroup_1132
-- Algebra.Bundles.AbelianGroup.Carrier
d_Carrier_1654 :: T_AbelianGroup_1636 -> ()
d_Carrier_1654 :: T_AbelianGroup_1636 -> ()
d_Carrier_1654 = T_AbelianGroup_1636 -> ()
forall a. a
erased
-- Algebra.Bundles.AbelianGroup._≈_
d__'8776'__1656 :: T_AbelianGroup_1636 -> AgdaAny -> AgdaAny -> ()
d__'8776'__1656 :: T_AbelianGroup_1636 -> AgdaAny -> AgdaAny -> ()
d__'8776'__1656 = T_AbelianGroup_1636 -> AgdaAny -> AgdaAny -> ()
forall a. a
erased
-- Algebra.Bundles.AbelianGroup._∙_
d__'8729'__1658 ::
  T_AbelianGroup_1636 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__1658 :: T_AbelianGroup_1636 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__1658 T_AbelianGroup_1636
v0
  = case T_AbelianGroup_1636 -> T_AbelianGroup_1636
forall a b. a -> b
coe T_AbelianGroup_1636
v0 of
      C_AbelianGroup'46'constructor_29855 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny
v4 AgdaAny -> AgdaAny
v5 T_IsAbelianGroup_1132
v6 -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v3
      T_AbelianGroup_1636
_ -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.AbelianGroup.ε
d_ε_1660 :: T_AbelianGroup_1636 -> AgdaAny
d_ε_1660 :: T_AbelianGroup_1636 -> AgdaAny
d_ε_1660 T_AbelianGroup_1636
v0
  = case T_AbelianGroup_1636 -> T_AbelianGroup_1636
forall a b. a -> b
coe T_AbelianGroup_1636
v0 of
      C_AbelianGroup'46'constructor_29855 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny
v4 AgdaAny -> AgdaAny
v5 T_IsAbelianGroup_1132
v6 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v4
      T_AbelianGroup_1636
_ -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.AbelianGroup._⁻¹
d__'8315''185'_1662 :: T_AbelianGroup_1636 -> AgdaAny -> AgdaAny
d__'8315''185'_1662 :: T_AbelianGroup_1636 -> AgdaAny -> AgdaAny
d__'8315''185'_1662 T_AbelianGroup_1636
v0
  = case T_AbelianGroup_1636 -> T_AbelianGroup_1636
forall a b. a -> b
coe T_AbelianGroup_1636
v0 of
      C_AbelianGroup'46'constructor_29855 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny
v4 AgdaAny -> AgdaAny
v5 T_IsAbelianGroup_1132
v6 -> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v5
      T_AbelianGroup_1636
_ -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.AbelianGroup.isAbelianGroup
d_isAbelianGroup_1664 ::
  T_AbelianGroup_1636 ->
  MAlonzo.Code.Algebra.Structures.T_IsAbelianGroup_1132
d_isAbelianGroup_1664 :: T_AbelianGroup_1636 -> T_IsAbelianGroup_1132
d_isAbelianGroup_1664 T_AbelianGroup_1636
v0
  = case T_AbelianGroup_1636 -> T_AbelianGroup_1636
forall a b. a -> b
coe T_AbelianGroup_1636
v0 of
      C_AbelianGroup'46'constructor_29855 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny
v4 AgdaAny -> AgdaAny
v5 T_IsAbelianGroup_1132
v6 -> T_IsAbelianGroup_1132 -> T_IsAbelianGroup_1132
forall a b. a -> b
coe T_IsAbelianGroup_1132
v6
      T_AbelianGroup_1636
_ -> T_IsAbelianGroup_1132
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.AbelianGroup._._//_
d__'47''47'__1668 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_AbelianGroup_1636 -> AgdaAny -> AgdaAny -> AgdaAny
d__'47''47'__1668 :: () -> () -> T_AbelianGroup_1636 -> AgdaAny -> AgdaAny -> AgdaAny
d__'47''47'__1668 ~()
v0 ~()
v1 T_AbelianGroup_1636
v2 = T_AbelianGroup_1636 -> AgdaAny -> AgdaAny -> AgdaAny
du__'47''47'__1668 T_AbelianGroup_1636
v2
du__'47''47'__1668 ::
  T_AbelianGroup_1636 -> AgdaAny -> AgdaAny -> AgdaAny
du__'47''47'__1668 :: T_AbelianGroup_1636 -> AgdaAny -> AgdaAny -> AgdaAny
du__'47''47'__1668 T_AbelianGroup_1636
v0
  = let v1 :: AgdaAny -> AgdaAny -> AgdaAny
v1 = T_AbelianGroup_1636 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__1658 (T_AbelianGroup_1636 -> T_AbelianGroup_1636
forall a b. a -> b
coe T_AbelianGroup_1636
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: AgdaAny -> AgdaAny
v2 = T_AbelianGroup_1636 -> AgdaAny -> AgdaAny
d__'8315''185'_1662 (T_AbelianGroup_1636 -> T_AbelianGroup_1636
forall a b. a -> b
coe T_AbelianGroup_1636
v0) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (((AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du__'47''47'__1098 ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v1)
            ((AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v2)))
-- Algebra.Bundles.AbelianGroup._.assoc
d_assoc_1670 ::
  T_AbelianGroup_1636 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_1670 :: T_AbelianGroup_1636 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_1670 T_AbelianGroup_1636
v0
  = (T_IsSemigroup_472 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsSemigroup_472 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_assoc_482
      ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
         ((T_IsGroup_1036 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsGroup_1036 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_1050
            ((T_IsAbelianGroup_1132 -> T_IsGroup_1036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsAbelianGroup_1132 -> T_IsGroup_1036
MAlonzo.Code.Algebra.Structures.d_isGroup_1144
               ((T_AbelianGroup_1636 -> T_IsAbelianGroup_1132)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_AbelianGroup_1636 -> T_IsAbelianGroup_1132
d_isAbelianGroup_1664 (T_AbelianGroup_1636 -> AgdaAny
forall a b. a -> b
coe T_AbelianGroup_1636
v0)))))
-- Algebra.Bundles.AbelianGroup._.comm
d_comm_1672 :: T_AbelianGroup_1636 -> AgdaAny -> AgdaAny -> AgdaAny
d_comm_1672 :: T_AbelianGroup_1636 -> AgdaAny -> AgdaAny -> AgdaAny
d_comm_1672 T_AbelianGroup_1636
v0
  = (T_IsAbelianGroup_1132 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsAbelianGroup_1132 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_comm_1146
      ((T_AbelianGroup_1636 -> T_IsAbelianGroup_1132)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_AbelianGroup_1636 -> T_IsAbelianGroup_1132
d_isAbelianGroup_1664 (T_AbelianGroup_1636 -> AgdaAny
forall a b. a -> b
coe T_AbelianGroup_1636
v0))
-- Algebra.Bundles.AbelianGroup._.identity
d_identity_1674 ::
  T_AbelianGroup_1636 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_identity_1674 :: T_AbelianGroup_1636 -> T_Σ_14
d_identity_1674 T_AbelianGroup_1636
v0
  = (T_IsMonoid_686 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsMonoid_686 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_identity_698
      ((T_IsGroup_1036 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsGroup_1036 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_1050
         ((T_IsAbelianGroup_1132 -> T_IsGroup_1036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsAbelianGroup_1132 -> T_IsGroup_1036
MAlonzo.Code.Algebra.Structures.d_isGroup_1144
            ((T_AbelianGroup_1636 -> T_IsAbelianGroup_1132)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_AbelianGroup_1636 -> T_IsAbelianGroup_1132
d_isAbelianGroup_1664 (T_AbelianGroup_1636 -> AgdaAny
forall a b. a -> b
coe T_AbelianGroup_1636
v0))))
-- Algebra.Bundles.AbelianGroup._.identityʳ
d_identity'691'_1676 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_AbelianGroup_1636 -> AgdaAny -> AgdaAny
d_identity'691'_1676 :: () -> () -> T_AbelianGroup_1636 -> AgdaAny -> AgdaAny
d_identity'691'_1676 ~()
v0 ~()
v1 T_AbelianGroup_1636
v2 = T_AbelianGroup_1636 -> AgdaAny -> AgdaAny
du_identity'691'_1676 T_AbelianGroup_1636
v2
du_identity'691'_1676 :: T_AbelianGroup_1636 -> AgdaAny -> AgdaAny
du_identity'691'_1676 :: T_AbelianGroup_1636 -> AgdaAny -> AgdaAny
du_identity'691'_1676 T_AbelianGroup_1636
v0
  = let v1 :: T_IsAbelianGroup_1132
v1 = T_AbelianGroup_1636 -> T_IsAbelianGroup_1132
d_isAbelianGroup_1664 (T_AbelianGroup_1636 -> T_AbelianGroup_1636
forall a b. a -> b
coe T_AbelianGroup_1636
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsGroup_1036
v2
             = T_IsAbelianGroup_1132 -> T_IsGroup_1036
MAlonzo.Code.Algebra.Structures.d_isGroup_1144 (T_IsAbelianGroup_1132 -> T_IsAbelianGroup_1132
forall a b. a -> b
coe T_IsAbelianGroup_1132
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsMonoid_686 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoid_686 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_identity'691'_728
            ((T_IsGroup_1036 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1036 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_1050 (T_IsGroup_1036 -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1036
v2))))
-- Algebra.Bundles.AbelianGroup._.identityˡ
d_identity'737'_1678 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_AbelianGroup_1636 -> AgdaAny -> AgdaAny
d_identity'737'_1678 :: () -> () -> T_AbelianGroup_1636 -> AgdaAny -> AgdaAny
d_identity'737'_1678 ~()
v0 ~()
v1 T_AbelianGroup_1636
v2 = T_AbelianGroup_1636 -> AgdaAny -> AgdaAny
du_identity'737'_1678 T_AbelianGroup_1636
v2
du_identity'737'_1678 :: T_AbelianGroup_1636 -> AgdaAny -> AgdaAny
du_identity'737'_1678 :: T_AbelianGroup_1636 -> AgdaAny -> AgdaAny
du_identity'737'_1678 T_AbelianGroup_1636
v0
  = let v1 :: T_IsAbelianGroup_1132
v1 = T_AbelianGroup_1636 -> T_IsAbelianGroup_1132
d_isAbelianGroup_1664 (T_AbelianGroup_1636 -> T_AbelianGroup_1636
forall a b. a -> b
coe T_AbelianGroup_1636
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsGroup_1036
v2
             = T_IsAbelianGroup_1132 -> T_IsGroup_1036
MAlonzo.Code.Algebra.Structures.d_isGroup_1144 (T_IsAbelianGroup_1132 -> T_IsAbelianGroup_1132
forall a b. a -> b
coe T_IsAbelianGroup_1132
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsMonoid_686 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoid_686 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_identity'737'_726
            ((T_IsGroup_1036 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1036 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_1050 (T_IsGroup_1036 -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1036
v2))))
-- Algebra.Bundles.AbelianGroup._.inverse
d_inverse_1680 ::
  T_AbelianGroup_1636 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_inverse_1680 :: T_AbelianGroup_1636 -> T_Σ_14
d_inverse_1680 T_AbelianGroup_1636
v0
  = (T_IsGroup_1036 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsGroup_1036 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_inverse_1052
      ((T_IsAbelianGroup_1132 -> T_IsGroup_1036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsAbelianGroup_1132 -> T_IsGroup_1036
MAlonzo.Code.Algebra.Structures.d_isGroup_1144
         ((T_AbelianGroup_1636 -> T_IsAbelianGroup_1132)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_AbelianGroup_1636 -> T_IsAbelianGroup_1132
d_isAbelianGroup_1664 (T_AbelianGroup_1636 -> AgdaAny
forall a b. a -> b
coe T_AbelianGroup_1636
v0)))
-- Algebra.Bundles.AbelianGroup._.inverseʳ
d_inverse'691'_1682 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_AbelianGroup_1636 -> AgdaAny -> AgdaAny
d_inverse'691'_1682 :: () -> () -> T_AbelianGroup_1636 -> AgdaAny -> AgdaAny
d_inverse'691'_1682 ~()
v0 ~()
v1 T_AbelianGroup_1636
v2 = T_AbelianGroup_1636 -> AgdaAny -> AgdaAny
du_inverse'691'_1682 T_AbelianGroup_1636
v2
du_inverse'691'_1682 :: T_AbelianGroup_1636 -> AgdaAny -> AgdaAny
du_inverse'691'_1682 :: T_AbelianGroup_1636 -> AgdaAny -> AgdaAny
du_inverse'691'_1682 T_AbelianGroup_1636
v0
  = let v1 :: T_IsAbelianGroup_1132
v1 = T_AbelianGroup_1636 -> T_IsAbelianGroup_1132
d_isAbelianGroup_1664 (T_AbelianGroup_1636 -> T_AbelianGroup_1636
forall a b. a -> b
coe T_AbelianGroup_1636
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsGroup_1036 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsGroup_1036 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_inverse'691'_1108
         ((T_IsAbelianGroup_1132 -> T_IsGroup_1036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132 -> T_IsGroup_1036
MAlonzo.Code.Algebra.Structures.d_isGroup_1144 (T_IsAbelianGroup_1132 -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132
v1)))
-- Algebra.Bundles.AbelianGroup._.inverseˡ
d_inverse'737'_1684 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_AbelianGroup_1636 -> AgdaAny -> AgdaAny
d_inverse'737'_1684 :: () -> () -> T_AbelianGroup_1636 -> AgdaAny -> AgdaAny
d_inverse'737'_1684 ~()
v0 ~()
v1 T_AbelianGroup_1636
v2 = T_AbelianGroup_1636 -> AgdaAny -> AgdaAny
du_inverse'737'_1684 T_AbelianGroup_1636
v2
du_inverse'737'_1684 :: T_AbelianGroup_1636 -> AgdaAny -> AgdaAny
du_inverse'737'_1684 :: T_AbelianGroup_1636 -> AgdaAny -> AgdaAny
du_inverse'737'_1684 T_AbelianGroup_1636
v0
  = let v1 :: T_IsAbelianGroup_1132
v1 = T_AbelianGroup_1636 -> T_IsAbelianGroup_1132
d_isAbelianGroup_1664 (T_AbelianGroup_1636 -> T_AbelianGroup_1636
forall a b. a -> b
coe T_AbelianGroup_1636
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsGroup_1036 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsGroup_1036 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_inverse'737'_1106
         ((T_IsAbelianGroup_1132 -> T_IsGroup_1036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132 -> T_IsGroup_1036
MAlonzo.Code.Algebra.Structures.d_isGroup_1144 (T_IsAbelianGroup_1132 -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132
v1)))
-- Algebra.Bundles.AbelianGroup._.isCommutativeMagma
d_isCommutativeMagma_1686 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_AbelianGroup_1636 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMagma_212
d_isCommutativeMagma_1686 :: () -> () -> T_AbelianGroup_1636 -> T_IsCommutativeMagma_212
d_isCommutativeMagma_1686 ~()
v0 ~()
v1 T_AbelianGroup_1636
v2
  = T_AbelianGroup_1636 -> T_IsCommutativeMagma_212
du_isCommutativeMagma_1686 T_AbelianGroup_1636
v2
du_isCommutativeMagma_1686 ::
  T_AbelianGroup_1636 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMagma_212
du_isCommutativeMagma_1686 :: T_AbelianGroup_1636 -> T_IsCommutativeMagma_212
du_isCommutativeMagma_1686 T_AbelianGroup_1636
v0
  = let v1 :: T_IsAbelianGroup_1132
v1 = T_AbelianGroup_1636 -> T_IsAbelianGroup_1132
d_isAbelianGroup_1664 (T_AbelianGroup_1636 -> T_AbelianGroup_1636
forall a b. a -> b
coe T_AbelianGroup_1636
v0) in
    AgdaAny -> T_IsCommutativeMagma_212
forall a b. a -> b
coe
      (let v2 :: t
v2
             = (T_IsAbelianGroup_1132 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> t
forall a b. a -> b
coe
                 T_IsAbelianGroup_1132 -> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.du_isCommutativeMonoid_1204
                 (T_IsAbelianGroup_1132 -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsCommutativeSemigroup_548 -> T_IsCommutativeMagma_212)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCommutativeSemigroup_548 -> T_IsCommutativeMagma_212
MAlonzo.Code.Algebra.Structures.du_isCommutativeMagma_586
            ((T_IsCommutativeMonoid_736 -> T_IsCommutativeSemigroup_548)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsCommutativeMonoid_736 -> T_IsCommutativeSemigroup_548
MAlonzo.Code.Algebra.Structures.du_isCommutativeSemigroup_786
               (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2))))
-- Algebra.Bundles.AbelianGroup._.isCommutativeMonoid
d_isCommutativeMonoid_1688 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_AbelianGroup_1636 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMonoid_736
d_isCommutativeMonoid_1688 :: () -> () -> T_AbelianGroup_1636 -> T_IsCommutativeMonoid_736
d_isCommutativeMonoid_1688 ~()
v0 ~()
v1 T_AbelianGroup_1636
v2
  = T_AbelianGroup_1636 -> T_IsCommutativeMonoid_736
du_isCommutativeMonoid_1688 T_AbelianGroup_1636
v2
du_isCommutativeMonoid_1688 ::
  T_AbelianGroup_1636 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMonoid_736
du_isCommutativeMonoid_1688 :: T_AbelianGroup_1636 -> T_IsCommutativeMonoid_736
du_isCommutativeMonoid_1688 T_AbelianGroup_1636
v0
  = (T_IsAbelianGroup_1132 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> T_IsCommutativeMonoid_736
forall a b. a -> b
coe
      T_IsAbelianGroup_1132 -> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.du_isCommutativeMonoid_1204
      ((T_AbelianGroup_1636 -> T_IsAbelianGroup_1132)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_AbelianGroup_1636 -> T_IsAbelianGroup_1132
d_isAbelianGroup_1664 (T_AbelianGroup_1636 -> AgdaAny
forall a b. a -> b
coe T_AbelianGroup_1636
v0))
-- Algebra.Bundles.AbelianGroup._.isCommutativeSemigroup
d_isCommutativeSemigroup_1690 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_AbelianGroup_1636 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_548
d_isCommutativeSemigroup_1690 :: () -> () -> T_AbelianGroup_1636 -> T_IsCommutativeSemigroup_548
d_isCommutativeSemigroup_1690 ~()
v0 ~()
v1 T_AbelianGroup_1636
v2
  = T_AbelianGroup_1636 -> T_IsCommutativeSemigroup_548
du_isCommutativeSemigroup_1690 T_AbelianGroup_1636
v2
du_isCommutativeSemigroup_1690 ::
  T_AbelianGroup_1636 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_548
du_isCommutativeSemigroup_1690 :: T_AbelianGroup_1636 -> T_IsCommutativeSemigroup_548
du_isCommutativeSemigroup_1690 T_AbelianGroup_1636
v0
  = let v1 :: T_IsAbelianGroup_1132
v1 = T_AbelianGroup_1636 -> T_IsAbelianGroup_1132
d_isAbelianGroup_1664 (T_AbelianGroup_1636 -> T_AbelianGroup_1636
forall a b. a -> b
coe T_AbelianGroup_1636
v0) in
    AgdaAny -> T_IsCommutativeSemigroup_548
forall a b. a -> b
coe
      ((T_IsCommutativeMonoid_736 -> T_IsCommutativeSemigroup_548)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCommutativeMonoid_736 -> T_IsCommutativeSemigroup_548
MAlonzo.Code.Algebra.Structures.du_isCommutativeSemigroup_786
         ((T_IsAbelianGroup_1132 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsAbelianGroup_1132 -> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.du_isCommutativeMonoid_1204
            (T_IsAbelianGroup_1132 -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132
v1)))
-- Algebra.Bundles.AbelianGroup._.isEquivalence
d_isEquivalence_1692 ::
  T_AbelianGroup_1636 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_1692 :: T_AbelianGroup_1636 -> T_IsEquivalence_26
d_isEquivalence_1692 T_AbelianGroup_1636
v0
  = (T_IsMagma_176 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
      ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480
         ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
            ((T_IsGroup_1036 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsGroup_1036 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_1050
               ((T_IsAbelianGroup_1132 -> T_IsGroup_1036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsAbelianGroup_1132 -> T_IsGroup_1036
MAlonzo.Code.Algebra.Structures.d_isGroup_1144
                  ((T_AbelianGroup_1636 -> T_IsAbelianGroup_1132)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_AbelianGroup_1636 -> T_IsAbelianGroup_1132
d_isAbelianGroup_1664 (T_AbelianGroup_1636 -> AgdaAny
forall a b. a -> b
coe T_AbelianGroup_1636
v0))))))
-- Algebra.Bundles.AbelianGroup._.isGroup
d_isGroup_1694 ::
  T_AbelianGroup_1636 ->
  MAlonzo.Code.Algebra.Structures.T_IsGroup_1036
d_isGroup_1694 :: T_AbelianGroup_1636 -> T_IsGroup_1036
d_isGroup_1694 T_AbelianGroup_1636
v0
  = (T_IsAbelianGroup_1132 -> T_IsGroup_1036)
-> AgdaAny -> T_IsGroup_1036
forall a b. a -> b
coe
      T_IsAbelianGroup_1132 -> T_IsGroup_1036
MAlonzo.Code.Algebra.Structures.d_isGroup_1144
      ((T_AbelianGroup_1636 -> T_IsAbelianGroup_1132)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_AbelianGroup_1636 -> T_IsAbelianGroup_1132
d_isAbelianGroup_1664 (T_AbelianGroup_1636 -> AgdaAny
forall a b. a -> b
coe T_AbelianGroup_1636
v0))
-- Algebra.Bundles.AbelianGroup._.isInvertibleMagma
d_isInvertibleMagma_1696 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_AbelianGroup_1636 ->
  MAlonzo.Code.Algebra.Structures.T_IsInvertibleMagma_924
d_isInvertibleMagma_1696 :: () -> () -> T_AbelianGroup_1636 -> T_IsInvertibleMagma_924
d_isInvertibleMagma_1696 ~()
v0 ~()
v1 T_AbelianGroup_1636
v2 = T_AbelianGroup_1636 -> T_IsInvertibleMagma_924
du_isInvertibleMagma_1696 T_AbelianGroup_1636
v2
du_isInvertibleMagma_1696 ::
  T_AbelianGroup_1636 ->
  MAlonzo.Code.Algebra.Structures.T_IsInvertibleMagma_924
du_isInvertibleMagma_1696 :: T_AbelianGroup_1636 -> T_IsInvertibleMagma_924
du_isInvertibleMagma_1696 T_AbelianGroup_1636
v0
  = let v1 :: T_IsAbelianGroup_1132
v1 = T_AbelianGroup_1636 -> T_IsAbelianGroup_1132
d_isAbelianGroup_1664 (T_AbelianGroup_1636 -> T_AbelianGroup_1636
forall a b. a -> b
coe T_AbelianGroup_1636
v0) in
    AgdaAny -> T_IsInvertibleMagma_924
forall a b. a -> b
coe
      ((T_IsGroup_1036 -> T_IsInvertibleMagma_924) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsGroup_1036 -> T_IsInvertibleMagma_924
MAlonzo.Code.Algebra.Structures.du_isInvertibleMagma_1122
         ((T_IsAbelianGroup_1132 -> T_IsGroup_1036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132 -> T_IsGroup_1036
MAlonzo.Code.Algebra.Structures.d_isGroup_1144 (T_IsAbelianGroup_1132 -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132
v1)))
-- Algebra.Bundles.AbelianGroup._.isInvertibleUnitalMagma
d_isInvertibleUnitalMagma_1698 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_AbelianGroup_1636 ->
  MAlonzo.Code.Algebra.Structures.T_IsInvertibleUnitalMagma_976
d_isInvertibleUnitalMagma_1698 :: () -> () -> T_AbelianGroup_1636 -> T_IsInvertibleUnitalMagma_976
d_isInvertibleUnitalMagma_1698 ~()
v0 ~()
v1 T_AbelianGroup_1636
v2
  = T_AbelianGroup_1636 -> T_IsInvertibleUnitalMagma_976
du_isInvertibleUnitalMagma_1698 T_AbelianGroup_1636
v2
du_isInvertibleUnitalMagma_1698 ::
  T_AbelianGroup_1636 ->
  MAlonzo.Code.Algebra.Structures.T_IsInvertibleUnitalMagma_976
du_isInvertibleUnitalMagma_1698 :: T_AbelianGroup_1636 -> T_IsInvertibleUnitalMagma_976
du_isInvertibleUnitalMagma_1698 T_AbelianGroup_1636
v0
  = let v1 :: T_IsAbelianGroup_1132
v1 = T_AbelianGroup_1636 -> T_IsAbelianGroup_1132
d_isAbelianGroup_1664 (T_AbelianGroup_1636 -> T_AbelianGroup_1636
forall a b. a -> b
coe T_AbelianGroup_1636
v0) in
    AgdaAny -> T_IsInvertibleUnitalMagma_976
forall a b. a -> b
coe
      ((T_IsGroup_1036 -> T_IsInvertibleUnitalMagma_976)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsGroup_1036 -> T_IsInvertibleUnitalMagma_976
MAlonzo.Code.Algebra.Structures.du_isInvertibleUnitalMagma_1124
         ((T_IsAbelianGroup_1132 -> T_IsGroup_1036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132 -> T_IsGroup_1036
MAlonzo.Code.Algebra.Structures.d_isGroup_1144 (T_IsAbelianGroup_1132 -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132
v1)))
-- Algebra.Bundles.AbelianGroup._.isMagma
d_isMagma_1700 ::
  T_AbelianGroup_1636 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_176
d_isMagma_1700 :: T_AbelianGroup_1636 -> T_IsMagma_176
d_isMagma_1700 T_AbelianGroup_1636
v0
  = (T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> T_IsMagma_176
forall a b. a -> b
coe
      T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480
      ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
         ((T_IsGroup_1036 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsGroup_1036 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_1050
            ((T_IsAbelianGroup_1132 -> T_IsGroup_1036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsAbelianGroup_1132 -> T_IsGroup_1036
MAlonzo.Code.Algebra.Structures.d_isGroup_1144
               ((T_AbelianGroup_1636 -> T_IsAbelianGroup_1132)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_AbelianGroup_1636 -> T_IsAbelianGroup_1132
d_isAbelianGroup_1664 (T_AbelianGroup_1636 -> AgdaAny
forall a b. a -> b
coe T_AbelianGroup_1636
v0)))))
-- Algebra.Bundles.AbelianGroup._.isMonoid
d_isMonoid_1702 ::
  T_AbelianGroup_1636 ->
  MAlonzo.Code.Algebra.Structures.T_IsMonoid_686
d_isMonoid_1702 :: T_AbelianGroup_1636 -> T_IsMonoid_686
d_isMonoid_1702 T_AbelianGroup_1636
v0
  = (T_IsGroup_1036 -> T_IsMonoid_686) -> AgdaAny -> T_IsMonoid_686
forall a b. a -> b
coe
      T_IsGroup_1036 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_1050
      ((T_IsAbelianGroup_1132 -> T_IsGroup_1036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsAbelianGroup_1132 -> T_IsGroup_1036
MAlonzo.Code.Algebra.Structures.d_isGroup_1144
         ((T_AbelianGroup_1636 -> T_IsAbelianGroup_1132)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_AbelianGroup_1636 -> T_IsAbelianGroup_1132
d_isAbelianGroup_1664 (T_AbelianGroup_1636 -> AgdaAny
forall a b. a -> b
coe T_AbelianGroup_1636
v0)))
-- Algebra.Bundles.AbelianGroup._.isPartialEquivalence
d_isPartialEquivalence_1704 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_AbelianGroup_1636 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_1704 :: () -> () -> T_AbelianGroup_1636 -> T_IsPartialEquivalence_16
d_isPartialEquivalence_1704 ~()
v0 ~()
v1 T_AbelianGroup_1636
v2
  = T_AbelianGroup_1636 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_1704 T_AbelianGroup_1636
v2
du_isPartialEquivalence_1704 ::
  T_AbelianGroup_1636 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_1704 :: T_AbelianGroup_1636 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_1704 T_AbelianGroup_1636
v0
  = let v1 :: T_IsAbelianGroup_1132
v1 = T_AbelianGroup_1636 -> T_IsAbelianGroup_1132
d_isAbelianGroup_1664 (T_AbelianGroup_1636 -> T_AbelianGroup_1636
forall a b. a -> b
coe T_AbelianGroup_1636
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsGroup_1036
v2
             = T_IsAbelianGroup_1132 -> T_IsGroup_1036
MAlonzo.Code.Algebra.Structures.d_isGroup_1144 (T_IsAbelianGroup_1132 -> T_IsAbelianGroup_1132
forall a b. a -> b
coe T_IsAbelianGroup_1132
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsMonoid_686
v3
                = T_IsGroup_1036 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_1050 (T_IsGroup_1036 -> T_IsGroup_1036
forall a b. a -> b
coe T_IsGroup_1036
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsSemigroup_472
v4
                   = T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsMagma_176
v5 = T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (T_IsSemigroup_472 -> T_IsSemigroup_472
forall a b. a -> b
coe T_IsSemigroup_472
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  ((T_IsEquivalence_26 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsEquivalence_26 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
                     ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v5)))))))
-- Algebra.Bundles.AbelianGroup._.isSemigroup
d_isSemigroup_1706 ::
  T_AbelianGroup_1636 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_472
d_isSemigroup_1706 :: T_AbelianGroup_1636 -> T_IsSemigroup_472
d_isSemigroup_1706 T_AbelianGroup_1636
v0
  = (T_IsMonoid_686 -> T_IsSemigroup_472)
-> AgdaAny -> T_IsSemigroup_472
forall a b. a -> b
coe
      T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
      ((T_IsGroup_1036 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsGroup_1036 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_1050
         ((T_IsAbelianGroup_1132 -> T_IsGroup_1036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsAbelianGroup_1132 -> T_IsGroup_1036
MAlonzo.Code.Algebra.Structures.d_isGroup_1144
            ((T_AbelianGroup_1636 -> T_IsAbelianGroup_1132)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_AbelianGroup_1636 -> T_IsAbelianGroup_1132
d_isAbelianGroup_1664 (T_AbelianGroup_1636 -> AgdaAny
forall a b. a -> b
coe T_AbelianGroup_1636
v0))))
-- Algebra.Bundles.AbelianGroup._.isUnitalMagma
d_isUnitalMagma_1708 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_AbelianGroup_1636 ->
  MAlonzo.Code.Algebra.Structures.T_IsUnitalMagma_642
d_isUnitalMagma_1708 :: () -> () -> T_AbelianGroup_1636 -> T_IsUnitalMagma_642
d_isUnitalMagma_1708 ~()
v0 ~()
v1 T_AbelianGroup_1636
v2 = T_AbelianGroup_1636 -> T_IsUnitalMagma_642
du_isUnitalMagma_1708 T_AbelianGroup_1636
v2
du_isUnitalMagma_1708 ::
  T_AbelianGroup_1636 ->
  MAlonzo.Code.Algebra.Structures.T_IsUnitalMagma_642
du_isUnitalMagma_1708 :: T_AbelianGroup_1636 -> T_IsUnitalMagma_642
du_isUnitalMagma_1708 T_AbelianGroup_1636
v0
  = let v1 :: T_IsAbelianGroup_1132
v1 = T_AbelianGroup_1636 -> T_IsAbelianGroup_1132
d_isAbelianGroup_1664 (T_AbelianGroup_1636 -> T_AbelianGroup_1636
forall a b. a -> b
coe T_AbelianGroup_1636
v0) in
    AgdaAny -> T_IsUnitalMagma_642
forall a b. a -> b
coe
      (let v2 :: T_IsGroup_1036
v2
             = T_IsAbelianGroup_1132 -> T_IsGroup_1036
MAlonzo.Code.Algebra.Structures.d_isGroup_1144 (T_IsAbelianGroup_1132 -> T_IsAbelianGroup_1132
forall a b. a -> b
coe T_IsAbelianGroup_1132
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsMonoid_686 -> T_IsUnitalMagma_642) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoid_686 -> T_IsUnitalMagma_642
MAlonzo.Code.Algebra.Structures.du_isUnitalMagma_730
            ((T_IsGroup_1036 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1036 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_1050 (T_IsGroup_1036 -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1036
v2))))
-- Algebra.Bundles.AbelianGroup._.refl
d_refl_1710 :: T_AbelianGroup_1636 -> AgdaAny -> AgdaAny
d_refl_1710 :: T_AbelianGroup_1636 -> AgdaAny -> AgdaAny
d_refl_1710 T_AbelianGroup_1636
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_34
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
         ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480
            ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
               ((T_IsGroup_1036 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsGroup_1036 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_1050
                  ((T_IsAbelianGroup_1132 -> T_IsGroup_1036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsAbelianGroup_1132 -> T_IsGroup_1036
MAlonzo.Code.Algebra.Structures.d_isGroup_1144
                     ((T_AbelianGroup_1636 -> T_IsAbelianGroup_1132)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_AbelianGroup_1636 -> T_IsAbelianGroup_1132
d_isAbelianGroup_1664 (T_AbelianGroup_1636 -> AgdaAny
forall a b. a -> b
coe T_AbelianGroup_1636
v0)))))))
-- Algebra.Bundles.AbelianGroup._.reflexive
d_reflexive_1712 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_AbelianGroup_1636 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_1712 :: ()
-> ()
-> T_AbelianGroup_1636
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_1712 ~()
v0 ~()
v1 T_AbelianGroup_1636
v2 = T_AbelianGroup_1636
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_1712 T_AbelianGroup_1636
v2
du_reflexive_1712 ::
  T_AbelianGroup_1636 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_1712 :: T_AbelianGroup_1636
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_1712 T_AbelianGroup_1636
v0
  = let v1 :: T_IsAbelianGroup_1132
v1 = T_AbelianGroup_1636 -> T_IsAbelianGroup_1132
d_isAbelianGroup_1664 (T_AbelianGroup_1636 -> T_AbelianGroup_1636
forall a b. a -> b
coe T_AbelianGroup_1636
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsGroup_1036
v2
             = T_IsAbelianGroup_1132 -> T_IsGroup_1036
MAlonzo.Code.Algebra.Structures.d_isGroup_1144 (T_IsAbelianGroup_1132 -> T_IsAbelianGroup_1132
forall a b. a -> b
coe T_IsAbelianGroup_1132
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsMonoid_686
v3
                = T_IsGroup_1036 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_1050 (T_IsGroup_1036 -> T_IsGroup_1036
forall a b. a -> b
coe T_IsGroup_1036
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsSemigroup_472
v4
                   = T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsMagma_176
v5 = T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (T_IsSemigroup_472 -> T_IsSemigroup_472
forall a b. a -> b
coe T_IsSemigroup_472
v4) in
                (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
                  (\ AgdaAny
v6 AgdaAny
v7 AgdaAny
v8 ->
                     (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                       T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
                       ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v5))
                       AgdaAny
v6)))))
-- Algebra.Bundles.AbelianGroup._.setoid
d_setoid_1714 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_AbelianGroup_1636 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_1714 :: () -> () -> T_AbelianGroup_1636 -> T_Setoid_44
d_setoid_1714 ~()
v0 ~()
v1 T_AbelianGroup_1636
v2 = T_AbelianGroup_1636 -> T_Setoid_44
du_setoid_1714 T_AbelianGroup_1636
v2
du_setoid_1714 ::
  T_AbelianGroup_1636 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_1714 :: T_AbelianGroup_1636 -> T_Setoid_44
du_setoid_1714 T_AbelianGroup_1636
v0
  = let v1 :: T_IsAbelianGroup_1132
v1 = T_AbelianGroup_1636 -> T_IsAbelianGroup_1132
d_isAbelianGroup_1664 (T_AbelianGroup_1636 -> T_AbelianGroup_1636
forall a b. a -> b
coe T_AbelianGroup_1636
v0) in
    AgdaAny -> T_Setoid_44
forall a b. a -> b
coe
      (let v2 :: T_IsGroup_1036
v2
             = T_IsAbelianGroup_1132 -> T_IsGroup_1036
MAlonzo.Code.Algebra.Structures.d_isGroup_1144 (T_IsAbelianGroup_1132 -> T_IsAbelianGroup_1132
forall a b. a -> b
coe T_IsAbelianGroup_1132
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsMonoid_686
v3
                = T_IsGroup_1036 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_1050 (T_IsGroup_1036 -> T_IsGroup_1036
forall a b. a -> b
coe T_IsGroup_1036
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsSemigroup_472
v4
                   = T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               ((T_IsMagma_176 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsMagma_176 -> T_Setoid_44
MAlonzo.Code.Algebra.Structures.du_setoid_200
                  ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v4))))))
-- Algebra.Bundles.AbelianGroup._.sym
d_sym_1716 ::
  T_AbelianGroup_1636 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_1716 :: T_AbelianGroup_1636 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_1716 T_AbelianGroup_1636
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_36
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
         ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480
            ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
               ((T_IsGroup_1036 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsGroup_1036 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_1050
                  ((T_IsAbelianGroup_1132 -> T_IsGroup_1036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsAbelianGroup_1132 -> T_IsGroup_1036
MAlonzo.Code.Algebra.Structures.d_isGroup_1144
                     ((T_AbelianGroup_1636 -> T_IsAbelianGroup_1132)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_AbelianGroup_1636 -> T_IsAbelianGroup_1132
d_isAbelianGroup_1664 (T_AbelianGroup_1636 -> AgdaAny
forall a b. a -> b
coe T_AbelianGroup_1636
v0)))))))
-- Algebra.Bundles.AbelianGroup._.trans
d_trans_1718 ::
  T_AbelianGroup_1636 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_1718 :: T_AbelianGroup_1636
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_1718 T_AbelianGroup_1636
v0
  = (T_IsEquivalence_26
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_38
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
         ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480
            ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
               ((T_IsGroup_1036 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsGroup_1036 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_1050
                  ((T_IsAbelianGroup_1132 -> T_IsGroup_1036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsAbelianGroup_1132 -> T_IsGroup_1036
MAlonzo.Code.Algebra.Structures.d_isGroup_1144
                     ((T_AbelianGroup_1636 -> T_IsAbelianGroup_1132)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_AbelianGroup_1636 -> T_IsAbelianGroup_1132
d_isAbelianGroup_1664 (T_AbelianGroup_1636 -> AgdaAny
forall a b. a -> b
coe T_AbelianGroup_1636
v0)))))))
-- Algebra.Bundles.AbelianGroup._.uniqueʳ-⁻¹
d_unique'691''45''8315''185'_1720 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_AbelianGroup_1636 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_unique'691''45''8315''185'_1720 :: ()
-> ()
-> T_AbelianGroup_1636
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_unique'691''45''8315''185'_1720 ~()
v0 ~()
v1 T_AbelianGroup_1636
v2
  = T_AbelianGroup_1636 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_unique'691''45''8315''185'_1720 T_AbelianGroup_1636
v2
du_unique'691''45''8315''185'_1720 ::
  T_AbelianGroup_1636 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_unique'691''45''8315''185'_1720 :: T_AbelianGroup_1636 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_unique'691''45''8315''185'_1720 T_AbelianGroup_1636
v0
  = let v1 :: AgdaAny -> AgdaAny -> AgdaAny
v1 = T_AbelianGroup_1636 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__1658 (T_AbelianGroup_1636 -> T_AbelianGroup_1636
forall a b. a -> b
coe T_AbelianGroup_1636
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: AgdaAny
v2 = T_AbelianGroup_1636 -> AgdaAny
d_ε_1660 (T_AbelianGroup_1636 -> T_AbelianGroup_1636
forall a b. a -> b
coe T_AbelianGroup_1636
v0) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: AgdaAny -> AgdaAny
v3 = T_AbelianGroup_1636 -> AgdaAny -> AgdaAny
d__'8315''185'_1662 (T_AbelianGroup_1636 -> T_AbelianGroup_1636
forall a b. a -> b
coe T_AbelianGroup_1636
v0) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsAbelianGroup_1132
v4 = T_AbelianGroup_1636 -> T_IsAbelianGroup_1132
d_isAbelianGroup_1664 (T_AbelianGroup_1636 -> T_AbelianGroup_1636
forall a b. a -> b
coe T_AbelianGroup_1636
v0) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (((AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> (AgdaAny -> AgdaAny)
 -> T_IsGroup_1036
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsGroup_1036
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.du_unique'691''45''8315''185'_1120
                  ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v1) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2) ((AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v3)
                  ((T_IsAbelianGroup_1132 -> T_IsGroup_1036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132 -> T_IsGroup_1036
MAlonzo.Code.Algebra.Structures.d_isGroup_1144 (T_IsAbelianGroup_1132 -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132
v4))))))
-- Algebra.Bundles.AbelianGroup._.uniqueˡ-⁻¹
d_unique'737''45''8315''185'_1722 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_AbelianGroup_1636 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_unique'737''45''8315''185'_1722 :: ()
-> ()
-> T_AbelianGroup_1636
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_unique'737''45''8315''185'_1722 ~()
v0 ~()
v1 T_AbelianGroup_1636
v2
  = T_AbelianGroup_1636 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_unique'737''45''8315''185'_1722 T_AbelianGroup_1636
v2
du_unique'737''45''8315''185'_1722 ::
  T_AbelianGroup_1636 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_unique'737''45''8315''185'_1722 :: T_AbelianGroup_1636 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_unique'737''45''8315''185'_1722 T_AbelianGroup_1636
v0
  = let v1 :: AgdaAny -> AgdaAny -> AgdaAny
v1 = T_AbelianGroup_1636 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__1658 (T_AbelianGroup_1636 -> T_AbelianGroup_1636
forall a b. a -> b
coe T_AbelianGroup_1636
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: AgdaAny
v2 = T_AbelianGroup_1636 -> AgdaAny
d_ε_1660 (T_AbelianGroup_1636 -> T_AbelianGroup_1636
forall a b. a -> b
coe T_AbelianGroup_1636
v0) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: AgdaAny -> AgdaAny
v3 = T_AbelianGroup_1636 -> AgdaAny -> AgdaAny
d__'8315''185'_1662 (T_AbelianGroup_1636 -> T_AbelianGroup_1636
forall a b. a -> b
coe T_AbelianGroup_1636
v0) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsAbelianGroup_1132
v4 = T_AbelianGroup_1636 -> T_IsAbelianGroup_1132
d_isAbelianGroup_1664 (T_AbelianGroup_1636 -> T_AbelianGroup_1636
forall a b. a -> b
coe T_AbelianGroup_1636
v0) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (((AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> (AgdaAny -> AgdaAny)
 -> T_IsGroup_1036
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsGroup_1036
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.du_unique'737''45''8315''185'_1114
                  ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v1) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2) ((AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v3)
                  ((T_IsAbelianGroup_1132 -> T_IsGroup_1036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132 -> T_IsGroup_1036
MAlonzo.Code.Algebra.Structures.d_isGroup_1144 (T_IsAbelianGroup_1132 -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132
v4))))))
-- Algebra.Bundles.AbelianGroup._.⁻¹-cong
d_'8315''185''45'cong_1724 ::
  T_AbelianGroup_1636 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8315''185''45'cong_1724 :: T_AbelianGroup_1636 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8315''185''45'cong_1724 T_AbelianGroup_1636
v0
  = (T_IsGroup_1036 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsGroup_1036 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8315''185''45'cong_1054
      ((T_IsAbelianGroup_1132 -> T_IsGroup_1036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsAbelianGroup_1132 -> T_IsGroup_1036
MAlonzo.Code.Algebra.Structures.d_isGroup_1144
         ((T_AbelianGroup_1636 -> T_IsAbelianGroup_1132)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_AbelianGroup_1636 -> T_IsAbelianGroup_1132
d_isAbelianGroup_1664 (T_AbelianGroup_1636 -> AgdaAny
forall a b. a -> b
coe T_AbelianGroup_1636
v0)))
-- Algebra.Bundles.AbelianGroup._.∙-cong
d_'8729''45'cong_1726 ::
  T_AbelianGroup_1636 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_1726 :: T_AbelianGroup_1636
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_1726 T_AbelianGroup_1636
v0
  = (T_IsMagma_176
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsMagma_176
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_186
      ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480
         ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
            ((T_IsGroup_1036 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsGroup_1036 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_1050
               ((T_IsAbelianGroup_1132 -> T_IsGroup_1036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsAbelianGroup_1132 -> T_IsGroup_1036
MAlonzo.Code.Algebra.Structures.d_isGroup_1144
                  ((T_AbelianGroup_1636 -> T_IsAbelianGroup_1132)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_AbelianGroup_1636 -> T_IsAbelianGroup_1132
d_isAbelianGroup_1664 (T_AbelianGroup_1636 -> AgdaAny
forall a b. a -> b
coe T_AbelianGroup_1636
v0))))))
-- Algebra.Bundles.AbelianGroup._.∙-congʳ
d_'8729''45'cong'691'_1728 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_AbelianGroup_1636 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_1728 :: ()
-> ()
-> T_AbelianGroup_1636
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_1728 ~()
v0 ~()
v1 T_AbelianGroup_1636
v2
  = T_AbelianGroup_1636
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1728 T_AbelianGroup_1636
v2
du_'8729''45'cong'691'_1728 ::
  T_AbelianGroup_1636 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1728 :: T_AbelianGroup_1636
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1728 T_AbelianGroup_1636
v0
  = let v1 :: T_IsAbelianGroup_1132
v1 = T_AbelianGroup_1636 -> T_IsAbelianGroup_1132
d_isAbelianGroup_1664 (T_AbelianGroup_1636 -> T_AbelianGroup_1636
forall a b. a -> b
coe T_AbelianGroup_1636
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsGroup_1036
v2
             = T_IsAbelianGroup_1132 -> T_IsGroup_1036
MAlonzo.Code.Algebra.Structures.d_isGroup_1144 (T_IsAbelianGroup_1132 -> T_IsAbelianGroup_1132
forall a b. a -> b
coe T_IsAbelianGroup_1132
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsMonoid_686
v3
                = T_IsGroup_1036 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_1050 (T_IsGroup_1036 -> T_IsGroup_1036
forall a b. a -> b
coe T_IsGroup_1036
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsSemigroup_472
v4
                   = T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'691'_206
                  ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v4))))))
-- Algebra.Bundles.AbelianGroup._.∙-congˡ
d_'8729''45'cong'737'_1730 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_AbelianGroup_1636 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_1730 :: ()
-> ()
-> T_AbelianGroup_1636
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_1730 ~()
v0 ~()
v1 T_AbelianGroup_1636
v2
  = T_AbelianGroup_1636
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1730 T_AbelianGroup_1636
v2
du_'8729''45'cong'737'_1730 ::
  T_AbelianGroup_1636 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1730 :: T_AbelianGroup_1636
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1730 T_AbelianGroup_1636
v0
  = let v1 :: T_IsAbelianGroup_1132
v1 = T_AbelianGroup_1636 -> T_IsAbelianGroup_1132
d_isAbelianGroup_1664 (T_AbelianGroup_1636 -> T_AbelianGroup_1636
forall a b. a -> b
coe T_AbelianGroup_1636
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsGroup_1036
v2
             = T_IsAbelianGroup_1132 -> T_IsGroup_1036
MAlonzo.Code.Algebra.Structures.d_isGroup_1144 (T_IsAbelianGroup_1132 -> T_IsAbelianGroup_1132
forall a b. a -> b
coe T_IsAbelianGroup_1132
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsMonoid_686
v3
                = T_IsGroup_1036 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_1050 (T_IsGroup_1036 -> T_IsGroup_1036
forall a b. a -> b
coe T_IsGroup_1036
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsSemigroup_472
v4
                   = T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'737'_202
                  ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v4))))))
-- Algebra.Bundles.AbelianGroup.group
d_group_1732 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_AbelianGroup_1636 -> T_Group_1520
d_group_1732 :: () -> () -> T_AbelianGroup_1636 -> T_Group_1520
d_group_1732 ~()
v0 ~()
v1 T_AbelianGroup_1636
v2 = T_AbelianGroup_1636 -> T_Group_1520
du_group_1732 T_AbelianGroup_1636
v2
du_group_1732 :: T_AbelianGroup_1636 -> T_Group_1520
du_group_1732 :: T_AbelianGroup_1636 -> T_Group_1520
du_group_1732 T_AbelianGroup_1636
v0
  = ((AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> (AgdaAny -> AgdaAny)
 -> T_IsGroup_1036
 -> T_Group_1520)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsGroup_1036
-> T_Group_1520
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsGroup_1036
-> T_Group_1520
C_Group'46'constructor_27303 (T_AbelianGroup_1636 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__1658 (T_AbelianGroup_1636 -> T_AbelianGroup_1636
forall a b. a -> b
coe T_AbelianGroup_1636
v0))
      (T_AbelianGroup_1636 -> AgdaAny
d_ε_1660 (T_AbelianGroup_1636 -> T_AbelianGroup_1636
forall a b. a -> b
coe T_AbelianGroup_1636
v0)) (T_AbelianGroup_1636 -> AgdaAny -> AgdaAny
d__'8315''185'_1662 (T_AbelianGroup_1636 -> T_AbelianGroup_1636
forall a b. a -> b
coe T_AbelianGroup_1636
v0))
      (T_IsAbelianGroup_1132 -> T_IsGroup_1036
MAlonzo.Code.Algebra.Structures.d_isGroup_1144
         ((T_AbelianGroup_1636 -> T_IsAbelianGroup_1132)
-> AgdaAny -> T_IsAbelianGroup_1132
forall a b. a -> b
coe T_AbelianGroup_1636 -> T_IsAbelianGroup_1132
d_isAbelianGroup_1664 (T_AbelianGroup_1636 -> AgdaAny
forall a b. a -> b
coe T_AbelianGroup_1636
v0)))
-- Algebra.Bundles.AbelianGroup._._≉_
d__'8777'__1736 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_AbelianGroup_1636 -> AgdaAny -> AgdaAny -> ()
d__'8777'__1736 :: () -> () -> T_AbelianGroup_1636 -> AgdaAny -> AgdaAny -> ()
d__'8777'__1736 = () -> () -> T_AbelianGroup_1636 -> AgdaAny -> AgdaAny -> ()
forall a. a
erased
-- Algebra.Bundles.AbelianGroup._.invertibleMagma
d_invertibleMagma_1738 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_AbelianGroup_1636 -> T_InvertibleMagma_1360
d_invertibleMagma_1738 :: () -> () -> T_AbelianGroup_1636 -> T_InvertibleMagma_1360
d_invertibleMagma_1738 ~()
v0 ~()
v1 T_AbelianGroup_1636
v2 = T_AbelianGroup_1636 -> T_InvertibleMagma_1360
du_invertibleMagma_1738 T_AbelianGroup_1636
v2
du_invertibleMagma_1738 ::
  T_AbelianGroup_1636 -> T_InvertibleMagma_1360
du_invertibleMagma_1738 :: T_AbelianGroup_1636 -> T_InvertibleMagma_1360
du_invertibleMagma_1738 T_AbelianGroup_1636
v0
  = (T_Group_1520 -> T_InvertibleMagma_1360)
-> AgdaAny -> T_InvertibleMagma_1360
forall a b. a -> b
coe T_Group_1520 -> T_InvertibleMagma_1360
du_invertibleMagma_1628 ((T_AbelianGroup_1636 -> T_Group_1520) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_AbelianGroup_1636 -> T_Group_1520
du_group_1732 (T_AbelianGroup_1636 -> AgdaAny
forall a b. a -> b
coe T_AbelianGroup_1636
v0))
-- Algebra.Bundles.AbelianGroup._.invertibleUnitalMagma
d_invertibleUnitalMagma_1740 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_AbelianGroup_1636 -> T_InvertibleUnitalMagma_1434
d_invertibleUnitalMagma_1740 :: () -> () -> T_AbelianGroup_1636 -> T_InvertibleUnitalMagma_1434
d_invertibleUnitalMagma_1740 ~()
v0 ~()
v1 T_AbelianGroup_1636
v2
  = T_AbelianGroup_1636 -> T_InvertibleUnitalMagma_1434
du_invertibleUnitalMagma_1740 T_AbelianGroup_1636
v2
du_invertibleUnitalMagma_1740 ::
  T_AbelianGroup_1636 -> T_InvertibleUnitalMagma_1434
du_invertibleUnitalMagma_1740 :: T_AbelianGroup_1636 -> T_InvertibleUnitalMagma_1434
du_invertibleUnitalMagma_1740 T_AbelianGroup_1636
v0
  = (T_Group_1520 -> T_InvertibleUnitalMagma_1434)
-> AgdaAny -> T_InvertibleUnitalMagma_1434
forall a b. a -> b
coe T_Group_1520 -> T_InvertibleUnitalMagma_1434
du_invertibleUnitalMagma_1630 ((T_AbelianGroup_1636 -> T_Group_1520) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_AbelianGroup_1636 -> T_Group_1520
du_group_1732 (T_AbelianGroup_1636 -> AgdaAny
forall a b. a -> b
coe T_AbelianGroup_1636
v0))
-- Algebra.Bundles.AbelianGroup._.magma
d_magma_1742 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_AbelianGroup_1636 -> T_Magma_68
d_magma_1742 :: () -> () -> T_AbelianGroup_1636 -> T_Magma_68
d_magma_1742 ~()
v0 ~()
v1 T_AbelianGroup_1636
v2 = T_AbelianGroup_1636 -> T_Magma_68
du_magma_1742 T_AbelianGroup_1636
v2
du_magma_1742 :: T_AbelianGroup_1636 -> T_Magma_68
du_magma_1742 :: T_AbelianGroup_1636 -> T_Magma_68
du_magma_1742 T_AbelianGroup_1636
v0
  = let v1 :: t
v1 = (T_AbelianGroup_1636 -> T_Group_1520) -> AgdaAny -> t
forall a b. a -> b
coe T_AbelianGroup_1636 -> T_Group_1520
du_group_1732 (T_AbelianGroup_1636 -> AgdaAny
forall a b. a -> b
coe T_AbelianGroup_1636
v0) in
    AgdaAny -> T_Magma_68
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_Group_1520 -> T_Monoid_882) -> AgdaAny -> t
forall a b. a -> b
coe T_Group_1520 -> T_Monoid_882
du_monoid_1612 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_Semigroup_536 -> T_Magma_68) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semigroup_536 -> T_Magma_68
du_magma_584 ((T_Monoid_882 -> T_Semigroup_536) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Monoid_882 -> T_Semigroup_536
du_semigroup_944 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2))))
-- Algebra.Bundles.AbelianGroup._.monoid
d_monoid_1744 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_AbelianGroup_1636 -> T_Monoid_882
d_monoid_1744 :: () -> () -> T_AbelianGroup_1636 -> T_Monoid_882
d_monoid_1744 ~()
v0 ~()
v1 T_AbelianGroup_1636
v2 = T_AbelianGroup_1636 -> T_Monoid_882
du_monoid_1744 T_AbelianGroup_1636
v2
du_monoid_1744 :: T_AbelianGroup_1636 -> T_Monoid_882
du_monoid_1744 :: T_AbelianGroup_1636 -> T_Monoid_882
du_monoid_1744 T_AbelianGroup_1636
v0 = (T_Group_1520 -> T_Monoid_882) -> AgdaAny -> T_Monoid_882
forall a b. a -> b
coe T_Group_1520 -> T_Monoid_882
du_monoid_1612 ((T_AbelianGroup_1636 -> T_Group_1520) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_AbelianGroup_1636 -> T_Group_1520
du_group_1732 (T_AbelianGroup_1636 -> AgdaAny
forall a b. a -> b
coe T_AbelianGroup_1636
v0))
-- Algebra.Bundles.AbelianGroup._.rawGroup
d_rawGroup_1746 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_AbelianGroup_1636 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawGroup_96
d_rawGroup_1746 :: () -> () -> T_AbelianGroup_1636 -> T_RawGroup_96
d_rawGroup_1746 ~()
v0 ~()
v1 T_AbelianGroup_1636
v2 = T_AbelianGroup_1636 -> T_RawGroup_96
du_rawGroup_1746 T_AbelianGroup_1636
v2
du_rawGroup_1746 ::
  T_AbelianGroup_1636 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawGroup_96
du_rawGroup_1746 :: T_AbelianGroup_1636 -> T_RawGroup_96
du_rawGroup_1746 T_AbelianGroup_1636
v0
  = (T_Group_1520 -> T_RawGroup_96) -> AgdaAny -> T_RawGroup_96
forall a b. a -> b
coe T_Group_1520 -> T_RawGroup_96
du_rawGroup_1610 ((T_AbelianGroup_1636 -> T_Group_1520) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_AbelianGroup_1636 -> T_Group_1520
du_group_1732 (T_AbelianGroup_1636 -> AgdaAny
forall a b. a -> b
coe T_AbelianGroup_1636
v0))
-- Algebra.Bundles.AbelianGroup._.rawMagma
d_rawMagma_1748 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_AbelianGroup_1636 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
d_rawMagma_1748 :: () -> () -> T_AbelianGroup_1636 -> T_RawMagma_36
d_rawMagma_1748 ~()
v0 ~()
v1 T_AbelianGroup_1636
v2 = T_AbelianGroup_1636 -> T_RawMagma_36
du_rawMagma_1748 T_AbelianGroup_1636
v2
du_rawMagma_1748 ::
  T_AbelianGroup_1636 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
du_rawMagma_1748 :: T_AbelianGroup_1636 -> T_RawMagma_36
du_rawMagma_1748 T_AbelianGroup_1636
v0
  = let v1 :: t
v1 = (T_AbelianGroup_1636 -> T_Group_1520) -> AgdaAny -> t
forall a b. a -> b
coe T_AbelianGroup_1636 -> T_Group_1520
du_group_1732 (T_AbelianGroup_1636 -> AgdaAny
forall a b. a -> b
coe T_AbelianGroup_1636
v0) in
    AgdaAny -> T_RawMagma_36
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_Group_1520 -> T_Monoid_882) -> AgdaAny -> t
forall a b. a -> b
coe T_Group_1520 -> T_Monoid_882
du_monoid_1612 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: t
v3 = (T_Monoid_882 -> T_Semigroup_536) -> AgdaAny -> t
forall a b. a -> b
coe T_Monoid_882 -> T_Semigroup_536
du_semigroup_944 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_Magma_68 -> T_RawMagma_36) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Magma_68 -> T_RawMagma_36
du_rawMagma_112 ((T_Semigroup_536 -> T_Magma_68) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semigroup_536 -> T_Magma_68
du_magma_584 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3)))))
-- Algebra.Bundles.AbelianGroup._.rawMonoid
d_rawMonoid_1750 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_AbelianGroup_1636 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMonoid_64
d_rawMonoid_1750 :: () -> () -> T_AbelianGroup_1636 -> T_RawMonoid_64
d_rawMonoid_1750 ~()
v0 ~()
v1 T_AbelianGroup_1636
v2 = T_AbelianGroup_1636 -> T_RawMonoid_64
du_rawMonoid_1750 T_AbelianGroup_1636
v2
du_rawMonoid_1750 ::
  T_AbelianGroup_1636 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMonoid_64
du_rawMonoid_1750 :: T_AbelianGroup_1636 -> T_RawMonoid_64
du_rawMonoid_1750 T_AbelianGroup_1636
v0
  = let v1 :: t
v1 = (T_AbelianGroup_1636 -> T_Group_1520) -> AgdaAny -> t
forall a b. a -> b
coe T_AbelianGroup_1636 -> T_Group_1520
du_group_1732 (T_AbelianGroup_1636 -> AgdaAny
forall a b. a -> b
coe T_AbelianGroup_1636
v0) in
    AgdaAny -> T_RawMonoid_64
forall a b. a -> b
coe ((T_Monoid_882 -> T_RawMonoid_64) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Monoid_882 -> T_RawMonoid_64
du_rawMonoid_954 ((T_Group_1520 -> T_Monoid_882) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Group_1520 -> T_Monoid_882
du_monoid_1612 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1)))
-- Algebra.Bundles.AbelianGroup._.semigroup
d_semigroup_1752 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_AbelianGroup_1636 -> T_Semigroup_536
d_semigroup_1752 :: () -> () -> T_AbelianGroup_1636 -> T_Semigroup_536
d_semigroup_1752 ~()
v0 ~()
v1 T_AbelianGroup_1636
v2 = T_AbelianGroup_1636 -> T_Semigroup_536
du_semigroup_1752 T_AbelianGroup_1636
v2
du_semigroup_1752 :: T_AbelianGroup_1636 -> T_Semigroup_536
du_semigroup_1752 :: T_AbelianGroup_1636 -> T_Semigroup_536
du_semigroup_1752 T_AbelianGroup_1636
v0
  = let v1 :: t
v1 = (T_AbelianGroup_1636 -> T_Group_1520) -> AgdaAny -> t
forall a b. a -> b
coe T_AbelianGroup_1636 -> T_Group_1520
du_group_1732 (T_AbelianGroup_1636 -> AgdaAny
forall a b. a -> b
coe T_AbelianGroup_1636
v0) in
    AgdaAny -> T_Semigroup_536
forall a b. a -> b
coe ((T_Monoid_882 -> T_Semigroup_536) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Monoid_882 -> T_Semigroup_536
du_semigroup_944 ((T_Group_1520 -> T_Monoid_882) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Group_1520 -> T_Monoid_882
du_monoid_1612 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1)))
-- Algebra.Bundles.AbelianGroup.commutativeMonoid
d_commutativeMonoid_1754 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_AbelianGroup_1636 -> T_CommutativeMonoid_962
d_commutativeMonoid_1754 :: () -> () -> T_AbelianGroup_1636 -> T_CommutativeMonoid_962
d_commutativeMonoid_1754 ~()
v0 ~()
v1 T_AbelianGroup_1636
v2 = T_AbelianGroup_1636 -> T_CommutativeMonoid_962
du_commutativeMonoid_1754 T_AbelianGroup_1636
v2
du_commutativeMonoid_1754 ::
  T_AbelianGroup_1636 -> T_CommutativeMonoid_962
du_commutativeMonoid_1754 :: T_AbelianGroup_1636 -> T_CommutativeMonoid_962
du_commutativeMonoid_1754 T_AbelianGroup_1636
v0
  = ((AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny -> T_IsCommutativeMonoid_736 -> T_CommutativeMonoid_962)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_CommutativeMonoid_962
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> T_IsCommutativeMonoid_736 -> T_CommutativeMonoid_962
C_CommutativeMonoid'46'constructor_17931 (T_AbelianGroup_1636 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__1658 (T_AbelianGroup_1636 -> T_AbelianGroup_1636
forall a b. a -> b
coe T_AbelianGroup_1636
v0))
      (T_AbelianGroup_1636 -> AgdaAny
d_ε_1660 (T_AbelianGroup_1636 -> T_AbelianGroup_1636
forall a b. a -> b
coe T_AbelianGroup_1636
v0))
      ((T_IsAbelianGroup_1132 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsAbelianGroup_1132 -> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.du_isCommutativeMonoid_1204
         ((T_AbelianGroup_1636 -> T_IsAbelianGroup_1132)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_AbelianGroup_1636 -> T_IsAbelianGroup_1132
d_isAbelianGroup_1664 (T_AbelianGroup_1636 -> AgdaAny
forall a b. a -> b
coe T_AbelianGroup_1636
v0)))
-- Algebra.Bundles.AbelianGroup._.commutativeMagma
d_commutativeMagma_1758 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_AbelianGroup_1636 -> T_CommutativeMagma_180
d_commutativeMagma_1758 :: () -> () -> T_AbelianGroup_1636 -> T_CommutativeMagma_180
d_commutativeMagma_1758 ~()
v0 ~()
v1 T_AbelianGroup_1636
v2 = T_AbelianGroup_1636 -> T_CommutativeMagma_180
du_commutativeMagma_1758 T_AbelianGroup_1636
v2
du_commutativeMagma_1758 ::
  T_AbelianGroup_1636 -> T_CommutativeMagma_180
du_commutativeMagma_1758 :: T_AbelianGroup_1636 -> T_CommutativeMagma_180
du_commutativeMagma_1758 T_AbelianGroup_1636
v0
  = let v1 :: t
v1 = (T_AbelianGroup_1636 -> T_CommutativeMonoid_962) -> AgdaAny -> t
forall a b. a -> b
coe T_AbelianGroup_1636 -> T_CommutativeMonoid_962
du_commutativeMonoid_1754 (T_AbelianGroup_1636 -> AgdaAny
forall a b. a -> b
coe T_AbelianGroup_1636
v0) in
    AgdaAny -> T_CommutativeMagma_180
forall a b. a -> b
coe
      ((T_CommutativeSemigroup_662 -> T_CommutativeMagma_180)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_CommutativeSemigroup_662 -> T_CommutativeMagma_180
du_commutativeMagma_726
         ((T_CommutativeMonoid_962 -> T_CommutativeSemigroup_662)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeMonoid_962 -> T_CommutativeSemigroup_662
du_commutativeSemigroup_1048 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1)))
-- Algebra.Bundles.AbelianGroup._.commutativeSemigroup
d_commutativeSemigroup_1760 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_AbelianGroup_1636 -> T_CommutativeSemigroup_662
d_commutativeSemigroup_1760 :: () -> () -> T_AbelianGroup_1636 -> T_CommutativeSemigroup_662
d_commutativeSemigroup_1760 ~()
v0 ~()
v1 T_AbelianGroup_1636
v2
  = T_AbelianGroup_1636 -> T_CommutativeSemigroup_662
du_commutativeSemigroup_1760 T_AbelianGroup_1636
v2
du_commutativeSemigroup_1760 ::
  T_AbelianGroup_1636 -> T_CommutativeSemigroup_662
du_commutativeSemigroup_1760 :: T_AbelianGroup_1636 -> T_CommutativeSemigroup_662
du_commutativeSemigroup_1760 T_AbelianGroup_1636
v0
  = (T_CommutativeMonoid_962 -> T_CommutativeSemigroup_662)
-> AgdaAny -> T_CommutativeSemigroup_662
forall a b. a -> b
coe
      T_CommutativeMonoid_962 -> T_CommutativeSemigroup_662
du_commutativeSemigroup_1048
      ((T_AbelianGroup_1636 -> T_CommutativeMonoid_962)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_AbelianGroup_1636 -> T_CommutativeMonoid_962
du_commutativeMonoid_1754 (T_AbelianGroup_1636 -> AgdaAny
forall a b. a -> b
coe T_AbelianGroup_1636
v0))
-- Algebra.Bundles.NearSemiring
d_NearSemiring_1766 :: p -> p -> ()
d_NearSemiring_1766 p
a0 p
a1 = ()
data T_NearSemiring_1766
  = C_NearSemiring'46'constructor_32269 (AgdaAny ->
                                         AgdaAny -> AgdaAny)
                                        (AgdaAny -> AgdaAny -> AgdaAny) AgdaAny
                                        MAlonzo.Code.Algebra.Structures.T_IsNearSemiring_1218
-- Algebra.Bundles.NearSemiring.Carrier
d_Carrier_1784 :: T_NearSemiring_1766 -> ()
d_Carrier_1784 :: T_NearSemiring_1766 -> ()
d_Carrier_1784 = T_NearSemiring_1766 -> ()
forall a. a
erased
-- Algebra.Bundles.NearSemiring._≈_
d__'8776'__1786 :: T_NearSemiring_1766 -> AgdaAny -> AgdaAny -> ()
d__'8776'__1786 :: T_NearSemiring_1766 -> AgdaAny -> AgdaAny -> ()
d__'8776'__1786 = T_NearSemiring_1766 -> AgdaAny -> AgdaAny -> ()
forall a. a
erased
-- Algebra.Bundles.NearSemiring._+_
d__'43'__1788 ::
  T_NearSemiring_1766 -> AgdaAny -> AgdaAny -> AgdaAny
d__'43'__1788 :: T_NearSemiring_1766 -> AgdaAny -> AgdaAny -> AgdaAny
d__'43'__1788 T_NearSemiring_1766
v0
  = case T_NearSemiring_1766 -> T_NearSemiring_1766
forall a b. a -> b
coe T_NearSemiring_1766
v0 of
      C_NearSemiring'46'constructor_32269 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny
v5 T_IsNearSemiring_1218
v6 -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v3
      T_NearSemiring_1766
_ -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.NearSemiring._*_
d__'42'__1790 ::
  T_NearSemiring_1766 -> AgdaAny -> AgdaAny -> AgdaAny
d__'42'__1790 :: T_NearSemiring_1766 -> AgdaAny -> AgdaAny -> AgdaAny
d__'42'__1790 T_NearSemiring_1766
v0
  = case T_NearSemiring_1766 -> T_NearSemiring_1766
forall a b. a -> b
coe T_NearSemiring_1766
v0 of
      C_NearSemiring'46'constructor_32269 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny
v5 T_IsNearSemiring_1218
v6 -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v4
      T_NearSemiring_1766
_ -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.NearSemiring.0#
d_0'35'_1792 :: T_NearSemiring_1766 -> AgdaAny
d_0'35'_1792 :: T_NearSemiring_1766 -> AgdaAny
d_0'35'_1792 T_NearSemiring_1766
v0
  = case T_NearSemiring_1766 -> T_NearSemiring_1766
forall a b. a -> b
coe T_NearSemiring_1766
v0 of
      C_NearSemiring'46'constructor_32269 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny
v5 T_IsNearSemiring_1218
v6 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v5
      T_NearSemiring_1766
_ -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.NearSemiring.isNearSemiring
d_isNearSemiring_1794 ::
  T_NearSemiring_1766 ->
  MAlonzo.Code.Algebra.Structures.T_IsNearSemiring_1218
d_isNearSemiring_1794 :: T_NearSemiring_1766 -> T_IsNearSemiring_1218
d_isNearSemiring_1794 T_NearSemiring_1766
v0
  = case T_NearSemiring_1766 -> T_NearSemiring_1766
forall a b. a -> b
coe T_NearSemiring_1766
v0 of
      C_NearSemiring'46'constructor_32269 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny
v5 T_IsNearSemiring_1218
v6 -> T_IsNearSemiring_1218 -> T_IsNearSemiring_1218
forall a b. a -> b
coe T_IsNearSemiring_1218
v6
      T_NearSemiring_1766
_ -> T_IsNearSemiring_1218
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.NearSemiring._.*-assoc
d_'42''45'assoc_1798 ::
  T_NearSemiring_1766 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'assoc_1798 :: T_NearSemiring_1766 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'assoc_1798 T_NearSemiring_1766
v0
  = (T_IsNearSemiring_1218 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsNearSemiring_1218 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'42''45'assoc_1240
      ((T_NearSemiring_1766 -> T_IsNearSemiring_1218)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_NearSemiring_1766 -> T_IsNearSemiring_1218
d_isNearSemiring_1794 (T_NearSemiring_1766 -> AgdaAny
forall a b. a -> b
coe T_NearSemiring_1766
v0))
-- Algebra.Bundles.NearSemiring._.*-cong
d_'42''45'cong_1800 ::
  T_NearSemiring_1766 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'cong_1800 :: T_NearSemiring_1766
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'42''45'cong_1800 T_NearSemiring_1766
v0
  = (T_IsNearSemiring_1218
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsNearSemiring_1218
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'42''45'cong_1238
      ((T_NearSemiring_1766 -> T_IsNearSemiring_1218)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_NearSemiring_1766 -> T_IsNearSemiring_1218
d_isNearSemiring_1794 (T_NearSemiring_1766 -> AgdaAny
forall a b. a -> b
coe T_NearSemiring_1766
v0))
-- Algebra.Bundles.NearSemiring._.∙-congʳ
d_'8729''45'cong'691'_1802 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_NearSemiring_1766 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_1802 :: ()
-> ()
-> T_NearSemiring_1766
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_1802 ~()
v0 ~()
v1 T_NearSemiring_1766
v2
  = T_NearSemiring_1766
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1802 T_NearSemiring_1766
v2
du_'8729''45'cong'691'_1802 ::
  T_NearSemiring_1766 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1802 :: T_NearSemiring_1766
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1802 T_NearSemiring_1766
v0
  = let v1 :: T_IsNearSemiring_1218
v1 = T_NearSemiring_1766 -> T_IsNearSemiring_1218
d_isNearSemiring_1794 (T_NearSemiring_1766 -> T_NearSemiring_1766
forall a b. a -> b
coe T_NearSemiring_1766
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'691'_206
         ((T_IsNearSemiring_1218 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsNearSemiring_1218 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.du_'42''45'isMagma_1282 (T_IsNearSemiring_1218 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiring_1218
v1)))
-- Algebra.Bundles.NearSemiring._.∙-congˡ
d_'8729''45'cong'737'_1804 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_NearSemiring_1766 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_1804 :: ()
-> ()
-> T_NearSemiring_1766
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_1804 ~()
v0 ~()
v1 T_NearSemiring_1766
v2
  = T_NearSemiring_1766
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1804 T_NearSemiring_1766
v2
du_'8729''45'cong'737'_1804 ::
  T_NearSemiring_1766 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1804 :: T_NearSemiring_1766
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1804 T_NearSemiring_1766
v0
  = let v1 :: T_IsNearSemiring_1218
v1 = T_NearSemiring_1766 -> T_IsNearSemiring_1218
d_isNearSemiring_1794 (T_NearSemiring_1766 -> T_NearSemiring_1766
forall a b. a -> b
coe T_NearSemiring_1766
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'737'_202
         ((T_IsNearSemiring_1218 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsNearSemiring_1218 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.du_'42''45'isMagma_1282 (T_IsNearSemiring_1218 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiring_1218
v1)))
-- Algebra.Bundles.NearSemiring._.*-isMagma
d_'42''45'isMagma_1806 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_NearSemiring_1766 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_176
d_'42''45'isMagma_1806 :: () -> () -> T_NearSemiring_1766 -> T_IsMagma_176
d_'42''45'isMagma_1806 ~()
v0 ~()
v1 T_NearSemiring_1766
v2 = T_NearSemiring_1766 -> T_IsMagma_176
du_'42''45'isMagma_1806 T_NearSemiring_1766
v2
du_'42''45'isMagma_1806 ::
  T_NearSemiring_1766 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_176
du_'42''45'isMagma_1806 :: T_NearSemiring_1766 -> T_IsMagma_176
du_'42''45'isMagma_1806 T_NearSemiring_1766
v0
  = (T_IsNearSemiring_1218 -> T_IsMagma_176)
-> AgdaAny -> T_IsMagma_176
forall a b. a -> b
coe
      T_IsNearSemiring_1218 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.du_'42''45'isMagma_1282
      ((T_NearSemiring_1766 -> T_IsNearSemiring_1218)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_NearSemiring_1766 -> T_IsNearSemiring_1218
d_isNearSemiring_1794 (T_NearSemiring_1766 -> AgdaAny
forall a b. a -> b
coe T_NearSemiring_1766
v0))
-- Algebra.Bundles.NearSemiring._.*-isSemigroup
d_'42''45'isSemigroup_1808 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_NearSemiring_1766 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_472
d_'42''45'isSemigroup_1808 :: () -> () -> T_NearSemiring_1766 -> T_IsSemigroup_472
d_'42''45'isSemigroup_1808 ~()
v0 ~()
v1 T_NearSemiring_1766
v2
  = T_NearSemiring_1766 -> T_IsSemigroup_472
du_'42''45'isSemigroup_1808 T_NearSemiring_1766
v2
du_'42''45'isSemigroup_1808 ::
  T_NearSemiring_1766 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_472
du_'42''45'isSemigroup_1808 :: T_NearSemiring_1766 -> T_IsSemigroup_472
du_'42''45'isSemigroup_1808 T_NearSemiring_1766
v0
  = (T_IsNearSemiring_1218 -> T_IsSemigroup_472)
-> AgdaAny -> T_IsSemigroup_472
forall a b. a -> b
coe
      T_IsNearSemiring_1218 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.du_'42''45'isSemigroup_1284
      ((T_NearSemiring_1766 -> T_IsNearSemiring_1218)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_NearSemiring_1766 -> T_IsNearSemiring_1218
d_isNearSemiring_1794 (T_NearSemiring_1766 -> AgdaAny
forall a b. a -> b
coe T_NearSemiring_1766
v0))
-- Algebra.Bundles.NearSemiring._.assoc
d_assoc_1810 ::
  T_NearSemiring_1766 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_1810 :: T_NearSemiring_1766 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_1810 T_NearSemiring_1766
v0
  = (T_IsSemigroup_472 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsSemigroup_472 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_assoc_482
      ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
         ((T_IsNearSemiring_1218 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsNearSemiring_1218 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_'43''45'isMonoid_1236
            ((T_NearSemiring_1766 -> T_IsNearSemiring_1218)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_NearSemiring_1766 -> T_IsNearSemiring_1218
d_isNearSemiring_1794 (T_NearSemiring_1766 -> AgdaAny
forall a b. a -> b
coe T_NearSemiring_1766
v0))))
-- Algebra.Bundles.NearSemiring._.∙-cong
d_'8729''45'cong_1812 ::
  T_NearSemiring_1766 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_1812 :: T_NearSemiring_1766
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_1812 T_NearSemiring_1766
v0
  = (T_IsMagma_176
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsMagma_176
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_186
      ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480
         ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
            ((T_IsNearSemiring_1218 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsNearSemiring_1218 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_'43''45'isMonoid_1236
               ((T_NearSemiring_1766 -> T_IsNearSemiring_1218)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_NearSemiring_1766 -> T_IsNearSemiring_1218
d_isNearSemiring_1794 (T_NearSemiring_1766 -> AgdaAny
forall a b. a -> b
coe T_NearSemiring_1766
v0)))))
-- Algebra.Bundles.NearSemiring._.∙-congʳ
d_'8729''45'cong'691'_1814 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_NearSemiring_1766 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_1814 :: ()
-> ()
-> T_NearSemiring_1766
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_1814 ~()
v0 ~()
v1 T_NearSemiring_1766
v2
  = T_NearSemiring_1766
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1814 T_NearSemiring_1766
v2
du_'8729''45'cong'691'_1814 ::
  T_NearSemiring_1766 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1814 :: T_NearSemiring_1766
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1814 T_NearSemiring_1766
v0
  = let v1 :: T_IsNearSemiring_1218
v1 = T_NearSemiring_1766 -> T_IsNearSemiring_1218
d_isNearSemiring_1794 (T_NearSemiring_1766 -> T_NearSemiring_1766
forall a b. a -> b
coe T_NearSemiring_1766
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsMonoid_686
v2
             = T_IsNearSemiring_1218 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_'43''45'isMonoid_1236
                 (T_IsNearSemiring_1218 -> T_IsNearSemiring_1218
forall a b. a -> b
coe T_IsNearSemiring_1218
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_472
v3
                = T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'691'_206
               ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v3)))))
-- Algebra.Bundles.NearSemiring._.∙-congˡ
d_'8729''45'cong'737'_1816 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_NearSemiring_1766 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_1816 :: ()
-> ()
-> T_NearSemiring_1766
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_1816 ~()
v0 ~()
v1 T_NearSemiring_1766
v2
  = T_NearSemiring_1766
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1816 T_NearSemiring_1766
v2
du_'8729''45'cong'737'_1816 ::
  T_NearSemiring_1766 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1816 :: T_NearSemiring_1766
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1816 T_NearSemiring_1766
v0
  = let v1 :: T_IsNearSemiring_1218
v1 = T_NearSemiring_1766 -> T_IsNearSemiring_1218
d_isNearSemiring_1794 (T_NearSemiring_1766 -> T_NearSemiring_1766
forall a b. a -> b
coe T_NearSemiring_1766
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsMonoid_686
v2
             = T_IsNearSemiring_1218 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_'43''45'isMonoid_1236
                 (T_IsNearSemiring_1218 -> T_IsNearSemiring_1218
forall a b. a -> b
coe T_IsNearSemiring_1218
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_472
v3
                = T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'737'_202
               ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v3)))))
-- Algebra.Bundles.NearSemiring._.identity
d_identity_1818 ::
  T_NearSemiring_1766 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_identity_1818 :: T_NearSemiring_1766 -> T_Σ_14
d_identity_1818 T_NearSemiring_1766
v0
  = (T_IsMonoid_686 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsMonoid_686 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_identity_698
      ((T_IsNearSemiring_1218 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsNearSemiring_1218 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_'43''45'isMonoid_1236
         ((T_NearSemiring_1766 -> T_IsNearSemiring_1218)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_NearSemiring_1766 -> T_IsNearSemiring_1218
d_isNearSemiring_1794 (T_NearSemiring_1766 -> AgdaAny
forall a b. a -> b
coe T_NearSemiring_1766
v0)))
-- Algebra.Bundles.NearSemiring._.identityʳ
d_identity'691'_1820 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_NearSemiring_1766 -> AgdaAny -> AgdaAny
d_identity'691'_1820 :: () -> () -> T_NearSemiring_1766 -> AgdaAny -> AgdaAny
d_identity'691'_1820 ~()
v0 ~()
v1 T_NearSemiring_1766
v2 = T_NearSemiring_1766 -> AgdaAny -> AgdaAny
du_identity'691'_1820 T_NearSemiring_1766
v2
du_identity'691'_1820 :: T_NearSemiring_1766 -> AgdaAny -> AgdaAny
du_identity'691'_1820 :: T_NearSemiring_1766 -> AgdaAny -> AgdaAny
du_identity'691'_1820 T_NearSemiring_1766
v0
  = let v1 :: T_IsNearSemiring_1218
v1 = T_NearSemiring_1766 -> T_IsNearSemiring_1218
d_isNearSemiring_1794 (T_NearSemiring_1766 -> T_NearSemiring_1766
forall a b. a -> b
coe T_NearSemiring_1766
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsMonoid_686 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoid_686 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_identity'691'_728
         ((T_IsNearSemiring_1218 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsNearSemiring_1218 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_'43''45'isMonoid_1236 (T_IsNearSemiring_1218 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiring_1218
v1)))
-- Algebra.Bundles.NearSemiring._.identityˡ
d_identity'737'_1822 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_NearSemiring_1766 -> AgdaAny -> AgdaAny
d_identity'737'_1822 :: () -> () -> T_NearSemiring_1766 -> AgdaAny -> AgdaAny
d_identity'737'_1822 ~()
v0 ~()
v1 T_NearSemiring_1766
v2 = T_NearSemiring_1766 -> AgdaAny -> AgdaAny
du_identity'737'_1822 T_NearSemiring_1766
v2
du_identity'737'_1822 :: T_NearSemiring_1766 -> AgdaAny -> AgdaAny
du_identity'737'_1822 :: T_NearSemiring_1766 -> AgdaAny -> AgdaAny
du_identity'737'_1822 T_NearSemiring_1766
v0
  = let v1 :: T_IsNearSemiring_1218
v1 = T_NearSemiring_1766 -> T_IsNearSemiring_1218
d_isNearSemiring_1794 (T_NearSemiring_1766 -> T_NearSemiring_1766
forall a b. a -> b
coe T_NearSemiring_1766
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsMonoid_686 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoid_686 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_identity'737'_726
         ((T_IsNearSemiring_1218 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsNearSemiring_1218 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_'43''45'isMonoid_1236 (T_IsNearSemiring_1218 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiring_1218
v1)))
-- Algebra.Bundles.NearSemiring._.isMagma
d_isMagma_1824 ::
  T_NearSemiring_1766 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_176
d_isMagma_1824 :: T_NearSemiring_1766 -> T_IsMagma_176
d_isMagma_1824 T_NearSemiring_1766
v0
  = (T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> T_IsMagma_176
forall a b. a -> b
coe
      T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480
      ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
         ((T_IsNearSemiring_1218 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsNearSemiring_1218 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_'43''45'isMonoid_1236
            ((T_NearSemiring_1766 -> T_IsNearSemiring_1218)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_NearSemiring_1766 -> T_IsNearSemiring_1218
d_isNearSemiring_1794 (T_NearSemiring_1766 -> AgdaAny
forall a b. a -> b
coe T_NearSemiring_1766
v0))))
-- Algebra.Bundles.NearSemiring._.+-isMonoid
d_'43''45'isMonoid_1826 ::
  T_NearSemiring_1766 ->
  MAlonzo.Code.Algebra.Structures.T_IsMonoid_686
d_'43''45'isMonoid_1826 :: T_NearSemiring_1766 -> T_IsMonoid_686
d_'43''45'isMonoid_1826 T_NearSemiring_1766
v0
  = (T_IsNearSemiring_1218 -> T_IsMonoid_686)
-> AgdaAny -> T_IsMonoid_686
forall a b. a -> b
coe
      T_IsNearSemiring_1218 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_'43''45'isMonoid_1236
      ((T_NearSemiring_1766 -> T_IsNearSemiring_1218)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_NearSemiring_1766 -> T_IsNearSemiring_1218
d_isNearSemiring_1794 (T_NearSemiring_1766 -> AgdaAny
forall a b. a -> b
coe T_NearSemiring_1766
v0))
-- Algebra.Bundles.NearSemiring._.isSemigroup
d_isSemigroup_1828 ::
  T_NearSemiring_1766 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_472
d_isSemigroup_1828 :: T_NearSemiring_1766 -> T_IsSemigroup_472
d_isSemigroup_1828 T_NearSemiring_1766
v0
  = (T_IsMonoid_686 -> T_IsSemigroup_472)
-> AgdaAny -> T_IsSemigroup_472
forall a b. a -> b
coe
      T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
      ((T_IsNearSemiring_1218 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsNearSemiring_1218 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_'43''45'isMonoid_1236
         ((T_NearSemiring_1766 -> T_IsNearSemiring_1218)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_NearSemiring_1766 -> T_IsNearSemiring_1218
d_isNearSemiring_1794 (T_NearSemiring_1766 -> AgdaAny
forall a b. a -> b
coe T_NearSemiring_1766
v0)))
-- Algebra.Bundles.NearSemiring._.isUnitalMagma
d_isUnitalMagma_1830 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_NearSemiring_1766 ->
  MAlonzo.Code.Algebra.Structures.T_IsUnitalMagma_642
d_isUnitalMagma_1830 :: () -> () -> T_NearSemiring_1766 -> T_IsUnitalMagma_642
d_isUnitalMagma_1830 ~()
v0 ~()
v1 T_NearSemiring_1766
v2 = T_NearSemiring_1766 -> T_IsUnitalMagma_642
du_isUnitalMagma_1830 T_NearSemiring_1766
v2
du_isUnitalMagma_1830 ::
  T_NearSemiring_1766 ->
  MAlonzo.Code.Algebra.Structures.T_IsUnitalMagma_642
du_isUnitalMagma_1830 :: T_NearSemiring_1766 -> T_IsUnitalMagma_642
du_isUnitalMagma_1830 T_NearSemiring_1766
v0
  = let v1 :: T_IsNearSemiring_1218
v1 = T_NearSemiring_1766 -> T_IsNearSemiring_1218
d_isNearSemiring_1794 (T_NearSemiring_1766 -> T_NearSemiring_1766
forall a b. a -> b
coe T_NearSemiring_1766
v0) in
    AgdaAny -> T_IsUnitalMagma_642
forall a b. a -> b
coe
      ((T_IsMonoid_686 -> T_IsUnitalMagma_642) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoid_686 -> T_IsUnitalMagma_642
MAlonzo.Code.Algebra.Structures.du_isUnitalMagma_730
         ((T_IsNearSemiring_1218 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsNearSemiring_1218 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_'43''45'isMonoid_1236 (T_IsNearSemiring_1218 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiring_1218
v1)))
-- Algebra.Bundles.NearSemiring._.distribʳ
d_distrib'691'_1832 ::
  T_NearSemiring_1766 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_distrib'691'_1832 :: T_NearSemiring_1766 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_distrib'691'_1832 T_NearSemiring_1766
v0
  = (T_IsNearSemiring_1218 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsNearSemiring_1218 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_distrib'691'_1242
      ((T_NearSemiring_1766 -> T_IsNearSemiring_1218)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_NearSemiring_1766 -> T_IsNearSemiring_1218
d_isNearSemiring_1794 (T_NearSemiring_1766 -> AgdaAny
forall a b. a -> b
coe T_NearSemiring_1766
v0))
-- Algebra.Bundles.NearSemiring._.isEquivalence
d_isEquivalence_1834 ::
  T_NearSemiring_1766 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_1834 :: T_NearSemiring_1766 -> T_IsEquivalence_26
d_isEquivalence_1834 T_NearSemiring_1766
v0
  = (T_IsMagma_176 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
      ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480
         ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
            ((T_IsNearSemiring_1218 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsNearSemiring_1218 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_'43''45'isMonoid_1236
               ((T_NearSemiring_1766 -> T_IsNearSemiring_1218)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_NearSemiring_1766 -> T_IsNearSemiring_1218
d_isNearSemiring_1794 (T_NearSemiring_1766 -> AgdaAny
forall a b. a -> b
coe T_NearSemiring_1766
v0)))))
-- Algebra.Bundles.NearSemiring._.isPartialEquivalence
d_isPartialEquivalence_1836 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_NearSemiring_1766 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_1836 :: () -> () -> T_NearSemiring_1766 -> T_IsPartialEquivalence_16
d_isPartialEquivalence_1836 ~()
v0 ~()
v1 T_NearSemiring_1766
v2
  = T_NearSemiring_1766 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_1836 T_NearSemiring_1766
v2
du_isPartialEquivalence_1836 ::
  T_NearSemiring_1766 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_1836 :: T_NearSemiring_1766 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_1836 T_NearSemiring_1766
v0
  = let v1 :: T_IsNearSemiring_1218
v1 = T_NearSemiring_1766 -> T_IsNearSemiring_1218
d_isNearSemiring_1794 (T_NearSemiring_1766 -> T_NearSemiring_1766
forall a b. a -> b
coe T_NearSemiring_1766
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsMonoid_686
v2
             = T_IsNearSemiring_1218 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_'43''45'isMonoid_1236
                 (T_IsNearSemiring_1218 -> T_IsNearSemiring_1218
forall a b. a -> b
coe T_IsNearSemiring_1218
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_472
v3
                = T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsMagma_176
v4 = T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (T_IsSemigroup_472 -> T_IsSemigroup_472
forall a b. a -> b
coe T_IsSemigroup_472
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               ((T_IsEquivalence_26 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsEquivalence_26 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
                  ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v4))))))
-- Algebra.Bundles.NearSemiring._.refl
d_refl_1838 :: T_NearSemiring_1766 -> AgdaAny -> AgdaAny
d_refl_1838 :: T_NearSemiring_1766 -> AgdaAny -> AgdaAny
d_refl_1838 T_NearSemiring_1766
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_34
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
         ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480
            ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
               ((T_IsNearSemiring_1218 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsNearSemiring_1218 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_'43''45'isMonoid_1236
                  ((T_NearSemiring_1766 -> T_IsNearSemiring_1218)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_NearSemiring_1766 -> T_IsNearSemiring_1218
d_isNearSemiring_1794 (T_NearSemiring_1766 -> AgdaAny
forall a b. a -> b
coe T_NearSemiring_1766
v0))))))
-- Algebra.Bundles.NearSemiring._.reflexive
d_reflexive_1840 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_NearSemiring_1766 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_1840 :: ()
-> ()
-> T_NearSemiring_1766
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_1840 ~()
v0 ~()
v1 T_NearSemiring_1766
v2 = T_NearSemiring_1766
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_1840 T_NearSemiring_1766
v2
du_reflexive_1840 ::
  T_NearSemiring_1766 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_1840 :: T_NearSemiring_1766
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_1840 T_NearSemiring_1766
v0
  = let v1 :: T_IsNearSemiring_1218
v1 = T_NearSemiring_1766 -> T_IsNearSemiring_1218
d_isNearSemiring_1794 (T_NearSemiring_1766 -> T_NearSemiring_1766
forall a b. a -> b
coe T_NearSemiring_1766
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsMonoid_686
v2
             = T_IsNearSemiring_1218 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_'43''45'isMonoid_1236
                 (T_IsNearSemiring_1218 -> T_IsNearSemiring_1218
forall a b. a -> b
coe T_IsNearSemiring_1218
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_472
v3
                = T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsMagma_176
v4 = T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (T_IsSemigroup_472 -> T_IsSemigroup_472
forall a b. a -> b
coe T_IsSemigroup_472
v3) in
             (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
               (\ AgdaAny
v5 AgdaAny
v6 AgdaAny
v7 ->
                  (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                    T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
                    ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v4))
                    AgdaAny
v5))))
-- Algebra.Bundles.NearSemiring._.setoid
d_setoid_1842 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_NearSemiring_1766 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_1842 :: () -> () -> T_NearSemiring_1766 -> T_Setoid_44
d_setoid_1842 ~()
v0 ~()
v1 T_NearSemiring_1766
v2 = T_NearSemiring_1766 -> T_Setoid_44
du_setoid_1842 T_NearSemiring_1766
v2
du_setoid_1842 ::
  T_NearSemiring_1766 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_1842 :: T_NearSemiring_1766 -> T_Setoid_44
du_setoid_1842 T_NearSemiring_1766
v0
  = let v1 :: T_IsNearSemiring_1218
v1 = T_NearSemiring_1766 -> T_IsNearSemiring_1218
d_isNearSemiring_1794 (T_NearSemiring_1766 -> T_NearSemiring_1766
forall a b. a -> b
coe T_NearSemiring_1766
v0) in
    AgdaAny -> T_Setoid_44
forall a b. a -> b
coe
      (let v2 :: T_IsMonoid_686
v2
             = T_IsNearSemiring_1218 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_'43''45'isMonoid_1236
                 (T_IsNearSemiring_1218 -> T_IsNearSemiring_1218
forall a b. a -> b
coe T_IsNearSemiring_1218
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_472
v3
                = T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsMagma_176 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMagma_176 -> T_Setoid_44
MAlonzo.Code.Algebra.Structures.du_setoid_200
               ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v3)))))
-- Algebra.Bundles.NearSemiring._.sym
d_sym_1844 ::
  T_NearSemiring_1766 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_1844 :: T_NearSemiring_1766 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_1844 T_NearSemiring_1766
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_36
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
         ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480
            ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
               ((T_IsNearSemiring_1218 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsNearSemiring_1218 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_'43''45'isMonoid_1236
                  ((T_NearSemiring_1766 -> T_IsNearSemiring_1218)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_NearSemiring_1766 -> T_IsNearSemiring_1218
d_isNearSemiring_1794 (T_NearSemiring_1766 -> AgdaAny
forall a b. a -> b
coe T_NearSemiring_1766
v0))))))
-- Algebra.Bundles.NearSemiring._.trans
d_trans_1846 ::
  T_NearSemiring_1766 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_1846 :: T_NearSemiring_1766
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_1846 T_NearSemiring_1766
v0
  = (T_IsEquivalence_26
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_38
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
         ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480
            ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
               ((T_IsNearSemiring_1218 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsNearSemiring_1218 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_'43''45'isMonoid_1236
                  ((T_NearSemiring_1766 -> T_IsNearSemiring_1218)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_NearSemiring_1766 -> T_IsNearSemiring_1218
d_isNearSemiring_1794 (T_NearSemiring_1766 -> AgdaAny
forall a b. a -> b
coe T_NearSemiring_1766
v0))))))
-- Algebra.Bundles.NearSemiring._.zeroˡ
d_zero'737'_1848 :: T_NearSemiring_1766 -> AgdaAny -> AgdaAny
d_zero'737'_1848 :: T_NearSemiring_1766 -> AgdaAny -> AgdaAny
d_zero'737'_1848 T_NearSemiring_1766
v0
  = (T_IsNearSemiring_1218 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsNearSemiring_1218 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_zero'737'_1244
      ((T_NearSemiring_1766 -> T_IsNearSemiring_1218)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_NearSemiring_1766 -> T_IsNearSemiring_1218
d_isNearSemiring_1794 (T_NearSemiring_1766 -> AgdaAny
forall a b. a -> b
coe T_NearSemiring_1766
v0))
-- Algebra.Bundles.NearSemiring.rawNearSemiring
d_rawNearSemiring_1850 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_NearSemiring_1766 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawNearSemiring_134
d_rawNearSemiring_1850 :: () -> () -> T_NearSemiring_1766 -> T_RawNearSemiring_134
d_rawNearSemiring_1850 ~()
v0 ~()
v1 T_NearSemiring_1766
v2 = T_NearSemiring_1766 -> T_RawNearSemiring_134
du_rawNearSemiring_1850 T_NearSemiring_1766
v2
du_rawNearSemiring_1850 ::
  T_NearSemiring_1766 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawNearSemiring_134
du_rawNearSemiring_1850 :: T_NearSemiring_1766 -> T_RawNearSemiring_134
du_rawNearSemiring_1850 T_NearSemiring_1766
v0
  = ((AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> T_RawNearSemiring_134)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_RawNearSemiring_134
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_RawNearSemiring_134
MAlonzo.Code.Algebra.Bundles.Raw.C_RawNearSemiring'46'constructor_1729
      (T_NearSemiring_1766 -> AgdaAny -> AgdaAny -> AgdaAny
d__'43'__1788 (T_NearSemiring_1766 -> T_NearSemiring_1766
forall a b. a -> b
coe T_NearSemiring_1766
v0)) (T_NearSemiring_1766 -> AgdaAny -> AgdaAny -> AgdaAny
d__'42'__1790 (T_NearSemiring_1766 -> T_NearSemiring_1766
forall a b. a -> b
coe T_NearSemiring_1766
v0))
      (T_NearSemiring_1766 -> AgdaAny
d_0'35'_1792 (T_NearSemiring_1766 -> T_NearSemiring_1766
forall a b. a -> b
coe T_NearSemiring_1766
v0))
-- Algebra.Bundles.NearSemiring.+-monoid
d_'43''45'monoid_1852 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_NearSemiring_1766 -> T_Monoid_882
d_'43''45'monoid_1852 :: () -> () -> T_NearSemiring_1766 -> T_Monoid_882
d_'43''45'monoid_1852 ~()
v0 ~()
v1 T_NearSemiring_1766
v2 = T_NearSemiring_1766 -> T_Monoid_882
du_'43''45'monoid_1852 T_NearSemiring_1766
v2
du_'43''45'monoid_1852 :: T_NearSemiring_1766 -> T_Monoid_882
du_'43''45'monoid_1852 :: T_NearSemiring_1766 -> T_Monoid_882
du_'43''45'monoid_1852 T_NearSemiring_1766
v0
  = ((AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny -> T_IsMonoid_686 -> T_Monoid_882)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsMonoid_686
-> T_Monoid_882
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> T_IsMonoid_686 -> T_Monoid_882
C_Monoid'46'constructor_16157 (T_NearSemiring_1766 -> AgdaAny -> AgdaAny -> AgdaAny
d__'43'__1788 (T_NearSemiring_1766 -> T_NearSemiring_1766
forall a b. a -> b
coe T_NearSemiring_1766
v0))
      (T_NearSemiring_1766 -> AgdaAny
d_0'35'_1792 (T_NearSemiring_1766 -> T_NearSemiring_1766
forall a b. a -> b
coe T_NearSemiring_1766
v0))
      (T_IsNearSemiring_1218 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_'43''45'isMonoid_1236
         ((T_NearSemiring_1766 -> T_IsNearSemiring_1218)
-> AgdaAny -> T_IsNearSemiring_1218
forall a b. a -> b
coe T_NearSemiring_1766 -> T_IsNearSemiring_1218
d_isNearSemiring_1794 (T_NearSemiring_1766 -> AgdaAny
forall a b. a -> b
coe T_NearSemiring_1766
v0)))
-- Algebra.Bundles.NearSemiring._._≉_
d__'8777'__1856 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_NearSemiring_1766 -> AgdaAny -> AgdaAny -> ()
d__'8777'__1856 :: () -> () -> T_NearSemiring_1766 -> AgdaAny -> AgdaAny -> ()
d__'8777'__1856 = () -> () -> T_NearSemiring_1766 -> AgdaAny -> AgdaAny -> ()
forall a. a
erased
-- Algebra.Bundles.NearSemiring._.magma
d_magma_1858 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_NearSemiring_1766 -> T_Magma_68
d_magma_1858 :: () -> () -> T_NearSemiring_1766 -> T_Magma_68
d_magma_1858 ~()
v0 ~()
v1 T_NearSemiring_1766
v2 = T_NearSemiring_1766 -> T_Magma_68
du_magma_1858 T_NearSemiring_1766
v2
du_magma_1858 :: T_NearSemiring_1766 -> T_Magma_68
du_magma_1858 :: T_NearSemiring_1766 -> T_Magma_68
du_magma_1858 T_NearSemiring_1766
v0
  = let v1 :: t
v1 = (T_NearSemiring_1766 -> T_Monoid_882) -> AgdaAny -> t
forall a b. a -> b
coe T_NearSemiring_1766 -> T_Monoid_882
du_'43''45'monoid_1852 (T_NearSemiring_1766 -> AgdaAny
forall a b. a -> b
coe T_NearSemiring_1766
v0) in
    AgdaAny -> T_Magma_68
forall a b. a -> b
coe ((T_Semigroup_536 -> T_Magma_68) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semigroup_536 -> T_Magma_68
du_magma_584 ((T_Monoid_882 -> T_Semigroup_536) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Monoid_882 -> T_Semigroup_536
du_semigroup_944 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1)))
-- Algebra.Bundles.NearSemiring._.rawMagma
d_rawMagma_1860 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_NearSemiring_1766 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
d_rawMagma_1860 :: () -> () -> T_NearSemiring_1766 -> T_RawMagma_36
d_rawMagma_1860 ~()
v0 ~()
v1 T_NearSemiring_1766
v2 = T_NearSemiring_1766 -> T_RawMagma_36
du_rawMagma_1860 T_NearSemiring_1766
v2
du_rawMagma_1860 ::
  T_NearSemiring_1766 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
du_rawMagma_1860 :: T_NearSemiring_1766 -> T_RawMagma_36
du_rawMagma_1860 T_NearSemiring_1766
v0
  = let v1 :: t
v1 = (T_NearSemiring_1766 -> T_Monoid_882) -> AgdaAny -> t
forall a b. a -> b
coe T_NearSemiring_1766 -> T_Monoid_882
du_'43''45'monoid_1852 (T_NearSemiring_1766 -> AgdaAny
forall a b. a -> b
coe T_NearSemiring_1766
v0) in
    AgdaAny -> T_RawMagma_36
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_Monoid_882 -> T_Semigroup_536) -> AgdaAny -> t
forall a b. a -> b
coe T_Monoid_882 -> T_Semigroup_536
du_semigroup_944 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_Magma_68 -> T_RawMagma_36) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Magma_68 -> T_RawMagma_36
du_rawMagma_112 ((T_Semigroup_536 -> T_Magma_68) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semigroup_536 -> T_Magma_68
du_magma_584 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2))))
-- Algebra.Bundles.NearSemiring._.rawMonoid
d_rawMonoid_1862 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_NearSemiring_1766 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMonoid_64
d_rawMonoid_1862 :: () -> () -> T_NearSemiring_1766 -> T_RawMonoid_64
d_rawMonoid_1862 ~()
v0 ~()
v1 T_NearSemiring_1766
v2 = T_NearSemiring_1766 -> T_RawMonoid_64
du_rawMonoid_1862 T_NearSemiring_1766
v2
du_rawMonoid_1862 ::
  T_NearSemiring_1766 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMonoid_64
du_rawMonoid_1862 :: T_NearSemiring_1766 -> T_RawMonoid_64
du_rawMonoid_1862 T_NearSemiring_1766
v0
  = (T_Monoid_882 -> T_RawMonoid_64) -> AgdaAny -> T_RawMonoid_64
forall a b. a -> b
coe T_Monoid_882 -> T_RawMonoid_64
du_rawMonoid_954 ((T_NearSemiring_1766 -> T_Monoid_882) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_NearSemiring_1766 -> T_Monoid_882
du_'43''45'monoid_1852 (T_NearSemiring_1766 -> AgdaAny
forall a b. a -> b
coe T_NearSemiring_1766
v0))
-- Algebra.Bundles.NearSemiring._.semigroup
d_semigroup_1864 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_NearSemiring_1766 -> T_Semigroup_536
d_semigroup_1864 :: () -> () -> T_NearSemiring_1766 -> T_Semigroup_536
d_semigroup_1864 ~()
v0 ~()
v1 T_NearSemiring_1766
v2 = T_NearSemiring_1766 -> T_Semigroup_536
du_semigroup_1864 T_NearSemiring_1766
v2
du_semigroup_1864 :: T_NearSemiring_1766 -> T_Semigroup_536
du_semigroup_1864 :: T_NearSemiring_1766 -> T_Semigroup_536
du_semigroup_1864 T_NearSemiring_1766
v0
  = (T_Monoid_882 -> T_Semigroup_536) -> AgdaAny -> T_Semigroup_536
forall a b. a -> b
coe T_Monoid_882 -> T_Semigroup_536
du_semigroup_944 ((T_NearSemiring_1766 -> T_Monoid_882) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_NearSemiring_1766 -> T_Monoid_882
du_'43''45'monoid_1852 (T_NearSemiring_1766 -> AgdaAny
forall a b. a -> b
coe T_NearSemiring_1766
v0))
-- Algebra.Bundles.NearSemiring._.unitalMagma
d_unitalMagma_1866 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_NearSemiring_1766 -> T_UnitalMagma_814
d_unitalMagma_1866 :: () -> () -> T_NearSemiring_1766 -> T_UnitalMagma_814
d_unitalMagma_1866 ~()
v0 ~()
v1 T_NearSemiring_1766
v2 = T_NearSemiring_1766 -> T_UnitalMagma_814
du_unitalMagma_1866 T_NearSemiring_1766
v2
du_unitalMagma_1866 :: T_NearSemiring_1766 -> T_UnitalMagma_814
du_unitalMagma_1866 :: T_NearSemiring_1766 -> T_UnitalMagma_814
du_unitalMagma_1866 T_NearSemiring_1766
v0
  = (T_Monoid_882 -> T_UnitalMagma_814) -> AgdaAny -> T_UnitalMagma_814
forall a b. a -> b
coe T_Monoid_882 -> T_UnitalMagma_814
du_unitalMagma_956 ((T_NearSemiring_1766 -> T_Monoid_882) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_NearSemiring_1766 -> T_Monoid_882
du_'43''45'monoid_1852 (T_NearSemiring_1766 -> AgdaAny
forall a b. a -> b
coe T_NearSemiring_1766
v0))
-- Algebra.Bundles.NearSemiring.*-semigroup
d_'42''45'semigroup_1868 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_NearSemiring_1766 -> T_Semigroup_536
d_'42''45'semigroup_1868 :: () -> () -> T_NearSemiring_1766 -> T_Semigroup_536
d_'42''45'semigroup_1868 ~()
v0 ~()
v1 T_NearSemiring_1766
v2 = T_NearSemiring_1766 -> T_Semigroup_536
du_'42''45'semigroup_1868 T_NearSemiring_1766
v2
du_'42''45'semigroup_1868 :: T_NearSemiring_1766 -> T_Semigroup_536
du_'42''45'semigroup_1868 :: T_NearSemiring_1766 -> T_Semigroup_536
du_'42''45'semigroup_1868 T_NearSemiring_1766
v0
  = ((AgdaAny -> AgdaAny -> AgdaAny)
 -> T_IsSemigroup_472 -> T_Semigroup_536)
-> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> T_Semigroup_536
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsSemigroup_472 -> T_Semigroup_536
C_Semigroup'46'constructor_9793 (T_NearSemiring_1766 -> AgdaAny -> AgdaAny -> AgdaAny
d__'42'__1790 (T_NearSemiring_1766 -> T_NearSemiring_1766
forall a b. a -> b
coe T_NearSemiring_1766
v0))
      ((T_IsNearSemiring_1218 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsNearSemiring_1218 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.du_'42''45'isSemigroup_1284
         ((T_NearSemiring_1766 -> T_IsNearSemiring_1218)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_NearSemiring_1766 -> T_IsNearSemiring_1218
d_isNearSemiring_1794 (T_NearSemiring_1766 -> AgdaAny
forall a b. a -> b
coe T_NearSemiring_1766
v0)))
-- Algebra.Bundles.NearSemiring._.magma
d_magma_1872 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_NearSemiring_1766 -> T_Magma_68
d_magma_1872 :: () -> () -> T_NearSemiring_1766 -> T_Magma_68
d_magma_1872 ~()
v0 ~()
v1 T_NearSemiring_1766
v2 = T_NearSemiring_1766 -> T_Magma_68
du_magma_1872 T_NearSemiring_1766
v2
du_magma_1872 :: T_NearSemiring_1766 -> T_Magma_68
du_magma_1872 :: T_NearSemiring_1766 -> T_Magma_68
du_magma_1872 T_NearSemiring_1766
v0
  = (T_Semigroup_536 -> T_Magma_68) -> AgdaAny -> T_Magma_68
forall a b. a -> b
coe T_Semigroup_536 -> T_Magma_68
du_magma_584 ((T_NearSemiring_1766 -> T_Semigroup_536) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_NearSemiring_1766 -> T_Semigroup_536
du_'42''45'semigroup_1868 (T_NearSemiring_1766 -> AgdaAny
forall a b. a -> b
coe T_NearSemiring_1766
v0))
-- Algebra.Bundles.NearSemiring._.rawMagma
d_rawMagma_1874 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_NearSemiring_1766 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
d_rawMagma_1874 :: () -> () -> T_NearSemiring_1766 -> T_RawMagma_36
d_rawMagma_1874 ~()
v0 ~()
v1 T_NearSemiring_1766
v2 = T_NearSemiring_1766 -> T_RawMagma_36
du_rawMagma_1874 T_NearSemiring_1766
v2
du_rawMagma_1874 ::
  T_NearSemiring_1766 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
du_rawMagma_1874 :: T_NearSemiring_1766 -> T_RawMagma_36
du_rawMagma_1874 T_NearSemiring_1766
v0
  = let v1 :: t
v1 = (T_NearSemiring_1766 -> T_Semigroup_536) -> AgdaAny -> t
forall a b. a -> b
coe T_NearSemiring_1766 -> T_Semigroup_536
du_'42''45'semigroup_1868 (T_NearSemiring_1766 -> AgdaAny
forall a b. a -> b
coe T_NearSemiring_1766
v0) in
    AgdaAny -> T_RawMagma_36
forall a b. a -> b
coe ((T_Magma_68 -> T_RawMagma_36) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Magma_68 -> T_RawMagma_36
du_rawMagma_112 ((T_Semigroup_536 -> T_Magma_68) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semigroup_536 -> T_Magma_68
du_magma_584 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1)))
-- Algebra.Bundles.SemiringWithoutOne
d_SemiringWithoutOne_1880 :: p -> p -> ()
d_SemiringWithoutOne_1880 p
a0 p
a1 = ()
data T_SemiringWithoutOne_1880
  = C_SemiringWithoutOne'46'constructor_34609 (AgdaAny ->
                                               AgdaAny -> AgdaAny)
                                              (AgdaAny -> AgdaAny -> AgdaAny) AgdaAny
                                              MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutOne_1298
-- Algebra.Bundles.SemiringWithoutOne.Carrier
d_Carrier_1898 :: T_SemiringWithoutOne_1880 -> ()
d_Carrier_1898 :: T_SemiringWithoutOne_1880 -> ()
d_Carrier_1898 = T_SemiringWithoutOne_1880 -> ()
forall a. a
erased
-- Algebra.Bundles.SemiringWithoutOne._≈_
d__'8776'__1900 ::
  T_SemiringWithoutOne_1880 -> AgdaAny -> AgdaAny -> ()
d__'8776'__1900 :: T_SemiringWithoutOne_1880 -> AgdaAny -> AgdaAny -> ()
d__'8776'__1900 = T_SemiringWithoutOne_1880 -> AgdaAny -> AgdaAny -> ()
forall a. a
erased
-- Algebra.Bundles.SemiringWithoutOne._+_
d__'43'__1902 ::
  T_SemiringWithoutOne_1880 -> AgdaAny -> AgdaAny -> AgdaAny
d__'43'__1902 :: T_SemiringWithoutOne_1880 -> AgdaAny -> AgdaAny -> AgdaAny
d__'43'__1902 T_SemiringWithoutOne_1880
v0
  = case T_SemiringWithoutOne_1880 -> T_SemiringWithoutOne_1880
forall a b. a -> b
coe T_SemiringWithoutOne_1880
v0 of
      C_SemiringWithoutOne'46'constructor_34609 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny
v5 T_IsSemiringWithoutOne_1298
v6 -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v3
      T_SemiringWithoutOne_1880
_ -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.SemiringWithoutOne._*_
d__'42'__1904 ::
  T_SemiringWithoutOne_1880 -> AgdaAny -> AgdaAny -> AgdaAny
d__'42'__1904 :: T_SemiringWithoutOne_1880 -> AgdaAny -> AgdaAny -> AgdaAny
d__'42'__1904 T_SemiringWithoutOne_1880
v0
  = case T_SemiringWithoutOne_1880 -> T_SemiringWithoutOne_1880
forall a b. a -> b
coe T_SemiringWithoutOne_1880
v0 of
      C_SemiringWithoutOne'46'constructor_34609 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny
v5 T_IsSemiringWithoutOne_1298
v6 -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v4
      T_SemiringWithoutOne_1880
_ -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.SemiringWithoutOne.0#
d_0'35'_1906 :: T_SemiringWithoutOne_1880 -> AgdaAny
d_0'35'_1906 :: T_SemiringWithoutOne_1880 -> AgdaAny
d_0'35'_1906 T_SemiringWithoutOne_1880
v0
  = case T_SemiringWithoutOne_1880 -> T_SemiringWithoutOne_1880
forall a b. a -> b
coe T_SemiringWithoutOne_1880
v0 of
      C_SemiringWithoutOne'46'constructor_34609 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny
v5 T_IsSemiringWithoutOne_1298
v6 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v5
      T_SemiringWithoutOne_1880
_ -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.SemiringWithoutOne.isSemiringWithoutOne
d_isSemiringWithoutOne_1908 ::
  T_SemiringWithoutOne_1880 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutOne_1298
d_isSemiringWithoutOne_1908 :: T_SemiringWithoutOne_1880 -> T_IsSemiringWithoutOne_1298
d_isSemiringWithoutOne_1908 T_SemiringWithoutOne_1880
v0
  = case T_SemiringWithoutOne_1880 -> T_SemiringWithoutOne_1880
forall a b. a -> b
coe T_SemiringWithoutOne_1880
v0 of
      C_SemiringWithoutOne'46'constructor_34609 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny
v5 T_IsSemiringWithoutOne_1298
v6 -> T_IsSemiringWithoutOne_1298 -> T_IsSemiringWithoutOne_1298
forall a b. a -> b
coe T_IsSemiringWithoutOne_1298
v6
      T_SemiringWithoutOne_1880
_ -> T_IsSemiringWithoutOne_1298
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.SemiringWithoutOne._._≈_
d__'8776'__1912 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SemiringWithoutOne_1880 -> AgdaAny -> AgdaAny -> ()
d__'8776'__1912 :: () -> () -> T_SemiringWithoutOne_1880 -> AgdaAny -> AgdaAny -> ()
d__'8776'__1912 = () -> () -> T_SemiringWithoutOne_1880 -> AgdaAny -> AgdaAny -> ()
forall a. a
erased
-- Algebra.Bundles.SemiringWithoutOne._._≉_
d__'8777'__1914 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SemiringWithoutOne_1880 -> AgdaAny -> AgdaAny -> ()
d__'8777'__1914 :: () -> () -> T_SemiringWithoutOne_1880 -> AgdaAny -> AgdaAny -> ()
d__'8777'__1914 = () -> () -> T_SemiringWithoutOne_1880 -> AgdaAny -> AgdaAny -> ()
forall a. a
erased
-- Algebra.Bundles.SemiringWithoutOne._.*-assoc
d_'42''45'assoc_1916 ::
  T_SemiringWithoutOne_1880 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'assoc_1916 :: T_SemiringWithoutOne_1880
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'assoc_1916 T_SemiringWithoutOne_1880
v0
  = (T_IsSemiringWithoutOne_1298
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsSemiringWithoutOne_1298
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'42''45'assoc_1320
      ((T_SemiringWithoutOne_1880 -> T_IsSemiringWithoutOne_1298)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutOne_1880 -> T_IsSemiringWithoutOne_1298
d_isSemiringWithoutOne_1908 (T_SemiringWithoutOne_1880 -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutOne_1880
v0))
-- Algebra.Bundles.SemiringWithoutOne._.*-cong
d_'42''45'cong_1918 ::
  T_SemiringWithoutOne_1880 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'cong_1918 :: T_SemiringWithoutOne_1880
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'42''45'cong_1918 T_SemiringWithoutOne_1880
v0
  = (T_IsSemiringWithoutOne_1298
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsSemiringWithoutOne_1298
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'42''45'cong_1318
      ((T_SemiringWithoutOne_1880 -> T_IsSemiringWithoutOne_1298)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutOne_1880 -> T_IsSemiringWithoutOne_1298
d_isSemiringWithoutOne_1908 (T_SemiringWithoutOne_1880 -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutOne_1880
v0))
-- Algebra.Bundles.SemiringWithoutOne._.∙-congʳ
d_'8729''45'cong'691'_1920 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SemiringWithoutOne_1880 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_1920 :: ()
-> ()
-> T_SemiringWithoutOne_1880
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_1920 ~()
v0 ~()
v1 T_SemiringWithoutOne_1880
v2
  = T_SemiringWithoutOne_1880
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1920 T_SemiringWithoutOne_1880
v2
du_'8729''45'cong'691'_1920 ::
  T_SemiringWithoutOne_1880 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1920 :: T_SemiringWithoutOne_1880
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1920 T_SemiringWithoutOne_1880
v0
  = let v1 :: T_IsSemiringWithoutOne_1298
v1 = T_SemiringWithoutOne_1880 -> T_IsSemiringWithoutOne_1298
d_isSemiringWithoutOne_1908 (T_SemiringWithoutOne_1880 -> T_SemiringWithoutOne_1880
forall a b. a -> b
coe T_SemiringWithoutOne_1880
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'691'_206
         ((T_IsSemiringWithoutOne_1298 -> T_IsMagma_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemiringWithoutOne_1298 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.du_'42''45'isMagma_1360 (T_IsSemiringWithoutOne_1298 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_1298
v1)))
-- Algebra.Bundles.SemiringWithoutOne._.∙-congˡ
d_'8729''45'cong'737'_1922 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SemiringWithoutOne_1880 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_1922 :: ()
-> ()
-> T_SemiringWithoutOne_1880
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_1922 ~()
v0 ~()
v1 T_SemiringWithoutOne_1880
v2
  = T_SemiringWithoutOne_1880
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1922 T_SemiringWithoutOne_1880
v2
du_'8729''45'cong'737'_1922 ::
  T_SemiringWithoutOne_1880 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1922 :: T_SemiringWithoutOne_1880
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1922 T_SemiringWithoutOne_1880
v0
  = let v1 :: T_IsSemiringWithoutOne_1298
v1 = T_SemiringWithoutOne_1880 -> T_IsSemiringWithoutOne_1298
d_isSemiringWithoutOne_1908 (T_SemiringWithoutOne_1880 -> T_SemiringWithoutOne_1880
forall a b. a -> b
coe T_SemiringWithoutOne_1880
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'737'_202
         ((T_IsSemiringWithoutOne_1298 -> T_IsMagma_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemiringWithoutOne_1298 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.du_'42''45'isMagma_1360 (T_IsSemiringWithoutOne_1298 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_1298
v1)))
-- Algebra.Bundles.SemiringWithoutOne._.*-isMagma
d_'42''45'isMagma_1924 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SemiringWithoutOne_1880 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_176
d_'42''45'isMagma_1924 :: () -> () -> T_SemiringWithoutOne_1880 -> T_IsMagma_176
d_'42''45'isMagma_1924 ~()
v0 ~()
v1 T_SemiringWithoutOne_1880
v2 = T_SemiringWithoutOne_1880 -> T_IsMagma_176
du_'42''45'isMagma_1924 T_SemiringWithoutOne_1880
v2
du_'42''45'isMagma_1924 ::
  T_SemiringWithoutOne_1880 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_176
du_'42''45'isMagma_1924 :: T_SemiringWithoutOne_1880 -> T_IsMagma_176
du_'42''45'isMagma_1924 T_SemiringWithoutOne_1880
v0
  = (T_IsSemiringWithoutOne_1298 -> T_IsMagma_176)
-> AgdaAny -> T_IsMagma_176
forall a b. a -> b
coe
      T_IsSemiringWithoutOne_1298 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.du_'42''45'isMagma_1360
      ((T_SemiringWithoutOne_1880 -> T_IsSemiringWithoutOne_1298)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutOne_1880 -> T_IsSemiringWithoutOne_1298
d_isSemiringWithoutOne_1908 (T_SemiringWithoutOne_1880 -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutOne_1880
v0))
-- Algebra.Bundles.SemiringWithoutOne._.*-isSemigroup
d_'42''45'isSemigroup_1926 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SemiringWithoutOne_1880 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_472
d_'42''45'isSemigroup_1926 :: () -> () -> T_SemiringWithoutOne_1880 -> T_IsSemigroup_472
d_'42''45'isSemigroup_1926 ~()
v0 ~()
v1 T_SemiringWithoutOne_1880
v2
  = T_SemiringWithoutOne_1880 -> T_IsSemigroup_472
du_'42''45'isSemigroup_1926 T_SemiringWithoutOne_1880
v2
du_'42''45'isSemigroup_1926 ::
  T_SemiringWithoutOne_1880 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_472
du_'42''45'isSemigroup_1926 :: T_SemiringWithoutOne_1880 -> T_IsSemigroup_472
du_'42''45'isSemigroup_1926 T_SemiringWithoutOne_1880
v0
  = (T_IsSemiringWithoutOne_1298 -> T_IsSemigroup_472)
-> AgdaAny -> T_IsSemigroup_472
forall a b. a -> b
coe
      T_IsSemiringWithoutOne_1298 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.du_'42''45'isSemigroup_1362
      ((T_SemiringWithoutOne_1880 -> T_IsSemiringWithoutOne_1298)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutOne_1880 -> T_IsSemiringWithoutOne_1298
d_isSemiringWithoutOne_1908 (T_SemiringWithoutOne_1880 -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutOne_1880
v0))
-- Algebra.Bundles.SemiringWithoutOne._.comm
d_comm_1928 ::
  T_SemiringWithoutOne_1880 -> AgdaAny -> AgdaAny -> AgdaAny
d_comm_1928 :: T_SemiringWithoutOne_1880 -> AgdaAny -> AgdaAny -> AgdaAny
d_comm_1928 T_SemiringWithoutOne_1880
v0
  = (T_IsCommutativeMonoid_736 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsCommutativeMonoid_736 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_comm_748
      ((T_IsSemiringWithoutOne_1298 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiringWithoutOne_1298 -> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1316
         ((T_SemiringWithoutOne_1880 -> T_IsSemiringWithoutOne_1298)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutOne_1880 -> T_IsSemiringWithoutOne_1298
d_isSemiringWithoutOne_1908 (T_SemiringWithoutOne_1880 -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutOne_1880
v0)))
-- Algebra.Bundles.SemiringWithoutOne._.isCommutativeMagma
d_isCommutativeMagma_1930 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SemiringWithoutOne_1880 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMagma_212
d_isCommutativeMagma_1930 :: () -> () -> T_SemiringWithoutOne_1880 -> T_IsCommutativeMagma_212
d_isCommutativeMagma_1930 ~()
v0 ~()
v1 T_SemiringWithoutOne_1880
v2
  = T_SemiringWithoutOne_1880 -> T_IsCommutativeMagma_212
du_isCommutativeMagma_1930 T_SemiringWithoutOne_1880
v2
du_isCommutativeMagma_1930 ::
  T_SemiringWithoutOne_1880 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMagma_212
du_isCommutativeMagma_1930 :: T_SemiringWithoutOne_1880 -> T_IsCommutativeMagma_212
du_isCommutativeMagma_1930 T_SemiringWithoutOne_1880
v0
  = let v1 :: T_IsSemiringWithoutOne_1298
v1 = T_SemiringWithoutOne_1880 -> T_IsSemiringWithoutOne_1298
d_isSemiringWithoutOne_1908 (T_SemiringWithoutOne_1880 -> T_SemiringWithoutOne_1880
forall a b. a -> b
coe T_SemiringWithoutOne_1880
v0) in
    AgdaAny -> T_IsCommutativeMagma_212
forall a b. a -> b
coe
      (let v2 :: T_IsCommutativeMonoid_736
v2
             = T_IsSemiringWithoutOne_1298 -> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1316
                 (T_IsSemiringWithoutOne_1298 -> T_IsSemiringWithoutOne_1298
forall a b. a -> b
coe T_IsSemiringWithoutOne_1298
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsCommutativeSemigroup_548 -> T_IsCommutativeMagma_212)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCommutativeSemigroup_548 -> T_IsCommutativeMagma_212
MAlonzo.Code.Algebra.Structures.du_isCommutativeMagma_586
            ((T_IsCommutativeMonoid_736 -> T_IsCommutativeSemigroup_548)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsCommutativeMonoid_736 -> T_IsCommutativeSemigroup_548
MAlonzo.Code.Algebra.Structures.du_isCommutativeSemigroup_786
               (T_IsCommutativeMonoid_736 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v2))))
-- Algebra.Bundles.SemiringWithoutOne._.+-isCommutativeMonoid
d_'43''45'isCommutativeMonoid_1932 ::
  T_SemiringWithoutOne_1880 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1932 :: T_SemiringWithoutOne_1880 -> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_1932 T_SemiringWithoutOne_1880
v0
  = (T_IsSemiringWithoutOne_1298 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> T_IsCommutativeMonoid_736
forall a b. a -> b
coe
      T_IsSemiringWithoutOne_1298 -> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1316
      ((T_SemiringWithoutOne_1880 -> T_IsSemiringWithoutOne_1298)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutOne_1880 -> T_IsSemiringWithoutOne_1298
d_isSemiringWithoutOne_1908 (T_SemiringWithoutOne_1880 -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutOne_1880
v0))
-- Algebra.Bundles.SemiringWithoutOne._.isCommutativeSemigroup
d_isCommutativeSemigroup_1934 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SemiringWithoutOne_1880 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_548
d_isCommutativeSemigroup_1934 :: ()
-> () -> T_SemiringWithoutOne_1880 -> T_IsCommutativeSemigroup_548
d_isCommutativeSemigroup_1934 ~()
v0 ~()
v1 T_SemiringWithoutOne_1880
v2
  = T_SemiringWithoutOne_1880 -> T_IsCommutativeSemigroup_548
du_isCommutativeSemigroup_1934 T_SemiringWithoutOne_1880
v2
du_isCommutativeSemigroup_1934 ::
  T_SemiringWithoutOne_1880 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_548
du_isCommutativeSemigroup_1934 :: T_SemiringWithoutOne_1880 -> T_IsCommutativeSemigroup_548
du_isCommutativeSemigroup_1934 T_SemiringWithoutOne_1880
v0
  = let v1 :: T_IsSemiringWithoutOne_1298
v1 = T_SemiringWithoutOne_1880 -> T_IsSemiringWithoutOne_1298
d_isSemiringWithoutOne_1908 (T_SemiringWithoutOne_1880 -> T_SemiringWithoutOne_1880
forall a b. a -> b
coe T_SemiringWithoutOne_1880
v0) in
    AgdaAny -> T_IsCommutativeSemigroup_548
forall a b. a -> b
coe
      ((T_IsCommutativeMonoid_736 -> T_IsCommutativeSemigroup_548)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCommutativeMonoid_736 -> T_IsCommutativeSemigroup_548
MAlonzo.Code.Algebra.Structures.du_isCommutativeSemigroup_786
         ((T_IsSemiringWithoutOne_1298 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemiringWithoutOne_1298 -> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1316
            (T_IsSemiringWithoutOne_1298 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_1298
v1)))
-- Algebra.Bundles.SemiringWithoutOne._.isMonoid
d_isMonoid_1936 ::
  T_SemiringWithoutOne_1880 ->
  MAlonzo.Code.Algebra.Structures.T_IsMonoid_686
d_isMonoid_1936 :: T_SemiringWithoutOne_1880 -> T_IsMonoid_686
d_isMonoid_1936 T_SemiringWithoutOne_1880
v0
  = (T_IsCommutativeMonoid_736 -> T_IsMonoid_686)
-> AgdaAny -> T_IsMonoid_686
forall a b. a -> b
coe
      T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746
      ((T_IsSemiringWithoutOne_1298 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiringWithoutOne_1298 -> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1316
         ((T_SemiringWithoutOne_1880 -> T_IsSemiringWithoutOne_1298)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutOne_1880 -> T_IsSemiringWithoutOne_1298
d_isSemiringWithoutOne_1908 (T_SemiringWithoutOne_1880 -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutOne_1880
v0)))
-- Algebra.Bundles.SemiringWithoutOne._.Carrier
d_Carrier_1938 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SemiringWithoutOne_1880 -> ()
d_Carrier_1938 :: () -> () -> T_SemiringWithoutOne_1880 -> ()
d_Carrier_1938 = () -> () -> T_SemiringWithoutOne_1880 -> ()
forall a. a
erased
-- Algebra.Bundles.SemiringWithoutOne._.distrib
d_distrib_1940 ::
  T_SemiringWithoutOne_1880 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_distrib_1940 :: T_SemiringWithoutOne_1880 -> T_Σ_14
d_distrib_1940 T_SemiringWithoutOne_1880
v0
  = (T_IsSemiringWithoutOne_1298 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsSemiringWithoutOne_1298 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_distrib_1322
      ((T_SemiringWithoutOne_1880 -> T_IsSemiringWithoutOne_1298)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutOne_1880 -> T_IsSemiringWithoutOne_1298
d_isSemiringWithoutOne_1908 (T_SemiringWithoutOne_1880 -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutOne_1880
v0))
-- Algebra.Bundles.SemiringWithoutOne._.isEquivalence
d_isEquivalence_1942 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SemiringWithoutOne_1880 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_1942 :: () -> () -> T_SemiringWithoutOne_1880 -> T_IsEquivalence_26
d_isEquivalence_1942 ~()
v0 ~()
v1 T_SemiringWithoutOne_1880
v2 = T_SemiringWithoutOne_1880 -> T_IsEquivalence_26
du_isEquivalence_1942 T_SemiringWithoutOne_1880
v2
du_isEquivalence_1942 ::
  T_SemiringWithoutOne_1880 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
du_isEquivalence_1942 :: T_SemiringWithoutOne_1880 -> T_IsEquivalence_26
du_isEquivalence_1942 T_SemiringWithoutOne_1880
v0
  = let v1 :: T_IsSemiringWithoutOne_1298
v1 = T_SemiringWithoutOne_1880 -> T_IsSemiringWithoutOne_1298
d_isSemiringWithoutOne_1908 (T_SemiringWithoutOne_1880 -> T_SemiringWithoutOne_1880
forall a b. a -> b
coe T_SemiringWithoutOne_1880
v0) in
    AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      ((T_Setoid_44 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_Setoid_44 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60
         (let v2 :: T_IsMonoid_686
v2
                = T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746
                    ((T_IsSemiringWithoutOne_1298 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> T_IsCommutativeMonoid_736
forall a b. a -> b
coe
                       T_IsSemiringWithoutOne_1298 -> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1316
                       (T_IsSemiringWithoutOne_1298 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_1298
v1)) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v3 :: T_IsSemigroup_472
v3
                   = T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v2) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               ((T_IsMagma_176 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsMagma_176 -> T_Setoid_44
MAlonzo.Code.Algebra.Structures.du_setoid_200
                  ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v3))))))
-- Algebra.Bundles.SemiringWithoutOne._.isNearSemiring
d_isNearSemiring_1944 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SemiringWithoutOne_1880 ->
  MAlonzo.Code.Algebra.Structures.T_IsNearSemiring_1218
d_isNearSemiring_1944 :: () -> () -> T_SemiringWithoutOne_1880 -> T_IsNearSemiring_1218
d_isNearSemiring_1944 ~()
v0 ~()
v1 T_SemiringWithoutOne_1880
v2 = T_SemiringWithoutOne_1880 -> T_IsNearSemiring_1218
du_isNearSemiring_1944 T_SemiringWithoutOne_1880
v2
du_isNearSemiring_1944 ::
  T_SemiringWithoutOne_1880 ->
  MAlonzo.Code.Algebra.Structures.T_IsNearSemiring_1218
du_isNearSemiring_1944 :: T_SemiringWithoutOne_1880 -> T_IsNearSemiring_1218
du_isNearSemiring_1944 T_SemiringWithoutOne_1880
v0
  = (T_IsSemiringWithoutOne_1298 -> T_IsNearSemiring_1218)
-> AgdaAny -> T_IsNearSemiring_1218
forall a b. a -> b
coe
      T_IsSemiringWithoutOne_1298 -> T_IsNearSemiring_1218
MAlonzo.Code.Algebra.Structures.du_isNearSemiring_1374
      ((T_SemiringWithoutOne_1880 -> T_IsSemiringWithoutOne_1298)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutOne_1880 -> T_IsSemiringWithoutOne_1298
d_isSemiringWithoutOne_1908 (T_SemiringWithoutOne_1880 -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutOne_1880
v0))
-- Algebra.Bundles.SemiringWithoutOne._.isPartialEquivalence
d_isPartialEquivalence_1946 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SemiringWithoutOne_1880 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_1946 :: () -> () -> T_SemiringWithoutOne_1880 -> T_IsPartialEquivalence_16
d_isPartialEquivalence_1946 ~()
v0 ~()
v1 T_SemiringWithoutOne_1880
v2
  = T_SemiringWithoutOne_1880 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_1946 T_SemiringWithoutOne_1880
v2
du_isPartialEquivalence_1946 ::
  T_SemiringWithoutOne_1880 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_1946 :: T_SemiringWithoutOne_1880 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_1946 T_SemiringWithoutOne_1880
v0
  = let v1 :: T_IsSemiringWithoutOne_1298
v1 = T_SemiringWithoutOne_1880 -> T_IsSemiringWithoutOne_1298
d_isSemiringWithoutOne_1908 (T_SemiringWithoutOne_1880 -> T_SemiringWithoutOne_1880
forall a b. a -> b
coe T_SemiringWithoutOne_1880
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: b
v2
             = let v2 :: T_IsMonoid_686
v2
                     = T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746
                         ((T_IsSemiringWithoutOne_1298 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> T_IsCommutativeMonoid_736
forall a b. a -> b
coe
                            T_IsSemiringWithoutOne_1298 -> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1316
                            (T_IsSemiringWithoutOne_1298 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_1298
v1)) in
               AgdaAny -> b
forall a b. a -> b
coe
                 (let v3 :: T_IsSemigroup_472
v3
                        = T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v2) in
                  AgdaAny -> AgdaAny
forall a b. a -> b
coe
                    ((T_IsMagma_176 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                       T_IsMagma_176 -> T_Setoid_44
MAlonzo.Code.Algebra.Structures.du_setoid_200
                       ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v3)))) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsEquivalence_26 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsEquivalence_26 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
            ((T_Setoid_44 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_Setoid_44 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2))))
-- Algebra.Bundles.SemiringWithoutOne._.partialSetoid
d_partialSetoid_1948 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SemiringWithoutOne_1880 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
d_partialSetoid_1948 :: () -> () -> T_SemiringWithoutOne_1880 -> T_PartialSetoid_10
d_partialSetoid_1948 ~()
v0 ~()
v1 T_SemiringWithoutOne_1880
v2 = T_SemiringWithoutOne_1880 -> T_PartialSetoid_10
du_partialSetoid_1948 T_SemiringWithoutOne_1880
v2
du_partialSetoid_1948 ::
  T_SemiringWithoutOne_1880 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
du_partialSetoid_1948 :: T_SemiringWithoutOne_1880 -> T_PartialSetoid_10
du_partialSetoid_1948 T_SemiringWithoutOne_1880
v0
  = let v1 :: T_IsSemiringWithoutOne_1298
v1 = T_SemiringWithoutOne_1880 -> T_IsSemiringWithoutOne_1298
d_isSemiringWithoutOne_1908 (T_SemiringWithoutOne_1880 -> T_SemiringWithoutOne_1880
forall a b. a -> b
coe T_SemiringWithoutOne_1880
v0) in
    AgdaAny -> T_PartialSetoid_10
forall a b. a -> b
coe
      ((T_Setoid_44 -> T_PartialSetoid_10) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_Setoid_44 -> T_PartialSetoid_10
MAlonzo.Code.Relation.Binary.Bundles.du_partialSetoid_70
         (let v2 :: T_IsMonoid_686
v2
                = T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746
                    ((T_IsSemiringWithoutOne_1298 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> T_IsCommutativeMonoid_736
forall a b. a -> b
coe
                       T_IsSemiringWithoutOne_1298 -> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1316
                       (T_IsSemiringWithoutOne_1298 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_1298
v1)) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v3 :: T_IsSemigroup_472
v3
                   = T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v2) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               ((T_IsMagma_176 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsMagma_176 -> T_Setoid_44
MAlonzo.Code.Algebra.Structures.du_setoid_200
                  ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v3))))))
-- Algebra.Bundles.SemiringWithoutOne._.refl
d_refl_1950 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SemiringWithoutOne_1880 -> AgdaAny -> AgdaAny
d_refl_1950 :: () -> () -> T_SemiringWithoutOne_1880 -> AgdaAny -> AgdaAny
d_refl_1950 ~()
v0 ~()
v1 T_SemiringWithoutOne_1880
v2 = T_SemiringWithoutOne_1880 -> AgdaAny -> AgdaAny
du_refl_1950 T_SemiringWithoutOne_1880
v2
du_refl_1950 :: T_SemiringWithoutOne_1880 -> AgdaAny -> AgdaAny
du_refl_1950 :: T_SemiringWithoutOne_1880 -> AgdaAny -> AgdaAny
du_refl_1950 T_SemiringWithoutOne_1880
v0
  = let v1 :: T_IsSemiringWithoutOne_1298
v1 = T_SemiringWithoutOne_1880 -> T_IsSemiringWithoutOne_1298
d_isSemiringWithoutOne_1908 (T_SemiringWithoutOne_1880 -> T_SemiringWithoutOne_1880
forall a b. a -> b
coe T_SemiringWithoutOne_1880
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsEquivalence_26 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_34
         ((T_Setoid_44 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_Setoid_44 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60
            (let v2 :: T_IsMonoid_686
v2
                   = T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746
                       ((T_IsSemiringWithoutOne_1298 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> T_IsCommutativeMonoid_736
forall a b. a -> b
coe
                          T_IsSemiringWithoutOne_1298 -> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1316
                          (T_IsSemiringWithoutOne_1298 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_1298
v1)) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v3 :: T_IsSemigroup_472
v3
                      = T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v2) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  ((T_IsMagma_176 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsMagma_176 -> T_Setoid_44
MAlonzo.Code.Algebra.Structures.du_setoid_200
                     ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v3)))))))
-- Algebra.Bundles.SemiringWithoutOne._.reflexive
d_reflexive_1952 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SemiringWithoutOne_1880 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_1952 :: ()
-> ()
-> T_SemiringWithoutOne_1880
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_1952 ~()
v0 ~()
v1 T_SemiringWithoutOne_1880
v2 = T_SemiringWithoutOne_1880
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_1952 T_SemiringWithoutOne_1880
v2
du_reflexive_1952 ::
  T_SemiringWithoutOne_1880 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_1952 :: T_SemiringWithoutOne_1880
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_1952 T_SemiringWithoutOne_1880
v0
  = let v1 :: T_IsSemiringWithoutOne_1298
v1 = T_SemiringWithoutOne_1880 -> T_IsSemiringWithoutOne_1298
d_isSemiringWithoutOne_1908 (T_SemiringWithoutOne_1880 -> T_SemiringWithoutOne_1880
forall a b. a -> b
coe T_SemiringWithoutOne_1880
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: b
v2
             = let v2 :: T_IsMonoid_686
v2
                     = T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746
                         ((T_IsSemiringWithoutOne_1298 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> T_IsCommutativeMonoid_736
forall a b. a -> b
coe
                            T_IsSemiringWithoutOne_1298 -> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1316
                            (T_IsSemiringWithoutOne_1298 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_1298
v1)) in
               AgdaAny -> b
forall a b. a -> b
coe
                 (let v3 :: T_IsSemigroup_472
v3
                        = T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v2) in
                  AgdaAny -> AgdaAny
forall a b. a -> b
coe
                    ((T_IsMagma_176 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                       T_IsMagma_176 -> T_Setoid_44
MAlonzo.Code.Algebra.Structures.du_setoid_200
                       ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v3)))) in
       (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
         (\ AgdaAny
v3 AgdaAny
v4 AgdaAny
v5 ->
            (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
              T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
              ((T_Setoid_44 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                 T_Setoid_44 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2))
              AgdaAny
v3))
-- Algebra.Bundles.SemiringWithoutOne._.setoid
d_setoid_1954 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SemiringWithoutOne_1880 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_1954 :: () -> () -> T_SemiringWithoutOne_1880 -> T_Setoid_44
d_setoid_1954 ~()
v0 ~()
v1 T_SemiringWithoutOne_1880
v2 = T_SemiringWithoutOne_1880 -> T_Setoid_44
du_setoid_1954 T_SemiringWithoutOne_1880
v2
du_setoid_1954 ::
  T_SemiringWithoutOne_1880 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_1954 :: T_SemiringWithoutOne_1880 -> T_Setoid_44
du_setoid_1954 T_SemiringWithoutOne_1880
v0
  = let v1 :: T_IsSemiringWithoutOne_1298
v1 = T_SemiringWithoutOne_1880 -> T_IsSemiringWithoutOne_1298
d_isSemiringWithoutOne_1908 (T_SemiringWithoutOne_1880 -> T_SemiringWithoutOne_1880
forall a b. a -> b
coe T_SemiringWithoutOne_1880
v0) in
    AgdaAny -> T_Setoid_44
forall a b. a -> b
coe
      (let v2 :: T_IsCommutativeMonoid_736
v2
             = T_IsSemiringWithoutOne_1298 -> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1316
                 (T_IsSemiringWithoutOne_1298 -> T_IsSemiringWithoutOne_1298
forall a b. a -> b
coe T_IsSemiringWithoutOne_1298
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsMonoid_686
v3
                = T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746 (T_IsCommutativeMonoid_736 -> T_IsCommutativeMonoid_736
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsSemigroup_472
v4
                   = T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               ((T_IsMagma_176 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsMagma_176 -> T_Setoid_44
MAlonzo.Code.Algebra.Structures.du_setoid_200
                  ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v4))))))
-- Algebra.Bundles.SemiringWithoutOne._.sym
d_sym_1956 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SemiringWithoutOne_1880 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_1956 :: ()
-> ()
-> T_SemiringWithoutOne_1880
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_sym_1956 ~()
v0 ~()
v1 T_SemiringWithoutOne_1880
v2 = T_SemiringWithoutOne_1880
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_1956 T_SemiringWithoutOne_1880
v2
du_sym_1956 ::
  T_SemiringWithoutOne_1880 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_1956 :: T_SemiringWithoutOne_1880
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_1956 T_SemiringWithoutOne_1880
v0
  = let v1 :: T_IsSemiringWithoutOne_1298
v1 = T_SemiringWithoutOne_1880 -> T_IsSemiringWithoutOne_1298
d_isSemiringWithoutOne_1908 (T_SemiringWithoutOne_1880 -> T_SemiringWithoutOne_1880
forall a b. a -> b
coe T_SemiringWithoutOne_1880
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: b
v2
             = let v2 :: T_IsMonoid_686
v2
                     = T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746
                         ((T_IsSemiringWithoutOne_1298 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> T_IsCommutativeMonoid_736
forall a b. a -> b
coe
                            T_IsSemiringWithoutOne_1298 -> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1316
                            (T_IsSemiringWithoutOne_1298 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_1298
v1)) in
               AgdaAny -> b
forall a b. a -> b
coe
                 (let v3 :: T_IsSemigroup_472
v3
                        = T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v2) in
                  AgdaAny -> AgdaAny
forall a b. a -> b
coe
                    ((T_IsMagma_176 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                       T_IsMagma_176 -> T_Setoid_44
MAlonzo.Code.Algebra.Structures.du_setoid_200
                       ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v3)))) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_36
            ((T_Setoid_44 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_Setoid_44 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2))))
-- Algebra.Bundles.SemiringWithoutOne._.trans
d_trans_1958 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SemiringWithoutOne_1880 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_1958 :: ()
-> ()
-> T_SemiringWithoutOne_1880
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_trans_1958 ~()
v0 ~()
v1 T_SemiringWithoutOne_1880
v2 = T_SemiringWithoutOne_1880
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_1958 T_SemiringWithoutOne_1880
v2
du_trans_1958 ::
  T_SemiringWithoutOne_1880 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_1958 :: T_SemiringWithoutOne_1880
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_1958 T_SemiringWithoutOne_1880
v0
  = let v1 :: T_IsSemiringWithoutOne_1298
v1 = T_SemiringWithoutOne_1880 -> T_IsSemiringWithoutOne_1298
d_isSemiringWithoutOne_1908 (T_SemiringWithoutOne_1880 -> T_SemiringWithoutOne_1880
forall a b. a -> b
coe T_SemiringWithoutOne_1880
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: b
v2
             = let v2 :: T_IsMonoid_686
v2
                     = T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746
                         ((T_IsSemiringWithoutOne_1298 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> T_IsCommutativeMonoid_736
forall a b. a -> b
coe
                            T_IsSemiringWithoutOne_1298 -> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1316
                            (T_IsSemiringWithoutOne_1298 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_1298
v1)) in
               AgdaAny -> b
forall a b. a -> b
coe
                 (let v3 :: T_IsSemigroup_472
v3
                        = T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v2) in
                  AgdaAny -> AgdaAny
forall a b. a -> b
coe
                    ((T_IsMagma_176 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                       T_IsMagma_176 -> T_Setoid_44
MAlonzo.Code.Algebra.Structures.du_setoid_200
                       ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v3)))) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsEquivalence_26
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsEquivalence_26
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_38
            ((T_Setoid_44 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_Setoid_44 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2))))
-- Algebra.Bundles.SemiringWithoutOne._.zero
d_zero_1960 ::
  T_SemiringWithoutOne_1880 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_zero_1960 :: T_SemiringWithoutOne_1880 -> T_Σ_14
d_zero_1960 T_SemiringWithoutOne_1880
v0
  = (T_IsSemiringWithoutOne_1298 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsSemiringWithoutOne_1298 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_zero_1324
      ((T_SemiringWithoutOne_1880 -> T_IsSemiringWithoutOne_1298)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutOne_1880 -> T_IsSemiringWithoutOne_1298
d_isSemiringWithoutOne_1908 (T_SemiringWithoutOne_1880 -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutOne_1880
v0))
-- Algebra.Bundles.SemiringWithoutOne._.zeroʳ
d_zero'691'_1962 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SemiringWithoutOne_1880 -> AgdaAny -> AgdaAny
d_zero'691'_1962 :: () -> () -> T_SemiringWithoutOne_1880 -> AgdaAny -> AgdaAny
d_zero'691'_1962 ~()
v0 ~()
v1 T_SemiringWithoutOne_1880
v2 = T_SemiringWithoutOne_1880 -> AgdaAny -> AgdaAny
du_zero'691'_1962 T_SemiringWithoutOne_1880
v2
du_zero'691'_1962 ::
  T_SemiringWithoutOne_1880 -> AgdaAny -> AgdaAny
du_zero'691'_1962 :: T_SemiringWithoutOne_1880 -> AgdaAny -> AgdaAny
du_zero'691'_1962 T_SemiringWithoutOne_1880
v0
  = (T_IsSemiringWithoutOne_1298 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsSemiringWithoutOne_1298 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_zero'691'_1372
      ((T_SemiringWithoutOne_1880 -> T_IsSemiringWithoutOne_1298)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutOne_1880 -> T_IsSemiringWithoutOne_1298
d_isSemiringWithoutOne_1908 (T_SemiringWithoutOne_1880 -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutOne_1880
v0))
-- Algebra.Bundles.SemiringWithoutOne._.zeroˡ
d_zero'737'_1964 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SemiringWithoutOne_1880 -> AgdaAny -> AgdaAny
d_zero'737'_1964 :: () -> () -> T_SemiringWithoutOne_1880 -> AgdaAny -> AgdaAny
d_zero'737'_1964 ~()
v0 ~()
v1 T_SemiringWithoutOne_1880
v2 = T_SemiringWithoutOne_1880 -> AgdaAny -> AgdaAny
du_zero'737'_1964 T_SemiringWithoutOne_1880
v2
du_zero'737'_1964 ::
  T_SemiringWithoutOne_1880 -> AgdaAny -> AgdaAny
du_zero'737'_1964 :: T_SemiringWithoutOne_1880 -> AgdaAny -> AgdaAny
du_zero'737'_1964 T_SemiringWithoutOne_1880
v0
  = (T_IsSemiringWithoutOne_1298 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsSemiringWithoutOne_1298 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_zero'737'_1370
      ((T_SemiringWithoutOne_1880 -> T_IsSemiringWithoutOne_1298)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutOne_1880 -> T_IsSemiringWithoutOne_1298
d_isSemiringWithoutOne_1908 (T_SemiringWithoutOne_1880 -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutOne_1880
v0))
-- Algebra.Bundles.SemiringWithoutOne.nearSemiring
d_nearSemiring_1966 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SemiringWithoutOne_1880 -> T_NearSemiring_1766
d_nearSemiring_1966 :: () -> () -> T_SemiringWithoutOne_1880 -> T_NearSemiring_1766
d_nearSemiring_1966 ~()
v0 ~()
v1 T_SemiringWithoutOne_1880
v2 = T_SemiringWithoutOne_1880 -> T_NearSemiring_1766
du_nearSemiring_1966 T_SemiringWithoutOne_1880
v2
du_nearSemiring_1966 ::
  T_SemiringWithoutOne_1880 -> T_NearSemiring_1766
du_nearSemiring_1966 :: T_SemiringWithoutOne_1880 -> T_NearSemiring_1766
du_nearSemiring_1966 T_SemiringWithoutOne_1880
v0
  = ((AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> T_IsNearSemiring_1218
 -> T_NearSemiring_1766)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_NearSemiring_1766
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsNearSemiring_1218
-> T_NearSemiring_1766
C_NearSemiring'46'constructor_32269 (T_SemiringWithoutOne_1880 -> AgdaAny -> AgdaAny -> AgdaAny
d__'43'__1902 (T_SemiringWithoutOne_1880 -> T_SemiringWithoutOne_1880
forall a b. a -> b
coe T_SemiringWithoutOne_1880
v0))
      (T_SemiringWithoutOne_1880 -> AgdaAny -> AgdaAny -> AgdaAny
d__'42'__1904 (T_SemiringWithoutOne_1880 -> T_SemiringWithoutOne_1880
forall a b. a -> b
coe T_SemiringWithoutOne_1880
v0)) (T_SemiringWithoutOne_1880 -> AgdaAny
d_0'35'_1906 (T_SemiringWithoutOne_1880 -> T_SemiringWithoutOne_1880
forall a b. a -> b
coe T_SemiringWithoutOne_1880
v0))
      ((T_IsSemiringWithoutOne_1298 -> T_IsNearSemiring_1218)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiringWithoutOne_1298 -> T_IsNearSemiring_1218
MAlonzo.Code.Algebra.Structures.du_isNearSemiring_1374
         ((T_SemiringWithoutOne_1880 -> T_IsSemiringWithoutOne_1298)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutOne_1880 -> T_IsSemiringWithoutOne_1298
d_isSemiringWithoutOne_1908 (T_SemiringWithoutOne_1880 -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutOne_1880
v0)))
-- Algebra.Bundles.SemiringWithoutOne._.magma
d_magma_1970 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SemiringWithoutOne_1880 -> T_Magma_68
d_magma_1970 :: () -> () -> T_SemiringWithoutOne_1880 -> T_Magma_68
d_magma_1970 ~()
v0 ~()
v1 T_SemiringWithoutOne_1880
v2 = T_SemiringWithoutOne_1880 -> T_Magma_68
du_magma_1970 T_SemiringWithoutOne_1880
v2
du_magma_1970 :: T_SemiringWithoutOne_1880 -> T_Magma_68
du_magma_1970 :: T_SemiringWithoutOne_1880 -> T_Magma_68
du_magma_1970 T_SemiringWithoutOne_1880
v0
  = let v1 :: t
v1 = (T_SemiringWithoutOne_1880 -> T_NearSemiring_1766) -> AgdaAny -> t
forall a b. a -> b
coe T_SemiringWithoutOne_1880 -> T_NearSemiring_1766
du_nearSemiring_1966 (T_SemiringWithoutOne_1880 -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutOne_1880
v0) in
    AgdaAny -> T_Magma_68
forall a b. a -> b
coe ((T_Semigroup_536 -> T_Magma_68) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semigroup_536 -> T_Magma_68
du_magma_584 ((T_NearSemiring_1766 -> T_Semigroup_536) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_NearSemiring_1766 -> T_Semigroup_536
du_'42''45'semigroup_1868 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1)))
-- Algebra.Bundles.SemiringWithoutOne._.rawMagma
d_rawMagma_1972 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SemiringWithoutOne_1880 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
d_rawMagma_1972 :: () -> () -> T_SemiringWithoutOne_1880 -> T_RawMagma_36
d_rawMagma_1972 ~()
v0 ~()
v1 T_SemiringWithoutOne_1880
v2 = T_SemiringWithoutOne_1880 -> T_RawMagma_36
du_rawMagma_1972 T_SemiringWithoutOne_1880
v2
du_rawMagma_1972 ::
  T_SemiringWithoutOne_1880 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
du_rawMagma_1972 :: T_SemiringWithoutOne_1880 -> T_RawMagma_36
du_rawMagma_1972 T_SemiringWithoutOne_1880
v0
  = let v1 :: t
v1 = (T_SemiringWithoutOne_1880 -> T_NearSemiring_1766) -> AgdaAny -> t
forall a b. a -> b
coe T_SemiringWithoutOne_1880 -> T_NearSemiring_1766
du_nearSemiring_1966 (T_SemiringWithoutOne_1880 -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutOne_1880
v0) in
    AgdaAny -> T_RawMagma_36
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_NearSemiring_1766 -> T_Semigroup_536) -> AgdaAny -> t
forall a b. a -> b
coe T_NearSemiring_1766 -> T_Semigroup_536
du_'42''45'semigroup_1868 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_Magma_68 -> T_RawMagma_36) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Magma_68 -> T_RawMagma_36
du_rawMagma_112 ((T_Semigroup_536 -> T_Magma_68) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semigroup_536 -> T_Magma_68
du_magma_584 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2))))
-- Algebra.Bundles.SemiringWithoutOne._.*-semigroup
d_'42''45'semigroup_1974 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SemiringWithoutOne_1880 -> T_Semigroup_536
d_'42''45'semigroup_1974 :: () -> () -> T_SemiringWithoutOne_1880 -> T_Semigroup_536
d_'42''45'semigroup_1974 ~()
v0 ~()
v1 T_SemiringWithoutOne_1880
v2 = T_SemiringWithoutOne_1880 -> T_Semigroup_536
du_'42''45'semigroup_1974 T_SemiringWithoutOne_1880
v2
du_'42''45'semigroup_1974 ::
  T_SemiringWithoutOne_1880 -> T_Semigroup_536
du_'42''45'semigroup_1974 :: T_SemiringWithoutOne_1880 -> T_Semigroup_536
du_'42''45'semigroup_1974 T_SemiringWithoutOne_1880
v0
  = (T_NearSemiring_1766 -> T_Semigroup_536)
-> AgdaAny -> T_Semigroup_536
forall a b. a -> b
coe T_NearSemiring_1766 -> T_Semigroup_536
du_'42''45'semigroup_1868 ((T_SemiringWithoutOne_1880 -> T_NearSemiring_1766)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutOne_1880 -> T_NearSemiring_1766
du_nearSemiring_1966 (T_SemiringWithoutOne_1880 -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutOne_1880
v0))
-- Algebra.Bundles.SemiringWithoutOne._.magma
d_magma_1976 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SemiringWithoutOne_1880 -> T_Magma_68
d_magma_1976 :: () -> () -> T_SemiringWithoutOne_1880 -> T_Magma_68
d_magma_1976 ~()
v0 ~()
v1 T_SemiringWithoutOne_1880
v2 = T_SemiringWithoutOne_1880 -> T_Magma_68
du_magma_1976 T_SemiringWithoutOne_1880
v2
du_magma_1976 :: T_SemiringWithoutOne_1880 -> T_Magma_68
du_magma_1976 :: T_SemiringWithoutOne_1880 -> T_Magma_68
du_magma_1976 T_SemiringWithoutOne_1880
v0
  = let v1 :: t
v1 = (T_SemiringWithoutOne_1880 -> T_NearSemiring_1766) -> AgdaAny -> t
forall a b. a -> b
coe T_SemiringWithoutOne_1880 -> T_NearSemiring_1766
du_nearSemiring_1966 (T_SemiringWithoutOne_1880 -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutOne_1880
v0) in
    AgdaAny -> T_Magma_68
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_NearSemiring_1766 -> T_Monoid_882) -> AgdaAny -> t
forall a b. a -> b
coe T_NearSemiring_1766 -> T_Monoid_882
du_'43''45'monoid_1852 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_Semigroup_536 -> T_Magma_68) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semigroup_536 -> T_Magma_68
du_magma_584 ((T_Monoid_882 -> T_Semigroup_536) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Monoid_882 -> T_Semigroup_536
du_semigroup_944 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2))))
-- Algebra.Bundles.SemiringWithoutOne._.+-monoid
d_'43''45'monoid_1978 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SemiringWithoutOne_1880 -> T_Monoid_882
d_'43''45'monoid_1978 :: () -> () -> T_SemiringWithoutOne_1880 -> T_Monoid_882
d_'43''45'monoid_1978 ~()
v0 ~()
v1 T_SemiringWithoutOne_1880
v2 = T_SemiringWithoutOne_1880 -> T_Monoid_882
du_'43''45'monoid_1978 T_SemiringWithoutOne_1880
v2
du_'43''45'monoid_1978 :: T_SemiringWithoutOne_1880 -> T_Monoid_882
du_'43''45'monoid_1978 :: T_SemiringWithoutOne_1880 -> T_Monoid_882
du_'43''45'monoid_1978 T_SemiringWithoutOne_1880
v0
  = (T_NearSemiring_1766 -> T_Monoid_882) -> AgdaAny -> T_Monoid_882
forall a b. a -> b
coe T_NearSemiring_1766 -> T_Monoid_882
du_'43''45'monoid_1852 ((T_SemiringWithoutOne_1880 -> T_NearSemiring_1766)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutOne_1880 -> T_NearSemiring_1766
du_nearSemiring_1966 (T_SemiringWithoutOne_1880 -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutOne_1880
v0))
-- Algebra.Bundles.SemiringWithoutOne._.rawMagma
d_rawMagma_1980 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SemiringWithoutOne_1880 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
d_rawMagma_1980 :: () -> () -> T_SemiringWithoutOne_1880 -> T_RawMagma_36
d_rawMagma_1980 ~()
v0 ~()
v1 T_SemiringWithoutOne_1880
v2 = T_SemiringWithoutOne_1880 -> T_RawMagma_36
du_rawMagma_1980 T_SemiringWithoutOne_1880
v2
du_rawMagma_1980 ::
  T_SemiringWithoutOne_1880 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
du_rawMagma_1980 :: T_SemiringWithoutOne_1880 -> T_RawMagma_36
du_rawMagma_1980 T_SemiringWithoutOne_1880
v0
  = let v1 :: t
v1 = (T_SemiringWithoutOne_1880 -> T_NearSemiring_1766) -> AgdaAny -> t
forall a b. a -> b
coe T_SemiringWithoutOne_1880 -> T_NearSemiring_1766
du_nearSemiring_1966 (T_SemiringWithoutOne_1880 -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutOne_1880
v0) in
    AgdaAny -> T_RawMagma_36
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_NearSemiring_1766 -> T_Monoid_882) -> AgdaAny -> t
forall a b. a -> b
coe T_NearSemiring_1766 -> T_Monoid_882
du_'43''45'monoid_1852 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: t
v3 = (T_Monoid_882 -> T_Semigroup_536) -> AgdaAny -> t
forall a b. a -> b
coe T_Monoid_882 -> T_Semigroup_536
du_semigroup_944 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_Magma_68 -> T_RawMagma_36) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Magma_68 -> T_RawMagma_36
du_rawMagma_112 ((T_Semigroup_536 -> T_Magma_68) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semigroup_536 -> T_Magma_68
du_magma_584 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3)))))
-- Algebra.Bundles.SemiringWithoutOne._.rawMonoid
d_rawMonoid_1982 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SemiringWithoutOne_1880 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMonoid_64
d_rawMonoid_1982 :: () -> () -> T_SemiringWithoutOne_1880 -> T_RawMonoid_64
d_rawMonoid_1982 ~()
v0 ~()
v1 T_SemiringWithoutOne_1880
v2 = T_SemiringWithoutOne_1880 -> T_RawMonoid_64
du_rawMonoid_1982 T_SemiringWithoutOne_1880
v2
du_rawMonoid_1982 ::
  T_SemiringWithoutOne_1880 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMonoid_64
du_rawMonoid_1982 :: T_SemiringWithoutOne_1880 -> T_RawMonoid_64
du_rawMonoid_1982 T_SemiringWithoutOne_1880
v0
  = let v1 :: t
v1 = (T_SemiringWithoutOne_1880 -> T_NearSemiring_1766) -> AgdaAny -> t
forall a b. a -> b
coe T_SemiringWithoutOne_1880 -> T_NearSemiring_1766
du_nearSemiring_1966 (T_SemiringWithoutOne_1880 -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutOne_1880
v0) in
    AgdaAny -> T_RawMonoid_64
forall a b. a -> b
coe ((T_Monoid_882 -> T_RawMonoid_64) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Monoid_882 -> T_RawMonoid_64
du_rawMonoid_954 ((T_NearSemiring_1766 -> T_Monoid_882) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_NearSemiring_1766 -> T_Monoid_882
du_'43''45'monoid_1852 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1)))
-- Algebra.Bundles.SemiringWithoutOne._.semigroup
d_semigroup_1984 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SemiringWithoutOne_1880 -> T_Semigroup_536
d_semigroup_1984 :: () -> () -> T_SemiringWithoutOne_1880 -> T_Semigroup_536
d_semigroup_1984 ~()
v0 ~()
v1 T_SemiringWithoutOne_1880
v2 = T_SemiringWithoutOne_1880 -> T_Semigroup_536
du_semigroup_1984 T_SemiringWithoutOne_1880
v2
du_semigroup_1984 :: T_SemiringWithoutOne_1880 -> T_Semigroup_536
du_semigroup_1984 :: T_SemiringWithoutOne_1880 -> T_Semigroup_536
du_semigroup_1984 T_SemiringWithoutOne_1880
v0
  = let v1 :: t
v1 = (T_SemiringWithoutOne_1880 -> T_NearSemiring_1766) -> AgdaAny -> t
forall a b. a -> b
coe T_SemiringWithoutOne_1880 -> T_NearSemiring_1766
du_nearSemiring_1966 (T_SemiringWithoutOne_1880 -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutOne_1880
v0) in
    AgdaAny -> T_Semigroup_536
forall a b. a -> b
coe ((T_Monoid_882 -> T_Semigroup_536) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Monoid_882 -> T_Semigroup_536
du_semigroup_944 ((T_NearSemiring_1766 -> T_Monoid_882) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_NearSemiring_1766 -> T_Monoid_882
du_'43''45'monoid_1852 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1)))
-- Algebra.Bundles.SemiringWithoutOne._.unitalMagma
d_unitalMagma_1986 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SemiringWithoutOne_1880 -> T_UnitalMagma_814
d_unitalMagma_1986 :: () -> () -> T_SemiringWithoutOne_1880 -> T_UnitalMagma_814
d_unitalMagma_1986 ~()
v0 ~()
v1 T_SemiringWithoutOne_1880
v2 = T_SemiringWithoutOne_1880 -> T_UnitalMagma_814
du_unitalMagma_1986 T_SemiringWithoutOne_1880
v2
du_unitalMagma_1986 ::
  T_SemiringWithoutOne_1880 -> T_UnitalMagma_814
du_unitalMagma_1986 :: T_SemiringWithoutOne_1880 -> T_UnitalMagma_814
du_unitalMagma_1986 T_SemiringWithoutOne_1880
v0
  = let v1 :: t
v1 = (T_SemiringWithoutOne_1880 -> T_NearSemiring_1766) -> AgdaAny -> t
forall a b. a -> b
coe T_SemiringWithoutOne_1880 -> T_NearSemiring_1766
du_nearSemiring_1966 (T_SemiringWithoutOne_1880 -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutOne_1880
v0) in
    AgdaAny -> T_UnitalMagma_814
forall a b. a -> b
coe ((T_Monoid_882 -> T_UnitalMagma_814) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Monoid_882 -> T_UnitalMagma_814
du_unitalMagma_956 ((T_NearSemiring_1766 -> T_Monoid_882) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_NearSemiring_1766 -> T_Monoid_882
du_'43''45'monoid_1852 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1)))
-- Algebra.Bundles.SemiringWithoutOne._.rawNearSemiring
d_rawNearSemiring_1988 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SemiringWithoutOne_1880 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawNearSemiring_134
d_rawNearSemiring_1988 :: () -> () -> T_SemiringWithoutOne_1880 -> T_RawNearSemiring_134
d_rawNearSemiring_1988 ~()
v0 ~()
v1 T_SemiringWithoutOne_1880
v2 = T_SemiringWithoutOne_1880 -> T_RawNearSemiring_134
du_rawNearSemiring_1988 T_SemiringWithoutOne_1880
v2
du_rawNearSemiring_1988 ::
  T_SemiringWithoutOne_1880 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawNearSemiring_134
du_rawNearSemiring_1988 :: T_SemiringWithoutOne_1880 -> T_RawNearSemiring_134
du_rawNearSemiring_1988 T_SemiringWithoutOne_1880
v0
  = (T_NearSemiring_1766 -> T_RawNearSemiring_134)
-> AgdaAny -> T_RawNearSemiring_134
forall a b. a -> b
coe T_NearSemiring_1766 -> T_RawNearSemiring_134
du_rawNearSemiring_1850 ((T_SemiringWithoutOne_1880 -> T_NearSemiring_1766)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutOne_1880 -> T_NearSemiring_1766
du_nearSemiring_1966 (T_SemiringWithoutOne_1880 -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutOne_1880
v0))
-- Algebra.Bundles.SemiringWithoutOne.+-commutativeMonoid
d_'43''45'commutativeMonoid_1990 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SemiringWithoutOne_1880 -> T_CommutativeMonoid_962
d_'43''45'commutativeMonoid_1990 :: () -> () -> T_SemiringWithoutOne_1880 -> T_CommutativeMonoid_962
d_'43''45'commutativeMonoid_1990 ~()
v0 ~()
v1 T_SemiringWithoutOne_1880
v2
  = T_SemiringWithoutOne_1880 -> T_CommutativeMonoid_962
du_'43''45'commutativeMonoid_1990 T_SemiringWithoutOne_1880
v2
du_'43''45'commutativeMonoid_1990 ::
  T_SemiringWithoutOne_1880 -> T_CommutativeMonoid_962
du_'43''45'commutativeMonoid_1990 :: T_SemiringWithoutOne_1880 -> T_CommutativeMonoid_962
du_'43''45'commutativeMonoid_1990 T_SemiringWithoutOne_1880
v0
  = ((AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny -> T_IsCommutativeMonoid_736 -> T_CommutativeMonoid_962)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsCommutativeMonoid_736
-> T_CommutativeMonoid_962
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> T_IsCommutativeMonoid_736 -> T_CommutativeMonoid_962
C_CommutativeMonoid'46'constructor_17931 (T_SemiringWithoutOne_1880 -> AgdaAny -> AgdaAny -> AgdaAny
d__'43'__1902 (T_SemiringWithoutOne_1880 -> T_SemiringWithoutOne_1880
forall a b. a -> b
coe T_SemiringWithoutOne_1880
v0))
      (T_SemiringWithoutOne_1880 -> AgdaAny
d_0'35'_1906 (T_SemiringWithoutOne_1880 -> T_SemiringWithoutOne_1880
forall a b. a -> b
coe T_SemiringWithoutOne_1880
v0))
      (T_IsSemiringWithoutOne_1298 -> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1316
         ((T_SemiringWithoutOne_1880 -> T_IsSemiringWithoutOne_1298)
-> AgdaAny -> T_IsSemiringWithoutOne_1298
forall a b. a -> b
coe T_SemiringWithoutOne_1880 -> T_IsSemiringWithoutOne_1298
d_isSemiringWithoutOne_1908 (T_SemiringWithoutOne_1880 -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutOne_1880
v0)))
-- Algebra.Bundles.SemiringWithoutOne._.commutativeMagma
d_commutativeMagma_1994 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SemiringWithoutOne_1880 -> T_CommutativeMagma_180
d_commutativeMagma_1994 :: () -> () -> T_SemiringWithoutOne_1880 -> T_CommutativeMagma_180
d_commutativeMagma_1994 ~()
v0 ~()
v1 T_SemiringWithoutOne_1880
v2 = T_SemiringWithoutOne_1880 -> T_CommutativeMagma_180
du_commutativeMagma_1994 T_SemiringWithoutOne_1880
v2
du_commutativeMagma_1994 ::
  T_SemiringWithoutOne_1880 -> T_CommutativeMagma_180
du_commutativeMagma_1994 :: T_SemiringWithoutOne_1880 -> T_CommutativeMagma_180
du_commutativeMagma_1994 T_SemiringWithoutOne_1880
v0
  = let v1 :: t
v1 = (T_SemiringWithoutOne_1880 -> T_CommutativeMonoid_962)
-> AgdaAny -> t
forall a b. a -> b
coe T_SemiringWithoutOne_1880 -> T_CommutativeMonoid_962
du_'43''45'commutativeMonoid_1990 (T_SemiringWithoutOne_1880 -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutOne_1880
v0) in
    AgdaAny -> T_CommutativeMagma_180
forall a b. a -> b
coe
      ((T_CommutativeSemigroup_662 -> T_CommutativeMagma_180)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_CommutativeSemigroup_662 -> T_CommutativeMagma_180
du_commutativeMagma_726
         ((T_CommutativeMonoid_962 -> T_CommutativeSemigroup_662)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeMonoid_962 -> T_CommutativeSemigroup_662
du_commutativeSemigroup_1048 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1)))
-- Algebra.Bundles.SemiringWithoutOne._.commutativeSemigroup
d_commutativeSemigroup_1996 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SemiringWithoutOne_1880 -> T_CommutativeSemigroup_662
d_commutativeSemigroup_1996 :: () -> () -> T_SemiringWithoutOne_1880 -> T_CommutativeSemigroup_662
d_commutativeSemigroup_1996 ~()
v0 ~()
v1 T_SemiringWithoutOne_1880
v2
  = T_SemiringWithoutOne_1880 -> T_CommutativeSemigroup_662
du_commutativeSemigroup_1996 T_SemiringWithoutOne_1880
v2
du_commutativeSemigroup_1996 ::
  T_SemiringWithoutOne_1880 -> T_CommutativeSemigroup_662
du_commutativeSemigroup_1996 :: T_SemiringWithoutOne_1880 -> T_CommutativeSemigroup_662
du_commutativeSemigroup_1996 T_SemiringWithoutOne_1880
v0
  = (T_CommutativeMonoid_962 -> T_CommutativeSemigroup_662)
-> AgdaAny -> T_CommutativeSemigroup_662
forall a b. a -> b
coe
      T_CommutativeMonoid_962 -> T_CommutativeSemigroup_662
du_commutativeSemigroup_1048
      ((T_SemiringWithoutOne_1880 -> T_CommutativeMonoid_962)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutOne_1880 -> T_CommutativeMonoid_962
du_'43''45'commutativeMonoid_1990 (T_SemiringWithoutOne_1880 -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutOne_1880
v0))
-- Algebra.Bundles.CommutativeSemiringWithoutOne
d_CommutativeSemiringWithoutOne_2002 :: p -> p -> ()
d_CommutativeSemiringWithoutOne_2002 p
a0 p
a1 = ()
data T_CommutativeSemiringWithoutOne_2002
  = C_CommutativeSemiringWithoutOne'46'constructor_36869 (AgdaAny ->
                                                          AgdaAny -> AgdaAny)
                                                         (AgdaAny -> AgdaAny -> AgdaAny) AgdaAny
                                                         MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiringWithoutOne_1382
-- Algebra.Bundles.CommutativeSemiringWithoutOne.Carrier
d_Carrier_2020 :: T_CommutativeSemiringWithoutOne_2002 -> ()
d_Carrier_2020 :: T_CommutativeSemiringWithoutOne_2002 -> ()
d_Carrier_2020 = T_CommutativeSemiringWithoutOne_2002 -> ()
forall a. a
erased
-- Algebra.Bundles.CommutativeSemiringWithoutOne._≈_
d__'8776'__2022 ::
  T_CommutativeSemiringWithoutOne_2002 -> AgdaAny -> AgdaAny -> ()
d__'8776'__2022 :: T_CommutativeSemiringWithoutOne_2002 -> AgdaAny -> AgdaAny -> ()
d__'8776'__2022 = T_CommutativeSemiringWithoutOne_2002 -> AgdaAny -> AgdaAny -> ()
forall a. a
erased
-- Algebra.Bundles.CommutativeSemiringWithoutOne._+_
d__'43'__2024 ::
  T_CommutativeSemiringWithoutOne_2002 ->
  AgdaAny -> AgdaAny -> AgdaAny
d__'43'__2024 :: T_CommutativeSemiringWithoutOne_2002
-> AgdaAny -> AgdaAny -> AgdaAny
d__'43'__2024 T_CommutativeSemiringWithoutOne_2002
v0
  = case T_CommutativeSemiringWithoutOne_2002
-> T_CommutativeSemiringWithoutOne_2002
forall a b. a -> b
coe T_CommutativeSemiringWithoutOne_2002
v0 of
      C_CommutativeSemiringWithoutOne'46'constructor_36869 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny
v5 T_IsCommutativeSemiringWithoutOne_1382
v6
        -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v3
      T_CommutativeSemiringWithoutOne_2002
_ -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.CommutativeSemiringWithoutOne._*_
d__'42'__2026 ::
  T_CommutativeSemiringWithoutOne_2002 ->
  AgdaAny -> AgdaAny -> AgdaAny
d__'42'__2026 :: T_CommutativeSemiringWithoutOne_2002
-> AgdaAny -> AgdaAny -> AgdaAny
d__'42'__2026 T_CommutativeSemiringWithoutOne_2002
v0
  = case T_CommutativeSemiringWithoutOne_2002
-> T_CommutativeSemiringWithoutOne_2002
forall a b. a -> b
coe T_CommutativeSemiringWithoutOne_2002
v0 of
      C_CommutativeSemiringWithoutOne'46'constructor_36869 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny
v5 T_IsCommutativeSemiringWithoutOne_1382
v6
        -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v4
      T_CommutativeSemiringWithoutOne_2002
_ -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.CommutativeSemiringWithoutOne.0#
d_0'35'_2028 :: T_CommutativeSemiringWithoutOne_2002 -> AgdaAny
d_0'35'_2028 :: T_CommutativeSemiringWithoutOne_2002 -> AgdaAny
d_0'35'_2028 T_CommutativeSemiringWithoutOne_2002
v0
  = case T_CommutativeSemiringWithoutOne_2002
-> T_CommutativeSemiringWithoutOne_2002
forall a b. a -> b
coe T_CommutativeSemiringWithoutOne_2002
v0 of
      C_CommutativeSemiringWithoutOne'46'constructor_36869 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny
v5 T_IsCommutativeSemiringWithoutOne_1382
v6
        -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v5
      T_CommutativeSemiringWithoutOne_2002
_ -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.CommutativeSemiringWithoutOne.isCommutativeSemiringWithoutOne
d_isCommutativeSemiringWithoutOne_2030 ::
  T_CommutativeSemiringWithoutOne_2002 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiringWithoutOne_1382
d_isCommutativeSemiringWithoutOne_2030 :: T_CommutativeSemiringWithoutOne_2002
-> T_IsCommutativeSemiringWithoutOne_1382
d_isCommutativeSemiringWithoutOne_2030 T_CommutativeSemiringWithoutOne_2002
v0
  = case T_CommutativeSemiringWithoutOne_2002
-> T_CommutativeSemiringWithoutOne_2002
forall a b. a -> b
coe T_CommutativeSemiringWithoutOne_2002
v0 of
      C_CommutativeSemiringWithoutOne'46'constructor_36869 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny
v5 T_IsCommutativeSemiringWithoutOne_1382
v6
        -> T_IsCommutativeSemiringWithoutOne_1382
-> T_IsCommutativeSemiringWithoutOne_1382
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1382
v6
      T_CommutativeSemiringWithoutOne_2002
_ -> T_IsCommutativeSemiringWithoutOne_1382
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.CommutativeSemiringWithoutOne._._≈_
d__'8776'__2034 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeSemiringWithoutOne_2002 -> AgdaAny -> AgdaAny -> ()
d__'8776'__2034 :: ()
-> ()
-> T_CommutativeSemiringWithoutOne_2002
-> AgdaAny
-> AgdaAny
-> ()
d__'8776'__2034 = ()
-> ()
-> T_CommutativeSemiringWithoutOne_2002
-> AgdaAny
-> AgdaAny
-> ()
forall a. a
erased
-- Algebra.Bundles.CommutativeSemiringWithoutOne._._≉_
d__'8777'__2036 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeSemiringWithoutOne_2002 -> AgdaAny -> AgdaAny -> ()
d__'8777'__2036 :: ()
-> ()
-> T_CommutativeSemiringWithoutOne_2002
-> AgdaAny
-> AgdaAny
-> ()
d__'8777'__2036 = ()
-> ()
-> T_CommutativeSemiringWithoutOne_2002
-> AgdaAny
-> AgdaAny
-> ()
forall a. a
erased
-- Algebra.Bundles.CommutativeSemiringWithoutOne._.*-assoc
d_'42''45'assoc_2038 ::
  T_CommutativeSemiringWithoutOne_2002 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'assoc_2038 :: T_CommutativeSemiringWithoutOne_2002
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'assoc_2038 T_CommutativeSemiringWithoutOne_2002
v0
  = (T_IsSemiringWithoutOne_1298
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsSemiringWithoutOne_1298
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'42''45'assoc_1320
      ((T_IsCommutativeSemiringWithoutOne_1382
 -> T_IsSemiringWithoutOne_1298)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCommutativeSemiringWithoutOne_1382
-> T_IsSemiringWithoutOne_1298
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutOne_1394
         ((T_CommutativeSemiringWithoutOne_2002
 -> T_IsCommutativeSemiringWithoutOne_1382)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemiringWithoutOne_2002
-> T_IsCommutativeSemiringWithoutOne_1382
d_isCommutativeSemiringWithoutOne_2030 (T_CommutativeSemiringWithoutOne_2002 -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemiringWithoutOne_2002
v0)))
-- Algebra.Bundles.CommutativeSemiringWithoutOne._.*-comm
d_'42''45'comm_2040 ::
  T_CommutativeSemiringWithoutOne_2002 ->
  AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'comm_2040 :: T_CommutativeSemiringWithoutOne_2002
-> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'comm_2040 T_CommutativeSemiringWithoutOne_2002
v0
  = (T_IsCommutativeSemiringWithoutOne_1382
 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsCommutativeSemiringWithoutOne_1382
-> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'42''45'comm_1396
      ((T_CommutativeSemiringWithoutOne_2002
 -> T_IsCommutativeSemiringWithoutOne_1382)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemiringWithoutOne_2002
-> T_IsCommutativeSemiringWithoutOne_1382
d_isCommutativeSemiringWithoutOne_2030 (T_CommutativeSemiringWithoutOne_2002 -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemiringWithoutOne_2002
v0))
-- Algebra.Bundles.CommutativeSemiringWithoutOne._.*-cong
d_'42''45'cong_2042 ::
  T_CommutativeSemiringWithoutOne_2002 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'cong_2042 :: T_CommutativeSemiringWithoutOne_2002
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'42''45'cong_2042 T_CommutativeSemiringWithoutOne_2002
v0
  = (T_IsSemiringWithoutOne_1298
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsSemiringWithoutOne_1298
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'42''45'cong_1318
      ((T_IsCommutativeSemiringWithoutOne_1382
 -> T_IsSemiringWithoutOne_1298)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCommutativeSemiringWithoutOne_1382
-> T_IsSemiringWithoutOne_1298
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutOne_1394
         ((T_CommutativeSemiringWithoutOne_2002
 -> T_IsCommutativeSemiringWithoutOne_1382)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemiringWithoutOne_2002
-> T_IsCommutativeSemiringWithoutOne_1382
d_isCommutativeSemiringWithoutOne_2030 (T_CommutativeSemiringWithoutOne_2002 -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemiringWithoutOne_2002
v0)))
-- Algebra.Bundles.CommutativeSemiringWithoutOne._.∙-congʳ
d_'8729''45'cong'691'_2044 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeSemiringWithoutOne_2002 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_2044 :: ()
-> ()
-> T_CommutativeSemiringWithoutOne_2002
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_2044 ~()
v0 ~()
v1 T_CommutativeSemiringWithoutOne_2002
v2
  = T_CommutativeSemiringWithoutOne_2002
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_2044 T_CommutativeSemiringWithoutOne_2002
v2
du_'8729''45'cong'691'_2044 ::
  T_CommutativeSemiringWithoutOne_2002 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_2044 :: T_CommutativeSemiringWithoutOne_2002
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_2044 T_CommutativeSemiringWithoutOne_2002
v0
  = let v1 :: T_IsCommutativeSemiringWithoutOne_1382
v1 = T_CommutativeSemiringWithoutOne_2002
-> T_IsCommutativeSemiringWithoutOne_1382
d_isCommutativeSemiringWithoutOne_2030 (T_CommutativeSemiringWithoutOne_2002
-> T_CommutativeSemiringWithoutOne_2002
forall a b. a -> b
coe T_CommutativeSemiringWithoutOne_2002
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemiringWithoutOne_1298
v2
             = T_IsCommutativeSemiringWithoutOne_1382
-> T_IsSemiringWithoutOne_1298
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutOne_1394
                 (T_IsCommutativeSemiringWithoutOne_1382
-> T_IsCommutativeSemiringWithoutOne_1382
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1382
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'691'_206
            ((T_IsSemiringWithoutOne_1298 -> T_IsMagma_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemiringWithoutOne_1298 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.du_'42''45'isMagma_1360 (T_IsSemiringWithoutOne_1298 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_1298
v2))))
-- Algebra.Bundles.CommutativeSemiringWithoutOne._.∙-congˡ
d_'8729''45'cong'737'_2046 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeSemiringWithoutOne_2002 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_2046 :: ()
-> ()
-> T_CommutativeSemiringWithoutOne_2002
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_2046 ~()
v0 ~()
v1 T_CommutativeSemiringWithoutOne_2002
v2
  = T_CommutativeSemiringWithoutOne_2002
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_2046 T_CommutativeSemiringWithoutOne_2002
v2
du_'8729''45'cong'737'_2046 ::
  T_CommutativeSemiringWithoutOne_2002 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_2046 :: T_CommutativeSemiringWithoutOne_2002
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_2046 T_CommutativeSemiringWithoutOne_2002
v0
  = let v1 :: T_IsCommutativeSemiringWithoutOne_1382
v1 = T_CommutativeSemiringWithoutOne_2002
-> T_IsCommutativeSemiringWithoutOne_1382
d_isCommutativeSemiringWithoutOne_2030 (T_CommutativeSemiringWithoutOne_2002
-> T_CommutativeSemiringWithoutOne_2002
forall a b. a -> b
coe T_CommutativeSemiringWithoutOne_2002
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemiringWithoutOne_1298
v2
             = T_IsCommutativeSemiringWithoutOne_1382
-> T_IsSemiringWithoutOne_1298
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutOne_1394
                 (T_IsCommutativeSemiringWithoutOne_1382
-> T_IsCommutativeSemiringWithoutOne_1382
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1382
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'737'_202
            ((T_IsSemiringWithoutOne_1298 -> T_IsMagma_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemiringWithoutOne_1298 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.du_'42''45'isMagma_1360 (T_IsSemiringWithoutOne_1298 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_1298
v2))))
-- Algebra.Bundles.CommutativeSemiringWithoutOne._.isCommutativeMagma
d_isCommutativeMagma_2048 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeSemiringWithoutOne_2002 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMagma_212
d_isCommutativeMagma_2048 :: ()
-> ()
-> T_CommutativeSemiringWithoutOne_2002
-> T_IsCommutativeMagma_212
d_isCommutativeMagma_2048 ~()
v0 ~()
v1 T_CommutativeSemiringWithoutOne_2002
v2
  = T_CommutativeSemiringWithoutOne_2002 -> T_IsCommutativeMagma_212
du_isCommutativeMagma_2048 T_CommutativeSemiringWithoutOne_2002
v2
du_isCommutativeMagma_2048 ::
  T_CommutativeSemiringWithoutOne_2002 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMagma_212
du_isCommutativeMagma_2048 :: T_CommutativeSemiringWithoutOne_2002 -> T_IsCommutativeMagma_212
du_isCommutativeMagma_2048 T_CommutativeSemiringWithoutOne_2002
v0
  = let v1 :: T_IsCommutativeSemiringWithoutOne_1382
v1 = T_CommutativeSemiringWithoutOne_2002
-> T_IsCommutativeSemiringWithoutOne_1382
d_isCommutativeSemiringWithoutOne_2030 (T_CommutativeSemiringWithoutOne_2002
-> T_CommutativeSemiringWithoutOne_2002
forall a b. a -> b
coe T_CommutativeSemiringWithoutOne_2002
v0) in
    AgdaAny -> T_IsCommutativeMagma_212
forall a b. a -> b
coe
      ((T_IsCommutativeSemigroup_548 -> T_IsCommutativeMagma_212)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCommutativeSemigroup_548 -> T_IsCommutativeMagma_212
MAlonzo.Code.Algebra.Structures.du_isCommutativeMagma_586
         ((T_IsCommutativeSemiringWithoutOne_1382
 -> T_IsCommutativeSemigroup_548)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCommutativeSemiringWithoutOne_1382
-> T_IsCommutativeSemigroup_548
MAlonzo.Code.Algebra.Structures.du_'42''45'isCommutativeSemigroup_1454
            (T_IsCommutativeSemiringWithoutOne_1382 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1382
v1)))
-- Algebra.Bundles.CommutativeSemiringWithoutOne._.*-isCommutativeSemigroup
d_'42''45'isCommutativeSemigroup_2050 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeSemiringWithoutOne_2002 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_548
d_'42''45'isCommutativeSemigroup_2050 :: ()
-> ()
-> T_CommutativeSemiringWithoutOne_2002
-> T_IsCommutativeSemigroup_548
d_'42''45'isCommutativeSemigroup_2050 ~()
v0 ~()
v1 T_CommutativeSemiringWithoutOne_2002
v2
  = T_CommutativeSemiringWithoutOne_2002
-> T_IsCommutativeSemigroup_548
du_'42''45'isCommutativeSemigroup_2050 T_CommutativeSemiringWithoutOne_2002
v2
du_'42''45'isCommutativeSemigroup_2050 ::
  T_CommutativeSemiringWithoutOne_2002 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_548
du_'42''45'isCommutativeSemigroup_2050 :: T_CommutativeSemiringWithoutOne_2002
-> T_IsCommutativeSemigroup_548
du_'42''45'isCommutativeSemigroup_2050 T_CommutativeSemiringWithoutOne_2002
v0
  = (T_IsCommutativeSemiringWithoutOne_1382
 -> T_IsCommutativeSemigroup_548)
-> AgdaAny -> T_IsCommutativeSemigroup_548
forall a b. a -> b
coe
      T_IsCommutativeSemiringWithoutOne_1382
-> T_IsCommutativeSemigroup_548
MAlonzo.Code.Algebra.Structures.du_'42''45'isCommutativeSemigroup_1454
      ((T_CommutativeSemiringWithoutOne_2002
 -> T_IsCommutativeSemiringWithoutOne_1382)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemiringWithoutOne_2002
-> T_IsCommutativeSemiringWithoutOne_1382
d_isCommutativeSemiringWithoutOne_2030 (T_CommutativeSemiringWithoutOne_2002 -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemiringWithoutOne_2002
v0))
-- Algebra.Bundles.CommutativeSemiringWithoutOne._.*-isMagma
d_'42''45'isMagma_2052 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeSemiringWithoutOne_2002 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_176
d_'42''45'isMagma_2052 :: () -> () -> T_CommutativeSemiringWithoutOne_2002 -> T_IsMagma_176
d_'42''45'isMagma_2052 ~()
v0 ~()
v1 T_CommutativeSemiringWithoutOne_2002
v2 = T_CommutativeSemiringWithoutOne_2002 -> T_IsMagma_176
du_'42''45'isMagma_2052 T_CommutativeSemiringWithoutOne_2002
v2
du_'42''45'isMagma_2052 ::
  T_CommutativeSemiringWithoutOne_2002 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_176
du_'42''45'isMagma_2052 :: T_CommutativeSemiringWithoutOne_2002 -> T_IsMagma_176
du_'42''45'isMagma_2052 T_CommutativeSemiringWithoutOne_2002
v0
  = let v1 :: T_IsCommutativeSemiringWithoutOne_1382
v1 = T_CommutativeSemiringWithoutOne_2002
-> T_IsCommutativeSemiringWithoutOne_1382
d_isCommutativeSemiringWithoutOne_2030 (T_CommutativeSemiringWithoutOne_2002
-> T_CommutativeSemiringWithoutOne_2002
forall a b. a -> b
coe T_CommutativeSemiringWithoutOne_2002
v0) in
    AgdaAny -> T_IsMagma_176
forall a b. a -> b
coe
      ((T_IsSemiringWithoutOne_1298 -> T_IsMagma_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiringWithoutOne_1298 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.du_'42''45'isMagma_1360
         ((T_IsCommutativeSemiringWithoutOne_1382
 -> T_IsSemiringWithoutOne_1298)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCommutativeSemiringWithoutOne_1382
-> T_IsSemiringWithoutOne_1298
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutOne_1394
            (T_IsCommutativeSemiringWithoutOne_1382 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1382
v1)))
-- Algebra.Bundles.CommutativeSemiringWithoutOne._.*-isSemigroup
d_'42''45'isSemigroup_2054 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeSemiringWithoutOne_2002 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_472
d_'42''45'isSemigroup_2054 :: ()
-> () -> T_CommutativeSemiringWithoutOne_2002 -> T_IsSemigroup_472
d_'42''45'isSemigroup_2054 ~()
v0 ~()
v1 T_CommutativeSemiringWithoutOne_2002
v2
  = T_CommutativeSemiringWithoutOne_2002 -> T_IsSemigroup_472
du_'42''45'isSemigroup_2054 T_CommutativeSemiringWithoutOne_2002
v2
du_'42''45'isSemigroup_2054 ::
  T_CommutativeSemiringWithoutOne_2002 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_472
du_'42''45'isSemigroup_2054 :: T_CommutativeSemiringWithoutOne_2002 -> T_IsSemigroup_472
du_'42''45'isSemigroup_2054 T_CommutativeSemiringWithoutOne_2002
v0
  = let v1 :: T_IsCommutativeSemiringWithoutOne_1382
v1 = T_CommutativeSemiringWithoutOne_2002
-> T_IsCommutativeSemiringWithoutOne_1382
d_isCommutativeSemiringWithoutOne_2030 (T_CommutativeSemiringWithoutOne_2002
-> T_CommutativeSemiringWithoutOne_2002
forall a b. a -> b
coe T_CommutativeSemiringWithoutOne_2002
v0) in
    AgdaAny -> T_IsSemigroup_472
forall a b. a -> b
coe
      ((T_IsSemiringWithoutOne_1298 -> T_IsSemigroup_472)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiringWithoutOne_1298 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.du_'42''45'isSemigroup_1362
         ((T_IsCommutativeSemiringWithoutOne_1382
 -> T_IsSemiringWithoutOne_1298)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCommutativeSemiringWithoutOne_1382
-> T_IsSemiringWithoutOne_1298
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutOne_1394
            (T_IsCommutativeSemiringWithoutOne_1382 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1382
v1)))
-- Algebra.Bundles.CommutativeSemiringWithoutOne._.comm
d_comm_2056 ::
  T_CommutativeSemiringWithoutOne_2002 ->
  AgdaAny -> AgdaAny -> AgdaAny
d_comm_2056 :: T_CommutativeSemiringWithoutOne_2002
-> AgdaAny -> AgdaAny -> AgdaAny
d_comm_2056 T_CommutativeSemiringWithoutOne_2002
v0
  = (T_IsCommutativeMonoid_736 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsCommutativeMonoid_736 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_comm_748
      ((T_IsSemiringWithoutOne_1298 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiringWithoutOne_1298 -> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1316
         ((T_IsCommutativeSemiringWithoutOne_1382
 -> T_IsSemiringWithoutOne_1298)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCommutativeSemiringWithoutOne_1382
-> T_IsSemiringWithoutOne_1298
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutOne_1394
            ((T_CommutativeSemiringWithoutOne_2002
 -> T_IsCommutativeSemiringWithoutOne_1382)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemiringWithoutOne_2002
-> T_IsCommutativeSemiringWithoutOne_1382
d_isCommutativeSemiringWithoutOne_2030 (T_CommutativeSemiringWithoutOne_2002 -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemiringWithoutOne_2002
v0))))
-- Algebra.Bundles.CommutativeSemiringWithoutOne._.isCommutativeMagma
d_isCommutativeMagma_2058 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeSemiringWithoutOne_2002 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMagma_212
d_isCommutativeMagma_2058 :: ()
-> ()
-> T_CommutativeSemiringWithoutOne_2002
-> T_IsCommutativeMagma_212
d_isCommutativeMagma_2058 ~()
v0 ~()
v1 T_CommutativeSemiringWithoutOne_2002
v2
  = T_CommutativeSemiringWithoutOne_2002 -> T_IsCommutativeMagma_212
du_isCommutativeMagma_2058 T_CommutativeSemiringWithoutOne_2002
v2
du_isCommutativeMagma_2058 ::
  T_CommutativeSemiringWithoutOne_2002 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMagma_212
du_isCommutativeMagma_2058 :: T_CommutativeSemiringWithoutOne_2002 -> T_IsCommutativeMagma_212
du_isCommutativeMagma_2058 T_CommutativeSemiringWithoutOne_2002
v0
  = let v1 :: T_IsCommutativeSemiringWithoutOne_1382
v1 = T_CommutativeSemiringWithoutOne_2002
-> T_IsCommutativeSemiringWithoutOne_1382
d_isCommutativeSemiringWithoutOne_2030 (T_CommutativeSemiringWithoutOne_2002
-> T_CommutativeSemiringWithoutOne_2002
forall a b. a -> b
coe T_CommutativeSemiringWithoutOne_2002
v0) in
    AgdaAny -> T_IsCommutativeMagma_212
forall a b. a -> b
coe
      (let v2 :: T_IsSemiringWithoutOne_1298
v2
             = T_IsCommutativeSemiringWithoutOne_1382
-> T_IsSemiringWithoutOne_1298
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutOne_1394
                 (T_IsCommutativeSemiringWithoutOne_1382
-> T_IsCommutativeSemiringWithoutOne_1382
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1382
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsCommutativeMonoid_736
v3
                = T_IsSemiringWithoutOne_1298 -> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1316
                    (T_IsSemiringWithoutOne_1298 -> T_IsSemiringWithoutOne_1298
forall a b. a -> b
coe T_IsSemiringWithoutOne_1298
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsCommutativeSemigroup_548 -> T_IsCommutativeMagma_212)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsCommutativeSemigroup_548 -> T_IsCommutativeMagma_212
MAlonzo.Code.Algebra.Structures.du_isCommutativeMagma_586
               ((T_IsCommutativeMonoid_736 -> T_IsCommutativeSemigroup_548)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsCommutativeMonoid_736 -> T_IsCommutativeSemigroup_548
MAlonzo.Code.Algebra.Structures.du_isCommutativeSemigroup_786
                  (T_IsCommutativeMonoid_736 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v3)))))
-- Algebra.Bundles.CommutativeSemiringWithoutOne._.+-isCommutativeMonoid
d_'43''45'isCommutativeMonoid_2060 ::
  T_CommutativeSemiringWithoutOne_2002 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_2060 :: T_CommutativeSemiringWithoutOne_2002 -> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_2060 T_CommutativeSemiringWithoutOne_2002
v0
  = (T_IsSemiringWithoutOne_1298 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> T_IsCommutativeMonoid_736
forall a b. a -> b
coe
      T_IsSemiringWithoutOne_1298 -> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1316
      ((T_IsCommutativeSemiringWithoutOne_1382
 -> T_IsSemiringWithoutOne_1298)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCommutativeSemiringWithoutOne_1382
-> T_IsSemiringWithoutOne_1298
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutOne_1394
         ((T_CommutativeSemiringWithoutOne_2002
 -> T_IsCommutativeSemiringWithoutOne_1382)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemiringWithoutOne_2002
-> T_IsCommutativeSemiringWithoutOne_1382
d_isCommutativeSemiringWithoutOne_2030 (T_CommutativeSemiringWithoutOne_2002 -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemiringWithoutOne_2002
v0)))
-- Algebra.Bundles.CommutativeSemiringWithoutOne._.isCommutativeSemigroup
d_isCommutativeSemigroup_2062 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeSemiringWithoutOne_2002 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_548
d_isCommutativeSemigroup_2062 :: ()
-> ()
-> T_CommutativeSemiringWithoutOne_2002
-> T_IsCommutativeSemigroup_548
d_isCommutativeSemigroup_2062 ~()
v0 ~()
v1 T_CommutativeSemiringWithoutOne_2002
v2
  = T_CommutativeSemiringWithoutOne_2002
-> T_IsCommutativeSemigroup_548
du_isCommutativeSemigroup_2062 T_CommutativeSemiringWithoutOne_2002
v2
du_isCommutativeSemigroup_2062 ::
  T_CommutativeSemiringWithoutOne_2002 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_548
du_isCommutativeSemigroup_2062 :: T_CommutativeSemiringWithoutOne_2002
-> T_IsCommutativeSemigroup_548
du_isCommutativeSemigroup_2062 T_CommutativeSemiringWithoutOne_2002
v0
  = let v1 :: T_IsCommutativeSemiringWithoutOne_1382
v1 = T_CommutativeSemiringWithoutOne_2002
-> T_IsCommutativeSemiringWithoutOne_1382
d_isCommutativeSemiringWithoutOne_2030 (T_CommutativeSemiringWithoutOne_2002
-> T_CommutativeSemiringWithoutOne_2002
forall a b. a -> b
coe T_CommutativeSemiringWithoutOne_2002
v0) in
    AgdaAny -> T_IsCommutativeSemigroup_548
forall a b. a -> b
coe
      (let v2 :: T_IsSemiringWithoutOne_1298
v2
             = T_IsCommutativeSemiringWithoutOne_1382
-> T_IsSemiringWithoutOne_1298
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutOne_1394
                 (T_IsCommutativeSemiringWithoutOne_1382
-> T_IsCommutativeSemiringWithoutOne_1382
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1382
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsCommutativeMonoid_736 -> T_IsCommutativeSemigroup_548)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCommutativeMonoid_736 -> T_IsCommutativeSemigroup_548
MAlonzo.Code.Algebra.Structures.du_isCommutativeSemigroup_786
            ((T_IsSemiringWithoutOne_1298 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemiringWithoutOne_1298 -> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1316
               (T_IsSemiringWithoutOne_1298 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_1298
v2))))
-- Algebra.Bundles.CommutativeSemiringWithoutOne._.isMonoid
d_isMonoid_2064 ::
  T_CommutativeSemiringWithoutOne_2002 ->
  MAlonzo.Code.Algebra.Structures.T_IsMonoid_686
d_isMonoid_2064 :: T_CommutativeSemiringWithoutOne_2002 -> T_IsMonoid_686
d_isMonoid_2064 T_CommutativeSemiringWithoutOne_2002
v0
  = (T_IsCommutativeMonoid_736 -> T_IsMonoid_686)
-> AgdaAny -> T_IsMonoid_686
forall a b. a -> b
coe
      T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746
      ((T_IsSemiringWithoutOne_1298 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiringWithoutOne_1298 -> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1316
         ((T_IsCommutativeSemiringWithoutOne_1382
 -> T_IsSemiringWithoutOne_1298)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCommutativeSemiringWithoutOne_1382
-> T_IsSemiringWithoutOne_1298
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutOne_1394
            ((T_CommutativeSemiringWithoutOne_2002
 -> T_IsCommutativeSemiringWithoutOne_1382)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemiringWithoutOne_2002
-> T_IsCommutativeSemiringWithoutOne_1382
d_isCommutativeSemiringWithoutOne_2030 (T_CommutativeSemiringWithoutOne_2002 -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemiringWithoutOne_2002
v0))))
-- Algebra.Bundles.CommutativeSemiringWithoutOne._.Carrier
d_Carrier_2066 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeSemiringWithoutOne_2002 -> ()
d_Carrier_2066 :: () -> () -> T_CommutativeSemiringWithoutOne_2002 -> ()
d_Carrier_2066 = () -> () -> T_CommutativeSemiringWithoutOne_2002 -> ()
forall a. a
erased
-- Algebra.Bundles.CommutativeSemiringWithoutOne._.distrib
d_distrib_2068 ::
  T_CommutativeSemiringWithoutOne_2002 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_distrib_2068 :: T_CommutativeSemiringWithoutOne_2002 -> T_Σ_14
d_distrib_2068 T_CommutativeSemiringWithoutOne_2002
v0
  = (T_IsSemiringWithoutOne_1298 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsSemiringWithoutOne_1298 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_distrib_1322
      ((T_IsCommutativeSemiringWithoutOne_1382
 -> T_IsSemiringWithoutOne_1298)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCommutativeSemiringWithoutOne_1382
-> T_IsSemiringWithoutOne_1298
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutOne_1394
         ((T_CommutativeSemiringWithoutOne_2002
 -> T_IsCommutativeSemiringWithoutOne_1382)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemiringWithoutOne_2002
-> T_IsCommutativeSemiringWithoutOne_1382
d_isCommutativeSemiringWithoutOne_2030 (T_CommutativeSemiringWithoutOne_2002 -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemiringWithoutOne_2002
v0)))
-- Algebra.Bundles.CommutativeSemiringWithoutOne._.isEquivalence
d_isEquivalence_2070 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeSemiringWithoutOne_2002 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_2070 :: ()
-> () -> T_CommutativeSemiringWithoutOne_2002 -> T_IsEquivalence_26
d_isEquivalence_2070 ~()
v0 ~()
v1 T_CommutativeSemiringWithoutOne_2002
v2 = T_CommutativeSemiringWithoutOne_2002 -> T_IsEquivalence_26
du_isEquivalence_2070 T_CommutativeSemiringWithoutOne_2002
v2
du_isEquivalence_2070 ::
  T_CommutativeSemiringWithoutOne_2002 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
du_isEquivalence_2070 :: T_CommutativeSemiringWithoutOne_2002 -> T_IsEquivalence_26
du_isEquivalence_2070 T_CommutativeSemiringWithoutOne_2002
v0
  = let v1 :: T_IsCommutativeSemiringWithoutOne_1382
v1 = T_CommutativeSemiringWithoutOne_2002
-> T_IsCommutativeSemiringWithoutOne_1382
d_isCommutativeSemiringWithoutOne_2030 (T_CommutativeSemiringWithoutOne_2002
-> T_CommutativeSemiringWithoutOne_2002
forall a b. a -> b
coe T_CommutativeSemiringWithoutOne_2002
v0) in
    AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      (let v2 :: T_IsSemiringWithoutOne_1298
v2
             = T_IsCommutativeSemiringWithoutOne_1382
-> T_IsSemiringWithoutOne_1298
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutOne_1394
                 (T_IsCommutativeSemiringWithoutOne_1382
-> T_IsCommutativeSemiringWithoutOne_1382
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1382
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_Setoid_44 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_Setoid_44 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60
            (let v3 :: T_IsMonoid_686
v3
                   = T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746
                       ((T_IsSemiringWithoutOne_1298 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> T_IsCommutativeMonoid_736
forall a b. a -> b
coe
                          T_IsSemiringWithoutOne_1298 -> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1316
                          (T_IsSemiringWithoutOne_1298 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_1298
v2)) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v4 :: T_IsSemigroup_472
v4
                      = T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v3) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  ((T_IsMagma_176 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsMagma_176 -> T_Setoid_44
MAlonzo.Code.Algebra.Structures.du_setoid_200
                     ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v4)))))))
-- Algebra.Bundles.CommutativeSemiringWithoutOne._.isNearSemiring
d_isNearSemiring_2072 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeSemiringWithoutOne_2002 ->
  MAlonzo.Code.Algebra.Structures.T_IsNearSemiring_1218
d_isNearSemiring_2072 :: ()
-> ()
-> T_CommutativeSemiringWithoutOne_2002
-> T_IsNearSemiring_1218
d_isNearSemiring_2072 ~()
v0 ~()
v1 T_CommutativeSemiringWithoutOne_2002
v2 = T_CommutativeSemiringWithoutOne_2002 -> T_IsNearSemiring_1218
du_isNearSemiring_2072 T_CommutativeSemiringWithoutOne_2002
v2
du_isNearSemiring_2072 ::
  T_CommutativeSemiringWithoutOne_2002 ->
  MAlonzo.Code.Algebra.Structures.T_IsNearSemiring_1218
du_isNearSemiring_2072 :: T_CommutativeSemiringWithoutOne_2002 -> T_IsNearSemiring_1218
du_isNearSemiring_2072 T_CommutativeSemiringWithoutOne_2002
v0
  = let v1 :: T_IsCommutativeSemiringWithoutOne_1382
v1 = T_CommutativeSemiringWithoutOne_2002
-> T_IsCommutativeSemiringWithoutOne_1382
d_isCommutativeSemiringWithoutOne_2030 (T_CommutativeSemiringWithoutOne_2002
-> T_CommutativeSemiringWithoutOne_2002
forall a b. a -> b
coe T_CommutativeSemiringWithoutOne_2002
v0) in
    AgdaAny -> T_IsNearSemiring_1218
forall a b. a -> b
coe
      ((T_IsSemiringWithoutOne_1298 -> T_IsNearSemiring_1218)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiringWithoutOne_1298 -> T_IsNearSemiring_1218
MAlonzo.Code.Algebra.Structures.du_isNearSemiring_1374
         ((T_IsCommutativeSemiringWithoutOne_1382
 -> T_IsSemiringWithoutOne_1298)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCommutativeSemiringWithoutOne_1382
-> T_IsSemiringWithoutOne_1298
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutOne_1394
            (T_IsCommutativeSemiringWithoutOne_1382 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1382
v1)))
-- Algebra.Bundles.CommutativeSemiringWithoutOne._.isPartialEquivalence
d_isPartialEquivalence_2074 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeSemiringWithoutOne_2002 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_2074 :: ()
-> ()
-> T_CommutativeSemiringWithoutOne_2002
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_2074 ~()
v0 ~()
v1 T_CommutativeSemiringWithoutOne_2002
v2
  = T_CommutativeSemiringWithoutOne_2002 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_2074 T_CommutativeSemiringWithoutOne_2002
v2
du_isPartialEquivalence_2074 ::
  T_CommutativeSemiringWithoutOne_2002 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_2074 :: T_CommutativeSemiringWithoutOne_2002 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_2074 T_CommutativeSemiringWithoutOne_2002
v0
  = let v1 :: T_IsCommutativeSemiringWithoutOne_1382
v1 = T_CommutativeSemiringWithoutOne_2002
-> T_IsCommutativeSemiringWithoutOne_1382
d_isCommutativeSemiringWithoutOne_2030 (T_CommutativeSemiringWithoutOne_2002
-> T_CommutativeSemiringWithoutOne_2002
forall a b. a -> b
coe T_CommutativeSemiringWithoutOne_2002
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsSemiringWithoutOne_1298
v2
             = T_IsCommutativeSemiringWithoutOne_1382
-> T_IsSemiringWithoutOne_1298
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutOne_1394
                 (T_IsCommutativeSemiringWithoutOne_1382
-> T_IsCommutativeSemiringWithoutOne_1382
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1382
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: b
v3
                = let v3 :: T_IsMonoid_686
v3
                        = T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746
                            ((T_IsSemiringWithoutOne_1298 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> T_IsCommutativeMonoid_736
forall a b. a -> b
coe
                               T_IsSemiringWithoutOne_1298 -> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1316
                               (T_IsSemiringWithoutOne_1298 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_1298
v2)) in
                  AgdaAny -> b
forall a b. a -> b
coe
                    (let v4 :: T_IsSemigroup_472
v4
                           = T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v3) in
                     AgdaAny -> AgdaAny
forall a b. a -> b
coe
                       ((T_IsMagma_176 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                          T_IsMagma_176 -> T_Setoid_44
MAlonzo.Code.Algebra.Structures.du_setoid_200
                          ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v4)))) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsEquivalence_26 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsEquivalence_26 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
               ((T_Setoid_44 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_Setoid_44 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60
                  (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3)))))
-- Algebra.Bundles.CommutativeSemiringWithoutOne._.isSemiringWithoutOne
d_isSemiringWithoutOne_2076 ::
  T_CommutativeSemiringWithoutOne_2002 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutOne_1298
d_isSemiringWithoutOne_2076 :: T_CommutativeSemiringWithoutOne_2002 -> T_IsSemiringWithoutOne_1298
d_isSemiringWithoutOne_2076 T_CommutativeSemiringWithoutOne_2002
v0
  = (T_IsCommutativeSemiringWithoutOne_1382
 -> T_IsSemiringWithoutOne_1298)
-> AgdaAny -> T_IsSemiringWithoutOne_1298
forall a b. a -> b
coe
      T_IsCommutativeSemiringWithoutOne_1382
-> T_IsSemiringWithoutOne_1298
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutOne_1394
      ((T_CommutativeSemiringWithoutOne_2002
 -> T_IsCommutativeSemiringWithoutOne_1382)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemiringWithoutOne_2002
-> T_IsCommutativeSemiringWithoutOne_1382
d_isCommutativeSemiringWithoutOne_2030 (T_CommutativeSemiringWithoutOne_2002 -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemiringWithoutOne_2002
v0))
-- Algebra.Bundles.CommutativeSemiringWithoutOne._.partialSetoid
d_partialSetoid_2078 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeSemiringWithoutOne_2002 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
d_partialSetoid_2078 :: ()
-> () -> T_CommutativeSemiringWithoutOne_2002 -> T_PartialSetoid_10
d_partialSetoid_2078 ~()
v0 ~()
v1 T_CommutativeSemiringWithoutOne_2002
v2 = T_CommutativeSemiringWithoutOne_2002 -> T_PartialSetoid_10
du_partialSetoid_2078 T_CommutativeSemiringWithoutOne_2002
v2
du_partialSetoid_2078 ::
  T_CommutativeSemiringWithoutOne_2002 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
du_partialSetoid_2078 :: T_CommutativeSemiringWithoutOne_2002 -> T_PartialSetoid_10
du_partialSetoid_2078 T_CommutativeSemiringWithoutOne_2002
v0
  = let v1 :: T_IsCommutativeSemiringWithoutOne_1382
v1 = T_CommutativeSemiringWithoutOne_2002
-> T_IsCommutativeSemiringWithoutOne_1382
d_isCommutativeSemiringWithoutOne_2030 (T_CommutativeSemiringWithoutOne_2002
-> T_CommutativeSemiringWithoutOne_2002
forall a b. a -> b
coe T_CommutativeSemiringWithoutOne_2002
v0) in
    AgdaAny -> T_PartialSetoid_10
forall a b. a -> b
coe
      (let v2 :: T_IsSemiringWithoutOne_1298
v2
             = T_IsCommutativeSemiringWithoutOne_1382
-> T_IsSemiringWithoutOne_1298
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutOne_1394
                 (T_IsCommutativeSemiringWithoutOne_1382
-> T_IsCommutativeSemiringWithoutOne_1382
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1382
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_Setoid_44 -> T_PartialSetoid_10) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_Setoid_44 -> T_PartialSetoid_10
MAlonzo.Code.Relation.Binary.Bundles.du_partialSetoid_70
            (let v3 :: T_IsMonoid_686
v3
                   = T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746
                       ((T_IsSemiringWithoutOne_1298 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> T_IsCommutativeMonoid_736
forall a b. a -> b
coe
                          T_IsSemiringWithoutOne_1298 -> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1316
                          (T_IsSemiringWithoutOne_1298 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_1298
v2)) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v4 :: T_IsSemigroup_472
v4
                      = T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v3) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  ((T_IsMagma_176 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsMagma_176 -> T_Setoid_44
MAlonzo.Code.Algebra.Structures.du_setoid_200
                     ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v4)))))))
-- Algebra.Bundles.CommutativeSemiringWithoutOne._.refl
d_refl_2080 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeSemiringWithoutOne_2002 -> AgdaAny -> AgdaAny
d_refl_2080 :: ()
-> () -> T_CommutativeSemiringWithoutOne_2002 -> AgdaAny -> AgdaAny
d_refl_2080 ~()
v0 ~()
v1 T_CommutativeSemiringWithoutOne_2002
v2 = T_CommutativeSemiringWithoutOne_2002 -> AgdaAny -> AgdaAny
du_refl_2080 T_CommutativeSemiringWithoutOne_2002
v2
du_refl_2080 ::
  T_CommutativeSemiringWithoutOne_2002 -> AgdaAny -> AgdaAny
du_refl_2080 :: T_CommutativeSemiringWithoutOne_2002 -> AgdaAny -> AgdaAny
du_refl_2080 T_CommutativeSemiringWithoutOne_2002
v0
  = let v1 :: T_IsCommutativeSemiringWithoutOne_1382
v1 = T_CommutativeSemiringWithoutOne_2002
-> T_IsCommutativeSemiringWithoutOne_1382
d_isCommutativeSemiringWithoutOne_2030 (T_CommutativeSemiringWithoutOne_2002
-> T_CommutativeSemiringWithoutOne_2002
forall a b. a -> b
coe T_CommutativeSemiringWithoutOne_2002
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemiringWithoutOne_1298
v2
             = T_IsCommutativeSemiringWithoutOne_1382
-> T_IsSemiringWithoutOne_1298
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutOne_1394
                 (T_IsCommutativeSemiringWithoutOne_1382
-> T_IsCommutativeSemiringWithoutOne_1382
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1382
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsEquivalence_26 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_34
            ((T_Setoid_44 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_Setoid_44 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60
               (let v3 :: T_IsMonoid_686
v3
                      = T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746
                          ((T_IsSemiringWithoutOne_1298 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> T_IsCommutativeMonoid_736
forall a b. a -> b
coe
                             T_IsSemiringWithoutOne_1298 -> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1316
                             (T_IsSemiringWithoutOne_1298 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_1298
v2)) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (let v4 :: T_IsSemigroup_472
v4
                         = T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v3) in
                   AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     ((T_IsMagma_176 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsMagma_176 -> T_Setoid_44
MAlonzo.Code.Algebra.Structures.du_setoid_200
                        ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v4))))))))
-- Algebra.Bundles.CommutativeSemiringWithoutOne._.reflexive
d_reflexive_2082 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeSemiringWithoutOne_2002 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_2082 :: ()
-> ()
-> T_CommutativeSemiringWithoutOne_2002
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_2082 ~()
v0 ~()
v1 T_CommutativeSemiringWithoutOne_2002
v2 = T_CommutativeSemiringWithoutOne_2002
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_2082 T_CommutativeSemiringWithoutOne_2002
v2
du_reflexive_2082 ::
  T_CommutativeSemiringWithoutOne_2002 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_2082 :: T_CommutativeSemiringWithoutOne_2002
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_2082 T_CommutativeSemiringWithoutOne_2002
v0
  = let v1 :: T_IsCommutativeSemiringWithoutOne_1382
v1 = T_CommutativeSemiringWithoutOne_2002
-> T_IsCommutativeSemiringWithoutOne_1382
d_isCommutativeSemiringWithoutOne_2030 (T_CommutativeSemiringWithoutOne_2002
-> T_CommutativeSemiringWithoutOne_2002
forall a b. a -> b
coe T_CommutativeSemiringWithoutOne_2002
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemiringWithoutOne_1298
v2
             = T_IsCommutativeSemiringWithoutOne_1382
-> T_IsSemiringWithoutOne_1298
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutOne_1394
                 (T_IsCommutativeSemiringWithoutOne_1382
-> T_IsCommutativeSemiringWithoutOne_1382
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1382
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: b
v3
                = let v3 :: T_IsMonoid_686
v3
                        = T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746
                            ((T_IsSemiringWithoutOne_1298 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> T_IsCommutativeMonoid_736
forall a b. a -> b
coe
                               T_IsSemiringWithoutOne_1298 -> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1316
                               (T_IsSemiringWithoutOne_1298 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_1298
v2)) in
                  AgdaAny -> b
forall a b. a -> b
coe
                    (let v4 :: T_IsSemigroup_472
v4
                           = T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v3) in
                     AgdaAny -> AgdaAny
forall a b. a -> b
coe
                       ((T_IsMagma_176 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                          T_IsMagma_176 -> T_Setoid_44
MAlonzo.Code.Algebra.Structures.du_setoid_200
                          ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v4)))) in
          (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
            (\ AgdaAny
v4 AgdaAny
v5 AgdaAny
v6 ->
               (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                 T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
                 ((T_Setoid_44 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                    T_Setoid_44 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3))
                 AgdaAny
v4)))
-- Algebra.Bundles.CommutativeSemiringWithoutOne._.setoid
d_setoid_2084 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeSemiringWithoutOne_2002 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_2084 :: () -> () -> T_CommutativeSemiringWithoutOne_2002 -> T_Setoid_44
d_setoid_2084 ~()
v0 ~()
v1 T_CommutativeSemiringWithoutOne_2002
v2 = T_CommutativeSemiringWithoutOne_2002 -> T_Setoid_44
du_setoid_2084 T_CommutativeSemiringWithoutOne_2002
v2
du_setoid_2084 ::
  T_CommutativeSemiringWithoutOne_2002 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_2084 :: T_CommutativeSemiringWithoutOne_2002 -> T_Setoid_44
du_setoid_2084 T_CommutativeSemiringWithoutOne_2002
v0
  = let v1 :: T_IsCommutativeSemiringWithoutOne_1382
v1 = T_CommutativeSemiringWithoutOne_2002
-> T_IsCommutativeSemiringWithoutOne_1382
d_isCommutativeSemiringWithoutOne_2030 (T_CommutativeSemiringWithoutOne_2002
-> T_CommutativeSemiringWithoutOne_2002
forall a b. a -> b
coe T_CommutativeSemiringWithoutOne_2002
v0) in
    AgdaAny -> T_Setoid_44
forall a b. a -> b
coe
      (let v2 :: T_IsSemiringWithoutOne_1298
v2
             = T_IsCommutativeSemiringWithoutOne_1382
-> T_IsSemiringWithoutOne_1298
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutOne_1394
                 (T_IsCommutativeSemiringWithoutOne_1382
-> T_IsCommutativeSemiringWithoutOne_1382
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1382
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsCommutativeMonoid_736
v3
                = T_IsSemiringWithoutOne_1298 -> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1316
                    (T_IsSemiringWithoutOne_1298 -> T_IsSemiringWithoutOne_1298
forall a b. a -> b
coe T_IsSemiringWithoutOne_1298
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsMonoid_686
v4
                   = T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746 (T_IsCommutativeMonoid_736 -> T_IsCommutativeMonoid_736
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsSemigroup_472
v5
                      = T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  ((T_IsMagma_176 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsMagma_176 -> T_Setoid_44
MAlonzo.Code.Algebra.Structures.du_setoid_200
                     ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v5)))))))
-- Algebra.Bundles.CommutativeSemiringWithoutOne._.sym
d_sym_2086 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeSemiringWithoutOne_2002 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_2086 :: ()
-> ()
-> T_CommutativeSemiringWithoutOne_2002
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_sym_2086 ~()
v0 ~()
v1 T_CommutativeSemiringWithoutOne_2002
v2 = T_CommutativeSemiringWithoutOne_2002
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_2086 T_CommutativeSemiringWithoutOne_2002
v2
du_sym_2086 ::
  T_CommutativeSemiringWithoutOne_2002 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_2086 :: T_CommutativeSemiringWithoutOne_2002
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_2086 T_CommutativeSemiringWithoutOne_2002
v0
  = let v1 :: T_IsCommutativeSemiringWithoutOne_1382
v1 = T_CommutativeSemiringWithoutOne_2002
-> T_IsCommutativeSemiringWithoutOne_1382
d_isCommutativeSemiringWithoutOne_2030 (T_CommutativeSemiringWithoutOne_2002
-> T_CommutativeSemiringWithoutOne_2002
forall a b. a -> b
coe T_CommutativeSemiringWithoutOne_2002
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemiringWithoutOne_1298
v2
             = T_IsCommutativeSemiringWithoutOne_1382
-> T_IsSemiringWithoutOne_1298
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutOne_1394
                 (T_IsCommutativeSemiringWithoutOne_1382
-> T_IsCommutativeSemiringWithoutOne_1382
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1382
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: b
v3
                = let v3 :: T_IsMonoid_686
v3
                        = T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746
                            ((T_IsSemiringWithoutOne_1298 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> T_IsCommutativeMonoid_736
forall a b. a -> b
coe
                               T_IsSemiringWithoutOne_1298 -> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1316
                               (T_IsSemiringWithoutOne_1298 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_1298
v2)) in
                  AgdaAny -> b
forall a b. a -> b
coe
                    (let v4 :: T_IsSemigroup_472
v4
                           = T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v3) in
                     AgdaAny -> AgdaAny
forall a b. a -> b
coe
                       ((T_IsMagma_176 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                          T_IsMagma_176 -> T_Setoid_44
MAlonzo.Code.Algebra.Structures.du_setoid_200
                          ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v4)))) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_36
               ((T_Setoid_44 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_Setoid_44 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60
                  (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3)))))
-- Algebra.Bundles.CommutativeSemiringWithoutOne._.trans
d_trans_2088 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeSemiringWithoutOne_2002 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_2088 :: ()
-> ()
-> T_CommutativeSemiringWithoutOne_2002
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_trans_2088 ~()
v0 ~()
v1 T_CommutativeSemiringWithoutOne_2002
v2 = T_CommutativeSemiringWithoutOne_2002
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_2088 T_CommutativeSemiringWithoutOne_2002
v2
du_trans_2088 ::
  T_CommutativeSemiringWithoutOne_2002 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_2088 :: T_CommutativeSemiringWithoutOne_2002
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_2088 T_CommutativeSemiringWithoutOne_2002
v0
  = let v1 :: T_IsCommutativeSemiringWithoutOne_1382
v1 = T_CommutativeSemiringWithoutOne_2002
-> T_IsCommutativeSemiringWithoutOne_1382
d_isCommutativeSemiringWithoutOne_2030 (T_CommutativeSemiringWithoutOne_2002
-> T_CommutativeSemiringWithoutOne_2002
forall a b. a -> b
coe T_CommutativeSemiringWithoutOne_2002
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemiringWithoutOne_1298
v2
             = T_IsCommutativeSemiringWithoutOne_1382
-> T_IsSemiringWithoutOne_1298
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutOne_1394
                 (T_IsCommutativeSemiringWithoutOne_1382
-> T_IsCommutativeSemiringWithoutOne_1382
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1382
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: b
v3
                = let v3 :: T_IsMonoid_686
v3
                        = T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746
                            ((T_IsSemiringWithoutOne_1298 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> T_IsCommutativeMonoid_736
forall a b. a -> b
coe
                               T_IsSemiringWithoutOne_1298 -> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1316
                               (T_IsSemiringWithoutOne_1298 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_1298
v2)) in
                  AgdaAny -> b
forall a b. a -> b
coe
                    (let v4 :: T_IsSemigroup_472
v4
                           = T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v3) in
                     AgdaAny -> AgdaAny
forall a b. a -> b
coe
                       ((T_IsMagma_176 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                          T_IsMagma_176 -> T_Setoid_44
MAlonzo.Code.Algebra.Structures.du_setoid_200
                          ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v4)))) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsEquivalence_26
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsEquivalence_26
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_38
               ((T_Setoid_44 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_Setoid_44 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60
                  (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3)))))
-- Algebra.Bundles.CommutativeSemiringWithoutOne._.zero
d_zero_2090 ::
  T_CommutativeSemiringWithoutOne_2002 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_zero_2090 :: T_CommutativeSemiringWithoutOne_2002 -> T_Σ_14
d_zero_2090 T_CommutativeSemiringWithoutOne_2002
v0
  = (T_IsSemiringWithoutOne_1298 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsSemiringWithoutOne_1298 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_zero_1324
      ((T_IsCommutativeSemiringWithoutOne_1382
 -> T_IsSemiringWithoutOne_1298)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCommutativeSemiringWithoutOne_1382
-> T_IsSemiringWithoutOne_1298
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutOne_1394
         ((T_CommutativeSemiringWithoutOne_2002
 -> T_IsCommutativeSemiringWithoutOne_1382)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemiringWithoutOne_2002
-> T_IsCommutativeSemiringWithoutOne_1382
d_isCommutativeSemiringWithoutOne_2030 (T_CommutativeSemiringWithoutOne_2002 -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemiringWithoutOne_2002
v0)))
-- Algebra.Bundles.CommutativeSemiringWithoutOne._.zeroʳ
d_zero'691'_2092 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeSemiringWithoutOne_2002 -> AgdaAny -> AgdaAny
d_zero'691'_2092 :: ()
-> () -> T_CommutativeSemiringWithoutOne_2002 -> AgdaAny -> AgdaAny
d_zero'691'_2092 ~()
v0 ~()
v1 T_CommutativeSemiringWithoutOne_2002
v2 = T_CommutativeSemiringWithoutOne_2002 -> AgdaAny -> AgdaAny
du_zero'691'_2092 T_CommutativeSemiringWithoutOne_2002
v2
du_zero'691'_2092 ::
  T_CommutativeSemiringWithoutOne_2002 -> AgdaAny -> AgdaAny
du_zero'691'_2092 :: T_CommutativeSemiringWithoutOne_2002 -> AgdaAny -> AgdaAny
du_zero'691'_2092 T_CommutativeSemiringWithoutOne_2002
v0
  = let v1 :: T_IsCommutativeSemiringWithoutOne_1382
v1 = T_CommutativeSemiringWithoutOne_2002
-> T_IsCommutativeSemiringWithoutOne_1382
d_isCommutativeSemiringWithoutOne_2030 (T_CommutativeSemiringWithoutOne_2002
-> T_CommutativeSemiringWithoutOne_2002
forall a b. a -> b
coe T_CommutativeSemiringWithoutOne_2002
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsSemiringWithoutOne_1298 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiringWithoutOne_1298 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_zero'691'_1372
         ((T_IsCommutativeSemiringWithoutOne_1382
 -> T_IsSemiringWithoutOne_1298)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCommutativeSemiringWithoutOne_1382
-> T_IsSemiringWithoutOne_1298
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutOne_1394
            (T_IsCommutativeSemiringWithoutOne_1382 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1382
v1)))
-- Algebra.Bundles.CommutativeSemiringWithoutOne._.zeroˡ
d_zero'737'_2094 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeSemiringWithoutOne_2002 -> AgdaAny -> AgdaAny
d_zero'737'_2094 :: ()
-> () -> T_CommutativeSemiringWithoutOne_2002 -> AgdaAny -> AgdaAny
d_zero'737'_2094 ~()
v0 ~()
v1 T_CommutativeSemiringWithoutOne_2002
v2 = T_CommutativeSemiringWithoutOne_2002 -> AgdaAny -> AgdaAny
du_zero'737'_2094 T_CommutativeSemiringWithoutOne_2002
v2
du_zero'737'_2094 ::
  T_CommutativeSemiringWithoutOne_2002 -> AgdaAny -> AgdaAny
du_zero'737'_2094 :: T_CommutativeSemiringWithoutOne_2002 -> AgdaAny -> AgdaAny
du_zero'737'_2094 T_CommutativeSemiringWithoutOne_2002
v0
  = let v1 :: T_IsCommutativeSemiringWithoutOne_1382
v1 = T_CommutativeSemiringWithoutOne_2002
-> T_IsCommutativeSemiringWithoutOne_1382
d_isCommutativeSemiringWithoutOne_2030 (T_CommutativeSemiringWithoutOne_2002
-> T_CommutativeSemiringWithoutOne_2002
forall a b. a -> b
coe T_CommutativeSemiringWithoutOne_2002
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsSemiringWithoutOne_1298 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiringWithoutOne_1298 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_zero'737'_1370
         ((T_IsCommutativeSemiringWithoutOne_1382
 -> T_IsSemiringWithoutOne_1298)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCommutativeSemiringWithoutOne_1382
-> T_IsSemiringWithoutOne_1298
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutOne_1394
            (T_IsCommutativeSemiringWithoutOne_1382 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1382
v1)))
-- Algebra.Bundles.CommutativeSemiringWithoutOne.semiringWithoutOne
d_semiringWithoutOne_2096 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeSemiringWithoutOne_2002 -> T_SemiringWithoutOne_1880
d_semiringWithoutOne_2096 :: ()
-> ()
-> T_CommutativeSemiringWithoutOne_2002
-> T_SemiringWithoutOne_1880
d_semiringWithoutOne_2096 ~()
v0 ~()
v1 T_CommutativeSemiringWithoutOne_2002
v2
  = T_CommutativeSemiringWithoutOne_2002 -> T_SemiringWithoutOne_1880
du_semiringWithoutOne_2096 T_CommutativeSemiringWithoutOne_2002
v2
du_semiringWithoutOne_2096 ::
  T_CommutativeSemiringWithoutOne_2002 -> T_SemiringWithoutOne_1880
du_semiringWithoutOne_2096 :: T_CommutativeSemiringWithoutOne_2002 -> T_SemiringWithoutOne_1880
du_semiringWithoutOne_2096 T_CommutativeSemiringWithoutOne_2002
v0
  = ((AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> T_IsSemiringWithoutOne_1298
 -> T_SemiringWithoutOne_1880)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsSemiringWithoutOne_1298
-> T_SemiringWithoutOne_1880
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsSemiringWithoutOne_1298
-> T_SemiringWithoutOne_1880
C_SemiringWithoutOne'46'constructor_34609 (T_CommutativeSemiringWithoutOne_2002
-> AgdaAny -> AgdaAny -> AgdaAny
d__'43'__2024 (T_CommutativeSemiringWithoutOne_2002
-> T_CommutativeSemiringWithoutOne_2002
forall a b. a -> b
coe T_CommutativeSemiringWithoutOne_2002
v0))
      (T_CommutativeSemiringWithoutOne_2002
-> AgdaAny -> AgdaAny -> AgdaAny
d__'42'__2026 (T_CommutativeSemiringWithoutOne_2002
-> T_CommutativeSemiringWithoutOne_2002
forall a b. a -> b
coe T_CommutativeSemiringWithoutOne_2002
v0)) (T_CommutativeSemiringWithoutOne_2002 -> AgdaAny
d_0'35'_2028 (T_CommutativeSemiringWithoutOne_2002
-> T_CommutativeSemiringWithoutOne_2002
forall a b. a -> b
coe T_CommutativeSemiringWithoutOne_2002
v0))
      (T_IsCommutativeSemiringWithoutOne_1382
-> T_IsSemiringWithoutOne_1298
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutOne_1394
         ((T_CommutativeSemiringWithoutOne_2002
 -> T_IsCommutativeSemiringWithoutOne_1382)
-> AgdaAny -> T_IsCommutativeSemiringWithoutOne_1382
forall a b. a -> b
coe T_CommutativeSemiringWithoutOne_2002
-> T_IsCommutativeSemiringWithoutOne_1382
d_isCommutativeSemiringWithoutOne_2030 (T_CommutativeSemiringWithoutOne_2002 -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemiringWithoutOne_2002
v0)))
-- Algebra.Bundles.CommutativeSemiringWithoutOne._.magma
d_magma_2100 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeSemiringWithoutOne_2002 -> T_Magma_68
d_magma_2100 :: () -> () -> T_CommutativeSemiringWithoutOne_2002 -> T_Magma_68
d_magma_2100 ~()
v0 ~()
v1 T_CommutativeSemiringWithoutOne_2002
v2 = T_CommutativeSemiringWithoutOne_2002 -> T_Magma_68
du_magma_2100 T_CommutativeSemiringWithoutOne_2002
v2
du_magma_2100 :: T_CommutativeSemiringWithoutOne_2002 -> T_Magma_68
du_magma_2100 :: T_CommutativeSemiringWithoutOne_2002 -> T_Magma_68
du_magma_2100 T_CommutativeSemiringWithoutOne_2002
v0
  = let v1 :: t
v1 = (T_CommutativeSemiringWithoutOne_2002 -> T_SemiringWithoutOne_1880)
-> AgdaAny -> t
forall a b. a -> b
coe T_CommutativeSemiringWithoutOne_2002 -> T_SemiringWithoutOne_1880
du_semiringWithoutOne_2096 (T_CommutativeSemiringWithoutOne_2002 -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemiringWithoutOne_2002
v0) in
    AgdaAny -> T_Magma_68
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_SemiringWithoutOne_1880 -> T_NearSemiring_1766) -> AgdaAny -> t
forall a b. a -> b
coe T_SemiringWithoutOne_1880 -> T_NearSemiring_1766
du_nearSemiring_1966 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_Semigroup_536 -> T_Magma_68) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semigroup_536 -> T_Magma_68
du_magma_584 ((T_NearSemiring_1766 -> T_Semigroup_536) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_NearSemiring_1766 -> T_Semigroup_536
