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

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

module MAlonzo.Code.Algebra.Bundles where

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

-- Algebra.Bundles.RawMagma
d_RawMagma_8 :: p -> p -> ()
d_RawMagma_8 p
a0 p
a1 = ()
newtype T_RawMagma_8
  = C_RawMagma'46'constructor_79 (AgdaAny -> AgdaAny -> AgdaAny)
-- Algebra.Bundles.RawMagma.Carrier
d_Carrier_20 :: T_RawMagma_8 -> ()
d_Carrier_20 :: T_RawMagma_8 -> ()
d_Carrier_20 = T_RawMagma_8 -> ()
forall a. a
erased
-- Algebra.Bundles.RawMagma._≈_
d__'8776'__22 :: T_RawMagma_8 -> AgdaAny -> AgdaAny -> ()
d__'8776'__22 :: T_RawMagma_8 -> AgdaAny -> AgdaAny -> ()
d__'8776'__22 = T_RawMagma_8 -> AgdaAny -> AgdaAny -> ()
forall a. a
erased
-- Algebra.Bundles.RawMagma._∙_
d__'8729'__24 :: T_RawMagma_8 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__24 :: T_RawMagma_8 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__24 T_RawMagma_8
v0
  = case T_RawMagma_8 -> T_RawMagma_8
forall a b. a -> b
coe T_RawMagma_8
v0 of
      C_RawMagma'46'constructor_79 AgdaAny -> AgdaAny -> AgdaAny
v3 -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v3
      T_RawMagma_8
_ -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.RawMagma._≉_
d__'8777'__26 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_RawMagma_8 -> AgdaAny -> AgdaAny -> ()
d__'8777'__26 :: () -> () -> T_RawMagma_8 -> AgdaAny -> AgdaAny -> ()
d__'8777'__26 = () -> () -> T_RawMagma_8 -> AgdaAny -> AgdaAny -> ()
forall a. a
erased
-- Algebra.Bundles.Magma
d_Magma_36 :: p -> p -> ()
d_Magma_36 p
a0 p
a1 = ()
data T_Magma_36
  = C_Magma'46'constructor_581 (AgdaAny -> AgdaAny -> AgdaAny)
                               MAlonzo.Code.Algebra.Structures.T_IsMagma_86
-- Algebra.Bundles.Magma.Carrier
d_Carrier_50 :: T_Magma_36 -> ()
d_Carrier_50 :: T_Magma_36 -> ()
d_Carrier_50 = T_Magma_36 -> ()
forall a. a
erased
-- Algebra.Bundles.Magma._≈_
d__'8776'__52 :: T_Magma_36 -> AgdaAny -> AgdaAny -> ()
d__'8776'__52 :: T_Magma_36 -> AgdaAny -> AgdaAny -> ()
d__'8776'__52 = T_Magma_36 -> AgdaAny -> AgdaAny -> ()
forall a. a
erased
-- Algebra.Bundles.Magma._∙_
d__'8729'__54 :: T_Magma_36 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__54 :: T_Magma_36 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__54 T_Magma_36
v0
  = case T_Magma_36 -> T_Magma_36
forall a b. a -> b
coe T_Magma_36
v0 of
      C_Magma'46'constructor_581 AgdaAny -> AgdaAny -> AgdaAny
v3 T_IsMagma_86
v4 -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v3
      T_Magma_36
_ -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.Magma.isMagma
d_isMagma_56 ::
  T_Magma_36 -> MAlonzo.Code.Algebra.Structures.T_IsMagma_86
d_isMagma_56 :: T_Magma_36 -> T_IsMagma_86
d_isMagma_56 T_Magma_36
v0
  = case T_Magma_36 -> T_Magma_36
forall a b. a -> b
coe T_Magma_36
v0 of
      C_Magma'46'constructor_581 AgdaAny -> AgdaAny -> AgdaAny
v3 T_IsMagma_86
v4 -> T_IsMagma_86 -> T_IsMagma_86
forall a b. a -> b
coe T_IsMagma_86
v4
      T_Magma_36
_ -> T_IsMagma_86
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.Magma._.isEquivalence
d_isEquivalence_60 ::
  T_Magma_36 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_60 :: T_Magma_36 -> T_IsEquivalence_26
d_isEquivalence_60 T_Magma_36
v0
  = (T_IsMagma_86 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      T_IsMagma_86 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_94
      ((T_Magma_36 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Magma_36 -> T_IsMagma_86
d_isMagma_56 (T_Magma_36 -> AgdaAny
forall a b. a -> b
coe T_Magma_36
v0))
-- Algebra.Bundles.Magma._.isPartialEquivalence
d_isPartialEquivalence_62 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Magma_36 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_62 :: () -> () -> T_Magma_36 -> T_IsPartialEquivalence_16
d_isPartialEquivalence_62 ~()
v0 ~()
v1 T_Magma_36
v2
  = T_Magma_36 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_62 T_Magma_36
v2
du_isPartialEquivalence_62 ::
  T_Magma_36 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_62 :: T_Magma_36 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_62 T_Magma_36
v0
  = let v1 :: T_IsMagma_86
v1 = T_Magma_36 -> T_IsMagma_86
d_isMagma_56 (T_Magma_36 -> T_Magma_36
forall a b. a -> b
coe T_Magma_36
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_86 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_94 (T_IsMagma_86 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86
v1)))
-- Algebra.Bundles.Magma._.refl
d_refl_64 :: T_Magma_36 -> AgdaAny -> AgdaAny
d_refl_64 :: T_Magma_36 -> AgdaAny -> AgdaAny
d_refl_64 T_Magma_36
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_86 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_86 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_94
         ((T_Magma_36 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Magma_36 -> T_IsMagma_86
d_isMagma_56 (T_Magma_36 -> AgdaAny
forall a b. a -> b
coe T_Magma_36
v0)))
-- Algebra.Bundles.Magma._.reflexive
d_reflexive_66 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Magma_36 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_66 :: ()
-> ()
-> T_Magma_36
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_66 ~()
v0 ~()
v1 T_Magma_36
v2 = T_Magma_36 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_66 T_Magma_36
v2
du_reflexive_66 ::
  T_Magma_36 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_66 :: T_Magma_36 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_66 T_Magma_36
v0
  = let v1 :: T_IsMagma_86
v1 = T_Magma_36 -> T_IsMagma_86
d_isMagma_56 (T_Magma_36 -> T_Magma_36
forall a b. a -> b
coe T_Magma_36
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_86 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_94 (T_IsMagma_86 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86
v1))
           AgdaAny
v2)
-- Algebra.Bundles.Magma._.setoid
d_setoid_68 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Magma_36 -> MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_68 :: () -> () -> T_Magma_36 -> T_Setoid_44
d_setoid_68 ~()
v0 ~()
v1 T_Magma_36
v2 = T_Magma_36 -> T_Setoid_44
du_setoid_68 T_Magma_36
v2
du_setoid_68 ::
  T_Magma_36 -> MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_68 :: T_Magma_36 -> T_Setoid_44
du_setoid_68 T_Magma_36
v0
  = (T_IsMagma_86 -> T_Setoid_44) -> AgdaAny -> T_Setoid_44
forall a b. a -> b
coe
      T_IsMagma_86 -> T_Setoid_44
MAlonzo.Code.Algebra.Structures.du_setoid_110
      ((T_Magma_36 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Magma_36 -> T_IsMagma_86
d_isMagma_56 (T_Magma_36 -> AgdaAny
forall a b. a -> b
coe T_Magma_36
v0))
-- Algebra.Bundles.Magma._.sym
d_sym_70 :: T_Magma_36 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_70 :: T_Magma_36 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_70 T_Magma_36
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_86 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_86 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_94
         ((T_Magma_36 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Magma_36 -> T_IsMagma_86
d_isMagma_56 (T_Magma_36 -> AgdaAny
forall a b. a -> b
coe T_Magma_36
v0)))
-- Algebra.Bundles.Magma._.trans
d_trans_72 ::
  T_Magma_36 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_72 :: T_Magma_36
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_72 T_Magma_36
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_86 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_86 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_94
         ((T_Magma_36 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Magma_36 -> T_IsMagma_86
d_isMagma_56 (T_Magma_36 -> AgdaAny
forall a b. a -> b
coe T_Magma_36
v0)))
-- Algebra.Bundles.Magma._.∙-cong
d_'8729''45'cong_74 ::
  T_Magma_36 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_74 :: T_Magma_36
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_74 T_Magma_36
v0
  = (T_IsMagma_86
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsMagma_86
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_96
      ((T_Magma_36 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Magma_36 -> T_IsMagma_86
d_isMagma_56 (T_Magma_36 -> AgdaAny
forall a b. a -> b
coe T_Magma_36
v0))
-- Algebra.Bundles.Magma._.∙-congʳ
d_'8729''45'cong'691'_76 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Magma_36 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_76 :: ()
-> ()
-> T_Magma_36
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_76 ~()
v0 ~()
v1 T_Magma_36
v2 = T_Magma_36 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_76 T_Magma_36
v2
du_'8729''45'cong'691'_76 ::
  T_Magma_36 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_76 :: T_Magma_36 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_76 T_Magma_36
v0
  = (T_IsMagma_86
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsMagma_86 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'691'_116
      ((T_Magma_36 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Magma_36 -> T_IsMagma_86
d_isMagma_56 (T_Magma_36 -> AgdaAny
forall a b. a -> b
coe T_Magma_36
v0))
-- Algebra.Bundles.Magma._.∙-congˡ
d_'8729''45'cong'737'_78 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Magma_36 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_78 :: ()
-> ()
-> T_Magma_36
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_78 ~()
v0 ~()
v1 T_Magma_36
v2 = T_Magma_36 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_78 T_Magma_36
v2
du_'8729''45'cong'737'_78 ::
  T_Magma_36 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_78 :: T_Magma_36 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_78 T_Magma_36
v0
  = (T_IsMagma_86
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsMagma_86 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'737'_112
      ((T_Magma_36 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Magma_36 -> T_IsMagma_86
d_isMagma_56 (T_Magma_36 -> AgdaAny
forall a b. a -> b
coe T_Magma_36
v0))
-- Algebra.Bundles.Magma.rawMagma
d_rawMagma_80 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Magma_36 -> T_RawMagma_8
d_rawMagma_80 :: () -> () -> T_Magma_36 -> T_RawMagma_8
d_rawMagma_80 ~()
v0 ~()
v1 T_Magma_36
v2 = T_Magma_36 -> T_RawMagma_8
du_rawMagma_80 T_Magma_36
v2
du_rawMagma_80 :: T_Magma_36 -> T_RawMagma_8
du_rawMagma_80 :: T_Magma_36 -> T_RawMagma_8
du_rawMagma_80 T_Magma_36
v0
  = ((AgdaAny -> AgdaAny -> AgdaAny) -> T_RawMagma_8)
-> (AgdaAny -> AgdaAny -> AgdaAny) -> T_RawMagma_8
forall a b. a -> b
coe (AgdaAny -> AgdaAny -> AgdaAny) -> T_RawMagma_8
C_RawMagma'46'constructor_79 (T_Magma_36 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__54 (T_Magma_36 -> T_Magma_36
forall a b. a -> b
coe T_Magma_36
v0))
-- Algebra.Bundles.Magma._._≉_
d__'8777'__84 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Magma_36 -> AgdaAny -> AgdaAny -> ()
d__'8777'__84 :: () -> () -> T_Magma_36 -> AgdaAny -> AgdaAny -> ()
d__'8777'__84 = () -> () -> T_Magma_36 -> AgdaAny -> AgdaAny -> ()
forall a. a
erased
-- Algebra.Bundles.SelectiveMagma
d_SelectiveMagma_90 :: p -> p -> ()
d_SelectiveMagma_90 p
a0 p
a1 = ()
data T_SelectiveMagma_90
  = C_SelectiveMagma'46'constructor_1577 (AgdaAny ->
                                          AgdaAny -> AgdaAny)
                                         MAlonzo.Code.Algebra.Structures.T_IsSelectiveMagma_158
-- Algebra.Bundles.SelectiveMagma.Carrier
d_Carrier_104 :: T_SelectiveMagma_90 -> ()
d_Carrier_104 :: T_SelectiveMagma_90 -> ()
d_Carrier_104 = T_SelectiveMagma_90 -> ()
forall a. a
erased
-- Algebra.Bundles.SelectiveMagma._≈_
d__'8776'__106 :: T_SelectiveMagma_90 -> AgdaAny -> AgdaAny -> ()
d__'8776'__106 :: T_SelectiveMagma_90 -> AgdaAny -> AgdaAny -> ()
d__'8776'__106 = T_SelectiveMagma_90 -> AgdaAny -> AgdaAny -> ()
forall a. a
erased
-- Algebra.Bundles.SelectiveMagma._∙_
d__'8729'__108 ::
  T_SelectiveMagma_90 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__108 :: T_SelectiveMagma_90 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__108 T_SelectiveMagma_90
v0
  = case T_SelectiveMagma_90 -> T_SelectiveMagma_90
forall a b. a -> b
coe T_SelectiveMagma_90
v0 of
      C_SelectiveMagma'46'constructor_1577 AgdaAny -> AgdaAny -> AgdaAny
v3 T_IsSelectiveMagma_158
v4 -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v3
      T_SelectiveMagma_90
_ -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.SelectiveMagma.isSelectiveMagma
d_isSelectiveMagma_110 ::
  T_SelectiveMagma_90 ->
  MAlonzo.Code.Algebra.Structures.T_IsSelectiveMagma_158
d_isSelectiveMagma_110 :: T_SelectiveMagma_90 -> T_IsSelectiveMagma_158
d_isSelectiveMagma_110 T_SelectiveMagma_90
v0
  = case T_SelectiveMagma_90 -> T_SelectiveMagma_90
forall a b. a -> b
coe T_SelectiveMagma_90
v0 of
      C_SelectiveMagma'46'constructor_1577 AgdaAny -> AgdaAny -> AgdaAny
v3 T_IsSelectiveMagma_158
v4 -> T_IsSelectiveMagma_158 -> T_IsSelectiveMagma_158
forall a b. a -> b
coe T_IsSelectiveMagma_158
v4
      T_SelectiveMagma_90
_ -> T_IsSelectiveMagma_158
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.SelectiveMagma._.isEquivalence
d_isEquivalence_114 ::
  T_SelectiveMagma_90 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_114 :: T_SelectiveMagma_90 -> T_IsEquivalence_26
d_isEquivalence_114 T_SelectiveMagma_90
v0
  = (T_IsMagma_86 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      T_IsMagma_86 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_94
      ((T_IsSelectiveMagma_158 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSelectiveMagma_158 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_166
         ((T_SelectiveMagma_90 -> T_IsSelectiveMagma_158)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SelectiveMagma_90 -> T_IsSelectiveMagma_158
d_isSelectiveMagma_110 (T_SelectiveMagma_90 -> AgdaAny
forall a b. a -> b
coe T_SelectiveMagma_90
v0)))
-- Algebra.Bundles.SelectiveMagma._.isMagma
d_isMagma_116 ::
