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

-- 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 :: AgdaAny
v1 = (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) 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
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 :: AgdaAny
v1 = (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) 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
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 :: AgdaAny
v1 = (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) 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
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 :: AgdaAny
v1 = (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) in
    AgdaAny -> T_RawMagma_36
forall a b. a -> b
coe
      (let v2 :: AgdaAny
v2 = (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
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
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 :: AgdaAny
v1 = (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) 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
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 :: AgdaAny
v1 = (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) 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
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 :: AgdaAny
v1 = (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) in
    AgdaAny -> T_RawMagma_36
forall a b. a -> b
coe
      (let v2 :: AgdaAny
v2 = (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
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
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 :: AgdaAny
v1 = (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) 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
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 :: AgdaAny
v1 = (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) in
    AgdaAny -> T_RawMagma_36
forall a b. a -> b
coe
      (let v2 :: AgdaAny
v2 = (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
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
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 :: AgdaAny
v1 = (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) 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
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 :: AgdaAny
v1 = (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) in
    AgdaAny -> T_Magma_68
forall a b. a -> b
coe
      (let v2 :: AgdaAny
v2 = (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
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
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 :: AgdaAny
v1 = (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) in
    AgdaAny -> T_RawMagma_36
forall a b. a -> b
coe
      (let v2 :: AgdaAny
v2 = (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
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: AgdaAny
v3 = (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
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
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 :: AgdaAny
v1 = (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) 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
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 :: AgdaAny
v1 = (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) 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
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 :: AgdaAny
v1 = (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) 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
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 :: AgdaAny
v1 = (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) 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
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 :: AgdaAny
v1 = (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) in
    AgdaAny -> T_Magma_68
forall a b. a -> b
coe
      (let v2 :: AgdaAny
v2 = (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
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
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 :: AgdaAny
v1 = (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) in
    AgdaAny -> T_RawMagma_36
forall a b. a -> b
coe
      (let v2 :: AgdaAny
v2 = (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
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: AgdaAny
v3 = (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
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
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 :: AgdaAny
v1 = (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) 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
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 :: AgdaAny
v1 = (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) 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
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 :: AgdaAny
v1 = (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) 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
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 :: AgdaAny
v1 = (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) 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
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 :: AgdaAny
v1 = (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) 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
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 :: AgdaAny
v1 = (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) in
    AgdaAny -> T_RawMagma_36
forall a b. a -> b
coe
      (let v2 :: AgdaAny
v2 = (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
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
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 :: AgdaAny
v2
             = (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) 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
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 :: AgdaAny
v1 = (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) in
    AgdaAny -> T_Magma_68
forall a b. a -> b
coe
      (let v2 :: AgdaAny
v2 = (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
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
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 :: AgdaAny
v1 = (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) in
    AgdaAny -> T_RawMagma_36
forall a b. a -> b
coe
      (let v2 :: AgdaAny
v2 = (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
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: AgdaAny
v3 = (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
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
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 :: AgdaAny
v1 = (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) 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
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 :: AgdaAny
v1 = (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) 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
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 :: AgdaAny
v1 = (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) 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
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 :: AgdaAny
v1 = (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) 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
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 :: AgdaAny
v1 = (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) in
    AgdaAny -> T_RawMagma_36
forall a b. a -> b
coe
      (let v2 :: AgdaAny
v2 = (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
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
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