du_'42''45'semigroup_1868 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2))))
-- Algebra.Bundles.CommutativeSemiringWithoutOne._.rawMagma
d_rawMagma_2102 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeSemiringWithoutOne_2002 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
d_rawMagma_2102 :: () -> () -> T_CommutativeSemiringWithoutOne_2002 -> T_RawMagma_36
d_rawMagma_2102 ~()
v0 ~()
v1 T_CommutativeSemiringWithoutOne_2002
v2 = T_CommutativeSemiringWithoutOne_2002 -> T_RawMagma_36
du_rawMagma_2102 T_CommutativeSemiringWithoutOne_2002
v2
du_rawMagma_2102 ::
  T_CommutativeSemiringWithoutOne_2002 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
du_rawMagma_2102 :: T_CommutativeSemiringWithoutOne_2002 -> T_RawMagma_36
du_rawMagma_2102 T_CommutativeSemiringWithoutOne_2002
v0
  = let v1 :: t
v1 = (T_CommutativeSemiringWithoutOne_2002 -> T_SemiringWithoutOne_1880)
-> AgdaAny -> t
forall a b. a -> b
coe T_CommutativeSemiringWithoutOne_2002 -> T_SemiringWithoutOne_1880
du_semiringWithoutOne_2096 (T_CommutativeSemiringWithoutOne_2002 -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemiringWithoutOne_2002
v0) in
    AgdaAny -> T_RawMagma_36
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_SemiringWithoutOne_1880 -> T_NearSemiring_1766) -> AgdaAny -> t
forall a b. a -> b
coe T_SemiringWithoutOne_1880 -> T_NearSemiring_1766
du_nearSemiring_1966 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: t
v3 = (T_NearSemiring_1766 -> T_Semigroup_536) -> AgdaAny -> t
forall a b. a -> b
coe T_NearSemiring_1766 -> T_Semigroup_536
du_'42''45'semigroup_1868 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_Magma_68 -> T_RawMagma_36) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Magma_68 -> T_RawMagma_36
du_rawMagma_112 ((T_Semigroup_536 -> T_Magma_68) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semigroup_536 -> T_Magma_68
du_magma_584 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3)))))
-- Algebra.Bundles.CommutativeSemiringWithoutOne._.*-semigroup
d_'42''45'semigroup_2104 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeSemiringWithoutOne_2002 -> T_Semigroup_536
d_'42''45'semigroup_2104 :: () -> () -> T_CommutativeSemiringWithoutOne_2002 -> T_Semigroup_536
d_'42''45'semigroup_2104 ~()
v0 ~()
v1 T_CommutativeSemiringWithoutOne_2002
v2 = T_CommutativeSemiringWithoutOne_2002 -> T_Semigroup_536
du_'42''45'semigroup_2104 T_CommutativeSemiringWithoutOne_2002
v2
du_'42''45'semigroup_2104 ::
  T_CommutativeSemiringWithoutOne_2002 -> T_Semigroup_536
du_'42''45'semigroup_2104 :: T_CommutativeSemiringWithoutOne_2002 -> T_Semigroup_536
du_'42''45'semigroup_2104 T_CommutativeSemiringWithoutOne_2002
v0
  = let v1 :: t
v1 = (T_CommutativeSemiringWithoutOne_2002 -> T_SemiringWithoutOne_1880)
-> AgdaAny -> t
forall a b. a -> b
coe T_CommutativeSemiringWithoutOne_2002 -> T_SemiringWithoutOne_1880
du_semiringWithoutOne_2096 (T_CommutativeSemiringWithoutOne_2002 -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemiringWithoutOne_2002
v0) in
    AgdaAny -> T_Semigroup_536
forall a b. a -> b
coe
      ((T_NearSemiring_1766 -> T_Semigroup_536) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_NearSemiring_1766 -> T_Semigroup_536
du_'42''45'semigroup_1868 ((T_SemiringWithoutOne_1880 -> T_NearSemiring_1766)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutOne_1880 -> T_NearSemiring_1766
du_nearSemiring_1966 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1)))
-- Algebra.Bundles.CommutativeSemiringWithoutOne._.+-commutativeMonoid
d_'43''45'commutativeMonoid_2106 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeSemiringWithoutOne_2002 -> T_CommutativeMonoid_962
d_'43''45'commutativeMonoid_2106 :: ()
-> ()
-> T_CommutativeSemiringWithoutOne_2002
-> T_CommutativeMonoid_962
d_'43''45'commutativeMonoid_2106 ~()
v0 ~()
v1 T_CommutativeSemiringWithoutOne_2002
v2
  = T_CommutativeSemiringWithoutOne_2002 -> T_CommutativeMonoid_962
du_'43''45'commutativeMonoid_2106 T_CommutativeSemiringWithoutOne_2002
v2
du_'43''45'commutativeMonoid_2106 ::
  T_CommutativeSemiringWithoutOne_2002 -> T_CommutativeMonoid_962
du_'43''45'commutativeMonoid_2106 :: T_CommutativeSemiringWithoutOne_2002 -> T_CommutativeMonoid_962
du_'43''45'commutativeMonoid_2106 T_CommutativeSemiringWithoutOne_2002
v0
  = (T_SemiringWithoutOne_1880 -> T_CommutativeMonoid_962)
-> AgdaAny -> T_CommutativeMonoid_962
forall a b. a -> b
coe
      T_SemiringWithoutOne_1880 -> T_CommutativeMonoid_962
du_'43''45'commutativeMonoid_1990
      ((T_CommutativeSemiringWithoutOne_2002 -> T_SemiringWithoutOne_1880)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemiringWithoutOne_2002 -> T_SemiringWithoutOne_1880
du_semiringWithoutOne_2096 (T_CommutativeSemiringWithoutOne_2002 -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemiringWithoutOne_2002
v0))
-- Algebra.Bundles.CommutativeSemiringWithoutOne._.commutativeSemigroup
d_commutativeSemigroup_2108 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeSemiringWithoutOne_2002 -> T_CommutativeSemigroup_662
d_commutativeSemigroup_2108 :: ()
-> ()
-> T_CommutativeSemiringWithoutOne_2002
-> T_CommutativeSemigroup_662
d_commutativeSemigroup_2108 ~()
v0 ~()
v1 T_CommutativeSemiringWithoutOne_2002
v2
  = T_CommutativeSemiringWithoutOne_2002 -> T_CommutativeSemigroup_662
du_commutativeSemigroup_2108 T_CommutativeSemiringWithoutOne_2002
v2
du_commutativeSemigroup_2108 ::
  T_CommutativeSemiringWithoutOne_2002 -> T_CommutativeSemigroup_662
du_commutativeSemigroup_2108 :: T_CommutativeSemiringWithoutOne_2002 -> T_CommutativeSemigroup_662
du_commutativeSemigroup_2108 T_CommutativeSemiringWithoutOne_2002
v0
  = let v1 :: t
v1 = (T_CommutativeSemiringWithoutOne_2002 -> T_SemiringWithoutOne_1880)
-> AgdaAny -> t
forall a b. a -> b
coe T_CommutativeSemiringWithoutOne_2002 -> T_SemiringWithoutOne_1880
du_semiringWithoutOne_2096 (T_CommutativeSemiringWithoutOne_2002 -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemiringWithoutOne_2002
v0) in
    AgdaAny -> T_CommutativeSemigroup_662
forall a b. a -> b
coe
      ((T_CommutativeMonoid_962 -> T_CommutativeSemigroup_662)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_CommutativeMonoid_962 -> T_CommutativeSemigroup_662
du_commutativeSemigroup_1048
         ((T_SemiringWithoutOne_1880 -> T_CommutativeMonoid_962)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutOne_1880 -> T_CommutativeMonoid_962
du_'43''45'commutativeMonoid_1990 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1)))
-- Algebra.Bundles.CommutativeSemiringWithoutOne._.magma
d_magma_2110 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeSemiringWithoutOne_2002 -> T_Magma_68
d_magma_2110 :: () -> () -> T_CommutativeSemiringWithoutOne_2002 -> T_Magma_68
d_magma_2110 ~()
v0 ~()
v1 T_CommutativeSemiringWithoutOne_2002
v2 = T_CommutativeSemiringWithoutOne_2002 -> T_Magma_68
du_magma_2110 T_CommutativeSemiringWithoutOne_2002
v2
du_magma_2110 :: T_CommutativeSemiringWithoutOne_2002 -> T_Magma_68
du_magma_2110 :: T_CommutativeSemiringWithoutOne_2002 -> T_Magma_68
du_magma_2110 T_CommutativeSemiringWithoutOne_2002
v0
  = let v1 :: t
v1 = (T_CommutativeSemiringWithoutOne_2002 -> T_SemiringWithoutOne_1880)
-> AgdaAny -> t
forall a b. a -> b
coe T_CommutativeSemiringWithoutOne_2002 -> T_SemiringWithoutOne_1880
du_semiringWithoutOne_2096 (T_CommutativeSemiringWithoutOne_2002 -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemiringWithoutOne_2002
v0) in
    AgdaAny -> T_Magma_68
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_SemiringWithoutOne_1880 -> T_NearSemiring_1766) -> AgdaAny -> t
forall a b. a -> b
coe T_SemiringWithoutOne_1880 -> T_NearSemiring_1766
du_nearSemiring_1966 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: t
v3 = (T_NearSemiring_1766 -> T_Monoid_882) -> AgdaAny -> t
forall a b. a -> b
coe T_NearSemiring_1766 -> T_Monoid_882
du_'43''45'monoid_1852 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_Semigroup_536 -> T_Magma_68) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semigroup_536 -> T_Magma_68
du_magma_584 ((T_Monoid_882 -> T_Semigroup_536) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Monoid_882 -> T_Semigroup_536
du_semigroup_944 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3)))))
-- Algebra.Bundles.CommutativeSemiringWithoutOne._.+-monoid
d_'43''45'monoid_2112 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeSemiringWithoutOne_2002 -> T_Monoid_882
d_'43''45'monoid_2112 :: () -> () -> T_CommutativeSemiringWithoutOne_2002 -> T_Monoid_882
d_'43''45'monoid_2112 ~()
v0 ~()
v1 T_CommutativeSemiringWithoutOne_2002
v2 = T_CommutativeSemiringWithoutOne_2002 -> T_Monoid_882
du_'43''45'monoid_2112 T_CommutativeSemiringWithoutOne_2002
v2
du_'43''45'monoid_2112 ::
  T_CommutativeSemiringWithoutOne_2002 -> T_Monoid_882
du_'43''45'monoid_2112 :: T_CommutativeSemiringWithoutOne_2002 -> T_Monoid_882
du_'43''45'monoid_2112 T_CommutativeSemiringWithoutOne_2002
v0
  = let v1 :: t
v1 = (T_CommutativeSemiringWithoutOne_2002 -> T_SemiringWithoutOne_1880)
-> AgdaAny -> t
forall a b. a -> b
coe T_CommutativeSemiringWithoutOne_2002 -> T_SemiringWithoutOne_1880
du_semiringWithoutOne_2096 (T_CommutativeSemiringWithoutOne_2002 -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemiringWithoutOne_2002
v0) in
    AgdaAny -> T_Monoid_882
forall a b. a -> b
coe
      ((T_NearSemiring_1766 -> T_Monoid_882) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_NearSemiring_1766 -> T_Monoid_882
du_'43''45'monoid_1852 ((T_SemiringWithoutOne_1880 -> T_NearSemiring_1766)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutOne_1880 -> T_NearSemiring_1766
du_nearSemiring_1966 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1)))
-- Algebra.Bundles.CommutativeSemiringWithoutOne._.rawMagma
d_rawMagma_2114 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeSemiringWithoutOne_2002 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
d_rawMagma_2114 :: () -> () -> T_CommutativeSemiringWithoutOne_2002 -> T_RawMagma_36
d_rawMagma_2114 ~()
v0 ~()
v1 T_CommutativeSemiringWithoutOne_2002
v2 = T_CommutativeSemiringWithoutOne_2002 -> T_RawMagma_36
du_rawMagma_2114 T_CommutativeSemiringWithoutOne_2002
v2
du_rawMagma_2114 ::
  T_CommutativeSemiringWithoutOne_2002 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
du_rawMagma_2114 :: T_CommutativeSemiringWithoutOne_2002 -> T_RawMagma_36
du_rawMagma_2114 T_CommutativeSemiringWithoutOne_2002
v0
  = let v1 :: t
v1 = (T_CommutativeSemiringWithoutOne_2002 -> T_SemiringWithoutOne_1880)
-> AgdaAny -> t
forall a b. a -> b
coe T_CommutativeSemiringWithoutOne_2002 -> T_SemiringWithoutOne_1880
du_semiringWithoutOne_2096 (T_CommutativeSemiringWithoutOne_2002 -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemiringWithoutOne_2002
v0) in
    AgdaAny -> T_RawMagma_36
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_SemiringWithoutOne_1880 -> T_NearSemiring_1766) -> AgdaAny -> t
forall a b. a -> b
coe T_SemiringWithoutOne_1880 -> T_NearSemiring_1766
du_nearSemiring_1966 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: t
v3 = (T_NearSemiring_1766 -> T_Monoid_882) -> AgdaAny -> t
forall a b. a -> b
coe T_NearSemiring_1766 -> T_Monoid_882
du_'43''45'monoid_1852 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: t
v4 = (T_Monoid_882 -> T_Semigroup_536) -> AgdaAny -> t
forall a b. a -> b
coe T_Monoid_882 -> T_Semigroup_536
du_semigroup_944 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_Magma_68 -> T_RawMagma_36) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Magma_68 -> T_RawMagma_36
du_rawMagma_112 ((T_Semigroup_536 -> T_Magma_68) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semigroup_536 -> T_Magma_68
du_magma_584 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v4))))))
-- Algebra.Bundles.CommutativeSemiringWithoutOne._.rawMonoid
d_rawMonoid_2116 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeSemiringWithoutOne_2002 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMonoid_64
d_rawMonoid_2116 :: () -> () -> T_CommutativeSemiringWithoutOne_2002 -> T_RawMonoid_64
d_rawMonoid_2116 ~()
v0 ~()
v1 T_CommutativeSemiringWithoutOne_2002
v2 = T_CommutativeSemiringWithoutOne_2002 -> T_RawMonoid_64
du_rawMonoid_2116 T_CommutativeSemiringWithoutOne_2002
v2
du_rawMonoid_2116 ::
  T_CommutativeSemiringWithoutOne_2002 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMonoid_64
du_rawMonoid_2116 :: T_CommutativeSemiringWithoutOne_2002 -> T_RawMonoid_64
du_rawMonoid_2116 T_CommutativeSemiringWithoutOne_2002
v0
  = let v1 :: t
v1 = (T_CommutativeSemiringWithoutOne_2002 -> T_SemiringWithoutOne_1880)
-> AgdaAny -> t
forall a b. a -> b
coe T_CommutativeSemiringWithoutOne_2002 -> T_SemiringWithoutOne_1880
du_semiringWithoutOne_2096 (T_CommutativeSemiringWithoutOne_2002 -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemiringWithoutOne_2002
v0) in
    AgdaAny -> T_RawMonoid_64
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_SemiringWithoutOne_1880 -> T_NearSemiring_1766) -> AgdaAny -> t
forall a b. a -> b
coe T_SemiringWithoutOne_1880 -> T_NearSemiring_1766
du_nearSemiring_1966 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_Monoid_882 -> T_RawMonoid_64) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Monoid_882 -> T_RawMonoid_64
du_rawMonoid_954 ((T_NearSemiring_1766 -> T_Monoid_882) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_NearSemiring_1766 -> T_Monoid_882
du_'43''45'monoid_1852 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2))))
-- Algebra.Bundles.CommutativeSemiringWithoutOne._.semigroup
d_semigroup_2118 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeSemiringWithoutOne_2002 -> T_Semigroup_536
d_semigroup_2118 :: () -> () -> T_CommutativeSemiringWithoutOne_2002 -> T_Semigroup_536
d_semigroup_2118 ~()
v0 ~()
v1 T_CommutativeSemiringWithoutOne_2002
v2 = T_CommutativeSemiringWithoutOne_2002 -> T_Semigroup_536
du_semigroup_2118 T_CommutativeSemiringWithoutOne_2002
v2
du_semigroup_2118 ::
  T_CommutativeSemiringWithoutOne_2002 -> T_Semigroup_536
du_semigroup_2118 :: T_CommutativeSemiringWithoutOne_2002 -> T_Semigroup_536
du_semigroup_2118 T_CommutativeSemiringWithoutOne_2002
v0
  = let v1 :: t
v1 = (T_CommutativeSemiringWithoutOne_2002 -> T_SemiringWithoutOne_1880)
-> AgdaAny -> t
forall a b. a -> b
coe T_CommutativeSemiringWithoutOne_2002 -> T_SemiringWithoutOne_1880
du_semiringWithoutOne_2096 (T_CommutativeSemiringWithoutOne_2002 -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemiringWithoutOne_2002
v0) in
    AgdaAny -> T_Semigroup_536
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_SemiringWithoutOne_1880 -> T_NearSemiring_1766) -> AgdaAny -> t
forall a b. a -> b
coe T_SemiringWithoutOne_1880 -> T_NearSemiring_1766
du_nearSemiring_1966 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_Monoid_882 -> T_Semigroup_536) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Monoid_882 -> T_Semigroup_536
du_semigroup_944 ((T_NearSemiring_1766 -> T_Monoid_882) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_NearSemiring_1766 -> T_Monoid_882
du_'43''45'monoid_1852 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2))))
-- Algebra.Bundles.CommutativeSemiringWithoutOne._.unitalMagma
d_unitalMagma_2120 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeSemiringWithoutOne_2002 -> T_UnitalMagma_814
d_unitalMagma_2120 :: ()
-> () -> T_CommutativeSemiringWithoutOne_2002 -> T_UnitalMagma_814
d_unitalMagma_2120 ~()
v0 ~()
v1 T_CommutativeSemiringWithoutOne_2002
v2 = T_CommutativeSemiringWithoutOne_2002 -> T_UnitalMagma_814
du_unitalMagma_2120 T_CommutativeSemiringWithoutOne_2002
v2
du_unitalMagma_2120 ::
  T_CommutativeSemiringWithoutOne_2002 -> T_UnitalMagma_814
du_unitalMagma_2120 :: T_CommutativeSemiringWithoutOne_2002 -> T_UnitalMagma_814
du_unitalMagma_2120 T_CommutativeSemiringWithoutOne_2002
v0
  = let v1 :: t
v1 = (T_CommutativeSemiringWithoutOne_2002 -> T_SemiringWithoutOne_1880)
-> AgdaAny -> t
forall a b. a -> b
coe T_CommutativeSemiringWithoutOne_2002 -> T_SemiringWithoutOne_1880
du_semiringWithoutOne_2096 (T_CommutativeSemiringWithoutOne_2002 -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemiringWithoutOne_2002
v0) in
    AgdaAny -> T_UnitalMagma_814
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_SemiringWithoutOne_1880 -> T_NearSemiring_1766) -> AgdaAny -> t
forall a b. a -> b
coe T_SemiringWithoutOne_1880 -> T_NearSemiring_1766
du_nearSemiring_1966 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_Monoid_882 -> T_UnitalMagma_814) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Monoid_882 -> T_UnitalMagma_814
du_unitalMagma_956 ((T_NearSemiring_1766 -> T_Monoid_882) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_NearSemiring_1766 -> T_Monoid_882
du_'43''45'monoid_1852 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2))))
-- Algebra.Bundles.CommutativeSemiringWithoutOne._.nearSemiring
d_nearSemiring_2122 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeSemiringWithoutOne_2002 -> T_NearSemiring_1766
d_nearSemiring_2122 :: ()
-> ()
-> T_CommutativeSemiringWithoutOne_2002
-> T_NearSemiring_1766
d_nearSemiring_2122 ~()
v0 ~()
v1 T_CommutativeSemiringWithoutOne_2002
v2 = T_CommutativeSemiringWithoutOne_2002 -> T_NearSemiring_1766
du_nearSemiring_2122 T_CommutativeSemiringWithoutOne_2002
v2
du_nearSemiring_2122 ::
  T_CommutativeSemiringWithoutOne_2002 -> T_NearSemiring_1766
du_nearSemiring_2122 :: T_CommutativeSemiringWithoutOne_2002 -> T_NearSemiring_1766
du_nearSemiring_2122 T_CommutativeSemiringWithoutOne_2002
v0
  = (T_SemiringWithoutOne_1880 -> T_NearSemiring_1766)
-> AgdaAny -> T_NearSemiring_1766
forall a b. a -> b
coe
      T_SemiringWithoutOne_1880 -> T_NearSemiring_1766
du_nearSemiring_1966 ((T_CommutativeSemiringWithoutOne_2002 -> T_SemiringWithoutOne_1880)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemiringWithoutOne_2002 -> T_SemiringWithoutOne_1880
du_semiringWithoutOne_2096 (T_CommutativeSemiringWithoutOne_2002 -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemiringWithoutOne_2002
v0))
-- Algebra.Bundles.CommutativeSemiringWithoutOne._.rawNearSemiring
d_rawNearSemiring_2124 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeSemiringWithoutOne_2002 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawNearSemiring_134
d_rawNearSemiring_2124 :: ()
-> ()
-> T_CommutativeSemiringWithoutOne_2002
-> T_RawNearSemiring_134
d_rawNearSemiring_2124 ~()
v0 ~()
v1 T_CommutativeSemiringWithoutOne_2002
v2 = T_CommutativeSemiringWithoutOne_2002 -> T_RawNearSemiring_134
du_rawNearSemiring_2124 T_CommutativeSemiringWithoutOne_2002
v2
du_rawNearSemiring_2124 ::
  T_CommutativeSemiringWithoutOne_2002 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawNearSemiring_134
du_rawNearSemiring_2124 :: T_CommutativeSemiringWithoutOne_2002 -> T_RawNearSemiring_134
du_rawNearSemiring_2124 T_CommutativeSemiringWithoutOne_2002
v0
  = let v1 :: t
v1 = (T_CommutativeSemiringWithoutOne_2002 -> T_SemiringWithoutOne_1880)
-> AgdaAny -> t
forall a b. a -> b
coe T_CommutativeSemiringWithoutOne_2002 -> T_SemiringWithoutOne_1880
du_semiringWithoutOne_2096 (T_CommutativeSemiringWithoutOne_2002 -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemiringWithoutOne_2002
v0) in
    AgdaAny -> T_RawNearSemiring_134
forall a b. a -> b
coe
      ((T_NearSemiring_1766 -> T_RawNearSemiring_134)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_NearSemiring_1766 -> T_RawNearSemiring_134
du_rawNearSemiring_1850 ((T_SemiringWithoutOne_1880 -> T_NearSemiring_1766)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutOne_1880 -> T_NearSemiring_1766
du_nearSemiring_1966 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1)))
-- Algebra.Bundles.SemiringWithoutAnnihilatingZero
d_SemiringWithoutAnnihilatingZero_2130 :: p -> p -> ()
d_SemiringWithoutAnnihilatingZero_2130 p
a0 p
a1 = ()
data T_SemiringWithoutAnnihilatingZero_2130
  = C_SemiringWithoutAnnihilatingZero'46'constructor_38993 (AgdaAny ->
                                                            AgdaAny -> AgdaAny)
                                                           (AgdaAny -> AgdaAny -> AgdaAny) AgdaAny
                                                           AgdaAny
                                                           MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutAnnihilatingZero_1468
-- Algebra.Bundles.SemiringWithoutAnnihilatingZero.Carrier
d_Carrier_2150 :: T_SemiringWithoutAnnihilatingZero_2130 -> ()
d_Carrier_2150 :: T_SemiringWithoutAnnihilatingZero_2130 -> ()
d_Carrier_2150 = T_SemiringWithoutAnnihilatingZero_2130 -> ()
forall a. a
erased
-- Algebra.Bundles.SemiringWithoutAnnihilatingZero._≈_
d__'8776'__2152 ::
  T_SemiringWithoutAnnihilatingZero_2130 -> AgdaAny -> AgdaAny -> ()
d__'8776'__2152 :: T_SemiringWithoutAnnihilatingZero_2130 -> AgdaAny -> AgdaAny -> ()
d__'8776'__2152 = T_SemiringWithoutAnnihilatingZero_2130 -> AgdaAny -> AgdaAny -> ()
forall a. a
erased
-- Algebra.Bundles.SemiringWithoutAnnihilatingZero._+_
d__'43'__2154 ::
  T_SemiringWithoutAnnihilatingZero_2130 ->
  AgdaAny -> AgdaAny -> AgdaAny
d__'43'__2154 :: T_SemiringWithoutAnnihilatingZero_2130
-> AgdaAny -> AgdaAny -> AgdaAny
d__'43'__2154 T_SemiringWithoutAnnihilatingZero_2130
v0
  = case T_SemiringWithoutAnnihilatingZero_2130
-> T_SemiringWithoutAnnihilatingZero_2130
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_2130
v0 of
      C_SemiringWithoutAnnihilatingZero'46'constructor_38993 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny
v5 AgdaAny
v6 T_IsSemiringWithoutAnnihilatingZero_1468
v7
        -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v3
      T_SemiringWithoutAnnihilatingZero_2130
_ -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.SemiringWithoutAnnihilatingZero._*_
d__'42'__2156 ::
  T_SemiringWithoutAnnihilatingZero_2130 ->
  AgdaAny -> AgdaAny -> AgdaAny
d__'42'__2156 :: T_SemiringWithoutAnnihilatingZero_2130
-> AgdaAny -> AgdaAny -> AgdaAny
d__'42'__2156 T_SemiringWithoutAnnihilatingZero_2130
v0
  = case T_SemiringWithoutAnnihilatingZero_2130
-> T_SemiringWithoutAnnihilatingZero_2130
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_2130
v0 of
      C_SemiringWithoutAnnihilatingZero'46'constructor_38993 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny
v5 AgdaAny
v6 T_IsSemiringWithoutAnnihilatingZero_1468
v7
        -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v4
      T_SemiringWithoutAnnihilatingZero_2130
_ -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.SemiringWithoutAnnihilatingZero.0#
d_0'35'_2158 :: T_SemiringWithoutAnnihilatingZero_2130 -> AgdaAny
d_0'35'_2158 :: T_SemiringWithoutAnnihilatingZero_2130 -> AgdaAny
d_0'35'_2158 T_SemiringWithoutAnnihilatingZero_2130
v0
  = case T_SemiringWithoutAnnihilatingZero_2130
-> T_SemiringWithoutAnnihilatingZero_2130
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_2130
v0 of
      C_SemiringWithoutAnnihilatingZero'46'constructor_38993 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny
v5 AgdaAny
v6 T_IsSemiringWithoutAnnihilatingZero_1468
v7
        -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v5
      T_SemiringWithoutAnnihilatingZero_2130
_ -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.SemiringWithoutAnnihilatingZero.1#
d_1'35'_2160 :: T_SemiringWithoutAnnihilatingZero_2130 -> AgdaAny
d_1'35'_2160 :: T_SemiringWithoutAnnihilatingZero_2130 -> AgdaAny
d_1'35'_2160 T_SemiringWithoutAnnihilatingZero_2130
v0
  = case T_SemiringWithoutAnnihilatingZero_2130
-> T_SemiringWithoutAnnihilatingZero_2130
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_2130
v0 of
      C_SemiringWithoutAnnihilatingZero'46'constructor_38993 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny
v5 AgdaAny
v6 T_IsSemiringWithoutAnnihilatingZero_1468
v7
        -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v6
      T_SemiringWithoutAnnihilatingZero_2130
_ -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.SemiringWithoutAnnihilatingZero.isSemiringWithoutAnnihilatingZero
d_isSemiringWithoutAnnihilatingZero_2162 ::
  T_SemiringWithoutAnnihilatingZero_2130 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_2162 :: T_SemiringWithoutAnnihilatingZero_2130
-> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_2162 T_SemiringWithoutAnnihilatingZero_2130
v0
  = case T_SemiringWithoutAnnihilatingZero_2130
-> T_SemiringWithoutAnnihilatingZero_2130
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_2130
v0 of
      C_SemiringWithoutAnnihilatingZero'46'constructor_38993 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny
v5 AgdaAny
v6 T_IsSemiringWithoutAnnihilatingZero_1468
v7
        -> T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsSemiringWithoutAnnihilatingZero_1468
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
v7
      T_SemiringWithoutAnnihilatingZero_2130
_ -> T_IsSemiringWithoutAnnihilatingZero_1468
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.SemiringWithoutAnnihilatingZero._.*-assoc
d_'42''45'assoc_2166 ::
  T_SemiringWithoutAnnihilatingZero_2130 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'assoc_2166 :: T_SemiringWithoutAnnihilatingZero_2130
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'assoc_2166 T_SemiringWithoutAnnihilatingZero_2130
v0
  = (T_IsSemiringWithoutAnnihilatingZero_1468
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsSemiringWithoutAnnihilatingZero_1468
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'42''45'assoc_1492
      ((T_SemiringWithoutAnnihilatingZero_2130
 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_2130
-> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_2162 (T_SemiringWithoutAnnihilatingZero_2130 -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_2130
v0))
-- Algebra.Bundles.SemiringWithoutAnnihilatingZero._.*-cong
d_'42''45'cong_2168 ::
  T_SemiringWithoutAnnihilatingZero_2130 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'cong_2168 :: T_SemiringWithoutAnnihilatingZero_2130
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'42''45'cong_2168 T_SemiringWithoutAnnihilatingZero_2130
v0
  = (T_IsSemiringWithoutAnnihilatingZero_1468
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsSemiringWithoutAnnihilatingZero_1468
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'42''45'cong_1490
      ((T_SemiringWithoutAnnihilatingZero_2130
 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_2130
-> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_2162 (T_SemiringWithoutAnnihilatingZero_2130 -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_2130
v0))
-- Algebra.Bundles.SemiringWithoutAnnihilatingZero._.∙-congʳ
d_'8729''45'cong'691'_2170 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SemiringWithoutAnnihilatingZero_2130 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_2170 :: ()
-> ()
-> T_SemiringWithoutAnnihilatingZero_2130
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_2170 ~()
v0 ~()
v1 T_SemiringWithoutAnnihilatingZero_2130
v2
  = T_SemiringWithoutAnnihilatingZero_2130
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_2170 T_SemiringWithoutAnnihilatingZero_2130
v2
du_'8729''45'cong'691'_2170 ::
  T_SemiringWithoutAnnihilatingZero_2130 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_2170 :: T_SemiringWithoutAnnihilatingZero_2130
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_2170 T_SemiringWithoutAnnihilatingZero_2130
v0
  = let v1 :: T_IsSemiringWithoutAnnihilatingZero_1468
v1 = T_SemiringWithoutAnnihilatingZero_2130
-> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_2162 (T_SemiringWithoutAnnihilatingZero_2130
-> T_SemiringWithoutAnnihilatingZero_2130
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_2130
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: t
v2
             = (T_IsSemiringWithoutAnnihilatingZero_1468 -> T_IsMonoid_686)
-> AgdaAny -> t
forall a b. a -> b
coe
                 T_IsSemiringWithoutAnnihilatingZero_1468 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.du_'42''45'isMonoid_1550
                 (T_IsSemiringWithoutAnnihilatingZero_1468 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_472
v3
                = T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (AgdaAny -> T_IsMonoid_686
forall a b. a -> b
coe AgdaAny
forall a. a
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'691'_206
               ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v3)))))
-- Algebra.Bundles.SemiringWithoutAnnihilatingZero._.∙-congˡ
d_'8729''45'cong'737'_2172 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SemiringWithoutAnnihilatingZero_2130 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_2172 :: ()
-> ()
-> T_SemiringWithoutAnnihilatingZero_2130
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_2172 ~()
v0 ~()
v1 T_SemiringWithoutAnnihilatingZero_2130
v2
  = T_SemiringWithoutAnnihilatingZero_2130
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_2172 T_SemiringWithoutAnnihilatingZero_2130
v2
du_'8729''45'cong'737'_2172 ::
  T_SemiringWithoutAnnihilatingZero_2130 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_2172 :: T_SemiringWithoutAnnihilatingZero_2130
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_2172 T_SemiringWithoutAnnihilatingZero_2130
v0
  = let v1 :: T_IsSemiringWithoutAnnihilatingZero_1468
v1 = T_SemiringWithoutAnnihilatingZero_2130
-> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_2162 (T_SemiringWithoutAnnihilatingZero_2130
-> T_SemiringWithoutAnnihilatingZero_2130
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_2130
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: t
v2
             = (T_IsSemiringWithoutAnnihilatingZero_1468 -> T_IsMonoid_686)
-> AgdaAny -> t
forall a b. a -> b
coe
                 T_IsSemiringWithoutAnnihilatingZero_1468 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.du_'42''45'isMonoid_1550
                 (T_IsSemiringWithoutAnnihilatingZero_1468 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_472
v3
                = T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (AgdaAny -> T_IsMonoid_686
forall a b. a -> b
coe AgdaAny
forall a. a
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'737'_202
               ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v3)))))
-- Algebra.Bundles.SemiringWithoutAnnihilatingZero._.*-identity
d_'42''45'identity_2174 ::
  T_SemiringWithoutAnnihilatingZero_2130 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'42''45'identity_2174 :: T_SemiringWithoutAnnihilatingZero_2130 -> T_Σ_14
d_'42''45'identity_2174 T_SemiringWithoutAnnihilatingZero_2130
v0
  = (T_IsSemiringWithoutAnnihilatingZero_1468 -> T_Σ_14)
-> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsSemiringWithoutAnnihilatingZero_1468 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_'42''45'identity_1494
      ((T_SemiringWithoutAnnihilatingZero_2130
 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_2130
-> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_2162 (T_SemiringWithoutAnnihilatingZero_2130 -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_2130
v0))
-- Algebra.Bundles.SemiringWithoutAnnihilatingZero._.identityʳ
d_identity'691'_2176 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SemiringWithoutAnnihilatingZero_2130 -> AgdaAny -> AgdaAny
d_identity'691'_2176 :: ()
-> ()
-> T_SemiringWithoutAnnihilatingZero_2130
-> AgdaAny
-> AgdaAny
d_identity'691'_2176 ~()
v0 ~()
v1 T_SemiringWithoutAnnihilatingZero_2130
v2 = T_SemiringWithoutAnnihilatingZero_2130 -> AgdaAny -> AgdaAny
du_identity'691'_2176 T_SemiringWithoutAnnihilatingZero_2130
v2
du_identity'691'_2176 ::
  T_SemiringWithoutAnnihilatingZero_2130 -> AgdaAny -> AgdaAny
du_identity'691'_2176 :: T_SemiringWithoutAnnihilatingZero_2130 -> AgdaAny -> AgdaAny
du_identity'691'_2176 T_SemiringWithoutAnnihilatingZero_2130
v0
  = let v1 :: T_IsSemiringWithoutAnnihilatingZero_1468
v1 = T_SemiringWithoutAnnihilatingZero_2130
-> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_2162 (T_SemiringWithoutAnnihilatingZero_2130
-> T_SemiringWithoutAnnihilatingZero_2130
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_2130
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsMonoid_686 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoid_686 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_identity'691'_728
         ((T_IsSemiringWithoutAnnihilatingZero_1468 -> T_IsMonoid_686)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemiringWithoutAnnihilatingZero_1468 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.du_'42''45'isMonoid_1550 (T_IsSemiringWithoutAnnihilatingZero_1468 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
v1)))
-- Algebra.Bundles.SemiringWithoutAnnihilatingZero._.identityˡ
d_identity'737'_2178 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SemiringWithoutAnnihilatingZero_2130 -> AgdaAny -> AgdaAny
d_identity'737'_2178 :: ()
-> ()
-> T_SemiringWithoutAnnihilatingZero_2130
-> AgdaAny
-> AgdaAny
d_identity'737'_2178 ~()
v0 ~()
v1 T_SemiringWithoutAnnihilatingZero_2130
v2 = T_SemiringWithoutAnnihilatingZero_2130 -> AgdaAny -> AgdaAny
du_identity'737'_2178 T_SemiringWithoutAnnihilatingZero_2130
v2
du_identity'737'_2178 ::
  T_SemiringWithoutAnnihilatingZero_2130 -> AgdaAny -> AgdaAny
du_identity'737'_2178 :: T_SemiringWithoutAnnihilatingZero_2130 -> AgdaAny -> AgdaAny
du_identity'737'_2178 T_SemiringWithoutAnnihilatingZero_2130
v0
  = let v1 :: T_IsSemiringWithoutAnnihilatingZero_1468
v1 = T_SemiringWithoutAnnihilatingZero_2130
-> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_2162 (T_SemiringWithoutAnnihilatingZero_2130
-> T_SemiringWithoutAnnihilatingZero_2130
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_2130
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsMonoid_686 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoid_686 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_identity'737'_726
         ((T_IsSemiringWithoutAnnihilatingZero_1468 -> T_IsMonoid_686)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemiringWithoutAnnihilatingZero_1468 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.du_'42''45'isMonoid_1550 (T_IsSemiringWithoutAnnihilatingZero_1468 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
v1)))
-- Algebra.Bundles.SemiringWithoutAnnihilatingZero._.*-isMagma
d_'42''45'isMagma_2180 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SemiringWithoutAnnihilatingZero_2130 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_176
d_'42''45'isMagma_2180 :: () -> () -> T_SemiringWithoutAnnihilatingZero_2130 -> T_IsMagma_176
d_'42''45'isMagma_2180 ~()
v0 ~()
v1 T_SemiringWithoutAnnihilatingZero_2130
v2 = T_SemiringWithoutAnnihilatingZero_2130 -> T_IsMagma_176
du_'42''45'isMagma_2180 T_SemiringWithoutAnnihilatingZero_2130
v2
du_'42''45'isMagma_2180 ::
  T_SemiringWithoutAnnihilatingZero_2130 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_176
du_'42''45'isMagma_2180 :: T_SemiringWithoutAnnihilatingZero_2130 -> T_IsMagma_176
du_'42''45'isMagma_2180 T_SemiringWithoutAnnihilatingZero_2130
v0
  = (T_IsSemiringWithoutAnnihilatingZero_1468 -> T_IsMagma_176)
-> AgdaAny -> T_IsMagma_176
forall a b. a -> b
coe
      T_IsSemiringWithoutAnnihilatingZero_1468 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.du_'42''45'isMagma_1546
      ((T_SemiringWithoutAnnihilatingZero_2130
 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_2130
-> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_2162 (T_SemiringWithoutAnnihilatingZero_2130 -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_2130
v0))
-- Algebra.Bundles.SemiringWithoutAnnihilatingZero._.*-isMonoid
d_'42''45'isMonoid_2182 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SemiringWithoutAnnihilatingZero_2130 ->
  MAlonzo.Code.Algebra.Structures.T_IsMonoid_686
d_'42''45'isMonoid_2182 :: ()
-> () -> T_SemiringWithoutAnnihilatingZero_2130 -> T_IsMonoid_686
d_'42''45'isMonoid_2182 ~()
v0 ~()
v1 T_SemiringWithoutAnnihilatingZero_2130
v2 = T_SemiringWithoutAnnihilatingZero_2130 -> T_IsMonoid_686
du_'42''45'isMonoid_2182 T_SemiringWithoutAnnihilatingZero_2130
v2
du_'42''45'isMonoid_2182 ::
  T_SemiringWithoutAnnihilatingZero_2130 ->
  MAlonzo.Code.Algebra.Structures.T_IsMonoid_686
du_'42''45'isMonoid_2182 :: T_SemiringWithoutAnnihilatingZero_2130 -> T_IsMonoid_686
du_'42''45'isMonoid_2182 T_SemiringWithoutAnnihilatingZero_2130
v0
  = (T_IsSemiringWithoutAnnihilatingZero_1468 -> T_IsMonoid_686)
-> AgdaAny -> T_IsMonoid_686
forall a b. a -> b
coe
      T_IsSemiringWithoutAnnihilatingZero_1468 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.du_'42''45'isMonoid_1550
      ((T_SemiringWithoutAnnihilatingZero_2130
 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_2130
-> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_2162 (T_SemiringWithoutAnnihilatingZero_2130 -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_2130
v0))
-- Algebra.Bundles.SemiringWithoutAnnihilatingZero._.*-isSemigroup
d_'42''45'isSemigroup_2184 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SemiringWithoutAnnihilatingZero_2130 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_472
d_'42''45'isSemigroup_2184 :: ()
-> ()
-> T_SemiringWithoutAnnihilatingZero_2130
-> T_IsSemigroup_472
d_'42''45'isSemigroup_2184 ~()
v0 ~()
v1 T_SemiringWithoutAnnihilatingZero_2130
v2
  = T_SemiringWithoutAnnihilatingZero_2130 -> T_IsSemigroup_472
du_'42''45'isSemigroup_2184 T_SemiringWithoutAnnihilatingZero_2130
v2
du_'42''45'isSemigroup_2184 ::
  T_SemiringWithoutAnnihilatingZero_2130 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_472
du_'42''45'isSemigroup_2184 :: T_SemiringWithoutAnnihilatingZero_2130 -> T_IsSemigroup_472
du_'42''45'isSemigroup_2184 T_SemiringWithoutAnnihilatingZero_2130
v0
  = (T_IsSemiringWithoutAnnihilatingZero_1468 -> T_IsSemigroup_472)
-> AgdaAny -> T_IsSemigroup_472
forall a b. a -> b
coe
      T_IsSemiringWithoutAnnihilatingZero_1468 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.du_'42''45'isSemigroup_1548
      ((T_SemiringWithoutAnnihilatingZero_2130
 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_2130
-> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_2162 (T_SemiringWithoutAnnihilatingZero_2130 -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_2130
v0))
-- Algebra.Bundles.SemiringWithoutAnnihilatingZero._.assoc
d_assoc_2186 ::
  T_SemiringWithoutAnnihilatingZero_2130 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_2186 :: T_SemiringWithoutAnnihilatingZero_2130
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_2186 T_SemiringWithoutAnnihilatingZero_2130
v0
  = (T_IsSemigroup_472 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsSemigroup_472 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_assoc_482
      ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
         ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746
            ((T_IsSemiringWithoutAnnihilatingZero_1468
 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
               ((T_SemiringWithoutAnnihilatingZero_2130
 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_2130
-> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_2162 (T_SemiringWithoutAnnihilatingZero_2130 -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_2130
v0)))))
-- Algebra.Bundles.SemiringWithoutAnnihilatingZero._.comm
d_comm_2188 ::
  T_SemiringWithoutAnnihilatingZero_2130 ->
  AgdaAny -> AgdaAny -> AgdaAny
d_comm_2188 :: T_SemiringWithoutAnnihilatingZero_2130
-> AgdaAny -> AgdaAny -> AgdaAny
d_comm_2188 T_SemiringWithoutAnnihilatingZero_2130
v0
  = (T_IsCommutativeMonoid_736 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsCommutativeMonoid_736 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_comm_748
      ((T_IsSemiringWithoutAnnihilatingZero_1468
 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
         ((T_SemiringWithoutAnnihilatingZero_2130
 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_2130
-> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_2162 (T_SemiringWithoutAnnihilatingZero_2130 -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_2130
v0)))
-- Algebra.Bundles.SemiringWithoutAnnihilatingZero._.∙-cong
d_'8729''45'cong_2190 ::
  T_SemiringWithoutAnnihilatingZero_2130 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_2190 :: T_SemiringWithoutAnnihilatingZero_2130
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_2190 T_SemiringWithoutAnnihilatingZero_2130
v0
  = (T_IsMagma_176
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsMagma_176
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_186
      ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480
         ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
            ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746
               ((T_IsSemiringWithoutAnnihilatingZero_1468
 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
                  ((T_SemiringWithoutAnnihilatingZero_2130
 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_2130
-> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_2162 (T_SemiringWithoutAnnihilatingZero_2130 -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_2130
v0))))))
-- Algebra.Bundles.SemiringWithoutAnnihilatingZero._.∙-congʳ
d_'8729''45'cong'691'_2192 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SemiringWithoutAnnihilatingZero_2130 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_2192 :: ()
-> ()
-> T_SemiringWithoutAnnihilatingZero_2130
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_2192 ~()
v0 ~()
v1 T_SemiringWithoutAnnihilatingZero_2130
v2
  = T_SemiringWithoutAnnihilatingZero_2130
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_2192 T_SemiringWithoutAnnihilatingZero_2130
v2
du_'8729''45'cong'691'_2192 ::
  T_SemiringWithoutAnnihilatingZero_2130 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_2192 :: T_SemiringWithoutAnnihilatingZero_2130
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_2192 T_SemiringWithoutAnnihilatingZero_2130
v0
  = let v1 :: T_IsSemiringWithoutAnnihilatingZero_1468
v1 = T_SemiringWithoutAnnihilatingZero_2130
-> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_2162 (T_SemiringWithoutAnnihilatingZero_2130
-> T_SemiringWithoutAnnihilatingZero_2130
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_2130
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsCommutativeMonoid_736
v2
             = T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
                 (T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsSemiringWithoutAnnihilatingZero_1468
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsMonoid_686
v3
                = T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746 (T_IsCommutativeMonoid_736 -> T_IsCommutativeMonoid_736
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsSemigroup_472
v4
                   = T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'691'_206
                  ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v4))))))
-- Algebra.Bundles.SemiringWithoutAnnihilatingZero._.∙-congˡ
d_'8729''45'cong'737'_2194 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SemiringWithoutAnnihilatingZero_2130 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_2194 :: ()
-> ()
-> T_SemiringWithoutAnnihilatingZero_2130
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_2194 ~()
v0 ~()
v1 T_SemiringWithoutAnnihilatingZero_2130
v2
  = T_SemiringWithoutAnnihilatingZero_2130
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_2194 T_SemiringWithoutAnnihilatingZero_2130
v2
du_'8729''45'cong'737'_2194 ::
  T_SemiringWithoutAnnihilatingZero_2130 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_2194 :: T_SemiringWithoutAnnihilatingZero_2130
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_2194 T_SemiringWithoutAnnihilatingZero_2130
v0
  = let v1 :: T_IsSemiringWithoutAnnihilatingZero_1468
v1 = T_SemiringWithoutAnnihilatingZero_2130
-> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_2162 (T_SemiringWithoutAnnihilatingZero_2130
-> T_SemiringWithoutAnnihilatingZero_2130
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_2130
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsCommutativeMonoid_736
v2
             = T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
                 (T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsSemiringWithoutAnnihilatingZero_1468
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsMonoid_686
v3
                = T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746 (T_IsCommutativeMonoid_736 -> T_IsCommutativeMonoid_736
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsSemigroup_472
v4
                   = T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'737'_202
                  ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v4))))))
-- Algebra.Bundles.SemiringWithoutAnnihilatingZero._.identity
d_identity_2196 ::
  T_SemiringWithoutAnnihilatingZero_2130 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_identity_2196 :: T_SemiringWithoutAnnihilatingZero_2130 -> T_Σ_14
d_identity_2196 T_SemiringWithoutAnnihilatingZero_2130
v0
  = (T_IsMonoid_686 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsMonoid_686 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_identity_698
      ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746
         ((T_IsSemiringWithoutAnnihilatingZero_1468
 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
            ((T_SemiringWithoutAnnihilatingZero_2130
 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_2130
-> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_2162 (T_SemiringWithoutAnnihilatingZero_2130 -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_2130
v0))))
-- Algebra.Bundles.SemiringWithoutAnnihilatingZero._.identityʳ
d_identity'691'_2198 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SemiringWithoutAnnihilatingZero_2130 -> AgdaAny -> AgdaAny
d_identity'691'_2198 :: ()
-> ()
-> T_SemiringWithoutAnnihilatingZero_2130
-> AgdaAny
-> AgdaAny
d_identity'691'_2198 ~()
v0 ~()
v1 T_SemiringWithoutAnnihilatingZero_2130
v2 = T_SemiringWithoutAnnihilatingZero_2130 -> AgdaAny -> AgdaAny
du_identity'691'_2198 T_SemiringWithoutAnnihilatingZero_2130
v2
du_identity'691'_2198 ::
  T_SemiringWithoutAnnihilatingZero_2130 -> AgdaAny -> AgdaAny
du_identity'691'_2198 :: T_SemiringWithoutAnnihilatingZero_2130 -> AgdaAny -> AgdaAny
du_identity'691'_2198 T_SemiringWithoutAnnihilatingZero_2130
v0
  = let v1 :: T_IsSemiringWithoutAnnihilatingZero_1468
v1 = T_SemiringWithoutAnnihilatingZero_2130
-> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_2162 (T_SemiringWithoutAnnihilatingZero_2130
-> T_SemiringWithoutAnnihilatingZero_2130
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_2130
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsCommutativeMonoid_736
v2
             = T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
                 (T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsSemiringWithoutAnnihilatingZero_1468
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsMonoid_686 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoid_686 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_identity'691'_728
            ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746 (T_IsCommutativeMonoid_736 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v2))))
-- Algebra.Bundles.SemiringWithoutAnnihilatingZero._.identityˡ
d_identity'737'_2200 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SemiringWithoutAnnihilatingZero_2130 -> AgdaAny -> AgdaAny
d_identity'737'_2200 :: ()
-> ()
-> T_SemiringWithoutAnnihilatingZero_2130
-> AgdaAny
-> AgdaAny
d_identity'737'_2200 ~()
v0 ~()
v1 T_SemiringWithoutAnnihilatingZero_2130
v2 = T_SemiringWithoutAnnihilatingZero_2130 -> AgdaAny -> AgdaAny
du_identity'737'_2200 T_SemiringWithoutAnnihilatingZero_2130
v2
du_identity'737'_2200 ::
  T_SemiringWithoutAnnihilatingZero_2130 -> AgdaAny -> AgdaAny
du_identity'737'_2200 :: T_SemiringWithoutAnnihilatingZero_2130 -> AgdaAny -> AgdaAny
du_identity'737'_2200 T_SemiringWithoutAnnihilatingZero_2130
v0
  = let v1 :: T_IsSemiringWithoutAnnihilatingZero_1468
v1 = T_SemiringWithoutAnnihilatingZero_2130
-> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_2162 (T_SemiringWithoutAnnihilatingZero_2130
-> T_SemiringWithoutAnnihilatingZero_2130
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_2130
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsCommutativeMonoid_736
v2
             = T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
                 (T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsSemiringWithoutAnnihilatingZero_1468
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsMonoid_686 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoid_686 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_identity'737'_726
            ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746 (T_IsCommutativeMonoid_736 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v2))))
-- Algebra.Bundles.SemiringWithoutAnnihilatingZero._.isCommutativeMagma
d_isCommutativeMagma_2202 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SemiringWithoutAnnihilatingZero_2130 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMagma_212
d_isCommutativeMagma_2202 :: ()
-> ()
-> T_SemiringWithoutAnnihilatingZero_2130
-> T_IsCommutativeMagma_212
d_isCommutativeMagma_2202 ~()
v0 ~()
v1 T_SemiringWithoutAnnihilatingZero_2130
v2
  = T_SemiringWithoutAnnihilatingZero_2130 -> T_IsCommutativeMagma_212
du_isCommutativeMagma_2202 T_SemiringWithoutAnnihilatingZero_2130
v2
du_isCommutativeMagma_2202 ::
  T_SemiringWithoutAnnihilatingZero_2130 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMagma_212
du_isCommutativeMagma_2202 :: T_SemiringWithoutAnnihilatingZero_2130 -> T_IsCommutativeMagma_212
du_isCommutativeMagma_2202 T_SemiringWithoutAnnihilatingZero_2130
v0
  = let v1 :: T_IsSemiringWithoutAnnihilatingZero_1468
v1 = T_SemiringWithoutAnnihilatingZero_2130
-> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_2162 (T_SemiringWithoutAnnihilatingZero_2130
-> T_SemiringWithoutAnnihilatingZero_2130
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_2130
v0) in
    AgdaAny -> T_IsCommutativeMagma_212
forall a b. a -> b
coe
      (let v2 :: T_IsCommutativeMonoid_736
v2
             = T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
                 (T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsSemiringWithoutAnnihilatingZero_1468
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsCommutativeSemigroup_548 -> T_IsCommutativeMagma_212)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCommutativeSemigroup_548 -> T_IsCommutativeMagma_212
MAlonzo.Code.Algebra.Structures.du_isCommutativeMagma_586
            ((T_IsCommutativeMonoid_736 -> T_IsCommutativeSemigroup_548)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsCommutativeMonoid_736 -> T_IsCommutativeSemigroup_548
MAlonzo.Code.Algebra.Structures.du_isCommutativeSemigroup_786
               (T_IsCommutativeMonoid_736 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v2))))
-- Algebra.Bundles.SemiringWithoutAnnihilatingZero._.+-isCommutativeMonoid
d_'43''45'isCommutativeMonoid_2204 ::
  T_SemiringWithoutAnnihilatingZero_2130 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_2204 :: T_SemiringWithoutAnnihilatingZero_2130 -> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_2204 T_SemiringWithoutAnnihilatingZero_2130
v0
  = (T_IsSemiringWithoutAnnihilatingZero_1468
 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> T_IsCommutativeMonoid_736
forall a b. a -> b
coe
      T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
      ((T_SemiringWithoutAnnihilatingZero_2130
 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_2130
-> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_2162 (T_SemiringWithoutAnnihilatingZero_2130 -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_2130
v0))
-- Algebra.Bundles.SemiringWithoutAnnihilatingZero._.isCommutativeSemigroup
d_isCommutativeSemigroup_2206 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SemiringWithoutAnnihilatingZero_2130 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_548
d_isCommutativeSemigroup_2206 :: ()
-> ()
-> T_SemiringWithoutAnnihilatingZero_2130
-> T_IsCommutativeSemigroup_548
d_isCommutativeSemigroup_2206 ~()
v0 ~()
v1 T_SemiringWithoutAnnihilatingZero_2130
v2
  = T_SemiringWithoutAnnihilatingZero_2130
-> T_IsCommutativeSemigroup_548
du_isCommutativeSemigroup_2206 T_SemiringWithoutAnnihilatingZero_2130
v2
du_isCommutativeSemigroup_2206 ::
  T_SemiringWithoutAnnihilatingZero_2130 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_548
du_isCommutativeSemigroup_2206 :: T_SemiringWithoutAnnihilatingZero_2130
-> T_IsCommutativeSemigroup_548
du_isCommutativeSemigroup_2206 T_SemiringWithoutAnnihilatingZero_2130
v0
  = let v1 :: T_IsSemiringWithoutAnnihilatingZero_1468
v1 = T_SemiringWithoutAnnihilatingZero_2130
-> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_2162 (T_SemiringWithoutAnnihilatingZero_2130
-> T_SemiringWithoutAnnihilatingZero_2130
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_2130
v0) in
    AgdaAny -> T_IsCommutativeSemigroup_548
forall a b. a -> b
coe
      ((T_IsCommutativeMonoid_736 -> T_IsCommutativeSemigroup_548)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCommutativeMonoid_736 -> T_IsCommutativeSemigroup_548
MAlonzo.Code.Algebra.Structures.du_isCommutativeSemigroup_786
         ((T_IsSemiringWithoutAnnihilatingZero_1468
 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
            (T_IsSemiringWithoutAnnihilatingZero_1468 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
v1)))
-- Algebra.Bundles.SemiringWithoutAnnihilatingZero._.isMagma
d_isMagma_2208 ::
  T_SemiringWithoutAnnihilatingZero_2130 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_176
d_isMagma_2208 :: T_SemiringWithoutAnnihilatingZero_2130 -> T_IsMagma_176
d_isMagma_2208 T_SemiringWithoutAnnihilatingZero_2130
v0
  = (T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> T_IsMagma_176
forall a b. a -> b
coe
      T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480
      ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
         ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746
            ((T_IsSemiringWithoutAnnihilatingZero_1468
 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
               ((T_SemiringWithoutAnnihilatingZero_2130
 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_2130
-> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_2162 (T_SemiringWithoutAnnihilatingZero_2130 -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_2130
v0)))))
-- Algebra.Bundles.SemiringWithoutAnnihilatingZero._.isMonoid
d_isMonoid_2210 ::
  T_SemiringWithoutAnnihilatingZero_2130 ->
  MAlonzo.Code.Algebra.Structures.T_IsMonoid_686
d_isMonoid_2210 :: T_SemiringWithoutAnnihilatingZero_2130 -> T_IsMonoid_686
d_isMonoid_2210 T_SemiringWithoutAnnihilatingZero_2130
v0
  = (T_IsCommutativeMonoid_736 -> T_IsMonoid_686)
-> AgdaAny -> T_IsMonoid_686
forall a b. a -> b
coe
      T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746
      ((T_IsSemiringWithoutAnnihilatingZero_1468
 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
         ((T_SemiringWithoutAnnihilatingZero_2130
 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_2130
-> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_2162 (T_SemiringWithoutAnnihilatingZero_2130 -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_2130
v0)))
-- Algebra.Bundles.SemiringWithoutAnnihilatingZero._.isSemigroup
d_isSemigroup_2212 ::
  T_SemiringWithoutAnnihilatingZero_2130 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_472
d_isSemigroup_2212 :: T_SemiringWithoutAnnihilatingZero_2130 -> T_IsSemigroup_472
d_isSemigroup_2212 T_SemiringWithoutAnnihilatingZero_2130
v0
  = (T_IsMonoid_686 -> T_IsSemigroup_472)
-> AgdaAny -> T_IsSemigroup_472
forall a b. a -> b
coe
      T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
      ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746
         ((T_IsSemiringWithoutAnnihilatingZero_1468
 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
            ((T_SemiringWithoutAnnihilatingZero_2130
 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_2130
-> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_2162 (T_SemiringWithoutAnnihilatingZero_2130 -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_2130
v0))))
-- Algebra.Bundles.SemiringWithoutAnnihilatingZero._.isUnitalMagma
d_isUnitalMagma_2214 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SemiringWithoutAnnihilatingZero_2130 ->
  MAlonzo.Code.Algebra.Structures.T_IsUnitalMagma_642
d_isUnitalMagma_2214 :: ()
-> ()
-> T_SemiringWithoutAnnihilatingZero_2130
-> T_IsUnitalMagma_642
d_isUnitalMagma_2214 ~()
v0 ~()
v1 T_SemiringWithoutAnnihilatingZero_2130
v2 = T_SemiringWithoutAnnihilatingZero_2130 -> T_IsUnitalMagma_642
du_isUnitalMagma_2214 T_SemiringWithoutAnnihilatingZero_2130
v2
du_isUnitalMagma_2214 ::
  T_SemiringWithoutAnnihilatingZero_2130 ->
  MAlonzo.Code.Algebra.Structures.T_IsUnitalMagma_642
du_isUnitalMagma_2214 :: T_SemiringWithoutAnnihilatingZero_2130 -> T_IsUnitalMagma_642
du_isUnitalMagma_2214 T_SemiringWithoutAnnihilatingZero_2130
v0
  = let v1 :: T_IsSemiringWithoutAnnihilatingZero_1468
v1 = T_SemiringWithoutAnnihilatingZero_2130
-> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_2162 (T_SemiringWithoutAnnihilatingZero_2130
-> T_SemiringWithoutAnnihilatingZero_2130
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_2130
v0) in
    AgdaAny -> T_IsUnitalMagma_642
forall a b. a -> b
coe
      (let v2 :: T_IsCommutativeMonoid_736
v2
             = T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
                 (T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsSemiringWithoutAnnihilatingZero_1468
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsMonoid_686 -> T_IsUnitalMagma_642) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoid_686 -> T_IsUnitalMagma_642
MAlonzo.Code.Algebra.Structures.du_isUnitalMagma_730
            ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746 (T_IsCommutativeMonoid_736 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v2))))
-- Algebra.Bundles.SemiringWithoutAnnihilatingZero._.distrib
d_distrib_2216 ::
  T_SemiringWithoutAnnihilatingZero_2130 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_distrib_2216 :: T_SemiringWithoutAnnihilatingZero_2130 -> T_Σ_14
d_distrib_2216 T_SemiringWithoutAnnihilatingZero_2130
v0
  = (T_IsSemiringWithoutAnnihilatingZero_1468 -> T_Σ_14)
-> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsSemiringWithoutAnnihilatingZero_1468 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_distrib_1496
      ((T_SemiringWithoutAnnihilatingZero_2130
 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_2130
-> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_2162 (T_SemiringWithoutAnnihilatingZero_2130 -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_2130
v0))
-- Algebra.Bundles.SemiringWithoutAnnihilatingZero._.distribʳ
d_distrib'691'_2218 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SemiringWithoutAnnihilatingZero_2130 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_distrib'691'_2218 :: ()
-> ()
-> T_SemiringWithoutAnnihilatingZero_2130
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_distrib'691'_2218 ~()
v0 ~()
v1 T_SemiringWithoutAnnihilatingZero_2130
v2 = T_SemiringWithoutAnnihilatingZero_2130
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'691'_2218 T_SemiringWithoutAnnihilatingZero_2130
v2
du_distrib'691'_2218 ::
  T_SemiringWithoutAnnihilatingZero_2130 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'691'_2218 :: T_SemiringWithoutAnnihilatingZero_2130
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'691'_2218 T_SemiringWithoutAnnihilatingZero_2130
v0
  = (T_IsSemiringWithoutAnnihilatingZero_1468
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsSemiringWithoutAnnihilatingZero_1468
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_distrib'691'_1500
      ((T_SemiringWithoutAnnihilatingZero_2130
 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_2130
-> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_2162 (T_SemiringWithoutAnnihilatingZero_2130 -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_2130
v0))
-- Algebra.Bundles.SemiringWithoutAnnihilatingZero._.distribˡ
d_distrib'737'_2220 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SemiringWithoutAnnihilatingZero_2130 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_distrib'737'_2220 :: ()
-> ()
-> T_SemiringWithoutAnnihilatingZero_2130
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_distrib'737'_2220 ~()
v0 ~()
v1 T_SemiringWithoutAnnihilatingZero_2130
v2 = T_SemiringWithoutAnnihilatingZero_2130
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'737'_2220 T_SemiringWithoutAnnihilatingZero_2130
v2
du_distrib'737'_2220 ::
  T_SemiringWithoutAnnihilatingZero_2130 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'737'_2220 :: T_SemiringWithoutAnnihilatingZero_2130
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'737'_2220 T_SemiringWithoutAnnihilatingZero_2130
v0
  = (T_IsSemiringWithoutAnnihilatingZero_1468
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsSemiringWithoutAnnihilatingZero_1468
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_distrib'737'_1498
      ((T_SemiringWithoutAnnihilatingZero_2130
 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_2130
-> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_2162 (T_SemiringWithoutAnnihilatingZero_2130 -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_2130
v0))
-- Algebra.Bundles.SemiringWithoutAnnihilatingZero._.isEquivalence
d_isEquivalence_2222 ::
  T_SemiringWithoutAnnihilatingZero_2130 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_2222 :: T_SemiringWithoutAnnihilatingZero_2130 -> T_IsEquivalence_26
d_isEquivalence_2222 T_SemiringWithoutAnnihilatingZero_2130
v0
  = (T_IsMagma_176 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
      ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480
         ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
            ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746
               ((T_IsSemiringWithoutAnnihilatingZero_1468
 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
                  ((T_SemiringWithoutAnnihilatingZero_2130
 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_2130
-> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_2162 (T_SemiringWithoutAnnihilatingZero_2130 -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_2130
v0))))))
-- Algebra.Bundles.SemiringWithoutAnnihilatingZero._.isPartialEquivalence
d_isPartialEquivalence_2224 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SemiringWithoutAnnihilatingZero_2130 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_2224 :: ()
-> ()
-> T_SemiringWithoutAnnihilatingZero_2130
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_2224 ~()
v0 ~()
v1 T_SemiringWithoutAnnihilatingZero_2130
v2
  = T_SemiringWithoutAnnihilatingZero_2130 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_2224 T_SemiringWithoutAnnihilatingZero_2130
v2
du_isPartialEquivalence_2224 ::
  T_SemiringWithoutAnnihilatingZero_2130 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_2224 :: T_SemiringWithoutAnnihilatingZero_2130 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_2224 T_SemiringWithoutAnnihilatingZero_2130
v0
  = let v1 :: T_IsSemiringWithoutAnnihilatingZero_1468
v1 = T_SemiringWithoutAnnihilatingZero_2130
-> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_2162 (T_SemiringWithoutAnnihilatingZero_2130
-> T_SemiringWithoutAnnihilatingZero_2130
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_2130
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsCommutativeMonoid_736
v2
             = T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
                 (T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsSemiringWithoutAnnihilatingZero_1468
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsMonoid_686
v3
                = T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746 (T_IsCommutativeMonoid_736 -> T_IsCommutativeMonoid_736
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsSemigroup_472
v4
                   = T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsMagma_176
v5 = T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (T_IsSemigroup_472 -> T_IsSemigroup_472
forall a b. a -> b
coe T_IsSemigroup_472
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  ((T_IsEquivalence_26 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsEquivalence_26 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
                     ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v5)))))))
-- Algebra.Bundles.SemiringWithoutAnnihilatingZero._.refl
d_refl_2226 ::
  T_SemiringWithoutAnnihilatingZero_2130 -> AgdaAny -> AgdaAny
d_refl_2226 :: T_SemiringWithoutAnnihilatingZero_2130 -> AgdaAny -> AgdaAny
d_refl_2226 T_SemiringWithoutAnnihilatingZero_2130
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_34
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
         ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480
            ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
               ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746
                  ((T_IsSemiringWithoutAnnihilatingZero_1468
 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
                     ((T_SemiringWithoutAnnihilatingZero_2130
 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_2130
-> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_2162 (T_SemiringWithoutAnnihilatingZero_2130 -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_2130
v0)))))))
-- Algebra.Bundles.SemiringWithoutAnnihilatingZero._.reflexive
d_reflexive_2228 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SemiringWithoutAnnihilatingZero_2130 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_2228 :: ()
-> ()
-> T_SemiringWithoutAnnihilatingZero_2130
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_2228 ~()
v0 ~()
v1 T_SemiringWithoutAnnihilatingZero_2130
v2 = T_SemiringWithoutAnnihilatingZero_2130
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_2228 T_SemiringWithoutAnnihilatingZero_2130
v2
du_reflexive_2228 ::
  T_SemiringWithoutAnnihilatingZero_2130 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_2228 :: T_SemiringWithoutAnnihilatingZero_2130
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_2228 T_SemiringWithoutAnnihilatingZero_2130
v0
  = let v1 :: T_IsSemiringWithoutAnnihilatingZero_1468
v1 = T_SemiringWithoutAnnihilatingZero_2130
-> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_2162 (T_SemiringWithoutAnnihilatingZero_2130
-> T_SemiringWithoutAnnihilatingZero_2130
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_2130
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsCommutativeMonoid_736
v2
             = T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
                 (T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsSemiringWithoutAnnihilatingZero_1468
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsMonoid_686
v3
                = T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746 (T_IsCommutativeMonoid_736 -> T_IsCommutativeMonoid_736
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsSemigroup_472
v4
                   = T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsMagma_176
v5 = T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (T_IsSemigroup_472 -> T_IsSemigroup_472
forall a b. a -> b
coe T_IsSemigroup_472
v4) in
                (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
                  (\ AgdaAny
v6 AgdaAny
v7 AgdaAny
v8 ->
                     (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                       T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
                       ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v5))
                       AgdaAny
v6)))))
-- Algebra.Bundles.SemiringWithoutAnnihilatingZero._.setoid
d_setoid_2230 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SemiringWithoutAnnihilatingZero_2130 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_2230 :: () -> () -> T_SemiringWithoutAnnihilatingZero_2130 -> T_Setoid_44
d_setoid_2230 ~()
v0 ~()
v1 T_SemiringWithoutAnnihilatingZero_2130
v2 = T_SemiringWithoutAnnihilatingZero_2130 -> T_Setoid_44
du_setoid_2230 T_SemiringWithoutAnnihilatingZero_2130
v2
du_setoid_2230 ::
  T_SemiringWithoutAnnihilatingZero_2130 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_2230 :: T_SemiringWithoutAnnihilatingZero_2130 -> T_Setoid_44
du_setoid_2230 T_SemiringWithoutAnnihilatingZero_2130
v0
  = let v1 :: T_IsSemiringWithoutAnnihilatingZero_1468
v1 = T_SemiringWithoutAnnihilatingZero_2130
-> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_2162 (T_SemiringWithoutAnnihilatingZero_2130
-> T_SemiringWithoutAnnihilatingZero_2130
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_2130
v0) in
    AgdaAny -> T_Setoid_44
forall a b. a -> b
coe
      (let v2 :: T_IsCommutativeMonoid_736
v2
             = T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
                 (T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsSemiringWithoutAnnihilatingZero_1468
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsMonoid_686
v3
                = T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746 (T_IsCommutativeMonoid_736 -> T_IsCommutativeMonoid_736
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsSemigroup_472
v4
                   = T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               ((T_IsMagma_176 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsMagma_176 -> T_Setoid_44
MAlonzo.Code.Algebra.Structures.du_setoid_200
                  ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v4))))))
-- Algebra.Bundles.SemiringWithoutAnnihilatingZero._.sym
d_sym_2232 ::
  T_SemiringWithoutAnnihilatingZero_2130 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_2232 :: T_SemiringWithoutAnnihilatingZero_2130
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_2232 T_SemiringWithoutAnnihilatingZero_2130
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_36
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
         ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480
            ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
               ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746
                  ((T_IsSemiringWithoutAnnihilatingZero_1468
 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
                     ((T_SemiringWithoutAnnihilatingZero_2130
 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_2130
-> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_2162 (T_SemiringWithoutAnnihilatingZero_2130 -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_2130
v0)))))))
-- Algebra.Bundles.SemiringWithoutAnnihilatingZero._.trans
d_trans_2234 ::
  T_SemiringWithoutAnnihilatingZero_2130 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_2234 :: T_SemiringWithoutAnnihilatingZero_2130
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_2234 T_SemiringWithoutAnnihilatingZero_2130
v0
  = (T_IsEquivalence_26
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_38
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
         ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480
            ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
               ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746
                  ((T_IsSemiringWithoutAnnihilatingZero_1468
 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
                     ((T_SemiringWithoutAnnihilatingZero_2130
 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_2130
-> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_2162 (T_SemiringWithoutAnnihilatingZero_2130 -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_2130
v0)))))))
-- Algebra.Bundles.SemiringWithoutAnnihilatingZero.rawSemiring
d_rawSemiring_2236 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SemiringWithoutAnnihilatingZero_2130 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawSemiring_174
d_rawSemiring_2236 :: ()
-> ()
-> T_SemiringWithoutAnnihilatingZero_2130
-> T_RawSemiring_174
d_rawSemiring_2236 ~()
v0 ~()
v1 T_SemiringWithoutAnnihilatingZero_2130
v2 = T_SemiringWithoutAnnihilatingZero_2130 -> T_RawSemiring_174
du_rawSemiring_2236 T_SemiringWithoutAnnihilatingZero_2130
v2
du_rawSemiring_2236 ::
  T_SemiringWithoutAnnihilatingZero_2130 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawSemiring_174
du_rawSemiring_2236 :: T_SemiringWithoutAnnihilatingZero_2130 -> T_RawSemiring_174
du_rawSemiring_2236 T_SemiringWithoutAnnihilatingZero_2130
v0
  = ((AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> AgdaAny
 -> T_RawSemiring_174)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_RawSemiring_174
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_RawSemiring_174
MAlonzo.Code.Algebra.Bundles.Raw.C_RawSemiring'46'constructor_2353
      (T_SemiringWithoutAnnihilatingZero_2130
-> AgdaAny -> AgdaAny -> AgdaAny
d__'43'__2154 (T_SemiringWithoutAnnihilatingZero_2130
-> T_SemiringWithoutAnnihilatingZero_2130
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_2130
v0)) (T_SemiringWithoutAnnihilatingZero_2130
-> AgdaAny -> AgdaAny -> AgdaAny
d__'42'__2156 (T_SemiringWithoutAnnihilatingZero_2130
-> T_SemiringWithoutAnnihilatingZero_2130
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_2130
v0))
      (T_SemiringWithoutAnnihilatingZero_2130 -> AgdaAny
d_0'35'_2158 (T_SemiringWithoutAnnihilatingZero_2130
-> T_SemiringWithoutAnnihilatingZero_2130
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_2130
v0)) (T_SemiringWithoutAnnihilatingZero_2130 -> AgdaAny
d_1'35'_2160 (T_SemiringWithoutAnnihilatingZero_2130
-> T_SemiringWithoutAnnihilatingZero_2130
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_2130
v0))
-- Algebra.Bundles.SemiringWithoutAnnihilatingZero._.rawNearSemiring
d_rawNearSemiring_2240 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SemiringWithoutAnnihilatingZero_2130 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawNearSemiring_134
d_rawNearSemiring_2240 :: ()
-> ()
-> T_SemiringWithoutAnnihilatingZero_2130
-> T_RawNearSemiring_134
d_rawNearSemiring_2240 ~()
v0 ~()
v1 T_SemiringWithoutAnnihilatingZero_2130
v2 = T_SemiringWithoutAnnihilatingZero_2130 -> T_RawNearSemiring_134
du_rawNearSemiring_2240 T_SemiringWithoutAnnihilatingZero_2130
v2
du_rawNearSemiring_2240 ::
  T_SemiringWithoutAnnihilatingZero_2130 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawNearSemiring_134
du_rawNearSemiring_2240 :: T_SemiringWithoutAnnihilatingZero_2130 -> T_RawNearSemiring_134
du_rawNearSemiring_2240 T_SemiringWithoutAnnihilatingZero_2130
v0
  = (T_RawSemiring_174 -> T_RawNearSemiring_134)
-> AgdaAny -> T_RawNearSemiring_134
forall a b. a -> b
coe
      T_RawSemiring_174 -> T_RawNearSemiring_134
MAlonzo.Code.Algebra.Bundles.Raw.du_rawNearSemiring_204
      ((T_SemiringWithoutAnnihilatingZero_2130 -> T_RawSemiring_174)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_2130 -> T_RawSemiring_174
du_rawSemiring_2236 (T_SemiringWithoutAnnihilatingZero_2130 -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_2130
v0))
-- Algebra.Bundles.SemiringWithoutAnnihilatingZero.+-commutativeMonoid
d_'43''45'commutativeMonoid_2242 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SemiringWithoutAnnihilatingZero_2130 -> T_CommutativeMonoid_962
d_'43''45'commutativeMonoid_2242 :: ()
-> ()
-> T_SemiringWithoutAnnihilatingZero_2130
-> T_CommutativeMonoid_962
d_'43''45'commutativeMonoid_2242 ~()
v0 ~()
v1 T_SemiringWithoutAnnihilatingZero_2130
v2
  = T_SemiringWithoutAnnihilatingZero_2130 -> T_CommutativeMonoid_962
du_'43''45'commutativeMonoid_2242 T_SemiringWithoutAnnihilatingZero_2130
v2
du_'43''45'commutativeMonoid_2242 ::
  T_SemiringWithoutAnnihilatingZero_2130 -> T_CommutativeMonoid_962
du_'43''45'commutativeMonoid_2242 :: T_SemiringWithoutAnnihilatingZero_2130 -> T_CommutativeMonoid_962
du_'43''45'commutativeMonoid_2242 T_SemiringWithoutAnnihilatingZero_2130
v0
  = ((AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny -> T_IsCommutativeMonoid_736 -> T_CommutativeMonoid_962)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsCommutativeMonoid_736
-> T_CommutativeMonoid_962
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> T_IsCommutativeMonoid_736 -> T_CommutativeMonoid_962
C_CommutativeMonoid'46'constructor_17931 (T_SemiringWithoutAnnihilatingZero_2130
-> AgdaAny -> AgdaAny -> AgdaAny
d__'43'__2154 (T_SemiringWithoutAnnihilatingZero_2130
-> T_SemiringWithoutAnnihilatingZero_2130
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_2130
v0))
      (T_SemiringWithoutAnnihilatingZero_2130 -> AgdaAny
d_0'35'_2158 (T_SemiringWithoutAnnihilatingZero_2130
-> T_SemiringWithoutAnnihilatingZero_2130
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_2130
v0))
      (T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
         ((T_SemiringWithoutAnnihilatingZero_2130
 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> T_IsSemiringWithoutAnnihilatingZero_1468
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_2130
-> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_2162 (T_SemiringWithoutAnnihilatingZero_2130 -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_2130
v0)))
-- Algebra.Bundles.SemiringWithoutAnnihilatingZero._._≉_
d__'8777'__2246 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SemiringWithoutAnnihilatingZero_2130 -> AgdaAny -> AgdaAny -> ()
d__'8777'__2246 :: ()
-> ()
-> T_SemiringWithoutAnnihilatingZero_2130
-> AgdaAny
-> AgdaAny
-> ()
d__'8777'__2246 = ()
-> ()
-> T_SemiringWithoutAnnihilatingZero_2130
-> AgdaAny
-> AgdaAny
-> ()
forall a. a
erased
-- Algebra.Bundles.SemiringWithoutAnnihilatingZero._.commutativeMagma
d_commutativeMagma_2248 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SemiringWithoutAnnihilatingZero_2130 -> T_CommutativeMagma_180
d_commutativeMagma_2248 :: ()
-> ()
-> T_SemiringWithoutAnnihilatingZero_2130
-> T_CommutativeMagma_180
d_commutativeMagma_2248 ~()
v0 ~()
v1 T_SemiringWithoutAnnihilatingZero_2130
v2 = T_SemiringWithoutAnnihilatingZero_2130 -> T_CommutativeMagma_180
du_commutativeMagma_2248 T_SemiringWithoutAnnihilatingZero_2130
v2
du_commutativeMagma_2248 ::
  T_SemiringWithoutAnnihilatingZero_2130 -> T_CommutativeMagma_180
du_commutativeMagma_2248 :: T_SemiringWithoutAnnihilatingZero_2130 -> T_CommutativeMagma_180
du_commutativeMagma_2248 T_SemiringWithoutAnnihilatingZero_2130
v0
  = let v1 :: t
v1 = (T_SemiringWithoutAnnihilatingZero_2130 -> T_CommutativeMonoid_962)
-> AgdaAny -> t
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_2130 -> T_CommutativeMonoid_962
du_'43''45'commutativeMonoid_2242 (T_SemiringWithoutAnnihilatingZero_2130 -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_2130
v0) in
    AgdaAny -> T_CommutativeMagma_180
forall a b. a -> b
coe
      ((T_CommutativeSemigroup_662 -> T_CommutativeMagma_180)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_CommutativeSemigroup_662 -> T_CommutativeMagma_180
du_commutativeMagma_726
         ((T_CommutativeMonoid_962 -> T_CommutativeSemigroup_662)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeMonoid_962 -> T_CommutativeSemigroup_662
du_commutativeSemigroup_1048 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1)))
-- Algebra.Bundles.SemiringWithoutAnnihilatingZero._.commutativeSemigroup
d_commutativeSemigroup_2250 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SemiringWithoutAnnihilatingZero_2130 ->
  T_CommutativeSemigroup_662
d_commutativeSemigroup_2250 :: ()
-> ()
-> T_SemiringWithoutAnnihilatingZero_2130
-> T_CommutativeSemigroup_662
d_commutativeSemigroup_2250 ~()
v0 ~()
v1 T_SemiringWithoutAnnihilatingZero_2130
v2
  = T_SemiringWithoutAnnihilatingZero_2130
-> T_CommutativeSemigroup_662
du_commutativeSemigroup_2250 T_SemiringWithoutAnnihilatingZero_2130
v2
du_commutativeSemigroup_2250 ::
  T_SemiringWithoutAnnihilatingZero_2130 ->
  T_CommutativeSemigroup_662
du_commutativeSemigroup_2250 :: T_SemiringWithoutAnnihilatingZero_2130
-> T_CommutativeSemigroup_662
du_commutativeSemigroup_2250 T_SemiringWithoutAnnihilatingZero_2130
v0
  = (T_CommutativeMonoid_962 -> T_CommutativeSemigroup_662)
-> AgdaAny -> T_CommutativeSemigroup_662
forall a b. a -> b
coe
      T_CommutativeMonoid_962 -> T_CommutativeSemigroup_662
du_commutativeSemigroup_1048
      ((T_SemiringWithoutAnnihilatingZero_2130 -> T_CommutativeMonoid_962)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_2130 -> T_CommutativeMonoid_962
du_'43''45'commutativeMonoid_2242 (T_SemiringWithoutAnnihilatingZero_2130 -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_2130
v0))
-- Algebra.Bundles.SemiringWithoutAnnihilatingZero._.magma
d_magma_2252 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SemiringWithoutAnnihilatingZero_2130 -> T_Magma_68
d_magma_2252 :: () -> () -> T_SemiringWithoutAnnihilatingZero_2130 -> T_Magma_68
d_magma_2252 ~()
v0 ~()
v1 T_SemiringWithoutAnnihilatingZero_2130
v2 = T_SemiringWithoutAnnihilatingZero_2130 -> T_Magma_68
du_magma_2252 T_SemiringWithoutAnnihilatingZero_2130
v2
du_magma_2252 ::
  T_SemiringWithoutAnnihilatingZero_2130 -> T_Magma_68
du_magma_2252 :: T_SemiringWithoutAnnihilatingZero_2130 -> T_Magma_68
du_magma_2252 T_SemiringWithoutAnnihilatingZero_2130
v0
  = let v1 :: t
v1 = (T_SemiringWithoutAnnihilatingZero_2130 -> T_CommutativeMonoid_962)
-> AgdaAny -> t
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_2130 -> T_CommutativeMonoid_962
du_'43''45'commutativeMonoid_2242 (T_SemiringWithoutAnnihilatingZero_2130 -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_2130
v0) in
    AgdaAny -> T_Magma_68
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_CommutativeMonoid_962 -> T_Monoid_882) -> AgdaAny -> t
forall a b. a -> b
coe T_CommutativeMonoid_962 -> T_Monoid_882
du_monoid_1032 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_Semigroup_536 -> T_Magma_68) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semigroup_536 -> T_Magma_68
du_magma_584 ((T_Monoid_882 -> T_Semigroup_536) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Monoid_882 -> T_Semigroup_536
du_semigroup_944 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2))))
-- Algebra.Bundles.SemiringWithoutAnnihilatingZero._.monoid
d_monoid_2254 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SemiringWithoutAnnihilatingZero_2130 -> T_Monoid_882
d_monoid_2254 :: () -> () -> T_SemiringWithoutAnnihilatingZero_2130 -> T_Monoid_882
d_monoid_2254 ~()
v0 ~()
v1 T_SemiringWithoutAnnihilatingZero_2130
v2 = T_SemiringWithoutAnnihilatingZero_2130 -> T_Monoid_882
du_monoid_2254 T_SemiringWithoutAnnihilatingZero_2130
v2
du_monoid_2254 ::
  T_SemiringWithoutAnnihilatingZero_2130 -> T_Monoid_882
du_monoid_2254 :: T_SemiringWithoutAnnihilatingZero_2130 -> T_Monoid_882
du_monoid_2254 T_SemiringWithoutAnnihilatingZero_2130
v0
  = (T_CommutativeMonoid_962 -> T_Monoid_882)
-> AgdaAny -> T_Monoid_882
forall a b. a -> b
coe
      T_CommutativeMonoid_962 -> T_Monoid_882
du_monoid_1032 ((T_SemiringWithoutAnnihilatingZero_2130 -> T_CommutativeMonoid_962)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_2130 -> T_CommutativeMonoid_962
du_'43''45'commutativeMonoid_2242 (T_SemiringWithoutAnnihilatingZero_2130 -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_2130
v0))
-- Algebra.Bundles.SemiringWithoutAnnihilatingZero._.rawMagma
d_rawMagma_2256 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SemiringWithoutAnnihilatingZero_2130 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
d_rawMagma_2256 :: () -> () -> T_SemiringWithoutAnnihilatingZero_2130 -> T_RawMagma_36
d_rawMagma_2256 ~()
v0 ~()
v1 T_SemiringWithoutAnnihilatingZero_2130
v2 = T_SemiringWithoutAnnihilatingZero_2130 -> T_RawMagma_36
du_rawMagma_2256 T_SemiringWithoutAnnihilatingZero_2130
v2
du_rawMagma_2256 ::
  T_SemiringWithoutAnnihilatingZero_2130 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
du_rawMagma_2256 :: T_SemiringWithoutAnnihilatingZero_2130 -> T_RawMagma_36
du_rawMagma_2256 T_SemiringWithoutAnnihilatingZero_2130
v0
  = let v1 :: t
v1 = (T_SemiringWithoutAnnihilatingZero_2130 -> T_CommutativeMonoid_962)
-> AgdaAny -> t
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_2130 -> T_CommutativeMonoid_962
du_'43''45'commutativeMonoid_2242 (T_SemiringWithoutAnnihilatingZero_2130 -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_2130
v0) in
    AgdaAny -> T_RawMagma_36
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_CommutativeMonoid_962 -> T_Monoid_882) -> AgdaAny -> t
forall a b. a -> b
coe T_CommutativeMonoid_962 -> T_Monoid_882
du_monoid_1032 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: t
v3 = (T_Monoid_882 -> T_Semigroup_536) -> AgdaAny -> t
forall a b. a -> b
coe T_Monoid_882 -> T_Semigroup_536
du_semigroup_944 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_Magma_68 -> T_RawMagma_36) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Magma_68 -> T_RawMagma_36
du_rawMagma_112 ((T_Semigroup_536 -> T_Magma_68) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semigroup_536 -> T_Magma_68
du_magma_584 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3)))))
-- Algebra.Bundles.SemiringWithoutAnnihilatingZero._.rawMonoid
d_rawMonoid_2258 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SemiringWithoutAnnihilatingZero_2130 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMonoid_64
d_rawMonoid_2258 :: ()
-> () -> T_SemiringWithoutAnnihilatingZero_2130 -> T_RawMonoid_64
d_rawMonoid_2258 ~()
v0 ~()
v1 T_SemiringWithoutAnnihilatingZero_2130
v2 = T_SemiringWithoutAnnihilatingZero_2130 -> T_RawMonoid_64
du_rawMonoid_2258 T_SemiringWithoutAnnihilatingZero_2130
v2
du_rawMonoid_2258 ::
  T_SemiringWithoutAnnihilatingZero_2130 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMonoid_64
du_rawMonoid_2258 :: T_SemiringWithoutAnnihilatingZero_2130 -> T_RawMonoid_64
du_rawMonoid_2258 T_SemiringWithoutAnnihilatingZero_2130
v0
  = let v1 :: t
v1 = (T_SemiringWithoutAnnihilatingZero_2130 -> T_CommutativeMonoid_962)
-> AgdaAny -> t
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_2130 -> T_CommutativeMonoid_962
du_'43''45'commutativeMonoid_2242 (T_SemiringWithoutAnnihilatingZero_2130 -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_2130
v0) in
    AgdaAny -> T_RawMonoid_64
forall a b. a -> b
coe ((T_Monoid_882 -> T_RawMonoid_64) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Monoid_882 -> T_RawMonoid_64
du_rawMonoid_954 ((T_CommutativeMonoid_962 -> T_Monoid_882) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeMonoid_962 -> T_Monoid_882
du_monoid_1032 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1)))
-- Algebra.Bundles.SemiringWithoutAnnihilatingZero._.semigroup
d_semigroup_2260 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SemiringWithoutAnnihilatingZero_2130 -> T_Semigroup_536
d_semigroup_2260 :: ()
-> () -> T_SemiringWithoutAnnihilatingZero_2130 -> T_Semigroup_536
d_semigroup_2260 ~()
v0 ~()
v1 T_SemiringWithoutAnnihilatingZero_2130
v2 = T_SemiringWithoutAnnihilatingZero_2130 -> T_Semigroup_536
du_semigroup_2260 T_SemiringWithoutAnnihilatingZero_2130
v2
du_semigroup_2260 ::
  T_SemiringWithoutAnnihilatingZero_2130 -> T_Semigroup_536
du_semigroup_2260 :: T_SemiringWithoutAnnihilatingZero_2130 -> T_Semigroup_536
du_semigroup_2260 T_SemiringWithoutAnnihilatingZero_2130
v0
  = let v1 :: t
v1 = (T_SemiringWithoutAnnihilatingZero_2130 -> T_CommutativeMonoid_962)
-> AgdaAny -> t
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_2130 -> T_CommutativeMonoid_962
du_'43''45'commutativeMonoid_2242 (T_SemiringWithoutAnnihilatingZero_2130 -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_2130
v0) in
    AgdaAny -> T_Semigroup_536
forall a b. a -> b
coe ((T_Monoid_882 -> T_Semigroup_536) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Monoid_882 -> T_Semigroup_536
du_semigroup_944 ((T_CommutativeMonoid_962 -> T_Monoid_882) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeMonoid_962 -> T_Monoid_882
du_monoid_1032 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1)))
-- Algebra.Bundles.SemiringWithoutAnnihilatingZero._.unitalMagma
d_unitalMagma_2262 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SemiringWithoutAnnihilatingZero_2130 -> T_UnitalMagma_814
d_unitalMagma_2262 :: ()
-> ()
-> T_SemiringWithoutAnnihilatingZero_2130
-> T_UnitalMagma_814
d_unitalMagma_2262 ~()
v0 ~()
v1 T_SemiringWithoutAnnihilatingZero_2130
v2 = T_SemiringWithoutAnnihilatingZero_2130 -> T_UnitalMagma_814
du_unitalMagma_2262 T_SemiringWithoutAnnihilatingZero_2130
v2
du_unitalMagma_2262 ::
  T_SemiringWithoutAnnihilatingZero_2130 -> T_UnitalMagma_814
du_unitalMagma_2262 :: T_SemiringWithoutAnnihilatingZero_2130 -> T_UnitalMagma_814
du_unitalMagma_2262 T_SemiringWithoutAnnihilatingZero_2130
v0
  = let v1 :: t
v1 = (T_SemiringWithoutAnnihilatingZero_2130 -> T_CommutativeMonoid_962)
-> AgdaAny -> t
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_2130 -> T_CommutativeMonoid_962
du_'43''45'commutativeMonoid_2242 (T_SemiringWithoutAnnihilatingZero_2130 -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_2130
v0) in
    AgdaAny -> T_UnitalMagma_814
forall a b. a -> b
coe ((T_Monoid_882 -> T_UnitalMagma_814) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Monoid_882 -> T_UnitalMagma_814
du_unitalMagma_956 ((T_CommutativeMonoid_962 -> T_Monoid_882) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeMonoid_962 -> T_Monoid_882
du_monoid_1032 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1)))
-- Algebra.Bundles.SemiringWithoutAnnihilatingZero.*-monoid
d_'42''45'monoid_2264 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SemiringWithoutAnnihilatingZero_2130 -> T_Monoid_882
d_'42''45'monoid_2264 :: () -> () -> T_SemiringWithoutAnnihilatingZero_2130 -> T_Monoid_882
d_'42''45'monoid_2264 ~()
v0 ~()
v1 T_SemiringWithoutAnnihilatingZero_2130
v2 = T_SemiringWithoutAnnihilatingZero_2130 -> T_Monoid_882
du_'42''45'monoid_2264 T_SemiringWithoutAnnihilatingZero_2130
v2
du_'42''45'monoid_2264 ::
  T_SemiringWithoutAnnihilatingZero_2130 -> T_Monoid_882
du_'42''45'monoid_2264 :: T_SemiringWithoutAnnihilatingZero_2130 -> T_Monoid_882
du_'42''45'monoid_2264 T_SemiringWithoutAnnihilatingZero_2130
v0
  = ((AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny -> T_IsMonoid_686 -> T_Monoid_882)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_Monoid_882
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> T_IsMonoid_686 -> T_Monoid_882
C_Monoid'46'constructor_16157 (T_SemiringWithoutAnnihilatingZero_2130
-> AgdaAny -> AgdaAny -> AgdaAny
d__'42'__2156 (T_SemiringWithoutAnnihilatingZero_2130
-> T_SemiringWithoutAnnihilatingZero_2130
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_2130
v0))
      (T_SemiringWithoutAnnihilatingZero_2130 -> AgdaAny
d_1'35'_2160 (T_SemiringWithoutAnnihilatingZero_2130
-> T_SemiringWithoutAnnihilatingZero_2130
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_2130
v0))
      ((T_IsSemiringWithoutAnnihilatingZero_1468 -> T_IsMonoid_686)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiringWithoutAnnihilatingZero_1468 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.du_'42''45'isMonoid_1550
         ((T_SemiringWithoutAnnihilatingZero_2130
 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_2130
-> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_2162 (T_SemiringWithoutAnnihilatingZero_2130 -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_2130
v0)))
-- Algebra.Bundles.SemiringWithoutAnnihilatingZero._.magma
d_magma_2268 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SemiringWithoutAnnihilatingZero_2130 -> T_Magma_68
d_magma_2268 :: () -> () -> T_SemiringWithoutAnnihilatingZero_2130 -> T_Magma_68
d_magma_2268 ~()
v0 ~()
v1 T_SemiringWithoutAnnihilatingZero_2130
v2 = T_SemiringWithoutAnnihilatingZero_2130 -> T_Magma_68
du_magma_2268 T_SemiringWithoutAnnihilatingZero_2130
v2
du_magma_2268 ::
  T_SemiringWithoutAnnihilatingZero_2130 -> T_Magma_68
du_magma_2268 :: T_SemiringWithoutAnnihilatingZero_2130 -> T_Magma_68
du_magma_2268 T_SemiringWithoutAnnihilatingZero_2130
v0
  = let v1 :: t
v1 = (T_SemiringWithoutAnnihilatingZero_2130 -> T_Monoid_882)
-> AgdaAny -> t
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_2130 -> T_Monoid_882
du_'42''45'monoid_2264 (T_SemiringWithoutAnnihilatingZero_2130 -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_2130
v0) in
    AgdaAny -> T_Magma_68
forall a b. a -> b
coe ((T_Semigroup_536 -> T_Magma_68) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semigroup_536 -> T_Magma_68
du_magma_584 ((T_Monoid_882 -> T_Semigroup_536) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Monoid_882 -> T_Semigroup_536
du_semigroup_944 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1)))
-- Algebra.Bundles.SemiringWithoutAnnihilatingZero._.rawMagma
d_rawMagma_2270 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SemiringWithoutAnnihilatingZero_2130 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
d_rawMagma_2270 :: () -> () -> T_SemiringWithoutAnnihilatingZero_2130 -> T_RawMagma_36
d_rawMagma_2270 ~()
v0 ~()
v1 T_SemiringWithoutAnnihilatingZero_2130
v2 = T_SemiringWithoutAnnihilatingZero_2130 -> T_RawMagma_36
du_rawMagma_2270 T_SemiringWithoutAnnihilatingZero_2130
v2
du_rawMagma_2270 ::
  T_SemiringWithoutAnnihilatingZero_2130 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
du_rawMagma_2270 :: T_SemiringWithoutAnnihilatingZero_2130 -> T_RawMagma_36
du_rawMagma_2270 T_SemiringWithoutAnnihilatingZero_2130
v0
  = let v1 :: t
v1 = (T_SemiringWithoutAnnihilatingZero_2130 -> T_Monoid_882)
-> AgdaAny -> t
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_2130 -> T_Monoid_882
du_'42''45'monoid_2264 (T_SemiringWithoutAnnihilatingZero_2130 -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_2130
v0) in
    AgdaAny -> T_RawMagma_36
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_Monoid_882 -> T_Semigroup_536) -> AgdaAny -> t
forall a b. a -> b
coe T_Monoid_882 -> T_Semigroup_536
du_semigroup_944 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_Magma_68 -> T_RawMagma_36) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Magma_68 -> T_RawMagma_36
du_rawMagma_112 ((T_Semigroup_536 -> T_Magma_68) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semigroup_536 -> T_Magma_68
du_magma_584 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2))))
-- Algebra.Bundles.SemiringWithoutAnnihilatingZero._.rawMonoid
d_rawMonoid_2272 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SemiringWithoutAnnihilatingZero_2130 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMonoid_64
d_rawMonoid_2272 :: ()
-> () -> T_SemiringWithoutAnnihilatingZero_2130 -> T_RawMonoid_64
d_rawMonoid_2272 ~()
v0 ~()
v1 T_SemiringWithoutAnnihilatingZero_2130
v2 = T_SemiringWithoutAnnihilatingZero_2130 -> T_RawMonoid_64
du_rawMonoid_2272 T_SemiringWithoutAnnihilatingZero_2130
v2
du_rawMonoid_2272 ::
  T_SemiringWithoutAnnihilatingZero_2130 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMonoid_64
du_rawMonoid_2272 :: T_SemiringWithoutAnnihilatingZero_2130 -> T_RawMonoid_64
du_rawMonoid_2272 T_SemiringWithoutAnnihilatingZero_2130
v0
  = (T_Monoid_882 -> T_RawMonoid_64) -> AgdaAny -> T_RawMonoid_64
forall a b. a -> b
coe T_Monoid_882 -> T_RawMonoid_64
du_rawMonoid_954 ((T_SemiringWithoutAnnihilatingZero_2130 -> T_Monoid_882)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_2130 -> T_Monoid_882
du_'42''45'monoid_2264 (T_SemiringWithoutAnnihilatingZero_2130 -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_2130
v0))
-- Algebra.Bundles.SemiringWithoutAnnihilatingZero._.semigroup
d_semigroup_2274 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SemiringWithoutAnnihilatingZero_2130 -> T_Semigroup_536
d_semigroup_2274 :: ()
-> () -> T_SemiringWithoutAnnihilatingZero_2130 -> T_Semigroup_536
d_semigroup_2274 ~()
v0 ~()
v1 T_SemiringWithoutAnnihilatingZero_2130
v2 = T_SemiringWithoutAnnihilatingZero_2130 -> T_Semigroup_536
du_semigroup_2274 T_SemiringWithoutAnnihilatingZero_2130
v2
du_semigroup_2274 ::
  T_SemiringWithoutAnnihilatingZero_2130 -> T_Semigroup_536
du_semigroup_2274 :: T_SemiringWithoutAnnihilatingZero_2130 -> T_Semigroup_536
du_semigroup_2274 T_SemiringWithoutAnnihilatingZero_2130
v0
  = (T_Monoid_882 -> T_Semigroup_536) -> AgdaAny -> T_Semigroup_536
forall a b. a -> b
coe T_Monoid_882 -> T_Semigroup_536
du_semigroup_944 ((T_SemiringWithoutAnnihilatingZero_2130 -> T_Monoid_882)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_2130 -> T_Monoid_882
du_'42''45'monoid_2264 (T_SemiringWithoutAnnihilatingZero_2130 -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_2130
v0))
-- Algebra.Bundles.Semiring
d_Semiring_2280 :: p -> p -> ()
d_Semiring_2280 p
a0 p
a1 = ()
data T_Semiring_2280
  = C_Semiring'46'constructor_41765 (AgdaAny -> AgdaAny -> AgdaAny)
                                    (AgdaAny -> AgdaAny -> AgdaAny) AgdaAny AgdaAny
                                    MAlonzo.Code.Algebra.Structures.T_IsSemiring_1570
-- Algebra.Bundles.Semiring.Carrier
d_Carrier_2300 :: T_Semiring_2280 -> ()
d_Carrier_2300 :: T_Semiring_2280 -> ()
d_Carrier_2300 = T_Semiring_2280 -> ()
forall a. a
erased
-- Algebra.Bundles.Semiring._≈_
d__'8776'__2302 :: T_Semiring_2280 -> AgdaAny -> AgdaAny -> ()
d__'8776'__2302 :: T_Semiring_2280 -> AgdaAny -> AgdaAny -> ()
d__'8776'__2302 = T_Semiring_2280 -> AgdaAny -> AgdaAny -> ()
forall a. a
erased
-- Algebra.Bundles.Semiring._+_
d__'43'__2304 :: T_Semiring_2280 -> AgdaAny -> AgdaAny -> AgdaAny
d__'43'__2304 :: T_Semiring_2280 -> AgdaAny -> AgdaAny -> AgdaAny
d__'43'__2304 T_Semiring_2280
v0
  = case T_Semiring_2280 -> T_Semiring_2280
forall a b. a -> b
coe T_Semiring_2280
v0 of
      C_Semiring'46'constructor_41765 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny
v5 AgdaAny
v6 T_IsSemiring_1570
v7 -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v3
      T_Semiring_2280
_ -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.Semiring._*_
d__'42'__2306 :: T_Semiring_2280 -> AgdaAny -> AgdaAny -> AgdaAny
d__'42'__2306 :: T_Semiring_2280 -> AgdaAny -> AgdaAny -> AgdaAny
d__'42'__2306 T_Semiring_2280
v0
  = case T_Semiring_2280 -> T_Semiring_2280
forall a b. a -> b
coe T_Semiring_2280
v0 of
      C_Semiring'46'constructor_41765 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny
v5 AgdaAny
v6 T_IsSemiring_1570
v7 -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v4
      T_Semiring_2280
_ -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.Semiring.0#
d_0'35'_2308 :: T_Semiring_2280 -> AgdaAny
d_0'35'_2308 :: T_Semiring_2280 -> AgdaAny
d_0'35'_2308 T_Semiring_2280
v0
  = case T_Semiring_2280 -> T_Semiring_2280
forall a b. a -> b
coe T_Semiring_2280
v0 of
      C_Semiring'46'constructor_41765 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny
v5 AgdaAny
v6 T_IsSemiring_1570
v7 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v5
      T_Semiring_2280
_ -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.Semiring.1#
d_1'35'_2310 :: T_Semiring_2280 -> AgdaAny
d_1'35'_2310 :: T_Semiring_2280 -> AgdaAny
d_1'35'_2310 T_Semiring_2280
v0
  = case T_Semiring_2280 -> T_Semiring_2280
forall a b. a -> b
coe T_Semiring_2280
v0 of
      C_Semiring'46'constructor_41765 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny
v5 AgdaAny
v6 T_IsSemiring_1570
v7 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v6
      T_Semiring_2280
_ -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.Semiring.isSemiring
d_isSemiring_2312 ::
  T_Semiring_2280 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemiring_1570
d_isSemiring_2312 :: T_Semiring_2280 -> T_IsSemiring_1570
d_isSemiring_2312 T_Semiring_2280
v0
  = case T_Semiring_2280 -> T_Semiring_2280
forall a b. a -> b
coe T_Semiring_2280
v0 of
      C_Semiring'46'constructor_41765 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny
v5 AgdaAny
v6 T_IsSemiring_1570
v7 -> T_IsSemiring_1570 -> T_IsSemiring_1570
forall a b. a -> b
coe T_IsSemiring_1570
v7
      T_Semiring_2280
_ -> T_IsSemiring_1570
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.Semiring._.*-assoc
d_'42''45'assoc_2316 ::
  T_Semiring_2280 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'assoc_2316 :: T_Semiring_2280 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'assoc_2316 T_Semiring_2280
v0
  = (T_IsSemiringWithoutAnnihilatingZero_1468
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsSemiringWithoutAnnihilatingZero_1468
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'42''45'assoc_1492
      ((T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
         ((T_Semiring_2280 -> T_IsSemiring_1570) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semiring_2280 -> T_IsSemiring_1570
d_isSemiring_2312 (T_Semiring_2280 -> AgdaAny
forall a b. a -> b
coe T_Semiring_2280
v0)))
-- Algebra.Bundles.Semiring._.*-cong
d_'42''45'cong_2318 ::
  T_Semiring_2280 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'cong_2318 :: T_Semiring_2280
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'42''45'cong_2318 T_Semiring_2280
v0
  = (T_IsSemiringWithoutAnnihilatingZero_1468
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsSemiringWithoutAnnihilatingZero_1468
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'42''45'cong_1490
      ((T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
         ((T_Semiring_2280 -> T_IsSemiring_1570) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semiring_2280 -> T_IsSemiring_1570
d_isSemiring_2312 (T_Semiring_2280 -> AgdaAny
forall a b. a -> b
coe T_Semiring_2280
v0)))
-- Algebra.Bundles.Semiring._.∙-congʳ
d_'8729''45'cong'691'_2320 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Semiring_2280 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_2320 :: ()
-> ()
-> T_Semiring_2280
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_2320 ~()
v0 ~()
v1 T_Semiring_2280
v2
  = T_Semiring_2280
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_2320 T_Semiring_2280
v2
du_'8729''45'cong'691'_2320 ::
  T_Semiring_2280 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_2320 :: T_Semiring_2280
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_2320 T_Semiring_2280
v0
  = let v1 :: T_IsSemiring_1570
v1 = T_Semiring_2280 -> T_IsSemiring_1570
d_isSemiring_2312 (T_Semiring_2280 -> T_Semiring_2280
forall a b. a -> b
coe T_Semiring_2280
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemiringWithoutAnnihilatingZero_1468
v2
             = T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                 (T_IsSemiring_1570 -> T_IsSemiring_1570
forall a b. a -> b
coe T_IsSemiring_1570
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: t
v3
                = (T_IsSemiringWithoutAnnihilatingZero_1468 -> T_IsMonoid_686)
-> AgdaAny -> t
forall a b. a -> b
coe
                    T_IsSemiringWithoutAnnihilatingZero_1468 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.du_'42''45'isMonoid_1550
                    (T_IsSemiringWithoutAnnihilatingZero_1468 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsSemigroup_472
v4
                   = T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (AgdaAny -> T_IsMonoid_686
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'691'_206
                  ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v4))))))
-- Algebra.Bundles.Semiring._.∙-congˡ
d_'8729''45'cong'737'_2322 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Semiring_2280 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_2322 :: ()
-> ()
-> T_Semiring_2280
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_2322 ~()
v0 ~()
v1 T_Semiring_2280
v2
  = T_Semiring_2280
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_2322 T_Semiring_2280
v2
du_'8729''45'cong'737'_2322 ::
  T_Semiring_2280 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_2322 :: T_Semiring_2280
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_2322 T_Semiring_2280
v0
  = let v1 :: T_IsSemiring_1570
v1 = T_Semiring_2280 -> T_IsSemiring_1570
d_isSemiring_2312 (T_Semiring_2280 -> T_Semiring_2280
forall a b. a -> b
coe T_Semiring_2280
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemiringWithoutAnnihilatingZero_1468
v2
             = T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                 (T_IsSemiring_1570 -> T_IsSemiring_1570
forall a b. a -> b
coe T_IsSemiring_1570
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: t
v3
                = (T_IsSemiringWithoutAnnihilatingZero_1468 -> T_IsMonoid_686)
-> AgdaAny -> t
forall a b. a -> b
coe
                    T_IsSemiringWithoutAnnihilatingZero_1468 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.du_'42''45'isMonoid_1550
                    (T_IsSemiringWithoutAnnihilatingZero_1468 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsSemigroup_472
v4
                   = T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (AgdaAny -> T_IsMonoid_686
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'737'_202
                  ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v4))))))
-- Algebra.Bundles.Semiring._.*-identity
d_'42''45'identity_2324 ::
  T_Semiring_2280 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'42''45'identity_2324 :: T_Semiring_2280 -> T_Σ_14
d_'42''45'identity_2324 T_Semiring_2280
v0
  = (T_IsSemiringWithoutAnnihilatingZero_1468 -> T_Σ_14)
-> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsSemiringWithoutAnnihilatingZero_1468 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_'42''45'identity_1494
      ((T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
         ((T_Semiring_2280 -> T_IsSemiring_1570) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semiring_2280 -> T_IsSemiring_1570
d_isSemiring_2312 (T_Semiring_2280 -> AgdaAny
forall a b. a -> b
coe T_Semiring_2280
v0)))
-- Algebra.Bundles.Semiring._.identityʳ
d_identity'691'_2326 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Semiring_2280 -> AgdaAny -> AgdaAny
d_identity'691'_2326 :: () -> () -> T_Semiring_2280 -> AgdaAny -> AgdaAny
d_identity'691'_2326 ~()
v0 ~()
v1 T_Semiring_2280
v2 = T_Semiring_2280 -> AgdaAny -> AgdaAny
du_identity'691'_2326 T_Semiring_2280
v2
du_identity'691'_2326 :: T_Semiring_2280 -> AgdaAny -> AgdaAny
du_identity'691'_2326 :: T_Semiring_2280 -> AgdaAny -> AgdaAny
du_identity'691'_2326 T_Semiring_2280
v0
  = let v1 :: T_IsSemiring_1570
v1 = T_Semiring_2280 -> T_IsSemiring_1570
d_isSemiring_2312 (T_Semiring_2280 -> T_Semiring_2280
forall a b. a -> b
coe T_Semiring_2280
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemiringWithoutAnnihilatingZero_1468
v2
             = T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                 (T_IsSemiring_1570 -> T_IsSemiring_1570
forall a b. a -> b
coe T_IsSemiring_1570
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsMonoid_686 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoid_686 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_identity'691'_728
            ((T_IsSemiringWithoutAnnihilatingZero_1468 -> T_IsMonoid_686)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemiringWithoutAnnihilatingZero_1468 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.du_'42''45'isMonoid_1550
               (T_IsSemiringWithoutAnnihilatingZero_1468 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
v2))))
-- Algebra.Bundles.Semiring._.identityˡ
d_identity'737'_2328 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Semiring_2280 -> AgdaAny -> AgdaAny
d_identity'737'_2328 :: () -> () -> T_Semiring_2280 -> AgdaAny -> AgdaAny
d_identity'737'_2328 ~()
v0 ~()
v1 T_Semiring_2280
v2 = T_Semiring_2280 -> AgdaAny -> AgdaAny
du_identity'737'_2328 T_Semiring_2280
v2
du_identity'737'_2328 :: T_Semiring_2280 -> AgdaAny -> AgdaAny
du_identity'737'_2328 :: T_Semiring_2280 -> AgdaAny -> AgdaAny
du_identity'737'_2328 T_Semiring_2280
v0
  = let v1 :: T_IsSemiring_1570
v1 = T_Semiring_2280 -> T_IsSemiring_1570
d_isSemiring_2312 (T_Semiring_2280 -> T_Semiring_2280
forall a b. a -> b
coe T_Semiring_2280
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemiringWithoutAnnihilatingZero_1468
v2
             = T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                 (T_IsSemiring_1570 -> T_IsSemiring_1570
forall a b. a -> b
coe T_IsSemiring_1570
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsMonoid_686 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoid_686 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_identity'737'_726
            ((T_IsSemiringWithoutAnnihilatingZero_1468 -> T_IsMonoid_686)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemiringWithoutAnnihilatingZero_1468 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.du_'42''45'isMonoid_1550
               (T_IsSemiringWithoutAnnihilatingZero_1468 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
v2))))
-- Algebra.Bundles.Semiring._.*-isMagma
d_'42''45'isMagma_2330 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Semiring_2280 -> MAlonzo.Code.Algebra.Structures.T_IsMagma_176
d_'42''45'isMagma_2330 :: () -> () -> T_Semiring_2280 -> T_IsMagma_176
d_'42''45'isMagma_2330 ~()
v0 ~()
v1 T_Semiring_2280
v2 = T_Semiring_2280 -> T_IsMagma_176
du_'42''45'isMagma_2330 T_Semiring_2280
v2
du_'42''45'isMagma_2330 ::
  T_Semiring_2280 -> MAlonzo.Code.Algebra.Structures.T_IsMagma_176
du_'42''45'isMagma_2330 :: T_Semiring_2280 -> T_IsMagma_176
du_'42''45'isMagma_2330 T_Semiring_2280
v0
  = let v1 :: T_IsSemiring_1570
v1 = T_Semiring_2280 -> T_IsSemiring_1570
d_isSemiring_2312 (T_Semiring_2280 -> T_Semiring_2280
forall a b. a -> b
coe T_Semiring_2280
v0) in
    AgdaAny -> T_IsMagma_176
forall a b. a -> b
coe
      ((T_IsSemiringWithoutAnnihilatingZero_1468 -> T_IsMagma_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiringWithoutAnnihilatingZero_1468 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.du_'42''45'isMagma_1546
         ((T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
            (T_IsSemiring_1570 -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1570
v1)))
-- Algebra.Bundles.Semiring._.*-isMonoid
d_'42''45'isMonoid_2332 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Semiring_2280 -> MAlonzo.Code.Algebra.Structures.T_IsMonoid_686
d_'42''45'isMonoid_2332 :: () -> () -> T_Semiring_2280 -> T_IsMonoid_686
d_'42''45'isMonoid_2332 ~()
v0 ~()
v1 T_Semiring_2280
v2 = T_Semiring_2280 -> T_IsMonoid_686
du_'42''45'isMonoid_2332 T_Semiring_2280
v2
du_'42''45'isMonoid_2332 ::
  T_Semiring_2280 -> MAlonzo.Code.Algebra.Structures.T_IsMonoid_686
du_'42''45'isMonoid_2332 :: T_Semiring_2280 -> T_IsMonoid_686
du_'42''45'isMonoid_2332 T_Semiring_2280
v0
  = let v1 :: T_IsSemiring_1570
v1 = T_Semiring_2280 -> T_IsSemiring_1570
d_isSemiring_2312 (T_Semiring_2280 -> T_Semiring_2280
forall a b. a -> b
coe T_Semiring_2280
v0) in
    AgdaAny -> T_IsMonoid_686
forall a b. a -> b
coe
      ((T_IsSemiringWithoutAnnihilatingZero_1468 -> T_IsMonoid_686)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiringWithoutAnnihilatingZero_1468 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.du_'42''45'isMonoid_1550
         ((T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
            (T_IsSemiring_1570 -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1570
v1)))
-- Algebra.Bundles.Semiring._.*-isSemigroup
d_'42''45'isSemigroup_2334 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Semiring_2280 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_472
d_'42''45'isSemigroup_2334 :: () -> () -> T_Semiring_2280 -> T_IsSemigroup_472
d_'42''45'isSemigroup_2334 ~()
v0 ~()
v1 T_Semiring_2280
v2
  = T_Semiring_2280 -> T_IsSemigroup_472
du_'42''45'isSemigroup_2334 T_Semiring_2280
v2
du_'42''45'isSemigroup_2334 ::
  T_Semiring_2280 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_472
du_'42''45'isSemigroup_2334 :: T_Semiring_2280 -> T_IsSemigroup_472
du_'42''45'isSemigroup_2334 T_Semiring_2280
v0
  = let v1 :: T_IsSemiring_1570
v1 = T_Semiring_2280 -> T_IsSemiring_1570
d_isSemiring_2312 (T_Semiring_2280 -> T_Semiring_2280
forall a b. a -> b
coe T_Semiring_2280
v0) in
    AgdaAny -> T_IsSemigroup_472
forall a b. a -> b
coe
      ((T_IsSemiringWithoutAnnihilatingZero_1468 -> T_IsSemigroup_472)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiringWithoutAnnihilatingZero_1468 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.du_'42''45'isSemigroup_1548
         ((T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
            (T_IsSemiring_1570 -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1570
v1)))
-- Algebra.Bundles.Semiring._.assoc
d_assoc_2336 ::
  T_Semiring_2280 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_2336 :: T_Semiring_2280 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_2336 T_Semiring_2280
v0
  = (T_IsSemigroup_472 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsSemigroup_472 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_assoc_482
      ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
         ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746
            ((T_IsSemiringWithoutAnnihilatingZero_1468
 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
               ((T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                  ((T_Semiring_2280 -> T_IsSemiring_1570) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semiring_2280 -> T_IsSemiring_1570
d_isSemiring_2312 (T_Semiring_2280 -> AgdaAny
forall a b. a -> b
coe T_Semiring_2280
v0))))))
-- Algebra.Bundles.Semiring._.comm
d_comm_2338 :: T_Semiring_2280 -> AgdaAny -> AgdaAny -> AgdaAny
d_comm_2338 :: T_Semiring_2280 -> AgdaAny -> AgdaAny -> AgdaAny
d_comm_2338 T_Semiring_2280
v0
  = (T_IsCommutativeMonoid_736 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsCommutativeMonoid_736 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_comm_748
      ((T_IsSemiringWithoutAnnihilatingZero_1468
 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
         ((T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
            ((T_Semiring_2280 -> T_IsSemiring_1570) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semiring_2280 -> T_IsSemiring_1570
d_isSemiring_2312 (T_Semiring_2280 -> AgdaAny
forall a b. a -> b
coe T_Semiring_2280
v0))))
-- Algebra.Bundles.Semiring._.∙-cong
d_'8729''45'cong_2340 ::
  T_Semiring_2280 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_2340 :: T_Semiring_2280
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_2340 T_Semiring_2280
v0
  = (T_IsMagma_176
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsMagma_176
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_186
      ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480
         ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
            ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746
               ((T_IsSemiringWithoutAnnihilatingZero_1468
 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
                  ((T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                     ((T_Semiring_2280 -> T_IsSemiring_1570) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semiring_2280 -> T_IsSemiring_1570
d_isSemiring_2312 (T_Semiring_2280 -> AgdaAny
forall a b. a -> b
coe T_Semiring_2280
v0)))))))
-- Algebra.Bundles.Semiring._.∙-congʳ
d_'8729''45'cong'691'_2342 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Semiring_2280 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_2342 :: ()
-> ()
-> T_Semiring_2280
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_2342 ~()
v0 ~()
v1 T_Semiring_2280
v2
  = T_Semiring_2280
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_2342 T_Semiring_2280
v2
du_'8729''45'cong'691'_2342 ::
  T_Semiring_2280 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_2342 :: T_Semiring_2280
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_2342 T_Semiring_2280
v0
  = let v1 :: T_IsSemiring_1570
v1 = T_Semiring_2280 -> T_IsSemiring_1570
d_isSemiring_2312 (T_Semiring_2280 -> T_Semiring_2280
forall a b. a -> b
coe T_Semiring_2280
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemiringWithoutAnnihilatingZero_1468
v2
             = T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                 (T_IsSemiring_1570 -> T_IsSemiring_1570
forall a b. a -> b
coe T_IsSemiring_1570
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsCommutativeMonoid_736
v3
                = T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
                    (T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsSemiringWithoutAnnihilatingZero_1468
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsMonoid_686
v4
                   = T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746 (T_IsCommutativeMonoid_736 -> T_IsCommutativeMonoid_736
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsSemigroup_472
v5
                      = T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'691'_206
                     ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v5)))))))
-- Algebra.Bundles.Semiring._.∙-congˡ
d_'8729''45'cong'737'_2344 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Semiring_2280 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_2344 :: ()
-> ()
-> T_Semiring_2280
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_2344 ~()
v0 ~()
v1 T_Semiring_2280
v2
  = T_Semiring_2280
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_2344 T_Semiring_2280
v2
du_'8729''45'cong'737'_2344 ::
  T_Semiring_2280 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_2344 :: T_Semiring_2280
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_2344 T_Semiring_2280
v0
  = let v1 :: T_IsSemiring_1570
v1 = T_Semiring_2280 -> T_IsSemiring_1570
d_isSemiring_2312 (T_Semiring_2280 -> T_Semiring_2280
forall a b. a -> b
coe T_Semiring_2280
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemiringWithoutAnnihilatingZero_1468
v2
             = T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                 (T_IsSemiring_1570 -> T_IsSemiring_1570
forall a b. a -> b
coe T_IsSemiring_1570
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsCommutativeMonoid_736
v3
                = T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
                    (T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsSemiringWithoutAnnihilatingZero_1468
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsMonoid_686
v4
                   = T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746 (T_IsCommutativeMonoid_736 -> T_IsCommutativeMonoid_736
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsSemigroup_472
v5
                      = T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'737'_202
                     ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v5)))))))
-- Algebra.Bundles.Semiring._.identity
d_identity_2346 ::
  T_Semiring_2280 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_identity_2346 :: T_Semiring_2280 -> T_Σ_14
d_identity_2346 T_Semiring_2280
v0
  = (T_IsMonoid_686 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsMonoid_686 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_identity_698
      ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746
         ((T_IsSemiringWithoutAnnihilatingZero_1468
 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
            ((T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
               ((T_Semiring_2280 -> T_IsSemiring_1570) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semiring_2280 -> T_IsSemiring_1570
d_isSemiring_2312 (T_Semiring_2280 -> AgdaAny
forall a b. a -> b
coe T_Semiring_2280
v0)))))
-- Algebra.Bundles.Semiring._.identityʳ
d_identity'691'_2348 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Semiring_2280 -> AgdaAny -> AgdaAny
d_identity'691'_2348 :: () -> () -> T_Semiring_2280 -> AgdaAny -> AgdaAny
d_identity'691'_2348 ~()
v0 ~()
v1 T_Semiring_2280
v2 = T_Semiring_2280 -> AgdaAny -> AgdaAny
du_identity'691'_2348 T_Semiring_2280
v2
du_identity'691'_2348 :: T_Semiring_2280 -> AgdaAny -> AgdaAny
du_identity'691'_2348 :: T_Semiring_2280 -> AgdaAny -> AgdaAny
du_identity'691'_2348 T_Semiring_2280
v0
  = let v1 :: T_IsSemiring_1570
v1 = T_Semiring_2280 -> T_IsSemiring_1570
d_isSemiring_2312 (T_Semiring_2280 -> T_Semiring_2280
forall a b. a -> b
coe T_Semiring_2280
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemiringWithoutAnnihilatingZero_1468
v2
             = T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                 (T_IsSemiring_1570 -> T_IsSemiring_1570
forall a b. a -> b
coe T_IsSemiring_1570
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsCommutativeMonoid_736
v3
                = T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
                    (T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsSemiringWithoutAnnihilatingZero_1468
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsMonoid_686 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_686 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_identity'691'_728
               ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746 (T_IsCommutativeMonoid_736 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v3)))))
-- Algebra.Bundles.Semiring._.identityˡ
d_identity'737'_2350 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Semiring_2280 -> AgdaAny -> AgdaAny
d_identity'737'_2350 :: () -> () -> T_Semiring_2280 -> AgdaAny -> AgdaAny
d_identity'737'_2350 ~()
v0 ~()
v1 T_Semiring_2280
v2 = T_Semiring_2280 -> AgdaAny -> AgdaAny
du_identity'737'_2350 T_Semiring_2280
v2
du_identity'737'_2350 :: T_Semiring_2280 -> AgdaAny -> AgdaAny
du_identity'737'_2350 :: T_Semiring_2280 -> AgdaAny -> AgdaAny
du_identity'737'_2350 T_Semiring_2280
v0
  = let v1 :: T_IsSemiring_1570
v1 = T_Semiring_2280 -> T_IsSemiring_1570
d_isSemiring_2312 (T_Semiring_2280 -> T_Semiring_2280
forall a b. a -> b
coe T_Semiring_2280
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemiringWithoutAnnihilatingZero_1468
v2
             = T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                 (T_IsSemiring_1570 -> T_IsSemiring_1570
forall a b. a -> b
coe T_IsSemiring_1570
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsCommutativeMonoid_736
v3
                = T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
                    (T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsSemiringWithoutAnnihilatingZero_1468
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsMonoid_686 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_686 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_identity'737'_726
               ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746 (T_IsCommutativeMonoid_736 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v3)))))
-- Algebra.Bundles.Semiring._.isCommutativeMagma
d_isCommutativeMagma_2352 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Semiring_2280 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMagma_212
d_isCommutativeMagma_2352 :: () -> () -> T_Semiring_2280 -> T_IsCommutativeMagma_212
d_isCommutativeMagma_2352 ~()
v0 ~()
v1 T_Semiring_2280
v2
  = T_Semiring_2280 -> T_IsCommutativeMagma_212
du_isCommutativeMagma_2352 T_Semiring_2280
v2
du_isCommutativeMagma_2352 ::
  T_Semiring_2280 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMagma_212
du_isCommutativeMagma_2352 :: T_Semiring_2280 -> T_IsCommutativeMagma_212
du_isCommutativeMagma_2352 T_Semiring_2280
v0
  = let v1 :: T_IsSemiring_1570
v1 = T_Semiring_2280 -> T_IsSemiring_1570
d_isSemiring_2312 (T_Semiring_2280 -> T_Semiring_2280
forall a b. a -> b
coe T_Semiring_2280
v0) in
    AgdaAny -> T_IsCommutativeMagma_212
forall a b. a -> b
coe
      (let v2 :: T_IsSemiringWithoutAnnihilatingZero_1468
v2
             = T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                 (T_IsSemiring_1570 -> T_IsSemiring_1570
forall a b. a -> b
coe T_IsSemiring_1570
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsCommutativeMonoid_736
v3
                = T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
                    (T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsSemiringWithoutAnnihilatingZero_1468
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsCommutativeSemigroup_548 -> T_IsCommutativeMagma_212)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsCommutativeSemigroup_548 -> T_IsCommutativeMagma_212
MAlonzo.Code.Algebra.Structures.du_isCommutativeMagma_586
               ((T_IsCommutativeMonoid_736 -> T_IsCommutativeSemigroup_548)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsCommutativeMonoid_736 -> T_IsCommutativeSemigroup_548
MAlonzo.Code.Algebra.Structures.du_isCommutativeSemigroup_786
                  (T_IsCommutativeMonoid_736 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v3)))))
-- Algebra.Bundles.Semiring._.+-isCommutativeMonoid
d_'43''45'isCommutativeMonoid_2354 ::
  T_Semiring_2280 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_2354 :: T_Semiring_2280 -> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_2354 T_Semiring_2280
v0
  = (T_IsSemiringWithoutAnnihilatingZero_1468
 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> T_IsCommutativeMonoid_736
forall a b. a -> b
coe
      T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
      ((T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
         ((T_Semiring_2280 -> T_IsSemiring_1570) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semiring_2280 -> T_IsSemiring_1570
d_isSemiring_2312 (T_Semiring_2280 -> AgdaAny
forall a b. a -> b
coe T_Semiring_2280
v0)))
-- Algebra.Bundles.Semiring._.isCommutativeSemigroup
d_isCommutativeSemigroup_2356 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Semiring_2280 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_548
d_isCommutativeSemigroup_2356 :: () -> () -> T_Semiring_2280 -> T_IsCommutativeSemigroup_548
d_isCommutativeSemigroup_2356 ~()
v0 ~()
v1 T_Semiring_2280
v2
  = T_Semiring_2280 -> T_IsCommutativeSemigroup_548
du_isCommutativeSemigroup_2356 T_Semiring_2280
v2
du_isCommutativeSemigroup_2356 ::
  T_Semiring_2280 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_548
du_isCommutativeSemigroup_2356 :: T_Semiring_2280 -> T_IsCommutativeSemigroup_548
du_isCommutativeSemigroup_2356 T_Semiring_2280
v0
  = let v1 :: T_IsSemiring_1570
v1 = T_Semiring_2280 -> T_IsSemiring_1570
d_isSemiring_2312 (T_Semiring_2280 -> T_Semiring_2280
forall a b. a -> b
coe T_Semiring_2280
v0) in
    AgdaAny -> T_IsCommutativeSemigroup_548
forall a b. a -> b
coe
      (let v2 :: T_IsSemiringWithoutAnnihilatingZero_1468
v2
             = T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                 (T_IsSemiring_1570 -> T_IsSemiring_1570
forall a b. a -> b
coe T_IsSemiring_1570
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsCommutativeMonoid_736 -> T_IsCommutativeSemigroup_548)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCommutativeMonoid_736 -> T_IsCommutativeSemigroup_548
MAlonzo.Code.Algebra.Structures.du_isCommutativeSemigroup_786
            ((T_IsSemiringWithoutAnnihilatingZero_1468
 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
               (T_IsSemiringWithoutAnnihilatingZero_1468 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
v2))))
-- Algebra.Bundles.Semiring._.isMagma
d_isMagma_2358 ::
  T_Semiring_2280 -> MAlonzo.Code.Algebra.Structures.T_IsMagma_176
d_isMagma_2358 :: T_Semiring_2280 -> T_IsMagma_176
d_isMagma_2358 T_Semiring_2280
v0
  = (T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> T_IsMagma_176
forall a b. a -> b
coe
      T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480
      ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
         ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746
            ((T_IsSemiringWithoutAnnihilatingZero_1468
 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
               ((T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                  ((T_Semiring_2280 -> T_IsSemiring_1570) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semiring_2280 -> T_IsSemiring_1570
d_isSemiring_2312 (T_Semiring_2280 -> AgdaAny
forall a b. a -> b
coe T_Semiring_2280
v0))))))
-- Algebra.Bundles.Semiring._.isMonoid
d_isMonoid_2360 ::
  T_Semiring_2280 -> MAlonzo.Code.Algebra.Structures.T_IsMonoid_686
d_isMonoid_2360 :: T_Semiring_2280 -> T_IsMonoid_686
d_isMonoid_2360 T_Semiring_2280
v0
  = (T_IsCommutativeMonoid_736 -> T_IsMonoid_686)
-> AgdaAny -> T_IsMonoid_686
forall a b. a -> b
coe
      T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746
      ((T_IsSemiringWithoutAnnihilatingZero_1468
 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
         ((T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
            ((T_Semiring_2280 -> T_IsSemiring_1570) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semiring_2280 -> T_IsSemiring_1570
d_isSemiring_2312 (T_Semiring_2280 -> AgdaAny
forall a b. a -> b
coe T_Semiring_2280
v0))))
-- Algebra.Bundles.Semiring._.isSemigroup
d_isSemigroup_2362 ::
  T_Semiring_2280 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_472
d_isSemigroup_2362 :: T_Semiring_2280 -> T_IsSemigroup_472
d_isSemigroup_2362 T_Semiring_2280
v0
  = (T_IsMonoid_686 -> T_IsSemigroup_472)
-> AgdaAny -> T_IsSemigroup_472
forall a b. a -> b
coe
      T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
      ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746
         ((T_IsSemiringWithoutAnnihilatingZero_1468
 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
            ((T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
               ((T_Semiring_2280 -> T_IsSemiring_1570) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semiring_2280 -> T_IsSemiring_1570
d_isSemiring_2312 (T_Semiring_2280 -> AgdaAny
forall a b. a -> b
coe T_Semiring_2280
v0)))))
-- Algebra.Bundles.Semiring._.isUnitalMagma
d_isUnitalMagma_2364 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Semiring_2280 ->
  MAlonzo.Code.Algebra.Structures.T_IsUnitalMagma_642
d_isUnitalMagma_2364 :: () -> () -> T_Semiring_2280 -> T_IsUnitalMagma_642
d_isUnitalMagma_2364 ~()
v0 ~()
v1 T_Semiring_2280
v2 = T_Semiring_2280 -> T_IsUnitalMagma_642
du_isUnitalMagma_2364 T_Semiring_2280
v2
du_isUnitalMagma_2364 ::
  T_Semiring_2280 ->
  MAlonzo.Code.Algebra.Structures.T_IsUnitalMagma_642
du_isUnitalMagma_2364 :: T_Semiring_2280 -> T_IsUnitalMagma_642
du_isUnitalMagma_2364 T_Semiring_2280
v0
  = let v1 :: T_IsSemiring_1570
v1 = T_Semiring_2280 -> T_IsSemiring_1570
d_isSemiring_2312 (T_Semiring_2280 -> T_Semiring_2280
forall a b. a -> b
coe T_Semiring_2280
v0) in
    AgdaAny -> T_IsUnitalMagma_642
forall a b. a -> b
coe
      (let v2 :: T_IsSemiringWithoutAnnihilatingZero_1468
v2
             = T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                 (T_IsSemiring_1570 -> T_IsSemiring_1570
forall a b. a -> b
coe T_IsSemiring_1570
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsCommutativeMonoid_736
v3
                = T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
                    (T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsSemiringWithoutAnnihilatingZero_1468
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsMonoid_686 -> T_IsUnitalMagma_642) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_686 -> T_IsUnitalMagma_642
MAlonzo.Code.Algebra.Structures.du_isUnitalMagma_730
               ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746 (T_IsCommutativeMonoid_736 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v3)))))
-- Algebra.Bundles.Semiring._.distrib
d_distrib_2366 ::
  T_Semiring_2280 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_distrib_2366 :: T_Semiring_2280 -> T_Σ_14
d_distrib_2366 T_Semiring_2280
v0
  = (T_IsSemiringWithoutAnnihilatingZero_1468 -> T_Σ_14)
-> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsSemiringWithoutAnnihilatingZero_1468 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_distrib_1496
      ((T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
         ((T_Semiring_2280 -> T_IsSemiring_1570) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semiring_2280 -> T_IsSemiring_1570
d_isSemiring_2312 (T_Semiring_2280 -> AgdaAny
forall a b. a -> b
coe T_Semiring_2280
v0)))
-- Algebra.Bundles.Semiring._.distribʳ
d_distrib'691'_2368 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Semiring_2280 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_distrib'691'_2368 :: ()
-> ()
-> T_Semiring_2280
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_distrib'691'_2368 ~()
v0 ~()
v1 T_Semiring_2280
v2 = T_Semiring_2280 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'691'_2368 T_Semiring_2280
v2
du_distrib'691'_2368 ::
  T_Semiring_2280 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'691'_2368 :: T_Semiring_2280 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'691'_2368 T_Semiring_2280
v0
  = let v1 :: T_IsSemiring_1570
v1 = T_Semiring_2280 -> T_IsSemiring_1570
d_isSemiring_2312 (T_Semiring_2280 -> T_Semiring_2280
forall a b. a -> b
coe T_Semiring_2280
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsSemiringWithoutAnnihilatingZero_1468
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiringWithoutAnnihilatingZero_1468
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_distrib'691'_1500
         ((T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
            (T_IsSemiring_1570 -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1570
v1)))
-- Algebra.Bundles.Semiring._.distribˡ
d_distrib'737'_2370 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Semiring_2280 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_distrib'737'_2370 :: ()
-> ()
-> T_Semiring_2280
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_distrib'737'_2370 ~()
v0 ~()
v1 T_Semiring_2280
v2 = T_Semiring_2280 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'737'_2370 T_Semiring_2280
v2
du_distrib'737'_2370 ::
  T_Semiring_2280 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'737'_2370 :: T_Semiring_2280 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'737'_2370 T_Semiring_2280
v0
  = let v1 :: T_IsSemiring_1570
v1 = T_Semiring_2280 -> T_IsSemiring_1570
d_isSemiring_2312 (T_Semiring_2280 -> T_Semiring_2280
forall a b. a -> b
coe T_Semiring_2280
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsSemiringWithoutAnnihilatingZero_1468
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiringWithoutAnnihilatingZero_1468
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_distrib'737'_1498
         ((T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
            (T_IsSemiring_1570 -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1570
v1)))
-- Algebra.Bundles.Semiring._.isEquivalence
d_isEquivalence_2372 ::
  T_Semiring_2280 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_2372 :: T_Semiring_2280 -> T_IsEquivalence_26
d_isEquivalence_2372 T_Semiring_2280
v0
  = (T_IsMagma_176 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
      ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480
         ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
            ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746
               ((T_IsSemiringWithoutAnnihilatingZero_1468
 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
                  ((T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                     ((T_Semiring_2280 -> T_IsSemiring_1570) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semiring_2280 -> T_IsSemiring_1570
d_isSemiring_2312 (T_Semiring_2280 -> AgdaAny
forall a b. a -> b
coe T_Semiring_2280
v0)))))))
-- Algebra.Bundles.Semiring._.isNearSemiring
d_isNearSemiring_2374 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Semiring_2280 ->
  MAlonzo.Code.Algebra.Structures.T_IsNearSemiring_1218
d_isNearSemiring_2374 :: () -> () -> T_Semiring_2280 -> T_IsNearSemiring_1218
d_isNearSemiring_2374 ~()
v0 ~()
v1 T_Semiring_2280
v2 = T_Semiring_2280 -> T_IsNearSemiring_1218
du_isNearSemiring_2374 T_Semiring_2280
v2
du_isNearSemiring_2374 ::
  T_Semiring_2280 ->
  MAlonzo.Code.Algebra.Structures.T_IsNearSemiring_1218
du_isNearSemiring_2374 :: T_Semiring_2280 -> T_IsNearSemiring_1218
du_isNearSemiring_2374 T_Semiring_2280
v0
  = let v1 :: T_IsSemiring_1570
v1 = T_Semiring_2280 -> T_IsSemiring_1570
d_isSemiring_2312 (T_Semiring_2280 -> T_Semiring_2280
forall a b. a -> b
coe T_Semiring_2280
v0) in
    AgdaAny -> T_IsNearSemiring_1218
forall a b. a -> b
coe
      ((T_IsSemiringWithoutOne_1298 -> T_IsNearSemiring_1218)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiringWithoutOne_1298 -> T_IsNearSemiring_1218
MAlonzo.Code.Algebra.Structures.du_isNearSemiring_1374
         ((T_IsSemiring_1570 -> T_IsSemiringWithoutOne_1298)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemiring_1570 -> T_IsSemiringWithoutOne_1298
MAlonzo.Code.Algebra.Structures.du_isSemiringWithoutOne_1660
            (T_IsSemiring_1570 -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1570
v1)))
-- Algebra.Bundles.Semiring._.isPartialEquivalence
d_isPartialEquivalence_2376 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Semiring_2280 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_2376 :: () -> () -> T_Semiring_2280 -> T_IsPartialEquivalence_16
d_isPartialEquivalence_2376 ~()
v0 ~()
v1 T_Semiring_2280
v2
  = T_Semiring_2280 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_2376 T_Semiring_2280
v2
du_isPartialEquivalence_2376 ::
  T_Semiring_2280 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_2376 :: T_Semiring_2280 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_2376 T_Semiring_2280
v0
  = let v1 :: T_IsSemiring_1570
v1 = T_Semiring_2280 -> T_IsSemiring_1570
d_isSemiring_2312 (T_Semiring_2280 -> T_Semiring_2280
forall a b. a -> b
coe T_Semiring_2280
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsSemiringWithoutAnnihilatingZero_1468
v2
             = T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                 (T_IsSemiring_1570 -> T_IsSemiring_1570
forall a b. a -> b
coe T_IsSemiring_1570
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsCommutativeMonoid_736
v3
                = T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
                    (T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsSemiringWithoutAnnihilatingZero_1468
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsMonoid_686
v4
                   = T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746 (T_IsCommutativeMonoid_736 -> T_IsCommutativeMonoid_736
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsSemigroup_472
v5
                      = T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (let v6 :: T_IsMagma_176
v6 = T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (T_IsSemigroup_472 -> T_IsSemigroup_472
forall a b. a -> b
coe T_IsSemigroup_472
v5) in
                   AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     ((T_IsEquivalence_26 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsEquivalence_26 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
                        ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v6))))))))
-- Algebra.Bundles.Semiring._.isSemiringWithoutAnnihilatingZero
d_isSemiringWithoutAnnihilatingZero_2378 ::
  T_Semiring_2280 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_2378 :: T_Semiring_2280 -> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_2378 T_Semiring_2280
v0
  = (T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> T_IsSemiringWithoutAnnihilatingZero_1468
forall a b. a -> b
coe
      T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
      ((T_Semiring_2280 -> T_IsSemiring_1570) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semiring_2280 -> T_IsSemiring_1570
d_isSemiring_2312 (T_Semiring_2280 -> AgdaAny
forall a b. a -> b
coe T_Semiring_2280
v0))
-- Algebra.Bundles.Semiring._.isSemiringWithoutOne
d_isSemiringWithoutOne_2380 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Semiring_2280 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutOne_1298
d_isSemiringWithoutOne_2380 :: () -> () -> T_Semiring_2280 -> T_IsSemiringWithoutOne_1298
d_isSemiringWithoutOne_2380 ~()
v0 ~()
v1 T_Semiring_2280
v2
  = T_Semiring_2280 -> T_IsSemiringWithoutOne_1298
du_isSemiringWithoutOne_2380 T_Semiring_2280
v2
du_isSemiringWithoutOne_2380 ::
  T_Semiring_2280 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutOne_1298
du_isSemiringWithoutOne_2380 :: T_Semiring_2280 -> T_IsSemiringWithoutOne_1298
du_isSemiringWithoutOne_2380 T_Semiring_2280
v0
  = (T_IsSemiring_1570 -> T_IsSemiringWithoutOne_1298)
-> AgdaAny -> T_IsSemiringWithoutOne_1298
forall a b. a -> b
coe
      T_IsSemiring_1570 -> T_IsSemiringWithoutOne_1298
MAlonzo.Code.Algebra.Structures.du_isSemiringWithoutOne_1660
      ((T_Semiring_2280 -> T_IsSemiring_1570) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semiring_2280 -> T_IsSemiring_1570
d_isSemiring_2312 (T_Semiring_2280 -> AgdaAny
forall a b. a -> b
coe T_Semiring_2280
v0))
-- Algebra.Bundles.Semiring._.refl
d_refl_2382 :: T_Semiring_2280 -> AgdaAny -> AgdaAny
d_refl_2382 :: T_Semiring_2280 -> AgdaAny -> AgdaAny
d_refl_2382 T_Semiring_2280
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_34
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
         ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480
            ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
               ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746
                  ((T_IsSemiringWithoutAnnihilatingZero_1468
 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
                     ((T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                        ((T_Semiring_2280 -> T_IsSemiring_1570) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semiring_2280 -> T_IsSemiring_1570
d_isSemiring_2312 (T_Semiring_2280 -> AgdaAny
forall a b. a -> b
coe T_Semiring_2280
v0))))))))
-- Algebra.Bundles.Semiring._.reflexive
d_reflexive_2384 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Semiring_2280 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_2384 :: ()
-> ()
-> T_Semiring_2280
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_2384 ~()
v0 ~()
v1 T_Semiring_2280
v2 = T_Semiring_2280 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_2384 T_Semiring_2280
v2
du_reflexive_2384 ::
  T_Semiring_2280 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_2384 :: T_Semiring_2280 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_2384 T_Semiring_2280
v0
  = let v1 :: T_IsSemiring_1570
v1 = T_Semiring_2280 -> T_IsSemiring_1570
d_isSemiring_2312 (T_Semiring_2280 -> T_Semiring_2280
forall a b. a -> b
coe T_Semiring_2280
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemiringWithoutAnnihilatingZero_1468
v2
             = T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                 (T_IsSemiring_1570 -> T_IsSemiring_1570
forall a b. a -> b
coe T_IsSemiring_1570
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsCommutativeMonoid_736
v3
                = T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
                    (T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsSemiringWithoutAnnihilatingZero_1468
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsMonoid_686
v4
                   = T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746 (T_IsCommutativeMonoid_736 -> T_IsCommutativeMonoid_736
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsSemigroup_472
v5
                      = T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (let v6 :: T_IsMagma_176
v6 = T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (T_IsSemigroup_472 -> T_IsSemigroup_472
forall a b. a -> b
coe T_IsSemigroup_472
v5) in
                   (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
                     (\ AgdaAny
v7 AgdaAny
v8 AgdaAny
v9 ->
                        (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                          T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
                          ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v6))
                          AgdaAny
v7))))))
-- Algebra.Bundles.Semiring._.setoid
d_setoid_2386 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Semiring_2280 -> MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_2386 :: () -> () -> T_Semiring_2280 -> T_Setoid_44
d_setoid_2386 ~()
v0 ~()
v1 T_Semiring_2280
v2 = T_Semiring_2280 -> T_Setoid_44
du_setoid_2386 T_Semiring_2280
v2
du_setoid_2386 ::
  T_Semiring_2280 -> MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_2386 :: T_Semiring_2280 -> T_Setoid_44
du_setoid_2386 T_Semiring_2280
v0
  = let v1 :: T_IsSemiring_1570
v1 = T_Semiring_2280 -> T_IsSemiring_1570
d_isSemiring_2312 (T_Semiring_2280 -> T_Semiring_2280
forall a b. a -> b
coe T_Semiring_2280
v0) in
    AgdaAny -> T_Setoid_44
forall a b. a -> b
coe
      (let v2 :: T_IsSemiringWithoutAnnihilatingZero_1468
v2
             = T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                 (T_IsSemiring_1570 -> T_IsSemiring_1570
forall a b. a -> b
coe T_IsSemiring_1570
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsCommutativeMonoid_736
v3
                = T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
                    (T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsSemiringWithoutAnnihilatingZero_1468
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsMonoid_686
v4
                   = T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746 (T_IsCommutativeMonoid_736 -> T_IsCommutativeMonoid_736
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsSemigroup_472
v5
                      = T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  ((T_IsMagma_176 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsMagma_176 -> T_Setoid_44
MAlonzo.Code.Algebra.Structures.du_setoid_200
                     ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v5)))))))
-- Algebra.Bundles.Semiring._.sym
d_sym_2388 ::
  T_Semiring_2280 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_2388 :: T_Semiring_2280 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_2388 T_Semiring_2280
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_36
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
         ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480
            ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
               ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746
                  ((T_IsSemiringWithoutAnnihilatingZero_1468
 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
                     ((T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                        ((T_Semiring_2280 -> T_IsSemiring_1570) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semiring_2280 -> T_IsSemiring_1570
d_isSemiring_2312 (T_Semiring_2280 -> AgdaAny
forall a b. a -> b
coe T_Semiring_2280
v0))))))))
-- Algebra.Bundles.Semiring._.trans
d_trans_2390 ::
  T_Semiring_2280 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_2390 :: T_Semiring_2280
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_2390 T_Semiring_2280
v0
  = (T_IsEquivalence_26
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_38
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
         ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480
            ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
               ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746
                  ((T_IsSemiringWithoutAnnihilatingZero_1468
 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
                     ((T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                        ((T_Semiring_2280 -> T_IsSemiring_1570) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semiring_2280 -> T_IsSemiring_1570
d_isSemiring_2312 (T_Semiring_2280 -> AgdaAny
forall a b. a -> b
coe T_Semiring_2280
v0))))))))
-- Algebra.Bundles.Semiring._.zero
d_zero_2392 ::
  T_Semiring_2280 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_zero_2392 :: T_Semiring_2280 -> T_Σ_14
d_zero_2392 T_Semiring_2280
v0
  = (T_IsSemiring_1570 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsSemiring_1570 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_zero_1586
      ((T_Semiring_2280 -> T_IsSemiring_1570) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semiring_2280 -> T_IsSemiring_1570
d_isSemiring_2312 (T_Semiring_2280 -> AgdaAny
forall a b. a -> b
coe T_Semiring_2280
v0))
-- Algebra.Bundles.Semiring._.zeroʳ
d_zero'691'_2394 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Semiring_2280 -> AgdaAny -> AgdaAny
d_zero'691'_2394 :: () -> () -> T_Semiring_2280 -> AgdaAny -> AgdaAny
d_zero'691'_2394 ~()
v0 ~()
v1 T_Semiring_2280
v2 = T_Semiring_2280 -> AgdaAny -> AgdaAny
du_zero'691'_2394 T_Semiring_2280
v2
du_zero'691'_2394 :: T_Semiring_2280 -> AgdaAny -> AgdaAny
du_zero'691'_2394 :: T_Semiring_2280 -> AgdaAny -> AgdaAny
du_zero'691'_2394 T_Semiring_2280
v0
  = let v1 :: T_IsSemiring_1570
v1 = T_Semiring_2280 -> T_IsSemiring_1570
d_isSemiring_2312 (T_Semiring_2280 -> T_Semiring_2280
forall a b. a -> b
coe T_Semiring_2280
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsSemiringWithoutOne_1298 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiringWithoutOne_1298 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_zero'691'_1372
         ((T_IsSemiring_1570 -> T_IsSemiringWithoutOne_1298)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemiring_1570 -> T_IsSemiringWithoutOne_1298
MAlonzo.Code.Algebra.Structures.du_isSemiringWithoutOne_1660
            (T_IsSemiring_1570 -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1570
v1)))
-- Algebra.Bundles.Semiring._.zeroˡ
d_zero'737'_2396 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Semiring_2280 -> AgdaAny -> AgdaAny
d_zero'737'_2396 :: () -> () -> T_Semiring_2280 -> AgdaAny -> AgdaAny
d_zero'737'_2396 ~()
v0 ~()
v1 T_Semiring_2280
v2 = T_Semiring_2280 -> AgdaAny -> AgdaAny
du_zero'737'_2396 T_Semiring_2280
v2
du_zero'737'_2396 :: T_Semiring_2280 -> AgdaAny -> AgdaAny
du_zero'737'_2396 :: T_Semiring_2280 -> AgdaAny -> AgdaAny
du_zero'737'_2396 T_Semiring_2280
v0
  = let v1 :: T_IsSemiring_1570
v1 = T_Semiring_2280 -> T_IsSemiring_1570
d_isSemiring_2312 (T_Semiring_2280 -> T_Semiring_2280
forall a b. a -> b
coe T_Semiring_2280
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsSemiringWithoutOne_1298 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiringWithoutOne_1298 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_zero'737'_1370
         ((T_IsSemiring_1570 -> T_IsSemiringWithoutOne_1298)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemiring_1570 -> T_IsSemiringWithoutOne_1298
MAlonzo.Code.Algebra.Structures.du_isSemiringWithoutOne_1660
            (T_IsSemiring_1570 -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1570
v1)))
-- Algebra.Bundles.Semiring.semiringWithoutAnnihilatingZero
d_semiringWithoutAnnihilatingZero_2398 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Semiring_2280 -> T_SemiringWithoutAnnihilatingZero_2130
d_semiringWithoutAnnihilatingZero_2398 :: ()
-> () -> T_Semiring_2280 -> T_SemiringWithoutAnnihilatingZero_2130
d_semiringWithoutAnnihilatingZero_2398 ~()
v0 ~()
v1 T_Semiring_2280
v2
  = T_Semiring_2280 -> T_SemiringWithoutAnnihilatingZero_2130
du_semiringWithoutAnnihilatingZero_2398 T_Semiring_2280
v2
du_semiringWithoutAnnihilatingZero_2398 ::
  T_Semiring_2280 -> T_SemiringWithoutAnnihilatingZero_2130
du_semiringWithoutAnnihilatingZero_2398 :: T_Semiring_2280 -> T_SemiringWithoutAnnihilatingZero_2130
du_semiringWithoutAnnihilatingZero_2398 T_Semiring_2280
v0
  = ((AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> AgdaAny
 -> T_IsSemiringWithoutAnnihilatingZero_1468
 -> T_SemiringWithoutAnnihilatingZero_2130)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsSemiringWithoutAnnihilatingZero_1468
-> T_SemiringWithoutAnnihilatingZero_2130
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsSemiringWithoutAnnihilatingZero_1468
-> T_SemiringWithoutAnnihilatingZero_2130
C_SemiringWithoutAnnihilatingZero'46'constructor_38993
      (T_Semiring_2280 -> AgdaAny -> AgdaAny -> AgdaAny
d__'43'__2304 (T_Semiring_2280 -> T_Semiring_2280
forall a b. a -> b
coe T_Semiring_2280
v0)) (T_Semiring_2280 -> AgdaAny -> AgdaAny -> AgdaAny
d__'42'__2306 (T_Semiring_2280 -> T_Semiring_2280
forall a b. a -> b
coe T_Semiring_2280
v0))
      (T_Semiring_2280 -> AgdaAny
d_0'35'_2308 (T_Semiring_2280 -> T_Semiring_2280
forall a b. a -> b
coe T_Semiring_2280
v0)) (T_Semiring_2280 -> AgdaAny
d_1'35'_2310 (T_Semiring_2280 -> T_Semiring_2280
forall a b. a -> b
coe T_Semiring_2280
v0))
      (T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
         ((T_Semiring_2280 -> T_IsSemiring_1570)
-> AgdaAny -> T_IsSemiring_1570
forall a b. a -> b
coe T_Semiring_2280 -> T_IsSemiring_1570
d_isSemiring_2312 (T_Semiring_2280 -> AgdaAny
forall a b. a -> b
coe T_Semiring_2280
v0)))
-- Algebra.Bundles.Semiring._._≉_
d__'8777'__2402 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Semiring_2280 -> AgdaAny -> AgdaAny -> ()
d__'8777'__2402 :: () -> () -> T_Semiring_2280 -> AgdaAny -> AgdaAny -> ()
d__'8777'__2402 = () -> () -> T_Semiring_2280 -> AgdaAny -> AgdaAny -> ()
forall a. a
erased
-- Algebra.Bundles.Semiring._.magma
d_magma_2404 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Semiring_2280 -> T_Magma_68
d_magma_2404 :: () -> () -> T_Semiring_2280 -> T_Magma_68
d_magma_2404 ~()
v0 ~()
v1 T_Semiring_2280
v2 = T_Semiring_2280 -> T_Magma_68
du_magma_2404 T_Semiring_2280
v2
du_magma_2404 :: T_Semiring_2280 -> T_Magma_68
du_magma_2404 :: T_Semiring_2280 -> T_Magma_68
du_magma_2404 T_Semiring_2280
v0
  = let v1 :: t
v1 = (T_Semiring_2280 -> T_SemiringWithoutAnnihilatingZero_2130)
-> AgdaAny -> t
forall a b. a -> b
coe T_Semiring_2280 -> T_SemiringWithoutAnnihilatingZero_2130
du_semiringWithoutAnnihilatingZero_2398 (T_Semiring_2280 -> AgdaAny
forall a b. a -> b
coe T_Semiring_2280
v0) in
    AgdaAny -> T_Magma_68
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_SemiringWithoutAnnihilatingZero_2130 -> T_Monoid_882)
-> AgdaAny -> t
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_2130 -> T_Monoid_882
du_'42''45'monoid_2264 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_Semigroup_536 -> T_Magma_68) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semigroup_536 -> T_Magma_68
du_magma_584 ((T_Monoid_882 -> T_Semigroup_536) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Monoid_882 -> T_Semigroup_536
du_semigroup_944 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2))))
-- Algebra.Bundles.Semiring._.*-monoid
d_'42''45'monoid_2406 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Semiring_2280 -> T_Monoid_882
d_'42''45'monoid_2406 :: () -> () -> T_Semiring_2280 -> T_Monoid_882
d_'42''45'monoid_2406 ~()
v0 ~()
v1 T_Semiring_2280
v2 = T_Semiring_2280 -> T_Monoid_882
du_'42''45'monoid_2406 T_Semiring_2280
v2
du_'42''45'monoid_2406 :: T_Semiring_2280 -> T_Monoid_882
du_'42''45'monoid_2406 :: T_Semiring_2280 -> T_Monoid_882
du_'42''45'monoid_2406 T_Semiring_2280
v0
  = (T_SemiringWithoutAnnihilatingZero_2130 -> T_Monoid_882)
-> AgdaAny -> T_Monoid_882
forall a b. a -> b
coe
      T_SemiringWithoutAnnihilatingZero_2130 -> T_Monoid_882
du_'42''45'monoid_2264
      ((T_Semiring_2280 -> T_SemiringWithoutAnnihilatingZero_2130)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semiring_2280 -> T_SemiringWithoutAnnihilatingZero_2130
du_semiringWithoutAnnihilatingZero_2398 (T_Semiring_2280 -> AgdaAny
forall a b. a -> b
coe T_Semiring_2280
v0))
-- Algebra.Bundles.Semiring._.rawMagma
d_rawMagma_2408 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Semiring_2280 -> MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
d_rawMagma_2408 :: () -> () -> T_Semiring_2280 -> T_RawMagma_36
d_rawMagma_2408 ~()
v0 ~()
v1 T_Semiring_2280
v2 = T_Semiring_2280 -> T_RawMagma_36
du_rawMagma_2408 T_Semiring_2280
v2
du_rawMagma_2408 ::
  T_Semiring_2280 -> MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
du_rawMagma_2408 :: T_Semiring_2280 -> T_RawMagma_36
du_rawMagma_2408 T_Semiring_2280
v0
  = let v1 :: t
v1 = (T_Semiring_2280 -> T_SemiringWithoutAnnihilatingZero_2130)
-> AgdaAny -> t
forall a b. a -> b
coe T_Semiring_2280 -> T_SemiringWithoutAnnihilatingZero_2130
du_semiringWithoutAnnihilatingZero_2398 (T_Semiring_2280 -> AgdaAny
forall a b. a -> b
coe T_Semiring_2280
v0) in
    AgdaAny -> T_RawMagma_36
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_SemiringWithoutAnnihilatingZero_2130 -> T_Monoid_882)
-> AgdaAny -> t
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_2130 -> T_Monoid_882
du_'42''45'monoid_2264 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: t
v3 = (T_Monoid_882 -> T_Semigroup_536) -> AgdaAny -> t
forall a b. a -> b
coe T_Monoid_882 -> T_Semigroup_536
du_semigroup_944 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_Magma_68 -> T_RawMagma_36) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Magma_68 -> T_RawMagma_36
du_rawMagma_112 ((T_Semigroup_536 -> T_Magma_68) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semigroup_536 -> T_Magma_68
du_magma_584 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3)))))
-- Algebra.Bundles.Semiring._.rawMonoid
d_rawMonoid_2410 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Semiring_2280 -> MAlonzo.Code.Algebra.Bundles.Raw.T_RawMonoid_64
d_rawMonoid_2410 :: () -> () -> T_Semiring_2280 -> T_RawMonoid_64
d_rawMonoid_2410 ~()
v0 ~()
v1 T_Semiring_2280
v2 = T_Semiring_2280 -> T_RawMonoid_64
du_rawMonoid_2410 T_Semiring_2280
v2
du_rawMonoid_2410 ::
  T_Semiring_2280 -> MAlonzo.Code.Algebra.Bundles.Raw.T_RawMonoid_64
du_rawMonoid_2410 :: T_Semiring_2280 -> T_RawMonoid_64
du_rawMonoid_2410 T_Semiring_2280
v0
  = let v1 :: t
v1 = (T_Semiring_2280 -> T_SemiringWithoutAnnihilatingZero_2130)
-> AgdaAny -> t
forall a b. a -> b
coe T_Semiring_2280 -> T_SemiringWithoutAnnihilatingZero_2130
du_semiringWithoutAnnihilatingZero_2398 (T_Semiring_2280 -> AgdaAny
forall a b. a -> b
coe T_Semiring_2280
v0) in
    AgdaAny -> T_RawMonoid_64
forall a b. a -> b
coe ((T_Monoid_882 -> T_RawMonoid_64) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Monoid_882 -> T_RawMonoid_64
du_rawMonoid_954 ((T_SemiringWithoutAnnihilatingZero_2130 -> T_Monoid_882)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_2130 -> T_Monoid_882
du_'42''45'monoid_2264 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1)))
-- Algebra.Bundles.Semiring._.semigroup
d_semigroup_2412 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Semiring_2280 -> T_Semigroup_536
d_semigroup_2412 :: () -> () -> T_Semiring_2280 -> T_Semigroup_536
d_semigroup_2412 ~()
v0 ~()
v1 T_Semiring_2280
v2 = T_Semiring_2280 -> T_Semigroup_536
du_semigroup_2412 T_Semiring_2280
v2
du_semigroup_2412 :: T_Semiring_2280 -> T_Semigroup_536
du_semigroup_2412 :: T_Semiring_2280 -> T_Semigroup_536
du_semigroup_2412 T_Semiring_2280
v0
  = let v1 :: t
v1 = (T_Semiring_2280 -> T_SemiringWithoutAnnihilatingZero_2130)
-> AgdaAny -> t
forall a b. a -> b
coe T_Semiring_2280 -> T_SemiringWithoutAnnihilatingZero_2130
du_semiringWithoutAnnihilatingZero_2398 (T_Semiring_2280 -> AgdaAny
forall a b. a -> b
coe T_Semiring_2280
v0) in
    AgdaAny -> T_Semigroup_536
forall a b. a -> b
coe ((T_Monoid_882 -> T_Semigroup_536) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Monoid_882 -> T_Semigroup_536
du_semigroup_944 ((T_SemiringWithoutAnnihilatingZero_2130 -> T_Monoid_882)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_2130 -> T_Monoid_882
du_'42''45'monoid_2264 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1)))
-- Algebra.Bundles.Semiring._.commutativeMagma
d_commutativeMagma_2414 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Semiring_2280 -> T_CommutativeMagma_180
d_commutativeMagma_2414 :: () -> () -> T_Semiring_2280 -> T_CommutativeMagma_180
d_commutativeMagma_2414 ~()
v0 ~()
v1 T_Semiring_2280
v2 = T_Semiring_2280 -> T_CommutativeMagma_180
du_commutativeMagma_2414 T_Semiring_2280
v2
du_commutativeMagma_2414 ::
  T_Semiring_2280 -> T_CommutativeMagma_180
du_commutativeMagma_2414 :: T_Semiring_2280 -> T_CommutativeMagma_180
du_commutativeMagma_2414 T_Semiring_2280
v0
  = let v1 :: t
v1 = (T_Semiring_2280 -> T_SemiringWithoutAnnihilatingZero_2130)
-> AgdaAny -> t
forall a b. a -> b
coe T_Semiring_2280 -> T_SemiringWithoutAnnihilatingZero_2130
du_semiringWithoutAnnihilatingZero_2398 (T_Semiring_2280 -> AgdaAny
forall a b. a -> b
coe T_Semiring_2280
v0) in
    AgdaAny -> T_CommutativeMagma_180
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_SemiringWithoutAnnihilatingZero_2130 -> T_CommutativeMonoid_962)
-> AgdaAny -> t
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_2130 -> T_CommutativeMonoid_962
du_'43''45'commutativeMonoid_2242 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_CommutativeSemigroup_662 -> T_CommutativeMagma_180)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_CommutativeSemigroup_662 -> T_CommutativeMagma_180
du_commutativeMagma_726
            ((T_CommutativeMonoid_962 -> T_CommutativeSemigroup_662)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeMonoid_962 -> T_CommutativeSemigroup_662
du_commutativeSemigroup_1048 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2))))
-- Algebra.Bundles.Semiring._.+-commutativeMonoid
d_'43''45'commutativeMonoid_2416 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Semiring_2280 -> T_CommutativeMonoid_962
d_'43''45'commutativeMonoid_2416 :: () -> () -> T_Semiring_2280 -> T_CommutativeMonoid_962
d_'43''45'commutativeMonoid_2416 ~()
v0 ~()
v1 T_Semiring_2280
v2
  = T_Semiring_2280 -> T_CommutativeMonoid_962
du_'43''45'commutativeMonoid_2416 T_Semiring_2280
v2
du_'43''45'commutativeMonoid_2416 ::
  T_Semiring_2280 -> T_CommutativeMonoid_962
du_'43''45'commutativeMonoid_2416 :: T_Semiring_2280 -> T_CommutativeMonoid_962
du_'43''45'commutativeMonoid_2416 T_Semiring_2280
v0
  = (T_SemiringWithoutAnnihilatingZero_2130 -> T_CommutativeMonoid_962)
-> AgdaAny -> T_CommutativeMonoid_962
forall a b. a -> b
coe
      T_SemiringWithoutAnnihilatingZero_2130 -> T_CommutativeMonoid_962
du_'43''45'commutativeMonoid_2242
      ((T_Semiring_2280 -> T_SemiringWithoutAnnihilatingZero_2130)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semiring_2280 -> T_SemiringWithoutAnnihilatingZero_2130
du_semiringWithoutAnnihilatingZero_2398 (T_Semiring_2280 -> AgdaAny
forall a b. a -> b
coe T_Semiring_2280
v0))
-- Algebra.Bundles.Semiring._.commutativeSemigroup
d_commutativeSemigroup_2418 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Semiring_2280 -> T_CommutativeSemigroup_662
d_commutativeSemigroup_2418 :: () -> () -> T_Semiring_2280 -> T_CommutativeSemigroup_662
d_commutativeSemigroup_2418 ~()
v0 ~()
v1 T_Semiring_2280
v2
  = T_Semiring_2280 -> T_CommutativeSemigroup_662
du_commutativeSemigroup_2418 T_Semiring_2280
v2
du_commutativeSemigroup_2418 ::
  T_Semiring_2280 -> T_CommutativeSemigroup_662
du_commutativeSemigroup_2418 :: T_Semiring_2280 -> T_CommutativeSemigroup_662
du_commutativeSemigroup_2418 T_Semiring_2280
v0
  = let v1 :: t
v1 = (T_Semiring_2280 -> T_SemiringWithoutAnnihilatingZero_2130)
-> AgdaAny -> t
forall a b. a -> b
coe T_Semiring_2280 -> T_SemiringWithoutAnnihilatingZero_2130
du_semiringWithoutAnnihilatingZero_2398 (T_Semiring_2280 -> AgdaAny
forall a b. a -> b
coe T_Semiring_2280
v0) in
    AgdaAny -> T_CommutativeSemigroup_662
forall a b. a -> b
coe
      ((T_CommutativeMonoid_962 -> T_CommutativeSemigroup_662)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_CommutativeMonoid_962 -> T_CommutativeSemigroup_662
du_commutativeSemigroup_1048
         ((T_SemiringWithoutAnnihilatingZero_2130 -> T_CommutativeMonoid_962)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_2130 -> T_CommutativeMonoid_962
du_'43''45'commutativeMonoid_2242 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1)))
-- Algebra.Bundles.Semiring._.magma
d_magma_2420 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Semiring_2280 -> T_Magma_68
d_magma_2420 :: () -> () -> T_Semiring_2280 -> T_Magma_68
d_magma_2420 ~()
v0 ~()
v1 T_Semiring_2280
v2 = T_Semiring_2280 -> T_Magma_68
du_magma_2420 T_Semiring_2280
v2
du_magma_2420 :: T_Semiring_2280 -> T_Magma_68
du_magma_2420 :: T_Semiring_2280 -> T_Magma_68
du_magma_2420 T_Semiring_2280
v0
  = let v1 :: t
v1 = (T_Semiring_2280 -> T_SemiringWithoutAnnihilatingZero_2130)
-> AgdaAny -> t
forall a b. a -> b
coe T_Semiring_2280 -> T_SemiringWithoutAnnihilatingZero_2130
du_semiringWithoutAnnihilatingZero_2398 (T_Semiring_2280 -> AgdaAny
forall a b. a -> b
coe T_Semiring_2280
v0) in
    AgdaAny -> T_Magma_68
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_SemiringWithoutAnnihilatingZero_2130 -> T_CommutativeMonoid_962)
-> AgdaAny -> t
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_2130 -> T_CommutativeMonoid_962
du_'43''45'commutativeMonoid_2242 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: t
v3 = (T_CommutativeMonoid_962 -> T_Monoid_882) -> AgdaAny -> t
forall a b. a -> b
coe T_CommutativeMonoid_962 -> T_Monoid_882
du_monoid_1032 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_Semigroup_536 -> T_Magma_68) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semigroup_536 -> T_Magma_68
du_magma_584 ((T_Monoid_882 -> T_Semigroup_536) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Monoid_882 -> T_Semigroup_536
du_semigroup_944 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3)))))
-- Algebra.Bundles.Semiring._.monoid
d_monoid_2422 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Semiring_2280 -> T_Monoid_882
d_monoid_2422 :: () -> () -> T_Semiring_2280 -> T_Monoid_882
d_monoid_2422 ~()
v0 ~()
v1 T_Semiring_2280
v2 = T_Semiring_2280 -> T_Monoid_882
du_monoid_2422 T_Semiring_2280
v2
du_monoid_2422 :: T_Semiring_2280 -> T_Monoid_882
du_monoid_2422 :: T_Semiring_2280 -> T_Monoid_882
du_monoid_2422 T_Semiring_2280
v0
  = let v1 :: t
v1 = (T_Semiring_2280 -> T_SemiringWithoutAnnihilatingZero_2130)
-> AgdaAny -> t
forall a b. a -> b
coe T_Semiring_2280 -> T_SemiringWithoutAnnihilatingZero_2130
du_semiringWithoutAnnihilatingZero_2398 (T_Semiring_2280 -> AgdaAny
forall a b. a -> b
coe T_Semiring_2280
v0) in
    AgdaAny -> T_Monoid_882
forall a b. a -> b
coe
      ((T_CommutativeMonoid_962 -> T_Monoid_882) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_CommutativeMonoid_962 -> T_Monoid_882
du_monoid_1032 ((T_SemiringWithoutAnnihilatingZero_2130 -> T_CommutativeMonoid_962)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_2130 -> T_CommutativeMonoid_962
du_'43''45'commutativeMonoid_2242 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1)))
-- Algebra.Bundles.Semiring._.rawMagma
d_rawMagma_2424 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Semiring_2280 -> MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
d_rawMagma_2424 :: () -> () -> T_Semiring_2280 -> T_RawMagma_36
d_rawMagma_2424 ~()
v0 ~()
v1 T_Semiring_2280
v2 = T_Semiring_2280 -> T_RawMagma_36
du_rawMagma_2424 T_Semiring_2280
v2
du_rawMagma_2424 ::
  T_Semiring_2280 -> MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
du_rawMagma_2424 :: T_Semiring_2280 -> T_RawMagma_36
du_rawMagma_2424 T_Semiring_2280
v0
  = let v1 :: t
v1 = (T_Semiring_2280 -> T_SemiringWithoutAnnihilatingZero_2130)
-> AgdaAny -> t
forall a b. a -> b
coe T_Semiring_2280 -> T_SemiringWithoutAnnihilatingZero_2130
du_semiringWithoutAnnihilatingZero_2398 (T_Semiring_2280 -> AgdaAny
forall a b. a -> b
coe T_Semiring_2280
v0) in
    AgdaAny -> T_RawMagma_36
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_SemiringWithoutAnnihilatingZero_2130 -> T_CommutativeMonoid_962)
-> AgdaAny -> t
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_2130 -> T_CommutativeMonoid_962
du_'43''45'commutativeMonoid_2242 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: t
v3 = (T_CommutativeMonoid_962 -> T_Monoid_882) -> AgdaAny -> t
forall a b. a -> b
coe T_CommutativeMonoid_962 -> T_Monoid_882
du_monoid_1032 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: t
v4 = (T_Monoid_882 -> T_Semigroup_536) -> AgdaAny -> t
forall a b. a -> b
coe T_Monoid_882 -> T_Semigroup_536
du_semigroup_944 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_Magma_68 -> T_RawMagma_36) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Magma_68 -> T_RawMagma_36
du_rawMagma_112 ((T_Semigroup_536 -> T_Magma_68) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semigroup_536 -> T_Magma_68
du_magma_584 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v4))))))
-- Algebra.Bundles.Semiring._.rawMonoid
d_rawMonoid_2426 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Semiring_2280 -> MAlonzo.Code.Algebra.Bundles.Raw.T_RawMonoid_64
d_rawMonoid_2426 :: () -> () -> T_Semiring_2280 -> T_RawMonoid_64
d_rawMonoid_2426 ~()
v0 ~()
v1 T_Semiring_2280
v2 = T_Semiring_2280 -> T_RawMonoid_64
du_rawMonoid_2426 T_Semiring_2280
v2
du_rawMonoid_2426 ::
  T_Semiring_2280 -> MAlonzo.Code.Algebra.Bundles.Raw.T_RawMonoid_64
du_rawMonoid_2426 :: T_Semiring_2280 -> T_RawMonoid_64
du_rawMonoid_2426 T_Semiring_2280
v0
  = let v1 :: t
v1 = (T_Semiring_2280 -> T_SemiringWithoutAnnihilatingZero_2130)
-> AgdaAny -> t
forall a b. a -> b
coe T_Semiring_2280 -> T_SemiringWithoutAnnihilatingZero_2130
du_semiringWithoutAnnihilatingZero_2398 (T_Semiring_2280 -> AgdaAny
forall a b. a -> b
coe T_Semiring_2280
v0) in
    AgdaAny -> T_RawMonoid_64
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_SemiringWithoutAnnihilatingZero_2130 -> T_CommutativeMonoid_962)
-> AgdaAny -> t
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_2130 -> T_CommutativeMonoid_962
du_'43''45'commutativeMonoid_2242 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_Monoid_882 -> T_RawMonoid_64) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Monoid_882 -> T_RawMonoid_64
du_rawMonoid_954 ((T_CommutativeMonoid_962 -> T_Monoid_882) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeMonoid_962 -> T_Monoid_882
du_monoid_1032 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2))))
-- Algebra.Bundles.Semiring._.semigroup
d_semigroup_2428 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Semiring_2280 -> T_Semigroup_536
d_semigroup_2428 :: () -> () -> T_Semiring_2280 -> T_Semigroup_536
d_semigroup_2428 ~()
v0 ~()
v1 T_Semiring_2280
v2 = T_Semiring_2280 -> T_Semigroup_536
du_semigroup_2428 T_Semiring_2280
v2
du_semigroup_2428 :: T_Semiring_2280 -> T_Semigroup_536
du_semigroup_2428 :: T_Semiring_2280 -> T_Semigroup_536
du_semigroup_2428 T_Semiring_2280
v0
  = let v1 :: t
v1 = (T_Semiring_2280 -> T_SemiringWithoutAnnihilatingZero_2130)
-> AgdaAny -> t
forall a b. a -> b
coe T_Semiring_2280 -> T_SemiringWithoutAnnihilatingZero_2130
du_semiringWithoutAnnihilatingZero_2398 (T_Semiring_2280 -> AgdaAny
forall a b. a -> b
coe T_Semiring_2280
v0) in
    AgdaAny -> T_Semigroup_536
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_SemiringWithoutAnnihilatingZero_2130 -> T_CommutativeMonoid_962)
-> AgdaAny -> t
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_2130 -> T_CommutativeMonoid_962
du_'43''45'commutativeMonoid_2242 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_Monoid_882 -> T_Semigroup_536) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Monoid_882 -> T_Semigroup_536
du_semigroup_944 ((T_CommutativeMonoid_962 -> T_Monoid_882) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeMonoid_962 -> T_Monoid_882
du_monoid_1032 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2))))
-- Algebra.Bundles.Semiring._.unitalMagma
d_unitalMagma_2430 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Semiring_2280 -> T_UnitalMagma_814
d_unitalMagma_2430 :: () -> () -> T_Semiring_2280 -> T_UnitalMagma_814
d_unitalMagma_2430 ~()
v0 ~()
v1 T_Semiring_2280
v2 = T_Semiring_2280 -> T_UnitalMagma_814
du_unitalMagma_2430 T_Semiring_2280
v2
du_unitalMagma_2430 :: T_Semiring_2280 -> T_UnitalMagma_814
du_unitalMagma_2430 :: T_Semiring_2280 -> T_UnitalMagma_814
du_unitalMagma_2430 T_Semiring_2280
v0
  = let v1 :: t
v1 = (T_Semiring_2280 -> T_SemiringWithoutAnnihilatingZero_2130)
-> AgdaAny -> t
forall a b. a -> b
coe T_Semiring_2280 -> T_SemiringWithoutAnnihilatingZero_2130
du_semiringWithoutAnnihilatingZero_2398 (T_Semiring_2280 -> AgdaAny
forall a b. a -> b
coe T_Semiring_2280
v0) in
    AgdaAny -> T_UnitalMagma_814
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_SemiringWithoutAnnihilatingZero_2130 -> T_CommutativeMonoid_962)
-> AgdaAny -> t
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_2130 -> T_CommutativeMonoid_962
du_'43''45'commutativeMonoid_2242 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_Monoid_882 -> T_UnitalMagma_814) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Monoid_882 -> T_UnitalMagma_814
du_unitalMagma_956 ((T_CommutativeMonoid_962 -> T_Monoid_882) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeMonoid_962 -> T_Monoid_882
du_monoid_1032 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2))))
-- Algebra.Bundles.Semiring._.rawNearSemiring
d_rawNearSemiring_2432 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Semiring_2280 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawNearSemiring_134
d_rawNearSemiring_2432 :: () -> () -> T_Semiring_2280 -> T_RawNearSemiring_134
d_rawNearSemiring_2432 ~()
v0 ~()
v1 T_Semiring_2280
v2 = T_Semiring_2280 -> T_RawNearSemiring_134
du_rawNearSemiring_2432 T_Semiring_2280
v2
du_rawNearSemiring_2432 ::
  T_Semiring_2280 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawNearSemiring_134
du_rawNearSemiring_2432 :: T_Semiring_2280 -> T_RawNearSemiring_134
du_rawNearSemiring_2432 T_Semiring_2280
v0
  = let v1 :: t
v1 = (T_Semiring_2280 -> T_SemiringWithoutAnnihilatingZero_2130)
-> AgdaAny -> t
forall a b. a -> b
coe T_Semiring_2280 -> T_SemiringWithoutAnnihilatingZero_2130
du_semiringWithoutAnnihilatingZero_2398 (T_Semiring_2280 -> AgdaAny
forall a b. a -> b
coe T_Semiring_2280
v0) in
    AgdaAny -> T_RawNearSemiring_134
forall a b. a -> b
coe
      ((T_RawSemiring_174 -> T_RawNearSemiring_134) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_RawSemiring_174 -> T_RawNearSemiring_134
MAlonzo.Code.Algebra.Bundles.Raw.du_rawNearSemiring_204
         ((T_SemiringWithoutAnnihilatingZero_2130 -> T_RawSemiring_174)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_2130 -> T_RawSemiring_174
du_rawSemiring_2236 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1)))
-- Algebra.Bundles.Semiring._.rawSemiring
d_rawSemiring_2434 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Semiring_2280 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawSemiring_174
d_rawSemiring_2434 :: () -> () -> T_Semiring_2280 -> T_RawSemiring_174
d_rawSemiring_2434 ~()
v0 ~()
v1 T_Semiring_2280
v2 = T_Semiring_2280 -> T_RawSemiring_174
du_rawSemiring_2434 T_Semiring_2280
v2
du_rawSemiring_2434 ::
  T_Semiring_2280 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawSemiring_174
du_rawSemiring_2434 :: T_Semiring_2280 -> T_RawSemiring_174
du_rawSemiring_2434 T_Semiring_2280
v0
  = (T_SemiringWithoutAnnihilatingZero_2130 -> T_RawSemiring_174)
-> AgdaAny -> T_RawSemiring_174
forall a b. a -> b
coe
      T_SemiringWithoutAnnihilatingZero_2130 -> T_RawSemiring_174
du_rawSemiring_2236
      ((T_Semiring_2280 -> T_SemiringWithoutAnnihilatingZero_2130)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semiring_2280 -> T_SemiringWithoutAnnihilatingZero_2130
du_semiringWithoutAnnihilatingZero_2398 (T_Semiring_2280 -> AgdaAny
forall a b. a -> b
coe T_Semiring_2280
v0))
-- Algebra.Bundles.Semiring.semiringWithoutOne
d_semiringWithoutOne_2436 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Semiring_2280 -> T_SemiringWithoutOne_1880
d_semiringWithoutOne_2436 :: () -> () -> T_Semiring_2280 -> T_SemiringWithoutOne_1880
d_semiringWithoutOne_2436 ~()
v0 ~()
v1 T_Semiring_2280
v2
  = T_Semiring_2280 -> T_SemiringWithoutOne_1880
du_semiringWithoutOne_2436 T_Semiring_2280
v2
du_semiringWithoutOne_2436 ::
  T_Semiring_2280 -> T_SemiringWithoutOne_1880
du_semiringWithoutOne_2436 :: T_Semiring_2280 -> T_SemiringWithoutOne_1880
du_semiringWithoutOne_2436 T_Semiring_2280
v0
  = ((AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> T_IsSemiringWithoutOne_1298
 -> T_SemiringWithoutOne_1880)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_SemiringWithoutOne_1880
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsSemiringWithoutOne_1298
-> T_SemiringWithoutOne_1880
C_SemiringWithoutOne'46'constructor_34609 (T_Semiring_2280 -> AgdaAny -> AgdaAny -> AgdaAny
d__'43'__2304 (T_Semiring_2280 -> T_Semiring_2280
forall a b. a -> b
coe T_Semiring_2280
v0))
      (T_Semiring_2280 -> AgdaAny -> AgdaAny -> AgdaAny
d__'42'__2306 (T_Semiring_2280 -> T_Semiring_2280
forall a b. a -> b
coe T_Semiring_2280
v0)) (T_Semiring_2280 -> AgdaAny
d_0'35'_2308 (T_Semiring_2280 -> T_Semiring_2280
forall a b. a -> b
coe T_Semiring_2280
v0))
      ((T_IsSemiring_1570 -> T_IsSemiringWithoutOne_1298)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiring_1570 -> T_IsSemiringWithoutOne_1298
MAlonzo.Code.Algebra.Structures.du_isSemiringWithoutOne_1660
         ((T_Semiring_2280 -> T_IsSemiring_1570) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semiring_2280 -> T_IsSemiring_1570
d_isSemiring_2312 (T_Semiring_2280 -> AgdaAny
forall a b. a -> b
coe T_Semiring_2280
v0)))
-- Algebra.Bundles.Semiring._.nearSemiring
d_nearSemiring_2440 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Semiring_2280 -> T_NearSemiring_1766
d_nearSemiring_2440 :: () -> () -> T_Semiring_2280 -> T_NearSemiring_1766
d_nearSemiring_2440 ~()
v0 ~()
v1 T_Semiring_2280
v2 = T_Semiring_2280 -> T_NearSemiring_1766
du_nearSemiring_2440 T_Semiring_2280
v2
du_nearSemiring_2440 :: T_Semiring_2280 -> T_NearSemiring_1766
du_nearSemiring_2440 :: T_Semiring_2280 -> T_NearSemiring_1766
du_nearSemiring_2440 T_Semiring_2280
v0
  = (T_SemiringWithoutOne_1880 -> T_NearSemiring_1766)
-> AgdaAny -> T_NearSemiring_1766
forall a b. a -> b
coe
      T_SemiringWithoutOne_1880 -> T_NearSemiring_1766
du_nearSemiring_1966 ((T_Semiring_2280 -> T_SemiringWithoutOne_1880)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semiring_2280 -> T_SemiringWithoutOne_1880
du_semiringWithoutOne_2436 (T_Semiring_2280 -> AgdaAny
forall a b. a -> b
coe T_Semiring_2280
v0))
-- Algebra.Bundles.CommutativeSemiring
d_CommutativeSemiring_2446 :: p -> p -> ()
d_CommutativeSemiring_2446 p
a0 p
a1 = ()
data T_CommutativeSemiring_2446
  = C_CommutativeSemiring'46'constructor_44731 (AgdaAny ->
                                                AgdaAny -> AgdaAny)
                                               (AgdaAny -> AgdaAny -> AgdaAny) AgdaAny AgdaAny
                                               MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiring_1678
-- Algebra.Bundles.CommutativeSemiring.Carrier
d_Carrier_2466 :: T_CommutativeSemiring_2446 -> ()
d_Carrier_2466 :: T_CommutativeSemiring_2446 -> ()
d_Carrier_2466 = T_CommutativeSemiring_2446 -> ()
forall a. a
erased
-- Algebra.Bundles.CommutativeSemiring._≈_
d__'8776'__2468 ::
  T_CommutativeSemiring_2446 -> AgdaAny -> AgdaAny -> ()
d__'8776'__2468 :: T_CommutativeSemiring_2446 -> AgdaAny -> AgdaAny -> ()
d__'8776'__2468 = T_CommutativeSemiring_2446 -> AgdaAny -> AgdaAny -> ()
forall a. a
erased
-- Algebra.Bundles.CommutativeSemiring._+_
d__'43'__2470 ::
  T_CommutativeSemiring_2446 -> AgdaAny -> AgdaAny -> AgdaAny
d__'43'__2470 :: T_CommutativeSemiring_2446 -> AgdaAny -> AgdaAny -> AgdaAny
d__'43'__2470 T_CommutativeSemiring_2446
v0
  = case T_CommutativeSemiring_2446 -> T_CommutativeSemiring_2446
forall a b. a -> b
coe T_CommutativeSemiring_2446
v0 of
      C_CommutativeSemiring'46'constructor_44731 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny
v5 AgdaAny
v6 T_IsCommutativeSemiring_1678
v7 -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v3
      T_CommutativeSemiring_2446
_ -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.CommutativeSemiring._*_
d__'42'__2472 ::
  T_CommutativeSemiring_2446 -> AgdaAny -> AgdaAny -> AgdaAny
d__'42'__2472 :: T_CommutativeSemiring_2446 -> AgdaAny -> AgdaAny -> AgdaAny
d__'42'__2472 T_CommutativeSemiring_2446
v0
  = case T_CommutativeSemiring_2446 -> T_CommutativeSemiring_2446
forall a b. a -> b
coe T_CommutativeSemiring_2446
v0 of
      C_CommutativeSemiring'46'constructor_44731 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny
v5 AgdaAny
v6 T_IsCommutativeSemiring_1678
v7 -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v4
      T_CommutativeSemiring_2446
_ -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.CommutativeSemiring.0#
d_0'35'_2474 :: T_CommutativeSemiring_2446 -> AgdaAny
d_0'35'_2474 :: T_CommutativeSemiring_2446 -> AgdaAny
d_0'35'_2474 T_CommutativeSemiring_2446
v0
  = case T_CommutativeSemiring_2446 -> T_CommutativeSemiring_2446
forall a b. a -> b
coe T_CommutativeSemiring_2446
v0 of
      C_CommutativeSemiring'46'constructor_44731 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny
v5 AgdaAny
v6 T_IsCommutativeSemiring_1678
v7 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v5
      T_CommutativeSemiring_2446
_ -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.CommutativeSemiring.1#
d_1'35'_2476 :: T_CommutativeSemiring_2446 -> AgdaAny
d_1'35'_2476 :: T_CommutativeSemiring_2446 -> AgdaAny
d_1'35'_2476 T_CommutativeSemiring_2446
v0
  = case T_CommutativeSemiring_2446 -> T_CommutativeSemiring_2446
forall a b. a -> b
coe T_CommutativeSemiring_2446
v0 of
      C_CommutativeSemiring'46'constructor_44731 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny
v5 AgdaAny
v6 T_IsCommutativeSemiring_1678
v7 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v6
      T_CommutativeSemiring_2446
_ -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.CommutativeSemiring.isCommutativeSemiring
d_isCommutativeSemiring_2478 ::
  T_CommutativeSemiring_2446 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiring_1678
d_isCommutativeSemiring_2478 :: T_CommutativeSemiring_2446 -> T_IsCommutativeSemiring_1678
d_isCommutativeSemiring_2478 T_CommutativeSemiring_2446
v0
  = case T_CommutativeSemiring_2446 -> T_CommutativeSemiring_2446
forall a b. a -> b
coe T_CommutativeSemiring_2446
v0 of
      C_CommutativeSemiring'46'constructor_44731 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny
v5 AgdaAny
v6 T_IsCommutativeSemiring_1678
v7 -> T_IsCommutativeSemiring_1678 -> T_IsCommutativeSemiring_1678
forall a b. a -> b
coe T_IsCommutativeSemiring_1678
v7
      T_CommutativeSemiring_2446
_ -> T_IsCommutativeSemiring_1678
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.CommutativeSemiring._.*-assoc
d_'42''45'assoc_2482 ::
  T_CommutativeSemiring_2446 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'assoc_2482 :: T_CommutativeSemiring_2446
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'assoc_2482 T_CommutativeSemiring_2446
v0
  = (T_IsSemiringWithoutAnnihilatingZero_1468
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsSemiringWithoutAnnihilatingZero_1468
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'42''45'assoc_1492
      ((T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
         ((T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570
MAlonzo.Code.Algebra.Structures.d_isSemiring_1692
            ((T_CommutativeSemiring_2446 -> T_IsCommutativeSemiring_1678)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemiring_2446 -> T_IsCommutativeSemiring_1678
d_isCommutativeSemiring_2478 (T_CommutativeSemiring_2446 -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemiring_2446
v0))))
-- Algebra.Bundles.CommutativeSemiring._.*-comm
d_'42''45'comm_2484 ::
  T_CommutativeSemiring_2446 -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'comm_2484 :: T_CommutativeSemiring_2446 -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'comm_2484 T_CommutativeSemiring_2446
v0
  = (T_IsCommutativeSemiring_1678 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsCommutativeSemiring_1678 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'42''45'comm_1694
      ((T_CommutativeSemiring_2446 -> T_IsCommutativeSemiring_1678)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemiring_2446 -> T_IsCommutativeSemiring_1678
d_isCommutativeSemiring_2478 (T_CommutativeSemiring_2446 -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemiring_2446
v0))
-- Algebra.Bundles.CommutativeSemiring._.*-cong
d_'42''45'cong_2486 ::
  T_CommutativeSemiring_2446 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'cong_2486 :: T_CommutativeSemiring_2446
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'42''45'cong_2486 T_CommutativeSemiring_2446
v0
  = (T_IsSemiringWithoutAnnihilatingZero_1468
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsSemiringWithoutAnnihilatingZero_1468
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'42''45'cong_1490
      ((T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
         ((T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570
MAlonzo.Code.Algebra.Structures.d_isSemiring_1692
            ((T_CommutativeSemiring_2446 -> T_IsCommutativeSemiring_1678)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemiring_2446 -> T_IsCommutativeSemiring_1678
d_isCommutativeSemiring_2478 (T_CommutativeSemiring_2446 -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemiring_2446
v0))))
-- Algebra.Bundles.CommutativeSemiring._.∙-congʳ
d_'8729''45'cong'691'_2488 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeSemiring_2446 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_2488 :: ()
-> ()
-> T_CommutativeSemiring_2446
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_2488 ~()
v0 ~()
v1 T_CommutativeSemiring_2446
v2
  = T_CommutativeSemiring_2446
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_2488 T_CommutativeSemiring_2446
v2
du_'8729''45'cong'691'_2488 ::
  T_CommutativeSemiring_2446 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_2488 :: T_CommutativeSemiring_2446
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_2488 T_CommutativeSemiring_2446
v0
  = let v1 :: T_IsCommutativeSemiring_1678
v1 = T_CommutativeSemiring_2446 -> T_IsCommutativeSemiring_1678
d_isCommutativeSemiring_2478 (T_CommutativeSemiring_2446 -> T_CommutativeSemiring_2446
forall a b. a -> b
coe T_CommutativeSemiring_2446
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemiring_1570
v2
             = T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570
MAlonzo.Code.Algebra.Structures.d_isSemiring_1692 (T_IsCommutativeSemiring_1678 -> T_IsCommutativeSemiring_1678
forall a b. a -> b
coe T_IsCommutativeSemiring_1678
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemiringWithoutAnnihilatingZero_1468
v3
                = T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                    (T_IsSemiring_1570 -> T_IsSemiring_1570
forall a b. a -> b
coe T_IsSemiring_1570
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: t
v4
                   = (T_IsSemiringWithoutAnnihilatingZero_1468 -> T_IsMonoid_686)
-> AgdaAny -> t
forall a b. a -> b
coe
                       T_IsSemiringWithoutAnnihilatingZero_1468 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.du_'42''45'isMonoid_1550
                       (T_IsSemiringWithoutAnnihilatingZero_1468 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsSemigroup_472
v5
                      = T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (AgdaAny -> T_IsMonoid_686
forall a b. a -> b
coe AgdaAny
forall a. a
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'691'_206
                     ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v5)))))))
-- Algebra.Bundles.CommutativeSemiring._.∙-congˡ
d_'8729''45'cong'737'_2490 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeSemiring_2446 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_2490 :: ()
-> ()
-> T_CommutativeSemiring_2446
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_2490 ~()
v0 ~()
v1 T_CommutativeSemiring_2446
v2
  = T_CommutativeSemiring_2446
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_2490 T_CommutativeSemiring_2446
v2
du_'8729''45'cong'737'_2490 ::
  T_CommutativeSemiring_2446 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_2490 :: T_CommutativeSemiring_2446
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_2490 T_CommutativeSemiring_2446
v0
  = let v1 :: T_IsCommutativeSemiring_1678
v1 = T_CommutativeSemiring_2446 -> T_IsCommutativeSemiring_1678
d_isCommutativeSemiring_2478 (T_CommutativeSemiring_2446 -> T_CommutativeSemiring_2446
forall a b. a -> b
coe T_CommutativeSemiring_2446
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemiring_1570
v2
             = T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570
MAlonzo.Code.Algebra.Structures.d_isSemiring_1692 (T_IsCommutativeSemiring_1678 -> T_IsCommutativeSemiring_1678
forall a b. a -> b
coe T_IsCommutativeSemiring_1678
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemiringWithoutAnnihilatingZero_1468
v3
                = T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                    (T_IsSemiring_1570 -> T_IsSemiring_1570
forall a b. a -> b
coe T_IsSemiring_1570
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: t
v4
                   = (T_IsSemiringWithoutAnnihilatingZero_1468 -> T_IsMonoid_686)
-> AgdaAny -> t
forall a b. a -> b
coe
                       T_IsSemiringWithoutAnnihilatingZero_1468 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.du_'42''45'isMonoid_1550
                       (T_IsSemiringWithoutAnnihilatingZero_1468 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsSemigroup_472
v5
                      = T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (AgdaAny -> T_IsMonoid_686
forall a b. a -> b
coe AgdaAny
forall a. a
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'737'_202
                     ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v5)))))))
-- Algebra.Bundles.CommutativeSemiring._.*-identity
d_'42''45'identity_2492 ::
  T_CommutativeSemiring_2446 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'42''45'identity_2492 :: T_CommutativeSemiring_2446 -> T_Σ_14
d_'42''45'identity_2492 T_CommutativeSemiring_2446
v0
  = (T_IsSemiringWithoutAnnihilatingZero_1468 -> T_Σ_14)
-> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsSemiringWithoutAnnihilatingZero_1468 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_'42''45'identity_1494
      ((T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
         ((T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570
MAlonzo.Code.Algebra.Structures.d_isSemiring_1692
            ((T_CommutativeSemiring_2446 -> T_IsCommutativeSemiring_1678)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemiring_2446 -> T_IsCommutativeSemiring_1678
d_isCommutativeSemiring_2478 (T_CommutativeSemiring_2446 -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemiring_2446
v0))))
-- Algebra.Bundles.CommutativeSemiring._.identityʳ
d_identity'691'_2494 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeSemiring_2446 -> AgdaAny -> AgdaAny
d_identity'691'_2494 :: () -> () -> T_CommutativeSemiring_2446 -> AgdaAny -> AgdaAny
d_identity'691'_2494 ~()
v0 ~()
v1 T_CommutativeSemiring_2446
v2 = T_CommutativeSemiring_2446 -> AgdaAny -> AgdaAny
du_identity'691'_2494 T_CommutativeSemiring_2446
v2
du_identity'691'_2494 ::
  T_CommutativeSemiring_2446 -> AgdaAny -> AgdaAny
du_identity'691'_2494 :: T_CommutativeSemiring_2446 -> AgdaAny -> AgdaAny
du_identity'691'_2494 T_CommutativeSemiring_2446
v0
  = let v1 :: T_IsCommutativeSemiring_1678
v1 = T_CommutativeSemiring_2446 -> T_IsCommutativeSemiring_1678
d_isCommutativeSemiring_2478 (T_CommutativeSemiring_2446 -> T_CommutativeSemiring_2446
forall a b. a -> b
coe T_CommutativeSemiring_2446
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemiring_1570
v2
             = T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570
MAlonzo.Code.Algebra.Structures.d_isSemiring_1692 (T_IsCommutativeSemiring_1678 -> T_IsCommutativeSemiring_1678
forall a b. a -> b
coe T_IsCommutativeSemiring_1678
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemiringWithoutAnnihilatingZero_1468
v3
                = T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                    (T_IsSemiring_1570 -> T_IsSemiring_1570
forall a b. a -> b
coe T_IsSemiring_1570
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsMonoid_686 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_686 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_identity'691'_728
               ((T_IsSemiringWithoutAnnihilatingZero_1468 -> T_IsMonoid_686)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsSemiringWithoutAnnihilatingZero_1468 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.du_'42''45'isMonoid_1550
                  (T_IsSemiringWithoutAnnihilatingZero_1468 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
v3)))))
-- Algebra.Bundles.CommutativeSemiring._.identityˡ
d_identity'737'_2496 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeSemiring_2446 -> AgdaAny -> AgdaAny
d_identity'737'_2496 :: () -> () -> T_CommutativeSemiring_2446 -> AgdaAny -> AgdaAny
d_identity'737'_2496 ~()
v0 ~()
v1 T_CommutativeSemiring_2446
v2 = T_CommutativeSemiring_2446 -> AgdaAny -> AgdaAny
du_identity'737'_2496 T_CommutativeSemiring_2446
v2
du_identity'737'_2496 ::
  T_CommutativeSemiring_2446 -> AgdaAny -> AgdaAny
du_identity'737'_2496 :: T_CommutativeSemiring_2446 -> AgdaAny -> AgdaAny
du_identity'737'_2496 T_CommutativeSemiring_2446
v0
  = let v1 :: T_IsCommutativeSemiring_1678
v1 = T_CommutativeSemiring_2446 -> T_IsCommutativeSemiring_1678
d_isCommutativeSemiring_2478 (T_CommutativeSemiring_2446 -> T_CommutativeSemiring_2446
forall a b. a -> b
coe T_CommutativeSemiring_2446
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemiring_1570
v2
             = T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570
MAlonzo.Code.Algebra.Structures.d_isSemiring_1692 (T_IsCommutativeSemiring_1678 -> T_IsCommutativeSemiring_1678
forall a b. a -> b
coe T_IsCommutativeSemiring_1678
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemiringWithoutAnnihilatingZero_1468
v3
                = T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                    (T_IsSemiring_1570 -> T_IsSemiring_1570
forall a b. a -> b
coe T_IsSemiring_1570
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsMonoid_686 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_686 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_identity'737'_726
               ((T_IsSemiringWithoutAnnihilatingZero_1468 -> T_IsMonoid_686)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsSemiringWithoutAnnihilatingZero_1468 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.du_'42''45'isMonoid_1550
                  (T_IsSemiringWithoutAnnihilatingZero_1468 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
v3)))))
-- Algebra.Bundles.CommutativeSemiring._.isCommutativeMagma
d_isCommutativeMagma_2498 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeSemiring_2446 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMagma_212
d_isCommutativeMagma_2498 :: () -> () -> T_CommutativeSemiring_2446 -> T_IsCommutativeMagma_212
d_isCommutativeMagma_2498 ~()
v0 ~()
v1 T_CommutativeSemiring_2446
v2
  = T_CommutativeSemiring_2446 -> T_IsCommutativeMagma_212
du_isCommutativeMagma_2498 T_CommutativeSemiring_2446
v2
du_isCommutativeMagma_2498 ::
  T_CommutativeSemiring_2446 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMagma_212
du_isCommutativeMagma_2498 :: T_CommutativeSemiring_2446 -> T_IsCommutativeMagma_212
du_isCommutativeMagma_2498 T_CommutativeSemiring_2446
v0
  = let v1 :: T_IsCommutativeSemiring_1678
v1 = T_CommutativeSemiring_2446 -> T_IsCommutativeSemiring_1678
d_isCommutativeSemiring_2478 (T_CommutativeSemiring_2446 -> T_CommutativeSemiring_2446
forall a b. a -> b
coe T_CommutativeSemiring_2446
v0) in
    AgdaAny -> T_IsCommutativeMagma_212
forall a b. a -> b
coe
      (let v2 :: t
v2
             = (T_IsCommutativeSemiring_1678
 -> T_IsCommutativeSemiringWithoutOne_1382)
-> AgdaAny -> t
forall a b. a -> b
coe
                 T_IsCommutativeSemiring_1678
-> T_IsCommutativeSemiringWithoutOne_1382
MAlonzo.Code.Algebra.Structures.du_isCommutativeSemiringWithoutOne_1780
                 (T_IsCommutativeSemiring_1678 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiring_1678
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsCommutativeSemigroup_548 -> T_IsCommutativeMagma_212)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCommutativeSemigroup_548 -> T_IsCommutativeMagma_212
MAlonzo.Code.Algebra.Structures.du_isCommutativeMagma_586
            ((T_IsCommutativeSemiringWithoutOne_1382
 -> T_IsCommutativeSemigroup_548)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsCommutativeSemiringWithoutOne_1382
-> T_IsCommutativeSemigroup_548
MAlonzo.Code.Algebra.Structures.du_'42''45'isCommutativeSemigroup_1454
               (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2))))
-- Algebra.Bundles.CommutativeSemiring._.*-isCommutativeMonoid
d_'42''45'isCommutativeMonoid_2500 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeSemiring_2446 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMonoid_736
d_'42''45'isCommutativeMonoid_2500 :: () -> () -> T_CommutativeSemiring_2446 -> T_IsCommutativeMonoid_736
d_'42''45'isCommutativeMonoid_2500 ~()
v0 ~()
v1 T_CommutativeSemiring_2446
v2
  = T_CommutativeSemiring_2446 -> T_IsCommutativeMonoid_736
du_'42''45'isCommutativeMonoid_2500 T_CommutativeSemiring_2446
v2
du_'42''45'isCommutativeMonoid_2500 ::
  T_CommutativeSemiring_2446 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMonoid_736
du_'42''45'isCommutativeMonoid_2500 :: T_CommutativeSemiring_2446 -> T_IsCommutativeMonoid_736
du_'42''45'isCommutativeMonoid_2500 T_CommutativeSemiring_2446
v0
  = (T_IsCommutativeSemiring_1678 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> T_IsCommutativeMonoid_736
forall a b. a -> b
coe
      T_IsCommutativeSemiring_1678 -> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.du_'42''45'isCommutativeMonoid_1788
      ((T_CommutativeSemiring_2446 -> T_IsCommutativeSemiring_1678)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemiring_2446 -> T_IsCommutativeSemiring_1678
d_isCommutativeSemiring_2478 (T_CommutativeSemiring_2446 -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemiring_2446
v0))
-- Algebra.Bundles.CommutativeSemiring._.*-isCommutativeSemigroup
d_'42''45'isCommutativeSemigroup_2502 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeSemiring_2446 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_548
d_'42''45'isCommutativeSemigroup_2502 :: ()
-> () -> T_CommutativeSemiring_2446 -> T_IsCommutativeSemigroup_548
d_'42''45'isCommutativeSemigroup_2502 ~()
v0 ~()
v1 T_CommutativeSemiring_2446
v2
  = T_CommutativeSemiring_2446 -> T_IsCommutativeSemigroup_548
du_'42''45'isCommutativeSemigroup_2502 T_CommutativeSemiring_2446
v2
du_'42''45'isCommutativeSemigroup_2502 ::
  T_CommutativeSemiring_2446 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_548
du_'42''45'isCommutativeSemigroup_2502 :: T_CommutativeSemiring_2446 -> T_IsCommutativeSemigroup_548
du_'42''45'isCommutativeSemigroup_2502 T_CommutativeSemiring_2446
v0
  = let v1 :: T_IsCommutativeSemiring_1678
v1 = T_CommutativeSemiring_2446 -> T_IsCommutativeSemiring_1678
d_isCommutativeSemiring_2478 (T_CommutativeSemiring_2446 -> T_CommutativeSemiring_2446
forall a b. a -> b
coe T_CommutativeSemiring_2446
v0) in
    AgdaAny -> T_IsCommutativeSemigroup_548
forall a b. a -> b
coe
      ((T_IsCommutativeSemiringWithoutOne_1382
 -> T_IsCommutativeSemigroup_548)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCommutativeSemiringWithoutOne_1382
-> T_IsCommutativeSemigroup_548
MAlonzo.Code.Algebra.Structures.du_'42''45'isCommutativeSemigroup_1454
         ((T_IsCommutativeSemiring_1678
 -> T_IsCommutativeSemiringWithoutOne_1382)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCommutativeSemiring_1678
-> T_IsCommutativeSemiringWithoutOne_1382
MAlonzo.Code.Algebra.Structures.du_isCommutativeSemiringWithoutOne_1780
            (T_IsCommutativeSemiring_1678 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiring_1678
v1)))
-- Algebra.Bundles.CommutativeSemiring._.*-isMagma
d_'42''45'isMagma_2504 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeSemiring_2446 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_176
d_'42''45'isMagma_2504 :: () -> () -> T_CommutativeSemiring_2446 -> T_IsMagma_176
d_'42''45'isMagma_2504 ~()
v0 ~()
v1 T_CommutativeSemiring_2446
v2 = T_CommutativeSemiring_2446 -> T_IsMagma_176
du_'42''45'isMagma_2504 T_CommutativeSemiring_2446
v2
du_'42''45'isMagma_2504 ::
  T_CommutativeSemiring_2446 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_176
du_'42''45'isMagma_2504 :: T_CommutativeSemiring_2446 -> T_IsMagma_176
du_'42''45'isMagma_2504 T_CommutativeSemiring_2446
v0
  = let v1 :: T_IsCommutativeSemiring_1678
v1 = T_CommutativeSemiring_2446 -> T_IsCommutativeSemiring_1678
d_isCommutativeSemiring_2478 (T_CommutativeSemiring_2446 -> T_CommutativeSemiring_2446
forall a b. a -> b
coe T_CommutativeSemiring_2446
v0) in
    AgdaAny -> T_IsMagma_176
forall a b. a -> b
coe
      (let v2 :: T_IsSemiring_1570
v2
             = T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570
MAlonzo.Code.Algebra.Structures.d_isSemiring_1692 (T_IsCommutativeSemiring_1678 -> T_IsCommutativeSemiring_1678
forall a b. a -> b
coe T_IsCommutativeSemiring_1678
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsSemiringWithoutAnnihilatingZero_1468 -> T_IsMagma_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemiringWithoutAnnihilatingZero_1468 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.du_'42''45'isMagma_1546
            ((T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
               (T_IsSemiring_1570 -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1570
v2))))
-- Algebra.Bundles.CommutativeSemiring._.*-isMonoid
d_'42''45'isMonoid_2506 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeSemiring_2446 ->
  MAlonzo.Code.Algebra.Structures.T_IsMonoid_686
d_'42''45'isMonoid_2506 :: () -> () -> T_CommutativeSemiring_2446 -> T_IsMonoid_686
d_'42''45'isMonoid_2506 ~()
v0 ~()
v1 T_CommutativeSemiring_2446
v2 = T_CommutativeSemiring_2446 -> T_IsMonoid_686
du_'42''45'isMonoid_2506 T_CommutativeSemiring_2446
v2
du_'42''45'isMonoid_2506 ::
  T_CommutativeSemiring_2446 ->
  MAlonzo.Code.Algebra.Structures.T_IsMonoid_686
du_'42''45'isMonoid_2506 :: T_CommutativeSemiring_2446 -> T_IsMonoid_686
du_'42''45'isMonoid_2506 T_CommutativeSemiring_2446
v0
  = let v1 :: T_IsCommutativeSemiring_1678
v1 = T_CommutativeSemiring_2446 -> T_IsCommutativeSemiring_1678
d_isCommutativeSemiring_2478 (T_CommutativeSemiring_2446 -> T_CommutativeSemiring_2446
forall a b. a -> b
coe T_CommutativeSemiring_2446
v0) in
    AgdaAny -> T_IsMonoid_686
forall a b. a -> b
coe
      (let v2 :: T_IsSemiring_1570
v2
             = T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570
MAlonzo.Code.Algebra.Structures.d_isSemiring_1692 (T_IsCommutativeSemiring_1678 -> T_IsCommutativeSemiring_1678
forall a b. a -> b
coe T_IsCommutativeSemiring_1678
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsSemiringWithoutAnnihilatingZero_1468 -> T_IsMonoid_686)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemiringWithoutAnnihilatingZero_1468 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.du_'42''45'isMonoid_1550
            ((T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
               (T_IsSemiring_1570 -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1570
v2))))
-- Algebra.Bundles.CommutativeSemiring._.*-isSemigroup
d_'42''45'isSemigroup_2508 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeSemiring_2446 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_472
d_'42''45'isSemigroup_2508 :: () -> () -> T_CommutativeSemiring_2446 -> T_IsSemigroup_472
d_'42''45'isSemigroup_2508 ~()
v0 ~()
v1 T_CommutativeSemiring_2446
v2
  = T_CommutativeSemiring_2446 -> T_IsSemigroup_472
du_'42''45'isSemigroup_2508 T_CommutativeSemiring_2446
v2
du_'42''45'isSemigroup_2508 ::
  T_CommutativeSemiring_2446 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_472
du_'42''45'isSemigroup_2508 :: T_CommutativeSemiring_2446 -> T_IsSemigroup_472
du_'42''45'isSemigroup_2508 T_CommutativeSemiring_2446
v0
  = let v1 :: T_IsCommutativeSemiring_1678
v1 = T_CommutativeSemiring_2446 -> T_IsCommutativeSemiring_1678
d_isCommutativeSemiring_2478 (T_CommutativeSemiring_2446 -> T_CommutativeSemiring_2446
forall a b. a -> b
coe T_CommutativeSemiring_2446
v0) in
    AgdaAny -> T_IsSemigroup_472
forall a b. a -> b
coe
      (let v2 :: T_IsSemiring_1570
v2
             = T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570
MAlonzo.Code.Algebra.Structures.d_isSemiring_1692 (T_IsCommutativeSemiring_1678 -> T_IsCommutativeSemiring_1678
forall a b. a -> b
coe T_IsCommutativeSemiring_1678
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsSemiringWithoutAnnihilatingZero_1468 -> T_IsSemigroup_472)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemiringWithoutAnnihilatingZero_1468 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.du_'42''45'isSemigroup_1548
            ((T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
               (T_IsSemiring_1570 -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1570
v2))))
-- Algebra.Bundles.CommutativeSemiring._.assoc
d_assoc_2510 ::
  T_CommutativeSemiring_2446 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_2510 :: T_CommutativeSemiring_2446
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_2510 T_CommutativeSemiring_2446
v0
  = (T_IsSemigroup_472 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsSemigroup_472 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_assoc_482
      ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
         ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746
            ((T_IsSemiringWithoutAnnihilatingZero_1468
 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
               ((T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                  ((T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570
MAlonzo.Code.Algebra.Structures.d_isSemiring_1692
                     ((T_CommutativeSemiring_2446 -> T_IsCommutativeSemiring_1678)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemiring_2446 -> T_IsCommutativeSemiring_1678
d_isCommutativeSemiring_2478 (T_CommutativeSemiring_2446 -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemiring_2446
v0)))))))
-- Algebra.Bundles.CommutativeSemiring._.comm
d_comm_2512 ::
  T_CommutativeSemiring_2446 -> AgdaAny -> AgdaAny -> AgdaAny
d_comm_2512 :: T_CommutativeSemiring_2446 -> AgdaAny -> AgdaAny -> AgdaAny
d_comm_2512 T_CommutativeSemiring_2446
v0
  = (T_IsCommutativeMonoid_736 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsCommutativeMonoid_736 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_comm_748
      ((T_IsSemiringWithoutAnnihilatingZero_1468
 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
         ((T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
            ((T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570
MAlonzo.Code.Algebra.Structures.d_isSemiring_1692
               ((T_CommutativeSemiring_2446 -> T_IsCommutativeSemiring_1678)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemiring_2446 -> T_IsCommutativeSemiring_1678
d_isCommutativeSemiring_2478 (T_CommutativeSemiring_2446 -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemiring_2446
v0)))))
-- Algebra.Bundles.CommutativeSemiring._.∙-cong
d_'8729''45'cong_2514 ::
  T_CommutativeSemiring_2446 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_2514 :: T_CommutativeSemiring_2446
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_2514 T_CommutativeSemiring_2446
v0
  = (T_IsMagma_176
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsMagma_176
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_186
      ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480
         ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
            ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746
               ((T_IsSemiringWithoutAnnihilatingZero_1468
 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
                  ((T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                     ((T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570
MAlonzo.Code.Algebra.Structures.d_isSemiring_1692
                        ((T_CommutativeSemiring_2446 -> T_IsCommutativeSemiring_1678)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemiring_2446 -> T_IsCommutativeSemiring_1678
d_isCommutativeSemiring_2478 (T_CommutativeSemiring_2446 -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemiring_2446
v0))))))))
-- Algebra.Bundles.CommutativeSemiring._.∙-congʳ
d_'8729''45'cong'691'_2516 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeSemiring_2446 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_2516 :: ()
-> ()
-> T_CommutativeSemiring_2446
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_2516 ~()
v0 ~()
v1 T_CommutativeSemiring_2446
v2
  = T_CommutativeSemiring_2446
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_2516 T_CommutativeSemiring_2446
v2
du_'8729''45'cong'691'_2516 ::
  T_CommutativeSemiring_2446 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_2516 :: T_CommutativeSemiring_2446
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_2516 T_CommutativeSemiring_2446
v0
  = let v1 :: T_IsCommutativeSemiring_1678
v1 = T_CommutativeSemiring_2446 -> T_IsCommutativeSemiring_1678
d_isCommutativeSemiring_2478 (T_CommutativeSemiring_2446 -> T_CommutativeSemiring_2446
forall a b. a -> b
coe T_CommutativeSemiring_2446
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemiring_1570
v2
             = T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570
MAlonzo.Code.Algebra.Structures.d_isSemiring_1692 (T_IsCommutativeSemiring_1678 -> T_IsCommutativeSemiring_1678
forall a b. a -> b
coe T_IsCommutativeSemiring_1678
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemiringWithoutAnnihilatingZero_1468
v3
                = T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                    (T_IsSemiring_1570 -> T_IsSemiring_1570
forall a b. a -> b
coe T_IsSemiring_1570
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsCommutativeMonoid_736
v4
                   = T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
                       (T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsSemiringWithoutAnnihilatingZero_1468
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsMonoid_686
v5
                      = T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746 (T_IsCommutativeMonoid_736 -> T_IsCommutativeMonoid_736
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (let v6 :: T_IsSemigroup_472
v6
                         = T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v5) in
                   AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'691'_206
                        ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v6))))))))
-- Algebra.Bundles.CommutativeSemiring._.∙-congˡ
d_'8729''45'cong'737'_2518 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeSemiring_2446 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_2518 :: ()
-> ()
-> T_CommutativeSemiring_2446
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_2518 ~()
v0 ~()
v1 T_CommutativeSemiring_2446
v2
  = T_CommutativeSemiring_2446
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_2518 T_CommutativeSemiring_2446
v2
du_'8729''45'cong'737'_2518 ::
  T_CommutativeSemiring_2446 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_2518 :: T_CommutativeSemiring_2446
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_2518 T_CommutativeSemiring_2446
v0
  = let v1 :: T_IsCommutativeSemiring_1678
v1 = T_CommutativeSemiring_2446 -> T_IsCommutativeSemiring_1678
d_isCommutativeSemiring_2478 (T_CommutativeSemiring_2446 -> T_CommutativeSemiring_2446
forall a b. a -> b
coe T_CommutativeSemiring_2446
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemiring_1570
v2
             = T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570
MAlonzo.Code.Algebra.Structures.d_isSemiring_1692 (T_IsCommutativeSemiring_1678 -> T_IsCommutativeSemiring_1678
forall a b. a -> b
coe T_IsCommutativeSemiring_1678
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemiringWithoutAnnihilatingZero_1468
v3
                = T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                    (T_IsSemiring_1570 -> T_IsSemiring_1570
forall a b. a -> b
coe T_IsSemiring_1570
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsCommutativeMonoid_736
v4
                   = T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
                       (T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsSemiringWithoutAnnihilatingZero_1468
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsMonoid_686
v5
                      = T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746 (T_IsCommutativeMonoid_736 -> T_IsCommutativeMonoid_736
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (let v6 :: T_IsSemigroup_472
v6
                         = T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v5) in
                   AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'737'_202
                        ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v6))))))))
-- Algebra.Bundles.CommutativeSemiring._.identity
d_identity_2520 ::
  T_CommutativeSemiring_2446 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_identity_2520 :: T_CommutativeSemiring_2446 -> T_Σ_14
d_identity_2520 T_CommutativeSemiring_2446
v0
  = (T_IsMonoid_686 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsMonoid_686 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_identity_698
      ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746
         ((T_IsSemiringWithoutAnnihilatingZero_1468
 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
            ((T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
               ((T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570
MAlonzo.Code.Algebra.Structures.d_isSemiring_1692
                  ((T_CommutativeSemiring_2446 -> T_IsCommutativeSemiring_1678)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemiring_2446 -> T_IsCommutativeSemiring_1678
d_isCommutativeSemiring_2478 (T_CommutativeSemiring_2446 -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemiring_2446
v0))))))
-- Algebra.Bundles.CommutativeSemiring._.identityʳ
d_identity'691'_2522 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeSemiring_2446 -> AgdaAny -> AgdaAny
d_identity'691'_2522 :: () -> () -> T_CommutativeSemiring_2446 -> AgdaAny -> AgdaAny
d_identity'691'_2522 ~()
v0 ~()
v1 T_CommutativeSemiring_2446
v2 = T_CommutativeSemiring_2446 -> AgdaAny -> AgdaAny
du_identity'691'_2522 T_CommutativeSemiring_2446
v2
du_identity'691'_2522 ::
  T_CommutativeSemiring_2446 -> AgdaAny -> AgdaAny
du_identity'691'_2522 :: T_CommutativeSemiring_2446 -> AgdaAny -> AgdaAny
du_identity'691'_2522 T_CommutativeSemiring_2446
v0
  = let v1 :: T_IsCommutativeSemiring_1678
v1 = T_CommutativeSemiring_2446 -> T_IsCommutativeSemiring_1678
d_isCommutativeSemiring_2478 (T_CommutativeSemiring_2446 -> T_CommutativeSemiring_2446
forall a b. a -> b
coe T_CommutativeSemiring_2446
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemiring_1570
v2
             = T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570
MAlonzo.Code.Algebra.Structures.d_isSemiring_1692 (T_IsCommutativeSemiring_1678 -> T_IsCommutativeSemiring_1678
forall a b. a -> b
coe T_IsCommutativeSemiring_1678
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemiringWithoutAnnihilatingZero_1468
v3
                = T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                    (T_IsSemiring_1570 -> T_IsSemiring_1570
forall a b. a -> b
coe T_IsSemiring_1570
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsCommutativeMonoid_736
v4
                   = T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
                       (T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsSemiringWithoutAnnihilatingZero_1468
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               ((T_IsMonoid_686 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsMonoid_686 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_identity'691'_728
                  ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746 (T_IsCommutativeMonoid_736 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v4))))))
-- Algebra.Bundles.CommutativeSemiring._.identityˡ
d_identity'737'_2524 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeSemiring_2446 -> AgdaAny -> AgdaAny
d_identity'737'_2524 :: () -> () -> T_CommutativeSemiring_2446 -> AgdaAny -> AgdaAny
d_identity'737'_2524 ~()
v0 ~()
v1 T_CommutativeSemiring_2446
v2 = T_CommutativeSemiring_2446 -> AgdaAny -> AgdaAny
du_identity'737'_2524 T_CommutativeSemiring_2446
v2
du_identity'737'_2524 ::
  T_CommutativeSemiring_2446 -> AgdaAny -> AgdaAny
du_identity'737'_2524 :: T_CommutativeSemiring_2446 -> AgdaAny -> AgdaAny
du_identity'737'_2524 T_CommutativeSemiring_2446
v0
  = let v1 :: T_IsCommutativeSemiring_1678
v1 = T_CommutativeSemiring_2446 -> T_IsCommutativeSemiring_1678
d_isCommutativeSemiring_2478 (T_CommutativeSemiring_2446 -> T_CommutativeSemiring_2446
forall a b. a -> b
coe T_CommutativeSemiring_2446
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemiring_1570
v2
             = T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570
MAlonzo.Code.Algebra.Structures.d_isSemiring_1692 (T_IsCommutativeSemiring_1678 -> T_IsCommutativeSemiring_1678
forall a b. a -> b
coe T_IsCommutativeSemiring_1678
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemiringWithoutAnnihilatingZero_1468
v3
                = T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                    (T_IsSemiring_1570 -> T_IsSemiring_1570
forall a b. a -> b
coe T_IsSemiring_1570
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsCommutativeMonoid_736
v4
                   = T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
                       (T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsSemiringWithoutAnnihilatingZero_1468
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               ((T_IsMonoid_686 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsMonoid_686 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_identity'737'_726
                  ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746 (T_IsCommutativeMonoid_736 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v4))))))
-- Algebra.Bundles.CommutativeSemiring._.isCommutativeMagma
d_isCommutativeMagma_2526 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeSemiring_2446 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMagma_212
d_isCommutativeMagma_2526 :: () -> () -> T_CommutativeSemiring_2446 -> T_IsCommutativeMagma_212
d_isCommutativeMagma_2526 ~()
v0 ~()
v1 T_CommutativeSemiring_2446
v2
  = T_CommutativeSemiring_2446 -> T_IsCommutativeMagma_212
du_isCommutativeMagma_2526 T_CommutativeSemiring_2446
v2
du_isCommutativeMagma_2526 ::
  T_CommutativeSemiring_2446 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMagma_212
du_isCommutativeMagma_2526 :: T_CommutativeSemiring_2446 -> T_IsCommutativeMagma_212
du_isCommutativeMagma_2526 T_CommutativeSemiring_2446
v0
  = let v1 :: T_IsCommutativeSemiring_1678
v1 = T_CommutativeSemiring_2446 -> T_IsCommutativeSemiring_1678
d_isCommutativeSemiring_2478 (T_CommutativeSemiring_2446 -> T_CommutativeSemiring_2446
forall a b. a -> b
coe T_CommutativeSemiring_2446
v0) in
    AgdaAny -> T_IsCommutativeMagma_212
forall a b. a -> b
coe
      (let v2 :: T_IsSemiring_1570
v2
             = T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570
MAlonzo.Code.Algebra.Structures.d_isSemiring_1692 (T_IsCommutativeSemiring_1678 -> T_IsCommutativeSemiring_1678
forall a b. a -> b
coe T_IsCommutativeSemiring_1678
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemiringWithoutAnnihilatingZero_1468
v3
                = T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                    (T_IsSemiring_1570 -> T_IsSemiring_1570
forall a b. a -> b
coe T_IsSemiring_1570
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsCommutativeMonoid_736
v4
                   = T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
                       (T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsSemiringWithoutAnnihilatingZero_1468
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               ((T_IsCommutativeSemigroup_548 -> T_IsCommutativeMagma_212)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsCommutativeSemigroup_548 -> T_IsCommutativeMagma_212
MAlonzo.Code.Algebra.Structures.du_isCommutativeMagma_586
                  ((T_IsCommutativeMonoid_736 -> T_IsCommutativeSemigroup_548)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsCommutativeMonoid_736 -> T_IsCommutativeSemigroup_548
MAlonzo.Code.Algebra.Structures.du_isCommutativeSemigroup_786
                     (T_IsCommutativeMonoid_736 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v4))))))
-- Algebra.Bundles.CommutativeSemiring._.+-isCommutativeMonoid
d_'43''45'isCommutativeMonoid_2528 ::
  T_CommutativeSemiring_2446 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_2528 :: T_CommutativeSemiring_2446 -> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_2528 T_CommutativeSemiring_2446
v0
  = (T_IsSemiringWithoutAnnihilatingZero_1468
 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> T_IsCommutativeMonoid_736
forall a b. a -> b
coe
      T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
      ((T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
         ((T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570
MAlonzo.Code.Algebra.Structures.d_isSemiring_1692
            ((T_CommutativeSemiring_2446 -> T_IsCommutativeSemiring_1678)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemiring_2446 -> T_IsCommutativeSemiring_1678
d_isCommutativeSemiring_2478 (T_CommutativeSemiring_2446 -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemiring_2446
v0))))
-- Algebra.Bundles.CommutativeSemiring._.isCommutativeSemigroup
d_isCommutativeSemigroup_2530 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeSemiring_2446 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_548
d_isCommutativeSemigroup_2530 :: ()
-> () -> T_CommutativeSemiring_2446 -> T_IsCommutativeSemigroup_548
d_isCommutativeSemigroup_2530 ~()
v0 ~()
v1 T_CommutativeSemiring_2446
v2
  = T_CommutativeSemiring_2446 -> T_IsCommutativeSemigroup_548
du_isCommutativeSemigroup_2530 T_CommutativeSemiring_2446
v2
du_isCommutativeSemigroup_2530 ::
  T_CommutativeSemiring_2446 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_548
du_isCommutativeSemigroup_2530 :: T_CommutativeSemiring_2446 -> T_IsCommutativeSemigroup_548
du_isCommutativeSemigroup_2530 T_CommutativeSemiring_2446
v0
  = let v1 :: T_IsCommutativeSemiring_1678
v1 = T_CommutativeSemiring_2446 -> T_IsCommutativeSemiring_1678
d_isCommutativeSemiring_2478 (T_CommutativeSemiring_2446 -> T_CommutativeSemiring_2446
forall a b. a -> b
coe T_CommutativeSemiring_2446
v0) in
    AgdaAny -> T_IsCommutativeSemigroup_548
forall a b. a -> b
coe
      (let v2 :: T_IsSemiring_1570
v2
             = T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570
MAlonzo.Code.Algebra.Structures.d_isSemiring_1692 (T_IsCommutativeSemiring_1678 -> T_IsCommutativeSemiring_1678
forall a b. a -> b
coe T_IsCommutativeSemiring_1678
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemiringWithoutAnnihilatingZero_1468
v3
                = T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                    (T_IsSemiring_1570 -> T_IsSemiring_1570
forall a b. a -> b
coe T_IsSemiring_1570
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsCommutativeMonoid_736 -> T_IsCommutativeSemigroup_548)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsCommutativeMonoid_736 -> T_IsCommutativeSemigroup_548
MAlonzo.Code.Algebra.Structures.du_isCommutativeSemigroup_786
               ((T_IsSemiringWithoutAnnihilatingZero_1468
 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