  T_SelectiveMagma_90 -> MAlonzo.Code.Algebra.Structures.T_IsMagma_86
d_isMagma_116 :: T_SelectiveMagma_90 -> T_IsMagma_86
d_isMagma_116 T_SelectiveMagma_90
v0
  = (T_IsSelectiveMagma_158 -> T_IsMagma_86) -> AgdaAny -> T_IsMagma_86
forall a b. a -> b
coe
      T_IsSelectiveMagma_158 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_166
      ((T_SelectiveMagma_90 -> T_IsSelectiveMagma_158)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SelectiveMagma_90 -> T_IsSelectiveMagma_158
d_isSelectiveMagma_110 (T_SelectiveMagma_90 -> AgdaAny
forall a b. a -> b
coe T_SelectiveMagma_90
v0))
-- Algebra.Bundles.SelectiveMagma._.isPartialEquivalence
d_isPartialEquivalence_118 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SelectiveMagma_90 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_118 :: () -> () -> T_SelectiveMagma_90 -> T_IsPartialEquivalence_16
d_isPartialEquivalence_118 ~()
v0 ~()
v1 T_SelectiveMagma_90
v2
  = T_SelectiveMagma_90 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_118 T_SelectiveMagma_90
v2
du_isPartialEquivalence_118 ::
  T_SelectiveMagma_90 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_118 :: T_SelectiveMagma_90 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_118 T_SelectiveMagma_90
v0
  = let v1 :: T_IsSelectiveMagma_158
v1 = T_SelectiveMagma_90 -> T_IsSelectiveMagma_158
d_isSelectiveMagma_110 (T_SelectiveMagma_90 -> T_SelectiveMagma_90
forall a b. a -> b
coe T_SelectiveMagma_90
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsMagma_86
v2 = T_IsSelectiveMagma_158 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_166 (T_IsSelectiveMagma_158 -> T_IsSelectiveMagma_158
forall a b. a -> b
coe T_IsSelectiveMagma_158
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_86 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_94 (T_IsMagma_86 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86
v2))))
-- Algebra.Bundles.SelectiveMagma._.refl
d_refl_120 :: T_SelectiveMagma_90 -> AgdaAny -> AgdaAny
d_refl_120 :: T_SelectiveMagma_90 -> AgdaAny -> AgdaAny
d_refl_120 T_SelectiveMagma_90
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_86 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_86 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_94
         ((T_IsSelectiveMagma_158 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSelectiveMagma_158 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_166
            ((T_SelectiveMagma_90 -> T_IsSelectiveMagma_158)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SelectiveMagma_90 -> T_IsSelectiveMagma_158
d_isSelectiveMagma_110 (T_SelectiveMagma_90 -> AgdaAny
forall a b. a -> b
coe T_SelectiveMagma_90
v0))))
-- Algebra.Bundles.SelectiveMagma._.reflexive
d_reflexive_122 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SelectiveMagma_90 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_122 :: ()
-> ()
-> T_SelectiveMagma_90
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_122 ~()
v0 ~()
v1 T_SelectiveMagma_90
v2 = T_SelectiveMagma_90
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_122 T_SelectiveMagma_90
v2
du_reflexive_122 ::
  T_SelectiveMagma_90 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_122 :: T_SelectiveMagma_90
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_122 T_SelectiveMagma_90
v0
  = let v1 :: T_IsSelectiveMagma_158
v1 = T_SelectiveMagma_90 -> T_IsSelectiveMagma_158
d_isSelectiveMagma_110 (T_SelectiveMagma_90 -> T_SelectiveMagma_90
forall a b. a -> b
coe T_SelectiveMagma_90
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsMagma_86
v2 = T_IsSelectiveMagma_158 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_166 (T_IsSelectiveMagma_158 -> T_IsSelectiveMagma_158
forall a b. a -> b
coe T_IsSelectiveMagma_158
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_86 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_94 (T_IsMagma_86 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86
v2))
              AgdaAny
v3))
-- Algebra.Bundles.SelectiveMagma._.sel
d_sel_124 ::
  T_SelectiveMagma_90 ->
  AgdaAny -> AgdaAny -> MAlonzo.Code.Data.Sum.Base.T__'8846'__30
d_sel_124 :: T_SelectiveMagma_90 -> AgdaAny -> AgdaAny -> T__'8846'__30
d_sel_124 T_SelectiveMagma_90
v0
  = (T_IsSelectiveMagma_158 -> AgdaAny -> AgdaAny -> T__'8846'__30)
-> AgdaAny -> AgdaAny -> AgdaAny -> T__'8846'__30
forall a b. a -> b
coe
      T_IsSelectiveMagma_158 -> AgdaAny -> AgdaAny -> T__'8846'__30
MAlonzo.Code.Algebra.Structures.d_sel_168
      ((T_SelectiveMagma_90 -> T_IsSelectiveMagma_158)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SelectiveMagma_90 -> T_IsSelectiveMagma_158
d_isSelectiveMagma_110 (T_SelectiveMagma_90 -> AgdaAny
forall a b. a -> b
coe T_SelectiveMagma_90
v0))
-- Algebra.Bundles.SelectiveMagma._.setoid
d_setoid_126 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SelectiveMagma_90 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_126 :: () -> () -> T_SelectiveMagma_90 -> T_Setoid_44
d_setoid_126 ~()
v0 ~()
v1 T_SelectiveMagma_90
v2 = T_SelectiveMagma_90 -> T_Setoid_44
du_setoid_126 T_SelectiveMagma_90
v2
du_setoid_126 ::
  T_SelectiveMagma_90 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_126 :: T_SelectiveMagma_90 -> T_Setoid_44
du_setoid_126 T_SelectiveMagma_90
v0
  = let v1 :: T_IsSelectiveMagma_158
v1 = T_SelectiveMagma_90 -> T_IsSelectiveMagma_158
d_isSelectiveMagma_110 (T_SelectiveMagma_90 -> T_SelectiveMagma_90
forall a b. a -> b
coe T_SelectiveMagma_90
v0) in
    AgdaAny -> T_Setoid_44
forall a b. a -> b
coe
      ((T_IsMagma_86 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_86 -> T_Setoid_44
MAlonzo.Code.Algebra.Structures.du_setoid_110
         ((T_IsSelectiveMagma_158 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSelectiveMagma_158 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_166 (T_IsSelectiveMagma_158 -> AgdaAny
forall a b. a -> b
coe T_IsSelectiveMagma_158
v1)))
-- Algebra.Bundles.SelectiveMagma._.sym
d_sym_128 ::
  T_SelectiveMagma_90 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_128 :: T_SelectiveMagma_90 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_128 T_SelectiveMagma_90
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_86 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_86 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_94
         ((T_IsSelectiveMagma_158 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSelectiveMagma_158 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_166
            ((T_SelectiveMagma_90 -> T_IsSelectiveMagma_158)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SelectiveMagma_90 -> T_IsSelectiveMagma_158
d_isSelectiveMagma_110 (T_SelectiveMagma_90 -> AgdaAny
forall a b. a -> b
coe T_SelectiveMagma_90
v0))))
-- Algebra.Bundles.SelectiveMagma._.trans
d_trans_130 ::
  T_SelectiveMagma_90 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_130 :: T_SelectiveMagma_90
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_130 T_SelectiveMagma_90
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_86 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_86 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_94
         ((T_IsSelectiveMagma_158 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSelectiveMagma_158 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_166
            ((T_SelectiveMagma_90 -> T_IsSelectiveMagma_158)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SelectiveMagma_90 -> T_IsSelectiveMagma_158
d_isSelectiveMagma_110 (T_SelectiveMagma_90 -> AgdaAny
forall a b. a -> b
coe T_SelectiveMagma_90
v0))))
-- Algebra.Bundles.SelectiveMagma._.∙-cong
d_'8729''45'cong_132 ::
  T_SelectiveMagma_90 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_132 :: T_SelectiveMagma_90
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_132 T_SelectiveMagma_90
v0
  = (T_IsMagma_86
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsMagma_86
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_96
      ((T_IsSelectiveMagma_158 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSelectiveMagma_158 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_166
         ((T_SelectiveMagma_90 -> T_IsSelectiveMagma_158)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SelectiveMagma_90 -> T_IsSelectiveMagma_158
d_isSelectiveMagma_110 (T_SelectiveMagma_90 -> AgdaAny
forall a b. a -> b
coe T_SelectiveMagma_90
v0)))
-- Algebra.Bundles.SelectiveMagma._.∙-congʳ
d_'8729''45'cong'691'_134 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SelectiveMagma_90 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_134 :: ()
-> ()
-> T_SelectiveMagma_90
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_134 ~()
v0 ~()
v1 T_SelectiveMagma_90
v2
  = T_SelectiveMagma_90
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_134 T_SelectiveMagma_90
v2
du_'8729''45'cong'691'_134 ::
  T_SelectiveMagma_90 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_134 :: T_SelectiveMagma_90
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_134 T_SelectiveMagma_90
v0
  = let v1 :: T_IsSelectiveMagma_158
v1 = T_SelectiveMagma_90 -> T_IsSelectiveMagma_158
d_isSelectiveMagma_110 (T_SelectiveMagma_90 -> T_SelectiveMagma_90
forall a b. a -> b
coe T_SelectiveMagma_90
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsMagma_86
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_86 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'691'_116
         ((T_IsSelectiveMagma_158 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSelectiveMagma_158 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_166 (T_IsSelectiveMagma_158 -> AgdaAny
forall a b. a -> b
coe T_IsSelectiveMagma_158
v1)))
-- Algebra.Bundles.SelectiveMagma._.∙-congˡ
d_'8729''45'cong'737'_136 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SelectiveMagma_90 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_136 :: ()
-> ()
-> T_SelectiveMagma_90
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_136 ~()
v0 ~()
v1 T_SelectiveMagma_90
v2
  = T_SelectiveMagma_90
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_136 T_SelectiveMagma_90
v2
du_'8729''45'cong'737'_136 ::
  T_SelectiveMagma_90 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_136 :: T_SelectiveMagma_90
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_136 T_SelectiveMagma_90
v0
  = let v1 :: T_IsSelectiveMagma_158
v1 = T_SelectiveMagma_90 -> T_IsSelectiveMagma_158
d_isSelectiveMagma_110 (T_SelectiveMagma_90 -> T_SelectiveMagma_90
forall a b. a -> b
coe T_SelectiveMagma_90
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsMagma_86
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_86 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'737'_112
         ((T_IsSelectiveMagma_158 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSelectiveMagma_158 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_166 (T_IsSelectiveMagma_158 -> AgdaAny
forall a b. a -> b
coe T_IsSelectiveMagma_158
v1)))
-- Algebra.Bundles.SelectiveMagma.magma
d_magma_138 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SelectiveMagma_90 -> T_Magma_36
d_magma_138 :: () -> () -> T_SelectiveMagma_90 -> T_Magma_36
d_magma_138 ~()
v0 ~()
v1 T_SelectiveMagma_90
v2 = T_SelectiveMagma_90 -> T_Magma_36
du_magma_138 T_SelectiveMagma_90
v2
du_magma_138 :: T_SelectiveMagma_90 -> T_Magma_36
du_magma_138 :: T_SelectiveMagma_90 -> T_Magma_36
du_magma_138 T_SelectiveMagma_90
v0
  = ((AgdaAny -> AgdaAny -> AgdaAny) -> T_IsMagma_86 -> T_Magma_36)
-> (AgdaAny -> AgdaAny -> AgdaAny) -> T_IsMagma_86 -> T_Magma_36
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny) -> T_IsMagma_86 -> T_Magma_36
C_Magma'46'constructor_581 (T_SelectiveMagma_90 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__108 (T_SelectiveMagma_90 -> T_SelectiveMagma_90
forall a b. a -> b
coe T_SelectiveMagma_90
v0))
      (T_IsSelectiveMagma_158 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_166
         ((T_SelectiveMagma_90 -> T_IsSelectiveMagma_158)
-> AgdaAny -> T_IsSelectiveMagma_158
forall a b. a -> b
coe T_SelectiveMagma_90 -> T_IsSelectiveMagma_158
d_isSelectiveMagma_110 (T_SelectiveMagma_90 -> AgdaAny
forall a b. a -> b
coe T_SelectiveMagma_90
v0)))
-- Algebra.Bundles.SelectiveMagma._.rawMagma
d_rawMagma_142 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SelectiveMagma_90 -> T_RawMagma_8
d_rawMagma_142 :: () -> () -> T_SelectiveMagma_90 -> T_RawMagma_8
d_rawMagma_142 ~()
v0 ~()
v1 T_SelectiveMagma_90
v2 = T_SelectiveMagma_90 -> T_RawMagma_8
du_rawMagma_142 T_SelectiveMagma_90
v2
du_rawMagma_142 :: T_SelectiveMagma_90 -> T_RawMagma_8
du_rawMagma_142 :: T_SelectiveMagma_90 -> T_RawMagma_8
du_rawMagma_142 T_SelectiveMagma_90
v0 = (T_Magma_36 -> T_RawMagma_8) -> AgdaAny -> T_RawMagma_8
forall a b. a -> b
coe T_Magma_36 -> T_RawMagma_8
du_rawMagma_80 ((T_SelectiveMagma_90 -> T_Magma_36) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SelectiveMagma_90 -> T_Magma_36
du_magma_138 (T_SelectiveMagma_90 -> AgdaAny
forall a b. a -> b
coe T_SelectiveMagma_90
v0))
-- Algebra.Bundles.CommutativeMagma
d_CommutativeMagma_148 :: p -> p -> ()
d_CommutativeMagma_148 p
a0 p
a1 = ()
data T_CommutativeMagma_148
  = C_CommutativeMagma'46'constructor_2623 (AgdaAny ->
                                            AgdaAny -> AgdaAny)
                                           MAlonzo.Code.Algebra.Structures.T_IsCommutativeMagma_122
-- Algebra.Bundles.CommutativeMagma.Carrier
d_Carrier_162 :: T_CommutativeMagma_148 -> ()
d_Carrier_162 :: T_CommutativeMagma_148 -> ()
d_Carrier_162 = T_CommutativeMagma_148 -> ()
forall a. a
erased
-- Algebra.Bundles.CommutativeMagma._≈_
d__'8776'__164 ::
  T_CommutativeMagma_148 -> AgdaAny -> AgdaAny -> ()
d__'8776'__164 :: T_CommutativeMagma_148 -> AgdaAny -> AgdaAny -> ()
d__'8776'__164 = T_CommutativeMagma_148 -> AgdaAny -> AgdaAny -> ()
forall a. a
erased
-- Algebra.Bundles.CommutativeMagma._∙_
d__'8729'__166 ::
  T_CommutativeMagma_148 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__166 :: T_CommutativeMagma_148 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__166 T_CommutativeMagma_148
v0
  = case T_CommutativeMagma_148 -> T_CommutativeMagma_148
forall a b. a -> b
coe T_CommutativeMagma_148
v0 of
      C_CommutativeMagma'46'constructor_2623 AgdaAny -> AgdaAny -> AgdaAny
v3 T_IsCommutativeMagma_122
v4 -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v3
      T_CommutativeMagma_148
_ -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.CommutativeMagma.isCommutativeMagma
d_isCommutativeMagma_168 ::
  T_CommutativeMagma_148 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMagma_122
d_isCommutativeMagma_168 :: T_CommutativeMagma_148 -> T_IsCommutativeMagma_122
d_isCommutativeMagma_168 T_CommutativeMagma_148
v0
  = case T_CommutativeMagma_148 -> T_CommutativeMagma_148
forall a b. a -> b
coe T_CommutativeMagma_148
v0 of
      C_CommutativeMagma'46'constructor_2623 AgdaAny -> AgdaAny -> AgdaAny
v3 T_IsCommutativeMagma_122
v4 -> T_IsCommutativeMagma_122 -> T_IsCommutativeMagma_122
forall a b. a -> b
coe T_IsCommutativeMagma_122
v4
      T_CommutativeMagma_148
_ -> T_IsCommutativeMagma_122
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.CommutativeMagma._.comm
d_comm_172 ::
  T_CommutativeMagma_148 -> AgdaAny -> AgdaAny -> AgdaAny
d_comm_172 :: T_CommutativeMagma_148 -> AgdaAny -> AgdaAny -> AgdaAny
d_comm_172 T_CommutativeMagma_148
v0
  = (T_IsCommutativeMagma_122 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsCommutativeMagma_122 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_comm_132
      ((T_CommutativeMagma_148 -> T_IsCommutativeMagma_122)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeMagma_148 -> T_IsCommutativeMagma_122
d_isCommutativeMagma_168 (T_CommutativeMagma_148 -> AgdaAny
forall a b. a -> b
coe T_CommutativeMagma_148
v0))
-- Algebra.Bundles.CommutativeMagma._.isEquivalence
d_isEquivalence_174 ::
  T_CommutativeMagma_148 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_174 :: T_CommutativeMagma_148 -> T_IsEquivalence_26
d_isEquivalence_174 T_CommutativeMagma_148
v0
  = (T_IsMagma_86 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      T_IsMagma_86 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_94
      ((T_IsCommutativeMagma_122 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCommutativeMagma_122 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_130
         ((T_CommutativeMagma_148 -> T_IsCommutativeMagma_122)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeMagma_148 -> T_IsCommutativeMagma_122
d_isCommutativeMagma_168 (T_CommutativeMagma_148 -> AgdaAny
forall a b. a -> b
coe T_CommutativeMagma_148
v0)))
-- Algebra.Bundles.CommutativeMagma._.isMagma
d_isMagma_176 ::
  T_CommutativeMagma_148 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_86
d_isMagma_176 :: T_CommutativeMagma_148 -> T_IsMagma_86
d_isMagma_176 T_CommutativeMagma_148
v0
  = (T_IsCommutativeMagma_122 -> T_IsMagma_86)
-> AgdaAny -> T_IsMagma_86
forall a b. a -> b
coe
      T_IsCommutativeMagma_122 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_130
      ((T_CommutativeMagma_148 -> T_IsCommutativeMagma_122)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeMagma_148 -> T_IsCommutativeMagma_122
d_isCommutativeMagma_168 (T_CommutativeMagma_148 -> AgdaAny
forall a b. a -> b
coe T_CommutativeMagma_148
v0))
-- Algebra.Bundles.CommutativeMagma._.isPartialEquivalence
d_isPartialEquivalence_178 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeMagma_148 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_178 :: () -> () -> T_CommutativeMagma_148 -> T_IsPartialEquivalence_16
d_isPartialEquivalence_178 ~()
v0 ~()
v1 T_CommutativeMagma_148
v2
  = T_CommutativeMagma_148 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_178 T_CommutativeMagma_148
v2
du_isPartialEquivalence_178 ::
  T_CommutativeMagma_148 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_178 :: T_CommutativeMagma_148 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_178 T_CommutativeMagma_148
v0
  = let v1 :: T_IsCommutativeMagma_122
v1 = T_CommutativeMagma_148 -> T_IsCommutativeMagma_122
d_isCommutativeMagma_168 (T_CommutativeMagma_148 -> T_CommutativeMagma_148
forall a b. a -> b
coe T_CommutativeMagma_148
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsMagma_86
v2 = T_IsCommutativeMagma_122 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_130 (T_IsCommutativeMagma_122 -> T_IsCommutativeMagma_122
forall a b. a -> b
coe T_IsCommutativeMagma_122
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_86 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_94 (T_IsMagma_86 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86
v2))))
-- Algebra.Bundles.CommutativeMagma._.refl
d_refl_180 :: T_CommutativeMagma_148 -> AgdaAny -> AgdaAny
d_refl_180 :: T_CommutativeMagma_148 -> AgdaAny -> AgdaAny
d_refl_180 T_CommutativeMagma_148
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_86 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_86 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_94
         ((T_IsCommutativeMagma_122 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCommutativeMagma_122 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_130
            ((T_CommutativeMagma_148 -> T_IsCommutativeMagma_122)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeMagma_148 -> T_IsCommutativeMagma_122
d_isCommutativeMagma_168 (T_CommutativeMagma_148 -> AgdaAny
forall a b. a -> b
coe T_CommutativeMagma_148
v0))))
-- Algebra.Bundles.CommutativeMagma._.reflexive
d_reflexive_182 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeMagma_148 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_182 :: ()
-> ()
-> T_CommutativeMagma_148
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_182 ~()
v0 ~()
v1 T_CommutativeMagma_148
v2 = T_CommutativeMagma_148
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_182 T_CommutativeMagma_148
v2
du_reflexive_182 ::
  T_CommutativeMagma_148 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_182 :: T_CommutativeMagma_148
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_182 T_CommutativeMagma_148
v0
  = let v1 :: T_IsCommutativeMagma_122
v1 = T_CommutativeMagma_148 -> T_IsCommutativeMagma_122
d_isCommutativeMagma_168 (T_CommutativeMagma_148 -> T_CommutativeMagma_148
forall a b. a -> b
coe T_CommutativeMagma_148
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsMagma_86
v2 = T_IsCommutativeMagma_122 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_130 (T_IsCommutativeMagma_122 -> T_IsCommutativeMagma_122
forall a b. a -> b
coe T_IsCommutativeMagma_122
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_86 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_94 (T_IsMagma_86 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86
v2))
              AgdaAny
v3))
-- Algebra.Bundles.CommutativeMagma._.setoid
d_setoid_184 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeMagma_148 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_184 :: () -> () -> T_CommutativeMagma_148 -> T_Setoid_44
d_setoid_184 ~()
v0 ~()
v1 T_CommutativeMagma_148
v2 = T_CommutativeMagma_148 -> T_Setoid_44
du_setoid_184 T_CommutativeMagma_148
v2
du_setoid_184 ::
  T_CommutativeMagma_148 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_184 :: T_CommutativeMagma_148 -> T_Setoid_44
du_setoid_184 T_CommutativeMagma_148
v0
  = let v1 :: T_IsCommutativeMagma_122
v1 = T_CommutativeMagma_148 -> T_IsCommutativeMagma_122
d_isCommutativeMagma_168 (T_CommutativeMagma_148 -> T_CommutativeMagma_148
forall a b. a -> b
coe T_CommutativeMagma_148
v0) in
    AgdaAny -> T_Setoid_44
forall a b. a -> b
coe
      ((T_IsMagma_86 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_86 -> T_Setoid_44
MAlonzo.Code.Algebra.Structures.du_setoid_110
         ((T_IsCommutativeMagma_122 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMagma_122 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_130 (T_IsCommutativeMagma_122 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMagma_122
v1)))
-- Algebra.Bundles.CommutativeMagma._.sym
d_sym_186 ::
  T_CommutativeMagma_148 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_186 :: T_CommutativeMagma_148 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_186 T_CommutativeMagma_148
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_86 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_86 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_94
         ((T_IsCommutativeMagma_122 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCommutativeMagma_122 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_130
            ((T_CommutativeMagma_148 -> T_IsCommutativeMagma_122)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeMagma_148 -> T_IsCommutativeMagma_122
d_isCommutativeMagma_168 (T_CommutativeMagma_148 -> AgdaAny
forall a b. a -> b
coe T_CommutativeMagma_148
v0))))
-- Algebra.Bundles.CommutativeMagma._.trans
d_trans_188 ::
  T_CommutativeMagma_148 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_188 :: T_CommutativeMagma_148
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_188 T_CommutativeMagma_148
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_86 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_86 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_94
         ((T_IsCommutativeMagma_122 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCommutativeMagma_122 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_130
            ((T_CommutativeMagma_148 -> T_IsCommutativeMagma_122)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeMagma_148 -> T_IsCommutativeMagma_122
d_isCommutativeMagma_168 (T_CommutativeMagma_148 -> AgdaAny
forall a b. a -> b
coe T_CommutativeMagma_148
v0))))
-- Algebra.Bundles.CommutativeMagma._.∙-cong
d_'8729''45'cong_190 ::
  T_CommutativeMagma_148 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_190 :: T_CommutativeMagma_148
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_190 T_CommutativeMagma_148
v0
  = (T_IsMagma_86
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsMagma_86
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_96
      ((T_IsCommutativeMagma_122 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCommutativeMagma_122 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_130
         ((T_CommutativeMagma_148 -> T_IsCommutativeMagma_122)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeMagma_148 -> T_IsCommutativeMagma_122
d_isCommutativeMagma_168 (T_CommutativeMagma_148 -> AgdaAny
forall a b. a -> b
coe T_CommutativeMagma_148
v0)))
-- Algebra.Bundles.CommutativeMagma._.∙-congʳ
d_'8729''45'cong'691'_192 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeMagma_148 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_192 :: ()
-> ()
-> T_CommutativeMagma_148
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_192 ~()
v0 ~()
v1 T_CommutativeMagma_148
v2
  = T_CommutativeMagma_148
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_192 T_CommutativeMagma_148
v2
du_'8729''45'cong'691'_192 ::
  T_CommutativeMagma_148 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_192 :: T_CommutativeMagma_148
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_192 T_CommutativeMagma_148
v0
  = let v1 :: T_IsCommutativeMagma_122
v1 = T_CommutativeMagma_148 -> T_IsCommutativeMagma_122
d_isCommutativeMagma_168 (T_CommutativeMagma_148 -> T_CommutativeMagma_148
forall a b. a -> b
coe T_CommutativeMagma_148
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsMagma_86
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_86 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'691'_116
         ((T_IsCommutativeMagma_122 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMagma_122 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_130 (T_IsCommutativeMagma_122 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMagma_122
v1)))
-- Algebra.Bundles.CommutativeMagma._.∙-congˡ
d_'8729''45'cong'737'_194 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeMagma_148 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_194 :: ()
-> ()
-> T_CommutativeMagma_148
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_194 ~()
v0 ~()
v1 T_CommutativeMagma_148
v2
  = T_CommutativeMagma_148
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_194 T_CommutativeMagma_148
v2
du_'8729''45'cong'737'_194 ::
  T_CommutativeMagma_148 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_194 :: T_CommutativeMagma_148
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_194 T_CommutativeMagma_148
v0
  = let v1 :: T_IsCommutativeMagma_122
v1 = T_CommutativeMagma_148 -> T_IsCommutativeMagma_122
d_isCommutativeMagma_168 (T_CommutativeMagma_148 -> T_CommutativeMagma_148
forall a b. a -> b
coe T_CommutativeMagma_148
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsMagma_86
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_86 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'737'_112
         ((T_IsCommutativeMagma_122 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMagma_122 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_130 (T_IsCommutativeMagma_122 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMagma_122
v1)))
-- Algebra.Bundles.CommutativeMagma.magma
d_magma_196 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeMagma_148 -> T_Magma_36
d_magma_196 :: () -> () -> T_CommutativeMagma_148 -> T_Magma_36
d_magma_196 ~()
v0 ~()
v1 T_CommutativeMagma_148
v2 = T_CommutativeMagma_148 -> T_Magma_36
du_magma_196 T_CommutativeMagma_148
v2
du_magma_196 :: T_CommutativeMagma_148 -> T_Magma_36
du_magma_196 :: T_CommutativeMagma_148 -> T_Magma_36
du_magma_196 T_CommutativeMagma_148
v0
  = ((AgdaAny -> AgdaAny -> AgdaAny) -> T_IsMagma_86 -> T_Magma_36)
-> (AgdaAny -> AgdaAny -> AgdaAny) -> T_IsMagma_86 -> T_Magma_36
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny) -> T_IsMagma_86 -> T_Magma_36