                  (T_IsSemiringWithoutAnnihilatingZero_1468 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
v3)))))
-- Algebra.Bundles.CommutativeSemiring._.isMagma
d_isMagma_2532 ::
  T_CommutativeSemiring_2446 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_176
d_isMagma_2532 :: T_CommutativeSemiring_2446 -> T_IsMagma_176
d_isMagma_2532 T_CommutativeSemiring_2446
v0
  = (T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> T_IsMagma_176
forall a b. a -> b
coe
      T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480
      ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
         ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746
            ((T_IsSemiringWithoutAnnihilatingZero_1468
 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
               ((T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                  ((T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570
MAlonzo.Code.Algebra.Structures.d_isSemiring_1692
                     ((T_CommutativeSemiring_2446 -> T_IsCommutativeSemiring_1678)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemiring_2446 -> T_IsCommutativeSemiring_1678
d_isCommutativeSemiring_2478 (T_CommutativeSemiring_2446 -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemiring_2446
v0)))))))
-- Algebra.Bundles.CommutativeSemiring._.isMonoid
d_isMonoid_2534 ::
  T_CommutativeSemiring_2446 ->
  MAlonzo.Code.Algebra.Structures.T_IsMonoid_686
d_isMonoid_2534 :: T_CommutativeSemiring_2446 -> T_IsMonoid_686
d_isMonoid_2534 T_CommutativeSemiring_2446
v0
  = (T_IsCommutativeMonoid_736 -> T_IsMonoid_686)
-> AgdaAny -> T_IsMonoid_686
forall a b. a -> b
coe
      T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746
      ((T_IsSemiringWithoutAnnihilatingZero_1468
 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
         ((T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
            ((T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570
MAlonzo.Code.Algebra.Structures.d_isSemiring_1692
               ((T_CommutativeSemiring_2446 -> T_IsCommutativeSemiring_1678)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemiring_2446 -> T_IsCommutativeSemiring_1678
d_isCommutativeSemiring_2478 (T_CommutativeSemiring_2446 -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemiring_2446
v0)))))
-- Algebra.Bundles.CommutativeSemiring._.isSemigroup
d_isSemigroup_2536 ::
  T_CommutativeSemiring_2446 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_472
d_isSemigroup_2536 :: T_CommutativeSemiring_2446 -> T_IsSemigroup_472
d_isSemigroup_2536 T_CommutativeSemiring_2446
v0
  = (T_IsMonoid_686 -> T_IsSemigroup_472)
-> AgdaAny -> T_IsSemigroup_472
forall a b. a -> b
coe
      T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
      ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746
         ((T_IsSemiringWithoutAnnihilatingZero_1468
 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
            ((T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
               ((T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570
MAlonzo.Code.Algebra.Structures.d_isSemiring_1692
                  ((T_CommutativeSemiring_2446 -> T_IsCommutativeSemiring_1678)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemiring_2446 -> T_IsCommutativeSemiring_1678
d_isCommutativeSemiring_2478 (T_CommutativeSemiring_2446 -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemiring_2446
v0))))))
-- Algebra.Bundles.CommutativeSemiring._.isUnitalMagma
d_isUnitalMagma_2538 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeSemiring_2446 ->
  MAlonzo.Code.Algebra.Structures.T_IsUnitalMagma_642
d_isUnitalMagma_2538 :: () -> () -> T_CommutativeSemiring_2446 -> T_IsUnitalMagma_642
d_isUnitalMagma_2538 ~()
v0 ~()
v1 T_CommutativeSemiring_2446
v2 = T_CommutativeSemiring_2446 -> T_IsUnitalMagma_642
du_isUnitalMagma_2538 T_CommutativeSemiring_2446
v2
du_isUnitalMagma_2538 ::
  T_CommutativeSemiring_2446 ->
  MAlonzo.Code.Algebra.Structures.T_IsUnitalMagma_642
du_isUnitalMagma_2538 :: T_CommutativeSemiring_2446 -> T_IsUnitalMagma_642
du_isUnitalMagma_2538 T_CommutativeSemiring_2446
v0
  = let v1 :: T_IsCommutativeSemiring_1678
v1 = T_CommutativeSemiring_2446 -> T_IsCommutativeSemiring_1678
d_isCommutativeSemiring_2478 (T_CommutativeSemiring_2446 -> T_CommutativeSemiring_2446
forall a b. a -> b
coe T_CommutativeSemiring_2446
v0) in
    AgdaAny -> T_IsUnitalMagma_642
forall a b. a -> b
coe
      (let v2 :: T_IsSemiring_1570
v2
             = T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570
MAlonzo.Code.Algebra.Structures.d_isSemiring_1692 (T_IsCommutativeSemiring_1678 -> T_IsCommutativeSemiring_1678
forall a b. a -> b
coe T_IsCommutativeSemiring_1678
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemiringWithoutAnnihilatingZero_1468
v3
                = T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                    (T_IsSemiring_1570 -> T_IsSemiring_1570
forall a b. a -> b
coe T_IsSemiring_1570
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsCommutativeMonoid_736
v4
                   = T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
                       (T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsSemiringWithoutAnnihilatingZero_1468
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               ((T_IsMonoid_686 -> T_IsUnitalMagma_642) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsMonoid_686 -> T_IsUnitalMagma_642
MAlonzo.Code.Algebra.Structures.du_isUnitalMagma_730
                  ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746 (T_IsCommutativeMonoid_736 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v4))))))
-- Algebra.Bundles.CommutativeSemiring._.distrib
d_distrib_2540 ::
  T_CommutativeSemiring_2446 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_distrib_2540 :: T_CommutativeSemiring_2446 -> T_Σ_14
d_distrib_2540 T_CommutativeSemiring_2446
v0
  = (T_IsSemiringWithoutAnnihilatingZero_1468 -> T_Σ_14)
-> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsSemiringWithoutAnnihilatingZero_1468 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_distrib_1496
      ((T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
         ((T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570
MAlonzo.Code.Algebra.Structures.d_isSemiring_1692
            ((T_CommutativeSemiring_2446 -> T_IsCommutativeSemiring_1678)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemiring_2446 -> T_IsCommutativeSemiring_1678
d_isCommutativeSemiring_2478 (T_CommutativeSemiring_2446 -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemiring_2446
v0))))
-- Algebra.Bundles.CommutativeSemiring._.distribʳ
d_distrib'691'_2542 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeSemiring_2446 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_distrib'691'_2542 :: ()
-> ()
-> T_CommutativeSemiring_2446
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_distrib'691'_2542 ~()
v0 ~()
v1 T_CommutativeSemiring_2446
v2 = T_CommutativeSemiring_2446
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'691'_2542 T_CommutativeSemiring_2446
v2
du_distrib'691'_2542 ::
  T_CommutativeSemiring_2446 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'691'_2542 :: T_CommutativeSemiring_2446
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'691'_2542 T_CommutativeSemiring_2446
v0
  = let v1 :: T_IsCommutativeSemiring_1678
v1 = T_CommutativeSemiring_2446 -> T_IsCommutativeSemiring_1678
d_isCommutativeSemiring_2478 (T_CommutativeSemiring_2446 -> T_CommutativeSemiring_2446
forall a b. a -> b
coe T_CommutativeSemiring_2446
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemiring_1570
v2
             = T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570
MAlonzo.Code.Algebra.Structures.d_isSemiring_1692 (T_IsCommutativeSemiring_1678 -> T_IsCommutativeSemiring_1678
forall a b. a -> b
coe T_IsCommutativeSemiring_1678
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsSemiringWithoutAnnihilatingZero_1468
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemiringWithoutAnnihilatingZero_1468
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_distrib'691'_1500
            ((T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
               (T_IsSemiring_1570 -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1570
v2))))
-- Algebra.Bundles.CommutativeSemiring._.distribˡ
d_distrib'737'_2544 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeSemiring_2446 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_distrib'737'_2544 :: ()
-> ()
-> T_CommutativeSemiring_2446
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_distrib'737'_2544 ~()
v0 ~()
v1 T_CommutativeSemiring_2446
v2 = T_CommutativeSemiring_2446
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'737'_2544 T_CommutativeSemiring_2446
v2
du_distrib'737'_2544 ::
  T_CommutativeSemiring_2446 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'737'_2544 :: T_CommutativeSemiring_2446
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'737'_2544 T_CommutativeSemiring_2446
v0
  = let v1 :: T_IsCommutativeSemiring_1678
v1 = T_CommutativeSemiring_2446 -> T_IsCommutativeSemiring_1678
d_isCommutativeSemiring_2478 (T_CommutativeSemiring_2446 -> T_CommutativeSemiring_2446
forall a b. a -> b
coe T_CommutativeSemiring_2446
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemiring_1570
v2
             = T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570
MAlonzo.Code.Algebra.Structures.d_isSemiring_1692 (T_IsCommutativeSemiring_1678 -> T_IsCommutativeSemiring_1678
forall a b. a -> b
coe T_IsCommutativeSemiring_1678
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsSemiringWithoutAnnihilatingZero_1468
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemiringWithoutAnnihilatingZero_1468
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_distrib'737'_1498
            ((T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
               (T_IsSemiring_1570 -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1570
v2))))
-- Algebra.Bundles.CommutativeSemiring._.isCommutativeSemiringWithoutOne
d_isCommutativeSemiringWithoutOne_2546 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeSemiring_2446 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiringWithoutOne_1382
d_isCommutativeSemiringWithoutOne_2546 :: ()
-> ()
-> T_CommutativeSemiring_2446
-> T_IsCommutativeSemiringWithoutOne_1382
d_isCommutativeSemiringWithoutOne_2546 ~()
v0 ~()
v1 T_CommutativeSemiring_2446
v2
  = T_CommutativeSemiring_2446
-> T_IsCommutativeSemiringWithoutOne_1382
du_isCommutativeSemiringWithoutOne_2546 T_CommutativeSemiring_2446
v2
du_isCommutativeSemiringWithoutOne_2546 ::
  T_CommutativeSemiring_2446 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiringWithoutOne_1382
du_isCommutativeSemiringWithoutOne_2546 :: T_CommutativeSemiring_2446
-> T_IsCommutativeSemiringWithoutOne_1382
du_isCommutativeSemiringWithoutOne_2546 T_CommutativeSemiring_2446
v0
  = (T_IsCommutativeSemiring_1678
 -> T_IsCommutativeSemiringWithoutOne_1382)
-> AgdaAny -> T_IsCommutativeSemiringWithoutOne_1382
forall a b. a -> b
coe
      T_IsCommutativeSemiring_1678
-> T_IsCommutativeSemiringWithoutOne_1382
MAlonzo.Code.Algebra.Structures.du_isCommutativeSemiringWithoutOne_1780
      ((T_CommutativeSemiring_2446 -> T_IsCommutativeSemiring_1678)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemiring_2446 -> T_IsCommutativeSemiring_1678
d_isCommutativeSemiring_2478 (T_CommutativeSemiring_2446 -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemiring_2446
v0))
-- Algebra.Bundles.CommutativeSemiring._.isEquivalence
d_isEquivalence_2548 ::
  T_CommutativeSemiring_2446 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_2548 :: T_CommutativeSemiring_2446 -> T_IsEquivalence_26
d_isEquivalence_2548 T_CommutativeSemiring_2446
v0
  = (T_IsMagma_176 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
      ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480
         ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
            ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746
               ((T_IsSemiringWithoutAnnihilatingZero_1468
 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
                  ((T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                     ((T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570
MAlonzo.Code.Algebra.Structures.d_isSemiring_1692
                        ((T_CommutativeSemiring_2446 -> T_IsCommutativeSemiring_1678)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemiring_2446 -> T_IsCommutativeSemiring_1678
d_isCommutativeSemiring_2478 (T_CommutativeSemiring_2446 -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemiring_2446
v0))))))))
-- Algebra.Bundles.CommutativeSemiring._.isNearSemiring
d_isNearSemiring_2550 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeSemiring_2446 ->
  MAlonzo.Code.Algebra.Structures.T_IsNearSemiring_1218
d_isNearSemiring_2550 :: () -> () -> T_CommutativeSemiring_2446 -> T_IsNearSemiring_1218
d_isNearSemiring_2550 ~()
v0 ~()
v1 T_CommutativeSemiring_2446
v2 = T_CommutativeSemiring_2446 -> T_IsNearSemiring_1218
du_isNearSemiring_2550 T_CommutativeSemiring_2446
v2
du_isNearSemiring_2550 ::
  T_CommutativeSemiring_2446 ->
  MAlonzo.Code.Algebra.Structures.T_IsNearSemiring_1218
du_isNearSemiring_2550 :: T_CommutativeSemiring_2446 -> T_IsNearSemiring_1218
du_isNearSemiring_2550 T_CommutativeSemiring_2446
v0
  = let v1 :: T_IsCommutativeSemiring_1678
v1 = T_CommutativeSemiring_2446 -> T_IsCommutativeSemiring_1678
d_isCommutativeSemiring_2478 (T_CommutativeSemiring_2446 -> T_CommutativeSemiring_2446
forall a b. a -> b
coe T_CommutativeSemiring_2446
v0) in
    AgdaAny -> T_IsNearSemiring_1218
forall a b. a -> b
coe
      (let v2 :: T_IsSemiring_1570
v2
             = T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570
MAlonzo.Code.Algebra.Structures.d_isSemiring_1692 (T_IsCommutativeSemiring_1678 -> T_IsCommutativeSemiring_1678
forall a b. a -> b
coe T_IsCommutativeSemiring_1678
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsSemiringWithoutOne_1298 -> T_IsNearSemiring_1218)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemiringWithoutOne_1298 -> T_IsNearSemiring_1218
MAlonzo.Code.Algebra.Structures.du_isNearSemiring_1374
            ((T_IsSemiring_1570 -> T_IsSemiringWithoutOne_1298)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemiring_1570 -> T_IsSemiringWithoutOne_1298
MAlonzo.Code.Algebra.Structures.du_isSemiringWithoutOne_1660
               (T_IsSemiring_1570 -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1570
v2))))
-- Algebra.Bundles.CommutativeSemiring._.isPartialEquivalence
d_isPartialEquivalence_2552 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeSemiring_2446 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_2552 :: () -> () -> T_CommutativeSemiring_2446 -> T_IsPartialEquivalence_16
d_isPartialEquivalence_2552 ~()
v0 ~()
v1 T_CommutativeSemiring_2446
v2
  = T_CommutativeSemiring_2446 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_2552 T_CommutativeSemiring_2446
v2
du_isPartialEquivalence_2552 ::
  T_CommutativeSemiring_2446 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_2552 :: T_CommutativeSemiring_2446 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_2552 T_CommutativeSemiring_2446
v0
  = let v1 :: T_IsCommutativeSemiring_1678
v1 = T_CommutativeSemiring_2446 -> T_IsCommutativeSemiring_1678
d_isCommutativeSemiring_2478 (T_CommutativeSemiring_2446 -> T_CommutativeSemiring_2446
forall a b. a -> b
coe T_CommutativeSemiring_2446
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsSemiring_1570
v2
             = T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570
MAlonzo.Code.Algebra.Structures.d_isSemiring_1692 (T_IsCommutativeSemiring_1678 -> T_IsCommutativeSemiring_1678
forall a b. a -> b
coe T_IsCommutativeSemiring_1678
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemiringWithoutAnnihilatingZero_1468
v3
                = T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                    (T_IsSemiring_1570 -> T_IsSemiring_1570
forall a b. a -> b
coe T_IsSemiring_1570
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsCommutativeMonoid_736
v4
                   = T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
                       (T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsSemiringWithoutAnnihilatingZero_1468
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsMonoid_686
v5
                      = T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746 (T_IsCommutativeMonoid_736 -> T_IsCommutativeMonoid_736
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (let v6 :: T_IsSemigroup_472
v6
                         = T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v5) in
                   AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     (let v7 :: T_IsMagma_176
v7 = T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (T_IsSemigroup_472 -> T_IsSemigroup_472
forall a b. a -> b
coe T_IsSemigroup_472
v6) in
                      AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        ((T_IsEquivalence_26 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_IsEquivalence_26 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
                           ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                              T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
                              (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v7)))))))))
-- Algebra.Bundles.CommutativeSemiring._.isSemiring
d_isSemiring_2554 ::
  T_CommutativeSemiring_2446 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemiring_1570
d_isSemiring_2554 :: T_CommutativeSemiring_2446 -> T_IsSemiring_1570
d_isSemiring_2554 T_CommutativeSemiring_2446
v0
  = (T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570)
-> AgdaAny -> T_IsSemiring_1570
forall a b. a -> b
coe
      T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570
MAlonzo.Code.Algebra.Structures.d_isSemiring_1692
      ((T_CommutativeSemiring_2446 -> T_IsCommutativeSemiring_1678)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemiring_2446 -> T_IsCommutativeSemiring_1678
d_isCommutativeSemiring_2478 (T_CommutativeSemiring_2446 -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemiring_2446
v0))
-- Algebra.Bundles.CommutativeSemiring._.isSemiringWithoutAnnihilatingZero
d_isSemiringWithoutAnnihilatingZero_2556 ::
  T_CommutativeSemiring_2446 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_2556 :: T_CommutativeSemiring_2446
-> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_2556 T_CommutativeSemiring_2446
v0
  = (T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> T_IsSemiringWithoutAnnihilatingZero_1468
forall a b. a -> b
coe
      T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
      ((T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570
MAlonzo.Code.Algebra.Structures.d_isSemiring_1692
         ((T_CommutativeSemiring_2446 -> T_IsCommutativeSemiring_1678)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemiring_2446 -> T_IsCommutativeSemiring_1678
d_isCommutativeSemiring_2478 (T_CommutativeSemiring_2446 -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemiring_2446
v0)))
-- Algebra.Bundles.CommutativeSemiring._.isSemiringWithoutOne
d_isSemiringWithoutOne_2558 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeSemiring_2446 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutOne_1298
d_isSemiringWithoutOne_2558 :: ()
-> () -> T_CommutativeSemiring_2446 -> T_IsSemiringWithoutOne_1298
d_isSemiringWithoutOne_2558 ~()
v0 ~()
v1 T_CommutativeSemiring_2446
v2
  = T_CommutativeSemiring_2446 -> T_IsSemiringWithoutOne_1298
du_isSemiringWithoutOne_2558 T_CommutativeSemiring_2446
v2
du_isSemiringWithoutOne_2558 ::
  T_CommutativeSemiring_2446 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutOne_1298
du_isSemiringWithoutOne_2558 :: T_CommutativeSemiring_2446 -> T_IsSemiringWithoutOne_1298
du_isSemiringWithoutOne_2558 T_CommutativeSemiring_2446
v0
  = let v1 :: T_IsCommutativeSemiring_1678
v1 = T_CommutativeSemiring_2446 -> T_IsCommutativeSemiring_1678
d_isCommutativeSemiring_2478 (T_CommutativeSemiring_2446 -> T_CommutativeSemiring_2446
forall a b. a -> b
coe T_CommutativeSemiring_2446
v0) in
    AgdaAny -> T_IsSemiringWithoutOne_1298
forall a b. a -> b
coe
      ((T_IsSemiring_1570 -> T_IsSemiringWithoutOne_1298)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiring_1570 -> T_IsSemiringWithoutOne_1298
MAlonzo.Code.Algebra.Structures.du_isSemiringWithoutOne_1660
         ((T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570
MAlonzo.Code.Algebra.Structures.d_isSemiring_1692 (T_IsCommutativeSemiring_1678 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiring_1678
v1)))
-- Algebra.Bundles.CommutativeSemiring._.refl
d_refl_2560 :: T_CommutativeSemiring_2446 -> AgdaAny -> AgdaAny
d_refl_2560 :: T_CommutativeSemiring_2446 -> AgdaAny -> AgdaAny
d_refl_2560 T_CommutativeSemiring_2446
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_34
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
         ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480
            ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
               ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746
                  ((T_IsSemiringWithoutAnnihilatingZero_1468
 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
                     ((T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                        ((T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570
MAlonzo.Code.Algebra.Structures.d_isSemiring_1692
                           ((T_CommutativeSemiring_2446 -> T_IsCommutativeSemiring_1678)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemiring_2446 -> T_IsCommutativeSemiring_1678
d_isCommutativeSemiring_2478 (T_CommutativeSemiring_2446 -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemiring_2446
v0)))))))))
-- Algebra.Bundles.CommutativeSemiring._.reflexive
d_reflexive_2562 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeSemiring_2446 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_2562 :: ()
-> ()
-> T_CommutativeSemiring_2446
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_2562 ~()
v0 ~()
v1 T_CommutativeSemiring_2446
v2 = T_CommutativeSemiring_2446
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_2562 T_CommutativeSemiring_2446
v2
du_reflexive_2562 ::
  T_CommutativeSemiring_2446 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_2562 :: T_CommutativeSemiring_2446
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_2562 T_CommutativeSemiring_2446
v0
  = let v1 :: T_IsCommutativeSemiring_1678
v1 = T_CommutativeSemiring_2446 -> T_IsCommutativeSemiring_1678
d_isCommutativeSemiring_2478 (T_CommutativeSemiring_2446 -> T_CommutativeSemiring_2446
forall a b. a -> b
coe T_CommutativeSemiring_2446
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemiring_1570
v2
             = T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570
MAlonzo.Code.Algebra.Structures.d_isSemiring_1692 (T_IsCommutativeSemiring_1678 -> T_IsCommutativeSemiring_1678
forall a b. a -> b
coe T_IsCommutativeSemiring_1678
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemiringWithoutAnnihilatingZero_1468
v3
                = T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                    (T_IsSemiring_1570 -> T_IsSemiring_1570
forall a b. a -> b
coe T_IsSemiring_1570
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsCommutativeMonoid_736
v4
                   = T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
                       (T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsSemiringWithoutAnnihilatingZero_1468
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsMonoid_686
v5
                      = T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746 (T_IsCommutativeMonoid_736 -> T_IsCommutativeMonoid_736
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (let v6 :: T_IsSemigroup_472
v6
                         = T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v5) in
                   AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     (let v7 :: T_IsMagma_176
v7 = T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (T_IsSemigroup_472 -> T_IsSemigroup_472
forall a b. a -> b
coe T_IsSemigroup_472
v6) in
                      (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
                        (\ AgdaAny
v8 AgdaAny
v9 AgdaAny
v10 ->
                           (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                             T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
                             ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v7))
                             AgdaAny
v8)))))))
-- Algebra.Bundles.CommutativeSemiring._.setoid
d_setoid_2564 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeSemiring_2446 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_2564 :: () -> () -> T_CommutativeSemiring_2446 -> T_Setoid_44
d_setoid_2564 ~()
v0 ~()
v1 T_CommutativeSemiring_2446
v2 = T_CommutativeSemiring_2446 -> T_Setoid_44
du_setoid_2564 T_CommutativeSemiring_2446
v2
du_setoid_2564 ::
  T_CommutativeSemiring_2446 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_2564 :: T_CommutativeSemiring_2446 -> T_Setoid_44
du_setoid_2564 T_CommutativeSemiring_2446
v0
  = let v1 :: T_IsCommutativeSemiring_1678
v1 = T_CommutativeSemiring_2446 -> T_IsCommutativeSemiring_1678
d_isCommutativeSemiring_2478 (T_CommutativeSemiring_2446 -> T_CommutativeSemiring_2446
forall a b. a -> b
coe T_CommutativeSemiring_2446
v0) in
    AgdaAny -> T_Setoid_44
forall a b. a -> b
coe
      (let v2 :: T_IsSemiring_1570
v2
             = T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570
MAlonzo.Code.Algebra.Structures.d_isSemiring_1692 (T_IsCommutativeSemiring_1678 -> T_IsCommutativeSemiring_1678
forall a b. a -> b
coe T_IsCommutativeSemiring_1678
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemiringWithoutAnnihilatingZero_1468
v3
                = T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                    (T_IsSemiring_1570 -> T_IsSemiring_1570
forall a b. a -> b
coe T_IsSemiring_1570
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsCommutativeMonoid_736
v4
                   = T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
                       (T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsSemiringWithoutAnnihilatingZero_1468
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsMonoid_686
v5
                      = T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746 (T_IsCommutativeMonoid_736 -> T_IsCommutativeMonoid_736
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (let v6 :: T_IsSemigroup_472
v6
                         = T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v5) in
                   AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     ((T_IsMagma_176 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsMagma_176 -> T_Setoid_44
MAlonzo.Code.Algebra.Structures.du_setoid_200
                        ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v6))))))))
-- Algebra.Bundles.CommutativeSemiring._.sym
d_sym_2566 ::
  T_CommutativeSemiring_2446 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_2566 :: T_CommutativeSemiring_2446
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_2566 T_CommutativeSemiring_2446
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_36
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
         ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480
            ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
               ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746
                  ((T_IsSemiringWithoutAnnihilatingZero_1468
 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
                     ((T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                        ((T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570
MAlonzo.Code.Algebra.Structures.d_isSemiring_1692
                           ((T_CommutativeSemiring_2446 -> T_IsCommutativeSemiring_1678)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemiring_2446 -> T_IsCommutativeSemiring_1678
d_isCommutativeSemiring_2478 (T_CommutativeSemiring_2446 -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemiring_2446
v0)))))))))
-- Algebra.Bundles.CommutativeSemiring._.trans
d_trans_2568 ::
  T_CommutativeSemiring_2446 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_2568 :: T_CommutativeSemiring_2446
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_2568 T_CommutativeSemiring_2446
v0
  = (T_IsEquivalence_26
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_38
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
         ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480
            ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
               ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746
                  ((T_IsSemiringWithoutAnnihilatingZero_1468
 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
                     ((T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                        ((T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570
MAlonzo.Code.Algebra.Structures.d_isSemiring_1692
                           ((T_CommutativeSemiring_2446 -> T_IsCommutativeSemiring_1678)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemiring_2446 -> T_IsCommutativeSemiring_1678
d_isCommutativeSemiring_2478 (T_CommutativeSemiring_2446 -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemiring_2446
v0)))))))))
-- Algebra.Bundles.CommutativeSemiring._.zero
d_zero_2570 ::
  T_CommutativeSemiring_2446 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_zero_2570 :: T_CommutativeSemiring_2446 -> T_Σ_14
d_zero_2570 T_CommutativeSemiring_2446
v0
  = (T_IsSemiring_1570 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsSemiring_1570 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_zero_1586
      ((T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570
MAlonzo.Code.Algebra.Structures.d_isSemiring_1692
         ((T_CommutativeSemiring_2446 -> T_IsCommutativeSemiring_1678)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemiring_2446 -> T_IsCommutativeSemiring_1678
d_isCommutativeSemiring_2478 (T_CommutativeSemiring_2446 -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemiring_2446
v0)))
-- Algebra.Bundles.CommutativeSemiring._.zeroʳ
d_zero'691'_2572 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeSemiring_2446 -> AgdaAny -> AgdaAny
d_zero'691'_2572 :: () -> () -> T_CommutativeSemiring_2446 -> AgdaAny -> AgdaAny
d_zero'691'_2572 ~()
v0 ~()
v1 T_CommutativeSemiring_2446
v2 = T_CommutativeSemiring_2446 -> AgdaAny -> AgdaAny
du_zero'691'_2572 T_CommutativeSemiring_2446
v2
du_zero'691'_2572 ::
  T_CommutativeSemiring_2446 -> AgdaAny -> AgdaAny
du_zero'691'_2572 :: T_CommutativeSemiring_2446 -> AgdaAny -> AgdaAny
du_zero'691'_2572 T_CommutativeSemiring_2446
v0
  = let v1 :: T_IsCommutativeSemiring_1678
v1 = T_CommutativeSemiring_2446 -> T_IsCommutativeSemiring_1678
d_isCommutativeSemiring_2478 (T_CommutativeSemiring_2446 -> T_CommutativeSemiring_2446
forall a b. a -> b
coe T_CommutativeSemiring_2446
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemiring_1570
v2
             = T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570
MAlonzo.Code.Algebra.Structures.d_isSemiring_1692 (T_IsCommutativeSemiring_1678 -> T_IsCommutativeSemiring_1678
forall a b. a -> b
coe T_IsCommutativeSemiring_1678
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsSemiringWithoutOne_1298 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemiringWithoutOne_1298 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_zero'691'_1372
            ((T_IsSemiring_1570 -> T_IsSemiringWithoutOne_1298)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemiring_1570 -> T_IsSemiringWithoutOne_1298
MAlonzo.Code.Algebra.Structures.du_isSemiringWithoutOne_1660
               (T_IsSemiring_1570 -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1570
v2))))
-- Algebra.Bundles.CommutativeSemiring._.zeroˡ
d_zero'737'_2574 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeSemiring_2446 -> AgdaAny -> AgdaAny
d_zero'737'_2574 :: () -> () -> T_CommutativeSemiring_2446 -> AgdaAny -> AgdaAny
d_zero'737'_2574 ~()
v0 ~()
v1 T_CommutativeSemiring_2446
v2 = T_CommutativeSemiring_2446 -> AgdaAny -> AgdaAny
du_zero'737'_2574 T_CommutativeSemiring_2446
v2
du_zero'737'_2574 ::
  T_CommutativeSemiring_2446 -> AgdaAny -> AgdaAny
du_zero'737'_2574 :: T_CommutativeSemiring_2446 -> AgdaAny -> AgdaAny
du_zero'737'_2574 T_CommutativeSemiring_2446
v0
  = let v1 :: T_IsCommutativeSemiring_1678
v1 = T_CommutativeSemiring_2446 -> T_IsCommutativeSemiring_1678
d_isCommutativeSemiring_2478 (T_CommutativeSemiring_2446 -> T_CommutativeSemiring_2446
forall a b. a -> b
coe T_CommutativeSemiring_2446
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemiring_1570
v2
             = T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570
MAlonzo.Code.Algebra.Structures.d_isSemiring_1692 (T_IsCommutativeSemiring_1678 -> T_IsCommutativeSemiring_1678
forall a b. a -> b
coe T_IsCommutativeSemiring_1678
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsSemiringWithoutOne_1298 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemiringWithoutOne_1298 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_zero'737'_1370
            ((T_IsSemiring_1570 -> T_IsSemiringWithoutOne_1298)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemiring_1570 -> T_IsSemiringWithoutOne_1298
MAlonzo.Code.Algebra.Structures.du_isSemiringWithoutOne_1660
               (T_IsSemiring_1570 -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1570
v2))))
-- Algebra.Bundles.CommutativeSemiring.semiring
d_semiring_2576 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeSemiring_2446 -> T_Semiring_2280
d_semiring_2576 :: () -> () -> T_CommutativeSemiring_2446 -> T_Semiring_2280
d_semiring_2576 ~()
v0 ~()
v1 T_CommutativeSemiring_2446
v2 = T_CommutativeSemiring_2446 -> T_Semiring_2280
du_semiring_2576 T_CommutativeSemiring_2446
v2
du_semiring_2576 :: T_CommutativeSemiring_2446 -> T_Semiring_2280
du_semiring_2576 :: T_CommutativeSemiring_2446 -> T_Semiring_2280
du_semiring_2576 T_CommutativeSemiring_2446
v0
  = ((AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> AgdaAny
 -> T_IsSemiring_1570
 -> T_Semiring_2280)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsSemiring_1570
-> T_Semiring_2280
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsSemiring_1570
-> T_Semiring_2280
C_Semiring'46'constructor_41765 (T_CommutativeSemiring_2446 -> AgdaAny -> AgdaAny -> AgdaAny
d__'43'__2470 (T_CommutativeSemiring_2446 -> T_CommutativeSemiring_2446
forall a b. a -> b
coe T_CommutativeSemiring_2446
v0))
      (T_CommutativeSemiring_2446 -> AgdaAny -> AgdaAny -> AgdaAny
d__'42'__2472 (T_CommutativeSemiring_2446 -> T_CommutativeSemiring_2446
forall a b. a -> b
coe T_CommutativeSemiring_2446
v0)) (T_CommutativeSemiring_2446 -> AgdaAny
d_0'35'_2474 (T_CommutativeSemiring_2446 -> T_CommutativeSemiring_2446
forall a b. a -> b
coe T_CommutativeSemiring_2446
v0))
      (T_CommutativeSemiring_2446 -> AgdaAny
d_1'35'_2476 (T_CommutativeSemiring_2446 -> T_CommutativeSemiring_2446
forall a b. a -> b
coe T_CommutativeSemiring_2446
v0))
      (T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570
MAlonzo.Code.Algebra.Structures.d_isSemiring_1692
         ((T_CommutativeSemiring_2446 -> T_IsCommutativeSemiring_1678)
-> AgdaAny -> T_IsCommutativeSemiring_1678
forall a b. a -> b
coe T_CommutativeSemiring_2446 -> T_IsCommutativeSemiring_1678
d_isCommutativeSemiring_2478 (T_CommutativeSemiring_2446 -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemiring_2446
v0)))
-- Algebra.Bundles.CommutativeSemiring._._≉_
d__'8777'__2580 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeSemiring_2446 -> AgdaAny -> AgdaAny -> ()
d__'8777'__2580 :: () -> () -> T_CommutativeSemiring_2446 -> AgdaAny -> AgdaAny -> ()
d__'8777'__2580 = () -> () -> T_CommutativeSemiring_2446 -> AgdaAny -> AgdaAny -> ()
forall a. a
erased
-- Algebra.Bundles.CommutativeSemiring._.magma
d_magma_2582 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeSemiring_2446 -> T_Magma_68
d_magma_2582 :: () -> () -> T_CommutativeSemiring_2446 -> T_Magma_68
d_magma_2582 ~()
v0 ~()
v1 T_CommutativeSemiring_2446
v2 = T_CommutativeSemiring_2446 -> T_Magma_68
du_magma_2582 T_CommutativeSemiring_2446
v2
du_magma_2582 :: T_CommutativeSemiring_2446 -> T_Magma_68
du_magma_2582 :: T_CommutativeSemiring_2446 -> T_Magma_68
du_magma_2582 T_CommutativeSemiring_2446
v0
  = let v1 :: t
v1 = (T_CommutativeSemiring_2446 -> T_Semiring_2280) -> AgdaAny -> t
forall a b. a -> b
coe T_CommutativeSemiring_2446 -> T_Semiring_2280
du_semiring_2576 (T_CommutativeSemiring_2446 -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemiring_2446
v0) in
    AgdaAny -> T_Magma_68
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_Semiring_2280 -> T_SemiringWithoutAnnihilatingZero_2130)
-> AgdaAny -> t
forall a b. a -> b
coe T_Semiring_2280 -> T_SemiringWithoutAnnihilatingZero_2130
du_semiringWithoutAnnihilatingZero_2398 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: t
v3 = (T_SemiringWithoutAnnihilatingZero_2130 -> T_Monoid_882)
-> AgdaAny -> t
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_2130 -> T_Monoid_882
du_'42''45'monoid_2264 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_Semigroup_536 -> T_Magma_68) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semigroup_536 -> T_Magma_68
du_magma_584 ((T_Monoid_882 -> T_Semigroup_536) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Monoid_882 -> T_Semigroup_536
du_semigroup_944 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3)))))
-- Algebra.Bundles.CommutativeSemiring._.*-monoid
d_'42''45'monoid_2584 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeSemiring_2446 -> T_Monoid_882
d_'42''45'monoid_2584 :: () -> () -> T_CommutativeSemiring_2446 -> T_Monoid_882
d_'42''45'monoid_2584 ~()
v0 ~()
v1 T_CommutativeSemiring_2446
v2 = T_CommutativeSemiring_2446 -> T_Monoid_882
du_'42''45'monoid_2584 T_CommutativeSemiring_2446
v2
du_'42''45'monoid_2584 ::
  T_CommutativeSemiring_2446 -> T_Monoid_882
du_'42''45'monoid_2584 :: T_CommutativeSemiring_2446 -> T_Monoid_882
du_'42''45'monoid_2584 T_CommutativeSemiring_2446
v0
  = let v1 :: t
v1 = (T_CommutativeSemiring_2446 -> T_Semiring_2280) -> AgdaAny -> t
forall a b. a -> b
coe T_CommutativeSemiring_2446 -> T_Semiring_2280
du_semiring_2576 (T_CommutativeSemiring_2446 -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemiring_2446
v0) in
    AgdaAny -> T_Monoid_882
forall a b. a -> b
coe
      ((T_SemiringWithoutAnnihilatingZero_2130 -> T_Monoid_882)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_SemiringWithoutAnnihilatingZero_2130 -> T_Monoid_882
du_'42''45'monoid_2264
         ((T_Semiring_2280 -> T_SemiringWithoutAnnihilatingZero_2130)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semiring_2280 -> T_SemiringWithoutAnnihilatingZero_2130
du_semiringWithoutAnnihilatingZero_2398 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1)))
-- Algebra.Bundles.CommutativeSemiring._.rawMagma
d_rawMagma_2586 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeSemiring_2446 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
d_rawMagma_2586 :: () -> () -> T_CommutativeSemiring_2446 -> T_RawMagma_36
d_rawMagma_2586 ~()
v0 ~()
v1 T_CommutativeSemiring_2446
v2 = T_CommutativeSemiring_2446 -> T_RawMagma_36
du_rawMagma_2586 T_CommutativeSemiring_2446
v2
du_rawMagma_2586 ::
  T_CommutativeSemiring_2446 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
du_rawMagma_2586 :: T_CommutativeSemiring_2446 -> T_RawMagma_36
du_rawMagma_2586 T_CommutativeSemiring_2446
v0
  = let v1 :: t
v1 = (T_CommutativeSemiring_2446 -> T_Semiring_2280) -> AgdaAny -> t
forall a b. a -> b
coe T_CommutativeSemiring_2446 -> T_Semiring_2280
du_semiring_2576 (T_CommutativeSemiring_2446 -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemiring_2446
v0) in
    AgdaAny -> T_RawMagma_36
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_Semiring_2280 -> T_SemiringWithoutAnnihilatingZero_2130)
-> AgdaAny -> t
forall a b. a -> b
coe T_Semiring_2280 -> T_SemiringWithoutAnnihilatingZero_2130
du_semiringWithoutAnnihilatingZero_2398 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: t
v3 = (T_SemiringWithoutAnnihilatingZero_2130 -> T_Monoid_882)
-> AgdaAny -> t
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_2130 -> T_Monoid_882
du_'42''45'monoid_2264 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: t
v4 = (T_Monoid_882 -> T_Semigroup_536) -> AgdaAny -> t
forall a b. a -> b
coe T_Monoid_882 -> T_Semigroup_536
du_semigroup_944 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_Magma_68 -> T_RawMagma_36) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Magma_68 -> T_RawMagma_36
du_rawMagma_112 ((T_Semigroup_536 -> T_Magma_68) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semigroup_536 -> T_Magma_68
du_magma_584 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v4))))))
-- Algebra.Bundles.CommutativeSemiring._.rawMonoid
d_rawMonoid_2588 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeSemiring_2446 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMonoid_64
d_rawMonoid_2588 :: () -> () -> T_CommutativeSemiring_2446 -> T_RawMonoid_64
d_rawMonoid_2588 ~()
v0 ~()
v1 T_CommutativeSemiring_2446
v2 = T_CommutativeSemiring_2446 -> T_RawMonoid_64
du_rawMonoid_2588 T_CommutativeSemiring_2446
v2
du_rawMonoid_2588 ::
  T_CommutativeSemiring_2446 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMonoid_64
du_rawMonoid_2588 :: T_CommutativeSemiring_2446 -> T_RawMonoid_64
du_rawMonoid_2588 T_CommutativeSemiring_2446
v0
  = let v1 :: t
v1 = (T_CommutativeSemiring_2446 -> T_Semiring_2280) -> AgdaAny -> t
forall a b. a -> b
coe T_CommutativeSemiring_2446 -> T_Semiring_2280
du_semiring_2576 (T_CommutativeSemiring_2446 -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemiring_2446
v0) in
    AgdaAny -> T_RawMonoid_64
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_Semiring_2280 -> T_SemiringWithoutAnnihilatingZero_2130)
-> AgdaAny -> t
forall a b. a -> b
coe T_Semiring_2280 -> T_SemiringWithoutAnnihilatingZero_2130
du_semiringWithoutAnnihilatingZero_2398 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_Monoid_882 -> T_RawMonoid_64) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Monoid_882 -> T_RawMonoid_64
du_rawMonoid_954 ((T_SemiringWithoutAnnihilatingZero_2130 -> T_Monoid_882)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_2130 -> T_Monoid_882
du_'42''45'monoid_2264 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2))))
-- Algebra.Bundles.CommutativeSemiring._.semigroup
d_semigroup_2590 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeSemiring_2446 -> T_Semigroup_536
d_semigroup_2590 :: () -> () -> T_CommutativeSemiring_2446 -> T_Semigroup_536
d_semigroup_2590 ~()
v0 ~()
v1 T_CommutativeSemiring_2446
v2 = T_CommutativeSemiring_2446 -> T_Semigroup_536
du_semigroup_2590 T_CommutativeSemiring_2446
v2
du_semigroup_2590 :: T_CommutativeSemiring_2446 -> T_Semigroup_536
du_semigroup_2590 :: T_CommutativeSemiring_2446 -> T_Semigroup_536
du_semigroup_2590 T_CommutativeSemiring_2446
v0
  = let v1 :: t
v1 = (T_CommutativeSemiring_2446 -> T_Semiring_2280) -> AgdaAny -> t
forall a b. a -> b
coe T_CommutativeSemiring_2446 -> T_Semiring_2280
du_semiring_2576 (T_CommutativeSemiring_2446 -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemiring_2446
v0) in
    AgdaAny -> T_Semigroup_536
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_Semiring_2280 -> T_SemiringWithoutAnnihilatingZero_2130)
-> AgdaAny -> t
forall a b. a -> b
coe T_Semiring_2280 -> T_SemiringWithoutAnnihilatingZero_2130
du_semiringWithoutAnnihilatingZero_2398 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_Monoid_882 -> T_Semigroup_536) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Monoid_882 -> T_Semigroup_536
du_semigroup_944 ((T_SemiringWithoutAnnihilatingZero_2130 -> T_Monoid_882)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_2130 -> T_Monoid_882
du_'42''45'monoid_2264 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2))))
-- Algebra.Bundles.CommutativeSemiring._.commutativeMagma
d_commutativeMagma_2592 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeSemiring_2446 -> T_CommutativeMagma_180
d_commutativeMagma_2592 :: () -> () -> T_CommutativeSemiring_2446 -> T_CommutativeMagma_180
d_commutativeMagma_2592 ~()
v0 ~()
v1 T_CommutativeSemiring_2446
v2 = T_CommutativeSemiring_2446 -> T_CommutativeMagma_180
du_commutativeMagma_2592 T_CommutativeSemiring_2446
v2
du_commutativeMagma_2592 ::
  T_CommutativeSemiring_2446 -> T_CommutativeMagma_180
du_commutativeMagma_2592 :: T_CommutativeSemiring_2446 -> T_CommutativeMagma_180
du_commutativeMagma_2592 T_CommutativeSemiring_2446
v0
  = let v1 :: t
v1 = (T_CommutativeSemiring_2446 -> T_Semiring_2280) -> AgdaAny -> t
forall a b. a -> b
coe T_CommutativeSemiring_2446 -> T_Semiring_2280
du_semiring_2576 (T_CommutativeSemiring_2446 -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemiring_2446
v0) in
    AgdaAny -> T_CommutativeMagma_180
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_Semiring_2280 -> T_SemiringWithoutAnnihilatingZero_2130)
-> AgdaAny -> t
forall a b. a -> b
coe T_Semiring_2280 -> T_SemiringWithoutAnnihilatingZero_2130
du_semiringWithoutAnnihilatingZero_2398 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: t
v3 = (T_SemiringWithoutAnnihilatingZero_2130 -> T_CommutativeMonoid_962)
-> AgdaAny -> t
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_2130 -> T_CommutativeMonoid_962
du_'43''45'commutativeMonoid_2242 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_CommutativeSemigroup_662 -> T_CommutativeMagma_180)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_CommutativeSemigroup_662 -> T_CommutativeMagma_180
du_commutativeMagma_726
               ((T_CommutativeMonoid_962 -> T_CommutativeSemigroup_662)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeMonoid_962 -> T_CommutativeSemigroup_662
du_commutativeSemigroup_1048 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3)))))
-- Algebra.Bundles.CommutativeSemiring._.+-commutativeMonoid
d_'43''45'commutativeMonoid_2594 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeSemiring_2446 -> T_CommutativeMonoid_962
d_'43''45'commutativeMonoid_2594 :: () -> () -> T_CommutativeSemiring_2446 -> T_CommutativeMonoid_962
d_'43''45'commutativeMonoid_2594 ~()
v0 ~()
v1 T_CommutativeSemiring_2446
v2
  = T_CommutativeSemiring_2446 -> T_CommutativeMonoid_962
du_'43''45'commutativeMonoid_2594 T_CommutativeSemiring_2446
v2
du_'43''45'commutativeMonoid_2594 ::
  T_CommutativeSemiring_2446 -> T_CommutativeMonoid_962
du_'43''45'commutativeMonoid_2594 :: T_CommutativeSemiring_2446 -> T_CommutativeMonoid_962
du_'43''45'commutativeMonoid_2594 T_CommutativeSemiring_2446
v0
  = let v1 :: t
v1 = (T_CommutativeSemiring_2446 -> T_Semiring_2280) -> AgdaAny -> t
forall a b. a -> b
coe T_CommutativeSemiring_2446 -> T_Semiring_2280
du_semiring_2576 (T_CommutativeSemiring_2446 -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemiring_2446
v0) in
    AgdaAny -> T_CommutativeMonoid_962
forall a b. a -> b
coe
      ((T_SemiringWithoutAnnihilatingZero_2130 -> T_CommutativeMonoid_962)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_SemiringWithoutAnnihilatingZero_2130 -> T_CommutativeMonoid_962
du_'43''45'commutativeMonoid_2242
         ((T_Semiring_2280 -> T_SemiringWithoutAnnihilatingZero_2130)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semiring_2280 -> T_SemiringWithoutAnnihilatingZero_2130
du_semiringWithoutAnnihilatingZero_2398 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1)))
-- Algebra.Bundles.CommutativeSemiring._.commutativeSemigroup
d_commutativeSemigroup_2596 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeSemiring_2446 -> T_CommutativeSemigroup_662
d_commutativeSemigroup_2596 :: ()
-> () -> T_CommutativeSemiring_2446 -> T_CommutativeSemigroup_662
d_commutativeSemigroup_2596 ~()
v0 ~()
v1 T_CommutativeSemiring_2446
v2
  = T_CommutativeSemiring_2446 -> T_CommutativeSemigroup_662
du_commutativeSemigroup_2596 T_CommutativeSemiring_2446
v2
du_commutativeSemigroup_2596 ::
  T_CommutativeSemiring_2446 -> T_CommutativeSemigroup_662
du_commutativeSemigroup_2596 :: T_CommutativeSemiring_2446 -> T_CommutativeSemigroup_662
du_commutativeSemigroup_2596 T_CommutativeSemiring_2446
v0
  = let v1 :: t
v1 = (T_CommutativeSemiring_2446 -> T_Semiring_2280) -> AgdaAny -> t
forall a b. a -> b
coe T_CommutativeSemiring_2446 -> T_Semiring_2280
du_semiring_2576 (T_CommutativeSemiring_2446 -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemiring_2446
v0) in
    AgdaAny -> T_CommutativeSemigroup_662
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_Semiring_2280 -> T_SemiringWithoutAnnihilatingZero_2130)
-> AgdaAny -> t
forall a b. a -> b
coe T_Semiring_2280 -> T_SemiringWithoutAnnihilatingZero_2130
du_semiringWithoutAnnihilatingZero_2398 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_CommutativeMonoid_962 -> T_CommutativeSemigroup_662)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_CommutativeMonoid_962 -> T_CommutativeSemigroup_662
du_commutativeSemigroup_1048
            ((T_SemiringWithoutAnnihilatingZero_2130 -> T_CommutativeMonoid_962)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_2130 -> T_CommutativeMonoid_962
du_'43''45'commutativeMonoid_2242 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2))))
-- Algebra.Bundles.CommutativeSemiring._.magma
d_magma_2598 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeSemiring_2446 -> T_Magma_68
d_magma_2598 :: () -> () -> T_CommutativeSemiring_2446 -> T_Magma_68
d_magma_2598 ~()
v0 ~()
v1 T_CommutativeSemiring_2446
v2 = T_CommutativeSemiring_2446 -> T_Magma_68
du_magma_2598 T_CommutativeSemiring_2446
v2
du_magma_2598 :: T_CommutativeSemiring_2446 -> T_Magma_68
du_magma_2598 :: T_CommutativeSemiring_2446 -> T_Magma_68
du_magma_2598 T_CommutativeSemiring_2446
v0
  = let v1 :: t
v1 = (T_CommutativeSemiring_2446 -> T_Semiring_2280) -> AgdaAny -> t
forall a b. a -> b
coe T_CommutativeSemiring_2446 -> T_Semiring_2280
du_semiring_2576 (T_CommutativeSemiring_2446 -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemiring_2446
v0) in
    AgdaAny -> T_Magma_68
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_Semiring_2280 -> T_SemiringWithoutAnnihilatingZero_2130)
-> AgdaAny -> t
forall a b. a -> b
coe T_Semiring_2280 -> T_SemiringWithoutAnnihilatingZero_2130
du_semiringWithoutAnnihilatingZero_2398 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: t
v3 = (T_SemiringWithoutAnnihilatingZero_2130 -> T_CommutativeMonoid_962)
-> AgdaAny -> t
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_2130 -> T_CommutativeMonoid_962
du_'43''45'commutativeMonoid_2242 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: t
v4 = (T_CommutativeMonoid_962 -> T_Monoid_882) -> AgdaAny -> t
forall a b. a -> b
coe T_CommutativeMonoid_962 -> T_Monoid_882
du_monoid_1032 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_Semigroup_536 -> T_Magma_68) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semigroup_536 -> T_Magma_68
du_magma_584 ((T_Monoid_882 -> T_Semigroup_536) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Monoid_882 -> T_Semigroup_536
du_semigroup_944 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v4))))))
-- Algebra.Bundles.CommutativeSemiring._.monoid
d_monoid_2600 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeSemiring_2446 -> T_Monoid_882
d_monoid_2600 :: () -> () -> T_CommutativeSemiring_2446 -> T_Monoid_882
d_monoid_2600 ~()
v0 ~()
v1 T_CommutativeSemiring_2446
v2 = T_CommutativeSemiring_2446 -> T_Monoid_882
du_monoid_2600 T_CommutativeSemiring_2446
v2
du_monoid_2600 :: T_CommutativeSemiring_2446 -> T_Monoid_882
du_monoid_2600 :: T_CommutativeSemiring_2446 -> T_Monoid_882
du_monoid_2600 T_CommutativeSemiring_2446
v0
  = let v1 :: t
v1 = (T_CommutativeSemiring_2446 -> T_Semiring_2280) -> AgdaAny -> t
forall a b. a -> b
coe T_CommutativeSemiring_2446 -> T_Semiring_2280
du_semiring_2576 (T_CommutativeSemiring_2446 -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemiring_2446
v0) in
    AgdaAny -> T_Monoid_882
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_Semiring_2280 -> T_SemiringWithoutAnnihilatingZero_2130)
-> AgdaAny -> t
forall a b. a -> b
coe T_Semiring_2280 -> T_SemiringWithoutAnnihilatingZero_2130
du_semiringWithoutAnnihilatingZero_2398 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_CommutativeMonoid_962 -> T_Monoid_882) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_CommutativeMonoid_962 -> T_Monoid_882
du_monoid_1032 ((T_SemiringWithoutAnnihilatingZero_2130 -> T_CommutativeMonoid_962)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_2130 -> T_CommutativeMonoid_962
du_'43''45'commutativeMonoid_2242 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2))))
-- Algebra.Bundles.CommutativeSemiring._.rawMagma
d_rawMagma_2602 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeSemiring_2446 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
d_rawMagma_2602 :: () -> () -> T_CommutativeSemiring_2446 -> T_RawMagma_36
d_rawMagma_2602 ~()
v0 ~()
v1 T_CommutativeSemiring_2446
v2 = T_CommutativeSemiring_2446 -> T_RawMagma_36
du_rawMagma_2602 T_CommutativeSemiring_2446
v2
du_rawMagma_2602 ::
  T_CommutativeSemiring_2446 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
du_rawMagma_2602 :: T_CommutativeSemiring_2446 -> T_RawMagma_36
du_rawMagma_2602 T_CommutativeSemiring_2446
v0
  = let v1 :: t
v1 = (T_CommutativeSemiring_2446 -> T_Semiring_2280) -> AgdaAny -> t
forall a b. a -> b
coe T_CommutativeSemiring_2446 -> T_Semiring_2280
du_semiring_2576 (T_CommutativeSemiring_2446 -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemiring_2446
v0) in
    AgdaAny -> T_RawMagma_36
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_Semiring_2280 -> T_SemiringWithoutAnnihilatingZero_2130)
-> AgdaAny -> t
forall a b. a -> b
coe T_Semiring_2280 -> T_SemiringWithoutAnnihilatingZero_2130
du_semiringWithoutAnnihilatingZero_2398 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: t
v3 = (T_SemiringWithoutAnnihilatingZero_2130 -> T_CommutativeMonoid_962)
-> AgdaAny -> t
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_2130 -> T_CommutativeMonoid_962
du_'43''45'commutativeMonoid_2242 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: t
v4 = (T_CommutativeMonoid_962 -> T_Monoid_882) -> AgdaAny -> t
forall a b. a -> b
coe T_CommutativeMonoid_962 -> T_Monoid_882
du_monoid_1032 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: t
v5 = (T_Monoid_882 -> T_Semigroup_536) -> AgdaAny -> t
forall a b. a -> b
coe T_Monoid_882 -> T_Semigroup_536
du_semigroup_944 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_Magma_68 -> T_RawMagma_36) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Magma_68 -> T_RawMagma_36
du_rawMagma_112 ((T_Semigroup_536 -> T_Magma_68) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semigroup_536 -> T_Magma_68
du_magma_584 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v5)))))))
-- Algebra.Bundles.CommutativeSemiring._.rawMonoid
d_rawMonoid_2604 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeSemiring_2446 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMonoid_64
d_rawMonoid_2604 :: () -> () -> T_CommutativeSemiring_2446 -> T_RawMonoid_64
d_rawMonoid_2604 ~()
v0 ~()
v1 T_CommutativeSemiring_2446
v2 = T_CommutativeSemiring_2446 -> T_RawMonoid_64
du_rawMonoid_2604 T_CommutativeSemiring_2446
v2
du_rawMonoid_2604 ::
  T_CommutativeSemiring_2446 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMonoid_64
du_rawMonoid_2604 :: T_CommutativeSemiring_2446 -> T_RawMonoid_64
du_rawMonoid_2604 T_CommutativeSemiring_2446
v0
  = let v1 :: t
v1 = (T_CommutativeSemiring_2446 -> T_Semiring_2280) -> AgdaAny -> t
forall a b. a -> b
coe T_CommutativeSemiring_2446 -> T_Semiring_2280
du_semiring_2576 (T_CommutativeSemiring_2446 -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemiring_2446
v0) in
    AgdaAny -> T_RawMonoid_64
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_Semiring_2280 -> T_SemiringWithoutAnnihilatingZero_2130)
-> AgdaAny -> t
forall a b. a -> b
coe T_Semiring_2280 -> T_SemiringWithoutAnnihilatingZero_2130
du_semiringWithoutAnnihilatingZero_2398 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: t
v3 = (T_SemiringWithoutAnnihilatingZero_2130 -> T_CommutativeMonoid_962)
-> AgdaAny -> t
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_2130 -> T_CommutativeMonoid_962
du_'43''45'commutativeMonoid_2242 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_Monoid_882 -> T_RawMonoid_64) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Monoid_882 -> T_RawMonoid_64
du_rawMonoid_954 ((T_CommutativeMonoid_962 -> T_Monoid_882) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeMonoid_962 -> T_Monoid_882
du_monoid_1032 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3)))))
-- Algebra.Bundles.CommutativeSemiring._.semigroup
d_semigroup_2606 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeSemiring_2446 -> T_Semigroup_536
d_semigroup_2606 :: () -> () -> T_CommutativeSemiring_2446 -> T_Semigroup_536
d_semigroup_2606 ~()
v0 ~()
v1 T_CommutativeSemiring_2446
v2 = T_CommutativeSemiring_2446 -> T_Semigroup_536
du_semigroup_2606 T_CommutativeSemiring_2446
v2
du_semigroup_2606 :: T_CommutativeSemiring_2446 -> T_Semigroup_536
du_semigroup_2606 :: T_CommutativeSemiring_2446 -> T_Semigroup_536
du_semigroup_2606 T_CommutativeSemiring_2446
v0
  = let v1 :: t
v1 = (T_CommutativeSemiring_2446 -> T_Semiring_2280) -> AgdaAny -> t
forall a b. a -> b
coe T_CommutativeSemiring_2446 -> T_Semiring_2280
du_semiring_2576 (T_CommutativeSemiring_2446 -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemiring_2446
v0) in
    AgdaAny -> T_Semigroup_536
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_Semiring_2280 -> T_SemiringWithoutAnnihilatingZero_2130)
-> AgdaAny -> t
forall a b. a -> b
coe T_Semiring_2280 -> T_SemiringWithoutAnnihilatingZero_2130
du_semiringWithoutAnnihilatingZero_2398 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: t
v3 = (T_SemiringWithoutAnnihilatingZero_2130 -> T_CommutativeMonoid_962)
-> AgdaAny -> t
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_2130 -> T_CommutativeMonoid_962
du_'43''45'commutativeMonoid_2242 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_Monoid_882 -> T_Semigroup_536) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Monoid_882 -> T_Semigroup_536
du_semigroup_944 ((T_CommutativeMonoid_962 -> T_Monoid_882) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeMonoid_962 -> T_Monoid_882
du_monoid_1032 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3)))))
-- Algebra.Bundles.CommutativeSemiring._.unitalMagma
d_unitalMagma_2608 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeSemiring_2446 -> T_UnitalMagma_814
d_unitalMagma_2608 :: () -> () -> T_CommutativeSemiring_2446 -> T_UnitalMagma_814
d_unitalMagma_2608 ~()
v0 ~()
v1 T_CommutativeSemiring_2446
v2 = T_CommutativeSemiring_2446 -> T_UnitalMagma_814
du_unitalMagma_2608 T_CommutativeSemiring_2446
v2
du_unitalMagma_2608 ::
  T_CommutativeSemiring_2446 -> T_UnitalMagma_814
du_unitalMagma_2608 :: T_CommutativeSemiring_2446 -> T_UnitalMagma_814
du_unitalMagma_2608 T_CommutativeSemiring_2446
v0
  = let v1 :: t
v1 = (T_CommutativeSemiring_2446 -> T_Semiring_2280) -> AgdaAny -> t
forall a b. a -> b
coe T_CommutativeSemiring_2446 -> T_Semiring_2280
du_semiring_2576 (T_CommutativeSemiring_2446 -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemiring_2446
v0) in
    AgdaAny -> T_UnitalMagma_814
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_Semiring_2280 -> T_SemiringWithoutAnnihilatingZero_2130)
-> AgdaAny -> t
forall a b. a -> b
coe T_Semiring_2280 -> T_SemiringWithoutAnnihilatingZero_2130
du_semiringWithoutAnnihilatingZero_2398 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: t
v3 = (T_SemiringWithoutAnnihilatingZero_2130 -> T_CommutativeMonoid_962)
-> AgdaAny -> t
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_2130 -> T_CommutativeMonoid_962
du_'43''45'commutativeMonoid_2242 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_Monoid_882 -> T_UnitalMagma_814) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Monoid_882 -> T_UnitalMagma_814
du_unitalMagma_956 ((T_CommutativeMonoid_962 -> T_Monoid_882) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeMonoid_962 -> T_Monoid_882
du_monoid_1032 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3)))))
-- Algebra.Bundles.CommutativeSemiring._.nearSemiring
d_nearSemiring_2610 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeSemiring_2446 -> T_NearSemiring_1766
d_nearSemiring_2610 :: () -> () -> T_CommutativeSemiring_2446 -> T_NearSemiring_1766
d_nearSemiring_2610 ~()
v0 ~()
v1 T_CommutativeSemiring_2446
v2 = T_CommutativeSemiring_2446 -> T_NearSemiring_1766
du_nearSemiring_2610 T_CommutativeSemiring_2446
v2
du_nearSemiring_2610 ::
  T_CommutativeSemiring_2446 -> T_NearSemiring_1766
du_nearSemiring_2610 :: T_CommutativeSemiring_2446 -> T_NearSemiring_1766
du_nearSemiring_2610 T_CommutativeSemiring_2446
v0
  = let v1 :: t
v1 = (T_CommutativeSemiring_2446 -> T_Semiring_2280) -> AgdaAny -> t
forall a b. a -> b
coe T_CommutativeSemiring_2446 -> T_Semiring_2280
du_semiring_2576 (T_CommutativeSemiring_2446 -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemiring_2446
v0) in
    AgdaAny -> T_NearSemiring_1766
forall a b. a -> b
coe
      ((T_SemiringWithoutOne_1880 -> T_NearSemiring_1766)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_SemiringWithoutOne_1880 -> T_NearSemiring_1766
du_nearSemiring_1966 ((T_Semiring_2280 -> T_SemiringWithoutOne_1880)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semiring_2280 -> T_SemiringWithoutOne_1880
du_semiringWithoutOne_2436 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1)))
-- Algebra.Bundles.CommutativeSemiring._.rawSemiring
d_rawSemiring_2612 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeSemiring_2446 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawSemiring_174
d_rawSemiring_2612 :: () -> () -> T_CommutativeSemiring_2446 -> T_RawSemiring_174
d_rawSemiring_2612 ~()
v0 ~()
v1 T_CommutativeSemiring_2446
v2 = T_CommutativeSemiring_2446 -> T_RawSemiring_174
du_rawSemiring_2612 T_CommutativeSemiring_2446
v2
du_rawSemiring_2612 ::
  T_CommutativeSemiring_2446 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawSemiring_174
du_rawSemiring_2612 :: T_CommutativeSemiring_2446 -> T_RawSemiring_174
du_rawSemiring_2612 T_CommutativeSemiring_2446
v0
  = let v1 :: t
v1 = (T_CommutativeSemiring_2446 -> T_Semiring_2280) -> AgdaAny -> t
forall a b. a -> b
coe T_CommutativeSemiring_2446 -> T_Semiring_2280
du_semiring_2576 (T_CommutativeSemiring_2446 -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemiring_2446
v0) in
    AgdaAny -> T_RawSemiring_174
forall a b. a -> b
coe
      ((T_SemiringWithoutAnnihilatingZero_2130 -> T_RawSemiring_174)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_SemiringWithoutAnnihilatingZero_2130 -> T_RawSemiring_174
du_rawSemiring_2236
         ((T_Semiring_2280 -> T_SemiringWithoutAnnihilatingZero_2130)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semiring_2280 -> T_SemiringWithoutAnnihilatingZero_2130
du_semiringWithoutAnnihilatingZero_2398 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1)))
-- Algebra.Bundles.CommutativeSemiring._.semiringWithoutAnnihilatingZero
d_semiringWithoutAnnihilatingZero_2614 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeSemiring_2446 ->
  T_SemiringWithoutAnnihilatingZero_2130
d_semiringWithoutAnnihilatingZero_2614 :: ()
-> ()
-> T_CommutativeSemiring_2446
-> T_SemiringWithoutAnnihilatingZero_2130
d_semiringWithoutAnnihilatingZero_2614 ~()
v0 ~()
v1 T_CommutativeSemiring_2446
v2
  = T_CommutativeSemiring_2446
-> T_SemiringWithoutAnnihilatingZero_2130
du_semiringWithoutAnnihilatingZero_2614 T_CommutativeSemiring_2446
v2
du_semiringWithoutAnnihilatingZero_2614 ::
  T_CommutativeSemiring_2446 ->
  T_SemiringWithoutAnnihilatingZero_2130
du_semiringWithoutAnnihilatingZero_2614 :: T_CommutativeSemiring_2446
-> T_SemiringWithoutAnnihilatingZero_2130
du_semiringWithoutAnnihilatingZero_2614 T_CommutativeSemiring_2446
v0
  = (T_Semiring_2280 -> T_SemiringWithoutAnnihilatingZero_2130)
-> AgdaAny -> T_SemiringWithoutAnnihilatingZero_2130
forall a b. a -> b
coe
      T_Semiring_2280 -> T_SemiringWithoutAnnihilatingZero_2130
du_semiringWithoutAnnihilatingZero_2398
      ((T_CommutativeSemiring_2446 -> T_Semiring_2280)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemiring_2446 -> T_Semiring_2280
du_semiring_2576 (T_CommutativeSemiring_2446 -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemiring_2446
v0))
-- Algebra.Bundles.CommutativeSemiring._.semiringWithoutOne
d_semiringWithoutOne_2616 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeSemiring_2446 -> T_SemiringWithoutOne_1880
d_semiringWithoutOne_2616 :: () -> () -> T_CommutativeSemiring_2446 -> T_SemiringWithoutOne_1880
d_semiringWithoutOne_2616 ~()
v0 ~()
v1 T_CommutativeSemiring_2446
v2
  = T_CommutativeSemiring_2446 -> T_SemiringWithoutOne_1880
du_semiringWithoutOne_2616 T_CommutativeSemiring_2446
v2
du_semiringWithoutOne_2616 ::
  T_CommutativeSemiring_2446 -> T_SemiringWithoutOne_1880
du_semiringWithoutOne_2616 :: T_CommutativeSemiring_2446 -> T_SemiringWithoutOne_1880
du_semiringWithoutOne_2616 T_CommutativeSemiring_2446
v0
  = (T_Semiring_2280 -> T_SemiringWithoutOne_1880)
-> AgdaAny -> T_SemiringWithoutOne_1880
forall a b. a -> b
coe T_Semiring_2280 -> T_SemiringWithoutOne_1880
du_semiringWithoutOne_2436 ((T_CommutativeSemiring_2446 -> T_Semiring_2280)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemiring_2446 -> T_Semiring_2280
du_semiring_2576 (T_CommutativeSemiring_2446 -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemiring_2446
v0))
-- Algebra.Bundles.CommutativeSemiring.*-commutativeMonoid
d_'42''45'commutativeMonoid_2618 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeSemiring_2446 -> T_CommutativeMonoid_962
d_'42''45'commutativeMonoid_2618 :: () -> () -> T_CommutativeSemiring_2446 -> T_CommutativeMonoid_962
d_'42''45'commutativeMonoid_2618 ~()
v0 ~()
v1 T_CommutativeSemiring_2446
v2
  = T_CommutativeSemiring_2446 -> T_CommutativeMonoid_962
du_'42''45'commutativeMonoid_2618 T_CommutativeSemiring_2446
v2
du_'42''45'commutativeMonoid_2618 ::
  T_CommutativeSemiring_2446 -> T_CommutativeMonoid_962
du_'42''45'commutativeMonoid_2618 :: T_CommutativeSemiring_2446 -> T_CommutativeMonoid_962
du_'42''45'commutativeMonoid_2618 T_CommutativeSemiring_2446
v0
  = ((AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny -> T_IsCommutativeMonoid_736 -> T_CommutativeMonoid_962)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_CommutativeMonoid_962
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> T_IsCommutativeMonoid_736 -> T_CommutativeMonoid_962
C_CommutativeMonoid'46'constructor_17931 (T_CommutativeSemiring_2446 -> AgdaAny -> AgdaAny -> AgdaAny
d__'42'__2472 (T_CommutativeSemiring_2446 -> T_CommutativeSemiring_2446
forall a b. a -> b
coe T_CommutativeSemiring_2446
v0))
      (T_CommutativeSemiring_2446 -> AgdaAny
d_1'35'_2476 (T_CommutativeSemiring_2446 -> T_CommutativeSemiring_2446
forall a b. a -> b
coe T_CommutativeSemiring_2446
v0))
      ((T_IsCommutativeSemiring_1678 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCommutativeSemiring_1678 -> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.du_'42''45'isCommutativeMonoid_1788
         ((T_CommutativeSemiring_2446 -> T_IsCommutativeSemiring_1678)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemiring_2446 -> T_IsCommutativeSemiring_1678
d_isCommutativeSemiring_2478 (T_CommutativeSemiring_2446 -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemiring_2446
v0)))
-- Algebra.Bundles.CommutativeSemiring._.commutativeMagma
d_commutativeMagma_2622 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeSemiring_2446 -> T_CommutativeMagma_180
d_commutativeMagma_2622 :: () -> () -> T_CommutativeSemiring_2446 -> T_CommutativeMagma_180
d_commutativeMagma_2622 ~()
v0 ~()
v1 T_CommutativeSemiring_2446
v2 = T_CommutativeSemiring_2446 -> T_CommutativeMagma_180
du_commutativeMagma_2622 T_CommutativeSemiring_2446
v2
du_commutativeMagma_2622 ::
  T_CommutativeSemiring_2446 -> T_CommutativeMagma_180
du_commutativeMagma_2622 :: T_CommutativeSemiring_2446 -> T_CommutativeMagma_180
du_commutativeMagma_2622 T_CommutativeSemiring_2446
v0
  = let v1 :: t
v1 = (T_CommutativeSemiring_2446 -> T_CommutativeMonoid_962)
-> AgdaAny -> t
forall a b. a -> b
coe T_CommutativeSemiring_2446 -> T_CommutativeMonoid_962
du_'42''45'commutativeMonoid_2618 (T_CommutativeSemiring_2446 -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemiring_2446
v0) in
    AgdaAny -> T_CommutativeMagma_180
forall a b. a -> b
coe
      ((T_CommutativeSemigroup_662 -> T_CommutativeMagma_180)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_CommutativeSemigroup_662 -> T_CommutativeMagma_180
du_commutativeMagma_726
         ((T_CommutativeMonoid_962 -> T_CommutativeSemigroup_662)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeMonoid_962 -> T_CommutativeSemigroup_662
du_commutativeSemigroup_1048 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1)))
-- Algebra.Bundles.CommutativeSemiring._.commutativeSemigroup
d_commutativeSemigroup_2624 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeSemiring_2446 -> T_CommutativeSemigroup_662
d_commutativeSemigroup_2624 :: ()
-> () -> T_CommutativeSemiring_2446 -> T_CommutativeSemigroup_662
d_commutativeSemigroup_2624 ~()
v0 ~()
v1 T_CommutativeSemiring_2446
v2
  = T_CommutativeSemiring_2446 -> T_CommutativeSemigroup_662
du_commutativeSemigroup_2624 T_CommutativeSemiring_2446
v2
du_commutativeSemigroup_2624 ::
  T_CommutativeSemiring_2446 -> T_CommutativeSemigroup_662
du_commutativeSemigroup_2624 :: T_CommutativeSemiring_2446 -> T_CommutativeSemigroup_662
du_commutativeSemigroup_2624 T_CommutativeSemiring_2446
v0
  = (T_CommutativeMonoid_962 -> T_CommutativeSemigroup_662)
-> AgdaAny -> T_CommutativeSemigroup_662
forall a b. a -> b
coe
      T_CommutativeMonoid_962 -> T_CommutativeSemigroup_662
du_commutativeSemigroup_1048
      ((T_CommutativeSemiring_2446 -> T_CommutativeMonoid_962)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemiring_2446 -> T_CommutativeMonoid_962
du_'42''45'commutativeMonoid_2618 (T_CommutativeSemiring_2446 -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemiring_2446
v0))
-- Algebra.Bundles.CommutativeSemiring.commutativeSemiringWithoutOne
d_commutativeSemiringWithoutOne_2626 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeSemiring_2446 -> T_CommutativeSemiringWithoutOne_2002
d_commutativeSemiringWithoutOne_2626 :: ()
-> ()
-> T_CommutativeSemiring_2446
-> T_CommutativeSemiringWithoutOne_2002
d_commutativeSemiringWithoutOne_2626 ~()
v0 ~()
v1 T_CommutativeSemiring_2446
v2
  = T_CommutativeSemiring_2446 -> T_CommutativeSemiringWithoutOne_2002
du_commutativeSemiringWithoutOne_2626 T_CommutativeSemiring_2446
v2
du_commutativeSemiringWithoutOne_2626 ::
  T_CommutativeSemiring_2446 -> T_CommutativeSemiringWithoutOne_2002
du_commutativeSemiringWithoutOne_2626 :: T_CommutativeSemiring_2446 -> T_CommutativeSemiringWithoutOne_2002
du_commutativeSemiringWithoutOne_2626 T_CommutativeSemiring_2446
v0
  = ((AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> T_IsCommutativeSemiringWithoutOne_1382
 -> T_CommutativeSemiringWithoutOne_2002)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_CommutativeSemiringWithoutOne_2002
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsCommutativeSemiringWithoutOne_1382
-> T_CommutativeSemiringWithoutOne_2002
C_CommutativeSemiringWithoutOne'46'constructor_36869
      (T_CommutativeSemiring_2446 -> AgdaAny -> AgdaAny -> AgdaAny
d__'43'__2470 (T_CommutativeSemiring_2446 -> T_CommutativeSemiring_2446
forall a b. a -> b
coe T_CommutativeSemiring_2446
v0)) (T_CommutativeSemiring_2446 -> AgdaAny -> AgdaAny -> AgdaAny
d__'42'__2472 (T_CommutativeSemiring_2446 -> T_CommutativeSemiring_2446
forall a b. a -> b
coe T_CommutativeSemiring_2446
v0))
      (T_CommutativeSemiring_2446 -> AgdaAny
d_0'35'_2474 (T_CommutativeSemiring_2446 -> T_CommutativeSemiring_2446
forall a b. a -> b
coe T_CommutativeSemiring_2446
v0))
      ((T_IsCommutativeSemiring_1678
 -> T_IsCommutativeSemiringWithoutOne_1382)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCommutativeSemiring_1678
-> T_IsCommutativeSemiringWithoutOne_1382
MAlonzo.Code.Algebra.Structures.du_isCommutativeSemiringWithoutOne_1780
         ((T_CommutativeSemiring_2446 -> T_IsCommutativeSemiring_1678)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemiring_2446 -> T_IsCommutativeSemiring_1678
d_isCommutativeSemiring_2478 (T_CommutativeSemiring_2446 -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemiring_2446
v0)))
-- Algebra.Bundles.CancellativeCommutativeSemiring
d_CancellativeCommutativeSemiring_2632 :: p -> p -> ()
d_CancellativeCommutativeSemiring_2632 p
a0 p
a1 = ()
data T_CancellativeCommutativeSemiring_2632
  = C_CancellativeCommutativeSemiring'46'constructor_48119 (AgdaAny ->
                                                            AgdaAny -> AgdaAny)
                                                           (AgdaAny -> AgdaAny -> AgdaAny) AgdaAny
                                                           AgdaAny
                                                           MAlonzo.Code.Algebra.Structures.T_IsCancellativeCommutativeSemiring_1798
-- Algebra.Bundles.CancellativeCommutativeSemiring.Carrier
d_Carrier_2652 :: T_CancellativeCommutativeSemiring_2632 -> ()
d_Carrier_2652 :: T_CancellativeCommutativeSemiring_2632 -> ()
d_Carrier_2652 = T_CancellativeCommutativeSemiring_2632 -> ()
forall a. a
erased
-- Algebra.Bundles.CancellativeCommutativeSemiring._≈_
d__'8776'__2654 ::
  T_CancellativeCommutativeSemiring_2632 -> AgdaAny -> AgdaAny -> ()
d__'8776'__2654 :: T_CancellativeCommutativeSemiring_2632 -> AgdaAny -> AgdaAny -> ()
d__'8776'__2654 = T_CancellativeCommutativeSemiring_2632 -> AgdaAny -> AgdaAny -> ()
forall a. a
erased
-- Algebra.Bundles.CancellativeCommutativeSemiring._+_
d__'43'__2656 ::
  T_CancellativeCommutativeSemiring_2632 ->
  AgdaAny -> AgdaAny -> AgdaAny
d__'43'__2656 :: T_CancellativeCommutativeSemiring_2632
-> AgdaAny -> AgdaAny -> AgdaAny
d__'43'__2656 T_CancellativeCommutativeSemiring_2632
v0
  = case T_CancellativeCommutativeSemiring_2632
-> T_CancellativeCommutativeSemiring_2632
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2632
v0 of
      C_CancellativeCommutativeSemiring'46'constructor_48119 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny
v5 AgdaAny
v6 T_IsCancellativeCommutativeSemiring_1798
v7
        -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v3
      T_CancellativeCommutativeSemiring_2632
_ -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.CancellativeCommutativeSemiring._*_
d__'42'__2658 ::
  T_CancellativeCommutativeSemiring_2632 ->
  AgdaAny -> AgdaAny -> AgdaAny
d__'42'__2658 :: T_CancellativeCommutativeSemiring_2632
-> AgdaAny -> AgdaAny -> AgdaAny
d__'42'__2658 T_CancellativeCommutativeSemiring_2632
v0
  = case T_CancellativeCommutativeSemiring_2632
-> T_CancellativeCommutativeSemiring_2632
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2632
v0 of
      C_CancellativeCommutativeSemiring'46'constructor_48119 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny
v5 AgdaAny
v6 T_IsCancellativeCommutativeSemiring_1798
v7
        -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v4
      T_CancellativeCommutativeSemiring_2632
_ -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.CancellativeCommutativeSemiring.0#
d_0'35'_2660 :: T_CancellativeCommutativeSemiring_2632 -> AgdaAny
d_0'35'_2660 :: T_CancellativeCommutativeSemiring_2632 -> AgdaAny
d_0'35'_2660 T_CancellativeCommutativeSemiring_2632
v0
  = case T_CancellativeCommutativeSemiring_2632
-> T_CancellativeCommutativeSemiring_2632
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2632
v0 of
      C_CancellativeCommutativeSemiring'46'constructor_48119 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny
v5 AgdaAny
v6 T_IsCancellativeCommutativeSemiring_1798
v7
        -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v5
      T_CancellativeCommutativeSemiring_2632
_ -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.CancellativeCommutativeSemiring.1#
d_1'35'_2662 :: T_CancellativeCommutativeSemiring_2632 -> AgdaAny
d_1'35'_2662 :: T_CancellativeCommutativeSemiring_2632 -> AgdaAny
d_1'35'_2662 T_CancellativeCommutativeSemiring_2632
v0
  = case T_CancellativeCommutativeSemiring_2632
-> T_CancellativeCommutativeSemiring_2632
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2632
v0 of
      C_CancellativeCommutativeSemiring'46'constructor_48119 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny
v5 AgdaAny
v6 T_IsCancellativeCommutativeSemiring_1798
v7
        -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v6
      T_CancellativeCommutativeSemiring_2632
_ -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.CancellativeCommutativeSemiring.isCancellativeCommutativeSemiring
d_isCancellativeCommutativeSemiring_2664 ::
  T_CancellativeCommutativeSemiring_2632 ->
  MAlonzo.Code.Algebra.Structures.T_IsCancellativeCommutativeSemiring_1798
d_isCancellativeCommutativeSemiring_2664 :: T_CancellativeCommutativeSemiring_2632
-> T_IsCancellativeCommutativeSemiring_1798
d_isCancellativeCommutativeSemiring_2664 T_CancellativeCommutativeSemiring_2632
v0
  = case T_CancellativeCommutativeSemiring_2632
-> T_CancellativeCommutativeSemiring_2632
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2632
v0 of
      C_CancellativeCommutativeSemiring'46'constructor_48119 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny
v5 AgdaAny
v6 T_IsCancellativeCommutativeSemiring_1798
v7
        -> T_IsCancellativeCommutativeSemiring_1798
-> T_IsCancellativeCommutativeSemiring_1798
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1798
v7
      T_CancellativeCommutativeSemiring_2632
_ -> T_IsCancellativeCommutativeSemiring_1798
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.CancellativeCommutativeSemiring._.*-assoc
d_'42''45'assoc_2668 ::
  T_CancellativeCommutativeSemiring_2632 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'assoc_2668 :: T_CancellativeCommutativeSemiring_2632
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'assoc_2668 T_CancellativeCommutativeSemiring_2632
v0
  = (T_IsSemiringWithoutAnnihilatingZero_1468
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsSemiringWithoutAnnihilatingZero_1468
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'42''45'assoc_1492
      ((T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
         ((T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570
MAlonzo.Code.Algebra.Structures.d_isSemiring_1692
            ((T_IsCancellativeCommutativeSemiring_1798
 -> T_IsCommutativeSemiring_1678)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsCancellativeCommutativeSemiring_1798
-> T_IsCommutativeSemiring_1678
MAlonzo.Code.Algebra.Structures.d_isCommutativeSemiring_1812
               ((T_CancellativeCommutativeSemiring_2632
 -> T_IsCancellativeCommutativeSemiring_1798)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2632
-> T_IsCancellativeCommutativeSemiring_1798
d_isCancellativeCommutativeSemiring_2664 (T_CancellativeCommutativeSemiring_2632 -> AgdaAny
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2632
v0)))))
-- Algebra.Bundles.CancellativeCommutativeSemiring._.*-cancelʳ-nonZero
d_'42''45'cancel'691''45'nonZero_2670 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CancellativeCommutativeSemiring_2632 ->
  AgdaAny ->
  AgdaAny ->
  AgdaAny ->
  (AgdaAny -> MAlonzo.Code.Data.Irrelevant.T_Irrelevant_20) ->
  AgdaAny -> AgdaAny
d_'42''45'cancel'691''45'nonZero_2670 :: ()
-> ()
-> T_CancellativeCommutativeSemiring_2632
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> (AgdaAny -> T_Irrelevant_20)
-> AgdaAny
-> AgdaAny
d_'42''45'cancel'691''45'nonZero_2670 ~()
v0 ~()
v1 T_CancellativeCommutativeSemiring_2632
v2
  = T_CancellativeCommutativeSemiring_2632
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> (AgdaAny -> T_Irrelevant_20)
-> AgdaAny
-> AgdaAny
du_'42''45'cancel'691''45'nonZero_2670 T_CancellativeCommutativeSemiring_2632
v2
du_'42''45'cancel'691''45'nonZero_2670 ::
  T_CancellativeCommutativeSemiring_2632 ->
  AgdaAny ->
  AgdaAny ->
  AgdaAny ->
  (AgdaAny -> MAlonzo.Code.Data.Irrelevant.T_Irrelevant_20) ->
  AgdaAny -> AgdaAny
du_'42''45'cancel'691''45'nonZero_2670 :: T_CancellativeCommutativeSemiring_2632
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> (AgdaAny -> T_Irrelevant_20)
-> AgdaAny
-> AgdaAny
du_'42''45'cancel'691''45'nonZero_2670 T_CancellativeCommutativeSemiring_2632
v0
  = ((AgdaAny -> AgdaAny -> AgdaAny)
 -> T_IsCancellativeCommutativeSemiring_1798
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> (AgdaAny -> T_Irrelevant_20)
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> (AgdaAny -> T_Irrelevant_20)
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsCancellativeCommutativeSemiring_1798
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> (AgdaAny -> T_Irrelevant_20)
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'42''45'cancel'691''45'nonZero_1912
      ((T_CancellativeCommutativeSemiring_2632
 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2632
-> AgdaAny -> AgdaAny -> AgdaAny
d__'42'__2658 (T_CancellativeCommutativeSemiring_2632 -> AgdaAny
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2632
v0))
      ((T_CancellativeCommutativeSemiring_2632
 -> T_IsCancellativeCommutativeSemiring_1798)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2632
-> T_IsCancellativeCommutativeSemiring_1798
d_isCancellativeCommutativeSemiring_2664 (T_CancellativeCommutativeSemiring_2632 -> AgdaAny
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2632
v0))
-- Algebra.Bundles.CancellativeCommutativeSemiring._.*-cancelˡ-nonZero
d_'42''45'cancel'737''45'nonZero_2672 ::
  T_CancellativeCommutativeSemiring_2632 ->
  AgdaAny ->
  AgdaAny ->
  AgdaAny ->
  (AgdaAny -> MAlonzo.Code.Data.Irrelevant.T_Irrelevant_20) ->
  AgdaAny -> AgdaAny
d_'42''45'cancel'737''45'nonZero_2672 :: T_CancellativeCommutativeSemiring_2632
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> (AgdaAny -> T_Irrelevant_20)
-> AgdaAny
-> AgdaAny
d_'42''45'cancel'737''45'nonZero_2672 T_CancellativeCommutativeSemiring_2632
v0
  = (T_IsCancellativeCommutativeSemiring_1798
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> (AgdaAny -> T_Irrelevant_20)
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> (AgdaAny -> T_Irrelevant_20)
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsCancellativeCommutativeSemiring_1798
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> (AgdaAny -> T_Irrelevant_20)
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'42''45'cancel'737''45'nonZero_1814
      ((T_CancellativeCommutativeSemiring_2632
 -> T_IsCancellativeCommutativeSemiring_1798)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2632
-> T_IsCancellativeCommutativeSemiring_1798
d_isCancellativeCommutativeSemiring_2664 (T_CancellativeCommutativeSemiring_2632 -> AgdaAny
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2632
v0))
-- Algebra.Bundles.CancellativeCommutativeSemiring._.*-comm
d_'42''45'comm_2674 ::
  T_CancellativeCommutativeSemiring_2632 ->
  AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'comm_2674 :: T_CancellativeCommutativeSemiring_2632
-> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'comm_2674 T_CancellativeCommutativeSemiring_2632
v0
  = (T_IsCommutativeSemiring_1678 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsCommutativeSemiring_1678 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'42''45'comm_1694
      ((T_IsCancellativeCommutativeSemiring_1798
 -> T_IsCommutativeSemiring_1678)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCancellativeCommutativeSemiring_1798
-> T_IsCommutativeSemiring_1678
MAlonzo.Code.Algebra.Structures.d_isCommutativeSemiring_1812
         ((T_CancellativeCommutativeSemiring_2632
 -> T_IsCancellativeCommutativeSemiring_1798)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2632
-> T_IsCancellativeCommutativeSemiring_1798
d_isCancellativeCommutativeSemiring_2664 (T_CancellativeCommutativeSemiring_2632 -> AgdaAny
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2632
v0)))
-- Algebra.Bundles.CancellativeCommutativeSemiring._.*-cong
d_'42''45'cong_2676 ::
  T_CancellativeCommutativeSemiring_2632 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'cong_2676 :: T_CancellativeCommutativeSemiring_2632
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'42''45'cong_2676 T_CancellativeCommutativeSemiring_2632
v0
  = (T_IsSemiringWithoutAnnihilatingZero_1468
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsSemiringWithoutAnnihilatingZero_1468
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'42''45'cong_1490
      ((T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
         ((T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570
MAlonzo.Code.Algebra.Structures.d_isSemiring_1692
            ((T_IsCancellativeCommutativeSemiring_1798
 -> T_IsCommutativeSemiring_1678)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsCancellativeCommutativeSemiring_1798
-> T_IsCommutativeSemiring_1678
MAlonzo.Code.Algebra.Structures.d_isCommutativeSemiring_1812
               ((T_CancellativeCommutativeSemiring_2632
 -> T_IsCancellativeCommutativeSemiring_1798)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2632
-> T_IsCancellativeCommutativeSemiring_1798
d_isCancellativeCommutativeSemiring_2664 (T_CancellativeCommutativeSemiring_2632 -> AgdaAny
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2632
v0)))))
-- Algebra.Bundles.CancellativeCommutativeSemiring._.∙-congʳ
d_'8729''45'cong'691'_2678 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CancellativeCommutativeSemiring_2632 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_2678 :: ()
-> ()
-> T_CancellativeCommutativeSemiring_2632
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_2678 ~()
v0 ~()
v1 T_CancellativeCommutativeSemiring_2632
v2
  = T_CancellativeCommutativeSemiring_2632
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_2678 T_CancellativeCommutativeSemiring_2632
v2
du_'8729''45'cong'691'_2678 ::
  T_CancellativeCommutativeSemiring_2632 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_2678 :: T_CancellativeCommutativeSemiring_2632
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_2678 T_CancellativeCommutativeSemiring_2632
v0
  = let v1 :: T_IsCancellativeCommutativeSemiring_1798
v1 = T_CancellativeCommutativeSemiring_2632
-> T_IsCancellativeCommutativeSemiring_1798
d_isCancellativeCommutativeSemiring_2664 (T_CancellativeCommutativeSemiring_2632
-> T_CancellativeCommutativeSemiring_2632
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2632
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsCommutativeSemiring_1678
v2
             = T_IsCancellativeCommutativeSemiring_1798
-> T_IsCommutativeSemiring_1678
MAlonzo.Code.Algebra.Structures.d_isCommutativeSemiring_1812
                 (T_IsCancellativeCommutativeSemiring_1798
-> T_IsCancellativeCommutativeSemiring_1798
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1798
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemiring_1570
v3
                = T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570
MAlonzo.Code.Algebra.Structures.d_isSemiring_1692 (T_IsCommutativeSemiring_1678 -> T_IsCommutativeSemiring_1678
forall a b. a -> b
coe T_IsCommutativeSemiring_1678
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsSemiringWithoutAnnihilatingZero_1468
v4
                   = T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                       (T_IsSemiring_1570 -> T_IsSemiring_1570
forall a b. a -> b
coe T_IsSemiring_1570
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: t
v5
                      = (T_IsSemiringWithoutAnnihilatingZero_1468 -> T_IsMonoid_686)
-> AgdaAny -> t
forall a b. a -> b
coe
                          T_IsSemiringWithoutAnnihilatingZero_1468 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.du_'42''45'isMonoid_1550
                          (T_IsSemiringWithoutAnnihilatingZero_1468 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (let v6 :: T_IsSemigroup_472
v6
                         = T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (AgdaAny -> T_IsMonoid_686
forall a b. a -> b
coe AgdaAny
forall a. a
v5) in
                   AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'691'_206
                        ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v6))))))))
-- Algebra.Bundles.CancellativeCommutativeSemiring._.∙-congˡ
d_'8729''45'cong'737'_2680 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CancellativeCommutativeSemiring_2632 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_2680 :: ()
-> ()
-> T_CancellativeCommutativeSemiring_2632
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_2680 ~()
v0 ~()
v1 T_CancellativeCommutativeSemiring_2632
v2
  = T_CancellativeCommutativeSemiring_2632
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_2680 T_CancellativeCommutativeSemiring_2632
v2
du_'8729''45'cong'737'_2680 ::
  T_CancellativeCommutativeSemiring_2632 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_2680 :: T_CancellativeCommutativeSemiring_2632
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_2680 T_CancellativeCommutativeSemiring_2632
v0
  = let v1 :: T_IsCancellativeCommutativeSemiring_1798
v1 = T_CancellativeCommutativeSemiring_2632
-> T_IsCancellativeCommutativeSemiring_1798
d_isCancellativeCommutativeSemiring_2664 (T_CancellativeCommutativeSemiring_2632
-> T_CancellativeCommutativeSemiring_2632
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2632
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsCommutativeSemiring_1678
v2
             = T_IsCancellativeCommutativeSemiring_1798
-> T_IsCommutativeSemiring_1678
MAlonzo.Code.Algebra.Structures.d_isCommutativeSemiring_1812
                 (T_IsCancellativeCommutativeSemiring_1798
-> T_IsCancellativeCommutativeSemiring_1798
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1798
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemiring_1570
v3
                = T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570
MAlonzo.Code.Algebra.Structures.d_isSemiring_1692 (T_IsCommutativeSemiring_1678 -> T_IsCommutativeSemiring_1678
forall a b. a -> b
coe T_IsCommutativeSemiring_1678
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsSemiringWithoutAnnihilatingZero_1468
v4
                   = T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                       (T_IsSemiring_1570 -> T_IsSemiring_1570
forall a b. a -> b
coe T_IsSemiring_1570
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: t
v5
                      = (T_IsSemiringWithoutAnnihilatingZero_1468 -> T_IsMonoid_686)
-> AgdaAny -> t
forall a b. a -> b
coe
                          T_IsSemiringWithoutAnnihilatingZero_1468 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.du_'42''45'isMonoid_1550
                          (T_IsSemiringWithoutAnnihilatingZero_1468 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (let v6 :: T_IsSemigroup_472
v6
                         = T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (AgdaAny -> T_IsMonoid_686
forall a b. a -> b
coe AgdaAny
forall a. a
v5) in
                   AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'737'_202
                        ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v6))))))))
-- Algebra.Bundles.CancellativeCommutativeSemiring._.*-identity
d_'42''45'identity_2682 ::
  T_CancellativeCommutativeSemiring_2632 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'42''45'identity_2682 :: T_CancellativeCommutativeSemiring_2632 -> T_Σ_14
d_'42''45'identity_2682 T_CancellativeCommutativeSemiring_2632
v0
  = (T_IsSemiringWithoutAnnihilatingZero_1468 -> T_Σ_14)
-> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsSemiringWithoutAnnihilatingZero_1468 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_'42''45'identity_1494
      ((T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
         ((T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570
MAlonzo.Code.Algebra.Structures.d_isSemiring_1692
            ((T_IsCancellativeCommutativeSemiring_1798
 -> T_IsCommutativeSemiring_1678)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsCancellativeCommutativeSemiring_1798
-> T_IsCommutativeSemiring_1678
MAlonzo.Code.Algebra.Structures.d_isCommutativeSemiring_1812
               ((T_CancellativeCommutativeSemiring_2632
 -> T_IsCancellativeCommutativeSemiring_1798)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2632
-> T_IsCancellativeCommutativeSemiring_1798
d_isCancellativeCommutativeSemiring_2664 (T_CancellativeCommutativeSemiring_2632 -> AgdaAny
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2632
v0)))))
-- Algebra.Bundles.CancellativeCommutativeSemiring._.identityʳ
d_identity'691'_2684 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CancellativeCommutativeSemiring_2632 -> AgdaAny -> AgdaAny
d_identity'691'_2684 :: ()
-> ()
-> T_CancellativeCommutativeSemiring_2632
-> AgdaAny
-> AgdaAny
d_identity'691'_2684 ~()
v0 ~()
v1 T_CancellativeCommutativeSemiring_2632
v2 = T_CancellativeCommutativeSemiring_2632 -> AgdaAny -> AgdaAny
du_identity'691'_2684 T_CancellativeCommutativeSemiring_2632
v2
du_identity'691'_2684 ::
  T_CancellativeCommutativeSemiring_2632 -> AgdaAny -> AgdaAny
du_identity'691'_2684 :: T_CancellativeCommutativeSemiring_2632 -> AgdaAny -> AgdaAny
du_identity'691'_2684 T_CancellativeCommutativeSemiring_2632
v0
  = let v1 :: T_IsCancellativeCommutativeSemiring_1798
v1 = T_CancellativeCommutativeSemiring_2632
-> T_IsCancellativeCommutativeSemiring_1798
d_isCancellativeCommutativeSemiring_2664 (T_CancellativeCommutativeSemiring_2632
-> T_CancellativeCommutativeSemiring_2632
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2632
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsCommutativeSemiring_1678
v2
             = T_IsCancellativeCommutativeSemiring_1798
-> T_IsCommutativeSemiring_1678
MAlonzo.Code.Algebra.Structures.d_isCommutativeSemiring_1812
                 (T_IsCancellativeCommutativeSemiring_1798
-> T_IsCancellativeCommutativeSemiring_1798
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1798
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemiring_1570
v3
                = T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570
MAlonzo.Code.Algebra.Structures.d_isSemiring_1692 (T_IsCommutativeSemiring_1678 -> T_IsCommutativeSemiring_1678
forall a b. a -> b
coe T_IsCommutativeSemiring_1678
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsSemiringWithoutAnnihilatingZero_1468
v4
                   = T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                       (T_IsSemiring_1570 -> T_IsSemiring_1570
forall a b. a -> b
coe T_IsSemiring_1570
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               ((T_IsMonoid_686 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsMonoid_686 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_identity'691'_728
                  ((T_IsSemiringWithoutAnnihilatingZero_1468 -> T_IsMonoid_686)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsSemiringWithoutAnnihilatingZero_1468 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.du_'42''45'isMonoid_1550
                     (T_IsSemiringWithoutAnnihilatingZero_1468 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
v4))))))
-- Algebra.Bundles.CancellativeCommutativeSemiring._.identityˡ
d_identity'737'_2686 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CancellativeCommutativeSemiring_2632 -> AgdaAny -> AgdaAny
d_identity'737'_2686 :: ()
-> ()
-> T_CancellativeCommutativeSemiring_2632
-> AgdaAny
-> AgdaAny
d_identity'737'_2686 ~()
v0 ~()
v1 T_CancellativeCommutativeSemiring_2632
v2 = T_CancellativeCommutativeSemiring_2632 -> AgdaAny -> AgdaAny
du_identity'737'_2686 T_CancellativeCommutativeSemiring_2632
v2
du_identity'737'_2686 ::
  T_CancellativeCommutativeSemiring_2632 -> AgdaAny -> AgdaAny
du_identity'737'_2686 :: T_CancellativeCommutativeSemiring_2632 -> AgdaAny -> AgdaAny
du_identity'737'_2686 T_CancellativeCommutativeSemiring_2632
v0
  = let v1 :: T_IsCancellativeCommutativeSemiring_1798
v1 = T_CancellativeCommutativeSemiring_2632
-> T_IsCancellativeCommutativeSemiring_1798
d_isCancellativeCommutativeSemiring_2664 (T_CancellativeCommutativeSemiring_2632
-> T_CancellativeCommutativeSemiring_2632
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2632
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsCommutativeSemiring_1678
v2
             = T_IsCancellativeCommutativeSemiring_1798
-> T_IsCommutativeSemiring_1678
MAlonzo.Code.Algebra.Structures.d_isCommutativeSemiring_1812
                 (T_IsCancellativeCommutativeSemiring_1798
-> T_IsCancellativeCommutativeSemiring_1798
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1798
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemiring_1570
v3
                = T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570
MAlonzo.Code.Algebra.Structures.d_isSemiring_1692 (T_IsCommutativeSemiring_1678 -> T_IsCommutativeSemiring_1678
forall a b. a -> b
coe T_IsCommutativeSemiring_1678
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsSemiringWithoutAnnihilatingZero_1468
v4
                   = T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                       (T_IsSemiring_1570 -> T_IsSemiring_1570
forall a b. a -> b
coe T_IsSemiring_1570
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               ((T_IsMonoid_686 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsMonoid_686 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_identity'737'_726
                  ((T_IsSemiringWithoutAnnihilatingZero_1468 -> T_IsMonoid_686)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsSemiringWithoutAnnihilatingZero_1468 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.du_'42''45'isMonoid_1550
                     (T_IsSemiringWithoutAnnihilatingZero_1468 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
v4))))))
-- Algebra.Bundles.CancellativeCommutativeSemiring._.isCommutativeMagma
d_isCommutativeMagma_2688 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CancellativeCommutativeSemiring_2632 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMagma_212
d_isCommutativeMagma_2688 :: ()
-> ()
-> T_CancellativeCommutativeSemiring_2632
-> T_IsCommutativeMagma_212
d_isCommutativeMagma_2688 ~()
v0 ~()
v1 T_CancellativeCommutativeSemiring_2632
v2
  = T_CancellativeCommutativeSemiring_2632 -> T_IsCommutativeMagma_212
du_isCommutativeMagma_2688 T_CancellativeCommutativeSemiring_2632
v2
du_isCommutativeMagma_2688 ::
  T_CancellativeCommutativeSemiring_2632 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMagma_212
du_isCommutativeMagma_2688 :: T_CancellativeCommutativeSemiring_2632 -> T_IsCommutativeMagma_212
du_isCommutativeMagma_2688 T_CancellativeCommutativeSemiring_2632
v0
  = let v1 :: T_IsCancellativeCommutativeSemiring_1798
v1 = T_CancellativeCommutativeSemiring_2632
-> T_IsCancellativeCommutativeSemiring_1798
d_isCancellativeCommutativeSemiring_2664 (T_CancellativeCommutativeSemiring_2632
-> T_CancellativeCommutativeSemiring_2632
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2632
v0) in
    AgdaAny -> T_IsCommutativeMagma_212
forall a b. a -> b
coe
      (let v2 :: T_IsCommutativeSemiring_1678
v2
             = T_IsCancellativeCommutativeSemiring_1798
-> T_IsCommutativeSemiring_1678
MAlonzo.Code.Algebra.Structures.d_isCommutativeSemiring_1812
                 (T_IsCancellativeCommutativeSemiring_1798
-> T_IsCancellativeCommutativeSemiring_1798
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1798
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: t
v3
                = (T_IsCommutativeSemiring_1678
 -> T_IsCommutativeSemiringWithoutOne_1382)
-> AgdaAny -> t
forall a b. a -> b
coe
                    T_IsCommutativeSemiring_1678
-> T_IsCommutativeSemiringWithoutOne_1382
MAlonzo.Code.Algebra.Structures.du_isCommutativeSemiringWithoutOne_1780
                    (T_IsCommutativeSemiring_1678 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiring_1678
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsCommutativeSemigroup_548 -> T_IsCommutativeMagma_212)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsCommutativeSemigroup_548 -> T_IsCommutativeMagma_212
MAlonzo.Code.Algebra.Structures.du_isCommutativeMagma_586
               ((T_IsCommutativeSemiringWithoutOne_1382
 -> T_IsCommutativeSemigroup_548)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsCommutativeSemiringWithoutOne_1382
-> T_IsCommutativeSemigroup_548
MAlonzo.Code.Algebra.Structures.du_'42''45'isCommutativeSemigroup_1454
                  (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3)))))
-- Algebra.Bundles.CancellativeCommutativeSemiring._.*-isCommutativeMonoid
d_'42''45'isCommutativeMonoid_2690 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CancellativeCommutativeSemiring_2632 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMonoid_736
d_'42''45'isCommutativeMonoid_2690 :: ()
-> ()
-> T_CancellativeCommutativeSemiring_2632
-> T_IsCommutativeMonoid_736
d_'42''45'isCommutativeMonoid_2690 ~()
v0 ~()
v1 T_CancellativeCommutativeSemiring_2632
v2
  = T_CancellativeCommutativeSemiring_2632 -> T_IsCommutativeMonoid_736
du_'42''45'isCommutativeMonoid_2690 T_CancellativeCommutativeSemiring_2632
v2
du_'42''45'isCommutativeMonoid_2690 ::
  T_CancellativeCommutativeSemiring_2632 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMonoid_736
du_'42''45'isCommutativeMonoid_2690 :: T_CancellativeCommutativeSemiring_2632 -> T_IsCommutativeMonoid_736
du_'42''45'isCommutativeMonoid_2690 T_CancellativeCommutativeSemiring_2632
v0
  = let v1 :: T_IsCancellativeCommutativeSemiring_1798
v1 = T_CancellativeCommutativeSemiring_2632
-> T_IsCancellativeCommutativeSemiring_1798
d_isCancellativeCommutativeSemiring_2664 (T_CancellativeCommutativeSemiring_2632
-> T_CancellativeCommutativeSemiring_2632
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2632
v0) in
    AgdaAny -> T_IsCommutativeMonoid_736
forall a b. a -> b
coe
      ((T_IsCommutativeSemiring_1678 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCommutativeSemiring_1678 -> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.du_'42''45'isCommutativeMonoid_1788
         ((T_IsCancellativeCommutativeSemiring_1798
 -> T_IsCommutativeSemiring_1678)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCancellativeCommutativeSemiring_1798
-> T_IsCommutativeSemiring_1678
MAlonzo.Code.Algebra.Structures.d_isCommutativeSemiring_1812
            (T_IsCancellativeCommutativeSemiring_1798 -> AgdaAny
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1798
v1)))
-- Algebra.Bundles.CancellativeCommutativeSemiring._.*-isCommutativeSemigroup
d_'42''45'isCommutativeSemigroup_2692 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CancellativeCommutativeSemiring_2632 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_548
d_'42''45'isCommutativeSemigroup_2692 :: ()
-> ()
-> T_CancellativeCommutativeSemiring_2632
-> T_IsCommutativeSemigroup_548
d_'42''45'isCommutativeSemigroup_2692 ~()
v0 ~()
v1 T_CancellativeCommutativeSemiring_2632
v2
  = T_CancellativeCommutativeSemiring_2632
-> T_IsCommutativeSemigroup_548
du_'42''45'isCommutativeSemigroup_2692 T_CancellativeCommutativeSemiring_2632
v2
du_'42''45'isCommutativeSemigroup_2692 ::
  T_CancellativeCommutativeSemiring_2632 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_548
du_'42''45'isCommutativeSemigroup_2692 :: T_CancellativeCommutativeSemiring_2632
-> T_IsCommutativeSemigroup_548
du_'42''45'isCommutativeSemigroup_2692 T_CancellativeCommutativeSemiring_2632
v0
  = let v1 :: T_IsCancellativeCommutativeSemiring_1798
v1 = T_CancellativeCommutativeSemiring_2632
-> T_IsCancellativeCommutativeSemiring_1798
d_isCancellativeCommutativeSemiring_2664 (T_CancellativeCommutativeSemiring_2632
-> T_CancellativeCommutativeSemiring_2632
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2632
v0) in
    AgdaAny -> T_IsCommutativeSemigroup_548
forall a b. a -> b
coe
      (let v2 :: T_IsCommutativeSemiring_1678
v2
             = T_IsCancellativeCommutativeSemiring_1798
-> T_IsCommutativeSemiring_1678
MAlonzo.Code.Algebra.Structures.d_isCommutativeSemiring_1812
                 (T_IsCancellativeCommutativeSemiring_1798
-> T_IsCancellativeCommutativeSemiring_1798
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1798
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsCommutativeSemiringWithoutOne_1382
 -> T_IsCommutativeSemigroup_548)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCommutativeSemiringWithoutOne_1382
-> T_IsCommutativeSemigroup_548
MAlonzo.Code.Algebra.Structures.du_'42''45'isCommutativeSemigroup_1454
            ((T_IsCommutativeSemiring_1678
 -> T_IsCommutativeSemiringWithoutOne_1382)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsCommutativeSemiring_1678
-> T_IsCommutativeSemiringWithoutOne_1382
MAlonzo.Code.Algebra.Structures.du_isCommutativeSemiringWithoutOne_1780
               (T_IsCommutativeSemiring_1678 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiring_1678
v2))))
-- Algebra.Bundles.CancellativeCommutativeSemiring._.*-isMagma
d_'42''45'isMagma_2694 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CancellativeCommutativeSemiring_2632 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_176
d_'42''45'isMagma_2694 :: () -> () -> T_CancellativeCommutativeSemiring_2632 -> T_IsMagma_176
d_'42''45'isMagma_2694 ~()
v0 ~()
v1 T_CancellativeCommutativeSemiring_2632
v2 = T_CancellativeCommutativeSemiring_2632 -> T_IsMagma_176
du_'42''45'isMagma_2694 T_CancellativeCommutativeSemiring_2632
v2
du_'42''45'isMagma_2694 ::
  T_CancellativeCommutativeSemiring_2632 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_176
du_'42''45'isMagma_2694 :: T_CancellativeCommutativeSemiring_2632 -> T_IsMagma_176
du_'42''45'isMagma_2694 T_CancellativeCommutativeSemiring_2632
v0
  = let v1 :: T_IsCancellativeCommutativeSemiring_1798
v1 = T_CancellativeCommutativeSemiring_2632
-> T_IsCancellativeCommutativeSemiring_1798
d_isCancellativeCommutativeSemiring_2664 (T_CancellativeCommutativeSemiring_2632
-> T_CancellativeCommutativeSemiring_2632
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2632
v0) in
    AgdaAny -> T_IsMagma_176
forall a b. a -> b
coe
      (let v2 :: T_IsCommutativeSemiring_1678
v2
             = T_IsCancellativeCommutativeSemiring_1798
-> T_IsCommutativeSemiring_1678
MAlonzo.Code.Algebra.Structures.d_isCommutativeSemiring_1812
                 (T_IsCancellativeCommutativeSemiring_1798
-> T_IsCancellativeCommutativeSemiring_1798
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1798
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemiring_1570
v3
                = T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570
MAlonzo.Code.Algebra.Structures.d_isSemiring_1692 (T_IsCommutativeSemiring_1678 -> T_IsCommutativeSemiring_1678
forall a b. a -> b
coe T_IsCommutativeSemiring_1678
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsSemiringWithoutAnnihilatingZero_1468 -> T_IsMagma_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemiringWithoutAnnihilatingZero_1468 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.du_'42''45'isMagma_1546
               ((T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                  (T_IsSemiring_1570 -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1570
v3)))))
-- Algebra.Bundles.CancellativeCommutativeSemiring._.*-isMonoid
d_'42''45'isMonoid_2696 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CancellativeCommutativeSemiring_2632 ->
  MAlonzo.Code.Algebra.Structures.T_IsMonoid_686
d_'42''45'isMonoid_2696 :: ()
-> () -> T_CancellativeCommutativeSemiring_2632 -> T_IsMonoid_686
d_'42''45'isMonoid_2696 ~()
v0 ~()
v1 T_CancellativeCommutativeSemiring_2632
v2 = T_CancellativeCommutativeSemiring_2632 -> T_IsMonoid_686
du_'42''45'isMonoid_2696 T_CancellativeCommutativeSemiring_2632
v2
du_'42''45'isMonoid_2696 ::
  T_CancellativeCommutativeSemiring_2632 ->
  MAlonzo.Code.Algebra.Structures.T_IsMonoid_686
du_'42''45'isMonoid_2696 :: T_CancellativeCommutativeSemiring_2632 -> T_IsMonoid_686
du_'42''45'isMonoid_2696 T_CancellativeCommutativeSemiring_2632
v0
  = let v1 :: T_IsCancellativeCommutativeSemiring_1798
v1 = T_CancellativeCommutativeSemiring_2632
-> T_IsCancellativeCommutativeSemiring_1798
d_isCancellativeCommutativeSemiring_2664 (T_CancellativeCommutativeSemiring_2632
-> T_CancellativeCommutativeSemiring_2632
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2632
v0) in
    AgdaAny -> T_IsMonoid_686
forall a b. a -> b
coe
      (let v2 :: T_IsCommutativeSemiring_1678
v2
             = T_IsCancellativeCommutativeSemiring_1798
-> T_IsCommutativeSemiring_1678
MAlonzo.Code.Algebra.Structures.d_isCommutativeSemiring_1812
                 (T_IsCancellativeCommutativeSemiring_1798
-> T_IsCancellativeCommutativeSemiring_1798
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1798
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemiring_1570
v3
                = T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570
MAlonzo.Code.Algebra.Structures.d_isSemiring_1692 (T_IsCommutativeSemiring_1678 -> T_IsCommutativeSemiring_1678
forall a b. a -> b
coe T_IsCommutativeSemiring_1678
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsSemiringWithoutAnnihilatingZero_1468 -> T_IsMonoid_686)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemiringWithoutAnnihilatingZero_1468 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.du_'42''45'isMonoid_1550
               ((T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                  (T_IsSemiring_1570 -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1570
v3)))))
-- Algebra.Bundles.CancellativeCommutativeSemiring._.*-isSemigroup
d_'42''45'isSemigroup_2698 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CancellativeCommutativeSemiring_2632 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_472
d_'42''45'isSemigroup_2698 :: ()
-> ()
-> T_CancellativeCommutativeSemiring_2632
-> T_IsSemigroup_472
d_'42''45'isSemigroup_2698 ~()
v0 ~()
v1 T_CancellativeCommutativeSemiring_2632
v2
  = T_CancellativeCommutativeSemiring_2632 -> T_IsSemigroup_472
du_'42''45'isSemigroup_2698 T_CancellativeCommutativeSemiring_2632
v2
du_'42''45'isSemigroup_2698 ::
  T_CancellativeCommutativeSemiring_2632 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_472
du_'42''45'isSemigroup_2698 :: T_CancellativeCommutativeSemiring_2632 -> T_IsSemigroup_472
du_'42''45'isSemigroup_2698 T_CancellativeCommutativeSemiring_2632
v0
  = let v1 :: T_IsCancellativeCommutativeSemiring_1798
v1 = T_CancellativeCommutativeSemiring_2632
-> T_IsCancellativeCommutativeSemiring_1798
d_isCancellativeCommutativeSemiring_2664 (T_CancellativeCommutativeSemiring_2632
-> T_CancellativeCommutativeSemiring_2632
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2632
v0) in
    AgdaAny -> T_IsSemigroup_472
forall a b. a -> b
coe
      (let v2 :: T_IsCommutativeSemiring_1678
v2
             = T_IsCancellativeCommutativeSemiring_1798
-> T_IsCommutativeSemiring_1678
MAlonzo.Code.Algebra.Structures.d_isCommutativeSemiring_1812
                 (T_IsCancellativeCommutativeSemiring_1798
-> T_IsCancellativeCommutativeSemiring_1798
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1798
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemiring_1570
v3
                = T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570
MAlonzo.Code.Algebra.Structures.d_isSemiring_1692 (T_IsCommutativeSemiring_1678 -> T_IsCommutativeSemiring_1678
forall a b. a -> b
coe T_IsCommutativeSemiring_1678
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsSemiringWithoutAnnihilatingZero_1468 -> T_IsSemigroup_472)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemiringWithoutAnnihilatingZero_1468 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.du_'42''45'isSemigroup_1548
               ((T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                  (T_IsSemiring_1570 -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1570
v3)))))
-- Algebra.Bundles.CancellativeCommutativeSemiring._.assoc
d_assoc_2700 ::
  T_CancellativeCommutativeSemiring_2632 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_2700 :: T_CancellativeCommutativeSemiring_2632
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_2700 T_CancellativeCommutativeSemiring_2632
v0
  = (T_IsSemigroup_472 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsSemigroup_472 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_assoc_482
      ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
         ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746
            ((T_IsSemiringWithoutAnnihilatingZero_1468
 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
               ((T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                  ((T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570
MAlonzo.Code.Algebra.Structures.d_isSemiring_1692
                     ((T_IsCancellativeCommutativeSemiring_1798
 -> T_IsCommutativeSemiring_1678)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsCancellativeCommutativeSemiring_1798
-> T_IsCommutativeSemiring_1678
MAlonzo.Code.Algebra.Structures.d_isCommutativeSemiring_1812
                        ((T_CancellativeCommutativeSemiring_2632
 -> T_IsCancellativeCommutativeSemiring_1798)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2632
-> T_IsCancellativeCommutativeSemiring_1798
d_isCancellativeCommutativeSemiring_2664 (T_CancellativeCommutativeSemiring_2632 -> AgdaAny
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2632
v0))))))))
-- Algebra.Bundles.CancellativeCommutativeSemiring._.comm
d_comm_2702 ::
  T_CancellativeCommutativeSemiring_2632 ->
  AgdaAny -> AgdaAny -> AgdaAny
d_comm_2702 :: T_CancellativeCommutativeSemiring_2632
-> AgdaAny -> AgdaAny -> AgdaAny
d_comm_2702 T_CancellativeCommutativeSemiring_2632
v0
  = (T_IsCommutativeMonoid_736 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsCommutativeMonoid_736 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_comm_748
      ((T_IsSemiringWithoutAnnihilatingZero_1468
 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
         ((T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
            ((T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570
MAlonzo.Code.Algebra.Structures.d_isSemiring_1692
               ((T_IsCancellativeCommutativeSemiring_1798
 -> T_IsCommutativeSemiring_1678)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsCancellativeCommutativeSemiring_1798
-> T_IsCommutativeSemiring_1678
MAlonzo.Code.Algebra.Structures.d_isCommutativeSemiring_1812
                  ((T_CancellativeCommutativeSemiring_2632
 -> T_IsCancellativeCommutativeSemiring_1798)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2632
-> T_IsCancellativeCommutativeSemiring_1798
d_isCancellativeCommutativeSemiring_2664 (T_CancellativeCommutativeSemiring_2632 -> AgdaAny
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2632
v0))))))
-- Algebra.Bundles.CancellativeCommutativeSemiring._.∙-cong
d_'8729''45'cong_2704 ::
  T_CancellativeCommutativeSemiring_2632 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_2704 :: T_CancellativeCommutativeSemiring_2632
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_2704 T_CancellativeCommutativeSemiring_2632
v0
  = (T_IsMagma_176
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsMagma_176
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_186
      ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480
         ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
            ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746
               ((T_IsSemiringWithoutAnnihilatingZero_1468
 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
                  ((T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                     ((T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570
MAlonzo.Code.Algebra.Structures.d_isSemiring_1692
                        ((T_IsCancellativeCommutativeSemiring_1798
 -> T_IsCommutativeSemiring_1678)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_IsCancellativeCommutativeSemiring_1798
-> T_IsCommutativeSemiring_1678
MAlonzo.Code.Algebra.Structures.d_isCommutativeSemiring_1812
                           ((T_CancellativeCommutativeSemiring_2632
 -> T_IsCancellativeCommutativeSemiring_1798)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2632
-> T_IsCancellativeCommutativeSemiring_1798
d_isCancellativeCommutativeSemiring_2664 (T_CancellativeCommutativeSemiring_2632 -> AgdaAny
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2632
v0)))))))))
-- Algebra.Bundles.CancellativeCommutativeSemiring._.∙-congʳ
d_'8729''45'cong'691'_2706 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CancellativeCommutativeSemiring_2632 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_2706 :: ()
-> ()
-> T_CancellativeCommutativeSemiring_2632
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_2706 ~()
v0 ~()
v1 T_CancellativeCommutativeSemiring_2632
v2
  = T_CancellativeCommutativeSemiring_2632
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_2706 T_CancellativeCommutativeSemiring_2632
v2
du_'8729''45'cong'691'_2706 ::
  T_CancellativeCommutativeSemiring_2632 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_2706 :: T_CancellativeCommutativeSemiring_2632
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_2706 T_CancellativeCommutativeSemiring_2632
v0
  = let v1 :: T_IsCancellativeCommutativeSemiring_1798
v1 = T_CancellativeCommutativeSemiring_2632
-> T_IsCancellativeCommutativeSemiring_1798
d_isCancellativeCommutativeSemiring_2664 (T_CancellativeCommutativeSemiring_2632
-> T_CancellativeCommutativeSemiring_2632
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2632
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsCommutativeSemiring_1678
v2
             = T_IsCancellativeCommutativeSemiring_1798
-> T_IsCommutativeSemiring_1678
MAlonzo.Code.Algebra.Structures.d_isCommutativeSemiring_1812
                 (T_IsCancellativeCommutativeSemiring_1798
-> T_IsCancellativeCommutativeSemiring_1798
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1798
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemiring_1570
v3
                = T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570
MAlonzo.Code.Algebra.Structures.d_isSemiring_1692 (T_IsCommutativeSemiring_1678 -> T_IsCommutativeSemiring_1678
forall a b. a -> b
coe T_IsCommutativeSemiring_1678
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsSemiringWithoutAnnihilatingZero_1468
v4
                   = T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                       (T_IsSemiring_1570 -> T_IsSemiring_1570
forall a b. a -> b
coe T_IsSemiring_1570
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsCommutativeMonoid_736
v5
                      = T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
                          (T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsSemiringWithoutAnnihilatingZero_1468
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (let v6 :: T_IsMonoid_686
v6
                         = T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746 (T_IsCommutativeMonoid_736 -> T_IsCommutativeMonoid_736
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v5) in
                   AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     (let v7 :: T_IsSemigroup_472
v7
                            = T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v6) in
                      AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'691'_206
                           ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v7)))))))))
-- Algebra.Bundles.CancellativeCommutativeSemiring._.∙-congˡ
d_'8729''45'cong'737'_2708 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CancellativeCommutativeSemiring_2632 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_2708 :: ()
-> ()
-> T_CancellativeCommutativeSemiring_2632
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_2708 ~()
v0 ~()
v1 T_CancellativeCommutativeSemiring_2632
v2
  = T_CancellativeCommutativeSemiring_2632
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_2708 T_CancellativeCommutativeSemiring_2632
v2
du_'8729''45'cong'737'_2708 ::
  T_CancellativeCommutativeSemiring_2632 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_2708 :: T_CancellativeCommutativeSemiring_2632
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_2708 T_CancellativeCommutativeSemiring_2632
v0
  = let v1 :: T_IsCancellativeCommutativeSemiring_1798
v1 = T_CancellativeCommutativeSemiring_2632
-> T_IsCancellativeCommutativeSemiring_1798
d_isCancellativeCommutativeSemiring_2664 (T_CancellativeCommutativeSemiring_2632
-> T_CancellativeCommutativeSemiring_2632
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2632
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsCommutativeSemiring_1678
v2
             = T_IsCancellativeCommutativeSemiring_1798
-> T_IsCommutativeSemiring_1678
MAlonzo.Code.Algebra.Structures.d_isCommutativeSemiring_1812
                 (T_IsCancellativeCommutativeSemiring_1798
-> T_IsCancellativeCommutativeSemiring_1798
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1798
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemiring_1570
v3
                = T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570
MAlonzo.Code.Algebra.Structures.d_isSemiring_1692 (T_IsCommutativeSemiring_1678 -> T_IsCommutativeSemiring_1678
forall a b. a -> b
coe T_IsCommutativeSemiring_1678
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsSemiringWithoutAnnihilatingZero_1468
v4
                   = T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                       (T_IsSemiring_1570 -> T_IsSemiring_1570
forall a b. a -> b
coe T_IsSemiring_1570
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsCommutativeMonoid_736
v5
                      = T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
                          (T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsSemiringWithoutAnnihilatingZero_1468
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (let v6 :: T_IsMonoid_686
v6
                         = T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746 (T_IsCommutativeMonoid_736 -> T_IsCommutativeMonoid_736
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v5) in
                   AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     (let v7 :: T_IsSemigroup_472
v7
                            = T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v6) in
                      AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'737'_202
                           ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v7)))))))))
-- Algebra.Bundles.CancellativeCommutativeSemiring._.identity
d_identity_2710 ::
  T_CancellativeCommutativeSemiring_2632 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_identity_2710 :: T_CancellativeCommutativeSemiring_2632 -> T_Σ_14
d_identity_2710 T_CancellativeCommutativeSemiring_2632
v0
  = (T_IsMonoid_686 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsMonoid_686 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_identity_698
      ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746
         ((T_IsSemiringWithoutAnnihilatingZero_1468
 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
            ((T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
               ((T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570
MAlonzo.Code.Algebra.Structures.d_isSemiring_1692
                  ((T_IsCancellativeCommutativeSemiring_1798
 -> T_IsCommutativeSemiring_1678)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsCancellativeCommutativeSemiring_1798
-> T_IsCommutativeSemiring_1678
MAlonzo.Code.Algebra.Structures.d_isCommutativeSemiring_1812
                     ((T_CancellativeCommutativeSemiring_2632
 -> T_IsCancellativeCommutativeSemiring_1798)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2632
-> T_IsCancellativeCommutativeSemiring_1798
d_isCancellativeCommutativeSemiring_2664 (T_CancellativeCommutativeSemiring_2632 -> AgdaAny
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2632
v0)))))))
-- Algebra.Bundles.CancellativeCommutativeSemiring._.identityʳ
d_identity'691'_2712 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CancellativeCommutativeSemiring_2632 -> AgdaAny -> AgdaAny
d_identity'691'_2712 :: ()
-> ()
-> T_CancellativeCommutativeSemiring_2632
-> AgdaAny
-> AgdaAny
d_identity'691'_2712 ~()
v0 ~()
v1 T_CancellativeCommutativeSemiring_2632
v2 = T_CancellativeCommutativeSemiring_2632 -> AgdaAny -> AgdaAny
du_identity'691'_2712 T_CancellativeCommutativeSemiring_2632
v2
du_identity'691'_2712 ::
  T_CancellativeCommutativeSemiring_2632 -> AgdaAny -> AgdaAny
du_identity'691'_2712 :: T_CancellativeCommutativeSemiring_2632 -> AgdaAny -> AgdaAny
du_identity'691'_2712 T_CancellativeCommutativeSemiring_2632
v0
  = let v1 :: T_IsCancellativeCommutativeSemiring_1798
v1 = T_CancellativeCommutativeSemiring_2632
-> T_IsCancellativeCommutativeSemiring_1798
d_isCancellativeCommutativeSemiring_2664 (T_CancellativeCommutativeSemiring_2632
-> T_CancellativeCommutativeSemiring_2632
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2632
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsCommutativeSemiring_1678
v2
             = T_IsCancellativeCommutativeSemiring_1798
-> T_IsCommutativeSemiring_1678
MAlonzo.Code.Algebra.Structures.d_isCommutativeSemiring_1812
                 (T_IsCancellativeCommutativeSemiring_1798
-> T_IsCancellativeCommutativeSemiring_1798
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1798
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemiring_1570
v3
                = T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570
MAlonzo.Code.Algebra.Structures.d_isSemiring_1692 (T_IsCommutativeSemiring_1678 -> T_IsCommutativeSemiring_1678
forall a b. a -> b
coe T_IsCommutativeSemiring_1678
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsSemiringWithoutAnnihilatingZero_1468
v4
                   = T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                       (T_IsSemiring_1570 -> T_IsSemiring_1570
forall a b. a -> b
coe T_IsSemiring_1570
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsCommutativeMonoid_736
v5
                      = T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
                          (T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsSemiringWithoutAnnihilatingZero_1468
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  ((T_IsMonoid_686 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsMonoid_686 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_identity'691'_728
                     ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746 (T_IsCommutativeMonoid_736 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v5)))))))
-- Algebra.Bundles.CancellativeCommutativeSemiring._.identityˡ
d_identity'737'_2714 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CancellativeCommutativeSemiring_2632 -> AgdaAny -> AgdaAny
d_identity'737'_2714 :: ()
-> ()
-> T_CancellativeCommutativeSemiring_2632
-> AgdaAny
-> AgdaAny
d_identity'737'_2714 ~()
v0 ~()
v1 T_CancellativeCommutativeSemiring_2632
v2 = T_CancellativeCommutativeSemiring_2632 -> AgdaAny -> AgdaAny
du_identity'737'_2714 T_CancellativeCommutativeSemiring_2632
v2
du_identity'737'_2714 ::
  T_CancellativeCommutativeSemiring_2632 -> AgdaAny -> AgdaAny
du_identity'737'_2714 :: T_CancellativeCommutativeSemiring_2632 -> AgdaAny -> AgdaAny
du_identity'737'_2714 T_CancellativeCommutativeSemiring_2632
v0
  = let v1 :: T_IsCancellativeCommutativeSemiring_1798
v1 = T_CancellativeCommutativeSemiring_2632
-> T_IsCancellativeCommutativeSemiring_1798
d_isCancellativeCommutativeSemiring_2664 (T_CancellativeCommutativeSemiring_2632
-> T_CancellativeCommutativeSemiring_2632
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2632
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsCommutativeSemiring_1678
v2
             = T_IsCancellativeCommutativeSemiring_1798
-> T_IsCommutativeSemiring_1678
MAlonzo.Code.Algebra.Structures.d_isCommutativeSemiring_1812
                 (T_IsCancellativeCommutativeSemiring_1798
-> T_IsCancellativeCommutativeSemiring_1798
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1798
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemiring_1570
v3
                = T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570
MAlonzo.Code.Algebra.Structures.d_isSemiring_1692 (T_IsCommutativeSemiring_1678 -> T_IsCommutativeSemiring_1678
forall a b. a -> b
coe T_IsCommutativeSemiring_1678
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsSemiringWithoutAnnihilatingZero_1468
v4
                   = T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                       (T_IsSemiring_1570 -> T_IsSemiring_1570
forall a b. a -> b
coe T_IsSemiring_1570
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsCommutativeMonoid_736
v5
                      = T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
                          (T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsSemiringWithoutAnnihilatingZero_1468
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  ((T_IsMonoid_686 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsMonoid_686 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_identity'737'_726
                     ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746 (T_IsCommutativeMonoid_736 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v5)))))))
-- Algebra.Bundles.CancellativeCommutativeSemiring._.isCommutativeMagma
d_isCommutativeMagma_2716 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CancellativeCommutativeSemiring_2632 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMagma_212
d_isCommutativeMagma_2716 :: ()
-> ()
-> T_CancellativeCommutativeSemiring_2632
-> T_IsCommutativeMagma_212
d_isCommutativeMagma_2716 ~()
v0 ~()
v1 T_CancellativeCommutativeSemiring_2632
v2
  = T_CancellativeCommutativeSemiring_2632 -> T_IsCommutativeMagma_212
du_isCommutativeMagma_2716 T_CancellativeCommutativeSemiring_2632
v2
du_isCommutativeMagma_2716 ::
  T_CancellativeCommutativeSemiring_2632 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMagma_212
du_isCommutativeMagma_2716 :: T_CancellativeCommutativeSemiring_2632 -> T_IsCommutativeMagma_212
du_isCommutativeMagma_2716 T_CancellativeCommutativeSemiring_2632
v0
  = let v1 :: T_IsCancellativeCommutativeSemiring_1798
v1 = T_CancellativeCommutativeSemiring_2632
-> T_IsCancellativeCommutativeSemiring_1798
d_isCancellativeCommutativeSemiring_2664 (T_CancellativeCommutativeSemiring_2632
-> T_CancellativeCommutativeSemiring_2632
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2632
v0) in
    AgdaAny -> T_IsCommutativeMagma_212
forall a b. a -> b
coe
      (let v2 :: T_IsCommutativeSemiring_1678
v2
             = T_IsCancellativeCommutativeSemiring_1798
-> T_IsCommutativeSemiring_1678
MAlonzo.Code.Algebra.Structures.d_isCommutativeSemiring_1812
                 (T_IsCancellativeCommutativeSemiring_1798
-> T_IsCancellativeCommutativeSemiring_1798
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1798
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemiring_1570
v3
                = T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570
MAlonzo.Code.Algebra.Structures.d_isSemiring_1692 (T_IsCommutativeSemiring_1678 -> T_IsCommutativeSemiring_1678
forall a b. a -> b
coe T_IsCommutativeSemiring_1678
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsSemiringWithoutAnnihilatingZero_1468
v4
                   = T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                       (T_IsSemiring_1570 -> T_IsSemiring_1570
forall a b. a -> b
coe T_IsSemiring_1570
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsCommutativeMonoid_736
v5
                      = T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
                          (T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsSemiringWithoutAnnihilatingZero_1468
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  ((T_IsCommutativeSemigroup_548 -> T_IsCommutativeMagma_212)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsCommutativeSemigroup_548 -> T_IsCommutativeMagma_212
MAlonzo.Code.Algebra.Structures.du_isCommutativeMagma_586
                     ((T_IsCommutativeMonoid_736 -> T_IsCommutativeSemigroup_548)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsCommutativeMonoid_736 -> T_IsCommutativeSemigroup_548
MAlonzo.Code.Algebra.Structures.du_isCommutativeSemigroup_786
                        (T_IsCommutativeMonoid_736 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v5)))))))
-- Algebra.Bundles.CancellativeCommutativeSemiring._.+-isCommutativeMonoid
d_'43''45'isCommutativeMonoid_2718 ::
  T_CancellativeCommutativeSemiring_2632 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_2718 :: T_CancellativeCommutativeSemiring_2632 -> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_2718 T_CancellativeCommutativeSemiring_2632
v0
  = (T_IsSemiringWithoutAnnihilatingZero_1468
 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> T_IsCommutativeMonoid_736
forall a b. a -> b
coe
      T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
      ((T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
         ((T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570
MAlonzo.Code.Algebra.Structures.d_isSemiring_1692
            ((T_IsCancellativeCommutativeSemiring_1798
 -> T_IsCommutativeSemiring_1678)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsCancellativeCommutativeSemiring_1798
-> T_IsCommutativeSemiring_1678
MAlonzo.Code.Algebra.Structures.d_isCommutativeSemiring_1812
               ((T_CancellativeCommutativeSemiring_2632
 -> T_IsCancellativeCommutativeSemiring_1798)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2632
-> T_IsCancellativeCommutativeSemiring_1798
d_isCancellativeCommutativeSemiring_2664 (T_CancellativeCommutativeSemiring_2632 -> AgdaAny
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2632
v0)))))
-- Algebra.Bundles.CancellativeCommutativeSemiring._.isCommutativeSemigroup
d_isCommutativeSemigroup_2720 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CancellativeCommutativeSemiring_2632 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_548
d_isCommutativeSemigroup_2720 :: ()
-> ()
-> T_CancellativeCommutativeSemiring_2632
-> T_IsCommutativeSemigroup_548
d_isCommutativeSemigroup_2720 ~()
v0 ~()
v1 T_CancellativeCommutativeSemiring_2632
v2
  = T_CancellativeCommutativeSemiring_2632
-> T_IsCommutativeSemigroup_548
du_isCommutativeSemigroup_2720 T_CancellativeCommutativeSemiring_2632
v2
du_isCommutativeSemigroup_2720 ::
  T_CancellativeCommutativeSemiring_2632 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_548
du_isCommutativeSemigroup_2720 :: T_CancellativeCommutativeSemiring_2632
-> T_IsCommutativeSemigroup_548
du_isCommutativeSemigroup_2720 T_CancellativeCommutativeSemiring_2632
v0
  = let v1 :: T_IsCancellativeCommutativeSemiring_1798
v1 = T_CancellativeCommutativeSemiring_2632
-> T_IsCancellativeCommutativeSemiring_1798
d_isCancellativeCommutativeSemiring_2664 (T_CancellativeCommutativeSemiring_2632
-> T_CancellativeCommutativeSemiring_2632
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2632
v0) in
    AgdaAny -> T_IsCommutativeSemigroup_548
forall a b. a -> b
coe
      (let v2 :: T_IsCommutativeSemiring_1678
v2
             = T_IsCancellativeCommutativeSemiring_1798
-> T_IsCommutativeSemiring_1678
MAlonzo.Code.Algebra.Structures.d_isCommutativeSemiring_1812
                 (T_IsCancellativeCommutativeSemiring_1798
-> T_IsCancellativeCommutativeSemiring_1798
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1798
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemiring_1570
v3
                = T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570
MAlonzo.Code.Algebra.Structures.d_isSemiring_1692 (T_IsCommutativeSemiring_1678 -> T_IsCommutativeSemiring_1678
forall a b. a -> b
coe T_IsCommutativeSemiring_1678
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsSemiringWithoutAnnihilatingZero_1468
v4
                   = T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                       (T_IsSemiring_1570 -> T_IsSemiring_1570
forall a b. a -> b
coe T_IsSemiring_1570
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               ((T_IsCommutativeMonoid_736 -> T_IsCommutativeSemigroup_548)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsCommutativeMonoid_736 -> T_IsCommutativeSemigroup_548
MAlonzo.Code.Algebra.Structures.du_isCommutativeSemigroup_786
                  ((T_IsSemiringWithoutAnnihilatingZero_1468
 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
                     (T_IsSemiringWithoutAnnihilatingZero_1468 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
v4))))))
-- Algebra.Bundles.CancellativeCommutativeSemiring._.isMagma
d_isMagma_2722 ::
  T_CancellativeCommutativeSemiring_2632 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_176
d_isMagma_2722 :: T_CancellativeCommutativeSemiring_2632 -> T_IsMagma_176
d_isMagma_2722 T_CancellativeCommutativeSemiring_2632
v0
  = (T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> T_IsMagma_176
forall a b. a -> b
coe
      T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480
      ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
         ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746
            ((T_IsSemiringWithoutAnnihilatingZero_1468
 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
               ((T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                  ((T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570
MAlonzo.Code.Algebra.Structures.d_isSemiring_1692
                     ((T_IsCancellativeCommutativeSemiring_1798
 -> T_IsCommutativeSemiring_1678)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsCancellativeCommutativeSemiring_1798
-> T_IsCommutativeSemiring_1678
MAlonzo.Code.Algebra.Structures.d_isCommutativeSemiring_1812
                        ((T_CancellativeCommutativeSemiring_2632
 -> T_IsCancellativeCommutativeSemiring_1798)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2632
-> T_IsCancellativeCommutativeSemiring_1798
d_isCancellativeCommutativeSemiring_2664 (T_CancellativeCommutativeSemiring_2632 -> AgdaAny
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2632
v0))))))))
-- Algebra.Bundles.CancellativeCommutativeSemiring._.isMonoid
d_isMonoid_2724 ::
  T_CancellativeCommutativeSemiring_2632 ->
  MAlonzo.Code.Algebra.Structures.T_IsMonoid_686
d_isMonoid_2724 :: T_CancellativeCommutativeSemiring_2632 -> T_IsMonoid_686
d_isMonoid_2724 T_CancellativeCommutativeSemiring_2632
v0
  = (T_IsCommutativeMonoid_736 -> T_IsMonoid_686)
-> AgdaAny -> T_IsMonoid_686
forall a b. a -> b
coe
      T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746
      ((T_IsSemiringWithoutAnnihilatingZero_1468
 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
         ((T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
            ((T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570
MAlonzo.Code.Algebra.Structures.d_isSemiring_1692
               ((T_IsCancellativeCommutativeSemiring_1798
 -> T_IsCommutativeSemiring_1678)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsCancellativeCommutativeSemiring_1798
-> T_IsCommutativeSemiring_1678
MAlonzo.Code.Algebra.Structures.d_isCommutativeSemiring_1812
                  ((T_CancellativeCommutativeSemiring_2632
 -> T_IsCancellativeCommutativeSemiring_1798)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2632
-> T_IsCancellativeCommutativeSemiring_1798
d_isCancellativeCommutativeSemiring_2664 (T_CancellativeCommutativeSemiring_2632 -> AgdaAny
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2632
v0))))))
-- Algebra.Bundles.CancellativeCommutativeSemiring._.isSemigroup
d_isSemigroup_2726 ::
  T_CancellativeCommutativeSemiring_2632 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_472
d_isSemigroup_2726 :: T_CancellativeCommutativeSemiring_2632 -> T_IsSemigroup_472
d_isSemigroup_2726 T_CancellativeCommutativeSemiring_2632
v0
  = (T_IsMonoid_686 -> T_IsSemigroup_472)
-> AgdaAny -> T_IsSemigroup_472
forall a b. a -> b
coe
      T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
      ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746
         ((T_IsSemiringWithoutAnnihilatingZero_1468
 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
            ((T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
               ((T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570
MAlonzo.Code.Algebra.Structures.d_isSemiring_1692
                  ((T_IsCancellativeCommutativeSemiring_1798
 -> T_IsCommutativeSemiring_1678)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsCancellativeCommutativeSemiring_1798
-> T_IsCommutativeSemiring_1678
MAlonzo.Code.Algebra.Structures.d_isCommutativeSemiring_1812
                     ((T_CancellativeCommutativeSemiring_2632
 -> T_IsCancellativeCommutativeSemiring_1798)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2632
-> T_IsCancellativeCommutativeSemiring_1798
d_isCancellativeCommutativeSemiring_2664 (T_CancellativeCommutativeSemiring_2632 -> AgdaAny
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2632
v0)))))))
-- Algebra.Bundles.CancellativeCommutativeSemiring._.isUnitalMagma
d_isUnitalMagma_2728 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CancellativeCommutativeSemiring_2632 ->
  MAlonzo.Code.Algebra.Structures.T_IsUnitalMagma_642
d_isUnitalMagma_2728 :: ()
-> ()
-> T_CancellativeCommutativeSemiring_2632
-> T_IsUnitalMagma_642
d_isUnitalMagma_2728 ~()
v0 ~()
v1 T_CancellativeCommutativeSemiring_2632
v2 = T_CancellativeCommutativeSemiring_2632 -> T_IsUnitalMagma_642
du_isUnitalMagma_2728 T_CancellativeCommutativeSemiring_2632
v2
du_isUnitalMagma_2728 ::
  T_CancellativeCommutativeSemiring_2632 ->
  MAlonzo.Code.Algebra.Structures.T_IsUnitalMagma_642
du_isUnitalMagma_2728 :: T_CancellativeCommutativeSemiring_2632 -> T_IsUnitalMagma_642
du_isUnitalMagma_2728 T_CancellativeCommutativeSemiring_2632
v0
  = let v1 :: T_IsCancellativeCommutativeSemiring_1798
v1 = T_CancellativeCommutativeSemiring_2632
-> T_IsCancellativeCommutativeSemiring_1798
d_isCancellativeCommutativeSemiring_2664 (T_CancellativeCommutativeSemiring_2632
-> T_CancellativeCommutativeSemiring_2632
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2632
v0) in
    AgdaAny -> T_IsUnitalMagma_642
forall a b. a -> b
coe
      (let v2 :: T_IsCommutativeSemiring_1678
v2
             = T_IsCancellativeCommutativeSemiring_1798
-> T_IsCommutativeSemiring_1678
MAlonzo.Code.Algebra.Structures.d_isCommutativeSemiring_1812
                 (T_IsCancellativeCommutativeSemiring_1798
-> T_IsCancellativeCommutativeSemiring_1798
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1798
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemiring_1570
v3
                = T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570
MAlonzo.Code.Algebra.Structures.d_isSemiring_1692 (T_IsCommutativeSemiring_1678 -> T_IsCommutativeSemiring_1678
forall a b. a -> b
coe T_IsCommutativeSemiring_1678
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsSemiringWithoutAnnihilatingZero_1468
v4
                   = T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                       (T_IsSemiring_1570 -> T_IsSemiring_1570
forall a b. a -> b
coe T_IsSemiring_1570
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsCommutativeMonoid_736
v5
                      = T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
                          (T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsSemiringWithoutAnnihilatingZero_1468
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  ((T_IsMonoid_686 -> T_IsUnitalMagma_642) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsMonoid_686 -> T_IsUnitalMagma_642
MAlonzo.Code.Algebra.Structures.du_isUnitalMagma_730
                     ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746 (T_IsCommutativeMonoid_736 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v5)))))))
-- Algebra.Bundles.CancellativeCommutativeSemiring._.distrib
d_distrib_2730 ::
  T_CancellativeCommutativeSemiring_2632 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_distrib_2730 :: T_CancellativeCommutativeSemiring_2632 -> T_Σ_14
d_distrib_2730 T_CancellativeCommutativeSemiring_2632
v0
  = (T_IsSemiringWithoutAnnihilatingZero_1468 -> T_Σ_14)
-> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsSemiringWithoutAnnihilatingZero_1468 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_distrib_1496
      ((T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
         ((T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570
MAlonzo.Code.Algebra.Structures.d_isSemiring_1692
            ((T_IsCancellativeCommutativeSemiring_1798
 -> T_IsCommutativeSemiring_1678)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsCancellativeCommutativeSemiring_1798
-> T_IsCommutativeSemiring_1678
MAlonzo.Code.Algebra.Structures.d_isCommutativeSemiring_1812
               ((T_CancellativeCommutativeSemiring_2632
 -> T_IsCancellativeCommutativeSemiring_1798)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2632
-> T_IsCancellativeCommutativeSemiring_1798
d_isCancellativeCommutativeSemiring_2664 (T_CancellativeCommutativeSemiring_2632 -> AgdaAny
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2632
v0)))))
-- Algebra.Bundles.CancellativeCommutativeSemiring._.distribʳ
d_distrib'691'_2732 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CancellativeCommutativeSemiring_2632 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_distrib'691'_2732 :: ()
-> ()
-> T_CancellativeCommutativeSemiring_2632
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_distrib'691'_2732 ~()
v0 ~()
v1 T_CancellativeCommutativeSemiring_2632
v2 = T_CancellativeCommutativeSemiring_2632
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'691'_2732 T_CancellativeCommutativeSemiring_2632
v2
du_distrib'691'_2732 ::
  T_CancellativeCommutativeSemiring_2632 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'691'_2732 :: T_CancellativeCommutativeSemiring_2632
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'691'_2732 T_CancellativeCommutativeSemiring_2632
v0
  = let v1 :: T_IsCancellativeCommutativeSemiring_1798
v1 = T_CancellativeCommutativeSemiring_2632
-> T_IsCancellativeCommutativeSemiring_1798
d_isCancellativeCommutativeSemiring_2664 (T_CancellativeCommutativeSemiring_2632
-> T_CancellativeCommutativeSemiring_2632
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2632
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsCommutativeSemiring_1678
v2
             = T_IsCancellativeCommutativeSemiring_1798
-> T_IsCommutativeSemiring_1678
MAlonzo.Code.Algebra.Structures.d_isCommutativeSemiring_1812
                 (T_IsCancellativeCommutativeSemiring_1798
-> T_IsCancellativeCommutativeSemiring_1798
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1798
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemiring_1570
v3
                = T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570
MAlonzo.Code.Algebra.Structures.d_isSemiring_1692 (T_IsCommutativeSemiring_1678 -> T_IsCommutativeSemiring_1678
forall a b. a -> b
coe T_IsCommutativeSemiring_1678
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsSemiringWithoutAnnihilatingZero_1468
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemiringWithoutAnnihilatingZero_1468
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_distrib'691'_1500
               ((T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                  (T_IsSemiring_1570 -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1570
v3)))))
-- Algebra.Bundles.CancellativeCommutativeSemiring._.distribˡ
d_distrib'737'_2734 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CancellativeCommutativeSemiring_2632 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_distrib'737'_2734 :: ()
-> ()
-> T_CancellativeCommutativeSemiring_2632
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_distrib'737'_2734 ~()
v0 ~()
v1 T_CancellativeCommutativeSemiring_2632
v2 = T_CancellativeCommutativeSemiring_2632
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'737'_2734 T_CancellativeCommutativeSemiring_2632
v2
du_distrib'737'_2734 ::
  T_CancellativeCommutativeSemiring_2632 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'737'_2734 :: T_CancellativeCommutativeSemiring_2632
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'737'_2734 T_CancellativeCommutativeSemiring_2632
v0
  = let v1 :: T_IsCancellativeCommutativeSemiring_1798
v1 = T_CancellativeCommutativeSemiring_2632
-> T_IsCancellativeCommutativeSemiring_1798
d_isCancellativeCommutativeSemiring_2664 (T_CancellativeCommutativeSemiring_2632
-> T_CancellativeCommutativeSemiring_2632
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2632
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsCommutativeSemiring_1678
v2
             = T_IsCancellativeCommutativeSemiring_1798
-> T_IsCommutativeSemiring_1678
MAlonzo.Code.Algebra.Structures.d_isCommutativeSemiring_1812
                 (T_IsCancellativeCommutativeSemiring_1798
-> T_IsCancellativeCommutativeSemiring_1798
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1798
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemiring_1570
v3
                = T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570
MAlonzo.Code.Algebra.Structures.d_isSemiring_1692 (T_IsCommutativeSemiring_1678 -> T_IsCommutativeSemiring_1678
forall a b. a -> b
coe T_IsCommutativeSemiring_1678
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsSemiringWithoutAnnihilatingZero_1468
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemiringWithoutAnnihilatingZero_1468
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_distrib'737'_1498
               ((T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                  (T_IsSemiring_1570 -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1570
v3)))))
-- Algebra.Bundles.CancellativeCommutativeSemiring._.isCommutativeSemiring
d_isCommutativeSemiring_2736 ::
  T_CancellativeCommutativeSemiring_2632 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiring_1678
d_isCommutativeSemiring_2736 :: T_CancellativeCommutativeSemiring_2632
-> T_IsCommutativeSemiring_1678
d_isCommutativeSemiring_2736 T_CancellativeCommutativeSemiring_2632
v0
  = (T_IsCancellativeCommutativeSemiring_1798
 -> T_IsCommutativeSemiring_1678)
-> AgdaAny -> T_IsCommutativeSemiring_1678
forall a b. a -> b
coe
      T_IsCancellativeCommutativeSemiring_1798
-> T_IsCommutativeSemiring_1678
MAlonzo.Code.Algebra.Structures.d_isCommutativeSemiring_1812
      ((T_CancellativeCommutativeSemiring_2632
 -> T_IsCancellativeCommutativeSemiring_1798)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2632
-> T_IsCancellativeCommutativeSemiring_1798
d_isCancellativeCommutativeSemiring_2664 (T_CancellativeCommutativeSemiring_2632 -> AgdaAny
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2632
v0))
-- Algebra.Bundles.CancellativeCommutativeSemiring._.isCommutativeSemiringWithoutOne
d_isCommutativeSemiringWithoutOne_2738 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CancellativeCommutativeSemiring_2632 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiringWithoutOne_1382
d_isCommutativeSemiringWithoutOne_2738 :: ()
-> ()
-> T_CancellativeCommutativeSemiring_2632
-> T_IsCommutativeSemiringWithoutOne_1382
d_isCommutativeSemiringWithoutOne_2738 ~()
v0 ~()
v1 T_CancellativeCommutativeSemiring_2632
v2
  = T_CancellativeCommutativeSemiring_2632
-> T_IsCommutativeSemiringWithoutOne_1382
du_isCommutativeSemiringWithoutOne_2738 T_CancellativeCommutativeSemiring_2632
v2
du_isCommutativeSemiringWithoutOne_2738 ::
  T_CancellativeCommutativeSemiring_2632 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiringWithoutOne_1382
du_isCommutativeSemiringWithoutOne_2738 :: T_CancellativeCommutativeSemiring_2632
-> T_IsCommutativeSemiringWithoutOne_1382
du_isCommutativeSemiringWithoutOne_2738 T_CancellativeCommutativeSemiring_2632
v0
  = let v1 :: T_IsCancellativeCommutativeSemiring_1798
v1 = T_CancellativeCommutativeSemiring_2632
-> T_IsCancellativeCommutativeSemiring_1798
d_isCancellativeCommutativeSemiring_2664 (T_CancellativeCommutativeSemiring_2632
-> T_CancellativeCommutativeSemiring_2632
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2632
v0) in
    AgdaAny -> T_IsCommutativeSemiringWithoutOne_1382
forall a b. a -> b
coe
      ((T_IsCommutativeSemiring_1678
 -> T_IsCommutativeSemiringWithoutOne_1382)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCommutativeSemiring_1678
-> T_IsCommutativeSemiringWithoutOne_1382
MAlonzo.Code.Algebra.Structures.du_isCommutativeSemiringWithoutOne_1780
         ((T_IsCancellativeCommutativeSemiring_1798
 -> T_IsCommutativeSemiring_1678)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCancellativeCommutativeSemiring_1798
-> T_IsCommutativeSemiring_1678
MAlonzo.Code.Algebra.Structures.d_isCommutativeSemiring_1812
            (T_IsCancellativeCommutativeSemiring_1798 -> AgdaAny
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1798
v1)))
-- Algebra.Bundles.CancellativeCommutativeSemiring._.isEquivalence
d_isEquivalence_2740 ::
  T_CancellativeCommutativeSemiring_2632 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_2740 :: T_CancellativeCommutativeSemiring_2632 -> T_IsEquivalence_26
d_isEquivalence_2740 T_CancellativeCommutativeSemiring_2632
v0
  = (T_IsMagma_176 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
      ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480
         ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
            ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746
               ((T_IsSemiringWithoutAnnihilatingZero_1468
 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
                  ((T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                     ((T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570
MAlonzo.Code.Algebra.Structures.d_isSemiring_1692
                        ((T_IsCancellativeCommutativeSemiring_1798
 -> T_IsCommutativeSemiring_1678)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_IsCancellativeCommutativeSemiring_1798
-> T_IsCommutativeSemiring_1678
MAlonzo.Code.Algebra.Structures.d_isCommutativeSemiring_1812
                           ((T_CancellativeCommutativeSemiring_2632
 -> T_IsCancellativeCommutativeSemiring_1798)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2632
-> T_IsCancellativeCommutativeSemiring_1798
d_isCancellativeCommutativeSemiring_2664 (T_CancellativeCommutativeSemiring_2632 -> AgdaAny
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2632
v0)))))))))
-- Algebra.Bundles.CancellativeCommutativeSemiring._.isNearSemiring
d_isNearSemiring_2742 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CancellativeCommutativeSemiring_2632 ->
  MAlonzo.Code.Algebra.Structures.T_IsNearSemiring_1218
d_isNearSemiring_2742 :: ()
-> ()
-> T_CancellativeCommutativeSemiring_2632
-> T_IsNearSemiring_1218
d_isNearSemiring_2742 ~()
v0 ~()
v1 T_CancellativeCommutativeSemiring_2632
v2 = T_CancellativeCommutativeSemiring_2632 -> T_IsNearSemiring_1218
du_isNearSemiring_2742 T_CancellativeCommutativeSemiring_2632
v2
du_isNearSemiring_2742 ::
  T_CancellativeCommutativeSemiring_2632 ->
  MAlonzo.Code.Algebra.Structures.T_IsNearSemiring_1218
du_isNearSemiring_2742 :: T_CancellativeCommutativeSemiring_2632 -> T_IsNearSemiring_1218
du_isNearSemiring_2742 T_CancellativeCommutativeSemiring_2632
v0
  = let v1 :: T_IsCancellativeCommutativeSemiring_1798
v1 = T_CancellativeCommutativeSemiring_2632
-> T_IsCancellativeCommutativeSemiring_1798
d_isCancellativeCommutativeSemiring_2664 (T_CancellativeCommutativeSemiring_2632
-> T_CancellativeCommutativeSemiring_2632
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2632
v0) in
    AgdaAny -> T_IsNearSemiring_1218
forall a b. a -> b
coe
      (let v2 :: T_IsCommutativeSemiring_1678
v2
             = T_IsCancellativeCommutativeSemiring_1798
-> T_IsCommutativeSemiring_1678
MAlonzo.Code.Algebra.Structures.d_isCommutativeSemiring_1812
                 (T_IsCancellativeCommutativeSemiring_1798
-> T_IsCancellativeCommutativeSemiring_1798
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1798
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemiring_1570
v3
                = T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570
MAlonzo.Code.Algebra.Structures.d_isSemiring_1692 (T_IsCommutativeSemiring_1678 -> T_IsCommutativeSemiring_1678
forall a b. a -> b
coe T_IsCommutativeSemiring_1678
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsSemiringWithoutOne_1298 -> T_IsNearSemiring_1218)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemiringWithoutOne_1298 -> T_IsNearSemiring_1218
MAlonzo.Code.Algebra.Structures.du_isNearSemiring_1374
               ((T_IsSemiring_1570 -> T_IsSemiringWithoutOne_1298)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsSemiring_1570 -> T_IsSemiringWithoutOne_1298
MAlonzo.Code.Algebra.Structures.du_isSemiringWithoutOne_1660
                  (T_IsSemiring_1570 -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1570
v3)))))
-- Algebra.Bundles.CancellativeCommutativeSemiring._.isPartialEquivalence
d_isPartialEquivalence_2744 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CancellativeCommutativeSemiring_2632 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_2744 :: ()
-> ()
-> T_CancellativeCommutativeSemiring_2632
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_2744 ~()
v0 ~()
v1 T_CancellativeCommutativeSemiring_2632
v2
  = T_CancellativeCommutativeSemiring_2632 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_2744 T_CancellativeCommutativeSemiring_2632
v2
du_isPartialEquivalence_2744 ::
  T_CancellativeCommutativeSemiring_2632 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_2744 :: T_CancellativeCommutativeSemiring_2632 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_2744 T_CancellativeCommutativeSemiring_2632
v0
  = let v1 :: T_IsCancellativeCommutativeSemiring_1798
v1 = T_CancellativeCommutativeSemiring_2632
-> T_IsCancellativeCommutativeSemiring_1798
d_isCancellativeCommutativeSemiring_2664 (T_CancellativeCommutativeSemiring_2632
-> T_CancellativeCommutativeSemiring_2632
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2632
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsCommutativeSemiring_1678
v2
             = T_IsCancellativeCommutativeSemiring_1798
-> T_IsCommutativeSemiring_1678
MAlonzo.Code.Algebra.Structures.d_isCommutativeSemiring_1812
                 (T_IsCancellativeCommutativeSemiring_1798
-> T_IsCancellativeCommutativeSemiring_1798
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1798
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemiring_1570
v3
                = T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570
MAlonzo.Code.Algebra.Structures.d_isSemiring_1692 (T_IsCommutativeSemiring_1678 -> T_IsCommutativeSemiring_1678
forall a b. a -> b
coe T_IsCommutativeSemiring_1678
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsSemiringWithoutAnnihilatingZero_1468
v4
                   = T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                       (T_IsSemiring_1570 -> T_IsSemiring_1570
forall a b. a -> b
coe T_IsSemiring_1570
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsCommutativeMonoid_736
v5
                      = T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
                          (T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsSemiringWithoutAnnihilatingZero_1468
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (let v6 :: T_IsMonoid_686
v6
                         = T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746 (T_IsCommutativeMonoid_736 -> T_IsCommutativeMonoid_736
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v5) in
                   AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     (let v7 :: T_IsSemigroup_472
v7
                            = T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v6) in
                      AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        (let v8 :: T_IsMagma_176
v8 = T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (T_IsSemigroup_472 -> T_IsSemigroup_472
forall a b. a -> b
coe T_IsSemigroup_472
v7) in
                         AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           ((T_IsEquivalence_26 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                              T_IsEquivalence_26 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
                              ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                 T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
                                 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v8))))))))))
-- Algebra.Bundles.CancellativeCommutativeSemiring._.isSemiring
d_isSemiring_2746 ::
  T_CancellativeCommutativeSemiring_2632 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemiring_1570
d_isSemiring_2746 :: T_CancellativeCommutativeSemiring_2632 -> T_IsSemiring_1570
d_isSemiring_2746 T_CancellativeCommutativeSemiring_2632
v0
  = (T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570)
-> AgdaAny -> T_IsSemiring_1570
forall a b. a -> b
coe
      T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570
MAlonzo.Code.Algebra.Structures.d_isSemiring_1692
      ((T_IsCancellativeCommutativeSemiring_1798
 -> T_IsCommutativeSemiring_1678)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCancellativeCommutativeSemiring_1798
-> T_IsCommutativeSemiring_1678
MAlonzo.Code.Algebra.Structures.d_isCommutativeSemiring_1812
         ((T_CancellativeCommutativeSemiring_2632
 -> T_IsCancellativeCommutativeSemiring_1798)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2632
-> T_IsCancellativeCommutativeSemiring_1798
d_isCancellativeCommutativeSemiring_2664 (T_CancellativeCommutativeSemiring_2632 -> AgdaAny
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2632
v0)))
-- Algebra.Bundles.CancellativeCommutativeSemiring._.isSemiringWithoutAnnihilatingZero
d_isSemiringWithoutAnnihilatingZero_2748 ::
  T_CancellativeCommutativeSemiring_2632 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_2748 :: T_CancellativeCommutativeSemiring_2632
-> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_2748 T_CancellativeCommutativeSemiring_2632
v0
  = (T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> T_IsSemiringWithoutAnnihilatingZero_1468
forall a b. a -> b
coe
      T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
      ((T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570
MAlonzo.Code.Algebra.Structures.d_isSemiring_1692
         ((T_IsCancellativeCommutativeSemiring_1798
 -> T_IsCommutativeSemiring_1678)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCancellativeCommutativeSemiring_1798
-> T_IsCommutativeSemiring_1678
MAlonzo.Code.Algebra.Structures.d_isCommutativeSemiring_1812
            ((T_CancellativeCommutativeSemiring_2632
 -> T_IsCancellativeCommutativeSemiring_1798)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2632
-> T_IsCancellativeCommutativeSemiring_1798
d_isCancellativeCommutativeSemiring_2664 (T_CancellativeCommutativeSemiring_2632 -> AgdaAny
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2632
v0))))
-- Algebra.Bundles.CancellativeCommutativeSemiring._.isSemiringWithoutOne
d_isSemiringWithoutOne_2750 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CancellativeCommutativeSemiring_2632 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutOne_1298
d_isSemiringWithoutOne_2750 :: ()
-> ()
-> T_CancellativeCommutativeSemiring_2632
-> T_IsSemiringWithoutOne_1298
d_isSemiringWithoutOne_2750 ~()
v0 ~()
v1 T_CancellativeCommutativeSemiring_2632
v2
  = T_CancellativeCommutativeSemiring_2632
-> T_IsSemiringWithoutOne_1298
du_isSemiringWithoutOne_2750 T_CancellativeCommutativeSemiring_2632
v2
du_isSemiringWithoutOne_2750 ::
  T_CancellativeCommutativeSemiring_2632 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutOne_1298
du_isSemiringWithoutOne_2750 :: T_CancellativeCommutativeSemiring_2632
-> T_IsSemiringWithoutOne_1298
du_isSemiringWithoutOne_2750 T_CancellativeCommutativeSemiring_2632
v0
  = let v1 :: T_IsCancellativeCommutativeSemiring_1798
v1 = T_CancellativeCommutativeSemiring_2632
-> T_IsCancellativeCommutativeSemiring_1798
d_isCancellativeCommutativeSemiring_2664 (T_CancellativeCommutativeSemiring_2632
-> T_CancellativeCommutativeSemiring_2632
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2632
v0) in
    AgdaAny -> T_IsSemiringWithoutOne_1298
forall a b. a -> b
coe
      (let v2 :: T_IsCommutativeSemiring_1678
v2
             = T_IsCancellativeCommutativeSemiring_1798
-> T_IsCommutativeSemiring_1678
MAlonzo.Code.Algebra.Structures.d_isCommutativeSemiring_1812
                 (T_IsCancellativeCommutativeSemiring_1798
-> T_IsCancellativeCommutativeSemiring_1798
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1798
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsSemiring_1570 -> T_IsSemiringWithoutOne_1298)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemiring_1570 -> T_IsSemiringWithoutOne_1298
MAlonzo.Code.Algebra.Structures.du_isSemiringWithoutOne_1660
            ((T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570
MAlonzo.Code.Algebra.Structures.d_isSemiring_1692 (T_IsCommutativeSemiring_1678 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiring_1678
v2))))
-- Algebra.Bundles.CancellativeCommutativeSemiring._.refl
d_refl_2752 ::
  T_CancellativeCommutativeSemiring_2632 -> AgdaAny -> AgdaAny
d_refl_2752 :: T_CancellativeCommutativeSemiring_2632 -> AgdaAny -> AgdaAny
d_refl_2752 T_CancellativeCommutativeSemiring_2632
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_34
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
         ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480
            ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
               ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746
                  ((T_IsSemiringWithoutAnnihilatingZero_1468
 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
                     ((T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                        ((T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570
MAlonzo.Code.Algebra.Structures.d_isSemiring_1692
                           ((T_IsCancellativeCommutativeSemiring_1798
 -> T_IsCommutativeSemiring_1678)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                              T_IsCancellativeCommutativeSemiring_1798
-> T_IsCommutativeSemiring_1678
MAlonzo.Code.Algebra.Structures.d_isCommutativeSemiring_1812
                              ((T_CancellativeCommutativeSemiring_2632
 -> T_IsCancellativeCommutativeSemiring_1798)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2632
-> T_IsCancellativeCommutativeSemiring_1798
d_isCancellativeCommutativeSemiring_2664 (T_CancellativeCommutativeSemiring_2632 -> AgdaAny
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2632
v0))))))))))
-- Algebra.Bundles.CancellativeCommutativeSemiring._.reflexive
d_reflexive_2754 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CancellativeCommutativeSemiring_2632 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_2754 :: ()
-> ()
-> T_CancellativeCommutativeSemiring_2632
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_2754 ~()
v0 ~()
v1 T_CancellativeCommutativeSemiring_2632
v2 = T_CancellativeCommutativeSemiring_2632
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_2754 T_CancellativeCommutativeSemiring_2632
v2
du_reflexive_2754 ::
  T_CancellativeCommutativeSemiring_2632 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_2754 :: T_CancellativeCommutativeSemiring_2632
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_2754 T_CancellativeCommutativeSemiring_2632
v0
  = let v1 :: T_IsCancellativeCommutativeSemiring_1798
v1 = T_CancellativeCommutativeSemiring_2632
-> T_IsCancellativeCommutativeSemiring_1798
d_isCancellativeCommutativeSemiring_2664 (T_CancellativeCommutativeSemiring_2632
-> T_CancellativeCommutativeSemiring_2632
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2632
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsCommutativeSemiring_1678
v2
             = T_IsCancellativeCommutativeSemiring_1798
-> T_IsCommutativeSemiring_1678
MAlonzo.Code.Algebra.Structures.d_isCommutativeSemiring_1812
                 (T_IsCancellativeCommutativeSemiring_1798
-> T_IsCancellativeCommutativeSemiring_1798
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1798
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemiring_1570
v3
                = T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570
MAlonzo.Code.Algebra.Structures.d_isSemiring_1692 (T_IsCommutativeSemiring_1678 -> T_IsCommutativeSemiring_1678
forall a b. a -> b
coe T_IsCommutativeSemiring_1678
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsSemiringWithoutAnnihilatingZero_1468
v4
                   = T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                       (T_IsSemiring_1570 -> T_IsSemiring_1570
forall a b. a -> b
coe T_IsSemiring_1570
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsCommutativeMonoid_736
v5
                      = T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
                          (T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsSemiringWithoutAnnihilatingZero_1468
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (let v6 :: T_IsMonoid_686
v6
                         = T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746 (T_IsCommutativeMonoid_736 -> T_IsCommutativeMonoid_736
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v5) in
                   AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     (let v7 :: T_IsSemigroup_472
v7
                            = T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v6) in
                      AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        (let v8 :: T_IsMagma_176
v8 = T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (T_IsSemigroup_472 -> T_IsSemigroup_472
forall a b. a -> b
coe T_IsSemigroup_472
v7) in
                         (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
                           (\ AgdaAny
v9 AgdaAny
v10 AgdaAny
v11 ->
                              (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
                                ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v8))
                                AgdaAny
v9))))))))
-- Algebra.Bundles.CancellativeCommutativeSemiring._.setoid
d_setoid_2756 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CancellativeCommutativeSemiring_2632 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_2756 :: () -> () -> T_CancellativeCommutativeSemiring_2632 -> T_Setoid_44
d_setoid_2756 ~()
v0 ~()
v1 T_CancellativeCommutativeSemiring_2632
v2 = T_CancellativeCommutativeSemiring_2632 -> T_Setoid_44
du_setoid_2756 T_CancellativeCommutativeSemiring_2632
v2
du_setoid_2756 ::
  T_CancellativeCommutativeSemiring_2632 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_2756 :: T_CancellativeCommutativeSemiring_2632 -> T_Setoid_44
du_setoid_2756 T_CancellativeCommutativeSemiring_2632
v0
  = let v1 :: T_IsCancellativeCommutativeSemiring_1798
v1 = T_CancellativeCommutativeSemiring_2632
-> T_IsCancellativeCommutativeSemiring_1798
d_isCancellativeCommutativeSemiring_2664 (T_CancellativeCommutativeSemiring_2632
-> T_CancellativeCommutativeSemiring_2632
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2632
v0) in
    AgdaAny -> T_Setoid_44
forall a b. a -> b
coe
      (let v2 :: T_IsCommutativeSemiring_1678
v2
             = T_IsCancellativeCommutativeSemiring_1798
-> T_IsCommutativeSemiring_1678
MAlonzo.Code.Algebra.Structures.d_isCommutativeSemiring_1812
                 (T_IsCancellativeCommutativeSemiring_1798
-> T_IsCancellativeCommutativeSemiring_1798
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1798
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemiring_1570
v3
                = T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570
MAlonzo.Code.Algebra.Structures.d_isSemiring_1692 (T_IsCommutativeSemiring_1678 -> T_IsCommutativeSemiring_1678
forall a b. a -> b
coe T_IsCommutativeSemiring_1678
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsSemiringWithoutAnnihilatingZero_1468
v4
                   = T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                       (T_IsSemiring_1570 -> T_IsSemiring_1570
forall a b. a -> b
coe T_IsSemiring_1570
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsCommutativeMonoid_736
v5
                      = T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
                          (T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsSemiringWithoutAnnihilatingZero_1468
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (let v6 :: T_IsMonoid_686
v6
                         = T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746 (T_IsCommutativeMonoid_736 -> T_IsCommutativeMonoid_736
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v5) in
                   AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     (let v7 :: T_IsSemigroup_472
v7
                            = T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v6) in
                      AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        ((T_IsMagma_176 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_IsMagma_176 -> T_Setoid_44
MAlonzo.Code.Algebra.Structures.du_setoid_200
                           ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v7)))))))))
-- Algebra.Bundles.CancellativeCommutativeSemiring._.sym
d_sym_2758 ::
  T_CancellativeCommutativeSemiring_2632 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_2758 :: T_CancellativeCommutativeSemiring_2632
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_2758 T_CancellativeCommutativeSemiring_2632
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_36
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
         ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480
            ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
               ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746
                  ((T_IsSemiringWithoutAnnihilatingZero_1468
 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
                     ((T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                        ((T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570
MAlonzo.Code.Algebra.Structures.d_isSemiring_1692
                           ((T_IsCancellativeCommutativeSemiring_1798
 -> T_IsCommutativeSemiring_1678)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                              T_IsCancellativeCommutativeSemiring_1798
-> T_IsCommutativeSemiring_1678
MAlonzo.Code.Algebra.Structures.d_isCommutativeSemiring_1812
                              ((T_CancellativeCommutativeSemiring_2632
 -> T_IsCancellativeCommutativeSemiring_1798)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2632
-> T_IsCancellativeCommutativeSemiring_1798
d_isCancellativeCommutativeSemiring_2664 (T_CancellativeCommutativeSemiring_2632 -> AgdaAny
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2632
v0))))))))))
-- Algebra.Bundles.CancellativeCommutativeSemiring._.trans
d_trans_2760 ::
  T_CancellativeCommutativeSemiring_2632 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_2760 :: T_CancellativeCommutativeSemiring_2632
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_2760 T_CancellativeCommutativeSemiring_2632
v0
  = (T_IsEquivalence_26
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_38
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
         ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480
            ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
               ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746
                  ((T_IsSemiringWithoutAnnihilatingZero_1468
 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
                     ((T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                        ((T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570
MAlonzo.Code.Algebra.Structures.d_isSemiring_1692
                           ((T_IsCancellativeCommutativeSemiring_1798
 -> T_IsCommutativeSemiring_1678)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                              T_IsCancellativeCommutativeSemiring_1798
-> T_IsCommutativeSemiring_1678
MAlonzo.Code.Algebra.Structures.d_isCommutativeSemiring_1812
                              ((T_CancellativeCommutativeSemiring_2632
 -> T_IsCancellativeCommutativeSemiring_1798)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2632
-> T_IsCancellativeCommutativeSemiring_1798
d_isCancellativeCommutativeSemiring_2664 (T_CancellativeCommutativeSemiring_2632 -> AgdaAny
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2632
v0))))))))))
-- Algebra.Bundles.CancellativeCommutativeSemiring._.zero
d_zero_2762 ::
  T_CancellativeCommutativeSemiring_2632 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_zero_2762 :: T_CancellativeCommutativeSemiring_2632 -> T_Σ_14
d_zero_2762 T_CancellativeCommutativeSemiring_2632
v0
  = (T_IsSemiring_1570 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsSemiring_1570 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_zero_1586
      ((T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570
MAlonzo.Code.Algebra.Structures.d_isSemiring_1692
         ((T_IsCancellativeCommutativeSemiring_1798
 -> T_IsCommutativeSemiring_1678)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCancellativeCommutativeSemiring_1798
-> T_IsCommutativeSemiring_1678
MAlonzo.Code.Algebra.Structures.d_isCommutativeSemiring_1812
            ((T_CancellativeCommutativeSemiring_2632
 -> T_IsCancellativeCommutativeSemiring_1798)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2632
-> T_IsCancellativeCommutativeSemiring_1798
d_isCancellativeCommutativeSemiring_2664 (T_CancellativeCommutativeSemiring_2632 -> AgdaAny
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2632
v0))))
-- Algebra.Bundles.CancellativeCommutativeSemiring._.zeroʳ
d_zero'691'_2764 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CancellativeCommutativeSemiring_2632 -> AgdaAny -> AgdaAny
d_zero'691'_2764 :: ()
-> ()
-> T_CancellativeCommutativeSemiring_2632
-> AgdaAny
-> AgdaAny
d_zero'691'_2764 ~()
v0 ~()
v1 T_CancellativeCommutativeSemiring_2632
v2 = T_CancellativeCommutativeSemiring_2632 -> AgdaAny -> AgdaAny
du_zero'691'_2764 T_CancellativeCommutativeSemiring_2632
v2
du_zero'691'_2764 ::
  T_CancellativeCommutativeSemiring_2632 -> AgdaAny -> AgdaAny
du_zero'691'_2764 :: T_CancellativeCommutativeSemiring_2632 -> AgdaAny -> AgdaAny
du_zero'691'_2764 T_CancellativeCommutativeSemiring_2632
v0
  = let v1 :: T_IsCancellativeCommutativeSemiring_1798
v1 = T_CancellativeCommutativeSemiring_2632
-> T_IsCancellativeCommutativeSemiring_1798
d_isCancellativeCommutativeSemiring_2664 (T_CancellativeCommutativeSemiring_2632
-> T_CancellativeCommutativeSemiring_2632
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2632
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsCommutativeSemiring_1678
v2
             = T_IsCancellativeCommutativeSemiring_1798
-> T_IsCommutativeSemiring_1678
MAlonzo.Code.Algebra.Structures.d_isCommutativeSemiring_1812
                 (T_IsCancellativeCommutativeSemiring_1798
-> T_IsCancellativeCommutativeSemiring_1798
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1798
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemiring_1570
v3
                = T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570
MAlonzo.Code.Algebra.Structures.d_isSemiring_1692 (T_IsCommutativeSemiring_1678 -> T_IsCommutativeSemiring_1678
forall a b. a -> b
coe T_IsCommutativeSemiring_1678
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsSemiringWithoutOne_1298 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemiringWithoutOne_1298 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_zero'691'_1372
               ((T_IsSemiring_1570 -> T_IsSemiringWithoutOne_1298)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsSemiring_1570 -> T_IsSemiringWithoutOne_1298
MAlonzo.Code.Algebra.Structures.du_isSemiringWithoutOne_1660
                  (T_IsSemiring_1570 -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1570
v3)))))
-- Algebra.Bundles.CancellativeCommutativeSemiring._.zeroˡ
d_zero'737'_2766 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CancellativeCommutativeSemiring_2632 -> AgdaAny -> AgdaAny
d_zero'737'_2766 :: ()
-> ()
-> T_CancellativeCommutativeSemiring_2632
-> AgdaAny
-> AgdaAny
d_zero'737'_2766 ~()
v0 ~()
v1 T_CancellativeCommutativeSemiring_2632
v2 = T_CancellativeCommutativeSemiring_2632 -> AgdaAny -> AgdaAny
du_zero'737'_2766 T_CancellativeCommutativeSemiring_2632
v2
du_zero'737'_2766 ::
  T_CancellativeCommutativeSemiring_2632 -> AgdaAny -> AgdaAny
du_zero'737'_2766 :: T_CancellativeCommutativeSemiring_2632 -> AgdaAny -> AgdaAny
du_zero'737'_2766 T_CancellativeCommutativeSemiring_2632
v0
  = let v1 :: T_IsCancellativeCommutativeSemiring_1798
v1 = T_CancellativeCommutativeSemiring_2632
-> T_IsCancellativeCommutativeSemiring_1798
d_isCancellativeCommutativeSemiring_2664 (T_CancellativeCommutativeSemiring_2632
-> T_CancellativeCommutativeSemiring_2632
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2632
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsCommutativeSemiring_1678
v2
             = T_IsCancellativeCommutativeSemiring_1798
-> T_IsCommutativeSemiring_1678
MAlonzo.Code.Algebra.Structures.d_isCommutativeSemiring_1812
                 (T_IsCancellativeCommutativeSemiring_1798
-> T_IsCancellativeCommutativeSemiring_1798
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1798
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemiring_1570
v3
                = T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570
MAlonzo.Code.Algebra.Structures.d_isSemiring_1692 (T_IsCommutativeSemiring_1678 -> T_IsCommutativeSemiring_1678
forall a b. a -> b
coe T_IsCommutativeSemiring_1678
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsSemiringWithoutOne_1298 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemiringWithoutOne_1298 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_zero'737'_1370
               ((T_IsSemiring_1570 -> T_IsSemiringWithoutOne_1298)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsSemiring_1570 -> T_IsSemiringWithoutOne_1298
MAlonzo.Code.Algebra.Structures.du_isSemiringWithoutOne_1660
                  (T_IsSemiring_1570 -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1570
v3)))))
-- Algebra.Bundles.CancellativeCommutativeSemiring.commutativeSemiring
d_commutativeSemiring_2768 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CancellativeCommutativeSemiring_2632 ->
  T_CommutativeSemiring_2446
d_commutativeSemiring_2768 :: ()
-> ()
-> T_CancellativeCommutativeSemiring_2632
-> T_CommutativeSemiring_2446
d_commutativeSemiring_2768 ~()
v0 ~()
v1 T_CancellativeCommutativeSemiring_2632
v2
  = T_CancellativeCommutativeSemiring_2632
-> T_CommutativeSemiring_2446
du_commutativeSemiring_2768 T_CancellativeCommutativeSemiring_2632
v2
du_commutativeSemiring_2768 ::
  T_CancellativeCommutativeSemiring_2632 ->
  T_CommutativeSemiring_2446
du_commutativeSemiring_2768 :: T_CancellativeCommutativeSemiring_2632
-> T_CommutativeSemiring_2446
du_commutativeSemiring_2768 T_CancellativeCommutativeSemiring_2632
v0
  = ((AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> AgdaAny
 -> T_IsCommutativeSemiring_1678
 -> T_CommutativeSemiring_2446)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsCommutativeSemiring_1678
-> T_CommutativeSemiring_2446
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsCommutativeSemiring_1678
-> T_CommutativeSemiring_2446
C_CommutativeSemiring'46'constructor_44731 (T_CancellativeCommutativeSemiring_2632
-> AgdaAny -> AgdaAny -> AgdaAny
d__'43'__2656 (T_CancellativeCommutativeSemiring_2632
-> T_CancellativeCommutativeSemiring_2632
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2632
v0))
      (T_CancellativeCommutativeSemiring_2632
-> AgdaAny -> AgdaAny -> AgdaAny
d__'42'__2658 (T_CancellativeCommutativeSemiring_2632
-> T_CancellativeCommutativeSemiring_2632
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2632
v0)) (T_CancellativeCommutativeSemiring_2632 -> AgdaAny
d_0'35'_2660 (T_CancellativeCommutativeSemiring_2632
-> T_CancellativeCommutativeSemiring_2632
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2632
v0))
      (T_CancellativeCommutativeSemiring_2632 -> AgdaAny
d_1'35'_2662 (T_CancellativeCommutativeSemiring_2632
-> T_CancellativeCommutativeSemiring_2632
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2632
v0))
      (T_IsCancellativeCommutativeSemiring_1798
-> T_IsCommutativeSemiring_1678
MAlonzo.Code.Algebra.Structures.d_isCommutativeSemiring_1812
         ((T_CancellativeCommutativeSemiring_2632
 -> T_IsCancellativeCommutativeSemiring_1798)
-> AgdaAny -> T_IsCancellativeCommutativeSemiring_1798
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2632
-> T_IsCancellativeCommutativeSemiring_1798
d_isCancellativeCommutativeSemiring_2664 (T_CancellativeCommutativeSemiring_2632 -> AgdaAny
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2632
v0)))
-- Algebra.Bundles.CancellativeCommutativeSemiring._._≉_
d__'8777'__2772 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CancellativeCommutativeSemiring_2632 -> AgdaAny -> AgdaAny -> ()
d__'8777'__2772 :: ()
-> ()
-> T_CancellativeCommutativeSemiring_2632
-> AgdaAny
-> AgdaAny
-> ()
d__'8777'__2772 = ()
-> ()
-> T_CancellativeCommutativeSemiring_2632
-> AgdaAny
-> AgdaAny
-> ()
forall a. a
erased
-- Algebra.Bundles.CancellativeCommutativeSemiring._.commutativeMagma
d_commutativeMagma_2774 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CancellativeCommutativeSemiring_2632 -> T_CommutativeMagma_180
d_commutativeMagma_2774 :: ()
-> ()
-> T_CancellativeCommutativeSemiring_2632
-> T_CommutativeMagma_180
d_commutativeMagma_2774 ~()
v0 ~()
v1 T_CancellativeCommutativeSemiring_2632
v2 = T_CancellativeCommutativeSemiring_2632 -> T_CommutativeMagma_180
du_commutativeMagma_2774 T_CancellativeCommutativeSemiring_2632
v2
du_commutativeMagma_2774 ::
  T_CancellativeCommutativeSemiring_2632 -> T_CommutativeMagma_180
du_commutativeMagma_2774 :: T_CancellativeCommutativeSemiring_2632 -> T_CommutativeMagma_180
du_commutativeMagma_2774 T_CancellativeCommutativeSemiring_2632
v0
  = let v1 :: t
v1 = (T_CancellativeCommutativeSemiring_2632
 -> T_CommutativeSemiring_2446)
-> AgdaAny -> t
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2632
-> T_CommutativeSemiring_2446
du_commutativeSemiring_2768 (T_CancellativeCommutativeSemiring_2632 -> AgdaAny
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2632
v0) in
    AgdaAny -> T_CommutativeMagma_180
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_CommutativeSemiring_2446 -> T_CommutativeMonoid_962)
-> AgdaAny -> t
forall a b. a -> b
coe T_CommutativeSemiring_2446 -> T_CommutativeMonoid_962
du_'42''45'commutativeMonoid_2618 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_CommutativeSemigroup_662 -> T_CommutativeMagma_180)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_CommutativeSemigroup_662 -> T_CommutativeMagma_180
du_commutativeMagma_726
            ((T_CommutativeMonoid_962 -> T_CommutativeSemigroup_662)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeMonoid_962 -> T_CommutativeSemigroup_662
du_commutativeSemigroup_1048 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2))))
-- Algebra.Bundles.CancellativeCommutativeSemiring._.*-commutativeMonoid
d_'42''45'commutativeMonoid_2776 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CancellativeCommutativeSemiring_2632 -> T_CommutativeMonoid_962
d_'42''45'commutativeMonoid_2776 :: ()
-> ()
-> T_CancellativeCommutativeSemiring_2632
-> T_CommutativeMonoid_962
d_'42''45'commutativeMonoid_2776 ~()
v0 ~()
v1 T_CancellativeCommutativeSemiring_2632
v2
  = T_CancellativeCommutativeSemiring_2632 -> T_CommutativeMonoid_962
du_'42''45'commutativeMonoid_2776 T_CancellativeCommutativeSemiring_2632
v2
du_'42''45'commutativeMonoid_2776 ::
  T_CancellativeCommutativeSemiring_2632 -> T_CommutativeMonoid_962
du_'42''45'commutativeMonoid_2776 :: T_CancellativeCommutativeSemiring_2632 -> T_CommutativeMonoid_962
du_'42''45'commutativeMonoid_2776 T_CancellativeCommutativeSemiring_2632
v0
  = (T_CommutativeSemiring_2446 -> T_CommutativeMonoid_962)
-> AgdaAny -> T_CommutativeMonoid_962
forall a b. a -> b
coe
      T_CommutativeSemiring_2446 -> T_CommutativeMonoid_962
du_'42''45'commutativeMonoid_2618
      ((T_CancellativeCommutativeSemiring_2632
 -> T_CommutativeSemiring_2446)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2632
-> T_CommutativeSemiring_2446
du_commutativeSemiring_2768 (T_CancellativeCommutativeSemiring_2632 -> AgdaAny
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2632
v0))
-- Algebra.Bundles.CancellativeCommutativeSemiring._.commutativeSemigroup
d_commutativeSemigroup_2778 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CancellativeCommutativeSemiring_2632 ->
  T_CommutativeSemigroup_662
d_commutativeSemigroup_2778 :: ()
-> ()
-> T_CancellativeCommutativeSemiring_2632
-> T_CommutativeSemigroup_662
d_commutativeSemigroup_2778 ~()
v0 ~()
v1 T_CancellativeCommutativeSemiring_2632
v2
  = T_CancellativeCommutativeSemiring_2632
-> T_CommutativeSemigroup_662
du_commutativeSemigroup_2778 T_CancellativeCommutativeSemiring_2632
v2
du_commutativeSemigroup_2778 ::
  T_CancellativeCommutativeSemiring_2632 ->
  T_CommutativeSemigroup_662
du_commutativeSemigroup_2778 :: T_CancellativeCommutativeSemiring_2632
-> T_CommutativeSemigroup_662
du_commutativeSemigroup_2778 T_CancellativeCommutativeSemiring_2632
v0
  = let v1 :: t
v1 = (T_CancellativeCommutativeSemiring_2632
 -> T_CommutativeSemiring_2446)
-> AgdaAny -> t
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2632
-> T_CommutativeSemiring_2446
du_commutativeSemiring_2768 (T_CancellativeCommutativeSemiring_2632 -> AgdaAny
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2632
v0) in
    AgdaAny -> T_CommutativeSemigroup_662
forall a b. a -> b
coe
      ((T_CommutativeMonoid_962 -> T_CommutativeSemigroup_662)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_CommutativeMonoid_962 -> T_CommutativeSemigroup_662
du_commutativeSemigroup_1048
         ((T_CommutativeSemiring_2446 -> T_CommutativeMonoid_962)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemiring_2446 -> T_CommutativeMonoid_962
du_'42''45'commutativeMonoid_2618 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1)))
-- Algebra.Bundles.CancellativeCommutativeSemiring._.magma
d_magma_2780 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CancellativeCommutativeSemiring_2632 -> T_Magma_68
d_magma_2780 :: () -> () -> T_CancellativeCommutativeSemiring_2632 -> T_Magma_68
d_magma_2780 ~()
v0 ~()
v1 T_CancellativeCommutativeSemiring_2632
v2 = T_CancellativeCommutativeSemiring_2632 -> T_Magma_68
du_magma_2780 T_CancellativeCommutativeSemiring_2632
v2
du_magma_2780 ::
  T_CancellativeCommutativeSemiring_2632 -> T_Magma_68
du_magma_2780 :: T_CancellativeCommutativeSemiring_2632 -> T_Magma_68
du_magma_2780 T_CancellativeCommutativeSemiring_2632
v0
  = let v1 :: t
v1 = (T_CancellativeCommutativeSemiring_2632
 -> T_CommutativeSemiring_2446)
-> AgdaAny -> t
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2632
-> T_CommutativeSemiring_2446
du_commutativeSemiring_2768 (T_CancellativeCommutativeSemiring_2632 -> AgdaAny
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2632
v0) in
    AgdaAny -> T_Magma_68
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_CommutativeSemiring_2446 -> T_Semiring_2280) -> AgdaAny -> t
forall a b. a -> b
coe T_CommutativeSemiring_2446 -> T_Semiring_2280
du_semiring_2576 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: t
v3 = (T_Semiring_2280 -> T_SemiringWithoutAnnihilatingZero_2130)
-> AgdaAny -> t
forall a b. a -> b
coe T_Semiring_2280 -> T_SemiringWithoutAnnihilatingZero_2130
du_semiringWithoutAnnihilatingZero_2398 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: t
v4 = (T_SemiringWithoutAnnihilatingZero_2130 -> T_Monoid_882)
-> AgdaAny -> t
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_2130 -> T_Monoid_882
du_'42''45'monoid_2264 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_Semigroup_536 -> T_Magma_68) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semigroup_536 -> T_Magma_68
du_magma_584 ((T_Monoid_882 -> T_Semigroup_536) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Monoid_882 -> T_Semigroup_536
du_semigroup_944 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v4))))))
-- Algebra.Bundles.CancellativeCommutativeSemiring._.*-monoid
d_'42''45'monoid_2782 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CancellativeCommutativeSemiring_2632 -> T_Monoid_882
d_'42''45'monoid_2782 :: () -> () -> T_CancellativeCommutativeSemiring_2632 -> T_Monoid_882
d_'42''45'monoid_2782 ~()
v0 ~()
v1 T_CancellativeCommutativeSemiring_2632
v2 = T_CancellativeCommutativeSemiring_2632 -> T_Monoid_882
du_'42''45'monoid_2782 T_CancellativeCommutativeSemiring_2632
v2
du_'42''45'monoid_2782 ::
  T_CancellativeCommutativeSemiring_2632 -> T_Monoid_882
du_'42''45'monoid_2782 :: T_CancellativeCommutativeSemiring_2632 -> T_Monoid_882
du_'42''45'monoid_2782 T_CancellativeCommutativeSemiring_2632
v0
  = let v1 :: t
v1 = (T_CancellativeCommutativeSemiring_2632
 -> T_CommutativeSemiring_2446)
-> AgdaAny -> t
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2632
-> T_CommutativeSemiring_2446
du_commutativeSemiring_2768 (T_CancellativeCommutativeSemiring_2632 -> AgdaAny
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2632
v0) in
    AgdaAny -> T_Monoid_882
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_CommutativeSemiring_2446 -> T_Semiring_2280) -> AgdaAny -> t
forall a b. a -> b
coe T_CommutativeSemiring_2446 -> T_Semiring_2280
du_semiring_2576 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_SemiringWithoutAnnihilatingZero_2130 -> T_Monoid_882)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_SemiringWithoutAnnihilatingZero_2130 -> T_Monoid_882
du_'42''45'monoid_2264
            ((T_Semiring_2280 -> T_SemiringWithoutAnnihilatingZero_2130)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semiring_2280 -> T_SemiringWithoutAnnihilatingZero_2130
du_semiringWithoutAnnihilatingZero_2398 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2))))
-- Algebra.Bundles.CancellativeCommutativeSemiring._.rawMagma
d_rawMagma_2784 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CancellativeCommutativeSemiring_2632 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
d_rawMagma_2784 :: () -> () -> T_CancellativeCommutativeSemiring_2632 -> T_RawMagma_36
d_rawMagma_2784 ~()
v0 ~()
v1 T_CancellativeCommutativeSemiring_2632
v2 = T_CancellativeCommutativeSemiring_2632 -> T_RawMagma_36
du_rawMagma_2784 T_CancellativeCommutativeSemiring_2632
v2
du_rawMagma_2784 ::
  T_CancellativeCommutativeSemiring_2632 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
du_rawMagma_2784 :: T_CancellativeCommutativeSemiring_2632 -> T_RawMagma_36
du_rawMagma_2784 T_CancellativeCommutativeSemiring_2632
v0
  = let v1 :: t
v1 = (T_CancellativeCommutativeSemiring_2632
 -> T_CommutativeSemiring_2446)
-> AgdaAny -> t
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2632
-> T_CommutativeSemiring_2446
du_commutativeSemiring_2768 (T_CancellativeCommutativeSemiring_2632 -> AgdaAny
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2632
v0) in
    AgdaAny -> T_RawMagma_36
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_CommutativeSemiring_2446 -> T_Semiring_2280) -> AgdaAny -> t
forall a b. a -> b
coe T_CommutativeSemiring_2446 -> T_Semiring_2280
du_semiring_2576 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: t
v3 = (T_Semiring_2280 -> T_SemiringWithoutAnnihilatingZero_2130)
-> AgdaAny -> t
forall a b. a -> b
coe T_Semiring_2280 -> T_SemiringWithoutAnnihilatingZero_2130
du_semiringWithoutAnnihilatingZero_2398 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: t
v4 = (T_SemiringWithoutAnnihilatingZero_2130 -> T_Monoid_882)
-> AgdaAny -> t
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_2130 -> T_Monoid_882
du_'42''45'monoid_2264 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: t
v5 = (T_Monoid_882 -> T_Semigroup_536) -> AgdaAny -> t
forall a b. a -> b
coe T_Monoid_882 -> T_Semigroup_536
du_semigroup_944 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_Magma_68 -> T_RawMagma_36) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Magma_68 -> T_RawMagma_36
du_rawMagma_112 ((T_Semigroup_536 -> T_Magma_68) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semigroup_536 -> T_Magma_68
du_magma_584 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v5)))))))
-- Algebra.Bundles.CancellativeCommutativeSemiring._.rawMonoid
d_rawMonoid_2786 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CancellativeCommutativeSemiring_2632 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMonoid_64
d_rawMonoid_2786 :: ()
-> () -> T_CancellativeCommutativeSemiring_2632 -> T_RawMonoid_64
d_rawMonoid_2786 ~()
v0 ~()
v1 T_CancellativeCommutativeSemiring_2632
v2 = T_CancellativeCommutativeSemiring_2632 -> T_RawMonoid_64
du_rawMonoid_2786 T_CancellativeCommutativeSemiring_2632
v2
du_rawMonoid_2786 ::
  T_CancellativeCommutativeSemiring_2632 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMonoid_64
du_rawMonoid_2786 :: T_CancellativeCommutativeSemiring_2632 -> T_RawMonoid_64
du_rawMonoid_2786 T_CancellativeCommutativeSemiring_2632
v0
  = let v1 :: t
v1 = (T_CancellativeCommutativeSemiring_2632
 -> T_CommutativeSemiring_2446)
-> AgdaAny -> t
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2632
-> T_CommutativeSemiring_2446
du_commutativeSemiring_2768 (T_CancellativeCommutativeSemiring_2632 -> AgdaAny
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2632
v0) in
    AgdaAny -> T_RawMonoid_64
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_CommutativeSemiring_2446 -> T_Semiring_2280) -> AgdaAny -> t
forall a b. a -> b
coe T_CommutativeSemiring_2446 -> T_Semiring_2280
du_semiring_2576 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: t
v3 = (T_Semiring_2280 -> T_SemiringWithoutAnnihilatingZero_2130)
-> AgdaAny -> t
forall a b. a -> b
coe T_Semiring_2280 -> T_SemiringWithoutAnnihilatingZero_2130
du_semiringWithoutAnnihilatingZero_2398 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_Monoid_882 -> T_RawMonoid_64) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Monoid_882 -> T_RawMonoid_64
du_rawMonoid_954 ((T_SemiringWithoutAnnihilatingZero_2130 -> T_Monoid_882)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_2130 -> T_Monoid_882
du_'42''45'monoid_2264 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3)))))
-- Algebra.Bundles.CancellativeCommutativeSemiring._.semigroup
d_semigroup_2788 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CancellativeCommutativeSemiring_2632 -> T_Semigroup_536
d_semigroup_2788 :: ()
-> () -> T_CancellativeCommutativeSemiring_2632 -> T_Semigroup_536
d_semigroup_2788 ~()
v0 ~()
v1 T_CancellativeCommutativeSemiring_2632
v2 = T_CancellativeCommutativeSemiring_2632 -> T_Semigroup_536
du_semigroup_2788 T_CancellativeCommutativeSemiring_2632
v2
du_semigroup_2788 ::
  T_CancellativeCommutativeSemiring_2632 -> T_Semigroup_536
du_semigroup_2788 :: T_CancellativeCommutativeSemiring_2632 -> T_Semigroup_536
du_semigroup_2788 T_CancellativeCommutativeSemiring_2632
v0
  = let v1 :: t
v1 = (T_CancellativeCommutativeSemiring_2632
 -> T_CommutativeSemiring_2446)
-> AgdaAny -> t
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2632
-> T_CommutativeSemiring_2446
du_commutativeSemiring_2768 (T_CancellativeCommutativeSemiring_2632 -> AgdaAny
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2632
v0) in
    AgdaAny -> T_Semigroup_536
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_CommutativeSemiring_2446 -> T_Semiring_2280) -> AgdaAny -> t
forall a b. a -> b
coe T_CommutativeSemiring_2446 -> T_Semiring_2280
du_semiring_2576 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: t
v3 = (T_Semiring_2280 -> T_SemiringWithoutAnnihilatingZero_2130)
-> AgdaAny -> t
forall a b. a -> b
coe T_Semiring_2280 -> T_SemiringWithoutAnnihilatingZero_2130
du_semiringWithoutAnnihilatingZero_2398 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_Monoid_882 -> T_Semigroup_536) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Monoid_882 -> T_Semigroup_536
du_semigroup_944 ((T_SemiringWithoutAnnihilatingZero_2130 -> T_Monoid_882)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_2130 -> T_Monoid_882
du_'42''45'monoid_2264 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3)))))
-- Algebra.Bundles.CancellativeCommutativeSemiring._.commutativeMagma
d_commutativeMagma_2790 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CancellativeCommutativeSemiring_2632 -> T_CommutativeMagma_180
d_commutativeMagma_2790 :: ()
-> ()
-> T_CancellativeCommutativeSemiring_2632
-> T_CommutativeMagma_180
d_commutativeMagma_2790 ~()
v0 ~()
v1 T_CancellativeCommutativeSemiring_2632
v2 = T_CancellativeCommutativeSemiring_2632 -> T_CommutativeMagma_180
du_commutativeMagma_2790 T_CancellativeCommutativeSemiring_2632
v2
du_commutativeMagma_2790 ::
  T_CancellativeCommutativeSemiring_2632 -> T_CommutativeMagma_180
du_commutativeMagma_2790 :: T_CancellativeCommutativeSemiring_2632 -> T_CommutativeMagma_180
du_commutativeMagma_2790 T_CancellativeCommutativeSemiring_2632
v0
  = let v1 :: t
v1 = (T_CancellativeCommutativeSemiring_2632
 -> T_CommutativeSemiring_2446)
-> AgdaAny -> t
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2632
-> T_CommutativeSemiring_2446
du_commutativeSemiring_2768 (T_CancellativeCommutativeSemiring_2632 -> AgdaAny
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2632
v0) in
    AgdaAny -> T_CommutativeMagma_180
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_CommutativeSemiring_2446 -> T_Semiring_2280) -> AgdaAny -> t
forall a b. a -> b
coe T_CommutativeSemiring_2446 -> T_Semiring_2280
du_semiring_2576 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: t
v3 = (T_Semiring_2280 -> T_SemiringWithoutAnnihilatingZero_2130)
-> AgdaAny -> t
forall a b. a -> b
coe T_Semiring_2280 -> T_SemiringWithoutAnnihilatingZero_2130
du_semiringWithoutAnnihilatingZero_2398 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: t
v4 = (T_SemiringWithoutAnnihilatingZero_2130 -> T_CommutativeMonoid_962)
-> AgdaAny -> t
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_2130 -> T_CommutativeMonoid_962
du_'43''45'commutativeMonoid_2242 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               ((T_CommutativeSemigroup_662 -> T_CommutativeMagma_180)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_CommutativeSemigroup_662 -> T_CommutativeMagma_180
du_commutativeMagma_726
                  ((T_CommutativeMonoid_962 -> T_CommutativeSemigroup_662)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeMonoid_962 -> T_CommutativeSemigroup_662
du_commutativeSemigroup_1048 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v4))))))
-- Algebra.Bundles.CancellativeCommutativeSemiring._.+-commutativeMonoid
d_'43''45'commutativeMonoid_2792 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CancellativeCommutativeSemiring_2632 -> T_CommutativeMonoid_962
d_'43''45'commutativeMonoid_2792 :: ()
-> ()
-> T_CancellativeCommutativeSemiring_2632
-> T_CommutativeMonoid_962
d_'43''45'commutativeMonoid_2792 ~()
v0 ~()
v1 T_CancellativeCommutativeSemiring_2632
v2
  = T_CancellativeCommutativeSemiring_2632 -> T_CommutativeMonoid_962
du_'43''45'commutativeMonoid_2792 T_CancellativeCommutativeSemiring_2632
v2
du_'43''45'commutativeMonoid_2792 ::
  T_CancellativeCommutativeSemiring_2632 -> T_CommutativeMonoid_962
du_'43''45'commutativeMonoid_2792 :: T_CancellativeCommutativeSemiring_2632 -> T_CommutativeMonoid_962
du_'43''45'commutativeMonoid_2792 T_CancellativeCommutativeSemiring_2632
v0
  = let v1 :: t
v1 = (T_CancellativeCommutativeSemiring_2632
 -> T_CommutativeSemiring_2446)
-> AgdaAny -> t
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2632
-> T_CommutativeSemiring_2446
du_commutativeSemiring_2768 (T_CancellativeCommutativeSemiring_2632 -> AgdaAny
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2632
v0) in
    AgdaAny -> T_CommutativeMonoid_962
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_CommutativeSemiring_2446 -> T_Semiring_2280) -> AgdaAny -> t
forall a b. a -> b
coe T_CommutativeSemiring_2446 -> T_Semiring_2280
du_semiring_2576 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_SemiringWithoutAnnihilatingZero_2130 -> T_CommutativeMonoid_962)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_SemiringWithoutAnnihilatingZero_2130 -> T_CommutativeMonoid_962
du_'43''45'commutativeMonoid_2242
            ((T_Semiring_2280 -> T_SemiringWithoutAnnihilatingZero_2130)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semiring_2280 -> T_SemiringWithoutAnnihilatingZero_2130
du_semiringWithoutAnnihilatingZero_2398 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2))))
-- Algebra.Bundles.CancellativeCommutativeSemiring._.commutativeSemigroup
d_commutativeSemigroup_2794 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CancellativeCommutativeSemiring_2632 ->
  T_CommutativeSemigroup_662
d_commutativeSemigroup_2794 :: ()
-> ()
-> T_CancellativeCommutativeSemiring_2632
-> T_CommutativeSemigroup_662
d_commutativeSemigroup_2794 ~()
v0 ~()
v1 T_CancellativeCommutativeSemiring_2632
v2
  = T_CancellativeCommutativeSemiring_2632
-> T_CommutativeSemigroup_662
du_commutativeSemigroup_2794 T_CancellativeCommutativeSemiring_2632
v2
du_commutativeSemigroup_2794 ::
  T_CancellativeCommutativeSemiring_2632 ->
  T_CommutativeSemigroup_662
du_commutativeSemigroup_2794 :: T_CancellativeCommutativeSemiring_2632
-> T_CommutativeSemigroup_662
du_commutativeSemigroup_2794 T_CancellativeCommutativeSemiring_2632
v0
  = let v1 :: t
v1 = (T_CancellativeCommutativeSemiring_2632
 -> T_CommutativeSemiring_2446)
-> AgdaAny -> t
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2632
-> T_CommutativeSemiring_2446
du_commutativeSemiring_2768 (T_CancellativeCommutativeSemiring_2632 -> AgdaAny
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2632
v0) in
    AgdaAny -> T_CommutativeSemigroup_662
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_CommutativeSemiring_2446 -> T_Semiring_2280) -> AgdaAny -> t
forall a b. a -> b
coe T_CommutativeSemiring_2446 -> T_Semiring_2280
du_semiring_2576 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: t
v3 = (T_Semiring_2280 -> T_SemiringWithoutAnnihilatingZero_2130)
-> AgdaAny -> t
forall a b. a -> b
coe T_Semiring_2280 -> T_SemiringWithoutAnnihilatingZero_2130
du_semiringWithoutAnnihilatingZero_2398 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_CommutativeMonoid_962 -> T_CommutativeSemigroup_662)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_CommutativeMonoid_962 -> T_CommutativeSemigroup_662
du_commutativeSemigroup_1048
               ((T_SemiringWithoutAnnihilatingZero_2130 -> T_CommutativeMonoid_962)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_2130 -> T_CommutativeMonoid_962
du_'43''45'commutativeMonoid_2242 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3)))))
-- Algebra.Bundles.CancellativeCommutativeSemiring._.magma
d_magma_2796 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CancellativeCommutativeSemiring_2632 -> T_Magma_68
d_magma_2796 :: () -> () -> T_CancellativeCommutativeSemiring_2632 -> T_Magma_68
d_magma_2796 ~()
v0 ~()
v1 T_CancellativeCommutativeSemiring_2632
v2 = T_CancellativeCommutativeSemiring_2632 -> T_Magma_68
du_magma_2796 T_CancellativeCommutativeSemiring_2632
v2
du_magma_2796 ::
  T_CancellativeCommutativeSemiring_2632 -> T_Magma_68
du_magma_2796 :: T_CancellativeCommutativeSemiring_2632 -> T_Magma_68
du_magma_2796 T_CancellativeCommutativeSemiring_2632
v0
  = let v1 :: t
v1 = (T_CancellativeCommutativeSemiring_2632
 -> T_CommutativeSemiring_2446)
-> AgdaAny -> t
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2632
-> T_CommutativeSemiring_2446
du_commutativeSemiring_2768 (T_CancellativeCommutativeSemiring_2632 -> AgdaAny
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2632
v0) in
    AgdaAny -> T_Magma_68
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_CommutativeSemiring_2446 -> T_Semiring_2280) -> AgdaAny -> t
forall a b. a -> b
coe T_CommutativeSemiring_2446 -> T_Semiring_2280
du_semiring_2576 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: t
v3 = (T_Semiring_2280 -> T_SemiringWithoutAnnihilatingZero_2130)
-> AgdaAny -> t
forall a b. a -> b
coe T_Semiring_2280 -> T_SemiringWithoutAnnihilatingZero_2130
du_semiringWithoutAnnihilatingZero_2398 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: t
v4 = (T_SemiringWithoutAnnihilatingZero_2130 -> T_CommutativeMonoid_962)
-> AgdaAny -> t
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_2130 -> T_CommutativeMonoid_962
du_'43''45'commutativeMonoid_2242 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: t
v5 = (T_CommutativeMonoid_962 -> T_Monoid_882) -> AgdaAny -> t
forall a b. a -> b
coe T_CommutativeMonoid_962 -> T_Monoid_882
du_monoid_1032 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_Semigroup_536 -> T_Magma_68) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semigroup_536 -> T_Magma_68
du_magma_584 ((T_Monoid_882 -> T_Semigroup_536) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Monoid_882 -> T_Semigroup_536
du_semigroup_944 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v5)))))))
-- Algebra.Bundles.CancellativeCommutativeSemiring._.monoid
d_monoid_2798 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CancellativeCommutativeSemiring_2632 -> T_Monoid_882
d_monoid_2798 :: () -> () -> T_CancellativeCommutativeSemiring_2632 -> T_Monoid_882
d_monoid_2798 ~()
v0 ~()
v1 T_CancellativeCommutativeSemiring_2632
v2 = T_CancellativeCommutativeSemiring_2632 -> T_Monoid_882
du_monoid_2798 T_CancellativeCommutativeSemiring_2632
v2
du_monoid_2798 ::
  T_CancellativeCommutativeSemiring_2632 -> T_Monoid_882
du_monoid_2798 :: T_CancellativeCommutativeSemiring_2632 -> T_Monoid_882
du_monoid_2798 T_CancellativeCommutativeSemiring_2632
v0
  = let v1 :: t
v1 = (T_CancellativeCommutativeSemiring_2632
 -> T_CommutativeSemiring_2446)
-> AgdaAny -> t
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2632
-> T_CommutativeSemiring_2446
du_commutativeSemiring_2768 (T_CancellativeCommutativeSemiring_2632 -> AgdaAny
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2632
v0) in
    AgdaAny -> T_Monoid_882
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_CommutativeSemiring_2446 -> T_Semiring_2280) -> AgdaAny -> t
forall a b. a -> b
coe T_CommutativeSemiring_2446 -> T_Semiring_2280
du_semiring_2576 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: t
v3 = (T_Semiring_2280 -> T_SemiringWithoutAnnihilatingZero_2130)
-> AgdaAny -> t
forall a b. a -> b
coe T_Semiring_2280 -> T_SemiringWithoutAnnihilatingZero_2130
du_semiringWithoutAnnihilatingZero_2398 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_CommutativeMonoid_962 -> T_Monoid_882) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_CommutativeMonoid_962 -> T_Monoid_882
du_monoid_1032 ((T_SemiringWithoutAnnihilatingZero_2130 -> T_CommutativeMonoid_962)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_2130 -> T_CommutativeMonoid_962
du_'43''45'commutativeMonoid_2242 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3)))))
-- Algebra.Bundles.CancellativeCommutativeSemiring._.rawMagma
d_rawMagma_2800 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CancellativeCommutativeSemiring_2632 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
d_rawMagma_2800 :: () -> () -> T_CancellativeCommutativeSemiring_2632 -> T_RawMagma_36
d_rawMagma_2800 ~()
v0 ~()
v1 T_CancellativeCommutativeSemiring_2632
v2 = T_CancellativeCommutativeSemiring_2632 -> T_RawMagma_36
du_rawMagma_2800 T_CancellativeCommutativeSemiring_2632
v2
du_rawMagma_2800 ::
  T_CancellativeCommutativeSemiring_2632 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
du_rawMagma_2800 :: T_CancellativeCommutativeSemiring_2632 -> T_RawMagma_36
du_rawMagma_2800 T_CancellativeCommutativeSemiring_2632
v0
  = let v1 :: t
v1 = (T_CancellativeCommutativeSemiring_2632
 -> T_CommutativeSemiring_2446)
-> AgdaAny -> t
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2632
-> T_CommutativeSemiring_2446
du_commutativeSemiring_2768 (T_CancellativeCommutativeSemiring_2632 -> AgdaAny
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2632
v0) in
    AgdaAny -> T_RawMagma_36
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_CommutativeSemiring_2446 -> T_Semiring_2280) -> AgdaAny -> t
forall a b. a -> b
coe T_CommutativeSemiring_2446 -> T_Semiring_2280
du_semiring_2576 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: t
v3 = (T_Semiring_2280 -> T_SemiringWithoutAnnihilatingZero_2130)
-> AgdaAny -> t
forall a b. a -> b
coe T_Semiring_2280 -> T_SemiringWithoutAnnihilatingZero_2130
du_semiringWithoutAnnihilatingZero_2398 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: t
v4 = (T_SemiringWithoutAnnihilatingZero_2130 -> T_CommutativeMonoid_962)
-> AgdaAny -> t
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_2130 -> T_CommutativeMonoid_962
du_'43''45'commutativeMonoid_2242 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: t
v5 = (T_CommutativeMonoid_962 -> T_Monoid_882) -> AgdaAny -> t
forall a b. a -> b
coe T_CommutativeMonoid_962 -> T_Monoid_882
du_monoid_1032 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (let v6 :: t
v6 = (T_Monoid_882 -> T_Semigroup_536) -> AgdaAny -> t
forall a b. a -> b
coe T_Monoid_882 -> T_Semigroup_536
du_semigroup_944 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v5) in
                   AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_Magma_68 -> T_RawMagma_36) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Magma_68 -> T_RawMagma_36
du_rawMagma_112 ((T_Semigroup_536 -> T_Magma_68) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semigroup_536 -> T_Magma_68
du_magma_584 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v6))))))))
-- Algebra.Bundles.CancellativeCommutativeSemiring._.rawMonoid
d_rawMonoid_2802 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CancellativeCommutativeSemiring_2632 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMonoid_64
d_rawMonoid_2802 :: ()
-> () -> T_CancellativeCommutativeSemiring_2632 -> T_RawMonoid_64
d_rawMonoid_2802 ~()
v0 ~()
v1 T_CancellativeCommutativeSemiring_2632
v2 = T_CancellativeCommutativeSemiring_2632 -> T_RawMonoid_64
du_rawMonoid_2802 T_CancellativeCommutativeSemiring_2632
v2
du_rawMonoid_2802 ::
  T_CancellativeCommutativeSemiring_2632 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMonoid_64
du_rawMonoid_2802 :: T_CancellativeCommutativeSemiring_2632 -> T_RawMonoid_64
du_rawMonoid_2802 T_CancellativeCommutativeSemiring_2632
v0
  = let v1 :: t
v1 = (T_CancellativeCommutativeSemiring_2632
 -> T_CommutativeSemiring_2446)
-> AgdaAny -> t
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2632
-> T_CommutativeSemiring_2446
du_commutativeSemiring_2768 (T_CancellativeCommutativeSemiring_2632 -> AgdaAny
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2632
v0) in
    AgdaAny -> T_RawMonoid_64
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_CommutativeSemiring_2446 -> T_Semiring_2280) -> AgdaAny -> t
forall a b. a -> b
coe T_CommutativeSemiring_2446 -> T_Semiring_2280
du_semiring_2576 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: t
v3 = (T_Semiring_2280 -> T_SemiringWithoutAnnihilatingZero_2130)
-> AgdaAny -> t
forall a b. a -> b
coe T_Semiring_2280 -> T_SemiringWithoutAnnihilatingZero_2130
du_semiringWithoutAnnihilatingZero_2398 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: t
v4 = (T_SemiringWithoutAnnihilatingZero_2130 -> T_CommutativeMonoid_962)
-> AgdaAny -> t
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_2130 -> T_CommutativeMonoid_962
du_'43''45'commutativeMonoid_2242 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_Monoid_882 -> T_RawMonoid_64) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Monoid_882 -> T_RawMonoid_64
du_rawMonoid_954 ((T_CommutativeMonoid_962 -> T_Monoid_882) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeMonoid_962 -> T_Monoid_882
du_monoid_1032 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v4))))))
-- Algebra.Bundles.CancellativeCommutativeSemiring._.semigroup
d_semigroup_2804 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CancellativeCommutativeSemiring_2632 -> T_Semigroup_536
d_semigroup_2804 :: ()
-> () -> T_CancellativeCommutativeSemiring_2632 -> T_Semigroup_536
d_semigroup_2804 ~()
v0 ~()
v1 T_CancellativeCommutativeSemiring_2632
v2 = T_CancellativeCommutativeSemiring_2632 -> T_Semigroup_536
du_semigroup_2804 T_CancellativeCommutativeSemiring_2632
v2
du_semigroup_2804 ::
  T_CancellativeCommutativeSemiring_2632 -> T_Semigroup_536
du_semigroup_2804 :: T_CancellativeCommutativeSemiring_2632 -> T_Semigroup_536
du_semigroup_2804 T_CancellativeCommutativeSemiring_2632
v0
  = let v1 :: t
v1 = (T_CancellativeCommutativeSemiring_2632
 -> T_CommutativeSemiring_2446)
-> AgdaAny -> t
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2632
-> T_CommutativeSemiring_2446
du_commutativeSemiring_2768 (T_CancellativeCommutativeSemiring_2632 -> AgdaAny
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2632
v0) in
    AgdaAny -> T_Semigroup_536
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_CommutativeSemiring_2446 -> T_Semiring_2280) -> AgdaAny -> t
forall a b. a -> b
coe T_CommutativeSemiring_2446 -> T_Semiring_2280
du_semiring_2576 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: t
v3 = (T_Semiring_2280 -> T_SemiringWithoutAnnihilatingZero_2130)
-> AgdaAny -> t
forall a b. a -> b
coe T_Semiring_2280 -> T_SemiringWithoutAnnihilatingZero_2130
du_semiringWithoutAnnihilatingZero_2398 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: t
v4 = (T_SemiringWithoutAnnihilatingZero_2130 -> T_CommutativeMonoid_962)
-> AgdaAny -> t
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_2130 -> T_CommutativeMonoid_962
du_'43''45'commutativeMonoid_2242 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_Monoid_882 -> T_Semigroup_536) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Monoid_882 -> T_Semigroup_536
du_semigroup_944 ((T_CommutativeMonoid_962 -> T_Monoid_882) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeMonoid_962 -> T_Monoid_882
du_monoid_1032 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v4))))))
-- Algebra.Bundles.CancellativeCommutativeSemiring._.unitalMagma
d_unitalMagma_2806 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CancellativeCommutativeSemiring_2632 -> T_UnitalMagma_814
d_unitalMagma_2806 :: ()
-> ()
-> T_CancellativeCommutativeSemiring_2632
-> T_UnitalMagma_814
d_unitalMagma_2806 ~()
v0 ~()
v1 T_CancellativeCommutativeSemiring_2632
v2 = T_CancellativeCommutativeSemiring_2632 -> T_UnitalMagma_814
du_unitalMagma_2806 T_CancellativeCommutativeSemiring_2632
v2
du_unitalMagma_2806 ::
  T_CancellativeCommutativeSemiring_2632 -> T_UnitalMagma_814
du_unitalMagma_2806 :: T_CancellativeCommutativeSemiring_2632 -> T_UnitalMagma_814
du_unitalMagma_2806 T_CancellativeCommutativeSemiring_2632
v0
  = let v1 :: t
v1 = (T_CancellativeCommutativeSemiring_2632
 -> T_CommutativeSemiring_2446)
-> AgdaAny -> t
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2632
-> T_CommutativeSemiring_2446
du_commutativeSemiring_2768 (T_CancellativeCommutativeSemiring_2632 -> AgdaAny
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2632
v0) in
    AgdaAny -> T_UnitalMagma_814
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_CommutativeSemiring_2446 -> T_Semiring_2280) -> AgdaAny -> t
forall a b. a -> b
coe T_CommutativeSemiring_2446 -> T_Semiring_2280
du_semiring_2576 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: t
v3 = (T_Semiring_2280 -> T_SemiringWithoutAnnihilatingZero_2130)
-> AgdaAny -> t
forall a b. a -> b
coe T_Semiring_2280 -> T_SemiringWithoutAnnihilatingZero_2130
du_semiringWithoutAnnihilatingZero_2398 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: t
v4 = (T_SemiringWithoutAnnihilatingZero_2130 -> T_CommutativeMonoid_962)
-> AgdaAny -> t
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_2130 -> T_CommutativeMonoid_962
du_'43''45'commutativeMonoid_2242 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_Monoid_882 -> T_UnitalMagma_814) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Monoid_882 -> T_UnitalMagma_814
du_unitalMagma_956 ((T_CommutativeMonoid_962 -> T_Monoid_882) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeMonoid_962 -> T_Monoid_882
du_monoid_1032 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v4))))))
-- Algebra.Bundles.CancellativeCommutativeSemiring._.nearSemiring
d_nearSemiring_2808 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CancellativeCommutativeSemiring_2632 -> T_NearSemiring_1766
d_nearSemiring_2808 :: ()
-> ()
-> T_CancellativeCommutativeSemiring_2632
-> T_NearSemiring_1766
d_nearSemiring_2808 ~()
v0 ~()
v1 T_CancellativeCommutativeSemiring_2632
v2 = T_CancellativeCommutativeSemiring_2632 -> T_NearSemiring_1766
du_nearSemiring_2808 T_CancellativeCommutativeSemiring_2632
v2
du_nearSemiring_2808 ::
  T_CancellativeCommutativeSemiring_2632 -> T_NearSemiring_1766
du_nearSemiring_2808 :: T_CancellativeCommutativeSemiring_2632 -> T_NearSemiring_1766
du_nearSemiring_2808 T_CancellativeCommutativeSemiring_2632
v0
  = let v1 :: t
v1 = (T_CancellativeCommutativeSemiring_2632
 -> T_CommutativeSemiring_2446)
-> AgdaAny -> t
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2632
-> T_CommutativeSemiring_2446
du_commutativeSemiring_2768 (T_CancellativeCommutativeSemiring_2632 -> AgdaAny
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2632
v0) in
    AgdaAny -> T_NearSemiring_1766
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_CommutativeSemiring_2446 -> T_Semiring_2280) -> AgdaAny -> t
forall a b. a -> b
coe T_CommutativeSemiring_2446 -> T_Semiring_2280
du_semiring_2576 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_SemiringWithoutOne_1880 -> T_NearSemiring_1766)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_SemiringWithoutOne_1880 -> T_NearSemiring_1766
du_nearSemiring_1966 ((T_Semiring_2280 -> T_SemiringWithoutOne_1880)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semiring_2280 -> T_SemiringWithoutOne_1880
du_semiringWithoutOne_2436 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2))))
-- Algebra.Bundles.CancellativeCommutativeSemiring._.rawSemiring
d_rawSemiring_2810 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CancellativeCommutativeSemiring_2632 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawSemiring_174
d_rawSemiring_2810 :: ()
-> ()
-> T_CancellativeCommutativeSemiring_2632
-> T_RawSemiring_174
d_rawSemiring_2810 ~()
v0 ~()
v1 T_CancellativeCommutativeSemiring_2632
v2 = T_CancellativeCommutativeSemiring_2632 -> T_RawSemiring_174
du_rawSemiring_2810 T_CancellativeCommutativeSemiring_2632
v2
du_rawSemiring_2810 ::
  T_CancellativeCommutativeSemiring_2632 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawSemiring_174
du_rawSemiring_2810 :: T_CancellativeCommutativeSemiring_2632 -> T_RawSemiring_174
du_rawSemiring_2810 T_CancellativeCommutativeSemiring_2632
v0
  = let v1 :: t
v1 = (T_CancellativeCommutativeSemiring_2632
 -> T_CommutativeSemiring_2446)
-> AgdaAny -> t
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2632
-> T_CommutativeSemiring_2446
du_commutativeSemiring_2768 (T_CancellativeCommutativeSemiring_2632 -> AgdaAny
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2632
v0) in
    AgdaAny -> T_RawSemiring_174
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_CommutativeSemiring_2446 -> T_Semiring_2280) -> AgdaAny -> t
forall a b. a -> b
coe T_CommutativeSemiring_2446 -> T_Semiring_2280
du_semiring_2576 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_SemiringWithoutAnnihilatingZero_2130 -> T_RawSemiring_174)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_SemiringWithoutAnnihilatingZero_2130 -> T_RawSemiring_174
du_rawSemiring_2236
            ((T_Semiring_2280 -> T_SemiringWithoutAnnihilatingZero_2130)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semiring_2280 -> T_SemiringWithoutAnnihilatingZero_2130
du_semiringWithoutAnnihilatingZero_2398 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2))))
-- Algebra.Bundles.CancellativeCommutativeSemiring._.semiring
d_semiring_2812 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CancellativeCommutativeSemiring_2632 -> T_Semiring_2280
d_semiring_2812 :: ()
-> () -> T_CancellativeCommutativeSemiring_2632 -> T_Semiring_2280
d_semiring_2812 ~()
v0 ~()
v1 T_CancellativeCommutativeSemiring_2632
v2 = T_CancellativeCommutativeSemiring_2632 -> T_Semiring_2280
du_semiring_2812 T_CancellativeCommutativeSemiring_2632
v2
du_semiring_2812 ::
  T_CancellativeCommutativeSemiring_2632 -> T_Semiring_2280
du_semiring_2812 :: T_CancellativeCommutativeSemiring_2632 -> T_Semiring_2280
du_semiring_2812 T_CancellativeCommutativeSemiring_2632
v0
  = (T_CommutativeSemiring_2446 -> T_Semiring_2280)
-> AgdaAny -> T_Semiring_2280
forall a b. a -> b
coe T_CommutativeSemiring_2446 -> T_Semiring_2280
du_semiring_2576 ((T_CancellativeCommutativeSemiring_2632
 -> T_CommutativeSemiring_2446)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2632
-> T_CommutativeSemiring_2446
du_commutativeSemiring_2768 (T_CancellativeCommutativeSemiring_2632 -> AgdaAny
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2632
v0))
-- Algebra.Bundles.CancellativeCommutativeSemiring._.semiringWithoutAnnihilatingZero
d_semiringWithoutAnnihilatingZero_2814 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CancellativeCommutativeSemiring_2632 ->
  T_SemiringWithoutAnnihilatingZero_2130
d_semiringWithoutAnnihilatingZero_2814 :: ()
-> ()
-> T_CancellativeCommutativeSemiring_2632
-> T_SemiringWithoutAnnihilatingZero_2130
d_semiringWithoutAnnihilatingZero_2814 ~()
v0 ~()
v1 T_CancellativeCommutativeSemiring_2632
v2
  = T_CancellativeCommutativeSemiring_2632
-> T_SemiringWithoutAnnihilatingZero_2130
du_semiringWithoutAnnihilatingZero_2814 T_CancellativeCommutativeSemiring_2632
v2
du_semiringWithoutAnnihilatingZero_2814 ::
  T_CancellativeCommutativeSemiring_2632 ->
  T_SemiringWithoutAnnihilatingZero_2130
du_semiringWithoutAnnihilatingZero_2814 :: T_CancellativeCommutativeSemiring_2632
-> T_SemiringWithoutAnnihilatingZero_2130
du_semiringWithoutAnnihilatingZero_2814 T_CancellativeCommutativeSemiring_2632
v0
  = let v1 :: t
v1 = (T_CancellativeCommutativeSemiring_2632
 -> T_CommutativeSemiring_2446)
-> AgdaAny -> t
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2632
-> T_CommutativeSemiring_2446
du_commutativeSemiring_2768 (T_CancellativeCommutativeSemiring_2632 -> AgdaAny
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2632
v0) in
    AgdaAny -> T_SemiringWithoutAnnihilatingZero_2130
forall a b. a -> b
coe
      ((T_Semiring_2280 -> T_SemiringWithoutAnnihilatingZero_2130)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_Semiring_2280 -> T_SemiringWithoutAnnihilatingZero_2130
du_semiringWithoutAnnihilatingZero_2398
         ((T_CommutativeSemiring_2446 -> T_Semiring_2280)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemiring_2446 -> T_Semiring_2280
du_semiring_2576 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1)))
-- Algebra.Bundles.CancellativeCommutativeSemiring._.semiringWithoutOne
d_semiringWithoutOne_2816 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CancellativeCommutativeSemiring_2632 -> T_SemiringWithoutOne_1880
d_semiringWithoutOne_2816 :: ()
-> ()
-> T_CancellativeCommutativeSemiring_2632
-> T_SemiringWithoutOne_1880
d_semiringWithoutOne_2816 ~()
v0 ~()
v1 T_CancellativeCommutativeSemiring_2632
v2
  = T_CancellativeCommutativeSemiring_2632 -> T_SemiringWithoutOne_1880
du_semiringWithoutOne_2816 T_CancellativeCommutativeSemiring_2632
v2
du_semiringWithoutOne_2816 ::
  T_CancellativeCommutativeSemiring_2632 -> T_SemiringWithoutOne_1880
du_semiringWithoutOne_2816 :: T_CancellativeCommutativeSemiring_2632 -> T_SemiringWithoutOne_1880
du_semiringWithoutOne_2816 T_CancellativeCommutativeSemiring_2632
v0
  = let v1 :: t
v1 = (T_CancellativeCommutativeSemiring_2632
 -> T_CommutativeSemiring_2446)
-> AgdaAny -> t
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2632
-> T_CommutativeSemiring_2446
du_commutativeSemiring_2768 (T_CancellativeCommutativeSemiring_2632 -> AgdaAny
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2632
v0) in
    AgdaAny -> T_SemiringWithoutOne_1880
forall a b. a -> b
coe
      ((T_Semiring_2280 -> T_SemiringWithoutOne_1880)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semiring_2280 -> T_SemiringWithoutOne_1880
du_semiringWithoutOne_2436 ((T_CommutativeSemiring_2446 -> T_Semiring_2280)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemiring_2446 -> T_Semiring_2280
du_semiring_2576 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1)))
-- Algebra.Bundles.IdempotentSemiring
d_IdempotentSemiring_2822 :: p -> p -> ()
d_IdempotentSemiring_2822 p
a0 p
a1 = ()
data T_IdempotentSemiring_2822
  = C_IdempotentSemiring'46'constructor_51015 (AgdaAny ->
                                               AgdaAny -> AgdaAny)
                                              (AgdaAny -> AgdaAny -> AgdaAny) AgdaAny AgdaAny
                                              MAlonzo.Code.Algebra.Structures.T_IsIdempotentSemiring_1922
-- Algebra.Bundles.IdempotentSemiring.Carrier
d_Carrier_2842 :: T_IdempotentSemiring_2822 -> ()
d_Carrier_2842 :: T_IdempotentSemiring_2822 -> ()
d_Carrier_2842 = T_IdempotentSemiring_2822 -> ()
forall a. a
erased
-- Algebra.Bundles.IdempotentSemiring._≈_
d__'8776'__2844 ::
  T_IdempotentSemiring_2822 -> AgdaAny -> AgdaAny -> ()
d__'8776'__2844 :: T_IdempotentSemiring_2822 -> AgdaAny -> AgdaAny -> ()
d__'8776'__2844 = T_IdempotentSemiring_2822 -> AgdaAny -> AgdaAny -> ()
forall a. a
erased
-- Algebra.Bundles.IdempotentSemiring._+_
d__'43'__2846 ::
  T_IdempotentSemiring_2822 -> AgdaAny -> AgdaAny -> AgdaAny
d__'43'__2846 :: T_IdempotentSemiring_2822 -> AgdaAny -> AgdaAny -> AgdaAny
d__'43'__2846 T_IdempotentSemiring_2822
v0
  = case T_IdempotentSemiring_2822 -> T_IdempotentSemiring_2822
forall a b. a -> b
coe T_IdempotentSemiring_2822
v0 of
      C_IdempotentSemiring'46'constructor_51015 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny
v5 AgdaAny
v6 T_IsIdempotentSemiring_1922
v7 -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v3
      T_IdempotentSemiring_2822
_ -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.IdempotentSemiring._*_
d__'42'__2848 ::
  T_IdempotentSemiring_2822 -> AgdaAny -> AgdaAny -> AgdaAny
d__'42'__2848 :: T_IdempotentSemiring_2822 -> AgdaAny -> AgdaAny -> AgdaAny
d__'42'__2848 T_IdempotentSemiring_2822
v0
  = case T_IdempotentSemiring_2822 -> T_IdempotentSemiring_2822
forall a b. a -> b
coe T_IdempotentSemiring_2822
v0 of
      C_IdempotentSemiring'46'constructor_51015 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny
v5 AgdaAny
v6 T_IsIdempotentSemiring_1922
v7 -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v4
      T_IdempotentSemiring_2822
_ -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.IdempotentSemiring.0#
d_0'35'_2850 :: T_IdempotentSemiring_2822 -> AgdaAny
d_0'35'_2850 :: T_IdempotentSemiring_2822 -> AgdaAny
d_0'35'_2850 T_IdempotentSemiring_2822
v0
  = case T_IdempotentSemiring_2822 -> T_IdempotentSemiring_2822
forall a b. a -> b
coe T_IdempotentSemiring_2822
v0 of
      C_IdempotentSemiring'46'constructor_51015 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny
v5 AgdaAny
v6 T_IsIdempotentSemiring_1922
v7 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v5
      T_IdempotentSemiring_2822
_ -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.IdempotentSemiring.1#
d_1'35'_2852 :: T_IdempotentSemiring_2822 -> AgdaAny
d_1'35'_2852 :: T_IdempotentSemiring_2822 -> AgdaAny
d_1'35'_2852 T_IdempotentSemiring_2822
v0
  = case T_IdempotentSemiring_2822 -> T_IdempotentSemiring_2822
forall a b. a -> b
coe T_IdempotentSemiring_2822
v0 of
      C_IdempotentSemiring'46'constructor_51015 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny
v5 AgdaAny
v6 T_IsIdempotentSemiring_1922
v7 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v6
      T_IdempotentSemiring_2822
_ -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.IdempotentSemiring.isIdempotentSemiring
d_isIdempotentSemiring_2854 ::
  T_IdempotentSemiring_2822 ->
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentSemiring_1922
d_isIdempotentSemiring_2854 :: T_IdempotentSemiring_2822 -> T_IsIdempotentSemiring_1922
d_isIdempotentSemiring_2854 T_IdempotentSemiring_2822
v0
  = case T_IdempotentSemiring_2822 -> T_IdempotentSemiring_2822
forall a b. a -> b
coe T_IdempotentSemiring_2822
v0 of
      C_IdempotentSemiring'46'constructor_51015 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny
v5 AgdaAny
v6 T_IsIdempotentSemiring_1922
v7 -> T_IsIdempotentSemiring_1922 -> T_IsIdempotentSemiring_1922
forall a b. a -> b
coe T_IsIdempotentSemiring_1922
v7
      T_IdempotentSemiring_2822
_ -> T_IsIdempotentSemiring_1922
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.IdempotentSemiring._.*-assoc
d_'42''45'assoc_2858 ::
  T_IdempotentSemiring_2822 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'assoc_2858 :: T_IdempotentSemiring_2822
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'assoc_2858 T_IdempotentSemiring_2822
v0
  = (T_IsSemiringWithoutAnnihilatingZero_1468
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsSemiringWithoutAnnihilatingZero_1468
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'42''45'assoc_1492
      ((T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
         ((T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570
MAlonzo.Code.Algebra.Structures.d_isSemiring_1936
            ((T_IdempotentSemiring_2822 -> T_IsIdempotentSemiring_1922)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IdempotentSemiring_2822 -> T_IsIdempotentSemiring_1922
d_isIdempotentSemiring_2854 (T_IdempotentSemiring_2822 -> AgdaAny
forall a b. a -> b
coe T_IdempotentSemiring_2822
v0))))
-- Algebra.Bundles.IdempotentSemiring._.*-cong
d_'42''45'cong_2860 ::
  T_IdempotentSemiring_2822 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'cong_2860 :: T_IdempotentSemiring_2822
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'42''45'cong_2860 T_IdempotentSemiring_2822
v0
  = (T_IsSemiringWithoutAnnihilatingZero_1468
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsSemiringWithoutAnnihilatingZero_1468
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'42''45'cong_1490
      ((T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
         ((T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570
MAlonzo.Code.Algebra.Structures.d_isSemiring_1936
            ((T_IdempotentSemiring_2822 -> T_IsIdempotentSemiring_1922)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IdempotentSemiring_2822 -> T_IsIdempotentSemiring_1922
d_isIdempotentSemiring_2854 (T_IdempotentSemiring_2822 -> AgdaAny
forall a b. a -> b
coe T_IdempotentSemiring_2822
v0))))
-- Algebra.Bundles.IdempotentSemiring._.∙-congʳ
d_'8729''45'cong'691'_2862 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentSemiring_2822 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_2862 :: ()
-> ()
-> T_IdempotentSemiring_2822
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_2862 ~()
v0 ~()
v1 T_IdempotentSemiring_2822
v2
  = T_IdempotentSemiring_2822
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_2862 T_IdempotentSemiring_2822
v2
du_'8729''45'cong'691'_2862 ::
  T_IdempotentSemiring_2822 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_2862 :: T_IdempotentSemiring_2822
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_2862 T_IdempotentSemiring_2822
v0
  = let v1 :: T_IsIdempotentSemiring_1922
v1 = T_IdempotentSemiring_2822 -> T_IsIdempotentSemiring_1922
d_isIdempotentSemiring_2854 (T_IdempotentSemiring_2822 -> T_IdempotentSemiring_2822
forall a b. a -> b
coe T_IdempotentSemiring_2822
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemiring_1570
v2
             = T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570
MAlonzo.Code.Algebra.Structures.d_isSemiring_1936 (T_IsIdempotentSemiring_1922 -> T_IsIdempotentSemiring_1922
forall a b. a -> b
coe T_IsIdempotentSemiring_1922
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemiringWithoutAnnihilatingZero_1468
v3
                = T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                    (T_IsSemiring_1570 -> T_IsSemiring_1570
forall a b. a -> b
coe T_IsSemiring_1570
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: t
v4
                   = (T_IsSemiringWithoutAnnihilatingZero_1468 -> T_IsMonoid_686)
-> AgdaAny -> t
forall a b. a -> b
coe
                       T_IsSemiringWithoutAnnihilatingZero_1468 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.du_'42''45'isMonoid_1550
                       (T_IsSemiringWithoutAnnihilatingZero_1468 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsSemigroup_472
v5
                      = T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (AgdaAny -> T_IsMonoid_686
forall a b. a -> b
coe AgdaAny
forall a. a
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'691'_206
                     ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v5)))))))
-- Algebra.Bundles.IdempotentSemiring._.∙-congˡ
d_'8729''45'cong'737'_2864 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentSemiring_2822 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_2864 :: ()
-> ()
-> T_IdempotentSemiring_2822
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_2864 ~()
v0 ~()
v1 T_IdempotentSemiring_2822
v2
  = T_IdempotentSemiring_2822
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_2864 T_IdempotentSemiring_2822
v2
du_'8729''45'cong'737'_2864 ::
  T_IdempotentSemiring_2822 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_2864 :: T_IdempotentSemiring_2822
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_2864 T_IdempotentSemiring_2822
v0
  = let v1 :: T_IsIdempotentSemiring_1922
v1 = T_IdempotentSemiring_2822 -> T_IsIdempotentSemiring_1922
d_isIdempotentSemiring_2854 (T_IdempotentSemiring_2822 -> T_IdempotentSemiring_2822
forall a b. a -> b
coe T_IdempotentSemiring_2822
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemiring_1570
v2
             = T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570
MAlonzo.Code.Algebra.Structures.d_isSemiring_1936 (T_IsIdempotentSemiring_1922 -> T_IsIdempotentSemiring_1922
forall a b. a -> b
coe T_IsIdempotentSemiring_1922
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemiringWithoutAnnihilatingZero_1468
v3
                = T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                    (T_IsSemiring_1570 -> T_IsSemiring_1570
forall a b. a -> b
coe T_IsSemiring_1570
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: t
v4
                   = (T_IsSemiringWithoutAnnihilatingZero_1468 -> T_IsMonoid_686)
-> AgdaAny -> t
forall a b. a -> b
coe
                       T_IsSemiringWithoutAnnihilatingZero_1468 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.du_'42''45'isMonoid_1550
                       (T_IsSemiringWithoutAnnihilatingZero_1468 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsSemigroup_472
v5
                      = T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (AgdaAny -> T_IsMonoid_686
forall a b. a -> b
coe AgdaAny
forall a. a
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'737'_202
                     ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v5)))))))
-- Algebra.Bundles.IdempotentSemiring._.*-identity
d_'42''45'identity_2866 ::
  T_IdempotentSemiring_2822 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'42''45'identity_2866 :: T_IdempotentSemiring_2822 -> T_Σ_14
d_'42''45'identity_2866 T_IdempotentSemiring_2822
v0
  = (T_IsSemiringWithoutAnnihilatingZero_1468 -> T_Σ_14)
-> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsSemiringWithoutAnnihilatingZero_1468 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_'42''45'identity_1494
      ((T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
         ((T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570
MAlonzo.Code.Algebra.Structures.d_isSemiring_1936
            ((T_IdempotentSemiring_2822 -> T_IsIdempotentSemiring_1922)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IdempotentSemiring_2822 -> T_IsIdempotentSemiring_1922
d_isIdempotentSemiring_2854 (T_IdempotentSemiring_2822 -> AgdaAny
forall a b. a -> b
coe T_IdempotentSemiring_2822
v0))))
-- Algebra.Bundles.IdempotentSemiring._.identityʳ
d_identity'691'_2868 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentSemiring_2822 -> AgdaAny -> AgdaAny
d_identity'691'_2868 :: () -> () -> T_IdempotentSemiring_2822 -> AgdaAny -> AgdaAny
d_identity'691'_2868 ~()
v0 ~()
v1 T_IdempotentSemiring_2822
v2 = T_IdempotentSemiring_2822 -> AgdaAny -> AgdaAny
du_identity'691'_2868 T_IdempotentSemiring_2822
v2
du_identity'691'_2868 ::
  T_IdempotentSemiring_2822 -> AgdaAny -> AgdaAny
du_identity'691'_2868 :: T_IdempotentSemiring_2822 -> AgdaAny -> AgdaAny
du_identity'691'_2868 T_IdempotentSemiring_2822
v0
  = let v1 :: T_IsIdempotentSemiring_1922
v1 = T_IdempotentSemiring_2822 -> T_IsIdempotentSemiring_1922
d_isIdempotentSemiring_2854 (T_IdempotentSemiring_2822 -> T_IdempotentSemiring_2822
forall a b. a -> b
coe T_IdempotentSemiring_2822
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemiring_1570
v2
             = T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570
MAlonzo.Code.Algebra.Structures.d_isSemiring_1936 (T_IsIdempotentSemiring_1922 -> T_IsIdempotentSemiring_1922
forall a b. a -> b
coe T_IsIdempotentSemiring_1922
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemiringWithoutAnnihilatingZero_1468
v3
                = T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                    (T_IsSemiring_1570 -> T_IsSemiring_1570
forall a b. a -> b
coe T_IsSemiring_1570
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsMonoid_686 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_686 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_identity'691'_728
               ((T_IsSemiringWithoutAnnihilatingZero_1468 -> T_IsMonoid_686)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsSemiringWithoutAnnihilatingZero_1468 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.du_'42''45'isMonoid_1550
                  (T_IsSemiringWithoutAnnihilatingZero_1468 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
v3)))))
-- Algebra.Bundles.IdempotentSemiring._.identityˡ
d_identity'737'_2870 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentSemiring_2822 -> AgdaAny -> AgdaAny
d_identity'737'_2870 :: () -> () -> T_IdempotentSemiring_2822 -> AgdaAny -> AgdaAny
d_identity'737'_2870 ~()
v0 ~()
v1 T_IdempotentSemiring_2822
v2 = T_IdempotentSemiring_2822 -> AgdaAny -> AgdaAny
du_identity'737'_2870 T_IdempotentSemiring_2822
v2
du_identity'737'_2870 ::
  T_IdempotentSemiring_2822 -> AgdaAny -> AgdaAny
du_identity'737'_2870 :: T_IdempotentSemiring_2822 -> AgdaAny -> AgdaAny
du_identity'737'_2870 T_IdempotentSemiring_2822
v0
  = let v1 :: T_IsIdempotentSemiring_1922
v1 = T_IdempotentSemiring_2822 -> T_IsIdempotentSemiring_1922
d_isIdempotentSemiring_2854 (T_IdempotentSemiring_2822 -> T_IdempotentSemiring_2822
forall a b. a -> b
coe T_IdempotentSemiring_2822
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemiring_1570
v2
             = T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570
MAlonzo.Code.Algebra.Structures.d_isSemiring_1936 (T_IsIdempotentSemiring_1922 -> T_IsIdempotentSemiring_1922
forall a b. a -> b
coe T_IsIdempotentSemiring_1922
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemiringWithoutAnnihilatingZero_1468
v3
                = T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                    (T_IsSemiring_1570 -> T_IsSemiring_1570
forall a b. a -> b
coe T_IsSemiring_1570
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsMonoid_686 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_686 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_identity'737'_726
               ((T_IsSemiringWithoutAnnihilatingZero_1468 -> T_IsMonoid_686)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsSemiringWithoutAnnihilatingZero_1468 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.du_'42''45'isMonoid_1550
                  (T_IsSemiringWithoutAnnihilatingZero_1468 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
v3)))))
-- Algebra.Bundles.IdempotentSemiring._.*-isMagma
d_'42''45'isMagma_2872 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentSemiring_2822 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_176
d_'42''45'isMagma_2872 :: () -> () -> T_IdempotentSemiring_2822 -> T_IsMagma_176
d_'42''45'isMagma_2872 ~()
v0 ~()
v1 T_IdempotentSemiring_2822
v2 = T_IdempotentSemiring_2822 -> T_IsMagma_176
du_'42''45'isMagma_2872 T_IdempotentSemiring_2822
v2
du_'42''45'isMagma_2872 ::
  T_IdempotentSemiring_2822 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_176
du_'42''45'isMagma_2872 :: T_IdempotentSemiring_2822 -> T_IsMagma_176
du_'42''45'isMagma_2872 T_IdempotentSemiring_2822
v0
  = let v1 :: T_IsIdempotentSemiring_1922
v1 = T_IdempotentSemiring_2822 -> T_IsIdempotentSemiring_1922
d_isIdempotentSemiring_2854 (T_IdempotentSemiring_2822 -> T_IdempotentSemiring_2822
forall a b. a -> b
coe T_IdempotentSemiring_2822
v0) in
    AgdaAny -> T_IsMagma_176
forall a b. a -> b
coe
      (let v2 :: T_IsSemiring_1570
v2
             = T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570
MAlonzo.Code.Algebra.Structures.d_isSemiring_1936 (T_IsIdempotentSemiring_1922 -> T_IsIdempotentSemiring_1922
forall a b. a -> b
coe T_IsIdempotentSemiring_1922
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsSemiringWithoutAnnihilatingZero_1468 -> T_IsMagma_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemiringWithoutAnnihilatingZero_1468 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.du_'42''45'isMagma_1546
            ((T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
               (T_IsSemiring_1570 -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1570
v2))))
-- Algebra.Bundles.IdempotentSemiring._.*-isMonoid
d_'42''45'isMonoid_2874 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentSemiring_2822 ->
  MAlonzo.Code.Algebra.Structures.T_IsMonoid_686
d_'42''45'isMonoid_2874 :: () -> () -> T_IdempotentSemiring_2822 -> T_IsMonoid_686
d_'42''45'isMonoid_2874 ~()
v0 ~()
v1 T_IdempotentSemiring_2822
v2 = T_IdempotentSemiring_2822 -> T_IsMonoid_686
du_'42''45'isMonoid_2874 T_IdempotentSemiring_2822
v2
du_'42''45'isMonoid_2874 ::
  T_IdempotentSemiring_2822 ->
  MAlonzo.Code.Algebra.Structures.T_IsMonoid_686
du_'42''45'isMonoid_2874 :: T_IdempotentSemiring_2822 -> T_IsMonoid_686
du_'42''45'isMonoid_2874 T_IdempotentSemiring_2822
v0
  = let v1 :: T_IsIdempotentSemiring_1922
v1 = T_IdempotentSemiring_2822 -> T_IsIdempotentSemiring_1922
d_isIdempotentSemiring_2854 (T_IdempotentSemiring_2822 -> T_IdempotentSemiring_2822
forall a b. a -> b
coe T_IdempotentSemiring_2822
v0) in
    AgdaAny -> T_IsMonoid_686
forall a b. a -> b
coe
      (let v2 :: T_IsSemiring_1570
v2
             = T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570
MAlonzo.Code.Algebra.Structures.d_isSemiring_1936 (T_IsIdempotentSemiring_1922 -> T_IsIdempotentSemiring_1922
forall a b. a -> b
coe T_IsIdempotentSemiring_1922
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsSemiringWithoutAnnihilatingZero_1468 -> T_IsMonoid_686)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemiringWithoutAnnihilatingZero_1468 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.du_'42''45'isMonoid_1550
            ((T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
               (T_IsSemiring_1570 -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1570
v2))))
-- Algebra.Bundles.IdempotentSemiring._.*-isSemigroup
d_'42''45'isSemigroup_2876 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentSemiring_2822 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_472
d_'42''45'isSemigroup_2876 :: () -> () -> T_IdempotentSemiring_2822 -> T_IsSemigroup_472
d_'42''45'isSemigroup_2876 ~()
v0 ~()
v1 T_IdempotentSemiring_2822
v2
  = T_IdempotentSemiring_2822 -> T_IsSemigroup_472
du_'42''45'isSemigroup_2876 T_IdempotentSemiring_2822
v2
du_'42''45'isSemigroup_2876 ::
  T_IdempotentSemiring_2822 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_472
du_'42''45'isSemigroup_2876 :: T_IdempotentSemiring_2822 -> T_IsSemigroup_472
du_'42''45'isSemigroup_2876 T_IdempotentSemiring_2822
v0
  = let v1 :: T_IsIdempotentSemiring_1922
v1 = T_IdempotentSemiring_2822 -> T_IsIdempotentSemiring_1922
d_isIdempotentSemiring_2854 (T_IdempotentSemiring_2822 -> T_IdempotentSemiring_2822
forall a b. a -> b
coe T_IdempotentSemiring_2822
v0) in
    AgdaAny -> T_IsSemigroup_472
forall a b. a -> b
coe
      (let v2 :: T_IsSemiring_1570
v2
             = T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570
MAlonzo.Code.Algebra.Structures.d_isSemiring_1936 (T_IsIdempotentSemiring_1922 -> T_IsIdempotentSemiring_1922
forall a b. a -> b
coe T_IsIdempotentSemiring_1922
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsSemiringWithoutAnnihilatingZero_1468 -> T_IsSemigroup_472)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemiringWithoutAnnihilatingZero_1468 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.du_'42''45'isSemigroup_1548
            ((T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
               (T_IsSemiring_1570 -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1570
v2))))
-- Algebra.Bundles.IdempotentSemiring._.assoc
d_assoc_2878 ::
  T_IdempotentSemiring_2822 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_2878 :: T_IdempotentSemiring_2822
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_2878 T_IdempotentSemiring_2822
v0
  = (T_IsSemigroup_472 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsSemigroup_472 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_assoc_482
      ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
         ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746
            ((T_IsSemiringWithoutAnnihilatingZero_1468
 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
               ((T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                  ((T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570
MAlonzo.Code.Algebra.Structures.d_isSemiring_1936
                     ((T_IdempotentSemiring_2822 -> T_IsIdempotentSemiring_1922)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IdempotentSemiring_2822 -> T_IsIdempotentSemiring_1922
d_isIdempotentSemiring_2854 (T_IdempotentSemiring_2822 -> AgdaAny
forall a b. a -> b
coe T_IdempotentSemiring_2822
v0)))))))
-- Algebra.Bundles.IdempotentSemiring._.comm
d_comm_2880 ::
  T_IdempotentSemiring_2822 -> AgdaAny -> AgdaAny -> AgdaAny
d_comm_2880 :: T_IdempotentSemiring_2822 -> AgdaAny -> AgdaAny -> AgdaAny
d_comm_2880 T_IdempotentSemiring_2822
v0
  = (T_IsCommutativeMonoid_736 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsCommutativeMonoid_736 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_comm_748
      ((T_IsSemiringWithoutAnnihilatingZero_1468
 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
         ((T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
            ((T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570
MAlonzo.Code.Algebra.Structures.d_isSemiring_1936
               ((T_IdempotentSemiring_2822 -> T_IsIdempotentSemiring_1922)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IdempotentSemiring_2822 -> T_IsIdempotentSemiring_1922
d_isIdempotentSemiring_2854 (T_IdempotentSemiring_2822 -> AgdaAny
forall a b. a -> b
coe T_IdempotentSemiring_2822
v0)))))
-- Algebra.Bundles.IdempotentSemiring._.∙-cong
d_'8729''45'cong_2882 ::
  T_IdempotentSemiring_2822 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_2882 :: T_IdempotentSemiring_2822
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_2882 T_IdempotentSemiring_2822
v0
  = (T_IsMagma_176
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsMagma_176
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_186
      ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480
         ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
            ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746
               ((T_IsSemiringWithoutAnnihilatingZero_1468
 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
                  ((T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                     ((T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570
MAlonzo.Code.Algebra.Structures.d_isSemiring_1936
                        ((T_IdempotentSemiring_2822 -> T_IsIdempotentSemiring_1922)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IdempotentSemiring_2822 -> T_IsIdempotentSemiring_1922
d_isIdempotentSemiring_2854 (T_IdempotentSemiring_2822 -> AgdaAny
forall a b. a -> b
coe T_IdempotentSemiring_2822
v0))))))))
-- Algebra.Bundles.IdempotentSemiring._.∙-congʳ
d_'8729''45'cong'691'_2884 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentSemiring_2822 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_2884 :: ()
-> ()
-> T_IdempotentSemiring_2822
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_2884 ~()
v0 ~()
v1 T_IdempotentSemiring_2822
v2
  = T_IdempotentSemiring_2822
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_2884 T_IdempotentSemiring_2822
v2
du_'8729''45'cong'691'_2884 ::
  T_IdempotentSemiring_2822 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_2884 :: T_IdempotentSemiring_2822
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_2884 T_IdempotentSemiring_2822
v0
  = let v1 :: T_IsIdempotentSemiring_1922
v1 = T_IdempotentSemiring_2822 -> T_IsIdempotentSemiring_1922
d_isIdempotentSemiring_2854 (T_IdempotentSemiring_2822 -> T_IdempotentSemiring_2822
forall a b. a -> b
coe T_IdempotentSemiring_2822
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemiring_1570
v2
             = T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570
MAlonzo.Code.Algebra.Structures.d_isSemiring_1936 (T_IsIdempotentSemiring_1922 -> T_IsIdempotentSemiring_1922
forall a b. a -> b
coe T_IsIdempotentSemiring_1922
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemiringWithoutAnnihilatingZero_1468
v3
                = T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                    (T_IsSemiring_1570 -> T_IsSemiring_1570
forall a b. a -> b
coe T_IsSemiring_1570
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsCommutativeMonoid_736
v4
                   = T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
                       (T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsSemiringWithoutAnnihilatingZero_1468
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsMonoid_686
v5
                      = T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746 (T_IsCommutativeMonoid_736 -> T_IsCommutativeMonoid_736
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (let v6 :: T_IsSemigroup_472
v6
                         = T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v5) in
                   AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'691'_206
                        ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v6))))))))
-- Algebra.Bundles.IdempotentSemiring._.∙-congˡ
d_'8729''45'cong'737'_2886 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentSemiring_2822 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_2886 :: ()
-> ()
-> T_IdempotentSemiring_2822
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_2886 ~()
v0 ~()
v1 T_IdempotentSemiring_2822
v2
  = T_IdempotentSemiring_2822
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_2886 T_IdempotentSemiring_2822
v2
du_'8729''45'cong'737'_2886 ::
  T_IdempotentSemiring_2822 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_2886 :: T_IdempotentSemiring_2822
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_2886 T_IdempotentSemiring_2822
v0
  = let v1 :: T_IsIdempotentSemiring_1922
v1 = T_IdempotentSemiring_2822 -> T_IsIdempotentSemiring_1922
d_isIdempotentSemiring_2854 (T_IdempotentSemiring_2822 -> T_IdempotentSemiring_2822
forall a b. a -> b
coe T_IdempotentSemiring_2822
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemiring_1570
v2
             = T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570
MAlonzo.Code.Algebra.Structures.d_isSemiring_1936 (T_IsIdempotentSemiring_1922 -> T_IsIdempotentSemiring_1922
forall a b. a -> b
coe T_IsIdempotentSemiring_1922
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemiringWithoutAnnihilatingZero_1468
v3
                = T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                    (T_IsSemiring_1570 -> T_IsSemiring_1570
forall a b. a -> b
coe T_IsSemiring_1570
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsCommutativeMonoid_736
v4
                   = T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
                       (T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsSemiringWithoutAnnihilatingZero_1468
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsMonoid_686
v5
                      = T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746 (T_IsCommutativeMonoid_736 -> T_IsCommutativeMonoid_736
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (let v6 :: T_IsSemigroup_472
v6
                         = T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v5) in
                   AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'737'_202
                        ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v6))))))))
-- Algebra.Bundles.IdempotentSemiring._.+-idem
d_'43''45'idem_2888 ::
  T_IdempotentSemiring_2822 -> AgdaAny -> AgdaAny
d_'43''45'idem_2888 :: T_IdempotentSemiring_2822 -> AgdaAny -> AgdaAny
d_'43''45'idem_2888 T_IdempotentSemiring_2822
v0
  = (T_IsIdempotentSemiring_1922 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsIdempotentSemiring_1922 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'43''45'idem_1938
      ((T_IdempotentSemiring_2822 -> T_IsIdempotentSemiring_1922)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IdempotentSemiring_2822 -> T_IsIdempotentSemiring_1922
d_isIdempotentSemiring_2854 (T_IdempotentSemiring_2822 -> AgdaAny
forall a b. a -> b
coe T_IdempotentSemiring_2822
v0))
-- Algebra.Bundles.IdempotentSemiring._.identity
d_identity_2890 ::
  T_IdempotentSemiring_2822 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_identity_2890 :: T_IdempotentSemiring_2822 -> T_Σ_14
d_identity_2890 T_IdempotentSemiring_2822
v0
  = (T_IsMonoid_686 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsMonoid_686 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_identity_698
      ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746
         ((T_IsSemiringWithoutAnnihilatingZero_1468
 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
            ((T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
               ((T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570
MAlonzo.Code.Algebra.Structures.d_isSemiring_1936
                  ((T_IdempotentSemiring_2822 -> T_IsIdempotentSemiring_1922)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IdempotentSemiring_2822 -> T_IsIdempotentSemiring_1922
d_isIdempotentSemiring_2854 (T_IdempotentSemiring_2822 -> AgdaAny
forall a b. a -> b
coe T_IdempotentSemiring_2822
v0))))))
-- Algebra.Bundles.IdempotentSemiring._.identityʳ
d_identity'691'_2892 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentSemiring_2822 -> AgdaAny -> AgdaAny
d_identity'691'_2892 :: () -> () -> T_IdempotentSemiring_2822 -> AgdaAny -> AgdaAny
d_identity'691'_2892 ~()
v0 ~()
v1 T_IdempotentSemiring_2822
v2 = T_IdempotentSemiring_2822 -> AgdaAny -> AgdaAny
du_identity'691'_2892 T_IdempotentSemiring_2822
v2
du_identity'691'_2892 ::
  T_IdempotentSemiring_2822 -> AgdaAny -> AgdaAny
du_identity'691'_2892 :: T_IdempotentSemiring_2822 -> AgdaAny -> AgdaAny
du_identity'691'_2892 T_IdempotentSemiring_2822
v0
  = let v1 :: T_IsIdempotentSemiring_1922
v1 = T_IdempotentSemiring_2822 -> T_IsIdempotentSemiring_1922
d_isIdempotentSemiring_2854 (T_IdempotentSemiring_2822 -> T_IdempotentSemiring_2822
forall a b. a -> b
coe T_IdempotentSemiring_2822
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemiring_1570
v2
             = T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570
MAlonzo.Code.Algebra.Structures.d_isSemiring_1936 (T_IsIdempotentSemiring_1922 -> T_IsIdempotentSemiring_1922
forall a b. a -> b
coe T_IsIdempotentSemiring_1922
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemiringWithoutAnnihilatingZero_1468
v3
                = T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                    (T_IsSemiring_1570 -> T_IsSemiring_1570
forall a b. a -> b
coe T_IsSemiring_1570
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsCommutativeMonoid_736
v4
                   = T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
                       (T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsSemiringWithoutAnnihilatingZero_1468
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               ((T_IsMonoid_686 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsMonoid_686 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_identity'691'_728
                  ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746 (T_IsCommutativeMonoid_736 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v4))))))
-- Algebra.Bundles.IdempotentSemiring._.identityˡ
d_identity'737'_2894 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentSemiring_2822 -> AgdaAny -> AgdaAny
d_identity'737'_2894 :: () -> () -> T_IdempotentSemiring_2822 -> AgdaAny -> AgdaAny
d_identity'737'_2894 ~()
v0 ~()
v1 T_IdempotentSemiring_2822
v2 = T_IdempotentSemiring_2822 -> AgdaAny -> AgdaAny
du_identity'737'_2894 T_IdempotentSemiring_2822
v2
du_identity'737'_2894 ::
  T_IdempotentSemiring_2822 -> AgdaAny -> AgdaAny
du_identity'737'_2894 :: T_IdempotentSemiring_2822 -> AgdaAny -> AgdaAny
du_identity'737'_2894 T_IdempotentSemiring_2822
v0
  = let v1 :: T_IsIdempotentSemiring_1922
v1 = T_IdempotentSemiring_2822 -> T_IsIdempotentSemiring_1922
d_isIdempotentSemiring_2854 (T_IdempotentSemiring_2822 -> T_IdempotentSemiring_2822
forall a b. a -> b
coe T_IdempotentSemiring_2822
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemiring_1570
v2
             = T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570
MAlonzo.Code.Algebra.Structures.d_isSemiring_1936 (T_IsIdempotentSemiring_1922 -> T_IsIdempotentSemiring_1922
forall a b. a -> b
coe T_IsIdempotentSemiring_1922
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemiringWithoutAnnihilatingZero_1468
v3
                = T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                    (T_IsSemiring_1570 -> T_IsSemiring_1570
forall a b. a -> b
coe T_IsSemiring_1570
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsCommutativeMonoid_736
v4
                   = T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
                       (T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsSemiringWithoutAnnihilatingZero_1468
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               ((T_IsMonoid_686 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsMonoid_686 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_identity'737'_726
                  ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746 (T_IsCommutativeMonoid_736 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v4))))))
-- Algebra.Bundles.IdempotentSemiring._.isBand
d_isBand_2896 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentSemiring_2822 ->
  MAlonzo.Code.Algebra.Structures.T_IsBand_508
d_isBand_2896 :: () -> () -> T_IdempotentSemiring_2822 -> T_IsBand_508
d_isBand_2896 ~()
v0 ~()
v1 T_IdempotentSemiring_2822
v2 = T_IdempotentSemiring_2822 -> T_IsBand_508
du_isBand_2896 T_IdempotentSemiring_2822
v2
du_isBand_2896 ::
  T_IdempotentSemiring_2822 ->
  MAlonzo.Code.Algebra.Structures.T_IsBand_508
du_isBand_2896 :: T_IdempotentSemiring_2822 -> T_IsBand_508
du_isBand_2896 T_IdempotentSemiring_2822
v0
  = let v1 :: T_IsIdempotentSemiring_1922
v1 = T_IdempotentSemiring_2822 -> T_IsIdempotentSemiring_1922
d_isIdempotentSemiring_2854 (T_IdempotentSemiring_2822 -> T_IdempotentSemiring_2822
forall a b. a -> b
coe T_IdempotentSemiring_2822
v0) in
    AgdaAny -> T_IsBand_508
forall a b. a -> b
coe
      (let v2 :: t
v2
             = (T_IsIdempotentSemiring_1922
 -> T_IsIdempotentCommutativeMonoid_852)
-> AgdaAny -> t
forall a b. a -> b
coe
                 T_IsIdempotentSemiring_1922 -> T_IsIdempotentCommutativeMonoid_852
MAlonzo.Code.Algebra.Structures.du_'43''45'isIdempotentCommutativeMonoid_2024
                 (T_IsIdempotentSemiring_1922 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentSemiring_1922
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsIdempotentMonoid_796 -> T_IsBand_508) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsIdempotentMonoid_796 -> T_IsBand_508
MAlonzo.Code.Algebra.Structures.du_isBand_846
            ((T_IsIdempotentCommutativeMonoid_852 -> T_IsIdempotentMonoid_796)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsIdempotentCommutativeMonoid_852 -> T_IsIdempotentMonoid_796
MAlonzo.Code.Algebra.Structures.du_isIdempotentMonoid_910
               (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2))))
-- Algebra.Bundles.IdempotentSemiring._.isCommutativeBand
d_isCommutativeBand_2898 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentSemiring_2822 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_590
d_isCommutativeBand_2898 :: () -> () -> T_IdempotentSemiring_2822 -> T_IsCommutativeBand_590
d_isCommutativeBand_2898 ~()
v0 ~()
v1 T_IdempotentSemiring_2822
v2 = T_IdempotentSemiring_2822 -> T_IsCommutativeBand_590
du_isCommutativeBand_2898 T_IdempotentSemiring_2822
v2
du_isCommutativeBand_2898 ::
  T_IdempotentSemiring_2822 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_590
du_isCommutativeBand_2898 :: T_IdempotentSemiring_2822 -> T_IsCommutativeBand_590
du_isCommutativeBand_2898 T_IdempotentSemiring_2822
v0
  = let v1 :: T_IsIdempotentSemiring_1922
v1 = T_IdempotentSemiring_2822 -> T_IsIdempotentSemiring_1922
d_isIdempotentSemiring_2854 (T_IdempotentSemiring_2822 -> T_IdempotentSemiring_2822
forall a b. a -> b
coe T_IdempotentSemiring_2822
v0) in
    AgdaAny -> T_IsCommutativeBand_590
forall a b. a -> b
coe
      ((T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeBand_590)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeBand_590
MAlonzo.Code.Algebra.Structures.du_isCommutativeBand_916
         ((T_IsIdempotentSemiring_1922
 -> T_IsIdempotentCommutativeMonoid_852)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsIdempotentSemiring_1922 -> T_IsIdempotentCommutativeMonoid_852
MAlonzo.Code.Algebra.Structures.du_'43''45'isIdempotentCommutativeMonoid_2024
            (T_IsIdempotentSemiring_1922 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentSemiring_1922
v1)))
-- Algebra.Bundles.IdempotentSemiring._.isCommutativeMagma
d_isCommutativeMagma_2900 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentSemiring_2822 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMagma_212
d_isCommutativeMagma_2900 :: () -> () -> T_IdempotentSemiring_2822 -> T_IsCommutativeMagma_212
d_isCommutativeMagma_2900 ~()
v0 ~()
v1 T_IdempotentSemiring_2822
v2
  = T_IdempotentSemiring_2822 -> T_IsCommutativeMagma_212
du_isCommutativeMagma_2900 T_IdempotentSemiring_2822
v2
du_isCommutativeMagma_2900 ::
  T_IdempotentSemiring_2822 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMagma_212
du_isCommutativeMagma_2900 :: T_IdempotentSemiring_2822 -> T_IsCommutativeMagma_212
du_isCommutativeMagma_2900 T_IdempotentSemiring_2822
v0
  = let v1 :: T_IsIdempotentSemiring_1922
v1 = T_IdempotentSemiring_2822 -> T_IsIdempotentSemiring_1922
d_isIdempotentSemiring_2854 (T_IdempotentSemiring_2822 -> T_IdempotentSemiring_2822
forall a b. a -> b
coe T_IdempotentSemiring_2822
v0) in
    AgdaAny -> T_IsCommutativeMagma_212
forall a b. a -> b
coe
      (let v2 :: T_IsSemiring_1570
v2
             = T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570
MAlonzo.Code.Algebra.Structures.d_isSemiring_1936 (T_IsIdempotentSemiring_1922 -> T_IsIdempotentSemiring_1922
forall a b. a -> b
coe T_IsIdempotentSemiring_1922
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemiringWithoutAnnihilatingZero_1468
v3
                = T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                    (T_IsSemiring_1570 -> T_IsSemiring_1570
forall a b. a -> b
coe T_IsSemiring_1570
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsCommutativeMonoid_736
v4
                   = T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
                       (T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsSemiringWithoutAnnihilatingZero_1468
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               ((T_IsCommutativeSemigroup_548 -> T_IsCommutativeMagma_212)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsCommutativeSemigroup_548 -> T_IsCommutativeMagma_212
MAlonzo.Code.Algebra.Structures.du_isCommutativeMagma_586
                  ((T_IsCommutativeMonoid_736 -> T_IsCommutativeSemigroup_548)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsCommutativeMonoid_736 -> T_IsCommutativeSemigroup_548
MAlonzo.Code.Algebra.Structures.du_isCommutativeSemigroup_786
                     (T_IsCommutativeMonoid_736 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v4))))))
-- Algebra.Bundles.IdempotentSemiring._.+-isCommutativeMonoid
d_'43''45'isCommutativeMonoid_2902 ::
  T_IdempotentSemiring_2822 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_2902 :: T_IdempotentSemiring_2822 -> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_2902 T_IdempotentSemiring_2822
v0
  = (T_IsSemiringWithoutAnnihilatingZero_1468
 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> T_IsCommutativeMonoid_736
forall a b. a -> b
coe
      T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
      ((T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
         ((T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570
MAlonzo.Code.Algebra.Structures.d_isSemiring_1936
            ((T_IdempotentSemiring_2822 -> T_IsIdempotentSemiring_1922)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IdempotentSemiring_2822 -> T_IsIdempotentSemiring_1922
d_isIdempotentSemiring_2854 (T_IdempotentSemiring_2822 -> AgdaAny
forall a b. a -> b
coe T_IdempotentSemiring_2822
v0))))
-- Algebra.Bundles.IdempotentSemiring._.isCommutativeSemigroup
d_isCommutativeSemigroup_2904 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentSemiring_2822 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_548
d_isCommutativeSemigroup_2904 :: ()
-> () -> T_IdempotentSemiring_2822 -> T_IsCommutativeSemigroup_548
d_isCommutativeSemigroup_2904 ~()
v0 ~()
v1 T_IdempotentSemiring_2822
v2
  = T_IdempotentSemiring_2822 -> T_IsCommutativeSemigroup_548
du_isCommutativeSemigroup_2904 T_IdempotentSemiring_2822
v2
du_isCommutativeSemigroup_2904 ::
  T_IdempotentSemiring_2822 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_548
du_isCommutativeSemigroup_2904 :: T_IdempotentSemiring_2822 -> T_IsCommutativeSemigroup_548
du_isCommutativeSemigroup_2904 T_IdempotentSemiring_2822
v0
  = let v1 :: T_IsIdempotentSemiring_1922
v1 = T_IdempotentSemiring_2822 -> T_IsIdempotentSemiring_1922
d_isIdempotentSemiring_2854 (T_IdempotentSemiring_2822 -> T_IdempotentSemiring_2822
forall a b. a -> b
coe T_IdempotentSemiring_2822
v0) in
    AgdaAny -> T_IsCommutativeSemigroup_548
forall a b. a -> b
coe
      (let v2 :: T_IsSemiring_1570
v2
             = T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570
MAlonzo.Code.Algebra.Structures.d_isSemiring_1936 (T_IsIdempotentSemiring_1922 -> T_IsIdempotentSemiring_1922
forall a b. a -> b
coe T_IsIdempotentSemiring_1922
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemiringWithoutAnnihilatingZero_1468
v3
                = T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                    (T_IsSemiring_1570 -> T_IsSemiring_1570
forall a b. a -> b
coe T_IsSemiring_1570
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsCommutativeMonoid_736 -> T_IsCommutativeSemigroup_548)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsCommutativeMonoid_736 -> T_IsCommutativeSemigroup_548
MAlonzo.Code.Algebra.Structures.du_isCommutativeSemigroup_786
               ((T_IsSemiringWithoutAnnihilatingZero_1468
 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
                  (T_IsSemiringWithoutAnnihilatingZero_1468 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
v3)))))
-- Algebra.Bundles.IdempotentSemiring._.+-isIdempotentCommutativeMonoid
d_'43''45'isIdempotentCommutativeMonoid_2906 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentSemiring_2822 ->
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_852
d_'43''45'isIdempotentCommutativeMonoid_2906 :: ()
-> ()
-> T_IdempotentSemiring_2822
-> T_IsIdempotentCommutativeMonoid_852
d_'43''45'isIdempotentCommutativeMonoid_2906 ~()
v0 ~()
v1 T_IdempotentSemiring_2822
v2
  = T_IdempotentSemiring_2822 -> T_IsIdempotentCommutativeMonoid_852
du_'43''45'isIdempotentCommutativeMonoid_2906 T_IdempotentSemiring_2822
v2
du_'43''45'isIdempotentCommutativeMonoid_2906 ::
  T_IdempotentSemiring_2822 ->
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_852
du_'43''45'isIdempotentCommutativeMonoid_2906 :: T_IdempotentSemiring_2822 -> T_IsIdempotentCommutativeMonoid_852
du_'43''45'isIdempotentCommutativeMonoid_2906 T_IdempotentSemiring_2822
v0
  = (T_IsIdempotentSemiring_1922
 -> T_IsIdempotentCommutativeMonoid_852)
-> AgdaAny -> T_IsIdempotentCommutativeMonoid_852
forall a b. a -> b
coe
      T_IsIdempotentSemiring_1922 -> T_IsIdempotentCommutativeMonoid_852
MAlonzo.Code.Algebra.Structures.du_'43''45'isIdempotentCommutativeMonoid_2024
      ((T_IdempotentSemiring_2822 -> T_IsIdempotentSemiring_1922)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IdempotentSemiring_2822 -> T_IsIdempotentSemiring_1922
d_isIdempotentSemiring_2854 (T_IdempotentSemiring_2822 -> AgdaAny
forall a b. a -> b
coe T_IdempotentSemiring_2822
v0))
-- Algebra.Bundles.IdempotentSemiring._.isIdempotentMonoid
d_isIdempotentMonoid_2908 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentSemiring_2822 ->
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentMonoid_796
d_isIdempotentMonoid_2908 :: () -> () -> T_IdempotentSemiring_2822 -> T_IsIdempotentMonoid_796
d_isIdempotentMonoid_2908 ~()
v0 ~()
v1 T_IdempotentSemiring_2822
v2
  = T_IdempotentSemiring_2822 -> T_IsIdempotentMonoid_796
du_isIdempotentMonoid_2908 T_IdempotentSemiring_2822
v2
du_isIdempotentMonoid_2908 ::
  T_IdempotentSemiring_2822 ->
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentMonoid_796
du_isIdempotentMonoid_2908 :: T_IdempotentSemiring_2822 -> T_IsIdempotentMonoid_796
du_isIdempotentMonoid_2908 T_IdempotentSemiring_2822
v0
  = let v1 :: T_IsIdempotentSemiring_1922
v1 = T_IdempotentSemiring_2822 -> T_IsIdempotentSemiring_1922
d_isIdempotentSemiring_2854 (T_IdempotentSemiring_2822 -> T_IdempotentSemiring_2822
forall a b. a -> b
coe T_IdempotentSemiring_2822
v0) in
    AgdaAny -> T_IsIdempotentMonoid_796
forall a b. a -> b
coe
      ((T_IsIdempotentCommutativeMonoid_852 -> T_IsIdempotentMonoid_796)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsIdempotentCommutativeMonoid_852 -> T_IsIdempotentMonoid_796
MAlonzo.Code.Algebra.Structures.du_isIdempotentMonoid_910
         ((T_IsIdempotentSemiring_1922
 -> T_IsIdempotentCommutativeMonoid_852)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsIdempotentSemiring_1922 -> T_IsIdempotentCommutativeMonoid_852
MAlonzo.Code.Algebra.Structures.du_'43''45'isIdempotentCommutativeMonoid_2024
            (T_IsIdempotentSemiring_1922 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentSemiring_1922
v1)))
-- Algebra.Bundles.IdempotentSemiring._.isMagma
d_isMagma_2910 ::
  T_IdempotentSemiring_2822 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_176
d_isMagma_2910 :: T_IdempotentSemiring_2822 -> T_IsMagma_176
d_isMagma_2910 T_IdempotentSemiring_2822
v0
  = (T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> T_IsMagma_176
forall a b. a -> b
coe
      T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480
      ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
         ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746
            ((T_IsSemiringWithoutAnnihilatingZero_1468
 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
               ((T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                  ((T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570
MAlonzo.Code.Algebra.Structures.d_isSemiring_1936
                     ((T_IdempotentSemiring_2822 -> T_IsIdempotentSemiring_1922)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IdempotentSemiring_2822 -> T_IsIdempotentSemiring_1922
d_isIdempotentSemiring_2854 (T_IdempotentSemiring_2822 -> AgdaAny
forall a b. a -> b
coe T_IdempotentSemiring_2822
v0)))))))
-- Algebra.Bundles.IdempotentSemiring._.isMonoid
d_isMonoid_2912 ::
  T_IdempotentSemiring_2822 ->
  MAlonzo.Code.Algebra.Structures.T_IsMonoid_686
d_isMonoid_2912 :: T_IdempotentSemiring_2822 -> T_IsMonoid_686
d_isMonoid_2912 T_IdempotentSemiring_2822
v0
  = (T_IsCommutativeMonoid_736 -> T_IsMonoid_686)
-> AgdaAny -> T_IsMonoid_686
forall a b. a -> b
coe
      T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746
      ((T_IsSemiringWithoutAnnihilatingZero_1468
 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
         ((T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
            ((T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570
MAlonzo.Code.Algebra.Structures.d_isSemiring_1936
               ((T_IdempotentSemiring_2822 -> T_IsIdempotentSemiring_1922)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IdempotentSemiring_2822 -> T_IsIdempotentSemiring_1922
d_isIdempotentSemiring_2854 (T_IdempotentSemiring_2822 -> AgdaAny
forall a b. a -> b
coe T_IdempotentSemiring_2822
v0)))))
-- Algebra.Bundles.IdempotentSemiring._.isSemigroup
d_isSemigroup_2914 ::
  T_IdempotentSemiring_2822 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_472
d_isSemigroup_2914 :: T_IdempotentSemiring_2822 -> T_IsSemigroup_472
d_isSemigroup_2914 T_IdempotentSemiring_2822
v0
  = (T_IsMonoid_686 -> T_IsSemigroup_472)
-> AgdaAny -> T_IsSemigroup_472
forall a b. a -> b
coe
      T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
      ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746
         ((T_IsSemiringWithoutAnnihilatingZero_1468
 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
            ((T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
               ((T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570
MAlonzo.Code.Algebra.Structures.d_isSemiring_1936
                  ((T_IdempotentSemiring_2822 -> T_IsIdempotentSemiring_1922)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IdempotentSemiring_2822 -> T_IsIdempotentSemiring_1922
d_isIdempotentSemiring_2854 (T_IdempotentSemiring_2822 -> AgdaAny
forall a b. a -> b
coe T_IdempotentSemiring_2822
v0))))))
-- Algebra.Bundles.IdempotentSemiring._.isUnitalMagma
d_isUnitalMagma_2916 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentSemiring_2822 ->
  MAlonzo.Code.Algebra.Structures.T_IsUnitalMagma_642
d_isUnitalMagma_2916 :: () -> () -> T_IdempotentSemiring_2822 -> T_IsUnitalMagma_642
d_isUnitalMagma_2916 ~()
v0 ~()
v1 T_IdempotentSemiring_2822
v2 = T_IdempotentSemiring_2822 -> T_IsUnitalMagma_642
du_isUnitalMagma_2916 T_IdempotentSemiring_2822
v2
du_isUnitalMagma_2916 ::
  T_IdempotentSemiring_2822 ->
  MAlonzo.Code.Algebra.Structures.T_IsUnitalMagma_642
du_isUnitalMagma_2916 :: T_IdempotentSemiring_2822 -> T_IsUnitalMagma_642
du_isUnitalMagma_2916 T_IdempotentSemiring_2822
v0
  = let v1 :: T_IsIdempotentSemiring_1922
v1 = T_IdempotentSemiring_2822 -> T_IsIdempotentSemiring_1922
d_isIdempotentSemiring_2854 (T_IdempotentSemiring_2822 -> T_IdempotentSemiring_2822
forall a b. a -> b
coe T_IdempotentSemiring_2822
v0) in
    AgdaAny -> T_IsUnitalMagma_642
forall a b. a -> b
coe
      (let v2 :: T_IsSemiring_1570
v2
             = T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570
MAlonzo.Code.Algebra.Structures.d_isSemiring_1936 (T_IsIdempotentSemiring_1922 -> T_IsIdempotentSemiring_1922
forall a b. a -> b
coe T_IsIdempotentSemiring_1922
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemiringWithoutAnnihilatingZero_1468
v3
                = T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                    (T_IsSemiring_1570 -> T_IsSemiring_1570
forall a b. a -> b
coe T_IsSemiring_1570
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsCommutativeMonoid_736
v4
                   = T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
                       (T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsSemiringWithoutAnnihilatingZero_1468
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               ((T_IsMonoid_686 -> T_IsUnitalMagma_642) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsMonoid_686 -> T_IsUnitalMagma_642
MAlonzo.Code.Algebra.Structures.du_isUnitalMagma_730
                  ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746 (T_IsCommutativeMonoid_736 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v4))))))
-- Algebra.Bundles.IdempotentSemiring._.distrib
d_distrib_2918 ::
  T_IdempotentSemiring_2822 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_distrib_2918 :: T_IdempotentSemiring_2822 -> T_Σ_14
d_distrib_2918 T_IdempotentSemiring_2822
v0
  = (T_IsSemiringWithoutAnnihilatingZero_1468 -> T_Σ_14)
-> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsSemiringWithoutAnnihilatingZero_1468 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_distrib_1496
      ((T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
         ((T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570
MAlonzo.Code.Algebra.Structures.d_isSemiring_1936
            ((T_IdempotentSemiring_2822 -> T_IsIdempotentSemiring_1922)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IdempotentSemiring_2822 -> T_IsIdempotentSemiring_1922
d_isIdempotentSemiring_2854 (T_IdempotentSemiring_2822 -> AgdaAny
forall a b. a -> b
coe T_IdempotentSemiring_2822
v0))))
-- Algebra.Bundles.IdempotentSemiring._.distribʳ
d_distrib'691'_2920 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentSemiring_2822 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_distrib'691'_2920 :: ()
-> ()
-> T_IdempotentSemiring_2822
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_distrib'691'_2920 ~()
v0 ~()
v1 T_IdempotentSemiring_2822
v2 = T_IdempotentSemiring_2822
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'691'_2920 T_IdempotentSemiring_2822
v2
du_distrib'691'_2920 ::
  T_IdempotentSemiring_2822 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'691'_2920 :: T_IdempotentSemiring_2822
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'691'_2920 T_IdempotentSemiring_2822
v0
  = let v1 :: T_IsIdempotentSemiring_1922
v1 = T_IdempotentSemiring_2822 -> T_IsIdempotentSemiring_1922
d_isIdempotentSemiring_2854 (T_IdempotentSemiring_2822 -> T_IdempotentSemiring_2822
forall a b. a -> b
coe T_IdempotentSemiring_2822
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemiring_1570
v2
             = T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570
MAlonzo.Code.Algebra.Structures.d_isSemiring_1936 (T_IsIdempotentSemiring_1922 -> T_IsIdempotentSemiring_1922
forall a b. a -> b
coe T_IsIdempotentSemiring_1922
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsSemiringWithoutAnnihilatingZero_1468
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemiringWithoutAnnihilatingZero_1468
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_distrib'691'_1500
            ((T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
               (T_IsSemiring_1570 -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1570
v2))))
-- Algebra.Bundles.IdempotentSemiring._.distribˡ
d_distrib'737'_2922 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentSemiring_2822 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_distrib'737'_2922 :: ()
-> ()
-> T_IdempotentSemiring_2822
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_distrib'737'_2922 ~()
v0 ~()
v1 T_IdempotentSemiring_2822
v2 = T_IdempotentSemiring_2822
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'737'_2922 T_IdempotentSemiring_2822
v2
du_distrib'737'_2922 ::
  T_IdempotentSemiring_2822 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'737'_2922 :: T_IdempotentSemiring_2822
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'737'_2922 T_IdempotentSemiring_2822
v0
  = let v1 :: T_IsIdempotentSemiring_1922
v1 = T_IdempotentSemiring_2822 -> T_IsIdempotentSemiring_1922
d_isIdempotentSemiring_2854 (T_IdempotentSemiring_2822 -> T_IdempotentSemiring_2822
forall a b. a -> b
coe T_IdempotentSemiring_2822
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemiring_1570
v2
             = T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570
MAlonzo.Code.Algebra.Structures.d_isSemiring_1936 (T_IsIdempotentSemiring_1922 -> T_IsIdempotentSemiring_1922
forall a b. a -> b
coe T_IsIdempotentSemiring_1922
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsSemiringWithoutAnnihilatingZero_1468
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemiringWithoutAnnihilatingZero_1468
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_distrib'737'_1498
            ((T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
               (T_IsSemiring_1570 -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1570
v2))))
-- Algebra.Bundles.IdempotentSemiring._.isEquivalence
d_isEquivalence_2924 ::
  T_IdempotentSemiring_2822 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_2924 :: T_IdempotentSemiring_2822 -> T_IsEquivalence_26
d_isEquivalence_2924 T_IdempotentSemiring_2822
v0
  = (T_IsMagma_176 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
      ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480
         ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
            ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746
               ((T_IsSemiringWithoutAnnihilatingZero_1468
 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
                  ((T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                     ((T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570
MAlonzo.Code.Algebra.Structures.d_isSemiring_1936
                        ((T_IdempotentSemiring_2822 -> T_IsIdempotentSemiring_1922)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IdempotentSemiring_2822 -> T_IsIdempotentSemiring_1922
d_isIdempotentSemiring_2854 (T_IdempotentSemiring_2822 -> AgdaAny
forall a b. a -> b
coe T_IdempotentSemiring_2822
v0))))))))
-- Algebra.Bundles.IdempotentSemiring._.isNearSemiring
d_isNearSemiring_2926 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentSemiring_2822 ->
  MAlonzo.Code.Algebra.Structures.T_IsNearSemiring_1218
d_isNearSemiring_2926 :: () -> () -> T_IdempotentSemiring_2822 -> T_IsNearSemiring_1218
d_isNearSemiring_2926 ~()
v0 ~()
v1 T_IdempotentSemiring_2822
v2 = T_IdempotentSemiring_2822 -> T_IsNearSemiring_1218
du_isNearSemiring_2926 T_IdempotentSemiring_2822
v2
du_isNearSemiring_2926 ::
  T_IdempotentSemiring_2822 ->
  MAlonzo.Code.Algebra.Structures.T_IsNearSemiring_1218
du_isNearSemiring_2926 :: T_IdempotentSemiring_2822 -> T_IsNearSemiring_1218
du_isNearSemiring_2926 T_IdempotentSemiring_2822
v0
  = let v1 :: T_IsIdempotentSemiring_1922
v1 = T_IdempotentSemiring_2822 -> T_IsIdempotentSemiring_1922
d_isIdempotentSemiring_2854 (T_IdempotentSemiring_2822 -> T_IdempotentSemiring_2822
forall a b. a -> b
coe T_IdempotentSemiring_2822
v0) in
    AgdaAny -> T_IsNearSemiring_1218
forall a b. a -> b
coe
      (let v2 :: T_IsSemiring_1570
v2
             = T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570
MAlonzo.Code.Algebra.Structures.d_isSemiring_1936 (T_IsIdempotentSemiring_1922 -> T_IsIdempotentSemiring_1922
forall a b. a -> b
coe T_IsIdempotentSemiring_1922
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsSemiringWithoutOne_1298 -> T_IsNearSemiring_1218)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemiringWithoutOne_1298 -> T_IsNearSemiring_1218
MAlonzo.Code.Algebra.Structures.du_isNearSemiring_1374
            ((T_IsSemiring_1570 -> T_IsSemiringWithoutOne_1298)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemiring_1570 -> T_IsSemiringWithoutOne_1298
MAlonzo.Code.Algebra.Structures.du_isSemiringWithoutOne_1660
               (T_IsSemiring_1570 -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1570
v2))))
-- Algebra.Bundles.IdempotentSemiring._.isPartialEquivalence
d_isPartialEquivalence_2928 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentSemiring_2822 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_2928 :: () -> () -> T_IdempotentSemiring_2822 -> T_IsPartialEquivalence_16
d_isPartialEquivalence_2928 ~()
v0 ~()
v1 T_IdempotentSemiring_2822
v2
  = T_IdempotentSemiring_2822 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_2928 T_IdempotentSemiring_2822
v2
du_isPartialEquivalence_2928 ::
  T_IdempotentSemiring_2822 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_2928 :: T_IdempotentSemiring_2822 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_2928 T_IdempotentSemiring_2822
v0
  = let v1 :: T_IsIdempotentSemiring_1922
v1 = T_IdempotentSemiring_2822 -> T_IsIdempotentSemiring_1922
d_isIdempotentSemiring_2854 (T_IdempotentSemiring_2822 -> T_IdempotentSemiring_2822
forall a b. a -> b
coe T_IdempotentSemiring_2822
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsSemiring_1570
v2
             = T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570
MAlonzo.Code.Algebra.Structures.d_isSemiring_1936 (T_IsIdempotentSemiring_1922 -> T_IsIdempotentSemiring_1922
forall a b. a -> b
coe T_IsIdempotentSemiring_1922
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemiringWithoutAnnihilatingZero_1468
v3
                = T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                    (T_IsSemiring_1570 -> T_IsSemiring_1570
forall a b. a -> b
coe T_IsSemiring_1570
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsCommutativeMonoid_736
v4
                   = T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
                       (T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsSemiringWithoutAnnihilatingZero_1468
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsMonoid_686
v5
                      = T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746 (T_IsCommutativeMonoid_736 -> T_IsCommutativeMonoid_736
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (let v6 :: T_IsSemigroup_472
v6
                         = T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v5) in
                   AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     (let v7 :: T_IsMagma_176
v7 = T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (T_IsSemigroup_472 -> T_IsSemigroup_472
forall a b. a -> b
coe T_IsSemigroup_472
v6) in
                      AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        ((T_IsEquivalence_26 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_IsEquivalence_26 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
                           ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                              T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
                              (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v7)))))))))
-- Algebra.Bundles.IdempotentSemiring._.isSemiring
d_isSemiring_2930 ::
  T_IdempotentSemiring_2822 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemiring_1570
d_isSemiring_2930 :: T_IdempotentSemiring_2822 -> T_IsSemiring_1570
d_isSemiring_2930 T_IdempotentSemiring_2822
v0
  = (T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570)
-> AgdaAny -> T_IsSemiring_1570
forall a b. a -> b
coe
      T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570
MAlonzo.Code.Algebra.Structures.d_isSemiring_1936
      ((T_IdempotentSemiring_2822 -> T_IsIdempotentSemiring_1922)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IdempotentSemiring_2822 -> T_IsIdempotentSemiring_1922
d_isIdempotentSemiring_2854 (T_IdempotentSemiring_2822 -> AgdaAny
forall a b. a -> b
coe T_IdempotentSemiring_2822
v0))
-- Algebra.Bundles.IdempotentSemiring._.isSemiringWithoutAnnihilatingZero
d_isSemiringWithoutAnnihilatingZero_2932 ::
  T_IdempotentSemiring_2822 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_2932 :: T_IdempotentSemiring_2822
-> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_2932 T_IdempotentSemiring_2822
v0
  = (T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> T_IsSemiringWithoutAnnihilatingZero_1468
forall a b. a -> b
coe
      T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
      ((T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570
MAlonzo.Code.Algebra.Structures.d_isSemiring_1936
         ((T_IdempotentSemiring_2822 -> T_IsIdempotentSemiring_1922)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IdempotentSemiring_2822 -> T_IsIdempotentSemiring_1922
d_isIdempotentSemiring_2854 (T_IdempotentSemiring_2822 -> AgdaAny
forall a b. a -> b
coe T_IdempotentSemiring_2822
v0)))
-- Algebra.Bundles.IdempotentSemiring._.isSemiringWithoutOne
d_isSemiringWithoutOne_2934 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentSemiring_2822 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutOne_1298
d_isSemiringWithoutOne_2934 :: ()
-> () -> T_IdempotentSemiring_2822 -> T_IsSemiringWithoutOne_1298
d_isSemiringWithoutOne_2934 ~()
v0 ~()
v1 T_IdempotentSemiring_2822
v2
  = T_IdempotentSemiring_2822 -> T_IsSemiringWithoutOne_1298
du_isSemiringWithoutOne_2934 T_IdempotentSemiring_2822
v2
du_isSemiringWithoutOne_2934 ::
  T_IdempotentSemiring_2822 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutOne_1298
du_isSemiringWithoutOne_2934 :: T_IdempotentSemiring_2822 -> T_IsSemiringWithoutOne_1298
du_isSemiringWithoutOne_2934 T_IdempotentSemiring_2822
v0
  = let v1 :: T_IsIdempotentSemiring_1922
v1 = T_IdempotentSemiring_2822 -> T_IsIdempotentSemiring_1922
d_isIdempotentSemiring_2854 (T_IdempotentSemiring_2822 -> T_IdempotentSemiring_2822
forall a b. a -> b
coe T_IdempotentSemiring_2822
v0) in
    AgdaAny -> T_IsSemiringWithoutOne_1298
forall a b. a -> b
coe
      ((T_IsSemiring_1570 -> T_IsSemiringWithoutOne_1298)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiring_1570 -> T_IsSemiringWithoutOne_1298
MAlonzo.Code.Algebra.Structures.du_isSemiringWithoutOne_1660
         ((T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570
MAlonzo.Code.Algebra.Structures.d_isSemiring_1936 (T_IsIdempotentSemiring_1922 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentSemiring_1922
v1)))
-- Algebra.Bundles.IdempotentSemiring._.refl
d_refl_2936 :: T_IdempotentSemiring_2822 -> AgdaAny -> AgdaAny
d_refl_2936 :: T_IdempotentSemiring_2822 -> AgdaAny -> AgdaAny
d_refl_2936 T_IdempotentSemiring_2822
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_34
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
         ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480
            ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
               ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746
                  ((T_IsSemiringWithoutAnnihilatingZero_1468
 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
                     ((T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                        ((T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570
MAlonzo.Code.Algebra.Structures.d_isSemiring_1936
                           ((T_IdempotentSemiring_2822 -> T_IsIdempotentSemiring_1922)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IdempotentSemiring_2822 -> T_IsIdempotentSemiring_1922
d_isIdempotentSemiring_2854 (T_IdempotentSemiring_2822 -> AgdaAny
forall a b. a -> b
coe T_IdempotentSemiring_2822
v0)))))))))
-- Algebra.Bundles.IdempotentSemiring._.reflexive
d_reflexive_2938 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentSemiring_2822 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_2938 :: ()
-> ()
-> T_IdempotentSemiring_2822
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_2938 ~()
v0 ~()
v1 T_IdempotentSemiring_2822
v2 = T_IdempotentSemiring_2822
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_2938 T_IdempotentSemiring_2822
v2
du_reflexive_2938 ::
  T_IdempotentSemiring_2822 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_2938 :: T_IdempotentSemiring_2822
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_2938 T_IdempotentSemiring_2822
v0
  = let v1 :: T_IsIdempotentSemiring_1922
v1 = T_IdempotentSemiring_2822 -> T_IsIdempotentSemiring_1922
d_isIdempotentSemiring_2854 (T_IdempotentSemiring_2822 -> T_IdempotentSemiring_2822
forall a b. a -> b
coe T_IdempotentSemiring_2822
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemiring_1570
v2
             = T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570
MAlonzo.Code.Algebra.Structures.d_isSemiring_1936 (T_IsIdempotentSemiring_1922 -> T_IsIdempotentSemiring_1922
forall a b. a -> b
coe T_IsIdempotentSemiring_1922
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemiringWithoutAnnihilatingZero_1468
v3
                = T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                    (T_IsSemiring_1570 -> T_IsSemiring_1570
forall a b. a -> b
coe T_IsSemiring_1570
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsCommutativeMonoid_736
v4
                   = T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
                       (T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsSemiringWithoutAnnihilatingZero_1468
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsMonoid_686
v5
                      = T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746 (T_IsCommutativeMonoid_736 -> T_IsCommutativeMonoid_736
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (let v6 :: T_IsSemigroup_472
v6
                         = T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v5) in
                   AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     (let v7 :: T_IsMagma_176
v7 = T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (T_IsSemigroup_472 -> T_IsSemigroup_472
forall a b. a -> b
coe T_IsSemigroup_472
v6) in
                      (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
                        (\ AgdaAny
v8 AgdaAny
v9 AgdaAny
v10 ->
                           (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                             T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
                             ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v7))
                             AgdaAny
v8)))))))
-- Algebra.Bundles.IdempotentSemiring._.setoid
d_setoid_2940 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentSemiring_2822 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_2940 :: () -> () -> T_IdempotentSemiring_2822 -> T_Setoid_44
d_setoid_2940 ~()
v0 ~()
v1 T_IdempotentSemiring_2822
v2 = T_IdempotentSemiring_2822 -> T_Setoid_44
du_setoid_2940 T_IdempotentSemiring_2822
v2
du_setoid_2940 ::
  T_IdempotentSemiring_2822 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_2940 :: T_IdempotentSemiring_2822 -> T_Setoid_44
du_setoid_2940 T_IdempotentSemiring_2822
v0
  = let v1 :: T_IsIdempotentSemiring_1922
v1 = T_IdempotentSemiring_2822 -> T_IsIdempotentSemiring_1922
d_isIdempotentSemiring_2854 (T_IdempotentSemiring_2822 -> T_IdempotentSemiring_2822
forall a b. a -> b
coe T_IdempotentSemiring_2822
v0) in
    AgdaAny -> T_Setoid_44
forall a b. a -> b
coe
      (let v2 :: T_IsSemiring_1570
v2
             = T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570
MAlonzo.Code.Algebra.Structures.d_isSemiring_1936 (T_IsIdempotentSemiring_1922 -> T_IsIdempotentSemiring_1922
forall a b. a -> b
coe T_IsIdempotentSemiring_1922
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemiringWithoutAnnihilatingZero_1468
v3
                = T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                    (T_IsSemiring_1570 -> T_IsSemiring_1570
forall a b. a -> b
coe T_IsSemiring_1570
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsCommutativeMonoid_736
v4
                   = T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
                       (T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsSemiringWithoutAnnihilatingZero_1468
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsMonoid_686
v5
                      = T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746 (T_IsCommutativeMonoid_736 -> T_IsCommutativeMonoid_736
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (let v6 :: T_IsSemigroup_472
v6
                         = T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v5) in
                   AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     ((T_IsMagma_176 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsMagma_176 -> T_Setoid_44
MAlonzo.Code.Algebra.Structures.du_setoid_200
                        ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v6))))))))
-- Algebra.Bundles.IdempotentSemiring._.sym
d_sym_2942 ::
  T_IdempotentSemiring_2822 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_2942 :: T_IdempotentSemiring_2822
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_2942 T_IdempotentSemiring_2822
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_36
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
         ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480
            ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
               ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746
                  ((T_IsSemiringWithoutAnnihilatingZero_1468
 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
                     ((T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                        ((T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570
MAlonzo.Code.Algebra.Structures.d_isSemiring_1936
                           ((T_IdempotentSemiring_2822 -> T_IsIdempotentSemiring_1922)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IdempotentSemiring_2822 -> T_IsIdempotentSemiring_1922
d_isIdempotentSemiring_2854 (T_IdempotentSemiring_2822 -> AgdaAny
forall a b. a -> b
coe T_IdempotentSemiring_2822
v0)))))))))
-- Algebra.Bundles.IdempotentSemiring._.trans
d_trans_2944 ::
  T_IdempotentSemiring_2822 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_2944 :: T_IdempotentSemiring_2822
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_2944 T_IdempotentSemiring_2822
v0
  = (T_IsEquivalence_26
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_38
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
         ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480
            ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
               ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746
                  ((T_IsSemiringWithoutAnnihilatingZero_1468
 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
                     ((T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                        ((T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570
MAlonzo.Code.Algebra.Structures.d_isSemiring_1936
                           ((T_IdempotentSemiring_2822 -> T_IsIdempotentSemiring_1922)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IdempotentSemiring_2822 -> T_IsIdempotentSemiring_1922
d_isIdempotentSemiring_2854 (T_IdempotentSemiring_2822 -> AgdaAny
forall a b. a -> b
coe T_IdempotentSemiring_2822
v0)))))))))
-- Algebra.Bundles.IdempotentSemiring._.zero
d_zero_2946 ::
  T_IdempotentSemiring_2822 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_zero_2946 :: T_IdempotentSemiring_2822 -> T_Σ_14
d_zero_2946 T_IdempotentSemiring_2822
v0
  = (T_IsSemiring_1570 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsSemiring_1570 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_zero_1586
      ((T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570
MAlonzo.Code.Algebra.Structures.d_isSemiring_1936
         ((T_IdempotentSemiring_2822 -> T_IsIdempotentSemiring_1922)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IdempotentSemiring_2822 -> T_IsIdempotentSemiring_1922
d_isIdempotentSemiring_2854 (T_IdempotentSemiring_2822 -> AgdaAny
forall a b. a -> b
coe T_IdempotentSemiring_2822
v0)))
-- Algebra.Bundles.IdempotentSemiring._.zeroʳ
d_zero'691'_2948 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentSemiring_2822 -> AgdaAny -> AgdaAny
d_zero'691'_2948 :: () -> () -> T_IdempotentSemiring_2822 -> AgdaAny -> AgdaAny
d_zero'691'_2948 ~()
v0 ~()
v1 T_IdempotentSemiring_2822
v2 = T_IdempotentSemiring_2822 -> AgdaAny -> AgdaAny
du_zero'691'_2948 T_IdempotentSemiring_2822
v2
du_zero'691'_2948 ::
  T_IdempotentSemiring_2822 -> AgdaAny -> AgdaAny
du_zero'691'_2948 :: T_IdempotentSemiring_2822 -> AgdaAny -> AgdaAny
du_zero'691'_2948 T_IdempotentSemiring_2822
v0
  = let v1 :: T_IsIdempotentSemiring_1922
v1 = T_IdempotentSemiring_2822 -> T_IsIdempotentSemiring_1922
d_isIdempotentSemiring_2854 (T_IdempotentSemiring_2822 -> T_IdempotentSemiring_2822
forall a b. a -> b
coe T_IdempotentSemiring_2822
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemiring_1570
v2
             = T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570
MAlonzo.Code.Algebra.Structures.d_isSemiring_1936 (T_IsIdempotentSemiring_1922 -> T_IsIdempotentSemiring_1922
forall a b. a -> b
coe T_IsIdempotentSemiring_1922
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsSemiringWithoutOne_1298 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemiringWithoutOne_1298 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_zero'691'_1372
            ((T_IsSemiring_1570 -> T_IsSemiringWithoutOne_1298)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemiring_1570 -> T_IsSemiringWithoutOne_1298
MAlonzo.Code.Algebra.Structures.du_isSemiringWithoutOne_1660
               (T_IsSemiring_1570 -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1570
v2))))
-- Algebra.Bundles.IdempotentSemiring._.zeroˡ
d_zero'737'_2950 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentSemiring_2822 -> AgdaAny -> AgdaAny
d_zero'737'_2950 :: () -> () -> T_IdempotentSemiring_2822 -> AgdaAny -> AgdaAny
d_zero'737'_2950 ~()
v0 ~()
v1 T_IdempotentSemiring_2822
v2 = T_IdempotentSemiring_2822 -> AgdaAny -> AgdaAny
du_zero'737'_2950 T_IdempotentSemiring_2822
v2
du_zero'737'_2950 ::
  T_IdempotentSemiring_2822 -> AgdaAny -> AgdaAny
du_zero'737'_2950 :: T_IdempotentSemiring_2822 -> AgdaAny -> AgdaAny
du_zero'737'_2950 T_IdempotentSemiring_2822
v0
  = let v1 :: T_IsIdempotentSemiring_1922
v1 = T_IdempotentSemiring_2822 -> T_IsIdempotentSemiring_1922
d_isIdempotentSemiring_2854 (T_IdempotentSemiring_2822 -> T_IdempotentSemiring_2822
forall a b. a -> b
coe T_IdempotentSemiring_2822
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemiring_1570
v2
             = T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570
MAlonzo.Code.Algebra.Structures.d_isSemiring_1936 (T_IsIdempotentSemiring_1922 -> T_IsIdempotentSemiring_1922
forall a b. a -> b
coe T_IsIdempotentSemiring_1922
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsSemiringWithoutOne_1298 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemiringWithoutOne_1298 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_zero'737'_1370
            ((T_IsSemiring_1570 -> T_IsSemiringWithoutOne_1298)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemiring_1570 -> T_IsSemiringWithoutOne_1298
MAlonzo.Code.Algebra.Structures.du_isSemiringWithoutOne_1660
               (T_IsSemiring_1570 -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1570
v2))))
-- Algebra.Bundles.IdempotentSemiring.semiring
d_semiring_2952 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentSemiring_2822 -> T_Semiring_2280
d_semiring_2952 :: () -> () -> T_IdempotentSemiring_2822 -> T_Semiring_2280
d_semiring_2952 ~()
v0 ~()
v1 T_IdempotentSemiring_2822
v2 = T_IdempotentSemiring_2822 -> T_Semiring_2280
du_semiring_2952 T_IdempotentSemiring_2822
v2
du_semiring_2952 :: T_IdempotentSemiring_2822 -> T_Semiring_2280
du_semiring_2952 :: T_IdempotentSemiring_2822 -> T_Semiring_2280
du_semiring_2952 T_IdempotentSemiring_2822
v0
  = ((AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> AgdaAny
 -> T_IsSemiring_1570
 -> T_Semiring_2280)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsSemiring_1570
-> T_Semiring_2280
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsSemiring_1570
-> T_Semiring_2280
C_Semiring'46'constructor_41765 (T_IdempotentSemiring_2822 -> AgdaAny -> AgdaAny -> AgdaAny
d__'43'__2846 (T_IdempotentSemiring_2822 -> T_IdempotentSemiring_2822
forall a b. a -> b
coe T_IdempotentSemiring_2822
v0))
      (T_IdempotentSemiring_2822 -> AgdaAny -> AgdaAny -> AgdaAny
d__'42'__2848 (T_IdempotentSemiring_2822 -> T_IdempotentSemiring_2822
forall a b. a -> b
coe T_IdempotentSemiring_2822
v0)) (T_IdempotentSemiring_2822 -> AgdaAny
d_0'35'_2850 (T_IdempotentSemiring_2822 -> T_IdempotentSemiring_2822
forall a b. a -> b
coe T_IdempotentSemiring_2822
v0))
      (T_IdempotentSemiring_2822 -> AgdaAny
d_1'35'_2852 (T_IdempotentSemiring_2822 -> T_IdempotentSemiring_2822
forall a b. a -> b
coe T_IdempotentSemiring_2822
v0))
      (T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570
MAlonzo.Code.Algebra.Structures.d_isSemiring_1936
         ((T_IdempotentSemiring_2822 -> T_IsIdempotentSemiring_1922)
-> AgdaAny -> T_IsIdempotentSemiring_1922
forall a b. a -> b
coe T_IdempotentSemiring_2822 -> T_IsIdempotentSemiring_1922
d_isIdempotentSemiring_2854 (T_IdempotentSemiring_2822 -> AgdaAny
forall a b. a -> b
coe T_IdempotentSemiring_2822
v0)))
-- Algebra.Bundles.IdempotentSemiring._._≉_
d__'8777'__2956 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentSemiring_2822 -> AgdaAny -> AgdaAny -> ()
d__'8777'__2956 :: () -> () -> T_IdempotentSemiring_2822 -> AgdaAny -> AgdaAny -> ()
d__'8777'__2956 = () -> () -> T_IdempotentSemiring_2822 -> AgdaAny -> AgdaAny -> ()
forall a. a
erased
-- Algebra.Bundles.IdempotentSemiring._.magma
d_magma_2958 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentSemiring_2822 -> T_Magma_68
d_magma_2958 :: () -> () -> T_IdempotentSemiring_2822 -> T_Magma_68
d_magma_2958 ~()
v0 ~()
v1 T_IdempotentSemiring_2822
v2 = T_IdempotentSemiring_2822 -> T_Magma_68
du_magma_2958 T_IdempotentSemiring_2822
v2
du_magma_2958 :: T_IdempotentSemiring_2822 -> T_Magma_68
du_magma_2958 :: T_IdempotentSemiring_2822 -> T_Magma_68
du_magma_2958 T_IdempotentSemiring_2822
v0
  = let v1 :: t
v1 = (T_IdempotentSemiring_2822 -> T_Semiring_2280) -> AgdaAny -> t
forall a b. a -> b
coe T_IdempotentSemiring_2822 -> T_Semiring_2280
du_semiring_2952 (T_IdempotentSemiring_2822 -> AgdaAny
forall a b. a -> b
coe T_IdempotentSemiring_2822
v0) in
    AgdaAny -> T_Magma_68
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_Semiring_2280 -> T_SemiringWithoutAnnihilatingZero_2130)
-> AgdaAny -> t
forall a b. a -> b
coe T_Semiring_2280 -> T_SemiringWithoutAnnihilatingZero_2130
du_semiringWithoutAnnihilatingZero_2398 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: t
v3 = (T_SemiringWithoutAnnihilatingZero_2130 -> T_Monoid_882)
-> AgdaAny -> t
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_2130 -> T_Monoid_882
du_'42''45'monoid_2264 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_Semigroup_536 -> T_Magma_68) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semigroup_536 -> T_Magma_68
du_magma_584 ((T_Monoid_882 -> T_Semigroup_536) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Monoid_882 -> T_Semigroup_536
du_semigroup_944 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3)))))
-- Algebra.Bundles.IdempotentSemiring._.*-monoid
d_'42''45'monoid_2960 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentSemiring_2822 -> T_Monoid_882
d_'42''45'monoid_2960 :: () -> () -> T_IdempotentSemiring_2822 -> T_Monoid_882
d_'42''45'monoid_2960 ~()
v0 ~()
v1 T_IdempotentSemiring_2822
v2 = T_IdempotentSemiring_2822 -> T_Monoid_882
du_'42''45'monoid_2960 T_IdempotentSemiring_2822
v2
du_'42''45'monoid_2960 :: T_IdempotentSemiring_2822 -> T_Monoid_882
du_'42''45'monoid_2960 :: T_IdempotentSemiring_2822 -> T_Monoid_882
du_'42''45'monoid_2960 T_IdempotentSemiring_2822
v0
  = let v1 :: t
v1 = (T_IdempotentSemiring_2822 -> T_Semiring_2280) -> AgdaAny -> t
forall a b. a -> b
coe T_IdempotentSemiring_2822 -> T_Semiring_2280
du_semiring_2952 (T_IdempotentSemiring_2822 -> AgdaAny
forall a b. a -> b
coe T_IdempotentSemiring_2822
v0) in
    AgdaAny -> T_Monoid_882
forall a b. a -> b
coe
      ((T_SemiringWithoutAnnihilatingZero_2130 -> T_Monoid_882)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_SemiringWithoutAnnihilatingZero_2130 -> T_Monoid_882
du_'42''45'monoid_2264
         ((T_Semiring_2280 -> T_SemiringWithoutAnnihilatingZero_2130)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semiring_2280 -> T_SemiringWithoutAnnihilatingZero_2130
du_semiringWithoutAnnihilatingZero_2398 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1)))
-- Algebra.Bundles.IdempotentSemiring._.rawMagma
d_rawMagma_2962 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentSemiring_2822 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
d_rawMagma_2962 :: () -> () -> T_IdempotentSemiring_2822 -> T_RawMagma_36
d_rawMagma_2962 ~()
v0 ~()
v1 T_IdempotentSemiring_2822
v2 = T_IdempotentSemiring_2822 -> T_RawMagma_36
du_rawMagma_2962 T_IdempotentSemiring_2822
v2
du_rawMagma_2962 ::
  T_IdempotentSemiring_2822 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
du_rawMagma_2962 :: T_IdempotentSemiring_2822 -> T_RawMagma_36
du_rawMagma_2962 T_IdempotentSemiring_2822
v0
  = let v1 :: t
v1 = (T_IdempotentSemiring_2822 -> T_Semiring_2280) -> AgdaAny -> t
forall a b. a -> b
coe T_IdempotentSemiring_2822 -> T_Semiring_2280
du_semiring_2952 (T_IdempotentSemiring_2822 -> AgdaAny
forall a b. a -> b
coe T_IdempotentSemiring_2822
v0) in
    AgdaAny -> T_RawMagma_36
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_Semiring_2280 -> T_SemiringWithoutAnnihilatingZero_2130)
-> AgdaAny -> t
forall a b. a -> b
coe T_Semiring_2280 -> T_SemiringWithoutAnnihilatingZero_2130
du_semiringWithoutAnnihilatingZero_2398 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: t
v3 = (T_SemiringWithoutAnnihilatingZero_2130 -> T_Monoid_882)
-> AgdaAny -> t
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_2130 -> T_Monoid_882
du_'42''45'monoid_2264 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: t
v4 = (T_Monoid_882 -> T_Semigroup_536) -> AgdaAny -> t
forall a b. a -> b
coe T_Monoid_882 -> T_Semigroup_536
du_semigroup_944 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_Magma_68 -> T_RawMagma_36) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Magma_68 -> T_RawMagma_36
du_rawMagma_112 ((T_Semigroup_536 -> T_Magma_68) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semigroup_536 -> T_Magma_68
du_magma_584 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v4))))))
-- Algebra.Bundles.IdempotentSemiring._.rawMonoid
d_rawMonoid_2964 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentSemiring_2822 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMonoid_64
d_rawMonoid_2964 :: () -> () -> T_IdempotentSemiring_2822 -> T_RawMonoid_64
d_rawMonoid_2964 ~()
v0 ~()
v1 T_IdempotentSemiring_2822
v2 = T_IdempotentSemiring_2822 -> T_RawMonoid_64
du_rawMonoid_2964 T_IdempotentSemiring_2822
v2
du_rawMonoid_2964 ::
  T_IdempotentSemiring_2822 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMonoid_64
du_rawMonoid_2964 :: T_IdempotentSemiring_2822 -> T_RawMonoid_64
du_rawMonoid_2964 T_IdempotentSemiring_2822
v0
  = let v1 :: t
v1 = (T_IdempotentSemiring_2822 -> T_Semiring_2280) -> AgdaAny -> t
forall a b. a -> b
coe T_IdempotentSemiring_2822 -> T_Semiring_2280
du_semiring_2952 (T_IdempotentSemiring_2822 -> AgdaAny
forall a b. a -> b
coe T_IdempotentSemiring_2822
v0) in
    AgdaAny -> T_RawMonoid_64
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_Semiring_2280 -> T_SemiringWithoutAnnihilatingZero_2130)
-> AgdaAny -> t
forall a b. a -> b
coe T_Semiring_2280 -> T_SemiringWithoutAnnihilatingZero_2130
du_semiringWithoutAnnihilatingZero_2398 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_Monoid_882 -> T_RawMonoid_64) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Monoid_882 -> T_RawMonoid_64
du_rawMonoid_954 ((T_SemiringWithoutAnnihilatingZero_2130 -> T_Monoid_882)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_2130 -> T_Monoid_882
du_'42''45'monoid_2264 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2))))
-- Algebra.Bundles.IdempotentSemiring._.semigroup
d_semigroup_2966 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentSemiring_2822 -> T_Semigroup_536
d_semigroup_2966 :: () -> () -> T_IdempotentSemiring_2822 -> T_Semigroup_536
d_semigroup_2966 ~()
v0 ~()
v1 T_IdempotentSemiring_2822
v2 = T_IdempotentSemiring_2822 -> T_Semigroup_536
du_semigroup_2966 T_IdempotentSemiring_2822
v2
du_semigroup_2966 :: T_IdempotentSemiring_2822 -> T_Semigroup_536
du_semigroup_2966 :: T_IdempotentSemiring_2822 -> T_Semigroup_536
du_semigroup_2966 T_IdempotentSemiring_2822
v0
  = let v1 :: t
v1 = (T_IdempotentSemiring_2822 -> T_Semiring_2280) -> AgdaAny -> t
forall a b. a -> b
coe T_IdempotentSemiring_2822 -> T_Semiring_2280
du_semiring_2952 (T_IdempotentSemiring_2822 -> AgdaAny
forall a b. a -> b
coe T_IdempotentSemiring_2822
v0) in
    AgdaAny -> T_Semigroup_536
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_Semiring_2280 -> T_SemiringWithoutAnnihilatingZero_2130)
-> AgdaAny -> t
forall a b. a -> b
coe T_Semiring_2280 -> T_SemiringWithoutAnnihilatingZero_2130
du_semiringWithoutAnnihilatingZero_2398 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_Monoid_882 -> T_Semigroup_536) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Monoid_882 -> T_Semigroup_536
du_semigroup_944 ((T_SemiringWithoutAnnihilatingZero_2130 -> T_Monoid_882)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_2130 -> T_Monoid_882
du_'42''45'monoid_2264 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2))))
-- Algebra.Bundles.IdempotentSemiring._.commutativeMagma
d_commutativeMagma_2968 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentSemiring_2822 -> T_CommutativeMagma_180
d_commutativeMagma_2968 :: () -> () -> T_IdempotentSemiring_2822 -> T_CommutativeMagma_180
d_commutativeMagma_2968 ~()
v0 ~()
v1 T_IdempotentSemiring_2822
v2 = T_IdempotentSemiring_2822 -> T_CommutativeMagma_180
du_commutativeMagma_2968 T_IdempotentSemiring_2822
v2
du_commutativeMagma_2968 ::
  T_IdempotentSemiring_2822 -> T_CommutativeMagma_180
du_commutativeMagma_2968 :: T_IdempotentSemiring_2822 -> T_CommutativeMagma_180
du_commutativeMagma_2968 T_IdempotentSemiring_2822
v0
  = let v1 :: t
v1 = (T_IdempotentSemiring_2822 -> T_Semiring_2280) -> AgdaAny -> t
forall a b. a -> b
coe T_IdempotentSemiring_2822 -> T_Semiring_2280
du_semiring_2952 (T_IdempotentSemiring_2822 -> AgdaAny
forall a b. a -> b
coe T_IdempotentSemiring_2822
v0) in
    AgdaAny -> T_CommutativeMagma_180
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_Semiring_2280 -> T_SemiringWithoutAnnihilatingZero_2130)
-> AgdaAny -> t
forall a b. a -> b
coe T_Semiring_2280 -> T_SemiringWithoutAnnihilatingZero_2130
du_semiringWithoutAnnihilatingZero_2398 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: t
v3 = (T_SemiringWithoutAnnihilatingZero_2130 -> T_CommutativeMonoid_962)
-> AgdaAny -> t
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_2130 -> T_CommutativeMonoid_962
du_'43''45'commutativeMonoid_2242 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_CommutativeSemigroup_662 -> T_CommutativeMagma_180)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_CommutativeSemigroup_662 -> T_CommutativeMagma_180
du_commutativeMagma_726
               ((T_CommutativeMonoid_962 -> T_CommutativeSemigroup_662)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeMonoid_962 -> T_CommutativeSemigroup_662
du_commutativeSemigroup_1048 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3)))))
-- Algebra.Bundles.IdempotentSemiring._.+-commutativeMonoid
d_'43''45'commutativeMonoid_2970 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentSemiring_2822 -> T_CommutativeMonoid_962
d_'43''45'commutativeMonoid_2970 :: () -> () -> T_IdempotentSemiring_2822 -> T_CommutativeMonoid_962
d_'43''45'commutativeMonoid_2970 ~()
v0 ~()
v1 T_IdempotentSemiring_2822
v2
  = T_IdempotentSemiring_2822 -> T_CommutativeMonoid_962
du_'43''45'commutativeMonoid_2970 T_IdempotentSemiring_2822
v2
du_'43''45'commutativeMonoid_2970 ::
  T_IdempotentSemiring_2822 -> T_CommutativeMonoid_962
du_'43''45'commutativeMonoid_2970 :: T_IdempotentSemiring_2822 -> T_CommutativeMonoid_962
du_'43''45'commutativeMonoid_2970 T_IdempotentSemiring_2822
v0
  = let v1 :: t
v1 = (T_IdempotentSemiring_2822 -> T_Semiring_2280) -> AgdaAny -> t
forall a b. a -> b
coe T_IdempotentSemiring_2822 -> T_Semiring_2280
du_semiring_2952 (T_IdempotentSemiring_2822 -> AgdaAny
forall a b. a -> b
coe T_IdempotentSemiring_2822
v0) in
    AgdaAny -> T_CommutativeMonoid_962
forall a b. a -> b
coe
      ((T_SemiringWithoutAnnihilatingZero_2130 -> T_CommutativeMonoid_962)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_SemiringWithoutAnnihilatingZero_2130 -> T_CommutativeMonoid_962
du_'43''45'commutativeMonoid_2242
         ((T_Semiring_2280 -> T_SemiringWithoutAnnihilatingZero_2130)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semiring_2280 -> T_SemiringWithoutAnnihilatingZero_2130
du_semiringWithoutAnnihilatingZero_2398 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1)))
-- Algebra.Bundles.IdempotentSemiring._.commutativeSemigroup
d_commutativeSemigroup_2972 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentSemiring_2822 -> T_CommutativeSemigroup_662
d_commutativeSemigroup_2972 :: () -> () -> T_IdempotentSemiring_2822 -> T_CommutativeSemigroup_662
d_commutativeSemigroup_2972 ~()
v0 ~()
v1 T_IdempotentSemiring_2822
v2
  = T_IdempotentSemiring_2822 -> T_CommutativeSemigroup_662
du_commutativeSemigroup_2972 T_IdempotentSemiring_2822
v2
du_commutativeSemigroup_2972 ::
  T_IdempotentSemiring_2822 -> T_CommutativeSemigroup_662
du_commutativeSemigroup_2972 :: T_IdempotentSemiring_2822 -> T_CommutativeSemigroup_662
du_commutativeSemigroup_2972 T_IdempotentSemiring_2822
v0
  = let v1 :: t
v1 = (T_IdempotentSemiring_2822 -> T_Semiring_2280) -> AgdaAny -> t
forall a b. a -> b
coe T_IdempotentSemiring_2822 -> T_Semiring_2280
du_semiring_2952 (T_IdempotentSemiring_2822 -> AgdaAny
forall a b. a -> b
coe T_IdempotentSemiring_2822
v0) in
    AgdaAny -> T_CommutativeSemigroup_662
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_Semiring_2280 -> T_SemiringWithoutAnnihilatingZero_2130)
-> AgdaAny -> t
forall a b. a -> b
coe T_Semiring_2280 -> T_SemiringWithoutAnnihilatingZero_2130
du_semiringWithoutAnnihilatingZero_2398 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_CommutativeMonoid_962 -> T_CommutativeSemigroup_662)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_CommutativeMonoid_962 -> T_CommutativeSemigroup_662
du_commutativeSemigroup_1048
            ((T_SemiringWithoutAnnihilatingZero_2130 -> T_CommutativeMonoid_962)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_2130 -> T_CommutativeMonoid_962
du_'43''45'commutativeMonoid_2242 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2))))
-- Algebra.Bundles.IdempotentSemiring._.magma
d_magma_2974 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentSemiring_2822 -> T_Magma_68
d_magma_2974 :: () -> () -> T_IdempotentSemiring_2822 -> T_Magma_68
d_magma_2974 ~()
v0 ~()
v1 T_IdempotentSemiring_2822
v2 = T_IdempotentSemiring_2822 -> T_Magma_68
du_magma_2974 T_IdempotentSemiring_2822
v2
du_magma_2974 :: T_IdempotentSemiring_2822 -> T_Magma_68
du_magma_2974 :: T_IdempotentSemiring_2822 -> T_Magma_68
du_magma_2974 T_IdempotentSemiring_2822
v0
  = let v1 :: t
v1 = (T_IdempotentSemiring_2822 -> T_Semiring_2280) -> AgdaAny -> t
forall a b. a -> b
coe T_IdempotentSemiring_2822 -> T_Semiring_2280
du_semiring_2952 (T_IdempotentSemiring_2822 -> AgdaAny
forall a b. a -> b
coe T_IdempotentSemiring_2822
v0) in
    AgdaAny -> T_Magma_68
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_Semiring_2280 -> T_SemiringWithoutAnnihilatingZero_2130)
-> AgdaAny -> t
forall a b. a -> b
coe T_Semiring_2280 -> T_SemiringWithoutAnnihilatingZero_2130
du_semiringWithoutAnnihilatingZero_2398 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: t
v3 = (T_SemiringWithoutAnnihilatingZero_2130 -> T_CommutativeMonoid_962)
-> AgdaAny -> t
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_2130 -> T_CommutativeMonoid_962
du_'43''45'commutativeMonoid_2242 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: t
v4 = (T_CommutativeMonoid_962 -> T_Monoid_882) -> AgdaAny -> t
forall a b. a -> b
coe T_CommutativeMonoid_962 -> T_Monoid_882
du_monoid_1032 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_Semigroup_536 -> T_Magma_68) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semigroup_536 -> T_Magma_68
du_magma_584 ((T_Monoid_882 -> T_Semigroup_536) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Monoid_882 -> T_Semigroup_536
du_semigroup_944 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v4))))))
-- Algebra.Bundles.IdempotentSemiring._.monoid
d_monoid_2976 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentSemiring_2822 -> T_Monoid_882
d_monoid_2976 :: () -> () -> T_IdempotentSemiring_2822 -> T_Monoid_882
d_monoid_2976 ~()
v0 ~()
v1 T_IdempotentSemiring_2822
v2 = T_IdempotentSemiring_2822 -> T_Monoid_882
du_monoid_2976 T_IdempotentSemiring_2822
v2
du_monoid_2976 :: T_IdempotentSemiring_2822 -> T_Monoid_882
du_monoid_2976 :: T_IdempotentSemiring_2822 -> T_Monoid_882
du_monoid_2976 T_IdempotentSemiring_2822
v0
  = let v1 :: t
v1 = (T_IdempotentSemiring_2822 -> T_Semiring_2280) -> AgdaAny -> t
forall a b. a -> b
coe T_IdempotentSemiring_2822 -> T_Semiring_2280
du_semiring_2952 (T_IdempotentSemiring_2822 -> AgdaAny
forall a b. a -> b
coe T_IdempotentSemiring_2822
v0) in
    AgdaAny -> T_Monoid_882
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_Semiring_2280 -> T_SemiringWithoutAnnihilatingZero_2130)
-> AgdaAny -> t
forall a b. a -> b
coe T_Semiring_2280 -> T_SemiringWithoutAnnihilatingZero_2130
du_semiringWithoutAnnihilatingZero_2398 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_CommutativeMonoid_962 -> T_Monoid_882) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_CommutativeMonoid_962 -> T_Monoid_882
du_monoid_1032 ((T_SemiringWithoutAnnihilatingZero_2130 -> T_CommutativeMonoid_962)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_2130 -> T_CommutativeMonoid_962
du_'43''45'commutativeMonoid_2242 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2))))
-- Algebra.Bundles.IdempotentSemiring._.rawMagma
d_rawMagma_2978 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentSemiring_2822 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
d_rawMagma_2978 :: () -> () -> T_IdempotentSemiring_2822 -> T_RawMagma_36
d_rawMagma_2978 ~()
v0 ~()
v1 T_IdempotentSemiring_2822
v2 = T_IdempotentSemiring_2822 -> T_RawMagma_36
du_rawMagma_2978 T_IdempotentSemiring_2822
v2
du_rawMagma_2978 ::
  T_IdempotentSemiring_2822 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
du_rawMagma_2978 :: T_IdempotentSemiring_2822 -> T_RawMagma_36
du_rawMagma_2978 T_IdempotentSemiring_2822
v0
  = let v1 :: t
v1 = (T_IdempotentSemiring_2822 -> T_Semiring_2280) -> AgdaAny -> t
forall a b. a -> b
coe T_IdempotentSemiring_2822 -> T_Semiring_2280
du_semiring_2952 (T_IdempotentSemiring_2822 -> AgdaAny
forall a b. a -> b
coe T_IdempotentSemiring_2822
v0) in
    AgdaAny -> T_RawMagma_36
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_Semiring_2280 -> T_SemiringWithoutAnnihilatingZero_2130)
-> AgdaAny -> t
forall a b. a -> b
coe T_Semiring_2280 -> T_SemiringWithoutAnnihilatingZero_2130
du_semiringWithoutAnnihilatingZero_2398 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: t
v3 = (T_SemiringWithoutAnnihilatingZero_2130 -> T_CommutativeMonoid_962)
-> AgdaAny -> t
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_2130 -> T_CommutativeMonoid_962
du_'43''45'commutativeMonoid_2242 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: t
v4 = (T_CommutativeMonoid_962 -> T_Monoid_882) -> AgdaAny -> t
forall a b. a -> b
coe T_CommutativeMonoid_962 -> T_Monoid_882
du_monoid_1032 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: t
v5 = (T_Monoid_882 -> T_Semigroup_536) -> AgdaAny -> t
forall a b. a -> b
coe T_Monoid_882 -> T_Semigroup_536
du_semigroup_944 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_Magma_68 -> T_RawMagma_36) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Magma_68 -> T_RawMagma_36
du_rawMagma_112 ((T_Semigroup_536 -> T_Magma_68) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semigroup_536 -> T_Magma_68
du_magma_584 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v5)))))))
-- Algebra.Bundles.IdempotentSemiring._.rawMonoid
d_rawMonoid_2980 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentSemiring_2822 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMonoid_64
d_rawMonoid_2980 :: () -> () -> T_IdempotentSemiring_2822 -> T_RawMonoid_64
d_rawMonoid_2980 ~()
v0 ~()
v1 T_IdempotentSemiring_2822
v2 = T_IdempotentSemiring_2822 -> T_RawMonoid_64
du_rawMonoid_2980 T_IdempotentSemiring_2822
v2
du_rawMonoid_2980 ::
  T_IdempotentSemiring_2822 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMonoid_64
du_rawMonoid_2980 :: T_IdempotentSemiring_2822 -> T_RawMonoid_64
du_rawMonoid_2980 T_IdempotentSemiring_2822
v0
  = let v1 :: t
v1 = (T_IdempotentSemiring_2822 -> T_Semiring_2280) -> AgdaAny -> t
forall a b. a -> b
coe T_IdempotentSemiring_2822 -> T_Semiring_2280
du_semiring_2952 (T_IdempotentSemiring_2822 -> AgdaAny
forall a b. a -> b
coe T_IdempotentSemiring_2822
v0) in
    AgdaAny -> T_RawMonoid_64
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_Semiring_2280 -> T_SemiringWithoutAnnihilatingZero_2130)
-> AgdaAny -> t
forall a b. a -> b
coe T_Semiring_2280 -> T_SemiringWithoutAnnihilatingZero_2130
du_semiringWithoutAnnihilatingZero_2398 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: t
v3 = (T_SemiringWithoutAnnihilatingZero_2130 -> T_CommutativeMonoid_962)
-> AgdaAny -> t
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_2130 -> T_CommutativeMonoid_962
du_'43''45'commutativeMonoid_2242 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_Monoid_882 -> T_RawMonoid_64) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Monoid_882 -> T_RawMonoid_64
du_rawMonoid_954 ((T_CommutativeMonoid_962 -> T_Monoid_882) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeMonoid_962 -> T_Monoid_882
du_monoid_1032 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3)))))
-- Algebra.Bundles.IdempotentSemiring._.semigroup
d_semigroup_2982 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentSemiring_2822 -> T_Semigroup_536
d_semigroup_2982 :: () -> () -> T_IdempotentSemiring_2822 -> T_Semigroup_536
d_semigroup_2982 ~()
v0 ~()
v1 T_IdempotentSemiring_2822
v2 = T_IdempotentSemiring_2822 -> T_Semigroup_536
du_semigroup_2982 T_IdempotentSemiring_2822
v2
du_semigroup_2982 :: T_IdempotentSemiring_2822 -> T_Semigroup_536
du_semigroup_2982 :: T_IdempotentSemiring_2822 -> T_Semigroup_536
du_semigroup_2982 T_IdempotentSemiring_2822
v0
  = let v1 :: t
v1 = (T_IdempotentSemiring_2822 -> T_Semiring_2280) -> AgdaAny -> t
forall a b. a -> b
coe T_IdempotentSemiring_2822 -> T_Semiring_2280
du_semiring_2952 (T_IdempotentSemiring_2822 -> AgdaAny
forall a b. a -> b
coe T_IdempotentSemiring_2822
v0) in
    AgdaAny -> T_Semigroup_536
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_Semiring_2280 -> T_SemiringWithoutAnnihilatingZero_2130)
-> AgdaAny -> t
forall a b. a -> b
coe T_Semiring_2280 -> T_SemiringWithoutAnnihilatingZero_2130
du_semiringWithoutAnnihilatingZero_2398 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: t
v3 = (T_SemiringWithoutAnnihilatingZero_2130 -> T_CommutativeMonoid_962)
-> AgdaAny -> t
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_2130 -> T_CommutativeMonoid_962
du_'43''45'commutativeMonoid_2242 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_Monoid_882 -> T_Semigroup_536) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Monoid_882 -> T_Semigroup_536
du_semigroup_944 ((T_CommutativeMonoid_962 -> T_Monoid_882) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeMonoid_962 -> T_Monoid_882
du_monoid_1032 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3)))))
-- Algebra.Bundles.IdempotentSemiring._.unitalMagma
d_unitalMagma_2984 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentSemiring_2822 -> T_UnitalMagma_814
d_unitalMagma_2984 :: () -> () -> T_IdempotentSemiring_2822 -> T_UnitalMagma_814
d_unitalMagma_2984 ~()
v0 ~()
v1 T_IdempotentSemiring_2822
v2 = T_IdempotentSemiring_2822 -> T_UnitalMagma_814
du_unitalMagma_2984 T_IdempotentSemiring_2822
v2
du_unitalMagma_2984 ::
  T_IdempotentSemiring_2822 -> T_UnitalMagma_814
du_unitalMagma_2984 :: T_IdempotentSemiring_2822 -> T_UnitalMagma_814
du_unitalMagma_2984 T_IdempotentSemiring_2822
v0
  = let v1 :: t
v1 = (T_IdempotentSemiring_2822 -> T_Semiring_2280) -> AgdaAny -> t
forall a b. a -> b
coe T_IdempotentSemiring_2822 -> T_Semiring_2280
du_semiring_2952 (T_IdempotentSemiring_2822 -> AgdaAny
forall a b. a -> b
coe T_IdempotentSemiring_2822
v0) in
    AgdaAny -> T_UnitalMagma_814
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_Semiring_2280 -> T_SemiringWithoutAnnihilatingZero_2130)
-> AgdaAny -> t
forall a b. a -> b
coe T_Semiring_2280 -> T_SemiringWithoutAnnihilatingZero_2130
du_semiringWithoutAnnihilatingZero_2398 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: t
v3 = (T_SemiringWithoutAnnihilatingZero_2130 -> T_CommutativeMonoid_962)
-> AgdaAny -> t
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_2130 -> T_CommutativeMonoid_962
du_'43''45'commutativeMonoid_2242 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_Monoid_882 -> T_UnitalMagma_814) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Monoid_882 -> T_UnitalMagma_814
du_unitalMagma_956 ((T_CommutativeMonoid_962 -> T_Monoid_882) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeMonoid_962 -> T_Monoid_882
du_monoid_1032 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3)))))
-- Algebra.Bundles.IdempotentSemiring._.nearSemiring
d_nearSemiring_2986 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentSemiring_2822 -> T_NearSemiring_1766
d_nearSemiring_2986 :: () -> () -> T_IdempotentSemiring_2822 -> T_NearSemiring_1766
d_nearSemiring_2986 ~()
v0 ~()
v1 T_IdempotentSemiring_2822
v2 = T_IdempotentSemiring_2822 -> T_NearSemiring_1766
du_nearSemiring_2986 T_IdempotentSemiring_2822
v2
du_nearSemiring_2986 ::
  T_IdempotentSemiring_2822 -> T_NearSemiring_1766
du_nearSemiring_2986 :: T_IdempotentSemiring_2822 -> T_NearSemiring_1766
du_nearSemiring_2986 T_IdempotentSemiring_2822
v0
  = let v1 :: t
v1 = (T_IdempotentSemiring_2822 -> T_Semiring_2280) -> AgdaAny -> t
forall a b. a -> b
coe T_IdempotentSemiring_2822 -> T_Semiring_2280
du_semiring_2952 (T_IdempotentSemiring_2822 -> AgdaAny
forall a b. a -> b
coe T_IdempotentSemiring_2822
v0) in
    AgdaAny -> T_NearSemiring_1766
forall a b. a -> b
coe
      ((T_SemiringWithoutOne_1880 -> T_NearSemiring_1766)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_SemiringWithoutOne_1880 -> T_NearSemiring_1766
du_nearSemiring_1966 ((T_Semiring_2280 -> T_SemiringWithoutOne_1880)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semiring_2280 -> T_SemiringWithoutOne_1880
du_semiringWithoutOne_2436 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1)))
-- Algebra.Bundles.IdempotentSemiring._.rawSemiring
d_rawSemiring_2988 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentSemiring_2822 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawSemiring_174
d_rawSemiring_2988 :: () -> () -> T_IdempotentSemiring_2822 -> T_RawSemiring_174
d_rawSemiring_2988 ~()
v0 ~()
v1 T_IdempotentSemiring_2822
v2 = T_IdempotentSemiring_2822 -> T_RawSemiring_174
du_rawSemiring_2988 T_IdempotentSemiring_2822
v2
du_rawSemiring_2988 ::
  T_IdempotentSemiring_2822 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawSemiring_174
du_rawSemiring_2988 :: T_IdempotentSemiring_2822 -> T_RawSemiring_174
du_rawSemiring_2988 T_IdempotentSemiring_2822
v0
  = let v1 :: t
v1 = (T_IdempotentSemiring_2822 -> T_Semiring_2280) -> AgdaAny -> t
forall a b. a -> b
coe T_IdempotentSemiring_2822 -> T_Semiring_2280
du_semiring_2952 (T_IdempotentSemiring_2822 -> AgdaAny
forall a b. a -> b
coe T_IdempotentSemiring_2822
v0) in
    AgdaAny -> T_RawSemiring_174
forall a b. a -> b
coe
      ((T_SemiringWithoutAnnihilatingZero_2130 -> T_RawSemiring_174)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_SemiringWithoutAnnihilatingZero_2130 -> T_RawSemiring_174
du_rawSemiring_2236
         ((T_Semiring_2280 -> T_SemiringWithoutAnnihilatingZero_2130)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semiring_2280 -> T_SemiringWithoutAnnihilatingZero_2130
du_semiringWithoutAnnihilatingZero_2398 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1)))
-- Algebra.Bundles.IdempotentSemiring._.semiringWithoutAnnihilatingZero
d_semiringWithoutAnnihilatingZero_2990 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentSemiring_2822 -> T_SemiringWithoutAnnihilatingZero_2130
d_semiringWithoutAnnihilatingZero_2990 :: ()
-> ()
-> T_IdempotentSemiring_2822
-> T_SemiringWithoutAnnihilatingZero_2130
d_semiringWithoutAnnihilatingZero_2990 ~()
v0 ~()
v1 T_IdempotentSemiring_2822
v2
  = T_IdempotentSemiring_2822 -> T_SemiringWithoutAnnihilatingZero_2130
du_semiringWithoutAnnihilatingZero_2990 T_IdempotentSemiring_2822
v2
du_semiringWithoutAnnihilatingZero_2990 ::
  T_IdempotentSemiring_2822 -> T_SemiringWithoutAnnihilatingZero_2130
du_semiringWithoutAnnihilatingZero_2990 :: T_IdempotentSemiring_2822 -> T_SemiringWithoutAnnihilatingZero_2130
du_semiringWithoutAnnihilatingZero_2990 T_IdempotentSemiring_2822
v0
  = (T_Semiring_2280 -> T_SemiringWithoutAnnihilatingZero_2130)
-> AgdaAny -> T_SemiringWithoutAnnihilatingZero_2130
forall a b. a -> b
coe
      T_Semiring_2280 -> T_SemiringWithoutAnnihilatingZero_2130
du_semiringWithoutAnnihilatingZero_2398
      ((T_IdempotentSemiring_2822 -> T_Semiring_2280)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IdempotentSemiring_2822 -> T_Semiring_2280
du_semiring_2952 (T_IdempotentSemiring_2822 -> AgdaAny
forall a b. a -> b
coe T_IdempotentSemiring_2822
v0))
-- Algebra.Bundles.IdempotentSemiring._.semiringWithoutOne
d_semiringWithoutOne_2992 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentSemiring_2822 -> T_SemiringWithoutOne_1880
d_semiringWithoutOne_2992 :: () -> () -> T_IdempotentSemiring_2822 -> T_SemiringWithoutOne_1880
d_semiringWithoutOne_2992 ~()
v0 ~()
v1 T_IdempotentSemiring_2822
v2
  = T_IdempotentSemiring_2822 -> T_SemiringWithoutOne_1880
du_semiringWithoutOne_2992 T_IdempotentSemiring_2822
v2
du_semiringWithoutOne_2992 ::
  T_IdempotentSemiring_2822 -> T_SemiringWithoutOne_1880
du_semiringWithoutOne_2992 :: T_IdempotentSemiring_2822 -> T_SemiringWithoutOne_1880
du_semiringWithoutOne_2992 T_IdempotentSemiring_2822
v0
  = (T_Semiring_2280 -> T_SemiringWithoutOne_1880)
-> AgdaAny -> T_SemiringWithoutOne_1880
forall a b. a -> b
coe T_Semiring_2280 -> T_SemiringWithoutOne_1880
du_semiringWithoutOne_2436 ((T_IdempotentSemiring_2822 -> T_Semiring_2280)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IdempotentSemiring_2822 -> T_Semiring_2280
du_semiring_2952 (T_IdempotentSemiring_2822 -> AgdaAny
forall a b. a -> b
coe T_IdempotentSemiring_2822
v0))
-- Algebra.Bundles.IdempotentSemiring.+-idempotentCommutativeMonoid
d_'43''45'idempotentCommutativeMonoid_2994 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentSemiring_2822 -> T_IdempotentCommutativeMonoid_1148
d_'43''45'idempotentCommutativeMonoid_2994 :: ()
-> ()
-> T_IdempotentSemiring_2822
-> T_IdempotentCommutativeMonoid_1148
d_'43''45'idempotentCommutativeMonoid_2994 ~()
v0 ~()
v1 T_IdempotentSemiring_2822
v2
  = T_IdempotentSemiring_2822 -> T_IdempotentCommutativeMonoid_1148
du_'43''45'idempotentCommutativeMonoid_2994 T_IdempotentSemiring_2822
v2
du_'43''45'idempotentCommutativeMonoid_2994 ::
  T_IdempotentSemiring_2822 -> T_IdempotentCommutativeMonoid_1148
du_'43''45'idempotentCommutativeMonoid_2994 :: T_IdempotentSemiring_2822 -> T_IdempotentCommutativeMonoid_1148
du_'43''45'idempotentCommutativeMonoid_2994 T_IdempotentSemiring_2822
v0
  = ((AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> T_IsIdempotentCommutativeMonoid_852
 -> T_IdempotentCommutativeMonoid_1148)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IdempotentCommutativeMonoid_1148
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsIdempotentCommutativeMonoid_852
-> T_IdempotentCommutativeMonoid_1148
C_IdempotentCommutativeMonoid'46'constructor_21499
      (T_IdempotentSemiring_2822 -> AgdaAny -> AgdaAny -> AgdaAny
d__'43'__2846 (T_IdempotentSemiring_2822 -> T_IdempotentSemiring_2822
forall a b. a -> b
coe T_IdempotentSemiring_2822
v0)) (T_IdempotentSemiring_2822 -> AgdaAny
d_0'35'_2850 (T_IdempotentSemiring_2822 -> T_IdempotentSemiring_2822
forall a b. a -> b
coe T_IdempotentSemiring_2822
v0))
      ((T_IsIdempotentSemiring_1922
 -> T_IsIdempotentCommutativeMonoid_852)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsIdempotentSemiring_1922 -> T_IsIdempotentCommutativeMonoid_852
MAlonzo.Code.Algebra.Structures.du_'43''45'isIdempotentCommutativeMonoid_2024
         ((T_IdempotentSemiring_2822 -> T_IsIdempotentSemiring_1922)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IdempotentSemiring_2822 -> T_IsIdempotentSemiring_1922
d_isIdempotentSemiring_2854 (T_IdempotentSemiring_2822 -> AgdaAny
forall a b. a -> b
coe T_IdempotentSemiring_2822
v0)))
-- Algebra.Bundles.IdempotentSemiring._.band
d_band_2998 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentSemiring_2822 -> T_Band_596
d_band_2998 :: () -> () -> T_IdempotentSemiring_2822 -> T_Band_596
d_band_2998 ~()
v0 ~()
v1 T_IdempotentSemiring_2822
v2 = T_IdempotentSemiring_2822 -> T_Band_596
du_band_2998 T_IdempotentSemiring_2822
v2
du_band_2998 :: T_IdempotentSemiring_2822 -> T_Band_596
du_band_2998 :: T_IdempotentSemiring_2822 -> T_Band_596
du_band_2998 T_IdempotentSemiring_2822
v0
  = let v1 :: t
v1
          = (T_IdempotentSemiring_2822 -> T_IdempotentCommutativeMonoid_1148)
-> AgdaAny -> t
forall a b. a -> b
coe T_IdempotentSemiring_2822 -> T_IdempotentCommutativeMonoid_1148
du_'43''45'idempotentCommutativeMonoid_2994 (T_IdempotentSemiring_2822 -> AgdaAny
forall a b. a -> b
coe T_IdempotentSemiring_2822
v0) in
    AgdaAny -> T_Band_596
forall a b. a -> b
coe ((T_CommutativeBand_732 -> T_Band_596) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeBand_732 -> T_Band_596
du_band_792 ((T_IdempotentCommutativeMonoid_1148 -> T_CommutativeBand_732)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1148 -> T_CommutativeBand_732
du_commutativeBand_1232 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1)))
-- Algebra.Bundles.IdempotentSemiring._.commutativeBand
d_commutativeBand_3000 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentSemiring_2822 -> T_CommutativeBand_732
d_commutativeBand_3000 :: () -> () -> T_IdempotentSemiring_2822 -> T_CommutativeBand_732
d_commutativeBand_3000 ~()
v0 ~()
v1 T_IdempotentSemiring_2822
v2 = T_IdempotentSemiring_2822 -> T_CommutativeBand_732
du_commutativeBand_3000 T_IdempotentSemiring_2822
v2
du_commutativeBand_3000 ::
  T_IdempotentSemiring_2822 -> T_CommutativeBand_732
du_commutativeBand_3000 :: T_IdempotentSemiring_2822 -> T_CommutativeBand_732
du_commutativeBand_3000 T_IdempotentSemiring_2822
v0
  = (T_IdempotentCommutativeMonoid_1148 -> T_CommutativeBand_732)
-> AgdaAny -> T_CommutativeBand_732
forall a b. a -> b
coe
      T_IdempotentCommutativeMonoid_1148 -> T_CommutativeBand_732
du_commutativeBand_1232
      ((T_IdempotentSemiring_2822 -> T_IdempotentCommutativeMonoid_1148)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IdempotentSemiring_2822 -> T_IdempotentCommutativeMonoid_1148
du_'43''45'idempotentCommutativeMonoid_2994 (T_IdempotentSemiring_2822 -> AgdaAny
forall a b. a -> b
coe T_IdempotentSemiring_2822
v0))
-- Algebra.Bundles.IdempotentSemiring._.idempotentMonoid
d_idempotentMonoid_3002 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentSemiring_2822 -> T_IdempotentMonoid_1058
d_idempotentMonoid_3002 :: () -> () -> T_IdempotentSemiring_2822 -> T_IdempotentMonoid_1058
d_idempotentMonoid_3002 ~()
v0 ~()
v1 T_IdempotentSemiring_2822
v2 = T_IdempotentSemiring_2822 -> T_IdempotentMonoid_1058
du_idempotentMonoid_3002 T_IdempotentSemiring_2822
v2
du_idempotentMonoid_3002 ::
  T_IdempotentSemiring_2822 -> T_IdempotentMonoid_1058
du_idempotentMonoid_3002 :: T_IdempotentSemiring_2822 -> T_IdempotentMonoid_1058
du_idempotentMonoid_3002 T_IdempotentSemiring_2822
v0
  = (T_IdempotentCommutativeMonoid_1148 -> T_IdempotentMonoid_1058)
-> AgdaAny -> T_IdempotentMonoid_1058
forall a b. a -> b
coe
      T_IdempotentCommutativeMonoid_1148 -> T_IdempotentMonoid_1058
du_idempotentMonoid_1230
      ((T_IdempotentSemiring_2822 -> T_IdempotentCommutativeMonoid_1148)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IdempotentSemiring_2822 -> T_IdempotentCommutativeMonoid_1148
du_'43''45'idempotentCommutativeMonoid_2994 (T_IdempotentSemiring_2822 -> AgdaAny
forall a b. a -> b
coe T_IdempotentSemiring_2822
v0))
-- Algebra.Bundles.KleeneAlgebra
d_KleeneAlgebra_3008 :: p -> p -> ()
d_KleeneAlgebra_3008 p
a0 p
a1 = ()
data T_KleeneAlgebra_3008
  = C_KleeneAlgebra'46'constructor_54207 (AgdaAny ->
                                          AgdaAny -> AgdaAny)
                                         (AgdaAny -> AgdaAny -> AgdaAny) (AgdaAny -> AgdaAny)
                                         AgdaAny AgdaAny
                                         MAlonzo.Code.Algebra.Structures.T_IsKleeneAlgebra_2044
-- Algebra.Bundles.KleeneAlgebra.Carrier
d_Carrier_3030 :: T_KleeneAlgebra_3008 -> ()
d_Carrier_3030 :: T_KleeneAlgebra_3008 -> ()
d_Carrier_3030 = T_KleeneAlgebra_3008 -> ()
forall a. a
erased
-- Algebra.Bundles.KleeneAlgebra._≈_
d__'8776'__3032 :: T_KleeneAlgebra_3008 -> AgdaAny -> AgdaAny -> ()
d__'8776'__3032 :: T_KleeneAlgebra_3008 -> AgdaAny -> AgdaAny -> ()
d__'8776'__3032 = T_KleeneAlgebra_3008 -> AgdaAny -> AgdaAny -> ()
forall a. a
erased
-- Algebra.Bundles.KleeneAlgebra._+_
d__'43'__3034 ::
  T_KleeneAlgebra_3008 -> AgdaAny -> AgdaAny -> AgdaAny
d__'43'__3034 :: T_KleeneAlgebra_3008 -> AgdaAny -> AgdaAny -> AgdaAny
d__'43'__3034 T_KleeneAlgebra_3008
v0
  = case T_KleeneAlgebra_3008 -> T_KleeneAlgebra_3008
forall a b. a -> b
coe T_KleeneAlgebra_3008
v0 of
      C_KleeneAlgebra'46'constructor_54207 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny
v5 AgdaAny
v6 AgdaAny
v7 T_IsKleeneAlgebra_2044
v8 -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v3
      T_KleeneAlgebra_3008
_ -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.KleeneAlgebra._*_
d__'42'__3036 ::
  T_KleeneAlgebra_3008 -> AgdaAny -> AgdaAny -> AgdaAny
d__'42'__3036 :: T_KleeneAlgebra_3008 -> AgdaAny -> AgdaAny -> AgdaAny
d__'42'__3036 T_KleeneAlgebra_3008
v0
  = case T_KleeneAlgebra_3008 -> T_KleeneAlgebra_3008
forall a b. a -> b
coe T_KleeneAlgebra_3008
v0 of
      C_KleeneAlgebra'46'constructor_54207 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny
v5 AgdaAny
v6 AgdaAny
v7 T_IsKleeneAlgebra_2044
v8 -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v4
      T_KleeneAlgebra_3008
_ -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.KleeneAlgebra._⋆
d__'8902'_3038 :: T_KleeneAlgebra_3008 -> AgdaAny -> AgdaAny
d__'8902'_3038 :: T_KleeneAlgebra_3008 -> AgdaAny -> AgdaAny
d__'8902'_3038 T_KleeneAlgebra_3008
v0
  = case T_KleeneAlgebra_3008 -> T_KleeneAlgebra_3008
forall a b. a -> b
coe T_KleeneAlgebra_3008
v0 of
      C_KleeneAlgebra'46'constructor_54207 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny
v5 AgdaAny
v6 AgdaAny
v7 T_IsKleeneAlgebra_2044
v8 -> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v5
      T_KleeneAlgebra_3008
_ -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.KleeneAlgebra.0#
d_0'35'_3040 :: T_KleeneAlgebra_3008 -> AgdaAny
d_0'35'_3040 :: T_KleeneAlgebra_3008 -> AgdaAny
d_0'35'_3040 T_KleeneAlgebra_3008
v0
  = case T_KleeneAlgebra_3008 -> T_KleeneAlgebra_3008
forall a b. a -> b
coe T_KleeneAlgebra_3008
v0 of
      C_KleeneAlgebra'46'constructor_54207 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny
v5 AgdaAny
v6 AgdaAny
v7 T_IsKleeneAlgebra_2044
v8 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v6
      T_KleeneAlgebra_3008
_ -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.KleeneAlgebra.1#
d_1'35'_3042 :: T_KleeneAlgebra_3008 -> AgdaAny
d_1'35'_3042 :: T_KleeneAlgebra_3008 -> AgdaAny
d_1'35'_3042 T_KleeneAlgebra_3008
v0
  = case T_KleeneAlgebra_3008 -> T_KleeneAlgebra_3008
forall a b. a -> b
coe T_KleeneAlgebra_3008
v0 of
      C_KleeneAlgebra'46'constructor_54207 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny
v5 AgdaAny
v6 AgdaAny
v7 T_IsKleeneAlgebra_2044
v8 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v7
      T_KleeneAlgebra_3008
_ -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.KleeneAlgebra.isKleeneAlgebra
d_isKleeneAlgebra_3044 ::
  T_KleeneAlgebra_3008 ->
  MAlonzo.Code.Algebra.Structures.T_IsKleeneAlgebra_2044
d_isKleeneAlgebra_3044 :: T_KleeneAlgebra_3008 -> T_IsKleeneAlgebra_2044
d_isKleeneAlgebra_3044 T_KleeneAlgebra_3008
v0
  = case T_KleeneAlgebra_3008 -> T_KleeneAlgebra_3008
forall a b. a -> b
coe T_KleeneAlgebra_3008
v0 of
      C_KleeneAlgebra'46'constructor_54207 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny
v5 AgdaAny
v6 AgdaAny
v7 T_IsKleeneAlgebra_2044
v8 -> T_IsKleeneAlgebra_2044 -> T_IsKleeneAlgebra_2044
forall a b. a -> b
coe T_IsKleeneAlgebra_2044
v8
      T_KleeneAlgebra_3008
_ -> T_IsKleeneAlgebra_2044
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.KleeneAlgebra._.*-assoc
d_'42''45'assoc_3048 ::
  T_KleeneAlgebra_3008 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'assoc_3048 :: T_KleeneAlgebra_3008 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'assoc_3048 T_KleeneAlgebra_3008
v0
  = (T_IsSemiringWithoutAnnihilatingZero_1468
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsSemiringWithoutAnnihilatingZero_1468
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'42''45'assoc_1492
      ((T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
         ((T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570
MAlonzo.Code.Algebra.Structures.d_isSemiring_1936
            ((T_IsKleeneAlgebra_2044 -> T_IsIdempotentSemiring_1922)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsKleeneAlgebra_2044 -> T_IsIdempotentSemiring_1922
MAlonzo.Code.Algebra.Structures.d_isIdempotentSemiring_2062
               ((T_KleeneAlgebra_3008 -> T_IsKleeneAlgebra_2044)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_KleeneAlgebra_3008 -> T_IsKleeneAlgebra_2044
d_isKleeneAlgebra_3044 (T_KleeneAlgebra_3008 -> AgdaAny
forall a b. a -> b
coe T_KleeneAlgebra_3008
v0)))))
-- Algebra.Bundles.KleeneAlgebra._.*-cong
d_'42''45'cong_3050 ::
  T_KleeneAlgebra_3008 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'cong_3050 :: T_KleeneAlgebra_3008
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'42''45'cong_3050 T_KleeneAlgebra_3008
v0
  = (T_IsSemiringWithoutAnnihilatingZero_1468
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsSemiringWithoutAnnihilatingZero_1468
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'42''45'cong_1490
      ((T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
         ((T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570
MAlonzo.Code.Algebra.Structures.d_isSemiring_1936
            ((T_IsKleeneAlgebra_2044 -> T_IsIdempotentSemiring_1922)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsKleeneAlgebra_2044 -> T_IsIdempotentSemiring_1922
MAlonzo.Code.Algebra.Structures.d_isIdempotentSemiring_2062
               ((T_KleeneAlgebra_3008 -> T_IsKleeneAlgebra_2044)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_KleeneAlgebra_3008 -> T_IsKleeneAlgebra_2044
d_isKleeneAlgebra_3044 (T_KleeneAlgebra_3008 -> AgdaAny
forall a b. a -> b
coe T_KleeneAlgebra_3008
v0)))))
-- Algebra.Bundles.KleeneAlgebra._.∙-congʳ
d_'8729''45'cong'691'_3052 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_KleeneAlgebra_3008 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_3052 :: ()
-> ()
-> T_KleeneAlgebra_3008
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_3052 ~()
v0 ~()
v1 T_KleeneAlgebra_3008
v2
  = T_KleeneAlgebra_3008
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_3052 T_KleeneAlgebra_3008
v2
du_'8729''45'cong'691'_3052 ::
  T_KleeneAlgebra_3008 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_3052 :: T_KleeneAlgebra_3008
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_3052 T_KleeneAlgebra_3008
v0
  = let v1 :: T_IsKleeneAlgebra_2044
v1 = T_KleeneAlgebra_3008 -> T_IsKleeneAlgebra_2044
d_isKleeneAlgebra_3044 (T_KleeneAlgebra_3008 -> T_KleeneAlgebra_3008
forall a b. a -> b
coe T_KleeneAlgebra_3008
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsIdempotentSemiring_1922
v2
             = T_IsKleeneAlgebra_2044 -> T_IsIdempotentSemiring_1922
MAlonzo.Code.Algebra.Structures.d_isIdempotentSemiring_2062
                 (T_IsKleeneAlgebra_2044 -> T_IsKleeneAlgebra_2044
forall a b. a -> b
coe T_IsKleeneAlgebra_2044
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemiring_1570
v3
                = T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570
MAlonzo.Code.Algebra.Structures.d_isSemiring_1936 (T_IsIdempotentSemiring_1922 -> T_IsIdempotentSemiring_1922
forall a b. a -> b
coe T_IsIdempotentSemiring_1922
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsSemiringWithoutAnnihilatingZero_1468
v4
                   = T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                       (T_IsSemiring_1570 -> T_IsSemiring_1570
forall a b. a -> b
coe T_IsSemiring_1570
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: t
v5
                      = (T_IsSemiringWithoutAnnihilatingZero_1468 -> T_IsMonoid_686)
-> AgdaAny -> t
forall a b. a -> b
coe
                          T_IsSemiringWithoutAnnihilatingZero_1468 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.du_'42''45'isMonoid_1550
                          (T_IsSemiringWithoutAnnihilatingZero_1468 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (let v6 :: T_IsSemigroup_472
v6
                         = T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (AgdaAny -> T_IsMonoid_686
forall a b. a -> b
coe AgdaAny
forall a. a
v5) in
                   AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'691'_206
                        ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v6))))))))
-- Algebra.Bundles.KleeneAlgebra._.∙-congˡ
d_'8729''45'cong'737'_3054 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_KleeneAlgebra_3008 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_3054 :: ()
-> ()
-> T_KleeneAlgebra_3008
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_3054 ~()
v0 ~()
v1 T_KleeneAlgebra_3008
v2
  = T_KleeneAlgebra_3008
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_3054 T_KleeneAlgebra_3008
v2
du_'8729''45'cong'737'_3054 ::
  T_KleeneAlgebra_3008 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_3054 :: T_KleeneAlgebra_3008
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_3054 T_KleeneAlgebra_3008
v0
  = let v1 :: T_IsKleeneAlgebra_2044
v1 = T_KleeneAlgebra_3008 -> T_IsKleeneAlgebra_2044
d_isKleeneAlgebra_3044 (T_KleeneAlgebra_3008 -> T_KleeneAlgebra_3008
forall a b. a -> b
coe T_KleeneAlgebra_3008
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsIdempotentSemiring_1922
v2
             = T_IsKleeneAlgebra_2044 -> T_IsIdempotentSemiring_1922
MAlonzo.Code.Algebra.Structures.d_isIdempotentSemiring_2062
                 (T_IsKleeneAlgebra_2044 -> T_IsKleeneAlgebra_2044
forall a b. a -> b
coe T_IsKleeneAlgebra_2044
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemiring_1570
v3
                = T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570
MAlonzo.Code.Algebra.Structures.d_isSemiring_1936 (T_IsIdempotentSemiring_1922 -> T_IsIdempotentSemiring_1922
forall a b. a -> b
coe T_IsIdempotentSemiring_1922
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsSemiringWithoutAnnihilatingZero_1468
v4
                   = T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                       (T_IsSemiring_1570 -> T_IsSemiring_1570
forall a b. a -> b
coe T_IsSemiring_1570
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: t
v5
                      = (T_IsSemiringWithoutAnnihilatingZero_1468 -> T_IsMonoid_686)
-> AgdaAny -> t
forall a b. a -> b
coe
                          T_IsSemiringWithoutAnnihilatingZero_1468 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.du_'42''45'isMonoid_1550
                          (T_IsSemiringWithoutAnnihilatingZero_1468 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (let v6 :: T_IsSemigroup_472
v6
                         = T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (AgdaAny -> T_IsMonoid_686
forall a b. a -> b
coe AgdaAny
forall a. a
v5) in
                   AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'737'_202
                        ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v6))))))))
-- Algebra.Bundles.KleeneAlgebra._.*-identity
d_'42''45'identity_3056 ::
  T_KleeneAlgebra_3008 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'42''45'identity_3056 :: T_KleeneAlgebra_3008 -> T_Σ_14
d_'42''45'identity_3056 T_KleeneAlgebra_3008
v0
  = (T_IsSemiringWithoutAnnihilatingZero_1468 -> T_Σ_14)
-> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsSemiringWithoutAnnihilatingZero_1468 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_'42''45'identity_1494
      ((T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
         ((T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570
MAlonzo.Code.Algebra.Structures.d_isSemiring_1936
            ((T_IsKleeneAlgebra_2044 -> T_IsIdempotentSemiring_1922)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsKleeneAlgebra_2044 -> T_IsIdempotentSemiring_1922
MAlonzo.Code.Algebra.Structures.d_isIdempotentSemiring_2062
               ((T_KleeneAlgebra_3008 -> T_IsKleeneAlgebra_2044)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_KleeneAlgebra_3008 -> T_IsKleeneAlgebra_2044
d_isKleeneAlgebra_3044 (T_KleeneAlgebra_3008 -> AgdaAny
forall a b. a -> b
coe T_KleeneAlgebra_3008
v0)))))
-- Algebra.Bundles.KleeneAlgebra._.identityʳ
d_identity'691'_3058 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_KleeneAlgebra_3008 -> AgdaAny -> AgdaAny
d_identity'691'_3058 :: () -> () -> T_KleeneAlgebra_3008 -> AgdaAny -> AgdaAny
d_identity'691'_3058 ~()
v0 ~()
v1 T_KleeneAlgebra_3008
v2 = T_KleeneAlgebra_3008 -> AgdaAny -> AgdaAny
du_identity'691'_3058 T_KleeneAlgebra_3008
v2
du_identity'691'_3058 :: T_KleeneAlgebra_3008 -> AgdaAny -> AgdaAny
du_identity'691'_3058 :: T_KleeneAlgebra_3008 -> AgdaAny -> AgdaAny
du_identity'691'_3058 T_KleeneAlgebra_3008
v0
  = let v1 :: T_IsKleeneAlgebra_2044
v1 = T_KleeneAlgebra_3008 -> T_IsKleeneAlgebra_2044
d_isKleeneAlgebra_3044 (T_KleeneAlgebra_3008 -> T_KleeneAlgebra_3008
forall a b. a -> b
coe T_KleeneAlgebra_3008
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsIdempotentSemiring_1922
v2
             = T_IsKleeneAlgebra_2044 -> T_IsIdempotentSemiring_1922
MAlonzo.Code.Algebra.Structures.d_isIdempotentSemiring_2062
                 (T_IsKleeneAlgebra_2044 -> T_IsKleeneAlgebra_2044
forall a b. a -> b
coe T_IsKleeneAlgebra_2044
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemiring_1570
v3
                = T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570
MAlonzo.Code.Algebra.Structures.d_isSemiring_1936 (T_IsIdempotentSemiring_1922 -> T_IsIdempotentSemiring_1922
forall a b. a -> b
coe T_IsIdempotentSemiring_1922
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsSemiringWithoutAnnihilatingZero_1468
v4
                   = T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                       (T_IsSemiring_1570 -> T_IsSemiring_1570
forall a b. a -> b
coe T_IsSemiring_1570
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               ((T_IsMonoid_686 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsMonoid_686 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_identity'691'_728
                  ((T_IsSemiringWithoutAnnihilatingZero_1468 -> T_IsMonoid_686)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsSemiringWithoutAnnihilatingZero_1468 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.du_'42''45'isMonoid_1550
                     (T_IsSemiringWithoutAnnihilatingZero_1468 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
v4))))))
-- Algebra.Bundles.KleeneAlgebra._.identityˡ
d_identity'737'_3060 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_KleeneAlgebra_3008 -> AgdaAny -> AgdaAny
d_identity'737'_3060 :: () -> () -> T_KleeneAlgebra_3008 -> AgdaAny -> AgdaAny
d_identity'737'_3060 ~()
v0 ~()
v1 T_KleeneAlgebra_3008
v2 = T_KleeneAlgebra_3008 -> AgdaAny -> AgdaAny
du_identity'737'_3060 T_KleeneAlgebra_3008
v2
du_identity'737'_3060 :: T_KleeneAlgebra_3008 -> AgdaAny -> AgdaAny
du_identity'737'_3060 :: T_KleeneAlgebra_3008 -> AgdaAny -> AgdaAny
du_identity'737'_3060 T_KleeneAlgebra_3008
v0
  = let v1 :: T_IsKleeneAlgebra_2044
v1 = T_KleeneAlgebra_3008 -> T_IsKleeneAlgebra_2044
d_isKleeneAlgebra_3044 (T_KleeneAlgebra_3008 -> T_KleeneAlgebra_3008
forall a b. a -> b
coe T_KleeneAlgebra_3008
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsIdempotentSemiring_1922
v2
             = T_IsKleeneAlgebra_2044 -> T_IsIdempotentSemiring_1922
MAlonzo.Code.Algebra.Structures.d_isIdempotentSemiring_2062
                 (T_IsKleeneAlgebra_2044 -> T_IsKleeneAlgebra_2044
forall a b. a -> b
coe T_IsKleeneAlgebra_2044
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemiring_1570
v3
                = T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570
MAlonzo.Code.Algebra.Structures.d_isSemiring_1936 (T_IsIdempotentSemiring_1922 -> T_IsIdempotentSemiring_1922
forall a b. a -> b
coe T_IsIdempotentSemiring_1922
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsSemiringWithoutAnnihilatingZero_1468
v4
                   = T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                       (T_IsSemiring_1570 -> T_IsSemiring_1570
forall a b. a -> b
coe T_IsSemiring_1570
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               ((T_IsMonoid_686 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsMonoid_686 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_identity'737'_726
                  ((T_IsSemiringWithoutAnnihilatingZero_1468 -> T_IsMonoid_686)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsSemiringWithoutAnnihilatingZero_1468 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.du_'42''45'isMonoid_1550
                     (T_IsSemiringWithoutAnnihilatingZero_1468 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
v4))))))
-- Algebra.Bundles.KleeneAlgebra._.*-isMagma
d_'42''45'isMagma_3062 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_KleeneAlgebra_3008 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_176
d_'42''45'isMagma_3062 :: () -> () -> T_KleeneAlgebra_3008 -> T_IsMagma_176
d_'42''45'isMagma_3062 ~()
v0 ~()
v1 T_KleeneAlgebra_3008
v2 = T_KleeneAlgebra_3008 -> T_IsMagma_176
du_'42''45'isMagma_3062 T_KleeneAlgebra_3008
v2
du_'42''45'isMagma_3062 ::
  T_KleeneAlgebra_3008 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_176
du_'42''45'isMagma_3062 :: T_KleeneAlgebra_3008 -> T_IsMagma_176
du_'42''45'isMagma_3062 T_KleeneAlgebra_3008
v0
  = let v1 :: T_IsKleeneAlgebra_2044
v1 = T_KleeneAlgebra_3008 -> T_IsKleeneAlgebra_2044
d_isKleeneAlgebra_3044 (T_KleeneAlgebra_3008 -> T_KleeneAlgebra_3008
forall a b. a -> b
coe T_KleeneAlgebra_3008
v0) in
    AgdaAny -> T_IsMagma_176
forall a b. a -> b
coe
      (let v2 :: T_IsIdempotentSemiring_1922
v2
             = T_IsKleeneAlgebra_2044 -> T_IsIdempotentSemiring_1922
MAlonzo.Code.Algebra.Structures.d_isIdempotentSemiring_2062
                 (T_IsKleeneAlgebra_2044 -> T_IsKleeneAlgebra_2044
forall a b. a -> b
coe T_IsKleeneAlgebra_2044
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemiring_1570
v3
                = T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570
MAlonzo.Code.Algebra.Structures.d_isSemiring_1936 (T_IsIdempotentSemiring_1922 -> T_IsIdempotentSemiring_1922
forall a b. a -> b
coe T_IsIdempotentSemiring_1922
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsSemiringWithoutAnnihilatingZero_1468 -> T_IsMagma_176)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemiringWithoutAnnihilatingZero_1468 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.du_'42''45'isMagma_1546
               ((T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                  (T_IsSemiring_1570 -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1570
v3)))))
-- Algebra.Bundles.KleeneAlgebra._.*-isMonoid
d_'42''45'isMonoid_3064 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_KleeneAlgebra_3008 ->
  MAlonzo.Code.Algebra.Structures.T_IsMonoid_686
d_'42''45'isMonoid_3064 :: () -> () -> T_KleeneAlgebra_3008 -> T_IsMonoid_686
d_'42''45'isMonoid_3064 ~()
v0 ~()
v1 T_KleeneAlgebra_3008
v2 = T_KleeneAlgebra_3008 -> T_IsMonoid_686
du_'42''45'isMonoid_3064 T_KleeneAlgebra_3008
v2
du_'42''45'isMonoid_3064 ::
  T_KleeneAlgebra_3008 ->
  MAlonzo.Code.Algebra.Structures.T_IsMonoid_686
du_'42''45'isMonoid_3064 :: T_KleeneAlgebra_3008 -> T_IsMonoid_686
du_'42''45'isMonoid_3064 T_KleeneAlgebra_3008
v0
  = let v1 :: T_IsKleeneAlgebra_2044
v1 = T_KleeneAlgebra_3008 -> T_IsKleeneAlgebra_2044
d_isKleeneAlgebra_3044 (T_KleeneAlgebra_3008 -> T_KleeneAlgebra_3008
forall a b. a -> b
coe T_KleeneAlgebra_3008
v0) in
    AgdaAny -> T_IsMonoid_686
forall a b. a -> b
coe
      (let v2 :: T_IsIdempotentSemiring_1922
v2
             = T_IsKleeneAlgebra_2044 -> T_IsIdempotentSemiring_1922
MAlonzo.Code.Algebra.Structures.d_isIdempotentSemiring_2062
                 (T_IsKleeneAlgebra_2044 -> T_IsKleeneAlgebra_2044
forall a b. a -> b
coe T_IsKleeneAlgebra_2044
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemiring_1570
v3
                = T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570
MAlonzo.Code.Algebra.Structures.d_isSemiring_1936 (T_IsIdempotentSemiring_1922 -> T_IsIdempotentSemiring_1922
forall a b. a -> b
coe T_IsIdempotentSemiring_1922
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsSemiringWithoutAnnihilatingZero_1468 -> T_IsMonoid_686)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemiringWithoutAnnihilatingZero_1468 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.du_'42''45'isMonoid_1550
               ((T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                  (T_IsSemiring_1570 -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1570
v3)))))
-- Algebra.Bundles.KleeneAlgebra._.*-isSemigroup
d_'42''45'isSemigroup_3066 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_KleeneAlgebra_3008 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_472
d_'42''45'isSemigroup_3066 :: () -> () -> T_KleeneAlgebra_3008 -> T_IsSemigroup_472
d_'42''45'isSemigroup_3066 ~()
v0 ~()
v1 T_KleeneAlgebra_3008
v2
  = T_KleeneAlgebra_3008 -> T_IsSemigroup_472
du_'42''45'isSemigroup_3066 T_KleeneAlgebra_3008
v2
du_'42''45'isSemigroup_3066 ::
  T_KleeneAlgebra_3008 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_472
du_'42''45'isSemigroup_3066 :: T_KleeneAlgebra_3008 -> T_IsSemigroup_472
du_'42''45'isSemigroup_3066 T_KleeneAlgebra_3008
v0
  = let v1 :: T_IsKleeneAlgebra_2044
v1 = T_KleeneAlgebra_3008 -> T_IsKleeneAlgebra_2044
d_isKleeneAlgebra_3044 (T_KleeneAlgebra_3008 -> T_KleeneAlgebra_3008
forall a b. a -> b
coe T_KleeneAlgebra_3008
v0) in
    AgdaAny -> T_IsSemigroup_472
forall a b. a -> b
coe
      (let v2 :: T_IsIdempotentSemiring_1922
v2
             = T_IsKleeneAlgebra_2044 -> T_IsIdempotentSemiring_1922
MAlonzo.Code.Algebra.Structures.d_isIdempotentSemiring_2062
                 (T_IsKleeneAlgebra_2044 -> T_IsKleeneAlgebra_2044
forall a b. a -> b
coe T_IsKleeneAlgebra_2044
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemiring_1570
v3
                = T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570
MAlonzo.Code.Algebra.Structures.d_isSemiring_1936 (T_IsIdempotentSemiring_1922 -> T_IsIdempotentSemiring_1922
forall a b. a -> b
coe T_IsIdempotentSemiring_1922
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsSemiringWithoutAnnihilatingZero_1468 -> T_IsSemigroup_472)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemiringWithoutAnnihilatingZero_1468 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.du_'42''45'isSemigroup_1548
               ((T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                  (T_IsSemiring_1570 -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1570
v3)))))
-- Algebra.Bundles.KleeneAlgebra._.assoc
d_assoc_3068 ::
  T_KleeneAlgebra_3008 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_3068 :: T_KleeneAlgebra_3008 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_3068 T_KleeneAlgebra_3008
v0
  = (T_IsSemigroup_472 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsSemigroup_472 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_assoc_482
      ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
         ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746
            ((T_IsSemiringWithoutAnnihilatingZero_1468
 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
               ((T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                  ((T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570
MAlonzo.Code.Algebra.Structures.d_isSemiring_1936
                     ((T_IsKleeneAlgebra_2044 -> T_IsIdempotentSemiring_1922)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsKleeneAlgebra_2044 -> T_IsIdempotentSemiring_1922
MAlonzo.Code.Algebra.Structures.d_isIdempotentSemiring_2062
                        ((T_KleeneAlgebra_3008 -> T_IsKleeneAlgebra_2044)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_KleeneAlgebra_3008 -> T_IsKleeneAlgebra_2044
d_isKleeneAlgebra_3044 (T_KleeneAlgebra_3008 -> AgdaAny
forall a b. a -> b
coe T_KleeneAlgebra_3008
v0))))))))
-- Algebra.Bundles.KleeneAlgebra._.comm
d_comm_3070 ::
  T_KleeneAlgebra_3008 -> AgdaAny -> AgdaAny -> AgdaAny
d_comm_3070 :: T_KleeneAlgebra_3008 -> AgdaAny -> AgdaAny -> AgdaAny
d_comm_3070 T_KleeneAlgebra_3008
v0
  = (T_IsCommutativeMonoid_736 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsCommutativeMonoid_736 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_comm_748
      ((T_IsSemiringWithoutAnnihilatingZero_1468
 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
         ((T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
            ((T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570
MAlonzo.Code.Algebra.Structures.d_isSemiring_1936
               ((T_IsKleeneAlgebra_2044 -> T_IsIdempotentSemiring_1922)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsKleeneAlgebra_2044 -> T_IsIdempotentSemiring_1922
MAlonzo.Code.Algebra.Structures.d_isIdempotentSemiring_2062
                  ((T_KleeneAlgebra_3008 -> T_IsKleeneAlgebra_2044)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_KleeneAlgebra_3008 -> T_IsKleeneAlgebra_2044
d_isKleeneAlgebra_3044 (T_KleeneAlgebra_3008 -> AgdaAny
forall a b. a -> b
coe T_KleeneAlgebra_3008
v0))))))
-- Algebra.Bundles.KleeneAlgebra._.∙-cong
d_'8729''45'cong_3072 ::
  T_KleeneAlgebra_3008 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_3072 :: T_KleeneAlgebra_3008
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_3072 T_KleeneAlgebra_3008
v0
  = (T_IsMagma_176
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsMagma_176
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_186
      ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480
         ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
            ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746
               ((T_IsSemiringWithoutAnnihilatingZero_1468
 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
                  ((T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                     ((T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570
MAlonzo.Code.Algebra.Structures.d_isSemiring_1936
                        ((T_IsKleeneAlgebra_2044 -> T_IsIdempotentSemiring_1922)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_IsKleeneAlgebra_2044 -> T_IsIdempotentSemiring_1922
MAlonzo.Code.Algebra.Structures.d_isIdempotentSemiring_2062
                           ((T_KleeneAlgebra_3008 -> T_IsKleeneAlgebra_2044)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_KleeneAlgebra_3008 -> T_IsKleeneAlgebra_2044
d_isKleeneAlgebra_3044 (T_KleeneAlgebra_3008 -> AgdaAny
forall a b. a -> b
coe T_KleeneAlgebra_3008
v0)))))))))
-- Algebra.Bundles.KleeneAlgebra._.∙-congʳ
d_'8729''45'cong'691'_3074 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_KleeneAlgebra_3008 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_3074 :: ()
-> ()
-> T_KleeneAlgebra_3008
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_3074 ~()
v0 ~()
v1 T_KleeneAlgebra_3008
v2
  = T_KleeneAlgebra_3008
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_3074 T_KleeneAlgebra_3008
v2
du_'8729''45'cong'691'_3074 ::
  T_KleeneAlgebra_3008 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_3074 :: T_KleeneAlgebra_3008
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_3074 T_KleeneAlgebra_3008
v0
  = let v1 :: T_IsKleeneAlgebra_2044
v1 = T_KleeneAlgebra_3008 -> T_IsKleeneAlgebra_2044
d_isKleeneAlgebra_3044 (T_KleeneAlgebra_3008 -> T_KleeneAlgebra_3008
forall a b. a -> b
coe T_KleeneAlgebra_3008
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsIdempotentSemiring_1922
v2
             = T_IsKleeneAlgebra_2044 -> T_IsIdempotentSemiring_1922
MAlonzo.Code.Algebra.Structures.d_isIdempotentSemiring_2062
                 (T_IsKleeneAlgebra_2044 -> T_IsKleeneAlgebra_2044
forall a b. a -> b
coe T_IsKleeneAlgebra_2044
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemiring_1570
v3
                = T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570
MAlonzo.Code.Algebra.Structures.d_isSemiring_1936 (T_IsIdempotentSemiring_1922 -> T_IsIdempotentSemiring_1922
forall a b. a -> b
coe T_IsIdempotentSemiring_1922
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsSemiringWithoutAnnihilatingZero_1468
v4
                   = T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                       (T_IsSemiring_1570 -> T_IsSemiring_1570
forall a b. a -> b
coe T_IsSemiring_1570
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsCommutativeMonoid_736
v5
                      = T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
                          (T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsSemiringWithoutAnnihilatingZero_1468
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (let v6 :: T_IsMonoid_686
v6
                         = T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746 (T_IsCommutativeMonoid_736 -> T_IsCommutativeMonoid_736
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v5) in
                   AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     (let v7 :: T_IsSemigroup_472
v7
                            = T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v6) in
                      AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'691'_206
                           ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v7)))))))))
-- Algebra.Bundles.KleeneAlgebra._.∙-congˡ
d_'8729''45'cong'737'_3076 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_KleeneAlgebra_3008 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_3076 :: ()
-> ()
-> T_KleeneAlgebra_3008
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_3076 ~()
v0 ~()
v1 T_KleeneAlgebra_3008
v2
  = T_KleeneAlgebra_3008
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_3076 T_KleeneAlgebra_3008
v2
du_'8729''45'cong'737'_3076 ::
  T_KleeneAlgebra_3008 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_3076 :: T_KleeneAlgebra_3008
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_3076 T_KleeneAlgebra_3008
v0
  = let v1 :: T_IsKleeneAlgebra_2044
v1 = T_KleeneAlgebra_3008 -> T_IsKleeneAlgebra_2044
d_isKleeneAlgebra_3044 (T_KleeneAlgebra_3008 -> T_KleeneAlgebra_3008
forall a b. a -> b
coe T_KleeneAlgebra_3008
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsIdempotentSemiring_1922
v2
             = T_IsKleeneAlgebra_2044 -> T_IsIdempotentSemiring_1922
MAlonzo.Code.Algebra.Structures.d_isIdempotentSemiring_2062
                 (T_IsKleeneAlgebra_2044 -> T_IsKleeneAlgebra_2044
forall a b. a -> b
coe T_IsKleeneAlgebra_2044
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemiring_1570
v3
                = T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570
MAlonzo.Code.Algebra.Structures.d_isSemiring_1936 (T_IsIdempotentSemiring_1922 -> T_IsIdempotentSemiring_1922
forall a b. a -> b
coe T_IsIdempotentSemiring_1922
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsSemiringWithoutAnnihilatingZero_1468
v4
                   = T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                       (T_IsSemiring_1570 -> T_IsSemiring_1570
forall a b. a -> b
coe T_IsSemiring_1570
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsCommutativeMonoid_736
v5
                      = T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
                          (T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsSemiringWithoutAnnihilatingZero_1468
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (let v6 :: T_IsMonoid_686
v6
                         = T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746 (T_IsCommutativeMonoid_736 -> T_IsCommutativeMonoid_736
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v5) in
                   AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     (let v7 :: T_IsSemigroup_472
v7
                            = T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v6) in
                      AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'737'_202
                           ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v7)))))))))
-- Algebra.Bundles.KleeneAlgebra._.+-idem
d_'43''45'idem_3078 :: T_KleeneAlgebra_3008 -> AgdaAny -> AgdaAny
d_'43''45'idem_3078 :: T_KleeneAlgebra_3008 -> AgdaAny -> AgdaAny
d_'43''45'idem_3078 T_KleeneAlgebra_3008
v0
  = (T_IsIdempotentSemiring_1922 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsIdempotentSemiring_1922 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'43''45'idem_1938
      ((T_IsKleeneAlgebra_2044 -> T_IsIdempotentSemiring_1922)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsKleeneAlgebra_2044 -> T_IsIdempotentSemiring_1922
MAlonzo.Code.Algebra.Structures.d_isIdempotentSemiring_2062
         ((T_KleeneAlgebra_3008 -> T_IsKleeneAlgebra_2044)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_KleeneAlgebra_3008 -> T_IsKleeneAlgebra_2044
d_isKleeneAlgebra_3044 (T_KleeneAlgebra_3008 -> AgdaAny
forall a b. a -> b
coe T_KleeneAlgebra_3008
v0)))
-- Algebra.Bundles.KleeneAlgebra._.identity
d_identity_3080 ::
  T_KleeneAlgebra_3008 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_identity_3080 :: T_KleeneAlgebra_3008 -> T_Σ_14
d_identity_3080 T_KleeneAlgebra_3008
v0
  = (T_IsMonoid_686 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsMonoid_686 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_identity_698
      ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746
         ((T_IsSemiringWithoutAnnihilatingZero_1468
 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
            ((T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
               ((T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570
MAlonzo.Code.Algebra.Structures.d_isSemiring_1936
                  ((T_IsKleeneAlgebra_2044 -> T_IsIdempotentSemiring_1922)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsKleeneAlgebra_2044 -> T_IsIdempotentSemiring_1922
MAlonzo.Code.Algebra.Structures.d_isIdempotentSemiring_2062
                     ((T_KleeneAlgebra_3008 -> T_IsKleeneAlgebra_2044)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_KleeneAlgebra_3008 -> T_IsKleeneAlgebra_2044
d_isKleeneAlgebra_3044 (T_KleeneAlgebra_3008 -> AgdaAny
forall a b. a -> b
coe T_KleeneAlgebra_3008
v0)))))))
-- Algebra.Bundles.KleeneAlgebra._.identityʳ
d_identity'691'_3082 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_KleeneAlgebra_3008 -> AgdaAny -> AgdaAny
d_identity'691'_3082 :: () -> () -> T_KleeneAlgebra_3008 -> AgdaAny -> AgdaAny
d_identity'691'_3082 ~()
v0 ~()
v1 T_KleeneAlgebra_3008
v2 = T_KleeneAlgebra_3008 -> AgdaAny -> AgdaAny
du_identity'691'_3082 T_KleeneAlgebra_3008
v2
du_identity'691'_3082 :: T_KleeneAlgebra_3008 -> AgdaAny -> AgdaAny
du_identity'691'_3082 :: T_KleeneAlgebra_3008 -> AgdaAny -> AgdaAny
du_identity'691'_3082 T_KleeneAlgebra_3008
v0
  = let v1 :: T_IsKleeneAlgebra_2044
v1 = T_KleeneAlgebra_3008 -> T_IsKleeneAlgebra_2044
d_isKleeneAlgebra_3044 (T_KleeneAlgebra_3008 -> T_KleeneAlgebra_3008
forall a b. a -> b
coe T_KleeneAlgebra_3008
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsIdempotentSemiring_1922
v2
             = T_IsKleeneAlgebra_2044 -> T_IsIdempotentSemiring_1922
MAlonzo.Code.Algebra.Structures.d_isIdempotentSemiring_2062
                 (T_IsKleeneAlgebra_2044 -> T_IsKleeneAlgebra_2044
forall a b. a -> b
coe T_IsKleeneAlgebra_2044
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemiring_1570
v3
                = T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570
MAlonzo.Code.Algebra.Structures.d_isSemiring_1936 (T_IsIdempotentSemiring_1922 -> T_IsIdempotentSemiring_1922
forall a b. a -> b
coe T_IsIdempotentSemiring_1922
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsSemiringWithoutAnnihilatingZero_1468
v4
                   = T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                       (T_IsSemiring_1570 -> T_IsSemiring_1570
forall a b. a -> b
coe T_IsSemiring_1570
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsCommutativeMonoid_736
v5
                      = T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
                          (T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsSemiringWithoutAnnihilatingZero_1468
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  ((T_IsMonoid_686 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsMonoid_686 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_identity'691'_728
                     ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746 (T_IsCommutativeMonoid_736 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v5)))))))
-- Algebra.Bundles.KleeneAlgebra._.identityˡ
d_identity'737'_3084 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_KleeneAlgebra_3008 -> AgdaAny -> AgdaAny
d_identity'737'_3084 :: () -> () -> T_KleeneAlgebra_3008 -> AgdaAny -> AgdaAny
d_identity'737'_3084 ~()
v0 ~()
v1 T_KleeneAlgebra_3008
v2 = T_KleeneAlgebra_3008 -> AgdaAny -> AgdaAny
du_identity'737'_3084 T_KleeneAlgebra_3008
v2
du_identity'737'_3084 :: T_KleeneAlgebra_3008 -> AgdaAny -> AgdaAny
du_identity'737'_3084 :: T_KleeneAlgebra_3008 -> AgdaAny -> AgdaAny
du_identity'737'_3084 T_KleeneAlgebra_3008
v0
  = let v1 :: T_IsKleeneAlgebra_2044
v1 = T_KleeneAlgebra_3008 -> T_IsKleeneAlgebra_2044
d_isKleeneAlgebra_3044 (T_KleeneAlgebra_3008 -> T_KleeneAlgebra_3008
forall a b. a -> b
coe T_KleeneAlgebra_3008
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsIdempotentSemiring_1922
v2
             = T_IsKleeneAlgebra_2044 -> T_IsIdempotentSemiring_1922
MAlonzo.Code.Algebra.Structures.d_isIdempotentSemiring_2062
                 (T_IsKleeneAlgebra_2044 -> T_IsKleeneAlgebra_2044
forall a b. a -> b
coe T_IsKleeneAlgebra_2044
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemiring_1570
v3
                = T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570
MAlonzo.Code.Algebra.Structures.d_isSemiring_1936 (T_IsIdempotentSemiring_1922 -> T_IsIdempotentSemiring_1922
forall a b. a -> b
coe T_IsIdempotentSemiring_1922
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsSemiringWithoutAnnihilatingZero_1468
v4
                   = T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                       (T_IsSemiring_1570 -> T_IsSemiring_1570
forall a b. a -> b
coe T_IsSemiring_1570
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsCommutativeMonoid_736
v5
                      = T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
                          (T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsSemiringWithoutAnnihilatingZero_1468
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  ((T_IsMonoid_686 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsMonoid_686 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_identity'737'_726
                     ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746 (T_IsCommutativeMonoid_736 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v5)))))))
-- Algebra.Bundles.KleeneAlgebra._.isBand
d_isBand_3086 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_KleeneAlgebra_3008 ->
  MAlonzo.Code.Algebra.Structures.T_IsBand_508
d_isBand_3086 :: () -> () -> T_KleeneAlgebra_3008 -> T_IsBand_508
d_isBand_3086 ~()
v0 ~()
v1 T_KleeneAlgebra_3008
v2 = T_KleeneAlgebra_3008 -> T_IsBand_508
du_isBand_3086 T_KleeneAlgebra_3008
v2
du_isBand_3086 ::
  T_KleeneAlgebra_3008 ->
  MAlonzo.Code.Algebra.Structures.T_IsBand_508
du_isBand_3086 :: T_KleeneAlgebra_3008 -> T_IsBand_508
du_isBand_3086 T_KleeneAlgebra_3008
v0
  = let v1 :: T_IsKleeneAlgebra_2044
v1 = T_KleeneAlgebra_3008 -> T_IsKleeneAlgebra_2044
d_isKleeneAlgebra_3044 (T_KleeneAlgebra_3008 -> T_KleeneAlgebra_3008
forall a b. a -> b
coe T_KleeneAlgebra_3008
v0) in
    AgdaAny -> T_IsBand_508
forall a b. a -> b
coe
      (let v2 :: T_IsIdempotentSemiring_1922
v2
             = T_IsKleeneAlgebra_2044 -> T_IsIdempotentSemiring_1922
MAlonzo.Code.Algebra.Structures.d_isIdempotentSemiring_2062
                 (T_IsKleeneAlgebra_2044 -> T_IsKleeneAlgebra_2044
forall a b. a -> b
coe T_IsKleeneAlgebra_2044
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: t
v3
                = (T_IsIdempotentSemiring_1922
 -> T_IsIdempotentCommutativeMonoid_852)
-> AgdaAny -> t
forall a b. a -> b
coe
                    T_IsIdempotentSemiring_1922 -> T_IsIdempotentCommutativeMonoid_852
MAlonzo.Code.Algebra.Structures.du_'43''45'isIdempotentCommutativeMonoid_2024
                    (T_IsIdempotentSemiring_1922 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentSemiring_1922
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsIdempotentMonoid_796 -> T_IsBand_508) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsIdempotentMonoid_796 -> T_IsBand_508
MAlonzo.Code.Algebra.Structures.du_isBand_846
               ((T_IsIdempotentCommutativeMonoid_852 -> T_IsIdempotentMonoid_796)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsIdempotentCommutativeMonoid_852 -> T_IsIdempotentMonoid_796
MAlonzo.Code.Algebra.Structures.du_isIdempotentMonoid_910
                  (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3)))))
-- Algebra.Bundles.KleeneAlgebra._.isCommutativeBand
d_isCommutativeBand_3088 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_KleeneAlgebra_3008 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_590
d_isCommutativeBand_3088 :: () -> () -> T_KleeneAlgebra_3008 -> T_IsCommutativeBand_590
d_isCommutativeBand_3088 ~()
v0 ~()
v1 T_KleeneAlgebra_3008
v2 = T_KleeneAlgebra_3008 -> T_IsCommutativeBand_590
du_isCommutativeBand_3088 T_KleeneAlgebra_3008
v2
du_isCommutativeBand_3088 ::
  T_KleeneAlgebra_3008 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_590
du_isCommutativeBand_3088 :: T_KleeneAlgebra_3008 -> T_IsCommutativeBand_590
du_isCommutativeBand_3088 T_KleeneAlgebra_3008
v0
  = let v1 :: T_IsKleeneAlgebra_2044
v1 = T_KleeneAlgebra_3008 -> T_IsKleeneAlgebra_2044
d_isKleeneAlgebra_3044 (T_KleeneAlgebra_3008 -> T_KleeneAlgebra_3008
forall a b. a -> b
coe T_KleeneAlgebra_3008
v0) in
    AgdaAny -> T_IsCommutativeBand_590
forall a b. a -> b
coe
      (let v2 :: T_IsIdempotentSemiring_1922
v2
             = T_IsKleeneAlgebra_2044 -> T_IsIdempotentSemiring_1922
MAlonzo.Code.Algebra.Structures.d_isIdempotentSemiring_2062
                 (T_IsKleeneAlgebra_2044 -> T_IsKleeneAlgebra_2044
forall a b. a -> b
coe T_IsKleeneAlgebra_2044
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeBand_590)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsIdempotentCommutativeMonoid_852 -> T_IsCommutativeBand_590
MAlonzo.Code.Algebra.Structures.du_isCommutativeBand_916
            ((T_IsIdempotentSemiring_1922
 -> T_IsIdempotentCommutativeMonoid_852)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsIdempotentSemiring_1922 -> T_IsIdempotentCommutativeMonoid_852
MAlonzo.Code.Algebra.Structures.du_'43''45'isIdempotentCommutativeMonoid_2024
               (T_IsIdempotentSemiring_1922 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentSemiring_1922
v2))))
-- Algebra.Bundles.KleeneAlgebra._.isCommutativeMagma
d_isCommutativeMagma_3090 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_KleeneAlgebra_3008 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMagma_212
d_isCommutativeMagma_3090 :: () -> () -> T_KleeneAlgebra_3008 -> T_IsCommutativeMagma_212
d_isCommutativeMagma_3090 ~()
v0 ~()
v1 T_KleeneAlgebra_3008
v2
  = T_KleeneAlgebra_3008 -> T_IsCommutativeMagma_212
du_isCommutativeMagma_3090 T_KleeneAlgebra_3008
v2
du_isCommutativeMagma_3090 ::
  T_KleeneAlgebra_3008 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMagma_212
du_isCommutativeMagma_3090 :: T_KleeneAlgebra_3008 -> T_IsCommutativeMagma_212
du_isCommutativeMagma_3090 T_KleeneAlgebra_3008
v0
  = let v1 :: T_IsKleeneAlgebra_2044
v1 = T_KleeneAlgebra_3008 -> T_IsKleeneAlgebra_2044
d_isKleeneAlgebra_3044 (T_KleeneAlgebra_3008 -> T_KleeneAlgebra_3008
forall a b. a -> b
coe T_KleeneAlgebra_3008
v0) in
    AgdaAny -> T_IsCommutativeMagma_212
forall a b. a -> b
coe
      (let v2 :: T_IsIdempotentSemiring_1922
v2
             = T_IsKleeneAlgebra_2044 -> T_IsIdempotentSemiring_1922
MAlonzo.Code.Algebra.Structures.d_isIdempotentSemiring_2062
                 (T_IsKleeneAlgebra_2044 -> T_IsKleeneAlgebra_2044
forall a b. a -> b
coe T_IsKleeneAlgebra_2044
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemiring_1570
v3
                = T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570
MAlonzo.Code.Algebra.Structures.d_isSemiring_1936 (T_IsIdempotentSemiring_1922 -> T_IsIdempotentSemiring_1922
forall a b. a -> b
coe T_IsIdempotentSemiring_1922
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsSemiringWithoutAnnihilatingZero_1468
v4
                   = T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                       (T_IsSemiring_1570 -> T_IsSemiring_1570
forall a b. a -> b
coe T_IsSemiring_1570
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsCommutativeMonoid_736
v5
                      = T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
                          (T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsSemiringWithoutAnnihilatingZero_1468
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  ((T_IsCommutativeSemigroup_548 -> T_IsCommutativeMagma_212)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsCommutativeSemigroup_548 -> T_IsCommutativeMagma_212
MAlonzo.Code.Algebra.Structures.du_isCommutativeMagma_586
                     ((T_IsCommutativeMonoid_736 -> T_IsCommutativeSemigroup_548)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsCommutativeMonoid_736 -> T_IsCommutativeSemigroup_548
MAlonzo.Code.Algebra.Structures.du_isCommutativeSemigroup_786
                        (T_IsCommutativeMonoid_736 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v5)))))))
-- Algebra.Bundles.KleeneAlgebra._.+-isCommutativeMonoid
d_'43''45'isCommutativeMonoid_3092 ::
  T_KleeneAlgebra_3008 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_3092 :: T_KleeneAlgebra_3008 -> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_3092 T_KleeneAlgebra_3008
v0
  = (T_IsSemiringWithoutAnnihilatingZero_1468
 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> T_IsCommutativeMonoid_736
forall a b. a -> b
coe
      T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
      ((T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
         ((T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570
MAlonzo.Code.Algebra.Structures.d_isSemiring_1936
            ((T_IsKleeneAlgebra_2044 -> T_IsIdempotentSemiring_1922)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsKleeneAlgebra_2044 -> T_IsIdempotentSemiring_1922
MAlonzo.Code.Algebra.Structures.d_isIdempotentSemiring_2062
               ((T_KleeneAlgebra_3008 -> T_IsKleeneAlgebra_2044)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_KleeneAlgebra_3008 -> T_IsKleeneAlgebra_2044
d_isKleeneAlgebra_3044 (T_KleeneAlgebra_3008 -> AgdaAny
forall a b. a -> b
coe T_KleeneAlgebra_3008
v0)))))
-- Algebra.Bundles.KleeneAlgebra._.isCommutativeSemigroup
d_isCommutativeSemigroup_3094 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_KleeneAlgebra_3008 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_548
d_isCommutativeSemigroup_3094 :: () -> () -> T_KleeneAlgebra_3008 -> T_IsCommutativeSemigroup_548
d_isCommutativeSemigroup_3094 ~()
v0 ~()
v1 T_KleeneAlgebra_3008
v2
  = T_KleeneAlgebra_3008 -> T_IsCommutativeSemigroup_548
du_isCommutativeSemigroup_3094 T_KleeneAlgebra_3008
v2
du_isCommutativeSemigroup_3094 ::
  T_KleeneAlgebra_3008 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_548
du_isCommutativeSemigroup_3094 :: T_KleeneAlgebra_3008 -> T_IsCommutativeSemigroup_548
du_isCommutativeSemigroup_3094 T_KleeneAlgebra_3008
v0
  = let v1 :: T_IsKleeneAlgebra_2044
v1 = T_KleeneAlgebra_3008 -> T_IsKleeneAlgebra_2044
d_isKleeneAlgebra_3044 (T_KleeneAlgebra_3008 -> T_KleeneAlgebra_3008
forall a b. a -> b
coe T_KleeneAlgebra_3008
v0) in
    AgdaAny -> T_IsCommutativeSemigroup_548
forall a b. a -> b
coe
      (let v2 :: T_IsIdempotentSemiring_1922
v2
             = T_IsKleeneAlgebra_2044 -> T_IsIdempotentSemiring_1922
MAlonzo.Code.Algebra.Structures.d_isIdempotentSemiring_2062
                 (T_IsKleeneAlgebra_2044 -> T_IsKleeneAlgebra_2044
forall a b. a -> b
coe T_IsKleeneAlgebra_2044
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemiring_1570
v3
                = T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570
MAlonzo.Code.Algebra.Structures.d_isSemiring_1936 (T_IsIdempotentSemiring_1922 -> T_IsIdempotentSemiring_1922
forall a b. a -> b
coe T_IsIdempotentSemiring_1922
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsSemiringWithoutAnnihilatingZero_1468
v4
                   = T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                       (T_IsSemiring_1570 -> T_IsSemiring_1570
forall a b. a -> b
coe T_IsSemiring_1570
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               ((T_IsCommutativeMonoid_736 -> T_IsCommutativeSemigroup_548)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsCommutativeMonoid_736 -> T_IsCommutativeSemigroup_548
MAlonzo.Code.Algebra.Structures.du_isCommutativeSemigroup_786
                  ((T_IsSemiringWithoutAnnihilatingZero_1468
 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
                     (T_IsSemiringWithoutAnnihilatingZero_1468 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
v4))))))
-- Algebra.Bundles.KleeneAlgebra._.+-isIdempotentCommutativeMonoid
d_'43''45'isIdempotentCommutativeMonoid_3096 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_KleeneAlgebra_3008 ->
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_852
d_'43''45'isIdempotentCommutativeMonoid_3096 :: ()
-> ()
-> T_KleeneAlgebra_3008
-> T_IsIdempotentCommutativeMonoid_852
d_'43''45'isIdempotentCommutativeMonoid_3096 ~()
v0 ~()
v1 T_KleeneAlgebra_3008
v2
  = T_KleeneAlgebra_3008 -> T_IsIdempotentCommutativeMonoid_852
du_'43''45'isIdempotentCommutativeMonoid_3096 T_KleeneAlgebra_3008
v2
du_'43''45'isIdempotentCommutativeMonoid_3096 ::
  T_KleeneAlgebra_3008 ->
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_852
du_'43''45'isIdempotentCommutativeMonoid_3096 :: T_KleeneAlgebra_3008 -> T_IsIdempotentCommutativeMonoid_852
du_'43''45'isIdempotentCommutativeMonoid_3096 T_KleeneAlgebra_3008
v0
  = let v1 :: T_IsKleeneAlgebra_2044
v1 = T_KleeneAlgebra_3008 -> T_IsKleeneAlgebra_2044
d_isKleeneAlgebra_3044 (T_KleeneAlgebra_3008 -> T_KleeneAlgebra_3008
forall a b. a -> b
coe T_KleeneAlgebra_3008
v0) in
    AgdaAny -> T_IsIdempotentCommutativeMonoid_852
forall a b. a -> b
coe
      ((T_IsIdempotentSemiring_1922
 -> T_IsIdempotentCommutativeMonoid_852)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsIdempotentSemiring_1922 -> T_IsIdempotentCommutativeMonoid_852
MAlonzo.Code.Algebra.Structures.du_'43''45'isIdempotentCommutativeMonoid_2024
         ((T_IsKleeneAlgebra_2044 -> T_IsIdempotentSemiring_1922)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsKleeneAlgebra_2044 -> T_IsIdempotentSemiring_1922
MAlonzo.Code.Algebra.Structures.d_isIdempotentSemiring_2062
            (T_IsKleeneAlgebra_2044 -> AgdaAny
forall a b. a -> b
coe T_IsKleeneAlgebra_2044
v1)))
-- Algebra.Bundles.KleeneAlgebra._.isIdempotentMonoid
d_isIdempotentMonoid_3098 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_KleeneAlgebra_3008 ->
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentMonoid_796
d_isIdempotentMonoid_3098 :: () -> () -> T_KleeneAlgebra_3008 -> T_IsIdempotentMonoid_796
d_isIdempotentMonoid_3098 ~()
v0 ~()
v1 T_KleeneAlgebra_3008
v2
  = T_KleeneAlgebra_3008 -> T_IsIdempotentMonoid_796
du_isIdempotentMonoid_3098 T_KleeneAlgebra_3008
v2
du_isIdempotentMonoid_3098 ::
  T_KleeneAlgebra_3008 ->
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentMonoid_796
du_isIdempotentMonoid_3098 :: T_KleeneAlgebra_3008 -> T_IsIdempotentMonoid_796
du_isIdempotentMonoid_3098 T_KleeneAlgebra_3008
v0
  = let v1 :: T_IsKleeneAlgebra_2044
v1 = T_KleeneAlgebra_3008 -> T_IsKleeneAlgebra_2044
d_isKleeneAlgebra_3044 (T_KleeneAlgebra_3008 -> T_KleeneAlgebra_3008
forall a b. a -> b
coe T_KleeneAlgebra_3008
v0) in
    AgdaAny -> T_IsIdempotentMonoid_796
forall a b. a -> b
coe
      (let v2 :: T_IsIdempotentSemiring_1922
v2
             = T_IsKleeneAlgebra_2044 -> T_IsIdempotentSemiring_1922
MAlonzo.Code.Algebra.Structures.d_isIdempotentSemiring_2062
                 (T_IsKleeneAlgebra_2044 -> T_IsKleeneAlgebra_2044
forall a b. a -> b
coe T_IsKleeneAlgebra_2044
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsIdempotentCommutativeMonoid_852 -> T_IsIdempotentMonoid_796)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsIdempotentCommutativeMonoid_852 -> T_IsIdempotentMonoid_796
MAlonzo.Code.Algebra.Structures.du_isIdempotentMonoid_910
            ((T_IsIdempotentSemiring_1922
 -> T_IsIdempotentCommutativeMonoid_852)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsIdempotentSemiring_1922 -> T_IsIdempotentCommutativeMonoid_852
MAlonzo.Code.Algebra.Structures.du_'43''45'isIdempotentCommutativeMonoid_2024
               (T_IsIdempotentSemiring_1922 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentSemiring_1922
v2))))
-- Algebra.Bundles.KleeneAlgebra._.isMagma
d_isMagma_3100 ::
  T_KleeneAlgebra_3008 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_176
d_isMagma_3100 :: T_KleeneAlgebra_3008 -> T_IsMagma_176
d_isMagma_3100 T_KleeneAlgebra_3008
v0
  = (T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> T_IsMagma_176
forall a b. a -> b
coe
      T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480
      ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
         ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746
            ((T_IsSemiringWithoutAnnihilatingZero_1468
 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
               ((T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                  ((T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570
MAlonzo.Code.Algebra.Structures.d_isSemiring_1936
                     ((T_IsKleeneAlgebra_2044 -> T_IsIdempotentSemiring_1922)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsKleeneAlgebra_2044 -> T_IsIdempotentSemiring_1922
MAlonzo.Code.Algebra.Structures.d_isIdempotentSemiring_2062
                        ((T_KleeneAlgebra_3008 -> T_IsKleeneAlgebra_2044)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_KleeneAlgebra_3008 -> T_IsKleeneAlgebra_2044
d_isKleeneAlgebra_3044 (T_KleeneAlgebra_3008 -> AgdaAny
forall a b. a -> b
coe T_KleeneAlgebra_3008
v0))))))))
-- Algebra.Bundles.KleeneAlgebra._.isMonoid
d_isMonoid_3102 ::
  T_KleeneAlgebra_3008 ->
  MAlonzo.Code.Algebra.Structures.T_IsMonoid_686
d_isMonoid_3102 :: T_KleeneAlgebra_3008 -> T_IsMonoid_686
d_isMonoid_3102 T_KleeneAlgebra_3008
v0
  = (T_IsCommutativeMonoid_736 -> T_IsMonoid_686)
-> AgdaAny -> T_IsMonoid_686
forall a b. a -> b
coe
      T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746
      ((T_IsSemiringWithoutAnnihilatingZero_1468
 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
         ((T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
            ((T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570
MAlonzo.Code.Algebra.Structures.d_isSemiring_1936
               ((T_IsKleeneAlgebra_2044 -> T_IsIdempotentSemiring_1922)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsKleeneAlgebra_2044 -> T_IsIdempotentSemiring_1922
MAlonzo.Code.Algebra.Structures.d_isIdempotentSemiring_2062
                  ((T_KleeneAlgebra_3008 -> T_IsKleeneAlgebra_2044)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_KleeneAlgebra_3008 -> T_IsKleeneAlgebra_2044
d_isKleeneAlgebra_3044 (T_KleeneAlgebra_3008 -> AgdaAny
forall a b. a -> b
coe T_KleeneAlgebra_3008
v0))))))
-- Algebra.Bundles.KleeneAlgebra._.isSemigroup
d_isSemigroup_3104 ::
  T_KleeneAlgebra_3008 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_472
d_isSemigroup_3104 :: T_KleeneAlgebra_3008 -> T_IsSemigroup_472
d_isSemigroup_3104 T_KleeneAlgebra_3008
v0
  = (T_IsMonoid_686 -> T_IsSemigroup_472)
-> AgdaAny -> T_IsSemigroup_472
forall a b. a -> b
coe
      T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
      ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746
         ((T_IsSemiringWithoutAnnihilatingZero_1468
 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
            ((T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
               ((T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570
MAlonzo.Code.Algebra.Structures.d_isSemiring_1936
                  ((T_IsKleeneAlgebra_2044 -> T_IsIdempotentSemiring_1922)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsKleeneAlgebra_2044 -> T_IsIdempotentSemiring_1922
MAlonzo.Code.Algebra.Structures.d_isIdempotentSemiring_2062
                     ((T_KleeneAlgebra_3008 -> T_IsKleeneAlgebra_2044)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_KleeneAlgebra_3008 -> T_IsKleeneAlgebra_2044
d_isKleeneAlgebra_3044 (T_KleeneAlgebra_3008 -> AgdaAny
forall a b. a -> b
coe T_KleeneAlgebra_3008
v0)))))))
-- Algebra.Bundles.KleeneAlgebra._.isUnitalMagma
d_isUnitalMagma_3106 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_KleeneAlgebra_3008 ->
  MAlonzo.Code.Algebra.Structures.T_IsUnitalMagma_642
d_isUnitalMagma_3106 :: () -> () -> T_KleeneAlgebra_3008 -> T_IsUnitalMagma_642
d_isUnitalMagma_3106 ~()
v0 ~()
v1 T_KleeneAlgebra_3008
v2 = T_KleeneAlgebra_3008 -> T_IsUnitalMagma_642
du_isUnitalMagma_3106 T_KleeneAlgebra_3008
v2
du_isUnitalMagma_3106 ::
  T_KleeneAlgebra_3008 ->
  MAlonzo.Code.Algebra.Structures.T_IsUnitalMagma_642
du_isUnitalMagma_3106 :: T_KleeneAlgebra_3008 -> T_IsUnitalMagma_642
du_isUnitalMagma_3106 T_KleeneAlgebra_3008
v0
  = let v1 :: T_IsKleeneAlgebra_2044
v1 = T_KleeneAlgebra_3008 -> T_IsKleeneAlgebra_2044
d_isKleeneAlgebra_3044 (T_KleeneAlgebra_3008 -> T_KleeneAlgebra_3008
forall a b. a -> b
coe T_KleeneAlgebra_3008
v0) in
    AgdaAny -> T_IsUnitalMagma_642
forall a b. a -> b
coe
      (let v2 :: T_IsIdempotentSemiring_1922
v2
             = T_IsKleeneAlgebra_2044 -> T_IsIdempotentSemiring_1922
MAlonzo.Code.Algebra.Structures.d_isIdempotentSemiring_2062
                 (T_IsKleeneAlgebra_2044 -> T_IsKleeneAlgebra_2044
forall a b. a -> b
coe T_IsKleeneAlgebra_2044
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemiring_1570
v3
                = T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570
MAlonzo.Code.Algebra.Structures.d_isSemiring_1936 (T_IsIdempotentSemiring_1922 -> T_IsIdempotentSemiring_1922
forall a b. a -> b
coe T_IsIdempotentSemiring_1922
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsSemiringWithoutAnnihilatingZero_1468
v4
                   = T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                       (T_IsSemiring_1570 -> T_IsSemiring_1570
forall a b. a -> b
coe T_IsSemiring_1570
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsCommutativeMonoid_736
v5
                      = T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
                          (T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsSemiringWithoutAnnihilatingZero_1468
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  ((T_IsMonoid_686 -> T_IsUnitalMagma_642) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsMonoid_686 -> T_IsUnitalMagma_642
MAlonzo.Code.Algebra.Structures.du_isUnitalMagma_730
                     ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746 (T_IsCommutativeMonoid_736 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v5)))))))
-- Algebra.Bundles.KleeneAlgebra._.distrib
d_distrib_3108 ::
  T_KleeneAlgebra_3008 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_distrib_3108 :: T_KleeneAlgebra_3008 -> T_Σ_14
d_distrib_3108 T_KleeneAlgebra_3008
v0
  = (T_IsSemiringWithoutAnnihilatingZero_1468 -> T_Σ_14)
-> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsSemiringWithoutAnnihilatingZero_1468 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_distrib_1496
      ((T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
         ((T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570
MAlonzo.Code.Algebra.Structures.d_isSemiring_1936
            ((T_IsKleeneAlgebra_2044 -> T_IsIdempotentSemiring_1922)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsKleeneAlgebra_2044 -> T_IsIdempotentSemiring_1922
MAlonzo.Code.Algebra.Structures.d_isIdempotentSemiring_2062
               ((T_KleeneAlgebra_3008 -> T_IsKleeneAlgebra_2044)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_KleeneAlgebra_3008 -> T_IsKleeneAlgebra_2044
d_isKleeneAlgebra_3044 (T_KleeneAlgebra_3008 -> AgdaAny
forall a b. a -> b
coe T_KleeneAlgebra_3008
v0)))))
-- Algebra.Bundles.KleeneAlgebra._.distribʳ
d_distrib'691'_3110 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_KleeneAlgebra_3008 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_distrib'691'_3110 :: ()
-> ()
-> T_KleeneAlgebra_3008
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_distrib'691'_3110 ~()
v0 ~()
v1 T_KleeneAlgebra_3008
v2 = T_KleeneAlgebra_3008 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'691'_3110 T_KleeneAlgebra_3008
v2
du_distrib'691'_3110 ::
  T_KleeneAlgebra_3008 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'691'_3110 :: T_KleeneAlgebra_3008 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'691'_3110 T_KleeneAlgebra_3008
v0
  = let v1 :: T_IsKleeneAlgebra_2044
v1 = T_KleeneAlgebra_3008 -> T_IsKleeneAlgebra_2044
d_isKleeneAlgebra_3044 (T_KleeneAlgebra_3008 -> T_KleeneAlgebra_3008
forall a b. a -> b
coe T_KleeneAlgebra_3008
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsIdempotentSemiring_1922
v2
             = T_IsKleeneAlgebra_2044 -> T_IsIdempotentSemiring_1922
MAlonzo.Code.Algebra.Structures.d_isIdempotentSemiring_2062
                 (T_IsKleeneAlgebra_2044 -> T_IsKleeneAlgebra_2044
forall a b. a -> b
coe T_IsKleeneAlgebra_2044
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemiring_1570
v3
                = T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570
MAlonzo.Code.Algebra.Structures.d_isSemiring_1936 (T_IsIdempotentSemiring_1922 -> T_IsIdempotentSemiring_1922
forall a b. a -> b
coe T_IsIdempotentSemiring_1922
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsSemiringWithoutAnnihilatingZero_1468
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemiringWithoutAnnihilatingZero_1468
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_distrib'691'_1500
               ((T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                  (T_IsSemiring_1570 -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1570
v3)))))
-- Algebra.Bundles.KleeneAlgebra._.distribˡ
d_distrib'737'_3112 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_KleeneAlgebra_3008 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_distrib'737'_3112 :: ()
-> ()
-> T_KleeneAlgebra_3008
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_distrib'737'_3112 ~()
v0 ~()
v1 T_KleeneAlgebra_3008
v2 = T_KleeneAlgebra_3008 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'737'_3112 T_KleeneAlgebra_3008
v2
du_distrib'737'_3112 ::
  T_KleeneAlgebra_3008 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'737'_3112 :: T_KleeneAlgebra_3008 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'737'_3112 T_KleeneAlgebra_3008
v0
  = let v1 :: T_IsKleeneAlgebra_2044
v1 = T_KleeneAlgebra_3008 -> T_IsKleeneAlgebra_2044
d_isKleeneAlgebra_3044 (T_KleeneAlgebra_3008 -> T_KleeneAlgebra_3008
forall a b. a -> b
coe T_KleeneAlgebra_3008
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsIdempotentSemiring_1922
v2
             = T_IsKleeneAlgebra_2044 -> T_IsIdempotentSemiring_1922
MAlonzo.Code.Algebra.Structures.d_isIdempotentSemiring_2062
                 (T_IsKleeneAlgebra_2044 -> T_IsKleeneAlgebra_2044
forall a b. a -> b
coe T_IsKleeneAlgebra_2044
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemiring_1570
v3
                = T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570
MAlonzo.Code.Algebra.Structures.d_isSemiring_1936 (T_IsIdempotentSemiring_1922 -> T_IsIdempotentSemiring_1922
forall a b. a -> b
coe T_IsIdempotentSemiring_1922
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsSemiringWithoutAnnihilatingZero_1468
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemiringWithoutAnnihilatingZero_1468
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_distrib'737'_1498
               ((T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                  (T_IsSemiring_1570 -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1570
v3)))))
-- Algebra.Bundles.KleeneAlgebra._.isEquivalence
d_isEquivalence_3114 ::
  T_KleeneAlgebra_3008 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_3114 :: T_KleeneAlgebra_3008 -> T_IsEquivalence_26
d_isEquivalence_3114 T_KleeneAlgebra_3008
v0
  = (T_IsMagma_176 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
      ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480
         ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
            ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746
               ((T_IsSemiringWithoutAnnihilatingZero_1468
 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
                  ((T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                     ((T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570
MAlonzo.Code.Algebra.Structures.d_isSemiring_1936
                        ((T_IsKleeneAlgebra_2044 -> T_IsIdempotentSemiring_1922)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_IsKleeneAlgebra_2044 -> T_IsIdempotentSemiring_1922
MAlonzo.Code.Algebra.Structures.d_isIdempotentSemiring_2062
                           ((T_KleeneAlgebra_3008 -> T_IsKleeneAlgebra_2044)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_KleeneAlgebra_3008 -> T_IsKleeneAlgebra_2044
d_isKleeneAlgebra_3044 (T_KleeneAlgebra_3008 -> AgdaAny
forall a b. a -> b
coe T_KleeneAlgebra_3008
v0)))))))))
-- Algebra.Bundles.KleeneAlgebra._.isIdempotentSemiring
d_isIdempotentSemiring_3116 ::
  T_KleeneAlgebra_3008 ->
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentSemiring_1922
d_isIdempotentSemiring_3116 :: T_KleeneAlgebra_3008 -> T_IsIdempotentSemiring_1922
d_isIdempotentSemiring_3116 T_KleeneAlgebra_3008
v0
  = (T_IsKleeneAlgebra_2044 -> T_IsIdempotentSemiring_1922)
-> AgdaAny -> T_IsIdempotentSemiring_1922
forall a b. a -> b
coe
      T_IsKleeneAlgebra_2044 -> T_IsIdempotentSemiring_1922
MAlonzo.Code.Algebra.Structures.d_isIdempotentSemiring_2062
      ((T_KleeneAlgebra_3008 -> T_IsKleeneAlgebra_2044)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_KleeneAlgebra_3008 -> T_IsKleeneAlgebra_2044
d_isKleeneAlgebra_3044 (T_KleeneAlgebra_3008 -> AgdaAny
forall a b. a -> b
coe T_KleeneAlgebra_3008
v0))
-- Algebra.Bundles.KleeneAlgebra._.isNearSemiring
d_isNearSemiring_3118 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_KleeneAlgebra_3008 ->
  MAlonzo.Code.Algebra.Structures.T_IsNearSemiring_1218
d_isNearSemiring_3118 :: () -> () -> T_KleeneAlgebra_3008 -> T_IsNearSemiring_1218
d_isNearSemiring_3118 ~()
v0 ~()
v1 T_KleeneAlgebra_3008
v2 = T_KleeneAlgebra_3008 -> T_IsNearSemiring_1218
du_isNearSemiring_3118 T_KleeneAlgebra_3008
v2
du_isNearSemiring_3118 ::
  T_KleeneAlgebra_3008 ->
  MAlonzo.Code.Algebra.Structures.T_IsNearSemiring_1218
du_isNearSemiring_3118 :: T_KleeneAlgebra_3008 -> T_IsNearSemiring_1218
du_isNearSemiring_3118 T_KleeneAlgebra_3008
v0
  = let v1 :: T_IsKleeneAlgebra_2044
v1 = T_KleeneAlgebra_3008 -> T_IsKleeneAlgebra_2044
d_isKleeneAlgebra_3044 (T_KleeneAlgebra_3008 -> T_KleeneAlgebra_3008
forall a b. a -> b
coe T_KleeneAlgebra_3008
v0) in
    AgdaAny -> T_IsNearSemiring_1218
forall a b. a -> b
coe
      (let v2 :: T_IsIdempotentSemiring_1922
v2
             = T_IsKleeneAlgebra_2044 -> T_IsIdempotentSemiring_1922
MAlonzo.Code.Algebra.Structures.d_isIdempotentSemiring_2062
                 (T_IsKleeneAlgebra_2044 -> T_IsKleeneAlgebra_2044
forall a b. a -> b
coe T_IsKleeneAlgebra_2044
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemiring_1570
v3
                = T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570
MAlonzo.Code.Algebra.Structures.d_isSemiring_1936 (T_IsIdempotentSemiring_1922 -> T_IsIdempotentSemiring_1922
forall a b. a -> b
coe T_IsIdempotentSemiring_1922
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsSemiringWithoutOne_1298 -> T_IsNearSemiring_1218)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemiringWithoutOne_1298 -> T_IsNearSemiring_1218
MAlonzo.Code.Algebra.Structures.du_isNearSemiring_1374
               ((T_IsSemiring_1570 -> T_IsSemiringWithoutOne_1298)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsSemiring_1570 -> T_IsSemiringWithoutOne_1298
MAlonzo.Code.Algebra.Structures.du_isSemiringWithoutOne_1660
                  (T_IsSemiring_1570 -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1570
v3)))))
-- Algebra.Bundles.KleeneAlgebra._.isPartialEquivalence
d_isPartialEquivalence_3120 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_KleeneAlgebra_3008 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_3120 :: () -> () -> T_KleeneAlgebra_3008 -> T_IsPartialEquivalence_16
d_isPartialEquivalence_3120 ~()
v0 ~()
v1 T_KleeneAlgebra_3008
v2
  = T_KleeneAlgebra_3008 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_3120 T_KleeneAlgebra_3008
v2
du_isPartialEquivalence_3120 ::
  T_KleeneAlgebra_3008 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_3120 :: T_KleeneAlgebra_3008 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_3120 T_KleeneAlgebra_3008
v0
  = let v1 :: T_IsKleeneAlgebra_2044
v1 = T_KleeneAlgebra_3008 -> T_IsKleeneAlgebra_2044
d_isKleeneAlgebra_3044 (T_KleeneAlgebra_3008 -> T_KleeneAlgebra_3008
forall a b. a -> b
coe T_KleeneAlgebra_3008
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsIdempotentSemiring_1922
v2
             = T_IsKleeneAlgebra_2044 -> T_IsIdempotentSemiring_1922
MAlonzo.Code.Algebra.Structures.d_isIdempotentSemiring_2062
                 (T_IsKleeneAlgebra_2044 -> T_IsKleeneAlgebra_2044
forall a b. a -> b
coe T_IsKleeneAlgebra_2044
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemiring_1570
v3
                = T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570
MAlonzo.Code.Algebra.Structures.d_isSemiring_1936 (T_IsIdempotentSemiring_1922 -> T_IsIdempotentSemiring_1922
forall a b. a -> b
coe T_IsIdempotentSemiring_1922
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsSemiringWithoutAnnihilatingZero_1468
v4
                   = T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                       (T_IsSemiring_1570 -> T_IsSemiring_1570
forall a b. a -> b
coe T_IsSemiring_1570
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsCommutativeMonoid_736
v5
                      = T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
                          (T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsSemiringWithoutAnnihilatingZero_1468
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (let v6 :: T_IsMonoid_686
v6
                         = T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746 (T_IsCommutativeMonoid_736 -> T_IsCommutativeMonoid_736
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v5) in
                   AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     (let v7 :: T_IsSemigroup_472
v7
                            = T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v6) in
                      AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        (let v8 :: T_IsMagma_176
v8 = T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (T_IsSemigroup_472 -> T_IsSemigroup_472
forall a b. a -> b
coe T_IsSemigroup_472
v7) in
                         AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           ((T_IsEquivalence_26 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                              T_IsEquivalence_26 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
                              ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                 T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
                                 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v8))))))))))
-- Algebra.Bundles.KleeneAlgebra._.isSemiring
d_isSemiring_3122 ::
  T_KleeneAlgebra_3008 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemiring_1570
d_isSemiring_3122 :: T_KleeneAlgebra_3008 -> T_IsSemiring_1570
d_isSemiring_3122 T_KleeneAlgebra_3008
v0
  = (T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570)
-> AgdaAny -> T_IsSemiring_1570
forall a b. a -> b
coe
      T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570
MAlonzo.Code.Algebra.Structures.d_isSemiring_1936
      ((T_IsKleeneAlgebra_2044 -> T_IsIdempotentSemiring_1922)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsKleeneAlgebra_2044 -> T_IsIdempotentSemiring_1922
MAlonzo.Code.Algebra.Structures.d_isIdempotentSemiring_2062
         ((T_KleeneAlgebra_3008 -> T_IsKleeneAlgebra_2044)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_KleeneAlgebra_3008 -> T_IsKleeneAlgebra_2044
d_isKleeneAlgebra_3044 (T_KleeneAlgebra_3008 -> AgdaAny
forall a b. a -> b
coe T_KleeneAlgebra_3008
v0)))
-- Algebra.Bundles.KleeneAlgebra._.isSemiringWithoutAnnihilatingZero
d_isSemiringWithoutAnnihilatingZero_3124 ::
  T_KleeneAlgebra_3008 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_3124 :: T_KleeneAlgebra_3008 -> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_3124 T_KleeneAlgebra_3008
v0
  = (T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> T_IsSemiringWithoutAnnihilatingZero_1468
forall a b. a -> b
coe
      T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
      ((T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570
MAlonzo.Code.Algebra.Structures.d_isSemiring_1936
         ((T_IsKleeneAlgebra_2044 -> T_IsIdempotentSemiring_1922)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsKleeneAlgebra_2044 -> T_IsIdempotentSemiring_1922
MAlonzo.Code.Algebra.Structures.d_isIdempotentSemiring_2062
            ((T_KleeneAlgebra_3008 -> T_IsKleeneAlgebra_2044)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_KleeneAlgebra_3008 -> T_IsKleeneAlgebra_2044
d_isKleeneAlgebra_3044 (T_KleeneAlgebra_3008 -> AgdaAny
forall a b. a -> b
coe T_KleeneAlgebra_3008
v0))))
-- Algebra.Bundles.KleeneAlgebra._.isSemiringWithoutOne
d_isSemiringWithoutOne_3126 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_KleeneAlgebra_3008 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutOne_1298
d_isSemiringWithoutOne_3126 :: () -> () -> T_KleeneAlgebra_3008 -> T_IsSemiringWithoutOne_1298
d_isSemiringWithoutOne_3126 ~()
v0 ~()
v1 T_KleeneAlgebra_3008
v2
  = T_KleeneAlgebra_3008 -> T_IsSemiringWithoutOne_1298
du_isSemiringWithoutOne_3126 T_KleeneAlgebra_3008
v2
du_isSemiringWithoutOne_3126 ::
  T_KleeneAlgebra_3008 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutOne_1298
du_isSemiringWithoutOne_3126 :: T_KleeneAlgebra_3008 -> T_IsSemiringWithoutOne_1298
du_isSemiringWithoutOne_3126 T_KleeneAlgebra_3008
v0
  = let v1 :: T_IsKleeneAlgebra_2044
v1 = T_KleeneAlgebra_3008 -> T_IsKleeneAlgebra_2044
d_isKleeneAlgebra_3044 (T_KleeneAlgebra_3008 -> T_KleeneAlgebra_3008
forall a b. a -> b
coe T_KleeneAlgebra_3008
v0) in
    AgdaAny -> T_IsSemiringWithoutOne_1298
forall a b. a -> b
coe
      (let v2 :: T_IsIdempotentSemiring_1922
v2
             = T_IsKleeneAlgebra_2044 -> T_IsIdempotentSemiring_1922
MAlonzo.Code.Algebra.Structures.d_isIdempotentSemiring_2062
                 (T_IsKleeneAlgebra_2044 -> T_IsKleeneAlgebra_2044
forall a b. a -> b
coe T_IsKleeneAlgebra_2044
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsSemiring_1570 -> T_IsSemiringWithoutOne_1298)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemiring_1570 -> T_IsSemiringWithoutOne_1298
MAlonzo.Code.Algebra.Structures.du_isSemiringWithoutOne_1660
            ((T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570
MAlonzo.Code.Algebra.Structures.d_isSemiring_1936 (T_IsIdempotentSemiring_1922 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentSemiring_1922
v2))))
-- Algebra.Bundles.KleeneAlgebra._.refl
d_refl_3128 :: T_KleeneAlgebra_3008 -> AgdaAny -> AgdaAny
d_refl_3128 :: T_KleeneAlgebra_3008 -> AgdaAny -> AgdaAny
d_refl_3128 T_KleeneAlgebra_3008
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_34
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
         ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480
            ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
               ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746
                  ((T_IsSemiringWithoutAnnihilatingZero_1468
 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
                     ((T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                        ((T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570
MAlonzo.Code.Algebra.Structures.d_isSemiring_1936
                           ((T_IsKleeneAlgebra_2044 -> T_IsIdempotentSemiring_1922)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                              T_IsKleeneAlgebra_2044 -> T_IsIdempotentSemiring_1922
MAlonzo.Code.Algebra.Structures.d_isIdempotentSemiring_2062
                              ((T_KleeneAlgebra_3008 -> T_IsKleeneAlgebra_2044)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_KleeneAlgebra_3008 -> T_IsKleeneAlgebra_2044
d_isKleeneAlgebra_3044 (T_KleeneAlgebra_3008 -> AgdaAny
forall a b. a -> b
coe T_KleeneAlgebra_3008
v0))))))))))
-- Algebra.Bundles.KleeneAlgebra._.reflexive
d_reflexive_3130 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_KleeneAlgebra_3008 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_3130 :: ()
-> ()
-> T_KleeneAlgebra_3008
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_3130 ~()
v0 ~()
v1 T_KleeneAlgebra_3008
v2 = T_KleeneAlgebra_3008
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_3130 T_KleeneAlgebra_3008
v2
du_reflexive_3130 ::
  T_KleeneAlgebra_3008 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_3130 :: T_KleeneAlgebra_3008
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_3130 T_KleeneAlgebra_3008
v0
  = let v1 :: T_IsKleeneAlgebra_2044
v1 = T_KleeneAlgebra_3008 -> T_IsKleeneAlgebra_2044
d_isKleeneAlgebra_3044 (T_KleeneAlgebra_3008 -> T_KleeneAlgebra_3008
forall a b. a -> b
coe T_KleeneAlgebra_3008
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsIdempotentSemiring_1922
v2
             = T_IsKleeneAlgebra_2044 -> T_IsIdempotentSemiring_1922
MAlonzo.Code.Algebra.Structures.d_isIdempotentSemiring_2062
                 (T_IsKleeneAlgebra_2044 -> T_IsKleeneAlgebra_2044
forall a b. a -> b
coe T_IsKleeneAlgebra_2044
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemiring_1570
v3
                = T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570
MAlonzo.Code.Algebra.Structures.d_isSemiring_1936 (T_IsIdempotentSemiring_1922 -> T_IsIdempotentSemiring_1922
forall a b. a -> b
coe T_IsIdempotentSemiring_1922
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsSemiringWithoutAnnihilatingZero_1468
v4
                   = T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                       (T_IsSemiring_1570 -> T_IsSemiring_1570
forall a b. a -> b
coe T_IsSemiring_1570
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsCommutativeMonoid_736
v5
                      = T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
                          (T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsSemiringWithoutAnnihilatingZero_1468
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (let v6 :: T_IsMonoid_686
v6
                         = T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746 (T_IsCommutativeMonoid_736 -> T_IsCommutativeMonoid_736
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v5) in
                   AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     (let v7 :: T_IsSemigroup_472
v7
                            = T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v6) in
                      AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        (let v8 :: T_IsMagma_176
v8 = T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (T_IsSemigroup_472 -> T_IsSemigroup_472
forall a b. a -> b
coe T_IsSemigroup_472
v7) in
                         (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
                           (\ AgdaAny
v9 AgdaAny
v10 AgdaAny
v11 ->
                              (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
                                ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v8))
                                AgdaAny
v9))))))))
-- Algebra.Bundles.KleeneAlgebra._.setoid
d_setoid_3132 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_KleeneAlgebra_3008 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_3132 :: () -> () -> T_KleeneAlgebra_3008 -> T_Setoid_44
d_setoid_3132 ~()
v0 ~()
v1 T_KleeneAlgebra_3008
v2 = T_KleeneAlgebra_3008 -> T_Setoid_44
du_setoid_3132 T_KleeneAlgebra_3008
v2
du_setoid_3132 ::
  T_KleeneAlgebra_3008 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_3132 :: T_KleeneAlgebra_3008 -> T_Setoid_44
du_setoid_3132 T_KleeneAlgebra_3008
v0
  = let v1 :: T_IsKleeneAlgebra_2044
v1 = T_KleeneAlgebra_3008 -> T_IsKleeneAlgebra_2044
d_isKleeneAlgebra_3044 (T_KleeneAlgebra_3008 -> T_KleeneAlgebra_3008
forall a b. a -> b
coe T_KleeneAlgebra_3008
v0) in
    AgdaAny -> T_Setoid_44
forall a b. a -> b
coe
      (let v2 :: T_IsIdempotentSemiring_1922
v2
             = T_IsKleeneAlgebra_2044 -> T_IsIdempotentSemiring_1922
MAlonzo.Code.Algebra.Structures.d_isIdempotentSemiring_2062
                 (T_IsKleeneAlgebra_2044 -> T_IsKleeneAlgebra_2044
forall a b. a -> b
coe T_IsKleeneAlgebra_2044
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemiring_1570
v3
                = T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570
MAlonzo.Code.Algebra.Structures.d_isSemiring_1936 (T_IsIdempotentSemiring_1922 -> T_IsIdempotentSemiring_1922
forall a b. a -> b
coe T_IsIdempotentSemiring_1922
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsSemiringWithoutAnnihilatingZero_1468
v4
                   = T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                       (T_IsSemiring_1570 -> T_IsSemiring_1570
forall a b. a -> b
coe T_IsSemiring_1570
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsCommutativeMonoid_736
v5
                      = T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
                          (T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsSemiringWithoutAnnihilatingZero_1468
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1468
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (let v6 :: T_IsMonoid_686
v6
                         = T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746 (T_IsCommutativeMonoid_736 -> T_IsCommutativeMonoid_736
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v5) in
                   AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     (let v7 :: T_IsSemigroup_472
v7
                            = T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v6) in
                      AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        ((T_IsMagma_176 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_IsMagma_176 -> T_Setoid_44
MAlonzo.Code.Algebra.Structures.du_setoid_200
                           ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v7)))))))))
-- Algebra.Bundles.KleeneAlgebra._.starDestructive
d_starDestructive_3134 ::
  T_KleeneAlgebra_3008 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_starDestructive_3134 :: T_KleeneAlgebra_3008 -> T_Σ_14
d_starDestructive_3134 T_KleeneAlgebra_3008
v0
  = (T_IsKleeneAlgebra_2044 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsKleeneAlgebra_2044 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_starDestructive_2066
      ((T_KleeneAlgebra_3008 -> T_IsKleeneAlgebra_2044)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_KleeneAlgebra_3008 -> T_IsKleeneAlgebra_2044
d_isKleeneAlgebra_3044 (T_KleeneAlgebra_3008 -> AgdaAny
forall a b. a -> b
coe T_KleeneAlgebra_3008
v0))
-- Algebra.Bundles.KleeneAlgebra._.starDestructiveʳ
d_starDestructive'691'_3136 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_KleeneAlgebra_3008 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_starDestructive'691'_3136 :: ()
-> ()
-> T_KleeneAlgebra_3008
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_starDestructive'691'_3136 ~()
v0 ~()
v1 T_KleeneAlgebra_3008
v2
  = T_KleeneAlgebra_3008
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_starDestructive'691'_3136 T_KleeneAlgebra_3008
v2
du_starDestructive'691'_3136 ::
  T_KleeneAlgebra_3008 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_starDestructive'691'_3136 :: T_KleeneAlgebra_3008
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_starDestructive'691'_3136 T_KleeneAlgebra_3008
v0
  = (T_IsKleeneAlgebra_2044
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsKleeneAlgebra_2044
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_starDestructive'691'_2170
      ((T_KleeneAlgebra_3008 -> T_IsKleeneAlgebra_2044)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_KleeneAlgebra_3008 -> T_IsKleeneAlgebra_2044
d_isKleeneAlgebra_3044 (T_KleeneAlgebra_3008 -> AgdaAny
forall a b. a -> b
coe T_KleeneAlgebra_3008
v0))
-- Algebra.Bundles.KleeneAlgebra._.starDestructiveˡ
d_starDestructive'737'_3138 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_KleeneAlgebra_3008 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_starDestructive'737'_3138 :: ()
-> ()
-> T_KleeneAlgebra_3008
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_starDestructive'737'_3138 ~()
v0 ~()
v1 T_KleeneAlgebra_3008
v2
  = T_KleeneAlgebra_3008
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_starDestructive'737'_3138 T_KleeneAlgebra_3008
v2
du_starDestructive'737'_3138 ::
  T_KleeneAlgebra_3008 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_starDestructive'737'_3138 :: T_KleeneAlgebra_3008
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_starDestructive'737'_3138 T_KleeneAlgebra_3008
v0
  = (T_IsKleeneAlgebra_2044
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsKleeneAlgebra_2044
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_starDestructive'737'_2168
      ((T_KleeneAlgebra_3008 -> T_IsKleeneAlgebra_2044)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_KleeneAlgebra_3008 -> T_IsKleeneAlgebra_2044
d_isKleeneAlgebra_3044 (T_KleeneAlgebra_3008 -> AgdaAny
forall a b. a -> b
coe T_KleeneAlgebra_3008
v0))
-- Algebra.Bundles.KleeneAlgebra._.starExpansive
d_starExpansive_3140 ::
  T_KleeneAlgebra_3008 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_starExpansive_3140 :: T_KleeneAlgebra_3008 -> T_Σ_14
d_starExpansive_3140 T_KleeneAlgebra_3008
v0
  = (T_IsKleeneAlgebra_2044 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsKleeneAlgebra_2044 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_starExpansive_2064
      ((T_KleeneAlgebra_3008 -> T_IsKleeneAlgebra_2044)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_KleeneAlgebra_3008 -> T_IsKleeneAlgebra_2044
d_isKleeneAlgebra_3044 (T_KleeneAlgebra_3008 -> AgdaAny
forall a b. a -> b
coe T_KleeneAlgebra_3008
v0))
-- Algebra.Bundles.KleeneAlgebra._.starExpansiveʳ
d_starExpansive'691'_3142 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_KleeneAlgebra_3008 -> AgdaAny -> AgdaAny
d_starExpansive'691'_3142 :: () -> () -> T_KleeneAlgebra_3008 -> AgdaAny -> AgdaAny
d_starExpansive'691'_3142 ~()
v0 ~()
v1 T_KleeneAlgebra_3008
v2
  = T_KleeneAlgebra_3008 -> AgdaAny -> AgdaAny
du_starExpansive'691'_3142 T_KleeneAlgebra_3008
v2
du_starExpansive'691'_3142 ::
  T_KleeneAlgebra_3008 -> AgdaAny -> AgdaAny
du_starExpansive'691'_3142 :: T_KleeneAlgebra_3008 -> AgdaAny -> AgdaAny
du_starExpansive'691'_3142 T_KleeneAlgebra_3008
v0
  = (T_IsKleeneAlgebra_2044 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsKleeneAlgebra_2044 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_starExpansive'691'_2166
      ((T_KleeneAlgebra_3008 -> T_IsKleeneAlgebra_2044)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_KleeneAlgebra_3008 -> T_IsKleeneAlgebra_2044
d_isKleeneAlgebra_3044 (T_KleeneAlgebra_3008 -> AgdaAny
forall a b. a -> b
coe T_KleeneAlgebra_3008
v0))
-- Algebra.Bundles.KleeneAlgebra._.starExpansiveˡ
d_starExpansive'737'_3144 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_KleeneAlgebra_3008 -> AgdaAny -> AgdaAny
d_starExpansive'737'_3144 :: () -> () -> T_KleeneAlgebra_3008 -> AgdaAny -> AgdaAny
d_starExpansive'737'_3144 ~()
v0 ~()
v1 T_KleeneAlgebra_3008
v2
  = T_KleeneAlgebra_3008 -> AgdaAny -> AgdaAny
du_starExpansive'737'_3144 T_KleeneAlgebra_3008
v2
du_starExpansive'737'_3144 ::
  T_KleeneAlgebra_3008 -> AgdaAny -> AgdaAny
du_starExpansive'737'_3144 :: T_KleeneAlgebra_3008 -> AgdaAny -> AgdaAny
du_starExpansive'737'_3144 T_KleeneAlgebra_3008
v0
  = (T_IsKleeneAlgebra_2044 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsKleeneAlgebra_2044 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_starExpansive'737'_2164
      ((T_KleeneAlgebra_3008 -> T_IsKleeneAlgebra_2044)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_KleeneAlgebra_3008 -> T_IsKleeneAlgebra_2044
d_isKleeneAlgebra_3044 (T_KleeneAlgebra_3008 -> AgdaAny
forall a b. a -> b
coe T_KleeneAlgebra_3008
v0))
-- Algebra.Bundles.KleeneAlgebra._.sym
d_sym_3146 ::
  T_KleeneAlgebra_3008 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_3146 :: T_KleeneAlgebra_3008 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_3146 T_KleeneAlgebra_3008
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_36
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
         ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480
            ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
               ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746
                  ((T_IsSemiringWithoutAnnihilatingZero_1468
 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
                     ((T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                        ((T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570
MAlonzo.Code.Algebra.Structures.d_isSemiring_1936
                           ((T_IsKleeneAlgebra_2044 -> T_IsIdempotentSemiring_1922)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                              T_IsKleeneAlgebra_2044 -> T_IsIdempotentSemiring_1922
MAlonzo.Code.Algebra.Structures.d_isIdempotentSemiring_2062
                              ((T_KleeneAlgebra_3008 -> T_IsKleeneAlgebra_2044)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_KleeneAlgebra_3008 -> T_IsKleeneAlgebra_2044
d_isKleeneAlgebra_3044 (T_KleeneAlgebra_3008 -> AgdaAny
forall a b. a -> b
coe T_KleeneAlgebra_3008
v0))))))))))
-- Algebra.Bundles.KleeneAlgebra._.trans
d_trans_3148 ::
  T_KleeneAlgebra_3008 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_3148 :: T_KleeneAlgebra_3008
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_3148 T_KleeneAlgebra_3008
v0
  = (T_IsEquivalence_26
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_38
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
         ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480
            ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
               ((T_IsCommutativeMonoid_736 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746
                  ((T_IsSemiringWithoutAnnihilatingZero_1468
 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsSemiringWithoutAnnihilatingZero_1468
-> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1488
                     ((T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
                        ((T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570
MAlonzo.Code.Algebra.Structures.d_isSemiring_1936
                           ((T_IsKleeneAlgebra_2044 -> T_IsIdempotentSemiring_1922)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                              T_IsKleeneAlgebra_2044 -> T_IsIdempotentSemiring_1922
MAlonzo.Code.Algebra.Structures.d_isIdempotentSemiring_2062
                              ((T_KleeneAlgebra_3008 -> T_IsKleeneAlgebra_2044)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_KleeneAlgebra_3008 -> T_IsKleeneAlgebra_2044
d_isKleeneAlgebra_3044 (T_KleeneAlgebra_3008 -> AgdaAny
forall a b. a -> b
coe T_KleeneAlgebra_3008
v0))))))))))
-- Algebra.Bundles.KleeneAlgebra._.zero
d_zero_3150 ::
  T_KleeneAlgebra_3008 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_zero_3150 :: T_KleeneAlgebra_3008 -> T_Σ_14
d_zero_3150 T_KleeneAlgebra_3008
v0
  = (T_IsSemiring_1570 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsSemiring_1570 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_zero_1586
      ((T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570
MAlonzo.Code.Algebra.Structures.d_isSemiring_1936
         ((T_IsKleeneAlgebra_2044 -> T_IsIdempotentSemiring_1922)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsKleeneAlgebra_2044 -> T_IsIdempotentSemiring_1922
MAlonzo.Code.Algebra.Structures.d_isIdempotentSemiring_2062
            ((T_KleeneAlgebra_3008 -> T_IsKleeneAlgebra_2044)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_KleeneAlgebra_3008 -> T_IsKleeneAlgebra_2044
d_isKleeneAlgebra_3044 (T_KleeneAlgebra_3008 -> AgdaAny
forall a b. a -> b
coe T_KleeneAlgebra_3008
v0))))
-- Algebra.Bundles.KleeneAlgebra._.zeroʳ
d_zero'691'_3152 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_KleeneAlgebra_3008 -> AgdaAny -> AgdaAny
d_zero'691'_3152 :: () -> () -> T_KleeneAlgebra_3008 -> AgdaAny -> AgdaAny
d_zero'691'_3152 ~()
v0 ~()
v1 T_KleeneAlgebra_3008
v2 = T_KleeneAlgebra_3008 -> AgdaAny -> AgdaAny
du_zero'691'_3152 T_KleeneAlgebra_3008
v2
du_zero'691'_3152 :: T_KleeneAlgebra_3008 -> AgdaAny -> AgdaAny
du_zero'691'_3152 :: T_KleeneAlgebra_3008 -> AgdaAny -> AgdaAny
du_zero'691'_3152 T_KleeneAlgebra_3008
v0
  = let v1 :: T_IsKleeneAlgebra_2044
v1 = T_KleeneAlgebra_3008 -> T_IsKleeneAlgebra_2044
d_isKleeneAlgebra_3044 (T_KleeneAlgebra_3008 -> T_KleeneAlgebra_3008
forall a b. a -> b
coe T_KleeneAlgebra_3008
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsIdempotentSemiring_1922
v2
             = T_IsKleeneAlgebra_2044 -> T_IsIdempotentSemiring_1922
MAlonzo.Code.Algebra.Structures.d_isIdempotentSemiring_2062
                 (T_IsKleeneAlgebra_2044 -> T_IsKleeneAlgebra_2044
forall a b. a -> b
coe T_IsKleeneAlgebra_2044
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemiring_1570
v3
                = T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570
MAlonzo.Code.Algebra.Structures.d_isSemiring_1936 (T_IsIdempotentSemiring_1922 -> T_IsIdempotentSemiring_1922
forall a b. a -> b
coe T_IsIdempotentSemiring_1922
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsSemiringWithoutOne_1298 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemiringWithoutOne_1298 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_zero'691'_1372
               ((T_IsSemiring_1570 -> T_IsSemiringWithoutOne_1298)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsSemiring_1570 -> T_IsSemiringWithoutOne_1298
MAlonzo.Code.Algebra.Structures.du_isSemiringWithoutOne_1660
                  (T_IsSemiring_1570 -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1570
v3)))))
-- Algebra.Bundles.KleeneAlgebra._.zeroˡ
d_zero'737'_3154 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_KleeneAlgebra_3008 -> AgdaAny -> AgdaAny
d_zero'737'_3154 :: () -> () -> T_KleeneAlgebra_3008 -> AgdaAny -> AgdaAny
d_zero'737'_3154 ~()
v0 ~()
v1 T_KleeneAlgebra_3008
v2 = T_KleeneAlgebra_3008 -> AgdaAny -> AgdaAny
du_zero'737'_3154 T_KleeneAlgebra_3008
v2
du_zero'737'_3154 :: T_KleeneAlgebra_3008 -> AgdaAny -> AgdaAny
du_zero'737'_3154 :: T_KleeneAlgebra_3008 -> AgdaAny -> AgdaAny
du_zero'737'_3154 T_KleeneAlgebra_3008
v0
  = let v1 :: T_IsKleeneAlgebra_2044
v1 = T_KleeneAlgebra_3008 -> T_IsKleeneAlgebra_2044
d_isKleeneAlgebra_3044 (T_KleeneAlgebra_3008 -> T_KleeneAlgebra_3008
forall a b. a -> b
coe T_KleeneAlgebra_3008
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsIdempotentSemiring_1922
v2
             = T_IsKleeneAlgebra_2044 -> T_IsIdempotentSemiring_1922
MAlonzo.Code.Algebra.Structures.d_isIdempotentSemiring_2062
                 (T_IsKleeneAlgebra_2044 -> T_IsKleeneAlgebra_2044
forall a b. a -> b
coe T_IsKleeneAlgebra_2044
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemiring_1570
v3
                = T_IsIdempotentSemiring_1922 -> T_IsSemiring_1570
MAlonzo.Code.Algebra.Structures.d_isSemiring_1936 (T_IsIdempotentSemiring_1922 -> T_IsIdempotentSemiring_1922
forall a b. a -> b
coe T_IsIdempotentSemiring_1922
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsSemiringWithoutOne_1298 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemiringWithoutOne_1298 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_zero'737'_1370
               ((T_IsSemiring_1570 -> T_IsSemiringWithoutOne_1298)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsSemiring_1570 -> T_IsSemiringWithoutOne_1298
MAlonzo.Code.Algebra.Structures.du_isSemiringWithoutOne_1660
                  (T_IsSemiring_1570 -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1570
v3)))))
-- Algebra.Bundles.KleeneAlgebra.idempotentSemiring
d_idempotentSemiring_3156 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_KleeneAlgebra_3008 -> T_IdempotentSemiring_2822
d_idempotentSemiring_3156 :: () -> () -> T_KleeneAlgebra_3008 -> T_IdempotentSemiring_2822
d_idempotentSemiring_3156 ~()
v0 ~()
v1 T_KleeneAlgebra_3008
v2
  = T_KleeneAlgebra_3008 -> T_IdempotentSemiring_2822
du_idempotentSemiring_3156 T_KleeneAlgebra_3008
v2
du_idempotentSemiring_3156 ::
  T_KleeneAlgebra_3008 -> T_IdempotentSemiring_2822
du_idempotentSemiring_3156 :: T_KleeneAlgebra_3008 -> T_IdempotentSemiring_2822
du_idempotentSemiring_3156 T_KleeneAlgebra_3008
v0
  = ((AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> AgdaAny
 -> T_IsIdempotentSemiring_1922
 -> T_IdempotentSemiring_2822)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsIdempotentSemiring_1922
-> T_IdempotentSemiring_2822
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsIdempotentSemiring_1922
-> T_IdempotentSemiring_2822
C_IdempotentSemiring'46'constructor_51015 (T_KleeneAlgebra_3008 -> AgdaAny -> AgdaAny -> AgdaAny
d__'43'__3034 (T_KleeneAlgebra_3008 -> T_KleeneAlgebra_3008
forall a b. a -> b
coe T_KleeneAlgebra_3008
v0))
      (T_KleeneAlgebra_3008 -> AgdaAny -> AgdaAny -> AgdaAny
d__'42'__3036 (T_KleeneAlgebra_3008 -> T_KleeneAlgebra_3008
forall a b. a -> b
coe T_KleeneAlgebra_3008
v0)) (T_KleeneAlgebra_3008 -> AgdaAny
d_0'35'_3040 (T_KleeneAlgebra_3008 -> T_KleeneAlgebra_3008
forall a b. a -> b
coe T_KleeneAlgebra_3008
v0))
      (T_KleeneAlgebra_3008 -> AgdaAny
d_1'35'_3042 (T_KleeneAlgebra_3008 -> T_KleeneAlgebra_3008
forall a b. a -> b
coe T_KleeneAlgebra_3008
v0))
      (T_IsKleeneAlgebra_2044 -> T_IsIdempotentSemiring_1922
MAlonzo.Code.Algebra.Structures.d_isIdempotentSemiring_2062
         ((T_KleeneAlgebra_3008 -> T_IsKleeneAlgebra_2044)
-> AgdaAny -> T_IsKleeneAlgebra_2044
forall a b. a -> b
coe T_KleeneAlgebra_3008 -> T_IsKleeneAlgebra_2044
d_isKleeneAlgebra_3044 (T_KleeneAlgebra_3008 -> AgdaAny
forall a b. a -> b
coe T_KleeneAlgebra_3008
v0)))
-- Algebra.Bundles.KleeneAlgebra._._≉_
d__'8777'__3160 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_KleeneAlgebra_3008 -> AgdaAny -> AgdaAny -> ()
d__'8777'__3160 :: () -> () -> T_KleeneAlgebra_3008 -> AgdaAny -> AgdaAny -> ()
d__'8777'__3160 = () -> () -> T_KleeneAlgebra_3008 -> AgdaAny -> AgdaAny -> ()
forall a. a
erased
-- Algebra.Bundles.KleeneAlgebra._.magma
d_magma_3162 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_KleeneAlgebra_3008 -> T_Magma_68
d_magma_3162 :: () -> () -> T_KleeneAlgebra_3008 -> T_Magma_68
d_magma_3162 ~()
v0 ~()
v1 T_KleeneAlgebra_3008
v2 = T_KleeneAlgebra_3008 -> T_Magma_68
du_magma_3162 T_KleeneAlgebra_3008
v2
du_magma_3162 :: T_KleeneAlgebra_3008 -> T_Magma_68
du_magma_3162 :: T_KleeneAlgebra_3008 -> T_Magma_68
du_magma_3162 T_KleeneAlgebra_3008
v0
  = let v1 :: t
v1 = (T_KleeneAlgebra_3008 -> T_IdempotentSemiring_2822) -> AgdaAny -> t
forall a b. a -> b
coe T_KleeneAlgebra_3008 -> T_IdempotentSemiring_2822
du_idempotentSemiring_3156 (T_KleeneAlgebra_3008 -> AgdaAny
forall a b. a -> b
coe T_KleeneAlgebra_3008
v0) in
    AgdaAny -> T_Magma_68
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_IdempotentSemiring_2822 -> T_Semiring_2280) -> AgdaAny -> t
forall a b. a -> b
coe T_IdempotentSemiring_2822 -> T_Semiring_2280
du_semiring_2952 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: t
v3 = (T_Semiring_2280 -> T_SemiringWithoutAnnihilatingZero_2130)
-> AgdaAny -> t
forall a b. a -> b
coe T_Semiring_2280 -> T_SemiringWithoutAnnihilatingZero_2130
du_semiringWithoutAnnihilatingZero_2398 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: t
v4 = (T_SemiringWithoutAnnihilatingZero_2130 -> T_Monoid_882)