C_Magma'46'constructor_581 (T_CommutativeMagma_148 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__166 (T_CommutativeMagma_148 -> T_CommutativeMagma_148
forall a b. a -> b
coe T_CommutativeMagma_148
v0))
      (T_IsCommutativeMagma_122 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_130
         ((T_CommutativeMagma_148 -> T_IsCommutativeMagma_122)
-> AgdaAny -> T_IsCommutativeMagma_122
forall a b. a -> b
coe T_CommutativeMagma_148 -> T_IsCommutativeMagma_122
d_isCommutativeMagma_168 (T_CommutativeMagma_148 -> AgdaAny
forall a b. a -> b
coe T_CommutativeMagma_148
v0)))
-- Algebra.Bundles.CommutativeMagma._.rawMagma
d_rawMagma_200 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeMagma_148 -> T_RawMagma_8
d_rawMagma_200 :: () -> () -> T_CommutativeMagma_148 -> T_RawMagma_8
d_rawMagma_200 ~()
v0 ~()
v1 T_CommutativeMagma_148
v2 = T_CommutativeMagma_148 -> T_RawMagma_8
du_rawMagma_200 T_CommutativeMagma_148
v2
du_rawMagma_200 :: T_CommutativeMagma_148 -> T_RawMagma_8
du_rawMagma_200 :: T_CommutativeMagma_148 -> T_RawMagma_8
du_rawMagma_200 T_CommutativeMagma_148
v0 = (T_Magma_36 -> T_RawMagma_8) -> AgdaAny -> T_RawMagma_8
forall a b. a -> b
coe T_Magma_36 -> T_RawMagma_8
du_rawMagma_80 ((T_CommutativeMagma_148 -> T_Magma_36) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeMagma_148 -> T_Magma_36
du_magma_196 (T_CommutativeMagma_148 -> AgdaAny
forall a b. a -> b
coe T_CommutativeMagma_148
v0))
-- Algebra.Bundles.Semigroup
d_Semigroup_206 :: p -> p -> ()
d_Semigroup_206 p
a0 p
a1 = ()
data T_Semigroup_206
  = C_Semigroup'46'constructor_3669 (AgdaAny -> AgdaAny -> AgdaAny)
                                    MAlonzo.Code.Algebra.Structures.T_IsSemigroup_194
-- Algebra.Bundles.Semigroup.Carrier
d_Carrier_220 :: T_Semigroup_206 -> ()
d_Carrier_220 :: T_Semigroup_206 -> ()
d_Carrier_220 = T_Semigroup_206 -> ()
forall a. a
erased
-- Algebra.Bundles.Semigroup._≈_
d__'8776'__222 :: T_Semigroup_206 -> AgdaAny -> AgdaAny -> ()
d__'8776'__222 :: T_Semigroup_206 -> AgdaAny -> AgdaAny -> ()
d__'8776'__222 = T_Semigroup_206 -> AgdaAny -> AgdaAny -> ()
forall a. a
erased
-- Algebra.Bundles.Semigroup._∙_
d__'8729'__224 :: T_Semigroup_206 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__224 :: T_Semigroup_206 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__224 T_Semigroup_206
v0
  = case T_Semigroup_206 -> T_Semigroup_206
forall a b. a -> b
coe T_Semigroup_206
v0 of
      C_Semigroup'46'constructor_3669 AgdaAny -> AgdaAny -> AgdaAny
v3 T_IsSemigroup_194
v4 -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v3
      T_Semigroup_206
_ -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.Semigroup.isSemigroup
d_isSemigroup_226 ::
  T_Semigroup_206 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_194
d_isSemigroup_226 :: T_Semigroup_206 -> T_IsSemigroup_194
d_isSemigroup_226 T_Semigroup_206
v0
  = case T_Semigroup_206 -> T_Semigroup_206
forall a b. a -> b
coe T_Semigroup_206
v0 of
      C_Semigroup'46'constructor_3669 AgdaAny -> AgdaAny -> AgdaAny
v3 T_IsSemigroup_194
v4 -> T_IsSemigroup_194 -> T_IsSemigroup_194
forall a b. a -> b
coe T_IsSemigroup_194
v4
      T_Semigroup_206
_ -> T_IsSemigroup_194
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.Semigroup._.assoc
d_assoc_230 ::
  T_Semigroup_206 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_230 :: T_Semigroup_206 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_230 T_Semigroup_206
v0
  = (T_IsSemigroup_194 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsSemigroup_194 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_assoc_204
      ((T_Semigroup_206 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semigroup_206 -> T_IsSemigroup_194
d_isSemigroup_226 (T_Semigroup_206 -> AgdaAny
forall a b. a -> b
coe T_Semigroup_206
v0))
-- Algebra.Bundles.Semigroup._.isEquivalence
d_isEquivalence_232 ::
  T_Semigroup_206 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_232 :: T_Semigroup_206 -> T_IsEquivalence_26
d_isEquivalence_232 T_Semigroup_206
v0
  = (T_IsMagma_86 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      T_IsMagma_86 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_94
      ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202
         ((T_Semigroup_206 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semigroup_206 -> T_IsSemigroup_194
d_isSemigroup_226 (T_Semigroup_206 -> AgdaAny
forall a b. a -> b
coe T_Semigroup_206
v0)))
-- Algebra.Bundles.Semigroup._.isMagma
d_isMagma_234 ::
  T_Semigroup_206 -> MAlonzo.Code.Algebra.Structures.T_IsMagma_86
d_isMagma_234 :: T_Semigroup_206 -> T_IsMagma_86
d_isMagma_234 T_Semigroup_206
v0
  = (T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> T_IsMagma_86
forall a b. a -> b
coe
      T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202
      ((T_Semigroup_206 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semigroup_206 -> T_IsSemigroup_194
d_isSemigroup_226 (T_Semigroup_206 -> AgdaAny
forall a b. a -> b
coe T_Semigroup_206
v0))
-- Algebra.Bundles.Semigroup._.isPartialEquivalence
d_isPartialEquivalence_236 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Semigroup_206 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_236 :: () -> () -> T_Semigroup_206 -> T_IsPartialEquivalence_16
d_isPartialEquivalence_236 ~()
v0 ~()
v1 T_Semigroup_206
v2
  = T_Semigroup_206 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_236 T_Semigroup_206
v2
du_isPartialEquivalence_236 ::
  T_Semigroup_206 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_236 :: T_Semigroup_206 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_236 T_Semigroup_206
v0
  = let v1 :: T_IsSemigroup_194
v1 = T_Semigroup_206 -> T_IsSemigroup_194
d_isSemigroup_226 (T_Semigroup_206 -> T_Semigroup_206
forall a b. a -> b
coe T_Semigroup_206
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsMagma_86
v2 = T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202 (T_IsSemigroup_194 -> T_IsSemigroup_194
forall a b. a -> b
coe T_IsSemigroup_194
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_86 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_94 (T_IsMagma_86 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86
v2))))
-- Algebra.Bundles.Semigroup._.refl
d_refl_238 :: T_Semigroup_206 -> AgdaAny -> AgdaAny
d_refl_238 :: T_Semigroup_206 -> AgdaAny -> AgdaAny
d_refl_238 T_Semigroup_206
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_86 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_86 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_94
         ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202
            ((T_Semigroup_206 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semigroup_206 -> T_IsSemigroup_194
d_isSemigroup_226 (T_Semigroup_206 -> AgdaAny
forall a b. a -> b
coe T_Semigroup_206
v0))))
-- Algebra.Bundles.Semigroup._.reflexive
d_reflexive_240 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Semigroup_206 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_240 :: ()
-> ()
-> T_Semigroup_206
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_240 ~()
v0 ~()
v1 T_Semigroup_206
v2 = T_Semigroup_206 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_240 T_Semigroup_206
v2
du_reflexive_240 ::
  T_Semigroup_206 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_240 :: T_Semigroup_206 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_240 T_Semigroup_206
v0
  = let v1 :: T_IsSemigroup_194
v1 = T_Semigroup_206 -> T_IsSemigroup_194
d_isSemigroup_226 (T_Semigroup_206 -> T_Semigroup_206
forall a b. a -> b
coe T_Semigroup_206
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsMagma_86
v2 = T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202 (T_IsSemigroup_194 -> T_IsSemigroup_194
forall a b. a -> b
coe T_IsSemigroup_194
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_86 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_94 (T_IsMagma_86 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86
v2))
              AgdaAny
v3))
-- Algebra.Bundles.Semigroup._.setoid
d_setoid_242 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Semigroup_206 -> MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_242 :: () -> () -> T_Semigroup_206 -> T_Setoid_44
d_setoid_242 ~()
v0 ~()
v1 T_Semigroup_206
v2 = T_Semigroup_206 -> T_Setoid_44
du_setoid_242 T_Semigroup_206
v2
du_setoid_242 ::
  T_Semigroup_206 -> MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_242 :: T_Semigroup_206 -> T_Setoid_44
du_setoid_242 T_Semigroup_206
v0
  = let v1 :: T_IsSemigroup_194
v1 = T_Semigroup_206 -> T_IsSemigroup_194
d_isSemigroup_226 (T_Semigroup_206 -> T_Semigroup_206
forall a b. a -> b
coe T_Semigroup_206
v0) in
    AgdaAny -> T_Setoid_44
forall a b. a -> b
coe
      ((T_IsMagma_86 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_86 -> T_Setoid_44
MAlonzo.Code.Algebra.Structures.du_setoid_110
         ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202 (T_IsSemigroup_194 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194
v1)))
-- Algebra.Bundles.Semigroup._.sym
d_sym_244 ::
  T_Semigroup_206 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_244 :: T_Semigroup_206 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_244 T_Semigroup_206
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_86 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_86 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_94
         ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202
            ((T_Semigroup_206 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semigroup_206 -> T_IsSemigroup_194
d_isSemigroup_226 (T_Semigroup_206 -> AgdaAny
forall a b. a -> b
coe T_Semigroup_206
v0))))
-- Algebra.Bundles.Semigroup._.trans
d_trans_246 ::
  T_Semigroup_206 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_246 :: T_Semigroup_206
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_246 T_Semigroup_206
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_86 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_86 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_94
         ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202
            ((T_Semigroup_206 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semigroup_206 -> T_IsSemigroup_194
d_isSemigroup_226 (T_Semigroup_206 -> AgdaAny
forall a b. a -> b
coe T_Semigroup_206
v0))))
-- Algebra.Bundles.Semigroup._.∙-cong
d_'8729''45'cong_248 ::
  T_Semigroup_206 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_248 :: T_Semigroup_206
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_248 T_Semigroup_206
v0
  = (T_IsMagma_86
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsMagma_86
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_96
      ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202
         ((T_Semigroup_206 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semigroup_206 -> T_IsSemigroup_194
d_isSemigroup_226 (T_Semigroup_206 -> AgdaAny
forall a b. a -> b
coe T_Semigroup_206
v0)))
-- Algebra.Bundles.Semigroup._.∙-congʳ
d_'8729''45'cong'691'_250 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Semigroup_206 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_250 :: ()
-> ()
-> T_Semigroup_206
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_250 ~()
v0 ~()
v1 T_Semigroup_206
v2
  = T_Semigroup_206
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_250 T_Semigroup_206
v2
du_'8729''45'cong'691'_250 ::
  T_Semigroup_206 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_250 :: T_Semigroup_206
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_250 T_Semigroup_206
v0
  = let v1 :: T_IsSemigroup_194
v1 = T_Semigroup_206 -> T_IsSemigroup_194
d_isSemigroup_226 (T_Semigroup_206 -> T_Semigroup_206
forall a b. a -> b
coe T_Semigroup_206
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsMagma_86
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_86 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'691'_116
         ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202 (T_IsSemigroup_194 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194
v1)))
-- Algebra.Bundles.Semigroup._.∙-congˡ
d_'8729''45'cong'737'_252 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Semigroup_206 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_252 :: ()
-> ()
-> T_Semigroup_206
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_252 ~()
v0 ~()
v1 T_Semigroup_206
v2
  = T_Semigroup_206
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_252 T_Semigroup_206
v2
du_'8729''45'cong'737'_252 ::
  T_Semigroup_206 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_252 :: T_Semigroup_206
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_252 T_Semigroup_206
v0
  = let v1 :: T_IsSemigroup_194
v1 = T_Semigroup_206 -> T_IsSemigroup_194
d_isSemigroup_226 (T_Semigroup_206 -> T_Semigroup_206
forall a b. a -> b
coe T_Semigroup_206
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsMagma_86
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_86 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'737'_112
         ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202 (T_IsSemigroup_194 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194
v1)))
-- Algebra.Bundles.Semigroup.magma
d_magma_254 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Semigroup_206 -> T_Magma_36
d_magma_254 :: () -> () -> T_Semigroup_206 -> T_Magma_36
d_magma_254 ~()
v0 ~()
v1 T_Semigroup_206
v2 = T_Semigroup_206 -> T_Magma_36
du_magma_254 T_Semigroup_206
v2
du_magma_254 :: T_Semigroup_206 -> T_Magma_36
du_magma_254 :: T_Semigroup_206 -> T_Magma_36
du_magma_254 T_Semigroup_206
v0
  = ((AgdaAny -> AgdaAny -> AgdaAny) -> T_IsMagma_86 -> T_Magma_36)
-> (AgdaAny -> AgdaAny -> AgdaAny) -> T_IsMagma_86 -> T_Magma_36
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny) -> T_IsMagma_86 -> T_Magma_36
C_Magma'46'constructor_581 (T_Semigroup_206 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__224 (T_Semigroup_206 -> T_Semigroup_206