-> AgdaAny -> t
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_2130 -> T_Monoid_882
du_'42''45'monoid_2264 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_Semigroup_536 -> T_Magma_68) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semigroup_536 -> T_Magma_68
du_magma_584 ((T_Monoid_882 -> T_Semigroup_536) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Monoid_882 -> T_Semigroup_536
du_semigroup_944 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v4))))))
-- Algebra.Bundles.KleeneAlgebra._.*-monoid
d_'42''45'monoid_3164 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_KleeneAlgebra_3008 -> T_Monoid_882
d_'42''45'monoid_3164 :: () -> () -> T_KleeneAlgebra_3008 -> T_Monoid_882
d_'42''45'monoid_3164 ~()
v0 ~()
v1 T_KleeneAlgebra_3008
v2 = T_KleeneAlgebra_3008 -> T_Monoid_882
du_'42''45'monoid_3164 T_KleeneAlgebra_3008
v2
du_'42''45'monoid_3164 :: T_KleeneAlgebra_3008 -> T_Monoid_882
du_'42''45'monoid_3164 :: T_KleeneAlgebra_3008 -> T_Monoid_882
du_'42''45'monoid_3164 T_KleeneAlgebra_3008
v0
  = let v1 :: t
v1 = (T_KleeneAlgebra_3008 -> T_IdempotentSemiring_2822) -> AgdaAny -> t
forall a b. a -> b
coe T_KleeneAlgebra_3008 -> T_IdempotentSemiring_2822
du_idempotentSemiring_3156 (T_KleeneAlgebra_3008 -> AgdaAny
forall a b. a -> b
coe T_KleeneAlgebra_3008
v0) in
    AgdaAny -> T_Monoid_882
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_IdempotentSemiring_2822 -> T_Semiring_2280) -> AgdaAny -> t
forall a b. a -> b
coe T_IdempotentSemiring_2822 -> T_Semiring_2280
du_semiring_2952 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_SemiringWithoutAnnihilatingZero_2130 -> T_Monoid_882)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_SemiringWithoutAnnihilatingZero_2130 -> T_Monoid_882
du_'42''45'monoid_2264
            ((T_Semiring_2280 -> T_SemiringWithoutAnnihilatingZero_2130)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semiring_2280 -> T_SemiringWithoutAnnihilatingZero_2130
du_semiringWithoutAnnihilatingZero_2398 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2))))
-- Algebra.Bundles.KleeneAlgebra._.rawMagma
d_rawMagma_3166 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_KleeneAlgebra_3008 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
d_rawMagma_3166 :: () -> () -> T_KleeneAlgebra_3008 -> T_RawMagma_36
d_rawMagma_3166 ~()
v0 ~()
v1 T_KleeneAlgebra_3008
v2 = T_KleeneAlgebra_3008 -> T_RawMagma_36
du_rawMagma_3166 T_KleeneAlgebra_3008
v2
du_rawMagma_3166 ::
  T_KleeneAlgebra_3008 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
du_rawMagma_3166 :: T_KleeneAlgebra_3008 -> T_RawMagma_36
du_rawMagma_3166 T_KleeneAlgebra_3008
v0
  = let v1 :: t
v1 = (T_KleeneAlgebra_3008 -> T_IdempotentSemiring_2822) -> AgdaAny -> t
forall a b. a -> b
coe T_KleeneAlgebra_3008 -> T_IdempotentSemiring_2822
du_idempotentSemiring_3156 (T_KleeneAlgebra_3008 -> AgdaAny
forall a b. a -> b
coe T_KleeneAlgebra_3008
v0) in
    AgdaAny -> T_RawMagma_36
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_IdempotentSemiring_2822 -> T_Semiring_2280) -> AgdaAny -> t
forall a b. a -> b
coe T_IdempotentSemiring_2822 -> T_Semiring_2280
du_semiring_2952 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: t
v3 = (T_Semiring_2280 -> T_SemiringWithoutAnnihilatingZero_2130)
-> AgdaAny -> t
forall a b. a -> b
coe T_Semiring_2280 -> T_SemiringWithoutAnnihilatingZero_2130
du_semiringWithoutAnnihilatingZero_2398 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: t
v4 = (T_SemiringWithoutAnnihilatingZero_2130 -> T_Monoid_882)
-> AgdaAny -> t
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_2130 -> T_Monoid_882
du_'42''45'monoid_2264 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: t
v5 = (T_Monoid_882 -> T_Semigroup_536) -> AgdaAny -> t
forall a b. a -> b
coe T_Monoid_882 -> T_Semigroup_536
du_semigroup_944 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_Magma_68 -> T_RawMagma_36) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Magma_68 -> T_RawMagma_36
du_rawMagma_112 ((T_Semigroup_536 -> T_Magma_68) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semigroup_536 -> T_Magma_68
du_magma_584 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v5)))))))
-- Algebra.Bundles.KleeneAlgebra._.rawMonoid
d_rawMonoid_3168 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_KleeneAlgebra_3008 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMonoid_64
d_rawMonoid_3168 :: () -> () -> T_KleeneAlgebra_3008 -> T_RawMonoid_64
d_rawMonoid_3168 ~()
v0 ~()
v1 T_KleeneAlgebra_3008
v2 = T_KleeneAlgebra_3008 -> T_RawMonoid_64
du_rawMonoid_3168 T_KleeneAlgebra_3008
v2
du_rawMonoid_3168 ::
  T_KleeneAlgebra_3008 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMonoid_64
du_rawMonoid_3168 :: T_KleeneAlgebra_3008 -> T_RawMonoid_64
du_rawMonoid_3168 T_KleeneAlgebra_3008
v0
  = let v1 :: t
v1 = (T_KleeneAlgebra_3008 -> T_IdempotentSemiring_2822) -> AgdaAny -> t
forall a b. a -> b
coe T_KleeneAlgebra_3008 -> T_IdempotentSemiring_2822
du_idempotentSemiring_3156 (T_KleeneAlgebra_3008 -> AgdaAny
forall a b. a -> b
coe T_KleeneAlgebra_3008
v0) in
    AgdaAny -> T_RawMonoid_64
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_IdempotentSemiring_2822 -> T_Semiring_2280) -> AgdaAny -> t
forall a b. a -> b
coe T_IdempotentSemiring_2822 -> T_Semiring_2280
du_semiring_2952 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: t
v3 = (T_Semiring_2280 -> T_SemiringWithoutAnnihilatingZero_2130)
-> AgdaAny -> t
forall a b. a -> b
coe T_Semiring_2280 -> T_SemiringWithoutAnnihilatingZero_2130
du_semiringWithoutAnnihilatingZero_2398 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_Monoid_882 -> T_RawMonoid_64) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Monoid_882 -> T_RawMonoid_64
du_rawMonoid_954 ((T_SemiringWithoutAnnihilatingZero_2130 -> T_Monoid_882)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_2130 -> T_Monoid_882
du_'42''45'monoid_2264 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3)))))
-- Algebra.Bundles.KleeneAlgebra._.semigroup
d_semigroup_3170 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_KleeneAlgebra_3008 -> T_Semigroup_536
d_semigroup_3170 :: () -> () -> T_KleeneAlgebra_3008 -> T_Semigroup_536
d_semigroup_3170 ~()
v0 ~()
v1 T_KleeneAlgebra_3008
v2 = T_KleeneAlgebra_3008 -> T_Semigroup_536
du_semigroup_3170 T_KleeneAlgebra_3008
v2
du_semigroup_3170 :: T_KleeneAlgebra_3008 -> T_Semigroup_536
du_semigroup_3170 :: T_KleeneAlgebra_3008 -> T_Semigroup_536
du_semigroup_3170 T_KleeneAlgebra_3008
v0
  = let v1 :: t
v1 = (T_KleeneAlgebra_3008 -> T_IdempotentSemiring_2822) -> AgdaAny -> t
forall a b. a -> b
coe T_KleeneAlgebra_3008 -> T_IdempotentSemiring_2822
du_idempotentSemiring_3156 (T_KleeneAlgebra_3008 -> AgdaAny
forall a b. a -> b
coe T_KleeneAlgebra_3008
v0) in
    AgdaAny -> T_Semigroup_536
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_IdempotentSemiring_2822 -> T_Semiring_2280) -> AgdaAny -> t
forall a b. a -> b
coe T_IdempotentSemiring_2822 -> T_Semiring_2280
du_semiring_2952 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: t
v3 = (T_Semiring_2280 -> T_SemiringWithoutAnnihilatingZero_2130)
-> AgdaAny -> t
forall a b. a -> b
coe T_Semiring_2280 -> T_SemiringWithoutAnnihilatingZero_2130
du_semiringWithoutAnnihilatingZero_2398 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_Monoid_882 -> T_Semigroup_536) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Monoid_882 -> T_Semigroup_536
du_semigroup_944 ((T_SemiringWithoutAnnihilatingZero_2130 -> T_Monoid_882)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_2130 -> T_Monoid_882
du_'42''45'monoid_2264 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3)))))
-- Algebra.Bundles.KleeneAlgebra._.commutativeMagma
d_commutativeMagma_3172 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_KleeneAlgebra_3008 -> T_CommutativeMagma_180
d_commutativeMagma_3172 :: () -> () -> T_KleeneAlgebra_3008 -> T_CommutativeMagma_180
d_commutativeMagma_3172 ~()
v0 ~()
v1 T_KleeneAlgebra_3008
v2 = T_KleeneAlgebra_3008 -> T_CommutativeMagma_180
du_commutativeMagma_3172 T_KleeneAlgebra_3008
v2
du_commutativeMagma_3172 ::
  T_KleeneAlgebra_3008 -> T_CommutativeMagma_180
du_commutativeMagma_3172 :: T_KleeneAlgebra_3008 -> T_CommutativeMagma_180
du_commutativeMagma_3172 T_KleeneAlgebra_3008
v0
  = let v1 :: t
v1 = (T_KleeneAlgebra_3008 -> T_IdempotentSemiring_2822) -> AgdaAny -> t
forall a b. a -> b
coe T_KleeneAlgebra_3008 -> T_IdempotentSemiring_2822
du_idempotentSemiring_3156 (T_KleeneAlgebra_3008 -> AgdaAny
forall a b. a -> b
coe T_KleeneAlgebra_3008
v0) in
    AgdaAny -> T_CommutativeMagma_180
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_IdempotentSemiring_2822 -> T_Semiring_2280) -> AgdaAny -> t
forall a b. a -> b
coe T_IdempotentSemiring_2822 -> T_Semiring_2280
du_semiring_2952 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: t
v3 = (T_Semiring_2280 -> T_SemiringWithoutAnnihilatingZero_2130)
-> AgdaAny -> t
forall a b. a -> b
coe T_Semiring_2280 -> T_SemiringWithoutAnnihilatingZero_2130
du_semiringWithoutAnnihilatingZero_2398 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: t
v4 = (T_SemiringWithoutAnnihilatingZero_2130 -> T_CommutativeMonoid_962)
-> AgdaAny -> t
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_2130 -> T_CommutativeMonoid_962
du_'43''45'commutativeMonoid_2242 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               ((T_CommutativeSemigroup_662 -> T_CommutativeMagma_180)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_CommutativeSemigroup_662 -> T_CommutativeMagma_180
du_commutativeMagma_726
                  ((T_CommutativeMonoid_962 -> T_CommutativeSemigroup_662)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeMonoid_962 -> T_CommutativeSemigroup_662
du_commutativeSemigroup_1048 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v4))))))
-- Algebra.Bundles.KleeneAlgebra._.+-commutativeMonoid
d_'43''45'commutativeMonoid_3174 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_KleeneAlgebra_3008 -> T_CommutativeMonoid_962
d_'43''45'commutativeMonoid_3174 :: () -> () -> T_KleeneAlgebra_3008 -> T_CommutativeMonoid_962
d_'43''45'commutativeMonoid_3174 ~()
v0 ~()
v1 T_KleeneAlgebra_3008
v2
  = T_KleeneAlgebra_3008 -> T_CommutativeMonoid_962
du_'43''45'commutativeMonoid_3174 T_KleeneAlgebra_3008
v2
du_'43''45'commutativeMonoid_3174 ::
  T_KleeneAlgebra_3008 -> T_CommutativeMonoid_962
du_'43''45'commutativeMonoid_3174 :: T_KleeneAlgebra_3008 -> T_CommutativeMonoid_962
du_'43''45'commutativeMonoid_3174 T_KleeneAlgebra_3008
v0
  = let v1 :: t
v1 = (T_KleeneAlgebra_3008 -> T_IdempotentSemiring_2822) -> AgdaAny -> t
forall a b. a -> b
coe T_KleeneAlgebra_3008 -> T_IdempotentSemiring_2822
du_idempotentSemiring_3156 (T_KleeneAlgebra_3008 -> AgdaAny
forall a b. a -> b
coe T_KleeneAlgebra_3008
v0) in
    AgdaAny -> T_CommutativeMonoid_962
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_IdempotentSemiring_2822 -> T_Semiring_2280) -> AgdaAny -> t
forall a b. a -> b
coe T_IdempotentSemiring_2822 -> T_Semiring_2280
du_semiring_2952 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_SemiringWithoutAnnihilatingZero_2130 -> T_CommutativeMonoid_962)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_SemiringWithoutAnnihilatingZero_2130 -> T_CommutativeMonoid_962
du_'43''45'commutativeMonoid_2242
            ((T_Semiring_2280 -> T_SemiringWithoutAnnihilatingZero_2130)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semiring_2280 -> T_SemiringWithoutAnnihilatingZero_2130
du_semiringWithoutAnnihilatingZero_2398 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2))))
-- Algebra.Bundles.KleeneAlgebra._.commutativeSemigroup
d_commutativeSemigroup_3176 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_KleeneAlgebra_3008 -> T_CommutativeSemigroup_662
d_commutativeSemigroup_3176 :: () -> () -> T_KleeneAlgebra_3008 -> T_CommutativeSemigroup_662
d_commutativeSemigroup_3176 ~()
v0 ~()
v1 T_KleeneAlgebra_3008
v2
  = T_KleeneAlgebra_3008 -> T_CommutativeSemigroup_662
du_commutativeSemigroup_3176 T_KleeneAlgebra_3008
v2
du_commutativeSemigroup_3176 ::
  T_KleeneAlgebra_3008 -> T_CommutativeSemigroup_662
du_commutativeSemigroup_3176 :: T_KleeneAlgebra_3008 -> T_CommutativeSemigroup_662
du_commutativeSemigroup_3176 T_KleeneAlgebra_3008
v0
  = let v1 :: t
v1 = (T_KleeneAlgebra_3008 -> T_IdempotentSemiring_2822) -> AgdaAny -> t
forall a b. a -> b
coe T_KleeneAlgebra_3008 -> T_IdempotentSemiring_2822
du_idempotentSemiring_3156 (T_KleeneAlgebra_3008 -> AgdaAny
forall a b. a -> b
coe T_KleeneAlgebra_3008
v0) in
    AgdaAny -> T_CommutativeSemigroup_662
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_IdempotentSemiring_2822 -> T_Semiring_2280) -> AgdaAny -> t
forall a b. a -> b
coe T_IdempotentSemiring_2822 -> T_Semiring_2280
du_semiring_2952 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: t
v3 = (T_Semiring_2280 -> T_SemiringWithoutAnnihilatingZero_2130)
-> AgdaAny -> t
forall a b. a -> b
coe T_Semiring_2280 -> T_SemiringWithoutAnnihilatingZero_2130
du_semiringWithoutAnnihilatingZero_2398 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_CommutativeMonoid_962 -> T_CommutativeSemigroup_662)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_CommutativeMonoid_962 -> T_CommutativeSemigroup_662
du_commutativeSemigroup_1048
               ((T_SemiringWithoutAnnihilatingZero_2130 -> T_CommutativeMonoid_962)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_2130 -> T_CommutativeMonoid_962
du_'43''45'commutativeMonoid_2242 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3)))))
-- Algebra.Bundles.KleeneAlgebra._.magma
d_magma_3178 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_KleeneAlgebra_3008 -> T_Magma_68
d_magma_3178 :: () -> () -> T_KleeneAlgebra_3008 -> T_Magma_68
d_magma_3178 ~()
v0 ~()
v1 T_KleeneAlgebra_3008
v2 = T_KleeneAlgebra_3008 -> T_Magma_68
du_magma_3178 T_KleeneAlgebra_3008
v2
du_magma_3178 :: T_KleeneAlgebra_3008 -> T_Magma_68
du_magma_3178 :: T_KleeneAlgebra_3008 -> T_Magma_68
du_magma_3178 T_KleeneAlgebra_3008
v0
  = let v1 :: t
v1 = (T_KleeneAlgebra_3008 -> T_IdempotentSemiring_2822) -> AgdaAny -> t
forall a b. a -> b
coe T_KleeneAlgebra_3008 -> T_IdempotentSemiring_2822
du_idempotentSemiring_3156 (T_KleeneAlgebra_3008 -> AgdaAny
forall a b. a -> b
coe T_KleeneAlgebra_3008
v0) in
    AgdaAny -> T_Magma_68
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_IdempotentSemiring_2822 -> T_Semiring_2280) -> AgdaAny -> t
forall a b. a -> b
coe T_IdempotentSemiring_2822 -> T_Semiring_2280
du_semiring_2952 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: t
v3 = (T_Semiring_2280 -> T_SemiringWithoutAnnihilatingZero_2130)
-> AgdaAny -> t
forall a b. a -> b
coe T_Semiring_2280 -> T_SemiringWithoutAnnihilatingZero_2130
du_semiringWithoutAnnihilatingZero_2398 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: t
v4 = (T_SemiringWithoutAnnihilatingZero_2130 -> T_CommutativeMonoid_962)
-> AgdaAny -> t
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_2130 -> T_CommutativeMonoid_962
du_'43''45'commutativeMonoid_2242 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: t
v5 = (T_CommutativeMonoid_962 -> T_Monoid_882) -> AgdaAny -> t
forall a b. a -> b
coe T_CommutativeMonoid_962 -> T_Monoid_882
du_monoid_1032 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_Semigroup_536 -> T_Magma_68) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semigroup_536 -> T_Magma_68
du_magma_584 ((T_Monoid_882 -> T_Semigroup_536) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Monoid_882 -> T_Semigroup_536
du_semigroup_944 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v5)))))))
-- Algebra.Bundles.KleeneAlgebra._.monoid
d_monoid_3180 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_KleeneAlgebra_3008 -> T_Monoid_882
d_monoid_3180 :: () -> () -> T_KleeneAlgebra_3008 -> T_Monoid_882
d_monoid_3180 ~()
v0 ~()
v1 T_KleeneAlgebra_3008
v2 = T_KleeneAlgebra_3008 -> T_Monoid_882
du_monoid_3180 T_KleeneAlgebra_3008
v2
du_monoid_3180 :: T_KleeneAlgebra_3008 -> T_Monoid_882
du_monoid_3180 :: T_KleeneAlgebra_3008 -> T_Monoid_882
du_monoid_3180 T_KleeneAlgebra_3008
v0
  = let v1 :: t
v1 = (T_KleeneAlgebra_3008 -> T_IdempotentSemiring_2822) -> AgdaAny -> t
forall a b. a -> b
coe T_KleeneAlgebra_3008 -> T_IdempotentSemiring_2822
du_idempotentSemiring_3156 (T_KleeneAlgebra_3008 -> AgdaAny
forall a b. a -> b
coe T_KleeneAlgebra_3008
v0) in
    AgdaAny -> T_Monoid_882
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_IdempotentSemiring_2822 -> T_Semiring_2280) -> AgdaAny -> t
forall a b. a -> b
coe T_IdempotentSemiring_2822 -> T_Semiring_2280
du_semiring_2952 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: t
v3 = (T_Semiring_2280 -> T_SemiringWithoutAnnihilatingZero_2130)
-> AgdaAny -> t
forall a b. a -> b
coe T_Semiring_2280 -> T_SemiringWithoutAnnihilatingZero_2130
du_semiringWithoutAnnihilatingZero_2398 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_CommutativeMonoid_962 -> T_Monoid_882) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_CommutativeMonoid_962 -> T_Monoid_882
du_monoid_1032 ((T_SemiringWithoutAnnihilatingZero_2130 -> T_CommutativeMonoid_962)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_2130 -> T_CommutativeMonoid_962
du_'43''45'commutativeMonoid_2242 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3)))))
-- Algebra.Bundles.KleeneAlgebra._.rawMagma
d_rawMagma_3182 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_KleeneAlgebra_3008 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
d_rawMagma_3182 :: () -> () -> T_KleeneAlgebra_3008 -> T_RawMagma_36
d_rawMagma_3182 ~()
v0 ~()
v1 T_KleeneAlgebra_3008
v2 = T_KleeneAlgebra_3008 -> T_RawMagma_36
du_rawMagma_3182 T_KleeneAlgebra_3008
v2
du_rawMagma_3182 ::
  T_KleeneAlgebra_3008 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
du_rawMagma_3182 :: T_KleeneAlgebra_3008 -> T_RawMagma_36
du_rawMagma_3182 T_KleeneAlgebra_3008
v0
  = let v1 :: t
v1 = (T_KleeneAlgebra_3008 -> T_IdempotentSemiring_2822) -> AgdaAny -> t
forall a b. a -> b
coe T_KleeneAlgebra_3008 -> T_IdempotentSemiring_2822
du_idempotentSemiring_3156 (T_KleeneAlgebra_3008 -> AgdaAny
forall a b. a -> b
coe T_KleeneAlgebra_3008
v0) in
    AgdaAny -> T_RawMagma_36
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_IdempotentSemiring_2822 -> T_Semiring_2280) -> AgdaAny -> t
forall a b. a -> b
coe T_IdempotentSemiring_2822 -> T_Semiring_2280
du_semiring_2952 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: t
v3 = (T_Semiring_2280 -> T_SemiringWithoutAnnihilatingZero_2130)
-> AgdaAny -> t
forall a b. a -> b
coe T_Semiring_2280 -> T_SemiringWithoutAnnihilatingZero_2130
du_semiringWithoutAnnihilatingZero_2398 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: t
v4 = (T_SemiringWithoutAnnihilatingZero_2130 -> T_CommutativeMonoid_962)
-> AgdaAny -> t
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_2130 -> T_CommutativeMonoid_962
du_'43''45'commutativeMonoid_2242 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: t
v5 = (T_CommutativeMonoid_962 -> T_Monoid_882) -> AgdaAny -> t
forall a b. a -> b
coe T_CommutativeMonoid_962 -> T_Monoid_882
du_monoid_1032 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (let v6 :: t
v6 = (T_Monoid_882 -> T_Semigroup_536) -> AgdaAny -> t
forall a b. a -> b
coe T_Monoid_882 -> T_Semigroup_536
du_semigroup_944 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v5) in
                   AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_Magma_68 -> T_RawMagma_36) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Magma_68 -> T_RawMagma_36
du_rawMagma_112 ((T_Semigroup_536 -> T_Magma_68) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semigroup_536 -> T_Magma_68
du_magma_584 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v6))))))))
-- Algebra.Bundles.KleeneAlgebra._.rawMonoid
d_rawMonoid_3184 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_KleeneAlgebra_3008 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMonoid_64
d_rawMonoid_3184 :: () -> () -> T_KleeneAlgebra_3008 -> T_RawMonoid_64
d_rawMonoid_3184 ~()
v0 ~()
v1 T_KleeneAlgebra_3008
v2 = T_KleeneAlgebra_3008 -> T_RawMonoid_64
du_rawMonoid_3184 T_KleeneAlgebra_3008
v2
du_rawMonoid_3184 ::
  T_KleeneAlgebra_3008 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMonoid_64
du_rawMonoid_3184 :: T_KleeneAlgebra_3008 -> T_RawMonoid_64
du_rawMonoid_3184 T_KleeneAlgebra_3008
v0
  = let v1 :: t
v1 = (T_KleeneAlgebra_3008 -> T_IdempotentSemiring_2822) -> AgdaAny -> t
forall a b. a -> b
coe T_KleeneAlgebra_3008 -> T_IdempotentSemiring_2822
du_idempotentSemiring_3156 (T_KleeneAlgebra_3008 -> AgdaAny
forall a b. a -> b
coe T_KleeneAlgebra_3008
v0) in
    AgdaAny -> T_RawMonoid_64
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_IdempotentSemiring_2822 -> T_Semiring_2280) -> AgdaAny -> t
forall a b. a -> b
coe T_IdempotentSemiring_2822 -> T_Semiring_2280
du_semiring_2952 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: t
v3 = (T_Semiring_2280 -> T_SemiringWithoutAnnihilatingZero_2130)
-> AgdaAny -> t
forall a b. a -> b
coe T_Semiring_2280 -> T_SemiringWithoutAnnihilatingZero_2130
du_semiringWithoutAnnihilatingZero_2398 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: t
v4 = (T_SemiringWithoutAnnihilatingZero_2130 -> T_CommutativeMonoid_962)
-> AgdaAny -> t
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_2130 -> T_CommutativeMonoid_962
du_'43''45'commutativeMonoid_2242 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_Monoid_882 -> T_RawMonoid_64) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Monoid_882 -> T_RawMonoid_64
du_rawMonoid_954 ((T_CommutativeMonoid_962 -> T_Monoid_882) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeMonoid_962 -> T_Monoid_882
du_monoid_1032 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v4))))))
-- Algebra.Bundles.KleeneAlgebra._.semigroup
d_semigroup_3186 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_KleeneAlgebra_3008 -> T_Semigroup_536
d_semigroup_3186 :: () -> () -> T_KleeneAlgebra_3008 -> T_Semigroup_536
d_semigroup_3186 ~()
v0 ~()
v1 T_KleeneAlgebra_3008
v2 = T_KleeneAlgebra_3008 -> T_Semigroup_536
du_semigroup_3186 T_KleeneAlgebra_3008
v2
du_semigroup_3186 :: T_KleeneAlgebra_3008 -> T_Semigroup_536
du_semigroup_3186 :: T_KleeneAlgebra_3008 -> T_Semigroup_536
du_semigroup_3186 T_KleeneAlgebra_3008
v0
  = let v1 :: t
v1 = (T_KleeneAlgebra_3008 -> T_IdempotentSemiring_2822) -> AgdaAny -> t
forall a b. a -> b
coe T_KleeneAlgebra_3008 -> T_IdempotentSemiring_2822
du_idempotentSemiring_3156 (T_KleeneAlgebra_3008 -> AgdaAny
forall a b. a -> b
coe T_KleeneAlgebra_3008
v0) in
    AgdaAny -> T_Semigroup_536
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_IdempotentSemiring_2822 -> T_Semiring_2280) -> AgdaAny -> t
forall a b. a -> b
coe T_IdempotentSemiring_2822 -> T_Semiring_2280
du_semiring_2952 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: t
v3 = (T_Semiring_2280 -> T_SemiringWithoutAnnihilatingZero_2130)
-> AgdaAny -> t
forall a b. a -> b
coe T_Semiring_2280 -> T_SemiringWithoutAnnihilatingZero_2130
du_semiringWithoutAnnihilatingZero_2398 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: t
v4 = (T_SemiringWithoutAnnihilatingZero_2130 -> T_CommutativeMonoid_962)
-> AgdaAny -> t
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_2130 -> T_CommutativeMonoid_962
du_'43''45'commutativeMonoid_2242 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_Monoid_882 -> T_Semigroup_536) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Monoid_882 -> T_Semigroup_536
du_semigroup_944 ((T_CommutativeMonoid_962 -> T_Monoid_882) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeMonoid_962 -> T_Monoid_882
du_monoid_1032 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v4))))))
-- Algebra.Bundles.KleeneAlgebra._.unitalMagma
d_unitalMagma_3188 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_KleeneAlgebra_3008 -> T_UnitalMagma_814
d_unitalMagma_3188 :: () -> () -> T_KleeneAlgebra_3008 -> T_UnitalMagma_814
d_unitalMagma_3188 ~()
v0 ~()
v1 T_KleeneAlgebra_3008
v2 = T_KleeneAlgebra_3008 -> T_UnitalMagma_814
du_unitalMagma_3188 T_KleeneAlgebra_3008
v2
du_unitalMagma_3188 :: T_KleeneAlgebra_3008 -> T_UnitalMagma_814
du_unitalMagma_3188 :: T_KleeneAlgebra_3008 -> T_UnitalMagma_814
du_unitalMagma_3188 T_KleeneAlgebra_3008
v0
  = let v1 :: t
v1 = (T_KleeneAlgebra_3008 -> T_IdempotentSemiring_2822) -> AgdaAny -> t
forall a b. a -> b
coe T_KleeneAlgebra_3008 -> T_IdempotentSemiring_2822
du_idempotentSemiring_3156 (T_KleeneAlgebra_3008 -> AgdaAny
forall a b. a -> b
coe T_KleeneAlgebra_3008
v0) in
    AgdaAny -> T_UnitalMagma_814
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_IdempotentSemiring_2822 -> T_Semiring_2280) -> AgdaAny -> t
forall a b. a -> b
coe T_IdempotentSemiring_2822 -> T_Semiring_2280
du_semiring_2952 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: t
v3 = (T_Semiring_2280 -> T_SemiringWithoutAnnihilatingZero_2130)
-> AgdaAny -> t
forall a b. a -> b
coe T_Semiring_2280 -> T_SemiringWithoutAnnihilatingZero_2130
du_semiringWithoutAnnihilatingZero_2398 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: t
v4 = (T_SemiringWithoutAnnihilatingZero_2130 -> T_CommutativeMonoid_962)
-> AgdaAny -> t
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_2130 -> T_CommutativeMonoid_962
du_'43''45'commutativeMonoid_2242 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_Monoid_882 -> T_UnitalMagma_814) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Monoid_882 -> T_UnitalMagma_814
du_unitalMagma_956 ((T_CommutativeMonoid_962 -> T_Monoid_882) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeMonoid_962 -> T_Monoid_882
du_monoid_1032 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v4))))))
-- Algebra.Bundles.KleeneAlgebra._.nearSemiring
d_nearSemiring_3190 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_KleeneAlgebra_3008 -> T_NearSemiring_1766
d_nearSemiring_3190 :: () -> () -> T_KleeneAlgebra_3008 -> T_NearSemiring_1766
d_nearSemiring_3190 ~()
v0 ~()
v1 T_KleeneAlgebra_3008
v2 = T_KleeneAlgebra_3008 -> T_NearSemiring_1766
du_nearSemiring_3190 T_KleeneAlgebra_3008
v2
du_nearSemiring_3190 :: T_KleeneAlgebra_3008 -> T_NearSemiring_1766
du_nearSemiring_3190 :: T_KleeneAlgebra_3008 -> T_NearSemiring_1766
du_nearSemiring_3190 T_KleeneAlgebra_3008
v0
  = let v1 :: t
v1 = (T_KleeneAlgebra_3008 -> T_IdempotentSemiring_2822) -> AgdaAny -> t
forall a b. a -> b
coe T_KleeneAlgebra_3008 -> T_IdempotentSemiring_2822
du_idempotentSemiring_3156 (T_KleeneAlgebra_3008 -> AgdaAny
forall a b. a -> b
coe T_KleeneAlgebra_3008
v0) in
    AgdaAny -> T_NearSemiring_1766
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_IdempotentSemiring_2822 -> T_Semiring_2280) -> AgdaAny -> t
forall a b. a -> b
coe T_IdempotentSemiring_2822 -> T_Semiring_2280
du_semiring_2952 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_SemiringWithoutOne_1880 -> T_NearSemiring_1766)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_SemiringWithoutOne_1880 -> T_NearSemiring_1766
du_nearSemiring_1966 ((T_Semiring_2280 -> T_SemiringWithoutOne_1880)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semiring_2280 -> T_SemiringWithoutOne_1880
du_semiringWithoutOne_2436 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2))))
-- Algebra.Bundles.KleeneAlgebra._.rawSemiring
d_rawSemiring_3192 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_KleeneAlgebra_3008 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawSemiring_174
d_rawSemiring_3192 :: () -> () -> T_KleeneAlgebra_3008 -> T_RawSemiring_174
d_rawSemiring_3192 ~()
v0 ~()
v1 T_KleeneAlgebra_3008
v2 = T_KleeneAlgebra_3008 -> T_RawSemiring_174
du_rawSemiring_3192 T_KleeneAlgebra_3008
v2
du_rawSemiring_3192 ::
  T_KleeneAlgebra_3008 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawSemiring_174
du_rawSemiring_3192 :: T_KleeneAlgebra_3008 -> T_RawSemiring_174
du_rawSemiring_3192 T_KleeneAlgebra_3008
v0
  = let v1 :: t
v1 = (T_KleeneAlgebra_3008 -> T_IdempotentSemiring_2822) -> AgdaAny -> t
forall a b. a -> b
coe T_KleeneAlgebra_3008 -> T_IdempotentSemiring_2822
du_idempotentSemiring_3156 (T_KleeneAlgebra_3008 -> AgdaAny
forall a b. a -> b
coe T_KleeneAlgebra_3008
v0) in
    AgdaAny -> T_RawSemiring_174
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_IdempotentSemiring_2822 -> T_Semiring_2280) -> AgdaAny -> t
forall a b. a -> b
coe T_IdempotentSemiring_2822 -> T_Semiring_2280
du_semiring_2952 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_SemiringWithoutAnnihilatingZero_2130 -> T_RawSemiring_174)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_SemiringWithoutAnnihilatingZero_2130 -> T_RawSemiring_174
du_rawSemiring_2236
            ((T_Semiring_2280 -> T_SemiringWithoutAnnihilatingZero_2130)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semiring_2280 -> T_SemiringWithoutAnnihilatingZero_2130
du_semiringWithoutAnnihilatingZero_2398 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2))))
-- Algebra.Bundles.KleeneAlgebra._.semiring
d_semiring_3194 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_KleeneAlgebra_3008 -> T_Semiring_2280
d_semiring_3194 :: () -> () -> T_KleeneAlgebra_3008 -> T_Semiring_2280
d_semiring_3194 ~()
v0 ~()
v1 T_KleeneAlgebra_3008
v2 = T_KleeneAlgebra_3008 -> T_Semiring_2280
du_semiring_3194 T_KleeneAlgebra_3008
v2
du_semiring_3194 :: T_KleeneAlgebra_3008 -> T_Semiring_2280
du_semiring_3194 :: T_KleeneAlgebra_3008 -> T_Semiring_2280
du_semiring_3194 T_KleeneAlgebra_3008
v0
  = (T_IdempotentSemiring_2822 -> T_Semiring_2280)
-> AgdaAny -> T_Semiring_2280
forall a b. a -> b
coe T_IdempotentSemiring_2822 -> T_Semiring_2280
du_semiring_2952 ((T_KleeneAlgebra_3008 -> T_IdempotentSemiring_2822)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_KleeneAlgebra_3008 -> T_IdempotentSemiring_2822
du_idempotentSemiring_3156 (T_KleeneAlgebra_3008 -> AgdaAny
forall a b. a -> b
coe T_KleeneAlgebra_3008
v0))
-- Algebra.Bundles.KleeneAlgebra._.semiringWithoutAnnihilatingZero
d_semiringWithoutAnnihilatingZero_3196 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_KleeneAlgebra_3008 -> T_SemiringWithoutAnnihilatingZero_2130
d_semiringWithoutAnnihilatingZero_3196 :: ()
-> ()
-> T_KleeneAlgebra_3008
-> T_SemiringWithoutAnnihilatingZero_2130
d_semiringWithoutAnnihilatingZero_3196 ~()
v0 ~()
v1 T_KleeneAlgebra_3008
v2
  = T_KleeneAlgebra_3008 -> T_SemiringWithoutAnnihilatingZero_2130
du_semiringWithoutAnnihilatingZero_3196 T_KleeneAlgebra_3008
v2
du_semiringWithoutAnnihilatingZero_3196 ::
  T_KleeneAlgebra_3008 -> T_SemiringWithoutAnnihilatingZero_2130
du_semiringWithoutAnnihilatingZero_3196 :: T_KleeneAlgebra_3008 -> T_SemiringWithoutAnnihilatingZero_2130
du_semiringWithoutAnnihilatingZero_3196 T_KleeneAlgebra_3008
v0
  = let v1 :: t
v1 = (T_KleeneAlgebra_3008 -> T_IdempotentSemiring_2822) -> AgdaAny -> t
forall a b. a -> b
coe T_KleeneAlgebra_3008 -> T_IdempotentSemiring_2822
du_idempotentSemiring_3156 (T_KleeneAlgebra_3008 -> AgdaAny
forall a b. a -> b
coe T_KleeneAlgebra_3008
v0) in
    AgdaAny -> T_SemiringWithoutAnnihilatingZero_2130
forall a b. a -> b
coe
      ((T_Semiring_2280 -> T_SemiringWithoutAnnihilatingZero_2130)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_Semiring_2280 -> T_SemiringWithoutAnnihilatingZero_2130
du_semiringWithoutAnnihilatingZero_2398
         ((T_IdempotentSemiring_2822 -> T_Semiring_2280)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IdempotentSemiring_2822 -> T_Semiring_2280
du_semiring_2952 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1)))
-- Algebra.Bundles.KleeneAlgebra._.semiringWithoutOne
d_semiringWithoutOne_3198 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_KleeneAlgebra_3008 -> T_SemiringWithoutOne_1880
d_semiringWithoutOne_3198 :: () -> () -> T_KleeneAlgebra_3008 -> T_SemiringWithoutOne_1880
d_semiringWithoutOne_3198 ~()
v0 ~()
v1 T_KleeneAlgebra_3008
v2
  = T_KleeneAlgebra_3008 -> T_SemiringWithoutOne_1880
du_semiringWithoutOne_3198 T_KleeneAlgebra_3008
v2
du_semiringWithoutOne_3198 ::
  T_KleeneAlgebra_3008 -> T_SemiringWithoutOne_1880
du_semiringWithoutOne_3198 :: T_KleeneAlgebra_3008 -> T_SemiringWithoutOne_1880
du_semiringWithoutOne_3198 T_KleeneAlgebra_3008
v0
  = let v1 :: t
v1 = (T_KleeneAlgebra_3008 -> T_IdempotentSemiring_2822) -> AgdaAny -> t
forall a b. a -> b
coe T_KleeneAlgebra_3008 -> T_IdempotentSemiring_2822
du_idempotentSemiring_3156 (T_KleeneAlgebra_3008 -> AgdaAny
forall a b. a -> b
coe T_KleeneAlgebra_3008
v0) in
    AgdaAny -> T_SemiringWithoutOne_1880
forall a b. a -> b
coe
      ((T_Semiring_2280 -> T_SemiringWithoutOne_1880)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semiring_2280 -> T_SemiringWithoutOne_1880
du_semiringWithoutOne_2436 ((T_IdempotentSemiring_2822 -> T_Semiring_2280)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IdempotentSemiring_2822 -> T_Semiring_2280
du_semiring_2952 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1)))
-- Algebra.Bundles.Quasiring
d_Quasiring_3204 :: p -> p -> ()
d_Quasiring_3204 p
a0 p
a1 = ()
data T_Quasiring_3204
  = C_Quasiring'46'constructor_57285 (AgdaAny -> AgdaAny -> AgdaAny)
                                     (AgdaAny -> AgdaAny -> AgdaAny) AgdaAny AgdaAny
                                     MAlonzo.Code.Algebra.Structures.T_IsQuasiring_2180
-- Algebra.Bundles.Quasiring.Carrier
d_Carrier_3224 :: T_Quasiring_3204 -> ()
d_Carrier_3224 :: T_Quasiring_3204 -> ()
d_Carrier_3224 = T_Quasiring_3204 -> ()
forall a. a
erased
-- Algebra.Bundles.Quasiring._≈_
d__'8776'__3226 :: T_Quasiring_3204 -> AgdaAny -> AgdaAny -> ()
d__'8776'__3226 :: T_Quasiring_3204 -> AgdaAny -> AgdaAny -> ()
d__'8776'__3226 = T_Quasiring_3204 -> AgdaAny -> AgdaAny -> ()
forall a. a
erased
-- Algebra.Bundles.Quasiring._+_
d__'43'__3228 :: T_Quasiring_3204 -> AgdaAny -> AgdaAny -> AgdaAny
d__'43'__3228 :: T_Quasiring_3204 -> AgdaAny -> AgdaAny -> AgdaAny
d__'43'__3228 T_Quasiring_3204
v0
  = case T_Quasiring_3204 -> T_Quasiring_3204
forall a b. a -> b
coe T_Quasiring_3204
v0 of
      C_Quasiring'46'constructor_57285 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny
v5 AgdaAny
v6 T_IsQuasiring_2180
v7 -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v3
      T_Quasiring_3204
_ -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.Quasiring._*_
d__'42'__3230 :: T_Quasiring_3204 -> AgdaAny -> AgdaAny -> AgdaAny
d__'42'__3230 :: T_Quasiring_3204 -> AgdaAny -> AgdaAny -> AgdaAny
d__'42'__3230 T_Quasiring_3204
v0
  = case T_Quasiring_3204 -> T_Quasiring_3204
forall a b. a -> b
coe T_Quasiring_3204
v0 of
      C_Quasiring'46'constructor_57285 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny
v5 AgdaAny
v6 T_IsQuasiring_2180
v7 -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v4
      T_Quasiring_3204
_ -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.Quasiring.0#
d_0'35'_3232 :: T_Quasiring_3204 -> AgdaAny
d_0'35'_3232 :: T_Quasiring_3204 -> AgdaAny
d_0'35'_3232 T_Quasiring_3204
v0
  = case T_Quasiring_3204 -> T_Quasiring_3204
forall a b. a -> b
coe T_Quasiring_3204
v0 of
      C_Quasiring'46'constructor_57285 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny
v5 AgdaAny
v6 T_IsQuasiring_2180
v7 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v5
      T_Quasiring_3204
_ -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.Quasiring.1#
d_1'35'_3234 :: T_Quasiring_3204 -> AgdaAny
d_1'35'_3234 :: T_Quasiring_3204 -> AgdaAny
d_1'35'_3234 T_Quasiring_3204
v0
  = case T_Quasiring_3204 -> T_Quasiring_3204
forall a b. a -> b
coe T_Quasiring_3204
v0 of
      C_Quasiring'46'constructor_57285 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny
v5 AgdaAny
v6 T_IsQuasiring_2180
v7 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v6
      T_Quasiring_3204
_ -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.Quasiring.isQuasiring
d_isQuasiring_3236 ::
  T_Quasiring_3204 ->
  MAlonzo.Code.Algebra.Structures.T_IsQuasiring_2180
d_isQuasiring_3236 :: T_Quasiring_3204 -> T_IsQuasiring_2180
d_isQuasiring_3236 T_Quasiring_3204
v0
  = case T_Quasiring_3204 -> T_Quasiring_3204
forall a b. a -> b
coe T_Quasiring_3204
v0 of
      C_Quasiring'46'constructor_57285 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny
v5 AgdaAny
v6 T_IsQuasiring_2180
v7 -> T_IsQuasiring_2180 -> T_IsQuasiring_2180
forall a b. a -> b
coe T_IsQuasiring_2180
v7
      T_Quasiring_3204
_ -> T_IsQuasiring_2180
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.Quasiring._.*-assoc
d_'42''45'assoc_3240 ::
  T_Quasiring_3204 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'assoc_3240 :: T_Quasiring_3204 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'assoc_3240 T_Quasiring_3204
v0
  = (T_IsQuasiring_2180 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsQuasiring_2180 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'42''45'assoc_2206
      ((T_Quasiring_3204 -> T_IsQuasiring_2180) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Quasiring_3204 -> T_IsQuasiring_2180
d_isQuasiring_3236 (T_Quasiring_3204 -> AgdaAny
forall a b. a -> b
coe T_Quasiring_3204
v0))
-- Algebra.Bundles.Quasiring._.*-cong
d_'42''45'cong_3242 ::
  T_Quasiring_3204 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'cong_3242 :: T_Quasiring_3204
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'42''45'cong_3242 T_Quasiring_3204
v0
  = (T_IsQuasiring_2180
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsQuasiring_2180
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'42''45'cong_2204
      ((T_Quasiring_3204 -> T_IsQuasiring_2180) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Quasiring_3204 -> T_IsQuasiring_2180
d_isQuasiring_3236 (T_Quasiring_3204 -> AgdaAny
forall a b. a -> b
coe T_Quasiring_3204
v0))
-- Algebra.Bundles.Quasiring._.∙-congʳ
d_'8729''45'cong'691'_3244 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Quasiring_3204 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_3244 :: ()
-> ()
-> T_Quasiring_3204
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_3244 ~()
v0 ~()
v1 T_Quasiring_3204
v2
  = T_Quasiring_3204
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_3244 T_Quasiring_3204
v2
du_'8729''45'cong'691'_3244 ::
  T_Quasiring_3204 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_3244 :: T_Quasiring_3204
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_3244 T_Quasiring_3204
v0
  = let v1 :: T_IsQuasiring_2180
v1 = T_Quasiring_3204 -> T_IsQuasiring_2180
d_isQuasiring_3236 (T_Quasiring_3204 -> T_Quasiring_3204
forall a b. a -> b
coe T_Quasiring_3204
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: t
v2
             = (T_IsQuasiring_2180 -> T_IsMonoid_686) -> AgdaAny -> t
forall a b. a -> b
coe
                 T_IsQuasiring_2180 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.du_'42''45'isMonoid_2266
                 (T_IsQuasiring_2180 -> AgdaAny
forall a b. a -> b
coe T_IsQuasiring_2180
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_472
v3
                = T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (AgdaAny -> T_IsMonoid_686
forall a b. a -> b
coe AgdaAny
forall a. a
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'691'_206
               ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v3)))))
-- Algebra.Bundles.Quasiring._.∙-congˡ
d_'8729''45'cong'737'_3246 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Quasiring_3204 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_3246 :: ()
-> ()
-> T_Quasiring_3204
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_3246 ~()
v0 ~()
v1 T_Quasiring_3204
v2
  = T_Quasiring_3204
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_3246 T_Quasiring_3204
v2
du_'8729''45'cong'737'_3246 ::
  T_Quasiring_3204 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_3246 :: T_Quasiring_3204
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_3246 T_Quasiring_3204
v0
  = let v1 :: T_IsQuasiring_2180
v1 = T_Quasiring_3204 -> T_IsQuasiring_2180
d_isQuasiring_3236 (T_Quasiring_3204 -> T_Quasiring_3204
forall a b. a -> b
coe T_Quasiring_3204
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: t
v2
             = (T_IsQuasiring_2180 -> T_IsMonoid_686) -> AgdaAny -> t
forall a b. a -> b
coe
                 T_IsQuasiring_2180 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.du_'42''45'isMonoid_2266
                 (T_IsQuasiring_2180 -> AgdaAny
forall a b. a -> b
coe T_IsQuasiring_2180
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_472
v3
                = T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (AgdaAny -> T_IsMonoid_686
forall a b. a -> b
coe AgdaAny
forall a. a
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'737'_202
               ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v3)))))
-- Algebra.Bundles.Quasiring._.*-identity
d_'42''45'identity_3248 ::
  T_Quasiring_3204 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'42''45'identity_3248 :: T_Quasiring_3204 -> T_Σ_14
d_'42''45'identity_3248 T_Quasiring_3204
v0
  = (T_IsQuasiring_2180 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsQuasiring_2180 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_'42''45'identity_2208
      ((T_Quasiring_3204 -> T_IsQuasiring_2180) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Quasiring_3204 -> T_IsQuasiring_2180
d_isQuasiring_3236 (T_Quasiring_3204 -> AgdaAny
forall a b. a -> b
coe T_Quasiring_3204
v0))
-- Algebra.Bundles.Quasiring._.identityʳ
d_identity'691'_3250 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Quasiring_3204 -> AgdaAny -> AgdaAny
d_identity'691'_3250 :: () -> () -> T_Quasiring_3204 -> AgdaAny -> AgdaAny
d_identity'691'_3250 ~()
v0 ~()
v1 T_Quasiring_3204
v2 = T_Quasiring_3204 -> AgdaAny -> AgdaAny
du_identity'691'_3250 T_Quasiring_3204
v2
du_identity'691'_3250 :: T_Quasiring_3204 -> AgdaAny -> AgdaAny
du_identity'691'_3250 :: T_Quasiring_3204 -> AgdaAny -> AgdaAny
du_identity'691'_3250 T_Quasiring_3204
v0
  = let v1 :: T_IsQuasiring_2180
v1 = T_Quasiring_3204 -> T_IsQuasiring_2180
d_isQuasiring_3236 (T_Quasiring_3204 -> T_Quasiring_3204
forall a b. a -> b
coe T_Quasiring_3204
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsMonoid_686 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoid_686 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_identity'691'_728
         ((T_IsQuasiring_2180 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsQuasiring_2180 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.du_'42''45'isMonoid_2266 (T_IsQuasiring_2180 -> AgdaAny
forall a b. a -> b
coe T_IsQuasiring_2180
v1)))
-- Algebra.Bundles.Quasiring._.identityˡ
d_identity'737'_3252 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Quasiring_3204 -> AgdaAny -> AgdaAny
d_identity'737'_3252 :: () -> () -> T_Quasiring_3204 -> AgdaAny -> AgdaAny
d_identity'737'_3252 ~()
v0 ~()
v1 T_Quasiring_3204
v2 = T_Quasiring_3204 -> AgdaAny -> AgdaAny
du_identity'737'_3252 T_Quasiring_3204
v2
du_identity'737'_3252 :: T_Quasiring_3204 -> AgdaAny -> AgdaAny
du_identity'737'_3252 :: T_Quasiring_3204 -> AgdaAny -> AgdaAny
du_identity'737'_3252 T_Quasiring_3204
v0
  = let v1 :: T_IsQuasiring_2180
v1 = T_Quasiring_3204 -> T_IsQuasiring_2180
d_isQuasiring_3236 (T_Quasiring_3204 -> T_Quasiring_3204
forall a b. a -> b
coe T_Quasiring_3204
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsMonoid_686 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoid_686 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_identity'737'_726
         ((T_IsQuasiring_2180 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsQuasiring_2180 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.du_'42''45'isMonoid_2266 (T_IsQuasiring_2180 -> AgdaAny
forall a b. a -> b
coe T_IsQuasiring_2180
v1)))
-- Algebra.Bundles.Quasiring._.*-isMagma
d_'42''45'isMagma_3254 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Quasiring_3204 -> MAlonzo.Code.Algebra.Structures.T_IsMagma_176
d_'42''45'isMagma_3254 :: () -> () -> T_Quasiring_3204 -> T_IsMagma_176
d_'42''45'isMagma_3254 ~()
v0 ~()
v1 T_Quasiring_3204
v2 = T_Quasiring_3204 -> T_IsMagma_176
du_'42''45'isMagma_3254 T_Quasiring_3204
v2
du_'42''45'isMagma_3254 ::
  T_Quasiring_3204 -> MAlonzo.Code.Algebra.Structures.T_IsMagma_176
du_'42''45'isMagma_3254 :: T_Quasiring_3204 -> T_IsMagma_176
du_'42''45'isMagma_3254 T_Quasiring_3204
v0
  = (T_IsQuasiring_2180 -> T_IsMagma_176) -> AgdaAny -> T_IsMagma_176
forall a b. a -> b
coe
      T_IsQuasiring_2180 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.du_'42''45'isMagma_2262
      ((T_Quasiring_3204 -> T_IsQuasiring_2180) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Quasiring_3204 -> T_IsQuasiring_2180
d_isQuasiring_3236 (T_Quasiring_3204 -> AgdaAny
forall a b. a -> b
coe T_Quasiring_3204
v0))
-- Algebra.Bundles.Quasiring._.*-isMonoid
d_'42''45'isMonoid_3256 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Quasiring_3204 -> MAlonzo.Code.Algebra.Structures.T_IsMonoid_686
d_'42''45'isMonoid_3256 :: () -> () -> T_Quasiring_3204 -> T_IsMonoid_686
d_'42''45'isMonoid_3256 ~()
v0 ~()
v1 T_Quasiring_3204
v2 = T_Quasiring_3204 -> T_IsMonoid_686
du_'42''45'isMonoid_3256 T_Quasiring_3204
v2
du_'42''45'isMonoid_3256 ::
  T_Quasiring_3204 -> MAlonzo.Code.Algebra.Structures.T_IsMonoid_686
du_'42''45'isMonoid_3256 :: T_Quasiring_3204 -> T_IsMonoid_686
du_'42''45'isMonoid_3256 T_Quasiring_3204
v0
  = (T_IsQuasiring_2180 -> T_IsMonoid_686) -> AgdaAny -> T_IsMonoid_686
forall a b. a -> b
coe
      T_IsQuasiring_2180 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.du_'42''45'isMonoid_2266
      ((T_Quasiring_3204 -> T_IsQuasiring_2180) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Quasiring_3204 -> T_IsQuasiring_2180
d_isQuasiring_3236 (T_Quasiring_3204 -> AgdaAny
forall a b. a -> b
coe T_Quasiring_3204
v0))
-- Algebra.Bundles.Quasiring._.*-isSemigroup
d_'42''45'isSemigroup_3258 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Quasiring_3204 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_472
d_'42''45'isSemigroup_3258 :: () -> () -> T_Quasiring_3204 -> T_IsSemigroup_472
d_'42''45'isSemigroup_3258 ~()
v0 ~()
v1 T_Quasiring_3204
v2
  = T_Quasiring_3204 -> T_IsSemigroup_472
du_'42''45'isSemigroup_3258 T_Quasiring_3204
v2
du_'42''45'isSemigroup_3258 ::
  T_Quasiring_3204 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_472
du_'42''45'isSemigroup_3258 :: T_Quasiring_3204 -> T_IsSemigroup_472
du_'42''45'isSemigroup_3258 T_Quasiring_3204
v0
  = (T_IsQuasiring_2180 -> T_IsSemigroup_472)
-> AgdaAny -> T_IsSemigroup_472
forall a b. a -> b
coe
      T_IsQuasiring_2180 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.du_'42''45'isSemigroup_2264
      ((T_Quasiring_3204 -> T_IsQuasiring_2180) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Quasiring_3204 -> T_IsQuasiring_2180
d_isQuasiring_3236 (T_Quasiring_3204 -> AgdaAny
forall a b. a -> b
coe T_Quasiring_3204
v0))
-- Algebra.Bundles.Quasiring._.assoc
d_assoc_3260 ::
  T_Quasiring_3204 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_3260 :: T_Quasiring_3204 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_3260 T_Quasiring_3204
v0
  = (T_IsSemigroup_472 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsSemigroup_472 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_assoc_482
      ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
         ((T_IsQuasiring_2180 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsQuasiring_2180 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_'43''45'isMonoid_2202
            ((T_Quasiring_3204 -> T_IsQuasiring_2180) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Quasiring_3204 -> T_IsQuasiring_2180
d_isQuasiring_3236 (T_Quasiring_3204 -> AgdaAny
forall a b. a -> b
coe T_Quasiring_3204
v0))))
-- Algebra.Bundles.Quasiring._.∙-cong
d_'8729''45'cong_3262 ::
  T_Quasiring_3204 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_3262 :: T_Quasiring_3204
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_3262 T_Quasiring_3204
v0
  = (T_IsMagma_176
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsMagma_176
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_186
      ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480
         ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
            ((T_IsQuasiring_2180 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsQuasiring_2180 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_'43''45'isMonoid_2202
               ((T_Quasiring_3204 -> T_IsQuasiring_2180) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Quasiring_3204 -> T_IsQuasiring_2180
d_isQuasiring_3236 (T_Quasiring_3204 -> AgdaAny
forall a b. a -> b
coe T_Quasiring_3204
v0)))))
-- Algebra.Bundles.Quasiring._.∙-congʳ
d_'8729''45'cong'691'_3264 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Quasiring_3204 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_3264 :: ()
-> ()
-> T_Quasiring_3204
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_3264 ~()
v0 ~()
v1 T_Quasiring_3204
v2
  = T_Quasiring_3204
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_3264 T_Quasiring_3204
v2
du_'8729''45'cong'691'_3264 ::
  T_Quasiring_3204 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_3264 :: T_Quasiring_3204
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_3264 T_Quasiring_3204
v0
  = let v1 :: T_IsQuasiring_2180
v1 = T_Quasiring_3204 -> T_IsQuasiring_2180
d_isQuasiring_3236 (T_Quasiring_3204 -> T_Quasiring_3204
forall a b. a -> b
coe T_Quasiring_3204
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsMonoid_686
v2
             = T_IsQuasiring_2180 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_'43''45'isMonoid_2202
                 (T_IsQuasiring_2180 -> T_IsQuasiring_2180
forall a b. a -> b
coe T_IsQuasiring_2180
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_472
v3
                = T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'691'_206
               ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v3)))))
-- Algebra.Bundles.Quasiring._.∙-congˡ
d_'8729''45'cong'737'_3266 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Quasiring_3204 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_3266 :: ()
-> ()
-> T_Quasiring_3204
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_3266 ~()
v0 ~()
v1 T_Quasiring_3204
v2
  = T_Quasiring_3204
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_3266 T_Quasiring_3204
v2
du_'8729''45'cong'737'_3266 ::
  T_Quasiring_3204 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_3266 :: T_Quasiring_3204
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_3266 T_Quasiring_3204
v0
  = let v1 :: T_IsQuasiring_2180
v1 = T_Quasiring_3204 -> T_IsQuasiring_2180
d_isQuasiring_3236 (T_Quasiring_3204 -> T_Quasiring_3204
forall a b. a -> b
coe T_Quasiring_3204
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsMonoid_686
v2
             = T_IsQuasiring_2180 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_'43''45'isMonoid_2202
                 (T_IsQuasiring_2180 -> T_IsQuasiring_2180
forall a b. a -> b
coe T_IsQuasiring_2180
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_472
v3
                = T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'737'_202
               ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v3)))))
-- Algebra.Bundles.Quasiring._.identity
d_identity_3268 ::
  T_Quasiring_3204 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_identity_3268 :: T_Quasiring_3204 -> T_Σ_14
d_identity_3268 T_Quasiring_3204
v0
  = (T_IsMonoid_686 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsMonoid_686 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_identity_698
      ((T_IsQuasiring_2180 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsQuasiring_2180 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_'43''45'isMonoid_2202
         ((T_Quasiring_3204 -> T_IsQuasiring_2180) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Quasiring_3204 -> T_IsQuasiring_2180
d_isQuasiring_3236 (T_Quasiring_3204 -> AgdaAny
forall a b. a -> b
coe T_Quasiring_3204
v0)))
-- Algebra.Bundles.Quasiring._.identityʳ
d_identity'691'_3270 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Quasiring_3204 -> AgdaAny -> AgdaAny
d_identity'691'_3270 :: () -> () -> T_Quasiring_3204 -> AgdaAny -> AgdaAny
d_identity'691'_3270 ~()
v0 ~()
v1 T_Quasiring_3204
v2 = T_Quasiring_3204 -> AgdaAny -> AgdaAny
du_identity'691'_3270 T_Quasiring_3204
v2
du_identity'691'_3270 :: T_Quasiring_3204 -> AgdaAny -> AgdaAny
du_identity'691'_3270 :: T_Quasiring_3204 -> AgdaAny -> AgdaAny
du_identity'691'_3270 T_Quasiring_3204
v0
  = let v1 :: T_IsQuasiring_2180
v1 = T_Quasiring_3204 -> T_IsQuasiring_2180
d_isQuasiring_3236 (T_Quasiring_3204 -> T_Quasiring_3204
forall a b. a -> b
coe T_Quasiring_3204
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsMonoid_686 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoid_686 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_identity'691'_728
         ((T_IsQuasiring_2180 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsQuasiring_2180 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_'43''45'isMonoid_2202 (T_IsQuasiring_2180 -> AgdaAny
forall a b. a -> b
coe T_IsQuasiring_2180
v1)))
-- Algebra.Bundles.Quasiring._.identityˡ
d_identity'737'_3272 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Quasiring_3204 -> AgdaAny -> AgdaAny
d_identity'737'_3272 :: () -> () -> T_Quasiring_3204 -> AgdaAny -> AgdaAny
d_identity'737'_3272 ~()
v0 ~()
v1 T_Quasiring_3204
v2 = T_Quasiring_3204 -> AgdaAny -> AgdaAny
du_identity'737'_3272 T_Quasiring_3204
v2
du_identity'737'_3272 :: T_Quasiring_3204 -> AgdaAny -> AgdaAny
du_identity'737'_3272 :: T_Quasiring_3204 -> AgdaAny -> AgdaAny
du_identity'737'_3272 T_Quasiring_3204
v0
  = let v1 :: T_IsQuasiring_2180
v1 = T_Quasiring_3204 -> T_IsQuasiring_2180
d_isQuasiring_3236 (T_Quasiring_3204 -> T_Quasiring_3204
forall a b. a -> b
coe T_Quasiring_3204
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsMonoid_686 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoid_686 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_identity'737'_726
         ((T_IsQuasiring_2180 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsQuasiring_2180 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_'43''45'isMonoid_2202 (T_IsQuasiring_2180 -> AgdaAny
forall a b. a -> b
coe T_IsQuasiring_2180
v1)))
-- Algebra.Bundles.Quasiring._.isMagma
d_isMagma_3274 ::
  T_Quasiring_3204 -> MAlonzo.Code.Algebra.Structures.T_IsMagma_176
d_isMagma_3274 :: T_Quasiring_3204 -> T_IsMagma_176
d_isMagma_3274 T_Quasiring_3204
v0
  = (T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> T_IsMagma_176
forall a b. a -> b
coe
      T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480
      ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
         ((T_IsQuasiring_2180 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsQuasiring_2180 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_'43''45'isMonoid_2202
            ((T_Quasiring_3204 -> T_IsQuasiring_2180) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Quasiring_3204 -> T_IsQuasiring_2180
d_isQuasiring_3236 (T_Quasiring_3204 -> AgdaAny
forall a b. a -> b
coe T_Quasiring_3204
v0))))
-- Algebra.Bundles.Quasiring._.+-isMonoid
d_'43''45'isMonoid_3276 ::
  T_Quasiring_3204 -> MAlonzo.Code.Algebra.Structures.T_IsMonoid_686
d_'43''45'isMonoid_3276 :: T_Quasiring_3204 -> T_IsMonoid_686
d_'43''45'isMonoid_3276 T_Quasiring_3204
v0
  = (T_IsQuasiring_2180 -> T_IsMonoid_686) -> AgdaAny -> T_IsMonoid_686
forall a b. a -> b
coe
      T_IsQuasiring_2180 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_'43''45'isMonoid_2202
      ((T_Quasiring_3204 -> T_IsQuasiring_2180) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Quasiring_3204 -> T_IsQuasiring_2180
d_isQuasiring_3236 (T_Quasiring_3204 -> AgdaAny
forall a b. a -> b
coe T_Quasiring_3204
v0))
-- Algebra.Bundles.Quasiring._.isSemigroup
d_isSemigroup_3278 ::
  T_Quasiring_3204 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_472
d_isSemigroup_3278 :: T_Quasiring_3204 -> T_IsSemigroup_472
d_isSemigroup_3278 T_Quasiring_3204
v0
  = (T_IsMonoid_686 -> T_IsSemigroup_472)
-> AgdaAny -> T_IsSemigroup_472
forall a b. a -> b
coe
      T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
      ((T_IsQuasiring_2180 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsQuasiring_2180 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_'43''45'isMonoid_2202
         ((T_Quasiring_3204 -> T_IsQuasiring_2180) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Quasiring_3204 -> T_IsQuasiring_2180
d_isQuasiring_3236 (T_Quasiring_3204 -> AgdaAny
forall a b. a -> b
coe T_Quasiring_3204
v0)))
-- Algebra.Bundles.Quasiring._.isUnitalMagma
d_isUnitalMagma_3280 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Quasiring_3204 ->
  MAlonzo.Code.Algebra.Structures.T_IsUnitalMagma_642
d_isUnitalMagma_3280 :: () -> () -> T_Quasiring_3204 -> T_IsUnitalMagma_642
d_isUnitalMagma_3280 ~()
v0 ~()
v1 T_Quasiring_3204
v2 = T_Quasiring_3204 -> T_IsUnitalMagma_642
du_isUnitalMagma_3280 T_Quasiring_3204
v2
du_isUnitalMagma_3280 ::
  T_Quasiring_3204 ->
  MAlonzo.Code.Algebra.Structures.T_IsUnitalMagma_642
du_isUnitalMagma_3280 :: T_Quasiring_3204 -> T_IsUnitalMagma_642
du_isUnitalMagma_3280 T_Quasiring_3204
v0
  = let v1 :: T_IsQuasiring_2180
v1 = T_Quasiring_3204 -> T_IsQuasiring_2180
d_isQuasiring_3236 (T_Quasiring_3204 -> T_Quasiring_3204
forall a b. a -> b
coe T_Quasiring_3204
v0) in
    AgdaAny -> T_IsUnitalMagma_642
forall a b. a -> b
coe
      ((T_IsMonoid_686 -> T_IsUnitalMagma_642) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoid_686 -> T_IsUnitalMagma_642
MAlonzo.Code.Algebra.Structures.du_isUnitalMagma_730
         ((T_IsQuasiring_2180 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsQuasiring_2180 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_'43''45'isMonoid_2202 (T_IsQuasiring_2180 -> AgdaAny
forall a b. a -> b
coe T_IsQuasiring_2180
v1)))
-- Algebra.Bundles.Quasiring._.distrib
d_distrib_3282 ::
  T_Quasiring_3204 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_distrib_3282 :: T_Quasiring_3204 -> T_Σ_14
d_distrib_3282 T_Quasiring_3204
v0
  = (T_IsQuasiring_2180 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsQuasiring_2180 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_distrib_2210
      ((T_Quasiring_3204 -> T_IsQuasiring_2180) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Quasiring_3204 -> T_IsQuasiring_2180
d_isQuasiring_3236 (T_Quasiring_3204 -> AgdaAny
forall a b. a -> b
coe T_Quasiring_3204
v0))
-- Algebra.Bundles.Quasiring._.distribʳ
d_distrib'691'_3284 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Quasiring_3204 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_distrib'691'_3284 :: ()
-> ()
-> T_Quasiring_3204
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_distrib'691'_3284 ~()
v0 ~()
v1 T_Quasiring_3204
v2 = T_Quasiring_3204 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'691'_3284 T_Quasiring_3204
v2
du_distrib'691'_3284 ::
  T_Quasiring_3204 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'691'_3284 :: T_Quasiring_3204 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'691'_3284 T_Quasiring_3204
v0
  = (T_IsQuasiring_2180 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsQuasiring_2180 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_distrib'691'_2252
      ((T_Quasiring_3204 -> T_IsQuasiring_2180) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Quasiring_3204 -> T_IsQuasiring_2180
d_isQuasiring_3236 (T_Quasiring_3204 -> AgdaAny
forall a b. a -> b
coe T_Quasiring_3204
v0))
-- Algebra.Bundles.Quasiring._.distribˡ
d_distrib'737'_3286 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Quasiring_3204 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_distrib'737'_3286 :: ()
-> ()
-> T_Quasiring_3204
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_distrib'737'_3286 ~()
v0 ~()
v1 T_Quasiring_3204
v2 = T_Quasiring_3204 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'737'_3286 T_Quasiring_3204
v2
du_distrib'737'_3286 ::
  T_Quasiring_3204 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'737'_3286 :: T_Quasiring_3204 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'737'_3286 T_Quasiring_3204
v0
  = (T_IsQuasiring_2180 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsQuasiring_2180 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_distrib'737'_2250
      ((T_Quasiring_3204 -> T_IsQuasiring_2180) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Quasiring_3204 -> T_IsQuasiring_2180
d_isQuasiring_3236 (T_Quasiring_3204 -> AgdaAny
forall a b. a -> b
coe T_Quasiring_3204
v0))
-- Algebra.Bundles.Quasiring._.identityʳ
d_identity'691'_3288 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Quasiring_3204 -> AgdaAny -> AgdaAny
d_identity'691'_3288 :: () -> () -> T_Quasiring_3204 -> AgdaAny -> AgdaAny
d_identity'691'_3288 ~()
v0 ~()
v1 T_Quasiring_3204
v2 = T_Quasiring_3204 -> AgdaAny -> AgdaAny
du_identity'691'_3288 T_Quasiring_3204
v2
du_identity'691'_3288 :: T_Quasiring_3204 -> AgdaAny -> AgdaAny
du_identity'691'_3288 :: T_Quasiring_3204 -> AgdaAny -> AgdaAny
du_identity'691'_3288 T_Quasiring_3204
v0
  = (T_IsQuasiring_2180 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsQuasiring_2180 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_identity'691'_2260
      ((T_Quasiring_3204 -> T_IsQuasiring_2180) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Quasiring_3204 -> T_IsQuasiring_2180
d_isQuasiring_3236 (T_Quasiring_3204 -> AgdaAny
forall a b. a -> b
coe T_Quasiring_3204
v0))
-- Algebra.Bundles.Quasiring._.identityˡ
d_identity'737'_3290 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Quasiring_3204 -> AgdaAny -> AgdaAny
d_identity'737'_3290 :: () -> () -> T_Quasiring_3204 -> AgdaAny -> AgdaAny
d_identity'737'_3290 ~()
v0 ~()
v1 T_Quasiring_3204
v2 = T_Quasiring_3204 -> AgdaAny -> AgdaAny
du_identity'737'_3290 T_Quasiring_3204
v2
du_identity'737'_3290 :: T_Quasiring_3204 -> AgdaAny -> AgdaAny
du_identity'737'_3290 :: T_Quasiring_3204 -> AgdaAny -> AgdaAny
du_identity'737'_3290 T_Quasiring_3204
v0
  = (T_IsQuasiring_2180 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsQuasiring_2180 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_identity'737'_2258
      ((T_Quasiring_3204 -> T_IsQuasiring_2180) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Quasiring_3204 -> T_IsQuasiring_2180
d_isQuasiring_3236 (T_Quasiring_3204 -> AgdaAny
forall a b. a -> b
coe T_Quasiring_3204
v0))
-- Algebra.Bundles.Quasiring._.isEquivalence
d_isEquivalence_3292 ::
  T_Quasiring_3204 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_3292 :: T_Quasiring_3204 -> T_IsEquivalence_26
d_isEquivalence_3292 T_Quasiring_3204
v0
  = (T_IsMagma_176 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
      ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480
         ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
            ((T_IsQuasiring_2180 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsQuasiring_2180 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_'43''45'isMonoid_2202
               ((T_Quasiring_3204 -> T_IsQuasiring_2180) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Quasiring_3204 -> T_IsQuasiring_2180
d_isQuasiring_3236 (T_Quasiring_3204 -> AgdaAny
forall a b. a -> b
coe T_Quasiring_3204
v0)))))
-- Algebra.Bundles.Quasiring._.isPartialEquivalence
d_isPartialEquivalence_3294 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Quasiring_3204 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_3294 :: () -> () -> T_Quasiring_3204 -> T_IsPartialEquivalence_16
d_isPartialEquivalence_3294 ~()
v0 ~()
v1 T_Quasiring_3204
v2
  = T_Quasiring_3204 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_3294 T_Quasiring_3204
v2
du_isPartialEquivalence_3294 ::
  T_Quasiring_3204 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_3294 :: T_Quasiring_3204 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_3294 T_Quasiring_3204
v0
  = let v1 :: T_IsQuasiring_2180
v1 = T_Quasiring_3204 -> T_IsQuasiring_2180
d_isQuasiring_3236 (T_Quasiring_3204 -> T_Quasiring_3204
forall a b. a -> b
coe T_Quasiring_3204
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsMonoid_686
v2
             = T_IsQuasiring_2180 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_'43''45'isMonoid_2202
                 (T_IsQuasiring_2180 -> T_IsQuasiring_2180
forall a b. a -> b
coe T_IsQuasiring_2180
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_472
v3
                = T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsMagma_176
v4 = T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (T_IsSemigroup_472 -> T_IsSemigroup_472
forall a b. a -> b
coe T_IsSemigroup_472
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               ((T_IsEquivalence_26 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsEquivalence_26 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
                  ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v4))))))
-- Algebra.Bundles.Quasiring._.refl
d_refl_3296 :: T_Quasiring_3204 -> AgdaAny -> AgdaAny
d_refl_3296 :: T_Quasiring_3204 -> AgdaAny -> AgdaAny
d_refl_3296 T_Quasiring_3204
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_34
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
         ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480
            ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
               ((T_IsQuasiring_2180 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsQuasiring_2180 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_'43''45'isMonoid_2202
                  ((T_Quasiring_3204 -> T_IsQuasiring_2180) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Quasiring_3204 -> T_IsQuasiring_2180
d_isQuasiring_3236 (T_Quasiring_3204 -> AgdaAny
forall a b. a -> b
coe T_Quasiring_3204
v0))))))
-- Algebra.Bundles.Quasiring._.reflexive
d_reflexive_3298 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Quasiring_3204 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_3298 :: ()
-> ()
-> T_Quasiring_3204
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_3298 ~()
v0 ~()
v1 T_Quasiring_3204
v2 = T_Quasiring_3204 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_3298 T_Quasiring_3204
v2
du_reflexive_3298 ::
  T_Quasiring_3204 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_3298 :: T_Quasiring_3204 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_3298 T_Quasiring_3204
v0
  = let v1 :: T_IsQuasiring_2180
v1 = T_Quasiring_3204 -> T_IsQuasiring_2180
d_isQuasiring_3236 (T_Quasiring_3204 -> T_Quasiring_3204
forall a b. a -> b
coe T_Quasiring_3204
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsMonoid_686
v2
             = T_IsQuasiring_2180 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_'43''45'isMonoid_2202
                 (T_IsQuasiring_2180 -> T_IsQuasiring_2180
forall a b. a -> b
coe T_IsQuasiring_2180
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_472
v3
                = T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsMagma_176
v4 = T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (T_IsSemigroup_472 -> T_IsSemigroup_472
forall a b. a -> b
coe T_IsSemigroup_472
v3) in
             (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
               (\ AgdaAny
v5 AgdaAny
v6 AgdaAny
v7 ->
                  (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                    T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
                    ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v4))
                    AgdaAny
v5))))
-- Algebra.Bundles.Quasiring._.setoid
d_setoid_3300 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Quasiring_3204 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_3300 :: () -> () -> T_Quasiring_3204 -> T_Setoid_44
d_setoid_3300 ~()
v0 ~()
v1 T_Quasiring_3204
v2 = T_Quasiring_3204 -> T_Setoid_44
du_setoid_3300 T_Quasiring_3204
v2
du_setoid_3300 ::
  T_Quasiring_3204 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_3300 :: T_Quasiring_3204 -> T_Setoid_44
du_setoid_3300 T_Quasiring_3204
v0
  = let v1 :: T_IsQuasiring_2180
v1 = T_Quasiring_3204 -> T_IsQuasiring_2180
d_isQuasiring_3236 (T_Quasiring_3204 -> T_Quasiring_3204
forall a b. a -> b
coe T_Quasiring_3204
v0) in
    AgdaAny -> T_Setoid_44
forall a b. a -> b
coe
      (let v2 :: T_IsMonoid_686
v2
             = T_IsQuasiring_2180 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_'43''45'isMonoid_2202
                 (T_IsQuasiring_2180 -> T_IsQuasiring_2180
forall a b. a -> b
coe T_IsQuasiring_2180
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_472
v3
                = T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsMagma_176 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMagma_176 -> T_Setoid_44
MAlonzo.Code.Algebra.Structures.du_setoid_200
               ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v3)))))
-- Algebra.Bundles.Quasiring._.sym
d_sym_3302 ::
  T_Quasiring_3204 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_3302 :: T_Quasiring_3204 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_3302 T_Quasiring_3204
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_36
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
         ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480
            ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
               ((T_IsQuasiring_2180 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsQuasiring_2180 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_'43''45'isMonoid_2202
                  ((T_Quasiring_3204 -> T_IsQuasiring_2180) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Quasiring_3204 -> T_IsQuasiring_2180
d_isQuasiring_3236 (T_Quasiring_3204 -> AgdaAny
forall a b. a -> b
coe T_Quasiring_3204
v0))))))
-- Algebra.Bundles.Quasiring._.trans
d_trans_3304 ::
  T_Quasiring_3204 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_3304 :: T_Quasiring_3204
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_3304 T_Quasiring_3204
v0
  = (T_IsEquivalence_26
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_38
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
         ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480
            ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
               ((T_IsQuasiring_2180 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsQuasiring_2180 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_'43''45'isMonoid_2202
                  ((T_Quasiring_3204 -> T_IsQuasiring_2180) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Quasiring_3204 -> T_IsQuasiring_2180
d_isQuasiring_3236 (T_Quasiring_3204 -> AgdaAny
forall a b. a -> b
coe T_Quasiring_3204
v0))))))
-- Algebra.Bundles.Quasiring._.zero
d_zero_3306 ::
  T_Quasiring_3204 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_zero_3306 :: T_Quasiring_3204 -> T_Σ_14
d_zero_3306 T_Quasiring_3204
v0
  = (T_IsQuasiring_2180 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsQuasiring_2180 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_zero_2212
      ((T_Quasiring_3204 -> T_IsQuasiring_2180) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Quasiring_3204 -> T_IsQuasiring_2180
d_isQuasiring_3236 (T_Quasiring_3204 -> AgdaAny
forall a b. a -> b
coe T_Quasiring_3204
v0))
-- Algebra.Bundles.Quasiring._.zeroʳ
d_zero'691'_3308 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Quasiring_3204 -> AgdaAny -> AgdaAny
d_zero'691'_3308 :: () -> () -> T_Quasiring_3204 -> AgdaAny -> AgdaAny
d_zero'691'_3308 ~()
v0 ~()
v1 T_Quasiring_3204
v2 = T_Quasiring_3204 -> AgdaAny -> AgdaAny
du_zero'691'_3308 T_Quasiring_3204
v2
du_zero'691'_3308 :: T_Quasiring_3204 -> AgdaAny -> AgdaAny
du_zero'691'_3308 :: T_Quasiring_3204 -> AgdaAny -> AgdaAny
du_zero'691'_3308 T_Quasiring_3204
v0
  = (T_IsQuasiring_2180 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsQuasiring_2180 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_zero'691'_2256
      ((T_Quasiring_3204 -> T_IsQuasiring_2180) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Quasiring_3204 -> T_IsQuasiring_2180
d_isQuasiring_3236 (T_Quasiring_3204 -> AgdaAny
forall a b. a -> b
coe T_Quasiring_3204
v0))
-- Algebra.Bundles.Quasiring._.zeroˡ
d_zero'737'_3310 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Quasiring_3204 -> AgdaAny -> AgdaAny
d_zero'737'_3310 :: () -> () -> T_Quasiring_3204 -> AgdaAny -> AgdaAny
d_zero'737'_3310 ~()
v0 ~()
v1 T_Quasiring_3204
v2 = T_Quasiring_3204 -> AgdaAny -> AgdaAny
du_zero'737'_3310 T_Quasiring_3204
v2
du_zero'737'_3310 :: T_Quasiring_3204 -> AgdaAny -> AgdaAny
du_zero'737'_3310 :: T_Quasiring_3204 -> AgdaAny -> AgdaAny
du_zero'737'_3310 T_Quasiring_3204
v0
  = (T_IsQuasiring_2180 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsQuasiring_2180 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_zero'737'_2254
      ((T_Quasiring_3204 -> T_IsQuasiring_2180) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Quasiring_3204 -> T_IsQuasiring_2180
d_isQuasiring_3236 (T_Quasiring_3204 -> AgdaAny
forall a b. a -> b
coe T_Quasiring_3204
v0))
-- Algebra.Bundles.Quasiring.+-monoid
d_'43''45'monoid_3312 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Quasiring_3204 -> T_Monoid_882
d_'43''45'monoid_3312 :: () -> () -> T_Quasiring_3204 -> T_Monoid_882
d_'43''45'monoid_3312 ~()
v0 ~()
v1 T_Quasiring_3204
v2 = T_Quasiring_3204 -> T_Monoid_882
du_'43''45'monoid_3312 T_Quasiring_3204
v2
du_'43''45'monoid_3312 :: T_Quasiring_3204 -> T_Monoid_882
du_'43''45'monoid_3312 :: T_Quasiring_3204 -> T_Monoid_882
du_'43''45'monoid_3312 T_Quasiring_3204
v0
  = ((AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny -> T_IsMonoid_686 -> T_Monoid_882)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsMonoid_686
-> T_Monoid_882
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> T_IsMonoid_686 -> T_Monoid_882
C_Monoid'46'constructor_16157 (T_Quasiring_3204 -> AgdaAny -> AgdaAny -> AgdaAny
d__'43'__3228 (T_Quasiring_3204 -> T_Quasiring_3204
forall a b. a -> b
coe T_Quasiring_3204
v0))
      (T_Quasiring_3204 -> AgdaAny
d_0'35'_3232 (T_Quasiring_3204 -> T_Quasiring_3204
forall a b. a -> b
coe T_Quasiring_3204
v0))
      (T_IsQuasiring_2180 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_'43''45'isMonoid_2202
         ((T_Quasiring_3204 -> T_IsQuasiring_2180)
-> AgdaAny -> T_IsQuasiring_2180
forall a b. a -> b
coe T_Quasiring_3204 -> T_IsQuasiring_2180
d_isQuasiring_3236 (T_Quasiring_3204 -> AgdaAny
forall a b. a -> b
coe T_Quasiring_3204
v0)))
-- Algebra.Bundles.Quasiring._._≉_
d__'8777'__3316 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Quasiring_3204 -> AgdaAny -> AgdaAny -> ()
d__'8777'__3316 :: () -> () -> T_Quasiring_3204 -> AgdaAny -> AgdaAny -> ()
d__'8777'__3316 = () -> () -> T_Quasiring_3204 -> AgdaAny -> AgdaAny -> ()
forall a. a
erased
-- Algebra.Bundles.Quasiring._.magma
d_magma_3318 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Quasiring_3204 -> T_Magma_68
d_magma_3318 :: () -> () -> T_Quasiring_3204 -> T_Magma_68
d_magma_3318 ~()
v0 ~()
v1 T_Quasiring_3204
v2 = T_Quasiring_3204 -> T_Magma_68
du_magma_3318 T_Quasiring_3204
v2
du_magma_3318 :: T_Quasiring_3204 -> T_Magma_68
du_magma_3318 :: T_Quasiring_3204 -> T_Magma_68
du_magma_3318 T_Quasiring_3204
v0
  = let v1 :: t
v1 = (T_Quasiring_3204 -> T_Monoid_882) -> AgdaAny -> t
forall a b. a -> b
coe T_Quasiring_3204 -> T_Monoid_882
du_'43''45'monoid_3312 (T_Quasiring_3204 -> AgdaAny
forall a b. a -> b
coe T_Quasiring_3204
v0) in
    AgdaAny -> T_Magma_68
forall a b. a -> b
coe ((T_Semigroup_536 -> T_Magma_68) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semigroup_536 -> T_Magma_68
du_magma_584 ((T_Monoid_882 -> T_Semigroup_536) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Monoid_882 -> T_Semigroup_536
du_semigroup_944 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1)))
-- Algebra.Bundles.Quasiring._.rawMagma
d_rawMagma_3320 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Quasiring_3204 -> MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
d_rawMagma_3320 :: () -> () -> T_Quasiring_3204 -> T_RawMagma_36
d_rawMagma_3320 ~()
v0 ~()
v1 T_Quasiring_3204
v2 = T_Quasiring_3204 -> T_RawMagma_36
du_rawMagma_3320 T_Quasiring_3204
v2
du_rawMagma_3320 ::
  T_Quasiring_3204 -> MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
du_rawMagma_3320 :: T_Quasiring_3204 -> T_RawMagma_36
du_rawMagma_3320 T_Quasiring_3204
v0
  = let v1 :: t
v1 = (T_Quasiring_3204 -> T_Monoid_882) -> AgdaAny -> t
forall a b. a -> b
coe T_Quasiring_3204 -> T_Monoid_882
du_'43''45'monoid_3312 (T_Quasiring_3204 -> AgdaAny
forall a b. a -> b
coe T_Quasiring_3204
v0) in
    AgdaAny -> T_RawMagma_36
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_Monoid_882 -> T_Semigroup_536) -> AgdaAny -> t
forall a b. a -> b
coe T_Monoid_882 -> T_Semigroup_536
du_semigroup_944 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_Magma_68 -> T_RawMagma_36) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Magma_68 -> T_RawMagma_36
du_rawMagma_112 ((T_Semigroup_536 -> T_Magma_68) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semigroup_536 -> T_Magma_68
du_magma_584 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2))))
-- Algebra.Bundles.Quasiring._.rawMonoid
d_rawMonoid_3322 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Quasiring_3204 -> MAlonzo.Code.Algebra.Bundles.Raw.T_RawMonoid_64
d_rawMonoid_3322 :: () -> () -> T_Quasiring_3204 -> T_RawMonoid_64
d_rawMonoid_3322 ~()
v0 ~()
v1 T_Quasiring_3204
v2 = T_Quasiring_3204 -> T_RawMonoid_64
du_rawMonoid_3322 T_Quasiring_3204
v2
du_rawMonoid_3322 ::
  T_Quasiring_3204 -> MAlonzo.Code.Algebra.Bundles.Raw.T_RawMonoid_64
du_rawMonoid_3322 :: T_Quasiring_3204 -> T_RawMonoid_64
du_rawMonoid_3322 T_Quasiring_3204
v0
  = (T_Monoid_882 -> T_RawMonoid_64) -> AgdaAny -> T_RawMonoid_64
forall a b. a -> b
coe T_Monoid_882 -> T_RawMonoid_64
du_rawMonoid_954 ((T_Quasiring_3204 -> T_Monoid_882) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Quasiring_3204 -> T_Monoid_882
du_'43''45'monoid_3312 (T_Quasiring_3204 -> AgdaAny
forall a b. a -> b
coe T_Quasiring_3204
v0))
-- Algebra.Bundles.Quasiring._.semigroup
d_semigroup_3324 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Quasiring_3204 -> T_Semigroup_536
d_semigroup_3324 :: () -> () -> T_Quasiring_3204 -> T_Semigroup_536
d_semigroup_3324 ~()
v0 ~()
v1 T_Quasiring_3204
v2 = T_Quasiring_3204 -> T_Semigroup_536
du_semigroup_3324 T_Quasiring_3204
v2
du_semigroup_3324 :: T_Quasiring_3204 -> T_Semigroup_536
du_semigroup_3324 :: T_Quasiring_3204 -> T_Semigroup_536
du_semigroup_3324 T_Quasiring_3204
v0
  = (T_Monoid_882 -> T_Semigroup_536) -> AgdaAny -> T_Semigroup_536
forall a b. a -> b
coe T_Monoid_882 -> T_Semigroup_536
du_semigroup_944 ((T_Quasiring_3204 -> T_Monoid_882) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Quasiring_3204 -> T_Monoid_882
du_'43''45'monoid_3312 (T_Quasiring_3204 -> AgdaAny
forall a b. a -> b
coe T_Quasiring_3204
v0))
-- Algebra.Bundles.Quasiring._.unitalMagma
d_unitalMagma_3326 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Quasiring_3204 -> T_UnitalMagma_814
d_unitalMagma_3326 :: () -> () -> T_Quasiring_3204 -> T_UnitalMagma_814
d_unitalMagma_3326 ~()
v0 ~()
v1 T_Quasiring_3204
v2 = T_Quasiring_3204 -> T_UnitalMagma_814
du_unitalMagma_3326 T_Quasiring_3204
v2
du_unitalMagma_3326 :: T_Quasiring_3204 -> T_UnitalMagma_814
du_unitalMagma_3326 :: T_Quasiring_3204 -> T_UnitalMagma_814
du_unitalMagma_3326 T_Quasiring_3204
v0
  = (T_Monoid_882 -> T_UnitalMagma_814) -> AgdaAny -> T_UnitalMagma_814
forall a b. a -> b
coe T_Monoid_882 -> T_UnitalMagma_814
du_unitalMagma_956 ((T_Quasiring_3204 -> T_Monoid_882) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Quasiring_3204 -> T_Monoid_882
du_'43''45'monoid_3312 (T_Quasiring_3204 -> AgdaAny
forall a b. a -> b
coe T_Quasiring_3204
v0))
-- Algebra.Bundles.Quasiring.*-monoid
d_'42''45'monoid_3328 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Quasiring_3204 -> T_Monoid_882
d_'42''45'monoid_3328 :: () -> () -> T_Quasiring_3204 -> T_Monoid_882
d_'42''45'monoid_3328 ~()
v0 ~()
v1 T_Quasiring_3204
v2 = T_Quasiring_3204 -> T_Monoid_882
du_'42''45'monoid_3328 T_Quasiring_3204
v2
du_'42''45'monoid_3328 :: T_Quasiring_3204 -> T_Monoid_882
du_'42''45'monoid_3328 :: T_Quasiring_3204 -> T_Monoid_882
du_'42''45'monoid_3328 T_Quasiring_3204
v0
  = ((AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny -> T_IsMonoid_686 -> T_Monoid_882)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_Monoid_882
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> T_IsMonoid_686 -> T_Monoid_882
C_Monoid'46'constructor_16157 (T_Quasiring_3204 -> AgdaAny -> AgdaAny -> AgdaAny
d__'42'__3230 (T_Quasiring_3204 -> T_Quasiring_3204
forall a b. a -> b
coe T_Quasiring_3204
v0))
      (T_Quasiring_3204 -> AgdaAny
d_1'35'_3234 (T_Quasiring_3204 -> T_Quasiring_3204
forall a b. a -> b
coe T_Quasiring_3204
v0))
      ((T_IsQuasiring_2180 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsQuasiring_2180 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.du_'42''45'isMonoid_2266
         ((T_Quasiring_3204 -> T_IsQuasiring_2180) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Quasiring_3204 -> T_IsQuasiring_2180
d_isQuasiring_3236 (T_Quasiring_3204 -> AgdaAny
forall a b. a -> b
coe T_Quasiring_3204
v0)))
-- Algebra.Bundles.Quasiring._.magma
d_magma_3332 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Quasiring_3204 -> T_Magma_68
d_magma_3332 :: () -> () -> T_Quasiring_3204 -> T_Magma_68
d_magma_3332 ~()
v0 ~()
v1 T_Quasiring_3204
v2 = T_Quasiring_3204 -> T_Magma_68
du_magma_3332 T_Quasiring_3204
v2
du_magma_3332 :: T_Quasiring_3204 -> T_Magma_68
du_magma_3332 :: T_Quasiring_3204 -> T_Magma_68
du_magma_3332 T_Quasiring_3204
v0
  = let v1 :: t
v1 = (T_Quasiring_3204 -> T_Monoid_882) -> AgdaAny -> t
forall a b. a -> b
coe T_Quasiring_3204 -> T_Monoid_882
du_'42''45'monoid_3328 (T_Quasiring_3204 -> AgdaAny
forall a b. a -> b
coe T_Quasiring_3204
v0) in
    AgdaAny -> T_Magma_68
forall a b. a -> b
coe ((T_Semigroup_536 -> T_Magma_68) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semigroup_536 -> T_Magma_68
du_magma_584 ((T_Monoid_882 -> T_Semigroup_536) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Monoid_882 -> T_Semigroup_536
du_semigroup_944 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1)))
-- Algebra.Bundles.Quasiring._.rawMagma
d_rawMagma_3334 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Quasiring_3204 -> MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
d_rawMagma_3334 :: () -> () -> T_Quasiring_3204 -> T_RawMagma_36
d_rawMagma_3334 ~()
v0 ~()
v1 T_Quasiring_3204
v2 = T_Quasiring_3204 -> T_RawMagma_36
du_rawMagma_3334 T_Quasiring_3204
v2
du_rawMagma_3334 ::
  T_Quasiring_3204 -> MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
du_rawMagma_3334 :: T_Quasiring_3204 -> T_RawMagma_36
du_rawMagma_3334 T_Quasiring_3204
v0
  = let v1 :: t
v1 = (T_Quasiring_3204 -> T_Monoid_882) -> AgdaAny -> t
forall a b. a -> b
coe T_Quasiring_3204 -> T_Monoid_882
du_'42''45'monoid_3328 (T_Quasiring_3204 -> AgdaAny
forall a b. a -> b
coe T_Quasiring_3204
v0) in
    AgdaAny -> T_RawMagma_36
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_Monoid_882 -> T_Semigroup_536) -> AgdaAny -> t
forall a b. a -> b
coe T_Monoid_882 -> T_Semigroup_536
du_semigroup_944 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_Magma_68 -> T_RawMagma_36) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Magma_68 -> T_RawMagma_36
du_rawMagma_112 ((T_Semigroup_536 -> T_Magma_68) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semigroup_536 -> T_Magma_68
du_magma_584 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2))))
-- Algebra.Bundles.Quasiring._.rawMonoid
d_rawMonoid_3336 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Quasiring_3204 -> MAlonzo.Code.Algebra.Bundles.Raw.T_RawMonoid_64
d_rawMonoid_3336 :: () -> () -> T_Quasiring_3204 -> T_RawMonoid_64
d_rawMonoid_3336 ~()
v0 ~()
v1 T_Quasiring_3204
v2 = T_Quasiring_3204 -> T_RawMonoid_64
du_rawMonoid_3336 T_Quasiring_3204
v2
du_rawMonoid_3336 ::
  T_Quasiring_3204 -> MAlonzo.Code.Algebra.Bundles.Raw.T_RawMonoid_64
du_rawMonoid_3336 :: T_Quasiring_3204 -> T_RawMonoid_64
du_rawMonoid_3336 T_Quasiring_3204
v0
  = (T_Monoid_882 -> T_RawMonoid_64) -> AgdaAny -> T_RawMonoid_64
forall a b. a -> b
coe T_Monoid_882 -> T_RawMonoid_64
du_rawMonoid_954 ((T_Quasiring_3204 -> T_Monoid_882) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Quasiring_3204 -> T_Monoid_882
du_'42''45'monoid_3328 (T_Quasiring_3204 -> AgdaAny
forall a b. a -> b
coe T_Quasiring_3204
v0))
-- Algebra.Bundles.Quasiring._.semigroup
d_semigroup_3338 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Quasiring_3204 -> T_Semigroup_536
d_semigroup_3338 :: () -> () -> T_Quasiring_3204 -> T_Semigroup_536
d_semigroup_3338 ~()
v0 ~()
v1 T_Quasiring_3204
v2 = T_Quasiring_3204 -> T_Semigroup_536
du_semigroup_3338 T_Quasiring_3204
v2
du_semigroup_3338 :: T_Quasiring_3204 -> T_Semigroup_536
du_semigroup_3338 :: T_Quasiring_3204 -> T_Semigroup_536
du_semigroup_3338 T_Quasiring_3204
v0
  = (T_Monoid_882 -> T_Semigroup_536) -> AgdaAny -> T_Semigroup_536
forall a b. a -> b
coe T_Monoid_882 -> T_Semigroup_536
du_semigroup_944 ((T_Quasiring_3204 -> T_Monoid_882) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Quasiring_3204 -> T_Monoid_882
du_'42''45'monoid_3328 (T_Quasiring_3204 -> AgdaAny
forall a b. a -> b
coe T_Quasiring_3204
v0))
-- Algebra.Bundles.RingWithoutOne
d_RingWithoutOne_3344 :: p -> p -> ()
d_RingWithoutOne_3344 p
a0 p
a1 = ()
data T_RingWithoutOne_3344
  = C_RingWithoutOne'46'constructor_59923 (AgdaAny ->
                                           AgdaAny -> AgdaAny)
                                          (AgdaAny -> AgdaAny -> AgdaAny) (AgdaAny -> AgdaAny)
                                          AgdaAny
                                          MAlonzo.Code.Algebra.Structures.T_IsRingWithoutOne_2286
-- Algebra.Bundles.RingWithoutOne.Carrier
d_Carrier_3364 :: T_RingWithoutOne_3344 -> ()
d_Carrier_3364 :: T_RingWithoutOne_3344 -> ()
d_Carrier_3364 = T_RingWithoutOne_3344 -> ()
forall a. a
erased
-- Algebra.Bundles.RingWithoutOne._≈_
d__'8776'__3366 ::
  T_RingWithoutOne_3344 -> AgdaAny -> AgdaAny -> ()
d__'8776'__3366 :: T_RingWithoutOne_3344 -> AgdaAny -> AgdaAny -> ()
d__'8776'__3366 = T_RingWithoutOne_3344 -> AgdaAny -> AgdaAny -> ()
forall a. a
erased
-- Algebra.Bundles.RingWithoutOne._+_
d__'43'__3368 ::
  T_RingWithoutOne_3344 -> AgdaAny -> AgdaAny -> AgdaAny
d__'43'__3368 :: T_RingWithoutOne_3344 -> AgdaAny -> AgdaAny -> AgdaAny
d__'43'__3368 T_RingWithoutOne_3344
v0
  = case T_RingWithoutOne_3344 -> T_RingWithoutOne_3344
forall a b. a -> b
coe T_RingWithoutOne_3344
v0 of
      C_RingWithoutOne'46'constructor_59923 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny
v5 AgdaAny
v6 T_IsRingWithoutOne_2286
v7 -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v3
      T_RingWithoutOne_3344
_ -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.RingWithoutOne._*_
d__'42'__3370 ::
  T_RingWithoutOne_3344 -> AgdaAny -> AgdaAny -> AgdaAny
d__'42'__3370 :: T_RingWithoutOne_3344 -> AgdaAny -> AgdaAny -> AgdaAny
d__'42'__3370 T_RingWithoutOne_3344
v0
  = case T_RingWithoutOne_3344 -> T_RingWithoutOne_3344
forall a b. a -> b
coe T_RingWithoutOne_3344
v0 of
      C_RingWithoutOne'46'constructor_59923 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny
v5 AgdaAny
v6 T_IsRingWithoutOne_2286
v7 -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v4
      T_RingWithoutOne_3344
_ -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.RingWithoutOne.-_
d_'45'__3372 :: T_RingWithoutOne_3344 -> AgdaAny -> AgdaAny
d_'45'__3372 :: T_RingWithoutOne_3344 -> AgdaAny -> AgdaAny
d_'45'__3372 T_RingWithoutOne_3344
v0
  = case T_RingWithoutOne_3344 -> T_RingWithoutOne_3344
forall a b. a -> b
coe T_RingWithoutOne_3344
v0 of
      C_RingWithoutOne'46'constructor_59923 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny
v5 AgdaAny
v6 T_IsRingWithoutOne_2286
v7 -> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v5
      T_RingWithoutOne_3344
_ -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.RingWithoutOne.0#
d_0'35'_3374 :: T_RingWithoutOne_3344 -> AgdaAny
d_0'35'_3374 :: T_RingWithoutOne_3344 -> AgdaAny
d_0'35'_3374 T_RingWithoutOne_3344
v0
  = case T_RingWithoutOne_3344 -> T_RingWithoutOne_3344
forall a b. a -> b
coe T_RingWithoutOne_3344
v0 of
      C_RingWithoutOne'46'constructor_59923 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny
v5 AgdaAny
v6 T_IsRingWithoutOne_2286
v7 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v6
      T_RingWithoutOne_3344
_ -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.RingWithoutOne.isRingWithoutOne
d_isRingWithoutOne_3376 ::
  T_RingWithoutOne_3344 ->
  MAlonzo.Code.Algebra.Structures.T_IsRingWithoutOne_2286
d_isRingWithoutOne_3376 :: T_RingWithoutOne_3344 -> T_IsRingWithoutOne_2286
d_isRingWithoutOne_3376 T_RingWithoutOne_3344
v0
  = case T_RingWithoutOne_3344 -> T_RingWithoutOne_3344
forall a b. a -> b
coe T_RingWithoutOne_3344
v0 of
      C_RingWithoutOne'46'constructor_59923 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny
v5 AgdaAny
v6 T_IsRingWithoutOne_2286
v7 -> T_IsRingWithoutOne_2286 -> T_IsRingWithoutOne_2286
forall a b. a -> b
coe T_IsRingWithoutOne_2286
v7
      T_RingWithoutOne_3344
_ -> T_IsRingWithoutOne_2286
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.RingWithoutOne._._//_
d__'47''47'__3380 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_RingWithoutOne_3344 -> AgdaAny -> AgdaAny -> AgdaAny
d__'47''47'__3380 :: () -> () -> T_RingWithoutOne_3344 -> AgdaAny -> AgdaAny -> AgdaAny
d__'47''47'__3380 ~()
v0 ~()
v1 T_RingWithoutOne_3344
v2 = T_RingWithoutOne_3344 -> AgdaAny -> AgdaAny -> AgdaAny
du__'47''47'__3380 T_RingWithoutOne_3344
v2
du__'47''47'__3380 ::
  T_RingWithoutOne_3344 -> AgdaAny -> AgdaAny -> AgdaAny
du__'47''47'__3380 :: T_RingWithoutOne_3344 -> AgdaAny -> AgdaAny -> AgdaAny
du__'47''47'__3380 T_RingWithoutOne_3344
v0
  = let v1 :: AgdaAny -> AgdaAny -> AgdaAny
v1 = T_RingWithoutOne_3344 -> AgdaAny -> AgdaAny -> AgdaAny
d__'43'__3368 (T_RingWithoutOne_3344 -> T_RingWithoutOne_3344
forall a b. a -> b
coe T_RingWithoutOne_3344
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: AgdaAny -> AgdaAny
v2 = T_RingWithoutOne_3344 -> AgdaAny -> AgdaAny
d_'45'__3372 (T_RingWithoutOne_3344 -> T_RingWithoutOne_3344
forall a b. a -> b
coe T_RingWithoutOne_3344
v0) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (((AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du__'47''47'__1098 ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v1)
            ((AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v2)))
-- Algebra.Bundles.RingWithoutOne._.*-assoc
d_'42''45'assoc_3382 ::
  T_RingWithoutOne_3344 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'assoc_3382 :: T_RingWithoutOne_3344 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'assoc_3382 T_RingWithoutOne_3344
v0
  = (T_IsRingWithoutOne_2286
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsRingWithoutOne_2286 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'42''45'assoc_2308
      ((T_RingWithoutOne_3344 -> T_IsRingWithoutOne_2286)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_RingWithoutOne_3344 -> T_IsRingWithoutOne_2286
d_isRingWithoutOne_3376 (T_RingWithoutOne_3344 -> AgdaAny
forall a b. a -> b
coe T_RingWithoutOne_3344
v0))
-- Algebra.Bundles.RingWithoutOne._.*-cong
d_'42''45'cong_3384 ::
  T_RingWithoutOne_3344 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'cong_3384 :: T_RingWithoutOne_3344
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'42''45'cong_3384 T_RingWithoutOne_3344
v0
  = (T_IsRingWithoutOne_2286
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsRingWithoutOne_2286
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'42''45'cong_2306
      ((T_RingWithoutOne_3344 -> T_IsRingWithoutOne_2286)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_RingWithoutOne_3344 -> T_IsRingWithoutOne_2286
d_isRingWithoutOne_3376 (T_RingWithoutOne_3344 -> AgdaAny
forall a b. a -> b
coe T_RingWithoutOne_3344
v0))
-- Algebra.Bundles.RingWithoutOne._.∙-congʳ
d_'8729''45'cong'691'_3386 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_RingWithoutOne_3344 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_3386 :: ()
-> ()
-> T_RingWithoutOne_3344
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_3386 ~()
v0 ~()
v1 T_RingWithoutOne_3344
v2
  = T_RingWithoutOne_3344
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_3386 T_RingWithoutOne_3344
v2
du_'8729''45'cong'691'_3386 ::
  T_RingWithoutOne_3344 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_3386 :: T_RingWithoutOne_3344
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_3386 T_RingWithoutOne_3344
v0
  = let v1 :: T_IsRingWithoutOne_2286
v1 = T_RingWithoutOne_3344 -> T_IsRingWithoutOne_2286
d_isRingWithoutOne_3376 (T_RingWithoutOne_3344 -> T_RingWithoutOne_3344
forall a b. a -> b
coe T_RingWithoutOne_3344
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: t
v2
             = (T_IsRingWithoutOne_2286 -> T_IsSemigroup_472) -> AgdaAny -> t
forall a b. a -> b
coe
                 T_IsRingWithoutOne_2286 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.du_'42''45'isSemigroup_2390
                 (T_IsRingWithoutOne_2286 -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOne_2286
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'691'_206
            ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2))))
-- Algebra.Bundles.RingWithoutOne._.∙-congˡ
d_'8729''45'cong'737'_3388 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_RingWithoutOne_3344 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_3388 :: ()
-> ()
-> T_RingWithoutOne_3344
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_3388 ~()
v0 ~()
v1 T_RingWithoutOne_3344
v2
  = T_RingWithoutOne_3344
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_3388 T_RingWithoutOne_3344
v2
du_'8729''45'cong'737'_3388 ::
  T_RingWithoutOne_3344 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_3388 :: T_RingWithoutOne_3344
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_3388 T_RingWithoutOne_3344
v0
  = let v1 :: T_IsRingWithoutOne_2286
v1 = T_RingWithoutOne_3344 -> T_IsRingWithoutOne_2286
d_isRingWithoutOne_3376 (T_RingWithoutOne_3344 -> T_RingWithoutOne_3344
forall a b. a -> b
coe T_RingWithoutOne_3344
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: t
v2
             = (T_IsRingWithoutOne_2286 -> T_IsSemigroup_472) -> AgdaAny -> t
forall a b. a -> b
coe
                 T_IsRingWithoutOne_2286 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.du_'42''45'isSemigroup_2390
                 (T_IsRingWithoutOne_2286 -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOne_2286
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'737'_202
            ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2))))
-- Algebra.Bundles.RingWithoutOne._.*-isMagma
d_'42''45'isMagma_3390 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_RingWithoutOne_3344 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_176
d_'42''45'isMagma_3390 :: () -> () -> T_RingWithoutOne_3344 -> T_IsMagma_176
d_'42''45'isMagma_3390 ~()
v0 ~()
v1 T_RingWithoutOne_3344
v2 = T_RingWithoutOne_3344 -> T_IsMagma_176
du_'42''45'isMagma_3390 T_RingWithoutOne_3344
v2
du_'42''45'isMagma_3390 ::
  T_RingWithoutOne_3344 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_176
du_'42''45'isMagma_3390 :: T_RingWithoutOne_3344 -> T_IsMagma_176
du_'42''45'isMagma_3390 T_RingWithoutOne_3344
v0
  = (T_IsRingWithoutOne_2286 -> T_IsMagma_176)
-> AgdaAny -> T_IsMagma_176
forall a b. a -> b
coe
      T_IsRingWithoutOne_2286 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.du_'42''45'isMagma_2388
      ((T_RingWithoutOne_3344 -> T_IsRingWithoutOne_2286)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_RingWithoutOne_3344 -> T_IsRingWithoutOne_2286
d_isRingWithoutOne_3376 (T_RingWithoutOne_3344 -> AgdaAny
forall a b. a -> b
coe T_RingWithoutOne_3344
v0))
-- Algebra.Bundles.RingWithoutOne._.*-isSemigroup
d_'42''45'isSemigroup_3392 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_RingWithoutOne_3344 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_472
d_'42''45'isSemigroup_3392 :: () -> () -> T_RingWithoutOne_3344 -> T_IsSemigroup_472
d_'42''45'isSemigroup_3392 ~()
v0 ~()
v1 T_RingWithoutOne_3344
v2
  = T_RingWithoutOne_3344 -> T_IsSemigroup_472
du_'42''45'isSemigroup_3392 T_RingWithoutOne_3344
v2
du_'42''45'isSemigroup_3392 ::
  T_RingWithoutOne_3344 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_472
du_'42''45'isSemigroup_3392 :: T_RingWithoutOne_3344 -> T_IsSemigroup_472
du_'42''45'isSemigroup_3392 T_RingWithoutOne_3344
v0
  = (T_IsRingWithoutOne_2286 -> T_IsSemigroup_472)
-> AgdaAny -> T_IsSemigroup_472
forall a b. a -> b
coe
      T_IsRingWithoutOne_2286 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.du_'42''45'isSemigroup_2390
      ((T_RingWithoutOne_3344 -> T_IsRingWithoutOne_2286)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_RingWithoutOne_3344 -> T_IsRingWithoutOne_2286
d_isRingWithoutOne_3376 (T_RingWithoutOne_3344 -> AgdaAny
forall a b. a -> b
coe T_RingWithoutOne_3344
v0))
-- Algebra.Bundles.RingWithoutOne._.assoc
d_assoc_3394 ::
  T_RingWithoutOne_3344 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_3394 :: T_RingWithoutOne_3344 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_3394 T_RingWithoutOne_3344
v0
  = (T_IsSemigroup_472 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsSemigroup_472 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_assoc_482
      ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
         ((T_IsGroup_1036 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsGroup_1036 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_1050
            ((T_IsAbelianGroup_1132 -> T_IsGroup_1036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsAbelianGroup_1132 -> T_IsGroup_1036
MAlonzo.Code.Algebra.Structures.d_isGroup_1144
               ((T_IsRingWithoutOne_2286 -> T_IsAbelianGroup_1132)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsRingWithoutOne_2286 -> T_IsAbelianGroup_1132
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2304
                  ((T_RingWithoutOne_3344 -> T_IsRingWithoutOne_2286)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_RingWithoutOne_3344 -> T_IsRingWithoutOne_2286
d_isRingWithoutOne_3376 (T_RingWithoutOne_3344 -> AgdaAny
forall a b. a -> b
coe T_RingWithoutOne_3344
v0))))))
-- Algebra.Bundles.RingWithoutOne._.comm
d_comm_3396 ::
  T_RingWithoutOne_3344 -> AgdaAny -> AgdaAny -> AgdaAny
d_comm_3396 :: T_RingWithoutOne_3344 -> AgdaAny -> AgdaAny -> AgdaAny
d_comm_3396 T_RingWithoutOne_3344
v0
  = (T_IsAbelianGroup_1132 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsAbelianGroup_1132 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_comm_1146
      ((T_IsRingWithoutOne_2286 -> T_IsAbelianGroup_1132)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsRingWithoutOne_2286 -> T_IsAbelianGroup_1132
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2304
         ((T_RingWithoutOne_3344 -> T_IsRingWithoutOne_2286)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_RingWithoutOne_3344 -> T_IsRingWithoutOne_2286
d_isRingWithoutOne_3376 (T_RingWithoutOne_3344 -> AgdaAny
forall a b. a -> b
coe T_RingWithoutOne_3344
v0)))
-- Algebra.Bundles.RingWithoutOne._.∙-cong
d_'8729''45'cong_3398 ::
  T_RingWithoutOne_3344 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_3398 :: T_RingWithoutOne_3344
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_3398 T_RingWithoutOne_3344
v0
  = (T_IsMagma_176
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsMagma_176
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_186
      ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480
         ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
            ((T_IsGroup_1036 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsGroup_1036 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_1050
               ((T_IsAbelianGroup_1132 -> T_IsGroup_1036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsAbelianGroup_1132 -> T_IsGroup_1036
MAlonzo.Code.Algebra.Structures.d_isGroup_1144
                  ((T_IsRingWithoutOne_2286 -> T_IsAbelianGroup_1132)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsRingWithoutOne_2286 -> T_IsAbelianGroup_1132
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2304
                     ((T_RingWithoutOne_3344 -> T_IsRingWithoutOne_2286)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_RingWithoutOne_3344 -> T_IsRingWithoutOne_2286
d_isRingWithoutOne_3376 (T_RingWithoutOne_3344 -> AgdaAny
forall a b. a -> b
coe T_RingWithoutOne_3344
v0)))))))
-- Algebra.Bundles.RingWithoutOne._.∙-congʳ
d_'8729''45'cong'691'_3400 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_RingWithoutOne_3344 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_3400 :: ()
-> ()
-> T_RingWithoutOne_3344
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_3400 ~()
v0 ~()
v1 T_RingWithoutOne_3344
v2
  = T_RingWithoutOne_3344
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_3400 T_RingWithoutOne_3344
v2
du_'8729''45'cong'691'_3400 ::
  T_RingWithoutOne_3344 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_3400 :: T_RingWithoutOne_3344
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_3400 T_RingWithoutOne_3344
v0
  = let v1 :: T_IsRingWithoutOne_2286
v1 = T_RingWithoutOne_3344 -> T_IsRingWithoutOne_2286
d_isRingWithoutOne_3376 (T_RingWithoutOne_3344 -> T_RingWithoutOne_3344
forall a b. a -> b
coe T_RingWithoutOne_3344
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsAbelianGroup_1132
v2
             = T_IsRingWithoutOne_2286 -> T_IsAbelianGroup_1132
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2304
                 (T_IsRingWithoutOne_2286 -> T_IsRingWithoutOne_2286
forall a b. a -> b
coe T_IsRingWithoutOne_2286
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsGroup_1036
v3
                = T_IsAbelianGroup_1132 -> T_IsGroup_1036
MAlonzo.Code.Algebra.Structures.d_isGroup_1144 (T_IsAbelianGroup_1132 -> T_IsAbelianGroup_1132
forall a b. a -> b
coe T_IsAbelianGroup_1132
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsMonoid_686
v4
                   = T_IsGroup_1036 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_1050 (T_IsGroup_1036 -> T_IsGroup_1036
forall a b. a -> b
coe T_IsGroup_1036
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsSemigroup_472
v5
                      = T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'691'_206
                     ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v5)))))))
-- Algebra.Bundles.RingWithoutOne._.∙-congˡ
d_'8729''45'cong'737'_3402 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_RingWithoutOne_3344 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_3402 :: ()
-> ()
-> T_RingWithoutOne_3344
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_3402 ~()
v0 ~()
v1 T_RingWithoutOne_3344
v2
  = T_RingWithoutOne_3344
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_3402 T_RingWithoutOne_3344
v2
du_'8729''45'cong'737'_3402 ::
  T_RingWithoutOne_3344 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_3402 :: T_RingWithoutOne_3344
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_3402 T_RingWithoutOne_3344
v0
  = let v1 :: T_IsRingWithoutOne_2286
v1 = T_RingWithoutOne_3344 -> T_IsRingWithoutOne_2286
d_isRingWithoutOne_3376 (T_RingWithoutOne_3344 -> T_RingWithoutOne_3344
forall a b. a -> b
coe T_RingWithoutOne_3344
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsAbelianGroup_1132
v2
             = T_IsRingWithoutOne_2286 -> T_IsAbelianGroup_1132
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2304
                 (T_IsRingWithoutOne_2286 -> T_IsRingWithoutOne_2286
forall a b. a -> b
coe T_IsRingWithoutOne_2286
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsGroup_1036
v3
                = T_IsAbelianGroup_1132 -> T_IsGroup_1036
MAlonzo.Code.Algebra.Structures.d_isGroup_1144 (T_IsAbelianGroup_1132 -> T_IsAbelianGroup_1132
forall a b. a -> b
coe T_IsAbelianGroup_1132
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsMonoid_686
v4
                   = T_IsGroup_1036 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_1050 (T_IsGroup_1036 -> T_IsGroup_1036
forall a b. a -> b
coe T_IsGroup_1036
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsSemigroup_472
v5
                      = T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'737'_202
                     ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v5)))))))
-- Algebra.Bundles.RingWithoutOne._.identity
d_identity_3404 ::
  T_RingWithoutOne_3344 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_identity_3404 :: T_RingWithoutOne_3344 -> T_Σ_14
d_identity_3404 T_RingWithoutOne_3344
v0
  = (T_IsMonoid_686 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsMonoid_686 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_identity_698
      ((T_IsGroup_1036 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsGroup_1036 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_1050
         ((T_IsAbelianGroup_1132 -> T_IsGroup_1036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsAbelianGroup_1132 -> T_IsGroup_1036
MAlonzo.Code.Algebra.Structures.d_isGroup_1144
            ((T_IsRingWithoutOne_2286 -> T_IsAbelianGroup_1132)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsRingWithoutOne_2286 -> T_IsAbelianGroup_1132
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2304
               ((T_RingWithoutOne_3344 -> T_IsRingWithoutOne_2286)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_RingWithoutOne_3344 -> T_IsRingWithoutOne_2286
d_isRingWithoutOne_3376 (T_RingWithoutOne_3344 -> AgdaAny
forall a b. a -> b
coe T_RingWithoutOne_3344
v0)))))
-- Algebra.Bundles.RingWithoutOne._.identityʳ
d_identity'691'_3406 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_RingWithoutOne_3344 -> AgdaAny -> AgdaAny
d_identity'691'_3406 :: () -> () -> T_RingWithoutOne_3344 -> AgdaAny -> AgdaAny
d_identity'691'_3406 ~()
v0 ~()
v1 T_RingWithoutOne_3344
v2 = T_RingWithoutOne_3344 -> AgdaAny -> AgdaAny
du_identity'691'_3406 T_RingWithoutOne_3344
v2
du_identity'691'_3406 ::
  T_RingWithoutOne_3344 -> AgdaAny -> AgdaAny
du_identity'691'_3406 :: T_RingWithoutOne_3344 -> AgdaAny -> AgdaAny
du_identity'691'_3406 T_RingWithoutOne_3344
v0
  = let v1 :: T_IsRingWithoutOne_2286
v1 = T_RingWithoutOne_3344 -> T_IsRingWithoutOne_2286
d_isRingWithoutOne_3376 (T_RingWithoutOne_3344 -> T_RingWithoutOne_3344
forall a b. a -> b
coe T_RingWithoutOne_3344
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsAbelianGroup_1132
v2
             = T_IsRingWithoutOne_2286 -> T_IsAbelianGroup_1132
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2304
                 (T_IsRingWithoutOne_2286 -> T_IsRingWithoutOne_2286
forall a b. a -> b
coe T_IsRingWithoutOne_2286
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsGroup_1036
v3
                = T_IsAbelianGroup_1132 -> T_IsGroup_1036
MAlonzo.Code.Algebra.Structures.d_isGroup_1144 (T_IsAbelianGroup_1132 -> T_IsAbelianGroup_1132
forall a b. a -> b
coe T_IsAbelianGroup_1132
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsMonoid_686 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_686 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_identity'691'_728
               ((T_IsGroup_1036 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1036 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_1050 (T_IsGroup_1036 -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1036
v3)))))
-- Algebra.Bundles.RingWithoutOne._.identityˡ
d_identity'737'_3408 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_RingWithoutOne_3344 -> AgdaAny -> AgdaAny
d_identity'737'_3408 :: () -> () -> T_RingWithoutOne_3344 -> AgdaAny -> AgdaAny
d_identity'737'_3408 ~()
v0 ~()
v1 T_RingWithoutOne_3344
v2 = T_RingWithoutOne_3344 -> AgdaAny -> AgdaAny
du_identity'737'_3408 T_RingWithoutOne_3344
v2
du_identity'737'_3408 ::
  T_RingWithoutOne_3344 -> AgdaAny -> AgdaAny
du_identity'737'_3408 :: T_RingWithoutOne_3344 -> AgdaAny -> AgdaAny
du_identity'737'_3408 T_RingWithoutOne_3344
v0
  = let v1 :: T_IsRingWithoutOne_2286
v1 = T_RingWithoutOne_3344 -> T_IsRingWithoutOne_2286
d_isRingWithoutOne_3376 (T_RingWithoutOne_3344 -> T_RingWithoutOne_3344
forall a b. a -> b
coe T_RingWithoutOne_3344
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsAbelianGroup_1132
v2
             = T_IsRingWithoutOne_2286 -> T_IsAbelianGroup_1132
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2304
                 (T_IsRingWithoutOne_2286 -> T_IsRingWithoutOne_2286
forall a b. a -> b
coe T_IsRingWithoutOne_2286
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsGroup_1036
v3
                = T_IsAbelianGroup_1132 -> T_IsGroup_1036
MAlonzo.Code.Algebra.Structures.d_isGroup_1144 (T_IsAbelianGroup_1132 -> T_IsAbelianGroup_1132
forall a b. a -> b
coe T_IsAbelianGroup_1132
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsMonoid_686 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_686 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_identity'737'_726
               ((T_IsGroup_1036 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1036 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_1050 (T_IsGroup_1036 -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1036
v3)))))
-- Algebra.Bundles.RingWithoutOne._.+-isAbelianGroup
d_'43''45'isAbelianGroup_3410 ::
  T_RingWithoutOne_3344 ->
  MAlonzo.Code.Algebra.Structures.T_IsAbelianGroup_1132
d_'43''45'isAbelianGroup_3410 :: T_RingWithoutOne_3344 -> T_IsAbelianGroup_1132
d_'43''45'isAbelianGroup_3410 T_RingWithoutOne_3344
v0
  = (T_IsRingWithoutOne_2286 -> T_IsAbelianGroup_1132)
-> AgdaAny -> T_IsAbelianGroup_1132
forall a b. a -> b
coe
      T_IsRingWithoutOne_2286 -> T_IsAbelianGroup_1132
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2304
      ((T_RingWithoutOne_3344 -> T_IsRingWithoutOne_2286)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_RingWithoutOne_3344 -> T_IsRingWithoutOne_2286
d_isRingWithoutOne_3376 (T_RingWithoutOne_3344 -> AgdaAny
forall a b. a -> b
coe T_RingWithoutOne_3344
v0))
-- Algebra.Bundles.RingWithoutOne._.isCommutativeMagma
d_isCommutativeMagma_3412 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_RingWithoutOne_3344 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMagma_212
d_isCommutativeMagma_3412 :: () -> () -> T_RingWithoutOne_3344 -> T_IsCommutativeMagma_212
d_isCommutativeMagma_3412 ~()
v0 ~()
v1 T_RingWithoutOne_3344
v2
  = T_RingWithoutOne_3344 -> T_IsCommutativeMagma_212
du_isCommutativeMagma_3412 T_RingWithoutOne_3344
v2
du_isCommutativeMagma_3412 ::
  T_RingWithoutOne_3344 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMagma_212
du_isCommutativeMagma_3412 :: T_RingWithoutOne_3344 -> T_IsCommutativeMagma_212
du_isCommutativeMagma_3412 T_RingWithoutOne_3344
v0
  = let v1 :: T_IsRingWithoutOne_2286
v1 = T_RingWithoutOne_3344 -> T_IsRingWithoutOne_2286
d_isRingWithoutOne_3376 (T_RingWithoutOne_3344 -> T_RingWithoutOne_3344
forall a b. a -> b
coe T_RingWithoutOne_3344
v0) in
    AgdaAny -> T_IsCommutativeMagma_212
forall a b. a -> b
coe
      (let v2 :: T_IsAbelianGroup_1132
v2
             = T_IsRingWithoutOne_2286 -> T_IsAbelianGroup_1132
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2304
                 (T_IsRingWithoutOne_2286 -> T_IsRingWithoutOne_2286
forall a b. a -> b
coe T_IsRingWithoutOne_2286
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: t
v3
                = (T_IsAbelianGroup_1132 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> t
forall a b. a -> b
coe
                    T_IsAbelianGroup_1132 -> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.du_isCommutativeMonoid_1204
                    (T_IsAbelianGroup_1132 -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsCommutativeSemigroup_548 -> T_IsCommutativeMagma_212)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsCommutativeSemigroup_548 -> T_IsCommutativeMagma_212
MAlonzo.Code.Algebra.Structures.du_isCommutativeMagma_586
               ((T_IsCommutativeMonoid_736 -> T_IsCommutativeSemigroup_548)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsCommutativeMonoid_736 -> T_IsCommutativeSemigroup_548
MAlonzo.Code.Algebra.Structures.du_isCommutativeSemigroup_786
                  (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3)))))
-- Algebra.Bundles.RingWithoutOne._.isCommutativeMonoid
d_isCommutativeMonoid_3414 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_RingWithoutOne_3344 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMonoid_736
d_isCommutativeMonoid_3414 :: () -> () -> T_RingWithoutOne_3344 -> T_IsCommutativeMonoid_736
d_isCommutativeMonoid_3414 ~()
v0 ~()
v1 T_RingWithoutOne_3344
v2
  = T_RingWithoutOne_3344 -> T_IsCommutativeMonoid_736
du_isCommutativeMonoid_3414 T_RingWithoutOne_3344
v2
du_isCommutativeMonoid_3414 ::
  T_RingWithoutOne_3344 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMonoid_736
du_isCommutativeMonoid_3414 :: T_RingWithoutOne_3344 -> T_IsCommutativeMonoid_736
du_isCommutativeMonoid_3414 T_RingWithoutOne_3344
v0
  = let v1 :: T_IsRingWithoutOne_2286
v1 = T_RingWithoutOne_3344 -> T_IsRingWithoutOne_2286
d_isRingWithoutOne_3376 (T_RingWithoutOne_3344 -> T_RingWithoutOne_3344
forall a b. a -> b
coe T_RingWithoutOne_3344
v0) in
    AgdaAny -> T_IsCommutativeMonoid_736
forall a b. a -> b
coe
      ((T_IsAbelianGroup_1132 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsAbelianGroup_1132 -> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.du_isCommutativeMonoid_1204
         ((T_IsRingWithoutOne_2286 -> T_IsAbelianGroup_1132)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsRingWithoutOne_2286 -> T_IsAbelianGroup_1132
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2304
            (T_IsRingWithoutOne_2286 -> AgdaAny
forall a b. a -> b
coe T_IsRingWithoutOne_2286
v1)))
-- Algebra.Bundles.RingWithoutOne._.isCommutativeSemigroup
d_isCommutativeSemigroup_3416 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_RingWithoutOne_3344 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_548
d_isCommutativeSemigroup_3416 :: () -> () -> T_RingWithoutOne_3344 -> T_IsCommutativeSemigroup_548
d_isCommutativeSemigroup_3416 ~()
v0 ~()
v1 T_RingWithoutOne_3344
v2
  = T_RingWithoutOne_3344 -> T_IsCommutativeSemigroup_548
du_isCommutativeSemigroup_3416 T_RingWithoutOne_3344
v2
du_isCommutativeSemigroup_3416 ::
  T_RingWithoutOne_3344 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_548
du_isCommutativeSemigroup_3416 :: T_RingWithoutOne_3344 -> T_IsCommutativeSemigroup_548
du_isCommutativeSemigroup_3416 T_RingWithoutOne_3344
v0
  = let v1 :: T_IsRingWithoutOne_2286
v1 = T_RingWithoutOne_3344 -> T_IsRingWithoutOne_2286
d_isRingWithoutOne_3376 (T_RingWithoutOne_3344 -> T_RingWithoutOne_3344
forall a b. a -> b
coe T_RingWithoutOne_3344
v0) in
    AgdaAny -> T_IsCommutativeSemigroup_548
forall a b. a -> b
coe
      (let v2 :: T_IsAbelianGroup_1132
v2
             = T_IsRingWithoutOne_2286 -> T_IsAbelianGroup_1132
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2304
                 (T_IsRingWithoutOne_2286 -> T_IsRingWithoutOne_2286
forall a b. a -> b
coe T_IsRingWithoutOne_2286
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsCommutativeMonoid_736 -> T_IsCommutativeSemigroup_548)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCommutativeMonoid_736 -> T_IsCommutativeSemigroup_548
MAlonzo.Code.Algebra.Structures.du_isCommutativeSemigroup_786
            ((T_IsAbelianGroup_1132 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsAbelianGroup_1132 -> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.du_isCommutativeMonoid_1204
               (T_IsAbelianGroup_1132 -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132
v2))))
-- Algebra.Bundles.RingWithoutOne._.isGroup
d_isGroup_3418 ::
  T_RingWithoutOne_3344 ->
  MAlonzo.Code.Algebra.Structures.T_IsGroup_1036
d_isGroup_3418 :: T_RingWithoutOne_3344 -> T_IsGroup_1036
d_isGroup_3418 T_RingWithoutOne_3344
v0
  = (T_IsAbelianGroup_1132 -> T_IsGroup_1036)
-> AgdaAny -> T_IsGroup_1036
forall a b. a -> b
coe
      T_IsAbelianGroup_1132 -> T_IsGroup_1036
MAlonzo.Code.Algebra.Structures.d_isGroup_1144
      ((T_IsRingWithoutOne_2286 -> T_IsAbelianGroup_1132)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsRingWithoutOne_2286 -> T_IsAbelianGroup_1132
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2304
         ((T_RingWithoutOne_3344 -> T_IsRingWithoutOne_2286)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_RingWithoutOne_3344 -> T_IsRingWithoutOne_2286
d_isRingWithoutOne_3376 (T_RingWithoutOne_3344 -> AgdaAny
forall a b. a -> b
coe T_RingWithoutOne_3344
v0)))
-- Algebra.Bundles.RingWithoutOne._.isInvertibleMagma
d_isInvertibleMagma_3420 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_RingWithoutOne_3344 ->
  MAlonzo.Code.Algebra.Structures.T_IsInvertibleMagma_924
d_isInvertibleMagma_3420 :: () -> () -> T_RingWithoutOne_3344 -> T_IsInvertibleMagma_924
d_isInvertibleMagma_3420 ~()
v0 ~()
v1 T_RingWithoutOne_3344
v2 = T_RingWithoutOne_3344 -> T_IsInvertibleMagma_924
du_isInvertibleMagma_3420 T_RingWithoutOne_3344
v2
du_isInvertibleMagma_3420 ::
  T_RingWithoutOne_3344 ->
  MAlonzo.Code.Algebra.Structures.T_IsInvertibleMagma_924
du_isInvertibleMagma_3420 :: T_RingWithoutOne_3344 -> T_IsInvertibleMagma_924
du_isInvertibleMagma_3420 T_RingWithoutOne_3344
v0
  = let v1 :: T_IsRingWithoutOne_2286
v1 = T_RingWithoutOne_3344 -> T_IsRingWithoutOne_2286
d_isRingWithoutOne_3376 (T_RingWithoutOne_3344 -> T_RingWithoutOne_3344
forall a b. a -> b
coe T_RingWithoutOne_3344
v0) in
    AgdaAny -> T_IsInvertibleMagma_924
forall a b. a -> b
coe
      (let v2 :: T_IsAbelianGroup_1132
v2
             = T_IsRingWithoutOne_2286 -> T_IsAbelianGroup_1132
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2304
                 (T_IsRingWithoutOne_2286 -> T_IsRingWithoutOne_2286
forall a b. a -> b
coe T_IsRingWithoutOne_2286
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsGroup_1036 -> T_IsInvertibleMagma_924) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsGroup_1036 -> T_IsInvertibleMagma_924
MAlonzo.Code.Algebra.Structures.du_isInvertibleMagma_1122
            ((T_IsAbelianGroup_1132 -> T_IsGroup_1036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132 -> T_IsGroup_1036
MAlonzo.Code.Algebra.Structures.d_isGroup_1144 (T_IsAbelianGroup_1132 -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132
v2))))
-- Algebra.Bundles.RingWithoutOne._.isInvertibleUnitalMagma
d_isInvertibleUnitalMagma_3422 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_RingWithoutOne_3344 ->
  MAlonzo.Code.Algebra.Structures.T_IsInvertibleUnitalMagma_976
d_isInvertibleUnitalMagma_3422 :: () -> () -> T_RingWithoutOne_3344 -> T_IsInvertibleUnitalMagma_976
d_isInvertibleUnitalMagma_3422 ~()
v0 ~()
v1 T_RingWithoutOne_3344
v2
  = T_RingWithoutOne_3344 -> T_IsInvertibleUnitalMagma_976
du_isInvertibleUnitalMagma_3422 T_RingWithoutOne_3344
v2
du_isInvertibleUnitalMagma_3422 ::
  T_RingWithoutOne_3344 ->
  MAlonzo.Code.Algebra.Structures.T_IsInvertibleUnitalMagma_976
du_isInvertibleUnitalMagma_3422 :: T_RingWithoutOne_3344 -> T_IsInvertibleUnitalMagma_976
du_isInvertibleUnitalMagma_3422 T_RingWithoutOne_3344
v0
  = let v1 :: T_IsRingWithoutOne_2286
v1 = T_RingWithoutOne_3344 -> T_IsRingWithoutOne_2286
d_isRingWithoutOne_3376 (T_RingWithoutOne_3344 -> T_RingWithoutOne_3344
forall a b. a -> b
coe T_RingWithoutOne_3344
v0) in
    AgdaAny -> T_IsInvertibleUnitalMagma_976
forall a b. a -> b
coe
      (let v2 :: T_IsAbelianGroup_1132
v2
             = T_IsRingWithoutOne_2286 -> T_IsAbelianGroup_1132
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2304
                 (T_IsRingWithoutOne_2286 -> T_IsRingWithoutOne_2286
forall a b. a -> b
coe T_IsRingWithoutOne_2286
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsGroup_1036 -> T_IsInvertibleUnitalMagma_976)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsGroup_1036 -> T_IsInvertibleUnitalMagma_976
MAlonzo.Code.Algebra.Structures.du_isInvertibleUnitalMagma_1124
            ((T_IsAbelianGroup_1132 -> T_IsGroup_1036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132 -> T_IsGroup_1036
MAlonzo.Code.Algebra.Structures.d_isGroup_1144 (T_IsAbelianGroup_1132 -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132
v2))))
-- Algebra.Bundles.RingWithoutOne._.isMagma
d_isMagma_3424 ::
  T_RingWithoutOne_3344 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_176
d_isMagma_3424 :: T_RingWithoutOne_3344 -> T_IsMagma_176
d_isMagma_3424 T_RingWithoutOne_3344
v0
  = (T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> T_IsMagma_176
forall a b. a -> b
coe
      T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480
      ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
         ((T_IsGroup_1036 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsGroup_1036 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_1050
            ((T_IsAbelianGroup_1132 -> T_IsGroup_1036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsAbelianGroup_1132 -> T_IsGroup_1036
MAlonzo.Code.Algebra.Structures.d_isGroup_1144
               ((T_IsRingWithoutOne_2286 -> T_IsAbelianGroup_1132)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsRingWithoutOne_2286 -> T_IsAbelianGroup_1132
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2304
                  ((T_RingWithoutOne_3344 -> T_IsRingWithoutOne_2286)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_RingWithoutOne_3344 -> T_IsRingWithoutOne_2286
d_isRingWithoutOne_3376 (T_RingWithoutOne_3344 -> AgdaAny
forall a b. a -> b
coe T_RingWithoutOne_3344
v0))))))
-- Algebra.Bundles.RingWithoutOne._.isMonoid
d_isMonoid_3426 ::
  T_RingWithoutOne_3344 ->
  MAlonzo.Code.Algebra.Structures.T_IsMonoid_686
d_isMonoid_3426 :: T_RingWithoutOne_3344 -> T_IsMonoid_686
d_isMonoid_3426 T_RingWithoutOne_3344
v0
  = (T_IsGroup_1036 -> T_IsMonoid_686) -> AgdaAny -> T_IsMonoid_686
forall a b. a -> b
coe
      T_IsGroup_1036 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_1050
      ((T_IsAbelianGroup_1132 -> T_IsGroup_1036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsAbelianGroup_1132 -> T_IsGroup_1036
MAlonzo.Code.Algebra.Structures.d_isGroup_1144
         ((T_IsRingWithoutOne_2286 -> T_IsAbelianGroup_1132)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsRingWithoutOne_2286 -> T_IsAbelianGroup_1132
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2304
            ((T_RingWithoutOne_3344 -> T_IsRingWithoutOne_2286)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_RingWithoutOne_3344 -> T_IsRingWithoutOne_2286
d_isRingWithoutOne_3376 (T_RingWithoutOne_3344 -> AgdaAny
forall a b. a -> b
coe T_RingWithoutOne_3344
v0))))
-- Algebra.Bundles.RingWithoutOne._.isSemigroup
d_isSemigroup_3428 ::
  T_RingWithoutOne_3344 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_472
d_isSemigroup_3428 :: T_RingWithoutOne_3344 -> T_IsSemigroup_472
d_isSemigroup_3428 T_RingWithoutOne_3344
v0
  = (T_IsMonoid_686 -> T_IsSemigroup_472)
-> AgdaAny -> T_IsSemigroup_472
forall a b. a -> b
coe
      T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
      ((T_IsGroup_1036 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsGroup_1036 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_1050
         ((T_IsAbelianGroup_1132 -> T_IsGroup_1036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsAbelianGroup_1132 -> T_IsGroup_1036
MAlonzo.Code.Algebra.Structures.d_isGroup_1144
            ((T_IsRingWithoutOne_2286 -> T_IsAbelianGroup_1132)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsRingWithoutOne_2286 -> T_IsAbelianGroup_1132
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2304
               ((T_RingWithoutOne_3344 -> T_IsRingWithoutOne_2286)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_RingWithoutOne_3344 -> T_IsRingWithoutOne_2286
d_isRingWithoutOne_3376 (T_RingWithoutOne_3344 -> AgdaAny
forall a b. a -> b
coe T_RingWithoutOne_3344
v0)))))
-- Algebra.Bundles.RingWithoutOne._.isUnitalMagma
d_isUnitalMagma_3430 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_RingWithoutOne_3344 ->
  MAlonzo.Code.Algebra.Structures.T_IsUnitalMagma_642
d_isUnitalMagma_3430 :: () -> () -> T_RingWithoutOne_3344 -> T_IsUnitalMagma_642
d_isUnitalMagma_3430 ~()
v0 ~()
v1 T_RingWithoutOne_3344
v2 = T_RingWithoutOne_3344 -> T_IsUnitalMagma_642
du_isUnitalMagma_3430 T_RingWithoutOne_3344
v2
du_isUnitalMagma_3430 ::
  T_RingWithoutOne_3344 ->
  MAlonzo.Code.Algebra.Structures.T_IsUnitalMagma_642
du_isUnitalMagma_3430 :: T_RingWithoutOne_3344 -> T_IsUnitalMagma_642
du_isUnitalMagma_3430 T_RingWithoutOne_3344
v0
  = let v1 :: T_IsRingWithoutOne_2286
v1 = T_RingWithoutOne_3344 -> T_IsRingWithoutOne_2286
d_isRingWithoutOne_3376 (T_RingWithoutOne_3344 -> T_RingWithoutOne_3344
forall a b. a -> b
coe T_RingWithoutOne_3344
v0) in
    AgdaAny -> T_IsUnitalMagma_642
forall a b. a -> b
coe
      (let v2 :: T_IsAbelianGroup_1132
v2
             = T_IsRingWithoutOne_2286 -> T_IsAbelianGroup_1132
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2304
                 (T_IsRingWithoutOne_2286 -> T_IsRingWithoutOne_2286
forall a b. a -> b
coe T_IsRingWithoutOne_2286
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsGroup_1036
v3
                = T_IsAbelianGroup_1132 -> T_IsGroup_1036
MAlonzo.Code.Algebra.Structures.d_isGroup_1144 (T_IsAbelianGroup_1132 -> T_IsAbelianGroup_1132
forall a b. a -> b
coe T_IsAbelianGroup_1132
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsMonoid_686 -> T_IsUnitalMagma_642) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_686 -> T_IsUnitalMagma_642
MAlonzo.Code.Algebra.Structures.du_isUnitalMagma_730
               ((T_IsGroup_1036 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1036 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_1050 (T_IsGroup_1036 -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1036
v3)))))
-- Algebra.Bundles.RingWithoutOne._.⁻¹-cong
d_'8315''185''45'cong_3432 ::
  T_RingWithoutOne_3344 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8315''185''45'cong_3432 :: T_RingWithoutOne_3344 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8315''185''45'cong_3432 T_RingWithoutOne_3344
v0
  = (T_IsGroup_1036 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsGroup_1036 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8315''185''45'cong_1054
      ((T_IsAbelianGroup_1132 -> T_IsGroup_1036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsAbelianGroup_1132 -> T_IsGroup_1036
MAlonzo.Code.Algebra.Structures.d_isGroup_1144
         ((T_IsRingWithoutOne_2286 -> T_IsAbelianGroup_1132)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsRingWithoutOne_2286 -> T_IsAbelianGroup_1132
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2304
            ((T_RingWithoutOne_3344 -> T_IsRingWithoutOne_2286)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_RingWithoutOne_3344 -> T_IsRingWithoutOne_2286
d_isRingWithoutOne_3376 (T_RingWithoutOne_3344 -> AgdaAny
forall a b. a -> b
coe T_RingWithoutOne_3344
v0))))
-- Algebra.Bundles.RingWithoutOne._.inverse
d_inverse_3434 ::
  T_RingWithoutOne_3344 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_inverse_3434 :: T_RingWithoutOne_3344 -> T_Σ_14
d_inverse_3434 T_RingWithoutOne_3344
v0
  = (T_IsGroup_1036 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsGroup_1036 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_inverse_1052
      ((T_IsAbelianGroup_1132 -> T_IsGroup_1036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsAbelianGroup_1132 -> T_IsGroup_1036
MAlonzo.Code.Algebra.Structures.d_isGroup_1144
         ((T_IsRingWithoutOne_2286 -> T_IsAbelianGroup_1132)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsRingWithoutOne_2286 -> T_IsAbelianGroup_1132
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2304
            ((T_RingWithoutOne_3344 -> T_IsRingWithoutOne_2286)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_RingWithoutOne_3344 -> T_IsRingWithoutOne_2286
d_isRingWithoutOne_3376 (T_RingWithoutOne_3344 -> AgdaAny
forall a b. a -> b
coe T_RingWithoutOne_3344
v0))))
-- Algebra.Bundles.RingWithoutOne._.inverseʳ
d_inverse'691'_3436 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_RingWithoutOne_3344 -> AgdaAny -> AgdaAny
d_inverse'691'_3436 :: () -> () -> T_RingWithoutOne_3344 -> AgdaAny -> AgdaAny
d_inverse'691'_3436 ~()
v0 ~()
v1 T_RingWithoutOne_3344
v2 = T_RingWithoutOne_3344 -> AgdaAny -> AgdaAny
du_inverse'691'_3436 T_RingWithoutOne_3344
v2
du_inverse'691'_3436 :: T_RingWithoutOne_3344 -> AgdaAny -> AgdaAny
du_inverse'691'_3436 :: T_RingWithoutOne_3344 -> AgdaAny -> AgdaAny
du_inverse'691'_3436 T_RingWithoutOne_3344
v0
  = let v1 :: T_IsRingWithoutOne_2286
v1 = T_RingWithoutOne_3344 -> T_IsRingWithoutOne_2286
d_isRingWithoutOne_3376 (T_RingWithoutOne_3344 -> T_RingWithoutOne_3344
forall a b. a -> b
coe T_RingWithoutOne_3344
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsAbelianGroup_1132
v2
             = T_IsRingWithoutOne_2286 -> T_IsAbelianGroup_1132
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2304
                 (T_IsRingWithoutOne_2286 -> T_IsRingWithoutOne_2286
forall a b. a -> b
coe T_IsRingWithoutOne_2286
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsGroup_1036 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsGroup_1036 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_inverse'691'_1108
            ((T_IsAbelianGroup_1132 -> T_IsGroup_1036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132 -> T_IsGroup_1036
MAlonzo.Code.Algebra.Structures.d_isGroup_1144 (T_IsAbelianGroup_1132 -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132
v2))))
-- Algebra.Bundles.RingWithoutOne._.inverseˡ
d_inverse'737'_3438 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_RingWithoutOne_3344 -> AgdaAny -> AgdaAny
d_inverse'737'_3438 :: () -> () -> T_RingWithoutOne_3344 -> AgdaAny -> AgdaAny
d_inverse'737'_3438 ~()
v0 ~()
v1 T_RingWithoutOne_3344
v2 = T_RingWithoutOne_3344 -> AgdaAny -> AgdaAny
du_inverse'737'_3438 T_RingWithoutOne_3344
v2
du_inverse'737'_3438 :: T_RingWithoutOne_3344 -> AgdaAny -> AgdaAny
du_inverse'737'_3438 :: T_RingWithoutOne_3344 -> AgdaAny -> AgdaAny
du_inverse'737'_3438 T_RingWithoutOne_3344
v0
  = let v1 :: T_IsRingWithoutOne_2286
v1 = T_RingWithoutOne_3344 -> T_IsRingWithoutOne_2286
d_isRingWithoutOne_3376 (T_RingWithoutOne_3344 -> T_RingWithoutOne_3344
forall a b. a -> b
coe T_RingWithoutOne_3344
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsAbelianGroup_1132
v2
             = T_IsRingWithoutOne_2286 -> T_IsAbelianGroup_1132
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2304
                 (T_IsRingWithoutOne_2286 -> T_IsRingWithoutOne_2286
forall a b. a -> b
coe T_IsRingWithoutOne_2286
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsGroup_1036 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsGroup_1036 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_inverse'737'_1106
            ((T_IsAbelianGroup_1132 -> T_IsGroup_1036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132 -> T_IsGroup_1036
MAlonzo.Code.Algebra.Structures.d_isGroup_1144 (T_IsAbelianGroup_1132 -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132
v2))))
-- Algebra.Bundles.RingWithoutOne._.distrib
d_distrib_3440 ::
  T_RingWithoutOne_3344 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_distrib_3440 :: T_RingWithoutOne_3344 -> T_Σ_14
d_distrib_3440 T_RingWithoutOne_3344
v0
  = (T_IsRingWithoutOne_2286 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsRingWithoutOne_2286 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_distrib_2310
      ((T_RingWithoutOne_3344 -> T_IsRingWithoutOne_2286)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_RingWithoutOne_3344 -> T_IsRingWithoutOne_2286
d_isRingWithoutOne_3376 (T_RingWithoutOne_3344 -> AgdaAny
forall a b. a -> b
coe T_RingWithoutOne_3344
v0))
-- Algebra.Bundles.RingWithoutOne._.distribʳ
d_distrib'691'_3442 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_RingWithoutOne_3344 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_distrib'691'_3442 :: ()
-> ()
-> T_RingWithoutOne_3344
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_distrib'691'_3442 ~()
v0 ~()
v1 T_RingWithoutOne_3344
v2 = T_RingWithoutOne_3344 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'691'_3442 T_RingWithoutOne_3344
v2
du_distrib'691'_3442 ::
  T_RingWithoutOne_3344 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'691'_3442 :: T_RingWithoutOne_3344 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'691'_3442 T_RingWithoutOne_3344
v0
  = (T_IsRingWithoutOne_2286
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsRingWithoutOne_2286 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_distrib'691'_2380
      ((T_RingWithoutOne_3344 -> T_IsRingWithoutOne_2286)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_RingWithoutOne_3344 -> T_IsRingWithoutOne_2286
d_isRingWithoutOne_3376 (T_RingWithoutOne_3344 -> AgdaAny
forall a b. a -> b
coe T_RingWithoutOne_3344
v0))
-- Algebra.Bundles.RingWithoutOne._.distribˡ
d_distrib'737'_3444 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_RingWithoutOne_3344 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_distrib'737'_3444 :: ()
-> ()
-> T_RingWithoutOne_3344
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_distrib'737'_3444 ~()
v0 ~()
v1 T_RingWithoutOne_3344
v2 = T_RingWithoutOne_3344 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'737'_3444 T_RingWithoutOne_3344
v2
du_distrib'737'_3444 ::
  T_RingWithoutOne_3344 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'737'_3444 :: T_RingWithoutOne_3344 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'737'_3444 T_RingWithoutOne_3344
v0
  = (T_IsRingWithoutOne_2286
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsRingWithoutOne_2286 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_distrib'737'_2378
      ((T_RingWithoutOne_3344 -> T_IsRingWithoutOne_2286)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_RingWithoutOne_3344 -> T_IsRingWithoutOne_2286
d_isRingWithoutOne_3376 (T_RingWithoutOne_3344 -> AgdaAny
forall a b. a -> b
coe T_RingWithoutOne_3344
v0))
-- Algebra.Bundles.RingWithoutOne._.isEquivalence
d_isEquivalence_3446 ::
  T_RingWithoutOne_3344 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_3446 :: T_RingWithoutOne_3344 -> T_IsEquivalence_26
d_isEquivalence_3446 T_RingWithoutOne_3344
v0
  = (T_IsMagma_176 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
      ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480
         ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
            ((T_IsGroup_1036 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsGroup_1036 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_1050
               ((T_IsAbelianGroup_1132 -> T_IsGroup_1036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsAbelianGroup_1132 -> T_IsGroup_1036
MAlonzo.Code.Algebra.Structures.d_isGroup_1144
                  ((T_IsRingWithoutOne_2286 -> T_IsAbelianGroup_1132)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsRingWithoutOne_2286 -> T_IsAbelianGroup_1132
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2304
                     ((T_RingWithoutOne_3344 -> T_IsRingWithoutOne_2286)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_RingWithoutOne_3344 -> T_IsRingWithoutOne_2286
d_isRingWithoutOne_3376 (T_RingWithoutOne_3344 -> AgdaAny
forall a b. a -> b
coe T_RingWithoutOne_3344
v0)))))))
-- Algebra.Bundles.RingWithoutOne._.isPartialEquivalence
d_isPartialEquivalence_3448 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_RingWithoutOne_3344 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_3448 :: () -> () -> T_RingWithoutOne_3344 -> T_IsPartialEquivalence_16
d_isPartialEquivalence_3448 ~()
v0 ~()
v1 T_RingWithoutOne_3344
v2
  = T_RingWithoutOne_3344 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_3448 T_RingWithoutOne_3344
v2
du_isPartialEquivalence_3448 ::
  T_RingWithoutOne_3344 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_3448 :: T_RingWithoutOne_3344 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_3448 T_RingWithoutOne_3344
v0
  = let v1 :: T_IsRingWithoutOne_2286
v1 = T_RingWithoutOne_3344 -> T_IsRingWithoutOne_2286
d_isRingWithoutOne_3376 (T_RingWithoutOne_3344 -> T_RingWithoutOne_3344
forall a b. a -> b
coe T_RingWithoutOne_3344
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsAbelianGroup_1132
v2
             = T_IsRingWithoutOne_2286 -> T_IsAbelianGroup_1132
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2304
                 (T_IsRingWithoutOne_2286 -> T_IsRingWithoutOne_2286
forall a b. a -> b
coe T_IsRingWithoutOne_2286
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsGroup_1036
v3
                = T_IsAbelianGroup_1132 -> T_IsGroup_1036
MAlonzo.Code.Algebra.Structures.d_isGroup_1144 (T_IsAbelianGroup_1132 -> T_IsAbelianGroup_1132
forall a b. a -> b
coe T_IsAbelianGroup_1132
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsMonoid_686
v4
                   = T_IsGroup_1036 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_1050 (T_IsGroup_1036 -> T_IsGroup_1036
forall a b. a -> b
coe T_IsGroup_1036
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsSemigroup_472
v5
                      = T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (let v6 :: T_IsMagma_176
v6 = T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (T_IsSemigroup_472 -> T_IsSemigroup_472
forall a b. a -> b
coe T_IsSemigroup_472
v5) in
                   AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     ((T_IsEquivalence_26 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsEquivalence_26 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
                        ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v6))))))))
-- Algebra.Bundles.RingWithoutOne._.refl
d_refl_3450 :: T_RingWithoutOne_3344 -> AgdaAny -> AgdaAny
d_refl_3450 :: T_RingWithoutOne_3344 -> AgdaAny -> AgdaAny
d_refl_3450 T_RingWithoutOne_3344
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_34
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
         ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480
            ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
               ((T_IsGroup_1036 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsGroup_1036 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_1050
                  ((T_IsAbelianGroup_1132 -> T_IsGroup_1036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsAbelianGroup_1132 -> T_IsGroup_1036
MAlonzo.Code.Algebra.Structures.d_isGroup_1144
                     ((T_IsRingWithoutOne_2286 -> T_IsAbelianGroup_1132)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsRingWithoutOne_2286 -> T_IsAbelianGroup_1132
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2304
                        ((T_RingWithoutOne_3344 -> T_IsRingWithoutOne_2286)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_RingWithoutOne_3344 -> T_IsRingWithoutOne_2286
d_isRingWithoutOne_3376 (T_RingWithoutOne_3344 -> AgdaAny
forall a b. a -> b
coe T_RingWithoutOne_3344
v0))))))))
-- Algebra.Bundles.RingWithoutOne._.reflexive
d_reflexive_3452 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_RingWithoutOne_3344 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_3452 :: ()
-> ()
-> T_RingWithoutOne_3344
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_3452 ~()
v0 ~()
v1 T_RingWithoutOne_3344
v2 = T_RingWithoutOne_3344
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_3452 T_RingWithoutOne_3344
v2
du_reflexive_3452 ::
  T_RingWithoutOne_3344 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_3452 :: T_RingWithoutOne_3344
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_3452 T_RingWithoutOne_3344
v0
  = let v1 :: T_IsRingWithoutOne_2286
v1 = T_RingWithoutOne_3344 -> T_IsRingWithoutOne_2286
d_isRingWithoutOne_3376 (T_RingWithoutOne_3344 -> T_RingWithoutOne_3344
forall a b. a -> b
coe T_RingWithoutOne_3344
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsAbelianGroup_1132
v2
             = T_IsRingWithoutOne_2286 -> T_IsAbelianGroup_1132
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2304
                 (T_IsRingWithoutOne_2286 -> T_IsRingWithoutOne_2286
forall a b. a -> b
coe T_IsRingWithoutOne_2286
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsGroup_1036
v3
                = T_IsAbelianGroup_1132 -> T_IsGroup_1036
MAlonzo.Code.Algebra.Structures.d_isGroup_1144 (T_IsAbelianGroup_1132 -> T_IsAbelianGroup_1132
forall a b. a -> b
coe T_IsAbelianGroup_1132
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsMonoid_686
v4
                   = T_IsGroup_1036 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_1050 (T_IsGroup_1036 -> T_IsGroup_1036
forall a b. a -> b
coe T_IsGroup_1036
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsSemigroup_472
v5
                      = T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (let v6 :: T_IsMagma_176
v6 = T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (T_IsSemigroup_472 -> T_IsSemigroup_472
forall a b. a -> b
coe T_IsSemigroup_472
v5) in
                   (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
                     (\ AgdaAny
v7 AgdaAny
v8 AgdaAny
v9 ->
                        (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                          T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
                          ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v6))
                          AgdaAny
v7))))))
-- Algebra.Bundles.RingWithoutOne._.setoid
d_setoid_3454 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_RingWithoutOne_3344 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_3454 :: () -> () -> T_RingWithoutOne_3344 -> T_Setoid_44
d_setoid_3454 ~()
v0 ~()
v1 T_RingWithoutOne_3344
v2 = T_RingWithoutOne_3344 -> T_Setoid_44
du_setoid_3454 T_RingWithoutOne_3344
v2
du_setoid_3454 ::
  T_RingWithoutOne_3344 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_3454 :: T_RingWithoutOne_3344 -> T_Setoid_44
du_setoid_3454 T_RingWithoutOne_3344
v0
  = let v1 :: T_IsRingWithoutOne_2286
v1 = T_RingWithoutOne_3344 -> T_IsRingWithoutOne_2286
d_isRingWithoutOne_3376 (T_RingWithoutOne_3344 -> T_RingWithoutOne_3344
forall a b. a -> b
coe T_RingWithoutOne_3344
v0) in
    AgdaAny -> T_Setoid_44
forall a b. a -> b
coe
      (let v2 :: T_IsAbelianGroup_1132
v2
             = T_IsRingWithoutOne_2286 -> T_IsAbelianGroup_1132
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2304
                 (T_IsRingWithoutOne_2286 -> T_IsRingWithoutOne_2286
forall a b. a -> b
coe T_IsRingWithoutOne_2286
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsGroup_1036
v3
                = T_IsAbelianGroup_1132 -> T_IsGroup_1036
MAlonzo.Code.Algebra.Structures.d_isGroup_1144 (T_IsAbelianGroup_1132 -> T_IsAbelianGroup_1132
forall a b. a -> b
coe T_IsAbelianGroup_1132
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsMonoid_686
v4
                   = T_IsGroup_1036 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_1050 (T_IsGroup_1036 -> T_IsGroup_1036
forall a b. a -> b
coe T_IsGroup_1036
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsSemigroup_472
v5
                      = T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  ((T_IsMagma_176 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsMagma_176 -> T_Setoid_44
MAlonzo.Code.Algebra.Structures.du_setoid_200
                     ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v5)))))))
-- Algebra.Bundles.RingWithoutOne._.sym
d_sym_3456 ::
  T_RingWithoutOne_3344 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_3456 :: T_RingWithoutOne_3344 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_3456 T_RingWithoutOne_3344
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_36
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
         ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480
            ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
               ((T_IsGroup_1036 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsGroup_1036 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_1050
                  ((T_IsAbelianGroup_1132 -> T_IsGroup_1036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsAbelianGroup_1132 -> T_IsGroup_1036
MAlonzo.Code.Algebra.Structures.d_isGroup_1144
                     ((T_IsRingWithoutOne_2286 -> T_IsAbelianGroup_1132)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsRingWithoutOne_2286 -> T_IsAbelianGroup_1132
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2304
                        ((T_RingWithoutOne_3344 -> T_IsRingWithoutOne_2286)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_RingWithoutOne_3344 -> T_IsRingWithoutOne_2286
d_isRingWithoutOne_3376 (T_RingWithoutOne_3344 -> AgdaAny
forall a b. a -> b
coe T_RingWithoutOne_3344
v0))))))))
-- Algebra.Bundles.RingWithoutOne._.trans
d_trans_3458 ::
  T_RingWithoutOne_3344 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_3458 :: T_RingWithoutOne_3344
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_3458 T_RingWithoutOne_3344
v0
  = (T_IsEquivalence_26
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_38
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
         ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480
            ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
               ((T_IsGroup_1036 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsGroup_1036 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_1050
                  ((T_IsAbelianGroup_1132 -> T_IsGroup_1036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsAbelianGroup_1132 -> T_IsGroup_1036
MAlonzo.Code.Algebra.Structures.d_isGroup_1144
                     ((T_IsRingWithoutOne_2286 -> T_IsAbelianGroup_1132)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsRingWithoutOne_2286 -> T_IsAbelianGroup_1132
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2304
                        ((T_RingWithoutOne_3344 -> T_IsRingWithoutOne_2286)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_RingWithoutOne_3344 -> T_IsRingWithoutOne_2286
d_isRingWithoutOne_3376 (T_RingWithoutOne_3344 -> AgdaAny
forall a b. a -> b
coe T_RingWithoutOne_3344
v0))))))))
-- Algebra.Bundles.RingWithoutOne._.uniqueʳ-⁻¹
d_unique'691''45''8315''185'_3460 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_RingWithoutOne_3344 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_unique'691''45''8315''185'_3460 :: ()
-> ()
-> T_RingWithoutOne_3344
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_unique'691''45''8315''185'_3460 ~()
v0 ~()
v1 T_RingWithoutOne_3344
v2
  = T_RingWithoutOne_3344 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_unique'691''45''8315''185'_3460 T_RingWithoutOne_3344
v2
du_unique'691''45''8315''185'_3460 ::
  T_RingWithoutOne_3344 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_unique'691''45''8315''185'_3460 :: T_RingWithoutOne_3344 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_unique'691''45''8315''185'_3460 T_RingWithoutOne_3344
v0
  = let v1 :: AgdaAny -> AgdaAny -> AgdaAny
v1 = T_RingWithoutOne_3344 -> AgdaAny -> AgdaAny -> AgdaAny
d__'43'__3368 (T_RingWithoutOne_3344 -> T_RingWithoutOne_3344
forall a b. a -> b
coe T_RingWithoutOne_3344
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: AgdaAny -> AgdaAny
v2 = T_RingWithoutOne_3344 -> AgdaAny -> AgdaAny
d_'45'__3372 (T_RingWithoutOne_3344 -> T_RingWithoutOne_3344
forall a b. a -> b
coe T_RingWithoutOne_3344
v0) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: AgdaAny
v3 = T_RingWithoutOne_3344 -> AgdaAny
d_0'35'_3374 (T_RingWithoutOne_3344 -> T_RingWithoutOne_3344
forall a b. a -> b
coe T_RingWithoutOne_3344
v0) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsRingWithoutOne_2286
v4 = T_RingWithoutOne_3344 -> T_IsRingWithoutOne_2286
d_isRingWithoutOne_3376 (T_RingWithoutOne_3344 -> T_RingWithoutOne_3344
forall a b. a -> b
coe T_RingWithoutOne_3344
v0) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsAbelianGroup_1132
v5
                      = T_IsRingWithoutOne_2286 -> T_IsAbelianGroup_1132
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2304
                          (T_IsRingWithoutOne_2286 -> T_IsRingWithoutOne_2286
forall a b. a -> b
coe T_IsRingWithoutOne_2286
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (((AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> (AgdaAny -> AgdaAny)
 -> T_IsGroup_1036
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsGroup_1036
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.du_unique'691''45''8315''185'_1120
                     ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v1) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3) ((AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v2)
                     ((T_IsAbelianGroup_1132 -> T_IsGroup_1036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132 -> T_IsGroup_1036
MAlonzo.Code.Algebra.Structures.d_isGroup_1144 (T_IsAbelianGroup_1132 -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132
v5)))))))
-- Algebra.Bundles.RingWithoutOne._.uniqueˡ-⁻¹
d_unique'737''45''8315''185'_3462 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_RingWithoutOne_3344 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_unique'737''45''8315''185'_3462 :: ()
-> ()
-> T_RingWithoutOne_3344
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_unique'737''45''8315''185'_3462 ~()
v0 ~()
v1 T_RingWithoutOne_3344
v2
  = T_RingWithoutOne_3344 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_unique'737''45''8315''185'_3462 T_RingWithoutOne_3344
v2
du_unique'737''45''8315''185'_3462 ::
  T_RingWithoutOne_3344 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_unique'737''45''8315''185'_3462 :: T_RingWithoutOne_3344 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_unique'737''45''8315''185'_3462 T_RingWithoutOne_3344
v0
  = let v1 :: AgdaAny -> AgdaAny -> AgdaAny
v1 = T_RingWithoutOne_3344 -> AgdaAny -> AgdaAny -> AgdaAny
d__'43'__3368 (T_RingWithoutOne_3344 -> T_RingWithoutOne_3344
forall a b. a -> b
coe T_RingWithoutOne_3344
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: AgdaAny -> AgdaAny
v2 = T_RingWithoutOne_3344 -> AgdaAny -> AgdaAny
d_'45'__3372 (T_RingWithoutOne_3344 -> T_RingWithoutOne_3344
forall a b. a -> b
coe T_RingWithoutOne_3344
v0) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: AgdaAny
v3 = T_RingWithoutOne_3344 -> AgdaAny
d_0'35'_3374 (T_RingWithoutOne_3344 -> T_RingWithoutOne_3344
forall a b. a -> b
coe T_RingWithoutOne_3344
v0) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsRingWithoutOne_2286
v4 = T_RingWithoutOne_3344 -> T_IsRingWithoutOne_2286
d_isRingWithoutOne_3376 (T_RingWithoutOne_3344 -> T_RingWithoutOne_3344
forall a b. a -> b
coe T_RingWithoutOne_3344
v0) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsAbelianGroup_1132
v5
                      = T_IsRingWithoutOne_2286 -> T_IsAbelianGroup_1132
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2304
                          (T_IsRingWithoutOne_2286 -> T_IsRingWithoutOne_2286
forall a b. a -> b
coe T_IsRingWithoutOne_2286
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (((AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> (AgdaAny -> AgdaAny)
 -> T_IsGroup_1036
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsGroup_1036
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.du_unique'737''45''8315''185'_1114
                     ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v1) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3) ((AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v2)
                     ((T_IsAbelianGroup_1132 -> T_IsGroup_1036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132 -> T_IsGroup_1036
MAlonzo.Code.Algebra.Structures.d_isGroup_1144 (T_IsAbelianGroup_1132 -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132
v5)))))))
-- Algebra.Bundles.RingWithoutOne._.zero
d_zero_3464 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_RingWithoutOne_3344 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_zero_3464 :: () -> () -> T_RingWithoutOne_3344 -> T_Σ_14
d_zero_3464 ~()
v0 ~()
v1 T_RingWithoutOne_3344
v2 = T_RingWithoutOne_3344 -> T_Σ_14
du_zero_3464 T_RingWithoutOne_3344
v2
du_zero_3464 ::
  T_RingWithoutOne_3344 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
du_zero_3464 :: T_RingWithoutOne_3344 -> T_Σ_14
du_zero_3464 T_RingWithoutOne_3344
v0
  = ((AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny)
 -> AgdaAny
 -> T_IsRingWithoutOne_2286
 -> T_Σ_14)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsRingWithoutOne_2286
-> T_Σ_14
MAlonzo.Code.Algebra.Structures.du_zero_2386
      ((T_RingWithoutOne_3344 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_RingWithoutOne_3344 -> AgdaAny -> AgdaAny -> AgdaAny
d__'43'__3368 (T_RingWithoutOne_3344 -> AgdaAny
forall a b. a -> b
coe T_RingWithoutOne_3344
v0)) ((T_RingWithoutOne_3344 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_RingWithoutOne_3344 -> AgdaAny -> AgdaAny -> AgdaAny
d__'42'__3370 (T_RingWithoutOne_3344 -> AgdaAny
forall a b. a -> b
coe T_RingWithoutOne_3344
v0))
      ((T_RingWithoutOne_3344 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_RingWithoutOne_3344 -> AgdaAny -> AgdaAny
d_'45'__3372 (T_RingWithoutOne_3344 -> AgdaAny
forall a b. a -> b
coe T_RingWithoutOne_3344
v0)) ((T_RingWithoutOne_3344 -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_RingWithoutOne_3344 -> AgdaAny
d_0'35'_3374 (T_RingWithoutOne_3344 -> AgdaAny
forall a b. a -> b
coe T_RingWithoutOne_3344
v0))
      ((T_RingWithoutOne_3344 -> T_IsRingWithoutOne_2286)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_RingWithoutOne_3344 -> T_IsRingWithoutOne_2286
d_isRingWithoutOne_3376 (T_RingWithoutOne_3344 -> AgdaAny
forall a b. a -> b
coe T_RingWithoutOne_3344
v0))
-- Algebra.Bundles.RingWithoutOne._.zeroʳ
d_zero'691'_3466 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_RingWithoutOne_3344 -> AgdaAny -> AgdaAny
d_zero'691'_3466 :: () -> () -> T_RingWithoutOne_3344 -> AgdaAny -> AgdaAny
d_zero'691'_3466 ~()
v0 ~()
v1 T_RingWithoutOne_3344
v2 = T_RingWithoutOne_3344 -> AgdaAny -> AgdaAny
du_zero'691'_3466 T_RingWithoutOne_3344
v2
du_zero'691'_3466 :: T_RingWithoutOne_3344 -> AgdaAny -> AgdaAny
du_zero'691'_3466 :: T_RingWithoutOne_3344 -> AgdaAny -> AgdaAny
du_zero'691'_3466 T_RingWithoutOne_3344
v0
  = ((AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny)
 -> AgdaAny
 -> T_IsRingWithoutOne_2286
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsRingWithoutOne_2286
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.du_zero'691'_2384
      ((T_RingWithoutOne_3344 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_RingWithoutOne_3344 -> AgdaAny -> AgdaAny -> AgdaAny
d__'43'__3368 (T_RingWithoutOne_3344 -> AgdaAny
forall a b. a -> b
coe T_RingWithoutOne_3344
v0)) ((T_RingWithoutOne_3344 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_RingWithoutOne_3344 -> AgdaAny -> AgdaAny -> AgdaAny
d__'42'__3370 (T_RingWithoutOne_3344 -> AgdaAny
forall a b. a -> b
coe T_RingWithoutOne_3344
v0))
      ((T_RingWithoutOne_3344 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_RingWithoutOne_3344 -> AgdaAny -> AgdaAny
d_'45'__3372 (T_RingWithoutOne_3344 -> AgdaAny
forall a b. a -> b
coe T_RingWithoutOne_3344
v0)) ((T_RingWithoutOne_3344 -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_RingWithoutOne_3344 -> AgdaAny
d_0'35'_3374 (T_RingWithoutOne_3344 -> AgdaAny
forall a b. a -> b
coe T_RingWithoutOne_3344
v0))
      ((T_RingWithoutOne_3344 -> T_IsRingWithoutOne_2286)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_RingWithoutOne_3344 -> T_IsRingWithoutOne_2286
d_isRingWithoutOne_3376 (T_RingWithoutOne_3344 -> AgdaAny
forall a b. a -> b
coe T_RingWithoutOne_3344
v0))
-- Algebra.Bundles.RingWithoutOne._.zeroˡ
d_zero'737'_3468 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_RingWithoutOne_3344 -> AgdaAny -> AgdaAny
d_zero'737'_3468 :: () -> () -> T_RingWithoutOne_3344 -> AgdaAny -> AgdaAny
d_zero'737'_3468 ~()
v0 ~()
v1 T_RingWithoutOne_3344
v2 = T_RingWithoutOne_3344 -> AgdaAny -> AgdaAny
du_zero'737'_3468 T_RingWithoutOne_3344
v2
du_zero'737'_3468 :: T_RingWithoutOne_3344 -> AgdaAny -> AgdaAny
du_zero'737'_3468 :: T_RingWithoutOne_3344 -> AgdaAny -> AgdaAny
du_zero'737'_3468 T_RingWithoutOne_3344
v0
  = ((AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny)
 -> AgdaAny
 -> T_IsRingWithoutOne_2286
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsRingWithoutOne_2286
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.du_zero'737'_2382
      ((T_RingWithoutOne_3344 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_RingWithoutOne_3344 -> AgdaAny -> AgdaAny -> AgdaAny
d__'43'__3368 (T_RingWithoutOne_3344 -> AgdaAny
forall a b. a -> b
coe T_RingWithoutOne_3344
v0)) ((T_RingWithoutOne_3344 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_RingWithoutOne_3344 -> AgdaAny -> AgdaAny -> AgdaAny
d__'42'__3370 (T_RingWithoutOne_3344 -> AgdaAny
forall a b. a -> b
coe T_RingWithoutOne_3344
v0))
      ((T_RingWithoutOne_3344 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_RingWithoutOne_3344 -> AgdaAny -> AgdaAny
d_'45'__3372 (T_RingWithoutOne_3344 -> AgdaAny
forall a b. a -> b
coe T_RingWithoutOne_3344
v0)) ((T_RingWithoutOne_3344 -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_RingWithoutOne_3344 -> AgdaAny
d_0'35'_3374 (T_RingWithoutOne_3344 -> AgdaAny
forall a b. a -> b
coe T_RingWithoutOne_3344
v0))
      ((T_RingWithoutOne_3344 -> T_IsRingWithoutOne_2286)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_RingWithoutOne_3344 -> T_IsRingWithoutOne_2286
d_isRingWithoutOne_3376 (T_RingWithoutOne_3344 -> AgdaAny
forall a b. a -> b
coe T_RingWithoutOne_3344
v0))
-- Algebra.Bundles.RingWithoutOne.+-abelianGroup
d_'43''45'abelianGroup_3470 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_RingWithoutOne_3344 -> T_AbelianGroup_1636
d_'43''45'abelianGroup_3470 :: () -> () -> T_RingWithoutOne_3344 -> T_AbelianGroup_1636
d_'43''45'abelianGroup_3470 ~()
v0 ~()
v1 T_RingWithoutOne_3344
v2
  = T_RingWithoutOne_3344 -> T_AbelianGroup_1636
du_'43''45'abelianGroup_3470 T_RingWithoutOne_3344
v2
du_'43''45'abelianGroup_3470 ::
  T_RingWithoutOne_3344 -> T_AbelianGroup_1636
du_'43''45'abelianGroup_3470 :: T_RingWithoutOne_3344 -> T_AbelianGroup_1636
du_'43''45'abelianGroup_3470 T_RingWithoutOne_3344
v0
  = ((AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> (AgdaAny -> AgdaAny)
 -> T_IsAbelianGroup_1132
 -> T_AbelianGroup_1636)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsAbelianGroup_1132
-> T_AbelianGroup_1636
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsAbelianGroup_1132
-> T_AbelianGroup_1636
C_AbelianGroup'46'constructor_29855 (T_RingWithoutOne_3344 -> AgdaAny -> AgdaAny -> AgdaAny
d__'43'__3368 (T_RingWithoutOne_3344 -> T_RingWithoutOne_3344
forall a b. a -> b
coe T_RingWithoutOne_3344
v0))
      (T_RingWithoutOne_3344 -> AgdaAny
d_0'35'_3374 (T_RingWithoutOne_3344 -> T_RingWithoutOne_3344
forall a b. a -> b
coe T_RingWithoutOne_3344
v0)) (T_RingWithoutOne_3344 -> AgdaAny -> AgdaAny
d_'45'__3372 (T_RingWithoutOne_3344 -> T_RingWithoutOne_3344
forall a b. a -> b
coe T_RingWithoutOne_3344
v0))
      (T_IsRingWithoutOne_2286 -> T_IsAbelianGroup_1132
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2304
         ((T_RingWithoutOne_3344 -> T_IsRingWithoutOne_2286)
-> AgdaAny -> T_IsRingWithoutOne_2286
forall a b. a -> b
coe T_RingWithoutOne_3344 -> T_IsRingWithoutOne_2286
d_isRingWithoutOne_3376 (T_RingWithoutOne_3344 -> AgdaAny
forall a b. a -> b
coe T_RingWithoutOne_3344
v0)))
-- Algebra.Bundles.RingWithoutOne.*-semigroup
d_'42''45'semigroup_3472 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_RingWithoutOne_3344 -> T_Semigroup_536
d_'42''45'semigroup_3472 :: () -> () -> T_RingWithoutOne_3344 -> T_Semigroup_536
d_'42''45'semigroup_3472 ~()
v0 ~()
v1 T_RingWithoutOne_3344
v2 = T_RingWithoutOne_3344 -> T_Semigroup_536
du_'42''45'semigroup_3472 T_RingWithoutOne_3344
v2
du_'42''45'semigroup_3472 ::
  T_RingWithoutOne_3344 -> T_Semigroup_536
du_'42''45'semigroup_3472 :: T_RingWithoutOne_3344 -> T_Semigroup_536
du_'42''45'semigroup_3472 T_RingWithoutOne_3344
v0
  = ((AgdaAny -> AgdaAny -> AgdaAny)
 -> T_IsSemigroup_472 -> T_Semigroup_536)
-> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> T_Semigroup_536
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsSemigroup_472 -> T_Semigroup_536
C_Semigroup'46'constructor_9793 (T_RingWithoutOne_3344 -> AgdaAny -> AgdaAny -> AgdaAny
d__'42'__3370 (T_RingWithoutOne_3344 -> T_RingWithoutOne_3344
forall a b. a -> b
coe T_RingWithoutOne_3344
v0))
      ((T_IsRingWithoutOne_2286 -> T_IsSemigroup_472)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsRingWithoutOne_2286 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.du_'42''45'isSemigroup_2390
         ((T_RingWithoutOne_3344 -> T_IsRingWithoutOne_2286)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_RingWithoutOne_3344 -> T_IsRingWithoutOne_2286
d_isRingWithoutOne_3376 (T_RingWithoutOne_3344 -> AgdaAny
forall a b. a -> b
coe T_RingWithoutOne_3344
v0)))
-- Algebra.Bundles.RingWithoutOne._.group
d_group_3476 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_RingWithoutOne_3344 -> T_Group_1520
d_group_3476 :: () -> () -> T_RingWithoutOne_3344 -> T_Group_1520
d_group_3476 ~()
v0 ~()
v1 T_RingWithoutOne_3344
v2 = T_RingWithoutOne_3344 -> T_Group_1520
du_group_3476 T_RingWithoutOne_3344
v2
du_group_3476 :: T_RingWithoutOne_3344 -> T_Group_1520
du_group_3476 :: T_RingWithoutOne_3344 -> T_Group_1520
du_group_3476 T_RingWithoutOne_3344
v0
  = (T_AbelianGroup_1636 -> T_Group_1520) -> AgdaAny -> T_Group_1520
forall a b. a -> b
coe T_AbelianGroup_1636 -> T_Group_1520
du_group_1732 ((T_RingWithoutOne_3344 -> T_AbelianGroup_1636)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_RingWithoutOne_3344 -> T_AbelianGroup_1636
du_'43''45'abelianGroup_3470 (T_RingWithoutOne_3344 -> AgdaAny
forall a b. a -> b
coe T_RingWithoutOne_3344
v0))
-- Algebra.Bundles.RingWithoutOne._.invertibleMagma
d_invertibleMagma_3478 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_RingWithoutOne_3344 -> T_InvertibleMagma_1360
d_invertibleMagma_3478 :: () -> () -> T_RingWithoutOne_3344 -> T_InvertibleMagma_1360
d_invertibleMagma_3478 ~()
v0 ~()
v1 T_RingWithoutOne_3344
v2 = T_RingWithoutOne_3344 -> T_InvertibleMagma_1360
du_invertibleMagma_3478 T_RingWithoutOne_3344
v2
du_invertibleMagma_3478 ::
  T_RingWithoutOne_3344 -> T_InvertibleMagma_1360
du_invertibleMagma_3478 :: T_RingWithoutOne_3344 -> T_InvertibleMagma_1360
du_invertibleMagma_3478 T_RingWithoutOne_3344
v0
  = let v1 :: t
v1 = (T_RingWithoutOne_3344 -> T_AbelianGroup_1636) -> AgdaAny -> t
forall a b. a -> b
coe T_RingWithoutOne_3344 -> T_AbelianGroup_1636
du_'43''45'abelianGroup_3470 (T_RingWithoutOne_3344 -> AgdaAny
forall a b. a -> b
coe T_RingWithoutOne_3344
v0) in
    AgdaAny -> T_InvertibleMagma_1360
forall a b. a -> b
coe ((T_Group_1520 -> T_InvertibleMagma_1360) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Group_1520 -> T_InvertibleMagma_1360
du_invertibleMagma_1628 ((T_AbelianGroup_1636 -> T_Group_1520) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_AbelianGroup_1636 -> T_Group_1520
du_group_1732 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1)))
-- Algebra.Bundles.RingWithoutOne._.invertibleUnitalMagma
d_invertibleUnitalMagma_3480 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_RingWithoutOne_3344 -> T_InvertibleUnitalMagma_1434
d_invertibleUnitalMagma_3480 :: () -> () -> T_RingWithoutOne_3344 -> T_InvertibleUnitalMagma_1434
d_invertibleUnitalMagma_3480 ~()
v0 ~()
v1 T_RingWithoutOne_3344
v2
  = T_RingWithoutOne_3344 -> T_InvertibleUnitalMagma_1434
du_invertibleUnitalMagma_3480 T_RingWithoutOne_3344
v2
du_invertibleUnitalMagma_3480 ::
  T_RingWithoutOne_3344 -> T_InvertibleUnitalMagma_1434
du_invertibleUnitalMagma_3480 :: T_RingWithoutOne_3344 -> T_InvertibleUnitalMagma_1434
du_invertibleUnitalMagma_3480 T_RingWithoutOne_3344
v0
  = let v1 :: t
v1 = (T_RingWithoutOne_3344 -> T_AbelianGroup_1636) -> AgdaAny -> t
forall a b. a -> b
coe T_RingWithoutOne_3344 -> T_AbelianGroup_1636
du_'43''45'abelianGroup_3470 (T_RingWithoutOne_3344 -> AgdaAny
forall a b. a -> b
coe T_RingWithoutOne_3344
v0) in
    AgdaAny -> T_InvertibleUnitalMagma_1434
forall a b. a -> b
coe
      ((T_Group_1520 -> T_InvertibleUnitalMagma_1434)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Group_1520 -> T_InvertibleUnitalMagma_1434
du_invertibleUnitalMagma_1630 ((T_AbelianGroup_1636 -> T_Group_1520) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_AbelianGroup_1636 -> T_Group_1520
du_group_1732 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1)))
-- Algebra.Bundles.RingWithoutOne._.magma
d_magma_3484 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_RingWithoutOne_3344 -> T_Magma_68
d_magma_3484 :: () -> () -> T_RingWithoutOne_3344 -> T_Magma_68
d_magma_3484 ~()
v0 ~()
v1 T_RingWithoutOne_3344
v2 = T_RingWithoutOne_3344 -> T_Magma_68
du_magma_3484 T_RingWithoutOne_3344
v2
du_magma_3484 :: T_RingWithoutOne_3344 -> T_Magma_68
du_magma_3484 :: T_RingWithoutOne_3344 -> T_Magma_68
du_magma_3484 T_RingWithoutOne_3344
v0
  = (T_Semigroup_536 -> T_Magma_68) -> AgdaAny -> T_Magma_68
forall a b. a -> b
coe T_Semigroup_536 -> T_Magma_68
du_magma_584 ((T_RingWithoutOne_3344 -> T_Semigroup_536) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_RingWithoutOne_3344 -> T_Semigroup_536
du_'42''45'semigroup_3472 (T_RingWithoutOne_3344 -> AgdaAny
forall a b. a -> b
coe T_RingWithoutOne_3344
v0))
-- Algebra.Bundles.RingWithoutOne._.rawMagma
d_rawMagma_3486 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_RingWithoutOne_3344 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
d_rawMagma_3486 :: () -> () -> T_RingWithoutOne_3344 -> T_RawMagma_36
d_rawMagma_3486 ~()
v0 ~()
v1 T_RingWithoutOne_3344
v2 = T_RingWithoutOne_3344 -> T_RawMagma_36
du_rawMagma_3486 T_RingWithoutOne_3344
v2
du_rawMagma_3486 ::
  T_RingWithoutOne_3344 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
du_rawMagma_3486 :: T_RingWithoutOne_3344 -> T_RawMagma_36
du_rawMagma_3486 T_RingWithoutOne_3344
v0
  = let v1 :: t
v1 = (T_RingWithoutOne_3344 -> T_Semigroup_536) -> AgdaAny -> t
forall a b. a -> b
coe T_RingWithoutOne_3344 -> T_Semigroup_536
du_'42''45'semigroup_3472 (T_RingWithoutOne_3344 -> AgdaAny
forall a b. a -> b
coe T_RingWithoutOne_3344
v0) in
    AgdaAny -> T_RawMagma_36
forall a b. a -> b
coe ((T_Magma_68 -> T_RawMagma_36) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Magma_68 -> T_RawMagma_36
du_rawMagma_112 ((T_Semigroup_536 -> T_Magma_68) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semigroup_536 -> T_Magma_68
du_magma_584 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1)))
-- Algebra.Bundles.NonAssociativeRing
d_NonAssociativeRing_3492 :: p -> p -> ()
d_NonAssociativeRing_3492 p
a0 p
a1 = ()
data T_NonAssociativeRing_3492
  = C_NonAssociativeRing'46'constructor_62767 (AgdaAny ->
                                               AgdaAny -> AgdaAny)
                                              (AgdaAny -> AgdaAny -> AgdaAny) (AgdaAny -> AgdaAny)
                                              AgdaAny AgdaAny
                                              MAlonzo.Code.Algebra.Structures.T_IsNonAssociativeRing_2408
-- Algebra.Bundles.NonAssociativeRing.Carrier
d_Carrier_3514 :: T_NonAssociativeRing_3492 -> ()
d_Carrier_3514 :: T_NonAssociativeRing_3492 -> ()
d_Carrier_3514 = T_NonAssociativeRing_3492 -> ()
forall a. a
erased
-- Algebra.Bundles.NonAssociativeRing._≈_
d__'8776'__3516 ::
  T_NonAssociativeRing_3492 -> AgdaAny -> AgdaAny -> ()
d__'8776'__3516 :: T_NonAssociativeRing_3492 -> AgdaAny -> AgdaAny -> ()
d__'8776'__3516 = T_NonAssociativeRing_3492 -> AgdaAny -> AgdaAny -> ()
forall a. a
erased
-- Algebra.Bundles.NonAssociativeRing._+_
d__'43'__3518 ::
  T_NonAssociativeRing_3492 -> AgdaAny -> AgdaAny -> AgdaAny
d__'43'__3518 :: T_NonAssociativeRing_3492 -> AgdaAny -> AgdaAny -> AgdaAny
d__'43'__3518 T_NonAssociativeRing_3492
v0
  = case T_NonAssociativeRing_3492 -> T_NonAssociativeRing_3492
forall a b. a -> b
coe T_NonAssociativeRing_3492
v0 of
      C_NonAssociativeRing'46'constructor_62767 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny
v5 AgdaAny
v6 AgdaAny
v7 T_IsNonAssociativeRing_2408
v8
        -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v3
      T_NonAssociativeRing_3492
_ -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.NonAssociativeRing._*_
d__'42'__3520 ::
  T_NonAssociativeRing_3492 -> AgdaAny -> AgdaAny -> AgdaAny
d__'42'__3520 :: T_NonAssociativeRing_3492 -> AgdaAny -> AgdaAny -> AgdaAny
d__'42'__3520 T_NonAssociativeRing_3492
v0
  = case T_NonAssociativeRing_3492 -> T_NonAssociativeRing_3492
forall a b. a -> b
coe T_NonAssociativeRing_3492
v0 of
      C_NonAssociativeRing'46'constructor_62767 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny
v5 AgdaAny
v6 AgdaAny
v7 T_IsNonAssociativeRing_2408
v8
        -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v4
      T_NonAssociativeRing_3492
_ -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.NonAssociativeRing.-_
d_'45'__3522 :: T_NonAssociativeRing_3492 -> AgdaAny -> AgdaAny
d_'45'__3522 :: T_NonAssociativeRing_3492 -> AgdaAny -> AgdaAny
d_'45'__3522 T_NonAssociativeRing_3492
v0
  = case T_NonAssociativeRing_3492 -> T_NonAssociativeRing_3492
forall a b. a -> b
coe T_NonAssociativeRing_3492
v0 of
      C_NonAssociativeRing'46'constructor_62767 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny
v5 AgdaAny
v6 AgdaAny
v7 T_IsNonAssociativeRing_2408
v8
        -> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v5
      T_NonAssociativeRing_3492
_ -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.NonAssociativeRing.0#
d_0'35'_3524 :: T_NonAssociativeRing_3492 -> AgdaAny
d_0'35'_3524 :: T_NonAssociativeRing_3492 -> AgdaAny
d_0'35'_3524 T_NonAssociativeRing_3492
v0
  = case T_NonAssociativeRing_3492 -> T_NonAssociativeRing_3492
forall a b. a -> b
coe T_NonAssociativeRing_3492
v0 of
      C_NonAssociativeRing'46'constructor_62767 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny
v5 AgdaAny
v6 AgdaAny
v7 T_IsNonAssociativeRing_2408
v8
        -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v6
      T_NonAssociativeRing_3492
_ -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.NonAssociativeRing.1#
d_1'35'_3526 :: T_NonAssociativeRing_3492 -> AgdaAny
d_1'35'_3526 :: T_NonAssociativeRing_3492 -> AgdaAny
d_1'35'_3526 T_NonAssociativeRing_3492
v0
  = case T_NonAssociativeRing_3492 -> T_NonAssociativeRing_3492
forall a b. a -> b
coe T_NonAssociativeRing_3492
v0 of
      C_NonAssociativeRing'46'constructor_62767 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny
v5 AgdaAny
v6 AgdaAny
v7 T_IsNonAssociativeRing_2408
v8
        -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v7
      T_NonAssociativeRing_3492
_ -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.NonAssociativeRing.isNonAssociativeRing
d_isNonAssociativeRing_3528 ::
  T_NonAssociativeRing_3492 ->
  MAlonzo.Code.Algebra.Structures.T_IsNonAssociativeRing_2408
d_isNonAssociativeRing_3528 :: T_NonAssociativeRing_3492 -> T_IsNonAssociativeRing_2408
d_isNonAssociativeRing_3528 T_NonAssociativeRing_3492
v0
  = case T_NonAssociativeRing_3492 -> T_NonAssociativeRing_3492
forall a b. a -> b
coe T_NonAssociativeRing_3492
v0 of
      C_NonAssociativeRing'46'constructor_62767 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny
v5 AgdaAny
v6 AgdaAny
v7 T_IsNonAssociativeRing_2408
v8
        -> T_IsNonAssociativeRing_2408 -> T_IsNonAssociativeRing_2408
forall a b. a -> b
coe T_IsNonAssociativeRing_2408
v8
      T_NonAssociativeRing_3492
_ -> T_IsNonAssociativeRing_2408
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.NonAssociativeRing._._//_
d__'47''47'__3532 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_NonAssociativeRing_3492 -> AgdaAny -> AgdaAny -> AgdaAny
d__'47''47'__3532 :: ()
-> () -> T_NonAssociativeRing_3492 -> AgdaAny -> AgdaAny -> AgdaAny
d__'47''47'__3532 ~()
v0 ~()
v1 T_NonAssociativeRing_3492
v2 = T_NonAssociativeRing_3492 -> AgdaAny -> AgdaAny -> AgdaAny
du__'47''47'__3532 T_NonAssociativeRing_3492
v2
du__'47''47'__3532 ::
  T_NonAssociativeRing_3492 -> AgdaAny -> AgdaAny -> AgdaAny
du__'47''47'__3532 :: T_NonAssociativeRing_3492 -> AgdaAny -> AgdaAny -> AgdaAny
du__'47''47'__3532 T_NonAssociativeRing_3492
v0
  = let v1 :: AgdaAny -> AgdaAny -> AgdaAny
v1 = T_NonAssociativeRing_3492 -> AgdaAny -> AgdaAny -> AgdaAny
d__'43'__3518 (T_NonAssociativeRing_3492 -> T_NonAssociativeRing_3492
forall a b. a -> b
coe T_NonAssociativeRing_3492
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: AgdaAny -> AgdaAny
v2 = T_NonAssociativeRing_3492 -> AgdaAny -> AgdaAny
d_'45'__3522 (T_NonAssociativeRing_3492 -> T_NonAssociativeRing_3492
forall a b. a -> b
coe T_NonAssociativeRing_3492
v0) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (((AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du__'47''47'__1098 ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v1)
            ((AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v2)))
-- Algebra.Bundles.NonAssociativeRing._.*-cong
d_'42''45'cong_3534 ::
  T_NonAssociativeRing_3492 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'cong_3534 :: T_NonAssociativeRing_3492
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'42''45'cong_3534 T_NonAssociativeRing_3492
v0
  = (T_IsNonAssociativeRing_2408
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsNonAssociativeRing_2408
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'42''45'cong_2432
      ((T_NonAssociativeRing_3492 -> T_IsNonAssociativeRing_2408)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_NonAssociativeRing_3492 -> T_IsNonAssociativeRing_2408
d_isNonAssociativeRing_3528 (T_NonAssociativeRing_3492 -> AgdaAny
forall a b. a -> b
coe T_NonAssociativeRing_3492
v0))
-- Algebra.Bundles.NonAssociativeRing._.∙-congʳ
d_'8729''45'cong'691'_3536 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_NonAssociativeRing_3492 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_3536 :: ()
-> ()
-> T_NonAssociativeRing_3492
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_3536 ~()
v0 ~()
v1 T_NonAssociativeRing_3492
v2
  = T_NonAssociativeRing_3492
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_3536 T_NonAssociativeRing_3492
v2
du_'8729''45'cong'691'_3536 ::
  T_NonAssociativeRing_3492 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_3536 :: T_NonAssociativeRing_3492
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_3536 T_NonAssociativeRing_3492
v0
  = let v1 :: T_IsNonAssociativeRing_2408
v1 = T_NonAssociativeRing_3492 -> T_IsNonAssociativeRing_2408
d_isNonAssociativeRing_3528 (T_NonAssociativeRing_3492 -> T_NonAssociativeRing_3492
forall a b. a -> b
coe T_NonAssociativeRing_3492
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: t
v2
             = (T_IsNonAssociativeRing_2408 -> T_IsUnitalMagma_642)
-> AgdaAny -> t
forall a b. a -> b
coe
                 T_IsNonAssociativeRing_2408 -> T_IsUnitalMagma_642
MAlonzo.Code.Algebra.Structures.du_'42''45'isUnitalMagma_2520
                 (T_IsNonAssociativeRing_2408 -> AgdaAny
forall a b. a -> b
coe T_IsNonAssociativeRing_2408
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'691'_206
            ((T_IsUnitalMagma_642 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsUnitalMagma_642 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_652 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2))))
-- Algebra.Bundles.NonAssociativeRing._.∙-congˡ
d_'8729''45'cong'737'_3538 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_NonAssociativeRing_3492 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_3538 :: ()
-> ()
-> T_NonAssociativeRing_3492
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_3538 ~()
v0 ~()
v1 T_NonAssociativeRing_3492
v2
  = T_NonAssociativeRing_3492
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_3538 T_NonAssociativeRing_3492
v2
du_'8729''45'cong'737'_3538 ::
  T_NonAssociativeRing_3492 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_3538 :: T_NonAssociativeRing_3492
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_3538 T_NonAssociativeRing_3492
v0
  = let v1 :: T_IsNonAssociativeRing_2408
v1 = T_NonAssociativeRing_3492 -> T_IsNonAssociativeRing_2408
d_isNonAssociativeRing_3528 (T_NonAssociativeRing_3492 -> T_NonAssociativeRing_3492
forall a b. a -> b
coe T_NonAssociativeRing_3492
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: t
v2
             = (T_IsNonAssociativeRing_2408 -> T_IsUnitalMagma_642)
-> AgdaAny -> t
forall a b. a -> b
coe
                 T_IsNonAssociativeRing_2408 -> T_IsUnitalMagma_642
MAlonzo.Code.Algebra.Structures.du_'42''45'isUnitalMagma_2520
                 (T_IsNonAssociativeRing_2408 -> AgdaAny
forall a b. a -> b
coe T_IsNonAssociativeRing_2408
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'737'_202
            ((T_IsUnitalMagma_642 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsUnitalMagma_642 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_652 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2))))
-- Algebra.Bundles.NonAssociativeRing._.*-identity
d_'42''45'identity_3540 ::
  T_NonAssociativeRing_3492 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'42''45'identity_3540 :: T_NonAssociativeRing_3492 -> T_Σ_14
d_'42''45'identity_3540 T_NonAssociativeRing_3492
v0
  = (T_IsNonAssociativeRing_2408 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsNonAssociativeRing_2408 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_'42''45'identity_2434
      ((T_NonAssociativeRing_3492 -> T_IsNonAssociativeRing_2408)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_NonAssociativeRing_3492 -> T_IsNonAssociativeRing_2408
d_isNonAssociativeRing_3528 (T_NonAssociativeRing_3492 -> AgdaAny
forall a b. a -> b
coe T_NonAssociativeRing_3492
v0))
-- Algebra.Bundles.NonAssociativeRing._.*-identityʳ
d_'42''45'identity'691'_3542 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_NonAssociativeRing_3492 -> AgdaAny -> AgdaAny
d_'42''45'identity'691'_3542 :: () -> () -> T_NonAssociativeRing_3492 -> AgdaAny -> AgdaAny
d_'42''45'identity'691'_3542 ~()
v0 ~()
v1 T_NonAssociativeRing_3492
v2
  = T_NonAssociativeRing_3492 -> AgdaAny -> AgdaAny
du_'42''45'identity'691'_3542 T_NonAssociativeRing_3492
v2
du_'42''45'identity'691'_3542 ::
  T_NonAssociativeRing_3492 -> AgdaAny -> AgdaAny
du_'42''45'identity'691'_3542 :: T_NonAssociativeRing_3492 -> AgdaAny -> AgdaAny
du_'42''45'identity'691'_3542 T_NonAssociativeRing_3492
v0
  = (T_IsNonAssociativeRing_2408 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsNonAssociativeRing_2408 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'42''45'identity'691'_2518
      ((T_NonAssociativeRing_3492 -> T_IsNonAssociativeRing_2408)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_NonAssociativeRing_3492 -> T_IsNonAssociativeRing_2408
d_isNonAssociativeRing_3528 (T_NonAssociativeRing_3492 -> AgdaAny
forall a b. a -> b
coe T_NonAssociativeRing_3492
v0))
-- Algebra.Bundles.NonAssociativeRing._.*-identityˡ
d_'42''45'identity'737'_3544 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_NonAssociativeRing_3492 -> AgdaAny -> AgdaAny
d_'42''45'identity'737'_3544 :: () -> () -> T_NonAssociativeRing_3492 -> AgdaAny -> AgdaAny
d_'42''45'identity'737'_3544 ~()
v0 ~()
v1 T_NonAssociativeRing_3492
v2
  = T_NonAssociativeRing_3492 -> AgdaAny -> AgdaAny
du_'42''45'identity'737'_3544 T_NonAssociativeRing_3492
v2
du_'42''45'identity'737'_3544 ::
  T_NonAssociativeRing_3492 -> AgdaAny -> AgdaAny
du_'42''45'identity'737'_3544 :: T_NonAssociativeRing_3492 -> AgdaAny -> AgdaAny
du_'42''45'identity'737'_3544 T_NonAssociativeRing_3492
v0
  = (T_IsNonAssociativeRing_2408 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsNonAssociativeRing_2408 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'42''45'identity'737'_2516
      ((T_NonAssociativeRing_3492 -> T_IsNonAssociativeRing_2408)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_NonAssociativeRing_3492 -> T_IsNonAssociativeRing_2408
d_isNonAssociativeRing_3528 (T_NonAssociativeRing_3492 -> AgdaAny
forall a b. a -> b
coe T_NonAssociativeRing_3492
v0))
-- Algebra.Bundles.NonAssociativeRing._.*-isMagma
d_'42''45'isMagma_3546 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_NonAssociativeRing_3492 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_176
d_'42''45'isMagma_3546 :: () -> () -> T_NonAssociativeRing_3492 -> T_IsMagma_176
d_'42''45'isMagma_3546 ~()
v0 ~()
v1 T_NonAssociativeRing_3492
v2 = T_NonAssociativeRing_3492 -> T_IsMagma_176
du_'42''45'isMagma_3546 T_NonAssociativeRing_3492
v2
du_'42''45'isMagma_3546 ::
  T_NonAssociativeRing_3492 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_176
du_'42''45'isMagma_3546 :: T_NonAssociativeRing_3492 -> T_IsMagma_176
du_'42''45'isMagma_3546 T_NonAssociativeRing_3492
v0
  = (T_IsNonAssociativeRing_2408 -> T_IsMagma_176)
-> AgdaAny -> T_IsMagma_176
forall a b. a -> b
coe
      T_IsNonAssociativeRing_2408 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.du_'42''45'isMagma_2514
      ((T_NonAssociativeRing_3492 -> T_IsNonAssociativeRing_2408)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_NonAssociativeRing_3492 -> T_IsNonAssociativeRing_2408
d_isNonAssociativeRing_3528 (T_NonAssociativeRing_3492 -> AgdaAny
forall a b. a -> b
coe T_NonAssociativeRing_3492
v0))
-- Algebra.Bundles.NonAssociativeRing._.*-isUnitalMagma
d_'42''45'isUnitalMagma_3548 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_NonAssociativeRing_3492 ->
  MAlonzo.Code.Algebra.Structures.T_IsUnitalMagma_642
d_'42''45'isUnitalMagma_3548 :: () -> () -> T_NonAssociativeRing_3492 -> T_IsUnitalMagma_642
d_'42''45'isUnitalMagma_3548 ~()
v0 ~()
v1 T_NonAssociativeRing_3492
v2
  = T_NonAssociativeRing_3492 -> T_IsUnitalMagma_642
du_'42''45'isUnitalMagma_3548 T_NonAssociativeRing_3492
v2
du_'42''45'isUnitalMagma_3548 ::
  T_NonAssociativeRing_3492 ->
  MAlonzo.Code.Algebra.Structures.T_IsUnitalMagma_642
du_'42''45'isUnitalMagma_3548 :: T_NonAssociativeRing_3492 -> T_IsUnitalMagma_642
du_'42''45'isUnitalMagma_3548 T_NonAssociativeRing_3492
v0
  = (T_IsNonAssociativeRing_2408 -> T_IsUnitalMagma_642)
-> AgdaAny -> T_IsUnitalMagma_642
forall a b. a -> b
coe
      T_IsNonAssociativeRing_2408 -> T_IsUnitalMagma_642
MAlonzo.Code.Algebra.Structures.du_'42''45'isUnitalMagma_2520
      ((T_NonAssociativeRing_3492 -> T_IsNonAssociativeRing_2408)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_NonAssociativeRing_3492 -> T_IsNonAssociativeRing_2408
d_isNonAssociativeRing_3528 (T_NonAssociativeRing_3492 -> AgdaAny
forall a b. a -> b
coe T_NonAssociativeRing_3492
v0))
-- Algebra.Bundles.NonAssociativeRing._.assoc
d_assoc_3550 ::
  T_NonAssociativeRing_3492 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_3550 :: T_NonAssociativeRing_3492
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_3550 T_NonAssociativeRing_3492
v0
  = (T_IsSemigroup_472 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsSemigroup_472 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_assoc_482
      ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
         ((T_IsGroup_1036 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsGroup_1036 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_1050
            ((T_IsAbelianGroup_1132 -> T_IsGroup_1036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsAbelianGroup_1132 -> T_IsGroup_1036
MAlonzo.Code.Algebra.Structures.d_isGroup_1144
               ((T_IsNonAssociativeRing_2408 -> T_IsAbelianGroup_1132)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsNonAssociativeRing_2408 -> T_IsAbelianGroup_1132
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2430
                  ((T_NonAssociativeRing_3492 -> T_IsNonAssociativeRing_2408)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_NonAssociativeRing_3492 -> T_IsNonAssociativeRing_2408
d_isNonAssociativeRing_3528 (T_NonAssociativeRing_3492 -> AgdaAny
forall a b. a -> b
coe T_NonAssociativeRing_3492
v0))))))
-- Algebra.Bundles.NonAssociativeRing._.comm
d_comm_3552 ::
  T_NonAssociativeRing_3492 -> AgdaAny -> AgdaAny -> AgdaAny
d_comm_3552 :: T_NonAssociativeRing_3492 -> AgdaAny -> AgdaAny -> AgdaAny
d_comm_3552 T_NonAssociativeRing_3492
v0
  = (T_IsAbelianGroup_1132 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsAbelianGroup_1132 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_comm_1146
      ((T_IsNonAssociativeRing_2408 -> T_IsAbelianGroup_1132)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsNonAssociativeRing_2408 -> T_IsAbelianGroup_1132
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2430
         ((T_NonAssociativeRing_3492 -> T_IsNonAssociativeRing_2408)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_NonAssociativeRing_3492 -> T_IsNonAssociativeRing_2408
d_isNonAssociativeRing_3528 (T_NonAssociativeRing_3492 -> AgdaAny
forall a b. a -> b
coe T_NonAssociativeRing_3492
v0)))
-- Algebra.Bundles.NonAssociativeRing._.∙-cong
d_'8729''45'cong_3554 ::
  T_NonAssociativeRing_3492 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_3554 :: T_NonAssociativeRing_3492
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_3554 T_NonAssociativeRing_3492
v0
  = (T_IsMagma_176
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsMagma_176
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_186
      ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480
         ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
            ((T_IsGroup_1036 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsGroup_1036 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_1050
               ((T_IsAbelianGroup_1132 -> T_IsGroup_1036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsAbelianGroup_1132 -> T_IsGroup_1036
MAlonzo.Code.Algebra.Structures.d_isGroup_1144
                  ((T_IsNonAssociativeRing_2408 -> T_IsAbelianGroup_1132)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsNonAssociativeRing_2408 -> T_IsAbelianGroup_1132
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2430
                     ((T_NonAssociativeRing_3492 -> T_IsNonAssociativeRing_2408)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_NonAssociativeRing_3492 -> T_IsNonAssociativeRing_2408
d_isNonAssociativeRing_3528 (T_NonAssociativeRing_3492 -> AgdaAny
forall a b. a -> b
coe T_NonAssociativeRing_3492
v0)))))))
-- Algebra.Bundles.NonAssociativeRing._.∙-congʳ
d_'8729''45'cong'691'_3556 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_NonAssociativeRing_3492 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_3556 :: ()
-> ()
-> T_NonAssociativeRing_3492
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_3556 ~()
v0 ~()
v1 T_NonAssociativeRing_3492
v2
  = T_NonAssociativeRing_3492
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_3556 T_NonAssociativeRing_3492
v2
du_'8729''45'cong'691'_3556 ::
  T_NonAssociativeRing_3492 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_3556 :: T_NonAssociativeRing_3492
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_3556 T_NonAssociativeRing_3492
v0
  = let v1 :: T_IsNonAssociativeRing_2408
v1 = T_NonAssociativeRing_3492 -> T_IsNonAssociativeRing_2408
d_isNonAssociativeRing_3528 (T_NonAssociativeRing_3492 -> T_NonAssociativeRing_3492
forall a b. a -> b
coe T_NonAssociativeRing_3492
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsAbelianGroup_1132
v2
             = T_IsNonAssociativeRing_2408 -> T_IsAbelianGroup_1132
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2430
                 (T_IsNonAssociativeRing_2408 -> T_IsNonAssociativeRing_2408
forall a b. a -> b
coe T_IsNonAssociativeRing_2408
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsGroup_1036
v3
                = T_IsAbelianGroup_1132 -> T_IsGroup_1036
MAlonzo.Code.Algebra.Structures.d_isGroup_1144 (T_IsAbelianGroup_1132 -> T_IsAbelianGroup_1132
forall a b. a -> b
coe T_IsAbelianGroup_1132
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsMonoid_686
v4
                   = T_IsGroup_1036 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_1050 (T_IsGroup_1036 -> T_IsGroup_1036
forall a b. a -> b
coe T_IsGroup_1036
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsSemigroup_472
v5
                      = T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'691'_206
                     ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v5)))))))
-- Algebra.Bundles.NonAssociativeRing._.∙-congˡ
d_'8729''45'cong'737'_3558 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_NonAssociativeRing_3492 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_3558 :: ()
-> ()
-> T_NonAssociativeRing_3492
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_3558 ~()
v0 ~()
v1 T_NonAssociativeRing_3492
v2
  = T_NonAssociativeRing_3492
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_3558 T_NonAssociativeRing_3492
v2
du_'8729''45'cong'737'_3558 ::
  T_NonAssociativeRing_3492 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_3558 :: T_NonAssociativeRing_3492
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_3558 T_NonAssociativeRing_3492
v0
  = let v1 :: T_IsNonAssociativeRing_2408
v1 = T_NonAssociativeRing_3492 -> T_IsNonAssociativeRing_2408
d_isNonAssociativeRing_3528 (T_NonAssociativeRing_3492 -> T_NonAssociativeRing_3492
forall a b. a -> b
coe T_NonAssociativeRing_3492
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsAbelianGroup_1132
v2
             = T_IsNonAssociativeRing_2408 -> T_IsAbelianGroup_1132
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2430
                 (T_IsNonAssociativeRing_2408 -> T_IsNonAssociativeRing_2408
forall a b. a -> b
coe T_IsNonAssociativeRing_2408
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsGroup_1036
v3
                = T_IsAbelianGroup_1132 -> T_IsGroup_1036
MAlonzo.Code.Algebra.Structures.d_isGroup_1144 (T_IsAbelianGroup_1132 -> T_IsAbelianGroup_1132
forall a b. a -> b
coe T_IsAbelianGroup_1132
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsMonoid_686
v4
                   = T_IsGroup_1036 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_1050 (T_IsGroup_1036 -> T_IsGroup_1036
forall a b. a -> b
coe T_IsGroup_1036
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsSemigroup_472
v5
                      = T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'737'_202
                     ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v5)))))))
-- Algebra.Bundles.NonAssociativeRing._.identity
d_identity_3560 ::
  T_NonAssociativeRing_3492 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_identity_3560 :: T_NonAssociativeRing_3492 -> T_Σ_14
d_identity_3560 T_NonAssociativeRing_3492
v0
  = (T_IsMonoid_686 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsMonoid_686 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_identity_698
      ((T_IsGroup_1036 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsGroup_1036 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_1050
         ((T_IsAbelianGroup_1132 -> T_IsGroup_1036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsAbelianGroup_1132 -> T_IsGroup_1036
MAlonzo.Code.Algebra.Structures.d_isGroup_1144
            ((T_IsNonAssociativeRing_2408 -> T_IsAbelianGroup_1132)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsNonAssociativeRing_2408 -> T_IsAbelianGroup_1132
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2430
               ((T_NonAssociativeRing_3492 -> T_IsNonAssociativeRing_2408)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_NonAssociativeRing_3492 -> T_IsNonAssociativeRing_2408
d_isNonAssociativeRing_3528 (T_NonAssociativeRing_3492 -> AgdaAny
forall a b. a -> b
coe T_NonAssociativeRing_3492
v0)))))
-- Algebra.Bundles.NonAssociativeRing._.identityʳ
d_identity'691'_3562 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_NonAssociativeRing_3492 -> AgdaAny -> AgdaAny
d_identity'691'_3562 :: () -> () -> T_NonAssociativeRing_3492 -> AgdaAny -> AgdaAny
d_identity'691'_3562 ~()
v0 ~()
v1 T_NonAssociativeRing_3492
v2 = T_NonAssociativeRing_3492 -> AgdaAny -> AgdaAny
du_identity'691'_3562 T_NonAssociativeRing_3492
v2
du_identity'691'_3562 ::
  T_NonAssociativeRing_3492 -> AgdaAny -> AgdaAny
du_identity'691'_3562 :: T_NonAssociativeRing_3492 -> AgdaAny -> AgdaAny
du_identity'691'_3562 T_NonAssociativeRing_3492
v0
  = let v1 :: T_IsNonAssociativeRing_2408
v1 = T_NonAssociativeRing_3492 -> T_IsNonAssociativeRing_2408
d_isNonAssociativeRing_3528 (T_NonAssociativeRing_3492 -> T_NonAssociativeRing_3492
forall a b. a -> b
coe T_NonAssociativeRing_3492
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsAbelianGroup_1132
v2
             = T_IsNonAssociativeRing_2408 -> T_IsAbelianGroup_1132
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2430
                 (T_IsNonAssociativeRing_2408 -> T_IsNonAssociativeRing_2408
forall a b. a -> b
coe T_IsNonAssociativeRing_2408
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsGroup_1036
v3
                = T_IsAbelianGroup_1132 -> T_IsGroup_1036
MAlonzo.Code.Algebra.Structures.d_isGroup_1144 (T_IsAbelianGroup_1132 -> T_IsAbelianGroup_1132
forall a b. a -> b
coe T_IsAbelianGroup_1132
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsMonoid_686 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_686 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_identity'691'_728
               ((T_IsGroup_1036 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1036 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_1050 (T_IsGroup_1036 -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1036
v3)))))
-- Algebra.Bundles.NonAssociativeRing._.identityˡ
d_identity'737'_3564 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_NonAssociativeRing_3492 -> AgdaAny -> AgdaAny
d_identity'737'_3564 :: () -> () -> T_NonAssociativeRing_3492 -> AgdaAny -> AgdaAny
d_identity'737'_3564 ~()
v0 ~()
v1 T_NonAssociativeRing_3492
v2 = T_NonAssociativeRing_3492 -> AgdaAny -> AgdaAny
du_identity'737'_3564 T_NonAssociativeRing_3492
v2
du_identity'737'_3564 ::
  T_NonAssociativeRing_3492 -> AgdaAny -> AgdaAny
du_identity'737'_3564 :: T_NonAssociativeRing_3492 -> AgdaAny -> AgdaAny
du_identity'737'_3564 T_NonAssociativeRing_3492
v0
  = let v1 :: T_IsNonAssociativeRing_2408
v1 = T_NonAssociativeRing_3492 -> T_IsNonAssociativeRing_2408
d_isNonAssociativeRing_3528 (T_NonAssociativeRing_3492 -> T_NonAssociativeRing_3492
forall a b. a -> b
coe T_NonAssociativeRing_3492
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsAbelianGroup_1132
v2
             = T_IsNonAssociativeRing_2408 -> T_IsAbelianGroup_1132
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2430
                 (T_IsNonAssociativeRing_2408 -> T_IsNonAssociativeRing_2408
forall a b. a -> b
coe T_IsNonAssociativeRing_2408
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsGroup_1036
v3
                = T_IsAbelianGroup_1132 -> T_IsGroup_1036
MAlonzo.Code.Algebra.Structures.d_isGroup_1144 (T_IsAbelianGroup_1132 -> T_IsAbelianGroup_1132
forall a b. a -> b
coe T_IsAbelianGroup_1132
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsMonoid_686 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_686 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_identity'737'_726
               ((T_IsGroup_1036 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1036 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_1050 (T_IsGroup_1036 -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1036
v3)))))
-- Algebra.Bundles.NonAssociativeRing._.+-isAbelianGroup
d_'43''45'isAbelianGroup_3566 ::
  T_NonAssociativeRing_3492 ->
  MAlonzo.Code.Algebra.Structures.T_IsAbelianGroup_1132
d_'43''45'isAbelianGroup_3566 :: T_NonAssociativeRing_3492 -> T_IsAbelianGroup_1132
d_'43''45'isAbelianGroup_3566 T_NonAssociativeRing_3492
v0
  = (T_IsNonAssociativeRing_2408 -> T_IsAbelianGroup_1132)
-> AgdaAny -> T_IsAbelianGroup_1132
forall a b. a -> b
coe
      T_IsNonAssociativeRing_2408 -> T_IsAbelianGroup_1132
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2430
      ((T_NonAssociativeRing_3492 -> T_IsNonAssociativeRing_2408)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_NonAssociativeRing_3492 -> T_IsNonAssociativeRing_2408
d_isNonAssociativeRing_3528 (T_NonAssociativeRing_3492 -> AgdaAny
forall a b. a -> b
coe T_NonAssociativeRing_3492
v0))
-- Algebra.Bundles.NonAssociativeRing._.isCommutativeMagma
d_isCommutativeMagma_3568 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_NonAssociativeRing_3492 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMagma_212
d_isCommutativeMagma_3568 :: () -> () -> T_NonAssociativeRing_3492 -> T_IsCommutativeMagma_212
d_isCommutativeMagma_3568 ~()
v0 ~()
v1 T_NonAssociativeRing_3492
v2
  = T_NonAssociativeRing_3492 -> T_IsCommutativeMagma_212
du_isCommutativeMagma_3568 T_NonAssociativeRing_3492
v2
du_isCommutativeMagma_3568 ::
  T_NonAssociativeRing_3492 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMagma_212
du_isCommutativeMagma_3568 :: T_NonAssociativeRing_3492 -> T_IsCommutativeMagma_212
du_isCommutativeMagma_3568 T_NonAssociativeRing_3492
v0
  = let v1 :: T_IsNonAssociativeRing_2408
v1 = T_NonAssociativeRing_3492 -> T_IsNonAssociativeRing_2408
d_isNonAssociativeRing_3528 (T_NonAssociativeRing_3492 -> T_NonAssociativeRing_3492
forall a b. a -> b
coe T_NonAssociativeRing_3492
v0) in
    AgdaAny -> T_IsCommutativeMagma_212
forall a b. a -> b
coe
      (let v2 :: T_IsAbelianGroup_1132
v2
             = T_IsNonAssociativeRing_2408 -> T_IsAbelianGroup_1132
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2430
                 (T_IsNonAssociativeRing_2408 -> T_IsNonAssociativeRing_2408
forall a b. a -> b
coe T_IsNonAssociativeRing_2408
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: t
v3
                = (T_IsAbelianGroup_1132 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> t
forall a b. a -> b
coe
                    T_IsAbelianGroup_1132 -> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.du_isCommutativeMonoid_1204
                    (T_IsAbelianGroup_1132 -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsCommutativeSemigroup_548 -> T_IsCommutativeMagma_212)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsCommutativeSemigroup_548 -> T_IsCommutativeMagma_212
MAlonzo.Code.Algebra.Structures.du_isCommutativeMagma_586
               ((T_IsCommutativeMonoid_736 -> T_IsCommutativeSemigroup_548)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsCommutativeMonoid_736 -> T_IsCommutativeSemigroup_548
MAlonzo.Code.Algebra.Structures.du_isCommutativeSemigroup_786
                  (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3)))))
-- Algebra.Bundles.NonAssociativeRing._.isCommutativeMonoid
d_isCommutativeMonoid_3570 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_NonAssociativeRing_3492 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMonoid_736
d_isCommutativeMonoid_3570 :: () -> () -> T_NonAssociativeRing_3492 -> T_IsCommutativeMonoid_736
d_isCommutativeMonoid_3570 ~()
v0 ~()
v1 T_NonAssociativeRing_3492
v2
  = T_NonAssociativeRing_3492 -> T_IsCommutativeMonoid_736
du_isCommutativeMonoid_3570 T_NonAssociativeRing_3492
v2
du_isCommutativeMonoid_3570 ::
  T_NonAssociativeRing_3492 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMonoid_736
du_isCommutativeMonoid_3570 :: T_NonAssociativeRing_3492 -> T_IsCommutativeMonoid_736
du_isCommutativeMonoid_3570 T_NonAssociativeRing_3492
v0
  = let v1 :: T_IsNonAssociativeRing_2408
v1 = T_NonAssociativeRing_3492 -> T_IsNonAssociativeRing_2408
d_isNonAssociativeRing_3528 (T_NonAssociativeRing_3492 -> T_NonAssociativeRing_3492
forall a b. a -> b
coe T_NonAssociativeRing_3492
v0) in
    AgdaAny -> T_IsCommutativeMonoid_736
forall a b. a -> b
coe
      ((T_IsAbelianGroup_1132 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsAbelianGroup_1132 -> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.du_isCommutativeMonoid_1204
         ((T_IsNonAssociativeRing_2408 -> T_IsAbelianGroup_1132)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsNonAssociativeRing_2408 -> T_IsAbelianGroup_1132
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2430
            (T_IsNonAssociativeRing_2408 -> AgdaAny
forall a b. a -> b
coe T_IsNonAssociativeRing_2408
v1)))
-- Algebra.Bundles.NonAssociativeRing._.isCommutativeSemigroup
d_isCommutativeSemigroup_3572 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_NonAssociativeRing_3492 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_548
d_isCommutativeSemigroup_3572 :: ()
-> () -> T_NonAssociativeRing_3492 -> T_IsCommutativeSemigroup_548
d_isCommutativeSemigroup_3572 ~()
v0 ~()
v1 T_NonAssociativeRing_3492
v2
  = T_NonAssociativeRing_3492 -> T_IsCommutativeSemigroup_548
du_isCommutativeSemigroup_3572 T_NonAssociativeRing_3492
v2
du_isCommutativeSemigroup_3572 ::
  T_NonAssociativeRing_3492 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_548
du_isCommutativeSemigroup_3572 :: T_NonAssociativeRing_3492 -> T_IsCommutativeSemigroup_548
du_isCommutativeSemigroup_3572 T_NonAssociativeRing_3492
v0
  = let v1 :: T_IsNonAssociativeRing_2408
v1 = T_NonAssociativeRing_3492 -> T_IsNonAssociativeRing_2408
d_isNonAssociativeRing_3528 (T_NonAssociativeRing_3492 -> T_NonAssociativeRing_3492
forall a b. a -> b
coe T_NonAssociativeRing_3492
v0) in
    AgdaAny -> T_IsCommutativeSemigroup_548
forall a b. a -> b
coe
      (let v2 :: T_IsAbelianGroup_1132
v2
             = T_IsNonAssociativeRing_2408 -> T_IsAbelianGroup_1132
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2430
                 (T_IsNonAssociativeRing_2408 -> T_IsNonAssociativeRing_2408
forall a b. a -> b
coe T_IsNonAssociativeRing_2408
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsCommutativeMonoid_736 -> T_IsCommutativeSemigroup_548)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCommutativeMonoid_736 -> T_IsCommutativeSemigroup_548
MAlonzo.Code.Algebra.Structures.du_isCommutativeSemigroup_786
            ((T_IsAbelianGroup_1132 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsAbelianGroup_1132 -> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.du_isCommutativeMonoid_1204
               (T_IsAbelianGroup_1132 -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132
v2))))
-- Algebra.Bundles.NonAssociativeRing._.isGroup
d_isGroup_3574 ::
  T_NonAssociativeRing_3492 ->
  MAlonzo.Code.Algebra.Structures.T_IsGroup_1036
d_isGroup_3574 :: T_NonAssociativeRing_3492 -> T_IsGroup_1036
d_isGroup_3574 T_NonAssociativeRing_3492
v0
  = (T_IsAbelianGroup_1132 -> T_IsGroup_1036)
-> AgdaAny -> T_IsGroup_1036
forall a b. a -> b
coe
      T_IsAbelianGroup_1132 -> T_IsGroup_1036
MAlonzo.Code.Algebra.Structures.d_isGroup_1144
      ((T_IsNonAssociativeRing_2408 -> T_IsAbelianGroup_1132)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsNonAssociativeRing_2408 -> T_IsAbelianGroup_1132
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2430
         ((T_NonAssociativeRing_3492 -> T_IsNonAssociativeRing_2408)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_NonAssociativeRing_3492 -> T_IsNonAssociativeRing_2408
d_isNonAssociativeRing_3528 (T_NonAssociativeRing_3492 -> AgdaAny
forall a b. a -> b
coe T_NonAssociativeRing_3492
v0)))
-- Algebra.Bundles.NonAssociativeRing._.isInvertibleMagma
d_isInvertibleMagma_3576 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_NonAssociativeRing_3492 ->
  MAlonzo.Code.Algebra.Structures.T_IsInvertibleMagma_924
d_isInvertibleMagma_3576 :: () -> () -> T_NonAssociativeRing_3492 -> T_IsInvertibleMagma_924
d_isInvertibleMagma_3576 ~()
v0 ~()
v1 T_NonAssociativeRing_3492
v2 = T_NonAssociativeRing_3492 -> T_IsInvertibleMagma_924
du_isInvertibleMagma_3576 T_NonAssociativeRing_3492
v2
du_isInvertibleMagma_3576 ::
  T_NonAssociativeRing_3492 ->
  MAlonzo.Code.Algebra.Structures.T_IsInvertibleMagma_924
du_isInvertibleMagma_3576 :: T_NonAssociativeRing_3492 -> T_IsInvertibleMagma_924
du_isInvertibleMagma_3576 T_NonAssociativeRing_3492
v0
  = let v1 :: T_IsNonAssociativeRing_2408
v1 = T_NonAssociativeRing_3492 -> T_IsNonAssociativeRing_2408
d_isNonAssociativeRing_3528 (T_NonAssociativeRing_3492 -> T_NonAssociativeRing_3492
forall a b. a -> b
coe T_NonAssociativeRing_3492
v0) in
    AgdaAny -> T_IsInvertibleMagma_924
forall a b. a -> b
coe
      (let v2 :: T_IsAbelianGroup_1132
v2
             = T_IsNonAssociativeRing_2408 -> T_IsAbelianGroup_1132
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2430
                 (T_IsNonAssociativeRing_2408 -> T_IsNonAssociativeRing_2408
forall a b. a -> b
coe T_IsNonAssociativeRing_2408
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsGroup_1036 -> T_IsInvertibleMagma_924) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsGroup_1036 -> T_IsInvertibleMagma_924
MAlonzo.Code.Algebra.Structures.du_isInvertibleMagma_1122
            ((T_IsAbelianGroup_1132 -> T_IsGroup_1036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132 -> T_IsGroup_1036
MAlonzo.Code.Algebra.Structures.d_isGroup_1144 (T_IsAbelianGroup_1132 -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132
v2))))
-- Algebra.Bundles.NonAssociativeRing._.isInvertibleUnitalMagma
d_isInvertibleUnitalMagma_3578 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_NonAssociativeRing_3492 ->
  MAlonzo.Code.Algebra.Structures.T_IsInvertibleUnitalMagma_976
d_isInvertibleUnitalMagma_3578 :: ()
-> () -> T_NonAssociativeRing_3492 -> T_IsInvertibleUnitalMagma_976
d_isInvertibleUnitalMagma_3578 ~()
v0 ~()
v1 T_NonAssociativeRing_3492
v2
  = T_NonAssociativeRing_3492 -> T_IsInvertibleUnitalMagma_976
du_isInvertibleUnitalMagma_3578 T_NonAssociativeRing_3492
v2
du_isInvertibleUnitalMagma_3578 ::
  T_NonAssociativeRing_3492 ->
  MAlonzo.Code.Algebra.Structures.T_IsInvertibleUnitalMagma_976
du_isInvertibleUnitalMagma_3578 :: T_NonAssociativeRing_3492 -> T_IsInvertibleUnitalMagma_976
du_isInvertibleUnitalMagma_3578 T_NonAssociativeRing_3492
v0
  = let v1 :: T_IsNonAssociativeRing_2408
v1 = T_NonAssociativeRing_3492 -> T_IsNonAssociativeRing_2408
d_isNonAssociativeRing_3528 (T_NonAssociativeRing_3492 -> T_NonAssociativeRing_3492
forall a b. a -> b
coe T_NonAssociativeRing_3492
v0) in
    AgdaAny -> T_IsInvertibleUnitalMagma_976
forall a b. a -> b
coe
      (let v2 :: T_IsAbelianGroup_1132
v2
             = T_IsNonAssociativeRing_2408 -> T_IsAbelianGroup_1132
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2430
                 (T_IsNonAssociativeRing_2408 -> T_IsNonAssociativeRing_2408
forall a b. a -> b
coe T_IsNonAssociativeRing_2408
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsGroup_1036 -> T_IsInvertibleUnitalMagma_976)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsGroup_1036 -> T_IsInvertibleUnitalMagma_976
MAlonzo.Code.Algebra.Structures.du_isInvertibleUnitalMagma_1124
            ((T_IsAbelianGroup_1132 -> T_IsGroup_1036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132 -> T_IsGroup_1036
MAlonzo.Code.Algebra.Structures.d_isGroup_1144 (T_IsAbelianGroup_1132 -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132
v2))))
-- Algebra.Bundles.NonAssociativeRing._.isMagma
d_isMagma_3580 ::
  T_NonAssociativeRing_3492 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_176
d_isMagma_3580 :: T_NonAssociativeRing_3492 -> T_IsMagma_176
d_isMagma_3580 T_NonAssociativeRing_3492
v0
  = (T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> T_IsMagma_176
forall a b. a -> b
coe
      T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480
      ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
         ((T_IsGroup_1036 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsGroup_1036 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_1050
            ((T_IsAbelianGroup_1132 -> T_IsGroup_1036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsAbelianGroup_1132 -> T_IsGroup_1036
MAlonzo.Code.Algebra.Structures.d_isGroup_1144
               ((T_IsNonAssociativeRing_2408 -> T_IsAbelianGroup_1132)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsNonAssociativeRing_2408 -> T_IsAbelianGroup_1132
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2430
                  ((T_NonAssociativeRing_3492 -> T_IsNonAssociativeRing_2408)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_NonAssociativeRing_3492 -> T_IsNonAssociativeRing_2408
d_isNonAssociativeRing_3528 (T_NonAssociativeRing_3492 -> AgdaAny
forall a b. a -> b
coe T_NonAssociativeRing_3492
v0))))))
-- Algebra.Bundles.NonAssociativeRing._.isMonoid
d_isMonoid_3582 ::
  T_NonAssociativeRing_3492 ->
  MAlonzo.Code.Algebra.Structures.T_IsMonoid_686
d_isMonoid_3582 :: T_NonAssociativeRing_3492 -> T_IsMonoid_686
d_isMonoid_3582 T_NonAssociativeRing_3492
v0
  = (T_IsGroup_1036 -> T_IsMonoid_686) -> AgdaAny -> T_IsMonoid_686
forall a b. a -> b
coe
      T_IsGroup_1036 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_1050
      ((T_IsAbelianGroup_1132 -> T_IsGroup_1036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsAbelianGroup_1132 -> T_IsGroup_1036
MAlonzo.Code.Algebra.Structures.d_isGroup_1144
         ((T_IsNonAssociativeRing_2408 -> T_IsAbelianGroup_1132)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsNonAssociativeRing_2408 -> T_IsAbelianGroup_1132
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2430
            ((T_NonAssociativeRing_3492 -> T_IsNonAssociativeRing_2408)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_NonAssociativeRing_3492 -> T_IsNonAssociativeRing_2408
d_isNonAssociativeRing_3528 (T_NonAssociativeRing_3492 -> AgdaAny
forall a b. a -> b
coe T_NonAssociativeRing_3492
v0))))
-- Algebra.Bundles.NonAssociativeRing._.isSemigroup
d_isSemigroup_3584 ::
  T_NonAssociativeRing_3492 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_472
d_isSemigroup_3584 :: T_NonAssociativeRing_3492 -> T_IsSemigroup_472
d_isSemigroup_3584 T_NonAssociativeRing_3492
v0
  = (T_IsMonoid_686 -> T_IsSemigroup_472)
-> AgdaAny -> T_IsSemigroup_472
forall a b. a -> b
coe
      T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
      ((T_IsGroup_1036 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsGroup_1036 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_1050
         ((T_IsAbelianGroup_1132 -> T_IsGroup_1036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsAbelianGroup_1132 -> T_IsGroup_1036
MAlonzo.Code.Algebra.Structures.d_isGroup_1144
            ((T_IsNonAssociativeRing_2408 -> T_IsAbelianGroup_1132)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsNonAssociativeRing_2408 -> T_IsAbelianGroup_1132
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2430
               ((T_NonAssociativeRing_3492 -> T_IsNonAssociativeRing_2408)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_NonAssociativeRing_3492 -> T_IsNonAssociativeRing_2408
d_isNonAssociativeRing_3528 (T_NonAssociativeRing_3492 -> AgdaAny
forall a b. a -> b
coe T_NonAssociativeRing_3492
v0)))))
-- Algebra.Bundles.NonAssociativeRing._.isUnitalMagma
d_isUnitalMagma_3586 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_NonAssociativeRing_3492 ->
  MAlonzo.Code.Algebra.Structures.T_IsUnitalMagma_642
d_isUnitalMagma_3586 :: () -> () -> T_NonAssociativeRing_3492 -> T_IsUnitalMagma_642
d_isUnitalMagma_3586 ~()
v0 ~()
v1 T_NonAssociativeRing_3492
v2 = T_NonAssociativeRing_3492 -> T_IsUnitalMagma_642
du_isUnitalMagma_3586 T_NonAssociativeRing_3492
v2
du_isUnitalMagma_3586 ::
  T_NonAssociativeRing_3492 ->
  MAlonzo.Code.Algebra.Structures.T_IsUnitalMagma_642
du_isUnitalMagma_3586 :: T_NonAssociativeRing_3492 -> T_IsUnitalMagma_642
du_isUnitalMagma_3586 T_NonAssociativeRing_3492
v0
  = let v1 :: T_IsNonAssociativeRing_2408
v1 = T_NonAssociativeRing_3492 -> T_IsNonAssociativeRing_2408
d_isNonAssociativeRing_3528 (T_NonAssociativeRing_3492 -> T_NonAssociativeRing_3492
forall a b. a -> b
coe T_NonAssociativeRing_3492
v0) in
    AgdaAny -> T_IsUnitalMagma_642
forall a b. a -> b
coe
      (let v2 :: T_IsAbelianGroup_1132
v2
             = T_IsNonAssociativeRing_2408 -> T_IsAbelianGroup_1132
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2430
                 (T_IsNonAssociativeRing_2408 -> T_IsNonAssociativeRing_2408
forall a b. a -> b
coe T_IsNonAssociativeRing_2408
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsGroup_1036
v3
                = T_IsAbelianGroup_1132 -> T_IsGroup_1036
MAlonzo.Code.Algebra.Structures.d_isGroup_1144 (T_IsAbelianGroup_1132 -> T_IsAbelianGroup_1132
forall a b. a -> b
coe T_IsAbelianGroup_1132
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsMonoid_686 -> T_IsUnitalMagma_642) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_686 -> T_IsUnitalMagma_642
MAlonzo.Code.Algebra.Structures.du_isUnitalMagma_730
               ((T_IsGroup_1036 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1036 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_1050 (T_IsGroup_1036 -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1036
v3)))))
-- Algebra.Bundles.NonAssociativeRing._.⁻¹-cong
d_'8315''185''45'cong_3588 ::
  T_NonAssociativeRing_3492 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8315''185''45'cong_3588 :: T_NonAssociativeRing_3492
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8315''185''45'cong_3588 T_NonAssociativeRing_3492
v0
  = (T_IsGroup_1036 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsGroup_1036 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8315''185''45'cong_1054
      ((T_IsAbelianGroup_1132 -> T_IsGroup_1036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsAbelianGroup_1132 -> T_IsGroup_1036
MAlonzo.Code.Algebra.Structures.d_isGroup_1144
         ((T_IsNonAssociativeRing_2408 -> T_IsAbelianGroup_1132)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsNonAssociativeRing_2408 -> T_IsAbelianGroup_1132
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2430
            ((T_NonAssociativeRing_3492 -> T_IsNonAssociativeRing_2408)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_NonAssociativeRing_3492 -> T_IsNonAssociativeRing_2408
d_isNonAssociativeRing_3528 (T_NonAssociativeRing_3492 -> AgdaAny
forall a b. a -> b
coe T_NonAssociativeRing_3492
v0))))
-- Algebra.Bundles.NonAssociativeRing._.inverse
d_inverse_3590 ::
  T_NonAssociativeRing_3492 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_inverse_3590 :: T_NonAssociativeRing_3492 -> T_Σ_14
d_inverse_3590 T_NonAssociativeRing_3492
v0
  = (T_IsGroup_1036 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsGroup_1036 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_inverse_1052
      ((T_IsAbelianGroup_1132 -> T_IsGroup_1036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsAbelianGroup_1132 -> T_IsGroup_1036
MAlonzo.Code.Algebra.Structures.d_isGroup_1144
         ((T_IsNonAssociativeRing_2408 -> T_IsAbelianGroup_1132)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsNonAssociativeRing_2408 -> T_IsAbelianGroup_1132
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2430
            ((T_NonAssociativeRing_3492 -> T_IsNonAssociativeRing_2408)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_NonAssociativeRing_3492 -> T_IsNonAssociativeRing_2408
d_isNonAssociativeRing_3528 (T_NonAssociativeRing_3492 -> AgdaAny
forall a b. a -> b
coe T_NonAssociativeRing_3492
v0))))
-- Algebra.Bundles.NonAssociativeRing._.inverseʳ
d_inverse'691'_3592 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_NonAssociativeRing_3492 -> AgdaAny -> AgdaAny
d_inverse'691'_3592 :: () -> () -> T_NonAssociativeRing_3492 -> AgdaAny -> AgdaAny
d_inverse'691'_3592 ~()
v0 ~()
v1 T_NonAssociativeRing_3492
v2 = T_NonAssociativeRing_3492 -> AgdaAny -> AgdaAny
du_inverse'691'_3592 T_NonAssociativeRing_3492
v2
du_inverse'691'_3592 ::
  T_NonAssociativeRing_3492 -> AgdaAny -> AgdaAny
du_inverse'691'_3592 :: T_NonAssociativeRing_3492 -> AgdaAny -> AgdaAny
du_inverse'691'_3592 T_NonAssociativeRing_3492
v0
  = let v1 :: T_IsNonAssociativeRing_2408
v1 = T_NonAssociativeRing_3492 -> T_IsNonAssociativeRing_2408
d_isNonAssociativeRing_3528 (T_NonAssociativeRing_3492 -> T_NonAssociativeRing_3492
forall a b. a -> b
coe T_NonAssociativeRing_3492
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsAbelianGroup_1132
v2
             = T_IsNonAssociativeRing_2408 -> T_IsAbelianGroup_1132
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2430
                 (T_IsNonAssociativeRing_2408 -> T_IsNonAssociativeRing_2408
forall a b. a -> b
coe T_IsNonAssociativeRing_2408
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsGroup_1036 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsGroup_1036 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_inverse'691'_1108
            ((T_IsAbelianGroup_1132 -> T_IsGroup_1036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132 -> T_IsGroup_1036
MAlonzo.Code.Algebra.Structures.d_isGroup_1144 (T_IsAbelianGroup_1132 -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132
v2))))
-- Algebra.Bundles.NonAssociativeRing._.inverseˡ
d_inverse'737'_3594 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_NonAssociativeRing_3492 -> AgdaAny -> AgdaAny
d_inverse'737'_3594 :: () -> () -> T_NonAssociativeRing_3492 -> AgdaAny -> AgdaAny
d_inverse'737'_3594 ~()
v0 ~()
v1 T_NonAssociativeRing_3492
v2 = T_NonAssociativeRing_3492 -> AgdaAny -> AgdaAny
du_inverse'737'_3594 T_NonAssociativeRing_3492
v2
du_inverse'737'_3594 ::
  T_NonAssociativeRing_3492 -> AgdaAny -> AgdaAny
du_inverse'737'_3594 :: T_NonAssociativeRing_3492 -> AgdaAny -> AgdaAny
du_inverse'737'_3594 T_NonAssociativeRing_3492
v0
  = let v1 :: T_IsNonAssociativeRing_2408
v1 = T_NonAssociativeRing_3492 -> T_IsNonAssociativeRing_2408
d_isNonAssociativeRing_3528 (T_NonAssociativeRing_3492 -> T_NonAssociativeRing_3492
forall a b. a -> b
coe T_NonAssociativeRing_3492
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsAbelianGroup_1132
v2
             = T_IsNonAssociativeRing_2408 -> T_IsAbelianGroup_1132
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2430
                 (T_IsNonAssociativeRing_2408 -> T_IsNonAssociativeRing_2408
forall a b. a -> b
coe T_IsNonAssociativeRing_2408
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsGroup_1036 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsGroup_1036 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_inverse'737'_1106
            ((T_IsAbelianGroup_1132 -> T_IsGroup_1036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132 -> T_IsGroup_1036
MAlonzo.Code.Algebra.Structures.d_isGroup_1144 (T_IsAbelianGroup_1132 -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132
v2))))
-- Algebra.Bundles.NonAssociativeRing._.distrib
d_distrib_3596 ::
  T_NonAssociativeRing_3492 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_distrib_3596 :: T_NonAssociativeRing_3492 -> T_Σ_14
d_distrib_3596 T_NonAssociativeRing_3492
v0
  = (T_IsNonAssociativeRing_2408 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsNonAssociativeRing_2408 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_distrib_2436
      ((T_NonAssociativeRing_3492 -> T_IsNonAssociativeRing_2408)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_NonAssociativeRing_3492 -> T_IsNonAssociativeRing_2408
d_isNonAssociativeRing_3528 (T_NonAssociativeRing_3492 -> AgdaAny
forall a b. a -> b
coe T_NonAssociativeRing_3492
v0))
-- Algebra.Bundles.NonAssociativeRing._.distribʳ
d_distrib'691'_3598 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_NonAssociativeRing_3492 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_distrib'691'_3598 :: ()
-> ()
-> T_NonAssociativeRing_3492
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_distrib'691'_3598 ~()
v0 ~()
v1 T_NonAssociativeRing_3492
v2 = T_NonAssociativeRing_3492
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'691'_3598 T_NonAssociativeRing_3492
v2
du_distrib'691'_3598 ::
  T_NonAssociativeRing_3492 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'691'_3598 :: T_NonAssociativeRing_3492
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'691'_3598 T_NonAssociativeRing_3492
v0
  = (T_IsNonAssociativeRing_2408
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsNonAssociativeRing_2408
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_distrib'691'_2512
      ((T_NonAssociativeRing_3492 -> T_IsNonAssociativeRing_2408)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_NonAssociativeRing_3492 -> T_IsNonAssociativeRing_2408
d_isNonAssociativeRing_3528 (T_NonAssociativeRing_3492 -> AgdaAny
forall a b. a -> b
coe T_NonAssociativeRing_3492
v0))
-- Algebra.Bundles.NonAssociativeRing._.distribˡ
d_distrib'737'_3600 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_NonAssociativeRing_3492 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_distrib'737'_3600 :: ()
-> ()
-> T_NonAssociativeRing_3492
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_distrib'737'_3600 ~()
v0 ~()
v1 T_NonAssociativeRing_3492
v2 = T_NonAssociativeRing_3492
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'737'_3600 T_NonAssociativeRing_3492
v2
du_distrib'737'_3600 ::
  T_NonAssociativeRing_3492 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'737'_3600 :: T_NonAssociativeRing_3492
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'737'_3600 T_NonAssociativeRing_3492
v0
  = (T_IsNonAssociativeRing_2408
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsNonAssociativeRing_2408
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_distrib'737'_2510
      ((T_NonAssociativeRing_3492 -> T_IsNonAssociativeRing_2408)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_NonAssociativeRing_3492 -> T_IsNonAssociativeRing_2408
d_isNonAssociativeRing_3528 (T_NonAssociativeRing_3492 -> AgdaAny
forall a b. a -> b
coe T_NonAssociativeRing_3492
v0))
-- Algebra.Bundles.NonAssociativeRing._.isEquivalence
d_isEquivalence_3602 ::
  T_NonAssociativeRing_3492 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_3602 :: T_NonAssociativeRing_3492 -> T_IsEquivalence_26
d_isEquivalence_3602 T_NonAssociativeRing_3492
v0
  = (T_IsMagma_176 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
      ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480
         ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
            ((T_IsGroup_1036 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsGroup_1036 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_1050
               ((T_IsAbelianGroup_1132 -> T_IsGroup_1036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsAbelianGroup_1132 -> T_IsGroup_1036
MAlonzo.Code.Algebra.Structures.d_isGroup_1144
                  ((T_IsNonAssociativeRing_2408 -> T_IsAbelianGroup_1132)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsNonAssociativeRing_2408 -> T_IsAbelianGroup_1132
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2430
                     ((T_NonAssociativeRing_3492 -> T_IsNonAssociativeRing_2408)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_NonAssociativeRing_3492 -> T_IsNonAssociativeRing_2408
d_isNonAssociativeRing_3528 (T_NonAssociativeRing_3492 -> AgdaAny
forall a b. a -> b
coe T_NonAssociativeRing_3492
v0)))))))
-- Algebra.Bundles.NonAssociativeRing._.isPartialEquivalence
d_isPartialEquivalence_3604 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_NonAssociativeRing_3492 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_3604 :: () -> () -> T_NonAssociativeRing_3492 -> T_IsPartialEquivalence_16
d_isPartialEquivalence_3604 ~()
v0 ~()
v1 T_NonAssociativeRing_3492
v2
  = T_NonAssociativeRing_3492 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_3604 T_NonAssociativeRing_3492
v2
du_isPartialEquivalence_3604 ::
  T_NonAssociativeRing_3492 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_3604 :: T_NonAssociativeRing_3492 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_3604 T_NonAssociativeRing_3492
v0
  = let v1 :: T_IsNonAssociativeRing_2408
v1 = T_NonAssociativeRing_3492 -> T_IsNonAssociativeRing_2408
d_isNonAssociativeRing_3528 (T_NonAssociativeRing_3492 -> T_NonAssociativeRing_3492
forall a b. a -> b
coe T_NonAssociativeRing_3492
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsAbelianGroup_1132
v2
             = T_IsNonAssociativeRing_2408 -> T_IsAbelianGroup_1132
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2430
                 (T_IsNonAssociativeRing_2408 -> T_IsNonAssociativeRing_2408
forall a b. a -> b
coe T_IsNonAssociativeRing_2408
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsGroup_1036
v3
                = T_IsAbelianGroup_1132 -> T_IsGroup_1036
MAlonzo.Code.Algebra.Structures.d_isGroup_1144 (T_IsAbelianGroup_1132 -> T_IsAbelianGroup_1132
forall a b. a -> b
coe T_IsAbelianGroup_1132
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsMonoid_686
v4
                   = T_IsGroup_1036 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_1050 (T_IsGroup_1036 -> T_IsGroup_1036
forall a b. a -> b
coe T_IsGroup_1036
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsSemigroup_472
v5
                      = T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (let v6 :: T_IsMagma_176
v6 = T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (T_IsSemigroup_472 -> T_IsSemigroup_472
forall a b. a -> b
coe T_IsSemigroup_472
v5) in
                   AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     ((T_IsEquivalence_26 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsEquivalence_26 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
                        ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v6))))))))
-- Algebra.Bundles.NonAssociativeRing._.refl
d_refl_3606 :: T_NonAssociativeRing_3492 -> AgdaAny -> AgdaAny
d_refl_3606 :: T_NonAssociativeRing_3492 -> AgdaAny -> AgdaAny
d_refl_3606 T_NonAssociativeRing_3492
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_34
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
         ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480
            ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
               ((T_IsGroup_1036 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsGroup_1036 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_1050
                  ((T_IsAbelianGroup_1132 -> T_IsGroup_1036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsAbelianGroup_1132 -> T_IsGroup_1036
MAlonzo.Code.Algebra.Structures.d_isGroup_1144
                     ((T_IsNonAssociativeRing_2408 -> T_IsAbelianGroup_1132)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsNonAssociativeRing_2408 -> T_IsAbelianGroup_1132
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2430
                        ((T_NonAssociativeRing_3492 -> T_IsNonAssociativeRing_2408)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_NonAssociativeRing_3492 -> T_IsNonAssociativeRing_2408
d_isNonAssociativeRing_3528 (T_NonAssociativeRing_3492 -> AgdaAny
forall a b. a -> b
coe T_NonAssociativeRing_3492
v0))))))))
-- Algebra.Bundles.NonAssociativeRing._.reflexive
d_reflexive_3608 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_NonAssociativeRing_3492 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_3608 :: ()
-> ()
-> T_NonAssociativeRing_3492
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_3608 ~()
v0 ~()
v1 T_NonAssociativeRing_3492
v2 = T_NonAssociativeRing_3492
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_3608 T_NonAssociativeRing_3492
v2
du_reflexive_3608 ::
  T_NonAssociativeRing_3492 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_3608 :: T_NonAssociativeRing_3492
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_3608 T_NonAssociativeRing_3492
v0
  = let v1 :: T_IsNonAssociativeRing_2408
v1 = T_NonAssociativeRing_3492 -> T_IsNonAssociativeRing_2408
d_isNonAssociativeRing_3528 (T_NonAssociativeRing_3492 -> T_NonAssociativeRing_3492
forall a b. a -> b
coe T_NonAssociativeRing_3492
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsAbelianGroup_1132
v2
             = T_IsNonAssociativeRing_2408 -> T_IsAbelianGroup_1132
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2430
                 (T_IsNonAssociativeRing_2408 -> T_IsNonAssociativeRing_2408
forall a b. a -> b
coe T_IsNonAssociativeRing_2408
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsGroup_1036
v3
                = T_IsAbelianGroup_1132 -> T_IsGroup_1036
MAlonzo.Code.Algebra.Structures.d_isGroup_1144 (T_IsAbelianGroup_1132 -> T_IsAbelianGroup_1132
forall a b. a -> b
coe T_IsAbelianGroup_1132
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsMonoid_686
v4
                   = T_IsGroup_1036 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_1050 (T_IsGroup_1036 -> T_IsGroup_1036
forall a b. a -> b
coe T_IsGroup_1036
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsSemigroup_472
v5
                      = T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (let v6 :: T_IsMagma_176
v6 = T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (T_IsSemigroup_472 -> T_IsSemigroup_472
forall a b. a -> b
coe T_IsSemigroup_472
v5) in
                   (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
                     (\ AgdaAny
v7 AgdaAny
v8 AgdaAny
v9 ->
                        (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                          T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
                          ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v6))
                          AgdaAny
v7))))))
-- Algebra.Bundles.NonAssociativeRing._.setoid
d_setoid_3610 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_NonAssociativeRing_3492 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_3610 :: () -> () -> T_NonAssociativeRing_3492 -> T_Setoid_44
d_setoid_3610 ~()
v0 ~()
v1 T_NonAssociativeRing_3492
v2 = T_NonAssociativeRing_3492 -> T_Setoid_44
du_setoid_3610 T_NonAssociativeRing_3492
v2
du_setoid_3610 ::
  T_NonAssociativeRing_3492 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_3610 :: T_NonAssociativeRing_3492 -> T_Setoid_44
du_setoid_3610 T_NonAssociativeRing_3492
v0
  = let v1 :: T_IsNonAssociativeRing_2408
v1 = T_NonAssociativeRing_3492 -> T_IsNonAssociativeRing_2408
d_isNonAssociativeRing_3528 (T_NonAssociativeRing_3492 -> T_NonAssociativeRing_3492
forall a b. a -> b
coe T_NonAssociativeRing_3492
v0) in
    AgdaAny -> T_Setoid_44
forall a b. a -> b
coe
      (let v2 :: T_IsAbelianGroup_1132
v2
             = T_IsNonAssociativeRing_2408 -> T_IsAbelianGroup_1132
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2430
                 (T_IsNonAssociativeRing_2408 -> T_IsNonAssociativeRing_2408
forall a b. a -> b
coe T_IsNonAssociativeRing_2408
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsGroup_1036
v3
                = T_IsAbelianGroup_1132 -> T_IsGroup_1036
MAlonzo.Code.Algebra.Structures.d_isGroup_1144 (T_IsAbelianGroup_1132 -> T_IsAbelianGroup_1132
forall a b. a -> b
coe T_IsAbelianGroup_1132
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsMonoid_686
v4
                   = T_IsGroup_1036 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_1050 (T_IsGroup_1036 -> T_IsGroup_1036
forall a b. a -> b
coe T_IsGroup_1036
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsSemigroup_472
v5
                      = T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  ((T_IsMagma_176 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsMagma_176 -> T_Setoid_44
MAlonzo.Code.Algebra.Structures.du_setoid_200
                     ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v5)))))))
-- Algebra.Bundles.NonAssociativeRing._.sym
d_sym_3612 ::
  T_NonAssociativeRing_3492 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_3612 :: T_NonAssociativeRing_3492
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_3612 T_NonAssociativeRing_3492
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_36
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
         ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480
            ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
               ((T_IsGroup_1036 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsGroup_1036 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_1050
                  ((T_IsAbelianGroup_1132 -> T_IsGroup_1036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsAbelianGroup_1132 -> T_IsGroup_1036
MAlonzo.Code.Algebra.Structures.d_isGroup_1144
                     ((T_IsNonAssociativeRing_2408 -> T_IsAbelianGroup_1132)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsNonAssociativeRing_2408 -> T_IsAbelianGroup_1132
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2430
                        ((T_NonAssociativeRing_3492 -> T_IsNonAssociativeRing_2408)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_NonAssociativeRing_3492 -> T_IsNonAssociativeRing_2408
d_isNonAssociativeRing_3528 (T_NonAssociativeRing_3492 -> AgdaAny
forall a b. a -> b
coe T_NonAssociativeRing_3492
v0))))))))
-- Algebra.Bundles.NonAssociativeRing._.trans
d_trans_3614 ::
  T_NonAssociativeRing_3492 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_3614 :: T_NonAssociativeRing_3492
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_3614 T_NonAssociativeRing_3492
v0
  = (T_IsEquivalence_26
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_38
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
         ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480
            ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
               ((T_IsGroup_1036 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsGroup_1036 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_1050
                  ((T_IsAbelianGroup_1132 -> T_IsGroup_1036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsAbelianGroup_1132 -> T_IsGroup_1036
MAlonzo.Code.Algebra.Structures.d_isGroup_1144
                     ((T_IsNonAssociativeRing_2408 -> T_IsAbelianGroup_1132)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsNonAssociativeRing_2408 -> T_IsAbelianGroup_1132
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2430
                        ((T_NonAssociativeRing_3492 -> T_IsNonAssociativeRing_2408)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_NonAssociativeRing_3492 -> T_IsNonAssociativeRing_2408
d_isNonAssociativeRing_3528 (T_NonAssociativeRing_3492 -> AgdaAny
forall a b. a -> b
coe T_NonAssociativeRing_3492
v0))))))))
-- Algebra.Bundles.NonAssociativeRing._.uniqueʳ-⁻¹
d_unique'691''45''8315''185'_3616 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_NonAssociativeRing_3492 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_unique'691''45''8315''185'_3616 :: ()
-> ()
-> T_NonAssociativeRing_3492
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_unique'691''45''8315''185'_3616 ~()
v0 ~()
v1 T_NonAssociativeRing_3492
v2
  = T_NonAssociativeRing_3492
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_unique'691''45''8315''185'_3616 T_NonAssociativeRing_3492
v2
du_unique'691''45''8315''185'_3616 ::
  T_NonAssociativeRing_3492 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_unique'691''45''8315''185'_3616 :: T_NonAssociativeRing_3492
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_unique'691''45''8315''185'_3616 T_NonAssociativeRing_3492
v0
  = let v1 :: AgdaAny -> AgdaAny -> AgdaAny
v1 = T_NonAssociativeRing_3492 -> AgdaAny -> AgdaAny -> AgdaAny
d__'43'__3518 (T_NonAssociativeRing_3492 -> T_NonAssociativeRing_3492
forall a b. a -> b
coe T_NonAssociativeRing_3492
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: AgdaAny -> AgdaAny
v2 = T_NonAssociativeRing_3492 -> AgdaAny -> AgdaAny
d_'45'__3522 (T_NonAssociativeRing_3492 -> T_NonAssociativeRing_3492
forall a b. a -> b
coe T_NonAssociativeRing_3492
v0) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: AgdaAny
v3 = T_NonAssociativeRing_3492 -> AgdaAny
d_0'35'_3524 (T_NonAssociativeRing_3492 -> T_NonAssociativeRing_3492
forall a b. a -> b
coe T_NonAssociativeRing_3492
v0) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsNonAssociativeRing_2408
v4 = T_NonAssociativeRing_3492 -> T_IsNonAssociativeRing_2408
d_isNonAssociativeRing_3528 (T_NonAssociativeRing_3492 -> T_NonAssociativeRing_3492
forall a b. a -> b
coe T_NonAssociativeRing_3492
v0) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsAbelianGroup_1132
v5
                      = T_IsNonAssociativeRing_2408 -> T_IsAbelianGroup_1132
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2430
                          (T_IsNonAssociativeRing_2408 -> T_IsNonAssociativeRing_2408
forall a b. a -> b
coe T_IsNonAssociativeRing_2408
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (((AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> (AgdaAny -> AgdaAny)
 -> T_IsGroup_1036
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsGroup_1036
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.du_unique'691''45''8315''185'_1120
                     ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v1) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3) ((AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v2)
                     ((T_IsAbelianGroup_1132 -> T_IsGroup_1036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132 -> T_IsGroup_1036
MAlonzo.Code.Algebra.Structures.d_isGroup_1144 (T_IsAbelianGroup_1132 -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132
v5)))))))
-- Algebra.Bundles.NonAssociativeRing._.uniqueˡ-⁻¹
d_unique'737''45''8315''185'_3618 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_NonAssociativeRing_3492 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_unique'737''45''8315''185'_3618 :: ()
-> ()
-> T_NonAssociativeRing_3492
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_unique'737''45''8315''185'_3618 ~()
v0 ~()
v1 T_NonAssociativeRing_3492
v2
  = T_NonAssociativeRing_3492
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_unique'737''45''8315''185'_3618 T_NonAssociativeRing_3492
v2
du_unique'737''45''8315''185'_3618 ::
  T_NonAssociativeRing_3492 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_unique'737''45''8315''185'_3618 :: T_NonAssociativeRing_3492
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_unique'737''45''8315''185'_3618 T_NonAssociativeRing_3492
v0
  = let v1 :: AgdaAny -> AgdaAny -> AgdaAny
v1 = T_NonAssociativeRing_3492 -> AgdaAny -> AgdaAny -> AgdaAny
d__'43'__3518 (T_NonAssociativeRing_3492 -> T_NonAssociativeRing_3492
forall a b. a -> b
coe T_NonAssociativeRing_3492
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: AgdaAny -> AgdaAny
v2 = T_NonAssociativeRing_3492 -> AgdaAny -> AgdaAny
d_'45'__3522 (T_NonAssociativeRing_3492 -> T_NonAssociativeRing_3492
forall a b. a -> b
coe T_NonAssociativeRing_3492
v0) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: AgdaAny
v3 = T_NonAssociativeRing_3492 -> AgdaAny
d_0'35'_3524 (T_NonAssociativeRing_3492 -> T_NonAssociativeRing_3492
forall a b. a -> b
coe T_NonAssociativeRing_3492
v0) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsNonAssociativeRing_2408
v4 = T_NonAssociativeRing_3492 -> T_IsNonAssociativeRing_2408
d_isNonAssociativeRing_3528 (T_NonAssociativeRing_3492 -> T_NonAssociativeRing_3492
forall a b. a -> b
coe T_NonAssociativeRing_3492
v0) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsAbelianGroup_1132
v5
                      = T_IsNonAssociativeRing_2408 -> T_IsAbelianGroup_1132
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2430
                          (T_IsNonAssociativeRing_2408 -> T_IsNonAssociativeRing_2408
forall a b. a -> b
coe T_IsNonAssociativeRing_2408
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (((AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> (AgdaAny -> AgdaAny)
 -> T_IsGroup_1036
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsGroup_1036
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.du_unique'737''45''8315''185'_1114
                     ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v1) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3) ((AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v2)
                     ((T_IsAbelianGroup_1132 -> T_IsGroup_1036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132 -> T_IsGroup_1036
MAlonzo.Code.Algebra.Structures.d_isGroup_1144 (T_IsAbelianGroup_1132 -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132
v5)))))))
-- Algebra.Bundles.NonAssociativeRing._.zero
d_zero_3620 ::
  T_NonAssociativeRing_3492 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_zero_3620 :: T_NonAssociativeRing_3492 -> T_Σ_14
d_zero_3620 T_NonAssociativeRing_3492
v0
  = (T_IsNonAssociativeRing_2408 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsNonAssociativeRing_2408 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_zero_2438
      ((T_NonAssociativeRing_3492 -> T_IsNonAssociativeRing_2408)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_NonAssociativeRing_3492 -> T_IsNonAssociativeRing_2408
d_isNonAssociativeRing_3528 (T_NonAssociativeRing_3492 -> AgdaAny
forall a b. a -> b
coe T_NonAssociativeRing_3492
v0))
-- Algebra.Bundles.NonAssociativeRing._.zeroʳ
d_zero'691'_3622 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_NonAssociativeRing_3492 -> AgdaAny -> AgdaAny
d_zero'691'_3622 :: () -> () -> T_NonAssociativeRing_3492 -> AgdaAny -> AgdaAny
d_zero'691'_3622 ~()
v0 ~()
v1 T_NonAssociativeRing_3492
v2 = T_NonAssociativeRing_3492 -> AgdaAny -> AgdaAny
du_zero'691'_3622 T_NonAssociativeRing_3492
v2
du_zero'691'_3622 ::
  T_NonAssociativeRing_3492 -> AgdaAny -> AgdaAny
du_zero'691'_3622 :: T_NonAssociativeRing_3492 -> AgdaAny -> AgdaAny
du_zero'691'_3622 T_NonAssociativeRing_3492
v0
  = (T_IsNonAssociativeRing_2408 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsNonAssociativeRing_2408 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_zero'691'_2508
      ((T_NonAssociativeRing_3492 -> T_IsNonAssociativeRing_2408)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_NonAssociativeRing_3492 -> T_IsNonAssociativeRing_2408
d_isNonAssociativeRing_3528 (T_NonAssociativeRing_3492 -> AgdaAny
forall a b. a -> b
coe T_NonAssociativeRing_3492
v0))
-- Algebra.Bundles.NonAssociativeRing._.zeroˡ
d_zero'737'_3624 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_NonAssociativeRing_3492 -> AgdaAny -> AgdaAny
d_zero'737'_3624 :: () -> () -> T_NonAssociativeRing_3492 -> AgdaAny -> AgdaAny
d_zero'737'_3624 ~()
v0 ~()
v1 T_NonAssociativeRing_3492
v2 = T_NonAssociativeRing_3492 -> AgdaAny -> AgdaAny
du_zero'737'_3624 T_NonAssociativeRing_3492
v2
du_zero'737'_3624 ::
  T_NonAssociativeRing_3492 -> AgdaAny -> AgdaAny
du_zero'737'_3624 :: T_NonAssociativeRing_3492 -> AgdaAny -> AgdaAny
du_zero'737'_3624 T_NonAssociativeRing_3492
v0
  = (T_IsNonAssociativeRing_2408 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsNonAssociativeRing_2408 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_zero'737'_2506
      ((T_NonAssociativeRing_3492 -> T_IsNonAssociativeRing_2408)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_NonAssociativeRing_3492 -> T_IsNonAssociativeRing_2408
d_isNonAssociativeRing_3528 (T_NonAssociativeRing_3492 -> AgdaAny
forall a b. a -> b
coe T_NonAssociativeRing_3492
v0))
-- Algebra.Bundles.NonAssociativeRing.+-abelianGroup
d_'43''45'abelianGroup_3626 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_NonAssociativeRing_3492 -> T_AbelianGroup_1636
d_'43''45'abelianGroup_3626 :: () -> () -> T_NonAssociativeRing_3492 -> T_AbelianGroup_1636
d_'43''45'abelianGroup_3626 ~()
v0 ~()
v1 T_NonAssociativeRing_3492
v2
  = T_NonAssociativeRing_3492 -> T_AbelianGroup_1636
du_'43''45'abelianGroup_3626 T_NonAssociativeRing_3492
v2
du_'43''45'abelianGroup_3626 ::
  T_NonAssociativeRing_3492 -> T_AbelianGroup_1636
du_'43''45'abelianGroup_3626 :: T_NonAssociativeRing_3492 -> T_AbelianGroup_1636
du_'43''45'abelianGroup_3626 T_NonAssociativeRing_3492
v0
  = ((AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> (AgdaAny -> AgdaAny)
 -> T_IsAbelianGroup_1132
 -> T_AbelianGroup_1636)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsAbelianGroup_1132
-> T_AbelianGroup_1636
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsAbelianGroup_1132
-> T_AbelianGroup_1636
C_AbelianGroup'46'constructor_29855 (T_NonAssociativeRing_3492 -> AgdaAny -> AgdaAny -> AgdaAny
d__'43'__3518 (T_NonAssociativeRing_3492 -> T_NonAssociativeRing_3492
forall a b. a -> b
coe T_NonAssociativeRing_3492
v0))
      (T_NonAssociativeRing_3492 -> AgdaAny
d_0'35'_3524 (T_NonAssociativeRing_3492 -> T_NonAssociativeRing_3492
forall a b. a -> b
coe T_NonAssociativeRing_3492
v0)) (T_NonAssociativeRing_3492 -> AgdaAny -> AgdaAny
d_'45'__3522 (T_NonAssociativeRing_3492 -> T_NonAssociativeRing_3492
forall a b. a -> b
coe T_NonAssociativeRing_3492
v0))
      (T_IsNonAssociativeRing_2408 -> T_IsAbelianGroup_1132
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2430
         ((T_NonAssociativeRing_3492 -> T_IsNonAssociativeRing_2408)
-> AgdaAny -> T_IsNonAssociativeRing_2408
forall a b. a -> b
coe T_NonAssociativeRing_3492 -> T_IsNonAssociativeRing_2408
d_isNonAssociativeRing_3528 (T_NonAssociativeRing_3492 -> AgdaAny
forall a b. a -> b
coe T_NonAssociativeRing_3492
v0)))
-- Algebra.Bundles.NonAssociativeRing._.group
d_group_3630 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_NonAssociativeRing_3492 -> T_Group_1520
d_group_3630 :: () -> () -> T_NonAssociativeRing_3492 -> T_Group_1520
d_group_3630 ~()
v0 ~()
v1 T_NonAssociativeRing_3492
v2 = T_NonAssociativeRing_3492 -> T_Group_1520
du_group_3630 T_NonAssociativeRing_3492
v2
du_group_3630 :: T_NonAssociativeRing_3492 -> T_Group_1520
du_group_3630 :: T_NonAssociativeRing_3492 -> T_Group_1520
du_group_3630 T_NonAssociativeRing_3492
v0
  = (T_AbelianGroup_1636 -> T_Group_1520) -> AgdaAny -> T_Group_1520
forall a b. a -> b
coe T_AbelianGroup_1636 -> T_Group_1520
du_group_1732 ((T_NonAssociativeRing_3492 -> T_AbelianGroup_1636)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_NonAssociativeRing_3492 -> T_AbelianGroup_1636
du_'43''45'abelianGroup_3626 (T_NonAssociativeRing_3492 -> AgdaAny
forall a b. a -> b
coe T_NonAssociativeRing_3492
v0))
-- Algebra.Bundles.NonAssociativeRing._.invertibleMagma
d_invertibleMagma_3632 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_NonAssociativeRing_3492 -> T_InvertibleMagma_1360
d_invertibleMagma_3632 :: () -> () -> T_NonAssociativeRing_3492 -> T_InvertibleMagma_1360
d_invertibleMagma_3632 ~()
v0 ~()
v1 T_NonAssociativeRing_3492
v2 = T_NonAssociativeRing_3492 -> T_InvertibleMagma_1360
du_invertibleMagma_3632 T_NonAssociativeRing_3492
v2
du_invertibleMagma_3632 ::
  T_NonAssociativeRing_3492 -> T_InvertibleMagma_1360
du_invertibleMagma_3632 :: T_NonAssociativeRing_3492 -> T_InvertibleMagma_1360
du_invertibleMagma_3632 T_NonAssociativeRing_3492
v0
  = let v1 :: t
v1 = (T_NonAssociativeRing_3492 -> T_AbelianGroup_1636) -> AgdaAny -> t
forall a b. a -> b
coe T_NonAssociativeRing_3492 -> T_AbelianGroup_1636
du_'43''45'abelianGroup_3626 (T_NonAssociativeRing_3492 -> AgdaAny
forall a b. a -> b
coe T_NonAssociativeRing_3492
v0) in
    AgdaAny -> T_InvertibleMagma_1360
forall a b. a -> b
coe ((T_Group_1520 -> T_InvertibleMagma_1360) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Group_1520 -> T_InvertibleMagma_1360
du_invertibleMagma_1628 ((T_AbelianGroup_1636 -> T_Group_1520) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_AbelianGroup_1636 -> T_Group_1520
du_group_1732 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1)))
-- Algebra.Bundles.NonAssociativeRing._.invertibleUnitalMagma
d_invertibleUnitalMagma_3634 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_NonAssociativeRing_3492 -> T_InvertibleUnitalMagma_1434
d_invertibleUnitalMagma_3634 :: ()
-> () -> T_NonAssociativeRing_3492 -> T_InvertibleUnitalMagma_1434
d_invertibleUnitalMagma_3634 ~()
v0 ~()
v1 T_NonAssociativeRing_3492
v2
  = T_NonAssociativeRing_3492 -> T_InvertibleUnitalMagma_1434
du_invertibleUnitalMagma_3634 T_NonAssociativeRing_3492
v2
du_invertibleUnitalMagma_3634 ::
  T_NonAssociativeRing_3492 -> T_InvertibleUnitalMagma_1434
du_invertibleUnitalMagma_3634 :: T_NonAssociativeRing_3492 -> T_InvertibleUnitalMagma_1434
du_invertibleUnitalMagma_3634 T_NonAssociativeRing_3492
v0
  = let v1 :: t
v1 = (T_NonAssociativeRing_3492 -> T_AbelianGroup_1636) -> AgdaAny -> t
forall a b. a -> b
coe T_NonAssociativeRing_3492 -> T_AbelianGroup_1636
du_'43''45'abelianGroup_3626 (T_NonAssociativeRing_3492 -> AgdaAny
forall a b. a -> b
coe T_NonAssociativeRing_3492
v0) in
    AgdaAny -> T_InvertibleUnitalMagma_1434
forall a b. a -> b
coe
      ((T_Group_1520 -> T_InvertibleUnitalMagma_1434)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Group_1520 -> T_InvertibleUnitalMagma_1434
du_invertibleUnitalMagma_1630 ((T_AbelianGroup_1636 -> T_Group_1520) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_AbelianGroup_1636 -> T_Group_1520
du_group_1732 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1)))
-- Algebra.Bundles.NonAssociativeRing.*-unitalMagma
d_'42''45'unitalMagma_3636 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_NonAssociativeRing_3492 -> T_UnitalMagma_814
d_'42''45'unitalMagma_3636 :: () -> () -> T_NonAssociativeRing_3492 -> T_UnitalMagma_814
d_'42''45'unitalMagma_3636 ~()
v0 ~()
v1 T_NonAssociativeRing_3492
v2
  = T_NonAssociativeRing_3492 -> T_UnitalMagma_814
du_'42''45'unitalMagma_3636 T_NonAssociativeRing_3492
v2
du_'42''45'unitalMagma_3636 ::
  T_NonAssociativeRing_3492 -> T_UnitalMagma_814
du_'42''45'unitalMagma_3636 :: T_NonAssociativeRing_3492 -> T_UnitalMagma_814
du_'42''45'unitalMagma_3636 T_NonAssociativeRing_3492
v0
  = ((AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny -> T_IsUnitalMagma_642 -> T_UnitalMagma_814)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_UnitalMagma_814
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> T_IsUnitalMagma_642 -> T_UnitalMagma_814
C_UnitalMagma'46'constructor_14927 (T_NonAssociativeRing_3492 -> AgdaAny -> AgdaAny -> AgdaAny
d__'42'__3520 (T_NonAssociativeRing_3492 -> T_NonAssociativeRing_3492
forall a b. a -> b
coe T_NonAssociativeRing_3492
v0))
      (T_NonAssociativeRing_3492 -> AgdaAny
d_1'35'_3526 (T_NonAssociativeRing_3492 -> T_NonAssociativeRing_3492
forall a b. a -> b
coe T_NonAssociativeRing_3492
v0))
      ((T_IsNonAssociativeRing_2408 -> T_IsUnitalMagma_642)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsNonAssociativeRing_2408 -> T_IsUnitalMagma_642
MAlonzo.Code.Algebra.Structures.du_'42''45'isUnitalMagma_2520
         ((T_NonAssociativeRing_3492 -> T_IsNonAssociativeRing_2408)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_NonAssociativeRing_3492 -> T_IsNonAssociativeRing_2408
d_isNonAssociativeRing_3528 (T_NonAssociativeRing_3492 -> AgdaAny
forall a b. a -> b
coe T_NonAssociativeRing_3492
v0)))
-- Algebra.Bundles.NonAssociativeRing._.identity
d_identity_3640 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_NonAssociativeRing_3492 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_identity_3640 :: () -> () -> T_NonAssociativeRing_3492 -> T_Σ_14
d_identity_3640 ~()
v0 ~()
v1 T_NonAssociativeRing_3492
v2 = T_NonAssociativeRing_3492 -> T_Σ_14
du_identity_3640 T_NonAssociativeRing_3492
v2
du_identity_3640 ::
  T_NonAssociativeRing_3492 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
du_identity_3640 :: T_NonAssociativeRing_3492 -> T_Σ_14
du_identity_3640 T_NonAssociativeRing_3492
v0
  = (T_IsNonAssociativeRing_2408 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsNonAssociativeRing_2408 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_'42''45'identity_2434
      ((T_NonAssociativeRing_3492 -> T_IsNonAssociativeRing_2408)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_NonAssociativeRing_3492 -> T_IsNonAssociativeRing_2408
d_isNonAssociativeRing_3528 (T_NonAssociativeRing_3492 -> AgdaAny
forall a b. a -> b
coe T_NonAssociativeRing_3492
v0))
-- Algebra.Bundles.NonAssociativeRing._.magma
d_magma_3642 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_NonAssociativeRing_3492 -> T_Magma_68
d_magma_3642 :: () -> () -> T_NonAssociativeRing_3492 -> T_Magma_68
d_magma_3642 ~()
v0 ~()
v1 T_NonAssociativeRing_3492
v2 = T_NonAssociativeRing_3492 -> T_Magma_68
du_magma_3642 T_NonAssociativeRing_3492
v2
du_magma_3642 :: T_NonAssociativeRing_3492 -> T_Magma_68
du_magma_3642 :: T_NonAssociativeRing_3492 -> T_Magma_68
du_magma_3642 T_NonAssociativeRing_3492
v0
  = (T_UnitalMagma_814 -> T_Magma_68) -> AgdaAny -> T_Magma_68
forall a b. a -> b
coe T_UnitalMagma_814 -> T_Magma_68
du_magma_870 ((T_NonAssociativeRing_3492 -> T_UnitalMagma_814)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_NonAssociativeRing_3492 -> T_UnitalMagma_814
du_'42''45'unitalMagma_3636 (T_NonAssociativeRing_3492 -> AgdaAny
forall a b. a -> b
coe T_NonAssociativeRing_3492
v0))
-- Algebra.Bundles.Nearring
d_Nearring_3648 :: p -> p -> ()
d_Nearring_3648 p
a0 p
a1 = ()
data T_Nearring_3648
  = C_Nearring'46'constructor_65771 (AgdaAny -> AgdaAny -> AgdaAny)
                                    (AgdaAny -> AgdaAny -> AgdaAny) (AgdaAny -> AgdaAny) AgdaAny
                                    AgdaAny MAlonzo.Code.Algebra.Structures.T_IsNearring_2538
-- Algebra.Bundles.Nearring.Carrier
d_Carrier_3670 :: T_Nearring_3648 -> ()
d_Carrier_3670 :: T_Nearring_3648 -> ()
d_Carrier_3670 = T_Nearring_3648 -> ()
forall a. a
erased
-- Algebra.Bundles.Nearring._≈_
d__'8776'__3672 :: T_Nearring_3648 -> AgdaAny -> AgdaAny -> ()
d__'8776'__3672 :: T_Nearring_3648 -> AgdaAny -> AgdaAny -> ()
d__'8776'__3672 = T_Nearring_3648 -> AgdaAny -> AgdaAny -> ()
forall a. a
erased
-- Algebra.Bundles.Nearring._+_
d__'43'__3674 :: T_Nearring_3648 -> AgdaAny -> AgdaAny -> AgdaAny
d__'43'__3674 :: T_Nearring_3648 -> AgdaAny -> AgdaAny -> AgdaAny
d__'43'__3674 T_Nearring_3648
v0
  = case T_Nearring_3648 -> T_Nearring_3648
forall a b. a -> b
coe T_Nearring_3648
v0 of
      C_Nearring'46'constructor_65771 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny
v5 AgdaAny
v6 AgdaAny
v7 T_IsNearring_2538
v8 -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v3
      T_Nearring_3648
_ -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.Nearring._*_
d__'42'__3676 :: T_Nearring_3648 -> AgdaAny -> AgdaAny -> AgdaAny
d__'42'__3676 :: T_Nearring_3648 -> AgdaAny -> AgdaAny -> AgdaAny
d__'42'__3676 T_Nearring_3648
v0
  = case T_Nearring_3648 -> T_Nearring_3648
forall a b. a -> b
coe T_Nearring_3648
v0 of
      C_Nearring'46'constructor_65771 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny
v5 AgdaAny
v6 AgdaAny
v7 T_IsNearring_2538
v8 -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v4
      T_Nearring_3648
_ -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.Nearring.-_
d_'45'__3678 :: T_Nearring_3648 -> AgdaAny -> AgdaAny
d_'45'__3678 :: T_Nearring_3648 -> AgdaAny -> AgdaAny
d_'45'__3678 T_Nearring_3648
v0
  = case T_Nearring_3648 -> T_Nearring_3648
forall a b. a -> b
coe T_Nearring_3648
v0 of
      C_Nearring'46'constructor_65771 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny
v5 AgdaAny
v6 AgdaAny
v7 T_IsNearring_2538
v8 -> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v5
      T_Nearring_3648
_ -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.Nearring.0#
d_0'35'_3680 :: T_Nearring_3648 -> AgdaAny
d_0'35'_3680 :: T_Nearring_3648 -> AgdaAny
d_0'35'_3680 T_Nearring_3648
v0
  = case T_Nearring_3648 -> T_Nearring_3648
forall a b. a -> b
coe T_Nearring_3648
v0 of
      C_Nearring'46'constructor_65771 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny
v5 AgdaAny
v6 AgdaAny
v7 T_IsNearring_2538
v8 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v6
      T_Nearring_3648
_ -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.Nearring.1#
d_1'35'_3682 :: T_Nearring_3648 -> AgdaAny
d_1'35'_3682 :: T_Nearring_3648 -> AgdaAny
d_1'35'_3682 T_Nearring_3648
v0
  = case T_Nearring_3648 -> T_Nearring_3648
forall a b. a -> b
coe T_Nearring_3648
v0 of
      C_Nearring'46'constructor_65771 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny
v5 AgdaAny
v6 AgdaAny
v7 T_IsNearring_2538
v8 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v7
      T_Nearring_3648
_ -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.Nearring.isNearring
d_isNearring_3684 ::
  T_Nearring_3648 ->
  MAlonzo.Code.Algebra.Structures.T_IsNearring_2538
d_isNearring_3684 :: T_Nearring_3648 -> T_IsNearring_2538
d_isNearring_3684 T_Nearring_3648
v0
  = case T_Nearring_3648 -> T_Nearring_3648
forall a b. a -> b
coe T_Nearring_3648
v0 of
      C_Nearring'46'constructor_65771 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny
v5 AgdaAny
v6 AgdaAny
v7 T_IsNearring_2538
v8 -> T_IsNearring_2538 -> T_IsNearring_2538
forall a b. a -> b
coe T_IsNearring_2538
v8
      T_Nearring_3648
_ -> T_IsNearring_2538
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.Nearring._.*-assoc
d_'42''45'assoc_3688 ::
  T_Nearring_3648 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'assoc_3688 :: T_Nearring_3648 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'assoc_3688 T_Nearring_3648
v0
  = (T_IsQuasiring_2180 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsQuasiring_2180 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'42''45'assoc_2206
      ((T_IsNearring_2538 -> T_IsQuasiring_2180) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsNearring_2538 -> T_IsQuasiring_2180
MAlonzo.Code.Algebra.Structures.d_isQuasiring_2556
         ((T_Nearring_3648 -> T_IsNearring_2538) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Nearring_3648 -> T_IsNearring_2538
d_isNearring_3684 (T_Nearring_3648 -> AgdaAny
forall a b. a -> b
coe T_Nearring_3648
v0)))
-- Algebra.Bundles.Nearring._.*-cong
d_'42''45'cong_3690 ::
  T_Nearring_3648 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'cong_3690 :: T_Nearring_3648
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'42''45'cong_3690 T_Nearring_3648
v0
  = (T_IsQuasiring_2180
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsQuasiring_2180
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'42''45'cong_2204
      ((T_IsNearring_2538 -> T_IsQuasiring_2180) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsNearring_2538 -> T_IsQuasiring_2180
MAlonzo.Code.Algebra.Structures.d_isQuasiring_2556
         ((T_Nearring_3648 -> T_IsNearring_2538) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Nearring_3648 -> T_IsNearring_2538
d_isNearring_3684 (T_Nearring_3648 -> AgdaAny
forall a b. a -> b
coe T_Nearring_3648
v0)))
-- Algebra.Bundles.Nearring._.∙-congʳ
d_'8729''45'cong'691'_3692 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Nearring_3648 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_3692 :: ()
-> ()
-> T_Nearring_3648
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_3692 ~()
v0 ~()
v1 T_Nearring_3648
v2
  = T_Nearring_3648
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_3692 T_Nearring_3648
v2
du_'8729''45'cong'691'_3692 ::
  T_Nearring_3648 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_3692 :: T_Nearring_3648
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_3692 T_Nearring_3648
v0
  = let v1 :: T_IsNearring_2538
v1 = T_Nearring_3648 -> T_IsNearring_2538
d_isNearring_3684 (T_Nearring_3648 -> T_Nearring_3648
forall a b. a -> b
coe T_Nearring_3648
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsQuasiring_2180
v2
             = T_IsNearring_2538 -> T_IsQuasiring_2180
MAlonzo.Code.Algebra.Structures.d_isQuasiring_2556 (T_IsNearring_2538 -> T_IsNearring_2538
forall a b. a -> b
coe T_IsNearring_2538
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: t
v3
                = (T_IsQuasiring_2180 -> T_IsMonoid_686) -> AgdaAny -> t
forall a b. a -> b
coe
                    T_IsQuasiring_2180 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.du_'42''45'isMonoid_2266
                    (T_IsQuasiring_2180 -> AgdaAny
forall a b. a -> b
coe T_IsQuasiring_2180
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsSemigroup_472
v4
                   = T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (AgdaAny -> T_IsMonoid_686
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'691'_206
                  ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v4))))))
-- Algebra.Bundles.Nearring._.∙-congˡ
d_'8729''45'cong'737'_3694 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Nearring_3648 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_3694 :: ()
-> ()
-> T_Nearring_3648
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_3694 ~()
v0 ~()
v1 T_Nearring_3648
v2
  = T_Nearring_3648
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_3694 T_Nearring_3648
v2
du_'8729''45'cong'737'_3694 ::
  T_Nearring_3648 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_3694 :: T_Nearring_3648
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_3694 T_Nearring_3648
v0
  = let v1 :: T_IsNearring_2538
v1 = T_Nearring_3648 -> T_IsNearring_2538
d_isNearring_3684 (T_Nearring_3648 -> T_Nearring_3648
forall a b. a -> b
coe T_Nearring_3648
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsQuasiring_2180
v2
             = T_IsNearring_2538 -> T_IsQuasiring_2180
MAlonzo.Code.Algebra.Structures.d_isQuasiring_2556 (T_IsNearring_2538 -> T_IsNearring_2538
forall a b. a -> b
coe T_IsNearring_2538
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: t
v3
                = (T_IsQuasiring_2180 -> T_IsMonoid_686) -> AgdaAny -> t
forall a b. a -> b
coe
                    T_IsQuasiring_2180 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.du_'42''45'isMonoid_2266
                    (T_IsQuasiring_2180 -> AgdaAny
forall a b. a -> b
coe T_IsQuasiring_2180
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsSemigroup_472
v4
                   = T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (AgdaAny -> T_IsMonoid_686
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'737'_202
                  ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v4))))))
-- Algebra.Bundles.Nearring._.*-identity
d_'42''45'identity_3696 ::
  T_Nearring_3648 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'42''45'identity_3696 :: T_Nearring_3648 -> T_Σ_14
d_'42''45'identity_3696 T_Nearring_3648
v0
  = (T_IsQuasiring_2180 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsQuasiring_2180 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_'42''45'identity_2208
      ((T_IsNearring_2538 -> T_IsQuasiring_2180) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsNearring_2538 -> T_IsQuasiring_2180
MAlonzo.Code.Algebra.Structures.d_isQuasiring_2556
         ((T_Nearring_3648 -> T_IsNearring_2538) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Nearring_3648 -> T_IsNearring_2538
d_isNearring_3684 (T_Nearring_3648 -> AgdaAny
forall a b. a -> b
coe T_Nearring_3648
v0)))
-- Algebra.Bundles.Nearring._.identityʳ
d_identity'691'_3698 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Nearring_3648 -> AgdaAny -> AgdaAny
d_identity'691'_3698 :: () -> () -> T_Nearring_3648 -> AgdaAny -> AgdaAny
d_identity'691'_3698 ~()
v0 ~()
v1 T_Nearring_3648
v2 = T_Nearring_3648 -> AgdaAny -> AgdaAny
du_identity'691'_3698 T_Nearring_3648
v2
du_identity'691'_3698 :: T_Nearring_3648 -> AgdaAny -> AgdaAny
du_identity'691'_3698 :: T_Nearring_3648 -> AgdaAny -> AgdaAny
du_identity'691'_3698 T_Nearring_3648
v0
  = let v1 :: T_IsNearring_2538
v1 = T_Nearring_3648 -> T_IsNearring_2538
d_isNearring_3684 (T_Nearring_3648 -> T_Nearring_3648
forall a b. a -> b
coe T_Nearring_3648
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsQuasiring_2180
v2
             = T_IsNearring_2538 -> T_IsQuasiring_2180
MAlonzo.Code.Algebra.Structures.d_isQuasiring_2556 (T_IsNearring_2538 -> T_IsNearring_2538
forall a b. a -> b
coe T_IsNearring_2538
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsMonoid_686 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoid_686 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_identity'691'_728
            ((T_IsQuasiring_2180 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsQuasiring_2180 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.du_'42''45'isMonoid_2266
               (T_IsQuasiring_2180 -> AgdaAny
forall a b. a -> b
coe T_IsQuasiring_2180
v2))))
-- Algebra.Bundles.Nearring._.identityˡ
d_identity'737'_3700 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Nearring_3648 -> AgdaAny -> AgdaAny
d_identity'737'_3700 :: () -> () -> T_Nearring_3648 -> AgdaAny -> AgdaAny
d_identity'737'_3700 ~()
v0 ~()
v1 T_Nearring_3648
v2 = T_Nearring_3648 -> AgdaAny -> AgdaAny
du_identity'737'_3700 T_Nearring_3648
v2
du_identity'737'_3700 :: T_Nearring_3648 -> AgdaAny -> AgdaAny
du_identity'737'_3700 :: T_Nearring_3648 -> AgdaAny -> AgdaAny
du_identity'737'_3700 T_Nearring_3648
v0
  = let v1 :: T_IsNearring_2538
v1 = T_Nearring_3648 -> T_IsNearring_2538
d_isNearring_3684 (T_Nearring_3648 -> T_Nearring_3648
forall a b. a -> b
coe T_Nearring_3648
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsQuasiring_2180
v2
             = T_IsNearring_2538 -> T_IsQuasiring_2180
MAlonzo.Code.Algebra.Structures.d_isQuasiring_2556 (T_IsNearring_2538 -> T_IsNearring_2538
forall a b. a -> b
coe T_IsNearring_2538
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsMonoid_686 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoid_686 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_identity'737'_726
            ((T_IsQuasiring_2180 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsQuasiring_2180 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.du_'42''45'isMonoid_2266
               (T_IsQuasiring_2180 -> AgdaAny
forall a b. a -> b
coe T_IsQuasiring_2180
v2))))
-- Algebra.Bundles.Nearring._.*-isMagma
d_'42''45'isMagma_3702 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Nearring_3648 -> MAlonzo.Code.Algebra.Structures.T_IsMagma_176
d_'42''45'isMagma_3702 :: () -> () -> T_Nearring_3648 -> T_IsMagma_176
d_'42''45'isMagma_3702 ~()
v0 ~()
v1 T_Nearring_3648
v2 = T_Nearring_3648 -> T_IsMagma_176
du_'42''45'isMagma_3702 T_Nearring_3648
v2
du_'42''45'isMagma_3702 ::
  T_Nearring_3648 -> MAlonzo.Code.Algebra.Structures.T_IsMagma_176
du_'42''45'isMagma_3702 :: T_Nearring_3648 -> T_IsMagma_176
du_'42''45'isMagma_3702 T_Nearring_3648
v0
  = let v1 :: T_IsNearring_2538
v1 = T_Nearring_3648 -> T_IsNearring_2538
d_isNearring_3684 (T_Nearring_3648 -> T_Nearring_3648
forall a b. a -> b
coe T_Nearring_3648
v0) in
    AgdaAny -> T_IsMagma_176
forall a b. a -> b
coe
      ((T_IsQuasiring_2180 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsQuasiring_2180 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.du_'42''45'isMagma_2262
         ((T_IsNearring_2538 -> T_IsQuasiring_2180) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearring_2538 -> T_IsQuasiring_2180
MAlonzo.Code.Algebra.Structures.d_isQuasiring_2556 (T_IsNearring_2538 -> AgdaAny
forall a b. a -> b
coe T_IsNearring_2538
v1)))
-- Algebra.Bundles.Nearring._.*-isMonoid
d_'42''45'isMonoid_3704 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Nearring_3648 -> MAlonzo.Code.Algebra.Structures.T_IsMonoid_686
d_'42''45'isMonoid_3704 :: () -> () -> T_Nearring_3648 -> T_IsMonoid_686
d_'42''45'isMonoid_3704 ~()
v0 ~()
v1 T_Nearring_3648
v2 = T_Nearring_3648 -> T_IsMonoid_686
du_'42''45'isMonoid_3704 T_Nearring_3648
v2
du_'42''45'isMonoid_3704 ::
  T_Nearring_3648 -> MAlonzo.Code.Algebra.Structures.T_IsMonoid_686
du_'42''45'isMonoid_3704 :: T_Nearring_3648 -> T_IsMonoid_686
du_'42''45'isMonoid_3704 T_Nearring_3648
v0
  = let v1 :: T_IsNearring_2538
v1 = T_Nearring_3648 -> T_IsNearring_2538
d_isNearring_3684 (T_Nearring_3648 -> T_Nearring_3648
forall a b. a -> b
coe T_Nearring_3648
v0) in
    AgdaAny -> T_IsMonoid_686
forall a b. a -> b
coe
      ((T_IsQuasiring_2180 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsQuasiring_2180 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.du_'42''45'isMonoid_2266
         ((T_IsNearring_2538 -> T_IsQuasiring_2180) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearring_2538 -> T_IsQuasiring_2180
MAlonzo.Code.Algebra.Structures.d_isQuasiring_2556 (T_IsNearring_2538 -> AgdaAny
forall a b. a -> b
coe T_IsNearring_2538
v1)))
-- Algebra.Bundles.Nearring._.*-isSemigroup
d_'42''45'isSemigroup_3706 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Nearring_3648 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_472
d_'42''45'isSemigroup_3706 :: () -> () -> T_Nearring_3648 -> T_IsSemigroup_472
d_'42''45'isSemigroup_3706 ~()
v0 ~()
v1 T_Nearring_3648
v2
  = T_Nearring_3648 -> T_IsSemigroup_472
du_'42''45'isSemigroup_3706 T_Nearring_3648
v2
du_'42''45'isSemigroup_3706 ::
  T_Nearring_3648 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_472
du_'42''45'isSemigroup_3706 :: T_Nearring_3648 -> T_IsSemigroup_472
du_'42''45'isSemigroup_3706 T_Nearring_3648
v0
  = let v1 :: T_IsNearring_2538
v1 = T_Nearring_3648 -> T_IsNearring_2538
d_isNearring_3684 (T_Nearring_3648 -> T_Nearring_3648
forall a b. a -> b
coe T_Nearring_3648
v0) in
    AgdaAny -> T_IsSemigroup_472
forall a b. a -> b
coe
      ((T_IsQuasiring_2180 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsQuasiring_2180 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.du_'42''45'isSemigroup_2264
         ((T_IsNearring_2538 -> T_IsQuasiring_2180) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearring_2538 -> T_IsQuasiring_2180
MAlonzo.Code.Algebra.Structures.d_isQuasiring_2556 (T_IsNearring_2538 -> AgdaAny
forall a b. a -> b
coe T_IsNearring_2538
v1)))
-- Algebra.Bundles.Nearring._.assoc
d_assoc_3708 ::
  T_Nearring_3648 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_3708 :: T_Nearring_3648 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_3708 T_Nearring_3648
v0
  = (T_IsSemigroup_472 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsSemigroup_472 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_assoc_482
      ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
         ((T_IsQuasiring_2180 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsQuasiring_2180 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_'43''45'isMonoid_2202
            ((T_IsNearring_2538 -> T_IsQuasiring_2180) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsNearring_2538 -> T_IsQuasiring_2180
MAlonzo.Code.Algebra.Structures.d_isQuasiring_2556
               ((T_Nearring_3648 -> T_IsNearring_2538) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Nearring_3648 -> T_IsNearring_2538
d_isNearring_3684 (T_Nearring_3648 -> AgdaAny
forall a b. a -> b
coe T_Nearring_3648
v0)))))
-- Algebra.Bundles.Nearring._.∙-cong
d_'8729''45'cong_3710 ::
  T_Nearring_3648 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_3710 :: T_Nearring_3648
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_3710 T_Nearring_3648
v0
  = (T_IsMagma_176
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsMagma_176
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_186
      ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480
         ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
            ((T_IsQuasiring_2180 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsQuasiring_2180 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_'43''45'isMonoid_2202
               ((T_IsNearring_2538 -> T_IsQuasiring_2180) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsNearring_2538 -> T_IsQuasiring_2180
MAlonzo.Code.Algebra.Structures.d_isQuasiring_2556
                  ((T_Nearring_3648 -> T_IsNearring_2538) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Nearring_3648 -> T_IsNearring_2538
d_isNearring_3684 (T_Nearring_3648 -> AgdaAny
forall a b. a -> b
coe T_Nearring_3648
v0))))))
-- Algebra.Bundles.Nearring._.∙-congʳ
d_'8729''45'cong'691'_3712 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Nearring_3648 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_3712 :: ()
-> ()
-> T_Nearring_3648
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_3712 ~()
v0 ~()
v1 T_Nearring_3648
v2
  = T_Nearring_3648
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_3712 T_Nearring_3648
v2
du_'8729''45'cong'691'_3712 ::
  T_Nearring_3648 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_3712 :: T_Nearring_3648
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_3712 T_Nearring_3648
v0
  = let v1 :: T_IsNearring_2538
v1 = T_Nearring_3648 -> T_IsNearring_2538
d_isNearring_3684 (T_Nearring_3648 -> T_Nearring_3648
forall a b. a -> b
coe T_Nearring_3648
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsQuasiring_2180
v2
             = T_IsNearring_2538 -> T_IsQuasiring_2180
MAlonzo.Code.Algebra.Structures.d_isQuasiring_2556 (T_IsNearring_2538 -> T_IsNearring_2538
forall a b. a -> b
coe T_IsNearring_2538
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsMonoid_686
v3
                = T_IsQuasiring_2180 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_'43''45'isMonoid_2202
                    (T_IsQuasiring_2180 -> T_IsQuasiring_2180
forall a b. a -> b
coe T_IsQuasiring_2180
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsSemigroup_472
v4
                   = T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'691'_206
                  ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v4))))))
-- Algebra.Bundles.Nearring._.∙-congˡ
d_'8729''45'cong'737'_3714 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Nearring_3648 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_3714 :: ()
-> ()
-> T_Nearring_3648
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_3714 ~()
v0 ~()
v1 T_Nearring_3648
v2
  = T_Nearring_3648
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_3714 T_Nearring_3648
v2
du_'8729''45'cong'737'_3714 ::
  T_Nearring_3648 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_3714 :: T_Nearring_3648
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_3714 T_Nearring_3648
v0
  = let v1 :: T_IsNearring_2538
v1 = T_Nearring_3648 -> T_IsNearring_2538
d_isNearring_3684 (T_Nearring_3648 -> T_Nearring_3648
forall a b. a -> b
coe T_Nearring_3648
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsQuasiring_2180
v2
             = T_IsNearring_2538 -> T_IsQuasiring_2180
MAlonzo.Code.Algebra.Structures.d_isQuasiring_2556 (T_IsNearring_2538 -> T_IsNearring_2538
forall a b. a -> b
coe T_IsNearring_2538
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsMonoid_686
v3
                = T_IsQuasiring_2180 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_'43''45'isMonoid_2202
                    (T_IsQuasiring_2180 -> T_IsQuasiring_2180
forall a b. a -> b
coe T_IsQuasiring_2180
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsSemigroup_472
v4
                   = T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'737'_202
                  ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v4))))))
-- Algebra.Bundles.Nearring._.identity
d_identity_3716 ::
  T_Nearring_3648 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_identity_3716 :: T_Nearring_3648 -> T_Σ_14
d_identity_3716 T_Nearring_3648
v0
  = (T_IsMonoid_686 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsMonoid_686 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_identity_698
      ((T_IsQuasiring_2180 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsQuasiring_2180 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_'43''45'isMonoid_2202
         ((T_IsNearring_2538 -> T_IsQuasiring_2180) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsNearring_2538 -> T_IsQuasiring_2180
MAlonzo.Code.Algebra.Structures.d_isQuasiring_2556
            ((T_Nearring_3648 -> T_IsNearring_2538) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Nearring_3648 -> T_IsNearring_2538
d_isNearring_3684 (T_Nearring_3648 -> AgdaAny
forall a b. a -> b
coe T_Nearring_3648
v0))))
-- Algebra.Bundles.Nearring._.identityʳ
d_identity'691'_3718 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Nearring_3648 -> AgdaAny -> AgdaAny
d_identity'691'_3718 :: () -> () -> T_Nearring_3648 -> AgdaAny -> AgdaAny
d_identity'691'_3718 ~()
v0 ~()
v1 T_Nearring_3648
v2 = T_Nearring_3648 -> AgdaAny -> AgdaAny
du_identity'691'_3718 T_Nearring_3648
v2
du_identity'691'_3718 :: T_Nearring_3648 -> AgdaAny -> AgdaAny
du_identity'691'_3718 :: T_Nearring_3648 -> AgdaAny -> AgdaAny
du_identity'691'_3718 T_Nearring_3648
v0
  = let v1 :: T_IsNearring_2538
v1 = T_Nearring_3648 -> T_IsNearring_2538
d_isNearring_3684 (T_Nearring_3648 -> T_Nearring_3648
forall a b. a -> b
coe T_Nearring_3648
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsQuasiring_2180
v2
             = T_IsNearring_2538 -> T_IsQuasiring_2180
MAlonzo.Code.Algebra.Structures.d_isQuasiring_2556 (T_IsNearring_2538 -> T_IsNearring_2538
forall a b. a -> b
coe T_IsNearring_2538
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsMonoid_686 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoid_686 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_identity'691'_728
            ((T_IsQuasiring_2180 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsQuasiring_2180 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_'43''45'isMonoid_2202 (T_IsQuasiring_2180 -> AgdaAny
forall a b. a -> b
coe T_IsQuasiring_2180
v2))))
-- Algebra.Bundles.Nearring._.identityˡ
d_identity'737'_3720 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Nearring_3648 -> AgdaAny -> AgdaAny
d_identity'737'_3720 :: () -> () -> T_Nearring_3648 -> AgdaAny -> AgdaAny
d_identity'737'_3720 ~()
v0 ~()
v1 T_Nearring_3648
v2 = T_Nearring_3648 -> AgdaAny -> AgdaAny
du_identity'737'_3720 T_Nearring_3648
v2
du_identity'737'_3720 :: T_Nearring_3648 -> AgdaAny -> AgdaAny
du_identity'737'_3720 :: T_Nearring_3648 -> AgdaAny -> AgdaAny
du_identity'737'_3720 T_Nearring_3648
v0
  = let v1 :: T_IsNearring_2538
v1 = T_Nearring_3648 -> T_IsNearring_2538
d_isNearring_3684 (T_Nearring_3648 -> T_Nearring_3648
forall a b. a -> b
coe T_Nearring_3648
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsQuasiring_2180
v2
             = T_IsNearring_2538 -> T_IsQuasiring_2180
MAlonzo.Code.Algebra.Structures.d_isQuasiring_2556 (T_IsNearring_2538 -> T_IsNearring_2538
forall a b. a -> b
coe T_IsNearring_2538
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsMonoid_686 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoid_686 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_identity'737'_726
            ((T_IsQuasiring_2180 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsQuasiring_2180 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_'43''45'isMonoid_2202 (T_IsQuasiring_2180 -> AgdaAny
forall a b. a -> b
coe T_IsQuasiring_2180
v2))))
-- Algebra.Bundles.Nearring._.+-inverse
d_'43''45'inverse_3722 ::
  T_Nearring_3648 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'43''45'inverse_3722 :: T_Nearring_3648 -> T_Σ_14
d_'43''45'inverse_3722 T_Nearring_3648
v0
  = (T_IsNearring_2538 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsNearring_2538 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_'43''45'inverse_2558
      ((T_Nearring_3648 -> T_IsNearring_2538) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Nearring_3648 -> T_IsNearring_2538
d_isNearring_3684 (T_Nearring_3648 -> AgdaAny
forall a b. a -> b
coe T_Nearring_3648
v0))
-- Algebra.Bundles.Nearring._.+-inverseʳ
d_'43''45'inverse'691'_3724 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Nearring_3648 -> AgdaAny -> AgdaAny
d_'43''45'inverse'691'_3724 :: () -> () -> T_Nearring_3648 -> AgdaAny -> AgdaAny
d_'43''45'inverse'691'_3724 ~()
v0 ~()
v1 T_Nearring_3648
v2
  = T_Nearring_3648 -> AgdaAny -> AgdaAny
du_'43''45'inverse'691'_3724 T_Nearring_3648
v2
du_'43''45'inverse'691'_3724 ::
  T_Nearring_3648 -> AgdaAny -> AgdaAny
du_'43''45'inverse'691'_3724 :: T_Nearring_3648 -> AgdaAny -> AgdaAny
du_'43''45'inverse'691'_3724 T_Nearring_3648
v0
  = (T_IsNearring_2538 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsNearring_2538 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'43''45'inverse'691'_2638
      ((T_Nearring_3648 -> T_IsNearring_2538) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Nearring_3648 -> T_IsNearring_2538
d_isNearring_3684 (T_Nearring_3648 -> AgdaAny
forall a b. a -> b
coe T_Nearring_3648
v0))
-- Algebra.Bundles.Nearring._.+-inverseˡ
d_'43''45'inverse'737'_3726 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Nearring_3648 -> AgdaAny -> AgdaAny
d_'43''45'inverse'737'_3726 :: () -> () -> T_Nearring_3648 -> AgdaAny -> AgdaAny
d_'43''45'inverse'737'_3726 ~()
v0 ~()
v1 T_Nearring_3648
v2
  = T_Nearring_3648 -> AgdaAny -> AgdaAny
du_'43''45'inverse'737'_3726 T_Nearring_3648
v2
du_'43''45'inverse'737'_3726 ::
  T_Nearring_3648 -> AgdaAny -> AgdaAny
du_'43''45'inverse'737'_3726 :: T_Nearring_3648 -> AgdaAny -> AgdaAny
du_'43''45'inverse'737'_3726 T_Nearring_3648
v0
  = (T_IsNearring_2538 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsNearring_2538 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'43''45'inverse'737'_2636
      ((T_Nearring_3648 -> T_IsNearring_2538) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Nearring_3648 -> T_IsNearring_2538
d_isNearring_3684 (T_Nearring_3648 -> AgdaAny
forall a b. a -> b
coe T_Nearring_3648
v0))
-- Algebra.Bundles.Nearring._.isMagma
d_isMagma_3728 ::
  T_Nearring_3648 -> MAlonzo.Code.Algebra.Structures.T_IsMagma_176
d_isMagma_3728 :: T_Nearring_3648 -> T_IsMagma_176
d_isMagma_3728 T_Nearring_3648
v0
  = (T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> T_IsMagma_176
forall a b. a -> b
coe
      T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480
      ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
         ((T_IsQuasiring_2180 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsQuasiring_2180 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_'43''45'isMonoid_2202
            ((T_IsNearring_2538 -> T_IsQuasiring_2180) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsNearring_2538 -> T_IsQuasiring_2180
MAlonzo.Code.Algebra.Structures.d_isQuasiring_2556
               ((T_Nearring_3648 -> T_IsNearring_2538) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Nearring_3648 -> T_IsNearring_2538
d_isNearring_3684 (T_Nearring_3648 -> AgdaAny
forall a b. a -> b
coe T_Nearring_3648
v0)))))
-- Algebra.Bundles.Nearring._.+-isMonoid
d_'43''45'isMonoid_3730 ::
  T_Nearring_3648 -> MAlonzo.Code.Algebra.Structures.T_IsMonoid_686
d_'43''45'isMonoid_3730 :: T_Nearring_3648 -> T_IsMonoid_686
d_'43''45'isMonoid_3730 T_Nearring_3648
v0
  = (T_IsQuasiring_2180 -> T_IsMonoid_686) -> AgdaAny -> T_IsMonoid_686
forall a b. a -> b
coe
      T_IsQuasiring_2180 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_'43''45'isMonoid_2202
      ((T_IsNearring_2538 -> T_IsQuasiring_2180) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsNearring_2538 -> T_IsQuasiring_2180
MAlonzo.Code.Algebra.Structures.d_isQuasiring_2556
         ((T_Nearring_3648 -> T_IsNearring_2538) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Nearring_3648 -> T_IsNearring_2538
d_isNearring_3684 (T_Nearring_3648 -> AgdaAny
forall a b. a -> b
coe T_Nearring_3648
v0)))
-- Algebra.Bundles.Nearring._.isSemigroup
d_isSemigroup_3732 ::
  T_Nearring_3648 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_472
d_isSemigroup_3732 :: T_Nearring_3648 -> T_IsSemigroup_472
d_isSemigroup_3732 T_Nearring_3648
v0
  = (T_IsMonoid_686 -> T_IsSemigroup_472)
-> AgdaAny -> T_IsSemigroup_472
forall a b. a -> b
coe
      T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
      ((T_IsQuasiring_2180 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsQuasiring_2180 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_'43''45'isMonoid_2202
         ((T_IsNearring_2538 -> T_IsQuasiring_2180) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsNearring_2538 -> T_IsQuasiring_2180
MAlonzo.Code.Algebra.Structures.d_isQuasiring_2556
            ((T_Nearring_3648 -> T_IsNearring_2538) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Nearring_3648 -> T_IsNearring_2538
d_isNearring_3684 (T_Nearring_3648 -> AgdaAny
forall a b. a -> b
coe T_Nearring_3648
v0))))
-- Algebra.Bundles.Nearring._.isUnitalMagma
d_isUnitalMagma_3734 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Nearring_3648 ->
  MAlonzo.Code.Algebra.Structures.T_IsUnitalMagma_642
d_isUnitalMagma_3734 :: () -> () -> T_Nearring_3648 -> T_IsUnitalMagma_642
d_isUnitalMagma_3734 ~()
v0 ~()
v1 T_Nearring_3648
v2 = T_Nearring_3648 -> T_IsUnitalMagma_642
du_isUnitalMagma_3734 T_Nearring_3648
v2
du_isUnitalMagma_3734 ::
  T_Nearring_3648 ->
  MAlonzo.Code.Algebra.Structures.T_IsUnitalMagma_642
du_isUnitalMagma_3734 :: T_Nearring_3648 -> T_IsUnitalMagma_642
du_isUnitalMagma_3734 T_Nearring_3648
v0
  = let v1 :: T_IsNearring_2538
v1 = T_Nearring_3648 -> T_IsNearring_2538
d_isNearring_3684 (T_Nearring_3648 -> T_Nearring_3648
forall a b. a -> b
coe T_Nearring_3648
v0) in
    AgdaAny -> T_IsUnitalMagma_642
forall a b. a -> b
coe
      (let v2 :: T_IsQuasiring_2180
v2
             = T_IsNearring_2538 -> T_IsQuasiring_2180
MAlonzo.Code.Algebra.Structures.d_isQuasiring_2556 (T_IsNearring_2538 -> T_IsNearring_2538
forall a b. a -> b
coe T_IsNearring_2538
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsMonoid_686 -> T_IsUnitalMagma_642) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoid_686 -> T_IsUnitalMagma_642
MAlonzo.Code.Algebra.Structures.du_isUnitalMagma_730
            ((T_IsQuasiring_2180 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsQuasiring_2180 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_'43''45'isMonoid_2202 (T_IsQuasiring_2180 -> AgdaAny
forall a b. a -> b
coe T_IsQuasiring_2180
v2))))
-- Algebra.Bundles.Nearring._.distrib
d_distrib_3736 ::
  T_Nearring_3648 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_distrib_3736 :: T_Nearring_3648 -> T_Σ_14
d_distrib_3736 T_Nearring_3648
v0
  = (T_IsQuasiring_2180 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsQuasiring_2180 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_distrib_2210
      ((T_IsNearring_2538 -> T_IsQuasiring_2180) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsNearring_2538 -> T_IsQuasiring_2180
MAlonzo.Code.Algebra.Structures.d_isQuasiring_2556
         ((T_Nearring_3648 -> T_IsNearring_2538) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Nearring_3648 -> T_IsNearring_2538
d_isNearring_3684 (T_Nearring_3648 -> AgdaAny
forall a b. a -> b
coe T_Nearring_3648
v0)))
-- Algebra.Bundles.Nearring._.distribʳ
d_distrib'691'_3738 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Nearring_3648 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_distrib'691'_3738 :: ()
-> ()
-> T_Nearring_3648
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_distrib'691'_3738 ~()
v0 ~()
v1 T_Nearring_3648
v2 = T_Nearring_3648 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'691'_3738 T_Nearring_3648
v2
du_distrib'691'_3738 ::
  T_Nearring_3648 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'691'_3738 :: T_Nearring_3648 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'691'_3738 T_Nearring_3648
v0
  = let v1 :: T_IsNearring_2538
v1 = T_Nearring_3648 -> T_IsNearring_2538
d_isNearring_3684 (T_Nearring_3648 -> T_Nearring_3648
forall a b. a -> b
coe T_Nearring_3648
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsQuasiring_2180 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsQuasiring_2180 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_distrib'691'_2252
         ((T_IsNearring_2538 -> T_IsQuasiring_2180) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearring_2538 -> T_IsQuasiring_2180
MAlonzo.Code.Algebra.Structures.d_isQuasiring_2556 (T_IsNearring_2538 -> AgdaAny
forall a b. a -> b
coe T_IsNearring_2538
v1)))
-- Algebra.Bundles.Nearring._.distribˡ
d_distrib'737'_3740 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Nearring_3648 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_distrib'737'_3740 :: ()
-> ()
-> T_Nearring_3648
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_distrib'737'_3740 ~()
v0 ~()
v1 T_Nearring_3648
v2 = T_Nearring_3648 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'737'_3740 T_Nearring_3648
v2
du_distrib'737'_3740 ::
  T_Nearring_3648 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'737'_3740 :: T_Nearring_3648 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'737'_3740 T_Nearring_3648
v0
  = let v1 :: T_IsNearring_2538
v1 = T_Nearring_3648 -> T_IsNearring_2538
d_isNearring_3684 (T_Nearring_3648 -> T_Nearring_3648
forall a b. a -> b
coe T_Nearring_3648
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsQuasiring_2180 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsQuasiring_2180 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_distrib'737'_2250
         ((T_IsNearring_2538 -> T_IsQuasiring_2180) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearring_2538 -> T_IsQuasiring_2180
MAlonzo.Code.Algebra.Structures.d_isQuasiring_2556 (T_IsNearring_2538 -> AgdaAny
forall a b. a -> b
coe T_IsNearring_2538
v1)))
-- Algebra.Bundles.Nearring._.identityʳ
d_identity'691'_3742 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Nearring_3648 -> AgdaAny -> AgdaAny
d_identity'691'_3742 :: () -> () -> T_Nearring_3648 -> AgdaAny -> AgdaAny
d_identity'691'_3742 ~()
v0 ~()
v1 T_Nearring_3648
v2 = T_Nearring_3648 -> AgdaAny -> AgdaAny
du_identity'691'_3742 T_Nearring_3648
v2
du_identity'691'_3742 :: T_Nearring_3648 -> AgdaAny -> AgdaAny
du_identity'691'_3742 :: T_Nearring_3648 -> AgdaAny -> AgdaAny
du_identity'691'_3742 T_Nearring_3648
v0
  = let v1 :: T_IsNearring_2538
v1 = T_Nearring_3648 -> T_IsNearring_2538
d_isNearring_3684 (T_Nearring_3648 -> T_Nearring_3648
forall a b. a -> b
coe T_Nearring_3648
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsQuasiring_2180 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsQuasiring_2180 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_identity'691'_2260
         ((T_IsNearring_2538 -> T_IsQuasiring_2180) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearring_2538 -> T_IsQuasiring_2180
MAlonzo.Code.Algebra.Structures.d_isQuasiring_2556 (T_IsNearring_2538 -> AgdaAny
forall a b. a -> b
coe T_IsNearring_2538
v1)))
-- Algebra.Bundles.Nearring._.identityˡ
d_identity'737'_3744 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Nearring_3648 -> AgdaAny -> AgdaAny
d_identity'737'_3744 :: () -> () -> T_Nearring_3648 -> AgdaAny -> AgdaAny
d_identity'737'_3744 ~()
v0 ~()
v1 T_Nearring_3648
v2 = T_Nearring_3648 -> AgdaAny -> AgdaAny
du_identity'737'_3744 T_Nearring_3648
v2
du_identity'737'_3744 :: T_Nearring_3648 -> AgdaAny -> AgdaAny
du_identity'737'_3744 :: T_Nearring_3648 -> AgdaAny -> AgdaAny
du_identity'737'_3744 T_Nearring_3648
v0
  = let v1 :: T_IsNearring_2538
v1 = T_Nearring_3648 -> T_IsNearring_2538
d_isNearring_3684 (T_Nearring_3648 -> T_Nearring_3648
forall a b. a -> b
coe T_Nearring_3648
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsQuasiring_2180 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsQuasiring_2180 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_identity'737'_2258
         ((T_IsNearring_2538 -> T_IsQuasiring_2180) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearring_2538 -> T_IsQuasiring_2180
MAlonzo.Code.Algebra.Structures.d_isQuasiring_2556 (T_IsNearring_2538 -> AgdaAny
forall a b. a -> b
coe T_IsNearring_2538
v1)))
-- Algebra.Bundles.Nearring._.isEquivalence
d_isEquivalence_3746 ::
  T_Nearring_3648 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_3746 :: T_Nearring_3648 -> T_IsEquivalence_26
d_isEquivalence_3746 T_Nearring_3648
v0
  = (T_IsMagma_176 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
      ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480
         ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
            ((T_IsQuasiring_2180 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsQuasiring_2180 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_'43''45'isMonoid_2202
               ((T_IsNearring_2538 -> T_IsQuasiring_2180) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsNearring_2538 -> T_IsQuasiring_2180
MAlonzo.Code.Algebra.Structures.d_isQuasiring_2556
                  ((T_Nearring_3648 -> T_IsNearring_2538) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Nearring_3648 -> T_IsNearring_2538
d_isNearring_3684 (T_Nearring_3648 -> AgdaAny
forall a b. a -> b
coe T_Nearring_3648
v0))))))
-- Algebra.Bundles.Nearring._.isPartialEquivalence
d_isPartialEquivalence_3748 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Nearring_3648 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_3748 :: () -> () -> T_Nearring_3648 -> T_IsPartialEquivalence_16
d_isPartialEquivalence_3748 ~()
v0 ~()
v1 T_Nearring_3648
v2
  = T_Nearring_3648 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_3748 T_Nearring_3648
v2
du_isPartialEquivalence_3748 ::
  T_Nearring_3648 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_3748 :: T_Nearring_3648 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_3748 T_Nearring_3648
v0
  = let v1 :: T_IsNearring_2538
v1 = T_Nearring_3648 -> T_IsNearring_2538
d_isNearring_3684 (T_Nearring_3648 -> T_Nearring_3648
forall a b. a -> b
coe T_Nearring_3648
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsQuasiring_2180
v2
             = T_IsNearring_2538 -> T_IsQuasiring_2180
MAlonzo.Code.Algebra.Structures.d_isQuasiring_2556 (T_IsNearring_2538 -> T_IsNearring_2538
forall a b. a -> b
coe T_IsNearring_2538
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsMonoid_686
v3
                = T_IsQuasiring_2180 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_'43''45'isMonoid_2202
                    (T_IsQuasiring_2180 -> T_IsQuasiring_2180
forall a b. a -> b
coe T_IsQuasiring_2180
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsSemigroup_472
v4
                   = T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsMagma_176
v5 = T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (T_IsSemigroup_472 -> T_IsSemigroup_472
forall a b. a -> b
coe T_IsSemigroup_472
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  ((T_IsEquivalence_26 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsEquivalence_26 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
                     ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v5)))))))
-- Algebra.Bundles.Nearring._.isQuasiring
d_isQuasiring_3750 ::
  T_Nearring_3648 ->
  MAlonzo.Code.Algebra.Structures.T_IsQuasiring_2180
d_isQuasiring_3750 :: T_Nearring_3648 -> T_IsQuasiring_2180
d_isQuasiring_3750 T_Nearring_3648
v0
  = (T_IsNearring_2538 -> T_IsQuasiring_2180)
-> AgdaAny -> T_IsQuasiring_2180
forall a b. a -> b
coe
      T_IsNearring_2538 -> T_IsQuasiring_2180
MAlonzo.Code.Algebra.Structures.d_isQuasiring_2556
      ((T_Nearring_3648 -> T_IsNearring_2538) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Nearring_3648 -> T_IsNearring_2538
d_isNearring_3684 (T_Nearring_3648 -> AgdaAny
forall a b. a -> b
coe T_Nearring_3648
v0))
-- Algebra.Bundles.Nearring._.refl
d_refl_3752 :: T_Nearring_3648 -> AgdaAny -> AgdaAny
d_refl_3752 :: T_Nearring_3648 -> AgdaAny -> AgdaAny
d_refl_3752 T_Nearring_3648
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_34
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
         ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480
            ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
               ((T_IsQuasiring_2180 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsQuasiring_2180 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_'43''45'isMonoid_2202
                  ((T_IsNearring_2538 -> T_IsQuasiring_2180) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsNearring_2538 -> T_IsQuasiring_2180
MAlonzo.Code.Algebra.Structures.d_isQuasiring_2556
                     ((T_Nearring_3648 -> T_IsNearring_2538) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Nearring_3648 -> T_IsNearring_2538
d_isNearring_3684 (T_Nearring_3648 -> AgdaAny
forall a b. a -> b
coe T_Nearring_3648
v0)))))))
-- Algebra.Bundles.Nearring._.reflexive
d_reflexive_3754 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Nearring_3648 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_3754 :: ()
-> ()
-> T_Nearring_3648
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_3754 ~()
v0 ~()
v1 T_Nearring_3648
v2 = T_Nearring_3648 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_3754 T_Nearring_3648
v2
du_reflexive_3754 ::
  T_Nearring_3648 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_3754 :: T_Nearring_3648 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_3754 T_Nearring_3648
v0
  = let v1 :: T_IsNearring_2538
v1 = T_Nearring_3648 -> T_IsNearring_2538
d_isNearring_3684 (T_Nearring_3648 -> T_Nearring_3648
forall a b. a -> b
coe T_Nearring_3648
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsQuasiring_2180
v2
             = T_IsNearring_2538 -> T_IsQuasiring_2180
MAlonzo.Code.Algebra.Structures.d_isQuasiring_2556 (T_IsNearring_2538 -> T_IsNearring_2538
forall a b. a -> b
coe T_IsNearring_2538
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsMonoid_686
v3
                = T_IsQuasiring_2180 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_'43''45'isMonoid_2202
                    (T_IsQuasiring_2180 -> T_IsQuasiring_2180
forall a b. a -> b
coe T_IsQuasiring_2180
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsSemigroup_472
v4
                   = T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsMagma_176
v5 = T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (T_IsSemigroup_472 -> T_IsSemigroup_472
forall a b. a -> b
coe T_IsSemigroup_472
v4) in
                (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
                  (\ AgdaAny
v6 AgdaAny
v7 AgdaAny
v8 ->
                     (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                       T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
                       ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v5))
                       AgdaAny
v6)))))
-- Algebra.Bundles.Nearring._.setoid
d_setoid_3756 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Nearring_3648 -> MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_3756 :: () -> () -> T_Nearring_3648 -> T_Setoid_44
d_setoid_3756 ~()
v0 ~()
v1 T_Nearring_3648
v2 = T_Nearring_3648 -> T_Setoid_44
du_setoid_3756 T_Nearring_3648
v2
du_setoid_3756 ::
  T_Nearring_3648 -> MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_3756 :: T_Nearring_3648 -> T_Setoid_44
du_setoid_3756 T_Nearring_3648
v0
  = let v1 :: T_IsNearring_2538
v1 = T_Nearring_3648 -> T_IsNearring_2538
d_isNearring_3684 (T_Nearring_3648 -> T_Nearring_3648
forall a b. a -> b
coe T_Nearring_3648
v0) in
    AgdaAny -> T_Setoid_44
forall a b. a -> b
coe
      (let v2 :: T_IsQuasiring_2180
v2
             = T_IsNearring_2538 -> T_IsQuasiring_2180
MAlonzo.Code.Algebra.Structures.d_isQuasiring_2556 (T_IsNearring_2538 -> T_IsNearring_2538
forall a b. a -> b
coe T_IsNearring_2538
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsMonoid_686
v3
                = T_IsQuasiring_2180 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_'43''45'isMonoid_2202
                    (T_IsQuasiring_2180 -> T_IsQuasiring_2180
forall a b. a -> b
coe T_IsQuasiring_2180
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsSemigroup_472
v4
                   = T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               ((T_IsMagma_176 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsMagma_176 -> T_Setoid_44
MAlonzo.Code.Algebra.Structures.du_setoid_200
                  ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v4))))))
-- Algebra.Bundles.Nearring._.sym
d_sym_3758 ::
  T_Nearring_3648 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_3758 :: T_Nearring_3648 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_3758 T_Nearring_3648
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_36
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
         ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480
            ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
               ((T_IsQuasiring_2180 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsQuasiring_2180 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_'43''45'isMonoid_2202
                  ((T_IsNearring_2538 -> T_IsQuasiring_2180) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsNearring_2538 -> T_IsQuasiring_2180
MAlonzo.Code.Algebra.Structures.d_isQuasiring_2556
                     ((T_Nearring_3648 -> T_IsNearring_2538) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Nearring_3648 -> T_IsNearring_2538
d_isNearring_3684 (T_Nearring_3648 -> AgdaAny
forall a b. a -> b
coe T_Nearring_3648
v0)))))))
-- Algebra.Bundles.Nearring._.trans
d_trans_3760 ::
  T_Nearring_3648 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_3760 :: T_Nearring_3648
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_3760 T_Nearring_3648
v0
  = (T_IsEquivalence_26
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_38
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
         ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480
            ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
               ((T_IsQuasiring_2180 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsQuasiring_2180 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_'43''45'isMonoid_2202
                  ((T_IsNearring_2538 -> T_IsQuasiring_2180) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsNearring_2538 -> T_IsQuasiring_2180
MAlonzo.Code.Algebra.Structures.d_isQuasiring_2556
                     ((T_Nearring_3648 -> T_IsNearring_2538) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Nearring_3648 -> T_IsNearring_2538
d_isNearring_3684 (T_Nearring_3648 -> AgdaAny
forall a b. a -> b
coe T_Nearring_3648
v0)))))))
-- Algebra.Bundles.Nearring._.zero
d_zero_3762 ::
  T_Nearring_3648 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_zero_3762 :: T_Nearring_3648 -> T_Σ_14
d_zero_3762 T_Nearring_3648
v0
  = (T_IsQuasiring_2180 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsQuasiring_2180 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_zero_2212
      ((T_IsNearring_2538 -> T_IsQuasiring_2180) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsNearring_2538 -> T_IsQuasiring_2180
MAlonzo.Code.Algebra.Structures.d_isQuasiring_2556
         ((T_Nearring_3648 -> T_IsNearring_2538) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Nearring_3648 -> T_IsNearring_2538
d_isNearring_3684 (T_Nearring_3648 -> AgdaAny
forall a b. a -> b
coe T_Nearring_3648
v0)))
-- Algebra.Bundles.Nearring._.zeroʳ
d_zero'691'_3764 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Nearring_3648 -> AgdaAny -> AgdaAny
d_zero'691'_3764 :: () -> () -> T_Nearring_3648 -> AgdaAny -> AgdaAny
d_zero'691'_3764 ~()
v0 ~()
v1 T_Nearring_3648
v2 = T_Nearring_3648 -> AgdaAny -> AgdaAny
du_zero'691'_3764 T_Nearring_3648
v2
du_zero'691'_3764 :: T_Nearring_3648 -> AgdaAny -> AgdaAny
du_zero'691'_3764 :: T_Nearring_3648 -> AgdaAny -> AgdaAny
du_zero'691'_3764 T_Nearring_3648
v0
  = let v1 :: T_IsNearring_2538
v1 = T_Nearring_3648 -> T_IsNearring_2538
d_isNearring_3684 (T_Nearring_3648 -> T_Nearring_3648
forall a b. a -> b
coe T_Nearring_3648
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsQuasiring_2180 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsQuasiring_2180 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_zero'691'_2256
         ((T_IsNearring_2538 -> T_IsQuasiring_2180) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearring_2538 -> T_IsQuasiring_2180
MAlonzo.Code.Algebra.Structures.d_isQuasiring_2556 (T_IsNearring_2538 -> AgdaAny
forall a b. a -> b
coe T_IsNearring_2538
v1)))
-- Algebra.Bundles.Nearring._.zeroˡ
d_zero'737'_3766 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Nearring_3648 -> AgdaAny -> AgdaAny
d_zero'737'_3766 :: () -> () -> T_Nearring_3648 -> AgdaAny -> AgdaAny
d_zero'737'_3766 ~()
v0 ~()
v1 T_Nearring_3648
v2 = T_Nearring_3648 -> AgdaAny -> AgdaAny
du_zero'737'_3766 T_Nearring_3648
v2
du_zero'737'_3766 :: T_Nearring_3648 -> AgdaAny -> AgdaAny
du_zero'737'_3766 :: T_Nearring_3648 -> AgdaAny -> AgdaAny
du_zero'737'_3766 T_Nearring_3648
v0
  = let v1 :: T_IsNearring_2538
v1 = T_Nearring_3648 -> T_IsNearring_2538
d_isNearring_3684 (T_Nearring_3648 -> T_Nearring_3648
forall a b. a -> b
coe T_Nearring_3648
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsQuasiring_2180 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsQuasiring_2180 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_zero'737'_2254
         ((T_IsNearring_2538 -> T_IsQuasiring_2180) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsNearring_2538 -> T_IsQuasiring_2180
MAlonzo.Code.Algebra.Structures.d_isQuasiring_2556 (T_IsNearring_2538 -> AgdaAny
forall a b. a -> b
coe T_IsNearring_2538
v1)))
-- Algebra.Bundles.Nearring._.⁻¹-cong
d_'8315''185''45'cong_3768 ::
  T_Nearring_3648 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8315''185''45'cong_3768 :: T_Nearring_3648 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8315''185''45'cong_3768 T_Nearring_3648
v0
  = (T_IsNearring_2538 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsNearring_2538 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8315''185''45'cong_2560
      ((T_Nearring_3648 -> T_IsNearring_2538) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Nearring_3648 -> T_IsNearring_2538
d_isNearring_3684 (T_Nearring_3648 -> AgdaAny
forall a b. a -> b
coe T_Nearring_3648
v0))
-- Algebra.Bundles.Nearring.quasiring
d_quasiring_3770 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Nearring_3648 -> T_Quasiring_3204
d_quasiring_3770 :: () -> () -> T_Nearring_3648 -> T_Quasiring_3204
d_quasiring_3770 ~()
v0 ~()
v1 T_Nearring_3648
v2 = T_Nearring_3648 -> T_Quasiring_3204
du_quasiring_3770 T_Nearring_3648
v2
du_quasiring_3770 :: T_Nearring_3648 -> T_Quasiring_3204
du_quasiring_3770 :: T_Nearring_3648 -> T_Quasiring_3204
du_quasiring_3770 T_Nearring_3648
v0
  = ((AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> AgdaAny
 -> T_IsQuasiring_2180
 -> T_Quasiring_3204)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsQuasiring_2180
-> T_Quasiring_3204
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsQuasiring_2180
-> T_Quasiring_3204
C_Quasiring'46'constructor_57285 (T_Nearring_3648 -> AgdaAny -> AgdaAny -> AgdaAny
d__'43'__3674 (T_Nearring_3648 -> T_Nearring_3648
forall a b. a -> b
coe T_Nearring_3648
v0))
      (T_Nearring_3648 -> AgdaAny -> AgdaAny -> AgdaAny
d__'42'__3676 (T_Nearring_3648 -> T_Nearring_3648
forall a b. a -> b
coe T_Nearring_3648
v0)) (T_Nearring_3648 -> AgdaAny
d_0'35'_3680 (T_Nearring_3648 -> T_Nearring_3648
forall a b. a -> b
coe T_Nearring_3648
v0))
      (T_Nearring_3648 -> AgdaAny
d_1'35'_3682 (T_Nearring_3648 -> T_Nearring_3648
forall a b. a -> b
coe T_Nearring_3648
v0))
      (T_IsNearring_2538 -> T_IsQuasiring_2180
MAlonzo.Code.Algebra.Structures.d_isQuasiring_2556
         ((T_Nearring_3648 -> T_IsNearring_2538)
-> AgdaAny -> T_IsNearring_2538
forall a b. a -> b
coe T_Nearring_3648 -> T_IsNearring_2538
d_isNearring_3684 (T_Nearring_3648 -> AgdaAny
forall a b. a -> b
coe T_Nearring_3648
v0)))
-- Algebra.Bundles.Nearring._._≉_
d__'8777'__3774 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Nearring_3648 -> AgdaAny -> AgdaAny -> ()
d__'8777'__3774 :: () -> () -> T_Nearring_3648 -> AgdaAny -> AgdaAny -> ()
d__'8777'__3774 = () -> () -> T_Nearring_3648 -> AgdaAny -> AgdaAny -> ()
forall a. a
erased
-- Algebra.Bundles.Nearring._.magma
d_magma_3776 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Nearring_3648 -> T_Magma_68
d_magma_3776 :: () -> () -> T_Nearring_3648 -> T_Magma_68
d_magma_3776 ~()
v0 ~()
v1 T_Nearring_3648
v2 = T_Nearring_3648 -> T_Magma_68
du_magma_3776 T_Nearring_3648
v2
du_magma_3776 :: T_Nearring_3648 -> T_Magma_68
du_magma_3776 :: T_Nearring_3648 -> T_Magma_68
du_magma_3776 T_Nearring_3648
v0
  = let v1 :: t
v1 = (T_Nearring_3648 -> T_Quasiring_3204) -> AgdaAny -> t
forall a b. a -> b
coe T_Nearring_3648 -> T_Quasiring_3204
du_quasiring_3770 (T_Nearring_3648 -> AgdaAny
forall a b. a -> b
coe T_Nearring_3648
v0) in
    AgdaAny -> T_Magma_68
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_Quasiring_3204 -> T_Monoid_882) -> AgdaAny -> t
forall a b. a -> b
coe T_Quasiring_3204 -> T_Monoid_882
du_'42''45'monoid_3328 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_Semigroup_536 -> T_Magma_68) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semigroup_536 -> T_Magma_68
du_magma_584 ((T_Monoid_882 -> T_Semigroup_536) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Monoid_882 -> T_Semigroup_536
du_semigroup_944 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2))))
-- Algebra.Bundles.Nearring._.*-monoid
d_'42''45'monoid_3778 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Nearring_3648 -> T_Monoid_882
d_'42''45'monoid_3778 :: () -> () -> T_Nearring_3648 -> T_Monoid_882
d_'42''45'monoid_3778 ~()
v0 ~()
v1 T_Nearring_3648
v2 = T_Nearring_3648 -> T_Monoid_882
du_'42''45'monoid_3778 T_Nearring_3648
v2
du_'42''45'monoid_3778 :: T_Nearring_3648 -> T_Monoid_882
du_'42''45'monoid_3778 :: T_Nearring_3648 -> T_Monoid_882
du_'42''45'monoid_3778 T_Nearring_3648
v0
  = (T_Quasiring_3204 -> T_Monoid_882) -> AgdaAny -> T_Monoid_882
forall a b. a -> b
coe T_Quasiring_3204 -> T_Monoid_882
du_'42''45'monoid_3328 ((T_Nearring_3648 -> T_Quasiring_3204) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Nearring_3648 -> T_Quasiring_3204
du_quasiring_3770 (T_Nearring_3648 -> AgdaAny
forall a b. a -> b
coe T_Nearring_3648
v0))
-- Algebra.Bundles.Nearring._.rawMagma
d_rawMagma_3780 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Nearring_3648 -> MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
d_rawMagma_3780 :: () -> () -> T_Nearring_3648 -> T_RawMagma_36
d_rawMagma_3780 ~()
v0 ~()
v1 T_Nearring_3648
v2 = T_Nearring_3648 -> T_RawMagma_36
du_rawMagma_3780 T_Nearring_3648
v2
du_rawMagma_3780 ::
  T_Nearring_3648 -> MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
du_rawMagma_3780 :: T_Nearring_3648 -> T_RawMagma_36
du_rawMagma_3780 T_Nearring_3648
v0
  = let v1 :: t
v1 = (T_Nearring_3648 -> T_Quasiring_3204) -> AgdaAny -> t
forall a b. a -> b
coe T_Nearring_3648 -> T_Quasiring_3204
du_quasiring_3770 (T_Nearring_3648 -> AgdaAny
forall a b. a -> b
coe T_Nearring_3648
v0) in
    AgdaAny -> T_RawMagma_36
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_Quasiring_3204 -> T_Monoid_882) -> AgdaAny -> t
forall a b. a -> b
coe T_Quasiring_3204 -> T_Monoid_882
du_'42''45'monoid_3328 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: t
v3 = (T_Monoid_882 -> T_Semigroup_536) -> AgdaAny -> t
forall a b. a -> b
coe T_Monoid_882 -> T_Semigroup_536
du_semigroup_944 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_Magma_68 -> T_RawMagma_36) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Magma_68 -> T_RawMagma_36
du_rawMagma_112 ((T_Semigroup_536 -> T_Magma_68) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semigroup_536 -> T_Magma_68
du_magma_584 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3)))))
-- Algebra.Bundles.Nearring._.semigroup
d_semigroup_3782 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Nearring_3648 -> T_Semigroup_536
d_semigroup_3782 :: () -> () -> T_Nearring_3648 -> T_Semigroup_536
d_semigroup_3782 ~()
v0 ~()
v1 T_Nearring_3648
v2 = T_Nearring_3648 -> T_Semigroup_536
du_semigroup_3782 T_Nearring_3648
v2
du_semigroup_3782 :: T_Nearring_3648 -> T_Semigroup_536
du_semigroup_3782 :: T_Nearring_3648 -> T_Semigroup_536
du_semigroup_3782 T_Nearring_3648
v0
  = let v1 :: t
v1 = (T_Nearring_3648 -> T_Quasiring_3204) -> AgdaAny -> t
forall a b. a -> b
coe T_Nearring_3648 -> T_Quasiring_3204
du_quasiring_3770 (T_Nearring_3648 -> AgdaAny
forall a b. a -> b
coe T_Nearring_3648
v0) in
    AgdaAny -> T_Semigroup_536
forall a b. a -> b
coe ((T_Monoid_882 -> T_Semigroup_536) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Monoid_882 -> T_Semigroup_536
du_semigroup_944 ((T_Quasiring_3204 -> T_Monoid_882) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Quasiring_3204 -> T_Monoid_882
du_'42''45'monoid_3328 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1)))
-- Algebra.Bundles.Nearring._.magma
d_magma_3784 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Nearring_3648 -> T_Magma_68
d_magma_3784 :: () -> () -> T_Nearring_3648 -> T_Magma_68
d_magma_3784 ~()
v0 ~()
v1 T_Nearring_3648
v2 = T_Nearring_3648 -> T_Magma_68
du_magma_3784 T_Nearring_3648
v2
du_magma_3784 :: T_Nearring_3648 -> T_Magma_68
du_magma_3784 :: T_Nearring_3648 -> T_Magma_68
du_magma_3784 T_Nearring_3648
v0
  = let v1 :: t
v1 = (T_Nearring_3648 -> T_Quasiring_3204) -> AgdaAny -> t
forall a b. a -> b
coe T_Nearring_3648 -> T_Quasiring_3204
du_quasiring_3770 (T_Nearring_3648 -> AgdaAny
forall a b. a -> b
coe T_Nearring_3648
v0) in
    AgdaAny -> T_Magma_68
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_Quasiring_3204 -> T_Monoid_882) -> AgdaAny -> t
forall a b. a -> b
coe T_Quasiring_3204 -> T_Monoid_882
du_'43''45'monoid_3312 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_Semigroup_536 -> T_Magma_68) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semigroup_536 -> T_Magma_68
du_magma_584 ((T_Monoid_882 -> T_Semigroup_536) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Monoid_882 -> T_Semigroup_536
du_semigroup_944 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2))))
-- Algebra.Bundles.Nearring._.+-monoid
d_'43''45'monoid_3786 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Nearring_3648 -> T_Monoid_882
d_'43''45'monoid_3786 :: () -> () -> T_Nearring_3648 -> T_Monoid_882
d_'43''45'monoid_3786 ~()
v0 ~()
v1 T_Nearring_3648
v2 = T_Nearring_3648 -> T_Monoid_882
du_'43''45'monoid_3786 T_Nearring_3648
v2
du_'43''45'monoid_3786 :: T_Nearring_3648 -> T_Monoid_882
du_'43''45'monoid_3786 :: T_Nearring_3648 -> T_Monoid_882
du_'43''45'monoid_3786 T_Nearring_3648
v0
  = (T_Quasiring_3204 -> T_Monoid_882) -> AgdaAny -> T_Monoid_882
forall a b. a -> b
coe T_Quasiring_3204 -> T_Monoid_882
du_'43''45'monoid_3312 ((T_Nearring_3648 -> T_Quasiring_3204) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Nearring_3648 -> T_Quasiring_3204
du_quasiring_3770 (T_Nearring_3648 -> AgdaAny
forall a b. a -> b
coe T_Nearring_3648
v0))
-- Algebra.Bundles.Nearring._.rawMagma
d_rawMagma_3788 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Nearring_3648 -> MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
d_rawMagma_3788 :: () -> () -> T_Nearring_3648 -> T_RawMagma_36
d_rawMagma_3788 ~()
v0 ~()
v1 T_Nearring_3648
v2 = T_Nearring_3648 -> T_RawMagma_36
du_rawMagma_3788 T_Nearring_3648
v2
du_rawMagma_3788 ::
  T_Nearring_3648 -> MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
du_rawMagma_3788 :: T_Nearring_3648 -> T_RawMagma_36
du_rawMagma_3788 T_Nearring_3648
v0
  = let v1 :: t
v1 = (T_Nearring_3648 -> T_Quasiring_3204) -> AgdaAny -> t
forall a b. a -> b
coe T_Nearring_3648 -> T_Quasiring_3204
du_quasiring_3770 (T_Nearring_3648 -> AgdaAny
forall a b. a -> b
coe T_Nearring_3648
v0) in
    AgdaAny -> T_RawMagma_36
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_Quasiring_3204 -> T_Monoid_882) -> AgdaAny -> t
forall a b. a -> b
coe T_Quasiring_3204 -> T_Monoid_882
du_'43''45'monoid_3312 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: t
v3 = (T_Monoid_882 -> T_Semigroup_536) -> AgdaAny -> t
forall a b. a -> b
coe T_Monoid_882 -> T_Semigroup_536
du_semigroup_944 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_Magma_68 -> T_RawMagma_36) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Magma_68 -> T_RawMagma_36
du_rawMagma_112 ((T_Semigroup_536 -> T_Magma_68) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semigroup_536 -> T_Magma_68
du_magma_584 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3)))))
-- Algebra.Bundles.Nearring._.rawMonoid
d_rawMonoid_3790 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Nearring_3648 -> MAlonzo.Code.Algebra.Bundles.Raw.T_RawMonoid_64
d_rawMonoid_3790 :: () -> () -> T_Nearring_3648 -> T_RawMonoid_64
d_rawMonoid_3790 ~()
v0 ~()
v1 T_Nearring_3648
v2 = T_Nearring_3648 -> T_RawMonoid_64
du_rawMonoid_3790 T_Nearring_3648
v2
du_rawMonoid_3790 ::
  T_Nearring_3648 -> MAlonzo.Code.Algebra.Bundles.Raw.T_RawMonoid_64
du_rawMonoid_3790 :: T_Nearring_3648 -> T_RawMonoid_64
du_rawMonoid_3790 T_Nearring_3648
v0
  = let v1 :: t
v1 = (T_Nearring_3648 -> T_Quasiring_3204) -> AgdaAny -> t
forall a b. a -> b
coe T_Nearring_3648 -> T_Quasiring_3204
du_quasiring_3770 (T_Nearring_3648 -> AgdaAny
forall a b. a -> b
coe T_Nearring_3648
v0) in
    AgdaAny -> T_RawMonoid_64
forall a b. a -> b
coe ((T_Monoid_882 -> T_RawMonoid_64) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Monoid_882 -> T_RawMonoid_64
du_rawMonoid_954 ((T_Quasiring_3204 -> T_Monoid_882) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Quasiring_3204 -> T_Monoid_882
du_'43''45'monoid_3312 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1)))
-- Algebra.Bundles.Nearring._.semigroup
d_semigroup_3792 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Nearring_3648 -> T_Semigroup_536
d_semigroup_3792 :: () -> () -> T_Nearring_3648 -> T_Semigroup_536
d_semigroup_3792 ~()
v0 ~()
v1 T_Nearring_3648
v2 = T_Nearring_3648 -> T_Semigroup_536
du_semigroup_3792 T_Nearring_3648
v2
du_semigroup_3792 :: T_Nearring_3648 -> T_Semigroup_536
du_semigroup_3792 :: T_Nearring_3648 -> T_Semigroup_536
du_semigroup_3792 T_Nearring_3648
v0
  = let v1 :: t
v1 = (T_Nearring_3648 -> T_Quasiring_3204) -> AgdaAny -> t
forall a b. a -> b
coe T_Nearring_3648 -> T_Quasiring_3204
du_quasiring_3770 (T_Nearring_3648 -> AgdaAny
forall a b. a -> b
coe T_Nearring_3648
v0) in
    AgdaAny -> T_Semigroup_536
forall a b. a -> b
coe ((T_Monoid_882 -> T_Semigroup_536) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Monoid_882 -> T_Semigroup_536
du_semigroup_944 ((T_Quasiring_3204 -> T_Monoid_882) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Quasiring_3204 -> T_Monoid_882
du_'43''45'monoid_3312 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1)))
-- Algebra.Bundles.Nearring._.unitalMagma
d_unitalMagma_3794 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Nearring_3648 -> T_UnitalMagma_814
d_unitalMagma_3794 :: () -> () -> T_Nearring_3648 -> T_UnitalMagma_814
d_unitalMagma_3794 ~()
v0 ~()
v1 T_Nearring_3648
v2 = T_Nearring_3648 -> T_UnitalMagma_814
du_unitalMagma_3794 T_Nearring_3648
v2
du_unitalMagma_3794 :: T_Nearring_3648 -> T_UnitalMagma_814
du_unitalMagma_3794 :: T_Nearring_3648 -> T_UnitalMagma_814
du_unitalMagma_3794 T_Nearring_3648
v0
  = let v1 :: t
v1 = (T_Nearring_3648 -> T_Quasiring_3204) -> AgdaAny -> t
forall a b. a -> b
coe T_Nearring_3648 -> T_Quasiring_3204
du_quasiring_3770 (T_Nearring_3648 -> AgdaAny
forall a b. a -> b
coe T_Nearring_3648
v0) in
    AgdaAny -> T_UnitalMagma_814
forall a b. a -> b
coe ((T_Monoid_882 -> T_UnitalMagma_814) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Monoid_882 -> T_UnitalMagma_814
du_unitalMagma_956 ((T_Quasiring_3204 -> T_Monoid_882) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Quasiring_3204 -> T_Monoid_882
du_'43''45'monoid_3312 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1)))
-- Algebra.Bundles.Ring
d_Ring_3800 :: p -> p -> ()
d_Ring_3800 p
a0 p
a1 = ()
data T_Ring_3800
  = C_Ring'46'constructor_68489 (AgdaAny -> AgdaAny -> AgdaAny)
                                (AgdaAny -> AgdaAny -> AgdaAny) (AgdaAny -> AgdaAny) AgdaAny
                                AgdaAny MAlonzo.Code.Algebra.Structures.T_IsRing_2650
-- Algebra.Bundles.Ring.Carrier
d_Carrier_3822 :: T_Ring_3800 -> ()
d_Carrier_3822 :: T_Ring_3800 -> ()
d_Carrier_3822 = T_Ring_3800 -> ()
forall a. a
erased
-- Algebra.Bundles.Ring._≈_
d__'8776'__3824 :: T_Ring_3800 -> AgdaAny -> AgdaAny -> ()
d__'8776'__3824 :: T_Ring_3800 -> AgdaAny -> AgdaAny -> ()
d__'8776'__3824 = T_Ring_3800 -> AgdaAny -> AgdaAny -> ()
forall a. a
erased
-- Algebra.Bundles.Ring._+_
d__'43'__3826 :: T_Ring_3800 -> AgdaAny -> AgdaAny -> AgdaAny
d__'43'__3826 :: T_Ring_3800 -> AgdaAny -> AgdaAny -> AgdaAny
d__'43'__3826 T_Ring_3800
v0
  = case T_Ring_3800 -> T_Ring_3800
forall a b. a -> b
coe T_Ring_3800
v0 of
      C_Ring'46'constructor_68489 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny
v5 AgdaAny
v6 AgdaAny
v7 T_IsRing_2650
v8 -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v3
      T_Ring_3800
_ -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.Ring._*_
d__'42'__3828 :: T_Ring_3800 -> AgdaAny -> AgdaAny -> AgdaAny
d__'42'__3828 :: T_Ring_3800 -> AgdaAny -> AgdaAny -> AgdaAny
d__'42'__3828 T_Ring_3800
v0
  = case T_Ring_3800 -> T_Ring_3800
forall a b. a -> b
coe T_Ring_3800
v0 of
      C_Ring'46'constructor_68489 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny
v5 AgdaAny
v6 AgdaAny
v7 T_IsRing_2650
v8 -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v4
      T_Ring_3800
_ -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.Ring.-_
d_'45'__3830 :: T_Ring_3800 -> AgdaAny -> AgdaAny
d_'45'__3830 :: T_Ring_3800 -> AgdaAny -> AgdaAny
d_'45'__3830 T_Ring_3800
v0
  = case T_Ring_3800 -> T_Ring_3800
forall a b. a -> b
coe T_Ring_3800
v0 of
      C_Ring'46'constructor_68489 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny
v5 AgdaAny
v6 AgdaAny
v7 T_IsRing_2650
v8 -> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v5
      T_Ring_3800
_ -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.Ring.0#
d_0'35'_3832 :: T_Ring_3800 -> AgdaAny
d_0'35'_3832 :: T_Ring_3800 -> AgdaAny
d_0'35'_3832 T_Ring_3800
v0
  = case T_Ring_3800 -> T_Ring_3800
forall a b. a -> b
coe T_Ring_3800
v0 of
      C_Ring'46'constructor_68489 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny
v5 AgdaAny
v6 AgdaAny
v7 T_IsRing_2650
v8 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v6
      T_Ring_3800
_ -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.Ring.1#
d_1'35'_3834 :: T_Ring_3800 -> AgdaAny
d_1'35'_3834 :: T_Ring_3800 -> AgdaAny
d_1'35'_3834 T_Ring_3800
v0
  = case T_Ring_3800 -> T_Ring_3800
forall a b. a -> b
coe T_Ring_3800
v0 of
      C_Ring'46'constructor_68489 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny
v5 AgdaAny
v6 AgdaAny
v7 T_IsRing_2650
v8 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v7
      T_Ring_3800
_ -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.Ring.isRing
d_isRing_3836 ::
  T_Ring_3800 -> MAlonzo.Code.Algebra.Structures.T_IsRing_2650
d_isRing_3836 :: T_Ring_3800 -> T_IsRing_2650
d_isRing_3836 T_Ring_3800
v0
  = case T_Ring_3800 -> T_Ring_3800
forall a b. a -> b
coe T_Ring_3800
v0 of
      C_Ring'46'constructor_68489 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny
v5 AgdaAny
v6 AgdaAny
v7 T_IsRing_2650
v8 -> T_IsRing_2650 -> T_IsRing_2650
forall a b. a -> b
coe T_IsRing_2650
v8
      T_Ring_3800
_ -> T_IsRing_2650
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.Ring._._//_
d__'47''47'__3840 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Ring_3800 -> AgdaAny -> AgdaAny -> AgdaAny
d__'47''47'__3840 :: () -> () -> T_Ring_3800 -> AgdaAny -> AgdaAny -> AgdaAny
d__'47''47'__3840 ~()
v0 ~()
v1 T_Ring_3800
v2 = T_Ring_3800 -> AgdaAny -> AgdaAny -> AgdaAny
du__'47''47'__3840 T_Ring_3800
v2
du__'47''47'__3840 :: T_Ring_3800 -> AgdaAny -> AgdaAny -> AgdaAny
du__'47''47'__3840 :: T_Ring_3800 -> AgdaAny -> AgdaAny -> AgdaAny
du__'47''47'__3840 T_Ring_3800
v0
  = let v1 :: AgdaAny -> AgdaAny -> AgdaAny
v1 = T_Ring_3800 -> AgdaAny -> AgdaAny -> AgdaAny
d__'43'__3826 (T_Ring_3800 -> T_Ring_3800
forall a b. a -> b
coe T_Ring_3800
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: AgdaAny -> AgdaAny
v2 = T_Ring_3800 -> AgdaAny -> AgdaAny
d_'45'__3830 (T_Ring_3800 -> T_Ring_3800
forall a b. a -> b
coe T_Ring_3800
v0) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (((AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du__'47''47'__1098 ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v1)
            ((AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v2)))
-- Algebra.Bundles.Ring._.*-assoc
d_'42''45'assoc_3842 ::
  T_Ring_3800 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'assoc_3842 :: T_Ring_3800 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'assoc_3842 T_Ring_3800
v0
  = (T_IsRing_2650 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsRing_2650 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'42''45'assoc_2676
      ((T_Ring_3800 -> T_IsRing_2650) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Ring_3800 -> T_IsRing_2650
d_isRing_3836 (T_Ring_3800 -> AgdaAny
forall a b. a -> b
coe T_Ring_3800
v0))
-- Algebra.Bundles.Ring._.*-cong
d_'42''45'cong_3844 ::
  T_Ring_3800 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'cong_3844 :: T_Ring_3800
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'42''45'cong_3844 T_Ring_3800
v0
  = (T_IsRing_2650
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsRing_2650
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'42''45'cong_2674
      ((T_Ring_3800 -> T_IsRing_2650) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Ring_3800 -> T_IsRing_2650
d_isRing_3836 (T_Ring_3800 -> AgdaAny
forall a b. a -> b
coe T_Ring_3800
v0))
-- Algebra.Bundles.Ring._.∙-congʳ
d_'8729''45'cong'691'_3846 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Ring_3800 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_3846 :: ()
-> ()
-> T_Ring_3800
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_3846 ~()
v0 ~()
v1 T_Ring_3800
v2
  = T_Ring_3800 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_3846 T_Ring_3800
v2
du_'8729''45'cong'691'_3846 ::
  T_Ring_3800 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_3846 :: T_Ring_3800 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_3846 T_Ring_3800
v0
  = let v1 :: T_IsRing_2650
v1 = T_Ring_3800 -> T_IsRing_2650
d_isRing_3836 (T_Ring_3800 -> T_Ring_3800
forall a b. a -> b
coe T_Ring_3800
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: t
v2
             = (T_IsRing_2650 -> T_IsRingWithoutOne_2286) -> AgdaAny -> t
forall a b. a -> b
coe
                 T_IsRing_2650 -> T_IsRingWithoutOne_2286
MAlonzo.Code.Algebra.Structures.du_isRingWithoutOne_2682
                 (T_IsRing_2650 -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: t
v3
                = (T_IsRingWithoutOne_2286 -> T_IsSemigroup_472) -> AgdaAny -> t
forall a b. a -> b
coe
                    T_IsRingWithoutOne_2286 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.du_'42''45'isSemigroup_2390
                    (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'691'_206
               ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3)))))
-- Algebra.Bundles.Ring._.∙-congˡ
d_'8729''45'cong'737'_3848 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Ring_3800 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_3848 :: ()
-> ()
-> T_Ring_3800
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_3848 ~()
v0 ~()
v1 T_Ring_3800
v2
  = T_Ring_3800 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_3848 T_Ring_3800
v2
du_'8729''45'cong'737'_3848 ::
  T_Ring_3800 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_3848 :: T_Ring_3800 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_3848 T_Ring_3800
v0
  = let v1 :: T_IsRing_2650
v1 = T_Ring_3800 -> T_IsRing_2650
d_isRing_3836 (T_Ring_3800 -> T_Ring_3800
forall a b. a -> b
coe T_Ring_3800
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: t
v2
             = (T_IsRing_2650 -> T_IsRingWithoutOne_2286) -> AgdaAny -> t
forall a b. a -> b
coe
                 T_IsRing_2650 -> T_IsRingWithoutOne_2286
MAlonzo.Code.Algebra.Structures.du_isRingWithoutOne_2682
                 (T_IsRing_2650 -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: t
v3
                = (T_IsRingWithoutOne_2286 -> T_IsSemigroup_472) -> AgdaAny -> t
forall a b. a -> b
coe
                    T_IsRingWithoutOne_2286 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.du_'42''45'isSemigroup_2390
                    (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'737'_202
               ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3)))))
-- Algebra.Bundles.Ring._.*-identity
d_'42''45'identity_3850 ::
  T_Ring_3800 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'42''45'identity_3850 :: T_Ring_3800 -> T_Σ_14
d_'42''45'identity_3850 T_Ring_3800
v0
  = (T_IsRing_2650 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsRing_2650 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_'42''45'identity_2678
      ((T_Ring_3800 -> T_IsRing_2650) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Ring_3800 -> T_IsRing_2650
d_isRing_3836 (T_Ring_3800 -> AgdaAny
forall a b. a -> b
coe T_Ring_3800
v0))
-- Algebra.Bundles.Ring._.identityʳ
d_identity'691'_3852 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Ring_3800 -> AgdaAny -> AgdaAny
d_identity'691'_3852 :: () -> () -> T_Ring_3800 -> AgdaAny -> AgdaAny
d_identity'691'_3852 ~()
v0 ~()
v1 T_Ring_3800
v2 = T_Ring_3800 -> AgdaAny -> AgdaAny
du_identity'691'_3852 T_Ring_3800
v2
du_identity'691'_3852 :: T_Ring_3800 -> AgdaAny -> AgdaAny
du_identity'691'_3852 :: T_Ring_3800 -> AgdaAny -> AgdaAny
du_identity'691'_3852 T_Ring_3800
v0
  = let v1 :: T_IsRing_2650
v1 = T_Ring_3800 -> T_IsRing_2650
d_isRing_3836 (T_Ring_3800 -> T_Ring_3800
forall a b. a -> b
coe T_Ring_3800
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsMonoid_686 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoid_686 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_identity'691'_728
         ((T_IsRing_2650 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsRing_2650 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.du_'42''45'isMonoid_2768 (T_IsRing_2650 -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650
v1)))
-- Algebra.Bundles.Ring._.identityˡ
d_identity'737'_3854 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Ring_3800 -> AgdaAny -> AgdaAny
d_identity'737'_3854 :: () -> () -> T_Ring_3800 -> AgdaAny -> AgdaAny
d_identity'737'_3854 ~()
v0 ~()
v1 T_Ring_3800
v2 = T_Ring_3800 -> AgdaAny -> AgdaAny
du_identity'737'_3854 T_Ring_3800
v2
du_identity'737'_3854 :: T_Ring_3800 -> AgdaAny -> AgdaAny
du_identity'737'_3854 :: T_Ring_3800 -> AgdaAny -> AgdaAny
du_identity'737'_3854 T_Ring_3800
v0
  = let v1 :: T_IsRing_2650
v1 = T_Ring_3800 -> T_IsRing_2650
d_isRing_3836 (T_Ring_3800 -> T_Ring_3800
forall a b. a -> b
coe T_Ring_3800
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsMonoid_686 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoid_686 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_identity'737'_726
         ((T_IsRing_2650 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsRing_2650 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.du_'42''45'isMonoid_2768 (T_IsRing_2650 -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650
v1)))
-- Algebra.Bundles.Ring._.*-isMagma
d_'42''45'isMagma_3856 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Ring_3800 -> MAlonzo.Code.Algebra.Structures.T_IsMagma_176
d_'42''45'isMagma_3856 :: () -> () -> T_Ring_3800 -> T_IsMagma_176
d_'42''45'isMagma_3856 ~()
v0 ~()
v1 T_Ring_3800
v2 = T_Ring_3800 -> T_IsMagma_176
du_'42''45'isMagma_3856 T_Ring_3800
v2
du_'42''45'isMagma_3856 ::
  T_Ring_3800 -> MAlonzo.Code.Algebra.Structures.T_IsMagma_176
du_'42''45'isMagma_3856 :: T_Ring_3800 -> T_IsMagma_176
du_'42''45'isMagma_3856 T_Ring_3800
v0
  = let v1 :: T_IsRing_2650
v1 = T_Ring_3800 -> T_IsRing_2650
d_isRing_3836 (T_Ring_3800 -> T_Ring_3800
forall a b. a -> b
coe T_Ring_3800
v0) in
    AgdaAny -> T_IsMagma_176
forall a b. a -> b
coe
      ((T_IsRingWithoutOne_2286 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsRingWithoutOne_2286 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.du_'42''45'isMagma_2388
         ((T_IsRing_2650 -> T_IsRingWithoutOne_2286) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsRing_2650 -> T_IsRingWithoutOne_2286
MAlonzo.Code.Algebra.Structures.du_isRingWithoutOne_2682 (T_IsRing_2650 -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650
v1)))
-- Algebra.Bundles.Ring._.*-isMonoid
d_'42''45'isMonoid_3858 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Ring_3800 -> MAlonzo.Code.Algebra.Structures.T_IsMonoid_686
d_'42''45'isMonoid_3858 :: () -> () -> T_Ring_3800 -> T_IsMonoid_686
d_'42''45'isMonoid_3858 ~()
v0 ~()
v1 T_Ring_3800
v2 = T_Ring_3800 -> T_IsMonoid_686
du_'42''45'isMonoid_3858 T_Ring_3800
v2
du_'42''45'isMonoid_3858 ::
  T_Ring_3800 -> MAlonzo.Code.Algebra.Structures.T_IsMonoid_686
du_'42''45'isMonoid_3858 :: T_Ring_3800 -> T_IsMonoid_686
du_'42''45'isMonoid_3858 T_Ring_3800
v0
  = (T_IsRing_2650 -> T_IsMonoid_686) -> AgdaAny -> T_IsMonoid_686
forall a b. a -> b
coe
      T_IsRing_2650 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.du_'42''45'isMonoid_2768
      ((T_Ring_3800 -> T_IsRing_2650) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Ring_3800 -> T_IsRing_2650
d_isRing_3836 (T_Ring_3800 -> AgdaAny
forall a b. a -> b
coe T_Ring_3800
v0))
-- Algebra.Bundles.Ring._.*-isSemigroup
d_'42''45'isSemigroup_3860 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Ring_3800 -> MAlonzo.Code.Algebra.Structures.T_IsSemigroup_472
d_'42''45'isSemigroup_3860 :: () -> () -> T_Ring_3800 -> T_IsSemigroup_472
d_'42''45'isSemigroup_3860 ~()
v0 ~()
v1 T_Ring_3800
v2
  = T_Ring_3800 -> T_IsSemigroup_472
du_'42''45'isSemigroup_3860 T_Ring_3800
v2
du_'42''45'isSemigroup_3860 ::
  T_Ring_3800 -> MAlonzo.Code.Algebra.Structures.T_IsSemigroup_472
du_'42''45'isSemigroup_3860 :: T_Ring_3800 -> T_IsSemigroup_472
du_'42''45'isSemigroup_3860 T_Ring_3800
v0
  = let v1 :: T_IsRing_2650
v1 = T_Ring_3800 -> T_IsRing_2650
d_isRing_3836 (T_Ring_3800 -> T_Ring_3800
forall a b. a -> b
coe T_Ring_3800
v0) in
    AgdaAny -> T_IsSemigroup_472
forall a b. a -> b
coe
      ((T_IsRingWithoutOne_2286 -> T_IsSemigroup_472)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsRingWithoutOne_2286 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.du_'42''45'isSemigroup_2390
         ((T_IsRing_2650 -> T_IsRingWithoutOne_2286) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsRing_2650 -> T_IsRingWithoutOne_2286
MAlonzo.Code.Algebra.Structures.du_isRingWithoutOne_2682 (T_IsRing_2650 -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650
v1)))
-- Algebra.Bundles.Ring._.assoc
d_assoc_3862 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Ring_3800 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_3862 :: () -> () -> T_Ring_3800 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_3862 ~()
v0 ~()
v1 T_Ring_3800
v2 = T_Ring_3800 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_assoc_3862 T_Ring_3800
v2
du_assoc_3862 ::
  T_Ring_3800 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_assoc_3862 :: T_Ring_3800 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_assoc_3862 T_Ring_3800
v0
  = let v1 :: T_IsRing_2650
v1 = T_Ring_3800 -> T_IsRing_2650
d_isRing_3836 (T_Ring_3800 -> T_Ring_3800
forall a b. a -> b
coe T_Ring_3800
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsSemigroup_472 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_472 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_assoc_482
         ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
            ((T_IsGroup_1036 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsGroup_1036 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_1050
               ((T_IsAbelianGroup_1132 -> T_IsGroup_1036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsAbelianGroup_1132 -> T_IsGroup_1036
MAlonzo.Code.Algebra.Structures.d_isGroup_1144
                  ((T_IsRing_2650 -> T_IsAbelianGroup_1132) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsRing_2650 -> T_IsAbelianGroup_1132
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2672
                     (T_IsRing_2650 -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650
v1))))))
-- Algebra.Bundles.Ring._.comm
d_comm_3864 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Ring_3800 -> AgdaAny -> AgdaAny -> AgdaAny
d_comm_3864 :: () -> () -> T_Ring_3800 -> AgdaAny -> AgdaAny -> AgdaAny
d_comm_3864 ~()
v0 ~()
v1 T_Ring_3800
v2 = T_Ring_3800 -> AgdaAny -> AgdaAny -> AgdaAny
du_comm_3864 T_Ring_3800
v2
du_comm_3864 :: T_Ring_3800 -> AgdaAny -> AgdaAny -> AgdaAny
du_comm_3864 :: T_Ring_3800 -> AgdaAny -> AgdaAny -> AgdaAny
du_comm_3864 T_Ring_3800
v0
  = let v1 :: T_IsRing_2650
v1 = T_Ring_3800 -> T_IsRing_2650
d_isRing_3836 (T_Ring_3800 -> T_Ring_3800
forall a b. a -> b
coe T_Ring_3800
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsAbelianGroup_1132 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsAbelianGroup_1132 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_comm_1146
         ((T_IsRing_2650 -> T_IsAbelianGroup_1132) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsRing_2650 -> T_IsAbelianGroup_1132
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2672
            (T_IsRing_2650 -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650
v1)))
-- Algebra.Bundles.Ring._.∙-cong
d_'8729''45'cong_3866 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Ring_3800 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_3866 :: ()
-> ()
-> T_Ring_3800
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_3866 ~()
v0 ~()
v1 T_Ring_3800
v2 = T_Ring_3800
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_'8729''45'cong_3866 T_Ring_3800
v2
du_'8729''45'cong_3866 ::
  T_Ring_3800 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong_3866 :: T_Ring_3800
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_'8729''45'cong_3866 T_Ring_3800
v0
  = let v1 :: T_IsRing_2650
v1 = T_Ring_3800 -> T_IsRing_2650
d_isRing_3836 (T_Ring_3800 -> T_Ring_3800
forall a b. a -> b
coe T_Ring_3800
v0) in
    AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      ((T_IsMagma_176
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_186
         ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480
            ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
               ((T_IsGroup_1036 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsGroup_1036 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_1050
                  ((T_IsAbelianGroup_1132 -> T_IsGroup_1036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsAbelianGroup_1132 -> T_IsGroup_1036
MAlonzo.Code.Algebra.Structures.d_isGroup_1144
                     ((T_IsRing_2650 -> T_IsAbelianGroup_1132) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsRing_2650 -> T_IsAbelianGroup_1132
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2672
                        (T_IsRing_2650 -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650
v1)))))))
-- Algebra.Bundles.Ring._.∙-congʳ
d_'8729''45'cong'691'_3868 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Ring_3800 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_3868 :: ()
-> ()
-> T_Ring_3800
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_3868 ~()
v0 ~()
v1 T_Ring_3800
v2
  = T_Ring_3800 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_3868 T_Ring_3800
v2
du_'8729''45'cong'691'_3868 ::
  T_Ring_3800 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_3868 :: T_Ring_3800 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_3868 T_Ring_3800
v0
  = let v1 :: T_IsRing_2650
v1 = T_Ring_3800 -> T_IsRing_2650
d_isRing_3836 (T_Ring_3800 -> T_Ring_3800
forall a b. a -> b
coe T_Ring_3800
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: t
v2
             = (T_IsRing_2650 -> T_IsRingWithoutOne_2286) -> AgdaAny -> t
forall a b. a -> b
coe
                 T_IsRing_2650 -> T_IsRingWithoutOne_2286
MAlonzo.Code.Algebra.Structures.du_isRingWithoutOne_2682
                 (T_IsRing_2650 -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsAbelianGroup_1132
v3
                = T_IsRingWithoutOne_2286 -> T_IsAbelianGroup_1132
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2304
                    (AgdaAny -> T_IsRingWithoutOne_2286
forall a b. a -> b
coe AgdaAny
forall a. a
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsGroup_1036
v4
                   = T_IsAbelianGroup_1132 -> T_IsGroup_1036
MAlonzo.Code.Algebra.Structures.d_isGroup_1144 (T_IsAbelianGroup_1132 -> T_IsAbelianGroup_1132
forall a b. a -> b
coe T_IsAbelianGroup_1132
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsMonoid_686
v5
                      = T_IsGroup_1036 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_1050 (T_IsGroup_1036 -> T_IsGroup_1036
forall a b. a -> b
coe T_IsGroup_1036
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (let v6 :: T_IsSemigroup_472
v6
                         = T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v5) in
                   AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'691'_206
                        ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v6))))))))
-- Algebra.Bundles.Ring._.∙-congˡ
d_'8729''45'cong'737'_3870 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Ring_3800 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_3870 :: ()
-> ()
-> T_Ring_3800
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_3870 ~()
v0 ~()
v1 T_Ring_3800
v2
  = T_Ring_3800 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_3870 T_Ring_3800
v2
du_'8729''45'cong'737'_3870 ::
  T_Ring_3800 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_3870 :: T_Ring_3800 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_3870 T_Ring_3800
v0
  = let v1 :: T_IsRing_2650
v1 = T_Ring_3800 -> T_IsRing_2650
d_isRing_3836 (T_Ring_3800 -> T_Ring_3800
forall a b. a -> b
coe T_Ring_3800
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: t
v2
             = (T_IsRing_2650 -> T_IsRingWithoutOne_2286) -> AgdaAny -> t
forall a b. a -> b
coe
                 T_IsRing_2650 -> T_IsRingWithoutOne_2286
MAlonzo.Code.Algebra.Structures.du_isRingWithoutOne_2682
                 (T_IsRing_2650 -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsAbelianGroup_1132
v3
                = T_IsRingWithoutOne_2286 -> T_IsAbelianGroup_1132
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2304
                    (AgdaAny -> T_IsRingWithoutOne_2286
forall a b. a -> b
coe AgdaAny
forall a. a
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsGroup_1036
v4
                   = T_IsAbelianGroup_1132 -> T_IsGroup_1036
MAlonzo.Code.Algebra.Structures.d_isGroup_1144 (T_IsAbelianGroup_1132 -> T_IsAbelianGroup_1132
forall a b. a -> b
coe T_IsAbelianGroup_1132
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsMonoid_686
v5
                      = T_IsGroup_1036 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_1050 (T_IsGroup_1036 -> T_IsGroup_1036
forall a b. a -> b
coe T_IsGroup_1036
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (let v6 :: T_IsSemigroup_472
v6
                         = T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v5) in
                   AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'737'_202
                        ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v6))))))))
-- Algebra.Bundles.Ring._.identity
d_identity_3872 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Ring_3800 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_identity_3872 :: () -> () -> T_Ring_3800 -> T_Σ_14
d_identity_3872 ~()
v0 ~()
v1 T_Ring_3800
v2 = T_Ring_3800 -> T_Σ_14
du_identity_3872 T_Ring_3800
v2
du_identity_3872 ::
  T_Ring_3800 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
du_identity_3872 :: T_Ring_3800 -> T_Σ_14
du_identity_3872 T_Ring_3800
v0
  = let v1 :: T_IsRing_2650
v1 = T_Ring_3800 -> T_IsRing_2650
d_isRing_3836 (T_Ring_3800 -> T_Ring_3800
forall a b. a -> b
coe T_Ring_3800
v0) in
    AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      ((T_IsMonoid_686 -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoid_686 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_identity_698
         ((T_IsGroup_1036 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsGroup_1036 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_1050
            ((T_IsAbelianGroup_1132 -> T_IsGroup_1036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsAbelianGroup_1132 -> T_IsGroup_1036
MAlonzo.Code.Algebra.Structures.d_isGroup_1144
               ((T_IsRing_2650 -> T_IsAbelianGroup_1132) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsRing_2650 -> T_IsAbelianGroup_1132
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2672
                  (T_IsRing_2650 -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650
v1)))))
-- Algebra.Bundles.Ring._.identityʳ
d_identity'691'_3874 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Ring_3800 -> AgdaAny -> AgdaAny
d_identity'691'_3874 :: () -> () -> T_Ring_3800 -> AgdaAny -> AgdaAny
d_identity'691'_3874 ~()
v0 ~()
v1 T_Ring_3800
v2 = T_Ring_3800 -> AgdaAny -> AgdaAny
du_identity'691'_3874 T_Ring_3800
v2
du_identity'691'_3874 :: T_Ring_3800 -> AgdaAny -> AgdaAny
du_identity'691'_3874 :: T_Ring_3800 -> AgdaAny -> AgdaAny
du_identity'691'_3874 T_Ring_3800
v0
  = let v1 :: T_IsRing_2650
v1 = T_Ring_3800 -> T_IsRing_2650
d_isRing_3836 (T_Ring_3800 -> T_Ring_3800
forall a b. a -> b
coe T_Ring_3800
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: t
v2
             = (T_IsRing_2650 -> T_IsRingWithoutOne_2286) -> AgdaAny -> t
forall a b. a -> b
coe
                 T_IsRing_2650 -> T_IsRingWithoutOne_2286
MAlonzo.Code.Algebra.Structures.du_isRingWithoutOne_2682
                 (T_IsRing_2650 -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsAbelianGroup_1132
v3
                = T_IsRingWithoutOne_2286 -> T_IsAbelianGroup_1132
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2304
                    (AgdaAny -> T_IsRingWithoutOne_2286
forall a b. a -> b
coe AgdaAny
forall a. a
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsGroup_1036
v4
                   = T_IsAbelianGroup_1132 -> T_IsGroup_1036
MAlonzo.Code.Algebra.Structures.d_isGroup_1144 (T_IsAbelianGroup_1132 -> T_IsAbelianGroup_1132
forall a b. a -> b
coe T_IsAbelianGroup_1132
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               ((T_IsMonoid_686 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsMonoid_686 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_identity'691'_728
                  ((T_IsGroup_1036 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1036 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_1050 (T_IsGroup_1036 -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1036
v4))))))
-- Algebra.Bundles.Ring._.identityˡ
d_identity'737'_3876 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Ring_3800 -> AgdaAny -> AgdaAny
d_identity'737'_3876 :: () -> () -> T_Ring_3800 -> AgdaAny -> AgdaAny
d_identity'737'_3876 ~()
v0 ~()
v1 T_Ring_3800
v2 = T_Ring_3800 -> AgdaAny -> AgdaAny
du_identity'737'_3876 T_Ring_3800
v2
du_identity'737'_3876 :: T_Ring_3800 -> AgdaAny -> AgdaAny
du_identity'737'_3876 :: T_Ring_3800 -> AgdaAny -> AgdaAny
du_identity'737'_3876 T_Ring_3800
v0
  = let v1 :: T_IsRing_2650
v1 = T_Ring_3800 -> T_IsRing_2650
d_isRing_3836 (T_Ring_3800 -> T_Ring_3800
forall a b. a -> b
coe T_Ring_3800
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: t
v2
             = (T_IsRing_2650 -> T_IsRingWithoutOne_2286) -> AgdaAny -> t
forall a b. a -> b
coe
                 T_IsRing_2650 -> T_IsRingWithoutOne_2286
MAlonzo.Code.Algebra.Structures.du_isRingWithoutOne_2682
                 (T_IsRing_2650 -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsAbelianGroup_1132
v3
                = T_IsRingWithoutOne_2286 -> T_IsAbelianGroup_1132
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2304
                    (AgdaAny -> T_IsRingWithoutOne_2286
forall a b. a -> b
coe AgdaAny
forall a. a
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsGroup_1036
v4
                   = T_IsAbelianGroup_1132 -> T_IsGroup_1036
MAlonzo.Code.Algebra.Structures.d_isGroup_1144 (T_IsAbelianGroup_1132 -> T_IsAbelianGroup_1132
forall a b. a -> b
coe T_IsAbelianGroup_1132
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               ((T_IsMonoid_686 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsMonoid_686 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_identity'737'_726
                  ((T_IsGroup_1036 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1036 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_1050 (T_IsGroup_1036 -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1036
v4))))))
-- Algebra.Bundles.Ring._.+-isAbelianGroup
d_'43''45'isAbelianGroup_3878 ::
  T_Ring_3800 ->
  MAlonzo.Code.Algebra.Structures.T_IsAbelianGroup_1132
d_'43''45'isAbelianGroup_3878 :: T_Ring_3800 -> T_IsAbelianGroup_1132
d_'43''45'isAbelianGroup_3878 T_Ring_3800
v0
  = (T_IsRing_2650 -> T_IsAbelianGroup_1132)
-> AgdaAny -> T_IsAbelianGroup_1132
forall a b. a -> b
coe
      T_IsRing_2650 -> T_IsAbelianGroup_1132
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2672
      ((T_Ring_3800 -> T_IsRing_2650) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Ring_3800 -> T_IsRing_2650
d_isRing_3836 (T_Ring_3800 -> AgdaAny
forall a b. a -> b
coe T_Ring_3800
v0))
-- Algebra.Bundles.Ring._.isCommutativeMagma
d_isCommutativeMagma_3880 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Ring_3800 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMagma_212
d_isCommutativeMagma_3880 :: () -> () -> T_Ring_3800 -> T_IsCommutativeMagma_212
d_isCommutativeMagma_3880 ~()
v0 ~()
v1 T_Ring_3800
v2
  = T_Ring_3800 -> T_IsCommutativeMagma_212
du_isCommutativeMagma_3880 T_Ring_3800
v2
du_isCommutativeMagma_3880 ::
  T_Ring_3800 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMagma_212
du_isCommutativeMagma_3880 :: T_Ring_3800 -> T_IsCommutativeMagma_212
du_isCommutativeMagma_3880 T_Ring_3800
v0
  = let v1 :: T_IsRing_2650
v1 = T_Ring_3800 -> T_IsRing_2650
d_isRing_3836 (T_Ring_3800 -> T_Ring_3800
forall a b. a -> b
coe T_Ring_3800
v0) in
    AgdaAny -> T_IsCommutativeMagma_212
forall a b. a -> b
coe
      (let v2 :: t
v2
             = (T_IsRing_2650 -> T_IsRingWithoutOne_2286) -> AgdaAny -> t
forall a b. a -> b
coe
                 T_IsRing_2650 -> T_IsRingWithoutOne_2286
MAlonzo.Code.Algebra.Structures.du_isRingWithoutOne_2682
                 (T_IsRing_2650 -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsAbelianGroup_1132
v3
                = T_IsRingWithoutOne_2286 -> T_IsAbelianGroup_1132
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2304
                    (AgdaAny -> T_IsRingWithoutOne_2286
forall a b. a -> b
coe AgdaAny
forall a. a
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: t
v4
                   = (T_IsAbelianGroup_1132 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> t
forall a b. a -> b
coe
                       T_IsAbelianGroup_1132 -> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.du_isCommutativeMonoid_1204
                       (T_IsAbelianGroup_1132 -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               ((T_IsCommutativeSemigroup_548 -> T_IsCommutativeMagma_212)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsCommutativeSemigroup_548 -> T_IsCommutativeMagma_212
MAlonzo.Code.Algebra.Structures.du_isCommutativeMagma_586
                  ((T_IsCommutativeMonoid_736 -> T_IsCommutativeSemigroup_548)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsCommutativeMonoid_736 -> T_IsCommutativeSemigroup_548
MAlonzo.Code.Algebra.Structures.du_isCommutativeSemigroup_786
                     (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v4))))))
-- Algebra.Bundles.Ring._.isCommutativeMonoid
d_isCommutativeMonoid_3882 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Ring_3800 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMonoid_736
d_isCommutativeMonoid_3882 :: () -> () -> T_Ring_3800 -> T_IsCommutativeMonoid_736
d_isCommutativeMonoid_3882 ~()
v0 ~()
v1 T_Ring_3800
v2
  = T_Ring_3800 -> T_IsCommutativeMonoid_736
du_isCommutativeMonoid_3882 T_Ring_3800
v2
du_isCommutativeMonoid_3882 ::
  T_Ring_3800 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMonoid_736
du_isCommutativeMonoid_3882 :: T_Ring_3800 -> T_IsCommutativeMonoid_736
du_isCommutativeMonoid_3882 T_Ring_3800
v0
  = let v1 :: T_IsRing_2650
v1 = T_Ring_3800 -> T_IsRing_2650
d_isRing_3836 (T_Ring_3800 -> T_Ring_3800
forall a b. a -> b
coe T_Ring_3800
v0) in
    AgdaAny -> T_IsCommutativeMonoid_736
forall a b. a -> b
coe
      (let v2 :: t
v2
             = (T_IsRing_2650 -> T_IsRingWithoutOne_2286) -> AgdaAny -> t
forall a b. a -> b
coe
                 T_IsRing_2650 -> T_IsRingWithoutOne_2286
MAlonzo.Code.Algebra.Structures.du_isRingWithoutOne_2682
                 (T_IsRing_2650 -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsAbelianGroup_1132 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsAbelianGroup_1132 -> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.du_isCommutativeMonoid_1204
            ((T_IsRingWithoutOne_2286 -> T_IsAbelianGroup_1132)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsRingWithoutOne_2286 -> T_IsAbelianGroup_1132
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2304
               (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2))))
-- Algebra.Bundles.Ring._.isCommutativeSemigroup
d_isCommutativeSemigroup_3884 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Ring_3800 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_548
d_isCommutativeSemigroup_3884 :: () -> () -> T_Ring_3800 -> T_IsCommutativeSemigroup_548
d_isCommutativeSemigroup_3884 ~()
v0 ~()
v1 T_Ring_3800
v2
  = T_Ring_3800 -> T_IsCommutativeSemigroup_548
du_isCommutativeSemigroup_3884 T_Ring_3800
v2
du_isCommutativeSemigroup_3884 ::
  T_Ring_3800 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_548
du_isCommutativeSemigroup_3884 :: T_Ring_3800 -> T_IsCommutativeSemigroup_548
du_isCommutativeSemigroup_3884 T_Ring_3800
v0
  = let v1 :: T_IsRing_2650
v1 = T_Ring_3800 -> T_IsRing_2650
d_isRing_3836 (T_Ring_3800 -> T_Ring_3800
forall a b. a -> b
coe T_Ring_3800
v0) in
    AgdaAny -> T_IsCommutativeSemigroup_548
forall a b. a -> b
coe
      (let v2 :: t
v2
             = (T_IsRing_2650 -> T_IsRingWithoutOne_2286) -> AgdaAny -> t
forall a b. a -> b
coe
                 T_IsRing_2650 -> T_IsRingWithoutOne_2286
MAlonzo.Code.Algebra.Structures.du_isRingWithoutOne_2682
                 (T_IsRing_2650 -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsAbelianGroup_1132
v3
                = T_IsRingWithoutOne_2286 -> T_IsAbelianGroup_1132
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2304
                    (AgdaAny -> T_IsRingWithoutOne_2286
forall a b. a -> b
coe AgdaAny
forall a. a
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsCommutativeMonoid_736 -> T_IsCommutativeSemigroup_548)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsCommutativeMonoid_736 -> T_IsCommutativeSemigroup_548
MAlonzo.Code.Algebra.Structures.du_isCommutativeSemigroup_786
               ((T_IsAbelianGroup_1132 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsAbelianGroup_1132 -> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.du_isCommutativeMonoid_1204
                  (T_IsAbelianGroup_1132 -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132
v3)))))
-- Algebra.Bundles.Ring._.isGroup
d_isGroup_3886 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Ring_3800 -> MAlonzo.Code.Algebra.Structures.T_IsGroup_1036
d_isGroup_3886 :: () -> () -> T_Ring_3800 -> T_IsGroup_1036
d_isGroup_3886 ~()
v0 ~()
v1 T_Ring_3800
v2 = T_Ring_3800 -> T_IsGroup_1036
du_isGroup_3886 T_Ring_3800
v2
du_isGroup_3886 ::
  T_Ring_3800 -> MAlonzo.Code.Algebra.Structures.T_IsGroup_1036
du_isGroup_3886 :: T_Ring_3800 -> T_IsGroup_1036
du_isGroup_3886 T_Ring_3800
v0
  = let v1 :: T_IsRing_2650
v1 = T_Ring_3800 -> T_IsRing_2650
d_isRing_3836 (T_Ring_3800 -> T_Ring_3800
forall a b. a -> b
coe T_Ring_3800
v0) in
    AgdaAny -> T_IsGroup_1036
forall a b. a -> b
coe
      ((T_IsAbelianGroup_1132 -> T_IsGroup_1036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsAbelianGroup_1132 -> T_IsGroup_1036
MAlonzo.Code.Algebra.Structures.d_isGroup_1144
         ((T_IsRing_2650 -> T_IsAbelianGroup_1132) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsRing_2650 -> T_IsAbelianGroup_1132
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2672
            (T_IsRing_2650 -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650
v1)))
-- Algebra.Bundles.Ring._.isInvertibleMagma
d_isInvertibleMagma_3888 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Ring_3800 ->
  MAlonzo.Code.Algebra.Structures.T_IsInvertibleMagma_924
d_isInvertibleMagma_3888 :: () -> () -> T_Ring_3800 -> T_IsInvertibleMagma_924
d_isInvertibleMagma_3888 ~()
v0 ~()
v1 T_Ring_3800
v2 = T_Ring_3800 -> T_IsInvertibleMagma_924
du_isInvertibleMagma_3888 T_Ring_3800
v2
du_isInvertibleMagma_3888 ::
  T_Ring_3800 ->
  MAlonzo.Code.Algebra.Structures.T_IsInvertibleMagma_924
du_isInvertibleMagma_3888 :: T_Ring_3800 -> T_IsInvertibleMagma_924
du_isInvertibleMagma_3888 T_Ring_3800
v0
  = let v1 :: T_IsRing_2650
v1 = T_Ring_3800 -> T_IsRing_2650
d_isRing_3836 (T_Ring_3800 -> T_Ring_3800
forall a b. a -> b
coe T_Ring_3800
v0) in
    AgdaAny -> T_IsInvertibleMagma_924
forall a b. a -> b
coe
      (let v2 :: t
v2
             = (T_IsRing_2650 -> T_IsRingWithoutOne_2286) -> AgdaAny -> t
forall a b. a -> b
coe
                 T_IsRing_2650 -> T_IsRingWithoutOne_2286
MAlonzo.Code.Algebra.Structures.du_isRingWithoutOne_2682
                 (T_IsRing_2650 -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsAbelianGroup_1132
v3
                = T_IsRingWithoutOne_2286 -> T_IsAbelianGroup_1132
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2304
                    (AgdaAny -> T_IsRingWithoutOne_2286
forall a b. a -> b
coe AgdaAny
forall a. a
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsGroup_1036 -> T_IsInvertibleMagma_924) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsGroup_1036 -> T_IsInvertibleMagma_924
MAlonzo.Code.Algebra.Structures.du_isInvertibleMagma_1122
               ((T_IsAbelianGroup_1132 -> T_IsGroup_1036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132 -> T_IsGroup_1036
MAlonzo.Code.Algebra.Structures.d_isGroup_1144 (T_IsAbelianGroup_1132 -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132
v3)))))
-- Algebra.Bundles.Ring._.isInvertibleUnitalMagma
d_isInvertibleUnitalMagma_3890 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Ring_3800 ->
  MAlonzo.Code.Algebra.Structures.T_IsInvertibleUnitalMagma_976
d_isInvertibleUnitalMagma_3890 :: () -> () -> T_Ring_3800 -> T_IsInvertibleUnitalMagma_976
d_isInvertibleUnitalMagma_3890 ~()
v0 ~()
v1 T_Ring_3800
v2
  = T_Ring_3800 -> T_IsInvertibleUnitalMagma_976
du_isInvertibleUnitalMagma_3890 T_Ring_3800
v2
du_isInvertibleUnitalMagma_3890 ::
  T_Ring_3800 ->
  MAlonzo.Code.Algebra.Structures.T_IsInvertibleUnitalMagma_976
du_isInvertibleUnitalMagma_3890 :: T_Ring_3800 -> T_IsInvertibleUnitalMagma_976
du_isInvertibleUnitalMagma_3890 T_Ring_3800
v0
  = let v1 :: T_IsRing_2650
v1 = T_Ring_3800 -> T_IsRing_2650
d_isRing_3836 (T_Ring_3800 -> T_Ring_3800
forall a b. a -> b
coe T_Ring_3800
v0) in
    AgdaAny -> T_IsInvertibleUnitalMagma_976
forall a b. a -> b
coe
      (let v2 :: t
v2
             = (T_IsRing_2650 -> T_IsRingWithoutOne_2286) -> AgdaAny -> t
forall a b. a -> b
coe
                 T_IsRing_2650 -> T_IsRingWithoutOne_2286
MAlonzo.Code.Algebra.Structures.du_isRingWithoutOne_2682
                 (T_IsRing_2650 -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsAbelianGroup_1132
v3
                = T_IsRingWithoutOne_2286 -> T_IsAbelianGroup_1132
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2304
                    (AgdaAny -> T_IsRingWithoutOne_2286
forall a b. a -> b
coe AgdaAny
forall a. a
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsGroup_1036 -> T_IsInvertibleUnitalMagma_976)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsGroup_1036 -> T_IsInvertibleUnitalMagma_976
MAlonzo.Code.Algebra.Structures.du_isInvertibleUnitalMagma_1124
               ((T_IsAbelianGroup_1132 -> T_IsGroup_1036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132 -> T_IsGroup_1036
MAlonzo.Code.Algebra.Structures.d_isGroup_1144 (T_IsAbelianGroup_1132 -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132
v3)))))
-- Algebra.Bundles.Ring._.isMagma
d_isMagma_3892 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Ring_3800 -> MAlonzo.Code.Algebra.Structures.T_IsMagma_176
d_isMagma_3892 :: () -> () -> T_Ring_3800 -> T_IsMagma_176
d_isMagma_3892 ~()
v0 ~()
v1 T_Ring_3800
v2 = T_Ring_3800 -> T_IsMagma_176
du_isMagma_3892 T_Ring_3800
v2
du_isMagma_3892 ::
  T_Ring_3800 -> MAlonzo.Code.Algebra.Structures.T_IsMagma_176
du_isMagma_3892 :: T_Ring_3800 -> T_IsMagma_176
du_isMagma_3892 T_Ring_3800
v0
  = let v1 :: T_IsRing_2650
v1 = T_Ring_3800 -> T_IsRing_2650
d_isRing_3836 (T_Ring_3800 -> T_Ring_3800
forall a b. a -> b
coe T_Ring_3800
v0) in
    AgdaAny -> T_IsMagma_176
forall a b. a -> b
coe
      ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480
         ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
            ((T_IsGroup_1036 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsGroup_1036 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_1050
               ((T_IsAbelianGroup_1132 -> T_IsGroup_1036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsAbelianGroup_1132 -> T_IsGroup_1036
MAlonzo.Code.Algebra.Structures.d_isGroup_1144
                  ((T_IsRing_2650 -> T_IsAbelianGroup_1132) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsRing_2650 -> T_IsAbelianGroup_1132
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2672
                     (T_IsRing_2650 -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650
v1))))))
-- Algebra.Bundles.Ring._.isMonoid
d_isMonoid_3894 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Ring_3800 -> MAlonzo.Code.Algebra.Structures.T_IsMonoid_686
d_isMonoid_3894 :: () -> () -> T_Ring_3800 -> T_IsMonoid_686
d_isMonoid_3894 ~()
v0 ~()
v1 T_Ring_3800
v2 = T_Ring_3800 -> T_IsMonoid_686
du_isMonoid_3894 T_Ring_3800
v2
du_isMonoid_3894 ::
  T_Ring_3800 -> MAlonzo.Code.Algebra.Structures.T_IsMonoid_686
du_isMonoid_3894 :: T_Ring_3800 -> T_IsMonoid_686
du_isMonoid_3894 T_Ring_3800
v0
  = let v1 :: T_IsRing_2650
v1 = T_Ring_3800 -> T_IsRing_2650
d_isRing_3836 (T_Ring_3800 -> T_Ring_3800
forall a b. a -> b
coe T_Ring_3800
v0) in
    AgdaAny -> T_IsMonoid_686
forall a b. a -> b
coe
      ((T_IsGroup_1036 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsGroup_1036 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_1050
         ((T_IsAbelianGroup_1132 -> T_IsGroup_1036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsAbelianGroup_1132 -> T_IsGroup_1036
MAlonzo.Code.Algebra.Structures.d_isGroup_1144
            ((T_IsRing_2650 -> T_IsAbelianGroup_1132) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsRing_2650 -> T_IsAbelianGroup_1132
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2672
               (T_IsRing_2650 -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650
v1))))
-- Algebra.Bundles.Ring._.isSemigroup
d_isSemigroup_3896 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Ring_3800 -> MAlonzo.Code.Algebra.Structures.T_IsSemigroup_472
d_isSemigroup_3896 :: () -> () -> T_Ring_3800 -> T_IsSemigroup_472
d_isSemigroup_3896 ~()
v0 ~()
v1 T_Ring_3800
v2 = T_Ring_3800 -> T_IsSemigroup_472
du_isSemigroup_3896 T_Ring_3800
v2
du_isSemigroup_3896 ::
  T_Ring_3800 -> MAlonzo.Code.Algebra.Structures.T_IsSemigroup_472
du_isSemigroup_3896 :: T_Ring_3800 -> T_IsSemigroup_472
du_isSemigroup_3896 T_Ring_3800
v0
  = let v1 :: T_IsRing_2650
v1 = T_Ring_3800 -> T_IsRing_2650
d_isRing_3836 (T_Ring_3800 -> T_Ring_3800
forall a b. a -> b
coe T_Ring_3800
v0) in
    AgdaAny -> T_IsSemigroup_472
forall a b. a -> b
coe
      ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
         ((T_IsGroup_1036 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsGroup_1036 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_1050
            ((T_IsAbelianGroup_1132 -> T_IsGroup_1036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsAbelianGroup_1132 -> T_IsGroup_1036
MAlonzo.Code.Algebra.Structures.d_isGroup_1144
               ((T_IsRing_2650 -> T_IsAbelianGroup_1132) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsRing_2650 -> T_IsAbelianGroup_1132
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2672
                  (T_IsRing_2650 -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650
v1)))))
-- Algebra.Bundles.Ring._.isUnitalMagma
d_isUnitalMagma_3898 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Ring_3800 -> MAlonzo.Code.Algebra.Structures.T_IsUnitalMagma_642
d_isUnitalMagma_3898 :: () -> () -> T_Ring_3800 -> T_IsUnitalMagma_642
d_isUnitalMagma_3898 ~()
v0 ~()
v1 T_Ring_3800
v2 = T_Ring_3800 -> T_IsUnitalMagma_642
du_isUnitalMagma_3898 T_Ring_3800
v2
du_isUnitalMagma_3898 ::
  T_Ring_3800 -> MAlonzo.Code.Algebra.Structures.T_IsUnitalMagma_642
du_isUnitalMagma_3898 :: T_Ring_3800 -> T_IsUnitalMagma_642
du_isUnitalMagma_3898 T_Ring_3800
v0
  = let v1 :: T_IsRing_2650
v1 = T_Ring_3800 -> T_IsRing_2650
d_isRing_3836 (T_Ring_3800 -> T_Ring_3800
forall a b. a -> b
coe T_Ring_3800
v0) in
    AgdaAny -> T_IsUnitalMagma_642
forall a b. a -> b
coe
      (let v2 :: t
v2
             = (T_IsRing_2650 -> T_IsRingWithoutOne_2286) -> AgdaAny -> t
forall a b. a -> b
coe
                 T_IsRing_2650 -> T_IsRingWithoutOne_2286
MAlonzo.Code.Algebra.Structures.du_isRingWithoutOne_2682
                 (T_IsRing_2650 -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsAbelianGroup_1132
v3
                = T_IsRingWithoutOne_2286 -> T_IsAbelianGroup_1132
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2304
                    (AgdaAny -> T_IsRingWithoutOne_2286
forall a b. a -> b
coe AgdaAny
forall a. a
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsGroup_1036
v4
                   = T_IsAbelianGroup_1132 -> T_IsGroup_1036
MAlonzo.Code.Algebra.Structures.d_isGroup_1144 (T_IsAbelianGroup_1132 -> T_IsAbelianGroup_1132
forall a b. a -> b
coe T_IsAbelianGroup_1132
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               ((T_IsMonoid_686 -> T_IsUnitalMagma_642) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsMonoid_686 -> T_IsUnitalMagma_642
MAlonzo.Code.Algebra.Structures.du_isUnitalMagma_730
                  ((T_IsGroup_1036 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1036 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_1050 (T_IsGroup_1036 -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1036
v4))))))
-- Algebra.Bundles.Ring._.⁻¹-cong
d_'8315''185''45'cong_3900 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Ring_3800 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8315''185''45'cong_3900 :: () -> () -> T_Ring_3800 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8315''185''45'cong_3900 ~()
v0 ~()
v1 T_Ring_3800
v2
  = T_Ring_3800 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8315''185''45'cong_3900 T_Ring_3800
v2
du_'8315''185''45'cong_3900 ::
  T_Ring_3800 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8315''185''45'cong_3900 :: T_Ring_3800 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8315''185''45'cong_3900 T_Ring_3800
v0
  = let v1 :: T_IsRing_2650
v1 = T_Ring_3800 -> T_IsRing_2650
d_isRing_3836 (T_Ring_3800 -> T_Ring_3800
forall a b. a -> b
coe T_Ring_3800
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsGroup_1036 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsGroup_1036 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8315''185''45'cong_1054
         ((T_IsAbelianGroup_1132 -> T_IsGroup_1036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsAbelianGroup_1132 -> T_IsGroup_1036
MAlonzo.Code.Algebra.Structures.d_isGroup_1144
            ((T_IsRing_2650 -> T_IsAbelianGroup_1132) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsRing_2650 -> T_IsAbelianGroup_1132
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2672
               (T_IsRing_2650 -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650
v1))))
-- Algebra.Bundles.Ring._.inverse
d_inverse_3902 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Ring_3800 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_inverse_3902 :: () -> () -> T_Ring_3800 -> T_Σ_14
d_inverse_3902 ~()
v0 ~()
v1 T_Ring_3800
v2 = T_Ring_3800 -> T_Σ_14
du_inverse_3902 T_Ring_3800
v2
du_inverse_3902 ::
  T_Ring_3800 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
du_inverse_3902 :: T_Ring_3800 -> T_Σ_14
du_inverse_3902 T_Ring_3800
v0
  = let v1 :: T_IsRing_2650
v1 = T_Ring_3800 -> T_IsRing_2650
d_isRing_3836 (T_Ring_3800 -> T_Ring_3800
forall a b. a -> b
coe T_Ring_3800
v0) in
    AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      ((T_IsGroup_1036 -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsGroup_1036 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_inverse_1052
         ((T_IsAbelianGroup_1132 -> T_IsGroup_1036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsAbelianGroup_1132 -> T_IsGroup_1036
MAlonzo.Code.Algebra.Structures.d_isGroup_1144
            ((T_IsRing_2650 -> T_IsAbelianGroup_1132) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsRing_2650 -> T_IsAbelianGroup_1132
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2672
               (T_IsRing_2650 -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650
v1))))
-- Algebra.Bundles.Ring._.inverseʳ
d_inverse'691'_3904 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Ring_3800 -> AgdaAny -> AgdaAny
d_inverse'691'_3904 :: () -> () -> T_Ring_3800 -> AgdaAny -> AgdaAny
d_inverse'691'_3904 ~()
v0 ~()
v1 T_Ring_3800
v2 = T_Ring_3800 -> AgdaAny -> AgdaAny
du_inverse'691'_3904 T_Ring_3800
v2
du_inverse'691'_3904 :: T_Ring_3800 -> AgdaAny -> AgdaAny
du_inverse'691'_3904 :: T_Ring_3800 -> AgdaAny -> AgdaAny
du_inverse'691'_3904 T_Ring_3800
v0
  = let v1 :: T_IsRing_2650
v1 = T_Ring_3800 -> T_IsRing_2650
d_isRing_3836 (T_Ring_3800 -> T_Ring_3800
forall a b. a -> b
coe T_Ring_3800
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: t
v2
             = (T_IsRing_2650 -> T_IsRingWithoutOne_2286) -> AgdaAny -> t
forall a b. a -> b
coe
                 T_IsRing_2650 -> T_IsRingWithoutOne_2286
MAlonzo.Code.Algebra.Structures.du_isRingWithoutOne_2682
                 (T_IsRing_2650 -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsAbelianGroup_1132
v3
                = T_IsRingWithoutOne_2286 -> T_IsAbelianGroup_1132
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2304
                    (AgdaAny -> T_IsRingWithoutOne_2286
forall a b. a -> b
coe AgdaAny
forall a. a
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsGroup_1036 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsGroup_1036 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_inverse'691'_1108
               ((T_IsAbelianGroup_1132 -> T_IsGroup_1036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132 -> T_IsGroup_1036
MAlonzo.Code.Algebra.Structures.d_isGroup_1144 (T_IsAbelianGroup_1132 -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132
v3)))))
-- Algebra.Bundles.Ring._.inverseˡ
d_inverse'737'_3906 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Ring_3800 -> AgdaAny -> AgdaAny
d_inverse'737'_3906 :: () -> () -> T_Ring_3800 -> AgdaAny -> AgdaAny
d_inverse'737'_3906 ~()
v0 ~()
v1 T_Ring_3800
v2 = T_Ring_3800 -> AgdaAny -> AgdaAny
du_inverse'737'_3906 T_Ring_3800
v2
du_inverse'737'_3906 :: T_Ring_3800 -> AgdaAny -> AgdaAny
du_inverse'737'_3906 :: T_Ring_3800 -> AgdaAny -> AgdaAny
du_inverse'737'_3906 T_Ring_3800
v0
  = let v1 :: T_IsRing_2650
v1 = T_Ring_3800 -> T_IsRing_2650
d_isRing_3836 (T_Ring_3800 -> T_Ring_3800
forall a b. a -> b
coe T_Ring_3800
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: t
v2
             = (T_IsRing_2650 -> T_IsRingWithoutOne_2286) -> AgdaAny -> t
forall a b. a -> b
coe
                 T_IsRing_2650 -> T_IsRingWithoutOne_2286
MAlonzo.Code.Algebra.Structures.du_isRingWithoutOne_2682
                 (T_IsRing_2650 -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsAbelianGroup_1132
v3
                = T_IsRingWithoutOne_2286 -> T_IsAbelianGroup_1132
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2304
                    (AgdaAny -> T_IsRingWithoutOne_2286
forall a b. a -> b
coe AgdaAny
forall a. a
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsGroup_1036 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsGroup_1036 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_inverse'737'_1106
               ((T_IsAbelianGroup_1132 -> T_IsGroup_1036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132 -> T_IsGroup_1036
MAlonzo.Code.Algebra.Structures.d_isGroup_1144 (T_IsAbelianGroup_1132 -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132
v3)))))
-- Algebra.Bundles.Ring._.distrib
d_distrib_3908 ::
  T_Ring_3800 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_distrib_3908 :: T_Ring_3800 -> T_Σ_14
d_distrib_3908 T_Ring_3800
v0
  = (T_IsRing_2650 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsRing_2650 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_distrib_2680
      ((T_Ring_3800 -> T_IsRing_2650) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Ring_3800 -> T_IsRing_2650
d_isRing_3836 (T_Ring_3800 -> AgdaAny
forall a b. a -> b
coe T_Ring_3800
v0))
-- Algebra.Bundles.Ring._.distribʳ
d_distrib'691'_3910 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Ring_3800 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_distrib'691'_3910 :: () -> () -> T_Ring_3800 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_distrib'691'_3910 ~()
v0 ~()
v1 T_Ring_3800
v2 = T_Ring_3800 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'691'_3910 T_Ring_3800
v2
du_distrib'691'_3910 ::
  T_Ring_3800 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'691'_3910 :: T_Ring_3800 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'691'_3910 T_Ring_3800
v0
  = let v1 :: T_IsRing_2650
v1 = T_Ring_3800 -> T_IsRing_2650
d_isRing_3836 (T_Ring_3800 -> T_Ring_3800
forall a b. a -> b
coe T_Ring_3800
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsRingWithoutOne_2286
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsRingWithoutOne_2286 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_distrib'691'_2380
         ((T_IsRing_2650 -> T_IsRingWithoutOne_2286) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsRing_2650 -> T_IsRingWithoutOne_2286
MAlonzo.Code.Algebra.Structures.du_isRingWithoutOne_2682 (T_IsRing_2650 -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650
v1)))
-- Algebra.Bundles.Ring._.distribˡ
d_distrib'737'_3912 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Ring_3800 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_distrib'737'_3912 :: () -> () -> T_Ring_3800 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_distrib'737'_3912 ~()
v0 ~()
v1 T_Ring_3800
v2 = T_Ring_3800 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'737'_3912 T_Ring_3800
v2
du_distrib'737'_3912 ::
  T_Ring_3800 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'737'_3912 :: T_Ring_3800 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'737'_3912 T_Ring_3800
v0
  = let v1 :: T_IsRing_2650
v1 = T_Ring_3800 -> T_IsRing_2650
d_isRing_3836 (T_Ring_3800 -> T_Ring_3800
forall a b. a -> b
coe T_Ring_3800
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsRingWithoutOne_2286
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsRingWithoutOne_2286 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_distrib'737'_2378
         ((T_IsRing_2650 -> T_IsRingWithoutOne_2286) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsRing_2650 -> T_IsRingWithoutOne_2286
MAlonzo.Code.Algebra.Structures.du_isRingWithoutOne_2682 (T_IsRing_2650 -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650
v1)))
-- Algebra.Bundles.Ring._.isEquivalence
d_isEquivalence_3914 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Ring_3800 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_3914 :: () -> () -> T_Ring_3800 -> T_IsEquivalence_26
d_isEquivalence_3914 ~()
v0 ~()
v1 T_Ring_3800
v2 = T_Ring_3800 -> T_IsEquivalence_26
du_isEquivalence_3914 T_Ring_3800
v2
du_isEquivalence_3914 ::
  T_Ring_3800 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
du_isEquivalence_3914 :: T_Ring_3800 -> T_IsEquivalence_26
du_isEquivalence_3914 T_Ring_3800
v0
  = let v1 :: T_IsRing_2650
v1 = T_Ring_3800 -> T_IsRing_2650
d_isRing_3836 (T_Ring_3800 -> T_Ring_3800
forall a b. a -> b
coe T_Ring_3800
v0) in
    AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
         ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480
            ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
               ((T_IsGroup_1036 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsGroup_1036 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_1050
                  ((T_IsAbelianGroup_1132 -> T_IsGroup_1036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsAbelianGroup_1132 -> T_IsGroup_1036
MAlonzo.Code.Algebra.Structures.d_isGroup_1144
                     ((T_IsRing_2650 -> T_IsAbelianGroup_1132) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsRing_2650 -> T_IsAbelianGroup_1132
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2672
                        (T_IsRing_2650 -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650
v1)))))))
-- Algebra.Bundles.Ring._.isNearSemiring
d_isNearSemiring_3916 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Ring_3800 ->
  MAlonzo.Code.Algebra.Structures.T_IsNearSemiring_1218
d_isNearSemiring_3916 :: () -> () -> T_Ring_3800 -> T_IsNearSemiring_1218
d_isNearSemiring_3916 ~()
v0 ~()
v1 T_Ring_3800
v2 = T_Ring_3800 -> T_IsNearSemiring_1218
du_isNearSemiring_3916 T_Ring_3800
v2
du_isNearSemiring_3916 ::
  T_Ring_3800 ->
  MAlonzo.Code.Algebra.Structures.T_IsNearSemiring_1218
du_isNearSemiring_3916 :: T_Ring_3800 -> T_IsNearSemiring_1218
du_isNearSemiring_3916 T_Ring_3800
v0
  = let v1 :: AgdaAny -> AgdaAny -> AgdaAny
v1 = T_Ring_3800 -> AgdaAny -> AgdaAny -> AgdaAny
d__'43'__3826 (T_Ring_3800 -> T_Ring_3800
forall a b. a -> b
coe T_Ring_3800
v0) in
    AgdaAny -> T_IsNearSemiring_1218
forall a b. a -> b
coe
      (let v2 :: AgdaAny -> AgdaAny -> AgdaAny
v2 = T_Ring_3800 -> AgdaAny -> AgdaAny -> AgdaAny
d__'42'__3828 (T_Ring_3800 -> T_Ring_3800
forall a b. a -> b
coe T_Ring_3800
v0) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: AgdaAny -> AgdaAny
v3 = T_Ring_3800 -> AgdaAny -> AgdaAny
d_'45'__3830 (T_Ring_3800 -> T_Ring_3800
forall a b. a -> b
coe T_Ring_3800
v0) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: AgdaAny
v4 = T_Ring_3800 -> AgdaAny
d_0'35'_3832 (T_Ring_3800 -> T_Ring_3800
forall a b. a -> b
coe T_Ring_3800
v0) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsRing_2650
v5 = T_Ring_3800 -> T_IsRing_2650
d_isRing_3836 (T_Ring_3800 -> T_Ring_3800
forall a b. a -> b
coe T_Ring_3800
v0) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (let v6 :: t
v6
                         = ((AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny)
 -> AgdaAny
 -> T_IsRing_2650
 -> T_IsSemiring_1570)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe
                             (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsRing_2650
-> T_IsSemiring_1570
MAlonzo.Code.Algebra.Structures.du_isSemiring_2778 ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v1)
                             ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v2) ((AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v3) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v4) (T_IsRing_2650 -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650
v5) in
                   AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     ((T_IsSemiringWithoutOne_1298 -> T_IsNearSemiring_1218)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsSemiringWithoutOne_1298 -> T_IsNearSemiring_1218
MAlonzo.Code.Algebra.Structures.du_isNearSemiring_1374
                        ((T_IsSemiring_1570 -> T_IsSemiringWithoutOne_1298)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_IsSemiring_1570 -> T_IsSemiringWithoutOne_1298
MAlonzo.Code.Algebra.Structures.du_isSemiringWithoutOne_1660
                           (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v6))))))))
-- Algebra.Bundles.Ring._.isPartialEquivalence
d_isPartialEquivalence_3918 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Ring_3800 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_3918 :: () -> () -> T_Ring_3800 -> T_IsPartialEquivalence_16
d_isPartialEquivalence_3918 ~()
v0 ~()
v1 T_Ring_3800
v2
  = T_Ring_3800 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_3918 T_Ring_3800
v2
du_isPartialEquivalence_3918 ::
  T_Ring_3800 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_3918 :: T_Ring_3800 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_3918 T_Ring_3800
v0
  = let v1 :: T_IsRing_2650
v1 = T_Ring_3800 -> T_IsRing_2650
d_isRing_3836 (T_Ring_3800 -> T_Ring_3800
forall a b. a -> b
coe T_Ring_3800
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: t
v2
             = (T_IsRing_2650 -> T_IsRingWithoutOne_2286) -> AgdaAny -> t
forall a b. a -> b
coe
                 T_IsRing_2650 -> T_IsRingWithoutOne_2286
MAlonzo.Code.Algebra.Structures.du_isRingWithoutOne_2682
                 (T_IsRing_2650 -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsAbelianGroup_1132
v3
                = T_IsRingWithoutOne_2286 -> T_IsAbelianGroup_1132
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2304
                    (AgdaAny -> T_IsRingWithoutOne_2286
forall a b. a -> b
coe AgdaAny
forall a. a
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsGroup_1036
v4
                   = T_IsAbelianGroup_1132 -> T_IsGroup_1036
MAlonzo.Code.Algebra.Structures.d_isGroup_1144 (T_IsAbelianGroup_1132 -> T_IsAbelianGroup_1132
forall a b. a -> b
coe T_IsAbelianGroup_1132
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsMonoid_686
v5
                      = T_IsGroup_1036 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_1050 (T_IsGroup_1036 -> T_IsGroup_1036
forall a b. a -> b
coe T_IsGroup_1036
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (let v6 :: T_IsSemigroup_472
v6
                         = T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v5) in
                   AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     (let v7 :: T_IsMagma_176
v7 = T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (T_IsSemigroup_472 -> T_IsSemigroup_472
forall a b. a -> b
coe T_IsSemigroup_472
v6) in
                      AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        ((T_IsEquivalence_26 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_IsEquivalence_26 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
                           ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                              T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
                              (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v7)))))))))
-- Algebra.Bundles.Ring._.isRingWithoutOne
d_isRingWithoutOne_3920 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Ring_3800 ->
  MAlonzo.Code.Algebra.Structures.T_IsRingWithoutOne_2286
d_isRingWithoutOne_3920 :: () -> () -> T_Ring_3800 -> T_IsRingWithoutOne_2286
d_isRingWithoutOne_3920 ~()
v0 ~()
v1 T_Ring_3800
v2 = T_Ring_3800 -> T_IsRingWithoutOne_2286
du_isRingWithoutOne_3920 T_Ring_3800
v2
du_isRingWithoutOne_3920 ::
  T_Ring_3800 ->
  MAlonzo.Code.Algebra.Structures.T_IsRingWithoutOne_2286
du_isRingWithoutOne_3920 :: T_Ring_3800 -> T_IsRingWithoutOne_2286
du_isRingWithoutOne_3920 T_Ring_3800
v0
  = (T_IsRing_2650 -> T_IsRingWithoutOne_2286)
-> AgdaAny -> T_IsRingWithoutOne_2286
forall a b. a -> b
coe
      T_IsRing_2650 -> T_IsRingWithoutOne_2286
MAlonzo.Code.Algebra.Structures.du_isRingWithoutOne_2682
      ((T_Ring_3800 -> T_IsRing_2650) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Ring_3800 -> T_IsRing_2650
d_isRing_3836 (T_Ring_3800 -> AgdaAny
forall a b. a -> b
coe T_Ring_3800
v0))
-- Algebra.Bundles.Ring._.isSemiring
d_isSemiring_3922 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Ring_3800 -> MAlonzo.Code.Algebra.Structures.T_IsSemiring_1570
d_isSemiring_3922 :: () -> () -> T_Ring_3800 -> T_IsSemiring_1570
d_isSemiring_3922 ~()
v0 ~()
v1 T_Ring_3800
v2 = T_Ring_3800 -> T_IsSemiring_1570
du_isSemiring_3922 T_Ring_3800
v2
du_isSemiring_3922 ::
  T_Ring_3800 -> MAlonzo.Code.Algebra.Structures.T_IsSemiring_1570
du_isSemiring_3922 :: T_Ring_3800 -> T_IsSemiring_1570
du_isSemiring_3922 T_Ring_3800
v0
  = ((AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny)
 -> AgdaAny
 -> T_IsRing_2650
 -> T_IsSemiring_1570)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> T_IsSemiring_1570
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsRing_2650
-> T_IsSemiring_1570
MAlonzo.Code.Algebra.Structures.du_isSemiring_2778
      ((T_Ring_3800 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Ring_3800 -> AgdaAny -> AgdaAny -> AgdaAny
d__'43'__3826 (T_Ring_3800 -> AgdaAny
forall a b. a -> b
coe T_Ring_3800
v0)) ((T_Ring_3800 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Ring_3800 -> AgdaAny -> AgdaAny -> AgdaAny
d__'42'__3828 (T_Ring_3800 -> AgdaAny
forall a b. a -> b
coe T_Ring_3800
v0))
      ((T_Ring_3800 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Ring_3800 -> AgdaAny -> AgdaAny
d_'45'__3830 (T_Ring_3800 -> AgdaAny
forall a b. a -> b
coe T_Ring_3800
v0)) ((T_Ring_3800 -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Ring_3800 -> AgdaAny
d_0'35'_3832 (T_Ring_3800 -> AgdaAny
forall a b. a -> b
coe T_Ring_3800
v0))
      ((T_Ring_3800 -> T_IsRing_2650) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Ring_3800 -> T_IsRing_2650
d_isRing_3836 (T_Ring_3800 -> AgdaAny
forall a b. a -> b
coe T_Ring_3800
v0))
-- Algebra.Bundles.Ring._.isSemiringWithoutAnnihilatingZero
d_isSemiringWithoutAnnihilatingZero_3924 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Ring_3800 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_3924 :: () -> () -> T_Ring_3800 -> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_3924 ~()
v0 ~()
v1 T_Ring_3800
v2
  = T_Ring_3800 -> T_IsSemiringWithoutAnnihilatingZero_1468
du_isSemiringWithoutAnnihilatingZero_3924 T_Ring_3800
v2
du_isSemiringWithoutAnnihilatingZero_3924 ::
  T_Ring_3800 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutAnnihilatingZero_1468
du_isSemiringWithoutAnnihilatingZero_3924 :: T_Ring_3800 -> T_IsSemiringWithoutAnnihilatingZero_1468
du_isSemiringWithoutAnnihilatingZero_3924 T_Ring_3800
v0
  = (T_IsRing_2650 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> T_IsSemiringWithoutAnnihilatingZero_1468
forall a b. a -> b
coe
      T_IsRing_2650 -> T_IsSemiringWithoutAnnihilatingZero_1468
MAlonzo.Code.Algebra.Structures.du_isSemiringWithoutAnnihilatingZero_2776
      ((T_Ring_3800 -> T_IsRing_2650) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Ring_3800 -> T_IsRing_2650
d_isRing_3836 (T_Ring_3800 -> AgdaAny
forall a b. a -> b
coe T_Ring_3800
v0))
-- Algebra.Bundles.Ring._.isSemiringWithoutOne
d_isSemiringWithoutOne_3926 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Ring_3800 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutOne_1298
d_isSemiringWithoutOne_3926 :: () -> () -> T_Ring_3800 -> T_IsSemiringWithoutOne_1298
d_isSemiringWithoutOne_3926 ~()
v0 ~()
v1 T_Ring_3800
v2
  = T_Ring_3800 -> T_IsSemiringWithoutOne_1298
du_isSemiringWithoutOne_3926 T_Ring_3800
v2
du_isSemiringWithoutOne_3926 ::
  T_Ring_3800 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutOne_1298
du_isSemiringWithoutOne_3926 :: T_Ring_3800 -> T_IsSemiringWithoutOne_1298
du_isSemiringWithoutOne_3926 T_Ring_3800
v0
  = let v1 :: AgdaAny -> AgdaAny -> AgdaAny
v1 = T_Ring_3800 -> AgdaAny -> AgdaAny -> AgdaAny
d__'43'__3826 (T_Ring_3800 -> T_Ring_3800
forall a b. a -> b
coe T_Ring_3800
v0) in
    AgdaAny -> T_IsSemiringWithoutOne_1298
forall a b. a -> b
coe
      (let v2 :: AgdaAny -> AgdaAny -> AgdaAny
v2 = T_Ring_3800 -> AgdaAny -> AgdaAny -> AgdaAny
d__'42'__3828 (T_Ring_3800 -> T_Ring_3800
forall a b. a -> b
coe T_Ring_3800
v0) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: AgdaAny -> AgdaAny
v3 = T_Ring_3800 -> AgdaAny -> AgdaAny
d_'45'__3830 (T_Ring_3800 -> T_Ring_3800
forall a b. a -> b
coe T_Ring_3800
v0) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: AgdaAny
v4 = T_Ring_3800 -> AgdaAny
d_0'35'_3832 (T_Ring_3800 -> T_Ring_3800
forall a b. a -> b
coe T_Ring_3800
v0) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsRing_2650
v5 = T_Ring_3800 -> T_IsRing_2650
d_isRing_3836 (T_Ring_3800 -> T_Ring_3800
forall a b. a -> b
coe T_Ring_3800
v0) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  ((T_IsSemiring_1570 -> T_IsSemiringWithoutOne_1298)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsSemiring_1570 -> T_IsSemiringWithoutOne_1298
MAlonzo.Code.Algebra.Structures.du_isSemiringWithoutOne_1660
                     (((AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny)
 -> AgdaAny
 -> T_IsRing_2650
 -> T_IsSemiring_1570)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsRing_2650
-> T_IsSemiring_1570
MAlonzo.Code.Algebra.Structures.du_isSemiring_2778 ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v1)
                        ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v2) ((AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v3) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v4) (T_IsRing_2650 -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650
v5)))))))
-- Algebra.Bundles.Ring._.refl
d_refl_3928 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Ring_3800 -> AgdaAny -> AgdaAny
d_refl_3928 :: () -> () -> T_Ring_3800 -> AgdaAny -> AgdaAny
d_refl_3928 ~()
v0 ~()
v1 T_Ring_3800
v2 = T_Ring_3800 -> AgdaAny -> AgdaAny
du_refl_3928 T_Ring_3800
v2
du_refl_3928 :: T_Ring_3800 -> AgdaAny -> AgdaAny
du_refl_3928 :: T_Ring_3800 -> AgdaAny -> AgdaAny
du_refl_3928 T_Ring_3800
v0
  = let v1 :: T_IsRing_2650
v1 = T_Ring_3800 -> T_IsRing_2650
d_isRing_3836 (T_Ring_3800 -> T_Ring_3800
forall a b. a -> b
coe T_Ring_3800
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsEquivalence_26 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_34
         ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
            ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480
               ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
                  ((T_IsGroup_1036 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsGroup_1036 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_1050
                     ((T_IsAbelianGroup_1132 -> T_IsGroup_1036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsAbelianGroup_1132 -> T_IsGroup_1036
MAlonzo.Code.Algebra.Structures.d_isGroup_1144
                        ((T_IsRing_2650 -> T_IsAbelianGroup_1132) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_IsRing_2650 -> T_IsAbelianGroup_1132
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2672
                           (T_IsRing_2650 -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650
v1))))))))
-- Algebra.Bundles.Ring._.reflexive
d_reflexive_3930 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Ring_3800 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_3930 :: ()
-> ()
-> T_Ring_3800
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_3930 ~()
v0 ~()
v1 T_Ring_3800
v2 = T_Ring_3800 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_3930 T_Ring_3800
v2
du_reflexive_3930 ::
  T_Ring_3800 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_3930 :: T_Ring_3800 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_3930 T_Ring_3800
v0
  = let v1 :: T_IsRing_2650
v1 = T_Ring_3800 -> T_IsRing_2650
d_isRing_3836 (T_Ring_3800 -> T_Ring_3800
forall a b. a -> b
coe T_Ring_3800
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: t
v2
             = (T_IsRing_2650 -> T_IsRingWithoutOne_2286) -> AgdaAny -> t
forall a b. a -> b
coe
                 T_IsRing_2650 -> T_IsRingWithoutOne_2286
MAlonzo.Code.Algebra.Structures.du_isRingWithoutOne_2682
                 (T_IsRing_2650 -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsAbelianGroup_1132
v3
                = T_IsRingWithoutOne_2286 -> T_IsAbelianGroup_1132
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2304
                    (AgdaAny -> T_IsRingWithoutOne_2286
forall a b. a -> b
coe AgdaAny
forall a. a
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsGroup_1036
v4
                   = T_IsAbelianGroup_1132 -> T_IsGroup_1036
MAlonzo.Code.Algebra.Structures.d_isGroup_1144 (T_IsAbelianGroup_1132 -> T_IsAbelianGroup_1132
forall a b. a -> b
coe T_IsAbelianGroup_1132
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsMonoid_686
v5
                      = T_IsGroup_1036 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_1050 (T_IsGroup_1036 -> T_IsGroup_1036
forall a b. a -> b
coe T_IsGroup_1036
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (let v6 :: T_IsSemigroup_472
v6
                         = T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v5) in
                   AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     (let v7 :: T_IsMagma_176
v7 = T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (T_IsSemigroup_472 -> T_IsSemigroup_472
forall a b. a -> b
coe T_IsSemigroup_472
v6) in
                      (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
                        (\ AgdaAny
v8 AgdaAny
v9 AgdaAny
v10 ->
                           (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                             T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
                             ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v7))
                             AgdaAny
v8)))))))
-- Algebra.Bundles.Ring._.setoid
d_setoid_3932 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Ring_3800 -> MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_3932 :: () -> () -> T_Ring_3800 -> T_Setoid_44
d_setoid_3932 ~()
v0 ~()
v1 T_Ring_3800
v2 = T_Ring_3800 -> T_Setoid_44
du_setoid_3932 T_Ring_3800
v2
du_setoid_3932 ::
  T_Ring_3800 -> MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_3932 :: T_Ring_3800 -> T_Setoid_44
du_setoid_3932 T_Ring_3800
v0
  = let v1 :: T_IsRing_2650
v1 = T_Ring_3800 -> T_IsRing_2650
d_isRing_3836 (T_Ring_3800 -> T_Ring_3800
forall a b. a -> b
coe T_Ring_3800
v0) in
    AgdaAny -> T_Setoid_44
forall a b. a -> b
coe
      (let v2 :: t
v2
             = (T_IsRing_2650 -> T_IsRingWithoutOne_2286) -> AgdaAny -> t
forall a b. a -> b
coe
                 T_IsRing_2650 -> T_IsRingWithoutOne_2286
MAlonzo.Code.Algebra.Structures.du_isRingWithoutOne_2682
                 (T_IsRing_2650 -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsAbelianGroup_1132
v3
                = T_IsRingWithoutOne_2286 -> T_IsAbelianGroup_1132
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2304
                    (AgdaAny -> T_IsRingWithoutOne_2286
forall a b. a -> b
coe AgdaAny
forall a. a
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsGroup_1036
v4
                   = T_IsAbelianGroup_1132 -> T_IsGroup_1036
MAlonzo.Code.Algebra.Structures.d_isGroup_1144 (T_IsAbelianGroup_1132 -> T_IsAbelianGroup_1132
forall a b. a -> b
coe T_IsAbelianGroup_1132
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsMonoid_686
v5
                      = T_IsGroup_1036 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_1050 (T_IsGroup_1036 -> T_IsGroup_1036
forall a b. a -> b
coe T_IsGroup_1036
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (let v6 :: T_IsSemigroup_472
v6
                         = T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v5) in
                   AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     ((T_IsMagma_176 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsMagma_176 -> T_Setoid_44
MAlonzo.Code.Algebra.Structures.du_setoid_200
                        ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v6))))))))
-- Algebra.Bundles.Ring._.sym
d_sym_3934 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Ring_3800 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_3934 :: () -> () -> T_Ring_3800 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_3934 ~()
v0 ~()
v1 T_Ring_3800
v2 = T_Ring_3800 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_3934 T_Ring_3800
v2
du_sym_3934 ::
  T_Ring_3800 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_3934 :: T_Ring_3800 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_3934 T_Ring_3800
v0
  = let v1 :: T_IsRing_2650
v1 = T_Ring_3800 -> T_IsRing_2650
d_isRing_3836 (T_Ring_3800 -> T_Ring_3800
forall a b. a -> b
coe T_Ring_3800
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_36
         ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
            ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480
               ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
                  ((T_IsGroup_1036 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsGroup_1036 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_1050
                     ((T_IsAbelianGroup_1132 -> T_IsGroup_1036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsAbelianGroup_1132 -> T_IsGroup_1036
MAlonzo.Code.Algebra.Structures.d_isGroup_1144
                        ((T_IsRing_2650 -> T_IsAbelianGroup_1132) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_IsRing_2650 -> T_IsAbelianGroup_1132
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2672
                           (T_IsRing_2650 -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650
v1))))))))
-- Algebra.Bundles.Ring._.trans
d_trans_3936 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Ring_3800 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_3936 :: ()
-> ()
-> T_Ring_3800
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_trans_3936 ~()
v0 ~()
v1 T_Ring_3800
v2 = T_Ring_3800
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_3936 T_Ring_3800
v2
du_trans_3936 ::
  T_Ring_3800 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_3936 :: T_Ring_3800
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_3936 T_Ring_3800
v0
  = let v1 :: T_IsRing_2650
v1 = T_Ring_3800 -> T_IsRing_2650
d_isRing_3836 (T_Ring_3800 -> T_Ring_3800
forall a b. a -> b
coe T_Ring_3800
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsEquivalence_26
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsEquivalence_26
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_38
         ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
            ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480
               ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
                  ((T_IsGroup_1036 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsGroup_1036 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_1050
                     ((T_IsAbelianGroup_1132 -> T_IsGroup_1036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsAbelianGroup_1132 -> T_IsGroup_1036
MAlonzo.Code.Algebra.Structures.d_isGroup_1144
                        ((T_IsRing_2650 -> T_IsAbelianGroup_1132) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_IsRing_2650 -> T_IsAbelianGroup_1132
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2672
                           (T_IsRing_2650 -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650
v1))))))))
-- Algebra.Bundles.Ring._.uniqueʳ-⁻¹
d_unique'691''45''8315''185'_3938 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Ring_3800 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_unique'691''45''8315''185'_3938 :: () -> () -> T_Ring_3800 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_unique'691''45''8315''185'_3938 ~()
v0 ~()
v1 T_Ring_3800
v2
  = T_Ring_3800 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_unique'691''45''8315''185'_3938 T_Ring_3800
v2
du_unique'691''45''8315''185'_3938 ::
  T_Ring_3800 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_unique'691''45''8315''185'_3938 :: T_Ring_3800 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_unique'691''45''8315''185'_3938 T_Ring_3800
v0
  = let v1 :: AgdaAny -> AgdaAny -> AgdaAny
v1 = T_Ring_3800 -> AgdaAny -> AgdaAny -> AgdaAny
d__'43'__3826 (T_Ring_3800 -> T_Ring_3800
forall a b. a -> b
coe T_Ring_3800
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: AgdaAny -> AgdaAny
v2 = T_Ring_3800 -> AgdaAny -> AgdaAny
d_'45'__3830 (T_Ring_3800 -> T_Ring_3800
forall a b. a -> b
coe T_Ring_3800
v0) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: AgdaAny
v3 = T_Ring_3800 -> AgdaAny
d_0'35'_3832 (T_Ring_3800 -> T_Ring_3800
forall a b. a -> b
coe T_Ring_3800
v0) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsRing_2650
v4 = T_Ring_3800 -> T_IsRing_2650
d_isRing_3836 (T_Ring_3800 -> T_Ring_3800
forall a b. a -> b
coe T_Ring_3800
v0) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: t
v5
                      = (T_IsRing_2650 -> T_IsRingWithoutOne_2286) -> AgdaAny -> t
forall a b. a -> b
coe
                          T_IsRing_2650 -> T_IsRingWithoutOne_2286
MAlonzo.Code.Algebra.Structures.du_isRingWithoutOne_2682
                          (T_IsRing_2650 -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (let v6 :: T_IsAbelianGroup_1132
v6
                         = T_IsRingWithoutOne_2286 -> T_IsAbelianGroup_1132
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2304
                             (AgdaAny -> T_IsRingWithoutOne_2286
forall a b. a -> b
coe AgdaAny
forall a. a
v5) in
                   AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     (((AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> (AgdaAny -> AgdaAny)
 -> T_IsGroup_1036
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsGroup_1036
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.du_unique'691''45''8315''185'_1120
                        ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v1) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3) ((AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v2)
                        ((T_IsAbelianGroup_1132 -> T_IsGroup_1036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132 -> T_IsGroup_1036
MAlonzo.Code.Algebra.Structures.d_isGroup_1144 (T_IsAbelianGroup_1132 -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132
v6))))))))
-- Algebra.Bundles.Ring._.uniqueˡ-⁻¹
d_unique'737''45''8315''185'_3940 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Ring_3800 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_unique'737''45''8315''185'_3940 :: () -> () -> T_Ring_3800 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_unique'737''45''8315''185'_3940 ~()
v0 ~()
v1 T_Ring_3800
v2
  = T_Ring_3800 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_unique'737''45''8315''185'_3940 T_Ring_3800
v2
du_unique'737''45''8315''185'_3940 ::
  T_Ring_3800 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_unique'737''45''8315''185'_3940 :: T_Ring_3800 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_unique'737''45''8315''185'_3940 T_Ring_3800
v0
  = let v1 :: AgdaAny -> AgdaAny -> AgdaAny
v1 = T_Ring_3800 -> AgdaAny -> AgdaAny -> AgdaAny
d__'43'__3826 (T_Ring_3800 -> T_Ring_3800
forall a b. a -> b
coe T_Ring_3800
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: AgdaAny -> AgdaAny
v2 = T_Ring_3800 -> AgdaAny -> AgdaAny
d_'45'__3830 (T_Ring_3800 -> T_Ring_3800
forall a b. a -> b
coe T_Ring_3800
v0) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: AgdaAny
v3 = T_Ring_3800 -> AgdaAny
d_0'35'_3832 (T_Ring_3800 -> T_Ring_3800
forall a b. a -> b
coe T_Ring_3800
v0) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsRing_2650
v4 = T_Ring_3800 -> T_IsRing_2650
d_isRing_3836 (T_Ring_3800 -> T_Ring_3800
forall a b. a -> b
coe T_Ring_3800
v0) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: t
v5
                      = (T_IsRing_2650 -> T_IsRingWithoutOne_2286) -> AgdaAny -> t
forall a b. a -> b
coe
                          T_IsRing_2650 -> T_IsRingWithoutOne_2286
MAlonzo.Code.Algebra.Structures.du_isRingWithoutOne_2682
                          (T_IsRing_2650 -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (let v6 :: T_IsAbelianGroup_1132
v6
                         = T_IsRingWithoutOne_2286 -> T_IsAbelianGroup_1132
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2304
                             (AgdaAny -> T_IsRingWithoutOne_2286
forall a b. a -> b
coe AgdaAny
forall a. a
v5) in
                   AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     (((AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> (AgdaAny -> AgdaAny)
 -> T_IsGroup_1036
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsGroup_1036
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.du_unique'737''45''8315''185'_1114
                        ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v1) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3) ((AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v2)
                        ((T_IsAbelianGroup_1132 -> T_IsGroup_1036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132 -> T_IsGroup_1036
MAlonzo.Code.Algebra.Structures.d_isGroup_1144 (T_IsAbelianGroup_1132 -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132
v6))))))))
-- Algebra.Bundles.Ring._.zero
d_zero_3942 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Ring_3800 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_zero_3942 :: () -> () -> T_Ring_3800 -> T_Σ_14
d_zero_3942 ~()
v0 ~()
v1 T_Ring_3800
v2 = T_Ring_3800 -> T_Σ_14
du_zero_3942 T_Ring_3800
v2
du_zero_3942 ::
  T_Ring_3800 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
du_zero_3942 :: T_Ring_3800 -> T_Σ_14
du_zero_3942 T_Ring_3800
v0
  = let v1 :: AgdaAny -> AgdaAny -> AgdaAny
v1 = T_Ring_3800 -> AgdaAny -> AgdaAny -> AgdaAny
d__'43'__3826 (T_Ring_3800 -> T_Ring_3800
forall a b. a -> b
coe T_Ring_3800
v0) in
    AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      (let v2 :: AgdaAny -> AgdaAny -> AgdaAny
v2 = T_Ring_3800 -> AgdaAny -> AgdaAny -> AgdaAny
d__'42'__3828 (T_Ring_3800 -> T_Ring_3800
forall a b. a -> b
coe T_Ring_3800
v0) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: AgdaAny -> AgdaAny
v3 = T_Ring_3800 -> AgdaAny -> AgdaAny
d_'45'__3830 (T_Ring_3800 -> T_Ring_3800
forall a b. a -> b
coe T_Ring_3800
v0) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: AgdaAny
v4 = T_Ring_3800 -> AgdaAny
d_0'35'_3832 (T_Ring_3800 -> T_Ring_3800
forall a b. a -> b
coe T_Ring_3800
v0) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsRing_2650
v5 = T_Ring_3800 -> T_IsRing_2650
d_isRing_3836 (T_Ring_3800 -> T_Ring_3800
forall a b. a -> b
coe T_Ring_3800
v0) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (((AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny)
 -> AgdaAny
 -> T_IsRingWithoutOne_2286
 -> T_Σ_14)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsRingWithoutOne_2286
-> T_Σ_14
MAlonzo.Code.Algebra.Structures.du_zero_2386 ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v1) ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v2)
                     ((AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v3) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v4)
                     ((T_IsRing_2650 -> T_IsRingWithoutOne_2286) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsRing_2650 -> T_IsRingWithoutOne_2286
MAlonzo.Code.Algebra.Structures.du_isRingWithoutOne_2682
                        (T_IsRing_2650 -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650
v5)))))))
-- Algebra.Bundles.Ring._.zeroʳ
d_zero'691'_3944 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Ring_3800 -> AgdaAny -> AgdaAny
d_zero'691'_3944 :: () -> () -> T_Ring_3800 -> AgdaAny -> AgdaAny
d_zero'691'_3944 ~()
v0 ~()
v1 T_Ring_3800
v2 = T_Ring_3800 -> AgdaAny -> AgdaAny
du_zero'691'_3944 T_Ring_3800
v2
du_zero'691'_3944 :: T_Ring_3800 -> AgdaAny -> AgdaAny
du_zero'691'_3944 :: T_Ring_3800 -> AgdaAny -> AgdaAny
du_zero'691'_3944 T_Ring_3800
v0
  = let v1 :: AgdaAny -> AgdaAny -> AgdaAny
v1 = T_Ring_3800 -> AgdaAny -> AgdaAny -> AgdaAny
d__'43'__3826 (T_Ring_3800 -> T_Ring_3800
forall a b. a -> b
coe T_Ring_3800
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: AgdaAny -> AgdaAny -> AgdaAny
v2 = T_Ring_3800 -> AgdaAny -> AgdaAny -> AgdaAny
d__'42'__3828 (T_Ring_3800 -> T_Ring_3800
forall a b. a -> b
coe T_Ring_3800
v0) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: AgdaAny -> AgdaAny
v3 = T_Ring_3800 -> AgdaAny -> AgdaAny
d_'45'__3830 (T_Ring_3800 -> T_Ring_3800
forall a b. a -> b
coe T_Ring_3800
v0) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: AgdaAny
v4 = T_Ring_3800 -> AgdaAny
d_0'35'_3832 (T_Ring_3800 -> T_Ring_3800
forall a b. a -> b
coe T_Ring_3800
v0) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsRing_2650
v5 = T_Ring_3800 -> T_IsRing_2650
d_isRing_3836 (T_Ring_3800 -> T_Ring_3800
forall a b. a -> b
coe T_Ring_3800
v0) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (((AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny)
 -> AgdaAny
 -> T_IsRingWithoutOne_2286
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsRingWithoutOne_2286
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.du_zero'691'_2384 ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v1) ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v2)
                     ((AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v3) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v4)
                     ((T_IsRing_2650 -> T_IsRingWithoutOne_2286) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsRing_2650 -> T_IsRingWithoutOne_2286
MAlonzo.Code.Algebra.Structures.du_isRingWithoutOne_2682
                        (T_IsRing_2650 -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650
v5)))))))
-- Algebra.Bundles.Ring._.zeroˡ
d_zero'737'_3946 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Ring_3800 -> AgdaAny -> AgdaAny
d_zero'737'_3946 :: () -> () -> T_Ring_3800 -> AgdaAny -> AgdaAny
d_zero'737'_3946 ~()
v0 ~()
v1 T_Ring_3800
v2 = T_Ring_3800 -> AgdaAny -> AgdaAny
du_zero'737'_3946 T_Ring_3800
v2
du_zero'737'_3946 :: T_Ring_3800 -> AgdaAny -> AgdaAny
du_zero'737'_3946 :: T_Ring_3800 -> AgdaAny -> AgdaAny
du_zero'737'_3946 T_Ring_3800
v0
  = let v1 :: AgdaAny -> AgdaAny -> AgdaAny
v1 = T_Ring_3800 -> AgdaAny -> AgdaAny -> AgdaAny
d__'43'__3826 (T_Ring_3800 -> T_Ring_3800
forall a b. a -> b
coe T_Ring_3800
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: AgdaAny -> AgdaAny -> AgdaAny
v2 = T_Ring_3800 -> AgdaAny -> AgdaAny -> AgdaAny
d__'42'__3828 (T_Ring_3800 -> T_Ring_3800
forall a b. a -> b
coe T_Ring_3800
v0) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: AgdaAny -> AgdaAny
v3 = T_Ring_3800 -> AgdaAny -> AgdaAny
d_'45'__3830 (T_Ring_3800 -> T_Ring_3800
forall a b. a -> b
coe T_Ring_3800
v0) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: AgdaAny
v4 = T_Ring_3800 -> AgdaAny
d_0'35'_3832 (T_Ring_3800 -> T_Ring_3800
forall a b. a -> b
coe T_Ring_3800
v0) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsRing_2650
v5 = T_Ring_3800 -> T_IsRing_2650
d_isRing_3836 (T_Ring_3800 -> T_Ring_3800
forall a b. a -> b
coe T_Ring_3800
v0) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (((AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny)
 -> AgdaAny
 -> T_IsRingWithoutOne_2286
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsRingWithoutOne_2286
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.du_zero'737'_2382 ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v1) ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v2)
                     ((AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v3) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v4)
                     ((T_IsRing_2650 -> T_IsRingWithoutOne_2286) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsRing_2650 -> T_IsRingWithoutOne_2286
MAlonzo.Code.Algebra.Structures.du_isRingWithoutOne_2682
                        (T_IsRing_2650 -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650
v5)))))))
-- Algebra.Bundles.Ring.+-abelianGroup
d_'43''45'abelianGroup_3948 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Ring_3800 -> T_AbelianGroup_1636
d_'43''45'abelianGroup_3948 :: () -> () -> T_Ring_3800 -> T_AbelianGroup_1636
d_'43''45'abelianGroup_3948 ~()
v0 ~()
v1 T_Ring_3800
v2
  = T_Ring_3800 -> T_AbelianGroup_1636
du_'43''45'abelianGroup_3948 T_Ring_3800
v2
du_'43''45'abelianGroup_3948 :: T_Ring_3800 -> T_AbelianGroup_1636
du_'43''45'abelianGroup_3948 :: T_Ring_3800 -> T_AbelianGroup_1636
du_'43''45'abelianGroup_3948 T_Ring_3800
v0
  = ((AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> (AgdaAny -> AgdaAny)
 -> T_IsAbelianGroup_1132
 -> T_AbelianGroup_1636)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsAbelianGroup_1132
-> T_AbelianGroup_1636
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsAbelianGroup_1132
-> T_AbelianGroup_1636
C_AbelianGroup'46'constructor_29855 (T_Ring_3800 -> AgdaAny -> AgdaAny -> AgdaAny
d__'43'__3826 (T_Ring_3800 -> T_Ring_3800
forall a b. a -> b
coe T_Ring_3800
v0))
      (T_Ring_3800 -> AgdaAny
d_0'35'_3832 (T_Ring_3800 -> T_Ring_3800
forall a b. a -> b
coe T_Ring_3800
v0)) (T_Ring_3800 -> AgdaAny -> AgdaAny
d_'45'__3830 (T_Ring_3800 -> T_Ring_3800
forall a b. a -> b
coe T_Ring_3800
v0))
      (T_IsRing_2650 -> T_IsAbelianGroup_1132
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2672
         ((T_Ring_3800 -> T_IsRing_2650) -> AgdaAny -> T_IsRing_2650
forall a b. a -> b
coe T_Ring_3800 -> T_IsRing_2650
d_isRing_3836 (T_Ring_3800 -> AgdaAny
forall a b. a -> b
coe T_Ring_3800
v0)))
-- Algebra.Bundles.Ring.ringWithoutOne
d_ringWithoutOne_3950 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Ring_3800 -> T_RingWithoutOne_3344
d_ringWithoutOne_3950 :: () -> () -> T_Ring_3800 -> T_RingWithoutOne_3344
d_ringWithoutOne_3950 ~()
v0 ~()
v1 T_Ring_3800
v2 = T_Ring_3800 -> T_RingWithoutOne_3344
du_ringWithoutOne_3950 T_Ring_3800
v2
du_ringWithoutOne_3950 :: T_Ring_3800 -> T_RingWithoutOne_3344
du_ringWithoutOne_3950 :: T_Ring_3800 -> T_RingWithoutOne_3344
du_ringWithoutOne_3950 T_Ring_3800
v0
  = ((AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny)
 -> AgdaAny
 -> T_IsRingWithoutOne_2286
 -> T_RingWithoutOne_3344)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_RingWithoutOne_3344
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsRingWithoutOne_2286
-> T_RingWithoutOne_3344
C_RingWithoutOne'46'constructor_59923 (T_Ring_3800 -> AgdaAny -> AgdaAny -> AgdaAny
d__'43'__3826 (T_Ring_3800 -> T_Ring_3800
forall a b. a -> b
coe T_Ring_3800
v0))
      (T_Ring_3800 -> AgdaAny -> AgdaAny -> AgdaAny
d__'42'__3828 (T_Ring_3800 -> T_Ring_3800
forall a b. a -> b
coe T_Ring_3800
v0)) (T_Ring_3800 -> AgdaAny -> AgdaAny
d_'45'__3830 (T_Ring_3800 -> T_Ring_3800
forall a b. a -> b
coe T_Ring_3800
v0))
      (T_Ring_3800 -> AgdaAny
d_0'35'_3832 (T_Ring_3800 -> T_Ring_3800
forall a b. a -> b
coe T_Ring_3800
v0))
      ((T_IsRing_2650 -> T_IsRingWithoutOne_2286) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsRing_2650 -> T_IsRingWithoutOne_2286
MAlonzo.Code.Algebra.Structures.du_isRingWithoutOne_2682
         ((T_Ring_3800 -> T_IsRing_2650) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Ring_3800 -> T_IsRing_2650
d_isRing_3836 (T_Ring_3800 -> AgdaAny
forall a b. a -> b
coe T_Ring_3800
v0)))
-- Algebra.Bundles.Ring.semiring
d_semiring_3952 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Ring_3800 -> T_Semiring_2280
d_semiring_3952 :: () -> () -> T_Ring_3800 -> T_Semiring_2280
d_semiring_3952 ~()
v0 ~()
v1 T_Ring_3800
v2 = T_Ring_3800 -> T_Semiring_2280
du_semiring_3952 T_Ring_3800
v2
du_semiring_3952 :: T_Ring_3800 -> T_Semiring_2280
du_semiring_3952 :: T_Ring_3800 -> T_Semiring_2280
du_semiring_3952 T_Ring_3800
v0
  = ((AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> AgdaAny
 -> T_IsSemiring_1570
 -> T_Semiring_2280)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> T_Semiring_2280
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsSemiring_1570
-> T_Semiring_2280
C_Semiring'46'constructor_41765 (T_Ring_3800 -> AgdaAny -> AgdaAny -> AgdaAny
d__'43'__3826 (T_Ring_3800 -> T_Ring_3800
forall a b. a -> b
coe T_Ring_3800
v0))
      (T_Ring_3800 -> AgdaAny -> AgdaAny -> AgdaAny
d__'42'__3828 (T_Ring_3800 -> T_Ring_3800
forall a b. a -> b
coe T_Ring_3800
v0)) (T_Ring_3800 -> AgdaAny
d_0'35'_3832 (T_Ring_3800 -> T_Ring_3800
forall a b. a -> b
coe T_Ring_3800
v0))
      (T_Ring_3800 -> AgdaAny
d_1'35'_3834 (T_Ring_3800 -> T_Ring_3800
forall a b. a -> b
coe T_Ring_3800
v0))
      (((AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny)
 -> AgdaAny
 -> T_IsRing_2650
 -> T_IsSemiring_1570)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsRing_2650
-> T_IsSemiring_1570
MAlonzo.Code.Algebra.Structures.du_isSemiring_2778
         ((T_Ring_3800 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Ring_3800 -> AgdaAny -> AgdaAny -> AgdaAny
d__'43'__3826 (T_Ring_3800 -> AgdaAny
forall a b. a -> b
coe T_Ring_3800
v0)) ((T_Ring_3800 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Ring_3800 -> AgdaAny -> AgdaAny -> AgdaAny
d__'42'__3828 (T_Ring_3800 -> AgdaAny
forall a b. a -> b
coe T_Ring_3800
v0))
         ((T_Ring_3800 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Ring_3800 -> AgdaAny -> AgdaAny
d_'45'__3830 (T_Ring_3800 -> AgdaAny
forall a b. a -> b
coe T_Ring_3800
v0)) ((T_Ring_3800 -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Ring_3800 -> AgdaAny
d_0'35'_3832 (T_Ring_3800 -> AgdaAny
forall a b. a -> b
coe T_Ring_3800
v0))
         ((T_Ring_3800 -> T_IsRing_2650) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Ring_3800 -> T_IsRing_2650
d_isRing_3836 (T_Ring_3800 -> AgdaAny
forall a b. a -> b
coe T_Ring_3800
v0)))
-- Algebra.Bundles.Ring._._≉_
d__'8777'__3956 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Ring_3800 -> AgdaAny -> AgdaAny -> ()
d__'8777'__3956 :: () -> () -> T_Ring_3800 -> AgdaAny -> AgdaAny -> ()
d__'8777'__3956 = () -> () -> T_Ring_3800 -> AgdaAny -> AgdaAny -> ()
forall a. a
erased
-- Algebra.Bundles.Ring._.magma
d_magma_3958 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 -> T_Ring_3800 -> T_Magma_68
d_magma_3958 :: () -> () -> T_Ring_3800 -> T_Magma_68
d_magma_3958 ~()
v0 ~()
v1 T_Ring_3800
v2 = T_Ring_3800 -> T_Magma_68
du_magma_3958 T_Ring_3800
v2
du_magma_3958 :: T_Ring_3800 -> T_Magma_68
du_magma_3958 :: T_Ring_3800 -> T_Magma_68
du_magma_3958 T_Ring_3800
v0
  = let v1 :: t
v1 = (T_Ring_3800 -> T_Semiring_2280) -> AgdaAny -> t
forall a b. a -> b
coe T_Ring_3800 -> T_Semiring_2280
du_semiring_3952 (T_Ring_3800 -> AgdaAny
forall a b. a -> b
coe T_Ring_3800
v0) in
    AgdaAny -> T_Magma_68
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_Semiring_2280 -> T_SemiringWithoutAnnihilatingZero_2130)
-> AgdaAny -> t
forall a b. a -> b
coe T_Semiring_2280 -> T_SemiringWithoutAnnihilatingZero_2130
du_semiringWithoutAnnihilatingZero_2398 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: t
v3 = (T_SemiringWithoutAnnihilatingZero_2130 -> T_Monoid_882)
-> AgdaAny -> t
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_2130 -> T_Monoid_882
du_'42''45'monoid_2264 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_Semigroup_536 -> T_Magma_68) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semigroup_536 -> T_Magma_68
du_magma_584 ((T_Monoid_882 -> T_Semigroup_536) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Monoid_882 -> T_Semigroup_536
du_semigroup_944 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3)))))
-- Algebra.Bundles.Ring._.*-monoid
d_'42''45'monoid_3960 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Ring_3800 -> T_Monoid_882
d_'42''45'monoid_3960 :: () -> () -> T_Ring_3800 -> T_Monoid_882
d_'42''45'monoid_3960 ~()
v0 ~()
v1 T_Ring_3800
v2 = T_Ring_3800 -> T_Monoid_882
du_'42''45'monoid_3960 T_Ring_3800
v2
du_'42''45'monoid_3960 :: T_Ring_3800 -> T_Monoid_882
du_'42''45'monoid_3960 :: T_Ring_3800 -> T_Monoid_882
du_'42''45'monoid_3960 T_Ring_3800
v0
  = let v1 :: t
v1 = (T_Ring_3800 -> T_Semiring_2280) -> AgdaAny -> t
forall a b. a -> b
coe T_Ring_3800 -> T_Semiring_2280
du_semiring_3952 (T_Ring_3800 -> AgdaAny
forall a b. a -> b
coe T_Ring_3800
v0) in
    AgdaAny -> T_Monoid_882
forall a b. a -> b
coe
      ((T_SemiringWithoutAnnihilatingZero_2130 -> T_Monoid_882)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_SemiringWithoutAnnihilatingZero_2130 -> T_Monoid_882
du_'42''45'monoid_2264
         ((T_Semiring_2280 -> T_SemiringWithoutAnnihilatingZero_2130)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semiring_2280 -> T_SemiringWithoutAnnihilatingZero_2130
du_semiringWithoutAnnihilatingZero_2398 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1)))
-- Algebra.Bundles.Ring._.rawMagma
d_rawMagma_3962 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Ring_3800 -> MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
d_rawMagma_3962 :: () -> () -> T_Ring_3800 -> T_RawMagma_36
d_rawMagma_3962 ~()
v0 ~()
v1 T_Ring_3800
v2 = T_Ring_3800 -> T_RawMagma_36
du_rawMagma_3962 T_Ring_3800
v2
du_rawMagma_3962 ::
  T_Ring_3800 -> MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
du_rawMagma_3962 :: T_Ring_3800 -> T_RawMagma_36
du_rawMagma_3962 T_Ring_3800
v0
  = let v1 :: t
v1 = (T_Ring_3800 -> T_Semiring_2280) -> AgdaAny -> t
forall a b. a -> b
coe T_Ring_3800 -> T_Semiring_2280
du_semiring_3952 (T_Ring_3800 -> AgdaAny
forall a b. a -> b
coe T_Ring_3800
v0) in
    AgdaAny -> T_RawMagma_36
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_Semiring_2280 -> T_SemiringWithoutAnnihilatingZero_2130)
-> AgdaAny -> t
forall a b. a -> b
coe T_Semiring_2280 -> T_SemiringWithoutAnnihilatingZero_2130
du_semiringWithoutAnnihilatingZero_2398 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: t
v3 = (T_SemiringWithoutAnnihilatingZero_2130 -> T_Monoid_882)
-> AgdaAny -> t
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_2130 -> T_Monoid_882
du_'42''45'monoid_2264 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: t
v4 = (T_Monoid_882 -> T_Semigroup_536) -> AgdaAny -> t
forall a b. a -> b
coe T_Monoid_882 -> T_Semigroup_536
du_semigroup_944 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_Magma_68 -> T_RawMagma_36) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Magma_68 -> T_RawMagma_36
du_rawMagma_112 ((T_Semigroup_536 -> T_Magma_68) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semigroup_536 -> T_Magma_68
du_magma_584 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v4))))))
-- Algebra.Bundles.Ring._.rawMonoid
d_rawMonoid_3964 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Ring_3800 -> MAlonzo.Code.Algebra.Bundles.Raw.T_RawMonoid_64
d_rawMonoid_3964 :: () -> () -> T_Ring_3800 -> T_RawMonoid_64
d_rawMonoid_3964 ~()
v0 ~()
v1 T_Ring_3800
v2 = T_Ring_3800 -> T_RawMonoid_64
du_rawMonoid_3964 T_Ring_3800
v2
du_rawMonoid_3964 ::
  T_Ring_3800 -> MAlonzo.Code.Algebra.Bundles.Raw.T_RawMonoid_64
du_rawMonoid_3964 :: T_Ring_3800 -> T_RawMonoid_64
du_rawMonoid_3964 T_Ring_3800
v0
  = let v1 :: t
v1 = (T_Ring_3800 -> T_Semiring_2280) -> AgdaAny -> t
forall a b. a -> b
coe T_Ring_3800 -> T_Semiring_2280
du_semiring_3952 (T_Ring_3800 -> AgdaAny
forall a b. a -> b
coe T_Ring_3800
v0) in
    AgdaAny -> T_RawMonoid_64
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_Semiring_2280 -> T_SemiringWithoutAnnihilatingZero_2130)
-> AgdaAny -> t
forall a b. a -> b
coe T_Semiring_2280 -> T_SemiringWithoutAnnihilatingZero_2130
du_semiringWithoutAnnihilatingZero_2398 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_Monoid_882 -> T_RawMonoid_64) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Monoid_882 -> T_RawMonoid_64
du_rawMonoid_954 ((T_SemiringWithoutAnnihilatingZero_2130 -> T_Monoid_882)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_2130 -> T_Monoid_882
du_'42''45'monoid_2264 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2))))
-- Algebra.Bundles.Ring._.semigroup
d_semigroup_3966 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Ring_3800 -> T_Semigroup_536
d_semigroup_3966 :: () -> () -> T_Ring_3800 -> T_Semigroup_536
d_semigroup_3966 ~()
v0 ~()
v1 T_Ring_3800
v2 = T_Ring_3800 -> T_Semigroup_536
du_semigroup_3966 T_Ring_3800
v2
du_semigroup_3966 :: T_Ring_3800 -> T_Semigroup_536
du_semigroup_3966 :: T_Ring_3800 -> T_Semigroup_536
du_semigroup_3966 T_Ring_3800
v0
  = let v1 :: t
v1 = (T_Ring_3800 -> T_Semiring_2280) -> AgdaAny -> t
forall a b. a -> b
coe T_Ring_3800 -> T_Semiring_2280
du_semiring_3952 (T_Ring_3800 -> AgdaAny
forall a b. a -> b
coe T_Ring_3800
v0) in
    AgdaAny -> T_Semigroup_536
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_Semiring_2280 -> T_SemiringWithoutAnnihilatingZero_2130)
-> AgdaAny -> t
forall a b. a -> b
coe T_Semiring_2280 -> T_SemiringWithoutAnnihilatingZero_2130
du_semiringWithoutAnnihilatingZero_2398 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_Monoid_882 -> T_Semigroup_536) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Monoid_882 -> T_Semigroup_536
du_semigroup_944 ((T_SemiringWithoutAnnihilatingZero_2130 -> T_Monoid_882)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_2130 -> T_Monoid_882
du_'42''45'monoid_2264 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2))))
-- Algebra.Bundles.Ring._.commutativeMagma
d_commutativeMagma_3968 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Ring_3800 -> T_CommutativeMagma_180
d_commutativeMagma_3968 :: () -> () -> T_Ring_3800 -> T_CommutativeMagma_180
d_commutativeMagma_3968 ~()
v0 ~()
v1 T_Ring_3800
v2 = T_Ring_3800 -> T_CommutativeMagma_180
du_commutativeMagma_3968 T_Ring_3800
v2
du_commutativeMagma_3968 :: T_Ring_3800 -> T_CommutativeMagma_180
du_commutativeMagma_3968 :: T_Ring_3800 -> T_CommutativeMagma_180
du_commutativeMagma_3968 T_Ring_3800
v0
  = let v1 :: t
v1 = (T_Ring_3800 -> T_Semiring_2280) -> AgdaAny -> t
forall a b. a -> b
coe T_Ring_3800 -> T_Semiring_2280
du_semiring_3952 (T_Ring_3800 -> AgdaAny
forall a b. a -> b
coe T_Ring_3800
v0) in
    AgdaAny -> T_CommutativeMagma_180
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_Semiring_2280 -> T_SemiringWithoutAnnihilatingZero_2130)
-> AgdaAny -> t
forall a b. a -> b
coe T_Semiring_2280 -> T_SemiringWithoutAnnihilatingZero_2130
du_semiringWithoutAnnihilatingZero_2398 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: t
v3 = (T_SemiringWithoutAnnihilatingZero_2130 -> T_CommutativeMonoid_962)
-> AgdaAny -> t
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_2130 -> T_CommutativeMonoid_962
du_'43''45'commutativeMonoid_2242 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_CommutativeSemigroup_662 -> T_CommutativeMagma_180)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_CommutativeSemigroup_662 -> T_CommutativeMagma_180
du_commutativeMagma_726
               ((T_CommutativeMonoid_962 -> T_CommutativeSemigroup_662)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeMonoid_962 -> T_CommutativeSemigroup_662
du_commutativeSemigroup_1048 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3)))))
-- Algebra.Bundles.Ring._.+-commutativeMonoid
d_'43''45'commutativeMonoid_3970 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Ring_3800 -> T_CommutativeMonoid_962
d_'43''45'commutativeMonoid_3970 :: () -> () -> T_Ring_3800 -> T_CommutativeMonoid_962
d_'43''45'commutativeMonoid_3970 ~()
v0 ~()
v1 T_Ring_3800
v2
  = T_Ring_3800 -> T_CommutativeMonoid_962
du_'43''45'commutativeMonoid_3970 T_Ring_3800
v2
du_'43''45'commutativeMonoid_3970 ::
  T_Ring_3800 -> T_CommutativeMonoid_962
du_'43''45'commutativeMonoid_3970 :: T_Ring_3800 -> T_CommutativeMonoid_962
du_'43''45'commutativeMonoid_3970 T_Ring_3800
v0
  = let v1 :: t
v1 = (T_Ring_3800 -> T_Semiring_2280) -> AgdaAny -> t
forall a b. a -> b
coe T_Ring_3800 -> T_Semiring_2280
du_semiring_3952 (T_Ring_3800 -> AgdaAny
forall a b. a -> b
coe T_Ring_3800
v0) in
    AgdaAny -> T_CommutativeMonoid_962
forall a b. a -> b
coe
      ((T_SemiringWithoutAnnihilatingZero_2130 -> T_CommutativeMonoid_962)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_SemiringWithoutAnnihilatingZero_2130 -> T_CommutativeMonoid_962
du_'43''45'commutativeMonoid_2242
         ((T_Semiring_2280 -> T_SemiringWithoutAnnihilatingZero_2130)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semiring_2280 -> T_SemiringWithoutAnnihilatingZero_2130
du_semiringWithoutAnnihilatingZero_2398 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1)))
-- Algebra.Bundles.Ring._.commutativeSemigroup
d_commutativeSemigroup_3972 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Ring_3800 -> T_CommutativeSemigroup_662
d_commutativeSemigroup_3972 :: () -> () -> T_Ring_3800 -> T_CommutativeSemigroup_662
d_commutativeSemigroup_3972 ~()
v0 ~()
v1 T_Ring_3800
v2
  = T_Ring_3800 -> T_CommutativeSemigroup_662
du_commutativeSemigroup_3972 T_Ring_3800
v2
du_commutativeSemigroup_3972 ::
  T_Ring_3800 -> T_CommutativeSemigroup_662
du_commutativeSemigroup_3972 :: T_Ring_3800 -> T_CommutativeSemigroup_662
du_commutativeSemigroup_3972 T_Ring_3800
v0
  = let v1 :: t
v1 = (T_Ring_3800 -> T_Semiring_2280) -> AgdaAny -> t
forall a b. a -> b
coe T_Ring_3800 -> T_Semiring_2280
du_semiring_3952 (T_Ring_3800 -> AgdaAny
forall a b. a -> b
coe T_Ring_3800
v0) in
    AgdaAny -> T_CommutativeSemigroup_662
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_Semiring_2280 -> T_SemiringWithoutAnnihilatingZero_2130)
-> AgdaAny -> t
forall a b. a -> b
coe T_Semiring_2280 -> T_SemiringWithoutAnnihilatingZero_2130
du_semiringWithoutAnnihilatingZero_2398 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_CommutativeMonoid_962 -> T_CommutativeSemigroup_662)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_CommutativeMonoid_962 -> T_CommutativeSemigroup_662
du_commutativeSemigroup_1048
            ((T_SemiringWithoutAnnihilatingZero_2130 -> T_CommutativeMonoid_962)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_2130 -> T_CommutativeMonoid_962
du_'43''45'commutativeMonoid_2242 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2))))
-- Algebra.Bundles.Ring._.magma
d_magma_3974 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 -> T_Ring_3800 -> T_Magma_68
d_magma_3974 :: () -> () -> T_Ring_3800 -> T_Magma_68
d_magma_3974 ~()
v0 ~()
v1 T_Ring_3800
v2 = T_Ring_3800 -> T_Magma_68
du_magma_3974 T_Ring_3800
v2
du_magma_3974 :: T_Ring_3800 -> T_Magma_68
du_magma_3974 :: T_Ring_3800 -> T_Magma_68
du_magma_3974 T_Ring_3800
v0
  = let v1 :: t
v1 = (T_Ring_3800 -> T_Semiring_2280) -> AgdaAny -> t
forall a b. a -> b
coe T_Ring_3800 -> T_Semiring_2280
du_semiring_3952 (T_Ring_3800 -> AgdaAny
forall a b. a -> b
coe T_Ring_3800
v0) in
    AgdaAny -> T_Magma_68
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_Semiring_2280 -> T_SemiringWithoutAnnihilatingZero_2130)
-> AgdaAny -> t
forall a b. a -> b
coe T_Semiring_2280 -> T_SemiringWithoutAnnihilatingZero_2130
du_semiringWithoutAnnihilatingZero_2398 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: t
v3 = (T_SemiringWithoutAnnihilatingZero_2130 -> T_CommutativeMonoid_962)
-> AgdaAny -> t
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_2130 -> T_CommutativeMonoid_962
du_'43''45'commutativeMonoid_2242 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: t
v4 = (T_CommutativeMonoid_962 -> T_Monoid_882) -> AgdaAny -> t
forall a b. a -> b
coe T_CommutativeMonoid_962 -> T_Monoid_882
du_monoid_1032 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_Semigroup_536 -> T_Magma_68) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semigroup_536 -> T_Magma_68
du_magma_584 ((T_Monoid_882 -> T_Semigroup_536) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Monoid_882 -> T_Semigroup_536
du_semigroup_944 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v4))))))
-- Algebra.Bundles.Ring._.monoid
d_monoid_3976 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Ring_3800 -> T_Monoid_882
d_monoid_3976 :: () -> () -> T_Ring_3800 -> T_Monoid_882
d_monoid_3976 ~()
v0 ~()
v1 T_Ring_3800
v2 = T_Ring_3800 -> T_Monoid_882
du_monoid_3976 T_Ring_3800
v2
du_monoid_3976 :: T_Ring_3800 -> T_Monoid_882
du_monoid_3976 :: T_Ring_3800 -> T_Monoid_882
du_monoid_3976 T_Ring_3800
v0
  = let v1 :: t
v1 = (T_Ring_3800 -> T_Semiring_2280) -> AgdaAny -> t
forall a b. a -> b
coe T_Ring_3800 -> T_Semiring_2280
du_semiring_3952 (T_Ring_3800 -> AgdaAny
forall a b. a -> b
coe T_Ring_3800
v0) in
    AgdaAny -> T_Monoid_882
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_Semiring_2280 -> T_SemiringWithoutAnnihilatingZero_2130)
-> AgdaAny -> t
forall a b. a -> b
coe T_Semiring_2280 -> T_SemiringWithoutAnnihilatingZero_2130
du_semiringWithoutAnnihilatingZero_2398 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_CommutativeMonoid_962 -> T_Monoid_882) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_CommutativeMonoid_962 -> T_Monoid_882
du_monoid_1032 ((T_SemiringWithoutAnnihilatingZero_2130 -> T_CommutativeMonoid_962)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_2130 -> T_CommutativeMonoid_962
du_'43''45'commutativeMonoid_2242 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2))))
-- Algebra.Bundles.Ring._.rawMagma
d_rawMagma_3978 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Ring_3800 -> MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
d_rawMagma_3978 :: () -> () -> T_Ring_3800 -> T_RawMagma_36
d_rawMagma_3978 ~()
v0 ~()
v1 T_Ring_3800
v2 = T_Ring_3800 -> T_RawMagma_36
du_rawMagma_3978 T_Ring_3800
v2
du_rawMagma_3978 ::
  T_Ring_3800 -> MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
du_rawMagma_3978 :: T_Ring_3800 -> T_RawMagma_36
du_rawMagma_3978 T_Ring_3800
v0
  = let v1 :: t
v1 = (T_Ring_3800 -> T_Semiring_2280) -> AgdaAny -> t
forall a b. a -> b
coe T_Ring_3800 -> T_Semiring_2280
du_semiring_3952 (T_Ring_3800 -> AgdaAny
forall a b. a -> b
coe T_Ring_3800
v0) in
    AgdaAny -> T_RawMagma_36
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_Semiring_2280 -> T_SemiringWithoutAnnihilatingZero_2130)
-> AgdaAny -> t
forall a b. a -> b
coe T_Semiring_2280 -> T_SemiringWithoutAnnihilatingZero_2130
du_semiringWithoutAnnihilatingZero_2398 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: t
v3 = (T_SemiringWithoutAnnihilatingZero_2130 -> T_CommutativeMonoid_962)
-> AgdaAny -> t
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_2130 -> T_CommutativeMonoid_962
du_'43''45'commutativeMonoid_2242 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: t
v4 = (T_CommutativeMonoid_962 -> T_Monoid_882) -> AgdaAny -> t
forall a b. a -> b
coe T_CommutativeMonoid_962 -> T_Monoid_882
du_monoid_1032 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: t
v5 = (T_Monoid_882 -> T_Semigroup_536) -> AgdaAny -> t
forall a b. a -> b
coe T_Monoid_882 -> T_Semigroup_536
du_semigroup_944 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_Magma_68 -> T_RawMagma_36) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Magma_68 -> T_RawMagma_36
du_rawMagma_112 ((T_Semigroup_536 -> T_Magma_68) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semigroup_536 -> T_Magma_68
du_magma_584 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v5)))))))
-- Algebra.Bundles.Ring._.rawMonoid
d_rawMonoid_3980 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Ring_3800 -> MAlonzo.Code.Algebra.Bundles.Raw.T_RawMonoid_64
d_rawMonoid_3980 :: () -> () -> T_Ring_3800 -> T_RawMonoid_64
d_rawMonoid_3980 ~()
v0 ~()
v1 T_Ring_3800
v2 = T_Ring_3800 -> T_RawMonoid_64
du_rawMonoid_3980 T_Ring_3800
v2
du_rawMonoid_3980 ::
  T_Ring_3800 -> MAlonzo.Code.Algebra.Bundles.Raw.T_RawMonoid_64
du_rawMonoid_3980 :: T_Ring_3800 -> T_RawMonoid_64
du_rawMonoid_3980 T_Ring_3800
v0
  = let v1 :: t
v1 = (T_Ring_3800 -> T_Semiring_2280) -> AgdaAny -> t
forall a b. a -> b
coe T_Ring_3800 -> T_Semiring_2280
du_semiring_3952 (T_Ring_3800 -> AgdaAny
forall a b. a -> b
coe T_Ring_3800
v0) in
    AgdaAny -> T_RawMonoid_64
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_Semiring_2280 -> T_SemiringWithoutAnnihilatingZero_2130)
-> AgdaAny -> t
forall a b. a -> b
coe T_Semiring_2280 -> T_SemiringWithoutAnnihilatingZero_2130
du_semiringWithoutAnnihilatingZero_2398 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: t
v3 = (T_SemiringWithoutAnnihilatingZero_2130 -> T_CommutativeMonoid_962)
-> AgdaAny -> t
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_2130 -> T_CommutativeMonoid_962
du_'43''45'commutativeMonoid_2242 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_Monoid_882 -> T_RawMonoid_64) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Monoid_882 -> T_RawMonoid_64
du_rawMonoid_954 ((T_CommutativeMonoid_962 -> T_Monoid_882) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeMonoid_962 -> T_Monoid_882
du_monoid_1032 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3)))))
-- Algebra.Bundles.Ring._.semigroup
d_semigroup_3982 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Ring_3800 -> T_Semigroup_536
d_semigroup_3982 :: () -> () -> T_Ring_3800 -> T_Semigroup_536
d_semigroup_3982 ~()
v0 ~()
v1 T_Ring_3800
v2 = T_Ring_3800 -> T_Semigroup_536
du_semigroup_3982 T_Ring_3800
v2
du_semigroup_3982 :: T_Ring_3800 -> T_Semigroup_536
du_semigroup_3982 :: T_Ring_3800 -> T_Semigroup_536
du_semigroup_3982 T_Ring_3800
v0
  = let v1 :: t
v1 = (T_Ring_3800 -> T_Semiring_2280) -> AgdaAny -> t
forall a b. a -> b
coe T_Ring_3800 -> T_Semiring_2280
du_semiring_3952 (T_Ring_3800 -> AgdaAny
forall a b. a -> b
coe T_Ring_3800
v0) in
    AgdaAny -> T_Semigroup_536
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_Semiring_2280 -> T_SemiringWithoutAnnihilatingZero_2130)
-> AgdaAny -> t
forall a b. a -> b
coe T_Semiring_2280 -> T_SemiringWithoutAnnihilatingZero_2130
du_semiringWithoutAnnihilatingZero_2398 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: t
v3 = (T_SemiringWithoutAnnihilatingZero_2130 -> T_CommutativeMonoid_962)
-> AgdaAny -> t
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_2130 -> T_CommutativeMonoid_962
du_'43''45'commutativeMonoid_2242 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_Monoid_882 -> T_Semigroup_536) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Monoid_882 -> T_Semigroup_536
du_semigroup_944 ((T_CommutativeMonoid_962 -> T_Monoid_882) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeMonoid_962 -> T_Monoid_882
du_monoid_1032 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3)))))
-- Algebra.Bundles.Ring._.unitalMagma
d_unitalMagma_3984 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Ring_3800 -> T_UnitalMagma_814
d_unitalMagma_3984 :: () -> () -> T_Ring_3800 -> T_UnitalMagma_814
d_unitalMagma_3984 ~()
v0 ~()
v1 T_Ring_3800
v2 = T_Ring_3800 -> T_UnitalMagma_814
du_unitalMagma_3984 T_Ring_3800
v2
du_unitalMagma_3984 :: T_Ring_3800 -> T_UnitalMagma_814
du_unitalMagma_3984 :: T_Ring_3800 -> T_UnitalMagma_814
du_unitalMagma_3984 T_Ring_3800
v0
  = let v1 :: t
v1 = (T_Ring_3800 -> T_Semiring_2280) -> AgdaAny -> t
forall a b. a -> b
coe T_Ring_3800 -> T_Semiring_2280
du_semiring_3952 (T_Ring_3800 -> AgdaAny
forall a b. a -> b
coe T_Ring_3800
v0) in
    AgdaAny -> T_UnitalMagma_814
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_Semiring_2280 -> T_SemiringWithoutAnnihilatingZero_2130)
-> AgdaAny -> t
forall a b. a -> b
coe T_Semiring_2280 -> T_SemiringWithoutAnnihilatingZero_2130
du_semiringWithoutAnnihilatingZero_2398 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: t
v3 = (T_SemiringWithoutAnnihilatingZero_2130 -> T_CommutativeMonoid_962)
-> AgdaAny -> t
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_2130 -> T_CommutativeMonoid_962
du_'43''45'commutativeMonoid_2242 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_Monoid_882 -> T_UnitalMagma_814) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Monoid_882 -> T_UnitalMagma_814
du_unitalMagma_956 ((T_CommutativeMonoid_962 -> T_Monoid_882) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeMonoid_962 -> T_Monoid_882
du_monoid_1032 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3)))))
-- Algebra.Bundles.Ring._.nearSemiring
d_nearSemiring_3986 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Ring_3800 -> T_NearSemiring_1766
d_nearSemiring_3986 :: () -> () -> T_Ring_3800 -> T_NearSemiring_1766
d_nearSemiring_3986 ~()
v0 ~()
v1 T_Ring_3800
v2 = T_Ring_3800 -> T_NearSemiring_1766
du_nearSemiring_3986 T_Ring_3800
v2
du_nearSemiring_3986 :: T_Ring_3800 -> T_NearSemiring_1766
du_nearSemiring_3986 :: T_Ring_3800 -> T_NearSemiring_1766
du_nearSemiring_3986 T_Ring_3800
v0
  = let v1 :: t
v1 = (T_Ring_3800 -> T_Semiring_2280) -> AgdaAny -> t
forall a b. a -> b
coe T_Ring_3800 -> T_Semiring_2280
du_semiring_3952 (T_Ring_3800 -> AgdaAny
forall a b. a -> b
coe T_Ring_3800
v0) in
    AgdaAny -> T_NearSemiring_1766
forall a b. a -> b
coe
      ((T_SemiringWithoutOne_1880 -> T_NearSemiring_1766)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_SemiringWithoutOne_1880 -> T_NearSemiring_1766
du_nearSemiring_1966 ((T_Semiring_2280 -> T_SemiringWithoutOne_1880)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semiring_2280 -> T_SemiringWithoutOne_1880
du_semiringWithoutOne_2436 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1)))
-- Algebra.Bundles.Ring._.semiringWithoutAnnihilatingZero
d_semiringWithoutAnnihilatingZero_3988 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Ring_3800 -> T_SemiringWithoutAnnihilatingZero_2130
d_semiringWithoutAnnihilatingZero_3988 :: () -> () -> T_Ring_3800 -> T_SemiringWithoutAnnihilatingZero_2130
d_semiringWithoutAnnihilatingZero_3988 ~()
v0 ~()
v1 T_Ring_3800
v2
  = T_Ring_3800 -> T_SemiringWithoutAnnihilatingZero_2130
du_semiringWithoutAnnihilatingZero_3988 T_Ring_3800
v2
du_semiringWithoutAnnihilatingZero_3988 ::
  T_Ring_3800 -> T_SemiringWithoutAnnihilatingZero_2130
du_semiringWithoutAnnihilatingZero_3988 :: T_Ring_3800 -> T_SemiringWithoutAnnihilatingZero_2130
du_semiringWithoutAnnihilatingZero_3988 T_Ring_3800
v0
  = (T_Semiring_2280 -> T_SemiringWithoutAnnihilatingZero_2130)
-> AgdaAny -> T_SemiringWithoutAnnihilatingZero_2130
forall a b. a -> b
coe
      T_Semiring_2280 -> T_SemiringWithoutAnnihilatingZero_2130
du_semiringWithoutAnnihilatingZero_2398
      ((T_Ring_3800 -> T_Semiring_2280) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Ring_3800 -> T_Semiring_2280
du_semiring_3952 (T_Ring_3800 -> AgdaAny
forall a b. a -> b
coe T_Ring_3800
v0))
-- Algebra.Bundles.Ring._.semiringWithoutOne
d_semiringWithoutOne_3990 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Ring_3800 -> T_SemiringWithoutOne_1880
d_semiringWithoutOne_3990 :: () -> () -> T_Ring_3800 -> T_SemiringWithoutOne_1880
d_semiringWithoutOne_3990 ~()
v0 ~()
v1 T_Ring_3800
v2
  = T_Ring_3800 -> T_SemiringWithoutOne_1880
du_semiringWithoutOne_3990 T_Ring_3800
v2
du_semiringWithoutOne_3990 ::
  T_Ring_3800 -> T_SemiringWithoutOne_1880
du_semiringWithoutOne_3990 :: T_Ring_3800 -> T_SemiringWithoutOne_1880
du_semiringWithoutOne_3990 T_Ring_3800
v0
  = (T_Semiring_2280 -> T_SemiringWithoutOne_1880)
-> AgdaAny -> T_SemiringWithoutOne_1880
forall a b. a -> b
coe T_Semiring_2280 -> T_SemiringWithoutOne_1880
du_semiringWithoutOne_2436 ((T_Ring_3800 -> T_Semiring_2280) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Ring_3800 -> T_Semiring_2280
du_semiring_3952 (T_Ring_3800 -> AgdaAny
forall a b. a -> b
coe T_Ring_3800
v0))
-- Algebra.Bundles.Ring._.rawNearSemiring
d_rawNearSemiring_3994 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Ring_3800 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawNearSemiring_134
d_rawNearSemiring_3994 :: () -> () -> T_Ring_3800 -> T_RawNearSemiring_134
d_rawNearSemiring_3994 ~()
v0 ~()
v1 T_Ring_3800
v2 = T_Ring_3800 -> T_RawNearSemiring_134
du_rawNearSemiring_3994 T_Ring_3800
v2
du_rawNearSemiring_3994 ::
  T_Ring_3800 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawNearSemiring_134
du_rawNearSemiring_3994 :: T_Ring_3800 -> T_RawNearSemiring_134
du_rawNearSemiring_3994 T_Ring_3800
v0
  = (T_NearSemiring_1766 -> T_RawNearSemiring_134)
-> AgdaAny -> T_RawNearSemiring_134
forall a b. a -> b
coe
      T_NearSemiring_1766 -> T_RawNearSemiring_134
du_rawNearSemiring_1850
      ((T_SemiringWithoutOne_1880 -> T_NearSemiring_1766)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_SemiringWithoutOne_1880 -> T_NearSemiring_1766
du_nearSemiring_1966
         ((T_Semiring_2280 -> T_SemiringWithoutOne_1880)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semiring_2280 -> T_SemiringWithoutOne_1880
du_semiringWithoutOne_2436 ((T_Ring_3800 -> T_Semiring_2280) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Ring_3800 -> T_Semiring_2280
du_semiring_3952 (T_Ring_3800 -> AgdaAny
forall a b. a -> b
coe T_Ring_3800
v0))))
-- Algebra.Bundles.Ring._.group
d_group_3998 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Ring_3800 -> T_Group_1520
d_group_3998 :: () -> () -> T_Ring_3800 -> T_Group_1520
d_group_3998 ~()
v0 ~()
v1 T_Ring_3800
v2 = T_Ring_3800 -> T_Group_1520
du_group_3998 T_Ring_3800
v2
du_group_3998 :: T_Ring_3800 -> T_Group_1520
du_group_3998 :: T_Ring_3800 -> T_Group_1520
du_group_3998 T_Ring_3800
v0
  = (T_AbelianGroup_1636 -> T_Group_1520) -> AgdaAny -> T_Group_1520
forall a b. a -> b
coe T_AbelianGroup_1636 -> T_Group_1520
du_group_1732 ((T_Ring_3800 -> T_AbelianGroup_1636) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Ring_3800 -> T_AbelianGroup_1636
du_'43''45'abelianGroup_3948 (T_Ring_3800 -> AgdaAny
forall a b. a -> b
coe T_Ring_3800
v0))
-- Algebra.Bundles.Ring._.invertibleMagma
d_invertibleMagma_4000 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Ring_3800 -> T_InvertibleMagma_1360
d_invertibleMagma_4000 :: () -> () -> T_Ring_3800 -> T_InvertibleMagma_1360
d_invertibleMagma_4000 ~()
v0 ~()
v1 T_Ring_3800
v2 = T_Ring_3800 -> T_InvertibleMagma_1360
du_invertibleMagma_4000 T_Ring_3800
v2
du_invertibleMagma_4000 :: T_Ring_3800 -> T_InvertibleMagma_1360
du_invertibleMagma_4000 :: T_Ring_3800 -> T_InvertibleMagma_1360
du_invertibleMagma_4000 T_Ring_3800
v0
  = let v1 :: t
v1 = (T_Ring_3800 -> T_AbelianGroup_1636) -> AgdaAny -> t
forall a b. a -> b
coe T_Ring_3800 -> T_AbelianGroup_1636
du_'43''45'abelianGroup_3948 (T_Ring_3800 -> AgdaAny
forall a b. a -> b
coe T_Ring_3800
v0) in
    AgdaAny -> T_InvertibleMagma_1360
forall a b. a -> b
coe ((T_Group_1520 -> T_InvertibleMagma_1360) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Group_1520 -> T_InvertibleMagma_1360
du_invertibleMagma_1628 ((T_AbelianGroup_1636 -> T_Group_1520) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_AbelianGroup_1636 -> T_Group_1520
du_group_1732 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1)))
-- Algebra.Bundles.Ring._.invertibleUnitalMagma
d_invertibleUnitalMagma_4002 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Ring_3800 -> T_InvertibleUnitalMagma_1434
d_invertibleUnitalMagma_4002 :: () -> () -> T_Ring_3800 -> T_InvertibleUnitalMagma_1434
d_invertibleUnitalMagma_4002 ~()
v0 ~()
v1 T_Ring_3800
v2
  = T_Ring_3800 -> T_InvertibleUnitalMagma_1434
du_invertibleUnitalMagma_4002 T_Ring_3800
v2
du_invertibleUnitalMagma_4002 ::
  T_Ring_3800 -> T_InvertibleUnitalMagma_1434
du_invertibleUnitalMagma_4002 :: T_Ring_3800 -> T_InvertibleUnitalMagma_1434
du_invertibleUnitalMagma_4002 T_Ring_3800
v0
  = let v1 :: t
v1 = (T_Ring_3800 -> T_AbelianGroup_1636) -> AgdaAny -> t
forall a b. a -> b
coe T_Ring_3800 -> T_AbelianGroup_1636
du_'43''45'abelianGroup_3948 (T_Ring_3800 -> AgdaAny
forall a b. a -> b
coe T_Ring_3800
v0) in
    AgdaAny -> T_InvertibleUnitalMagma_1434
forall a b. a -> b
coe
      ((T_Group_1520 -> T_InvertibleUnitalMagma_1434)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Group_1520 -> T_InvertibleUnitalMagma_1434
du_invertibleUnitalMagma_1630 ((T_AbelianGroup_1636 -> T_Group_1520) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_AbelianGroup_1636 -> T_Group_1520
du_group_1732 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1)))
-- Algebra.Bundles.Ring.rawRing
d_rawRing_4004 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Ring_3800 -> MAlonzo.Code.Algebra.Bundles.Raw.T_RawRing_268
d_rawRing_4004 :: () -> () -> T_Ring_3800 -> T_RawRing_268
d_rawRing_4004 ~()
v0 ~()
v1 T_Ring_3800
v2 = T_Ring_3800 -> T_RawRing_268
du_rawRing_4004 T_Ring_3800
v2
du_rawRing_4004 ::
  T_Ring_3800 -> MAlonzo.Code.Algebra.Bundles.Raw.T_RawRing_268
du_rawRing_4004 :: T_Ring_3800 -> T_RawRing_268
du_rawRing_4004 T_Ring_3800
v0
  = ((AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny)
 -> AgdaAny
 -> AgdaAny
 -> T_RawRing_268)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_RawRing_268
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_RawRing_268
MAlonzo.Code.Algebra.Bundles.Raw.C_RawRing'46'constructor_3857
      (T_Ring_3800 -> AgdaAny -> AgdaAny -> AgdaAny
d__'43'__3826 (T_Ring_3800 -> T_Ring_3800
forall a b. a -> b
coe T_Ring_3800
v0)) (T_Ring_3800 -> AgdaAny -> AgdaAny -> AgdaAny
d__'42'__3828 (T_Ring_3800 -> T_Ring_3800
forall a b. a -> b
coe T_Ring_3800
v0))
      (T_Ring_3800 -> AgdaAny -> AgdaAny
d_'45'__3830 (T_Ring_3800 -> T_Ring_3800
forall a b. a -> b
coe T_Ring_3800
v0)) (T_Ring_3800 -> AgdaAny
d_0'35'_3832 (T_Ring_3800 -> T_Ring_3800
forall a b. a -> b
coe T_Ring_3800
v0))
      (T_Ring_3800 -> AgdaAny
d_1'35'_3834 (T_Ring_3800 -> T_Ring_3800
forall a b. a -> b
coe T_Ring_3800