forall a b. a -> b
coe T_Semigroup_206
v0))
      (T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202
         ((T_Semigroup_206 -> T_IsSemigroup_194)
-> AgdaAny -> T_IsSemigroup_194
forall a b. a -> b
coe T_Semigroup_206 -> T_IsSemigroup_194
d_isSemigroup_226 (T_Semigroup_206 -> AgdaAny
forall a b. a -> b
coe T_Semigroup_206
v0)))
-- Algebra.Bundles.Semigroup._._≉_
d__'8777'__258 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Semigroup_206 -> AgdaAny -> AgdaAny -> ()
d__'8777'__258 :: () -> () -> T_Semigroup_206 -> AgdaAny -> AgdaAny -> ()
d__'8777'__258 = () -> () -> T_Semigroup_206 -> AgdaAny -> AgdaAny -> ()
forall a. a
erased
-- Algebra.Bundles.Semigroup._.rawMagma
d_rawMagma_260 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Semigroup_206 -> T_RawMagma_8
d_rawMagma_260 :: () -> () -> T_Semigroup_206 -> T_RawMagma_8
d_rawMagma_260 ~()
v0 ~()
v1 T_Semigroup_206
v2 = T_Semigroup_206 -> T_RawMagma_8
du_rawMagma_260 T_Semigroup_206
v2
du_rawMagma_260 :: T_Semigroup_206 -> T_RawMagma_8
du_rawMagma_260 :: T_Semigroup_206 -> T_RawMagma_8
du_rawMagma_260 T_Semigroup_206
v0 = (T_Magma_36 -> T_RawMagma_8) -> AgdaAny -> T_RawMagma_8
forall a b. a -> b
coe T_Magma_36 -> T_RawMagma_8
du_rawMagma_80 ((T_Semigroup_206 -> T_Magma_36) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semigroup_206 -> T_Magma_36
du_magma_254 (T_Semigroup_206 -> AgdaAny
forall a b. a -> b
coe T_Semigroup_206
v0))
-- Algebra.Bundles.Band
d_Band_266 :: p -> p -> ()
d_Band_266 p
a0 p
a1 = ()
data T_Band_266
  = C_Band'46'constructor_4745 (AgdaAny -> AgdaAny -> AgdaAny)
                               MAlonzo.Code.Algebra.Structures.T_IsBand_230
-- Algebra.Bundles.Band.Carrier
d_Carrier_280 :: T_Band_266 -> ()
d_Carrier_280 :: T_Band_266 -> ()
d_Carrier_280 = T_Band_266 -> ()
forall a. a
erased
-- Algebra.Bundles.Band._≈_
d__'8776'__282 :: T_Band_266 -> AgdaAny -> AgdaAny -> ()
d__'8776'__282 :: T_Band_266 -> AgdaAny -> AgdaAny -> ()
d__'8776'__282 = T_Band_266 -> AgdaAny -> AgdaAny -> ()
forall a. a
erased
-- Algebra.Bundles.Band._∙_
d__'8729'__284 :: T_Band_266 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__284 :: T_Band_266 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__284 T_Band_266
v0
  = case T_Band_266 -> T_Band_266
forall a b. a -> b
coe T_Band_266
v0 of
      C_Band'46'constructor_4745 AgdaAny -> AgdaAny -> AgdaAny
v3 T_IsBand_230
v4 -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v3
      T_Band_266
_ -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.Band.isBand
d_isBand_286 ::
  T_Band_266 -> MAlonzo.Code.Algebra.Structures.T_IsBand_230
d_isBand_286 :: T_Band_266 -> T_IsBand_230
d_isBand_286 T_Band_266
v0
  = case T_Band_266 -> T_Band_266
forall a b. a -> b
coe T_Band_266
v0 of
      C_Band'46'constructor_4745 AgdaAny -> AgdaAny -> AgdaAny
v3 T_IsBand_230
v4 -> T_IsBand_230 -> T_IsBand_230
forall a b. a -> b
coe T_IsBand_230
v4
      T_Band_266
_ -> T_IsBand_230
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.Band._.assoc
d_assoc_290 ::
  T_Band_266 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_290 :: T_Band_266 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_290 T_Band_266
v0
  = (T_IsSemigroup_194 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsSemigroup_194 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_assoc_204
      ((T_IsBand_230 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsBand_230 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_238
         ((T_Band_266 -> T_IsBand_230) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Band_266 -> T_IsBand_230
d_isBand_286 (T_Band_266 -> AgdaAny
forall a b. a -> b
coe T_Band_266
v0)))
-- Algebra.Bundles.Band._.idem
d_idem_292 :: T_Band_266 -> AgdaAny -> AgdaAny
d_idem_292 :: T_Band_266 -> AgdaAny -> AgdaAny
d_idem_292 T_Band_266
v0
  = (T_IsBand_230 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsBand_230 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_idem_240
      ((T_Band_266 -> T_IsBand_230) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Band_266 -> T_IsBand_230
d_isBand_286 (T_Band_266 -> AgdaAny
forall a b. a -> b
coe T_Band_266
v0))
-- Algebra.Bundles.Band._.isEquivalence
d_isEquivalence_294 ::
  T_Band_266 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_294 :: T_Band_266 -> T_IsEquivalence_26
d_isEquivalence_294 T_Band_266
v0
  = (T_IsMagma_86 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      T_IsMagma_86 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_94
      ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202
         ((T_IsBand_230 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsBand_230 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_238
            ((T_Band_266 -> T_IsBand_230) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Band_266 -> T_IsBand_230
d_isBand_286 (T_Band_266 -> AgdaAny
forall a b. a -> b
coe T_Band_266
v0))))
-- Algebra.Bundles.Band._.isMagma
d_isMagma_296 ::
  T_Band_266 -> MAlonzo.Code.Algebra.Structures.T_IsMagma_86
d_isMagma_296 :: T_Band_266 -> T_IsMagma_86
d_isMagma_296 T_Band_266
v0
  = (T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> T_IsMagma_86
forall a b. a -> b
coe
      T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202
      ((T_IsBand_230 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsBand_230 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_238
         ((T_Band_266 -> T_IsBand_230) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Band_266 -> T_IsBand_230
d_isBand_286 (T_Band_266 -> AgdaAny
forall a b. a -> b
coe T_Band_266
v0)))
-- Algebra.Bundles.Band._.isPartialEquivalence
d_isPartialEquivalence_298 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Band_266 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_298 :: () -> () -> T_Band_266 -> T_IsPartialEquivalence_16
d_isPartialEquivalence_298 ~()
v0 ~()
v1 T_Band_266
v2
  = T_Band_266 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_298 T_Band_266
v2
du_isPartialEquivalence_298 ::
  T_Band_266 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_298 :: T_Band_266 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_298 T_Band_266
v0
  = let v1 :: T_IsBand_230
v1 = T_Band_266 -> T_IsBand_230
d_isBand_286 (T_Band_266 -> T_Band_266
forall a b. a -> b
coe T_Band_266
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsSemigroup_194
v2
             = T_IsBand_230 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_238 (T_IsBand_230 -> T_IsBand_230
forall a b. a -> b
coe T_IsBand_230
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsMagma_86
v3 = T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202 (T_IsSemigroup_194 -> T_IsSemigroup_194
forall a b. a -> b
coe T_IsSemigroup_194
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_86 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsMagma_86 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_94 (T_IsMagma_86 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86
v3)))))
-- Algebra.Bundles.Band._.isSemigroup
d_isSemigroup_300 ::
  T_Band_266 -> MAlonzo.Code.Algebra.Structures.T_IsSemigroup_194
d_isSemigroup_300 :: T_Band_266 -> T_IsSemigroup_194
d_isSemigroup_300 T_Band_266
v0
  = (T_IsBand_230 -> T_IsSemigroup_194) -> AgdaAny -> T_IsSemigroup_194
forall a b. a -> b
coe
      T_IsBand_230 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_238
      ((T_Band_266 -> T_IsBand_230) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Band_266 -> T_IsBand_230
d_isBand_286 (T_Band_266 -> AgdaAny
forall a b. a -> b
coe T_Band_266
v0))
-- Algebra.Bundles.Band._.refl
d_refl_302 :: T_Band_266 -> AgdaAny -> AgdaAny
d_refl_302 :: T_Band_266 -> AgdaAny -> AgdaAny
d_refl_302 T_Band_266
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_86 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_86 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_94
         ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202
            ((T_IsBand_230 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsBand_230 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_238
               ((T_Band_266 -> T_IsBand_230) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Band_266 -> T_IsBand_230
d_isBand_286 (T_Band_266 -> AgdaAny
forall a b. a -> b
coe T_Band_266
v0)))))
-- Algebra.Bundles.Band._.reflexive
d_reflexive_304 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Band_266 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_304 :: ()
-> ()
-> T_Band_266
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_304 ~()
v0 ~()
v1 T_Band_266
v2 = T_Band_266 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_304 T_Band_266
v2
du_reflexive_304 ::
  T_Band_266 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_304 :: T_Band_266 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_304 T_Band_266
v0
  = let v1 :: T_IsBand_230
v1 = T_Band_266 -> T_IsBand_230
d_isBand_286 (T_Band_266 -> T_Band_266
forall a b. a -> b
coe T_Band_266
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemigroup_194
v2
             = T_IsBand_230 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_238 (T_IsBand_230 -> T_IsBand_230
forall a b. a -> b
coe T_IsBand_230
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsMagma_86
v3 = T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202 (T_IsSemigroup_194 -> T_IsSemigroup_194
forall a b. a -> b
coe T_IsSemigroup_194
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_86 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_94 (T_IsMagma_86 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86
v3))
                 AgdaAny
v4)))
-- Algebra.Bundles.Band._.setoid
d_setoid_306 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Band_266 -> MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_306 :: () -> () -> T_Band_266 -> T_Setoid_44
d_setoid_306 ~()
v0 ~()
v1 T_Band_266
v2 = T_Band_266 -> T_Setoid_44
du_setoid_306 T_Band_266
v2
du_setoid_306 ::
  T_Band_266 -> MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_306 :: T_Band_266 -> T_Setoid_44
du_setoid_306 T_Band_266
v0
  = let v1 :: T_IsBand_230
v1 = T_Band_266 -> T_IsBand_230
d_isBand_286 (T_Band_266 -> T_Band_266
forall a b. a -> b
coe T_Band_266
v0) in
    AgdaAny -> T_Setoid_44
forall a b. a -> b
coe
      (let v2 :: T_IsSemigroup_194
v2
             = T_IsBand_230 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_238 (T_IsBand_230 -> T_IsBand_230
forall a b. a -> b
coe T_IsBand_230
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsMagma_86 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMagma_86 -> T_Setoid_44
MAlonzo.Code.Algebra.Structures.du_setoid_110
            ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202 (T_IsSemigroup_194 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194
v2))))
-- Algebra.Bundles.Band._.sym
d_sym_308 :: T_Band_266 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_308 :: T_Band_266 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_308 T_Band_266
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_86 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_86 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_94
         ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202
            ((T_IsBand_230 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsBand_230 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_238
               ((T_Band_266 -> T_IsBand_230) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Band_266 -> T_IsBand_230
d_isBand_286 (T_Band_266 -> AgdaAny
forall a b. a -> b
coe T_Band_266
v0)))))
-- Algebra.Bundles.Band._.trans
d_trans_310 ::
  T_Band_266 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_310 :: T_Band_266
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_310 T_Band_266
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_86 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_86 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_94
         ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202
            ((T_IsBand_230 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsBand_230 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_238
               ((T_Band_266 -> T_IsBand_230) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Band_266 -> T_IsBand_230
d_isBand_286 (T_Band_266 -> AgdaAny
forall a b. a -> b
coe T_Band_266
v0)))))
-- Algebra.Bundles.Band._.∙-cong
d_'8729''45'cong_312 ::
  T_Band_266 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_312 :: T_Band_266
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_312 T_Band_266
v0
  = (T_IsMagma_86
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsMagma_86
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_96
      ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202
         ((T_IsBand_230 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsBand_230 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_238
            ((T_Band_266 -> T_IsBand_230) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Band_266 -> T_IsBand_230
d_isBand_286 (T_Band_266 -> AgdaAny
forall a b. a -> b
coe T_Band_266
v0))))
-- Algebra.Bundles.Band._.∙-congʳ
d_'8729''45'cong'691'_314 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Band_266 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_314 :: ()
-> ()
-> T_Band_266
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_314 ~()
v0 ~()
v1 T_Band_266
v2
  = T_Band_266 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_314 T_Band_266
v2
du_'8729''45'cong'691'_314 ::
  T_Band_266 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_314 :: T_Band_266 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_314 T_Band_266
v0
  = let v1 :: T_IsBand_230
v1 = T_Band_266 -> T_IsBand_230
d_isBand_286 (T_Band_266 -> T_Band_266
forall a b. a -> b
coe T_Band_266
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemigroup_194
v2