v0))
-- Algebra.Bundles.Ring._.+-rawGroup
d_'43''45'rawGroup_4008 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Ring_3800 -> MAlonzo.Code.Algebra.Bundles.Raw.T_RawGroup_96
d_'43''45'rawGroup_4008 :: () -> () -> T_Ring_3800 -> T_RawGroup_96
d_'43''45'rawGroup_4008 ~()
v0 ~()
v1 T_Ring_3800
v2 = T_Ring_3800 -> T_RawGroup_96
du_'43''45'rawGroup_4008 T_Ring_3800
v2
du_'43''45'rawGroup_4008 ::
  T_Ring_3800 -> MAlonzo.Code.Algebra.Bundles.Raw.T_RawGroup_96
du_'43''45'rawGroup_4008 :: T_Ring_3800 -> T_RawGroup_96
du_'43''45'rawGroup_4008 T_Ring_3800
v0
  = let v1 :: t
v1 = (T_Ring_3800 -> T_RawRing_268) -> AgdaAny -> t
forall a b. a -> b
coe T_Ring_3800 -> T_RawRing_268
du_rawRing_4004 (T_Ring_3800 -> AgdaAny
forall a b. a -> b
coe T_Ring_3800
v0) in
    AgdaAny -> T_RawGroup_96
forall a b. a -> b
coe
      ((T_RawRingWithoutOne_222 -> T_RawGroup_96) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_RawRingWithoutOne_222 -> T_RawGroup_96
MAlonzo.Code.Algebra.Bundles.Raw.du_'43''45'rawGroup_252
         ((T_RawRing_268 -> T_RawRingWithoutOne_222) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_RawRing_268 -> T_RawRingWithoutOne_222
MAlonzo.Code.Algebra.Bundles.Raw.du_rawRingWithoutOne_316
            (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1)))
-- Algebra.Bundles.Ring._.rawRingWithoutOne
d_rawRingWithoutOne_4010 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Ring_3800 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRingWithoutOne_222
d_rawRingWithoutOne_4010 :: () -> () -> T_Ring_3800 -> T_RawRingWithoutOne_222
d_rawRingWithoutOne_4010 ~()
v0 ~()
v1 T_Ring_3800
v2 = T_Ring_3800 -> T_RawRingWithoutOne_222
du_rawRingWithoutOne_4010 T_Ring_3800
v2
du_rawRingWithoutOne_4010 ::
  T_Ring_3800 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRingWithoutOne_222
du_rawRingWithoutOne_4010 :: T_Ring_3800 -> T_RawRingWithoutOne_222
du_rawRingWithoutOne_4010 T_Ring_3800
v0
  = (T_RawRing_268 -> T_RawRingWithoutOne_222)
-> AgdaAny -> T_RawRingWithoutOne_222
forall a b. a -> b
coe
      T_RawRing_268 -> T_RawRingWithoutOne_222
MAlonzo.Code.Algebra.Bundles.Raw.du_rawRingWithoutOne_316
      ((T_Ring_3800 -> T_RawRing_268) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Ring_3800 -> T_RawRing_268
du_rawRing_4004 (T_Ring_3800 -> AgdaAny
forall a b. a -> b
coe T_Ring_3800
v0))
-- Algebra.Bundles.CommutativeRing
d_CommutativeRing_4016 :: p -> p -> ()
d_CommutativeRing_4016 p
a0 p
a1 = ()
data T_CommutativeRing_4016
  = C_CommutativeRing'46'constructor_72553 (AgdaAny ->
                                            AgdaAny -> AgdaAny)
                                           (AgdaAny -> AgdaAny -> AgdaAny) (AgdaAny -> AgdaAny)
                                           AgdaAny AgdaAny
                                           MAlonzo.Code.Algebra.Structures.T_IsCommutativeRing_2796
-- Algebra.Bundles.CommutativeRing.Carrier
d_Carrier_4038 :: T_CommutativeRing_4016 -> ()
d_Carrier_4038 :: T_CommutativeRing_4016 -> ()
d_Carrier_4038 = T_CommutativeRing_4016 -> ()
forall a. a
erased
-- Algebra.Bundles.CommutativeRing._≈_
d__'8776'__4040 ::
  T_CommutativeRing_4016 -> AgdaAny -> AgdaAny -> ()
d__'8776'__4040 :: T_CommutativeRing_4016 -> AgdaAny -> AgdaAny -> ()
d__'8776'__4040 = T_CommutativeRing_4016 -> AgdaAny -> AgdaAny -> ()
forall a. a
erased
-- Algebra.Bundles.CommutativeRing._+_
d__'43'__4042 ::
  T_CommutativeRing_4016 -> AgdaAny -> AgdaAny -> AgdaAny
d__'43'__4042 :: T_CommutativeRing_4016 -> AgdaAny -> AgdaAny -> AgdaAny
d__'43'__4042 T_CommutativeRing_4016
v0
  = case T_CommutativeRing_4016 -> T_CommutativeRing_4016
forall a b. a -> b
coe T_CommutativeRing_4016
v0 of
      C_CommutativeRing'46'constructor_72553 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny
v5 AgdaAny
v6 AgdaAny
v7 T_IsCommutativeRing_2796
v8 -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v3
      T_CommutativeRing_4016
_ -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.CommutativeRing._*_
d__'42'__4044 ::
  T_CommutativeRing_4016 -> AgdaAny -> AgdaAny -> AgdaAny
d__'42'__4044 :: T_CommutativeRing_4016 -> AgdaAny -> AgdaAny -> AgdaAny
d__'42'__4044 T_CommutativeRing_4016
v0
  = case T_CommutativeRing_4016 -> T_CommutativeRing_4016
forall a b. a -> b
coe T_CommutativeRing_4016
v0 of
      C_CommutativeRing'46'constructor_72553 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny
v5 AgdaAny
v6 AgdaAny
v7 T_IsCommutativeRing_2796
v8 -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v4
      T_CommutativeRing_4016
_ -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.CommutativeRing.-_
d_'45'__4046 :: T_CommutativeRing_4016 -> AgdaAny -> AgdaAny
d_'45'__4046 :: T_CommutativeRing_4016 -> AgdaAny -> AgdaAny
d_'45'__4046 T_CommutativeRing_4016
v0
  = case T_CommutativeRing_4016 -> T_CommutativeRing_4016
forall a b. a -> b
coe T_CommutativeRing_4016
v0 of
      C_CommutativeRing'46'constructor_72553 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny
v5 AgdaAny
v6 AgdaAny
v7 T_IsCommutativeRing_2796
v8 -> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v5
      T_CommutativeRing_4016
_ -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.CommutativeRing.0#
d_0'35'_4048 :: T_CommutativeRing_4016 -> AgdaAny
d_0'35'_4048 :: T_CommutativeRing_4016 -> AgdaAny
d_0'35'_4048 T_CommutativeRing_4016
v0
  = case T_CommutativeRing_4016 -> T_CommutativeRing_4016
forall a b. a -> b
coe T_CommutativeRing_4016
v0 of
      C_CommutativeRing'46'constructor_72553 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny
v5 AgdaAny
v6 AgdaAny
v7 T_IsCommutativeRing_2796
v8 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v6
      T_CommutativeRing_4016
_ -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.CommutativeRing.1#
d_1'35'_4050 :: T_CommutativeRing_4016 -> AgdaAny
d_1'35'_4050 :: T_CommutativeRing_4016 -> AgdaAny
d_1'35'_4050 T_CommutativeRing_4016
v0
  = case T_CommutativeRing_4016 -> T_CommutativeRing_4016
forall a b. a -> b
coe T_CommutativeRing_4016
v0 of
      C_CommutativeRing'46'constructor_72553 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny
v5 AgdaAny
v6 AgdaAny
v7 T_IsCommutativeRing_2796
v8 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v7
      T_CommutativeRing_4016
_ -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.CommutativeRing.isCommutativeRing
d_isCommutativeRing_4052 ::
  T_CommutativeRing_4016 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeRing_2796
d_isCommutativeRing_4052 :: T_CommutativeRing_4016 -> T_IsCommutativeRing_2796
d_isCommutativeRing_4052 T_CommutativeRing_4016
v0
  = case T_CommutativeRing_4016 -> T_CommutativeRing_4016
forall a b. a -> b
coe T_CommutativeRing_4016
v0 of
      C_CommutativeRing'46'constructor_72553 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny
v5 AgdaAny
v6 AgdaAny
v7 T_IsCommutativeRing_2796
v8 -> T_IsCommutativeRing_2796 -> T_IsCommutativeRing_2796
forall a b. a -> b
coe T_IsCommutativeRing_2796
v8
      T_CommutativeRing_4016
_ -> T_IsCommutativeRing_2796
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.CommutativeRing._._//_
d__'47''47'__4056 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeRing_4016 -> AgdaAny -> AgdaAny -> AgdaAny
d__'47''47'__4056 :: () -> () -> T_CommutativeRing_4016 -> AgdaAny -> AgdaAny -> AgdaAny
d__'47''47'__4056 ~()
v0 ~()
v1 T_CommutativeRing_4016
v2 = T_CommutativeRing_4016 -> AgdaAny -> AgdaAny -> AgdaAny
du__'47''47'__4056 T_CommutativeRing_4016
v2
du__'47''47'__4056 ::
  T_CommutativeRing_4016 -> AgdaAny -> AgdaAny -> AgdaAny
du__'47''47'__4056 :: T_CommutativeRing_4016 -> AgdaAny -> AgdaAny -> AgdaAny
du__'47''47'__4056 T_CommutativeRing_4016
v0
  = let v1 :: AgdaAny -> AgdaAny -> AgdaAny
v1 = T_CommutativeRing_4016 -> AgdaAny -> AgdaAny -> AgdaAny
d__'43'__4042 (T_CommutativeRing_4016 -> T_CommutativeRing_4016
forall a b. a -> b
coe T_CommutativeRing_4016
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: AgdaAny -> AgdaAny
v2 = T_CommutativeRing_4016 -> AgdaAny -> AgdaAny
d_'45'__4046 (T_CommutativeRing_4016 -> T_CommutativeRing_4016
forall a b. a -> b
coe T_CommutativeRing_4016
v0) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (((AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du__'47''47'__1098 ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v1)
            ((AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v2)))
-- Algebra.Bundles.CommutativeRing._.*-assoc
d_'42''45'assoc_4058 ::
  T_CommutativeRing_4016 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'assoc_4058 :: T_CommutativeRing_4016 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'assoc_4058 T_CommutativeRing_4016
v0
  = (T_IsRing_2650 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsRing_2650 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'42''45'assoc_2676
      ((T_IsCommutativeRing_2796 -> T_IsRing_2650) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCommutativeRing_2796 -> T_IsRing_2650
MAlonzo.Code.Algebra.Structures.d_isRing_2812
         ((T_CommutativeRing_4016 -> T_IsCommutativeRing_2796)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeRing_4016 -> T_IsCommutativeRing_2796
d_isCommutativeRing_4052 (T_CommutativeRing_4016 -> AgdaAny
forall a b. a -> b
coe T_CommutativeRing_4016
v0)))
-- Algebra.Bundles.CommutativeRing._.*-comm
d_'42''45'comm_4060 ::
  T_CommutativeRing_4016 -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'comm_4060 :: T_CommutativeRing_4016 -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'comm_4060 T_CommutativeRing_4016
v0
  = (T_IsCommutativeRing_2796 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsCommutativeRing_2796 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'42''45'comm_2814
      ((T_CommutativeRing_4016 -> T_IsCommutativeRing_2796)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeRing_4016 -> T_IsCommutativeRing_2796
d_isCommutativeRing_4052 (T_CommutativeRing_4016 -> AgdaAny
forall a b. a -> b
coe T_CommutativeRing_4016
v0))
-- Algebra.Bundles.CommutativeRing._.*-cong
d_'42''45'cong_4062 ::
  T_CommutativeRing_4016 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'cong_4062 :: T_CommutativeRing_4016
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'42''45'cong_4062 T_CommutativeRing_4016
v0
  = (T_IsRing_2650
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsRing_2650
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'42''45'cong_2674
      ((T_IsCommutativeRing_2796 -> T_IsRing_2650) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCommutativeRing_2796 -> T_IsRing_2650
MAlonzo.Code.Algebra.Structures.d_isRing_2812
         ((T_CommutativeRing_4016 -> T_IsCommutativeRing_2796)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeRing_4016 -> T_IsCommutativeRing_2796
d_isCommutativeRing_4052 (T_CommutativeRing_4016 -> AgdaAny
forall a b. a -> b
coe T_CommutativeRing_4016
v0)))
-- Algebra.Bundles.CommutativeRing._.∙-congʳ
d_'8729''45'cong'691'_4064 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeRing_4016 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_4064 :: ()
-> ()
-> T_CommutativeRing_4016
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_4064 ~()
v0 ~()
v1 T_CommutativeRing_4016
v2
  = T_CommutativeRing_4016
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_4064 T_CommutativeRing_4016
v2
du_'8729''45'cong'691'_4064 ::
  T_CommutativeRing_4016 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_4064 :: T_CommutativeRing_4016
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_4064 T_CommutativeRing_4016
v0
  = let v1 :: T_IsCommutativeRing_2796
v1 = T_CommutativeRing_4016 -> T_IsCommutativeRing_2796
d_isCommutativeRing_4052 (T_CommutativeRing_4016 -> T_CommutativeRing_4016
forall a b. a -> b
coe T_CommutativeRing_4016
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsRing_2650
v2 = T_IsCommutativeRing_2796 -> T_IsRing_2650
MAlonzo.Code.Algebra.Structures.d_isRing_2812 (T_IsCommutativeRing_2796 -> T_IsCommutativeRing_2796
forall a b. a -> b
coe T_IsCommutativeRing_2796
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: t
v3
                = (T_IsRing_2650 -> T_IsRingWithoutOne_2286) -> AgdaAny -> t
forall a b. a -> b
coe
                    T_IsRing_2650 -> T_IsRingWithoutOne_2286
MAlonzo.Code.Algebra.Structures.du_isRingWithoutOne_2682
                    (T_IsRing_2650 -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: t
v4
                   = (T_IsRingWithoutOne_2286 -> T_IsSemigroup_472) -> AgdaAny -> t
forall a b. a -> b
coe
                       T_IsRingWithoutOne_2286 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.du_'42''45'isSemigroup_2390
                       (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'691'_206
                  ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v4))))))
-- Algebra.Bundles.CommutativeRing._.∙-congˡ
d_'8729''45'cong'737'_4066 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeRing_4016 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_4066 :: ()
-> ()
-> T_CommutativeRing_4016
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_4066 ~()
v0 ~()
v1 T_CommutativeRing_4016
v2
  = T_CommutativeRing_4016
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_4066 T_CommutativeRing_4016
v2
du_'8729''45'cong'737'_4066 ::
  T_CommutativeRing_4016 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_4066 :: T_CommutativeRing_4016
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_4066 T_CommutativeRing_4016
v0
  = let v1 :: T_IsCommutativeRing_2796
v1 = T_CommutativeRing_4016 -> T_IsCommutativeRing_2796
d_isCommutativeRing_4052 (T_CommutativeRing_4016 -> T_CommutativeRing_4016
forall a b. a -> b
coe T_CommutativeRing_4016
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsRing_2650
v2 = T_IsCommutativeRing_2796 -> T_IsRing_2650
MAlonzo.Code.Algebra.Structures.d_isRing_2812 (T_IsCommutativeRing_2796 -> T_IsCommutativeRing_2796
forall a b. a -> b
coe T_IsCommutativeRing_2796
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: t
v3
                = (T_IsRing_2650 -> T_IsRingWithoutOne_2286) -> AgdaAny -> t
forall a b. a -> b
coe
                    T_IsRing_2650 -> T_IsRingWithoutOne_2286
MAlonzo.Code.Algebra.Structures.du_isRingWithoutOne_2682
                    (T_IsRing_2650 -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: t
v4
                   = (T_IsRingWithoutOne_2286 -> T_IsSemigroup_472) -> AgdaAny -> t
forall a b. a -> b
coe
                       T_IsRingWithoutOne_2286 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.du_'42''45'isSemigroup_2390
                       (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'737'_202
                  ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v4))))))
-- Algebra.Bundles.CommutativeRing._.*-identity
d_'42''45'identity_4068 ::
  T_CommutativeRing_4016 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'42''45'identity_4068 :: T_CommutativeRing_4016 -> T_Σ_14
d_'42''45'identity_4068 T_CommutativeRing_4016
v0
  = (T_IsRing_2650 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsRing_2650 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_'42''45'identity_2678
      ((T_IsCommutativeRing_2796 -> T_IsRing_2650) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCommutativeRing_2796 -> T_IsRing_2650
MAlonzo.Code.Algebra.Structures.d_isRing_2812
         ((T_CommutativeRing_4016 -> T_IsCommutativeRing_2796)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeRing_4016 -> T_IsCommutativeRing_2796
d_isCommutativeRing_4052 (T_CommutativeRing_4016 -> AgdaAny
forall a b. a -> b
coe T_CommutativeRing_4016
v0)))
-- Algebra.Bundles.CommutativeRing._.identityʳ
d_identity'691'_4070 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeRing_4016 -> AgdaAny -> AgdaAny
d_identity'691'_4070 :: () -> () -> T_CommutativeRing_4016 -> AgdaAny -> AgdaAny
d_identity'691'_4070 ~()
v0 ~()
v1 T_CommutativeRing_4016
v2 = T_CommutativeRing_4016 -> AgdaAny -> AgdaAny
du_identity'691'_4070 T_CommutativeRing_4016
v2
du_identity'691'_4070 ::
  T_CommutativeRing_4016 -> AgdaAny -> AgdaAny
du_identity'691'_4070 :: T_CommutativeRing_4016 -> AgdaAny -> AgdaAny
du_identity'691'_4070 T_CommutativeRing_4016
v0
  = let v1 :: T_IsCommutativeRing_2796
v1 = T_CommutativeRing_4016 -> T_IsCommutativeRing_2796
d_isCommutativeRing_4052 (T_CommutativeRing_4016 -> T_CommutativeRing_4016
forall a b. a -> b
coe T_CommutativeRing_4016
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsRing_2650
v2 = T_IsCommutativeRing_2796 -> T_IsRing_2650
MAlonzo.Code.Algebra.Structures.d_isRing_2812 (T_IsCommutativeRing_2796 -> T_IsCommutativeRing_2796
forall a b. a -> b
coe T_IsCommutativeRing_2796
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsMonoid_686 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoid_686 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_identity'691'_728
            ((T_IsRing_2650 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsRing_2650 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.du_'42''45'isMonoid_2768
               (T_IsRing_2650 -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650
v2))))
-- Algebra.Bundles.CommutativeRing._.identityˡ
d_identity'737'_4072 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeRing_4016 -> AgdaAny -> AgdaAny
d_identity'737'_4072 :: () -> () -> T_CommutativeRing_4016 -> AgdaAny -> AgdaAny
d_identity'737'_4072 ~()
v0 ~()
v1 T_CommutativeRing_4016
v2 = T_CommutativeRing_4016 -> AgdaAny -> AgdaAny
du_identity'737'_4072 T_CommutativeRing_4016
v2
du_identity'737'_4072 ::
  T_CommutativeRing_4016 -> AgdaAny -> AgdaAny
du_identity'737'_4072 :: T_CommutativeRing_4016 -> AgdaAny -> AgdaAny
du_identity'737'_4072 T_CommutativeRing_4016
v0
  = let v1 :: T_IsCommutativeRing_2796
v1 = T_CommutativeRing_4016 -> T_IsCommutativeRing_2796
d_isCommutativeRing_4052 (T_CommutativeRing_4016 -> T_CommutativeRing_4016
forall a b. a -> b
coe T_CommutativeRing_4016
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsRing_2650
v2 = T_IsCommutativeRing_2796 -> T_IsRing_2650
MAlonzo.Code.Algebra.Structures.d_isRing_2812 (T_IsCommutativeRing_2796 -> T_IsCommutativeRing_2796
forall a b. a -> b
coe T_IsCommutativeRing_2796
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsMonoid_686 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoid_686 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_identity'737'_726
            ((T_IsRing_2650 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsRing_2650 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.du_'42''45'isMonoid_2768
               (T_IsRing_2650 -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650
v2))))
-- Algebra.Bundles.CommutativeRing._.isCommutativeMagma
d_isCommutativeMagma_4074 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeRing_4016 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMagma_212
d_isCommutativeMagma_4074 :: () -> () -> T_CommutativeRing_4016 -> T_IsCommutativeMagma_212
d_isCommutativeMagma_4074 ~()
v0 ~()
v1 T_CommutativeRing_4016
v2
  = T_CommutativeRing_4016 -> T_IsCommutativeMagma_212
du_isCommutativeMagma_4074 T_CommutativeRing_4016
v2
du_isCommutativeMagma_4074 ::
  T_CommutativeRing_4016 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMagma_212
du_isCommutativeMagma_4074 :: T_CommutativeRing_4016 -> T_IsCommutativeMagma_212
du_isCommutativeMagma_4074 T_CommutativeRing_4016
v0
  = let v1 :: AgdaAny -> AgdaAny -> AgdaAny
v1 = T_CommutativeRing_4016 -> AgdaAny -> AgdaAny -> AgdaAny
d__'43'__4042 (T_CommutativeRing_4016 -> T_CommutativeRing_4016
forall a b. a -> b
coe T_CommutativeRing_4016
v0) in
    AgdaAny -> T_IsCommutativeMagma_212
forall a b. a -> b
coe
      (let v2 :: AgdaAny -> AgdaAny -> AgdaAny
v2 = T_CommutativeRing_4016 -> AgdaAny -> AgdaAny -> AgdaAny
d__'42'__4044 (T_CommutativeRing_4016 -> T_CommutativeRing_4016
forall a b. a -> b
coe T_CommutativeRing_4016
v0) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: AgdaAny -> AgdaAny
v3 = T_CommutativeRing_4016 -> AgdaAny -> AgdaAny
d_'45'__4046 (T_CommutativeRing_4016 -> T_CommutativeRing_4016
forall a b. a -> b
coe T_CommutativeRing_4016
v0) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: AgdaAny
v4 = T_CommutativeRing_4016 -> AgdaAny
d_0'35'_4048 (T_CommutativeRing_4016 -> T_CommutativeRing_4016
forall a b. a -> b
coe T_CommutativeRing_4016
v0) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsCommutativeRing_2796
v5 = T_CommutativeRing_4016 -> T_IsCommutativeRing_2796
d_isCommutativeRing_4052 (T_CommutativeRing_4016 -> T_CommutativeRing_4016
forall a b. a -> b
coe T_CommutativeRing_4016
v0) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (let v6 :: t
v6
                         = ((AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny)
 -> AgdaAny
 -> T_IsCommutativeRing_2796
 -> T_IsCommutativeSemiring_1678)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe
                             (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsCommutativeRing_2796
-> T_IsCommutativeSemiring_1678
MAlonzo.Code.Algebra.Structures.du_isCommutativeSemiring_2926
                             ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v1) ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v2) ((AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v3) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v4) (T_IsCommutativeRing_2796 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeRing_2796
v5) in
                   AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     (let v7 :: t
v7
                            = (T_IsCommutativeSemiring_1678
 -> T_IsCommutativeSemiringWithoutOne_1382)
-> AgdaAny -> t
forall a b. a -> b
coe
                                T_IsCommutativeSemiring_1678
-> T_IsCommutativeSemiringWithoutOne_1382
MAlonzo.Code.Algebra.Structures.du_isCommutativeSemiringWithoutOne_1780
                                (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v6) in
                      AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        ((T_IsCommutativeSemigroup_548 -> T_IsCommutativeMagma_212)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_IsCommutativeSemigroup_548 -> T_IsCommutativeMagma_212
MAlonzo.Code.Algebra.Structures.du_isCommutativeMagma_586
                           ((T_IsCommutativeSemiringWithoutOne_1382
 -> T_IsCommutativeSemigroup_548)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                              T_IsCommutativeSemiringWithoutOne_1382
-> T_IsCommutativeSemigroup_548
MAlonzo.Code.Algebra.Structures.du_'42''45'isCommutativeSemigroup_1454
                              (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v7)))))))))
-- Algebra.Bundles.CommutativeRing._.*-isCommutativeMonoid
d_'42''45'isCommutativeMonoid_4076 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeRing_4016 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMonoid_736
d_'42''45'isCommutativeMonoid_4076 :: () -> () -> T_CommutativeRing_4016 -> T_IsCommutativeMonoid_736
d_'42''45'isCommutativeMonoid_4076 ~()
v0 ~()
v1 T_CommutativeRing_4016
v2
  = T_CommutativeRing_4016 -> T_IsCommutativeMonoid_736
du_'42''45'isCommutativeMonoid_4076 T_CommutativeRing_4016
v2
du_'42''45'isCommutativeMonoid_4076 ::
  T_CommutativeRing_4016 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMonoid_736
du_'42''45'isCommutativeMonoid_4076 :: T_CommutativeRing_4016 -> T_IsCommutativeMonoid_736
du_'42''45'isCommutativeMonoid_4076 T_CommutativeRing_4016
v0
  = let v1 :: AgdaAny -> AgdaAny -> AgdaAny
v1 = T_CommutativeRing_4016 -> AgdaAny -> AgdaAny -> AgdaAny
d__'43'__4042 (T_CommutativeRing_4016 -> T_CommutativeRing_4016
forall a b. a -> b
coe T_CommutativeRing_4016
v0) in
    AgdaAny -> T_IsCommutativeMonoid_736
forall a b. a -> b
coe
      (let v2 :: AgdaAny -> AgdaAny -> AgdaAny
v2 = T_CommutativeRing_4016 -> AgdaAny -> AgdaAny -> AgdaAny
d__'42'__4044 (T_CommutativeRing_4016 -> T_CommutativeRing_4016
forall a b. a -> b
coe T_CommutativeRing_4016
v0) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: AgdaAny -> AgdaAny
v3 = T_CommutativeRing_4016 -> AgdaAny -> AgdaAny
d_'45'__4046 (T_CommutativeRing_4016 -> T_CommutativeRing_4016
forall a b. a -> b
coe T_CommutativeRing_4016
v0) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: AgdaAny
v4 = T_CommutativeRing_4016 -> AgdaAny
d_0'35'_4048 (T_CommutativeRing_4016 -> T_CommutativeRing_4016
forall a b. a -> b
coe T_CommutativeRing_4016
v0) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsCommutativeRing_2796
v5 = T_CommutativeRing_4016 -> T_IsCommutativeRing_2796
d_isCommutativeRing_4052 (T_CommutativeRing_4016 -> T_CommutativeRing_4016
forall a b. a -> b
coe T_CommutativeRing_4016
v0) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  ((T_IsCommutativeSemiring_1678 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsCommutativeSemiring_1678 -> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.du_'42''45'isCommutativeMonoid_1788
                     (((AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny)
 -> AgdaAny
 -> T_IsCommutativeRing_2796
 -> T_IsCommutativeSemiring_1678)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsCommutativeRing_2796
-> T_IsCommutativeSemiring_1678
MAlonzo.Code.Algebra.Structures.du_isCommutativeSemiring_2926
                        ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v1) ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v2) ((AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v3) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v4) (T_IsCommutativeRing_2796 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeRing_2796
v5)))))))
-- Algebra.Bundles.CommutativeRing._.*-isCommutativeSemigroup
d_'42''45'isCommutativeSemigroup_4078 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeRing_4016 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_548
d_'42''45'isCommutativeSemigroup_4078 :: () -> () -> T_CommutativeRing_4016 -> T_IsCommutativeSemigroup_548
d_'42''45'isCommutativeSemigroup_4078 ~()
v0 ~()
v1 T_CommutativeRing_4016
v2
  = T_CommutativeRing_4016 -> T_IsCommutativeSemigroup_548
du_'42''45'isCommutativeSemigroup_4078 T_CommutativeRing_4016
v2
du_'42''45'isCommutativeSemigroup_4078 ::
  T_CommutativeRing_4016 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_548
du_'42''45'isCommutativeSemigroup_4078 :: T_CommutativeRing_4016 -> T_IsCommutativeSemigroup_548
du_'42''45'isCommutativeSemigroup_4078 T_CommutativeRing_4016
v0
  = let v1 :: AgdaAny -> AgdaAny -> AgdaAny
v1 = T_CommutativeRing_4016 -> AgdaAny -> AgdaAny -> AgdaAny
d__'43'__4042 (T_CommutativeRing_4016 -> T_CommutativeRing_4016
forall a b. a -> b
coe T_CommutativeRing_4016
v0) in
    AgdaAny -> T_IsCommutativeSemigroup_548
forall a b. a -> b
coe
      (let v2 :: AgdaAny -> AgdaAny -> AgdaAny
v2 = T_CommutativeRing_4016 -> AgdaAny -> AgdaAny -> AgdaAny
d__'42'__4044 (T_CommutativeRing_4016 -> T_CommutativeRing_4016
forall a b. a -> b
coe T_CommutativeRing_4016
v0) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: AgdaAny -> AgdaAny
v3 = T_CommutativeRing_4016 -> AgdaAny -> AgdaAny
d_'45'__4046 (T_CommutativeRing_4016 -> T_CommutativeRing_4016
forall a b. a -> b
coe T_CommutativeRing_4016
v0) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: AgdaAny
v4 = T_CommutativeRing_4016 -> AgdaAny
d_0'35'_4048 (T_CommutativeRing_4016 -> T_CommutativeRing_4016
forall a b. a -> b
coe T_CommutativeRing_4016
v0) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsCommutativeRing_2796
v5 = T_CommutativeRing_4016 -> T_IsCommutativeRing_2796
d_isCommutativeRing_4052 (T_CommutativeRing_4016 -> T_CommutativeRing_4016
forall a b. a -> b
coe T_CommutativeRing_4016
v0) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (let v6 :: t
v6
                         = ((AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny)
 -> AgdaAny
 -> T_IsCommutativeRing_2796
 -> T_IsCommutativeSemiring_1678)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe
                             (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsCommutativeRing_2796
-> T_IsCommutativeSemiring_1678
MAlonzo.Code.Algebra.Structures.du_isCommutativeSemiring_2926
                             ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v1) ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v2) ((AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v3) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v4) (T_IsCommutativeRing_2796 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeRing_2796
v5) in
                   AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     ((T_IsCommutativeSemiringWithoutOne_1382
 -> T_IsCommutativeSemigroup_548)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsCommutativeSemiringWithoutOne_1382
-> T_IsCommutativeSemigroup_548
MAlonzo.Code.Algebra.Structures.du_'42''45'isCommutativeSemigroup_1454
                        ((T_IsCommutativeSemiring_1678
 -> T_IsCommutativeSemiringWithoutOne_1382)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_IsCommutativeSemiring_1678
-> T_IsCommutativeSemiringWithoutOne_1382
MAlonzo.Code.Algebra.Structures.du_isCommutativeSemiringWithoutOne_1780
                           (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v6))))))))
-- Algebra.Bundles.CommutativeRing._.*-isMagma
d_'42''45'isMagma_4080 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeRing_4016 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_176
d_'42''45'isMagma_4080 :: () -> () -> T_CommutativeRing_4016 -> T_IsMagma_176
d_'42''45'isMagma_4080 ~()
v0 ~()
v1 T_CommutativeRing_4016
v2 = T_CommutativeRing_4016 -> T_IsMagma_176
du_'42''45'isMagma_4080 T_CommutativeRing_4016
v2
du_'42''45'isMagma_4080 ::
  T_CommutativeRing_4016 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_176
du_'42''45'isMagma_4080 :: T_CommutativeRing_4016 -> T_IsMagma_176
du_'42''45'isMagma_4080 T_CommutativeRing_4016
v0
  = let v1 :: T_IsCommutativeRing_2796
v1 = T_CommutativeRing_4016 -> T_IsCommutativeRing_2796
d_isCommutativeRing_4052 (T_CommutativeRing_4016 -> T_CommutativeRing_4016
forall a b. a -> b
coe T_CommutativeRing_4016
v0) in
    AgdaAny -> T_IsMagma_176
forall a b. a -> b
coe
      (let v2 :: T_IsRing_2650
v2 = T_IsCommutativeRing_2796 -> T_IsRing_2650
MAlonzo.Code.Algebra.Structures.d_isRing_2812 (T_IsCommutativeRing_2796 -> T_IsCommutativeRing_2796
forall a b. a -> b
coe T_IsCommutativeRing_2796
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsRingWithoutOne_2286 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsRingWithoutOne_2286 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.du_'42''45'isMagma_2388
            ((T_IsRing_2650 -> T_IsRingWithoutOne_2286) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsRing_2650 -> T_IsRingWithoutOne_2286
MAlonzo.Code.Algebra.Structures.du_isRingWithoutOne_2682
               (T_IsRing_2650 -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650
v2))))
-- Algebra.Bundles.CommutativeRing._.*-isMonoid
d_'42''45'isMonoid_4082 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeRing_4016 ->
  MAlonzo.Code.Algebra.Structures.T_IsMonoid_686
d_'42''45'isMonoid_4082 :: () -> () -> T_CommutativeRing_4016 -> T_IsMonoid_686
d_'42''45'isMonoid_4082 ~()
v0 ~()
v1 T_CommutativeRing_4016
v2 = T_CommutativeRing_4016 -> T_IsMonoid_686
du_'42''45'isMonoid_4082 T_CommutativeRing_4016
v2
du_'42''45'isMonoid_4082 ::
  T_CommutativeRing_4016 ->
  MAlonzo.Code.Algebra.Structures.T_IsMonoid_686
du_'42''45'isMonoid_4082 :: T_CommutativeRing_4016 -> T_IsMonoid_686
du_'42''45'isMonoid_4082 T_CommutativeRing_4016
v0
  = let v1 :: T_IsCommutativeRing_2796
v1 = T_CommutativeRing_4016 -> T_IsCommutativeRing_2796
d_isCommutativeRing_4052 (T_CommutativeRing_4016 -> T_CommutativeRing_4016
forall a b. a -> b
coe T_CommutativeRing_4016
v0) in
    AgdaAny -> T_IsMonoid_686
forall a b. a -> b
coe
      ((T_IsRing_2650 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsRing_2650 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.du_'42''45'isMonoid_2768
         ((T_IsCommutativeRing_2796 -> T_IsRing_2650) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeRing_2796 -> T_IsRing_2650
MAlonzo.Code.Algebra.Structures.d_isRing_2812 (T_IsCommutativeRing_2796 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeRing_2796
v1)))
-- Algebra.Bundles.CommutativeRing._.*-isSemigroup
d_'42''45'isSemigroup_4084 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeRing_4016 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_472
d_'42''45'isSemigroup_4084 :: () -> () -> T_CommutativeRing_4016 -> T_IsSemigroup_472
d_'42''45'isSemigroup_4084 ~()
v0 ~()
v1 T_CommutativeRing_4016
v2
  = T_CommutativeRing_4016 -> T_IsSemigroup_472
du_'42''45'isSemigroup_4084 T_CommutativeRing_4016
v2
du_'42''45'isSemigroup_4084 ::
  T_CommutativeRing_4016 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_472
du_'42''45'isSemigroup_4084 :: T_CommutativeRing_4016 -> T_IsSemigroup_472
du_'42''45'isSemigroup_4084 T_CommutativeRing_4016
v0
  = let v1 :: T_IsCommutativeRing_2796
v1 = T_CommutativeRing_4016 -> T_IsCommutativeRing_2796
d_isCommutativeRing_4052 (T_CommutativeRing_4016 -> T_CommutativeRing_4016
forall a b. a -> b
coe T_CommutativeRing_4016
v0) in
    AgdaAny -> T_IsSemigroup_472
forall a b. a -> b
coe
      (let v2 :: T_IsRing_2650
v2 = T_IsCommutativeRing_2796 -> T_IsRing_2650
MAlonzo.Code.Algebra.Structures.d_isRing_2812 (T_IsCommutativeRing_2796 -> T_IsCommutativeRing_2796
forall a b. a -> b
coe T_IsCommutativeRing_2796
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsRingWithoutOne_2286 -> T_IsSemigroup_472)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsRingWithoutOne_2286 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.du_'42''45'isSemigroup_2390
            ((T_IsRing_2650 -> T_IsRingWithoutOne_2286) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsRing_2650 -> T_IsRingWithoutOne_2286
MAlonzo.Code.Algebra.Structures.du_isRingWithoutOne_2682
               (T_IsRing_2650 -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650
v2))))
-- Algebra.Bundles.CommutativeRing._.assoc
d_assoc_4086 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeRing_4016 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_4086 :: ()
-> ()
-> T_CommutativeRing_4016
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_assoc_4086 ~()
v0 ~()
v1 T_CommutativeRing_4016
v2 = T_CommutativeRing_4016 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_assoc_4086 T_CommutativeRing_4016
v2
du_assoc_4086 ::
  T_CommutativeRing_4016 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_assoc_4086 :: T_CommutativeRing_4016 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_assoc_4086 T_CommutativeRing_4016
v0
  = let v1 :: T_IsCommutativeRing_2796
v1 = T_CommutativeRing_4016 -> T_IsCommutativeRing_2796
d_isCommutativeRing_4052 (T_CommutativeRing_4016 -> T_CommutativeRing_4016
forall a b. a -> b
coe T_CommutativeRing_4016
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsRing_2650
v2 = T_IsCommutativeRing_2796 -> T_IsRing_2650
MAlonzo.Code.Algebra.Structures.d_isRing_2812 (T_IsCommutativeRing_2796 -> T_IsCommutativeRing_2796
forall a b. a -> b
coe T_IsCommutativeRing_2796
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsSemigroup_472 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_472 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_assoc_482
            ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
               ((T_IsGroup_1036 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsGroup_1036 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_1050
                  ((T_IsAbelianGroup_1132 -> T_IsGroup_1036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsAbelianGroup_1132 -> T_IsGroup_1036
MAlonzo.Code.Algebra.Structures.d_isGroup_1144
                     ((T_IsRing_2650 -> T_IsAbelianGroup_1132) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsRing_2650 -> T_IsAbelianGroup_1132
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2672
                        (T_IsRing_2650 -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650
v2)))))))
-- Algebra.Bundles.CommutativeRing._.comm
d_comm_4088 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeRing_4016 -> AgdaAny -> AgdaAny -> AgdaAny
d_comm_4088 :: () -> () -> T_CommutativeRing_4016 -> AgdaAny -> AgdaAny -> AgdaAny
d_comm_4088 ~()
v0 ~()
v1 T_CommutativeRing_4016
v2 = T_CommutativeRing_4016 -> AgdaAny -> AgdaAny -> AgdaAny
du_comm_4088 T_CommutativeRing_4016
v2
du_comm_4088 ::
  T_CommutativeRing_4016 -> AgdaAny -> AgdaAny -> AgdaAny
du_comm_4088 :: T_CommutativeRing_4016 -> AgdaAny -> AgdaAny -> AgdaAny
du_comm_4088 T_CommutativeRing_4016
v0
  = let v1 :: T_IsCommutativeRing_2796
v1 = T_CommutativeRing_4016 -> T_IsCommutativeRing_2796
d_isCommutativeRing_4052 (T_CommutativeRing_4016 -> T_CommutativeRing_4016
forall a b. a -> b
coe T_CommutativeRing_4016
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsRing_2650
v2 = T_IsCommutativeRing_2796 -> T_IsRing_2650
MAlonzo.Code.Algebra.Structures.d_isRing_2812 (T_IsCommutativeRing_2796 -> T_IsCommutativeRing_2796
forall a b. a -> b
coe T_IsCommutativeRing_2796
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsAbelianGroup_1132 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsAbelianGroup_1132 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_comm_1146
            ((T_IsRing_2650 -> T_IsAbelianGroup_1132) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsRing_2650 -> T_IsAbelianGroup_1132
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2672
               (T_IsRing_2650 -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650
v2))))
-- Algebra.Bundles.CommutativeRing._.∙-cong
d_'8729''45'cong_4090 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeRing_4016 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_4090 :: ()
-> ()
-> T_CommutativeRing_4016
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_4090 ~()
v0 ~()
v1 T_CommutativeRing_4016
v2 = T_CommutativeRing_4016
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_'8729''45'cong_4090 T_CommutativeRing_4016
v2
du_'8729''45'cong_4090 ::
  T_CommutativeRing_4016 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong_4090 :: T_CommutativeRing_4016
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_'8729''45'cong_4090 T_CommutativeRing_4016
v0
  = let v1 :: T_IsCommutativeRing_2796
v1 = T_CommutativeRing_4016 -> T_IsCommutativeRing_2796
d_isCommutativeRing_4052 (T_CommutativeRing_4016 -> T_CommutativeRing_4016
forall a b. a -> b
coe T_CommutativeRing_4016
v0) in
    AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsRing_2650
v2 = T_IsCommutativeRing_2796 -> T_IsRing_2650
MAlonzo.Code.Algebra.Structures.d_isRing_2812 (T_IsCommutativeRing_2796 -> T_IsCommutativeRing_2796
forall a b. a -> b
coe T_IsCommutativeRing_2796
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsMagma_176
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMagma_176
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_186
            ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480
               ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
                  ((T_IsGroup_1036 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsGroup_1036 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_1050
                     ((T_IsAbelianGroup_1132 -> T_IsGroup_1036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsAbelianGroup_1132 -> T_IsGroup_1036
MAlonzo.Code.Algebra.Structures.d_isGroup_1144
                        ((T_IsRing_2650 -> T_IsAbelianGroup_1132) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_IsRing_2650 -> T_IsAbelianGroup_1132
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2672
                           (T_IsRing_2650 -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650
v2))))))))
-- Algebra.Bundles.CommutativeRing._.∙-congʳ
d_'8729''45'cong'691'_4092 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeRing_4016 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_4092 :: ()
-> ()
-> T_CommutativeRing_4016
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_4092 ~()
v0 ~()
v1 T_CommutativeRing_4016
v2
  = T_CommutativeRing_4016
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_4092 T_CommutativeRing_4016
v2
du_'8729''45'cong'691'_4092 ::
  T_CommutativeRing_4016 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_4092 :: T_CommutativeRing_4016
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_4092 T_CommutativeRing_4016
v0
  = let v1 :: T_IsCommutativeRing_2796
v1 = T_CommutativeRing_4016 -> T_IsCommutativeRing_2796
d_isCommutativeRing_4052 (T_CommutativeRing_4016 -> T_CommutativeRing_4016
forall a b. a -> b
coe T_CommutativeRing_4016
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsRing_2650
v2 = T_IsCommutativeRing_2796 -> T_IsRing_2650
MAlonzo.Code.Algebra.Structures.d_isRing_2812 (T_IsCommutativeRing_2796 -> T_IsCommutativeRing_2796
forall a b. a -> b
coe T_IsCommutativeRing_2796
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: t
v3
                = (T_IsRing_2650 -> T_IsRingWithoutOne_2286) -> AgdaAny -> t
forall a b. a -> b
coe
                    T_IsRing_2650 -> T_IsRingWithoutOne_2286
MAlonzo.Code.Algebra.Structures.du_isRingWithoutOne_2682
                    (T_IsRing_2650 -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsAbelianGroup_1132
v4
                   = T_IsRingWithoutOne_2286 -> T_IsAbelianGroup_1132
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2304
                       (AgdaAny -> T_IsRingWithoutOne_2286
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsGroup_1036
v5
                      = T_IsAbelianGroup_1132 -> T_IsGroup_1036
MAlonzo.Code.Algebra.Structures.d_isGroup_1144 (T_IsAbelianGroup_1132 -> T_IsAbelianGroup_1132
forall a b. a -> b
coe T_IsAbelianGroup_1132
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (let v6 :: T_IsMonoid_686
v6
                         = T_IsGroup_1036 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_1050 (T_IsGroup_1036 -> T_IsGroup_1036
forall a b. a -> b
coe T_IsGroup_1036
v5) in
                   AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     (let v7 :: T_IsSemigroup_472
v7
                            = T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v6) in
                      AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'691'_206
                           ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v7)))))))))
-- Algebra.Bundles.CommutativeRing._.∙-congˡ
d_'8729''45'cong'737'_4094 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeRing_4016 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_4094 :: ()
-> ()
-> T_CommutativeRing_4016
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_4094 ~()
v0 ~()
v1 T_CommutativeRing_4016
v2
  = T_CommutativeRing_4016
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_4094 T_CommutativeRing_4016
v2
du_'8729''45'cong'737'_4094 ::
  T_CommutativeRing_4016 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_4094 :: T_CommutativeRing_4016
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_4094 T_CommutativeRing_4016
v0
  = let v1 :: T_IsCommutativeRing_2796
v1 = T_CommutativeRing_4016 -> T_IsCommutativeRing_2796
d_isCommutativeRing_4052 (T_CommutativeRing_4016 -> T_CommutativeRing_4016
forall a b. a -> b
coe T_CommutativeRing_4016
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsRing_2650
v2 = T_IsCommutativeRing_2796 -> T_IsRing_2650
MAlonzo.Code.Algebra.Structures.d_isRing_2812 (T_IsCommutativeRing_2796 -> T_IsCommutativeRing_2796
forall a b. a -> b
coe T_IsCommutativeRing_2796
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: t
v3
                = (T_IsRing_2650 -> T_IsRingWithoutOne_2286) -> AgdaAny -> t
forall a b. a -> b
coe
                    T_IsRing_2650 -> T_IsRingWithoutOne_2286
MAlonzo.Code.Algebra.Structures.du_isRingWithoutOne_2682
                    (T_IsRing_2650 -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsAbelianGroup_1132
v4
                   = T_IsRingWithoutOne_2286 -> T_IsAbelianGroup_1132
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2304
                       (AgdaAny -> T_IsRingWithoutOne_2286
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsGroup_1036
v5
                      = T_IsAbelianGroup_1132 -> T_IsGroup_1036
MAlonzo.Code.Algebra.Structures.d_isGroup_1144 (T_IsAbelianGroup_1132 -> T_IsAbelianGroup_1132
forall a b. a -> b
coe T_IsAbelianGroup_1132
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (let v6 :: T_IsMonoid_686
v6
                         = T_IsGroup_1036 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_1050 (T_IsGroup_1036 -> T_IsGroup_1036
forall a b. a -> b
coe T_IsGroup_1036
v5) in
                   AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     (let v7 :: T_IsSemigroup_472
v7
                            = T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v6) in
                      AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'737'_202
                           ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v7)))))))))
-- Algebra.Bundles.CommutativeRing._.identity
d_identity_4096 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeRing_4016 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_identity_4096 :: () -> () -> T_CommutativeRing_4016 -> T_Σ_14
d_identity_4096 ~()
v0 ~()
v1 T_CommutativeRing_4016
v2 = T_CommutativeRing_4016 -> T_Σ_14
du_identity_4096 T_CommutativeRing_4016
v2
du_identity_4096 ::
  T_CommutativeRing_4016 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
du_identity_4096 :: T_CommutativeRing_4016 -> T_Σ_14
du_identity_4096 T_CommutativeRing_4016
v0
  = let v1 :: T_IsCommutativeRing_2796
v1 = T_CommutativeRing_4016 -> T_IsCommutativeRing_2796
d_isCommutativeRing_4052 (T_CommutativeRing_4016 -> T_CommutativeRing_4016
forall a b. a -> b
coe T_CommutativeRing_4016
v0) in
    AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      (let v2 :: T_IsRing_2650
v2 = T_IsCommutativeRing_2796 -> T_IsRing_2650
MAlonzo.Code.Algebra.Structures.d_isRing_2812 (T_IsCommutativeRing_2796 -> T_IsCommutativeRing_2796
forall a b. a -> b
coe T_IsCommutativeRing_2796
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsMonoid_686 -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoid_686 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_identity_698
            ((T_IsGroup_1036 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsGroup_1036 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_1050
               ((T_IsAbelianGroup_1132 -> T_IsGroup_1036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsAbelianGroup_1132 -> T_IsGroup_1036
MAlonzo.Code.Algebra.Structures.d_isGroup_1144
                  ((T_IsRing_2650 -> T_IsAbelianGroup_1132) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsRing_2650 -> T_IsAbelianGroup_1132
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2672
                     (T_IsRing_2650 -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650
v2))))))
-- Algebra.Bundles.CommutativeRing._.identityʳ
d_identity'691'_4098 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeRing_4016 -> AgdaAny -> AgdaAny
d_identity'691'_4098 :: () -> () -> T_CommutativeRing_4016 -> AgdaAny -> AgdaAny
d_identity'691'_4098 ~()
v0 ~()
v1 T_CommutativeRing_4016
v2 = T_CommutativeRing_4016 -> AgdaAny -> AgdaAny
du_identity'691'_4098 T_CommutativeRing_4016
v2
du_identity'691'_4098 ::
  T_CommutativeRing_4016 -> AgdaAny -> AgdaAny
du_identity'691'_4098 :: T_CommutativeRing_4016 -> AgdaAny -> AgdaAny
du_identity'691'_4098 T_CommutativeRing_4016
v0
  = let v1 :: T_IsCommutativeRing_2796
v1 = T_CommutativeRing_4016 -> T_IsCommutativeRing_2796
d_isCommutativeRing_4052 (T_CommutativeRing_4016 -> T_CommutativeRing_4016
forall a b. a -> b
coe T_CommutativeRing_4016
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsRing_2650
v2 = T_IsCommutativeRing_2796 -> T_IsRing_2650
MAlonzo.Code.Algebra.Structures.d_isRing_2812 (T_IsCommutativeRing_2796 -> T_IsCommutativeRing_2796
forall a b. a -> b
coe T_IsCommutativeRing_2796
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: t
v3
                = (T_IsRing_2650 -> T_IsRingWithoutOne_2286) -> AgdaAny -> t
forall a b. a -> b
coe
                    T_IsRing_2650 -> T_IsRingWithoutOne_2286
MAlonzo.Code.Algebra.Structures.du_isRingWithoutOne_2682
                    (T_IsRing_2650 -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsAbelianGroup_1132
v4
                   = T_IsRingWithoutOne_2286 -> T_IsAbelianGroup_1132
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2304
                       (AgdaAny -> T_IsRingWithoutOne_2286
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsGroup_1036
v5
                      = T_IsAbelianGroup_1132 -> T_IsGroup_1036
MAlonzo.Code.Algebra.Structures.d_isGroup_1144 (T_IsAbelianGroup_1132 -> T_IsAbelianGroup_1132
forall a b. a -> b
coe T_IsAbelianGroup_1132
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  ((T_IsMonoid_686 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsMonoid_686 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_identity'691'_728
                     ((T_IsGroup_1036 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1036 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_1050 (T_IsGroup_1036 -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1036
v5)))))))
-- Algebra.Bundles.CommutativeRing._.identityˡ
d_identity'737'_4100 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeRing_4016 -> AgdaAny -> AgdaAny
d_identity'737'_4100 :: () -> () -> T_CommutativeRing_4016 -> AgdaAny -> AgdaAny
d_identity'737'_4100 ~()
v0 ~()
v1 T_CommutativeRing_4016
v2 = T_CommutativeRing_4016 -> AgdaAny -> AgdaAny
du_identity'737'_4100 T_CommutativeRing_4016
v2
du_identity'737'_4100 ::
  T_CommutativeRing_4016 -> AgdaAny -> AgdaAny
du_identity'737'_4100 :: T_CommutativeRing_4016 -> AgdaAny -> AgdaAny
du_identity'737'_4100 T_CommutativeRing_4016
v0
  = let v1 :: T_IsCommutativeRing_2796
v1 = T_CommutativeRing_4016 -> T_IsCommutativeRing_2796
d_isCommutativeRing_4052 (T_CommutativeRing_4016 -> T_CommutativeRing_4016
forall a b. a -> b
coe T_CommutativeRing_4016
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsRing_2650
v2 = T_IsCommutativeRing_2796 -> T_IsRing_2650
MAlonzo.Code.Algebra.Structures.d_isRing_2812 (T_IsCommutativeRing_2796 -> T_IsCommutativeRing_2796
forall a b. a -> b
coe T_IsCommutativeRing_2796
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: t
v3
                = (T_IsRing_2650 -> T_IsRingWithoutOne_2286) -> AgdaAny -> t
forall a b. a -> b
coe
                    T_IsRing_2650 -> T_IsRingWithoutOne_2286
MAlonzo.Code.Algebra.Structures.du_isRingWithoutOne_2682
                    (T_IsRing_2650 -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsAbelianGroup_1132
v4
                   = T_IsRingWithoutOne_2286 -> T_IsAbelianGroup_1132
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2304
                       (AgdaAny -> T_IsRingWithoutOne_2286
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsGroup_1036
v5
                      = T_IsAbelianGroup_1132 -> T_IsGroup_1036
MAlonzo.Code.Algebra.Structures.d_isGroup_1144 (T_IsAbelianGroup_1132 -> T_IsAbelianGroup_1132
forall a b. a -> b
coe T_IsAbelianGroup_1132
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  ((T_IsMonoid_686 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsMonoid_686 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_identity'737'_726
                     ((T_IsGroup_1036 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1036 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_1050 (T_IsGroup_1036 -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1036
v5)))))))
-- Algebra.Bundles.CommutativeRing._.+-isAbelianGroup
d_'43''45'isAbelianGroup_4102 ::
  T_CommutativeRing_4016 ->
  MAlonzo.Code.Algebra.Structures.T_IsAbelianGroup_1132
d_'43''45'isAbelianGroup_4102 :: T_CommutativeRing_4016 -> T_IsAbelianGroup_1132
d_'43''45'isAbelianGroup_4102 T_CommutativeRing_4016
v0
  = (T_IsRing_2650 -> T_IsAbelianGroup_1132)
-> AgdaAny -> T_IsAbelianGroup_1132
forall a b. a -> b
coe
      T_IsRing_2650 -> T_IsAbelianGroup_1132
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2672
      ((T_IsCommutativeRing_2796 -> T_IsRing_2650) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCommutativeRing_2796 -> T_IsRing_2650
MAlonzo.Code.Algebra.Structures.d_isRing_2812
         ((T_CommutativeRing_4016 -> T_IsCommutativeRing_2796)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeRing_4016 -> T_IsCommutativeRing_2796
d_isCommutativeRing_4052 (T_CommutativeRing_4016 -> AgdaAny
forall a b. a -> b
coe T_CommutativeRing_4016
v0)))
-- Algebra.Bundles.CommutativeRing._.isCommutativeMagma
d_isCommutativeMagma_4104 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeRing_4016 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMagma_212
d_isCommutativeMagma_4104 :: () -> () -> T_CommutativeRing_4016 -> T_IsCommutativeMagma_212
d_isCommutativeMagma_4104 ~()
v0 ~()
v1 T_CommutativeRing_4016
v2
  = T_CommutativeRing_4016 -> T_IsCommutativeMagma_212
du_isCommutativeMagma_4104 T_CommutativeRing_4016
v2
du_isCommutativeMagma_4104 ::
  T_CommutativeRing_4016 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMagma_212
du_isCommutativeMagma_4104 :: T_CommutativeRing_4016 -> T_IsCommutativeMagma_212
du_isCommutativeMagma_4104 T_CommutativeRing_4016
v0
  = let v1 :: T_IsCommutativeRing_2796
v1 = T_CommutativeRing_4016 -> T_IsCommutativeRing_2796
d_isCommutativeRing_4052 (T_CommutativeRing_4016 -> T_CommutativeRing_4016
forall a b. a -> b
coe T_CommutativeRing_4016
v0) in
    AgdaAny -> T_IsCommutativeMagma_212
forall a b. a -> b
coe
      (let v2 :: T_IsRing_2650
v2 = T_IsCommutativeRing_2796 -> T_IsRing_2650
MAlonzo.Code.Algebra.Structures.d_isRing_2812 (T_IsCommutativeRing_2796 -> T_IsCommutativeRing_2796
forall a b. a -> b
coe T_IsCommutativeRing_2796
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: t
v3
                = (T_IsRing_2650 -> T_IsRingWithoutOne_2286) -> AgdaAny -> t
forall a b. a -> b
coe
                    T_IsRing_2650 -> T_IsRingWithoutOne_2286
MAlonzo.Code.Algebra.Structures.du_isRingWithoutOne_2682
                    (T_IsRing_2650 -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsAbelianGroup_1132
v4
                   = T_IsRingWithoutOne_2286 -> T_IsAbelianGroup_1132
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2304
                       (AgdaAny -> T_IsRingWithoutOne_2286
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: t
v5
                      = (T_IsAbelianGroup_1132 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> t
forall a b. a -> b
coe
                          T_IsAbelianGroup_1132 -> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.du_isCommutativeMonoid_1204
                          (T_IsAbelianGroup_1132 -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  ((T_IsCommutativeSemigroup_548 -> T_IsCommutativeMagma_212)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsCommutativeSemigroup_548 -> T_IsCommutativeMagma_212
MAlonzo.Code.Algebra.Structures.du_isCommutativeMagma_586
                     ((T_IsCommutativeMonoid_736 -> T_IsCommutativeSemigroup_548)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsCommutativeMonoid_736 -> T_IsCommutativeSemigroup_548
MAlonzo.Code.Algebra.Structures.du_isCommutativeSemigroup_786
                        (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v5)))))))
-- Algebra.Bundles.CommutativeRing._.isCommutativeMonoid
d_isCommutativeMonoid_4106 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeRing_4016 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMonoid_736
d_isCommutativeMonoid_4106 :: () -> () -> T_CommutativeRing_4016 -> T_IsCommutativeMonoid_736
d_isCommutativeMonoid_4106 ~()
v0 ~()
v1 T_CommutativeRing_4016
v2
  = T_CommutativeRing_4016 -> T_IsCommutativeMonoid_736
du_isCommutativeMonoid_4106 T_CommutativeRing_4016
v2
du_isCommutativeMonoid_4106 ::
  T_CommutativeRing_4016 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMonoid_736
du_isCommutativeMonoid_4106 :: T_CommutativeRing_4016 -> T_IsCommutativeMonoid_736
du_isCommutativeMonoid_4106 T_CommutativeRing_4016
v0
  = let v1 :: T_IsCommutativeRing_2796
v1 = T_CommutativeRing_4016 -> T_IsCommutativeRing_2796
d_isCommutativeRing_4052 (T_CommutativeRing_4016 -> T_CommutativeRing_4016
forall a b. a -> b
coe T_CommutativeRing_4016
v0) in
    AgdaAny -> T_IsCommutativeMonoid_736
forall a b. a -> b
coe
      (let v2 :: T_IsRing_2650
v2 = T_IsCommutativeRing_2796 -> T_IsRing_2650
MAlonzo.Code.Algebra.Structures.d_isRing_2812 (T_IsCommutativeRing_2796 -> T_IsCommutativeRing_2796
forall a b. a -> b
coe T_IsCommutativeRing_2796
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: t
v3
                = (T_IsRing_2650 -> T_IsRingWithoutOne_2286) -> AgdaAny -> t
forall a b. a -> b
coe
                    T_IsRing_2650 -> T_IsRingWithoutOne_2286
MAlonzo.Code.Algebra.Structures.du_isRingWithoutOne_2682
                    (T_IsRing_2650 -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsAbelianGroup_1132 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsAbelianGroup_1132 -> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.du_isCommutativeMonoid_1204
               ((T_IsRingWithoutOne_2286 -> T_IsAbelianGroup_1132)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsRingWithoutOne_2286 -> T_IsAbelianGroup_1132
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2304
                  (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3)))))
-- Algebra.Bundles.CommutativeRing._.isCommutativeSemigroup
d_isCommutativeSemigroup_4108 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeRing_4016 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_548
d_isCommutativeSemigroup_4108 :: () -> () -> T_CommutativeRing_4016 -> T_IsCommutativeSemigroup_548
d_isCommutativeSemigroup_4108 ~()
v0 ~()
v1 T_CommutativeRing_4016
v2
  = T_CommutativeRing_4016 -> T_IsCommutativeSemigroup_548
du_isCommutativeSemigroup_4108 T_CommutativeRing_4016
v2
du_isCommutativeSemigroup_4108 ::
  T_CommutativeRing_4016 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_548
du_isCommutativeSemigroup_4108 :: T_CommutativeRing_4016 -> T_IsCommutativeSemigroup_548
du_isCommutativeSemigroup_4108 T_CommutativeRing_4016
v0
  = let v1 :: T_IsCommutativeRing_2796
v1 = T_CommutativeRing_4016 -> T_IsCommutativeRing_2796
d_isCommutativeRing_4052 (T_CommutativeRing_4016 -> T_CommutativeRing_4016
forall a b. a -> b
coe T_CommutativeRing_4016
v0) in
    AgdaAny -> T_IsCommutativeSemigroup_548
forall a b. a -> b
coe
      (let v2 :: T_IsRing_2650
v2 = T_IsCommutativeRing_2796 -> T_IsRing_2650
MAlonzo.Code.Algebra.Structures.d_isRing_2812 (T_IsCommutativeRing_2796 -> T_IsCommutativeRing_2796
forall a b. a -> b
coe T_IsCommutativeRing_2796
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: t
v3
                = (T_IsRing_2650 -> T_IsRingWithoutOne_2286) -> AgdaAny -> t
forall a b. a -> b
coe
                    T_IsRing_2650 -> T_IsRingWithoutOne_2286
MAlonzo.Code.Algebra.Structures.du_isRingWithoutOne_2682
                    (T_IsRing_2650 -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsAbelianGroup_1132
v4
                   = T_IsRingWithoutOne_2286 -> T_IsAbelianGroup_1132
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2304
                       (AgdaAny -> T_IsRingWithoutOne_2286
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               ((T_IsCommutativeMonoid_736 -> T_IsCommutativeSemigroup_548)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsCommutativeMonoid_736 -> T_IsCommutativeSemigroup_548
MAlonzo.Code.Algebra.Structures.du_isCommutativeSemigroup_786
                  ((T_IsAbelianGroup_1132 -> T_IsCommutativeMonoid_736)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsAbelianGroup_1132 -> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.du_isCommutativeMonoid_1204
                     (T_IsAbelianGroup_1132 -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132
v4))))))
-- Algebra.Bundles.CommutativeRing._.isGroup
d_isGroup_4110 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeRing_4016 ->
  MAlonzo.Code.Algebra.Structures.T_IsGroup_1036
d_isGroup_4110 :: () -> () -> T_CommutativeRing_4016 -> T_IsGroup_1036
d_isGroup_4110 ~()
v0 ~()
v1 T_CommutativeRing_4016
v2 = T_CommutativeRing_4016 -> T_IsGroup_1036
du_isGroup_4110 T_CommutativeRing_4016
v2
du_isGroup_4110 ::
  T_CommutativeRing_4016 ->
  MAlonzo.Code.Algebra.Structures.T_IsGroup_1036
du_isGroup_4110 :: T_CommutativeRing_4016 -> T_IsGroup_1036
du_isGroup_4110 T_CommutativeRing_4016
v0
  = let v1 :: T_IsCommutativeRing_2796
v1 = T_CommutativeRing_4016 -> T_IsCommutativeRing_2796
d_isCommutativeRing_4052 (T_CommutativeRing_4016 -> T_CommutativeRing_4016
forall a b. a -> b
coe T_CommutativeRing_4016
v0) in
    AgdaAny -> T_IsGroup_1036
forall a b. a -> b
coe
      (let v2 :: T_IsRing_2650
v2 = T_IsCommutativeRing_2796 -> T_IsRing_2650
MAlonzo.Code.Algebra.Structures.d_isRing_2812 (T_IsCommutativeRing_2796 -> T_IsCommutativeRing_2796
forall a b. a -> b
coe T_IsCommutativeRing_2796
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsAbelianGroup_1132 -> T_IsGroup_1036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsAbelianGroup_1132 -> T_IsGroup_1036
MAlonzo.Code.Algebra.Structures.d_isGroup_1144
            ((T_IsRing_2650 -> T_IsAbelianGroup_1132) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsRing_2650 -> T_IsAbelianGroup_1132
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2672
               (T_IsRing_2650 -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650
v2))))
-- Algebra.Bundles.CommutativeRing._.isInvertibleMagma
d_isInvertibleMagma_4112 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeRing_4016 ->
  MAlonzo.Code.Algebra.Structures.T_IsInvertibleMagma_924
d_isInvertibleMagma_4112 :: () -> () -> T_CommutativeRing_4016 -> T_IsInvertibleMagma_924
d_isInvertibleMagma_4112 ~()
v0 ~()
v1 T_CommutativeRing_4016
v2 = T_CommutativeRing_4016 -> T_IsInvertibleMagma_924
du_isInvertibleMagma_4112 T_CommutativeRing_4016
v2
du_isInvertibleMagma_4112 ::
  T_CommutativeRing_4016 ->
  MAlonzo.Code.Algebra.Structures.T_IsInvertibleMagma_924
du_isInvertibleMagma_4112 :: T_CommutativeRing_4016 -> T_IsInvertibleMagma_924
du_isInvertibleMagma_4112 T_CommutativeRing_4016
v0
  = let v1 :: T_IsCommutativeRing_2796
v1 = T_CommutativeRing_4016 -> T_IsCommutativeRing_2796
d_isCommutativeRing_4052 (T_CommutativeRing_4016 -> T_CommutativeRing_4016
forall a b. a -> b
coe T_CommutativeRing_4016
v0) in
    AgdaAny -> T_IsInvertibleMagma_924
forall a b. a -> b
coe
      (let v2 :: T_IsRing_2650
v2 = T_IsCommutativeRing_2796 -> T_IsRing_2650
MAlonzo.Code.Algebra.Structures.d_isRing_2812 (T_IsCommutativeRing_2796 -> T_IsCommutativeRing_2796
forall a b. a -> b
coe T_IsCommutativeRing_2796
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: t
v3
                = (T_IsRing_2650 -> T_IsRingWithoutOne_2286) -> AgdaAny -> t
forall a b. a -> b
coe
                    T_IsRing_2650 -> T_IsRingWithoutOne_2286
MAlonzo.Code.Algebra.Structures.du_isRingWithoutOne_2682
                    (T_IsRing_2650 -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsAbelianGroup_1132
v4
                   = T_IsRingWithoutOne_2286 -> T_IsAbelianGroup_1132
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2304
                       (AgdaAny -> T_IsRingWithoutOne_2286
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               ((T_IsGroup_1036 -> T_IsInvertibleMagma_924) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsGroup_1036 -> T_IsInvertibleMagma_924
MAlonzo.Code.Algebra.Structures.du_isInvertibleMagma_1122
                  ((T_IsAbelianGroup_1132 -> T_IsGroup_1036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132 -> T_IsGroup_1036
MAlonzo.Code.Algebra.Structures.d_isGroup_1144 (T_IsAbelianGroup_1132 -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132
v4))))))
-- Algebra.Bundles.CommutativeRing._.isInvertibleUnitalMagma
d_isInvertibleUnitalMagma_4114 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeRing_4016 ->
  MAlonzo.Code.Algebra.Structures.T_IsInvertibleUnitalMagma_976
d_isInvertibleUnitalMagma_4114 :: () -> () -> T_CommutativeRing_4016 -> T_IsInvertibleUnitalMagma_976
d_isInvertibleUnitalMagma_4114 ~()
v0 ~()
v1 T_CommutativeRing_4016
v2
  = T_CommutativeRing_4016 -> T_IsInvertibleUnitalMagma_976
du_isInvertibleUnitalMagma_4114 T_CommutativeRing_4016
v2
du_isInvertibleUnitalMagma_4114 ::
  T_CommutativeRing_4016 ->
  MAlonzo.Code.Algebra.Structures.T_IsInvertibleUnitalMagma_976
du_isInvertibleUnitalMagma_4114 :: T_CommutativeRing_4016 -> T_IsInvertibleUnitalMagma_976
du_isInvertibleUnitalMagma_4114 T_CommutativeRing_4016
v0
  = let v1 :: T_IsCommutativeRing_2796
v1 = T_CommutativeRing_4016 -> T_IsCommutativeRing_2796
d_isCommutativeRing_4052 (T_CommutativeRing_4016 -> T_CommutativeRing_4016
forall a b. a -> b
coe T_CommutativeRing_4016
v0) in
    AgdaAny -> T_IsInvertibleUnitalMagma_976
forall a b. a -> b
coe
      (let v2 :: T_IsRing_2650
v2 = T_IsCommutativeRing_2796 -> T_IsRing_2650
MAlonzo.Code.Algebra.Structures.d_isRing_2812 (T_IsCommutativeRing_2796 -> T_IsCommutativeRing_2796
forall a b. a -> b
coe T_IsCommutativeRing_2796
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: t
v3
                = (T_IsRing_2650 -> T_IsRingWithoutOne_2286) -> AgdaAny -> t
forall a b. a -> b
coe
                    T_IsRing_2650 -> T_IsRingWithoutOne_2286
MAlonzo.Code.Algebra.Structures.du_isRingWithoutOne_2682
                    (T_IsRing_2650 -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsAbelianGroup_1132
v4
                   = T_IsRingWithoutOne_2286 -> T_IsAbelianGroup_1132
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2304
                       (AgdaAny -> T_IsRingWithoutOne_2286
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               ((T_IsGroup_1036 -> T_IsInvertibleUnitalMagma_976)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsGroup_1036 -> T_IsInvertibleUnitalMagma_976
MAlonzo.Code.Algebra.Structures.du_isInvertibleUnitalMagma_1124
                  ((T_IsAbelianGroup_1132 -> T_IsGroup_1036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132 -> T_IsGroup_1036
MAlonzo.Code.Algebra.Structures.d_isGroup_1144 (T_IsAbelianGroup_1132 -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132
v4))))))
-- Algebra.Bundles.CommutativeRing._.isMagma
d_isMagma_4116 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeRing_4016 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_176
d_isMagma_4116 :: () -> () -> T_CommutativeRing_4016 -> T_IsMagma_176
d_isMagma_4116 ~()
v0 ~()
v1 T_CommutativeRing_4016
v2 = T_CommutativeRing_4016 -> T_IsMagma_176
du_isMagma_4116 T_CommutativeRing_4016
v2
du_isMagma_4116 ::
  T_CommutativeRing_4016 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_176
du_isMagma_4116 :: T_CommutativeRing_4016 -> T_IsMagma_176
du_isMagma_4116 T_CommutativeRing_4016
v0
  = let v1 :: T_IsCommutativeRing_2796
v1 = T_CommutativeRing_4016 -> T_IsCommutativeRing_2796
d_isCommutativeRing_4052 (T_CommutativeRing_4016 -> T_CommutativeRing_4016
forall a b. a -> b
coe T_CommutativeRing_4016
v0) in
    AgdaAny -> T_IsMagma_176
forall a b. a -> b
coe
      (let v2 :: T_IsRing_2650
v2 = T_IsCommutativeRing_2796 -> T_IsRing_2650
MAlonzo.Code.Algebra.Structures.d_isRing_2812 (T_IsCommutativeRing_2796 -> T_IsCommutativeRing_2796
forall a b. a -> b
coe T_IsCommutativeRing_2796
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480
            ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
               ((T_IsGroup_1036 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsGroup_1036 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_1050
                  ((T_IsAbelianGroup_1132 -> T_IsGroup_1036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsAbelianGroup_1132 -> T_IsGroup_1036
MAlonzo.Code.Algebra.Structures.d_isGroup_1144
                     ((T_IsRing_2650 -> T_IsAbelianGroup_1132) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsRing_2650 -> T_IsAbelianGroup_1132
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2672
                        (T_IsRing_2650 -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650
v2)))))))
-- Algebra.Bundles.CommutativeRing._.isMonoid
d_isMonoid_4118 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeRing_4016 ->
  MAlonzo.Code.Algebra.Structures.T_IsMonoid_686
d_isMonoid_4118 :: () -> () -> T_CommutativeRing_4016 -> T_IsMonoid_686
d_isMonoid_4118 ~()
v0 ~()
v1 T_CommutativeRing_4016
v2 = T_CommutativeRing_4016 -> T_IsMonoid_686
du_isMonoid_4118 T_CommutativeRing_4016
v2
du_isMonoid_4118 ::
  T_CommutativeRing_4016 ->
  MAlonzo.Code.Algebra.Structures.T_IsMonoid_686
du_isMonoid_4118 :: T_CommutativeRing_4016 -> T_IsMonoid_686
du_isMonoid_4118 T_CommutativeRing_4016
v0
  = let v1 :: T_IsCommutativeRing_2796
v1 = T_CommutativeRing_4016 -> T_IsCommutativeRing_2796
d_isCommutativeRing_4052 (T_CommutativeRing_4016 -> T_CommutativeRing_4016
forall a b. a -> b
coe T_CommutativeRing_4016
v0) in
    AgdaAny -> T_IsMonoid_686
forall a b. a -> b
coe
      (let v2 :: T_IsRing_2650
v2 = T_IsCommutativeRing_2796 -> T_IsRing_2650
MAlonzo.Code.Algebra.Structures.d_isRing_2812 (T_IsCommutativeRing_2796 -> T_IsCommutativeRing_2796
forall a b. a -> b
coe T_IsCommutativeRing_2796
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsGroup_1036 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsGroup_1036 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_1050
            ((T_IsAbelianGroup_1132 -> T_IsGroup_1036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsAbelianGroup_1132 -> T_IsGroup_1036
MAlonzo.Code.Algebra.Structures.d_isGroup_1144
               ((T_IsRing_2650 -> T_IsAbelianGroup_1132) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsRing_2650 -> T_IsAbelianGroup_1132
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2672
                  (T_IsRing_2650 -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650
v2)))))
-- Algebra.Bundles.CommutativeRing._.isSemigroup
d_isSemigroup_4120 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeRing_4016 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_472
d_isSemigroup_4120 :: () -> () -> T_CommutativeRing_4016 -> T_IsSemigroup_472
d_isSemigroup_4120 ~()
v0 ~()
v1 T_CommutativeRing_4016
v2 = T_CommutativeRing_4016 -> T_IsSemigroup_472
du_isSemigroup_4120 T_CommutativeRing_4016
v2
du_isSemigroup_4120 ::
  T_CommutativeRing_4016 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_472
du_isSemigroup_4120 :: T_CommutativeRing_4016 -> T_IsSemigroup_472
du_isSemigroup_4120 T_CommutativeRing_4016
v0
  = let v1 :: T_IsCommutativeRing_2796
v1 = T_CommutativeRing_4016 -> T_IsCommutativeRing_2796
d_isCommutativeRing_4052 (T_CommutativeRing_4016 -> T_CommutativeRing_4016
forall a b. a -> b
coe T_CommutativeRing_4016
v0) in
    AgdaAny -> T_IsSemigroup_472
forall a b. a -> b
coe
      (let v2 :: T_IsRing_2650
v2 = T_IsCommutativeRing_2796 -> T_IsRing_2650
MAlonzo.Code.Algebra.Structures.d_isRing_2812 (T_IsCommutativeRing_2796 -> T_IsCommutativeRing_2796
forall a b. a -> b
coe T_IsCommutativeRing_2796
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
            ((T_IsGroup_1036 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsGroup_1036 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_1050
               ((T_IsAbelianGroup_1132 -> T_IsGroup_1036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsAbelianGroup_1132 -> T_IsGroup_1036
MAlonzo.Code.Algebra.Structures.d_isGroup_1144
                  ((T_IsRing_2650 -> T_IsAbelianGroup_1132) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsRing_2650 -> T_IsAbelianGroup_1132
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2672
                     (T_IsRing_2650 -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650
v2))))))
-- Algebra.Bundles.CommutativeRing._.isUnitalMagma
d_isUnitalMagma_4122 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeRing_4016 ->
  MAlonzo.Code.Algebra.Structures.T_IsUnitalMagma_642
d_isUnitalMagma_4122 :: () -> () -> T_CommutativeRing_4016 -> T_IsUnitalMagma_642
d_isUnitalMagma_4122 ~()
v0 ~()
v1 T_CommutativeRing_4016
v2 = T_CommutativeRing_4016 -> T_IsUnitalMagma_642
du_isUnitalMagma_4122 T_CommutativeRing_4016
v2
du_isUnitalMagma_4122 ::
  T_CommutativeRing_4016 ->
  MAlonzo.Code.Algebra.Structures.T_IsUnitalMagma_642
du_isUnitalMagma_4122 :: T_CommutativeRing_4016 -> T_IsUnitalMagma_642
du_isUnitalMagma_4122 T_CommutativeRing_4016
v0
  = let v1 :: T_IsCommutativeRing_2796
v1 = T_CommutativeRing_4016 -> T_IsCommutativeRing_2796
d_isCommutativeRing_4052 (T_CommutativeRing_4016 -> T_CommutativeRing_4016
forall a b. a -> b
coe T_CommutativeRing_4016
v0) in
    AgdaAny -> T_IsUnitalMagma_642
forall a b. a -> b
coe
      (let v2 :: T_IsRing_2650
v2 = T_IsCommutativeRing_2796 -> T_IsRing_2650
MAlonzo.Code.Algebra.Structures.d_isRing_2812 (T_IsCommutativeRing_2796 -> T_IsCommutativeRing_2796
forall a b. a -> b
coe T_IsCommutativeRing_2796
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: t
v3
                = (T_IsRing_2650 -> T_IsRingWithoutOne_2286) -> AgdaAny -> t
forall a b. a -> b
coe
                    T_IsRing_2650 -> T_IsRingWithoutOne_2286
MAlonzo.Code.Algebra.Structures.du_isRingWithoutOne_2682
                    (T_IsRing_2650 -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsAbelianGroup_1132
v4
                   = T_IsRingWithoutOne_2286 -> T_IsAbelianGroup_1132
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2304
                       (AgdaAny -> T_IsRingWithoutOne_2286
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsGroup_1036
v5
                      = T_IsAbelianGroup_1132 -> T_IsGroup_1036
MAlonzo.Code.Algebra.Structures.d_isGroup_1144 (T_IsAbelianGroup_1132 -> T_IsAbelianGroup_1132
forall a b. a -> b
coe T_IsAbelianGroup_1132
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  ((T_IsMonoid_686 -> T_IsUnitalMagma_642) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsMonoid_686 -> T_IsUnitalMagma_642
MAlonzo.Code.Algebra.Structures.du_isUnitalMagma_730
                     ((T_IsGroup_1036 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1036 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_1050 (T_IsGroup_1036 -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1036
v5)))))))
-- Algebra.Bundles.CommutativeRing._.⁻¹-cong
d_'8315''185''45'cong_4124 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeRing_4016 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8315''185''45'cong_4124 :: ()
-> ()
-> T_CommutativeRing_4016
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8315''185''45'cong_4124 ~()
v0 ~()
v1 T_CommutativeRing_4016
v2
  = T_CommutativeRing_4016 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8315''185''45'cong_4124 T_CommutativeRing_4016
v2
du_'8315''185''45'cong_4124 ::
  T_CommutativeRing_4016 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8315''185''45'cong_4124 :: T_CommutativeRing_4016 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8315''185''45'cong_4124 T_CommutativeRing_4016
v0
  = let v1 :: T_IsCommutativeRing_2796
v1 = T_CommutativeRing_4016 -> T_IsCommutativeRing_2796
d_isCommutativeRing_4052 (T_CommutativeRing_4016 -> T_CommutativeRing_4016
forall a b. a -> b
coe T_CommutativeRing_4016
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsRing_2650
v2 = T_IsCommutativeRing_2796 -> T_IsRing_2650
MAlonzo.Code.Algebra.Structures.d_isRing_2812 (T_IsCommutativeRing_2796 -> T_IsCommutativeRing_2796
forall a b. a -> b
coe T_IsCommutativeRing_2796
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsGroup_1036 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsGroup_1036 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8315''185''45'cong_1054
            ((T_IsAbelianGroup_1132 -> T_IsGroup_1036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsAbelianGroup_1132 -> T_IsGroup_1036
MAlonzo.Code.Algebra.Structures.d_isGroup_1144
               ((T_IsRing_2650 -> T_IsAbelianGroup_1132) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsRing_2650 -> T_IsAbelianGroup_1132
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2672
                  (T_IsRing_2650 -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650
v2)))))
-- Algebra.Bundles.CommutativeRing._.inverse
d_inverse_4126 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeRing_4016 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_inverse_4126 :: () -> () -> T_CommutativeRing_4016 -> T_Σ_14
d_inverse_4126 ~()
v0 ~()
v1 T_CommutativeRing_4016
v2 = T_CommutativeRing_4016 -> T_Σ_14
du_inverse_4126 T_CommutativeRing_4016
v2
du_inverse_4126 ::
  T_CommutativeRing_4016 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
du_inverse_4126 :: T_CommutativeRing_4016 -> T_Σ_14
du_inverse_4126 T_CommutativeRing_4016
v0
  = let v1 :: T_IsCommutativeRing_2796
v1 = T_CommutativeRing_4016 -> T_IsCommutativeRing_2796
d_isCommutativeRing_4052 (T_CommutativeRing_4016 -> T_CommutativeRing_4016
forall a b. a -> b
coe T_CommutativeRing_4016
v0) in
    AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      (let v2 :: T_IsRing_2650
v2 = T_IsCommutativeRing_2796 -> T_IsRing_2650
MAlonzo.Code.Algebra.Structures.d_isRing_2812 (T_IsCommutativeRing_2796 -> T_IsCommutativeRing_2796
forall a b. a -> b
coe T_IsCommutativeRing_2796
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsGroup_1036 -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsGroup_1036 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_inverse_1052
            ((T_IsAbelianGroup_1132 -> T_IsGroup_1036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsAbelianGroup_1132 -> T_IsGroup_1036
MAlonzo.Code.Algebra.Structures.d_isGroup_1144
               ((T_IsRing_2650 -> T_IsAbelianGroup_1132) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsRing_2650 -> T_IsAbelianGroup_1132
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2672
                  (T_IsRing_2650 -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650
v2)))))
-- Algebra.Bundles.CommutativeRing._.inverseʳ
d_inverse'691'_4128 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeRing_4016 -> AgdaAny -> AgdaAny
d_inverse'691'_4128 :: () -> () -> T_CommutativeRing_4016 -> AgdaAny -> AgdaAny
d_inverse'691'_4128 ~()
v0 ~()
v1 T_CommutativeRing_4016
v2 = T_CommutativeRing_4016 -> AgdaAny -> AgdaAny
du_inverse'691'_4128 T_CommutativeRing_4016
v2
du_inverse'691'_4128 ::
  T_CommutativeRing_4016 -> AgdaAny -> AgdaAny
du_inverse'691'_4128 :: T_CommutativeRing_4016 -> AgdaAny -> AgdaAny
du_inverse'691'_4128 T_CommutativeRing_4016
v0
  = let v1 :: T_IsCommutativeRing_2796
v1 = T_CommutativeRing_4016 -> T_IsCommutativeRing_2796
d_isCommutativeRing_4052 (T_CommutativeRing_4016 -> T_CommutativeRing_4016
forall a b. a -> b
coe T_CommutativeRing_4016
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsRing_2650
v2 = T_IsCommutativeRing_2796 -> T_IsRing_2650
MAlonzo.Code.Algebra.Structures.d_isRing_2812 (T_IsCommutativeRing_2796 -> T_IsCommutativeRing_2796
forall a b. a -> b
coe T_IsCommutativeRing_2796
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: t
v3
                = (T_IsRing_2650 -> T_IsRingWithoutOne_2286) -> AgdaAny -> t
forall a b. a -> b
coe
                    T_IsRing_2650 -> T_IsRingWithoutOne_2286
MAlonzo.Code.Algebra.Structures.du_isRingWithoutOne_2682
                    (T_IsRing_2650 -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsAbelianGroup_1132
v4
                   = T_IsRingWithoutOne_2286 -> T_IsAbelianGroup_1132
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2304
                       (AgdaAny -> T_IsRingWithoutOne_2286
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               ((T_IsGroup_1036 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsGroup_1036 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_inverse'691'_1108
                  ((T_IsAbelianGroup_1132 -> T_IsGroup_1036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132 -> T_IsGroup_1036
MAlonzo.Code.Algebra.Structures.d_isGroup_1144 (T_IsAbelianGroup_1132 -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132
v4))))))
-- Algebra.Bundles.CommutativeRing._.inverseˡ
d_inverse'737'_4130 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeRing_4016 -> AgdaAny -> AgdaAny
d_inverse'737'_4130 :: () -> () -> T_CommutativeRing_4016 -> AgdaAny -> AgdaAny
d_inverse'737'_4130 ~()
v0 ~()
v1 T_CommutativeRing_4016
v2 = T_CommutativeRing_4016 -> AgdaAny -> AgdaAny
du_inverse'737'_4130 T_CommutativeRing_4016
v2
du_inverse'737'_4130 ::
  T_CommutativeRing_4016 -> AgdaAny -> AgdaAny
du_inverse'737'_4130 :: T_CommutativeRing_4016 -> AgdaAny -> AgdaAny
du_inverse'737'_4130 T_CommutativeRing_4016
v0
  = let v1 :: T_IsCommutativeRing_2796
v1 = T_CommutativeRing_4016 -> T_IsCommutativeRing_2796
d_isCommutativeRing_4052 (T_CommutativeRing_4016 -> T_CommutativeRing_4016
forall a b. a -> b
coe T_CommutativeRing_4016
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsRing_2650
v2 = T_IsCommutativeRing_2796 -> T_IsRing_2650
MAlonzo.Code.Algebra.Structures.d_isRing_2812 (T_IsCommutativeRing_2796 -> T_IsCommutativeRing_2796
forall a b. a -> b
coe T_IsCommutativeRing_2796
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: t
v3
                = (T_IsRing_2650 -> T_IsRingWithoutOne_2286) -> AgdaAny -> t
forall a b. a -> b
coe
                    T_IsRing_2650 -> T_IsRingWithoutOne_2286
MAlonzo.Code.Algebra.Structures.du_isRingWithoutOne_2682
                    (T_IsRing_2650 -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsAbelianGroup_1132
v4
                   = T_IsRingWithoutOne_2286 -> T_IsAbelianGroup_1132
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2304
                       (AgdaAny -> T_IsRingWithoutOne_2286
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               ((T_IsGroup_1036 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsGroup_1036 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_inverse'737'_1106
                  ((T_IsAbelianGroup_1132 -> T_IsGroup_1036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132 -> T_IsGroup_1036
MAlonzo.Code.Algebra.Structures.d_isGroup_1144 (T_IsAbelianGroup_1132 -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132
v4))))))
-- Algebra.Bundles.CommutativeRing._.distrib
d_distrib_4132 ::
  T_CommutativeRing_4016 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_distrib_4132 :: T_CommutativeRing_4016 -> T_Σ_14
d_distrib_4132 T_CommutativeRing_4016
v0
  = (T_IsRing_2650 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsRing_2650 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_distrib_2680
      ((T_IsCommutativeRing_2796 -> T_IsRing_2650) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCommutativeRing_2796 -> T_IsRing_2650
MAlonzo.Code.Algebra.Structures.d_isRing_2812
         ((T_CommutativeRing_4016 -> T_IsCommutativeRing_2796)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeRing_4016 -> T_IsCommutativeRing_2796
d_isCommutativeRing_4052 (T_CommutativeRing_4016 -> AgdaAny
forall a b. a -> b
coe T_CommutativeRing_4016
v0)))
-- Algebra.Bundles.CommutativeRing._.distribʳ
d_distrib'691'_4134 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeRing_4016 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_distrib'691'_4134 :: ()
-> ()
-> T_CommutativeRing_4016
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_distrib'691'_4134 ~()
v0 ~()
v1 T_CommutativeRing_4016
v2 = T_CommutativeRing_4016 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'691'_4134 T_CommutativeRing_4016
v2
du_distrib'691'_4134 ::
  T_CommutativeRing_4016 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'691'_4134 :: T_CommutativeRing_4016 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'691'_4134 T_CommutativeRing_4016
v0
  = let v1 :: T_IsCommutativeRing_2796
v1 = T_CommutativeRing_4016 -> T_IsCommutativeRing_2796
d_isCommutativeRing_4052 (T_CommutativeRing_4016 -> T_CommutativeRing_4016
forall a b. a -> b
coe T_CommutativeRing_4016
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsRing_2650
v2 = T_IsCommutativeRing_2796 -> T_IsRing_2650
MAlonzo.Code.Algebra.Structures.d_isRing_2812 (T_IsCommutativeRing_2796 -> T_IsCommutativeRing_2796
forall a b. a -> b
coe T_IsCommutativeRing_2796
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsRingWithoutOne_2286
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsRingWithoutOne_2286 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_distrib'691'_2380
            ((T_IsRing_2650 -> T_IsRingWithoutOne_2286) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsRing_2650 -> T_IsRingWithoutOne_2286
MAlonzo.Code.Algebra.Structures.du_isRingWithoutOne_2682
               (T_IsRing_2650 -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650
v2))))
-- Algebra.Bundles.CommutativeRing._.distribˡ
d_distrib'737'_4136 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeRing_4016 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_distrib'737'_4136 :: ()
-> ()
-> T_CommutativeRing_4016
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_distrib'737'_4136 ~()
v0 ~()
v1 T_CommutativeRing_4016
v2 = T_CommutativeRing_4016 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'737'_4136 T_CommutativeRing_4016
v2
du_distrib'737'_4136 ::
  T_CommutativeRing_4016 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'737'_4136 :: T_CommutativeRing_4016 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'737'_4136 T_CommutativeRing_4016
v0
  = let v1 :: T_IsCommutativeRing_2796
v1 = T_CommutativeRing_4016 -> T_IsCommutativeRing_2796
d_isCommutativeRing_4052 (T_CommutativeRing_4016 -> T_CommutativeRing_4016
forall a b. a -> b
coe T_CommutativeRing_4016
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsRing_2650
v2 = T_IsCommutativeRing_2796 -> T_IsRing_2650
MAlonzo.Code.Algebra.Structures.d_isRing_2812 (T_IsCommutativeRing_2796 -> T_IsCommutativeRing_2796
forall a b. a -> b
coe T_IsCommutativeRing_2796
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsRingWithoutOne_2286
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsRingWithoutOne_2286 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_distrib'737'_2378
            ((T_IsRing_2650 -> T_IsRingWithoutOne_2286) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsRing_2650 -> T_IsRingWithoutOne_2286
MAlonzo.Code.Algebra.Structures.du_isRingWithoutOne_2682
               (T_IsRing_2650 -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650
v2))))
-- Algebra.Bundles.CommutativeRing._.isCommutativeSemiring
d_isCommutativeSemiring_4138 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeRing_4016 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiring_1678
d_isCommutativeSemiring_4138 :: () -> () -> T_CommutativeRing_4016 -> T_IsCommutativeSemiring_1678
d_isCommutativeSemiring_4138 ~()
v0 ~()
v1 T_CommutativeRing_4016
v2
  = T_CommutativeRing_4016 -> T_IsCommutativeSemiring_1678
du_isCommutativeSemiring_4138 T_CommutativeRing_4016
v2
du_isCommutativeSemiring_4138 ::
  T_CommutativeRing_4016 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiring_1678
du_isCommutativeSemiring_4138 :: T_CommutativeRing_4016 -> T_IsCommutativeSemiring_1678
du_isCommutativeSemiring_4138 T_CommutativeRing_4016
v0
  = ((AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny)
 -> AgdaAny
 -> T_IsCommutativeRing_2796
 -> T_IsCommutativeSemiring_1678)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> T_IsCommutativeSemiring_1678
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsCommutativeRing_2796
-> T_IsCommutativeSemiring_1678
MAlonzo.Code.Algebra.Structures.du_isCommutativeSemiring_2926
      ((T_CommutativeRing_4016 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeRing_4016 -> AgdaAny -> AgdaAny -> AgdaAny
d__'43'__4042 (T_CommutativeRing_4016 -> AgdaAny
forall a b. a -> b
coe T_CommutativeRing_4016
v0)) ((T_CommutativeRing_4016 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeRing_4016 -> AgdaAny -> AgdaAny -> AgdaAny
d__'42'__4044 (T_CommutativeRing_4016 -> AgdaAny
forall a b. a -> b
coe T_CommutativeRing_4016
v0))
      ((T_CommutativeRing_4016 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeRing_4016 -> AgdaAny -> AgdaAny
d_'45'__4046 (T_CommutativeRing_4016 -> AgdaAny
forall a b. a -> b
coe T_CommutativeRing_4016
v0)) ((T_CommutativeRing_4016 -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeRing_4016 -> AgdaAny
d_0'35'_4048 (T_CommutativeRing_4016 -> AgdaAny
forall a b. a -> b
coe T_CommutativeRing_4016
v0))
      ((T_CommutativeRing_4016 -> T_IsCommutativeRing_2796)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeRing_4016 -> T_IsCommutativeRing_2796
d_isCommutativeRing_4052 (T_CommutativeRing_4016 -> AgdaAny
forall a b. a -> b
coe T_CommutativeRing_4016
v0))
-- Algebra.Bundles.CommutativeRing._.isCommutativeSemiringWithoutOne
d_isCommutativeSemiringWithoutOne_4140 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeRing_4016 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiringWithoutOne_1382
d_isCommutativeSemiringWithoutOne_4140 :: ()
-> ()
-> T_CommutativeRing_4016
-> T_IsCommutativeSemiringWithoutOne_1382
d_isCommutativeSemiringWithoutOne_4140 ~()
v0 ~()
v1 T_CommutativeRing_4016
v2
  = T_CommutativeRing_4016 -> T_IsCommutativeSemiringWithoutOne_1382
du_isCommutativeSemiringWithoutOne_4140 T_CommutativeRing_4016
v2
du_isCommutativeSemiringWithoutOne_4140 ::
  T_CommutativeRing_4016 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiringWithoutOne_1382
du_isCommutativeSemiringWithoutOne_4140 :: T_CommutativeRing_4016 -> T_IsCommutativeSemiringWithoutOne_1382
du_isCommutativeSemiringWithoutOne_4140 T_CommutativeRing_4016
v0
  = let v1 :: AgdaAny -> AgdaAny -> AgdaAny
v1 = T_CommutativeRing_4016 -> AgdaAny -> AgdaAny -> AgdaAny
d__'43'__4042 (T_CommutativeRing_4016 -> T_CommutativeRing_4016
forall a b. a -> b
coe T_CommutativeRing_4016
v0) in
    AgdaAny -> T_IsCommutativeSemiringWithoutOne_1382
forall a b. a -> b
coe
      (let v2 :: AgdaAny -> AgdaAny -> AgdaAny
v2 = T_CommutativeRing_4016 -> AgdaAny -> AgdaAny -> AgdaAny
d__'42'__4044 (T_CommutativeRing_4016 -> T_CommutativeRing_4016
forall a b. a -> b
coe T_CommutativeRing_4016
v0) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: AgdaAny -> AgdaAny
v3 = T_CommutativeRing_4016 -> AgdaAny -> AgdaAny
d_'45'__4046 (T_CommutativeRing_4016 -> T_CommutativeRing_4016
forall a b. a -> b
coe T_CommutativeRing_4016
v0) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: AgdaAny
v4 = T_CommutativeRing_4016 -> AgdaAny
d_0'35'_4048 (T_CommutativeRing_4016 -> T_CommutativeRing_4016
forall a b. a -> b
coe T_CommutativeRing_4016
v0) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsCommutativeRing_2796
v5 = T_CommutativeRing_4016 -> T_IsCommutativeRing_2796
d_isCommutativeRing_4052 (T_CommutativeRing_4016 -> T_CommutativeRing_4016
forall a b. a -> b
coe T_CommutativeRing_4016
v0) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  ((T_IsCommutativeSemiring_1678
 -> T_IsCommutativeSemiringWithoutOne_1382)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsCommutativeSemiring_1678
-> T_IsCommutativeSemiringWithoutOne_1382
MAlonzo.Code.Algebra.Structures.du_isCommutativeSemiringWithoutOne_1780
                     (((AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny)
 -> AgdaAny
 -> T_IsCommutativeRing_2796
 -> T_IsCommutativeSemiring_1678)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsCommutativeRing_2796
-> T_IsCommutativeSemiring_1678
MAlonzo.Code.Algebra.Structures.du_isCommutativeSemiring_2926
                        ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v1) ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v2) ((AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v3) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v4) (T_IsCommutativeRing_2796 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeRing_2796
v5)))))))
-- Algebra.Bundles.CommutativeRing._.isEquivalence
d_isEquivalence_4142 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeRing_4016 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_4142 :: () -> () -> T_CommutativeRing_4016 -> T_IsEquivalence_26
d_isEquivalence_4142 ~()
v0 ~()
v1 T_CommutativeRing_4016
v2 = T_CommutativeRing_4016 -> T_IsEquivalence_26
du_isEquivalence_4142 T_CommutativeRing_4016
v2
du_isEquivalence_4142 ::
  T_CommutativeRing_4016 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
du_isEquivalence_4142 :: T_CommutativeRing_4016 -> T_IsEquivalence_26
du_isEquivalence_4142 T_CommutativeRing_4016
v0
  = let v1 :: T_IsCommutativeRing_2796
v1 = T_CommutativeRing_4016 -> T_IsCommutativeRing_2796
d_isCommutativeRing_4052 (T_CommutativeRing_4016 -> T_CommutativeRing_4016
forall a b. a -> b
coe T_CommutativeRing_4016
v0) in
    AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      (let v2 :: T_IsRing_2650
v2 = T_IsCommutativeRing_2796 -> T_IsRing_2650
MAlonzo.Code.Algebra.Structures.d_isRing_2812 (T_IsCommutativeRing_2796 -> T_IsCommutativeRing_2796
forall a b. a -> b
coe T_IsCommutativeRing_2796
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
            ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480
               ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
                  ((T_IsGroup_1036 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsGroup_1036 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_1050
                     ((T_IsAbelianGroup_1132 -> T_IsGroup_1036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsAbelianGroup_1132 -> T_IsGroup_1036
MAlonzo.Code.Algebra.Structures.d_isGroup_1144
                        ((T_IsRing_2650 -> T_IsAbelianGroup_1132) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_IsRing_2650 -> T_IsAbelianGroup_1132
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2672
                           (T_IsRing_2650 -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650
v2))))))))
-- Algebra.Bundles.CommutativeRing._.isNearSemiring
d_isNearSemiring_4144 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeRing_4016 ->
  MAlonzo.Code.Algebra.Structures.T_IsNearSemiring_1218
d_isNearSemiring_4144 :: () -> () -> T_CommutativeRing_4016 -> T_IsNearSemiring_1218
d_isNearSemiring_4144 ~()
v0 ~()
v1 T_CommutativeRing_4016
v2 = T_CommutativeRing_4016 -> T_IsNearSemiring_1218
du_isNearSemiring_4144 T_CommutativeRing_4016
v2
du_isNearSemiring_4144 ::
  T_CommutativeRing_4016 ->
  MAlonzo.Code.Algebra.Structures.T_IsNearSemiring_1218
du_isNearSemiring_4144 :: T_CommutativeRing_4016 -> T_IsNearSemiring_1218
du_isNearSemiring_4144 T_CommutativeRing_4016
v0
  = let v1 :: AgdaAny -> AgdaAny -> AgdaAny
v1 = T_CommutativeRing_4016 -> AgdaAny -> AgdaAny -> AgdaAny
d__'43'__4042 (T_CommutativeRing_4016 -> T_CommutativeRing_4016
forall a b. a -> b
coe T_CommutativeRing_4016
v0) in
    AgdaAny -> T_IsNearSemiring_1218
forall a b. a -> b
coe
      (let v2 :: AgdaAny -> AgdaAny -> AgdaAny
v2 = T_CommutativeRing_4016 -> AgdaAny -> AgdaAny -> AgdaAny
d__'42'__4044 (T_CommutativeRing_4016 -> T_CommutativeRing_4016
forall a b. a -> b
coe T_CommutativeRing_4016
v0) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: AgdaAny -> AgdaAny
v3 = T_CommutativeRing_4016 -> AgdaAny -> AgdaAny
d_'45'__4046 (T_CommutativeRing_4016 -> T_CommutativeRing_4016
forall a b. a -> b
coe T_CommutativeRing_4016
v0) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: AgdaAny
v4 = T_CommutativeRing_4016 -> AgdaAny
d_0'35'_4048 (T_CommutativeRing_4016 -> T_CommutativeRing_4016
forall a b. a -> b
coe T_CommutativeRing_4016
v0) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsCommutativeRing_2796
v5 = T_CommutativeRing_4016 -> T_IsCommutativeRing_2796
d_isCommutativeRing_4052 (T_CommutativeRing_4016 -> T_CommutativeRing_4016
forall a b. a -> b
coe T_CommutativeRing_4016
v0) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (let v6 :: T_IsRing_2650
v6 = T_IsCommutativeRing_2796 -> T_IsRing_2650
MAlonzo.Code.Algebra.Structures.d_isRing_2812 (T_IsCommutativeRing_2796 -> T_IsCommutativeRing_2796
forall a b. a -> b
coe T_IsCommutativeRing_2796
v5) in
                   AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     (let v7 :: t
v7
                            = ((AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny)
 -> AgdaAny
 -> T_IsRing_2650
 -> T_IsSemiring_1570)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe
                                (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsRing_2650
-> T_IsSemiring_1570
MAlonzo.Code.Algebra.Structures.du_isSemiring_2778 ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v1)
                                ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v2) ((AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v3) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v4) (T_IsRing_2650 -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650
v6) in
                      AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        ((T_IsSemiringWithoutOne_1298 -> T_IsNearSemiring_1218)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_IsSemiringWithoutOne_1298 -> T_IsNearSemiring_1218
MAlonzo.Code.Algebra.Structures.du_isNearSemiring_1374
                           ((T_IsSemiring_1570 -> T_IsSemiringWithoutOne_1298)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                              T_IsSemiring_1570 -> T_IsSemiringWithoutOne_1298
MAlonzo.Code.Algebra.Structures.du_isSemiringWithoutOne_1660
                              (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v7)))))))))
-- Algebra.Bundles.CommutativeRing._.isPartialEquivalence
d_isPartialEquivalence_4146 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeRing_4016 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_4146 :: () -> () -> T_CommutativeRing_4016 -> T_IsPartialEquivalence_16
d_isPartialEquivalence_4146 ~()
v0 ~()
v1 T_CommutativeRing_4016
v2
  = T_CommutativeRing_4016 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_4146 T_CommutativeRing_4016
v2
du_isPartialEquivalence_4146 ::
  T_CommutativeRing_4016 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_4146 :: T_CommutativeRing_4016 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_4146 T_CommutativeRing_4016
v0
  = let v1 :: T_IsCommutativeRing_2796
v1 = T_CommutativeRing_4016 -> T_IsCommutativeRing_2796
d_isCommutativeRing_4052 (T_CommutativeRing_4016 -> T_CommutativeRing_4016
forall a b. a -> b
coe T_CommutativeRing_4016
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsRing_2650
v2 = T_IsCommutativeRing_2796 -> T_IsRing_2650
MAlonzo.Code.Algebra.Structures.d_isRing_2812 (T_IsCommutativeRing_2796 -> T_IsCommutativeRing_2796
forall a b. a -> b
coe T_IsCommutativeRing_2796
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: t
v3
                = (T_IsRing_2650 -> T_IsRingWithoutOne_2286) -> AgdaAny -> t
forall a b. a -> b
coe
                    T_IsRing_2650 -> T_IsRingWithoutOne_2286
MAlonzo.Code.Algebra.Structures.du_isRingWithoutOne_2682
                    (T_IsRing_2650 -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsAbelianGroup_1132
v4
                   = T_IsRingWithoutOne_2286 -> T_IsAbelianGroup_1132
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2304
                       (AgdaAny -> T_IsRingWithoutOne_2286
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsGroup_1036
v5
                      = T_IsAbelianGroup_1132 -> T_IsGroup_1036
MAlonzo.Code.Algebra.Structures.d_isGroup_1144 (T_IsAbelianGroup_1132 -> T_IsAbelianGroup_1132
forall a b. a -> b
coe T_IsAbelianGroup_1132
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (let v6 :: T_IsMonoid_686
v6
                         = T_IsGroup_1036 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_1050 (T_IsGroup_1036 -> T_IsGroup_1036
forall a b. a -> b
coe T_IsGroup_1036
v5) in
                   AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     (let v7 :: T_IsSemigroup_472
v7
                            = T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v6) in
                      AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        (let v8 :: T_IsMagma_176
v8 = T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (T_IsSemigroup_472 -> T_IsSemigroup_472
forall a b. a -> b
coe T_IsSemigroup_472
v7) in
                         AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           ((T_IsEquivalence_26 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                              T_IsEquivalence_26 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
                              ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                 T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
                                 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v8))))))))))
-- Algebra.Bundles.CommutativeRing._.isRing
d_isRing_4148 ::
  T_CommutativeRing_4016 ->
  MAlonzo.Code.Algebra.Structures.T_IsRing_2650
d_isRing_4148 :: T_CommutativeRing_4016 -> T_IsRing_2650
d_isRing_4148 T_CommutativeRing_4016
v0
  = (T_IsCommutativeRing_2796 -> T_IsRing_2650)
-> AgdaAny -> T_IsRing_2650
forall a b. a -> b
coe
      T_IsCommutativeRing_2796 -> T_IsRing_2650
MAlonzo.Code.Algebra.Structures.d_isRing_2812
      ((T_CommutativeRing_4016 -> T_IsCommutativeRing_2796)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeRing_4016 -> T_IsCommutativeRing_2796
d_isCommutativeRing_4052 (T_CommutativeRing_4016 -> AgdaAny
forall a b. a -> b
coe T_CommutativeRing_4016
v0))
-- Algebra.Bundles.CommutativeRing._.isRingWithoutOne
d_isRingWithoutOne_4150 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeRing_4016 ->
  MAlonzo.Code.Algebra.Structures.T_IsRingWithoutOne_2286
d_isRingWithoutOne_4150 :: () -> () -> T_CommutativeRing_4016 -> T_IsRingWithoutOne_2286
d_isRingWithoutOne_4150 ~()
v0 ~()
v1 T_CommutativeRing_4016
v2 = T_CommutativeRing_4016 -> T_IsRingWithoutOne_2286
du_isRingWithoutOne_4150 T_CommutativeRing_4016
v2
du_isRingWithoutOne_4150 ::
  T_CommutativeRing_4016 ->
  MAlonzo.Code.Algebra.Structures.T_IsRingWithoutOne_2286
du_isRingWithoutOne_4150 :: T_CommutativeRing_4016 -> T_IsRingWithoutOne_2286
du_isRingWithoutOne_4150 T_CommutativeRing_4016
v0
  = let v1 :: T_IsCommutativeRing_2796
v1 = T_CommutativeRing_4016 -> T_IsCommutativeRing_2796
d_isCommutativeRing_4052 (T_CommutativeRing_4016 -> T_CommutativeRing_4016
forall a b. a -> b
coe T_CommutativeRing_4016
v0) in
    AgdaAny -> T_IsRingWithoutOne_2286
forall a b. a -> b
coe
      ((T_IsRing_2650 -> T_IsRingWithoutOne_2286) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsRing_2650 -> T_IsRingWithoutOne_2286
MAlonzo.Code.Algebra.Structures.du_isRingWithoutOne_2682
         ((T_IsCommutativeRing_2796 -> T_IsRing_2650) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeRing_2796 -> T_IsRing_2650
MAlonzo.Code.Algebra.Structures.d_isRing_2812 (T_IsCommutativeRing_2796 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeRing_2796
v1)))
-- Algebra.Bundles.CommutativeRing._.isSemiring
d_isSemiring_4152 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeRing_4016 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemiring_1570
d_isSemiring_4152 :: () -> () -> T_CommutativeRing_4016 -> T_IsSemiring_1570
d_isSemiring_4152 ~()
v0 ~()
v1 T_CommutativeRing_4016
v2 = T_CommutativeRing_4016 -> T_IsSemiring_1570
du_isSemiring_4152 T_CommutativeRing_4016
v2
du_isSemiring_4152 ::
  T_CommutativeRing_4016 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemiring_1570
du_isSemiring_4152 :: T_CommutativeRing_4016 -> T_IsSemiring_1570
du_isSemiring_4152 T_CommutativeRing_4016
v0
  = let v1 :: AgdaAny -> AgdaAny -> AgdaAny
v1 = T_CommutativeRing_4016 -> AgdaAny -> AgdaAny -> AgdaAny
d__'43'__4042 (T_CommutativeRing_4016 -> T_CommutativeRing_4016
forall a b. a -> b
coe T_CommutativeRing_4016
v0) in
    AgdaAny -> T_IsSemiring_1570
forall a b. a -> b
coe
      (let v2 :: AgdaAny -> AgdaAny -> AgdaAny
v2 = T_CommutativeRing_4016 -> AgdaAny -> AgdaAny -> AgdaAny
d__'42'__4044 (T_CommutativeRing_4016 -> T_CommutativeRing_4016
forall a b. a -> b
coe T_CommutativeRing_4016
v0) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: AgdaAny -> AgdaAny
v3 = T_CommutativeRing_4016 -> AgdaAny -> AgdaAny
d_'45'__4046 (T_CommutativeRing_4016 -> T_CommutativeRing_4016
forall a b. a -> b
coe T_CommutativeRing_4016
v0) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: AgdaAny
v4 = T_CommutativeRing_4016 -> AgdaAny
d_0'35'_4048 (T_CommutativeRing_4016 -> T_CommutativeRing_4016
forall a b. a -> b
coe T_CommutativeRing_4016
v0) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsCommutativeRing_2796
v5 = T_CommutativeRing_4016 -> T_IsCommutativeRing_2796
d_isCommutativeRing_4052 (T_CommutativeRing_4016 -> T_CommutativeRing_4016
forall a b. a -> b
coe T_CommutativeRing_4016
v0) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (((AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny)
 -> AgdaAny
 -> T_IsRing_2650
 -> T_IsSemiring_1570)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsRing_2650
-> T_IsSemiring_1570
MAlonzo.Code.Algebra.Structures.du_isSemiring_2778 ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v1)
                     ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v2) ((AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v3) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v4)
                     ((T_IsCommutativeRing_2796 -> T_IsRing_2650) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeRing_2796 -> T_IsRing_2650
MAlonzo.Code.Algebra.Structures.d_isRing_2812 (T_IsCommutativeRing_2796 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeRing_2796
v5)))))))
-- Algebra.Bundles.CommutativeRing._.isSemiringWithoutAnnihilatingZero
d_isSemiringWithoutAnnihilatingZero_4154 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeRing_4016 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_4154 :: ()
-> ()
-> T_CommutativeRing_4016
-> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_4154 ~()
v0 ~()
v1 T_CommutativeRing_4016
v2
  = T_CommutativeRing_4016 -> T_IsSemiringWithoutAnnihilatingZero_1468
du_isSemiringWithoutAnnihilatingZero_4154 T_CommutativeRing_4016
v2
du_isSemiringWithoutAnnihilatingZero_4154 ::
  T_CommutativeRing_4016 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutAnnihilatingZero_1468
du_isSemiringWithoutAnnihilatingZero_4154 :: T_CommutativeRing_4016 -> T_IsSemiringWithoutAnnihilatingZero_1468
du_isSemiringWithoutAnnihilatingZero_4154 T_CommutativeRing_4016
v0
  = let v1 :: T_IsCommutativeRing_2796
v1 = T_CommutativeRing_4016 -> T_IsCommutativeRing_2796
d_isCommutativeRing_4052 (T_CommutativeRing_4016 -> T_CommutativeRing_4016
forall a b. a -> b
coe T_CommutativeRing_4016
v0) in
    AgdaAny -> T_IsSemiringWithoutAnnihilatingZero_1468
forall a b. a -> b
coe
      ((T_IsRing_2650 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsRing_2650 -> T_IsSemiringWithoutAnnihilatingZero_1468
MAlonzo.Code.Algebra.Structures.du_isSemiringWithoutAnnihilatingZero_2776
         ((T_IsCommutativeRing_2796 -> T_IsRing_2650) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeRing_2796 -> T_IsRing_2650
MAlonzo.Code.Algebra.Structures.d_isRing_2812 (T_IsCommutativeRing_2796 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeRing_2796
v1)))
-- Algebra.Bundles.CommutativeRing._.isSemiringWithoutOne
d_isSemiringWithoutOne_4156 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeRing_4016 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutOne_1298
d_isSemiringWithoutOne_4156 :: () -> () -> T_CommutativeRing_4016 -> T_IsSemiringWithoutOne_1298
d_isSemiringWithoutOne_4156 ~()
v0 ~()
v1 T_CommutativeRing_4016
v2
  = T_CommutativeRing_4016 -> T_IsSemiringWithoutOne_1298
du_isSemiringWithoutOne_4156 T_CommutativeRing_4016
v2
du_isSemiringWithoutOne_4156 ::
  T_CommutativeRing_4016 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutOne_1298
du_isSemiringWithoutOne_4156 :: T_CommutativeRing_4016 -> T_IsSemiringWithoutOne_1298
du_isSemiringWithoutOne_4156 T_CommutativeRing_4016
v0
  = let v1 :: AgdaAny -> AgdaAny -> AgdaAny
v1 = T_CommutativeRing_4016 -> AgdaAny -> AgdaAny -> AgdaAny
d__'43'__4042 (T_CommutativeRing_4016 -> T_CommutativeRing_4016
forall a b. a -> b
coe T_CommutativeRing_4016
v0) in
    AgdaAny -> T_IsSemiringWithoutOne_1298
forall a b. a -> b
coe
      (let v2 :: AgdaAny -> AgdaAny -> AgdaAny
v2 = T_CommutativeRing_4016 -> AgdaAny -> AgdaAny -> AgdaAny
d__'42'__4044 (T_CommutativeRing_4016 -> T_CommutativeRing_4016
forall a b. a -> b
coe T_CommutativeRing_4016
v0) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: AgdaAny -> AgdaAny
v3 = T_CommutativeRing_4016 -> AgdaAny -> AgdaAny
d_'45'__4046 (T_CommutativeRing_4016 -> T_CommutativeRing_4016
forall a b. a -> b
coe T_CommutativeRing_4016
v0) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: AgdaAny
v4 = T_CommutativeRing_4016 -> AgdaAny
d_0'35'_4048 (T_CommutativeRing_4016 -> T_CommutativeRing_4016
forall a b. a -> b
coe T_CommutativeRing_4016
v0) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsCommutativeRing_2796
v5 = T_CommutativeRing_4016 -> T_IsCommutativeRing_2796
d_isCommutativeRing_4052 (T_CommutativeRing_4016 -> T_CommutativeRing_4016
forall a b. a -> b
coe T_CommutativeRing_4016
v0) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (let v6 :: T_IsRing_2650
v6 = T_IsCommutativeRing_2796 -> T_IsRing_2650
MAlonzo.Code.Algebra.Structures.d_isRing_2812 (T_IsCommutativeRing_2796 -> T_IsCommutativeRing_2796
forall a b. a -> b
coe T_IsCommutativeRing_2796
v5) in
                   AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     ((T_IsSemiring_1570 -> T_IsSemiringWithoutOne_1298)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsSemiring_1570 -> T_IsSemiringWithoutOne_1298
MAlonzo.Code.Algebra.Structures.du_isSemiringWithoutOne_1660
                        (((AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny)
 -> AgdaAny
 -> T_IsRing_2650
 -> T_IsSemiring_1570)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsRing_2650
-> T_IsSemiring_1570
MAlonzo.Code.Algebra.Structures.du_isSemiring_2778 ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v1)
                           ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v2) ((AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v3) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v4) (T_IsRing_2650 -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650
v6))))))))
-- Algebra.Bundles.CommutativeRing._.refl
d_refl_4158 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeRing_4016 -> AgdaAny -> AgdaAny
d_refl_4158 :: () -> () -> T_CommutativeRing_4016 -> AgdaAny -> AgdaAny
d_refl_4158 ~()
v0 ~()
v1 T_CommutativeRing_4016
v2 = T_CommutativeRing_4016 -> AgdaAny -> AgdaAny
du_refl_4158 T_CommutativeRing_4016
v2
du_refl_4158 :: T_CommutativeRing_4016 -> AgdaAny -> AgdaAny
du_refl_4158 :: T_CommutativeRing_4016 -> AgdaAny -> AgdaAny
du_refl_4158 T_CommutativeRing_4016
v0
  = let v1 :: T_IsCommutativeRing_2796
v1 = T_CommutativeRing_4016 -> T_IsCommutativeRing_2796
d_isCommutativeRing_4052 (T_CommutativeRing_4016 -> T_CommutativeRing_4016
forall a b. a -> b
coe T_CommutativeRing_4016
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsRing_2650
v2 = T_IsCommutativeRing_2796 -> T_IsRing_2650
MAlonzo.Code.Algebra.Structures.d_isRing_2812 (T_IsCommutativeRing_2796 -> T_IsCommutativeRing_2796
forall a b. a -> b
coe T_IsCommutativeRing_2796
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsEquivalence_26 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_34
            ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
               ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480
                  ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
                     ((T_IsGroup_1036 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsGroup_1036 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_1050
                        ((T_IsAbelianGroup_1132 -> T_IsGroup_1036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_IsAbelianGroup_1132 -> T_IsGroup_1036
MAlonzo.Code.Algebra.Structures.d_isGroup_1144
                           ((T_IsRing_2650 -> T_IsAbelianGroup_1132) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                              T_IsRing_2650 -> T_IsAbelianGroup_1132
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2672
                              (T_IsRing_2650 -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650
v2)))))))))
-- Algebra.Bundles.CommutativeRing._.reflexive
d_reflexive_4160 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeRing_4016 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_4160 :: ()
-> ()
-> T_CommutativeRing_4016
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_4160 ~()
v0 ~()
v1 T_CommutativeRing_4016
v2 = T_CommutativeRing_4016
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_4160 T_CommutativeRing_4016
v2
du_reflexive_4160 ::
  T_CommutativeRing_4016 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_4160 :: T_CommutativeRing_4016
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_4160 T_CommutativeRing_4016
v0
  = let v1 :: T_IsCommutativeRing_2796
v1 = T_CommutativeRing_4016 -> T_IsCommutativeRing_2796
d_isCommutativeRing_4052 (T_CommutativeRing_4016 -> T_CommutativeRing_4016
forall a b. a -> b
coe T_CommutativeRing_4016
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsRing_2650
v2 = T_IsCommutativeRing_2796 -> T_IsRing_2650
MAlonzo.Code.Algebra.Structures.d_isRing_2812 (T_IsCommutativeRing_2796 -> T_IsCommutativeRing_2796
forall a b. a -> b
coe T_IsCommutativeRing_2796
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: t
v3
                = (T_IsRing_2650 -> T_IsRingWithoutOne_2286) -> AgdaAny -> t
forall a b. a -> b
coe
                    T_IsRing_2650 -> T_IsRingWithoutOne_2286
MAlonzo.Code.Algebra.Structures.du_isRingWithoutOne_2682
                    (T_IsRing_2650 -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsAbelianGroup_1132
v4
                   = T_IsRingWithoutOne_2286 -> T_IsAbelianGroup_1132
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2304
                       (AgdaAny -> T_IsRingWithoutOne_2286
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsGroup_1036
v5
                      = T_IsAbelianGroup_1132 -> T_IsGroup_1036
MAlonzo.Code.Algebra.Structures.d_isGroup_1144 (T_IsAbelianGroup_1132 -> T_IsAbelianGroup_1132
forall a b. a -> b
coe T_IsAbelianGroup_1132
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (let v6 :: T_IsMonoid_686
v6
                         = T_IsGroup_1036 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_1050 (T_IsGroup_1036 -> T_IsGroup_1036
forall a b. a -> b
coe T_IsGroup_1036
v5) in
                   AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     (let v7 :: T_IsSemigroup_472
v7
                            = T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v6) in
                      AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        (let v8 :: T_IsMagma_176
v8 = T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (T_IsSemigroup_472 -> T_IsSemigroup_472
forall a b. a -> b
coe T_IsSemigroup_472
v7) in
                         (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
                           (\ AgdaAny
v9 AgdaAny
v10 AgdaAny
v11 ->
                              (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
                                ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v8))
                                AgdaAny
v9))))))))
-- Algebra.Bundles.CommutativeRing._.setoid
d_setoid_4162 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeRing_4016 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_4162 :: () -> () -> T_CommutativeRing_4016 -> T_Setoid_44
d_setoid_4162 ~()
v0 ~()
v1 T_CommutativeRing_4016
v2 = T_CommutativeRing_4016 -> T_Setoid_44
du_setoid_4162 T_CommutativeRing_4016
v2
du_setoid_4162 ::
  T_CommutativeRing_4016 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_4162 :: T_CommutativeRing_4016 -> T_Setoid_44
du_setoid_4162 T_CommutativeRing_4016
v0
  = let v1 :: T_IsCommutativeRing_2796
v1 = T_CommutativeRing_4016 -> T_IsCommutativeRing_2796
d_isCommutativeRing_4052 (T_CommutativeRing_4016 -> T_CommutativeRing_4016
forall a b. a -> b
coe T_CommutativeRing_4016
v0) in
    AgdaAny -> T_Setoid_44
forall a b. a -> b
coe
      (let v2 :: T_IsRing_2650
v2 = T_IsCommutativeRing_2796 -> T_IsRing_2650
MAlonzo.Code.Algebra.Structures.d_isRing_2812 (T_IsCommutativeRing_2796 -> T_IsCommutativeRing_2796
forall a b. a -> b
coe T_IsCommutativeRing_2796
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: t
v3
                = (T_IsRing_2650 -> T_IsRingWithoutOne_2286) -> AgdaAny -> t
forall a b. a -> b
coe
                    T_IsRing_2650 -> T_IsRingWithoutOne_2286
MAlonzo.Code.Algebra.Structures.du_isRingWithoutOne_2682
                    (T_IsRing_2650 -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsAbelianGroup_1132
v4
                   = T_IsRingWithoutOne_2286 -> T_IsAbelianGroup_1132
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2304
                       (AgdaAny -> T_IsRingWithoutOne_2286
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsGroup_1036
v5
                      = T_IsAbelianGroup_1132 -> T_IsGroup_1036
MAlonzo.Code.Algebra.Structures.d_isGroup_1144 (T_IsAbelianGroup_1132 -> T_IsAbelianGroup_1132
forall a b. a -> b
coe T_IsAbelianGroup_1132
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (let v6 :: T_IsMonoid_686
v6
                         = T_IsGroup_1036 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_1050 (T_IsGroup_1036 -> T_IsGroup_1036
forall a b. a -> b
coe T_IsGroup_1036
v5) in
                   AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     (let v7 :: T_IsSemigroup_472
v7
                            = T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (T_IsMonoid_686 -> T_IsMonoid_686
forall a b. a -> b
coe T_IsMonoid_686
v6) in
                      AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        ((T_IsMagma_176 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_IsMagma_176 -> T_Setoid_44
MAlonzo.Code.Algebra.Structures.du_setoid_200
                           ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v7)))))))))
-- Algebra.Bundles.CommutativeRing._.sym
d_sym_4164 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeRing_4016 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_4164 :: ()
-> ()
-> T_CommutativeRing_4016
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_sym_4164 ~()
v0 ~()
v1 T_CommutativeRing_4016
v2 = T_CommutativeRing_4016 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_4164 T_CommutativeRing_4016
v2
du_sym_4164 ::
  T_CommutativeRing_4016 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_4164 :: T_CommutativeRing_4016 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_4164 T_CommutativeRing_4016
v0
  = let v1 :: T_IsCommutativeRing_2796
v1 = T_CommutativeRing_4016 -> T_IsCommutativeRing_2796
d_isCommutativeRing_4052 (T_CommutativeRing_4016 -> T_CommutativeRing_4016
forall a b. a -> b
coe T_CommutativeRing_4016
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsRing_2650
v2 = T_IsCommutativeRing_2796 -> T_IsRing_2650
MAlonzo.Code.Algebra.Structures.d_isRing_2812 (T_IsCommutativeRing_2796 -> T_IsCommutativeRing_2796
forall a b. a -> b
coe T_IsCommutativeRing_2796
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_36
            ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
               ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480
                  ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
                     ((T_IsGroup_1036 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsGroup_1036 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_1050
                        ((T_IsAbelianGroup_1132 -> T_IsGroup_1036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_IsAbelianGroup_1132 -> T_IsGroup_1036
MAlonzo.Code.Algebra.Structures.d_isGroup_1144
                           ((T_IsRing_2650 -> T_IsAbelianGroup_1132) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                              T_IsRing_2650 -> T_IsAbelianGroup_1132
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2672
                              (T_IsRing_2650 -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650
v2)))))))))
-- Algebra.Bundles.CommutativeRing._.trans
d_trans_4166 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeRing_4016 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_4166 :: ()
-> ()
-> T_CommutativeRing_4016
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_trans_4166 ~()
v0 ~()
v1 T_CommutativeRing_4016
v2 = T_CommutativeRing_4016
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_4166 T_CommutativeRing_4016
v2
du_trans_4166 ::
  T_CommutativeRing_4016 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_4166 :: T_CommutativeRing_4016
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_4166 T_CommutativeRing_4016
v0
  = let v1 :: T_IsCommutativeRing_2796
v1 = T_CommutativeRing_4016 -> T_IsCommutativeRing_2796
d_isCommutativeRing_4052 (T_CommutativeRing_4016 -> T_CommutativeRing_4016
forall a b. a -> b
coe T_CommutativeRing_4016
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsRing_2650
v2 = T_IsCommutativeRing_2796 -> T_IsRing_2650
MAlonzo.Code.Algebra.Structures.d_isRing_2812 (T_IsCommutativeRing_2796 -> T_IsCommutativeRing_2796
forall a b. a -> b
coe T_IsCommutativeRing_2796
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsEquivalence_26
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsEquivalence_26
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_38
            ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
               ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480
                  ((T_IsMonoid_686 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696
                     ((T_IsGroup_1036 -> T_IsMonoid_686) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsGroup_1036 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_1050
                        ((T_IsAbelianGroup_1132 -> T_IsGroup_1036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_IsAbelianGroup_1132 -> T_IsGroup_1036
MAlonzo.Code.Algebra.Structures.d_isGroup_1144
                           ((T_IsRing_2650 -> T_IsAbelianGroup_1132) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                              T_IsRing_2650 -> T_IsAbelianGroup_1132
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2672
                              (T_IsRing_2650 -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650
v2)))))))))
-- Algebra.Bundles.CommutativeRing._.uniqueʳ-⁻¹
d_unique'691''45''8315''185'_4168 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeRing_4016 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_unique'691''45''8315''185'_4168 :: ()
-> ()
-> T_CommutativeRing_4016
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_unique'691''45''8315''185'_4168 ~()
v0 ~()
v1 T_CommutativeRing_4016
v2
  = T_CommutativeRing_4016 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_unique'691''45''8315''185'_4168 T_CommutativeRing_4016
v2
du_unique'691''45''8315''185'_4168 ::
  T_CommutativeRing_4016 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_unique'691''45''8315''185'_4168 :: T_CommutativeRing_4016 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_unique'691''45''8315''185'_4168 T_CommutativeRing_4016
v0
  = let v1 :: AgdaAny -> AgdaAny -> AgdaAny
v1 = T_CommutativeRing_4016 -> AgdaAny -> AgdaAny -> AgdaAny
d__'43'__4042 (T_CommutativeRing_4016 -> T_CommutativeRing_4016
forall a b. a -> b
coe T_CommutativeRing_4016
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: AgdaAny -> AgdaAny
v2 = T_CommutativeRing_4016 -> AgdaAny -> AgdaAny
d_'45'__4046 (T_CommutativeRing_4016 -> T_CommutativeRing_4016
forall a b. a -> b
coe T_CommutativeRing_4016
v0) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: AgdaAny
v3 = T_CommutativeRing_4016 -> AgdaAny
d_0'35'_4048 (T_CommutativeRing_4016 -> T_CommutativeRing_4016
forall a b. a -> b
coe T_CommutativeRing_4016
v0) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsCommutativeRing_2796
v4 = T_CommutativeRing_4016 -> T_IsCommutativeRing_2796
d_isCommutativeRing_4052 (T_CommutativeRing_4016 -> T_CommutativeRing_4016
forall a b. a -> b
coe T_CommutativeRing_4016
v0) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsRing_2650
v5 = T_IsCommutativeRing_2796 -> T_IsRing_2650
MAlonzo.Code.Algebra.Structures.d_isRing_2812 (T_IsCommutativeRing_2796 -> T_IsCommutativeRing_2796
forall a b. a -> b
coe T_IsCommutativeRing_2796
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (let v6 :: t
v6
                         = (T_IsRing_2650 -> T_IsRingWithoutOne_2286) -> AgdaAny -> t
forall a b. a -> b
coe
                             T_IsRing_2650 -> T_IsRingWithoutOne_2286
MAlonzo.Code.Algebra.Structures.du_isRingWithoutOne_2682
                             (T_IsRing_2650 -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650
v5) in
                   AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     (let v7 :: T_IsAbelianGroup_1132
v7
                            = T_IsRingWithoutOne_2286 -> T_IsAbelianGroup_1132
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2304
                                (AgdaAny -> T_IsRingWithoutOne_2286
forall a b. a -> b
coe AgdaAny
forall a. a
v6) in
                      AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        (((AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> (AgdaAny -> AgdaAny)
 -> T_IsGroup_1036
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsGroup_1036
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.du_unique'691''45''8315''185'_1120
                           ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v1) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3) ((AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v2)
                           ((T_IsAbelianGroup_1132 -> T_IsGroup_1036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                              T_IsAbelianGroup_1132 -> T_IsGroup_1036
MAlonzo.Code.Algebra.Structures.d_isGroup_1144 (T_IsAbelianGroup_1132 -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132
v7)))))))))
-- Algebra.Bundles.CommutativeRing._.uniqueˡ-⁻¹
d_unique'737''45''8315''185'_4170 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeRing_4016 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_unique'737''45''8315''185'_4170 :: ()
-> ()
-> T_CommutativeRing_4016
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_unique'737''45''8315''185'_4170 ~()
v0 ~()
v1 T_CommutativeRing_4016
v2
  = T_CommutativeRing_4016 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_unique'737''45''8315''185'_4170 T_CommutativeRing_4016
v2
du_unique'737''45''8315''185'_4170 ::
  T_CommutativeRing_4016 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_unique'737''45''8315''185'_4170 :: T_CommutativeRing_4016 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_unique'737''45''8315''185'_4170 T_CommutativeRing_4016
v0
  = let v1 :: AgdaAny -> AgdaAny -> AgdaAny
v1 = T_CommutativeRing_4016 -> AgdaAny -> AgdaAny -> AgdaAny
d__'43'__4042 (T_CommutativeRing_4016 -> T_CommutativeRing_4016
forall a b. a -> b
coe T_CommutativeRing_4016
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: AgdaAny -> AgdaAny
v2 = T_CommutativeRing_4016 -> AgdaAny -> AgdaAny
d_'45'__4046 (T_CommutativeRing_4016 -> T_CommutativeRing_4016
forall a b. a -> b
coe T_CommutativeRing_4016
v0) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: AgdaAny
v3 = T_CommutativeRing_4016 -> AgdaAny
d_0'35'_4048 (T_CommutativeRing_4016 -> T_CommutativeRing_4016
forall a b. a -> b
coe T_CommutativeRing_4016
v0) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsCommutativeRing_2796
v4 = T_CommutativeRing_4016 -> T_IsCommutativeRing_2796
d_isCommutativeRing_4052 (T_CommutativeRing_4016 -> T_CommutativeRing_4016
forall a b. a -> b
coe T_CommutativeRing_4016
v0) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsRing_2650
v5 = T_IsCommutativeRing_2796 -> T_IsRing_2650
MAlonzo.Code.Algebra.Structures.d_isRing_2812 (T_IsCommutativeRing_2796 -> T_IsCommutativeRing_2796
forall a b. a -> b
coe T_IsCommutativeRing_2796
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (let v6 :: t
v6
                         = (T_IsRing_2650 -> T_IsRingWithoutOne_2286) -> AgdaAny -> t
forall a b. a -> b
coe
                             T_IsRing_2650 -> T_IsRingWithoutOne_2286
MAlonzo.Code.Algebra.Structures.du_isRingWithoutOne_2682
                             (T_IsRing_2650 -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650
v5) in
                   AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     (let v7 :: T_IsAbelianGroup_1132
v7
                            = T_IsRingWithoutOne_2286 -> T_IsAbelianGroup_1132
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2304
                                (AgdaAny -> T_IsRingWithoutOne_2286
forall a b. a -> b
coe AgdaAny
forall a. a
v6) in
                      AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        (((AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> (AgdaAny -> AgdaAny)
 -> T_IsGroup_1036
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsGroup_1036
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.du_unique'737''45''8315''185'_1114
                           ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v1) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3) ((AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v2)
                           ((T_IsAbelianGroup_1132 -> T_IsGroup_1036) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                              T_IsAbelianGroup_1132 -> T_IsGroup_1036
MAlonzo.Code.Algebra.Structures.d_isGroup_1144 (T_IsAbelianGroup_1132 -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1132
v7)))))))))
-- Algebra.Bundles.CommutativeRing._.zero
d_zero_4172 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeRing_4016 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_zero_4172 :: () -> () -> T_CommutativeRing_4016 -> T_Σ_14
d_zero_4172 ~()
v0 ~()
v1 T_CommutativeRing_4016
v2 = T_CommutativeRing_4016 -> T_Σ_14
du_zero_4172 T_CommutativeRing_4016
v2
du_zero_4172 ::
  T_CommutativeRing_4016 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
du_zero_4172 :: T_CommutativeRing_4016 -> T_Σ_14
du_zero_4172 T_CommutativeRing_4016
v0
  = let v1 :: AgdaAny -> AgdaAny -> AgdaAny
v1 = T_CommutativeRing_4016 -> AgdaAny -> AgdaAny -> AgdaAny
d__'43'__4042 (T_CommutativeRing_4016 -> T_CommutativeRing_4016
forall a b. a -> b
coe T_CommutativeRing_4016
v0) in
    AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      (let v2 :: AgdaAny -> AgdaAny -> AgdaAny
v2 = T_CommutativeRing_4016 -> AgdaAny -> AgdaAny -> AgdaAny
d__'42'__4044 (T_CommutativeRing_4016 -> T_CommutativeRing_4016
forall a b. a -> b
coe T_CommutativeRing_4016
v0) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: AgdaAny -> AgdaAny
v3 = T_CommutativeRing_4016 -> AgdaAny -> AgdaAny
d_'45'__4046 (T_CommutativeRing_4016 -> T_CommutativeRing_4016
forall a b. a -> b
coe T_CommutativeRing_4016
v0) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: AgdaAny
v4 = T_CommutativeRing_4016 -> AgdaAny
d_0'35'_4048 (T_CommutativeRing_4016 -> T_CommutativeRing_4016
forall a b. a -> b
coe T_CommutativeRing_4016
v0) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsCommutativeRing_2796
v5 = T_CommutativeRing_4016 -> T_IsCommutativeRing_2796
d_isCommutativeRing_4052 (T_CommutativeRing_4016 -> T_CommutativeRing_4016
forall a b. a -> b
coe T_CommutativeRing_4016
v0) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (let v6 :: T_IsRing_2650
v6 = T_IsCommutativeRing_2796 -> T_IsRing_2650
MAlonzo.Code.Algebra.Structures.d_isRing_2812 (T_IsCommutativeRing_2796 -> T_IsCommutativeRing_2796
forall a b. a -> b
coe T_IsCommutativeRing_2796
v5) in
                   AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     (((AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny)
 -> AgdaAny
 -> T_IsRingWithoutOne_2286
 -> T_Σ_14)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsRingWithoutOne_2286
-> T_Σ_14
MAlonzo.Code.Algebra.Structures.du_zero_2386 ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v1) ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v2)
                        ((AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v3) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v4)
                        ((T_IsRing_2650 -> T_IsRingWithoutOne_2286) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_IsRing_2650 -> T_IsRingWithoutOne_2286
MAlonzo.Code.Algebra.Structures.du_isRingWithoutOne_2682
                           (T_IsRing_2650 -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650
v6))))))))
-- Algebra.Bundles.CommutativeRing._.zeroʳ
d_zero'691'_4174 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeRing_4016 -> AgdaAny -> AgdaAny
d_zero'691'_4174 :: () -> () -> T_CommutativeRing_4016 -> AgdaAny -> AgdaAny
d_zero'691'_4174 ~()
v0 ~()
v1 T_CommutativeRing_4016
v2 = T_CommutativeRing_4016 -> AgdaAny -> AgdaAny
du_zero'691'_4174 T_CommutativeRing_4016
v2
du_zero'691'_4174 :: T_CommutativeRing_4016 -> AgdaAny -> AgdaAny
du_zero'691'_4174 :: T_CommutativeRing_4016 -> AgdaAny -> AgdaAny
du_zero'691'_4174 T_CommutativeRing_4016
v0
  = let v1 :: AgdaAny -> AgdaAny -> AgdaAny
v1 = T_CommutativeRing_4016 -> AgdaAny -> AgdaAny -> AgdaAny
d__'43'__4042 (T_CommutativeRing_4016 -> T_CommutativeRing_4016
forall a b. a -> b
coe T_CommutativeRing_4016
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: AgdaAny -> AgdaAny -> AgdaAny
v2 = T_CommutativeRing_4016 -> AgdaAny -> AgdaAny -> AgdaAny
d__'42'__4044 (T_CommutativeRing_4016 -> T_CommutativeRing_4016
forall a b. a -> b
coe T_CommutativeRing_4016
v0) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: AgdaAny -> AgdaAny
v3 = T_CommutativeRing_4016 -> AgdaAny -> AgdaAny
d_'45'__4046 (T_CommutativeRing_4016 -> T_CommutativeRing_4016
forall a b. a -> b
coe T_CommutativeRing_4016
v0) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: AgdaAny
v4 = T_CommutativeRing_4016 -> AgdaAny
d_0'35'_4048 (T_CommutativeRing_4016 -> T_CommutativeRing_4016
forall a b. a -> b
coe T_CommutativeRing_4016
v0) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsCommutativeRing_2796
v5 = T_CommutativeRing_4016 -> T_IsCommutativeRing_2796
d_isCommutativeRing_4052 (T_CommutativeRing_4016 -> T_CommutativeRing_4016
forall a b. a -> b
coe T_CommutativeRing_4016
v0) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (let v6 :: T_IsRing_2650
v6 = T_IsCommutativeRing_2796 -> T_IsRing_2650
MAlonzo.Code.Algebra.Structures.d_isRing_2812 (T_IsCommutativeRing_2796 -> T_IsCommutativeRing_2796
forall a b. a -> b
coe T_IsCommutativeRing_2796
v5) in
                   AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     (((AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny)
 -> AgdaAny
 -> T_IsRingWithoutOne_2286
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsRingWithoutOne_2286
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.du_zero'691'_2384 ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v1) ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v2)
                        ((AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v3) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v4)
                        ((T_IsRing_2650 -> T_IsRingWithoutOne_2286) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_IsRing_2650 -> T_IsRingWithoutOne_2286
MAlonzo.Code.Algebra.Structures.du_isRingWithoutOne_2682
                           (T_IsRing_2650 -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650
v6))))))))
-- Algebra.Bundles.CommutativeRing._.zeroˡ
d_zero'737'_4176 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeRing_4016 -> AgdaAny -> AgdaAny
d_zero'737'_4176 :: () -> () -> T_CommutativeRing_4016 -> AgdaAny -> AgdaAny
d_zero'737'_4176 ~()
v0 ~()
v1 T_CommutativeRing_4016
v2 = T_CommutativeRing_4016 -> AgdaAny -> AgdaAny
du_zero'737'_4176 T_CommutativeRing_4016
v2
du_zero'737'_4176 :: T_CommutativeRing_4016 -> AgdaAny -> AgdaAny
du_zero'737'_4176 :: T_CommutativeRing_4016 -> AgdaAny -> AgdaAny
du_zero'737'_4176 T_CommutativeRing_4016
v0
  = let v1 :: AgdaAny -> AgdaAny -> AgdaAny
v1 = T_CommutativeRing_4016 -> AgdaAny -> AgdaAny -> AgdaAny
d__'43'__4042 (T_CommutativeRing_4016 -> T_CommutativeRing_4016
forall a b. a -> b
coe T_CommutativeRing_4016
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: AgdaAny -> AgdaAny -> AgdaAny
v2 = T_CommutativeRing_4016 -> AgdaAny -> AgdaAny -> AgdaAny
d__'42'__4044 (T_CommutativeRing_4016 -> T_CommutativeRing_4016
forall a b. a -> b
coe T_CommutativeRing_4016
v0) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: AgdaAny -> AgdaAny
v3 = T_CommutativeRing_4016 -> AgdaAny -> AgdaAny
d_'45'__4046 (T_CommutativeRing_4016 -> T_CommutativeRing_4016
forall a b. a -> b
coe T_CommutativeRing_4016
v0) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: AgdaAny
v4 = T_CommutativeRing_4016 -> AgdaAny
d_0'35'_4048 (T_CommutativeRing_4016 -> T_CommutativeRing_4016
forall a b. a -> b
coe T_CommutativeRing_4016
v0) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsCommutativeRing_2796
v5 = T_CommutativeRing_4016 -> T_IsCommutativeRing_2796
d_isCommutativeRing_4052 (T_CommutativeRing_4016 -> T_CommutativeRing_4016
forall a b. a -> b
coe T_CommutativeRing_4016
v0) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (let v6 :: T_IsRing_2650
v6 = T_IsCommutativeRing_2796 -> T_IsRing_2650
MAlonzo.Code.Algebra.Structures.d_isRing_2812 (T_IsCommutativeRing_2796 -> T_IsCommutativeRing_2796
forall a b. a -> b
coe T_IsCommutativeRing_2796
v5) in
                   AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     (((AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny)
 -> AgdaAny
 -> T_IsRingWithoutOne_2286
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsRingWithoutOne_2286
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.du_zero'737'_2382 ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v1) ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v2)
                        ((AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v3) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v4)
                        ((T_IsRing_2650 -> T_IsRingWithoutOne_2286) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_IsRing_2650 -> T_IsRingWithoutOne_2286
MAlonzo.Code.Algebra.Structures.du_isRingWithoutOne_2682
                           (T_IsRing_2650 -> AgdaAny
forall a b. a -> b
coe T_IsRing_2650
v6))))))))
-- Algebra.Bundles.CommutativeRing.ring
d_ring_4178 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeRing_4016 -> T_Ring_3800
d_ring_4178 :: () -> () -> T_CommutativeRing_4016 -> T_Ring_3800
d_ring_4178 ~()
v0 ~()
v1 T_CommutativeRing_4016
v2 = T_CommutativeRing_4016 -> T_Ring_3800
du_ring_4178 T_CommutativeRing_4016
v2
du_ring_4178 :: T_CommutativeRing_4016 -> T_Ring_3800
du_ring_4178 :: T_CommutativeRing_4016 -> T_Ring_3800
du_ring_4178 T_CommutativeRing_4016
v0
  = ((AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny)
 -> AgdaAny
 -> AgdaAny
 -> T_IsRing_2650
 -> T_Ring_3800)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsRing_2650
-> T_Ring_3800
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsRing_2650
-> T_Ring_3800
C_Ring'46'constructor_68489 (T_CommutativeRing_4016 -> AgdaAny -> AgdaAny -> AgdaAny
d__'43'__4042 (T_CommutativeRing_4016 -> T_CommutativeRing_4016
forall a b. a -> b
coe T_CommutativeRing_4016
v0))
      (T_CommutativeRing_4016 -> AgdaAny -> AgdaAny -> AgdaAny
d__'42'__4044 (T_CommutativeRing_4016 -> T_CommutativeRing_4016
forall a b. a -> b
coe T_CommutativeRing_4016
v0)) (T_CommutativeRing_4016 -> AgdaAny -> AgdaAny
d_'45'__4046 (T_CommutativeRing_4016 -> T_CommutativeRing_4016
forall a b. a -> b
coe T_CommutativeRing_4016
v0))
      (T_CommutativeRing_4016 -> AgdaAny
d_0'35'_4048 (T_CommutativeRing_4016 -> T_CommutativeRing_4016
forall a b. a -> b
coe T_CommutativeRing_4016
v0)) (T_CommutativeRing_4016 -> AgdaAny
d_1'35'_4050 (T_CommutativeRing_4016 -> T_CommutativeRing_4016
forall a b. a -> b
coe T_CommutativeRing_4016
v0))
      (T_IsCommutativeRing_2796 -> T_IsRing_2650
MAlonzo.Code.Algebra.Structures.d_isRing_2812
         ((T_CommutativeRing_4016 -> T_IsCommutativeRing_2796)
-> AgdaAny -> T_IsCommutativeRing_2796
forall a b. a -> b
coe T_CommutativeRing_4016 -> T_IsCommutativeRing_2796
d_isCommutativeRing_4052 (T_CommutativeRing_4016 -> AgdaAny
forall a b. a -> b
coe T_CommutativeRing_4016
v0)))
-- Algebra.Bundles.CommutativeRing._._≉_
d__'8777'__4182 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeRing_4016 -> AgdaAny -> AgdaAny -> ()
d__'8777'__4182 :: () -> () -> T_CommutativeRing_4016 -> AgdaAny -> AgdaAny -> ()
d__'8777'__4182 = () -> () -> T_CommutativeRing_4016 -> AgdaAny -> AgdaAny -> ()
forall a. a
erased
-- Algebra.Bundles.CommutativeRing._.+-abelianGroup
d_'43''45'abelianGroup_4184 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeRing_4016 -> T_AbelianGroup_1636
d_'43''45'abelianGroup_4184 :: () -> () -> T_CommutativeRing_4016 -> T_AbelianGroup_1636
d_'43''45'abelianGroup_4184 ~()
v0 ~()
v1 T_CommutativeRing_4016
v2
  = T_CommutativeRing_4016 -> T_AbelianGroup_1636
du_'43''45'abelianGroup_4184 T_CommutativeRing_4016
v2
du_'43''45'abelianGroup_4184 ::
  T_CommutativeRing_4016 -> T_AbelianGroup_1636
du_'43''45'abelianGroup_4184 :: T_CommutativeRing_4016 -> T_AbelianGroup_1636
du_'43''45'abelianGroup_4184 T_CommutativeRing_4016
v0
  = (T_Ring_3800 -> T_AbelianGroup_1636)
-> AgdaAny -> T_AbelianGroup_1636
forall a b. a -> b
coe T_Ring_3800 -> T_AbelianGroup_1636
du_'43''45'abelianGroup_3948 ((T_CommutativeRing_4016 -> T_Ring_3800) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeRing_4016 -> T_Ring_3800
du_ring_4178 (T_CommutativeRing_4016 -> AgdaAny
forall a b. a -> b
coe T_CommutativeRing_4016
v0))
-- Algebra.Bundles.CommutativeRing._.group
d_group_4186 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeRing_4016 -> T_Group_1520
d_group_4186 :: () -> () -> T_CommutativeRing_4016 -> T_Group_1520
d_group_4186 ~()
v0 ~()
v1 T_CommutativeRing_4016
v2 = T_CommutativeRing_4016 -> T_Group_1520
du_group_4186 T_CommutativeRing_4016
v2
du_group_4186 :: T_CommutativeRing_4016 -> T_Group_1520
du_group_4186 :: T_CommutativeRing_4016 -> T_Group_1520
du_group_4186 T_CommutativeRing_4016
v0
  = let v1 :: t
v1 = (T_CommutativeRing_4016 -> T_Ring_3800) -> AgdaAny -> t
forall a b. a -> b
coe T_CommutativeRing_4016 -> T_Ring_3800
du_ring_4178 (T_CommutativeRing_4016 -> AgdaAny
forall a b. a -> b
coe T_CommutativeRing_4016
v0) in
    AgdaAny -> T_Group_1520
forall a b. a -> b
coe ((T_AbelianGroup_1636 -> T_Group_1520) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_AbelianGroup_1636 -> T_Group_1520
du_group_1732 ((T_Ring_3800 -> T_AbelianGroup_1636) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Ring_3800 -> T_AbelianGroup_1636
du_'43''45'abelianGroup_3948 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1)))
-- Algebra.Bundles.CommutativeRing._.invertibleMagma
d_invertibleMagma_4188 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeRing_4016 -> T_InvertibleMagma_1360
d_invertibleMagma_4188 :: () -> () -> T_CommutativeRing_4016 -> T_InvertibleMagma_1360
d_invertibleMagma_4188 ~()
v0 ~()
v1 T_CommutativeRing_4016
v2 = T_CommutativeRing_4016 -> T_InvertibleMagma_1360
du_invertibleMagma_4188 T_CommutativeRing_4016
v2
du_invertibleMagma_4188 ::
  T_CommutativeRing_4016 -> T_InvertibleMagma_1360
du_invertibleMagma_4188 :: T_CommutativeRing_4016 -> T_InvertibleMagma_1360
du_invertibleMagma_4188 T_CommutativeRing_4016
v0
  = let v1 :: t
v1 = (T_CommutativeRing_4016 -> T_Ring_3800) -> AgdaAny -> t
forall a b. a -> b
coe T_CommutativeRing_4016 -> T_Ring_3800
du_ring_4178 (T_CommutativeRing_4016 -> AgdaAny
forall a b. a -> b
coe T_CommutativeRing_4016
v0) in
    AgdaAny -> T_InvertibleMagma_1360
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_Ring_3800 -> T_AbelianGroup_1636) -> AgdaAny -> t
forall a b. a -> b
coe T_Ring_3800 -> T_AbelianGroup_1636
du_'43''45'abelianGroup_3948 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_Group_1520 -> T_InvertibleMagma_1360) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Group_1520 -> T_InvertibleMagma_1360
du_invertibleMagma_1628 ((T_AbelianGroup_1636 -> T_Group_1520) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_AbelianGroup_1636 -> T_Group_1520
du_group_1732 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2))))
-- Algebra.Bundles.CommutativeRing._.invertibleUnitalMagma
d_invertibleUnitalMagma_4190 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeRing_4016 -> T_InvertibleUnitalMagma_1434
d_invertibleUnitalMagma_4190 :: () -> () -> T_CommutativeRing_4016 -> T_InvertibleUnitalMagma_1434
d_invertibleUnitalMagma_4190 ~()
v0 ~()
v1 T_CommutativeRing_4016
v2
  = T_CommutativeRing_4016 -> T_InvertibleUnitalMagma_1434
du_invertibleUnitalMagma_4190 T_CommutativeRing_4016
v2
du_invertibleUnitalMagma_4190 ::
  T_CommutativeRing_4016 -> T_InvertibleUnitalMagma_1434
du_invertibleUnitalMagma_4190 :: T_CommutativeRing_4016 -> T_InvertibleUnitalMagma_1434
du_invertibleUnitalMagma_4190 T_CommutativeRing_4016
v0
  = let v1 :: t
v1 = (T_CommutativeRing_4016 -> T_Ring_3800) -> AgdaAny -> t
forall a b. a -> b
coe T_CommutativeRing_4016 -> T_Ring_3800
du_ring_4178 (T_CommutativeRing_4016 -> AgdaAny
forall a b. a -> b
coe T_CommutativeRing_4016
v0) in
    AgdaAny -> T_InvertibleUnitalMagma_1434
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_Ring_3800 -> T_AbelianGroup_1636) -> AgdaAny -> t
forall a b. a -> b
coe T_Ring_3800 -> T_AbelianGroup_1636
du_'43''45'abelianGroup_3948 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_Group_1520 -> T_InvertibleUnitalMagma_1434)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Group_1520 -> T_InvertibleUnitalMagma_1434
du_invertibleUnitalMagma_1630 ((T_AbelianGroup_1636 -> T_Group_1520) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_AbelianGroup_1636 -> T_Group_1520
du_group_1732 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2))))
-- Algebra.Bundles.CommutativeRing._.rawRing
d_rawRing_4192 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeRing_4016 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRing_268
d_rawRing_4192 :: () -> () -> T_CommutativeRing_4016 -> T_RawRing_268
d_rawRing_4192 ~()
v0 ~()
v1 T_CommutativeRing_4016
v2 = T_CommutativeRing_4016 -> T_RawRing_268
du_rawRing_4192 T_CommutativeRing_4016
v2
du_rawRing_4192 ::
  T_CommutativeRing_4016 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawRing_268
du_rawRing_4192 :: T_CommutativeRing_4016 -> T_RawRing_268
du_rawRing_4192 T_CommutativeRing_4016
v0
  = (T_Ring_3800 -> T_RawRing_268) -> AgdaAny -> T_RawRing_268
forall a b. a -> b
coe T_Ring_3800 -> T_RawRing_268
du_rawRing_4004 ((T_CommutativeRing_4016 -> T_Ring_3800) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeRing_4016 -> T_Ring_3800
du_ring_4178 (T_CommutativeRing_4016 -> AgdaAny
forall a b. a -> b
coe T_CommutativeRing_4016
v0))
-- Algebra.Bundles.CommutativeRing.commutativeSemiring
d_commutativeSemiring_4194 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeRing_4016 -> T_CommutativeSemiring_2446
d_commutativeSemiring_4194 :: () -> () -> T_CommutativeRing_4016 -> T_CommutativeSemiring_2446
d_commutativeSemiring_4194 ~()
v0 ~()
v1 T_CommutativeRing_4016
v2
  = T_CommutativeRing_4016 -> T_CommutativeSemiring_2446
du_commutativeSemiring_4194 T_CommutativeRing_4016
v2
du_commutativeSemiring_4194 ::
  T_CommutativeRing_4016 -> T_CommutativeSemiring_2446
du_commutativeSemiring_4194 :: T_CommutativeRing_4016 -> T_CommutativeSemiring_2446
du_commutativeSemiring_4194 T_CommutativeRing_4016
v0
  = ((AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> AgdaAny
 -> T_IsCommutativeSemiring_1678
 -> T_CommutativeSemiring_2446)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> T_CommutativeSemiring_2446
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsCommutativeSemiring_1678
-> T_CommutativeSemiring_2446
C_CommutativeSemiring'46'constructor_44731 (T_CommutativeRing_4016 -> AgdaAny -> AgdaAny -> AgdaAny
d__'43'__4042 (T_CommutativeRing_4016 -> T_CommutativeRing_4016
forall a b. a -> b
coe T_CommutativeRing_4016
v0))
      (T_CommutativeRing_4016 -> AgdaAny -> AgdaAny -> AgdaAny
d__'42'__4044 (T_CommutativeRing_4016 -> T_CommutativeRing_4016
forall a b. a -> b
coe T_CommutativeRing_4016
v0)) (T_CommutativeRing_4016 -> AgdaAny
d_0'35'_4048 (T_CommutativeRing_4016 -> T_CommutativeRing_4016
forall a b. a -> b
coe T_CommutativeRing_4016
v0))
      (T_CommutativeRing_4016 -> AgdaAny
d_1'35'_4050 (T_CommutativeRing_4016 -> T_CommutativeRing_4016
forall a b. a -> b
coe T_CommutativeRing_4016
v0))
      (((AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny)
 -> AgdaAny
 -> T_IsCommutativeRing_2796
 -> T_IsCommutativeSemiring_1678)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsCommutativeRing_2796
-> T_IsCommutativeSemiring_1678
MAlonzo.Code.Algebra.Structures.du_isCommutativeSemiring_2926
         ((T_CommutativeRing_4016 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeRing_4016 -> AgdaAny -> AgdaAny -> AgdaAny
d__'43'__4042 (T_CommutativeRing_4016 -> AgdaAny
forall a b. a -> b
coe T_CommutativeRing_4016
v0)) ((T_CommutativeRing_4016 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeRing_4016 -> AgdaAny -> AgdaAny -> AgdaAny
d__'42'__4044 (T_CommutativeRing_4016 -> AgdaAny
forall a b. a -> b
coe T_CommutativeRing_4016
v0))
         ((T_CommutativeRing_4016 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeRing_4016 -> AgdaAny -> AgdaAny
d_'45'__4046 (T_CommutativeRing_4016 -> AgdaAny
forall a b. a -> b
coe T_CommutativeRing_4016
v0)) ((T_CommutativeRing_4016 -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeRing_4016 -> AgdaAny
d_0'35'_4048 (T_CommutativeRing_4016 -> AgdaAny
forall a b. a -> b
coe T_CommutativeRing_4016
v0))
         ((T_CommutativeRing_4016 -> T_IsCommutativeRing_2796)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeRing_4016 -> T_IsCommutativeRing_2796
d_isCommutativeRing_4052 (T_CommutativeRing_4016 -> AgdaAny
forall a b. a -> b
coe T_CommutativeRing_4016
v0)))
-- Algebra.Bundles.CommutativeRing._.commutativeMagma
d_commutativeMagma_4198 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeRing_4016 -> T_CommutativeMagma_180
d_commutativeMagma_4198 :: () -> () -> T_CommutativeRing_4016 -> T_CommutativeMagma_180
d_commutativeMagma_4198 ~()
v0 ~()
v1 T_CommutativeRing_4016
v2 = T_CommutativeRing_4016 -> T_CommutativeMagma_180
du_commutativeMagma_4198 T_CommutativeRing_4016
v2
du_commutativeMagma_4198 ::
  T_CommutativeRing_4016 -> T_CommutativeMagma_180
du_commutativeMagma_4198 :: T_CommutativeRing_4016 -> T_CommutativeMagma_180
du_commutativeMagma_4198 T_CommutativeRing_4016
v0
  = let v1 :: t
v1 = (T_CommutativeRing_4016 -> T_CommutativeSemiring_2446)
-> AgdaAny -> t
forall a b. a -> b
coe T_CommutativeRing_4016 -> T_CommutativeSemiring_2446
du_commutativeSemiring_4194 (T_CommutativeRing_4016 -> AgdaAny
forall a b. a -> b
coe T_CommutativeRing_4016
v0) in
    AgdaAny -> T_CommutativeMagma_180
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_CommutativeSemiring_2446 -> T_CommutativeMonoid_962)
-> AgdaAny -> t
forall a b. a -> b
coe T_CommutativeSemiring_2446 -> T_CommutativeMonoid_962
du_'42''45'commutativeMonoid_2618 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_CommutativeSemigroup_662 -> T_CommutativeMagma_180)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_CommutativeSemigroup_662 -> T_CommutativeMagma_180
du_commutativeMagma_726
            ((T_CommutativeMonoid_962 -> T_CommutativeSemigroup_662)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeMonoid_962 -> T_CommutativeSemigroup_662
du_commutativeSemigroup_1048 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2))))
-- Algebra.Bundles.CommutativeRing._.*-commutativeMonoid
d_'42''45'commutativeMonoid_4200 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeRing_4016 -> T_CommutativeMonoid_962
d_'42''45'commutativeMonoid_4200 :: () -> () -> T_CommutativeRing_4016 -> T_CommutativeMonoid_962
d_'42''45'commutativeMonoid_4200 ~()
v0 ~()
v1 T_CommutativeRing_4016
v2
  = T_CommutativeRing_4016 -> T_CommutativeMonoid_962
du_'42''45'commutativeMonoid_4200 T_CommutativeRing_4016
v2
du_'42''45'commutativeMonoid_4200 ::
  T_CommutativeRing_4016 -> T_CommutativeMonoid_962
du_'42''45'commutativeMonoid_4200 :: T_CommutativeRing_4016 -> T_CommutativeMonoid_962
du_'42''45'commutativeMonoid_4200 T_CommutativeRing_4016
v0
  = (T_CommutativeSemiring_2446 -> T_CommutativeMonoid_962)
-> AgdaAny -> T_CommutativeMonoid_962
forall a b. a -> b
coe
      T_CommutativeSemiring_2446 -> T_CommutativeMonoid_962
du_'42''45'commutativeMonoid_2618
      ((T_CommutativeRing_4016 -> T_CommutativeSemiring_2446)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeRing_4016 -> T_CommutativeSemiring_2446
du_commutativeSemiring_4194 (T_CommutativeRing_4016 -> AgdaAny
forall a b. a -> b
coe T_CommutativeRing_4016
v0))
-- Algebra.Bundles.CommutativeRing._.commutativeSemigroup
d_commutativeSemigroup_4202 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeRing_4016 -> T_CommutativeSemigroup_662
d_commutativeSemigroup_4202 :: () -> () -> T_CommutativeRing_4016 -> T_CommutativeSemigroup_662
d_commutativeSemigroup_4202 ~()
v0 ~()
v1 T_CommutativeRing_4016
v2
  = T_CommutativeRing_4016 -> T_CommutativeSemigroup_662
du_commutativeSemigroup_4202 T_CommutativeRing_4016
v2
du_commutativeSemigroup_4202 ::
  T_CommutativeRing_4016 -> T_CommutativeSemigroup_662
du_commutativeSemigroup_4202 :: T_CommutativeRing_4016 -> T_CommutativeSemigroup_662
du_commutativeSemigroup_4202 T_CommutativeRing_4016
v0
  = let v1 :: t
v1 = (T_CommutativeRing_4016 -> T_CommutativeSemiring_2446)
-> AgdaAny -> t
forall a b. a -> b
coe T_CommutativeRing_4016 -> T_CommutativeSemiring_2446
du_commutativeSemiring_4194 (T_CommutativeRing_4016 -> AgdaAny
forall a b. a -> b
coe T_CommutativeRing_4016
v0) in
    AgdaAny -> T_CommutativeSemigroup_662
forall a b. a -> b
coe
      ((T_CommutativeMonoid_962 -> T_CommutativeSemigroup_662)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_CommutativeMonoid_962 -> T_CommutativeSemigroup_662
du_commutativeSemigroup_1048
         ((T_CommutativeSemiring_2446 -> T_CommutativeMonoid_962)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemiring_2446 -> T_CommutativeMonoid_962
du_'42''45'commutativeMonoid_2618 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1)))
-- Algebra.Bundles.CommutativeRing._.magma
d_magma_4204 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeRing_4016 -> T_Magma_68
d_magma_4204 :: () -> () -> T_CommutativeRing_4016 -> T_Magma_68
d_magma_4204 ~()
v0 ~()
v1 T_CommutativeRing_4016
v2 = T_CommutativeRing_4016 -> T_Magma_68
du_magma_4204 T_CommutativeRing_4016
v2
du_magma_4204 :: T_CommutativeRing_4016 -> T_Magma_68
du_magma_4204 :: T_CommutativeRing_4016 -> T_Magma_68
du_magma_4204 T_CommutativeRing_4016
v0
  = let v1 :: t
v1 = (T_CommutativeRing_4016 -> T_CommutativeSemiring_2446)
-> AgdaAny -> t
forall a b. a -> b
coe T_CommutativeRing_4016 -> T_CommutativeSemiring_2446
du_commutativeSemiring_4194 (T_CommutativeRing_4016 -> AgdaAny
forall a b. a -> b
coe T_CommutativeRing_4016
v0) in
    AgdaAny -> T_Magma_68
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_CommutativeSemiring_2446 -> T_Semiring_2280) -> AgdaAny -> t
forall a b. a -> b
coe T_CommutativeSemiring_2446 -> T_Semiring_2280
du_semiring_2576 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: t
v3 = (T_Semiring_2280 -> T_SemiringWithoutAnnihilatingZero_2130)
-> AgdaAny -> t
forall a b. a -> b
coe T_Semiring_2280 -> T_SemiringWithoutAnnihilatingZero_2130
du_semiringWithoutAnnihilatingZero_2398 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: t
v4 = (T_SemiringWithoutAnnihilatingZero_2130 -> T_Monoid_882)
-> AgdaAny -> t
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_2130 -> T_Monoid_882
du_'42''45'monoid_2264 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_Semigroup_536 -> T_Magma_68) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semigroup_536 -> T_Magma_68
du_magma_584 ((T_Monoid_882 -> T_Semigroup_536) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Monoid_882 -> T_Semigroup_536
du_semigroup_944 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v4))))))
-- Algebra.Bundles.CommutativeRing._.*-monoid
d_'42''45'monoid_4206 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeRing_4016 -> T_Monoid_882
d_'42''45'monoid_4206 :: () -> () -> T_CommutativeRing_4016 -> T_Monoid_882
d_'42''45'monoid_4206 ~()
v0 ~()
v1 T_CommutativeRing_4016
v2 = T_CommutativeRing_4016 -> T_Monoid_882
du_'42''45'monoid_4206 T_CommutativeRing_4016
v2
du_'42''45'monoid_4206 :: T_CommutativeRing_4016 -> T_Monoid_882
du_'42''45'monoid_4206 :: T_CommutativeRing_4016 -> T_Monoid_882
du_'42''45'monoid_4206 T_CommutativeRing_4016
v0
  = let v1 :: t
v1 = (T_CommutativeRing_4016 -> T_CommutativeSemiring_2446)
-> AgdaAny -> t
forall a b. a -> b
coe T_CommutativeRing_4016 -> T_CommutativeSemiring_2446
du_commutativeSemiring_4194 (T_CommutativeRing_4016 -> AgdaAny
forall a b. a -> b
coe T_CommutativeRing_4016
v0) in
    AgdaAny -> T_Monoid_882
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_CommutativeSemiring_2446 -> T_Semiring_2280) -> AgdaAny -> t
forall a b. a -> b
coe T_CommutativeSemiring_2446 -> T_Semiring_2280
du_semiring_2576 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_SemiringWithoutAnnihilatingZero_2130 -> T_Monoid_882)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_SemiringWithoutAnnihilatingZero_2130 -> T_Monoid_882
du_'42''45'monoid_2264
            ((T_Semiring_2280 -> T_SemiringWithoutAnnihilatingZero_2130)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semiring_2280 -> T_SemiringWithoutAnnihilatingZero_2130
du_semiringWithoutAnnihilatingZero_2398 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2))))
-- Algebra.Bundles.CommutativeRing._.rawMagma
d_rawMagma_4208 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeRing_4016 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
d_rawMagma_4208 :: () -> () -> T_CommutativeRing_4016 -> T_RawMagma_36
d_rawMagma_4208 ~()
v0 ~()
v1 T_CommutativeRing_4016
v2 = T_CommutativeRing_4016 -> T_RawMagma_36
du_rawMagma_4208 T_CommutativeRing_4016
v2
du_rawMagma_4208 ::
  T_CommutativeRing_4016 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
du_rawMagma_4208 :: T_CommutativeRing_4016 -> T_RawMagma_36
du_rawMagma_4208 T_CommutativeRing_4016
v0
  = let v1 :: t
v1 = (T_CommutativeRing_4016 -> T_CommutativeSemiring_2446)
-> AgdaAny -> t
forall a b. a -> b
coe T_CommutativeRing_4016 -> T_CommutativeSemiring_2446
du_commutativeSemiring_4194 (T_CommutativeRing_4016 -> AgdaAny
forall a b. a -> b
coe T_CommutativeRing_4016
v0) in
    AgdaAny -> T_RawMagma_36
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_CommutativeSemiring_2446 -> T_Semiring_2280) -> AgdaAny -> t
forall a b. a -> b
coe T_CommutativeSemiring_2446 -> T_Semiring_2280
du_semiring_2576 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: t
v3 = (T_Semiring_2280 -> T_SemiringWithoutAnnihilatingZero_2130)
-> AgdaAny -> t
forall a b. a -> b
coe T_Semiring_2280 -> T_SemiringWithoutAnnihilatingZero_2130
du_semiringWithoutAnnihilatingZero_2398 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: t
v4 = (T_SemiringWithoutAnnihilatingZero_2130 -> T_Monoid_882)
-> AgdaAny -> t
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_2130 -> T_Monoid_882
du_'42''45'monoid_2264 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: t
v5 = (T_Monoid_882 -> T_Semigroup_536) -> AgdaAny -> t
forall a b. a -> b
coe T_Monoid_882 -> T_Semigroup_536
du_semigroup_944 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_Magma_68 -> T_RawMagma_36) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Magma_68 -> T_RawMagma_36
du_rawMagma_112 ((T_Semigroup_536 -> T_Magma_68) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semigroup_536 -> T_Magma_68
du_magma_584 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v5)))))))
-- Algebra.Bundles.CommutativeRing._.rawMonoid
d_rawMonoid_4210 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeRing_4016 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMonoid_64
d_rawMonoid_4210 :: () -> () -> T_CommutativeRing_4016 -> T_RawMonoid_64
d_rawMonoid_4210 ~()
v0 ~()
v1 T_CommutativeRing_4016
v2 = T_CommutativeRing_4016 -> T_RawMonoid_64
du_rawMonoid_4210 T_CommutativeRing_4016
v2
du_rawMonoid_4210 ::
  T_CommutativeRing_4016 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMonoid_64
du_rawMonoid_4210 :: T_CommutativeRing_4016 -> T_RawMonoid_64
du_rawMonoid_4210 T_CommutativeRing_4016
v0
  = let v1 :: t
v1 = (T_CommutativeRing_4016 -> T_CommutativeSemiring_2446)
-> AgdaAny -> t
forall a b. a -> b
coe T_CommutativeRing_4016 -> T_CommutativeSemiring_2446
du_commutativeSemiring_4194 (T_CommutativeRing_4016 -> AgdaAny
forall a b. a -> b
coe T_CommutativeRing_4016
v0) in
    AgdaAny -> T_RawMonoid_64
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_CommutativeSemiring_2446 -> T_Semiring_2280) -> AgdaAny -> t
forall a b. a -> b
coe T_CommutativeSemiring_2446 -> T_Semiring_2280
du_semiring_2576 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: t
v3 = (T_Semiring_2280 -> T_SemiringWithoutAnnihilatingZero_2130)
-> AgdaAny -> t
forall a b. a -> b
coe T_Semiring_2280 -> T_SemiringWithoutAnnihilatingZero_2130
du_semiringWithoutAnnihilatingZero_2398 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_Monoid_882 -> T_RawMonoid_64) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Monoid_882 -> T_RawMonoid_64
du_rawMonoid_954 ((T_SemiringWithoutAnnihilatingZero_2130 -> T_Monoid_882)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_2130 -> T_Monoid_882
du_'42''45'monoid_2264 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3)))))
-- Algebra.Bundles.CommutativeRing._.semigroup
d_semigroup_4212 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeRing_4016 -> T_Semigroup_536
d_semigroup_4212 :: () -> () -> T_CommutativeRing_4016 -> T_Semigroup_536
d_semigroup_4212 ~()
v0 ~()
v1 T_CommutativeRing_4016
v2 = T_CommutativeRing_4016 -> T_Semigroup_536
du_semigroup_4212 T_CommutativeRing_4016
v2
du_semigroup_4212 :: T_CommutativeRing_4016 -> T_Semigroup_536
du_semigroup_4212 :: T_CommutativeRing_4016 -> T_Semigroup_536
du_semigroup_4212 T_CommutativeRing_4016
v0
  = let v1 :: t
v1 = (T_CommutativeRing_4016 -> T_CommutativeSemiring_2446)
-> AgdaAny -> t
forall a b. a -> b
coe T_CommutativeRing_4016 -> T_CommutativeSemiring_2446
du_commutativeSemiring_4194 (T_CommutativeRing_4016 -> AgdaAny
forall a b. a -> b
coe T_CommutativeRing_4016
v0) in
    AgdaAny -> T_Semigroup_536
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_CommutativeSemiring_2446 -> T_Semiring_2280) -> AgdaAny -> t
forall a b. a -> b
coe T_CommutativeSemiring_2446 -> T_Semiring_2280
du_semiring_2576 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: t
v3 = (T_Semiring_2280 -> T_SemiringWithoutAnnihilatingZero_2130)
-> AgdaAny -> t
forall a b. a -> b
coe T_Semiring_2280 -> T_SemiringWithoutAnnihilatingZero_2130
du_semiringWithoutAnnihilatingZero_2398 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_Monoid_882 -> T_Semigroup_536) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Monoid_882 -> T_Semigroup_536
du_semigroup_944 ((T_SemiringWithoutAnnihilatingZero_2130 -> T_Monoid_882)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_2130 -> T_Monoid_882
du_'42''45'monoid_2264 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3)))))
-- Algebra.Bundles.CommutativeRing._.commutativeMagma
d_commutativeMagma_4214 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeRing_4016 -> T_CommutativeMagma_180
d_commutativeMagma_4214 :: () -> () -> T_CommutativeRing_4016 -> T_CommutativeMagma_180
d_commutativeMagma_4214 ~()
v0 ~()
v1 T_CommutativeRing_4016
v2 = T_CommutativeRing_4016 -> T_CommutativeMagma_180
du_commutativeMagma_4214 T_CommutativeRing_4016
v2
du_commutativeMagma_4214 ::
  T_CommutativeRing_4016 -> T_CommutativeMagma_180
du_commutativeMagma_4214 :: T_CommutativeRing_4016 -> T_CommutativeMagma_180
du_commutativeMagma_4214 T_CommutativeRing_4016
v0
  = let v1 :: t
v1 = (T_CommutativeRing_4016 -> T_CommutativeSemiring_2446)
-> AgdaAny -> t
forall a b. a -> b
coe T_CommutativeRing_4016 -> T_CommutativeSemiring_2446
du_commutativeSemiring_4194 (T_CommutativeRing_4016 -> AgdaAny
forall a b. a -> b
coe T_CommutativeRing_4016
v0) in
    AgdaAny -> T_CommutativeMagma_180
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_CommutativeSemiring_2446 -> T_Semiring_2280) -> AgdaAny -> t
forall a b. a -> b
coe T_CommutativeSemiring_2446 -> T_Semiring_2280
du_semiring_2576 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: t
v3 = (T_Semiring_2280 -> T_SemiringWithoutAnnihilatingZero_2130)
-> AgdaAny -> t
forall a b. a -> b
coe T_Semiring_2280 -> T_SemiringWithoutAnnihilatingZero_2130
du_semiringWithoutAnnihilatingZero_2398 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: t
v4 = (T_SemiringWithoutAnnihilatingZero_2130 -> T_CommutativeMonoid_962)
-> AgdaAny -> t
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_2130 -> T_CommutativeMonoid_962
du_'43''45'commutativeMonoid_2242 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               ((T_CommutativeSemigroup_662 -> T_CommutativeMagma_180)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_CommutativeSemigroup_662 -> T_CommutativeMagma_180
du_commutativeMagma_726
                  ((T_CommutativeMonoid_962 -> T_CommutativeSemigroup_662)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeMonoid_962 -> T_CommutativeSemigroup_662
du_commutativeSemigroup_1048 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v4))))))
-- Algebra.Bundles.CommutativeRing._.+-commutativeMonoid
d_'43''45'commutativeMonoid_4216 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeRing_4016 -> T_CommutativeMonoid_962
d_'43''45'commutativeMonoid_4216 :: () -> () -> T_CommutativeRing_4016 -> T_CommutativeMonoid_962
d_'43''45'commutativeMonoid_4216 ~()
v0 ~()
v1 T_CommutativeRing_4016
v2
  = T_CommutativeRing_4016 -> T_CommutativeMonoid_962
du_'43''45'commutativeMonoid_4216 T_CommutativeRing_4016
v2
du_'43''45'commutativeMonoid_4216 ::
  T_CommutativeRing_4016 -> T_CommutativeMonoid_962
du_'43''45'commutativeMonoid_4216 :: T_CommutativeRing_4016 -> T_CommutativeMonoid_962
du_'43''45'commutativeMonoid_4216 T_CommutativeRing_4016
v0
  = let v1 :: t
v1 = (T_CommutativeRing_4016 -> T_CommutativeSemiring_2446)
-> AgdaAny -> t
forall a b. a -> b
coe T_CommutativeRing_4016 -> T_CommutativeSemiring_2446
du_commutativeSemiring_4194 (T_CommutativeRing_4016 -> AgdaAny
forall a b. a -> b
coe T_CommutativeRing_4016
v0) in
    AgdaAny -> T_CommutativeMonoid_962
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_CommutativeSemiring_2446 -> T_Semiring_2280) -> AgdaAny -> t
forall a b. a -> b
coe T_CommutativeSemiring_2446 -> T_Semiring_2280
du_semiring_2576 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_SemiringWithoutAnnihilatingZero_2130 -> T_CommutativeMonoid_962)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_SemiringWithoutAnnihilatingZero_2130 -> T_CommutativeMonoid_962
du_'43''45'commutativeMonoid_2242
            ((T_Semiring_2280 -> T_SemiringWithoutAnnihilatingZero_2130)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semiring_2280 -> T_SemiringWithoutAnnihilatingZero_2130
du_semiringWithoutAnnihilatingZero_2398 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2))))
-- Algebra.Bundles.CommutativeRing._.commutativeSemigroup
d_commutativeSemigroup_4218 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeRing_4016 -> T_CommutativeSemigroup_662
d_commutativeSemigroup_4218 :: () -> () -> T_CommutativeRing_4016 -> T_CommutativeSemigroup_662
d_commutativeSemigroup_4218 ~()
v0 ~()
v1 T_CommutativeRing_4016
v2
  = T_CommutativeRing_4016 -> T_CommutativeSemigroup_662
du_commutativeSemigroup_4218 T_CommutativeRing_4016
v2
du_commutativeSemigroup_4218 ::
  T_CommutativeRing_4016 -> T_CommutativeSemigroup_662
du_commutativeSemigroup_4218 :: T_CommutativeRing_4016 -> T_CommutativeSemigroup_662
du_commutativeSemigroup_4218 T_CommutativeRing_4016
v0
  = let v1 :: t
v1 = (T_CommutativeRing_4016 -> T_CommutativeSemiring_2446)
-> AgdaAny -> t
forall a b. a -> b
coe T_CommutativeRing_4016 -> T_CommutativeSemiring_2446
du_commutativeSemiring_4194 (T_CommutativeRing_4016 -> AgdaAny
forall a b. a -> b
coe T_CommutativeRing_4016
v0) in
    AgdaAny -> T_CommutativeSemigroup_662
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_CommutativeSemiring_2446 -> T_Semiring_2280) -> AgdaAny -> t
forall a b. a -> b
coe T_CommutativeSemiring_2446 -> T_Semiring_2280
du_semiring_2576 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: t
v3 = (T_Semiring_2280 -> T_SemiringWithoutAnnihilatingZero_2130)
-> AgdaAny -> t
forall a b. a -> b
coe T_Semiring_2280 -> T_SemiringWithoutAnnihilatingZero_2130
du_semiringWithoutAnnihilatingZero_2398 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_CommutativeMonoid_962 -> T_CommutativeSemigroup_662)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_CommutativeMonoid_962 -> T_CommutativeSemigroup_662
du_commutativeSemigroup_1048
               ((T_SemiringWithoutAnnihilatingZero_2130 -> T_CommutativeMonoid_962)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_2130 -> T_CommutativeMonoid_962
du_'43''45'commutativeMonoid_2242 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3)))))
-- Algebra.Bundles.CommutativeRing._.magma
d_magma_4220 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeRing_4016 -> T_Magma_68
d_magma_4220 :: () -> () -> T_CommutativeRing_4016 -> T_Magma_68
d_magma_4220 ~()
v0 ~()
v1 T_CommutativeRing_4016
v2 = T_CommutativeRing_4016 -> T_Magma_68
du_magma_4220 T_CommutativeRing_4016
v2
du_magma_4220 :: T_CommutativeRing_4016 -> T_Magma_68
du_magma_4220 :: T_CommutativeRing_4016 -> T_Magma_68
du_magma_4220 T_CommutativeRing_4016
v0
  = let v1 :: t
v1 = (T_CommutativeRing_4016 -> T_CommutativeSemiring_2446)
-> AgdaAny -> t
forall a b. a -> b
coe T_CommutativeRing_4016 -> T_CommutativeSemiring_2446
du_commutativeSemiring_4194 (T_CommutativeRing_4016 -> AgdaAny
forall a b. a -> b
coe T_CommutativeRing_4016
v0) in
    AgdaAny -> T_Magma_68
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_CommutativeSemiring_2446 -> T_Semiring_2280) -> AgdaAny -> t
forall a b. a -> b
coe T_CommutativeSemiring_2446 -> T_Semiring_2280
du_semiring_2576 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: t
v3 = (T_Semiring_2280 -> T_SemiringWithoutAnnihilatingZero_2130)
-> AgdaAny -> t
forall a b. a -> b
coe T_Semiring_2280 -> T_SemiringWithoutAnnihilatingZero_2130
du_semiringWithoutAnnihilatingZero_2398 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: t
v4 = (T_SemiringWithoutAnnihilatingZero_2130 -> T_CommutativeMonoid_962)
-> AgdaAny -> t
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_2130 -> T_CommutativeMonoid_962
du_'43''45'commutativeMonoid_2242 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: t
v5 = (T_CommutativeMonoid_962 -> T_Monoid_882) -> AgdaAny -> t
forall a b. a -> b
coe T_CommutativeMonoid_962 -> T_Monoid_882
du_monoid_1032 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_Semigroup_536 -> T_Magma_68) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semigroup_536 -> T_Magma_68
du_magma_584 ((T_Monoid_882 -> T_Semigroup_536) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Monoid_882 -> T_Semigroup_536
du_semigroup_944 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v5)))))))
-- Algebra.Bundles.CommutativeRing._.monoid
d_monoid_4222 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeRing_4016 -> T_Monoid_882
d_monoid_4222 :: () -> () -> T_CommutativeRing_4016 -> T_Monoid_882
d_monoid_4222 ~()
v0 ~()
v1 T_CommutativeRing_4016
v2 = T_CommutativeRing_4016 -> T_Monoid_882
du_monoid_4222 T_CommutativeRing_4016
v2
du_monoid_4222 :: T_CommutativeRing_4016 -> T_Monoid_882
du_monoid_4222 :: T_CommutativeRing_4016 -> T_Monoid_882
du_monoid_4222 T_CommutativeRing_4016
v0
  = let v1 :: t
v1 = (T_CommutativeRing_4016 -> T_CommutativeSemiring_2446)
-> AgdaAny -> t
forall a b. a -> b
coe T_CommutativeRing_4016 -> T_CommutativeSemiring_2446
du_commutativeSemiring_4194 (T_CommutativeRing_4016 -> AgdaAny
forall a b. a -> b
coe T_CommutativeRing_4016
v0) in
    AgdaAny -> T_Monoid_882
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_CommutativeSemiring_2446 -> T_Semiring_2280) -> AgdaAny -> t
forall a b. a -> b
coe T_CommutativeSemiring_2446 -> T_Semiring_2280
du_semiring_2576 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: t
v3 = (T_Semiring_2280 -> T_SemiringWithoutAnnihilatingZero_2130)
-> AgdaAny -> t
forall a b. a -> b
coe T_Semiring_2280 -> T_SemiringWithoutAnnihilatingZero_2130
du_semiringWithoutAnnihilatingZero_2398 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_CommutativeMonoid_962 -> T_Monoid_882) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_CommutativeMonoid_962 -> T_Monoid_882
du_monoid_1032 ((T_SemiringWithoutAnnihilatingZero_2130 -> T_CommutativeMonoid_962)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_2130 -> T_CommutativeMonoid_962
du_'43''45'commutativeMonoid_2242 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3)))))
-- Algebra.Bundles.CommutativeRing._.rawMagma
d_rawMagma_4224 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeRing_4016 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
d_rawMagma_4224 :: () -> () -> T_CommutativeRing_4016 -> T_RawMagma_36
d_rawMagma_4224 ~()
v0 ~()
v1 T_CommutativeRing_4016
v2 = T_CommutativeRing_4016 -> T_RawMagma_36
du_rawMagma_4224 T_CommutativeRing_4016
v2
du_rawMagma_4224 ::
  T_CommutativeRing_4016 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
du_rawMagma_4224 :: T_CommutativeRing_4016 -> T_RawMagma_36
du_rawMagma_4224 T_CommutativeRing_4016
v0
  = let v1 :: t
v1 = (T_CommutativeRing_4016 -> T_CommutativeSemiring_2446)
-> AgdaAny -> t
forall a b. a -> b
coe T_CommutativeRing_4016 -> T_CommutativeSemiring_2446
du_commutativeSemiring_4194 (T_CommutativeRing_4016 -> AgdaAny
forall a b. a -> b
coe T_CommutativeRing_4016
v0) in
    AgdaAny -> T_RawMagma_36
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_CommutativeSemiring_2446 -> T_Semiring_2280) -> AgdaAny -> t
forall a b. a -> b
coe T_CommutativeSemiring_2446 -> T_Semiring_2280
du_semiring_2576 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: t
v3 = (T_Semiring_2280 -> T_SemiringWithoutAnnihilatingZero_2130)
-> AgdaAny -> t
forall a b. a -> b
coe T_Semiring_2280 -> T_SemiringWithoutAnnihilatingZero_2130
du_semiringWithoutAnnihilatingZero_2398 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: t
v4 = (T_SemiringWithoutAnnihilatingZero_2130 -> T_CommutativeMonoid_962)
-> AgdaAny -> t
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_2130 -> T_CommutativeMonoid_962
du_'43''45'commutativeMonoid_2242 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: t
v5 = (T_CommutativeMonoid_962 -> T_Monoid_882) -> AgdaAny -> t
forall a b. a -> b
coe T_CommutativeMonoid_962 -> T_Monoid_882
du_monoid_1032 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (let v6 :: t
v6 = (T_Monoid_882 -> T_Semigroup_536) -> AgdaAny -> t
forall a b. a -> b
coe T_Monoid_882 -> T_Semigroup_536
du_semigroup_944 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v5) in
                   AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_Magma_68 -> T_RawMagma_36) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Magma_68 -> T_RawMagma_36
du_rawMagma_112 ((T_Semigroup_536 -> T_Magma_68) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semigroup_536 -> T_Magma_68
du_magma_584 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v6))))))))
-- Algebra.Bundles.CommutativeRing._.rawMonoid
d_rawMonoid_4226 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeRing_4016 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMonoid_64
d_rawMonoid_4226 :: () -> () -> T_CommutativeRing_4016 -> T_RawMonoid_64
d_rawMonoid_4226 ~()
v0 ~()
v1 T_CommutativeRing_4016
v2 = T_CommutativeRing_4016 -> T_RawMonoid_64
du_rawMonoid_4226 T_CommutativeRing_4016
v2
du_rawMonoid_4226 ::
  T_CommutativeRing_4016 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMonoid_64
du_rawMonoid_4226 :: T_CommutativeRing_4016 -> T_RawMonoid_64
du_rawMonoid_4226 T_CommutativeRing_4016
v0
  = let v1 :: t
v1 = (T_CommutativeRing_4016 -> T_CommutativeSemiring_2446)
-> AgdaAny -> t
forall a b. a -> b
coe T_CommutativeRing_4016 -> T_CommutativeSemiring_2446
du_commutativeSemiring_4194 (T_CommutativeRing_4016 -> AgdaAny
forall a b. a -> b
coe T_CommutativeRing_4016
v0) in
    AgdaAny -> T_RawMonoid_64
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_CommutativeSemiring_2446 -> T_Semiring_2280) -> AgdaAny -> t
forall a b. a -> b
coe T_CommutativeSemiring_2446 -> T_Semiring_2280
du_semiring_2576 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: t
v3 = (T_Semiring_2280 -> T_SemiringWithoutAnnihilatingZero_2130)
-> AgdaAny -> t
forall a b. a -> b
coe T_Semiring_2280 -> T_SemiringWithoutAnnihilatingZero_2130
du_semiringWithoutAnnihilatingZero_2398 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: t
v4 = (T_SemiringWithoutAnnihilatingZero_2130 -> T_CommutativeMonoid_962)
-> AgdaAny -> t
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_2130 -> T_CommutativeMonoid_962
du_'43''45'commutativeMonoid_2242 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_Monoid_882 -> T_RawMonoid_64) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Monoid_882 -> T_RawMonoid_64
du_rawMonoid_954 ((T_CommutativeMonoid_962 -> T_Monoid_882) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeMonoid_962 -> T_Monoid_882
du_monoid_1032 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v4))))))
-- Algebra.Bundles.CommutativeRing._.semigroup
d_semigroup_4228 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeRing_4016 -> T_Semigroup_536
d_semigroup_4228 :: () -> () -> T_CommutativeRing_4016 -> T_Semigroup_536
d_semigroup_4228 ~()
v0 ~()
v1 T_CommutativeRing_4016
v2 = T_CommutativeRing_4016 -> T_Semigroup_536
du_semigroup_4228 T_CommutativeRing_4016
v2
du_semigroup_4228 :: T_CommutativeRing_4016 -> T_Semigroup_536
du_semigroup_4228 :: T_CommutativeRing_4016 -> T_Semigroup_536
du_semigroup_4228 T_CommutativeRing_4016
v0
  = let v1 :: t
v1 = (T_CommutativeRing_4016 -> T_CommutativeSemiring_2446)
-> AgdaAny -> t
forall a b. a -> b
coe T_CommutativeRing_4016 -> T_CommutativeSemiring_2446
du_commutativeSemiring_4194 (T_CommutativeRing_4016 -> AgdaAny
forall a b. a -> b
coe T_CommutativeRing_4016
v0) in
    AgdaAny -> T_Semigroup_536
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_CommutativeSemiring_2446 -> T_Semiring_2280) -> AgdaAny -> t
forall a b. a -> b
coe T_CommutativeSemiring_2446 -> T_Semiring_2280
du_semiring_2576 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: t
v3 = (T_Semiring_2280 -> T_SemiringWithoutAnnihilatingZero_2130)
-> AgdaAny -> t
forall a b. a -> b
coe T_Semiring_2280 -> T_SemiringWithoutAnnihilatingZero_2130
du_semiringWithoutAnnihilatingZero_2398 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: t
v4 = (T_SemiringWithoutAnnihilatingZero_2130 -> T_CommutativeMonoid_962)
-> AgdaAny -> t
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_2130 -> T_CommutativeMonoid_962
du_'43''45'commutativeMonoid_2242 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_Monoid_882 -> T_Semigroup_536) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Monoid_882 -> T_Semigroup_536
du_semigroup_944 ((T_CommutativeMonoid_962 -> T_Monoid_882) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeMonoid_962 -> T_Monoid_882
du_monoid_1032 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v4))))))
-- Algebra.Bundles.CommutativeRing._.unitalMagma
d_unitalMagma_4230 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeRing_4016 -> T_UnitalMagma_814
d_unitalMagma_4230 :: () -> () -> T_CommutativeRing_4016 -> T_UnitalMagma_814
d_unitalMagma_4230 ~()
v0 ~()
v1 T_CommutativeRing_4016
v2 = T_CommutativeRing_4016 -> T_UnitalMagma_814
du_unitalMagma_4230 T_CommutativeRing_4016
v2
du_unitalMagma_4230 :: T_CommutativeRing_4016 -> T_UnitalMagma_814
du_unitalMagma_4230 :: T_CommutativeRing_4016 -> T_UnitalMagma_814
du_unitalMagma_4230 T_CommutativeRing_4016
v0
  = let v1 :: t
v1 = (T_CommutativeRing_4016 -> T_CommutativeSemiring_2446)
-> AgdaAny -> t
forall a b. a -> b
coe T_CommutativeRing_4016 -> T_CommutativeSemiring_2446
du_commutativeSemiring_4194 (T_CommutativeRing_4016 -> AgdaAny
forall a b. a -> b
coe T_CommutativeRing_4016
v0) in
    AgdaAny -> T_UnitalMagma_814
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_CommutativeSemiring_2446 -> T_Semiring_2280) -> AgdaAny -> t
forall a b. a -> b
coe T_CommutativeSemiring_2446 -> T_Semiring_2280
du_semiring_2576 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: t
v3 = (T_Semiring_2280 -> T_SemiringWithoutAnnihilatingZero_2130)
-> AgdaAny -> t
forall a b. a -> b
coe T_Semiring_2280 -> T_SemiringWithoutAnnihilatingZero_2130
du_semiringWithoutAnnihilatingZero_2398 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: t
v4 = (T_SemiringWithoutAnnihilatingZero_2130 -> T_CommutativeMonoid_962)
-> AgdaAny -> t
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_2130 -> T_CommutativeMonoid_962
du_'43''45'commutativeMonoid_2242 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_Monoid_882 -> T_UnitalMagma_814) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Monoid_882 -> T_UnitalMagma_814
du_unitalMagma_956 ((T_CommutativeMonoid_962 -> T_Monoid_882) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeMonoid_962 -> T_Monoid_882
du_monoid_1032 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v4))))))
-- Algebra.Bundles.CommutativeRing._.commutativeSemiringWithoutOne
d_commutativeSemiringWithoutOne_4232 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeRing_4016 -> T_CommutativeSemiringWithoutOne_2002
d_commutativeSemiringWithoutOne_4232 :: ()
-> ()
-> T_CommutativeRing_4016
-> T_CommutativeSemiringWithoutOne_2002
d_commutativeSemiringWithoutOne_4232 ~()
v0 ~()
v1 T_CommutativeRing_4016
v2
  = T_CommutativeRing_4016 -> T_CommutativeSemiringWithoutOne_2002
du_commutativeSemiringWithoutOne_4232 T_CommutativeRing_4016
v2
du_commutativeSemiringWithoutOne_4232 ::
  T_CommutativeRing_4016 -> T_CommutativeSemiringWithoutOne_2002
du_commutativeSemiringWithoutOne_4232 :: T_CommutativeRing_4016 -> T_CommutativeSemiringWithoutOne_2002
du_commutativeSemiringWithoutOne_4232 T_CommutativeRing_4016
v0
  = (T_CommutativeSemiring_2446
 -> T_CommutativeSemiringWithoutOne_2002)
-> AgdaAny -> T_CommutativeSemiringWithoutOne_2002
forall a b. a -> b
coe
      T_CommutativeSemiring_2446 -> T_CommutativeSemiringWithoutOne_2002
du_commutativeSemiringWithoutOne_2626
      ((T_CommutativeRing_4016 -> T_CommutativeSemiring_2446)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeRing_4016 -> T_CommutativeSemiring_2446
du_commutativeSemiring_4194 (T_CommutativeRing_4016 -> AgdaAny
forall a b. a -> b
coe T_CommutativeRing_4016
v0))
-- Algebra.Bundles.CommutativeRing._.nearSemiring
d_nearSemiring_4234 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeRing_4016 -> T_NearSemiring_1766
d_nearSemiring_4234 :: () -> () -> T_CommutativeRing_4016 -> T_NearSemiring_1766
d_nearSemiring_4234 ~()
v0 ~()
v1 T_CommutativeRing_4016
v2 = T_CommutativeRing_4016 -> T_NearSemiring_1766
du_nearSemiring_4234 T_CommutativeRing_4016
v2
du_nearSemiring_4234 ::
  T_CommutativeRing_4016 -> T_NearSemiring_1766
du_nearSemiring_4234 :: T_CommutativeRing_4016 -> T_NearSemiring_1766
du_nearSemiring_4234 T_CommutativeRing_4016
v0
  = let v1 :: t
v1 = (T_CommutativeRing_4016 -> T_CommutativeSemiring_2446)
-> AgdaAny -> t
forall a b. a -> b
coe T_CommutativeRing_4016 -> T_CommutativeSemiring_2446
du_commutativeSemiring_4194 (T_CommutativeRing_4016 -> AgdaAny
forall a b. a -> b
coe T_CommutativeRing_4016
v0) in
    AgdaAny -> T_NearSemiring_1766
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_CommutativeSemiring_2446 -> T_Semiring_2280) -> AgdaAny -> t
forall a b. a -> b
coe T_CommutativeSemiring_2446 -> T_Semiring_2280
du_semiring_2576 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_SemiringWithoutOne_1880 -> T_NearSemiring_1766)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_SemiringWithoutOne_1880 -> T_NearSemiring_1766
du_nearSemiring_1966 ((T_Semiring_2280 -> T_SemiringWithoutOne_1880)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semiring_2280 -> T_SemiringWithoutOne_1880
du_semiringWithoutOne_2436 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2))))
-- Algebra.Bundles.CommutativeRing._.semiring
d_semiring_4236 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeRing_4016 -> T_Semiring_2280
d_semiring_4236 :: () -> () -> T_CommutativeRing_4016 -> T_Semiring_2280
d_semiring_4236 ~()
v0 ~()
v1 T_CommutativeRing_4016
v2 = T_CommutativeRing_4016 -> T_Semiring_2280
du_semiring_4236 T_CommutativeRing_4016
v2
du_semiring_4236 :: T_CommutativeRing_4016 -> T_Semiring_2280
du_semiring_4236 :: T_CommutativeRing_4016 -> T_Semiring_2280
du_semiring_4236 T_CommutativeRing_4016
v0
  = (T_CommutativeSemiring_2446 -> T_Semiring_2280)
-> AgdaAny -> T_Semiring_2280
forall a b. a -> b
coe T_CommutativeSemiring_2446 -> T_Semiring_2280
du_semiring_2576 ((T_CommutativeRing_4016 -> T_CommutativeSemiring_2446)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeRing_4016 -> T_CommutativeSemiring_2446
du_commutativeSemiring_4194 (T_CommutativeRing_4016 -> AgdaAny
forall a b. a -> b
coe T_CommutativeRing_4016
v0))
-- Algebra.Bundles.CommutativeRing._.semiringWithoutAnnihilatingZero
d_semiringWithoutAnnihilatingZero_4238 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeRing_4016 -> T_SemiringWithoutAnnihilatingZero_2130
d_semiringWithoutAnnihilatingZero_4238 :: ()
-> ()
-> T_CommutativeRing_4016
-> T_SemiringWithoutAnnihilatingZero_2130
d_semiringWithoutAnnihilatingZero_4238 ~()
v0 ~()
v1 T_CommutativeRing_4016
v2
  = T_CommutativeRing_4016 -> T_SemiringWithoutAnnihilatingZero_2130
du_semiringWithoutAnnihilatingZero_4238 T_CommutativeRing_4016
v2
du_semiringWithoutAnnihilatingZero_4238 ::
  T_CommutativeRing_4016 -> T_SemiringWithoutAnnihilatingZero_2130
du_semiringWithoutAnnihilatingZero_4238 :: T_CommutativeRing_4016 -> T_SemiringWithoutAnnihilatingZero_2130
du_semiringWithoutAnnihilatingZero_4238 T_CommutativeRing_4016
v0
  = let v1 :: t
v1 = (T_CommutativeRing_4016 -> T_CommutativeSemiring_2446)
-> AgdaAny -> t
forall a b. a -> b
coe T_CommutativeRing_4016 -> T_CommutativeSemiring_2446
du_commutativeSemiring_4194 (T_CommutativeRing_4016 -> AgdaAny
forall a b. a -> b
coe T_CommutativeRing_4016
v0) in
    AgdaAny -> T_SemiringWithoutAnnihilatingZero_2130
forall a b. a -> b
coe
      ((T_Semiring_2280 -> T_SemiringWithoutAnnihilatingZero_2130)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_Semiring_2280 -> T_SemiringWithoutAnnihilatingZero_2130
du_semiringWithoutAnnihilatingZero_2398
         ((T_CommutativeSemiring_2446 -> T_Semiring_2280)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemiring_2446 -> T_Semiring_2280
du_semiring_2576 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1)))
-- Algebra.Bundles.CommutativeRing._.semiringWithoutOne
d_semiringWithoutOne_4240 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeRing_4016 -> T_SemiringWithoutOne_1880
d_semiringWithoutOne_4240 :: () -> () -> T_CommutativeRing_4016 -> T_SemiringWithoutOne_1880
d_semiringWithoutOne_4240 ~()
v0 ~()
v1 T_CommutativeRing_4016
v2
  = T_CommutativeRing_4016 -> T_SemiringWithoutOne_1880
du_semiringWithoutOne_4240 T_CommutativeRing_4016
v2
du_semiringWithoutOne_4240 ::
  T_CommutativeRing_4016 -> T_SemiringWithoutOne_1880
du_semiringWithoutOne_4240 :: T_CommutativeRing_4016 -> T_SemiringWithoutOne_1880
du_semiringWithoutOne_4240 T_CommutativeRing_4016
v0
  = let v1 :: t
v1 = (T_CommutativeRing_4016 -> T_CommutativeSemiring_2446)
-> AgdaAny -> t
forall a b. a -> b
coe T_CommutativeRing_4016 -> T_CommutativeSemiring_2446
du_commutativeSemiring_4194 (T_CommutativeRing_4016 -> AgdaAny
forall a b. a -> b
coe T_CommutativeRing_4016
v0) in
    AgdaAny -> T_SemiringWithoutOne_1880
forall a b. a -> b
coe
      ((T_Semiring_2280 -> T_SemiringWithoutOne_1880)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semiring_2280 -> T_SemiringWithoutOne_1880
du_semiringWithoutOne_2436 ((T_CommutativeSemiring_2446 -> T_Semiring_2280)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemiring_2446 -> T_Semiring_2280
du_semiring_2576 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1)))
-- Algebra.Bundles.Quasigroup
d_Quasigroup_4246 :: p -> p -> ()
d_Quasigroup_4246 p
a0 p
a1 = ()
data T_Quasigroup_4246
  = C_Quasigroup'46'constructor_76277 (AgdaAny -> AgdaAny -> AgdaAny)
                                      (AgdaAny -> AgdaAny -> AgdaAny)
                                      (AgdaAny -> AgdaAny -> AgdaAny)
                                      MAlonzo.Code.Algebra.Structures.T_IsQuasigroup_2944
-- Algebra.Bundles.Quasigroup.Carrier
d_Carrier_4264 :: T_Quasigroup_4246 -> ()
d_Carrier_4264 :: T_Quasigroup_4246 -> ()
d_Carrier_4264 = T_Quasigroup_4246 -> ()
forall a. a
erased
-- Algebra.Bundles.Quasigroup._≈_
d__'8776'__4266 :: T_Quasigroup_4246 -> AgdaAny -> AgdaAny -> ()
d__'8776'__4266 :: T_Quasigroup_4246 -> AgdaAny -> AgdaAny -> ()
d__'8776'__4266 = T_Quasigroup_4246 -> AgdaAny -> AgdaAny -> ()
forall a. a
erased
-- Algebra.Bundles.Quasigroup._∙_
d__'8729'__4268 ::
  T_Quasigroup_4246 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__4268 :: T_Quasigroup_4246 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__4268 T_Quasigroup_4246
v0
  = case T_Quasigroup_4246 -> T_Quasigroup_4246
forall a b. a -> b
coe T_Quasigroup_4246
v0 of
      C_Quasigroup'46'constructor_76277 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny -> AgdaAny
v5 T_IsQuasigroup_2944
v6 -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v3
      T_Quasigroup_4246
_ -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.Quasigroup._\\_
d__'92''92'__4270 ::
  T_Quasigroup_4246 -> AgdaAny -> AgdaAny -> AgdaAny
d__'92''92'__4270 :: T_Quasigroup_4246 -> AgdaAny -> AgdaAny -> AgdaAny
d__'92''92'__4270 T_Quasigroup_4246
v0
  = case T_Quasigroup_4246 -> T_Quasigroup_4246
forall a b. a -> b
coe T_Quasigroup_4246
v0 of
      C_Quasigroup'46'constructor_76277 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny -> AgdaAny
v5 T_IsQuasigroup_2944
v6 -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v4
      T_Quasigroup_4246
_ -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.Quasigroup._//_
d__'47''47'__4272 ::
  T_Quasigroup_4246 -> AgdaAny -> AgdaAny -> AgdaAny
d__'47''47'__4272 :: T_Quasigroup_4246 -> AgdaAny -> AgdaAny -> AgdaAny
d__'47''47'__4272 T_Quasigroup_4246
v0
  = case T_Quasigroup_4246 -> T_Quasigroup_4246
forall a b. a -> b
coe T_Quasigroup_4246
v0 of
      C_Quasigroup'46'constructor_76277 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny -> AgdaAny
v5 T_IsQuasigroup_2944
v6 -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v5
      T_Quasigroup_4246
_ -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.Quasigroup.isQuasigroup
d_isQuasigroup_4274 ::
  T_Quasigroup_4246 ->
  MAlonzo.Code.Algebra.Structures.T_IsQuasigroup_2944
d_isQuasigroup_4274 :: T_Quasigroup_4246 -> T_IsQuasigroup_2944
d_isQuasigroup_4274 T_Quasigroup_4246
v0
  = case T_Quasigroup_4246 -> T_Quasigroup_4246
forall a b. a -> b
coe T_Quasigroup_4246
v0 of
      C_Quasigroup'46'constructor_76277 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny -> AgdaAny
v5 T_IsQuasigroup_2944
v6 -> T_IsQuasigroup_2944 -> T_IsQuasigroup_2944
forall a b. a -> b
coe T_IsQuasigroup_2944
v6
      T_Quasigroup_4246
_ -> T_IsQuasigroup_2944
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.Quasigroup._.//-cong
d_'47''47''45'cong_4278 ::
  T_Quasigroup_4246 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'47''47''45'cong_4278 :: T_Quasigroup_4246
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'47''47''45'cong_4278 T_Quasigroup_4246
v0
  = (T_IsQuasigroup_2944
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsQuasigroup_2944
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'47''47''45'cong_2966
      ((T_Quasigroup_4246 -> T_IsQuasigroup_2944) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Quasigroup_4246 -> T_IsQuasigroup_2944
d_isQuasigroup_4274 (T_Quasigroup_4246 -> AgdaAny
forall a b. a -> b
coe T_Quasigroup_4246
v0))
-- Algebra.Bundles.Quasigroup._.//-congʳ
d_'47''47''45'cong'691'_4280 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Quasigroup_4246 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'47''47''45'cong'691'_4280 :: ()
-> ()
-> T_Quasigroup_4246
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'47''47''45'cong'691'_4280 ~()
v0 ~()
v1 T_Quasigroup_4246
v2
  = T_Quasigroup_4246
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'47''47''45'cong'691'_4280 T_Quasigroup_4246
v2
du_'47''47''45'cong'691'_4280 ::
  T_Quasigroup_4246 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'47''47''45'cong'691'_4280 :: T_Quasigroup_4246
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'47''47''45'cong'691'_4280 T_Quasigroup_4246
v0
  = (T_IsQuasigroup_2944
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsQuasigroup_2944
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'47''47''45'cong'691'_3006
      ((T_Quasigroup_4246 -> T_IsQuasigroup_2944) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Quasigroup_4246 -> T_IsQuasigroup_2944
d_isQuasigroup_4274 (T_Quasigroup_4246 -> AgdaAny
forall a b. a -> b
coe T_Quasigroup_4246
v0))
-- Algebra.Bundles.Quasigroup._.//-congˡ
d_'47''47''45'cong'737'_4282 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Quasigroup_4246 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'47''47''45'cong'737'_4282 :: ()
-> ()
-> T_Quasigroup_4246
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'47''47''45'cong'737'_4282 ~()
v0 ~()
v1 T_Quasigroup_4246
v2
  = T_Quasigroup_4246
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'47''47''45'cong'737'_4282 T_Quasigroup_4246
v2
du_'47''47''45'cong'737'_4282 ::
  T_Quasigroup_4246 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'47''47''45'cong'737'_4282 :: T_Quasigroup_4246
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'47''47''45'cong'737'_4282 T_Quasigroup_4246
v0
  = (T_IsQuasigroup_2944
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsQuasigroup_2944
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'47''47''45'cong'737'_3002
      ((T_Quasigroup_4246 -> T_IsQuasigroup_2944) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Quasigroup_4246 -> T_IsQuasigroup_2944
d_isQuasigroup_4274 (T_Quasigroup_4246 -> AgdaAny
forall a b. a -> b
coe T_Quasigroup_4246
v0))
-- Algebra.Bundles.Quasigroup._.\\-cong
d_'92''92''45'cong_4284 ::
  T_Quasigroup_4246 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'92''92''45'cong_4284 :: T_Quasigroup_4246
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'92''92''45'cong_4284 T_Quasigroup_4246
v0
  = (T_IsQuasigroup_2944
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsQuasigroup_2944
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'92''92''45'cong_2964
      ((T_Quasigroup_4246 -> T_IsQuasigroup_2944) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Quasigroup_4246 -> T_IsQuasigroup_2944
d_isQuasigroup_4274 (T_Quasigroup_4246 -> AgdaAny
forall a b. a -> b
coe T_Quasigroup_4246
v0))
-- Algebra.Bundles.Quasigroup._.\\-congʳ
d_'92''92''45'cong'691'_4286 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Quasigroup_4246 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'92''92''45'cong'691'_4286 :: ()
-> ()
-> T_Quasigroup_4246
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'92''92''45'cong'691'_4286 ~()
v0 ~()
v1 T_Quasigroup_4246
v2
  = T_Quasigroup_4246
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'92''92''45'cong'691'_4286 T_Quasigroup_4246
v2
du_'92''92''45'cong'691'_4286 ::
  T_Quasigroup_4246 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'92''92''45'cong'691'_4286 :: T_Quasigroup_4246
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'92''92''45'cong'691'_4286 T_Quasigroup_4246
v0
  = (T_IsQuasigroup_2944
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsQuasigroup_2944
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'92''92''45'cong'691'_2998
      ((T_Quasigroup_4246 -> T_IsQuasigroup_2944) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Quasigroup_4246 -> T_IsQuasigroup_2944
d_isQuasigroup_4274 (T_Quasigroup_4246 -> AgdaAny
forall a b. a -> b
coe T_Quasigroup_4246
v0))
-- Algebra.Bundles.Quasigroup._.\\-congˡ
d_'92''92''45'cong'737'_4288 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Quasigroup_4246 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'92''92''45'cong'737'_4288 :: ()
-> ()
-> T_Quasigroup_4246
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'92''92''45'cong'737'_4288 ~()
v0 ~()
v1 T_Quasigroup_4246
v2
  = T_Quasigroup_4246
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'92''92''45'cong'737'_4288 T_Quasigroup_4246
v2
du_'92''92''45'cong'737'_4288 ::
  T_Quasigroup_4246 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'92''92''45'cong'737'_4288 :: T_Quasigroup_4246
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'92''92''45'cong'737'_4288 T_Quasigroup_4246
v0
  = (T_IsQuasigroup_2944
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsQuasigroup_2944
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'92''92''45'cong'737'_2994
      ((T_Quasigroup_4246 -> T_IsQuasigroup_2944) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Quasigroup_4246 -> T_IsQuasigroup_2944
d_isQuasigroup_4274 (T_Quasigroup_4246 -> AgdaAny
forall a b. a -> b
coe T_Quasigroup_4246
v0))
-- Algebra.Bundles.Quasigroup._.isEquivalence
d_isEquivalence_4290 ::
  T_Quasigroup_4246 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_4290 :: T_Quasigroup_4246 -> T_IsEquivalence_26
d_isEquivalence_4290 T_Quasigroup_4246
v0
  = (T_IsMagma_176 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
      ((T_IsQuasigroup_2944 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsQuasigroup_2944 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_2962
         ((T_Quasigroup_4246 -> T_IsQuasigroup_2944) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Quasigroup_4246 -> T_IsQuasigroup_2944
d_isQuasigroup_4274 (T_Quasigroup_4246 -> AgdaAny
forall a b. a -> b
coe T_Quasigroup_4246
v0)))
-- Algebra.Bundles.Quasigroup._.isMagma
d_isMagma_4292 ::
  T_Quasigroup_4246 -> MAlonzo.Code.Algebra.Structures.T_IsMagma_176
d_isMagma_4292 :: T_Quasigroup_4246 -> T_IsMagma_176
d_isMagma_4292 T_Quasigroup_4246
v0
  = (T_IsQuasigroup_2944 -> T_IsMagma_176) -> AgdaAny -> T_IsMagma_176
forall a b. a -> b
coe
      T_IsQuasigroup_2944 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_2962
      ((T_Quasigroup_4246 -> T_IsQuasigroup_2944) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Quasigroup_4246 -> T_IsQuasigroup_2944
d_isQuasigroup_4274 (T_Quasigroup_4246 -> AgdaAny
forall a b. a -> b
coe T_Quasigroup_4246
v0))
-- Algebra.Bundles.Quasigroup._.isPartialEquivalence
d_isPartialEquivalence_4294 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Quasigroup_4246 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_4294 :: () -> () -> T_Quasigroup_4246 -> T_IsPartialEquivalence_16
d_isPartialEquivalence_4294 ~()
v0 ~()
v1 T_Quasigroup_4246
v2
  = T_Quasigroup_4246 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_4294 T_Quasigroup_4246
v2
du_isPartialEquivalence_4294 ::
  T_Quasigroup_4246 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_4294 :: T_Quasigroup_4246 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_4294 T_Quasigroup_4246
v0
  = let v1 :: T_IsQuasigroup_2944
v1 = T_Quasigroup_4246 -> T_IsQuasigroup_2944
d_isQuasigroup_4274 (T_Quasigroup_4246 -> T_Quasigroup_4246
forall a b. a -> b
coe T_Quasigroup_4246
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsMagma_176
v2
             = T_IsQuasigroup_2944 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_2962 (T_IsQuasigroup_2944 -> T_IsQuasigroup_2944
forall a b. a -> b
coe T_IsQuasigroup_2944
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsEquivalence_26 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsEquivalence_26 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
            ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v2))))
-- Algebra.Bundles.Quasigroup._.leftDivides
d_leftDivides_4296 ::
  T_Quasigroup_4246 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_leftDivides_4296 :: T_Quasigroup_4246 -> T_Σ_14
d_leftDivides_4296 T_Quasigroup_4246
v0
  = (T_IsQuasigroup_2944 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsQuasigroup_2944 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_leftDivides_2968
      ((T_Quasigroup_4246 -> T_IsQuasigroup_2944) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Quasigroup_4246 -> T_IsQuasigroup_2944
d_isQuasigroup_4274 (T_Quasigroup_4246 -> AgdaAny
forall a b. a -> b
coe T_Quasigroup_4246
v0))
-- Algebra.Bundles.Quasigroup._.leftDividesʳ
d_leftDivides'691'_4298 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Quasigroup_4246 -> AgdaAny -> AgdaAny -> AgdaAny
d_leftDivides'691'_4298 :: () -> () -> T_Quasigroup_4246 -> AgdaAny -> AgdaAny -> AgdaAny
d_leftDivides'691'_4298 ~()
v0 ~()
v1 T_Quasigroup_4246
v2 = T_Quasigroup_4246 -> AgdaAny -> AgdaAny -> AgdaAny
du_leftDivides'691'_4298 T_Quasigroup_4246
v2
du_leftDivides'691'_4298 ::
  T_Quasigroup_4246 -> AgdaAny -> AgdaAny -> AgdaAny
du_leftDivides'691'_4298 :: T_Quasigroup_4246 -> AgdaAny -> AgdaAny -> AgdaAny
du_leftDivides'691'_4298 T_Quasigroup_4246
v0
  = (T_IsQuasigroup_2944 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsQuasigroup_2944 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_leftDivides'691'_3012
      ((T_Quasigroup_4246 -> T_IsQuasigroup_2944) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Quasigroup_4246 -> T_IsQuasigroup_2944
d_isQuasigroup_4274 (T_Quasigroup_4246 -> AgdaAny
forall a b. a -> b
coe T_Quasigroup_4246
v0))
-- Algebra.Bundles.Quasigroup._.leftDividesˡ
d_leftDivides'737'_4300 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Quasigroup_4246 -> AgdaAny -> AgdaAny -> AgdaAny
d_leftDivides'737'_4300 :: () -> () -> T_Quasigroup_4246 -> AgdaAny -> AgdaAny -> AgdaAny
d_leftDivides'737'_4300 ~()
v0 ~()
v1 T_Quasigroup_4246
v2 = T_Quasigroup_4246 -> AgdaAny -> AgdaAny -> AgdaAny
du_leftDivides'737'_4300 T_Quasigroup_4246
v2
du_leftDivides'737'_4300 ::
  T_Quasigroup_4246 -> AgdaAny -> AgdaAny -> AgdaAny
du_leftDivides'737'_4300 :: T_Quasigroup_4246 -> AgdaAny -> AgdaAny -> AgdaAny
du_leftDivides'737'_4300 T_Quasigroup_4246
v0
  = (T_IsQuasigroup_2944 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsQuasigroup_2944 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_leftDivides'737'_3010
      ((T_Quasigroup_4246 -> T_IsQuasigroup_2944) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Quasigroup_4246 -> T_IsQuasigroup_2944
d_isQuasigroup_4274 (T_Quasigroup_4246 -> AgdaAny
forall a b. a -> b
coe T_Quasigroup_4246
v0))
-- Algebra.Bundles.Quasigroup._.refl
d_refl_4302 :: T_Quasigroup_4246 -> AgdaAny -> AgdaAny
d_refl_4302 :: T_Quasigroup_4246 -> AgdaAny -> AgdaAny
d_refl_4302 T_Quasigroup_4246
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_34
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
         ((T_IsQuasigroup_2944 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsQuasigroup_2944 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_2962
            ((T_Quasigroup_4246 -> T_IsQuasigroup_2944) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Quasigroup_4246 -> T_IsQuasigroup_2944
d_isQuasigroup_4274 (T_Quasigroup_4246 -> AgdaAny
forall a b. a -> b
coe T_Quasigroup_4246
v0))))
-- Algebra.Bundles.Quasigroup._.reflexive
d_reflexive_4304 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Quasigroup_4246 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_4304 :: ()
-> ()
-> T_Quasigroup_4246
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_4304 ~()
v0 ~()
v1 T_Quasigroup_4246
v2 = T_Quasigroup_4246 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_4304 T_Quasigroup_4246
v2
du_reflexive_4304 ::
  T_Quasigroup_4246 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_4304 :: T_Quasigroup_4246 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_4304 T_Quasigroup_4246
v0
  = let v1 :: T_IsQuasigroup_2944
v1 = T_Quasigroup_4246 -> T_IsQuasigroup_2944
d_isQuasigroup_4274 (T_Quasigroup_4246 -> T_Quasigroup_4246
forall a b. a -> b
coe T_Quasigroup_4246
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsMagma_176
v2
             = T_IsQuasigroup_2944 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_2962 (T_IsQuasigroup_2944 -> T_IsQuasigroup_2944
forall a b. a -> b
coe T_IsQuasigroup_2944
v1) in
       (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
         (\ AgdaAny
v3 AgdaAny
v4 AgdaAny
v5 ->
            (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
              T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
              ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v2))
              AgdaAny
v3))
-- Algebra.Bundles.Quasigroup._.rightDivides
d_rightDivides_4306 ::
  T_Quasigroup_4246 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_rightDivides_4306 :: T_Quasigroup_4246 -> T_Σ_14
d_rightDivides_4306 T_Quasigroup_4246
v0
  = (T_IsQuasigroup_2944 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsQuasigroup_2944 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_rightDivides_2970
      ((T_Quasigroup_4246 -> T_IsQuasigroup_2944) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Quasigroup_4246 -> T_IsQuasigroup_2944
d_isQuasigroup_4274 (T_Quasigroup_4246 -> AgdaAny
forall a b. a -> b
coe T_Quasigroup_4246
v0))
-- Algebra.Bundles.Quasigroup._.rightDividesʳ
d_rightDivides'691'_4308 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Quasigroup_4246 -> AgdaAny -> AgdaAny -> AgdaAny
d_rightDivides'691'_4308 :: () -> () -> T_Quasigroup_4246 -> AgdaAny -> AgdaAny -> AgdaAny
d_rightDivides'691'_4308 ~()
v0 ~()
v1 T_Quasigroup_4246
v2 = T_Quasigroup_4246 -> AgdaAny -> AgdaAny -> AgdaAny
du_rightDivides'691'_4308 T_Quasigroup_4246
v2
du_rightDivides'691'_4308 ::
  T_Quasigroup_4246 -> AgdaAny -> AgdaAny -> AgdaAny
du_rightDivides'691'_4308 :: T_Quasigroup_4246 -> AgdaAny -> AgdaAny -> AgdaAny
du_rightDivides'691'_4308 T_Quasigroup_4246
v0
  = (T_IsQuasigroup_2944 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsQuasigroup_2944 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_rightDivides'691'_3016
      ((T_Quasigroup_4246 -> T_IsQuasigroup_2944) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Quasigroup_4246 -> T_IsQuasigroup_2944
d_isQuasigroup_4274 (T_Quasigroup_4246 -> AgdaAny
forall a b. a -> b
coe T_Quasigroup_4246
v0))
-- Algebra.Bundles.Quasigroup._.rightDividesˡ
d_rightDivides'737'_4310 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Quasigroup_4246 -> AgdaAny -> AgdaAny -> AgdaAny
d_rightDivides'737'_4310 :: () -> () -> T_Quasigroup_4246 -> AgdaAny -> AgdaAny -> AgdaAny
d_rightDivides'737'_4310 ~()
v0 ~()
v1 T_Quasigroup_4246
v2 = T_Quasigroup_4246 -> AgdaAny -> AgdaAny -> AgdaAny
du_rightDivides'737'_4310 T_Quasigroup_4246
v2
du_rightDivides'737'_4310 ::
  T_Quasigroup_4246 -> AgdaAny -> AgdaAny -> AgdaAny
du_rightDivides'737'_4310 :: T_Quasigroup_4246 -> AgdaAny -> AgdaAny -> AgdaAny
du_rightDivides'737'_4310 T_Quasigroup_4246
v0
  = (T_IsQuasigroup_2944 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsQuasigroup_2944 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_rightDivides'737'_3014
      ((T_Quasigroup_4246 -> T_IsQuasigroup_2944) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Quasigroup_4246 -> T_IsQuasigroup_2944
d_isQuasigroup_4274 (T_Quasigroup_4246 -> AgdaAny
forall a b. a -> b
coe T_Quasigroup_4246
v0))
-- Algebra.Bundles.Quasigroup._.setoid
d_setoid_4312 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Quasigroup_4246 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_4312 :: () -> () -> T_Quasigroup_4246 -> T_Setoid_44
d_setoid_4312 ~()
v0 ~()
v1 T_Quasigroup_4246
v2 = T_Quasigroup_4246 -> T_Setoid_44
du_setoid_4312 T_Quasigroup_4246
v2
du_setoid_4312 ::
  T_Quasigroup_4246 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_4312 :: T_Quasigroup_4246 -> T_Setoid_44
du_setoid_4312 T_Quasigroup_4246
v0
  = let v1 :: T_IsQuasigroup_2944
v1 = T_Quasigroup_4246 -> T_IsQuasigroup_2944
d_isQuasigroup_4274 (T_Quasigroup_4246 -> T_Quasigroup_4246
forall a b. a -> b
coe T_Quasigroup_4246
v0) in
    AgdaAny -> T_Setoid_44
forall a b. a -> b
coe
      ((T_IsMagma_176 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_Setoid_44
MAlonzo.Code.Algebra.Structures.du_setoid_200
         ((T_IsQuasigroup_2944 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroup_2944 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_2962 (T_IsQuasigroup_2944 -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroup_2944
v1)))
-- Algebra.Bundles.Quasigroup._.sym
d_sym_4314 ::
  T_Quasigroup_4246 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_4314 :: T_Quasigroup_4246 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_4314 T_Quasigroup_4246
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_36
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
         ((T_IsQuasigroup_2944 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsQuasigroup_2944 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_2962
            ((T_Quasigroup_4246 -> T_IsQuasigroup_2944) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Quasigroup_4246 -> T_IsQuasigroup_2944
d_isQuasigroup_4274 (T_Quasigroup_4246 -> AgdaAny
forall a b. a -> b
coe T_Quasigroup_4246
v0))))
-- Algebra.Bundles.Quasigroup._.trans
d_trans_4316 ::
  T_Quasigroup_4246 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_4316 :: T_Quasigroup_4246
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_4316 T_Quasigroup_4246
v0
  = (T_IsEquivalence_26
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_38
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
         ((T_IsQuasigroup_2944 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsQuasigroup_2944 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_2962
            ((T_Quasigroup_4246 -> T_IsQuasigroup_2944) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Quasigroup_4246 -> T_IsQuasigroup_2944
d_isQuasigroup_4274 (T_Quasigroup_4246 -> AgdaAny
forall a b. a -> b
coe T_Quasigroup_4246
v0))))
-- Algebra.Bundles.Quasigroup._.∙-cong
d_'8729''45'cong_4318 ::
  T_Quasigroup_4246 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_4318 :: T_Quasigroup_4246
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_4318 T_Quasigroup_4246
v0
  = (T_IsMagma_176
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsMagma_176
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_186
      ((T_IsQuasigroup_2944 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsQuasigroup_2944 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_2962
         ((T_Quasigroup_4246 -> T_IsQuasigroup_2944) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Quasigroup_4246 -> T_IsQuasigroup_2944
d_isQuasigroup_4274 (T_Quasigroup_4246 -> AgdaAny
forall a b. a -> b
coe T_Quasigroup_4246
v0)))
-- Algebra.Bundles.Quasigroup._.∙-congʳ
d_'8729''45'cong'691'_4320 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Quasigroup_4246 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_4320 :: ()
-> ()
-> T_Quasigroup_4246
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_4320 ~()
v0 ~()
v1 T_Quasigroup_4246
v2
  = T_Quasigroup_4246
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_4320 T_Quasigroup_4246
v2
du_'8729''45'cong'691'_4320 ::
  T_Quasigroup_4246 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_4320 :: T_Quasigroup_4246
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_4320 T_Quasigroup_4246
v0
  = let v1 :: T_IsQuasigroup_2944
v1 = T_Quasigroup_4246 -> T_IsQuasigroup_2944
d_isQuasigroup_4274 (T_Quasigroup_4246 -> T_Quasigroup_4246
forall a b. a -> b
coe T_Quasigroup_4246
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'691'_206
         ((T_IsQuasigroup_2944 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroup_2944 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_2962 (T_IsQuasigroup_2944 -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroup_2944
v1)))
-- Algebra.Bundles.Quasigroup._.∙-congˡ
d_'8729''45'cong'737'_4322 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Quasigroup_4246 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_4322 :: ()
-> ()
-> T_Quasigroup_4246
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_4322 ~()
v0 ~()
v1 T_Quasigroup_4246
v2
  = T_Quasigroup_4246
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_4322 T_Quasigroup_4246
v2
du_'8729''45'cong'737'_4322 ::
  T_Quasigroup_4246 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_4322 :: T_Quasigroup_4246
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_4322 T_Quasigroup_4246
v0
  = let v1 :: T_IsQuasigroup_2944
v1 = T_Quasigroup_4246 -> T_IsQuasigroup_2944
d_isQuasigroup_4274 (T_Quasigroup_4246 -> T_Quasigroup_4246
forall a b. a -> b
coe T_Quasigroup_4246
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'737'_202
         ((T_IsQuasigroup_2944 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroup_2944 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_2962 (T_IsQuasigroup_2944 -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroup_2944
v1)))
-- Algebra.Bundles.Quasigroup.magma
d_magma_4324 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Quasigroup_4246 -> T_Magma_68
d_magma_4324 :: () -> () -> T_Quasigroup_4246 -> T_Magma_68
d_magma_4324 ~()
v0 ~()
v1 T_Quasigroup_4246
v2 = T_Quasigroup_4246 -> T_Magma_68
du_magma_4324 T_Quasigroup_4246
v2
du_magma_4324 :: T_Quasigroup_4246 -> T_Magma_68
du_magma_4324 :: T_Quasigroup_4246 -> T_Magma_68
du_magma_4324 T_Quasigroup_4246
v0
  = ((AgdaAny -> AgdaAny -> AgdaAny) -> T_IsMagma_176 -> T_Magma_68)
-> (AgdaAny -> AgdaAny -> AgdaAny) -> T_IsMagma_176 -> T_Magma_68
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny) -> T_IsMagma_176 -> T_Magma_68
C_Magma'46'constructor_1279 (T_Quasigroup_4246 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__4268 (T_Quasigroup_4246 -> T_Quasigroup_4246
forall a b. a -> b
coe T_Quasigroup_4246
v0))
      (T_IsQuasigroup_2944 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_2962
         ((T_Quasigroup_4246 -> T_IsQuasigroup_2944)
-> AgdaAny -> T_IsQuasigroup_2944
forall a b. a -> b
coe T_Quasigroup_4246 -> T_IsQuasigroup_2944
d_isQuasigroup_4274 (T_Quasigroup_4246 -> AgdaAny
forall a b. a -> b
coe T_Quasigroup_4246
v0)))
-- Algebra.Bundles.Quasigroup._._≉_
d__'8777'__4328 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Quasigroup_4246 -> AgdaAny -> AgdaAny -> ()
d__'8777'__4328 :: () -> () -> T_Quasigroup_4246 -> AgdaAny -> AgdaAny -> ()
d__'8777'__4328 = () -> () -> T_Quasigroup_4246 -> AgdaAny -> AgdaAny -> ()
forall a. a
erased
-- Algebra.Bundles.Quasigroup._.rawMagma
d_rawMagma_4330 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Quasigroup_4246 -> MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
d_rawMagma_4330 :: () -> () -> T_Quasigroup_4246 -> T_RawMagma_36
d_rawMagma_4330 ~()
v0 ~()
v1 T_Quasigroup_4246
v2 = T_Quasigroup_4246 -> T_RawMagma_36
du_rawMagma_4330 T_Quasigroup_4246
v2
du_rawMagma_4330 ::
  T_Quasigroup_4246 -> MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
du_rawMagma_4330 :: T_Quasigroup_4246 -> T_RawMagma_36
du_rawMagma_4330 T_Quasigroup_4246
v0
  = (T_Magma_68 -> T_RawMagma_36) -> AgdaAny -> T_RawMagma_36
forall a b. a -> b
coe T_Magma_68 -> T_RawMagma_36
du_rawMagma_112 ((T_Quasigroup_4246 -> T_Magma_68) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Quasigroup_4246 -> T_Magma_68
du_magma_4324 (T_Quasigroup_4246 -> AgdaAny
forall a b. a -> b
coe T_Quasigroup_4246
v0))
-- Algebra.Bundles.Quasigroup.rawQuasigroup
d_rawQuasigroup_4332 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Quasigroup_4246 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawQuasigroup_326
d_rawQuasigroup_4332 :: () -> () -> T_Quasigroup_4246 -> T_RawQuasigroup_326
d_rawQuasigroup_4332 ~()
v0 ~()
v1 T_Quasigroup_4246
v2 = T_Quasigroup_4246 -> T_RawQuasigroup_326
du_rawQuasigroup_4332 T_Quasigroup_4246
v2
du_rawQuasigroup_4332 ::
  T_Quasigroup_4246 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawQuasigroup_326
du_rawQuasigroup_4332 :: T_Quasigroup_4246 -> T_RawQuasigroup_326
du_rawQuasigroup_4332 T_Quasigroup_4246
v0
  = ((AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> T_RawQuasigroup_326)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_RawQuasigroup_326
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_RawQuasigroup_326
MAlonzo.Code.Algebra.Bundles.Raw.C_RawQuasigroup'46'constructor_4731
      (T_Quasigroup_4246 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__4268 (T_Quasigroup_4246 -> T_Quasigroup_4246
forall a b. a -> b
coe T_Quasigroup_4246
v0)) (T_Quasigroup_4246 -> AgdaAny -> AgdaAny -> AgdaAny
d__'92''92'__4270 (T_Quasigroup_4246 -> T_Quasigroup_4246
forall a b. a -> b
coe T_Quasigroup_4246
v0))
      (T_Quasigroup_4246 -> AgdaAny -> AgdaAny -> AgdaAny
d__'47''47'__4272 (T_Quasigroup_4246 -> T_Quasigroup_4246
forall a b. a -> b
coe T_Quasigroup_4246
v0))
-- Algebra.Bundles.Quasigroup._.//-rawMagma
d_'47''47''45'rawMagma_4336 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Quasigroup_4246 -> MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
d_'47''47''45'rawMagma_4336 :: () -> () -> T_Quasigroup_4246 -> T_RawMagma_36
d_'47''47''45'rawMagma_4336 ~()
v0 ~()
v1 T_Quasigroup_4246
v2
  = T_Quasigroup_4246 -> T_RawMagma_36
du_'47''47''45'rawMagma_4336 T_Quasigroup_4246
v2
du_'47''47''45'rawMagma_4336 ::
  T_Quasigroup_4246 -> MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
du_'47''47''45'rawMagma_4336 :: T_Quasigroup_4246 -> T_RawMagma_36
du_'47''47''45'rawMagma_4336 T_Quasigroup_4246
v0
  = (T_RawQuasigroup_326 -> T_RawMagma_36) -> AgdaAny -> T_RawMagma_36
forall a b. a -> b
coe
      T_RawQuasigroup_326 -> T_RawMagma_36
MAlonzo.Code.Algebra.Bundles.Raw.du_'47''47''45'rawMagma_356
      ((T_Quasigroup_4246 -> T_RawQuasigroup_326) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Quasigroup_4246 -> T_RawQuasigroup_326
du_rawQuasigroup_4332 (T_Quasigroup_4246 -> AgdaAny
forall a b. a -> b
coe T_Quasigroup_4246
v0))
-- Algebra.Bundles.Quasigroup._.\\-rawMagma
d_'92''92''45'rawMagma_4338 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Quasigroup_4246 -> MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
d_'92''92''45'rawMagma_4338 :: () -> () -> T_Quasigroup_4246 -> T_RawMagma_36
d_'92''92''45'rawMagma_4338 ~()
v0 ~()
v1 T_Quasigroup_4246
v2
  = T_Quasigroup_4246 -> T_RawMagma_36
du_'92''92''45'rawMagma_4338 T_Quasigroup_4246
v2
du_'92''92''45'rawMagma_4338 ::
  T_Quasigroup_4246 -> MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
du_'92''92''45'rawMagma_4338 :: T_Quasigroup_4246 -> T_RawMagma_36
du_'92''92''45'rawMagma_4338 T_Quasigroup_4246
v0
  = (T_RawQuasigroup_326 -> T_RawMagma_36) -> AgdaAny -> T_RawMagma_36
forall a b. a -> b
coe
      T_RawQuasigroup_326 -> T_RawMagma_36
MAlonzo.Code.Algebra.Bundles.Raw.du_'92''92''45'rawMagma_354
      ((T_Quasigroup_4246 -> T_RawQuasigroup_326) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Quasigroup_4246 -> T_RawQuasigroup_326
du_rawQuasigroup_4332 (T_Quasigroup_4246 -> AgdaAny
forall a b. a -> b
coe T_Quasigroup_4246
v0))
-- Algebra.Bundles.Quasigroup._.∙-rawMagma
d_'8729''45'rawMagma_4340 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Quasigroup_4246 -> MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
d_'8729''45'rawMagma_4340 :: () -> () -> T_Quasigroup_4246 -> T_RawMagma_36
d_'8729''45'rawMagma_4340 ~()
v0 ~()
v1 T_Quasigroup_4246
v2
  = T_Quasigroup_4246 -> T_RawMagma_36
du_'8729''45'rawMagma_4340 T_Quasigroup_4246
v2
du_'8729''45'rawMagma_4340 ::
  T_Quasigroup_4246 -> MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
du_'8729''45'rawMagma_4340 :: T_Quasigroup_4246 -> T_RawMagma_36
du_'8729''45'rawMagma_4340 T_Quasigroup_4246
v0
  = (T_RawQuasigroup_326 -> T_RawMagma_36) -> AgdaAny -> T_RawMagma_36
forall a b. a -> b
coe
      T_RawQuasigroup_326 -> T_RawMagma_36
MAlonzo.Code.Algebra.Bundles.Raw.du_'8729''45'rawMagma_352
      ((T_Quasigroup_4246 -> T_RawQuasigroup_326) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Quasigroup_4246 -> T_RawQuasigroup_326
du_rawQuasigroup_4332 (T_Quasigroup_4246 -> AgdaAny
forall a b. a -> b
coe T_Quasigroup_4246
v0))
-- Algebra.Bundles.Loop
d_Loop_4346 :: p -> p -> ()
d_Loop_4346 p
a0 p
a1 = ()
data T_Loop_4346
  = C_Loop'46'constructor_78267 (AgdaAny -> AgdaAny -> AgdaAny)
                                (AgdaAny -> AgdaAny -> AgdaAny) (AgdaAny -> AgdaAny -> AgdaAny)
                                AgdaAny MAlonzo.Code.Algebra.Structures.T_IsLoop_3026
-- Algebra.Bundles.Loop.Carrier
d_Carrier_4366 :: T_Loop_4346 -> ()
d_Carrier_4366 :: T_Loop_4346 -> ()
d_Carrier_4366 = T_Loop_4346 -> ()
forall a. a
erased
-- Algebra.Bundles.Loop._≈_
d__'8776'__4368 :: T_Loop_4346 -> AgdaAny -> AgdaAny -> ()
d__'8776'__4368 :: T_Loop_4346 -> AgdaAny -> AgdaAny -> ()
d__'8776'__4368 = T_Loop_4346 -> AgdaAny -> AgdaAny -> ()
forall a. a
erased
-- Algebra.Bundles.Loop._∙_
d__'8729'__4370 :: T_Loop_4346 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__4370 :: T_Loop_4346 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__4370 T_Loop_4346
v0
  = case T_Loop_4346 -> T_Loop_4346
forall a b. a -> b
coe T_Loop_4346
v0 of
      C_Loop'46'constructor_78267 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny -> AgdaAny
v5 AgdaAny
v6 T_IsLoop_3026
v7 -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v3
      T_Loop_4346
_ -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.Loop._\\_
d__'92''92'__4372 :: T_Loop_4346 -> AgdaAny -> AgdaAny -> AgdaAny
d__'92''92'__4372 :: T_Loop_4346 -> AgdaAny -> AgdaAny -> AgdaAny
d__'92''92'__4372 T_Loop_4346
v0
  = case T_Loop_4346 -> T_Loop_4346
forall a b. a -> b
coe T_Loop_4346
v0 of
      C_Loop'46'constructor_78267 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny -> AgdaAny
v5 AgdaAny
v6 T_IsLoop_3026
v7 -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v4
      T_Loop_4346
_ -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.Loop._//_
d__'47''47'__4374 :: T_Loop_4346 -> AgdaAny -> AgdaAny -> AgdaAny
d__'47''47'__4374 :: T_Loop_4346 -> AgdaAny -> AgdaAny -> AgdaAny
d__'47''47'__4374 T_Loop_4346
v0
  = case T_Loop_4346 -> T_Loop_4346
forall a b. a -> b
coe T_Loop_4346
v0 of
      C_Loop'46'constructor_78267 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny -> AgdaAny
v5 AgdaAny
v6 T_IsLoop_3026
v7 -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v5
      T_Loop_4346
_ -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.Loop.ε
d_ε_4376 :: T_Loop_4346 -> AgdaAny
d_ε_4376 :: T_Loop_4346 -> AgdaAny
d_ε_4376 T_Loop_4346
v0
  = case T_Loop_4346 -> T_Loop_4346
forall a b. a -> b
coe T_Loop_4346
v0 of
      C_Loop'46'constructor_78267 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny -> AgdaAny
v5 AgdaAny
v6 T_IsLoop_3026
v7 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v6
      T_Loop_4346
_ -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.Loop.isLoop
d_isLoop_4378 ::
  T_Loop_4346 -> MAlonzo.Code.Algebra.Structures.T_IsLoop_3026
d_isLoop_4378 :: T_Loop_4346 -> T_IsLoop_3026
d_isLoop_4378 T_Loop_4346
v0
  = case T_Loop_4346 -> T_Loop_4346
forall a b. a -> b
coe T_Loop_4346
v0 of
      C_Loop'46'constructor_78267 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny -> AgdaAny
v5 AgdaAny
v6 T_IsLoop_3026
v7 -> T_IsLoop_3026 -> T_IsLoop_3026
forall a b. a -> b
coe T_IsLoop_3026
v7
      T_Loop_4346
_ -> T_IsLoop_3026
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.Loop._.//-cong
d_'47''47''45'cong_4382 ::