             = T_IsBand_230 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_238 (T_IsBand_230 -> T_IsBand_230
forall a b. a -> b
coe T_IsBand_230
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsMagma_86
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMagma_86 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'691'_116
            ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202 (T_IsSemigroup_194 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194
v2))))
-- Algebra.Bundles.Band._.∙-congˡ
d_'8729''45'cong'737'_316 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Band_266 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_316 :: ()
-> ()
-> T_Band_266
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_316 ~()
v0 ~()
v1 T_Band_266
v2
  = T_Band_266 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_316 T_Band_266
v2
du_'8729''45'cong'737'_316 ::
  T_Band_266 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_316 :: T_Band_266 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_316 T_Band_266
v0
  = let v1 :: T_IsBand_230
v1 = T_Band_266 -> T_IsBand_230
d_isBand_286 (T_Band_266 -> T_Band_266
forall a b. a -> b
coe T_Band_266
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemigroup_194
v2
             = T_IsBand_230 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_238 (T_IsBand_230 -> T_IsBand_230
forall a b. a -> b
coe T_IsBand_230
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsMagma_86
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMagma_86 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'737'_112
            ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202 (T_IsSemigroup_194 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194
v2))))
-- Algebra.Bundles.Band.semigroup
d_semigroup_318 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Band_266 -> T_Semigroup_206
d_semigroup_318 :: () -> () -> T_Band_266 -> T_Semigroup_206
d_semigroup_318 ~()
v0 ~()
v1 T_Band_266
v2 = T_Band_266 -> T_Semigroup_206
du_semigroup_318 T_Band_266
v2
du_semigroup_318 :: T_Band_266 -> T_Semigroup_206
du_semigroup_318 :: T_Band_266 -> T_Semigroup_206
du_semigroup_318 T_Band_266
v0
  = ((AgdaAny -> AgdaAny -> AgdaAny)
 -> T_IsSemigroup_194 -> T_Semigroup_206)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsSemigroup_194
-> T_Semigroup_206
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsSemigroup_194 -> T_Semigroup_206
C_Semigroup'46'constructor_3669 (T_Band_266 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__284 (T_Band_266 -> T_Band_266
forall a b. a -> b
coe T_Band_266
v0))
      (T_IsBand_230 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_238
         ((T_Band_266 -> T_IsBand_230) -> AgdaAny -> T_IsBand_230
forall a b. a -> b
coe T_Band_266 -> T_IsBand_230
d_isBand_286 (T_Band_266 -> AgdaAny
forall a b. a -> b
coe T_Band_266
v0)))
-- Algebra.Bundles.Band._._≉_
d__'8777'__322 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Band_266 -> AgdaAny -> AgdaAny -> ()
d__'8777'__322 :: () -> () -> T_Band_266 -> AgdaAny -> AgdaAny -> ()
d__'8777'__322 = () -> () -> T_Band_266 -> AgdaAny -> AgdaAny -> ()
forall a. a
erased
-- Algebra.Bundles.Band._.magma
d_magma_324 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 -> T_Band_266 -> T_Magma_36
d_magma_324 :: () -> () -> T_Band_266 -> T_Magma_36
d_magma_324 ~()
v0 ~()
v1 T_Band_266
v2 = T_Band_266 -> T_Magma_36
du_magma_324 T_Band_266
v2
du_magma_324 :: T_Band_266 -> T_Magma_36
du_magma_324 :: T_Band_266 -> T_Magma_36
du_magma_324 T_Band_266
v0 = (T_Semigroup_206 -> T_Magma_36) -> AgdaAny -> T_Magma_36
forall a b. a -> b
coe T_Semigroup_206 -> T_Magma_36
du_magma_254 ((T_Band_266 -> T_Semigroup_206) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Band_266 -> T_Semigroup_206
du_semigroup_318 (T_Band_266 -> AgdaAny
forall a b. a -> b
coe T_Band_266
v0))
-- Algebra.Bundles.Band._.rawMagma
d_rawMagma_326 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Band_266 -> T_RawMagma_8
d_rawMagma_326 :: () -> () -> T_Band_266 -> T_RawMagma_8
d_rawMagma_326 ~()
v0 ~()
v1 T_Band_266
v2 = T_Band_266 -> T_RawMagma_8
du_rawMagma_326 T_Band_266
v2
du_rawMagma_326 :: T_Band_266 -> T_RawMagma_8
du_rawMagma_326 :: T_Band_266 -> T_RawMagma_8
du_rawMagma_326 T_Band_266
v0
  = let v1 :: t
v1 = (T_Band_266 -> T_Semigroup_206) -> AgdaAny -> t
forall a b. a -> b
coe T_Band_266 -> T_Semigroup_206
du_semigroup_318 (T_Band_266 -> AgdaAny
forall a b. a -> b
coe T_Band_266
v0) in
    AgdaAny -> T_RawMagma_8
forall a b. a -> b
coe ((T_Magma_36 -> T_RawMagma_8) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Magma_36 -> T_RawMagma_8
du_rawMagma_80 ((T_Semigroup_206 -> T_Magma_36) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semigroup_206 -> T_Magma_36
du_magma_254 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1)))
-- Algebra.Bundles.CommutativeSemigroup
d_CommutativeSemigroup_332 :: p -> p -> ()
d_CommutativeSemigroup_332 p
a0 p
a1 = ()
data T_CommutativeSemigroup_332
  = C_CommutativeSemigroup'46'constructor_5887 (AgdaAny ->
                                                AgdaAny -> AgdaAny)
                                               MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_270
-- Algebra.Bundles.CommutativeSemigroup.Carrier
d_Carrier_346 :: T_CommutativeSemigroup_332 -> ()
d_Carrier_346 :: T_CommutativeSemigroup_332 -> ()
d_Carrier_346 = T_CommutativeSemigroup_332 -> ()
forall a. a
erased
-- Algebra.Bundles.CommutativeSemigroup._≈_
d__'8776'__348 ::
  T_CommutativeSemigroup_332 -> AgdaAny -> AgdaAny -> ()
d__'8776'__348 :: T_CommutativeSemigroup_332 -> AgdaAny -> AgdaAny -> ()
d__'8776'__348 = T_CommutativeSemigroup_332 -> AgdaAny -> AgdaAny -> ()
forall a. a
erased
-- Algebra.Bundles.CommutativeSemigroup._∙_
d__'8729'__350 ::
  T_CommutativeSemigroup_332 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__350 :: T_CommutativeSemigroup_332 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__350 T_CommutativeSemigroup_332
v0
  = case T_CommutativeSemigroup_332 -> T_CommutativeSemigroup_332
forall a b. a -> b
coe T_CommutativeSemigroup_332
v0 of
      C_CommutativeSemigroup'46'constructor_5887 AgdaAny -> AgdaAny -> AgdaAny
v3 T_IsCommutativeSemigroup_270
v4 -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v3
      T_CommutativeSemigroup_332
_ -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.CommutativeSemigroup.isCommutativeSemigroup
d_isCommutativeSemigroup_352 ::
  T_CommutativeSemigroup_332 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_270
d_isCommutativeSemigroup_352 :: T_CommutativeSemigroup_332 -> T_IsCommutativeSemigroup_270
d_isCommutativeSemigroup_352 T_CommutativeSemigroup_332
v0
  = case T_CommutativeSemigroup_332 -> T_CommutativeSemigroup_332
forall a b. a -> b
coe T_CommutativeSemigroup_332
v0 of
      C_CommutativeSemigroup'46'constructor_5887 AgdaAny -> AgdaAny -> AgdaAny
v3 T_IsCommutativeSemigroup_270
v4 -> T_IsCommutativeSemigroup_270 -> T_IsCommutativeSemigroup_270
forall a b. a -> b
coe T_IsCommutativeSemigroup_270
v4
      T_CommutativeSemigroup_332
_ -> T_IsCommutativeSemigroup_270
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.CommutativeSemigroup._.assoc
d_assoc_356 ::
  T_CommutativeSemigroup_332 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_356 :: T_CommutativeSemigroup_332
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_356 T_CommutativeSemigroup_332
v0
  = (T_IsSemigroup_194 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsSemigroup_194 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_assoc_204
      ((T_IsCommutativeSemigroup_270 -> T_IsSemigroup_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCommutativeSemigroup_270 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_278
         ((T_CommutativeSemigroup_332 -> T_IsCommutativeSemigroup_270)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemigroup_332 -> T_IsCommutativeSemigroup_270
d_isCommutativeSemigroup_352 (T_CommutativeSemigroup_332 -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemigroup_332
v0)))
-- Algebra.Bundles.CommutativeSemigroup._.comm
d_comm_358 ::
  T_CommutativeSemigroup_332 -> AgdaAny -> AgdaAny -> AgdaAny
d_comm_358 :: T_CommutativeSemigroup_332 -> AgdaAny -> AgdaAny -> AgdaAny
d_comm_358 T_CommutativeSemigroup_332
v0
  = (T_IsCommutativeSemigroup_270 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsCommutativeSemigroup_270 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_comm_280
      ((T_CommutativeSemigroup_332 -> T_IsCommutativeSemigroup_270)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemigroup_332 -> T_IsCommutativeSemigroup_270
d_isCommutativeSemigroup_352 (T_CommutativeSemigroup_332 -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemigroup_332
v0))
-- Algebra.Bundles.CommutativeSemigroup._.isCommutativeMagma
d_isCommutativeMagma_360 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeSemigroup_332 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMagma_122
d_isCommutativeMagma_360 :: () -> () -> T_CommutativeSemigroup_332 -> T_IsCommutativeMagma_122
d_isCommutativeMagma_360 ~()
v0 ~()
v1 T_CommutativeSemigroup_332
v2 = T_CommutativeSemigroup_332 -> T_IsCommutativeMagma_122
du_isCommutativeMagma_360 T_CommutativeSemigroup_332
v2
du_isCommutativeMagma_360 ::
  T_CommutativeSemigroup_332 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMagma_122
du_isCommutativeMagma_360 :: T_CommutativeSemigroup_332 -> T_IsCommutativeMagma_122
du_isCommutativeMagma_360 T_CommutativeSemigroup_332
v0
  = (T_IsCommutativeSemigroup_270 -> T_IsCommutativeMagma_122)
-> AgdaAny -> T_IsCommutativeMagma_122
forall a b. a -> b
coe
      T_IsCommutativeSemigroup_270 -> T_IsCommutativeMagma_122
MAlonzo.Code.Algebra.Structures.du_isCommutativeMagma_308
      ((T_CommutativeSemigroup_332 -> T_IsCommutativeSemigroup_270)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemigroup_332 -> T_IsCommutativeSemigroup_270
d_isCommutativeSemigroup_352 (T_CommutativeSemigroup_332 -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemigroup_332
v0))
-- Algebra.Bundles.CommutativeSemigroup._.isEquivalence
d_isEquivalence_362 ::
  T_CommutativeSemigroup_332 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_362 :: T_CommutativeSemigroup_332 -> T_IsEquivalence_26
d_isEquivalence_362 T_CommutativeSemigroup_332
v0
  = (T_IsMagma_86 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      T_IsMagma_86 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_94
      ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202
         ((T_IsCommutativeSemigroup_270 -> T_IsSemigroup_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCommutativeSemigroup_270 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_278
            ((T_CommutativeSemigroup_332 -> T_IsCommutativeSemigroup_270)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemigroup_332 -> T_IsCommutativeSemigroup_270
d_isCommutativeSemigroup_352 (T_CommutativeSemigroup_332 -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemigroup_332
v0))))
-- Algebra.Bundles.CommutativeSemigroup._.isMagma
d_isMagma_364 ::
  T_CommutativeSemigroup_332 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_86
d_isMagma_364 :: T_CommutativeSemigroup_332 -> T_IsMagma_86
d_isMagma_364 T_CommutativeSemigroup_332
v0
  = (T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> T_IsMagma_86
forall a b. a -> b
coe
      T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202
      ((T_IsCommutativeSemigroup_270 -> T_IsSemigroup_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCommutativeSemigroup_270 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_278
         ((T_CommutativeSemigroup_332 -> T_IsCommutativeSemigroup_270)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemigroup_332 -> T_IsCommutativeSemigroup_270
d_isCommutativeSemigroup_352 (T_CommutativeSemigroup_332 -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemigroup_332
v0)))
-- Algebra.Bundles.CommutativeSemigroup._.isPartialEquivalence
d_isPartialEquivalence_366 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeSemigroup_332 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_366 :: () -> () -> T_CommutativeSemigroup_332 -> T_IsPartialEquivalence_16
d_isPartialEquivalence_366 ~()
v0 ~()
v1 T_CommutativeSemigroup_332
v2
  = T_CommutativeSemigroup_332 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_366 T_CommutativeSemigroup_332
v2
du_isPartialEquivalence_366 ::
  T_CommutativeSemigroup_332 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_366 :: T_CommutativeSemigroup_332 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_366 T_CommutativeSemigroup_332
v0
  = let v1 :: T_IsCommutativeSemigroup_270
v1 = T_CommutativeSemigroup_332 -> T_IsCommutativeSemigroup_270
d_isCommutativeSemigroup_352 (T_CommutativeSemigroup_332 -> T_CommutativeSemigroup_332
forall a b. a -> b
coe T_CommutativeSemigroup_332
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsSemigroup_194
v2
             = T_IsCommutativeSemigroup_270 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_278 (T_IsCommutativeSemigroup_270 -> T_IsCommutativeSemigroup_270
forall a b. a -> b
coe T_IsCommutativeSemigroup_270
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsMagma_86
v3 = T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202 (T_IsSemigroup_194 -> T_IsSemigroup_194
forall a b. a -> b
coe T_IsSemigroup_194
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_86 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsMagma_86 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_94 (T_IsMagma_86 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86
v3)))))
-- Algebra.Bundles.CommutativeSemigroup._.isSemigroup
d_isSemigroup_368 ::
  T_CommutativeSemigroup_332 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_194
d_isSemigroup_368 :: T_CommutativeSemigroup_332 -> T_IsSemigroup_194
d_isSemigroup_368 T_CommutativeSemigroup_332
v0
  = (T_IsCommutativeSemigroup_270 -> T_IsSemigroup_194)
-> AgdaAny -> T_IsSemigroup_194
forall a b. a -> b
coe
      T_IsCommutativeSemigroup_270 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_278
      ((T_CommutativeSemigroup_332 -> T_IsCommutativeSemigroup_270)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemigroup_332 -> T_IsCommutativeSemigroup_270
d_isCommutativeSemigroup_352 (T_CommutativeSemigroup_332 -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemigroup_332
v0))
-- Algebra.Bundles.CommutativeSemigroup._.refl
d_refl_370 :: T_CommutativeSemigroup_332 -> AgdaAny -> AgdaAny
d_refl_370 :: T_CommutativeSemigroup_332 -> AgdaAny -> AgdaAny
d_refl_370 T_CommutativeSemigroup_332
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_86 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_86 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_94
         ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202
            ((T_IsCommutativeSemigroup_270 -> T_IsSemigroup_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsCommutativeSemigroup_270 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_278
               ((T_CommutativeSemigroup_332 -> T_IsCommutativeSemigroup_270)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemigroup_332 -> T_IsCommutativeSemigroup_270
d_isCommutativeSemigroup_352 (T_CommutativeSemigroup_332 -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemigroup_332
v0)))))
-- Algebra.Bundles.CommutativeSemigroup._.reflexive
d_reflexive_372 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeSemigroup_332 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_372 :: ()
-> ()
-> T_CommutativeSemigroup_332
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_372 ~()
v0 ~()
v1 T_CommutativeSemigroup_332
v2 = T_CommutativeSemigroup_332
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_372 T_CommutativeSemigroup_332
v2
du_reflexive_372 ::
  T_CommutativeSemigroup_332 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_372 :: T_CommutativeSemigroup_332
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_372 T_CommutativeSemigroup_332
v0
  = let v1 :: T_IsCommutativeSemigroup_270
v1 = T_CommutativeSemigroup_332 -> T_IsCommutativeSemigroup_270
d_isCommutativeSemigroup_352 (T_CommutativeSemigroup_332 -> T_CommutativeSemigroup_332
forall a b. a -> b
coe T_CommutativeSemigroup_332
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemigroup_194
v2
             = T_IsCommutativeSemigroup_270 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_278 (T_IsCommutativeSemigroup_270 -> T_IsCommutativeSemigroup_270
forall a b. a -> b
coe T_IsCommutativeSemigroup_270
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsMagma_86
v3 = T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202 (T_IsSemigroup_194 -> T_IsSemigroup_194
forall a b. a -> b
coe T_IsSemigroup_194
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_86 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_94 (T_IsMagma_86 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86
v3))
                 AgdaAny
v4)))
-- Algebra.Bundles.CommutativeSemigroup._.setoid
d_setoid_374 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeSemigroup_332 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_374 :: () -> () -> T_CommutativeSemigroup_332 -> T_Setoid_44
d_setoid_374 ~()
v0 ~()
v1 T_CommutativeSemigroup_332
v2 = T_CommutativeSemigroup_332 -> T_Setoid_44
du_setoid_374 T_CommutativeSemigroup_332
v2
du_setoid_374 ::
  T_CommutativeSemigroup_332 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_374 :: T_CommutativeSemigroup_332 -> T_Setoid_44
du_setoid_374 T_CommutativeSemigroup_332
v0
  = let v1 :: T_IsCommutativeSemigroup_270
v1 = T_CommutativeSemigroup_332 -> T_IsCommutativeSemigroup_270
d_isCommutativeSemigroup_352 (T_CommutativeSemigroup_332 -> T_CommutativeSemigroup_332
forall a b. a -> b
coe T_CommutativeSemigroup_332
v0) in
    AgdaAny -> T_Setoid_44
forall a b. a -> b
coe
      (let v2 :: T_IsSemigroup_194
v2
             = T_IsCommutativeSemigroup_270 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_278 (T_IsCommutativeSemigroup_270 -> T_IsCommutativeSemigroup_270
forall a b. a -> b
coe T_IsCommutativeSemigroup_270
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsMagma_86 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMagma_86 -> T_Setoid_44
MAlonzo.Code.Algebra.Structures.du_setoid_110
            ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202 (T_IsSemigroup_194 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194
v2))))
-- Algebra.Bundles.CommutativeSemigroup._.sym
d_sym_376 ::
  T_CommutativeSemigroup_332 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_376 :: T_CommutativeSemigroup_332
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_376 T_CommutativeSemigroup_332
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_86 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_86 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_94
         ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202
            ((T_IsCommutativeSemigroup_270 -> T_IsSemigroup_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsCommutativeSemigroup_270 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_278
               ((T_CommutativeSemigroup_332 -> T_IsCommutativeSemigroup_270)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemigroup_332 -> T_IsCommutativeSemigroup_270
d_isCommutativeSemigroup_352 (T_CommutativeSemigroup_332 -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemigroup_332
v0)))))
-- Algebra.Bundles.CommutativeSemigroup._.trans
d_trans_378 ::
  T_CommutativeSemigroup_332 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_378 :: T_CommutativeSemigroup_332
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_378 T_CommutativeSemigroup_332
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_86 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_86 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_94
         ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202
            ((T_IsCommutativeSemigroup_270 -> T_IsSemigroup_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsCommutativeSemigroup_270 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_278
               ((T_CommutativeSemigroup_332 -> T_IsCommutativeSemigroup_270)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemigroup_332 -> T_IsCommutativeSemigroup_270
d_isCommutativeSemigroup_352 (T_CommutativeSemigroup_332 -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemigroup_332
v0)))))
-- Algebra.Bundles.CommutativeSemigroup._.∙-cong
d_'8729''45'cong_380 ::
  T_CommutativeSemigroup_332 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_380 :: T_CommutativeSemigroup_332
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_380 T_CommutativeSemigroup_332
v0
  = (T_IsMagma_86
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsMagma_86
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_96
      ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202
         ((T_IsCommutativeSemigroup_270 -> T_IsSemigroup_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCommutativeSemigroup_270 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_278
            ((T_CommutativeSemigroup_332 -> T_IsCommutativeSemigroup_270)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemigroup_332 -> T_IsCommutativeSemigroup_270
d_isCommutativeSemigroup_352 (T_CommutativeSemigroup_332 -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemigroup_332
v0))))
-- Algebra.Bundles.CommutativeSemigroup._.∙-congʳ
d_'8729''45'cong'691'_382 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeSemigroup_332 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_382 :: ()
-> ()
-> T_CommutativeSemigroup_332
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_382 ~()
v0 ~()
v1 T_CommutativeSemigroup_332
v2
  = T_CommutativeSemigroup_332
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_382 T_CommutativeSemigroup_332
v2
du_'8729''45'cong'691'_382 ::
  T_CommutativeSemigroup_332 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_382 :: T_CommutativeSemigroup_332
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_382 T_CommutativeSemigroup_332
v0
  = let v1 :: T_IsCommutativeSemigroup_270
v1 = T_CommutativeSemigroup_332 -> T_IsCommutativeSemigroup_270
d_isCommutativeSemigroup_352 (T_CommutativeSemigroup_332 -> T_CommutativeSemigroup_332
forall a b. a -> b
coe T_CommutativeSemigroup_332
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemigroup_194
v2
             = T_IsCommutativeSemigroup_270 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_278 (T_IsCommutativeSemigroup_270 -> T_IsCommutativeSemigroup_270
forall a b. a -> b
coe T_IsCommutativeSemigroup_270
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsMagma_86
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMagma_86 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'691'_116
            ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202 (T_IsSemigroup_194 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194
v2))))
-- Algebra.Bundles.CommutativeSemigroup._.∙-congˡ
d_'8729''45'cong'737'_384 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeSemigroup_332 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_384 :: ()
-> ()
-> T_CommutativeSemigroup_332
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_384 ~()
v0 ~()
v1 T_CommutativeSemigroup_332
v2
  = T_CommutativeSemigroup_332
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_384 T_CommutativeSemigroup_332
v2
du_'8729''45'cong'737'_384 ::
  T_CommutativeSemigroup_332 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_384 :: T_CommutativeSemigroup_332
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_384 T_CommutativeSemigroup_332
v0
  = let v1 :: T_IsCommutativeSemigroup_270
v1 = T_CommutativeSemigroup_332 -> T_IsCommutativeSemigroup_270
d_isCommutativeSemigroup_352 (T_CommutativeSemigroup_332 -> T_CommutativeSemigroup_332
forall a b. a -> b
coe T_CommutativeSemigroup_332
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemigroup_194
v2
             = T_IsCommutativeSemigroup_270 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_278 (T_IsCommutativeSemigroup_270 -> T_IsCommutativeSemigroup_270
forall a b. a -> b
coe T_IsCommutativeSemigroup_270
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsMagma_86
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMagma_86 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'737'_112
            ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202 (T_IsSemigroup_194 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194
v2))))
-- Algebra.Bundles.CommutativeSemigroup.semigroup
d_semigroup_386 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeSemigroup_332 -> T_Semigroup_206
d_semigroup_386 :: () -> () -> T_CommutativeSemigroup_332 -> T_Semigroup_206
d_semigroup_386 ~()
v0 ~()
v1 T_CommutativeSemigroup_332
v2 = T_CommutativeSemigroup_332 -> T_Semigroup_206
du_semigroup_386 T_CommutativeSemigroup_332
v2
du_semigroup_386 :: T_CommutativeSemigroup_332 -> T_Semigroup_206
du_semigroup_386 :: T_CommutativeSemigroup_332 -> T_Semigroup_206
du_semigroup_386 T_CommutativeSemigroup_332
v0
  = ((AgdaAny -> AgdaAny -> AgdaAny)
 -> T_IsSemigroup_194 -> T_Semigroup_206)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsSemigroup_194
-> T_Semigroup_206
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsSemigroup_194 -> T_Semigroup_206
C_Semigroup'46'constructor_3669 (T_CommutativeSemigroup_332 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__350 (T_CommutativeSemigroup_332 -> T_CommutativeSemigroup_332
forall a b. a -> b
coe T_CommutativeSemigroup_332
v0))
      (T_IsCommutativeSemigroup_270 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_278
         ((T_CommutativeSemigroup_332 -> T_IsCommutativeSemigroup_270)
-> AgdaAny -> T_IsCommutativeSemigroup_270
forall a b. a -> b
coe T_CommutativeSemigroup_332 -> T_IsCommutativeSemigroup_270
d_isCommutativeSemigroup_352 (T_CommutativeSemigroup_332 -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemigroup_332
v0)))
-- Algebra.Bundles.CommutativeSemigroup._._≉_
d__'8777'__390 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeSemigroup_332 -> AgdaAny -> AgdaAny -> ()
d__'8777'__390 :: () -> () -> T_CommutativeSemigroup_332 -> AgdaAny -> AgdaAny -> ()
d__'8777'__390 = () -> () -> T_CommutativeSemigroup_332 -> AgdaAny -> AgdaAny -> ()
forall a. a
erased
-- Algebra.Bundles.CommutativeSemigroup._.magma
d_magma_392 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeSemigroup_332 -> T_Magma_36
d_magma_392 :: () -> () -> T_CommutativeSemigroup_332 -> T_Magma_36
d_magma_392 ~()
v0 ~()
v1 T_CommutativeSemigroup_332
v2 = T_CommutativeSemigroup_332 -> T_Magma_36
du_magma_392 T_CommutativeSemigroup_332
v2
du_magma_392 :: T_CommutativeSemigroup_332 -> T_Magma_36
du_magma_392 :: T_CommutativeSemigroup_332 -> T_Magma_36
du_magma_392 T_CommutativeSemigroup_332
v0 = (T_Semigroup_206 -> T_Magma_36) -> AgdaAny -> T_Magma_36
forall a b. a -> b
coe T_Semigroup_206 -> T_Magma_36
du_magma_254 ((T_CommutativeSemigroup_332 -> T_Semigroup_206)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemigroup_332 -> T_Semigroup_206
du_semigroup_386 (T_CommutativeSemigroup_332 -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemigroup_332
v0))
-- Algebra.Bundles.CommutativeSemigroup._.rawMagma
d_rawMagma_394 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeSemigroup_332 -> T_RawMagma_8
d_rawMagma_394 :: () -> () -> T_CommutativeSemigroup_332 -> T_RawMagma_8
d_rawMagma_394 ~()
v0 ~()
v1 T_CommutativeSemigroup_332
v2 = T_CommutativeSemigroup_332 -> T_RawMagma_8
du_rawMagma_394 T_CommutativeSemigroup_332
v2
du_rawMagma_394 :: T_CommutativeSemigroup_332 -> T_RawMagma_8
du_rawMagma_394 :: T_CommutativeSemigroup_332 -> T_RawMagma_8
du_rawMagma_394 T_CommutativeSemigroup_332
v0
  = let v1 :: t
v1 = (T_CommutativeSemigroup_332 -> T_Semigroup_206) -> AgdaAny -> t