  T_Loop_4346 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'47''47''45'cong_4382 :: T_Loop_4346
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'47''47''45'cong_4382 T_Loop_4346
v0
  = (T_IsQuasigroup_2944
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsQuasigroup_2944
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'47''47''45'cong_2966
      ((T_IsLoop_3026 -> T_IsQuasigroup_2944) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsLoop_3026 -> T_IsQuasigroup_2944
MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040
         ((T_Loop_4346 -> T_IsLoop_3026) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Loop_4346 -> T_IsLoop_3026
d_isLoop_4378 (T_Loop_4346 -> AgdaAny
forall a b. a -> b
coe T_Loop_4346
v0)))
-- Algebra.Bundles.Loop._.//-congʳ
d_'47''47''45'cong'691'_4384 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Loop_4346 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'47''47''45'cong'691'_4384 :: ()
-> ()
-> T_Loop_4346
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'47''47''45'cong'691'_4384 ~()
v0 ~()
v1 T_Loop_4346
v2
  = T_Loop_4346 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'47''47''45'cong'691'_4384 T_Loop_4346
v2
du_'47''47''45'cong'691'_4384 ::
  T_Loop_4346 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'47''47''45'cong'691'_4384 :: T_Loop_4346 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'47''47''45'cong'691'_4384 T_Loop_4346
v0
  = let v1 :: T_IsLoop_3026
v1 = T_Loop_4346 -> T_IsLoop_3026
d_isLoop_4378 (T_Loop_4346 -> T_Loop_4346
forall a b. a -> b
coe T_Loop_4346
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsQuasigroup_2944
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsQuasigroup_2944
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'47''47''45'cong'691'_3006
         ((T_IsLoop_3026 -> T_IsQuasigroup_2944) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLoop_3026 -> T_IsQuasigroup_2944
MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040 (T_IsLoop_3026 -> AgdaAny
forall a b. a -> b
coe T_IsLoop_3026
v1)))
-- Algebra.Bundles.Loop._.//-congˡ
d_'47''47''45'cong'737'_4386 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Loop_4346 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'47''47''45'cong'737'_4386 :: ()
-> ()
-> T_Loop_4346
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'47''47''45'cong'737'_4386 ~()
v0 ~()
v1 T_Loop_4346
v2
  = T_Loop_4346 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'47''47''45'cong'737'_4386 T_Loop_4346
v2
du_'47''47''45'cong'737'_4386 ::
  T_Loop_4346 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'47''47''45'cong'737'_4386 :: T_Loop_4346 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'47''47''45'cong'737'_4386 T_Loop_4346
v0
  = let v1 :: T_IsLoop_3026
v1 = T_Loop_4346 -> T_IsLoop_3026
d_isLoop_4378 (T_Loop_4346 -> T_Loop_4346
forall a b. a -> b
coe T_Loop_4346
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsQuasigroup_2944
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsQuasigroup_2944
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'47''47''45'cong'737'_3002
         ((T_IsLoop_3026 -> T_IsQuasigroup_2944) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLoop_3026 -> T_IsQuasigroup_2944
MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040 (T_IsLoop_3026 -> AgdaAny
forall a b. a -> b
coe T_IsLoop_3026
v1)))
-- Algebra.Bundles.Loop._.\\-cong
d_'92''92''45'cong_4388 ::
  T_Loop_4346 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'92''92''45'cong_4388 :: T_Loop_4346
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'92''92''45'cong_4388 T_Loop_4346
v0
  = (T_IsQuasigroup_2944
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsQuasigroup_2944
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'92''92''45'cong_2964
      ((T_IsLoop_3026 -> T_IsQuasigroup_2944) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsLoop_3026 -> T_IsQuasigroup_2944
MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040
         ((T_Loop_4346 -> T_IsLoop_3026) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Loop_4346 -> T_IsLoop_3026
d_isLoop_4378 (T_Loop_4346 -> AgdaAny
forall a b. a -> b
coe T_Loop_4346
v0)))
-- Algebra.Bundles.Loop._.\\-congʳ
d_'92''92''45'cong'691'_4390 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Loop_4346 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'92''92''45'cong'691'_4390 :: ()
-> ()
-> T_Loop_4346
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'92''92''45'cong'691'_4390 ~()
v0 ~()
v1 T_Loop_4346
v2
  = T_Loop_4346 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'92''92''45'cong'691'_4390 T_Loop_4346
v2
du_'92''92''45'cong'691'_4390 ::
  T_Loop_4346 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'92''92''45'cong'691'_4390 :: T_Loop_4346 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'92''92''45'cong'691'_4390 T_Loop_4346
v0
  = let v1 :: T_IsLoop_3026
v1 = T_Loop_4346 -> T_IsLoop_3026
d_isLoop_4378 (T_Loop_4346 -> T_Loop_4346
forall a b. a -> b
coe T_Loop_4346
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsQuasigroup_2944
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsQuasigroup_2944
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'92''92''45'cong'691'_2998
         ((T_IsLoop_3026 -> T_IsQuasigroup_2944) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLoop_3026 -> T_IsQuasigroup_2944
MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040 (T_IsLoop_3026 -> AgdaAny
forall a b. a -> b
coe T_IsLoop_3026
v1)))
-- Algebra.Bundles.Loop._.\\-congˡ
d_'92''92''45'cong'737'_4392 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Loop_4346 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'92''92''45'cong'737'_4392 :: ()
-> ()
-> T_Loop_4346
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'92''92''45'cong'737'_4392 ~()
v0 ~()
v1 T_Loop_4346
v2
  = T_Loop_4346 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'92''92''45'cong'737'_4392 T_Loop_4346
v2
du_'92''92''45'cong'737'_4392 ::
  T_Loop_4346 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'92''92''45'cong'737'_4392 :: T_Loop_4346 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'92''92''45'cong'737'_4392 T_Loop_4346
v0
  = let v1 :: T_IsLoop_3026
v1 = T_Loop_4346 -> T_IsLoop_3026
d_isLoop_4378 (T_Loop_4346 -> T_Loop_4346
forall a b. a -> b
coe T_Loop_4346
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsQuasigroup_2944
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsQuasigroup_2944
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'92''92''45'cong'737'_2994
         ((T_IsLoop_3026 -> T_IsQuasigroup_2944) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLoop_3026 -> T_IsQuasigroup_2944
MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040 (T_IsLoop_3026 -> AgdaAny
forall a b. a -> b
coe T_IsLoop_3026
v1)))
-- Algebra.Bundles.Loop._.identity
d_identity_4394 ::
  T_Loop_4346 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_identity_4394 :: T_Loop_4346 -> T_Σ_14
d_identity_4394 T_Loop_4346
v0
  = (T_IsLoop_3026 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsLoop_3026 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_identity_3042
      ((T_Loop_4346 -> T_IsLoop_3026) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Loop_4346 -> T_IsLoop_3026
d_isLoop_4378 (T_Loop_4346 -> AgdaAny
forall a b. a -> b
coe T_Loop_4346
v0))
-- Algebra.Bundles.Loop._.identityʳ
d_identity'691'_4396 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Loop_4346 -> AgdaAny -> AgdaAny
d_identity'691'_4396 :: () -> () -> T_Loop_4346 -> AgdaAny -> AgdaAny
d_identity'691'_4396 ~()
v0 ~()
v1 T_Loop_4346
v2 = T_Loop_4346 -> AgdaAny -> AgdaAny
du_identity'691'_4396 T_Loop_4346
v2
du_identity'691'_4396 :: T_Loop_4346 -> AgdaAny -> AgdaAny
du_identity'691'_4396 :: T_Loop_4346 -> AgdaAny -> AgdaAny
du_identity'691'_4396 T_Loop_4346
v0
  = (T_IsLoop_3026 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsLoop_3026 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_identity'691'_3094
      ((T_Loop_4346 -> T_IsLoop_3026) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Loop_4346 -> T_IsLoop_3026
d_isLoop_4378 (T_Loop_4346 -> AgdaAny
forall a b. a -> b
coe T_Loop_4346
v0))
-- Algebra.Bundles.Loop._.identityˡ
d_identity'737'_4398 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Loop_4346 -> AgdaAny -> AgdaAny
d_identity'737'_4398 :: () -> () -> T_Loop_4346 -> AgdaAny -> AgdaAny
d_identity'737'_4398 ~()
v0 ~()
v1 T_Loop_4346
v2 = T_Loop_4346 -> AgdaAny -> AgdaAny
du_identity'737'_4398 T_Loop_4346
v2
du_identity'737'_4398 :: T_Loop_4346 -> AgdaAny -> AgdaAny
du_identity'737'_4398 :: T_Loop_4346 -> AgdaAny -> AgdaAny
du_identity'737'_4398 T_Loop_4346
v0
  = (T_IsLoop_3026 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsLoop_3026 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_identity'737'_3092
      ((T_Loop_4346 -> T_IsLoop_3026) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Loop_4346 -> T_IsLoop_3026
d_isLoop_4378 (T_Loop_4346 -> AgdaAny
forall a b. a -> b
coe T_Loop_4346
v0))
-- Algebra.Bundles.Loop._.isEquivalence
d_isEquivalence_4400 ::
  T_Loop_4346 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_4400 :: T_Loop_4346 -> T_IsEquivalence_26
d_isEquivalence_4400 T_Loop_4346
v0
  = (T_IsMagma_176 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
      ((T_IsQuasigroup_2944 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsQuasigroup_2944 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_2962
         ((T_IsLoop_3026 -> T_IsQuasigroup_2944) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsLoop_3026 -> T_IsQuasigroup_2944
MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040
            ((T_Loop_4346 -> T_IsLoop_3026) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Loop_4346 -> T_IsLoop_3026
d_isLoop_4378 (T_Loop_4346 -> AgdaAny
forall a b. a -> b
coe T_Loop_4346
v0))))
-- Algebra.Bundles.Loop._.isMagma
d_isMagma_4402 ::
  T_Loop_4346 -> MAlonzo.Code.Algebra.Structures.T_IsMagma_176
d_isMagma_4402 :: T_Loop_4346 -> T_IsMagma_176
d_isMagma_4402 T_Loop_4346
v0
  = (T_IsQuasigroup_2944 -> T_IsMagma_176) -> AgdaAny -> T_IsMagma_176
forall a b. a -> b
coe
      T_IsQuasigroup_2944 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_2962
      ((T_IsLoop_3026 -> T_IsQuasigroup_2944) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsLoop_3026 -> T_IsQuasigroup_2944
MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040
         ((T_Loop_4346 -> T_IsLoop_3026) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Loop_4346 -> T_IsLoop_3026
d_isLoop_4378 (T_Loop_4346 -> AgdaAny
forall a b. a -> b
coe T_Loop_4346
v0)))
-- Algebra.Bundles.Loop._.isPartialEquivalence
d_isPartialEquivalence_4404 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Loop_4346 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_4404 :: () -> () -> T_Loop_4346 -> T_IsPartialEquivalence_16
d_isPartialEquivalence_4404 ~()
v0 ~()
v1 T_Loop_4346
v2
  = T_Loop_4346 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_4404 T_Loop_4346
v2
du_isPartialEquivalence_4404 ::
  T_Loop_4346 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_4404 :: T_Loop_4346 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_4404 T_Loop_4346
v0
  = let v1 :: T_IsLoop_3026
v1 = T_Loop_4346 -> T_IsLoop_3026
d_isLoop_4378 (T_Loop_4346 -> T_Loop_4346
forall a b. a -> b
coe T_Loop_4346
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsQuasigroup_2944
v2
             = T_IsLoop_3026 -> T_IsQuasigroup_2944
MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040 (T_IsLoop_3026 -> T_IsLoop_3026
forall a b. a -> b
coe T_IsLoop_3026
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsMagma_176
v3
                = T_IsQuasigroup_2944 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_2962 (T_IsQuasigroup_2944 -> T_IsQuasigroup_2944
forall a b. a -> b
coe T_IsQuasigroup_2944
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsEquivalence_26 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsEquivalence_26 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
               ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v3)))))
-- Algebra.Bundles.Loop._.isQuasigroup
d_isQuasigroup_4406 ::
  T_Loop_4346 -> MAlonzo.Code.Algebra.Structures.T_IsQuasigroup_2944
d_isQuasigroup_4406 :: T_Loop_4346 -> T_IsQuasigroup_2944
d_isQuasigroup_4406 T_Loop_4346
v0
  = (T_IsLoop_3026 -> T_IsQuasigroup_2944)
-> AgdaAny -> T_IsQuasigroup_2944
forall a b. a -> b
coe
      T_IsLoop_3026 -> T_IsQuasigroup_2944
MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040
      ((T_Loop_4346 -> T_IsLoop_3026) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Loop_4346 -> T_IsLoop_3026
d_isLoop_4378 (T_Loop_4346 -> AgdaAny
forall a b. a -> b
coe T_Loop_4346
v0))
-- Algebra.Bundles.Loop._.leftDivides
d_leftDivides_4408 ::
  T_Loop_4346 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_leftDivides_4408 :: T_Loop_4346 -> T_Σ_14
d_leftDivides_4408 T_Loop_4346
v0
  = (T_IsQuasigroup_2944 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsQuasigroup_2944 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_leftDivides_2968
      ((T_IsLoop_3026 -> T_IsQuasigroup_2944) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsLoop_3026 -> T_IsQuasigroup_2944
MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040
         ((T_Loop_4346 -> T_IsLoop_3026) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Loop_4346 -> T_IsLoop_3026
d_isLoop_4378 (T_Loop_4346 -> AgdaAny
forall a b. a -> b
coe T_Loop_4346
v0)))
-- Algebra.Bundles.Loop._.leftDividesʳ
d_leftDivides'691'_4410 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Loop_4346 -> AgdaAny -> AgdaAny -> AgdaAny
d_leftDivides'691'_4410 :: () -> () -> T_Loop_4346 -> AgdaAny -> AgdaAny -> AgdaAny
d_leftDivides'691'_4410 ~()
v0 ~()
v1 T_Loop_4346
v2 = T_Loop_4346 -> AgdaAny -> AgdaAny -> AgdaAny
du_leftDivides'691'_4410 T_Loop_4346
v2
du_leftDivides'691'_4410 ::
  T_Loop_4346 -> AgdaAny -> AgdaAny -> AgdaAny
du_leftDivides'691'_4410 :: T_Loop_4346 -> AgdaAny -> AgdaAny -> AgdaAny
du_leftDivides'691'_4410 T_Loop_4346
v0
  = let v1 :: T_IsLoop_3026
v1 = T_Loop_4346 -> T_IsLoop_3026
d_isLoop_4378 (T_Loop_4346 -> T_Loop_4346
forall a b. a -> b
coe T_Loop_4346
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsQuasigroup_2944 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsQuasigroup_2944 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_leftDivides'691'_3012
         ((T_IsLoop_3026 -> T_IsQuasigroup_2944) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLoop_3026 -> T_IsQuasigroup_2944
MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040 (T_IsLoop_3026 -> AgdaAny
forall a b. a -> b
coe T_IsLoop_3026
v1)))
-- Algebra.Bundles.Loop._.leftDividesˡ
d_leftDivides'737'_4412 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Loop_4346 -> AgdaAny -> AgdaAny -> AgdaAny
d_leftDivides'737'_4412 :: () -> () -> T_Loop_4346 -> AgdaAny -> AgdaAny -> AgdaAny
d_leftDivides'737'_4412 ~()
v0 ~()
v1 T_Loop_4346
v2 = T_Loop_4346 -> AgdaAny -> AgdaAny -> AgdaAny
du_leftDivides'737'_4412 T_Loop_4346
v2
du_leftDivides'737'_4412 ::
  T_Loop_4346 -> AgdaAny -> AgdaAny -> AgdaAny
du_leftDivides'737'_4412 :: T_Loop_4346 -> AgdaAny -> AgdaAny -> AgdaAny
du_leftDivides'737'_4412 T_Loop_4346
v0
  = let v1 :: T_IsLoop_3026
v1 = T_Loop_4346 -> T_IsLoop_3026
d_isLoop_4378 (T_Loop_4346 -> T_Loop_4346
forall a b. a -> b
coe T_Loop_4346
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsQuasigroup_2944 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsQuasigroup_2944 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_leftDivides'737'_3010
         ((T_IsLoop_3026 -> T_IsQuasigroup_2944) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLoop_3026 -> T_IsQuasigroup_2944
MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040 (T_IsLoop_3026 -> AgdaAny
forall a b. a -> b
coe T_IsLoop_3026
v1)))
-- Algebra.Bundles.Loop._.refl
d_refl_4414 :: T_Loop_4346 -> AgdaAny -> AgdaAny
d_refl_4414 :: T_Loop_4346 -> AgdaAny -> AgdaAny
d_refl_4414 T_Loop_4346
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_34
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
         ((T_IsQuasigroup_2944 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsQuasigroup_2944 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_2962
            ((T_IsLoop_3026 -> T_IsQuasigroup_2944) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsLoop_3026 -> T_IsQuasigroup_2944
MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040
               ((T_Loop_4346 -> T_IsLoop_3026) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Loop_4346 -> T_IsLoop_3026
d_isLoop_4378 (T_Loop_4346 -> AgdaAny
forall a b. a -> b
coe T_Loop_4346
v0)))))
-- Algebra.Bundles.Loop._.reflexive
d_reflexive_4416 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Loop_4346 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_4416 :: ()
-> ()
-> T_Loop_4346
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_4416 ~()
v0 ~()
v1 T_Loop_4346
v2 = T_Loop_4346 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_4416 T_Loop_4346
v2
du_reflexive_4416 ::
  T_Loop_4346 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_4416 :: T_Loop_4346 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_4416 T_Loop_4346
v0
  = let v1 :: T_IsLoop_3026
v1 = T_Loop_4346 -> T_IsLoop_3026
d_isLoop_4378 (T_Loop_4346 -> T_Loop_4346
forall a b. a -> b
coe T_Loop_4346
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsQuasigroup_2944
v2
             = T_IsLoop_3026 -> T_IsQuasigroup_2944
MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040 (T_IsLoop_3026 -> T_IsLoop_3026
forall a b. a -> b
coe T_IsLoop_3026
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsMagma_176
v3
                = T_IsQuasigroup_2944 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_2962 (T_IsQuasigroup_2944 -> T_IsQuasigroup_2944
forall a b. a -> b
coe T_IsQuasigroup_2944
v2) in
          (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
            (\ AgdaAny
v4 AgdaAny
v5 AgdaAny
v6 ->
               (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                 T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
                 ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v3))
                 AgdaAny
v4)))
-- Algebra.Bundles.Loop._.rightDivides
d_rightDivides_4418 ::
  T_Loop_4346 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_rightDivides_4418 :: T_Loop_4346 -> T_Σ_14
d_rightDivides_4418 T_Loop_4346
v0
  = (T_IsQuasigroup_2944 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsQuasigroup_2944 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_rightDivides_2970
      ((T_IsLoop_3026 -> T_IsQuasigroup_2944) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsLoop_3026 -> T_IsQuasigroup_2944
MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040
         ((T_Loop_4346 -> T_IsLoop_3026) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Loop_4346 -> T_IsLoop_3026
d_isLoop_4378 (T_Loop_4346 -> AgdaAny
forall a b. a -> b
coe T_Loop_4346
v0)))
-- Algebra.Bundles.Loop._.rightDividesʳ
d_rightDivides'691'_4420 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Loop_4346 -> AgdaAny -> AgdaAny -> AgdaAny
d_rightDivides'691'_4420 :: () -> () -> T_Loop_4346 -> AgdaAny -> AgdaAny -> AgdaAny
d_rightDivides'691'_4420 ~()
v0 ~()
v1 T_Loop_4346
v2 = T_Loop_4346 -> AgdaAny -> AgdaAny -> AgdaAny
du_rightDivides'691'_4420 T_Loop_4346
v2
du_rightDivides'691'_4420 ::
  T_Loop_4346 -> AgdaAny -> AgdaAny -> AgdaAny
du_rightDivides'691'_4420 :: T_Loop_4346 -> AgdaAny -> AgdaAny -> AgdaAny
du_rightDivides'691'_4420 T_Loop_4346
v0
  = let v1 :: T_IsLoop_3026
v1 = T_Loop_4346 -> T_IsLoop_3026
d_isLoop_4378 (T_Loop_4346 -> T_Loop_4346
forall a b. a -> b
coe T_Loop_4346
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsQuasigroup_2944 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsQuasigroup_2944 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_rightDivides'691'_3016
         ((T_IsLoop_3026 -> T_IsQuasigroup_2944) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLoop_3026 -> T_IsQuasigroup_2944
MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040 (T_IsLoop_3026 -> AgdaAny
forall a b. a -> b
coe T_IsLoop_3026
v1)))
-- Algebra.Bundles.Loop._.rightDividesˡ
d_rightDivides'737'_4422 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Loop_4346 -> AgdaAny -> AgdaAny -> AgdaAny
d_rightDivides'737'_4422 :: () -> () -> T_Loop_4346 -> AgdaAny -> AgdaAny -> AgdaAny
d_rightDivides'737'_4422 ~()
v0 ~()
v1 T_Loop_4346
v2 = T_Loop_4346 -> AgdaAny -> AgdaAny -> AgdaAny
du_rightDivides'737'_4422 T_Loop_4346
v2
du_rightDivides'737'_4422 ::
  T_Loop_4346 -> AgdaAny -> AgdaAny -> AgdaAny
du_rightDivides'737'_4422 :: T_Loop_4346 -> AgdaAny -> AgdaAny -> AgdaAny
du_rightDivides'737'_4422 T_Loop_4346
v0
  = let v1 :: T_IsLoop_3026
v1 = T_Loop_4346 -> T_IsLoop_3026
d_isLoop_4378 (T_Loop_4346 -> T_Loop_4346
forall a b. a -> b
coe T_Loop_4346
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsQuasigroup_2944 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsQuasigroup_2944 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_rightDivides'737'_3014
         ((T_IsLoop_3026 -> T_IsQuasigroup_2944) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLoop_3026 -> T_IsQuasigroup_2944
MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040 (T_IsLoop_3026 -> AgdaAny
forall a b. a -> b
coe T_IsLoop_3026
v1)))
-- Algebra.Bundles.Loop._.setoid
d_setoid_4424 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Loop_4346 -> MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_4424 :: () -> () -> T_Loop_4346 -> T_Setoid_44
d_setoid_4424 ~()
v0 ~()
v1 T_Loop_4346
v2 = T_Loop_4346 -> T_Setoid_44
du_setoid_4424 T_Loop_4346
v2
du_setoid_4424 ::
  T_Loop_4346 -> MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_4424 :: T_Loop_4346 -> T_Setoid_44
du_setoid_4424 T_Loop_4346
v0
  = let v1 :: T_IsLoop_3026
v1 = T_Loop_4346 -> T_IsLoop_3026
d_isLoop_4378 (T_Loop_4346 -> T_Loop_4346
forall a b. a -> b
coe T_Loop_4346
v0) in
    AgdaAny -> T_Setoid_44
forall a b. a -> b
coe
      (let v2 :: T_IsQuasigroup_2944
v2
             = T_IsLoop_3026 -> T_IsQuasigroup_2944
MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040 (T_IsLoop_3026 -> T_IsLoop_3026
forall a b. a -> b
coe T_IsLoop_3026
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsMagma_176 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMagma_176 -> T_Setoid_44
MAlonzo.Code.Algebra.Structures.du_setoid_200
            ((T_IsQuasigroup_2944 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroup_2944 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_2962 (T_IsQuasigroup_2944 -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroup_2944
v2))))
-- Algebra.Bundles.Loop._.sym
d_sym_4426 ::
  T_Loop_4346 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_4426 :: T_Loop_4346 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_4426 T_Loop_4346
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_36
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
         ((T_IsQuasigroup_2944 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsQuasigroup_2944 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_2962
            ((T_IsLoop_3026 -> T_IsQuasigroup_2944) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsLoop_3026 -> T_IsQuasigroup_2944
MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040
               ((T_Loop_4346 -> T_IsLoop_3026) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Loop_4346 -> T_IsLoop_3026
d_isLoop_4378 (T_Loop_4346 -> AgdaAny
forall a b. a -> b
coe T_Loop_4346
v0)))))
-- Algebra.Bundles.Loop._.trans
d_trans_4428 ::
  T_Loop_4346 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_4428 :: T_Loop_4346
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_4428 T_Loop_4346
v0
  = (T_IsEquivalence_26
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_38
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
         ((T_IsQuasigroup_2944 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsQuasigroup_2944 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_2962
            ((T_IsLoop_3026 -> T_IsQuasigroup_2944) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsLoop_3026 -> T_IsQuasigroup_2944
MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040
               ((T_Loop_4346 -> T_IsLoop_3026) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Loop_4346 -> T_IsLoop_3026
d_isLoop_4378 (T_Loop_4346 -> AgdaAny
forall a b. a -> b
coe T_Loop_4346
v0)))))
-- Algebra.Bundles.Loop._.∙-cong
d_'8729''45'cong_4430 ::
  T_Loop_4346 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_4430 :: T_Loop_4346
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_4430 T_Loop_4346
v0
  = (T_IsMagma_176
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsMagma_176
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_186
      ((T_IsQuasigroup_2944 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsQuasigroup_2944 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_2962
         ((T_IsLoop_3026 -> T_IsQuasigroup_2944) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsLoop_3026 -> T_IsQuasigroup_2944
MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040
            ((T_Loop_4346 -> T_IsLoop_3026) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Loop_4346 -> T_IsLoop_3026
d_isLoop_4378 (T_Loop_4346 -> AgdaAny
forall a b. a -> b
coe T_Loop_4346
v0))))
-- Algebra.Bundles.Loop._.∙-congʳ
d_'8729''45'cong'691'_4432 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Loop_4346 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_4432 :: ()
-> ()
-> T_Loop_4346
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_4432 ~()
v0 ~()
v1 T_Loop_4346
v2
  = T_Loop_4346 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_4432 T_Loop_4346
v2
du_'8729''45'cong'691'_4432 ::
  T_Loop_4346 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_4432 :: T_Loop_4346 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_4432 T_Loop_4346
v0
  = let v1 :: T_IsLoop_3026
v1 = T_Loop_4346 -> T_IsLoop_3026
d_isLoop_4378 (T_Loop_4346 -> T_Loop_4346
forall a b. a -> b
coe T_Loop_4346
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsQuasigroup_2944
v2
             = T_IsLoop_3026 -> T_IsQuasigroup_2944
MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040 (T_IsLoop_3026 -> T_IsLoop_3026
forall a b. a -> b
coe T_IsLoop_3026
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'691'_206
            ((T_IsQuasigroup_2944 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroup_2944 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_2962 (T_IsQuasigroup_2944 -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroup_2944
v2))))
-- Algebra.Bundles.Loop._.∙-congˡ
d_'8729''45'cong'737'_4434 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Loop_4346 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_4434 :: ()
-> ()
-> T_Loop_4346
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_4434 ~()
v0 ~()
v1 T_Loop_4346
v2
  = T_Loop_4346 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_4434 T_Loop_4346
v2
du_'8729''45'cong'737'_4434 ::
  T_Loop_4346 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_4434 :: T_Loop_4346 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_4434 T_Loop_4346
v0
  = let v1 :: T_IsLoop_3026
v1 = T_Loop_4346 -> T_IsLoop_3026
d_isLoop_4378 (T_Loop_4346 -> T_Loop_4346
forall a b. a -> b
coe T_Loop_4346
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsQuasigroup_2944
v2
             = T_IsLoop_3026 -> T_IsQuasigroup_2944
MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040 (T_IsLoop_3026 -> T_IsLoop_3026
forall a b. a -> b
coe T_IsLoop_3026
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'737'_202
            ((T_IsQuasigroup_2944 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroup_2944 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_2962 (T_IsQuasigroup_2944 -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroup_2944
v2))))
-- Algebra.Bundles.Loop.rawLoop
d_rawLoop_4436 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Loop_4346 -> MAlonzo.Code.Algebra.Bundles.Raw.T_RawLoop_366
d_rawLoop_4436 :: () -> () -> T_Loop_4346 -> T_RawLoop_366
d_rawLoop_4436 ~()
v0 ~()
v1 T_Loop_4346
v2 = T_Loop_4346 -> T_RawLoop_366
du_rawLoop_4436 T_Loop_4346
v2
du_rawLoop_4436 ::
  T_Loop_4346 -> MAlonzo.Code.Algebra.Bundles.Raw.T_RawLoop_366
du_rawLoop_4436 :: T_Loop_4346 -> T_RawLoop_366
du_rawLoop_4436 T_Loop_4346
v0
  = ((AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> T_RawLoop_366)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_RawLoop_366
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_RawLoop_366
MAlonzo.Code.Algebra.Bundles.Raw.C_RawLoop'46'constructor_5465
      (T_Loop_4346 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__4370 (T_Loop_4346 -> T_Loop_4346
forall a b. a -> b
coe T_Loop_4346
v0)) (T_Loop_4346 -> AgdaAny -> AgdaAny -> AgdaAny
d__'92''92'__4372 (T_Loop_4346 -> T_Loop_4346
forall a b. a -> b
coe T_Loop_4346
v0))
      (T_Loop_4346 -> AgdaAny -> AgdaAny -> AgdaAny
d__'47''47'__4374 (T_Loop_4346 -> T_Loop_4346
forall a b. a -> b
coe T_Loop_4346
v0)) (T_Loop_4346 -> AgdaAny
d_ε_4376 (T_Loop_4346 -> T_Loop_4346
forall a b. a -> b
coe T_Loop_4346
v0))
-- Algebra.Bundles.Loop.quasigroup
d_quasigroup_4438 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Loop_4346 -> T_Quasigroup_4246
d_quasigroup_4438 :: () -> () -> T_Loop_4346 -> T_Quasigroup_4246
d_quasigroup_4438 ~()
v0 ~()
v1 T_Loop_4346
v2 = T_Loop_4346 -> T_Quasigroup_4246
du_quasigroup_4438 T_Loop_4346
v2
du_quasigroup_4438 :: T_Loop_4346 -> T_Quasigroup_4246
du_quasigroup_4438 :: T_Loop_4346 -> T_Quasigroup_4246
du_quasigroup_4438 T_Loop_4346
v0
  = ((AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> T_IsQuasigroup_2944
 -> T_Quasigroup_4246)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsQuasigroup_2944
-> T_Quasigroup_4246
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsQuasigroup_2944
-> T_Quasigroup_4246
C_Quasigroup'46'constructor_76277 (T_Loop_4346 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__4370 (T_Loop_4346 -> T_Loop_4346
forall a b. a -> b
coe T_Loop_4346
v0))
      (T_Loop_4346 -> AgdaAny -> AgdaAny -> AgdaAny
d__'92''92'__4372 (T_Loop_4346 -> T_Loop_4346
forall a b. a -> b
coe T_Loop_4346
v0)) (T_Loop_4346 -> AgdaAny -> AgdaAny -> AgdaAny
d__'47''47'__4374 (T_Loop_4346 -> T_Loop_4346
forall a b. a -> b
coe T_Loop_4346
v0))
      (T_IsLoop_3026 -> T_IsQuasigroup_2944
MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040
         ((T_Loop_4346 -> T_IsLoop_3026) -> AgdaAny -> T_IsLoop_3026
forall a b. a -> b
coe T_Loop_4346 -> T_IsLoop_3026
d_isLoop_4378 (T_Loop_4346 -> AgdaAny
forall a b. a -> b
coe T_Loop_4346
v0)))
-- Algebra.Bundles.Loop._._≉_
d__'8777'__4442 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Loop_4346 -> AgdaAny -> AgdaAny -> ()
d__'8777'__4442 :: () -> () -> T_Loop_4346 -> AgdaAny -> AgdaAny -> ()
d__'8777'__4442 = () -> () -> T_Loop_4346 -> AgdaAny -> AgdaAny -> ()
forall a. a
erased
-- Algebra.Bundles.Loop._.//-rawMagma
d_'47''47''45'rawMagma_4444 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Loop_4346 -> MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
d_'47''47''45'rawMagma_4444 :: () -> () -> T_Loop_4346 -> T_RawMagma_36
d_'47''47''45'rawMagma_4444 ~()
v0 ~()
v1 T_Loop_4346
v2
  = T_Loop_4346 -> T_RawMagma_36
du_'47''47''45'rawMagma_4444 T_Loop_4346
v2
du_'47''47''45'rawMagma_4444 ::
  T_Loop_4346 -> MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
du_'47''47''45'rawMagma_4444 :: T_Loop_4346 -> T_RawMagma_36
du_'47''47''45'rawMagma_4444 T_Loop_4346
v0
  = let v1 :: t
v1 = (T_Loop_4346 -> T_Quasigroup_4246) -> AgdaAny -> t
forall a b. a -> b
coe T_Loop_4346 -> T_Quasigroup_4246
du_quasigroup_4438 (T_Loop_4346 -> AgdaAny
forall a b. a -> b
coe T_Loop_4346
v0) in
    AgdaAny -> T_RawMagma_36
forall a b. a -> b
coe
      ((T_RawQuasigroup_326 -> T_RawMagma_36) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_RawQuasigroup_326 -> T_RawMagma_36
MAlonzo.Code.Algebra.Bundles.Raw.du_'47''47''45'rawMagma_356
         ((T_Quasigroup_4246 -> T_RawQuasigroup_326) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Quasigroup_4246 -> T_RawQuasigroup_326
du_rawQuasigroup_4332 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1)))
-- Algebra.Bundles.Loop._.\\-rawMagma
d_'92''92''45'rawMagma_4446 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Loop_4346 -> MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
d_'92''92''45'rawMagma_4446 :: () -> () -> T_Loop_4346 -> T_RawMagma_36
d_'92''92''45'rawMagma_4446 ~()
v0 ~()
v1 T_Loop_4346
v2
  = T_Loop_4346 -> T_RawMagma_36
du_'92''92''45'rawMagma_4446 T_Loop_4346
v2
du_'92''92''45'rawMagma_4446 ::
  T_Loop_4346 -> MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
du_'92''92''45'rawMagma_4446 :: T_Loop_4346 -> T_RawMagma_36
du_'92''92''45'rawMagma_4446 T_Loop_4346
v0
  = let v1 :: t
v1 = (T_Loop_4346 -> T_Quasigroup_4246) -> AgdaAny -> t
forall a b. a -> b
coe T_Loop_4346 -> T_Quasigroup_4246
du_quasigroup_4438 (T_Loop_4346 -> AgdaAny
forall a b. a -> b
coe T_Loop_4346
v0) in
    AgdaAny -> T_RawMagma_36
forall a b. a -> b
coe
      ((T_RawQuasigroup_326 -> T_RawMagma_36) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_RawQuasigroup_326 -> T_RawMagma_36
MAlonzo.Code.Algebra.Bundles.Raw.du_'92''92''45'rawMagma_354
         ((T_Quasigroup_4246 -> T_RawQuasigroup_326) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Quasigroup_4246 -> T_RawQuasigroup_326
du_rawQuasigroup_4332 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1)))
-- Algebra.Bundles.Loop._.∙-rawMagma
d_'8729''45'rawMagma_4448 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Loop_4346 -> MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
d_'8729''45'rawMagma_4448 :: () -> () -> T_Loop_4346 -> T_RawMagma_36
d_'8729''45'rawMagma_4448 ~()
v0 ~()
v1 T_Loop_4346
v2
  = T_Loop_4346 -> T_RawMagma_36
du_'8729''45'rawMagma_4448 T_Loop_4346
v2
du_'8729''45'rawMagma_4448 ::
  T_Loop_4346 -> MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
du_'8729''45'rawMagma_4448 :: T_Loop_4346 -> T_RawMagma_36
du_'8729''45'rawMagma_4448 T_Loop_4346
v0
  = let v1 :: t
v1 = (T_Loop_4346 -> T_Quasigroup_4246) -> AgdaAny -> t
forall a b. a -> b
coe T_Loop_4346 -> T_Quasigroup_4246
du_quasigroup_4438 (T_Loop_4346 -> AgdaAny
forall a b. a -> b
coe T_Loop_4346
v0) in
    AgdaAny -> T_RawMagma_36
forall a b. a -> b
coe
      ((T_RawQuasigroup_326 -> T_RawMagma_36) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_RawQuasigroup_326 -> T_RawMagma_36
MAlonzo.Code.Algebra.Bundles.Raw.du_'8729''45'rawMagma_352
         ((T_Quasigroup_4246 -> T_RawQuasigroup_326) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Quasigroup_4246 -> T_RawQuasigroup_326
du_rawQuasigroup_4332 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1)))
-- Algebra.Bundles.LeftBolLoop
d_LeftBolLoop_4454 :: p -> p -> ()
d_LeftBolLoop_4454 p
a0 p
a1 = ()
data T_LeftBolLoop_4454
  = C_LeftBolLoop'46'constructor_80531 (AgdaAny ->
                                        AgdaAny -> AgdaAny)
                                       (AgdaAny -> AgdaAny -> AgdaAny)
                                       (AgdaAny -> AgdaAny -> AgdaAny) AgdaAny
                                       MAlonzo.Code.Algebra.Structures.T_IsLeftBolLoop_3104
-- Algebra.Bundles.LeftBolLoop.Carrier
d_Carrier_4474 :: T_LeftBolLoop_4454 -> ()
d_Carrier_4474 :: T_LeftBolLoop_4454 -> ()
d_Carrier_4474 = T_LeftBolLoop_4454 -> ()
forall a. a
erased
-- Algebra.Bundles.LeftBolLoop._≈_
d__'8776'__4476 :: T_LeftBolLoop_4454 -> AgdaAny -> AgdaAny -> ()
d__'8776'__4476 :: T_LeftBolLoop_4454 -> AgdaAny -> AgdaAny -> ()
d__'8776'__4476 = T_LeftBolLoop_4454 -> AgdaAny -> AgdaAny -> ()
forall a. a
erased
-- Algebra.Bundles.LeftBolLoop._∙_
d__'8729'__4478 ::
  T_LeftBolLoop_4454 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__4478 :: T_LeftBolLoop_4454 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__4478 T_LeftBolLoop_4454
v0
  = case T_LeftBolLoop_4454 -> T_LeftBolLoop_4454
forall a b. a -> b
coe T_LeftBolLoop_4454
v0 of
      C_LeftBolLoop'46'constructor_80531 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny -> AgdaAny
v5 AgdaAny
v6 T_IsLeftBolLoop_3104
v7 -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v3
      T_LeftBolLoop_4454
_ -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.LeftBolLoop._\\_
d__'92''92'__4480 ::
  T_LeftBolLoop_4454 -> AgdaAny -> AgdaAny -> AgdaAny
d__'92''92'__4480 :: T_LeftBolLoop_4454 -> AgdaAny -> AgdaAny -> AgdaAny
d__'92''92'__4480 T_LeftBolLoop_4454
v0
  = case T_LeftBolLoop_4454 -> T_LeftBolLoop_4454
forall a b. a -> b
coe T_LeftBolLoop_4454
v0 of
      C_LeftBolLoop'46'constructor_80531 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny -> AgdaAny
v5 AgdaAny
v6 T_IsLeftBolLoop_3104
v7 -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v4
      T_LeftBolLoop_4454
_ -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.LeftBolLoop._//_
d__'47''47'__4482 ::
  T_LeftBolLoop_4454 -> AgdaAny -> AgdaAny -> AgdaAny
d__'47''47'__4482 :: T_LeftBolLoop_4454 -> AgdaAny -> AgdaAny -> AgdaAny
d__'47''47'__4482 T_LeftBolLoop_4454
v0
  = case T_LeftBolLoop_4454 -> T_LeftBolLoop_4454
forall a b. a -> b
coe T_LeftBolLoop_4454
v0 of
      C_LeftBolLoop'46'constructor_80531 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny -> AgdaAny
v5 AgdaAny
v6 T_IsLeftBolLoop_3104
v7 -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v5
      T_LeftBolLoop_4454
_ -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.LeftBolLoop.ε
d_ε_4484 :: T_LeftBolLoop_4454 -> AgdaAny
d_ε_4484 :: T_LeftBolLoop_4454 -> AgdaAny
d_ε_4484 T_LeftBolLoop_4454
v0
  = case T_LeftBolLoop_4454 -> T_LeftBolLoop_4454
forall a b. a -> b
coe T_LeftBolLoop_4454
v0 of
      C_LeftBolLoop'46'constructor_80531 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny -> AgdaAny
v5 AgdaAny
v6 T_IsLeftBolLoop_3104
v7 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v6
      T_LeftBolLoop_4454
_ -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.LeftBolLoop.isLeftBolLoop
d_isLeftBolLoop_4486 ::
  T_LeftBolLoop_4454 ->
  MAlonzo.Code.Algebra.Structures.T_IsLeftBolLoop_3104
d_isLeftBolLoop_4486 :: T_LeftBolLoop_4454 -> T_IsLeftBolLoop_3104
d_isLeftBolLoop_4486 T_LeftBolLoop_4454
v0
  = case T_LeftBolLoop_4454 -> T_LeftBolLoop_4454
forall a b. a -> b
coe T_LeftBolLoop_4454
v0 of
      C_LeftBolLoop'46'constructor_80531 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny -> AgdaAny
v5 AgdaAny
v6 T_IsLeftBolLoop_3104
v7 -> T_IsLeftBolLoop_3104 -> T_IsLeftBolLoop_3104
forall a b. a -> b
coe T_IsLeftBolLoop_3104
v7
      T_LeftBolLoop_4454
_ -> T_IsLeftBolLoop_3104
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.LeftBolLoop._.//-cong
d_'47''47''45'cong_4490 ::
  T_LeftBolLoop_4454 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'47''47''45'cong_4490 :: T_LeftBolLoop_4454
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'47''47''45'cong_4490 T_LeftBolLoop_4454
v0
  = (T_IsQuasigroup_2944
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsQuasigroup_2944
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'47''47''45'cong_2966
      ((T_IsLoop_3026 -> T_IsQuasigroup_2944) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsLoop_3026 -> T_IsQuasigroup_2944
MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040
         ((T_IsLeftBolLoop_3104 -> T_IsLoop_3026) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsLeftBolLoop_3104 -> T_IsLoop_3026
MAlonzo.Code.Algebra.Structures.d_isLoop_3118
            ((T_LeftBolLoop_4454 -> T_IsLeftBolLoop_3104) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_LeftBolLoop_4454 -> T_IsLeftBolLoop_3104
d_isLeftBolLoop_4486 (T_LeftBolLoop_4454 -> AgdaAny
forall a b. a -> b
coe T_LeftBolLoop_4454
v0))))
-- Algebra.Bundles.LeftBolLoop._.//-congʳ
d_'47''47''45'cong'691'_4492 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_LeftBolLoop_4454 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'47''47''45'cong'691'_4492 :: ()
-> ()
-> T_LeftBolLoop_4454
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'47''47''45'cong'691'_4492 ~()
v0 ~()
v1 T_LeftBolLoop_4454
v2
  = T_LeftBolLoop_4454
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'47''47''45'cong'691'_4492 T_LeftBolLoop_4454
v2
du_'47''47''45'cong'691'_4492 ::
  T_LeftBolLoop_4454 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'47''47''45'cong'691'_4492 :: T_LeftBolLoop_4454
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'47''47''45'cong'691'_4492 T_LeftBolLoop_4454
v0
  = let v1 :: T_IsLeftBolLoop_3104
v1 = T_LeftBolLoop_4454 -> T_IsLeftBolLoop_3104
d_isLeftBolLoop_4486 (T_LeftBolLoop_4454 -> T_LeftBolLoop_4454
forall a b. a -> b
coe T_LeftBolLoop_4454
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsLoop_3026
v2 = T_IsLeftBolLoop_3104 -> T_IsLoop_3026
MAlonzo.Code.Algebra.Structures.d_isLoop_3118 (T_IsLeftBolLoop_3104 -> T_IsLeftBolLoop_3104
forall a b. a -> b
coe T_IsLeftBolLoop_3104
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsQuasigroup_2944
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsQuasigroup_2944
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'47''47''45'cong'691'_3006
            ((T_IsLoop_3026 -> T_IsQuasigroup_2944) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsLoop_3026 -> T_IsQuasigroup_2944
MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040 (T_IsLoop_3026 -> AgdaAny
forall a b. a -> b
coe T_IsLoop_3026
v2))))
-- Algebra.Bundles.LeftBolLoop._.//-congˡ
d_'47''47''45'cong'737'_4494 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_LeftBolLoop_4454 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'47''47''45'cong'737'_4494 :: ()
-> ()
-> T_LeftBolLoop_4454
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'47''47''45'cong'737'_4494 ~()
v0 ~()
v1 T_LeftBolLoop_4454
v2
  = T_LeftBolLoop_4454
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'47''47''45'cong'737'_4494 T_LeftBolLoop_4454
v2
du_'47''47''45'cong'737'_4494 ::
  T_LeftBolLoop_4454 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'47''47''45'cong'737'_4494 :: T_LeftBolLoop_4454
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'47''47''45'cong'737'_4494 T_LeftBolLoop_4454
v0
  = let v1 :: T_IsLeftBolLoop_3104
v1 = T_LeftBolLoop_4454 -> T_IsLeftBolLoop_3104
d_isLeftBolLoop_4486 (T_LeftBolLoop_4454 -> T_LeftBolLoop_4454
forall a b. a -> b
coe T_LeftBolLoop_4454
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsLoop_3026
v2 = T_IsLeftBolLoop_3104 -> T_IsLoop_3026
MAlonzo.Code.Algebra.Structures.d_isLoop_3118 (T_IsLeftBolLoop_3104 -> T_IsLeftBolLoop_3104
forall a b. a -> b
coe T_IsLeftBolLoop_3104
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsQuasigroup_2944
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsQuasigroup_2944
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'47''47''45'cong'737'_3002
            ((T_IsLoop_3026 -> T_IsQuasigroup_2944) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsLoop_3026 -> T_IsQuasigroup_2944
MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040 (T_IsLoop_3026 -> AgdaAny
forall a b. a -> b
coe T_IsLoop_3026
v2))))
-- Algebra.Bundles.LeftBolLoop._.\\-cong
d_'92''92''45'cong_4496 ::
  T_LeftBolLoop_4454 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'92''92''45'cong_4496 :: T_LeftBolLoop_4454
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'92''92''45'cong_4496 T_LeftBolLoop_4454
v0
  = (T_IsQuasigroup_2944
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsQuasigroup_2944
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'92''92''45'cong_2964
      ((T_IsLoop_3026 -> T_IsQuasigroup_2944) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsLoop_3026 -> T_IsQuasigroup_2944
MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040
         ((T_IsLeftBolLoop_3104 -> T_IsLoop_3026) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsLeftBolLoop_3104 -> T_IsLoop_3026
MAlonzo.Code.Algebra.Structures.d_isLoop_3118
            ((T_LeftBolLoop_4454 -> T_IsLeftBolLoop_3104) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_LeftBolLoop_4454 -> T_IsLeftBolLoop_3104
d_isLeftBolLoop_4486 (T_LeftBolLoop_4454 -> AgdaAny
forall a b. a -> b
coe T_LeftBolLoop_4454
v0))))
-- Algebra.Bundles.LeftBolLoop._.\\-congʳ
d_'92''92''45'cong'691'_4498 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_LeftBolLoop_4454 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'92''92''45'cong'691'_4498 :: ()
-> ()
-> T_LeftBolLoop_4454
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'92''92''45'cong'691'_4498 ~()
v0 ~()
v1 T_LeftBolLoop_4454
v2
  = T_LeftBolLoop_4454
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'92''92''45'cong'691'_4498 T_LeftBolLoop_4454
v2
du_'92''92''45'cong'691'_4498 ::
  T_LeftBolLoop_4454 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'92''92''45'cong'691'_4498 :: T_LeftBolLoop_4454
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'92''92''45'cong'691'_4498 T_LeftBolLoop_4454
v0
  = let v1 :: T_IsLeftBolLoop_3104
v1 = T_LeftBolLoop_4454 -> T_IsLeftBolLoop_3104
d_isLeftBolLoop_4486 (T_LeftBolLoop_4454 -> T_LeftBolLoop_4454
forall a b. a -> b
coe T_LeftBolLoop_4454
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsLoop_3026
v2 = T_IsLeftBolLoop_3104 -> T_IsLoop_3026
MAlonzo.Code.Algebra.Structures.d_isLoop_3118 (T_IsLeftBolLoop_3104 -> T_IsLeftBolLoop_3104
forall a b. a -> b
coe T_IsLeftBolLoop_3104
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsQuasigroup_2944
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsQuasigroup_2944
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'92''92''45'cong'691'_2998
            ((T_IsLoop_3026 -> T_IsQuasigroup_2944) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsLoop_3026 -> T_IsQuasigroup_2944
MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040 (T_IsLoop_3026 -> AgdaAny
forall a b. a -> b
coe T_IsLoop_3026
v2))))
-- Algebra.Bundles.LeftBolLoop._.\\-congˡ
d_'92''92''45'cong'737'_4500 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_LeftBolLoop_4454 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'92''92''45'cong'737'_4500 :: ()
-> ()
-> T_LeftBolLoop_4454
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'92''92''45'cong'737'_4500 ~()
v0 ~()
v1 T_LeftBolLoop_4454
v2
  = T_LeftBolLoop_4454
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'92''92''45'cong'737'_4500 T_LeftBolLoop_4454
v2
du_'92''92''45'cong'737'_4500 ::
  T_LeftBolLoop_4454 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'92''92''45'cong'737'_4500 :: T_LeftBolLoop_4454
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'92''92''45'cong'737'_4500 T_LeftBolLoop_4454
v0
  = let v1 :: T_IsLeftBolLoop_3104
v1 = T_LeftBolLoop_4454 -> T_IsLeftBolLoop_3104
d_isLeftBolLoop_4486 (T_LeftBolLoop_4454 -> T_LeftBolLoop_4454
forall a b. a -> b
coe T_LeftBolLoop_4454
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsLoop_3026
v2 = T_IsLeftBolLoop_3104 -> T_IsLoop_3026
MAlonzo.Code.Algebra.Structures.d_isLoop_3118 (T_IsLeftBolLoop_3104 -> T_IsLeftBolLoop_3104
forall a b. a -> b
coe T_IsLeftBolLoop_3104
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsQuasigroup_2944
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsQuasigroup_2944
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'92''92''45'cong'737'_2994
            ((T_IsLoop_3026 -> T_IsQuasigroup_2944) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsLoop_3026 -> T_IsQuasigroup_2944
MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040 (T_IsLoop_3026 -> AgdaAny
forall a b. a -> b
coe T_IsLoop_3026
v2))))
-- Algebra.Bundles.LeftBolLoop._.identity
d_identity_4502 ::
  T_LeftBolLoop_4454 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_identity_4502 :: T_LeftBolLoop_4454 -> T_Σ_14
d_identity_4502 T_LeftBolLoop_4454
v0
  = (T_IsLoop_3026 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsLoop_3026 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_identity_3042
      ((T_IsLeftBolLoop_3104 -> T_IsLoop_3026) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsLeftBolLoop_3104 -> T_IsLoop_3026
MAlonzo.Code.Algebra.Structures.d_isLoop_3118
         ((T_LeftBolLoop_4454 -> T_IsLeftBolLoop_3104) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_LeftBolLoop_4454 -> T_IsLeftBolLoop_3104
d_isLeftBolLoop_4486 (T_LeftBolLoop_4454 -> AgdaAny
forall a b. a -> b
coe T_LeftBolLoop_4454
v0)))
-- Algebra.Bundles.LeftBolLoop._.identityʳ
d_identity'691'_4504 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_LeftBolLoop_4454 -> AgdaAny -> AgdaAny
d_identity'691'_4504 :: () -> () -> T_LeftBolLoop_4454 -> AgdaAny -> AgdaAny
d_identity'691'_4504 ~()
v0 ~()
v1 T_LeftBolLoop_4454
v2 = T_LeftBolLoop_4454 -> AgdaAny -> AgdaAny
du_identity'691'_4504 T_LeftBolLoop_4454
v2
du_identity'691'_4504 :: T_LeftBolLoop_4454 -> AgdaAny -> AgdaAny
du_identity'691'_4504 :: T_LeftBolLoop_4454 -> AgdaAny -> AgdaAny
du_identity'691'_4504 T_LeftBolLoop_4454
v0
  = let v1 :: T_IsLeftBolLoop_3104
v1 = T_LeftBolLoop_4454 -> T_IsLeftBolLoop_3104
d_isLeftBolLoop_4486 (T_LeftBolLoop_4454 -> T_LeftBolLoop_4454
forall a b. a -> b
coe T_LeftBolLoop_4454
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsLoop_3026 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsLoop_3026 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_identity'691'_3094
         ((T_IsLeftBolLoop_3104 -> T_IsLoop_3026) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLeftBolLoop_3104 -> T_IsLoop_3026
MAlonzo.Code.Algebra.Structures.d_isLoop_3118 (T_IsLeftBolLoop_3104 -> AgdaAny
forall a b. a -> b
coe T_IsLeftBolLoop_3104
v1)))
-- Algebra.Bundles.LeftBolLoop._.identityˡ
d_identity'737'_4506 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_LeftBolLoop_4454 -> AgdaAny -> AgdaAny
d_identity'737'_4506 :: () -> () -> T_LeftBolLoop_4454 -> AgdaAny -> AgdaAny
d_identity'737'_4506 ~()
v0 ~()
v1 T_LeftBolLoop_4454
v2 = T_LeftBolLoop_4454 -> AgdaAny -> AgdaAny
du_identity'737'_4506 T_LeftBolLoop_4454
v2
du_identity'737'_4506 :: T_LeftBolLoop_4454 -> AgdaAny -> AgdaAny
du_identity'737'_4506 :: T_LeftBolLoop_4454 -> AgdaAny -> AgdaAny
du_identity'737'_4506 T_LeftBolLoop_4454
v0
  = let v1 :: T_IsLeftBolLoop_3104
v1 = T_LeftBolLoop_4454 -> T_IsLeftBolLoop_3104
d_isLeftBolLoop_4486 (T_LeftBolLoop_4454 -> T_LeftBolLoop_4454
forall a b. a -> b
coe T_LeftBolLoop_4454
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsLoop_3026 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsLoop_3026 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_identity'737'_3092
         ((T_IsLeftBolLoop_3104 -> T_IsLoop_3026) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLeftBolLoop_3104 -> T_IsLoop_3026
MAlonzo.Code.Algebra.Structures.d_isLoop_3118 (T_IsLeftBolLoop_3104 -> AgdaAny
forall a b. a -> b
coe T_IsLeftBolLoop_3104
v1)))
-- Algebra.Bundles.LeftBolLoop._.isEquivalence
d_isEquivalence_4508 ::
  T_LeftBolLoop_4454 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_4508 :: T_LeftBolLoop_4454 -> T_IsEquivalence_26
d_isEquivalence_4508 T_LeftBolLoop_4454
v0
  = (T_IsMagma_176 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
      ((T_IsQuasigroup_2944 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsQuasigroup_2944 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_2962
         ((T_IsLoop_3026 -> T_IsQuasigroup_2944) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsLoop_3026 -> T_IsQuasigroup_2944
MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040
            ((T_IsLeftBolLoop_3104 -> T_IsLoop_3026) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsLeftBolLoop_3104 -> T_IsLoop_3026
MAlonzo.Code.Algebra.Structures.d_isLoop_3118
               ((T_LeftBolLoop_4454 -> T_IsLeftBolLoop_3104) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_LeftBolLoop_4454 -> T_IsLeftBolLoop_3104
d_isLeftBolLoop_4486 (T_LeftBolLoop_4454 -> AgdaAny
forall a b. a -> b
coe T_LeftBolLoop_4454
v0)))))
-- Algebra.Bundles.LeftBolLoop._.isLoop
d_isLoop_4510 ::
  T_LeftBolLoop_4454 -> MAlonzo.Code.Algebra.Structures.T_IsLoop_3026
d_isLoop_4510 :: T_LeftBolLoop_4454 -> T_IsLoop_3026
d_isLoop_4510 T_LeftBolLoop_4454
v0
  = (T_IsLeftBolLoop_3104 -> T_IsLoop_3026) -> AgdaAny -> T_IsLoop_3026
forall a b. a -> b
coe
      T_IsLeftBolLoop_3104 -> T_IsLoop_3026
MAlonzo.Code.Algebra.Structures.d_isLoop_3118
      ((T_LeftBolLoop_4454 -> T_IsLeftBolLoop_3104) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_LeftBolLoop_4454 -> T_IsLeftBolLoop_3104
d_isLeftBolLoop_4486 (T_LeftBolLoop_4454 -> AgdaAny
forall a b. a -> b
coe T_LeftBolLoop_4454
v0))
-- Algebra.Bundles.LeftBolLoop._.isMagma
d_isMagma_4512 ::
  T_LeftBolLoop_4454 -> MAlonzo.Code.Algebra.Structures.T_IsMagma_176
d_isMagma_4512 :: T_LeftBolLoop_4454 -> T_IsMagma_176
d_isMagma_4512 T_LeftBolLoop_4454
v0
  = (T_IsQuasigroup_2944 -> T_IsMagma_176) -> AgdaAny -> T_IsMagma_176
forall a b. a -> b
coe
      T_IsQuasigroup_2944 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_2962
      ((T_IsLoop_3026 -> T_IsQuasigroup_2944) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsLoop_3026 -> T_IsQuasigroup_2944
MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040
         ((T_IsLeftBolLoop_3104 -> T_IsLoop_3026) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsLeftBolLoop_3104 -> T_IsLoop_3026
MAlonzo.Code.Algebra.Structures.d_isLoop_3118
            ((T_LeftBolLoop_4454 -> T_IsLeftBolLoop_3104) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_LeftBolLoop_4454 -> T_IsLeftBolLoop_3104
d_isLeftBolLoop_4486 (T_LeftBolLoop_4454 -> AgdaAny
forall a b. a -> b
coe T_LeftBolLoop_4454
v0))))
-- Algebra.Bundles.LeftBolLoop._.isPartialEquivalence
d_isPartialEquivalence_4514 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_LeftBolLoop_4454 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_4514 :: () -> () -> T_LeftBolLoop_4454 -> T_IsPartialEquivalence_16
d_isPartialEquivalence_4514 ~()
v0 ~()
v1 T_LeftBolLoop_4454
v2
  = T_LeftBolLoop_4454 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_4514 T_LeftBolLoop_4454
v2
du_isPartialEquivalence_4514 ::
  T_LeftBolLoop_4454 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_4514 :: T_LeftBolLoop_4454 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_4514 T_LeftBolLoop_4454
v0
  = let v1 :: T_IsLeftBolLoop_3104
v1 = T_LeftBolLoop_4454 -> T_IsLeftBolLoop_3104
d_isLeftBolLoop_4486 (T_LeftBolLoop_4454 -> T_LeftBolLoop_4454
forall a b. a -> b
coe T_LeftBolLoop_4454
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsLoop_3026
v2 = T_IsLeftBolLoop_3104 -> T_IsLoop_3026
MAlonzo.Code.Algebra.Structures.d_isLoop_3118 (T_IsLeftBolLoop_3104 -> T_IsLeftBolLoop_3104
forall a b. a -> b
coe T_IsLeftBolLoop_3104
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsQuasigroup_2944
v3
                = T_IsLoop_3026 -> T_IsQuasigroup_2944
MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040 (T_IsLoop_3026 -> T_IsLoop_3026
forall a b. a -> b
coe T_IsLoop_3026
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsMagma_176
v4
                   = T_IsQuasigroup_2944 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_2962 (T_IsQuasigroup_2944 -> T_IsQuasigroup_2944
forall a b. a -> b
coe T_IsQuasigroup_2944
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               ((T_IsEquivalence_26 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsEquivalence_26 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
                  ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v4))))))
-- Algebra.Bundles.LeftBolLoop._.isQuasigroup
d_isQuasigroup_4516 ::
  T_LeftBolLoop_4454 ->
  MAlonzo.Code.Algebra.Structures.T_IsQuasigroup_2944
d_isQuasigroup_4516 :: T_LeftBolLoop_4454 -> T_IsQuasigroup_2944
d_isQuasigroup_4516 T_LeftBolLoop_4454
v0
  = (T_IsLoop_3026 -> T_IsQuasigroup_2944)
-> AgdaAny -> T_IsQuasigroup_2944
forall a b. a -> b
coe
      T_IsLoop_3026 -> T_IsQuasigroup_2944
MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040
      ((T_IsLeftBolLoop_3104 -> T_IsLoop_3026) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsLeftBolLoop_3104 -> T_IsLoop_3026
MAlonzo.Code.Algebra.Structures.d_isLoop_3118
         ((T_LeftBolLoop_4454 -> T_IsLeftBolLoop_3104) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_LeftBolLoop_4454 -> T_IsLeftBolLoop_3104
d_isLeftBolLoop_4486 (T_LeftBolLoop_4454 -> AgdaAny
forall a b. a -> b
coe T_LeftBolLoop_4454
v0)))
-- Algebra.Bundles.LeftBolLoop._.leftBol
d_leftBol_4518 ::
  T_LeftBolLoop_4454 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_leftBol_4518 :: T_LeftBolLoop_4454 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_leftBol_4518 T_LeftBolLoop_4454
v0
  = (T_IsLeftBolLoop_3104 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsLeftBolLoop_3104 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_leftBol_3120
      ((T_LeftBolLoop_4454 -> T_IsLeftBolLoop_3104) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_LeftBolLoop_4454 -> T_IsLeftBolLoop_3104
d_isLeftBolLoop_4486 (T_LeftBolLoop_4454 -> AgdaAny
forall a b. a -> b
coe T_LeftBolLoop_4454
v0))
-- Algebra.Bundles.LeftBolLoop._.leftDivides
d_leftDivides_4520 ::
  T_LeftBolLoop_4454 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_leftDivides_4520 :: T_LeftBolLoop_4454 -> T_Σ_14
d_leftDivides_4520 T_LeftBolLoop_4454
v0
  = (T_IsQuasigroup_2944 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsQuasigroup_2944 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_leftDivides_2968
      ((T_IsLoop_3026 -> T_IsQuasigroup_2944) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsLoop_3026 -> T_IsQuasigroup_2944
MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040
         ((T_IsLeftBolLoop_3104 -> T_IsLoop_3026) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsLeftBolLoop_3104 -> T_IsLoop_3026
MAlonzo.Code.Algebra.Structures.d_isLoop_3118
            ((T_LeftBolLoop_4454 -> T_IsLeftBolLoop_3104) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_LeftBolLoop_4454 -> T_IsLeftBolLoop_3104
d_isLeftBolLoop_4486 (T_LeftBolLoop_4454 -> AgdaAny
forall a b. a -> b
coe T_LeftBolLoop_4454
v0))))
-- Algebra.Bundles.LeftBolLoop._.leftDividesʳ
d_leftDivides'691'_4522 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_LeftBolLoop_4454 -> AgdaAny -> AgdaAny -> AgdaAny
d_leftDivides'691'_4522 :: () -> () -> T_LeftBolLoop_4454 -> AgdaAny -> AgdaAny -> AgdaAny
d_leftDivides'691'_4522 ~()
v0 ~()
v1 T_LeftBolLoop_4454
v2 = T_LeftBolLoop_4454 -> AgdaAny -> AgdaAny -> AgdaAny
du_leftDivides'691'_4522 T_LeftBolLoop_4454
v2
du_leftDivides'691'_4522 ::
  T_LeftBolLoop_4454 -> AgdaAny -> AgdaAny -> AgdaAny
du_leftDivides'691'_4522 :: T_LeftBolLoop_4454 -> AgdaAny -> AgdaAny -> AgdaAny
du_leftDivides'691'_4522 T_LeftBolLoop_4454
v0
  = let v1 :: T_IsLeftBolLoop_3104
v1 = T_LeftBolLoop_4454 -> T_IsLeftBolLoop_3104
d_isLeftBolLoop_4486 (T_LeftBolLoop_4454 -> T_LeftBolLoop_4454
forall a b. a -> b
coe T_LeftBolLoop_4454
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsLoop_3026
v2 = T_IsLeftBolLoop_3104 -> T_IsLoop_3026
MAlonzo.Code.Algebra.Structures.d_isLoop_3118 (T_IsLeftBolLoop_3104 -> T_IsLeftBolLoop_3104
forall a b. a -> b
coe T_IsLeftBolLoop_3104
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsQuasigroup_2944 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsQuasigroup_2944 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_leftDivides'691'_3012
            ((T_IsLoop_3026 -> T_IsQuasigroup_2944) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsLoop_3026 -> T_IsQuasigroup_2944
MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040 (T_IsLoop_3026 -> AgdaAny
forall a b. a -> b
coe T_IsLoop_3026
v2))))
-- Algebra.Bundles.LeftBolLoop._.leftDividesˡ
d_leftDivides'737'_4524 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_LeftBolLoop_4454 -> AgdaAny -> AgdaAny -> AgdaAny
d_leftDivides'737'_4524 :: () -> () -> T_LeftBolLoop_4454 -> AgdaAny -> AgdaAny -> AgdaAny
d_leftDivides'737'_4524 ~()
v0 ~()
v1 T_LeftBolLoop_4454
v2 = T_LeftBolLoop_4454 -> AgdaAny -> AgdaAny -> AgdaAny
du_leftDivides'737'_4524 T_LeftBolLoop_4454
v2
du_leftDivides'737'_4524 ::
  T_LeftBolLoop_4454 -> AgdaAny -> AgdaAny -> AgdaAny
du_leftDivides'737'_4524 :: T_LeftBolLoop_4454 -> AgdaAny -> AgdaAny -> AgdaAny
du_leftDivides'737'_4524 T_LeftBolLoop_4454
v0
  = let v1 :: T_IsLeftBolLoop_3104
v1 = T_LeftBolLoop_4454 -> T_IsLeftBolLoop_3104
d_isLeftBolLoop_4486 (T_LeftBolLoop_4454 -> T_LeftBolLoop_4454
forall a b. a -> b
coe T_LeftBolLoop_4454
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsLoop_3026
v2 = T_IsLeftBolLoop_3104 -> T_IsLoop_3026
MAlonzo.Code.Algebra.Structures.d_isLoop_3118 (T_IsLeftBolLoop_3104 -> T_IsLeftBolLoop_3104
forall a b. a -> b
coe T_IsLeftBolLoop_3104
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsQuasigroup_2944 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsQuasigroup_2944 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_leftDivides'737'_3010
            ((T_IsLoop_3026 -> T_IsQuasigroup_2944) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsLoop_3026 -> T_IsQuasigroup_2944
MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040 (T_IsLoop_3026 -> AgdaAny
forall a b. a -> b
coe T_IsLoop_3026
v2))))
-- Algebra.Bundles.LeftBolLoop._.refl
d_refl_4526 :: T_LeftBolLoop_4454 -> AgdaAny -> AgdaAny
d_refl_4526 :: T_LeftBolLoop_4454 -> AgdaAny -> AgdaAny
d_refl_4526 T_LeftBolLoop_4454
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_34
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
         ((T_IsQuasigroup_2944 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsQuasigroup_2944 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_2962
            ((T_IsLoop_3026 -> T_IsQuasigroup_2944) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsLoop_3026 -> T_IsQuasigroup_2944
MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040
               ((T_IsLeftBolLoop_3104 -> T_IsLoop_3026) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsLeftBolLoop_3104 -> T_IsLoop_3026
MAlonzo.Code.Algebra.Structures.d_isLoop_3118
                  ((T_LeftBolLoop_4454 -> T_IsLeftBolLoop_3104) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_LeftBolLoop_4454 -> T_IsLeftBolLoop_3104
d_isLeftBolLoop_4486 (T_LeftBolLoop_4454 -> AgdaAny
forall a b. a -> b
coe T_LeftBolLoop_4454
v0))))))
-- Algebra.Bundles.LeftBolLoop._.reflexive
d_reflexive_4528 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_LeftBolLoop_4454 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_4528 :: ()
-> ()
-> T_LeftBolLoop_4454
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_4528 ~()
v0 ~()
v1 T_LeftBolLoop_4454
v2 = T_LeftBolLoop_4454
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_4528 T_LeftBolLoop_4454
v2
du_reflexive_4528 ::
  T_LeftBolLoop_4454 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_4528 :: T_LeftBolLoop_4454
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_4528 T_LeftBolLoop_4454
v0
  = let v1 :: T_IsLeftBolLoop_3104
v1 = T_LeftBolLoop_4454 -> T_IsLeftBolLoop_3104
d_isLeftBolLoop_4486 (T_LeftBolLoop_4454 -> T_LeftBolLoop_4454
forall a b. a -> b
coe T_LeftBolLoop_4454
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsLoop_3026
v2 = T_IsLeftBolLoop_3104 -> T_IsLoop_3026
MAlonzo.Code.Algebra.Structures.d_isLoop_3118 (T_IsLeftBolLoop_3104 -> T_IsLeftBolLoop_3104
forall a b. a -> b
coe T_IsLeftBolLoop_3104
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsQuasigroup_2944
v3
                = T_IsLoop_3026 -> T_IsQuasigroup_2944
MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040 (T_IsLoop_3026 -> T_IsLoop_3026
forall a b. a -> b
coe T_IsLoop_3026
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsMagma_176
v4
                   = T_IsQuasigroup_2944 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_2962 (T_IsQuasigroup_2944 -> T_IsQuasigroup_2944
forall a b. a -> b
coe T_IsQuasigroup_2944
v3) in
             (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
               (\ AgdaAny
v5 AgdaAny
v6 AgdaAny
v7 ->
                  (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                    T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
                    ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v4))
                    AgdaAny
v5))))
-- Algebra.Bundles.LeftBolLoop._.rightDivides
d_rightDivides_4530 ::
  T_LeftBolLoop_4454 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_rightDivides_4530 :: T_LeftBolLoop_4454 -> T_Σ_14
d_rightDivides_4530 T_LeftBolLoop_4454
v0
  = (T_IsQuasigroup_2944 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsQuasigroup_2944 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_rightDivides_2970
      ((T_IsLoop_3026 -> T_IsQuasigroup_2944) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsLoop_3026 -> T_IsQuasigroup_2944
MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040
         ((T_IsLeftBolLoop_3104 -> T_IsLoop_3026) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsLeftBolLoop_3104 -> T_IsLoop_3026
MAlonzo.Code.Algebra.Structures.d_isLoop_3118
            ((T_LeftBolLoop_4454 -> T_IsLeftBolLoop_3104) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_LeftBolLoop_4454 -> T_IsLeftBolLoop_3104
d_isLeftBolLoop_4486 (T_LeftBolLoop_4454 -> AgdaAny
forall a b. a -> b
coe T_LeftBolLoop_4454
v0))))
-- Algebra.Bundles.LeftBolLoop._.rightDividesʳ
d_rightDivides'691'_4532 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_LeftBolLoop_4454 -> AgdaAny -> AgdaAny -> AgdaAny
d_rightDivides'691'_4532 :: () -> () -> T_LeftBolLoop_4454 -> AgdaAny -> AgdaAny -> AgdaAny
d_rightDivides'691'_4532 ~()
v0 ~()
v1 T_LeftBolLoop_4454
v2 = T_LeftBolLoop_4454 -> AgdaAny -> AgdaAny -> AgdaAny
du_rightDivides'691'_4532 T_LeftBolLoop_4454
v2
du_rightDivides'691'_4532 ::
  T_LeftBolLoop_4454 -> AgdaAny -> AgdaAny -> AgdaAny
du_rightDivides'691'_4532 :: T_LeftBolLoop_4454 -> AgdaAny -> AgdaAny -> AgdaAny
du_rightDivides'691'_4532 T_LeftBolLoop_4454
v0
  = let v1 :: T_IsLeftBolLoop_3104
v1 = T_LeftBolLoop_4454 -> T_IsLeftBolLoop_3104
d_isLeftBolLoop_4486 (T_LeftBolLoop_4454 -> T_LeftBolLoop_4454
forall a b. a -> b
coe T_LeftBolLoop_4454
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsLoop_3026
v2 = T_IsLeftBolLoop_3104 -> T_IsLoop_3026
MAlonzo.Code.Algebra.Structures.d_isLoop_3118 (T_IsLeftBolLoop_3104 -> T_IsLeftBolLoop_3104
forall a b. a -> b
coe T_IsLeftBolLoop_3104
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsQuasigroup_2944 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsQuasigroup_2944 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_rightDivides'691'_3016
            ((T_IsLoop_3026 -> T_IsQuasigroup_2944) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsLoop_3026 -> T_IsQuasigroup_2944
MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040 (T_IsLoop_3026 -> AgdaAny
forall a b. a -> b
coe T_IsLoop_3026
v2))))
-- Algebra.Bundles.LeftBolLoop._.rightDividesˡ
d_rightDivides'737'_4534 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_LeftBolLoop_4454 -> AgdaAny -> AgdaAny -> AgdaAny
d_rightDivides'737'_4534 :: () -> () -> T_LeftBolLoop_4454 -> AgdaAny -> AgdaAny -> AgdaAny
d_rightDivides'737'_4534 ~()
v0 ~()
v1 T_LeftBolLoop_4454
v2 = T_LeftBolLoop_4454 -> AgdaAny -> AgdaAny -> AgdaAny
du_rightDivides'737'_4534 T_LeftBolLoop_4454
v2
du_rightDivides'737'_4534 ::
  T_LeftBolLoop_4454 -> AgdaAny -> AgdaAny -> AgdaAny
du_rightDivides'737'_4534 :: T_LeftBolLoop_4454 -> AgdaAny -> AgdaAny -> AgdaAny
du_rightDivides'737'_4534 T_LeftBolLoop_4454
v0
  = let v1 :: T_IsLeftBolLoop_3104
v1 = T_LeftBolLoop_4454 -> T_IsLeftBolLoop_3104
d_isLeftBolLoop_4486 (T_LeftBolLoop_4454 -> T_LeftBolLoop_4454
forall a b. a -> b
coe T_LeftBolLoop_4454
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsLoop_3026
v2 = T_IsLeftBolLoop_3104 -> T_IsLoop_3026
MAlonzo.Code.Algebra.Structures.d_isLoop_3118 (T_IsLeftBolLoop_3104 -> T_IsLeftBolLoop_3104
forall a b. a -> b
coe T_IsLeftBolLoop_3104
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsQuasigroup_2944 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsQuasigroup_2944 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_rightDivides'737'_3014
            ((T_IsLoop_3026 -> T_IsQuasigroup_2944) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsLoop_3026 -> T_IsQuasigroup_2944
MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040 (T_IsLoop_3026 -> AgdaAny
forall a b. a -> b
coe T_IsLoop_3026
v2))))
-- Algebra.Bundles.LeftBolLoop._.setoid
d_setoid_4536 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_LeftBolLoop_4454 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_4536 :: () -> () -> T_LeftBolLoop_4454 -> T_Setoid_44
d_setoid_4536 ~()
v0 ~()
v1 T_LeftBolLoop_4454
v2 = T_LeftBolLoop_4454 -> T_Setoid_44
du_setoid_4536 T_LeftBolLoop_4454
v2
du_setoid_4536 ::
  T_LeftBolLoop_4454 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_4536 :: T_LeftBolLoop_4454 -> T_Setoid_44
du_setoid_4536 T_LeftBolLoop_4454
v0
  = let v1 :: T_IsLeftBolLoop_3104
v1 = T_LeftBolLoop_4454 -> T_IsLeftBolLoop_3104
d_isLeftBolLoop_4486 (T_LeftBolLoop_4454 -> T_LeftBolLoop_4454
forall a b. a -> b
coe T_LeftBolLoop_4454
v0) in
    AgdaAny -> T_Setoid_44
forall a b. a -> b
coe
      (let v2 :: T_IsLoop_3026
v2 = T_IsLeftBolLoop_3104 -> T_IsLoop_3026
MAlonzo.Code.Algebra.Structures.d_isLoop_3118 (T_IsLeftBolLoop_3104 -> T_IsLeftBolLoop_3104
forall a b. a -> b
coe T_IsLeftBolLoop_3104
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsQuasigroup_2944
v3
                = T_IsLoop_3026 -> T_IsQuasigroup_2944
MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040 (T_IsLoop_3026 -> T_IsLoop_3026
forall a b. a -> b
coe T_IsLoop_3026
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsMagma_176 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMagma_176 -> T_Setoid_44
MAlonzo.Code.Algebra.Structures.du_setoid_200
               ((T_IsQuasigroup_2944 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroup_2944 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_2962 (T_IsQuasigroup_2944 -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroup_2944
v3)))))
-- Algebra.Bundles.LeftBolLoop._.sym
d_sym_4538 ::
  T_LeftBolLoop_4454 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_4538 :: T_LeftBolLoop_4454 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_4538 T_LeftBolLoop_4454
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_36
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
         ((T_IsQuasigroup_2944 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsQuasigroup_2944 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_2962
            ((T_IsLoop_3026 -> T_IsQuasigroup_2944) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsLoop_3026 -> T_IsQuasigroup_2944
MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040
               ((T_IsLeftBolLoop_3104 -> T_IsLoop_3026) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsLeftBolLoop_3104 -> T_IsLoop_3026
MAlonzo.Code.Algebra.Structures.d_isLoop_3118
                  ((T_LeftBolLoop_4454 -> T_IsLeftBolLoop_3104) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_LeftBolLoop_4454 -> T_IsLeftBolLoop_3104
d_isLeftBolLoop_4486 (T_LeftBolLoop_4454 -> AgdaAny
forall a b. a -> b
coe T_LeftBolLoop_4454
v0))))))
-- Algebra.Bundles.LeftBolLoop._.trans
d_trans_4540 ::
  T_LeftBolLoop_4454 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_4540 :: T_LeftBolLoop_4454
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_4540 T_LeftBolLoop_4454
v0
  = (T_IsEquivalence_26
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_38
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
         ((T_IsQuasigroup_2944 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsQuasigroup_2944 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_2962
            ((T_IsLoop_3026 -> T_IsQuasigroup_2944) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsLoop_3026 -> T_IsQuasigroup_2944
MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040
               ((T_IsLeftBolLoop_3104 -> T_IsLoop_3026) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsLeftBolLoop_3104 -> T_IsLoop_3026
MAlonzo.Code.Algebra.Structures.d_isLoop_3118
                  ((T_LeftBolLoop_4454 -> T_IsLeftBolLoop_3104) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_LeftBolLoop_4454 -> T_IsLeftBolLoop_3104
d_isLeftBolLoop_4486 (T_LeftBolLoop_4454 -> AgdaAny
forall a b. a -> b
coe T_LeftBolLoop_4454
v0))))))
-- Algebra.Bundles.LeftBolLoop._.∙-cong
d_'8729''45'cong_4542 ::
  T_LeftBolLoop_4454 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_4542 :: T_LeftBolLoop_4454
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_4542 T_LeftBolLoop_4454
v0
  = (T_IsMagma_176
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsMagma_176
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_186
      ((T_IsQuasigroup_2944 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsQuasigroup_2944 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_2962
         ((T_IsLoop_3026 -> T_IsQuasigroup_2944) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsLoop_3026 -> T_IsQuasigroup_2944
MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040
            ((T_IsLeftBolLoop_3104 -> T_IsLoop_3026) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsLeftBolLoop_3104 -> T_IsLoop_3026
MAlonzo.Code.Algebra.Structures.d_isLoop_3118
               ((T_LeftBolLoop_4454 -> T_IsLeftBolLoop_3104) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_LeftBolLoop_4454 -> T_IsLeftBolLoop_3104
d_isLeftBolLoop_4486 (T_LeftBolLoop_4454 -> AgdaAny
forall a b. a -> b
coe T_LeftBolLoop_4454
v0)))))
-- Algebra.Bundles.LeftBolLoop._.∙-congʳ
d_'8729''45'cong'691'_4544 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_LeftBolLoop_4454 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_4544 :: ()
-> ()
-> T_LeftBolLoop_4454
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_4544 ~()
v0 ~()
v1 T_LeftBolLoop_4454
v2
  = T_LeftBolLoop_4454
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_4544 T_LeftBolLoop_4454
v2
du_'8729''45'cong'691'_4544 ::
  T_LeftBolLoop_4454 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_4544 :: T_LeftBolLoop_4454
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_4544 T_LeftBolLoop_4454
v0
  = let v1 :: T_IsLeftBolLoop_3104
v1 = T_LeftBolLoop_4454 -> T_IsLeftBolLoop_3104
d_isLeftBolLoop_4486 (T_LeftBolLoop_4454 -> T_LeftBolLoop_4454
forall a b. a -> b
coe T_LeftBolLoop_4454
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsLoop_3026
v2 = T_IsLeftBolLoop_3104 -> T_IsLoop_3026
MAlonzo.Code.Algebra.Structures.d_isLoop_3118 (T_IsLeftBolLoop_3104 -> T_IsLeftBolLoop_3104
forall a b. a -> b
coe T_IsLeftBolLoop_3104
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsQuasigroup_2944
v3
                = T_IsLoop_3026 -> T_IsQuasigroup_2944
MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040 (T_IsLoop_3026 -> T_IsLoop_3026
forall a b. a -> b
coe T_IsLoop_3026
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'691'_206
               ((T_IsQuasigroup_2944 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroup_2944 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_2962 (T_IsQuasigroup_2944 -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroup_2944
v3)))))
-- Algebra.Bundles.LeftBolLoop._.∙-congˡ
d_'8729''45'cong'737'_4546 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_LeftBolLoop_4454 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_4546 :: ()
-> ()
-> T_LeftBolLoop_4454
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_4546 ~()
v0 ~()
v1 T_LeftBolLoop_4454
v2
  = T_LeftBolLoop_4454
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_4546 T_LeftBolLoop_4454
v2
du_'8729''45'cong'737'_4546 ::
  T_LeftBolLoop_4454 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_4546 :: T_LeftBolLoop_4454
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_4546 T_LeftBolLoop_4454
v0
  = let v1 :: T_IsLeftBolLoop_3104
v1 = T_LeftBolLoop_4454 -> T_IsLeftBolLoop_3104
d_isLeftBolLoop_4486 (T_LeftBolLoop_4454 -> T_LeftBolLoop_4454
forall a b. a -> b
coe T_LeftBolLoop_4454
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsLoop_3026
v2 = T_IsLeftBolLoop_3104 -> T_IsLoop_3026
MAlonzo.Code.Algebra.Structures.d_isLoop_3118 (T_IsLeftBolLoop_3104 -> T_IsLeftBolLoop_3104
forall a b. a -> b
coe T_IsLeftBolLoop_3104
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsQuasigroup_2944
v3
                = T_IsLoop_3026 -> T_IsQuasigroup_2944
MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040 (T_IsLoop_3026 -> T_IsLoop_3026
forall a b. a -> b
coe T_IsLoop_3026
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'737'_202
               ((T_IsQuasigroup_2944 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroup_2944 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_2962 (T_IsQuasigroup_2944 -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroup_2944
v3)))))
-- Algebra.Bundles.LeftBolLoop.loop
d_loop_4548 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_LeftBolLoop_4454 -> T_Loop_4346
d_loop_4548 :: () -> () -> T_LeftBolLoop_4454 -> T_Loop_4346
d_loop_4548 ~()
v0 ~()
v1 T_LeftBolLoop_4454
v2 = T_LeftBolLoop_4454 -> T_Loop_4346
du_loop_4548 T_LeftBolLoop_4454
v2
du_loop_4548 :: T_LeftBolLoop_4454 -> T_Loop_4346
du_loop_4548 :: T_LeftBolLoop_4454 -> T_Loop_4346
du_loop_4548 T_LeftBolLoop_4454
v0
  = ((AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> T_IsLoop_3026
 -> T_Loop_4346)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsLoop_3026
-> T_Loop_4346
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsLoop_3026
-> T_Loop_4346
C_Loop'46'constructor_78267 (T_LeftBolLoop_4454 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__4478 (T_LeftBolLoop_4454 -> T_LeftBolLoop_4454
forall a b. a -> b
coe T_LeftBolLoop_4454
v0))
      (T_LeftBolLoop_4454 -> AgdaAny -> AgdaAny -> AgdaAny
d__'92''92'__4480 (T_LeftBolLoop_4454 -> T_LeftBolLoop_4454
forall a b. a -> b
coe T_LeftBolLoop_4454
v0)) (T_LeftBolLoop_4454 -> AgdaAny -> AgdaAny -> AgdaAny
d__'47''47'__4482 (T_LeftBolLoop_4454 -> T_LeftBolLoop_4454
forall a b. a -> b
coe T_LeftBolLoop_4454
v0))
      (T_LeftBolLoop_4454 -> AgdaAny
d_ε_4484 (T_LeftBolLoop_4454 -> T_LeftBolLoop_4454
forall a b. a -> b
coe T_LeftBolLoop_4454
v0))
      (T_IsLeftBolLoop_3104 -> T_IsLoop_3026
MAlonzo.Code.Algebra.Structures.d_isLoop_3118
         ((T_LeftBolLoop_4454 -> T_IsLeftBolLoop_3104)
-> AgdaAny -> T_IsLeftBolLoop_3104
forall a b. a -> b
coe T_LeftBolLoop_4454 -> T_IsLeftBolLoop_3104
d_isLeftBolLoop_4486 (T_LeftBolLoop_4454 -> AgdaAny
forall a b. a -> b
coe T_LeftBolLoop_4454
v0)))
-- Algebra.Bundles.LeftBolLoop._.quasigroup
d_quasigroup_4552 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_LeftBolLoop_4454 -> T_Quasigroup_4246
d_quasigroup_4552 :: () -> () -> T_LeftBolLoop_4454 -> T_Quasigroup_4246
d_quasigroup_4552 ~()
v0 ~()
v1 T_LeftBolLoop_4454
v2 = T_LeftBolLoop_4454 -> T_Quasigroup_4246
du_quasigroup_4552 T_LeftBolLoop_4454
v2
du_quasigroup_4552 :: T_LeftBolLoop_4454 -> T_Quasigroup_4246
du_quasigroup_4552 :: T_LeftBolLoop_4454 -> T_Quasigroup_4246
du_quasigroup_4552 T_LeftBolLoop_4454
v0
  = (T_Loop_4346 -> T_Quasigroup_4246) -> AgdaAny -> T_Quasigroup_4246
forall a b. a -> b
coe T_Loop_4346 -> T_Quasigroup_4246
du_quasigroup_4438 ((T_LeftBolLoop_4454 -> T_Loop_4346) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_LeftBolLoop_4454 -> T_Loop_4346
du_loop_4548 (T_LeftBolLoop_4454 -> AgdaAny
forall a b. a -> b
coe T_LeftBolLoop_4454
v0))
-- Algebra.Bundles.RightBolLoop
d_RightBolLoop_4558 :: p -> p -> ()
d_RightBolLoop_4558 p
a0 p
a1 = ()
data T_RightBolLoop_4558
  = C_RightBolLoop'46'constructor_82729 (AgdaAny ->
                                         AgdaAny -> AgdaAny)
                                        (AgdaAny -> AgdaAny -> AgdaAny)
                                        (AgdaAny -> AgdaAny -> AgdaAny) AgdaAny
                                        MAlonzo.Code.Algebra.Structures.T_IsRightBolLoop_3186
-- Algebra.Bundles.RightBolLoop.Carrier
d_Carrier_4578 :: T_RightBolLoop_4558 -> ()
d_Carrier_4578 :: T_RightBolLoop_4558 -> ()
d_Carrier_4578 = T_RightBolLoop_4558 -> ()
forall a. a
erased
-- Algebra.Bundles.RightBolLoop._≈_
d__'8776'__4580 :: T_RightBolLoop_4558 -> AgdaAny -> AgdaAny -> ()
d__'8776'__4580 :: T_RightBolLoop_4558 -> AgdaAny -> AgdaAny -> ()
d__'8776'__4580 = T_RightBolLoop_4558 -> AgdaAny -> AgdaAny -> ()
forall a. a
erased
-- Algebra.Bundles.RightBolLoop._∙_
d__'8729'__4582 ::
  T_RightBolLoop_4558 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__4582 :: T_RightBolLoop_4558 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__4582 T_RightBolLoop_4558
v0
  = case T_RightBolLoop_4558 -> T_RightBolLoop_4558
forall a b. a -> b
coe T_RightBolLoop_4558
v0 of
      C_RightBolLoop'46'constructor_82729 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny -> AgdaAny
v5 AgdaAny
v6 T_IsRightBolLoop_3186
v7 -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v3
      T_RightBolLoop_4558
_ -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.RightBolLoop._\\_
d__'92''92'__4584 ::
  T_RightBolLoop_4558 -> AgdaAny -> AgdaAny -> AgdaAny
d__'92''92'__4584 :: T_RightBolLoop_4558 -> AgdaAny -> AgdaAny -> AgdaAny
d__'92''92'__4584 T_RightBolLoop_4558
v0
  = case T_RightBolLoop_4558 -> T_RightBolLoop_4558
forall a b. a -> b
coe T_RightBolLoop_4558
v0 of
      C_RightBolLoop'46'constructor_82729 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny -> AgdaAny
v5 AgdaAny
v6 T_IsRightBolLoop_3186
v7 -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v4
      T_RightBolLoop_4558
_ -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.RightBolLoop._//_
d__'47''47'__4586 ::
  T_RightBolLoop_4558 -> AgdaAny -> AgdaAny -> AgdaAny
d__'47''47'__4586 :: T_RightBolLoop_4558 -> AgdaAny -> AgdaAny -> AgdaAny
d__'47''47'__4586 T_RightBolLoop_4558
v0
  = case T_RightBolLoop_4558 -> T_RightBolLoop_4558
forall a b. a -> b
coe T_RightBolLoop_4558
v0 of
      C_RightBolLoop'46'constructor_82729 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny -> AgdaAny
v5 AgdaAny
v6 T_IsRightBolLoop_3186
v7 -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v5
      T_RightBolLoop_4558
_ -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.RightBolLoop.ε
d_ε_4588 :: T_RightBolLoop_4558 -> AgdaAny
d_ε_4588 :: T_RightBolLoop_4558 -> AgdaAny
d_ε_4588 T_RightBolLoop_4558
v0
  = case T_RightBolLoop_4558 -> T_RightBolLoop_4558
forall a b. a -> b
coe T_RightBolLoop_4558
v0 of
      C_RightBolLoop'46'constructor_82729 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny -> AgdaAny
v5 AgdaAny
v6 T_IsRightBolLoop_3186
v7 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v6
      T_RightBolLoop_4558
_ -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.RightBolLoop.isRightBolLoop
d_isRightBolLoop_4590 ::
  T_RightBolLoop_4558 ->
  MAlonzo.Code.Algebra.Structures.T_IsRightBolLoop_3186
d_isRightBolLoop_4590 :: T_RightBolLoop_4558 -> T_IsRightBolLoop_3186
d_isRightBolLoop_4590 T_RightBolLoop_4558
v0
  = case T_RightBolLoop_4558 -> T_RightBolLoop_4558
forall a b. a -> b
coe T_RightBolLoop_4558
v0 of
      C_RightBolLoop'46'constructor_82729 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny -> AgdaAny
v5 AgdaAny
v6 T_IsRightBolLoop_3186
v7 -> T_IsRightBolLoop_3186 -> T_IsRightBolLoop_3186
forall a b. a -> b
coe T_IsRightBolLoop_3186
v7
      T_RightBolLoop_4558
_ -> T_IsRightBolLoop_3186
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.RightBolLoop._.//-cong
d_'47''47''45'cong_4594 ::
  T_RightBolLoop_4558 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'47''47''45'cong_4594 :: T_RightBolLoop_4558
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'47''47''45'cong_4594 T_RightBolLoop_4558
v0
  = (T_IsQuasigroup_2944
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsQuasigroup_2944
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'47''47''45'cong_2966
      ((T_IsLoop_3026 -> T_IsQuasigroup_2944) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsLoop_3026 -> T_IsQuasigroup_2944
MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040
         ((T_IsRightBolLoop_3186 -> T_IsLoop_3026) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsRightBolLoop_3186 -> T_IsLoop_3026
MAlonzo.Code.Algebra.Structures.d_isLoop_3200
            ((T_RightBolLoop_4558 -> T_IsRightBolLoop_3186)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_RightBolLoop_4558 -> T_IsRightBolLoop_3186
d_isRightBolLoop_4590 (T_RightBolLoop_4558 -> AgdaAny
forall a b. a -> b
coe T_RightBolLoop_4558
v0))))
-- Algebra.Bundles.RightBolLoop._.//-congʳ
d_'47''47''45'cong'691'_4596 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_RightBolLoop_4558 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'47''47''45'cong'691'_4596 :: ()
-> ()
-> T_RightBolLoop_4558
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'47''47''45'cong'691'_4596 ~()
v0 ~()
v1 T_RightBolLoop_4558
v2
  = T_RightBolLoop_4558
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'47''47''45'cong'691'_4596 T_RightBolLoop_4558
v2
du_'47''47''45'cong'691'_4596 ::
  T_RightBolLoop_4558 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'47''47''45'cong'691'_4596 :: T_RightBolLoop_4558
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'47''47''45'cong'691'_4596 T_RightBolLoop_4558
v0
  = let v1 :: T_IsRightBolLoop_3186
v1 = T_RightBolLoop_4558 -> T_IsRightBolLoop_3186
d_isRightBolLoop_4590 (T_RightBolLoop_4558 -> T_RightBolLoop_4558
forall a b. a -> b
coe T_RightBolLoop_4558
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsLoop_3026
v2 = T_IsRightBolLoop_3186 -> T_IsLoop_3026
MAlonzo.Code.Algebra.Structures.d_isLoop_3200 (T_IsRightBolLoop_3186 -> T_IsRightBolLoop_3186
forall a b. a -> b
coe T_IsRightBolLoop_3186
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsQuasigroup_2944
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsQuasigroup_2944
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'47''47''45'cong'691'_3006
            ((T_IsLoop_3026 -> T_IsQuasigroup_2944) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsLoop_3026 -> T_IsQuasigroup_2944
MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040 (T_IsLoop_3026 -> AgdaAny
forall a b. a -> b
coe T_IsLoop_3026
v2))))
-- Algebra.Bundles.RightBolLoop._.//-congˡ
d_'47''47''45'cong'737'_4598 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_RightBolLoop_4558 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'47''47''45'cong'737'_4598 :: ()
-> ()
-> T_RightBolLoop_4558
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'47''47''45'cong'737'_4598 ~()
v0 ~()
v1 T_RightBolLoop_4558
v2
  = T_RightBolLoop_4558
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'47''47''45'cong'737'_4598 T_RightBolLoop_4558
v2
du_'47''47''45'cong'737'_4598 ::
  T_RightBolLoop_4558 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'47''47''45'cong'737'_4598 :: T_RightBolLoop_4558
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'47''47''45'cong'737'_4598 T_RightBolLoop_4558
v0
  = let v1 :: T_IsRightBolLoop_3186
v1 = T_RightBolLoop_4558 -> T_IsRightBolLoop_3186
d_isRightBolLoop_4590 (T_RightBolLoop_4558 -> T_RightBolLoop_4558
forall a b. a -> b
coe T_RightBolLoop_4558
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsLoop_3026
v2 = T_IsRightBolLoop_3186 -> T_IsLoop_3026
MAlonzo.Code.Algebra.Structures.d_isLoop_3200 (T_IsRightBolLoop_3186 -> T_IsRightBolLoop_3186
forall a b. a -> b
coe T_IsRightBolLoop_3186
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsQuasigroup_2944
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsQuasigroup_2944
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'47''47''45'cong'737'_3002
            ((T_IsLoop_3026 -> T_IsQuasigroup_2944) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsLoop_3026 -> T_IsQuasigroup_2944
MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040 (T_IsLoop_3026 -> AgdaAny
forall a b. a -> b
coe T_IsLoop_3026
v2))))
-- Algebra.Bundles.RightBolLoop._.\\-cong
d_'92''92''45'cong_4600 ::
  T_RightBolLoop_4558 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'92''92''45'cong_4600 :: T_RightBolLoop_4558
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'92''92''45'cong_4600 T_RightBolLoop_4558
v0
  = (T_IsQuasigroup_2944
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsQuasigroup_2944
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'92''92''45'cong_2964
      ((T_IsLoop_3026 -> T_IsQuasigroup_2944) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsLoop_3026 -> T_IsQuasigroup_2944
MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040
         ((T_IsRightBolLoop_3186 -> T_IsLoop_3026) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsRightBolLoop_3186 -> T_IsLoop_3026
MAlonzo.Code.Algebra.Structures.d_isLoop_3200
            ((T_RightBolLoop_4558 -> T_IsRightBolLoop_3186)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_RightBolLoop_4558 -> T_IsRightBolLoop_3186
d_isRightBolLoop_4590 (T_RightBolLoop_4558 -> AgdaAny
forall a b. a -> b
coe T_RightBolLoop_4558
v0))))
-- Algebra.Bundles.RightBolLoop._.\\-congʳ
d_'92''92''45'cong'691'_4602 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_RightBolLoop_4558 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'92''92''45'cong'691'_4602 :: ()
-> ()
-> T_RightBolLoop_4558
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'92''92''45'cong'691'_4602 ~()
v0 ~()
v1 T_RightBolLoop_4558
v2
  = T_RightBolLoop_4558
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'92''92''45'cong'691'_4602 T_RightBolLoop_4558
v2
du_'92''92''45'cong'691'_4602 ::
  T_RightBolLoop_4558 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'92''92''45'cong'691'_4602 :: T_RightBolLoop_4558
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'92''92''45'cong'691'_4602 T_RightBolLoop_4558
v0
  = let v1 :: T_IsRightBolLoop_3186
v1 = T_RightBolLoop_4558 -> T_IsRightBolLoop_3186
d_isRightBolLoop_4590 (T_RightBolLoop_4558 -> T_RightBolLoop_4558
forall a b. a -> b
coe T_RightBolLoop_4558
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsLoop_3026
v2 = T_IsRightBolLoop_3186 -> T_IsLoop_3026
MAlonzo.Code.Algebra.Structures.d_isLoop_3200 (T_IsRightBolLoop_3186 -> T_IsRightBolLoop_3186
forall a b. a -> b
coe T_IsRightBolLoop_3186
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsQuasigroup_2944
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsQuasigroup_2944
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'92''92''45'cong'691'_2998
            ((T_IsLoop_3026 -> T_IsQuasigroup_2944) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsLoop_3026 -> T_IsQuasigroup_2944
MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040 (T_IsLoop_3026 -> AgdaAny
forall a b. a -> b
coe T_IsLoop_3026
v2))))
-- Algebra.Bundles.RightBolLoop._.\\-congˡ
d_'92''92''45'cong'737'_4604 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_RightBolLoop_4558 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'92''92''45'cong'737'_4604 :: ()
-> ()
-> T_RightBolLoop_4558
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'92''92''45'cong'737'_4604 ~()
v0 ~()
v1 T_RightBolLoop_4558
v2
  = T_RightBolLoop_4558
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'92''92''45'cong'737'_4604 T_RightBolLoop_4558
v2
du_'92''92''45'cong'737'_4604 ::
  T_RightBolLoop_4558 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'92''92''45'cong'737'_4604 :: T_RightBolLoop_4558
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'92''92''45'cong'737'_4604 T_RightBolLoop_4558
v0
  = let v1 :: T_IsRightBolLoop_3186
v1 = T_RightBolLoop_4558 -> T_IsRightBolLoop_3186
d_isRightBolLoop_4590 (T_RightBolLoop_4558 -> T_RightBolLoop_4558
forall a b. a -> b
coe T_RightBolLoop_4558
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsLoop_3026
v2 = T_IsRightBolLoop_3186 -> T_IsLoop_3026
MAlonzo.Code.Algebra.Structures.d_isLoop_3200 (T_IsRightBolLoop_3186 -> T_IsRightBolLoop_3186
forall a b. a -> b
coe T_IsRightBolLoop_3186
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsQuasigroup_2944
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsQuasigroup_2944
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'92''92''45'cong'737'_2994
            ((T_IsLoop_3026 -> T_IsQuasigroup_2944) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsLoop_3026 -> T_IsQuasigroup_2944
MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040 (T_IsLoop_3026 -> AgdaAny
forall a b. a -> b
coe T_IsLoop_3026
v2))))
-- Algebra.Bundles.RightBolLoop._.identity
d_identity_4606 ::
  T_RightBolLoop_4558 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_identity_4606 :: T_RightBolLoop_4558 -> T_Σ_14
d_identity_4606 T_RightBolLoop_4558
v0
  = (T_IsLoop_3026 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsLoop_3026 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_identity_3042
      ((T_IsRightBolLoop_3186 -> T_IsLoop_3026) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsRightBolLoop_3186 -> T_IsLoop_3026
MAlonzo.Code.Algebra.Structures.d_isLoop_3200
         ((T_RightBolLoop_4558 -> T_IsRightBolLoop_3186)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_RightBolLoop_4558 -> T_IsRightBolLoop_3186
d_isRightBolLoop_4590 (T_RightBolLoop_4558 -> AgdaAny
forall a b. a -> b
coe T_RightBolLoop_4558
v0)))
-- Algebra.Bundles.RightBolLoop._.identityʳ
d_identity'691'_4608 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_RightBolLoop_4558 -> AgdaAny -> AgdaAny
d_identity'691'_4608 :: () -> () -> T_RightBolLoop_4558 -> AgdaAny -> AgdaAny
d_identity'691'_4608 ~()
v0 ~()
v1 T_RightBolLoop_4558
v2 = T_RightBolLoop_4558 -> AgdaAny -> AgdaAny
du_identity'691'_4608 T_RightBolLoop_4558
v2
du_identity'691'_4608 :: T_RightBolLoop_4558 -> AgdaAny -> AgdaAny
du_identity'691'_4608 :: T_RightBolLoop_4558 -> AgdaAny -> AgdaAny
du_identity'691'_4608 T_RightBolLoop_4558
v0
  = let v1 :: T_IsRightBolLoop_3186
v1 = T_RightBolLoop_4558 -> T_IsRightBolLoop_3186
d_isRightBolLoop_4590 (T_RightBolLoop_4558 -> T_RightBolLoop_4558
forall a b. a -> b
coe T_RightBolLoop_4558
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsLoop_3026 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsLoop_3026 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_identity'691'_3094
         ((T_IsRightBolLoop_3186 -> T_IsLoop_3026) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRightBolLoop_3186 -> T_IsLoop_3026
MAlonzo.Code.Algebra.Structures.d_isLoop_3200 (T_IsRightBolLoop_3186 -> AgdaAny
forall a b. a -> b
coe T_IsRightBolLoop_3186
v1)))
-- Algebra.Bundles.RightBolLoop._.identityˡ
d_identity'737'_4610 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_RightBolLoop_4558 -> AgdaAny -> AgdaAny
d_identity'737'_4610 :: () -> () -> T_RightBolLoop_4558 -> AgdaAny -> AgdaAny
d_identity'737'_4610 ~()
v0 ~()
v1 T_RightBolLoop_4558
v2 = T_RightBolLoop_4558 -> AgdaAny -> AgdaAny
du_identity'737'_4610 T_RightBolLoop_4558
v2
du_identity'737'_4610 :: T_RightBolLoop_4558 -> AgdaAny -> AgdaAny
du_identity'737'_4610 :: T_RightBolLoop_4558 -> AgdaAny -> AgdaAny
du_identity'737'_4610 T_RightBolLoop_4558
v0
  = let v1 :: T_IsRightBolLoop_3186
v1 = T_RightBolLoop_4558 -> T_IsRightBolLoop_3186
d_isRightBolLoop_4590 (T_RightBolLoop_4558 -> T_RightBolLoop_4558
forall a b. a -> b
coe T_RightBolLoop_4558
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsLoop_3026 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsLoop_3026 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_identity'737'_3092
         ((T_IsRightBolLoop_3186 -> T_IsLoop_3026) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRightBolLoop_3186 -> T_IsLoop_3026
MAlonzo.Code.Algebra.Structures.d_isLoop_3200 (T_IsRightBolLoop_3186 -> AgdaAny
forall a b. a -> b
coe T_IsRightBolLoop_3186
v1)))
-- Algebra.Bundles.RightBolLoop._.isEquivalence
d_isEquivalence_4612 ::
  T_RightBolLoop_4558 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_4612 :: T_RightBolLoop_4558 -> T_IsEquivalence_26
d_isEquivalence_4612 T_RightBolLoop_4558
v0
  = (T_IsMagma_176 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
      ((T_IsQuasigroup_2944 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsQuasigroup_2944 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_2962
         ((T_IsLoop_3026 -> T_IsQuasigroup_2944) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsLoop_3026 -> T_IsQuasigroup_2944
MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040
            ((T_IsRightBolLoop_3186 -> T_IsLoop_3026) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsRightBolLoop_3186 -> T_IsLoop_3026
MAlonzo.Code.Algebra.Structures.d_isLoop_3200
               ((T_RightBolLoop_4558 -> T_IsRightBolLoop_3186)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_RightBolLoop_4558 -> T_IsRightBolLoop_3186
d_isRightBolLoop_4590 (T_RightBolLoop_4558 -> AgdaAny
forall a b. a -> b
coe T_RightBolLoop_4558
v0)))))
-- Algebra.Bundles.RightBolLoop._.isLoop
d_isLoop_4614 ::
  T_RightBolLoop_4558 ->
  MAlonzo.Code.Algebra.Structures.T_IsLoop_3026
d_isLoop_4614 :: T_RightBolLoop_4558 -> T_IsLoop_3026
d_isLoop_4614 T_RightBolLoop_4558
v0
  = (T_IsRightBolLoop_3186 -> T_IsLoop_3026)
-> AgdaAny -> T_IsLoop_3026
forall a b. a -> b
coe
      T_IsRightBolLoop_3186 -> T_IsLoop_3026
MAlonzo.Code.Algebra.Structures.d_isLoop_3200
      ((T_RightBolLoop_4558 -> T_IsRightBolLoop_3186)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_RightBolLoop_4558 -> T_IsRightBolLoop_3186
d_isRightBolLoop_4590 (T_RightBolLoop_4558 -> AgdaAny
forall a b. a -> b
coe T_RightBolLoop_4558
v0))
-- Algebra.Bundles.RightBolLoop._.isMagma
d_isMagma_4616 ::
  T_RightBolLoop_4558 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_176
d_isMagma_4616 :: T_RightBolLoop_4558 -> T_IsMagma_176
d_isMagma_4616 T_RightBolLoop_4558
v0
  = (T_IsQuasigroup_2944 -> T_IsMagma_176) -> AgdaAny -> T_IsMagma_176
forall a b. a -> b
coe
      T_IsQuasigroup_2944 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_2962
      ((T_IsLoop_3026 -> T_IsQuasigroup_2944) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsLoop_3026 -> T_IsQuasigroup_2944
MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040
         ((T_IsRightBolLoop_3186 -> T_IsLoop_3026) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsRightBolLoop_3186 -> T_IsLoop_3026
MAlonzo.Code.Algebra.Structures.d_isLoop_3200
            ((T_RightBolLoop_4558 -> T_IsRightBolLoop_3186)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_RightBolLoop_4558 -> T_IsRightBolLoop_3186
d_isRightBolLoop_4590 (T_RightBolLoop_4558 -> AgdaAny
forall a b. a -> b
coe T_RightBolLoop_4558
v0))))
-- Algebra.Bundles.RightBolLoop._.isPartialEquivalence
d_isPartialEquivalence_4618 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_RightBolLoop_4558 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_4618 :: () -> () -> T_RightBolLoop_4558 -> T_IsPartialEquivalence_16
d_isPartialEquivalence_4618 ~()
v0 ~()
v1 T_RightBolLoop_4558
v2
  = T_RightBolLoop_4558 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_4618 T_RightBolLoop_4558
v2
du_isPartialEquivalence_4618 ::
  T_RightBolLoop_4558 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_4618 :: T_RightBolLoop_4558 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_4618 T_RightBolLoop_4558
v0
  = let v1 :: T_IsRightBolLoop_3186
v1 = T_RightBolLoop_4558 -> T_IsRightBolLoop_3186
d_isRightBolLoop_4590 (T_RightBolLoop_4558 -> T_RightBolLoop_4558
forall a b. a -> b
coe T_RightBolLoop_4558
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsLoop_3026
v2 = T_IsRightBolLoop_3186 -> T_IsLoop_3026
MAlonzo.Code.Algebra.Structures.d_isLoop_3200 (T_IsRightBolLoop_3186 -> T_IsRightBolLoop_3186
forall a b. a -> b
coe T_IsRightBolLoop_3186
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsQuasigroup_2944
v3
                = T_IsLoop_3026 -> T_IsQuasigroup_2944
MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040 (T_IsLoop_3026 -> T_IsLoop_3026
forall a b. a -> b
coe T_IsLoop_3026
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsMagma_176
v4
                   = T_IsQuasigroup_2944 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_2962 (T_IsQuasigroup_2944 -> T_IsQuasigroup_2944
forall a b. a -> b
coe T_IsQuasigroup_2944
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               ((T_IsEquivalence_26 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsEquivalence_26 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
                  ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v4))))))
-- Algebra.Bundles.RightBolLoop._.isQuasigroup
d_isQuasigroup_4620 ::
  T_RightBolLoop_4558 ->
  MAlonzo.Code.Algebra.Structures.T_IsQuasigroup_2944
d_isQuasigroup_4620 :: T_RightBolLoop_4558 -> T_IsQuasigroup_2944
d_isQuasigroup_4620 T_RightBolLoop_4558
v0
  = (T_IsLoop_3026 -> T_IsQuasigroup_2944)
-> AgdaAny -> T_IsQuasigroup_2944
forall a b. a -> b
coe
      T_IsLoop_3026 -> T_IsQuasigroup_2944
MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040
      ((T_IsRightBolLoop_3186 -> T_IsLoop_3026) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsRightBolLoop_3186 -> T_IsLoop_3026
MAlonzo.Code.Algebra.Structures.d_isLoop_3200
         ((T_RightBolLoop_4558 -> T_IsRightBolLoop_3186)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_RightBolLoop_4558 -> T_IsRightBolLoop_3186
d_isRightBolLoop_4590 (T_RightBolLoop_4558 -> AgdaAny
forall a b. a -> b
coe T_RightBolLoop_4558
v0)))
-- Algebra.Bundles.RightBolLoop._.leftDivides
d_leftDivides_4622 ::
  T_RightBolLoop_4558 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_leftDivides_4622 :: T_RightBolLoop_4558 -> T_Σ_14
d_leftDivides_4622 T_RightBolLoop_4558
v0
  = (T_IsQuasigroup_2944 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsQuasigroup_2944 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_leftDivides_2968
      ((T_IsLoop_3026 -> T_IsQuasigroup_2944) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsLoop_3026 -> T_IsQuasigroup_2944
MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040
         ((T_IsRightBolLoop_3186 -> T_IsLoop_3026) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsRightBolLoop_3186 -> T_IsLoop_3026
MAlonzo.Code.Algebra.Structures.d_isLoop_3200
            ((T_RightBolLoop_4558 -> T_IsRightBolLoop_3186)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_RightBolLoop_4558 -> T_IsRightBolLoop_3186
d_isRightBolLoop_4590 (T_RightBolLoop_4558 -> AgdaAny
forall a b. a -> b
coe T_RightBolLoop_4558
v0))))
-- Algebra.Bundles.RightBolLoop._.leftDividesʳ
d_leftDivides'691'_4624 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_RightBolLoop_4558 -> AgdaAny -> AgdaAny -> AgdaAny
d_leftDivides'691'_4624 :: () -> () -> T_RightBolLoop_4558 -> AgdaAny -> AgdaAny -> AgdaAny
d_leftDivides'691'_4624 ~()
v0 ~()
v1 T_RightBolLoop_4558
v2 = T_RightBolLoop_4558 -> AgdaAny -> AgdaAny -> AgdaAny
du_leftDivides'691'_4624 T_RightBolLoop_4558
v2
du_leftDivides'691'_4624 ::
  T_RightBolLoop_4558 -> AgdaAny -> AgdaAny -> AgdaAny
du_leftDivides'691'_4624 :: T_RightBolLoop_4558 -> AgdaAny -> AgdaAny -> AgdaAny
du_leftDivides'691'_4624 T_RightBolLoop_4558
v0
  = let v1 :: T_IsRightBolLoop_3186
v1 = T_RightBolLoop_4558 -> T_IsRightBolLoop_3186
d_isRightBolLoop_4590 (T_RightBolLoop_4558 -> T_RightBolLoop_4558
forall a b. a -> b
coe T_RightBolLoop_4558
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsLoop_3026
v2 = T_IsRightBolLoop_3186 -> T_IsLoop_3026
MAlonzo.Code.Algebra.Structures.d_isLoop_3200 (T_IsRightBolLoop_3186 -> T_IsRightBolLoop_3186
forall a b. a -> b
coe T_IsRightBolLoop_3186
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsQuasigroup_2944 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsQuasigroup_2944 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_leftDivides'691'_3012
            ((T_IsLoop_3026 -> T_IsQuasigroup_2944) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsLoop_3026 -> T_IsQuasigroup_2944
MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040 (T_IsLoop_3026 -> AgdaAny
forall a b. a -> b
coe T_IsLoop_3026
v2))))
-- Algebra.Bundles.RightBolLoop._.leftDividesˡ
d_leftDivides'737'_4626 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_RightBolLoop_4558 -> AgdaAny -> AgdaAny -> AgdaAny
d_leftDivides'737'_4626 :: () -> () -> T_RightBolLoop_4558 -> AgdaAny -> AgdaAny -> AgdaAny
d_leftDivides'737'_4626 ~()
v0 ~()
v1 T_RightBolLoop_4558
v2 = T_RightBolLoop_4558 -> AgdaAny -> AgdaAny -> AgdaAny
du_leftDivides'737'_4626 T_RightBolLoop_4558
v2
du_leftDivides'737'_4626 ::
  T_RightBolLoop_4558 -> AgdaAny -> AgdaAny -> AgdaAny
du_leftDivides'737'_4626 :: T_RightBolLoop_4558 -> AgdaAny -> AgdaAny -> AgdaAny
du_leftDivides'737'_4626 T_RightBolLoop_4558
v0
  = let v1 :: T_IsRightBolLoop_3186
v1 = T_RightBolLoop_4558 -> T_IsRightBolLoop_3186
d_isRightBolLoop_4590 (T_RightBolLoop_4558 -> T_RightBolLoop_4558
forall a b. a -> b
coe T_RightBolLoop_4558
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsLoop_3026
v2 = T_IsRightBolLoop_3186 -> T_IsLoop_3026
MAlonzo.Code.Algebra.Structures.d_isLoop_3200 (T_IsRightBolLoop_3186 -> T_IsRightBolLoop_3186
forall a b. a -> b
coe T_IsRightBolLoop_3186
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsQuasigroup_2944 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsQuasigroup_2944 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_leftDivides'737'_3010
            ((T_IsLoop_3026 -> T_IsQuasigroup_2944) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsLoop_3026 -> T_IsQuasigroup_2944
MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040 (T_IsLoop_3026 -> AgdaAny
forall a b. a -> b
coe T_IsLoop_3026
v2))))
-- Algebra.Bundles.RightBolLoop._.refl
d_refl_4628 :: T_RightBolLoop_4558 -> AgdaAny -> AgdaAny
d_refl_4628 :: T_RightBolLoop_4558 -> AgdaAny -> AgdaAny
d_refl_4628 T_RightBolLoop_4558
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_34
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
         ((T_IsQuasigroup_2944 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsQuasigroup_2944 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_2962
            ((T_IsLoop_3026 -> T_IsQuasigroup_2944) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsLoop_3026 -> T_IsQuasigroup_2944
MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040
               ((T_IsRightBolLoop_3186 -> T_IsLoop_3026) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsRightBolLoop_3186 -> T_IsLoop_3026
MAlonzo.Code.Algebra.Structures.d_isLoop_3200
                  ((T_RightBolLoop_4558 -> T_IsRightBolLoop_3186)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_RightBolLoop_4558 -> T_IsRightBolLoop_3186
d_isRightBolLoop_4590 (T_RightBolLoop_4558 -> AgdaAny
forall a b. a -> b
coe T_RightBolLoop_4558
v0))))))
-- Algebra.Bundles.RightBolLoop._.reflexive
d_reflexive_4630 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_RightBolLoop_4558 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_4630 :: ()
-> ()
-> T_RightBolLoop_4558
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_4630 ~()
v0 ~()
v1 T_RightBolLoop_4558
v2 = T_RightBolLoop_4558
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_4630 T_RightBolLoop_4558
v2
du_reflexive_4630 ::
  T_RightBolLoop_4558 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_4630 :: T_RightBolLoop_4558
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_4630 T_RightBolLoop_4558
v0
  = let v1 :: T_IsRightBolLoop_3186
v1 = T_RightBolLoop_4558 -> T_IsRightBolLoop_3186
d_isRightBolLoop_4590 (T_RightBolLoop_4558 -> T_RightBolLoop_4558
forall a b. a -> b
coe T_RightBolLoop_4558
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsLoop_3026
v2 = T_IsRightBolLoop_3186 -> T_IsLoop_3026
MAlonzo.Code.Algebra.Structures.d_isLoop_3200 (T_IsRightBolLoop_3186 -> T_IsRightBolLoop_3186
forall a b. a -> b
coe T_IsRightBolLoop_3186
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsQuasigroup_2944
v3
                = T_IsLoop_3026 -> T_IsQuasigroup_2944
MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040 (T_IsLoop_3026 -> T_IsLoop_3026
forall a b. a -> b
coe T_IsLoop_3026
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsMagma_176
v4
                   = T_IsQuasigroup_2944 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_2962 (T_IsQuasigroup_2944 -> T_IsQuasigroup_2944
forall a b. a -> b
coe T_IsQuasigroup_2944
v3) in
             (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
               (\ AgdaAny
v5 AgdaAny
v6 AgdaAny
v7 ->
                  (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                    T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
                    ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v4))
                    AgdaAny
v5))))
-- Algebra.Bundles.RightBolLoop._.rightBol
d_rightBol_4632 ::
  T_RightBolLoop_4558 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_rightBol_4632 :: T_RightBolLoop_4558 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_rightBol_4632 T_RightBolLoop_4558
v0
  = (T_IsRightBolLoop_3186 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsRightBolLoop_3186 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_rightBol_3202
      ((T_RightBolLoop_4558 -> T_IsRightBolLoop_3186)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_RightBolLoop_4558 -> T_IsRightBolLoop_3186
d_isRightBolLoop_4590 (T_RightBolLoop_4558 -> AgdaAny
forall a b. a -> b
coe T_RightBolLoop_4558
v0))
-- Algebra.Bundles.RightBolLoop._.rightDivides
d_rightDivides_4634 ::
  T_RightBolLoop_4558 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_rightDivides_4634 :: T_RightBolLoop_4558 -> T_Σ_14
d_rightDivides_4634 T_RightBolLoop_4558
v0
  = (T_IsQuasigroup_2944 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsQuasigroup_2944 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_rightDivides_2970
      ((T_IsLoop_3026 -> T_IsQuasigroup_2944) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsLoop_3026 -> T_IsQuasigroup_2944
MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040
         ((T_IsRightBolLoop_3186 -> T_IsLoop_3026) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsRightBolLoop_3186 -> T_IsLoop_3026
MAlonzo.Code.Algebra.Structures.d_isLoop_3200
            ((T_RightBolLoop_4558 -> T_IsRightBolLoop_3186)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_RightBolLoop_4558 -> T_IsRightBolLoop_3186
d_isRightBolLoop_4590 (T_RightBolLoop_4558 -> AgdaAny
forall a b. a -> b
coe T_RightBolLoop_4558
v0))))
-- Algebra.Bundles.RightBolLoop._.rightDividesʳ
d_rightDivides'691'_4636 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_RightBolLoop_4558 -> AgdaAny -> AgdaAny -> AgdaAny
d_rightDivides'691'_4636 :: () -> () -> T_RightBolLoop_4558 -> AgdaAny -> AgdaAny -> AgdaAny
d_rightDivides'691'_4636 ~()
v0 ~()
v1 T_RightBolLoop_4558
v2 = T_RightBolLoop_4558 -> AgdaAny -> AgdaAny -> AgdaAny
du_rightDivides'691'_4636 T_RightBolLoop_4558
v2
du_rightDivides'691'_4636 ::
  T_RightBolLoop_4558 -> AgdaAny -> AgdaAny -> AgdaAny
du_rightDivides'691'_4636 :: T_RightBolLoop_4558 -> AgdaAny -> AgdaAny -> AgdaAny
du_rightDivides'691'_4636 T_RightBolLoop_4558
v0
  = let v1 :: T_IsRightBolLoop_3186
v1 = T_RightBolLoop_4558 -> T_IsRightBolLoop_3186
d_isRightBolLoop_4590 (T_RightBolLoop_4558 -> T_RightBolLoop_4558
forall a b. a -> b
coe T_RightBolLoop_4558
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsLoop_3026
v2 = T_IsRightBolLoop_3186 -> T_IsLoop_3026
MAlonzo.Code.Algebra.Structures.d_isLoop_3200 (T_IsRightBolLoop_3186 -> T_IsRightBolLoop_3186
forall a b. a -> b
coe T_IsRightBolLoop_3186
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsQuasigroup_2944 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsQuasigroup_2944 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_rightDivides'691'_3016
            ((T_IsLoop_3026 -> T_IsQuasigroup_2944) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsLoop_3026 -> T_IsQuasigroup_2944
MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040 (T_IsLoop_3026 -> AgdaAny
forall a b. a -> b
coe T_IsLoop_3026
v2))))
-- Algebra.Bundles.RightBolLoop._.rightDividesˡ
d_rightDivides'737'_4638 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_RightBolLoop_4558 -> AgdaAny -> AgdaAny -> AgdaAny
d_rightDivides'737'_4638 :: () -> () -> T_RightBolLoop_4558 -> AgdaAny -> AgdaAny -> AgdaAny
d_rightDivides'737'_4638 ~()
v0 ~()
v1 T_RightBolLoop_4558
v2 = T_RightBolLoop_4558 -> AgdaAny -> AgdaAny -> AgdaAny
du_rightDivides'737'_4638 T_RightBolLoop_4558
v2
du_rightDivides'737'_4638 ::
  T_RightBolLoop_4558 -> AgdaAny -> AgdaAny -> AgdaAny
du_rightDivides'737'_4638 :: T_RightBolLoop_4558 -> AgdaAny -> AgdaAny -> AgdaAny
du_rightDivides'737'_4638 T_RightBolLoop_4558
v0
  = let v1 :: T_IsRightBolLoop_3186
v1 = T_RightBolLoop_4558 -> T_IsRightBolLoop_3186
d_isRightBolLoop_4590 (T_RightBolLoop_4558 -> T_RightBolLoop_4558
forall a b. a -> b
coe T_RightBolLoop_4558
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsLoop_3026
v2 = T_IsRightBolLoop_3186 -> T_IsLoop_3026
MAlonzo.Code.Algebra.Structures.d_isLoop_3200 (T_IsRightBolLoop_3186 -> T_IsRightBolLoop_3186
forall a b. a -> b
coe T_IsRightBolLoop_3186
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsQuasigroup_2944 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsQuasigroup_2944 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_rightDivides'737'_3014
            ((T_IsLoop_3026 -> T_IsQuasigroup_2944) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsLoop_3026 -> T_IsQuasigroup_2944
MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040 (T_IsLoop_3026 -> AgdaAny
forall a b. a -> b
coe T_IsLoop_3026
v2))))
-- Algebra.Bundles.RightBolLoop._.setoid
d_setoid_4640 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_RightBolLoop_4558 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_4640 :: () -> () -> T_RightBolLoop_4558 -> T_Setoid_44
d_setoid_4640 ~()
v0 ~()
v1 T_RightBolLoop_4558
v2 = T_RightBolLoop_4558 -> T_Setoid_44
du_setoid_4640 T_RightBolLoop_4558
v2
du_setoid_4640 ::
  T_RightBolLoop_4558 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_4640 :: T_RightBolLoop_4558 -> T_Setoid_44
du_setoid_4640 T_RightBolLoop_4558
v0
  = let v1 :: T_IsRightBolLoop_3186
v1 = T_RightBolLoop_4558 -> T_IsRightBolLoop_3186
d_isRightBolLoop_4590 (T_RightBolLoop_4558 -> T_RightBolLoop_4558
forall a b. a -> b
coe T_RightBolLoop_4558
v0) in
    AgdaAny -> T_Setoid_44
forall a b. a -> b
coe
      (let v2 :: T_IsLoop_3026
v2 = T_IsRightBolLoop_3186 -> T_IsLoop_3026
MAlonzo.Code.Algebra.Structures.d_isLoop_3200 (T_IsRightBolLoop_3186 -> T_IsRightBolLoop_3186
forall a b. a -> b
coe T_IsRightBolLoop_3186
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsQuasigroup_2944
v3
                = T_IsLoop_3026 -> T_IsQuasigroup_2944
MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040 (T_IsLoop_3026 -> T_IsLoop_3026
forall a b. a -> b
coe T_IsLoop_3026
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsMagma_176 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMagma_176 -> T_Setoid_44
MAlonzo.Code.Algebra.Structures.du_setoid_200
               ((T_IsQuasigroup_2944 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroup_2944 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_2962 (T_IsQuasigroup_2944 -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroup_2944
v3)))))
-- Algebra.Bundles.RightBolLoop._.sym
d_sym_4642 ::
  T_RightBolLoop_4558 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_4642 :: T_RightBolLoop_4558 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_4642 T_RightBolLoop_4558
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_36
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
         ((T_IsQuasigroup_2944 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsQuasigroup_2944 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_2962
            ((T_IsLoop_3026 -> T_IsQuasigroup_2944) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsLoop_3026 -> T_IsQuasigroup_2944
MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040
               ((T_IsRightBolLoop_3186 -> T_IsLoop_3026) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsRightBolLoop_3186 -> T_IsLoop_3026
MAlonzo.Code.Algebra.Structures.d_isLoop_3200
                  ((T_RightBolLoop_4558 -> T_IsRightBolLoop_3186)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_RightBolLoop_4558 -> T_IsRightBolLoop_3186
d_isRightBolLoop_4590 (T_RightBolLoop_4558 -> AgdaAny
forall a b. a -> b
coe T_RightBolLoop_4558
v0))))))
-- Algebra.Bundles.RightBolLoop._.trans
d_trans_4644 ::
  T_RightBolLoop_4558 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_4644 :: T_RightBolLoop_4558
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_4644 T_RightBolLoop_4558
v0
  = (T_IsEquivalence_26
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_38
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
         ((T_IsQuasigroup_2944 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsQuasigroup_2944 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_2962
            ((T_IsLoop_3026 -> T_IsQuasigroup_2944) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsLoop_3026 -> T_IsQuasigroup_2944
MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040
               ((T_IsRightBolLoop_3186 -> T_IsLoop_3026) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsRightBolLoop_3186 -> T_IsLoop_3026
MAlonzo.Code.Algebra.Structures.d_isLoop_3200
                  ((T_RightBolLoop_4558 -> T_IsRightBolLoop_3186)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_RightBolLoop_4558 -> T_IsRightBolLoop_3186
d_isRightBolLoop_4590 (T_RightBolLoop_4558 -> AgdaAny
forall a b. a -> b
coe T_RightBolLoop_4558
v0))))))
-- Algebra.Bundles.RightBolLoop._.∙-cong
d_'8729''45'cong_4646 ::
  T_RightBolLoop_4558 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_4646 :: T_RightBolLoop_4558
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_4646 T_RightBolLoop_4558
v0
  = (T_IsMagma_176
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsMagma_176
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_186
      ((T_IsQuasigroup_2944 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsQuasigroup_2944 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_2962
         ((T_IsLoop_3026 -> T_IsQuasigroup_2944) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsLoop_3026 -> T_IsQuasigroup_2944
MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040
            ((T_IsRightBolLoop_3186 -> T_IsLoop_3026) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsRightBolLoop_3186 -> T_IsLoop_3026
MAlonzo.Code.Algebra.Structures.d_isLoop_3200
               ((T_RightBolLoop_4558 -> T_IsRightBolLoop_3186)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_RightBolLoop_4558 -> T_IsRightBolLoop_3186
d_isRightBolLoop_4590 (T_RightBolLoop_4558 -> AgdaAny
forall a b. a -> b
coe T_RightBolLoop_4558
v0)))))
-- Algebra.Bundles.RightBolLoop._.∙-congʳ
d_'8729''45'cong'691'_4648 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_RightBolLoop_4558 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_4648 :: ()
-> ()
-> T_RightBolLoop_4558
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_4648 ~()
v0 ~()
v1 T_RightBolLoop_4558
v2
  = T_RightBolLoop_4558
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_4648 T_RightBolLoop_4558
v2
du_'8729''45'cong'691'_4648 ::
  T_RightBolLoop_4558 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_4648 :: T_RightBolLoop_4558
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_4648 T_RightBolLoop_4558
v0
  = let v1 :: T_IsRightBolLoop_3186
v1 = T_RightBolLoop_4558 -> T_IsRightBolLoop_3186
d_isRightBolLoop_4590 (T_RightBolLoop_4558 -> T_RightBolLoop_4558
forall a b. a -> b
coe T_RightBolLoop_4558
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsLoop_3026
v2 = T_IsRightBolLoop_3186 -> T_IsLoop_3026
MAlonzo.Code.Algebra.Structures.d_isLoop_3200 (T_IsRightBolLoop_3186 -> T_IsRightBolLoop_3186
forall a b. a -> b
coe T_IsRightBolLoop_3186
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsQuasigroup_2944
v3
                = T_IsLoop_3026 -> T_IsQuasigroup_2944
MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040 (T_IsLoop_3026 -> T_IsLoop_3026
forall a b. a -> b
coe T_IsLoop_3026
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'691'_206
               ((T_IsQuasigroup_2944 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroup_2944 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_2962 (T_IsQuasigroup_2944 -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroup_2944
v3)))))
-- Algebra.Bundles.RightBolLoop._.∙-congˡ
d_'8729''45'cong'737'_4650 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_RightBolLoop_4558 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_4650 :: ()
-> ()
-> T_RightBolLoop_4558
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_4650 ~()
v0 ~()
v1 T_RightBolLoop_4558
v2
  = T_RightBolLoop_4558
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_4650 T_RightBolLoop_4558
v2
du_'8729''45'cong'737'_4650 ::
  T_RightBolLoop_4558 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_4650 :: T_RightBolLoop_4558
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_4650 T_RightBolLoop_4558
v0
  = let v1 :: T_IsRightBolLoop_3186
v1 = T_RightBolLoop_4558 -> T_IsRightBolLoop_3186
d_isRightBolLoop_4590 (T_RightBolLoop_4558 -> T_RightBolLoop_4558
forall a b. a -> b
coe T_RightBolLoop_4558
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsLoop_3026
v2 = T_IsRightBolLoop_3186 -> T_IsLoop_3026
MAlonzo.Code.Algebra.Structures.d_isLoop_3200 (T_IsRightBolLoop_3186 -> T_IsRightBolLoop_3186
forall a b. a -> b
coe T_IsRightBolLoop_3186
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsQuasigroup_2944
v3
                = T_IsLoop_3026 -> T_IsQuasigroup_2944
MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040 (T_IsLoop_3026 -> T_IsLoop_3026
forall a b. a -> b
coe T_IsLoop_3026
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'737'_202
               ((T_IsQuasigroup_2944 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroup_2944 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_2962 (T_IsQuasigroup_2944 -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroup_2944
v3)))))
-- Algebra.Bundles.RightBolLoop.loop
d_loop_4652 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_RightBolLoop_4558 -> T_Loop_4346
d_loop_4652 :: () -> () -> T_RightBolLoop_4558 -> T_Loop_4346
d_loop_4652 ~()
v0 ~()
v1 T_RightBolLoop_4558
v2 = T_RightBolLoop_4558 -> T_Loop_4346
du_loop_4652 T_RightBolLoop_4558
v2
du_loop_4652 :: T_RightBolLoop_4558 -> T_Loop_4346
du_loop_4652 :: T_RightBolLoop_4558 -> T_Loop_4346
du_loop_4652 T_RightBolLoop_4558
v0
  = ((AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> T_IsLoop_3026
 -> T_Loop_4346)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsLoop_3026
-> T_Loop_4346
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsLoop_3026
-> T_Loop_4346
C_Loop'46'constructor_78267 (T_RightBolLoop_4558 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__4582 (T_RightBolLoop_4558 -> T_RightBolLoop_4558
forall a b. a -> b
coe T_RightBolLoop_4558
v0))
      (T_RightBolLoop_4558 -> AgdaAny -> AgdaAny -> AgdaAny
d__'92''92'__4584 (T_RightBolLoop_4558 -> T_RightBolLoop_4558
forall a b. a -> b
coe T_RightBolLoop_4558
v0)) (T_RightBolLoop_4558 -> AgdaAny -> AgdaAny -> AgdaAny
d__'47''47'__4586 (T_RightBolLoop_4558 -> T_RightBolLoop_4558
forall a b. a -> b
coe T_RightBolLoop_4558
v0))
      (T_RightBolLoop_4558 -> AgdaAny
d_ε_4588 (T_RightBolLoop_4558 -> T_RightBolLoop_4558
forall a b. a -> b
coe T_RightBolLoop_4558
v0))
      (T_IsRightBolLoop_3186 -> T_IsLoop_3026
MAlonzo.Code.Algebra.Structures.d_isLoop_3200
         ((T_RightBolLoop_4558 -> T_IsRightBolLoop_3186)
-> AgdaAny -> T_IsRightBolLoop_3186
forall a b. a -> b
coe T_RightBolLoop_4558 -> T_IsRightBolLoop_3186
d_isRightBolLoop_4590 (T_RightBolLoop_4558 -> AgdaAny
forall a b. a -> b
coe T_RightBolLoop_4558
v0)))
-- Algebra.Bundles.RightBolLoop._.quasigroup
d_quasigroup_4656 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_RightBolLoop_4558 -> T_Quasigroup_4246
d_quasigroup_4656 :: () -> () -> T_RightBolLoop_4558 -> T_Quasigroup_4246
d_quasigroup_4656 ~()
v0 ~()
v1 T_RightBolLoop_4558
v2 = T_RightBolLoop_4558 -> T_Quasigroup_4246
du_quasigroup_4656 T_RightBolLoop_4558
v2
du_quasigroup_4656 :: T_RightBolLoop_4558 -> T_Quasigroup_4246
du_quasigroup_4656 :: T_RightBolLoop_4558 -> T_Quasigroup_4246
du_quasigroup_4656 T_RightBolLoop_4558
v0
  = (T_Loop_4346 -> T_Quasigroup_4246) -> AgdaAny -> T_Quasigroup_4246
forall a b. a -> b
coe T_Loop_4346 -> T_Quasigroup_4246
du_quasigroup_4438 ((T_RightBolLoop_4558 -> T_Loop_4346) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_RightBolLoop_4558 -> T_Loop_4346
du_loop_4652 (T_RightBolLoop_4558 -> AgdaAny
forall a b. a -> b
coe T_RightBolLoop_4558
v0))
-- Algebra.Bundles.MoufangLoop
d_MoufangLoop_4662 :: p -> p -> ()
d_MoufangLoop_4662 p
a0 p
a1 = ()
data T_MoufangLoop_4662
  = C_MoufangLoop'46'constructor_84927 (AgdaAny ->
                                        AgdaAny -> AgdaAny)
                                       (AgdaAny -> AgdaAny -> AgdaAny)
                                       (AgdaAny -> AgdaAny -> AgdaAny) AgdaAny
                                       MAlonzo.Code.Algebra.Structures.T_IsMoufangLoop_3268
-- Algebra.Bundles.MoufangLoop.Carrier
d_Carrier_4682 :: T_MoufangLoop_4662 -> ()
d_Carrier_4682 :: T_MoufangLoop_4662 -> ()
d_Carrier_4682 = T_MoufangLoop_4662 -> ()
forall a. a
erased
-- Algebra.Bundles.MoufangLoop._≈_
d__'8776'__4684 :: T_MoufangLoop_4662 -> AgdaAny -> AgdaAny -> ()
d__'8776'__4684 :: T_MoufangLoop_4662 -> AgdaAny -> AgdaAny -> ()
d__'8776'__4684 = T_MoufangLoop_4662 -> AgdaAny -> AgdaAny -> ()
forall a. a
erased
-- Algebra.Bundles.MoufangLoop._∙_
d__'8729'__4686 ::
  T_MoufangLoop_4662 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__4686 :: T_MoufangLoop_4662 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__4686 T_MoufangLoop_4662
v0
  = case T_MoufangLoop_4662 -> T_MoufangLoop_4662
forall a b. a -> b
coe T_MoufangLoop_4662
v0 of
      C_MoufangLoop'46'constructor_84927 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny -> AgdaAny
v5 AgdaAny
v6 T_IsMoufangLoop_3268
v7 -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v3
      T_MoufangLoop_4662
_ -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.MoufangLoop._\\_
d__'92''92'__4688 ::
  T_MoufangLoop_4662 -> AgdaAny -> AgdaAny -> AgdaAny
d__'92''92'__4688 :: T_MoufangLoop_4662 -> AgdaAny -> AgdaAny -> AgdaAny
d__'92''92'__4688 T_MoufangLoop_4662
v0
  = case T_MoufangLoop_4662 -> T_MoufangLoop_4662
forall a b. a -> b
coe T_MoufangLoop_4662
v0 of
      C_MoufangLoop'46'constructor_84927 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny -> AgdaAny
v5 AgdaAny
v6 T_IsMoufangLoop_3268
v7 -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v4
      T_MoufangLoop_4662
_ -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.MoufangLoop._//_
d__'47''47'__4690 ::
  T_MoufangLoop_4662 -> AgdaAny -> AgdaAny -> AgdaAny
d__'47''47'__4690 :: T_MoufangLoop_4662 -> AgdaAny -> AgdaAny -> AgdaAny
d__'47''47'__4690 T_MoufangLoop_4662
v0
  = case T_MoufangLoop_4662 -> T_MoufangLoop_4662
forall a b. a -> b
coe T_MoufangLoop_4662
v0 of
      C_MoufangLoop'46'constructor_84927 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny -> AgdaAny
v5 AgdaAny
v6 T_IsMoufangLoop_3268
v7 -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v5
      T_MoufangLoop_4662
_ -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.MoufangLoop.ε
d_ε_4692 :: T_MoufangLoop_4662 -> AgdaAny
d_ε_4692 :: T_MoufangLoop_4662 -> AgdaAny
d_ε_4692 T_MoufangLoop_4662
v0
  = case T_MoufangLoop_4662 -> T_MoufangLoop_4662
forall a b. a -> b
coe T_MoufangLoop_4662
v0 of
      C_MoufangLoop'46'constructor_84927 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny -> AgdaAny
v5 AgdaAny
v6 T_IsMoufangLoop_3268
v7 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v6
      T_MoufangLoop_4662
_ -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.MoufangLoop.isMoufangLoop
d_isMoufangLoop_4694 ::
  T_MoufangLoop_4662 ->
  MAlonzo.Code.Algebra.Structures.T_IsMoufangLoop_3268
d_isMoufangLoop_4694 :: T_MoufangLoop_4662 -> T_IsMoufangLoop_3268
d_isMoufangLoop_4694 T_MoufangLoop_4662
v0
  = case T_MoufangLoop_4662 -> T_MoufangLoop_4662
forall a b. a -> b
coe T_MoufangLoop_4662
v0 of
      C_MoufangLoop'46'constructor_84927 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny -> AgdaAny
v5 AgdaAny
v6 T_IsMoufangLoop_3268
v7 -> T_IsMoufangLoop_3268 -> T_IsMoufangLoop_3268
forall a b. a -> b
coe T_IsMoufangLoop_3268
v7
      T_MoufangLoop_4662
_ -> T_IsMoufangLoop_3268
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.MoufangLoop._.//-cong
d_'47''47''45'cong_4698 ::
  T_MoufangLoop_4662 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'47''47''45'cong_4698 :: T_MoufangLoop_4662
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'47''47''45'cong_4698 T_MoufangLoop_4662
v0
  = (T_IsQuasigroup_2944
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsQuasigroup_2944
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'47''47''45'cong_2966
      ((T_IsLoop_3026 -> T_IsQuasigroup_2944) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsLoop_3026 -> T_IsQuasigroup_2944
MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040
         ((T_IsLeftBolLoop_3104 -> T_IsLoop_3026) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsLeftBolLoop_3104 -> T_IsLoop_3026
MAlonzo.Code.Algebra.Structures.d_isLoop_3118
            ((T_IsMoufangLoop_3268 -> T_IsLeftBolLoop_3104)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMoufangLoop_3268 -> T_IsLeftBolLoop_3104
MAlonzo.Code.Algebra.Structures.d_isLeftBolLoop_3284
               ((T_MoufangLoop_4662 -> T_IsMoufangLoop_3268) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_MoufangLoop_4662 -> T_IsMoufangLoop_3268
d_isMoufangLoop_4694 (T_MoufangLoop_4662 -> AgdaAny
forall a b. a -> b
coe T_MoufangLoop_4662
v0)))))
-- Algebra.Bundles.MoufangLoop._.//-congʳ
d_'47''47''45'cong'691'_4700 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_MoufangLoop_4662 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'47''47''45'cong'691'_4700 :: ()
-> ()
-> T_MoufangLoop_4662
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'47''47''45'cong'691'_4700 ~()
v0 ~()
v1 T_MoufangLoop_4662
v2
  = T_MoufangLoop_4662
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'47''47''45'cong'691'_4700 T_MoufangLoop_4662
v2
du_'47''47''45'cong'691'_4700 ::
  T_MoufangLoop_4662 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'47''47''45'cong'691'_4700 :: T_MoufangLoop_4662
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'47''47''45'cong'691'_4700 T_MoufangLoop_4662
v0
  = let v1 :: T_IsMoufangLoop_3268
v1 = T_MoufangLoop_4662 -> T_IsMoufangLoop_3268
d_isMoufangLoop_4694 (T_MoufangLoop_4662 -> T_MoufangLoop_4662
forall a b. a -> b
coe T_MoufangLoop_4662
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsLeftBolLoop_3104
v2
             = T_IsMoufangLoop_3268 -> T_IsLeftBolLoop_3104
MAlonzo.Code.Algebra.Structures.d_isLeftBolLoop_3284 (T_IsMoufangLoop_3268 -> T_IsMoufangLoop_3268
forall a b. a -> b
coe T_IsMoufangLoop_3268
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsLoop_3026
v3 = T_IsLeftBolLoop_3104 -> T_IsLoop_3026
MAlonzo.Code.Algebra.Structures.d_isLoop_3118 (T_IsLeftBolLoop_3104 -> T_IsLeftBolLoop_3104
forall a b. a -> b
coe T_IsLeftBolLoop_3104
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsQuasigroup_2944
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsQuasigroup_2944
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'47''47''45'cong'691'_3006
               ((T_IsLoop_3026 -> T_IsQuasigroup_2944) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsLoop_3026 -> T_IsQuasigroup_2944
MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040 (T_IsLoop_3026 -> AgdaAny
forall a b. a -> b
coe T_IsLoop_3026
v3)))))
-- Algebra.Bundles.MoufangLoop._.//-congˡ
d_'47''47''45'cong'737'_4702 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_MoufangLoop_4662 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'47''47''45'cong'737'_4702 :: ()
-> ()
-> T_MoufangLoop_4662
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'47''47''45'cong'737'_4702 ~()
v0 ~()
v1 T_MoufangLoop_4662
v2
  = T_MoufangLoop_4662
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'47''47''45'cong'737'_4702 T_MoufangLoop_4662
v2
du_'47''47''45'cong'737'_4702 ::
  T_MoufangLoop_4662 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'47''47''45'cong'737'_4702 :: T_MoufangLoop_4662
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'47''47''45'cong'737'_4702 T_MoufangLoop_4662
v0
  = let v1 :: T_IsMoufangLoop_3268
v1 = T_MoufangLoop_4662 -> T_IsMoufangLoop_3268
d_isMoufangLoop_4694 (T_MoufangLoop_4662 -> T_MoufangLoop_4662
forall a b. a -> b
coe T_MoufangLoop_4662
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsLeftBolLoop_3104
v2
             = T_IsMoufangLoop_3268 -> T_IsLeftBolLoop_3104
MAlonzo.Code.Algebra.Structures.d_isLeftBolLoop_3284 (T_IsMoufangLoop_3268 -> T_IsMoufangLoop_3268
forall a b. a -> b
coe T_IsMoufangLoop_3268
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsLoop_3026
v3 = T_IsLeftBolLoop_3104 -> T_IsLoop_3026
MAlonzo.Code.Algebra.Structures.d_isLoop_3118 (T_IsLeftBolLoop_3104 -> T_IsLeftBolLoop_3104
forall a b. a -> b
coe T_IsLeftBolLoop_3104
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsQuasigroup_2944
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsQuasigroup_2944
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'47''47''45'cong'737'_3002
               ((T_IsLoop_3026 -> T_IsQuasigroup_2944) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsLoop_3026 -> T_IsQuasigroup_2944
MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040 (T_IsLoop_3026 -> AgdaAny
forall a b. a -> b
coe T_IsLoop_3026
v3)))))
-- Algebra.Bundles.MoufangLoop._.\\-cong
d_'92''92''45'cong_4704 ::
  T_MoufangLoop_4662 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'92''92''45'cong_4704 :: T_MoufangLoop_4662
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'92''92''45'cong_4704 T_MoufangLoop_4662
v0
  = (T_IsQuasigroup_2944
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsQuasigroup_2944
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'92''92''45'cong_2964
      ((T_IsLoop_3026 -> T_IsQuasigroup_2944) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsLoop_3026 -> T_IsQuasigroup_2944
MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040
         ((T_IsLeftBolLoop_3104 -> T_IsLoop_3026) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsLeftBolLoop_3104 -> T_IsLoop_3026
MAlonzo.Code.Algebra.Structures.d_isLoop_3118
            ((T_IsMoufangLoop_3268 -> T_IsLeftBolLoop_3104)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMoufangLoop_3268 -> T_IsLeftBolLoop_3104
MAlonzo.Code.Algebra.Structures.d_isLeftBolLoop_3284
               ((T_MoufangLoop_4662 -> T_IsMoufangLoop_3268) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_MoufangLoop_4662 -> T_IsMoufangLoop_3268
d_isMoufangLoop_4694 (T_MoufangLoop_4662 -> AgdaAny
forall a b. a -> b
coe T_MoufangLoop_4662
v0)))))
-- Algebra.Bundles.MoufangLoop._.\\-congʳ
d_'92''92''45'cong'691'_4706 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_MoufangLoop_4662 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'92''92''45'cong'691'_4706 :: ()
-> ()
-> T_MoufangLoop_4662
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'92''92''45'cong'691'_4706 ~()
v0 ~()
v1 T_MoufangLoop_4662
v2
  = T_MoufangLoop_4662
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'92''92''45'cong'691'_4706 T_MoufangLoop_4662
v2
du_'92''92''45'cong'691'_4706 ::
  T_MoufangLoop_4662 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'92''92''45'cong'691'_4706 :: T_MoufangLoop_4662
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'92''92''45'cong'691'_4706 T_MoufangLoop_4662
v0
  = let v1 :: T_IsMoufangLoop_3268
v1 = T_MoufangLoop_4662 -> T_IsMoufangLoop_3268
d_isMoufangLoop_4694 (T_MoufangLoop_4662 -> T_MoufangLoop_4662
forall a b. a -> b
coe T_MoufangLoop_4662
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsLeftBolLoop_3104
v2
             = T_IsMoufangLoop_3268 -> T_IsLeftBolLoop_3104
MAlonzo.Code.Algebra.Structures.d_isLeftBolLoop_3284 (T_IsMoufangLoop_3268 -> T_IsMoufangLoop_3268
forall a b. a -> b
coe T_IsMoufangLoop_3268
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsLoop_3026
v3 = T_IsLeftBolLoop_3104 -> T_IsLoop_3026
MAlonzo.Code.Algebra.Structures.d_isLoop_3118 (T_IsLeftBolLoop_3104 -> T_IsLeftBolLoop_3104
forall a b. a -> b
coe T_IsLeftBolLoop_3104
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsQuasigroup_2944
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsQuasigroup_2944
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'92''92''45'cong'691'_2998
               ((T_IsLoop_3026 -> T_IsQuasigroup_2944) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsLoop_3026 -> T_IsQuasigroup_2944
MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040 (T_IsLoop_3026 -> AgdaAny
forall a b. a -> b
coe T_IsLoop_3026
v3)))))
-- Algebra.Bundles.MoufangLoop._.\\-congˡ
d_'92''92''45'cong'737'_4708 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_MoufangLoop_4662 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'92''92''45'cong'737'_4708 :: ()
-> ()
-> T_MoufangLoop_4662
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'92''92''45'cong'737'_4708 ~()
v0 ~()
v1 T_MoufangLoop_4662
v2
  = T_MoufangLoop_4662
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'92''92''45'cong'737'_4708 T_MoufangLoop_4662
v2
du_'92''92''45'cong'737'_4708 ::
  T_MoufangLoop_4662 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'92''92''45'cong'737'_4708 :: T_MoufangLoop_4662
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'92''92''45'cong'737'_4708 T_MoufangLoop_4662
v0
  = let v1 :: T_IsMoufangLoop_3268
v1 = T_MoufangLoop_4662 -> T_IsMoufangLoop_3268
d_isMoufangLoop_4694 (T_MoufangLoop_4662 -> T_MoufangLoop_4662
forall a b. a -> b
coe T_MoufangLoop_4662
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsLeftBolLoop_3104
v2
             = T_IsMoufangLoop_3268 -> T_IsLeftBolLoop_3104
MAlonzo.Code.Algebra.Structures.d_isLeftBolLoop_3284 (T_IsMoufangLoop_3268 -> T_IsMoufangLoop_3268
forall a b. a -> b
coe T_IsMoufangLoop_3268
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsLoop_3026
v3 = T_IsLeftBolLoop_3104 -> T_IsLoop_3026
MAlonzo.Code.Algebra.Structures.d_isLoop_3118 (T_IsLeftBolLoop_3104 -> T_IsLeftBolLoop_3104
forall a b. a -> b
coe T_IsLeftBolLoop_3104
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsQuasigroup_2944
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsQuasigroup_2944
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'92''92''45'cong'737'_2994
               ((T_IsLoop_3026 -> T_IsQuasigroup_2944) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsLoop_3026 -> T_IsQuasigroup_2944
MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040 (T_IsLoop_3026 -> AgdaAny
forall a b. a -> b
coe T_IsLoop_3026
v3)))))
-- Algebra.Bundles.MoufangLoop._.identical
d_identical_4710 ::
  T_MoufangLoop_4662 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_identical_4710 :: T_MoufangLoop_4662 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_identical_4710 T_MoufangLoop_4662
v0
  = (T_IsMoufangLoop_3268 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsMoufangLoop_3268 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_identical_3288
      ((T_MoufangLoop_4662 -> T_IsMoufangLoop_3268) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_MoufangLoop_4662 -> T_IsMoufangLoop_3268
d_isMoufangLoop_4694 (T_MoufangLoop_4662 -> AgdaAny
forall a b. a -> b
coe T_MoufangLoop_4662
v0))
-- Algebra.Bundles.MoufangLoop._.identity
d_identity_4712 ::
  T_MoufangLoop_4662 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_identity_4712 :: T_MoufangLoop_4662 -> T_Σ_14
d_identity_4712 T_MoufangLoop_4662
v0
  = (T_IsLoop_3026 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsLoop_3026 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_identity_3042
      ((T_IsLeftBolLoop_3104 -> T_IsLoop_3026) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsLeftBolLoop_3104 -> T_IsLoop_3026
MAlonzo.Code.Algebra.Structures.d_isLoop_3118
         ((T_IsMoufangLoop_3268 -> T_IsLeftBolLoop_3104)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMoufangLoop_3268 -> T_IsLeftBolLoop_3104
MAlonzo.Code.Algebra.Structures.d_isLeftBolLoop_3284
            ((T_MoufangLoop_4662 -> T_IsMoufangLoop_3268) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_MoufangLoop_4662 -> T_IsMoufangLoop_3268
d_isMoufangLoop_4694 (T_MoufangLoop_4662 -> AgdaAny
forall a b. a -> b
coe T_MoufangLoop_4662
v0))))
-- Algebra.Bundles.MoufangLoop._.identityʳ
d_identity'691'_4714 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_MoufangLoop_4662 -> AgdaAny -> AgdaAny
d_identity'691'_4714 :: () -> () -> T_MoufangLoop_4662 -> AgdaAny -> AgdaAny
d_identity'691'_4714 ~()
v0 ~()
v1 T_MoufangLoop_4662
v2 = T_MoufangLoop_4662 -> AgdaAny -> AgdaAny
du_identity'691'_4714 T_MoufangLoop_4662
v2
du_identity'691'_4714 :: T_MoufangLoop_4662 -> AgdaAny -> AgdaAny
du_identity'691'_4714 :: T_MoufangLoop_4662 -> AgdaAny -> AgdaAny
du_identity'691'_4714 T_MoufangLoop_4662
v0
  = let v1 :: T_IsMoufangLoop_3268
v1 = T_MoufangLoop_4662 -> T_IsMoufangLoop_3268
d_isMoufangLoop_4694 (T_MoufangLoop_4662 -> T_MoufangLoop_4662
forall a b. a -> b
coe T_MoufangLoop_4662
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsLeftBolLoop_3104
v2
             = T_IsMoufangLoop_3268 -> T_IsLeftBolLoop_3104
MAlonzo.Code.Algebra.Structures.d_isLeftBolLoop_3284 (T_IsMoufangLoop_3268 -> T_IsMoufangLoop_3268
forall a b. a -> b
coe T_IsMoufangLoop_3268
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsLoop_3026 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsLoop_3026 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_identity'691'_3094
            ((T_IsLeftBolLoop_3104 -> T_IsLoop_3026) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLeftBolLoop_3104 -> T_IsLoop_3026
MAlonzo.Code.Algebra.Structures.d_isLoop_3118 (T_IsLeftBolLoop_3104 -> AgdaAny
forall a b. a -> b
coe T_IsLeftBolLoop_3104
v2))))
-- Algebra.Bundles.MoufangLoop._.identityˡ
d_identity'737'_4716 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_MoufangLoop_4662 -> AgdaAny -> AgdaAny
d_identity'737'_4716 :: () -> () -> T_MoufangLoop_4662 -> AgdaAny -> AgdaAny
d_identity'737'_4716 ~()
v0 ~()
v1 T_MoufangLoop_4662
v2 = T_MoufangLoop_4662 -> AgdaAny -> AgdaAny
du_identity'737'_4716 T_MoufangLoop_4662
v2
du_identity'737'_4716 :: T_MoufangLoop_4662 -> AgdaAny -> AgdaAny
du_identity'737'_4716 :: T_MoufangLoop_4662 -> AgdaAny -> AgdaAny
du_identity'737'_4716 T_MoufangLoop_4662
v0
  = let v1 :: T_IsMoufangLoop_3268
v1 = T_MoufangLoop_4662 -> T_IsMoufangLoop_3268
d_isMoufangLoop_4694 (T_MoufangLoop_4662 -> T_MoufangLoop_4662
forall a b. a -> b
coe T_MoufangLoop_4662
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsLeftBolLoop_3104
v2
             = T_IsMoufangLoop_3268 -> T_IsLeftBolLoop_3104
MAlonzo.Code.Algebra.Structures.d_isLeftBolLoop_3284 (T_IsMoufangLoop_3268 -> T_IsMoufangLoop_3268
forall a b. a -> b
coe T_IsMoufangLoop_3268
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsLoop_3026 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsLoop_3026 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_identity'737'_3092
            ((T_IsLeftBolLoop_3104 -> T_IsLoop_3026) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLeftBolLoop_3104 -> T_IsLoop_3026
MAlonzo.Code.Algebra.Structures.d_isLoop_3118 (T_IsLeftBolLoop_3104 -> AgdaAny
forall a b. a -> b
coe T_IsLeftBolLoop_3104
v2))))
-- Algebra.Bundles.MoufangLoop._.isEquivalence
d_isEquivalence_4718 ::
  T_MoufangLoop_4662 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_4718 :: T_MoufangLoop_4662 -> T_IsEquivalence_26
d_isEquivalence_4718 T_MoufangLoop_4662
v0
  = (T_IsMagma_176 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
      ((T_IsQuasigroup_2944 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsQuasigroup_2944 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_2962
         ((T_IsLoop_3026 -> T_IsQuasigroup_2944) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsLoop_3026 -> T_IsQuasigroup_2944
MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040
            ((T_IsLeftBolLoop_3104 -> T_IsLoop_3026) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsLeftBolLoop_3104 -> T_IsLoop_3026
MAlonzo.Code.Algebra.Structures.d_isLoop_3118
               ((T_IsMoufangLoop_3268 -> T_IsLeftBolLoop_3104)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsMoufangLoop_3268 -> T_IsLeftBolLoop_3104
MAlonzo.Code.Algebra.Structures.d_isLeftBolLoop_3284
                  ((T_MoufangLoop_4662 -> T_IsMoufangLoop_3268) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_MoufangLoop_4662 -> T_IsMoufangLoop_3268
d_isMoufangLoop_4694 (T_MoufangLoop_4662 -> AgdaAny
forall a b. a -> b
coe T_MoufangLoop_4662
v0))))))
-- Algebra.Bundles.MoufangLoop._.isLeftBolLoop
d_isLeftBolLoop_4720 ::
  T_MoufangLoop_4662 ->
  MAlonzo.Code.Algebra.Structures.T_IsLeftBolLoop_3104
d_isLeftBolLoop_4720 :: T_MoufangLoop_4662 -> T_IsLeftBolLoop_3104
d_isLeftBolLoop_4720 T_MoufangLoop_4662
v0
  = (T_IsMoufangLoop_3268 -> T_IsLeftBolLoop_3104)
-> AgdaAny -> T_IsLeftBolLoop_3104
forall a b. a -> b
coe
      T_IsMoufangLoop_3268 -> T_IsLeftBolLoop_3104
MAlonzo.Code.Algebra.Structures.d_isLeftBolLoop_3284
      ((T_MoufangLoop_4662 -> T_IsMoufangLoop_3268) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_MoufangLoop_4662 -> T_IsMoufangLoop_3268
d_isMoufangLoop_4694 (T_MoufangLoop_4662 -> AgdaAny
forall a b. a -> b
coe T_MoufangLoop_4662
v0))
-- Algebra.Bundles.MoufangLoop._.isLoop
d_isLoop_4722 ::
  T_MoufangLoop_4662 -> MAlonzo.Code.Algebra.Structures.T_IsLoop_3026
d_isLoop_4722 :: T_MoufangLoop_4662 -> T_IsLoop_3026
d_isLoop_4722 T_MoufangLoop_4662
v0
  = (T_IsLeftBolLoop_3104 -> T_IsLoop_3026) -> AgdaAny -> T_IsLoop_3026
forall a b. a -> b
coe
      T_IsLeftBolLoop_3104 -> T_IsLoop_3026
MAlonzo.Code.Algebra.Structures.d_isLoop_3118
      ((T_IsMoufangLoop_3268 -> T_IsLeftBolLoop_3104)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMoufangLoop_3268 -> T_IsLeftBolLoop_3104
MAlonzo.Code.Algebra.Structures.d_isLeftBolLoop_3284
         ((T_MoufangLoop_4662 -> T_IsMoufangLoop_3268) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_MoufangLoop_4662 -> T_IsMoufangLoop_3268
d_isMoufangLoop_4694 (T_MoufangLoop_4662 -> AgdaAny
forall a b. a -> b
coe T_MoufangLoop_4662
v0)))
-- Algebra.Bundles.MoufangLoop._.isMagma
d_isMagma_4724 ::
  T_MoufangLoop_4662 -> MAlonzo.Code.Algebra.Structures.T_IsMagma_176
d_isMagma_4724 :: T_MoufangLoop_4662 -> T_IsMagma_176
d_isMagma_4724 T_MoufangLoop_4662
v0
  = (T_IsQuasigroup_2944 -> T_IsMagma_176) -> AgdaAny -> T_IsMagma_176
forall a b. a -> b
coe
      T_IsQuasigroup_2944 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_2962
      ((T_IsLoop_3026 -> T_IsQuasigroup_2944) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsLoop_3026 -> T_IsQuasigroup_2944
MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040
         ((T_IsLeftBolLoop_3104 -> T_IsLoop_3026) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsLeftBolLoop_3104 -> T_IsLoop_3026
MAlonzo.Code.Algebra.Structures.d_isLoop_3118
            ((T_IsMoufangLoop_3268 -> T_IsLeftBolLoop_3104)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMoufangLoop_3268 -> T_IsLeftBolLoop_3104
MAlonzo.Code.Algebra.Structures.d_isLeftBolLoop_3284
               ((T_MoufangLoop_4662 -> T_IsMoufangLoop_3268) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_MoufangLoop_4662 -> T_IsMoufangLoop_3268
d_isMoufangLoop_4694 (T_MoufangLoop_4662 -> AgdaAny
forall a b. a -> b
coe T_MoufangLoop_4662
v0)))))
-- Algebra.Bundles.MoufangLoop._.isPartialEquivalence
d_isPartialEquivalence_4726 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_MoufangLoop_4662 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_4726 :: () -> () -> T_MoufangLoop_4662 -> T_IsPartialEquivalence_16
d_isPartialEquivalence_4726 ~()
v0 ~()
v1 T_MoufangLoop_4662
v2
  = T_MoufangLoop_4662 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_4726 T_MoufangLoop_4662
v2
du_isPartialEquivalence_4726 ::
  T_MoufangLoop_4662 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_4726 :: T_MoufangLoop_4662 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_4726 T_MoufangLoop_4662
v0
  = let v1 :: T_IsMoufangLoop_3268
v1 = T_MoufangLoop_4662 -> T_IsMoufangLoop_3268
d_isMoufangLoop_4694 (T_MoufangLoop_4662 -> T_MoufangLoop_4662
forall a b. a -> b
coe T_MoufangLoop_4662
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsLeftBolLoop_3104
v2
             = T_IsMoufangLoop_3268 -> T_IsLeftBolLoop_3104
MAlonzo.Code.Algebra.Structures.d_isLeftBolLoop_3284 (T_IsMoufangLoop_3268 -> T_IsMoufangLoop_3268
forall a b. a -> b
coe T_IsMoufangLoop_3268
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsLoop_3026
v3 = T_IsLeftBolLoop_3104 -> T_IsLoop_3026
MAlonzo.Code.Algebra.Structures.d_isLoop_3118 (T_IsLeftBolLoop_3104 -> T_IsLeftBolLoop_3104
forall a b. a -> b
coe T_IsLeftBolLoop_3104
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsQuasigroup_2944
v4
                   = T_IsLoop_3026 -> T_IsQuasigroup_2944
MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040 (T_IsLoop_3026 -> T_IsLoop_3026
forall a b. a -> b
coe T_IsLoop_3026
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsMagma_176
v5
                      = T_IsQuasigroup_2944 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_2962 (T_IsQuasigroup_2944 -> T_IsQuasigroup_2944
forall a b. a -> b
coe T_IsQuasigroup_2944
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  ((T_IsEquivalence_26 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsEquivalence_26 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
                     ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v5)))))))
-- Algebra.Bundles.MoufangLoop._.isQuasigroup
d_isQuasigroup_4728 ::
  T_MoufangLoop_4662 ->
  MAlonzo.Code.Algebra.Structures.T_IsQuasigroup_2944
d_isQuasigroup_4728 :: T_MoufangLoop_4662 -> T_IsQuasigroup_2944
d_isQuasigroup_4728 T_MoufangLoop_4662
v0
  = (T_IsLoop_3026 -> T_IsQuasigroup_2944)
-> AgdaAny -> T_IsQuasigroup_2944
forall a b. a -> b
coe
      T_IsLoop_3026 -> T_IsQuasigroup_2944
MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040
      ((T_IsLeftBolLoop_3104 -> T_IsLoop_3026) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsLeftBolLoop_3104 -> T_IsLoop_3026
MAlonzo.Code.Algebra.Structures.d_isLoop_3118
         ((T_IsMoufangLoop_3268 -> T_IsLeftBolLoop_3104)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMoufangLoop_3268 -> T_IsLeftBolLoop_3104
MAlonzo.Code.Algebra.Structures.d_isLeftBolLoop_3284
            ((T_MoufangLoop_4662 -> T_IsMoufangLoop_3268) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_MoufangLoop_4662 -> T_IsMoufangLoop_3268
d_isMoufangLoop_4694 (T_MoufangLoop_4662 -> AgdaAny
forall a b. a -> b
coe T_MoufangLoop_4662
v0))))
-- Algebra.Bundles.MoufangLoop._.leftBol
d_leftBol_4730 ::
  T_MoufangLoop_4662 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_leftBol_4730 :: T_MoufangLoop_4662 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_leftBol_4730 T_MoufangLoop_4662
v0
  = (T_IsLeftBolLoop_3104 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsLeftBolLoop_3104 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_leftBol_3120
      ((T_IsMoufangLoop_3268 -> T_IsLeftBolLoop_3104)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMoufangLoop_3268 -> T_IsLeftBolLoop_3104
MAlonzo.Code.Algebra.Structures.d_isLeftBolLoop_3284
         ((T_MoufangLoop_4662 -> T_IsMoufangLoop_3268) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_MoufangLoop_4662 -> T_IsMoufangLoop_3268
d_isMoufangLoop_4694 (T_MoufangLoop_4662 -> AgdaAny
forall a b. a -> b
coe T_MoufangLoop_4662
v0)))
-- Algebra.Bundles.MoufangLoop._.leftDivides
d_leftDivides_4732 ::
  T_MoufangLoop_4662 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_leftDivides_4732 :: T_MoufangLoop_4662 -> T_Σ_14
d_leftDivides_4732 T_MoufangLoop_4662
v0
  = (T_IsQuasigroup_2944 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsQuasigroup_2944 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_leftDivides_2968
      ((T_IsLoop_3026 -> T_IsQuasigroup_2944) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsLoop_3026 -> T_IsQuasigroup_2944
MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040
         ((T_IsLeftBolLoop_3104 -> T_IsLoop_3026) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsLeftBolLoop_3104 -> T_IsLoop_3026
MAlonzo.Code.Algebra.Structures.d_isLoop_3118
            ((T_IsMoufangLoop_3268 -> T_IsLeftBolLoop_3104)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMoufangLoop_3268 -> T_IsLeftBolLoop_3104
MAlonzo.Code.Algebra.Structures.d_isLeftBolLoop_3284
               ((T_MoufangLoop_4662 -> T_IsMoufangLoop_3268) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_MoufangLoop_4662 -> T_IsMoufangLoop_3268
d_isMoufangLoop_4694 (T_MoufangLoop_4662 -> AgdaAny
forall a b. a -> b
coe T_MoufangLoop_4662
v0)))))
-- Algebra.Bundles.MoufangLoop._.leftDividesʳ
d_leftDivides'691'_4734 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_MoufangLoop_4662 -> AgdaAny -> AgdaAny -> AgdaAny
d_leftDivides'691'_4734 :: () -> () -> T_MoufangLoop_4662 -> AgdaAny -> AgdaAny -> AgdaAny
d_leftDivides'691'_4734 ~()
v0 ~()
v1 T_MoufangLoop_4662
v2 = T_MoufangLoop_4662 -> AgdaAny -> AgdaAny -> AgdaAny
du_leftDivides'691'_4734 T_MoufangLoop_4662
v2
du_leftDivides'691'_4734 ::
  T_MoufangLoop_4662 -> AgdaAny -> AgdaAny -> AgdaAny
du_leftDivides'691'_4734 :: T_MoufangLoop_4662 -> AgdaAny -> AgdaAny -> AgdaAny
du_leftDivides'691'_4734 T_MoufangLoop_4662
v0
  = let v1 :: T_IsMoufangLoop_3268
v1 = T_MoufangLoop_4662 -> T_IsMoufangLoop_3268
d_isMoufangLoop_4694 (T_MoufangLoop_4662 -> T_MoufangLoop_4662
forall a b. a -> b
coe T_MoufangLoop_4662
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsLeftBolLoop_3104
v2
             = T_IsMoufangLoop_3268 -> T_IsLeftBolLoop_3104
MAlonzo.Code.Algebra.Structures.d_isLeftBolLoop_3284 (T_IsMoufangLoop_3268 -> T_IsMoufangLoop_3268
forall a b. a -> b
coe T_IsMoufangLoop_3268
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsLoop_3026
v3 = T_IsLeftBolLoop_3104 -> T_IsLoop_3026
MAlonzo.Code.Algebra.Structures.d_isLoop_3118 (T_IsLeftBolLoop_3104 -> T_IsLeftBolLoop_3104
forall a b. a -> b
coe T_IsLeftBolLoop_3104
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsQuasigroup_2944 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsQuasigroup_2944 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_leftDivides'691'_3012
               ((T_IsLoop_3026 -> T_IsQuasigroup_2944) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsLoop_3026 -> T_IsQuasigroup_2944
MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040 (T_IsLoop_3026 -> AgdaAny
forall a b. a -> b
coe T_IsLoop_3026
v3)))))
-- Algebra.Bundles.MoufangLoop._.leftDividesˡ
d_leftDivides'737'_4736 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_MoufangLoop_4662 -> AgdaAny -> AgdaAny -> AgdaAny
d_leftDivides'737'_4736 :: () -> () -> T_MoufangLoop_4662 -> AgdaAny -> AgdaAny -> AgdaAny
d_leftDivides'737'_4736 ~()
v0 ~()
v1 T_MoufangLoop_4662
v2 = T_MoufangLoop_4662 -> AgdaAny -> AgdaAny -> AgdaAny
du_leftDivides'737'_4736 T_MoufangLoop_4662
v2
du_leftDivides'737'_4736 ::
  T_MoufangLoop_4662 -> AgdaAny -> AgdaAny -> AgdaAny
du_leftDivides'737'_4736 :: T_MoufangLoop_4662 -> AgdaAny -> AgdaAny -> AgdaAny
du_leftDivides'737'_4736 T_MoufangLoop_4662
v0
  = let v1 :: T_IsMoufangLoop_3268
v1 = T_MoufangLoop_4662 -> T_IsMoufangLoop_3268
d_isMoufangLoop_4694 (T_MoufangLoop_4662 -> T_MoufangLoop_4662
forall a b. a -> b
coe T_MoufangLoop_4662
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsLeftBolLoop_3104
v2
             = T_IsMoufangLoop_3268 -> T_IsLeftBolLoop_3104
MAlonzo.Code.Algebra.Structures.d_isLeftBolLoop_3284 (T_IsMoufangLoop_3268 -> T_IsMoufangLoop_3268
forall a b. a -> b
coe T_IsMoufangLoop_3268
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsLoop_3026
v3 = T_IsLeftBolLoop_3104 -> T_IsLoop_3026
MAlonzo.Code.Algebra.Structures.d_isLoop_3118 (T_IsLeftBolLoop_3104 -> T_IsLeftBolLoop_3104
forall a b. a -> b
coe T_IsLeftBolLoop_3104
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsQuasigroup_2944 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsQuasigroup_2944 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_leftDivides'737'_3010
               ((T_IsLoop_3026 -> T_IsQuasigroup_2944) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsLoop_3026 -> T_IsQuasigroup_2944
MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040 (T_IsLoop_3026 -> AgdaAny
forall a b. a -> b
coe T_IsLoop_3026
v3)))))
-- Algebra.Bundles.MoufangLoop._.refl
d_refl_4738 :: T_MoufangLoop_4662 -> AgdaAny -> AgdaAny
d_refl_4738 :: T_MoufangLoop_4662 -> AgdaAny -> AgdaAny
d_refl_4738 T_MoufangLoop_4662
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_34
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
         ((T_IsQuasigroup_2944 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsQuasigroup_2944 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_2962
            ((T_IsLoop_3026 -> T_IsQuasigroup_2944) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsLoop_3026 -> T_IsQuasigroup_2944
MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040
               ((T_IsLeftBolLoop_3104 -> T_IsLoop_3026) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsLeftBolLoop_3104 -> T_IsLoop_3026
MAlonzo.Code.Algebra.Structures.d_isLoop_3118
                  ((T_IsMoufangLoop_3268 -> T_IsLeftBolLoop_3104)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsMoufangLoop_3268 -> T_IsLeftBolLoop_3104
MAlonzo.Code.Algebra.Structures.d_isLeftBolLoop_3284
                     ((T_MoufangLoop_4662 -> T_IsMoufangLoop_3268) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_MoufangLoop_4662 -> T_IsMoufangLoop_3268
d_isMoufangLoop_4694 (T_MoufangLoop_4662 -> AgdaAny
forall a b. a -> b
coe T_MoufangLoop_4662
v0)))))))
-- Algebra.Bundles.MoufangLoop._.reflexive
d_reflexive_4740 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_MoufangLoop_4662 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_4740 :: ()
-> ()
-> T_MoufangLoop_4662
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_4740 ~()
v0 ~()
v1 T_MoufangLoop_4662
v2 = T_MoufangLoop_4662
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_4740 T_MoufangLoop_4662
v2
du_reflexive_4740 ::
  T_MoufangLoop_4662 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_4740 :: T_MoufangLoop_4662
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_4740 T_MoufangLoop_4662
v0
  = let v1 :: T_IsMoufangLoop_3268
v1 = T_MoufangLoop_4662 -> T_IsMoufangLoop_3268
d_isMoufangLoop_4694 (T_MoufangLoop_4662 -> T_MoufangLoop_4662
forall a b. a -> b
coe T_MoufangLoop_4662
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsLeftBolLoop_3104
v2
             = T_IsMoufangLoop_3268 -> T_IsLeftBolLoop_3104
MAlonzo.Code.Algebra.Structures.d_isLeftBolLoop_3284 (T_IsMoufangLoop_3268 -> T_IsMoufangLoop_3268
forall a b. a -> b
coe T_IsMoufangLoop_3268
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsLoop_3026
v3 = T_IsLeftBolLoop_3104 -> T_IsLoop_3026
MAlonzo.Code.Algebra.Structures.d_isLoop_3118 (T_IsLeftBolLoop_3104 -> T_IsLeftBolLoop_3104
forall a b. a -> b
coe T_IsLeftBolLoop_3104
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsQuasigroup_2944
v4
                   = T_IsLoop_3026 -> T_IsQuasigroup_2944
MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040 (T_IsLoop_3026 -> T_IsLoop_3026
forall a b. a -> b
coe T_IsLoop_3026
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsMagma_176
v5
                      = T_IsQuasigroup_2944 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_2962 (T_IsQuasigroup_2944 -> T_IsQuasigroup_2944
forall a b. a -> b
coe T_IsQuasigroup_2944
v4) in
                (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
                  (\ AgdaAny
v6 AgdaAny
v7 AgdaAny
v8 ->
                     (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                       T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
                       ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v5))
                       AgdaAny
v6)))))
-- Algebra.Bundles.MoufangLoop._.rightBol
d_rightBol_4742 ::
  T_MoufangLoop_4662 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_rightBol_4742 :: T_MoufangLoop_4662 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_rightBol_4742 T_MoufangLoop_4662
v0
  = (T_IsMoufangLoop_3268 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsMoufangLoop_3268 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_rightBol_3286
      ((T_MoufangLoop_4662 -> T_IsMoufangLoop_3268) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_MoufangLoop_4662 -> T_IsMoufangLoop_3268
d_isMoufangLoop_4694 (T_MoufangLoop_4662 -> AgdaAny
forall a b. a -> b
coe T_MoufangLoop_4662
v0))
-- Algebra.Bundles.MoufangLoop._.rightDivides
d_rightDivides_4744 ::
  T_MoufangLoop_4662 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_rightDivides_4744 :: T_MoufangLoop_4662 -> T_Σ_14
d_rightDivides_4744 T_MoufangLoop_4662
v0
  = (T_IsQuasigroup_2944 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsQuasigroup_2944 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_rightDivides_2970
      ((T_IsLoop_3026 -> T_IsQuasigroup_2944) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsLoop_3026 -> T_IsQuasigroup_2944
MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040
         ((T_IsLeftBolLoop_3104 -> T_IsLoop_3026) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsLeftBolLoop_3104 -> T_IsLoop_3026
MAlonzo.Code.Algebra.Structures.d_isLoop_3118
            ((T_IsMoufangLoop_3268 -> T_IsLeftBolLoop_3104)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMoufangLoop_3268 -> T_IsLeftBolLoop_3104
MAlonzo.Code.Algebra.Structures.d_isLeftBolLoop_3284
               ((T_MoufangLoop_4662 -> T_IsMoufangLoop_3268) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_MoufangLoop_4662 -> T_IsMoufangLoop_3268
d_isMoufangLoop_4694 (T_MoufangLoop_4662 -> AgdaAny
forall a b. a -> b
coe T_MoufangLoop_4662
v0)))))
-- Algebra.Bundles.MoufangLoop._.rightDividesʳ
d_rightDivides'691'_4746 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_MoufangLoop_4662 -> AgdaAny -> AgdaAny -> AgdaAny
d_rightDivides'691'_4746 :: () -> () -> T_MoufangLoop_4662 -> AgdaAny -> AgdaAny -> AgdaAny
d_rightDivides'691'_4746 ~()
v0 ~()
v1 T_MoufangLoop_4662
v2 = T_MoufangLoop_4662 -> AgdaAny -> AgdaAny -> AgdaAny
du_rightDivides'691'_4746 T_MoufangLoop_4662
v2
du_rightDivides'691'_4746 ::
  T_MoufangLoop_4662 -> AgdaAny -> AgdaAny -> AgdaAny
du_rightDivides'691'_4746 :: T_MoufangLoop_4662 -> AgdaAny -> AgdaAny -> AgdaAny
du_rightDivides'691'_4746 T_MoufangLoop_4662
v0
  = let v1 :: T_IsMoufangLoop_3268
v1 = T_MoufangLoop_4662 -> T_IsMoufangLoop_3268
d_isMoufangLoop_4694 (T_MoufangLoop_4662 -> T_MoufangLoop_4662
forall a b. a -> b
coe T_MoufangLoop_4662
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsLeftBolLoop_3104
v2
             = T_IsMoufangLoop_3268 -> T_IsLeftBolLoop_3104
MAlonzo.Code.Algebra.Structures.d_isLeftBolLoop_3284 (T_IsMoufangLoop_3268 -> T_IsMoufangLoop_3268
forall a b. a -> b
coe T_IsMoufangLoop_3268
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsLoop_3026
v3 = T_IsLeftBolLoop_3104 -> T_IsLoop_3026
MAlonzo.Code.Algebra.Structures.d_isLoop_3118 (T_IsLeftBolLoop_3104 -> T_IsLeftBolLoop_3104
forall a b. a -> b
coe T_IsLeftBolLoop_3104
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsQuasigroup_2944 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsQuasigroup_2944 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_rightDivides'691'_3016
               ((T_IsLoop_3026 -> T_IsQuasigroup_2944) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsLoop_3026 -> T_IsQuasigroup_2944
MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040 (T_IsLoop_3026 -> AgdaAny
forall a b. a -> b
coe T_IsLoop_3026
v3)))))
-- Algebra.Bundles.MoufangLoop._.rightDividesˡ
d_rightDivides'737'_4748 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_MoufangLoop_4662 -> AgdaAny -> AgdaAny -> AgdaAny
d_rightDivides'737'_4748 :: () -> () -> T_MoufangLoop_4662 -> AgdaAny -> AgdaAny -> AgdaAny
d_rightDivides'737'_4748 ~()
v0 ~()
v1 T_MoufangLoop_4662
v2 = T_MoufangLoop_4662 -> AgdaAny -> AgdaAny -> AgdaAny
du_rightDivides'737'_4748 T_MoufangLoop_4662
v2
du_rightDivides'737'_4748 ::
  T_MoufangLoop_4662 -> AgdaAny -> AgdaAny -> AgdaAny
du_rightDivides'737'_4748 :: T_MoufangLoop_4662 -> AgdaAny -> AgdaAny -> AgdaAny
du_rightDivides'737'_4748 T_MoufangLoop_4662
v0
  = let v1 :: T_IsMoufangLoop_3268
v1 = T_MoufangLoop_4662 -> T_IsMoufangLoop_3268
d_isMoufangLoop_4694 (T_MoufangLoop_4662 -> T_MoufangLoop_4662
forall a b. a -> b
coe T_MoufangLoop_4662
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsLeftBolLoop_3104
v2
             = T_IsMoufangLoop_3268 -> T_IsLeftBolLoop_3104
MAlonzo.Code.Algebra.Structures.d_isLeftBolLoop_3284 (T_IsMoufangLoop_3268 -> T_IsMoufangLoop_3268
forall a b. a -> b
coe T_IsMoufangLoop_3268
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsLoop_3026
v3 = T_IsLeftBolLoop_3104 -> T_IsLoop_3026
MAlonzo.Code.Algebra.Structures.d_isLoop_3118 (T_IsLeftBolLoop_3104 -> T_IsLeftBolLoop_3104
forall a b. a -> b
coe T_IsLeftBolLoop_3104
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsQuasigroup_2944 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsQuasigroup_2944 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_rightDivides'737'_3014
               ((T_IsLoop_3026 -> T_IsQuasigroup_2944) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsLoop_3026 -> T_IsQuasigroup_2944
MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040 (T_IsLoop_3026 -> AgdaAny
forall a b. a -> b
coe T_IsLoop_3026
v3)))))
-- Algebra.Bundles.MoufangLoop._.setoid
d_setoid_4750 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_MoufangLoop_4662 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_4750 :: () -> () -> T_MoufangLoop_4662 -> T_Setoid_44
d_setoid_4750 ~()
v0 ~()
v1 T_MoufangLoop_4662
v2 = T_MoufangLoop_4662 -> T_Setoid_44
du_setoid_4750 T_MoufangLoop_4662
v2
du_setoid_4750 ::
  T_MoufangLoop_4662 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_4750 :: T_MoufangLoop_4662 -> T_Setoid_44
du_setoid_4750 T_MoufangLoop_4662
v0
  = let v1 :: T_IsMoufangLoop_3268
v1 = T_MoufangLoop_4662 -> T_IsMoufangLoop_3268
d_isMoufangLoop_4694 (T_MoufangLoop_4662 -> T_MoufangLoop_4662
forall a b. a -> b
coe T_MoufangLoop_4662
v0) in
    AgdaAny -> T_Setoid_44
forall a b. a -> b
coe
      (let v2 :: T_IsLeftBolLoop_3104
v2
             = T_IsMoufangLoop_3268 -> T_IsLeftBolLoop_3104
MAlonzo.Code.Algebra.Structures.d_isLeftBolLoop_3284 (T_IsMoufangLoop_3268 -> T_IsMoufangLoop_3268
forall a b. a -> b
coe T_IsMoufangLoop_3268
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsLoop_3026
v3 = T_IsLeftBolLoop_3104 -> T_IsLoop_3026
MAlonzo.Code.Algebra.Structures.d_isLoop_3118 (T_IsLeftBolLoop_3104 -> T_IsLeftBolLoop_3104
forall a b. a -> b
coe T_IsLeftBolLoop_3104
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsQuasigroup_2944
v4
                   = T_IsLoop_3026 -> T_IsQuasigroup_2944
MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040 (T_IsLoop_3026 -> T_IsLoop_3026
forall a b. a -> b
coe T_IsLoop_3026
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               ((T_IsMagma_176 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsMagma_176 -> T_Setoid_44
MAlonzo.Code.Algebra.Structures.du_setoid_200
                  ((T_IsQuasigroup_2944 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroup_2944 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_2962 (T_IsQuasigroup_2944 -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroup_2944
v4))))))
-- Algebra.Bundles.MoufangLoop._.sym
d_sym_4752 ::
  T_MoufangLoop_4662 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_4752 :: T_MoufangLoop_4662 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_4752 T_MoufangLoop_4662
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_36
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
         ((T_IsQuasigroup_2944 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsQuasigroup_2944 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_2962
            ((T_IsLoop_3026 -> T_IsQuasigroup_2944) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsLoop_3026 -> T_IsQuasigroup_2944
MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040
               ((T_IsLeftBolLoop_3104 -> T_IsLoop_3026) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsLeftBolLoop_3104 -> T_IsLoop_3026
MAlonzo.Code.Algebra.Structures.d_isLoop_3118
                  ((T_IsMoufangLoop_3268 -> T_IsLeftBolLoop_3104)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsMoufangLoop_3268 -> T_IsLeftBolLoop_3104
MAlonzo.Code.Algebra.Structures.d_isLeftBolLoop_3284
                     ((T_MoufangLoop_4662 -> T_IsMoufangLoop_3268) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_MoufangLoop_4662 -> T_IsMoufangLoop_3268
d_isMoufangLoop_4694 (T_MoufangLoop_4662 -> AgdaAny
forall a b. a -> b
coe T_MoufangLoop_4662
v0)))))))
-- Algebra.Bundles.MoufangLoop._.trans
d_trans_4754 ::
  T_MoufangLoop_4662 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_4754 :: T_MoufangLoop_4662
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_4754 T_MoufangLoop_4662
v0
  = (T_IsEquivalence_26
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_38
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
         ((T_IsQuasigroup_2944 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsQuasigroup_2944 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_2962
            ((T_IsLoop_3026 -> T_IsQuasigroup_2944) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsLoop_3026 -> T_IsQuasigroup_2944
MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040
               ((T_IsLeftBolLoop_3104 -> T_IsLoop_3026) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsLeftBolLoop_3104 -> T_IsLoop_3026
MAlonzo.Code.Algebra.Structures.d_isLoop_3118
                  ((T_IsMoufangLoop_3268 -> T_IsLeftBolLoop_3104)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsMoufangLoop_3268 -> T_IsLeftBolLoop_3104
MAlonzo.Code.Algebra.Structures.d_isLeftBolLoop_3284
                     ((T_MoufangLoop_4662 -> T_IsMoufangLoop_3268) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_MoufangLoop_4662 -> T_IsMoufangLoop_3268
d_isMoufangLoop_4694 (T_MoufangLoop_4662 -> AgdaAny
forall a b. a -> b
coe T_MoufangLoop_4662
v0)))))))
-- Algebra.Bundles.MoufangLoop._.∙-cong
d_'8729''45'cong_4756 ::
  T_MoufangLoop_4662 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_4756 :: T_MoufangLoop_4662
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_4756 T_MoufangLoop_4662
v0
  = (T_IsMagma_176
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsMagma_176
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_186
      ((T_IsQuasigroup_2944 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsQuasigroup_2944 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_2962
         ((T_IsLoop_3026 -> T_IsQuasigroup_2944) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsLoop_3026 -> T_IsQuasigroup_2944
MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040
            ((T_IsLeftBolLoop_3104 -> T_IsLoop_3026) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsLeftBolLoop_3104 -> T_IsLoop_3026
MAlonzo.Code.Algebra.Structures.d_isLoop_3118
               ((T_IsMoufangLoop_3268 -> T_IsLeftBolLoop_3104)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsMoufangLoop_3268 -> T_IsLeftBolLoop_3104
MAlonzo.Code.Algebra.Structures.d_isLeftBolLoop_3284
                  ((T_MoufangLoop_4662 -> T_IsMoufangLoop_3268) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_MoufangLoop_4662 -> T_IsMoufangLoop_3268
d_isMoufangLoop_4694 (T_MoufangLoop_4662 -> AgdaAny
forall a b. a -> b
coe T_MoufangLoop_4662
v0))))))
-- Algebra.Bundles.MoufangLoop._.∙-congʳ
d_'8729''45'cong'691'_4758 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_MoufangLoop_4662 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_4758 :: ()
-> ()
-> T_MoufangLoop_4662
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_4758 ~()
v0 ~()
v1 T_MoufangLoop_4662
v2
  = T_MoufangLoop_4662
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_4758 T_MoufangLoop_4662
v2
du_'8729''45'cong'691'_4758 ::
  T_MoufangLoop_4662 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_4758 :: T_MoufangLoop_4662
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_4758 T_MoufangLoop_4662
v0
  = let v1 :: T_IsMoufangLoop_3268
v1 = T_MoufangLoop_4662 -> T_IsMoufangLoop_3268
d_isMoufangLoop_4694 (T_MoufangLoop_4662 -> T_MoufangLoop_4662
forall a b. a -> b
coe T_MoufangLoop_4662
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsLeftBolLoop_3104
v2
             = T_IsMoufangLoop_3268 -> T_IsLeftBolLoop_3104
MAlonzo.Code.Algebra.Structures.d_isLeftBolLoop_3284 (T_IsMoufangLoop_3268 -> T_IsMoufangLoop_3268
forall a b. a -> b
coe T_IsMoufangLoop_3268
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsLoop_3026
v3 = T_IsLeftBolLoop_3104 -> T_IsLoop_3026
MAlonzo.Code.Algebra.Structures.d_isLoop_3118 (T_IsLeftBolLoop_3104 -> T_IsLeftBolLoop_3104
forall a b. a -> b
coe T_IsLeftBolLoop_3104
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsQuasigroup_2944
v4
                   = T_IsLoop_3026 -> T_IsQuasigroup_2944
MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040 (T_IsLoop_3026 -> T_IsLoop_3026
forall a b. a -> b
coe T_IsLoop_3026
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'691'_206
                  ((T_IsQuasigroup_2944 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroup_2944 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_2962 (T_IsQuasigroup_2944 -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroup_2944
v4))))))
-- Algebra.Bundles.MoufangLoop._.∙-congˡ
d_'8729''45'cong'737'_4760 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_MoufangLoop_4662 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_4760 :: ()
-> ()
-> T_MoufangLoop_4662
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_4760 ~()
v0 ~()
v1 T_MoufangLoop_4662
v2
  = T_MoufangLoop_4662
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_4760 T_MoufangLoop_4662
v2
du_'8729''45'cong'737'_4760 ::
  T_MoufangLoop_4662 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_4760 :: T_MoufangLoop_4662
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_4760 T_MoufangLoop_4662
v0
  = let v1 :: T_IsMoufangLoop_3268
v1 = T_MoufangLoop_4662 -> T_IsMoufangLoop_3268
d_isMoufangLoop_4694 (T_MoufangLoop_4662 -> T_MoufangLoop_4662
forall a b. a -> b
coe T_MoufangLoop_4662
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsLeftBolLoop_3104
v2
             = T_IsMoufangLoop_3268 -> T_IsLeftBolLoop_3104
MAlonzo.Code.Algebra.Structures.d_isLeftBolLoop_3284 (T_IsMoufangLoop_3268 -> T_IsMoufangLoop_3268
forall a b. a -> b
coe T_IsMoufangLoop_3268
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsLoop_3026
v3 = T_IsLeftBolLoop_3104 -> T_IsLoop_3026
MAlonzo.Code.Algebra.Structures.d_isLoop_3118 (T_IsLeftBolLoop_3104 -> T_IsLeftBolLoop_3104
forall a b. a -> b
coe T_IsLeftBolLoop_3104
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsQuasigroup_2944
v4
                   = T_IsLoop_3026 -> T_IsQuasigroup_2944
MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040 (T_IsLoop_3026 -> T_IsLoop_3026
forall a b. a -> b
coe T_IsLoop_3026
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'737'_202
                  ((T_IsQuasigroup_2944 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroup_2944 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_2962 (T_IsQuasigroup_2944 -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroup_2944
v4))))))
-- Algebra.Bundles.MoufangLoop.leftBolLoop
d_leftBolLoop_4762 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_MoufangLoop_4662 -> T_LeftBolLoop_4454
d_leftBolLoop_4762 :: () -> () -> T_MoufangLoop_4662 -> T_LeftBolLoop_4454
d_leftBolLoop_4762 ~()
v0 ~()
v1 T_MoufangLoop_4662
v2 = T_MoufangLoop_4662 -> T_LeftBolLoop_4454
du_leftBolLoop_4762 T_MoufangLoop_4662
v2
du_leftBolLoop_4762 :: T_MoufangLoop_4662 -> T_LeftBolLoop_4454
du_leftBolLoop_4762 :: T_MoufangLoop_4662 -> T_LeftBolLoop_4454
du_leftBolLoop_4762 T_MoufangLoop_4662
v0
  = ((AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> T_IsLeftBolLoop_3104
 -> T_LeftBolLoop_4454)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsLeftBolLoop_3104
-> T_LeftBolLoop_4454
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsLeftBolLoop_3104
-> T_LeftBolLoop_4454
C_LeftBolLoop'46'constructor_80531 (T_MoufangLoop_4662 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__4686 (T_MoufangLoop_4662 -> T_MoufangLoop_4662
forall a b. a -> b
coe T_MoufangLoop_4662
v0))
      (T_MoufangLoop_4662 -> AgdaAny -> AgdaAny -> AgdaAny
d__'92''92'__4688 (T_MoufangLoop_4662 -> T_MoufangLoop_4662
forall a b. a -> b
coe T_MoufangLoop_4662
v0)) (T_MoufangLoop_4662 -> AgdaAny -> AgdaAny -> AgdaAny
d__'47''47'__4690 (T_MoufangLoop_4662 -> T_MoufangLoop_4662
forall a b. a -> b
coe T_MoufangLoop_4662
v0))
      (T_MoufangLoop_4662 -> AgdaAny
d_ε_4692 (T_MoufangLoop_4662 -> T_MoufangLoop_4662
forall a b. a -> b
coe T_MoufangLoop_4662
v0))
      (T_IsMoufangLoop_3268 -> T_IsLeftBolLoop_3104
MAlonzo.Code.Algebra.Structures.d_isLeftBolLoop_3284
         ((T_MoufangLoop_4662 -> T_IsMoufangLoop_3268)
-> AgdaAny -> T_IsMoufangLoop_3268
forall a b. a -> b
coe T_MoufangLoop_4662 -> T_IsMoufangLoop_3268
d_isMoufangLoop_4694 (T_MoufangLoop_4662 -> AgdaAny
forall a b. a -> b
coe T_MoufangLoop_4662
v0)))
-- Algebra.Bundles.MoufangLoop._.loop
d_loop_4766 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_MoufangLoop_4662 -> T_Loop_4346
d_loop_4766 :: () -> () -> T_MoufangLoop_4662 -> T_Loop_4346
d_loop_4766 ~()
v0 ~()
v1 T_MoufangLoop_4662
v2 = T_MoufangLoop_4662 -> T_Loop_4346
du_loop_4766 T_MoufangLoop_4662
v2
du_loop_4766 :: T_MoufangLoop_4662 -> T_Loop_4346
du_loop_4766 :: T_MoufangLoop_4662 -> T_Loop_4346
du_loop_4766 T_MoufangLoop_4662
v0
  = (T_LeftBolLoop_4454 -> T_Loop_4346) -> AgdaAny -> T_Loop_4346
forall a b. a -> b
coe T_LeftBolLoop_4454 -> T_Loop_4346
du_loop_4548 ((T_MoufangLoop_4662 -> T_LeftBolLoop_4454) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_MoufangLoop_4662 -> T_LeftBolLoop_4454
du_leftBolLoop_4762 (T_MoufangLoop_4662 -> AgdaAny
forall a b. a -> b
coe T_MoufangLoop_4662
v0))
-- Algebra.Bundles.MiddleBolLoop
d_MiddleBolLoop_4772 :: p -> p -> ()
d_MiddleBolLoop_4772 p
a0 p
a1 = ()
data T_MiddleBolLoop_4772
  = C_MiddleBolLoop'46'constructor_87215 (AgdaAny ->
                                          AgdaAny -> AgdaAny)
                                         (AgdaAny -> AgdaAny -> AgdaAny)
                                         (AgdaAny -> AgdaAny -> AgdaAny) AgdaAny
                                         MAlonzo.Code.Algebra.Structures.T_IsMiddleBolLoop_3358
-- Algebra.Bundles.MiddleBolLoop.Carrier
d_Carrier_4792 :: T_MiddleBolLoop_4772 -> ()
d_Carrier_4792 :: T_MiddleBolLoop_4772 -> ()
d_Carrier_4792 = T_MiddleBolLoop_4772 -> ()
forall a. a
erased
-- Algebra.Bundles.MiddleBolLoop._≈_
d__'8776'__4794 :: T_MiddleBolLoop_4772 -> AgdaAny -> AgdaAny -> ()
d__'8776'__4794 :: T_MiddleBolLoop_4772 -> AgdaAny -> AgdaAny -> ()
d__'8776'__4794 = T_MiddleBolLoop_4772 -> AgdaAny -> AgdaAny -> ()
forall a. a
erased
-- Algebra.Bundles.MiddleBolLoop._∙_
d__'8729'__4796 ::
  T_MiddleBolLoop_4772 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__4796 :: T_MiddleBolLoop_4772 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__4796 T_MiddleBolLoop_4772
v0
  = case T_MiddleBolLoop_4772 -> T_MiddleBolLoop_4772
forall a b. a -> b
coe T_MiddleBolLoop_4772
v0 of
      C_MiddleBolLoop'46'constructor_87215 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny -> AgdaAny
v5 AgdaAny
v6 T_IsMiddleBolLoop_3358
v7 -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v3
      T_MiddleBolLoop_4772
_ -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.MiddleBolLoop._\\_
d__'92''92'__4798 ::
  T_MiddleBolLoop_4772 -> AgdaAny -> AgdaAny -> AgdaAny
d__'92''92'__4798 :: T_MiddleBolLoop_4772 -> AgdaAny -> AgdaAny -> AgdaAny
d__'92''92'__4798 T_MiddleBolLoop_4772
v0
  = case T_MiddleBolLoop_4772 -> T_MiddleBolLoop_4772
forall a b. a -> b
coe T_MiddleBolLoop_4772
v0 of
      C_MiddleBolLoop'46'constructor_87215 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny -> AgdaAny
v5 AgdaAny
v6 T_IsMiddleBolLoop_3358
v7 -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v4
      T_MiddleBolLoop_4772
_ -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.MiddleBolLoop._//_
d__'47''47'__4800 ::
  T_MiddleBolLoop_4772 -> AgdaAny -> AgdaAny -> AgdaAny
d__'47''47'__4800 :: T_MiddleBolLoop_4772 -> AgdaAny -> AgdaAny -> AgdaAny
d__'47''47'__4800 T_MiddleBolLoop_4772
v0
  = case T_MiddleBolLoop_4772 -> T_MiddleBolLoop_4772
forall a b. a -> b
coe T_MiddleBolLoop_4772
v0 of
      C_MiddleBolLoop'46'constructor_87215 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny -> AgdaAny
v5 AgdaAny
v6 T_IsMiddleBolLoop_3358
v7 -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v5
      T_MiddleBolLoop_4772
_ -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.MiddleBolLoop.ε
d_ε_4802 :: T_MiddleBolLoop_4772 -> AgdaAny
d_ε_4802 :: T_MiddleBolLoop_4772 -> AgdaAny
d_ε_4802 T_MiddleBolLoop_4772
v0
  = case T_MiddleBolLoop_4772 -> T_MiddleBolLoop_4772
forall a b. a -> b
coe T_MiddleBolLoop_4772
v0 of
      C_MiddleBolLoop'46'constructor_87215 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny -> AgdaAny
v5 AgdaAny
v6 T_IsMiddleBolLoop_3358
v7 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v6
      T_MiddleBolLoop_4772
_ -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.MiddleBolLoop.isMiddleBolLoop
d_isMiddleBolLoop_4804 ::
  T_MiddleBolLoop_4772 ->
  MAlonzo.Code.Algebra.Structures.T_IsMiddleBolLoop_3358
d_isMiddleBolLoop_4804 :: T_MiddleBolLoop_4772 -> T_IsMiddleBolLoop_3358
d_isMiddleBolLoop_4804 T_MiddleBolLoop_4772
v0
  = case T_MiddleBolLoop_4772 -> T_MiddleBolLoop_4772
forall a b. a -> b
coe T_MiddleBolLoop_4772
v0 of
      C_MiddleBolLoop'46'constructor_87215 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny -> AgdaAny
v5 AgdaAny
v6 T_IsMiddleBolLoop_3358
v7 -> T_IsMiddleBolLoop_3358 -> T_IsMiddleBolLoop_3358
forall a b. a -> b
coe T_IsMiddleBolLoop_3358
v7
      T_MiddleBolLoop_4772
_ -> T_IsMiddleBolLoop_3358
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.MiddleBolLoop._.//-cong
d_'47''47''45'cong_4808 ::
  T_MiddleBolLoop_4772 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'47''47''45'cong_4808 :: T_MiddleBolLoop_4772
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'47''47''45'cong_4808 T_MiddleBolLoop_4772
v0
  = (T_IsQuasigroup_2944
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsQuasigroup_2944
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'47''47''45'cong_2966
      ((T_IsLoop_3026 -> T_IsQuasigroup_2944) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsLoop_3026 -> T_IsQuasigroup_2944
MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040
         ((T_IsMiddleBolLoop_3358 -> T_IsLoop_3026) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMiddleBolLoop_3358 -> T_IsLoop_3026
MAlonzo.Code.Algebra.Structures.d_isLoop_3372
            ((T_MiddleBolLoop_4772 -> T_IsMiddleBolLoop_3358)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_MiddleBolLoop_4772 -> T_IsMiddleBolLoop_3358
d_isMiddleBolLoop_4804 (T_MiddleBolLoop_4772 -> AgdaAny
forall a b. a -> b
coe T_MiddleBolLoop_4772
v0))))
-- Algebra.Bundles.MiddleBolLoop._.//-congʳ
d_'47''47''45'cong'691'_4810 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_MiddleBolLoop_4772 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'47''47''45'cong'691'_4810 :: ()
-> ()
-> T_MiddleBolLoop_4772
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'47''47''45'cong'691'_4810 ~()
v0 ~()
v1 T_MiddleBolLoop_4772
v2
  = T_MiddleBolLoop_4772
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'47''47''45'cong'691'_4810 T_MiddleBolLoop_4772
v2
du_'47''47''45'cong'691'_4810 ::
  T_MiddleBolLoop_4772 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'47''47''45'cong'691'_4810 :: T_MiddleBolLoop_4772
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'47''47''45'cong'691'_4810 T_MiddleBolLoop_4772
v0
  = let v1 :: T_IsMiddleBolLoop_3358
v1 = T_MiddleBolLoop_4772 -> T_IsMiddleBolLoop_3358
d_isMiddleBolLoop_4804 (T_MiddleBolLoop_4772 -> T_MiddleBolLoop_4772
forall a b. a -> b
coe T_MiddleBolLoop_4772
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsLoop_3026
v2 = T_IsMiddleBolLoop_3358 -> T_IsLoop_3026
MAlonzo.Code.Algebra.Structures.d_isLoop_3372 (T_IsMiddleBolLoop_3358 -> T_IsMiddleBolLoop_3358
forall a b. a -> b
coe T_IsMiddleBolLoop_3358
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsQuasigroup_2944
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsQuasigroup_2944
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'47''47''45'cong'691'_3006
            ((T_IsLoop_3026 -> T_IsQuasigroup_2944) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsLoop_3026 -> T_IsQuasigroup_2944
MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040 (T_IsLoop_3026 -> AgdaAny
forall a b. a -> b
coe T_IsLoop_3026
v2))))
-- Algebra.Bundles.MiddleBolLoop._.//-congˡ
d_'47''47''45'cong'737'_4812 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_MiddleBolLoop_4772 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'47''47''45'cong'737'_4812 :: ()
-> ()
-> T_MiddleBolLoop_4772
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'47''47''45'cong'737'_4812 ~()
v0 ~()
v1 T_MiddleBolLoop_4772
v2
  = T_MiddleBolLoop_4772
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'47''47''45'cong'737'_4812 T_MiddleBolLoop_4772
v2
du_'47''47''45'cong'737'_4812 ::
  T_MiddleBolLoop_4772 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'47''47''45'cong'737'_4812 :: T_MiddleBolLoop_4772
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'47''47''45'cong'737'_4812 T_MiddleBolLoop_4772
v0
  = let v1 :: T_IsMiddleBolLoop_3358
v1 = T_MiddleBolLoop_4772 -> T_IsMiddleBolLoop_3358
d_isMiddleBolLoop_4804 (T_MiddleBolLoop_4772 -> T_MiddleBolLoop_4772
forall a b. a -> b
coe T_MiddleBolLoop_4772
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsLoop_3026
v2 = T_IsMiddleBolLoop_3358 -> T_IsLoop_3026
MAlonzo.Code.Algebra.Structures.d_isLoop_3372 (T_IsMiddleBolLoop_3358 -> T_IsMiddleBolLoop_3358
forall a b. a -> b
coe T_IsMiddleBolLoop_3358
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsQuasigroup_2944
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsQuasigroup_2944
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'47''47''45'cong'737'_3002
            ((T_IsLoop_3026 -> T_IsQuasigroup_2944) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsLoop_3026 -> T_IsQuasigroup_2944
MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040 (T_IsLoop_3026 -> AgdaAny
forall a b. a -> b
coe T_IsLoop_3026
v2))))
-- Algebra.Bundles.MiddleBolLoop._.\\-cong
d_'92''92''45'cong_4814 ::
  T_MiddleBolLoop_4772 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'92''92''45'cong_4814 :: T_MiddleBolLoop_4772
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'92''92''45'cong_4814 T_MiddleBolLoop_4772
v0
  = (T_IsQuasigroup_2944
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsQuasigroup_2944
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'92''92''45'cong_2964
      ((T_IsLoop_3026 -> T_IsQuasigroup_2944) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsLoop_3026 -> T_IsQuasigroup_2944
MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040
         ((T_IsMiddleBolLoop_3358 -> T_IsLoop_3026) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMiddleBolLoop_3358 -> T_IsLoop_3026
MAlonzo.Code.Algebra.Structures.d_isLoop_3372
            ((T_MiddleBolLoop_4772 -> T_IsMiddleBolLoop_3358)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_MiddleBolLoop_4772 -> T_IsMiddleBolLoop_3358
d_isMiddleBolLoop_4804 (T_MiddleBolLoop_4772 -> AgdaAny
forall a b. a -> b
coe T_MiddleBolLoop_4772
v0))))
-- Algebra.Bundles.MiddleBolLoop._.\\-congʳ
d_'92''92''45'cong'691'_4816 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_MiddleBolLoop_4772 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'92''92''45'cong'691'_4816 :: ()
-> ()
-> T_MiddleBolLoop_4772
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'92''92''45'cong'691'_4816 ~()
v0 ~()
v1 T_MiddleBolLoop_4772
v2
  = T_MiddleBolLoop_4772
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'92''92''45'cong'691'_4816 T_MiddleBolLoop_4772
v2
du_'92''92''45'cong'691'_4816 ::
  T_MiddleBolLoop_4772 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'92''92''45'cong'691'_4816 :: T_MiddleBolLoop_4772
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'92''92''45'cong'691'_4816 T_MiddleBolLoop_4772
v0
  = let v1 :: T_IsMiddleBolLoop_3358
v1 = T_MiddleBolLoop_4772 -> T_IsMiddleBolLoop_3358
d_isMiddleBolLoop_4804 (T_MiddleBolLoop_4772 -> T_MiddleBolLoop_4772
forall a b. a -> b
coe T_MiddleBolLoop_4772
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsLoop_3026
v2 = T_IsMiddleBolLoop_3358 -> T_IsLoop_3026
MAlonzo.Code.Algebra.Structures.d_isLoop_3372 (T_IsMiddleBolLoop_3358 -> T_IsMiddleBolLoop_3358
forall a b. a -> b
coe T_IsMiddleBolLoop_3358
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsQuasigroup_2944
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsQuasigroup_2944
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'92''92''45'cong'691'_2998
            ((T_IsLoop_3026 -> T_IsQuasigroup_2944) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsLoop_3026 -> T_IsQuasigroup_2944
MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040 (T_IsLoop_3026 -> AgdaAny
forall a b. a -> b
coe T_IsLoop_3026
v2))))
-- Algebra.Bundles.MiddleBolLoop._.\\-congˡ
d_'92''92''45'cong'737'_4818 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_MiddleBolLoop_4772 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'92''92''45'cong'737'_4818 :: ()
-> ()
-> T_MiddleBolLoop_4772
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'92''92''45'cong'737'_4818 ~()
v0 ~()
v1 T_MiddleBolLoop_4772
v2
  = T_MiddleBolLoop_4772
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'92''92''45'cong'737'_4818 T_MiddleBolLoop_4772
v2
du_'92''92''45'cong'737'_4818 ::
  T_MiddleBolLoop_4772 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'92''92''45'cong'737'_4818 :: T_MiddleBolLoop_4772
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'92''92''45'cong'737'_4818 T_MiddleBolLoop_4772
v0
  = let v1 :: T_IsMiddleBolLoop_3358
v1 = T_MiddleBolLoop_4772 -> T_IsMiddleBolLoop_3358
d_isMiddleBolLoop_4804 (T_MiddleBolLoop_4772 -> T_MiddleBolLoop_4772
forall a b. a -> b
coe T_MiddleBolLoop_4772
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsLoop_3026
v2 = T_IsMiddleBolLoop_3358 -> T_IsLoop_3026
MAlonzo.Code.Algebra.Structures.d_isLoop_3372 (T_IsMiddleBolLoop_3358 -> T_IsMiddleBolLoop_3358
forall a b. a -> b
coe T_IsMiddleBolLoop_3358
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsQuasigroup_2944
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsQuasigroup_2944
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'92''92''45'cong'737'_2994
            ((T_IsLoop_3026 -> T_IsQuasigroup_2944) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsLoop_3026 -> T_IsQuasigroup_2944
MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040 (T_IsLoop_3026 -> AgdaAny
forall a b. a -> b
coe T_IsLoop_3026
v2))))
-- Algebra.Bundles.MiddleBolLoop._.identity
d_identity_4820 ::
  T_MiddleBolLoop_4772 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_identity_4820 :: T_MiddleBolLoop_4772 -> T_Σ_14
d_identity_4820 T_MiddleBolLoop_4772
v0
  = (T_IsLoop_3026 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsLoop_3026 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_identity_3042
      ((T_IsMiddleBolLoop_3358 -> T_IsLoop_3026) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMiddleBolLoop_3358 -> T_IsLoop_3026
MAlonzo.Code.Algebra.Structures.d_isLoop_3372
         ((T_MiddleBolLoop_4772 -> T_IsMiddleBolLoop_3358)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_MiddleBolLoop_4772 -> T_IsMiddleBolLoop_3358
d_isMiddleBolLoop_4804 (T_MiddleBolLoop_4772 -> AgdaAny
forall a b. a -> b
coe T_MiddleBolLoop_4772
v0)))
-- Algebra.Bundles.MiddleBolLoop._.identityʳ
d_identity'691'_4822 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_MiddleBolLoop_4772 -> AgdaAny -> AgdaAny
d_identity'691'_4822 :: () -> () -> T_MiddleBolLoop_4772 -> AgdaAny -> AgdaAny
d_identity'691'_4822 ~()
v0 ~()
v1 T_MiddleBolLoop_4772
v2 = T_MiddleBolLoop_4772 -> AgdaAny -> AgdaAny
du_identity'691'_4822 T_MiddleBolLoop_4772
v2
du_identity'691'_4822 :: T_MiddleBolLoop_4772 -> AgdaAny -> AgdaAny
du_identity'691'_4822 :: T_MiddleBolLoop_4772 -> AgdaAny -> AgdaAny
du_identity'691'_4822 T_MiddleBolLoop_4772
v0
  = let v1 :: T_IsMiddleBolLoop_3358
v1 = T_MiddleBolLoop_4772 -> T_IsMiddleBolLoop_3358
d_isMiddleBolLoop_4804 (T_MiddleBolLoop_4772 -> T_MiddleBolLoop_4772
forall a b. a -> b
coe T_MiddleBolLoop_4772
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsLoop_3026 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsLoop_3026 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_identity'691'_3094
         ((T_IsMiddleBolLoop_3358 -> T_IsLoop_3026) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMiddleBolLoop_3358 -> T_IsLoop_3026
MAlonzo.Code.Algebra.Structures.d_isLoop_3372 (T_IsMiddleBolLoop_3358 -> AgdaAny
forall a b. a -> b
coe T_IsMiddleBolLoop_3358
v1)))
-- Algebra.Bundles.MiddleBolLoop._.identityˡ
d_identity'737'_4824 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_MiddleBolLoop_4772 -> AgdaAny -> AgdaAny
d_identity'737'_4824 :: () -> () -> T_MiddleBolLoop_4772 -> AgdaAny -> AgdaAny
d_identity'737'_4824 ~()
v0 ~()
v1 T_MiddleBolLoop_4772
v2 = T_MiddleBolLoop_4772 -> AgdaAny -> AgdaAny
du_identity'737'_4824 T_MiddleBolLoop_4772
v2
du_identity'737'_4824 :: T_MiddleBolLoop_4772 -> AgdaAny -> AgdaAny
du_identity'737'_4824 :: T_MiddleBolLoop_4772 -> AgdaAny -> AgdaAny
du_identity'737'_4824 T_MiddleBolLoop_4772
v0
  = let v1 :: T_IsMiddleBolLoop_3358
v1 = T_MiddleBolLoop_4772 -> T_IsMiddleBolLoop_3358
d_isMiddleBolLoop_4804 (T_MiddleBolLoop_4772 -> T_MiddleBolLoop_4772
forall a b. a -> b
coe T_MiddleBolLoop_4772
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsLoop_3026 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsLoop_3026 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_identity'737'_3092
         ((T_IsMiddleBolLoop_3358 -> T_IsLoop_3026) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMiddleBolLoop_3358 -> T_IsLoop_3026
MAlonzo.Code.Algebra.Structures.d_isLoop_3372 (T_IsMiddleBolLoop_3358 -> AgdaAny
forall a b. a -> b
coe T_IsMiddleBolLoop_3358
v1)))
-- Algebra.Bundles.MiddleBolLoop._.isEquivalence
d_isEquivalence_4826 ::
  T_MiddleBolLoop_4772 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_4826 :: T_MiddleBolLoop_4772 -> T_IsEquivalence_26
d_isEquivalence_4826 T_MiddleBolLoop_4772
v0
  = (T_IsMagma_176 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
      ((T_IsQuasigroup_2944 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsQuasigroup_2944 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_2962
         ((T_IsLoop_3026 -> T_IsQuasigroup_2944) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsLoop_3026 -> T_IsQuasigroup_2944
MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040
            ((T_IsMiddleBolLoop_3358 -> T_IsLoop_3026) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMiddleBolLoop_3358 -> T_IsLoop_3026
MAlonzo.Code.Algebra.Structures.d_isLoop_3372
               ((T_MiddleBolLoop_4772 -> T_IsMiddleBolLoop_3358)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_MiddleBolLoop_4772 -> T_IsMiddleBolLoop_3358
d_isMiddleBolLoop_4804 (T_MiddleBolLoop_4772 -> AgdaAny
forall a b. a -> b
coe T_MiddleBolLoop_4772
v0)))))
-- Algebra.Bundles.MiddleBolLoop._.isLoop
d_isLoop_4828 ::
  T_MiddleBolLoop_4772 ->
  MAlonzo.Code.Algebra.Structures.T_IsLoop_3026
d_isLoop_4828 :: T_MiddleBolLoop_4772 -> T_IsLoop_3026
d_isLoop_4828 T_MiddleBolLoop_4772
v0
  = (T_IsMiddleBolLoop_3358 -> T_IsLoop_3026)
-> AgdaAny -> T_IsLoop_3026
forall a b. a -> b
coe
      T_IsMiddleBolLoop_3358 -> T_IsLoop_3026
MAlonzo.Code.Algebra.Structures.d_isLoop_3372
      ((T_MiddleBolLoop_4772 -> T_IsMiddleBolLoop_3358)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_MiddleBolLoop_4772 -> T_IsMiddleBolLoop_3358
d_isMiddleBolLoop_4804 (T_MiddleBolLoop_4772 -> AgdaAny
forall a b. a -> b
coe T_MiddleBolLoop_4772
v0))
-- Algebra.Bundles.MiddleBolLoop._.isMagma
d_isMagma_4830 ::
  T_MiddleBolLoop_4772 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_176
d_isMagma_4830 :: T_MiddleBolLoop_4772 -> T_IsMagma_176
d_isMagma_4830 T_MiddleBolLoop_4772
v0
  = (T_IsQuasigroup_2944 -> T_IsMagma_176) -> AgdaAny -> T_IsMagma_176
forall a b. a -> b
coe
      T_IsQuasigroup_2944 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_2962
      ((T_IsLoop_3026 -> T_IsQuasigroup_2944) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsLoop_3026 -> T_IsQuasigroup_2944
MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040
         ((T_IsMiddleBolLoop_3358 -> T_IsLoop_3026) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMiddleBolLoop_3358 -> T_IsLoop_3026
MAlonzo.Code.Algebra.Structures.d_isLoop_3372
            ((T_MiddleBolLoop_4772 -> T_IsMiddleBolLoop_3358)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_MiddleBolLoop_4772 -> T_IsMiddleBolLoop_3358
d_isMiddleBolLoop_4804 (T_MiddleBolLoop_4772 -> AgdaAny
forall a b. a -> b
coe T_MiddleBolLoop_4772
v0))))
-- Algebra.Bundles.MiddleBolLoop._.isPartialEquivalence
d_isPartialEquivalence_4832 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_MiddleBolLoop_4772 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_4832 :: () -> () -> T_MiddleBolLoop_4772 -> T_IsPartialEquivalence_16
d_isPartialEquivalence_4832 ~()
v0 ~()
v1 T_MiddleBolLoop_4772
v2
  = T_MiddleBolLoop_4772 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_4832 T_MiddleBolLoop_4772
v2
du_isPartialEquivalence_4832 ::
  T_MiddleBolLoop_4772 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_4832 :: T_MiddleBolLoop_4772 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_4832 T_MiddleBolLoop_4772
v0
  = let v1 :: T_IsMiddleBolLoop_3358
v1 = T_MiddleBolLoop_4772 -> T_IsMiddleBolLoop_3358
d_isMiddleBolLoop_4804 (T_MiddleBolLoop_4772 -> T_MiddleBolLoop_4772
forall a b. a -> b
coe T_MiddleBolLoop_4772
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsLoop_3026
v2 = T_IsMiddleBolLoop_3358 -> T_IsLoop_3026
MAlonzo.Code.Algebra.Structures.d_isLoop_3372 (T_IsMiddleBolLoop_3358 -> T_IsMiddleBolLoop_3358
forall a b. a -> b
coe T_IsMiddleBolLoop_3358
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsQuasigroup_2944
v3
                = T_IsLoop_3026 -> T_IsQuasigroup_2944
MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040 (T_IsLoop_3026 -> T_IsLoop_3026
forall a b. a -> b
coe T_IsLoop_3026
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsMagma_176
v4
                   = T_IsQuasigroup_2944 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_2962 (T_IsQuasigroup_2944 -> T_IsQuasigroup_2944
forall a b. a -> b
coe T_IsQuasigroup_2944
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               ((T_IsEquivalence_26 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsEquivalence_26 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
                  ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v4))))))
-- Algebra.Bundles.MiddleBolLoop._.isQuasigroup
d_isQuasigroup_4834 ::
  T_MiddleBolLoop_4772 ->
  MAlonzo.Code.Algebra.Structures.T_IsQuasigroup_2944
d_isQuasigroup_4834 :: T_MiddleBolLoop_4772 -> T_IsQuasigroup_2944
d_isQuasigroup_4834 T_MiddleBolLoop_4772
v0
  = (T_IsLoop_3026 -> T_IsQuasigroup_2944)
-> AgdaAny -> T_IsQuasigroup_2944
forall a b. a -> b
coe
      T_IsLoop_3026 -> T_IsQuasigroup_2944
MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040
      ((T_IsMiddleBolLoop_3358 -> T_IsLoop_3026) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMiddleBolLoop_3358 -> T_IsLoop_3026
MAlonzo.Code.Algebra.Structures.d_isLoop_3372
         ((T_MiddleBolLoop_4772 -> T_IsMiddleBolLoop_3358)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_MiddleBolLoop_4772 -> T_IsMiddleBolLoop_3358
d_isMiddleBolLoop_4804 (T_MiddleBolLoop_4772 -> AgdaAny
forall a b. a -> b
coe T_MiddleBolLoop_4772
v0)))
-- Algebra.Bundles.MiddleBolLoop._.leftDivides
d_leftDivides_4836 ::
  T_MiddleBolLoop_4772 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_leftDivides_4836 :: T_MiddleBolLoop_4772 -> T_Σ_14
d_leftDivides_4836 T_MiddleBolLoop_4772
v0
  = (T_IsQuasigroup_2944 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsQuasigroup_2944 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_leftDivides_2968
      ((T_IsLoop_3026 -> T_IsQuasigroup_2944) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsLoop_3026 -> T_IsQuasigroup_2944
MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040
         ((T_IsMiddleBolLoop_3358 -> T_IsLoop_3026) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMiddleBolLoop_3358 -> T_IsLoop_3026
MAlonzo.Code.Algebra.Structures.d_isLoop_3372
            ((T_MiddleBolLoop_4772 -> T_IsMiddleBolLoop_3358)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_MiddleBolLoop_4772 -> T_IsMiddleBolLoop_3358
d_isMiddleBolLoop_4804 (T_MiddleBolLoop_4772 -> AgdaAny
forall a b. a -> b
coe T_MiddleBolLoop_4772
v0))))
-- Algebra.Bundles.MiddleBolLoop._.leftDividesʳ
d_leftDivides'691'_4838 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_MiddleBolLoop_4772 -> AgdaAny -> AgdaAny -> AgdaAny
d_leftDivides'691'_4838 :: () -> () -> T_MiddleBolLoop_4772 -> AgdaAny -> AgdaAny -> AgdaAny
d_leftDivides'691'_4838 ~()
v0 ~()
v1 T_MiddleBolLoop_4772
v2 = T_MiddleBolLoop_4772 -> AgdaAny -> AgdaAny -> AgdaAny
du_leftDivides'691'_4838 T_MiddleBolLoop_4772
v2
du_leftDivides'691'_4838 ::
  T_MiddleBolLoop_4772 -> AgdaAny -> AgdaAny -> AgdaAny
du_leftDivides'691'_4838 :: T_MiddleBolLoop_4772 -> AgdaAny -> AgdaAny -> AgdaAny
du_leftDivides'691'_4838 T_MiddleBolLoop_4772
v0
  = let v1 :: T_IsMiddleBolLoop_3358
v1 = T_MiddleBolLoop_4772 -> T_IsMiddleBolLoop_3358
d_isMiddleBolLoop_4804 (T_MiddleBolLoop_4772 -> T_MiddleBolLoop_4772
forall a b. a -> b
coe T_MiddleBolLoop_4772
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsLoop_3026
v2 = T_IsMiddleBolLoop_3358 -> T_IsLoop_3026
MAlonzo.Code.Algebra.Structures.d_isLoop_3372 (T_IsMiddleBolLoop_3358 -> T_IsMiddleBolLoop_3358
forall a b. a -> b
coe T_IsMiddleBolLoop_3358
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsQuasigroup_2944 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsQuasigroup_2944 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_leftDivides'691'_3012
            ((T_IsLoop_3026 -> T_IsQuasigroup_2944) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsLoop_3026 -> T_IsQuasigroup_2944
MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040 (T_IsLoop_3026 -> AgdaAny
forall a b. a -> b
coe T_IsLoop_3026
v2))))
-- Algebra.Bundles.MiddleBolLoop._.leftDividesˡ
d_leftDivides'737'_4840 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_MiddleBolLoop_4772 -> AgdaAny -> AgdaAny -> AgdaAny
d_leftDivides'737'_4840 :: () -> () -> T_MiddleBolLoop_4772 -> AgdaAny -> AgdaAny -> AgdaAny
d_leftDivides'737'_4840 ~()
v0 ~()
v1 T_MiddleBolLoop_4772
v2 = T_MiddleBolLoop_4772 -> AgdaAny -> AgdaAny -> AgdaAny
du_leftDivides'737'_4840 T_MiddleBolLoop_4772
v2
du_leftDivides'737'_4840 ::
  T_MiddleBolLoop_4772 -> AgdaAny -> AgdaAny -> AgdaAny
du_leftDivides'737'_4840 :: T_MiddleBolLoop_4772 -> AgdaAny -> AgdaAny -> AgdaAny
du_leftDivides'737'_4840 T_MiddleBolLoop_4772
v0
  = let v1 :: T_IsMiddleBolLoop_3358
v1 = T_MiddleBolLoop_4772 -> T_IsMiddleBolLoop_3358
d_isMiddleBolLoop_4804 (T_MiddleBolLoop_4772 -> T_MiddleBolLoop_4772
forall a b. a -> b
coe T_MiddleBolLoop_4772
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsLoop_3026
v2 = T_IsMiddleBolLoop_3358 -> T_IsLoop_3026
MAlonzo.Code.Algebra.Structures.d_isLoop_3372 (T_IsMiddleBolLoop_3358 -> T_IsMiddleBolLoop_3358
forall a b. a -> b
coe T_IsMiddleBolLoop_3358
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsQuasigroup_2944 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsQuasigroup_2944 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_leftDivides'737'_3010
            ((T_IsLoop_3026 -> T_IsQuasigroup_2944) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsLoop_3026 -> T_IsQuasigroup_2944
MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040 (T_IsLoop_3026 -> AgdaAny
forall a b. a -> b
coe T_IsLoop_3026
v2))))
-- Algebra.Bundles.MiddleBolLoop._.middleBol
d_middleBol_4842 ::
  T_MiddleBolLoop_4772 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_middleBol_4842 :: T_MiddleBolLoop_4772 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_middleBol_4842 T_MiddleBolLoop_4772
v0
  = (T_IsMiddleBolLoop_3358
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsMiddleBolLoop_3358 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_middleBol_3374
      ((T_MiddleBolLoop_4772 -> T_IsMiddleBolLoop_3358)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_MiddleBolLoop_4772 -> T_IsMiddleBolLoop_3358
d_isMiddleBolLoop_4804 (T_MiddleBolLoop_4772 -> AgdaAny
forall a b. a -> b
coe T_MiddleBolLoop_4772
v0))
-- Algebra.Bundles.MiddleBolLoop._.refl
d_refl_4844 :: T_MiddleBolLoop_4772 -> AgdaAny -> AgdaAny
d_refl_4844 :: T_MiddleBolLoop_4772 -> AgdaAny -> AgdaAny
d_refl_4844 T_MiddleBolLoop_4772
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_34
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
         ((T_IsQuasigroup_2944 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsQuasigroup_2944 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_2962
            ((T_IsLoop_3026 -> T_IsQuasigroup_2944) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsLoop_3026 -> T_IsQuasigroup_2944
MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040
               ((T_IsMiddleBolLoop_3358 -> T_IsLoop_3026) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsMiddleBolLoop_3358 -> T_IsLoop_3026
MAlonzo.Code.Algebra.Structures.d_isLoop_3372
                  ((T_MiddleBolLoop_4772 -> T_IsMiddleBolLoop_3358)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_MiddleBolLoop_4772 -> T_IsMiddleBolLoop_3358
d_isMiddleBolLoop_4804 (T_MiddleBolLoop_4772 -> AgdaAny
forall a b. a -> b
coe T_MiddleBolLoop_4772
v0))))))
-- Algebra.Bundles.MiddleBolLoop._.reflexive
d_reflexive_4846 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_MiddleBolLoop_4772 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_4846 :: ()
-> ()
-> T_MiddleBolLoop_4772
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_4846 ~()
v0 ~()
v1 T_MiddleBolLoop_4772
v2 = T_MiddleBolLoop_4772
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_4846 T_MiddleBolLoop_4772
v2
du_reflexive_4846 ::
  T_MiddleBolLoop_4772 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_4846 :: T_MiddleBolLoop_4772
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_4846 T_MiddleBolLoop_4772
v0
  = let v1 :: T_IsMiddleBolLoop_3358
v1 = T_MiddleBolLoop_4772 -> T_IsMiddleBolLoop_3358
d_isMiddleBolLoop_4804 (T_MiddleBolLoop_4772 -> T_MiddleBolLoop_4772
forall a b. a -> b
coe T_MiddleBolLoop_4772
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsLoop_3026
v2 = T_IsMiddleBolLoop_3358 -> T_IsLoop_3026
MAlonzo.Code.Algebra.Structures.d_isLoop_3372 (T_IsMiddleBolLoop_3358 -> T_IsMiddleBolLoop_3358
forall a b. a -> b
coe T_IsMiddleBolLoop_3358
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsQuasigroup_2944
v3
                = T_IsLoop_3026 -> T_IsQuasigroup_2944
MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040 (T_IsLoop_3026 -> T_IsLoop_3026
forall a b. a -> b
coe T_IsLoop_3026
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsMagma_176
v4
                   = T_IsQuasigroup_2944 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_2962 (T_IsQuasigroup_2944 -> T_IsQuasigroup_2944
forall a b. a -> b
coe T_IsQuasigroup_2944
v3) in
             (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
               (\ AgdaAny
v5 AgdaAny
v6 AgdaAny
v7 ->
                  (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                    T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
                    ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v4))
                    AgdaAny
v5))))
-- Algebra.Bundles.MiddleBolLoop._.rightDivides
d_rightDivides_4848 ::
  T_MiddleBolLoop_4772 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_rightDivides_4848 :: T_MiddleBolLoop_4772 -> T_Σ_14
d_rightDivides_4848 T_MiddleBolLoop_4772
v0
  = (T_IsQuasigroup_2944 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsQuasigroup_2944 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_rightDivides_2970
      ((T_IsLoop_3026 -> T_IsQuasigroup_2944) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsLoop_3026 -> T_IsQuasigroup_2944
MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040
         ((T_IsMiddleBolLoop_3358 -> T_IsLoop_3026) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMiddleBolLoop_3358 -> T_IsLoop_3026
MAlonzo.Code.Algebra.Structures.d_isLoop_3372
            ((T_MiddleBolLoop_4772 -> T_IsMiddleBolLoop_3358)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_MiddleBolLoop_4772 -> T_IsMiddleBolLoop_3358
d_isMiddleBolLoop_4804 (T_MiddleBolLoop_4772 -> AgdaAny
forall a b. a -> b
coe T_MiddleBolLoop_4772
v0))))
-- Algebra.Bundles.MiddleBolLoop._.rightDividesʳ
d_rightDivides'691'_4850 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_MiddleBolLoop_4772 -> AgdaAny -> AgdaAny -> AgdaAny
d_rightDivides'691'_4850 :: () -> () -> T_MiddleBolLoop_4772 -> AgdaAny -> AgdaAny -> AgdaAny
d_rightDivides'691'_4850 ~()
v0 ~()
v1 T_MiddleBolLoop_4772
v2 = T_MiddleBolLoop_4772 -> AgdaAny -> AgdaAny -> AgdaAny
du_rightDivides'691'_4850 T_MiddleBolLoop_4772
v2
du_rightDivides'691'_4850 ::
  T_MiddleBolLoop_4772 -> AgdaAny -> AgdaAny -> AgdaAny
du_rightDivides'691'_4850 :: T_MiddleBolLoop_4772 -> AgdaAny -> AgdaAny -> AgdaAny
du_rightDivides'691'_4850 T_MiddleBolLoop_4772
v0
  = let v1 :: T_IsMiddleBolLoop_3358
v1 = T_MiddleBolLoop_4772 -> T_IsMiddleBolLoop_3358
d_isMiddleBolLoop_4804 (T_MiddleBolLoop_4772 -> T_MiddleBolLoop_4772
forall a b. a -> b
coe T_MiddleBolLoop_4772
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsLoop_3026
v2 = T_IsMiddleBolLoop_3358 -> T_IsLoop_3026
MAlonzo.Code.Algebra.Structures.d_isLoop_3372 (T_IsMiddleBolLoop_3358 -> T_IsMiddleBolLoop_3358
forall a b. a -> b
coe T_IsMiddleBolLoop_3358
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsQuasigroup_2944 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsQuasigroup_2944 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_rightDivides'691'_3016
            ((T_IsLoop_3026 -> T_IsQuasigroup_2944) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsLoop_3026 -> T_IsQuasigroup_2944
MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040 (T_IsLoop_3026 -> AgdaAny
forall a b. a -> b
coe T_IsLoop_3026
v2))))
-- Algebra.Bundles.MiddleBolLoop._.rightDividesˡ
d_rightDivides'737'_4852 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_MiddleBolLoop_4772 -> AgdaAny -> AgdaAny -> AgdaAny
d_rightDivides'737'_4852 :: () -> () -> T_MiddleBolLoop_4772 -> AgdaAny -> AgdaAny -> AgdaAny
d_rightDivides'737'_4852 ~()
v0 ~()
v1 T_MiddleBolLoop_4772
v2 = T_MiddleBolLoop_4772 -> AgdaAny -> AgdaAny -> AgdaAny
du_rightDivides'737'_4852 T_MiddleBolLoop_4772
v2
du_rightDivides'737'_4852 ::
  T_MiddleBolLoop_4772 -> AgdaAny -> AgdaAny -> AgdaAny
du_rightDivides'737'_4852 :: T_MiddleBolLoop_4772 -> AgdaAny -> AgdaAny -> AgdaAny
du_rightDivides'737'_4852 T_MiddleBolLoop_4772
v0
  = let v1 :: T_IsMiddleBolLoop_3358
v1 = T_MiddleBolLoop_4772 -> T_IsMiddleBolLoop_3358
d_isMiddleBolLoop_4804 (T_MiddleBolLoop_4772 -> T_MiddleBolLoop_4772
forall a b. a -> b
coe T_MiddleBolLoop_4772
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsLoop_3026
v2 = T_IsMiddleBolLoop_3358 -> T_IsLoop_3026
MAlonzo.Code.Algebra.Structures.d_isLoop_3372 (T_IsMiddleBolLoop_3358 -> T_IsMiddleBolLoop_3358
forall a b. a -> b
coe T_IsMiddleBolLoop_3358
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsQuasigroup_2944 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsQuasigroup_2944 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_rightDivides'737'_3014
            ((T_IsLoop_3026 -> T_IsQuasigroup_2944) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsLoop_3026 -> T_IsQuasigroup_2944
MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040 (T_IsLoop_3026 -> AgdaAny
forall a b. a -> b
coe T_IsLoop_3026
v2))))
-- Algebra.Bundles.MiddleBolLoop._.setoid
d_setoid_4854 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_MiddleBolLoop_4772 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_4854 :: () -> () -> T_MiddleBolLoop_4772 -> T_Setoid_44
d_setoid_4854 ~()
v0 ~()
v1 T_MiddleBolLoop_4772
v2 = T_MiddleBolLoop_4772 -> T_Setoid_44
du_setoid_4854 T_MiddleBolLoop_4772
v2
du_setoid_4854 ::
  T_MiddleBolLoop_4772 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_4854 :: T_MiddleBolLoop_4772 -> T_Setoid_44
du_setoid_4854 T_MiddleBolLoop_4772
v0
  = let v1 :: T_IsMiddleBolLoop_3358
v1 = T_MiddleBolLoop_4772 -> T_IsMiddleBolLoop_3358
d_isMiddleBolLoop_4804 (T_MiddleBolLoop_4772 -> T_MiddleBolLoop_4772
forall a b. a -> b
coe T_MiddleBolLoop_4772
v0) in
    AgdaAny -> T_Setoid_44
forall a b. a -> b
coe
      (let v2 :: T_IsLoop_3026
v2 = T_IsMiddleBolLoop_3358 -> T_IsLoop_3026
MAlonzo.Code.Algebra.Structures.d_isLoop_3372 (T_IsMiddleBolLoop_3358 -> T_IsMiddleBolLoop_3358
forall a b. a -> b
coe T_IsMiddleBolLoop_3358
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsQuasigroup_2944
v3
                = T_IsLoop_3026 -> T_IsQuasigroup_2944
MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040 (T_IsLoop_3026 -> T_IsLoop_3026
forall a b. a -> b
coe T_IsLoop_3026
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsMagma_176 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMagma_176 -> T_Setoid_44
MAlonzo.Code.Algebra.Structures.du_setoid_200
               ((T_IsQuasigroup_2944 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroup_2944 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_2962 (T_IsQuasigroup_2944 -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroup_2944
v3)))))
-- Algebra.Bundles.MiddleBolLoop._.sym
d_sym_4856 ::
  T_MiddleBolLoop_4772 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_4856 :: T_MiddleBolLoop_4772 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_4856 T_MiddleBolLoop_4772
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_36
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
         ((T_IsQuasigroup_2944 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsQuasigroup_2944 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_2962
            ((T_IsLoop_3026 -> T_IsQuasigroup_2944) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsLoop_3026 -> T_IsQuasigroup_2944
MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040
               ((T_IsMiddleBolLoop_3358 -> T_IsLoop_3026) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsMiddleBolLoop_3358 -> T_IsLoop_3026
MAlonzo.Code.Algebra.Structures.d_isLoop_3372
                  ((T_MiddleBolLoop_4772 -> T_IsMiddleBolLoop_3358)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_MiddleBolLoop_4772 -> T_IsMiddleBolLoop_3358
d_isMiddleBolLoop_4804 (T_MiddleBolLoop_4772 -> AgdaAny
forall a b. a -> b
coe T_MiddleBolLoop_4772
v0))))))
-- Algebra.Bundles.MiddleBolLoop._.trans
d_trans_4858 ::
  T_MiddleBolLoop_4772 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_4858 :: T_MiddleBolLoop_4772
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_4858 T_MiddleBolLoop_4772
v0
  = (T_IsEquivalence_26
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_38
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
         ((T_IsQuasigroup_2944 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsQuasigroup_2944 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_2962
            ((T_IsLoop_3026 -> T_IsQuasigroup_2944) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsLoop_3026 -> T_IsQuasigroup_2944
MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040
               ((T_IsMiddleBolLoop_3358 -> T_IsLoop_3026) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsMiddleBolLoop_3358 -> T_IsLoop_3026
MAlonzo.Code.Algebra.Structures.d_isLoop_3372
                  ((T_MiddleBolLoop_4772 -> T_IsMiddleBolLoop_3358)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_MiddleBolLoop_4772 -> T_IsMiddleBolLoop_3358
d_isMiddleBolLoop_4804 (T_MiddleBolLoop_4772 -> AgdaAny
forall a b. a -> b
coe T_MiddleBolLoop_4772
v0))))))
-- Algebra.Bundles.MiddleBolLoop._.∙-cong
d_'8729''45'cong_4860 ::
  T_MiddleBolLoop_4772 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_4860 :: T_MiddleBolLoop_4772
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_4860 T_MiddleBolLoop_4772
v0
  = (T_IsMagma_176
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsMagma_176
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_186
      ((T_IsQuasigroup_2944 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsQuasigroup_2944 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_2962
         ((T_IsLoop_3026 -> T_IsQuasigroup_2944) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsLoop_3026 -> T_IsQuasigroup_2944
MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040
            ((T_IsMiddleBolLoop_3358 -> T_IsLoop_3026) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMiddleBolLoop_3358 -> T_IsLoop_3026
MAlonzo.Code.Algebra.Structures.d_isLoop_3372
               ((T_MiddleBolLoop_4772 -> T_IsMiddleBolLoop_3358)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_MiddleBolLoop_4772 -> T_IsMiddleBolLoop_3358
d_isMiddleBolLoop_4804 (T_MiddleBolLoop_4772 -> AgdaAny
forall a b. a -> b
coe T_MiddleBolLoop_4772
v0)))))
-- Algebra.Bundles.MiddleBolLoop._.∙-congʳ
d_'8729''45'cong'691'_4862 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_MiddleBolLoop_4772 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_4862 :: ()
-> ()
-> T_MiddleBolLoop_4772
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_4862 ~()
v0 ~()
v1 T_MiddleBolLoop_4772
v2
  = T_MiddleBolLoop_4772
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_4862 T_MiddleBolLoop_4772
v2
du_'8729''45'cong'691'_4862 ::
  T_MiddleBolLoop_4772 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_4862 :: T_MiddleBolLoop_4772
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_4862 T_MiddleBolLoop_4772
v0
  = let v1 :: T_IsMiddleBolLoop_3358
v1 = T_MiddleBolLoop_4772 -> T_IsMiddleBolLoop_3358
d_isMiddleBolLoop_4804 (T_MiddleBolLoop_4772 -> T_MiddleBolLoop_4772
forall a b. a -> b
coe T_MiddleBolLoop_4772
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsLoop_3026
v2 = T_IsMiddleBolLoop_3358 -> T_IsLoop_3026
MAlonzo.Code.Algebra.Structures.d_isLoop_3372 (T_IsMiddleBolLoop_3358 -> T_IsMiddleBolLoop_3358
forall a b. a -> b
coe T_IsMiddleBolLoop_3358
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsQuasigroup_2944
v3
                = T_IsLoop_3026 -> T_IsQuasigroup_2944
MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040 (T_IsLoop_3026 -> T_IsLoop_3026
forall a b. a -> b
coe T_IsLoop_3026
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'691'_206
               ((T_IsQuasigroup_2944 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroup_2944 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_2962 (T_IsQuasigroup_2944 -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroup_2944
v3)))))
-- Algebra.Bundles.MiddleBolLoop._.∙-congˡ
d_'8729''45'cong'737'_4864 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_MiddleBolLoop_4772 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_4864 :: ()
-> ()
-> T_MiddleBolLoop_4772
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_4864 ~()
v0 ~()
v1 T_MiddleBolLoop_4772
v2
  = T_MiddleBolLoop_4772
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_4864 T_MiddleBolLoop_4772
v2
du_'8729''45'cong'737'_4864 ::
  T_MiddleBolLoop_4772 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_4864 :: T_MiddleBolLoop_4772
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_4864 T_MiddleBolLoop_4772
v0
  = let v1 :: T_IsMiddleBolLoop_3358
v1 = T_MiddleBolLoop_4772 -> T_IsMiddleBolLoop_3358
d_isMiddleBolLoop_4804 (T_MiddleBolLoop_4772 -> T_MiddleBolLoop_4772
forall a b. a -> b
coe T_MiddleBolLoop_4772
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsLoop_3026
v2 = T_IsMiddleBolLoop_3358 -> T_IsLoop_3026
MAlonzo.Code.Algebra.Structures.d_isLoop_3372 (T_IsMiddleBolLoop_3358 -> T_IsMiddleBolLoop_3358
forall a b. a -> b
coe T_IsMiddleBolLoop_3358
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsQuasigroup_2944
v3
                = T_IsLoop_3026 -> T_IsQuasigroup_2944
MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3040 (T_IsLoop_3026 -> T_IsLoop_3026
forall a b. a -> b
coe T_IsLoop_3026
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsMagma_176
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMagma_176
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'737'_202
               ((T_IsQuasigroup_2944 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroup_2944 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_2962 (T_IsQuasigroup_2944 -> AgdaAny
forall a b. a -> b
coe T_IsQuasigroup_2944
v3)))))
-- Algebra.Bundles.MiddleBolLoop.loop
d_loop_4866 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_MiddleBolLoop_4772 -> T_Loop_4346
d_loop_4866 :: () -> () -> T_MiddleBolLoop_4772 -> T_Loop_4346
d_loop_4866 ~()
v0 ~()
v1 T_MiddleBolLoop_4772
v2 = T_MiddleBolLoop_4772 -> T_Loop_4346
du_loop_4866 T_MiddleBolLoop_4772
v2
du_loop_4866 :: T_MiddleBolLoop_4772 -> T_Loop_4346
du_loop_4866 :: T_MiddleBolLoop_4772 -> T_Loop_4346
du_loop_4866 T_MiddleBolLoop_4772
v0
  = ((AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> T_IsLoop_3026
 -> T_Loop_4346)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsLoop_3026
-> T_Loop_4346
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsLoop_3026
-> T_Loop_4346
C_Loop'46'constructor_78267 (T_MiddleBolLoop_4772 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__4796 (T_MiddleBolLoop_4772 -> T_MiddleBolLoop_4772
forall a b. a -> b
coe T_MiddleBolLoop_4772
v0))
      (T_MiddleBolLoop_4772 -> AgdaAny -> AgdaAny -> AgdaAny
d__'92''92'__4798 (T_MiddleBolLoop_4772 -> T_MiddleBolLoop_4772
forall a b. a -> b
coe T_MiddleBolLoop_4772
v0)) (T_MiddleBolLoop_4772 -> AgdaAny -> AgdaAny -> AgdaAny
d__'47''47'__4800 (T_MiddleBolLoop_4772 -> T_MiddleBolLoop_4772
forall a b. a -> b
coe T_MiddleBolLoop_4772
v0))
      (T_MiddleBolLoop_4772 -> AgdaAny
d_ε_4802 (T_MiddleBolLoop_4772 -> T_MiddleBolLoop_4772
forall a b. a -> b
coe T_MiddleBolLoop_4772
v0))
      (T_IsMiddleBolLoop_3358 -> T_IsLoop_3026
MAlonzo.Code.Algebra.Structures.d_isLoop_3372
         ((T_MiddleBolLoop_4772 -> T_IsMiddleBolLoop_3358)
-> AgdaAny -> T_IsMiddleBolLoop_3358
forall a b. a -> b
coe T_MiddleBolLoop_4772 -> T_IsMiddleBolLoop_3358
d_isMiddleBolLoop_4804 (T_MiddleBolLoop_4772 -> AgdaAny
forall a b. a -> b
coe T_MiddleBolLoop_4772
v0)))
-- Algebra.Bundles.MiddleBolLoop._.quasigroup
d_quasigroup_4870 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_MiddleBolLoop_4772 -> T_Quasigroup_4246
d_quasigroup_4870 :: () -> () -> T_MiddleBolLoop_4772 -> T_Quasigroup_4246
d_quasigroup_4870 ~()
v0 ~()
v1 T_MiddleBolLoop_4772
v2 = T_MiddleBolLoop_4772 -> T_Quasigroup_4246
du_quasigroup_4870 T_MiddleBolLoop_4772
v2
du_quasigroup_4870 :: T_MiddleBolLoop_4772 -> T_Quasigroup_4246
du_quasigroup_4870 :: T_MiddleBolLoop_4772 -> T_Quasigroup_4246
du_quasigroup_4870 T_MiddleBolLoop_4772
v0
  = (T_Loop_4346 -> T_Quasigroup_4246) -> AgdaAny -> T_Quasigroup_4246
forall a b. a -> b
coe T_Loop_4346 -> T_Quasigroup_4246
du_quasigroup_4438 ((T_MiddleBolLoop_4772 -> T_Loop_4346) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_MiddleBolLoop_4772 -> T_Loop_4346
du_loop_4866 (T_MiddleBolLoop_4772 -> AgdaAny
forall a b. a -> b
coe T_MiddleBolLoop_4772
v0))