forall a b. a -> b
coe T_CommutativeSemigroup_332 -> T_Semigroup_206
du_semigroup_386 (T_CommutativeSemigroup_332 -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemigroup_332
v0) in
    AgdaAny -> T_RawMagma_8
forall a b. a -> b
coe ((T_Magma_36 -> T_RawMagma_8) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Magma_36 -> T_RawMagma_8
du_rawMagma_80 ((T_Semigroup_206 -> T_Magma_36) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semigroup_206 -> T_Magma_36
du_magma_254 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1)))
-- Algebra.Bundles.CommutativeSemigroup.commutativeMagma
d_commutativeMagma_396 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeSemigroup_332 -> T_CommutativeMagma_148
d_commutativeMagma_396 :: () -> () -> T_CommutativeSemigroup_332 -> T_CommutativeMagma_148
d_commutativeMagma_396 ~()
v0 ~()
v1 T_CommutativeSemigroup_332
v2 = T_CommutativeSemigroup_332 -> T_CommutativeMagma_148
du_commutativeMagma_396 T_CommutativeSemigroup_332
v2
du_commutativeMagma_396 ::
  T_CommutativeSemigroup_332 -> T_CommutativeMagma_148
du_commutativeMagma_396 :: T_CommutativeSemigroup_332 -> T_CommutativeMagma_148
du_commutativeMagma_396 T_CommutativeSemigroup_332
v0
  = ((AgdaAny -> AgdaAny -> AgdaAny)
 -> T_IsCommutativeMagma_122 -> T_CommutativeMagma_148)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_CommutativeMagma_148
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsCommutativeMagma_122 -> T_CommutativeMagma_148
C_CommutativeMagma'46'constructor_2623 (T_CommutativeSemigroup_332 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__350 (T_CommutativeSemigroup_332 -> T_CommutativeSemigroup_332
forall a b. a -> b
coe T_CommutativeSemigroup_332
v0))
      ((T_IsCommutativeSemigroup_270 -> T_IsCommutativeMagma_122)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCommutativeSemigroup_270 -> T_IsCommutativeMagma_122
MAlonzo.Code.Algebra.Structures.du_isCommutativeMagma_308
         ((T_CommutativeSemigroup_332 -> T_IsCommutativeSemigroup_270)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemigroup_332 -> T_IsCommutativeSemigroup_270
d_isCommutativeSemigroup_352 (T_CommutativeSemigroup_332 -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemigroup_332
v0)))
-- Algebra.Bundles.Semilattice
d_Semilattice_402 :: p -> p -> ()
d_Semilattice_402 p
a0 p
a1 = ()
data T_Semilattice_402
  = C_Semilattice'46'constructor_7205 (AgdaAny -> AgdaAny -> AgdaAny)
                                      MAlonzo.Code.Algebra.Structures.T_IsSemilattice_312
-- Algebra.Bundles.Semilattice.Carrier
d_Carrier_416 :: T_Semilattice_402 -> ()
d_Carrier_416 :: T_Semilattice_402 -> ()
d_Carrier_416 = T_Semilattice_402 -> ()
forall a. a
erased
-- Algebra.Bundles.Semilattice._≈_
d__'8776'__418 :: T_Semilattice_402 -> AgdaAny -> AgdaAny -> ()
d__'8776'__418 :: T_Semilattice_402 -> AgdaAny -> AgdaAny -> ()
d__'8776'__418 = T_Semilattice_402 -> AgdaAny -> AgdaAny -> ()
forall a. a
erased
-- Algebra.Bundles.Semilattice._∧_
d__'8743'__420 ::
  T_Semilattice_402 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8743'__420 :: T_Semilattice_402 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8743'__420 T_Semilattice_402
v0
  = case T_Semilattice_402 -> T_Semilattice_402
forall a b. a -> b
coe T_Semilattice_402
v0 of
      C_Semilattice'46'constructor_7205 AgdaAny -> AgdaAny -> AgdaAny
v3 T_IsSemilattice_312
v4 -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v3
      T_Semilattice_402
_ -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.Semilattice.isSemilattice
d_isSemilattice_422 ::
  T_Semilattice_402 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemilattice_312
d_isSemilattice_422 :: T_Semilattice_402 -> T_IsSemilattice_312
d_isSemilattice_422 T_Semilattice_402
v0
  = case T_Semilattice_402 -> T_Semilattice_402
forall a b. a -> b
coe T_Semilattice_402
v0 of
      C_Semilattice'46'constructor_7205 AgdaAny -> AgdaAny -> AgdaAny
v3 T_IsSemilattice_312
v4 -> T_IsSemilattice_312 -> T_IsSemilattice_312
forall a b. a -> b
coe T_IsSemilattice_312
v4
      T_Semilattice_402
_ -> T_IsSemilattice_312
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.Semilattice._.assoc
d_assoc_426 ::
  T_Semilattice_402 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_426 :: T_Semilattice_402 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_426 T_Semilattice_402
v0
  = (T_IsSemigroup_194 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsSemigroup_194 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_assoc_204
      ((T_IsBand_230 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsBand_230 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_238
         ((T_IsSemilattice_312 -> T_IsBand_230) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemilattice_312 -> T_IsBand_230
MAlonzo.Code.Algebra.Structures.d_isBand_320
            ((T_Semilattice_402 -> T_IsSemilattice_312) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semilattice_402 -> T_IsSemilattice_312
d_isSemilattice_422 (T_Semilattice_402 -> AgdaAny
forall a b. a -> b
coe T_Semilattice_402
v0))))
-- Algebra.Bundles.Semilattice._.comm
d_comm_428 :: T_Semilattice_402 -> AgdaAny -> AgdaAny -> AgdaAny
d_comm_428 :: T_Semilattice_402 -> AgdaAny -> AgdaAny -> AgdaAny
d_comm_428 T_Semilattice_402
v0
  = (T_IsSemilattice_312 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsSemilattice_312 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_comm_322
      ((T_Semilattice_402 -> T_IsSemilattice_312) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semilattice_402 -> T_IsSemilattice_312
d_isSemilattice_422 (T_Semilattice_402 -> AgdaAny
forall a b. a -> b
coe T_Semilattice_402
v0))
-- Algebra.Bundles.Semilattice._.idem
d_idem_430 :: T_Semilattice_402 -> AgdaAny -> AgdaAny
d_idem_430 :: T_Semilattice_402 -> AgdaAny -> AgdaAny
d_idem_430 T_Semilattice_402
v0
  = (T_IsBand_230 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsBand_230 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_idem_240
      ((T_IsSemilattice_312 -> T_IsBand_230) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemilattice_312 -> T_IsBand_230
MAlonzo.Code.Algebra.Structures.d_isBand_320
         ((T_Semilattice_402 -> T_IsSemilattice_312) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semilattice_402 -> T_IsSemilattice_312
d_isSemilattice_422 (T_Semilattice_402 -> AgdaAny
forall a b. a -> b
coe T_Semilattice_402
v0)))
-- Algebra.Bundles.Semilattice._.isBand
d_isBand_432 ::
  T_Semilattice_402 -> MAlonzo.Code.Algebra.Structures.T_IsBand_230
d_isBand_432 :: T_Semilattice_402 -> T_IsBand_230
d_isBand_432 T_Semilattice_402
v0
  = (T_IsSemilattice_312 -> T_IsBand_230) -> AgdaAny -> T_IsBand_230
forall a b. a -> b
coe
      T_IsSemilattice_312 -> T_IsBand_230
MAlonzo.Code.Algebra.Structures.d_isBand_320
      ((T_Semilattice_402 -> T_IsSemilattice_312) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semilattice_402 -> T_IsSemilattice_312
d_isSemilattice_422 (T_Semilattice_402 -> AgdaAny
forall a b. a -> b
coe T_Semilattice_402
v0))
-- Algebra.Bundles.Semilattice._.isEquivalence
d_isEquivalence_434 ::
  T_Semilattice_402 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_434 :: T_Semilattice_402 -> T_IsEquivalence_26
d_isEquivalence_434 T_Semilattice_402
v0
  = (T_IsMagma_86 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      T_IsMagma_86 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_94
      ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202
         ((T_IsBand_230 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsBand_230 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_238
            ((T_IsSemilattice_312 -> T_IsBand_230) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemilattice_312 -> T_IsBand_230
MAlonzo.Code.Algebra.Structures.d_isBand_320
               ((T_Semilattice_402 -> T_IsSemilattice_312) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semilattice_402 -> T_IsSemilattice_312
d_isSemilattice_422 (T_Semilattice_402 -> AgdaAny
forall a b. a -> b
coe T_Semilattice_402
v0)))))
-- Algebra.Bundles.Semilattice._.isMagma
d_isMagma_436 ::
  T_Semilattice_402 -> MAlonzo.Code.Algebra.Structures.T_IsMagma_86
d_isMagma_436 :: T_Semilattice_402 -> T_IsMagma_86
d_isMagma_436 T_Semilattice_402
v0
  = (T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> T_IsMagma_86
forall a b. a -> b
coe
      T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202
      ((T_IsBand_230 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsBand_230 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_238
         ((T_IsSemilattice_312 -> T_IsBand_230) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemilattice_312 -> T_IsBand_230
MAlonzo.Code.Algebra.Structures.d_isBand_320
            ((T_Semilattice_402 -> T_IsSemilattice_312) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semilattice_402 -> T_IsSemilattice_312
d_isSemilattice_422 (T_Semilattice_402 -> AgdaAny
forall a b. a -> b
coe T_Semilattice_402
v0))))
-- Algebra.Bundles.Semilattice._.isPartialEquivalence
d_isPartialEquivalence_438 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Semilattice_402 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_438 :: () -> () -> T_Semilattice_402 -> T_IsPartialEquivalence_16
d_isPartialEquivalence_438 ~()
v0 ~()
v1 T_Semilattice_402
v2
  = T_Semilattice_402 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_438 T_Semilattice_402
v2
du_isPartialEquivalence_438 ::
  T_Semilattice_402 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_438 :: T_Semilattice_402 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_438 T_Semilattice_402
v0
  = let v1 :: T_IsSemilattice_312
v1 = T_Semilattice_402 -> T_IsSemilattice_312
d_isSemilattice_422 (T_Semilattice_402 -> T_Semilattice_402
forall a b. a -> b
coe T_Semilattice_402
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsBand_230
v2 = T_IsSemilattice_312 -> T_IsBand_230
MAlonzo.Code.Algebra.Structures.d_isBand_320 (T_IsSemilattice_312 -> T_IsSemilattice_312
forall a b. a -> b
coe T_IsSemilattice_312
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_194
v3
                = T_IsBand_230 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_238 (T_IsBand_230 -> T_IsBand_230
forall a b. a -> b
coe T_IsBand_230
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsMagma_86
v4 = T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202 (T_IsSemigroup_194 -> T_IsSemigroup_194
forall a b. a -> b
coe T_IsSemigroup_194
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_86 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsMagma_86 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_94 (T_IsMagma_86 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86
v4))))))
-- Algebra.Bundles.Semilattice._.isSemigroup
d_isSemigroup_440 ::
  T_Semilattice_402 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_194
d_isSemigroup_440 :: T_Semilattice_402 -> T_IsSemigroup_194
d_isSemigroup_440 T_Semilattice_402
v0
  = (T_IsBand_230 -> T_IsSemigroup_194) -> AgdaAny -> T_IsSemigroup_194
forall a b. a -> b
coe
      T_IsBand_230 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_238
      ((T_IsSemilattice_312 -> T_IsBand_230) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemilattice_312 -> T_IsBand_230
MAlonzo.Code.Algebra.Structures.d_isBand_320
         ((T_Semilattice_402 -> T_IsSemilattice_312) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semilattice_402 -> T_IsSemilattice_312
d_isSemilattice_422 (T_Semilattice_402 -> AgdaAny
forall a b. a -> b
coe T_Semilattice_402
v0)))
-- Algebra.Bundles.Semilattice._.refl
d_refl_442 :: T_Semilattice_402 -> AgdaAny -> AgdaAny
d_refl_442 :: T_Semilattice_402 -> AgdaAny -> AgdaAny
d_refl_442 T_Semilattice_402
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_86 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_86 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_94
         ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202
            ((T_IsBand_230 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsBand_230 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_238
               ((T_IsSemilattice_312 -> T_IsBand_230) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsSemilattice_312 -> T_IsBand_230
MAlonzo.Code.Algebra.Structures.d_isBand_320
                  ((T_Semilattice_402 -> T_IsSemilattice_312) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semilattice_402 -> T_IsSemilattice_312
d_isSemilattice_422 (T_Semilattice_402 -> AgdaAny
forall a b. a -> b
coe T_Semilattice_402
v0))))))
-- Algebra.Bundles.Semilattice._.reflexive
d_reflexive_444 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Semilattice_402 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_444 :: ()
-> ()
-> T_Semilattice_402
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_444 ~()
v0 ~()
v1 T_Semilattice_402
v2 = T_Semilattice_402 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_444 T_Semilattice_402
v2
du_reflexive_444 ::
  T_Semilattice_402 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_444 :: T_Semilattice_402 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_444 T_Semilattice_402
v0
  = let v1 :: T_IsSemilattice_312
v1 = T_Semilattice_402 -> T_IsSemilattice_312
d_isSemilattice_422 (T_Semilattice_402 -> T_Semilattice_402
forall a b. a -> b
coe T_Semilattice_402
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsBand_230
v2 = T_IsSemilattice_312 -> T_IsBand_230
MAlonzo.Code.Algebra.Structures.d_isBand_320 (T_IsSemilattice_312 -> T_IsSemilattice_312
forall a b. a -> b
coe T_IsSemilattice_312
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_194
v3
                = T_IsBand_230 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_238 (T_IsBand_230 -> T_IsBand_230
forall a b. a -> b
coe T_IsBand_230
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsMagma_86
v4 = T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202 (T_IsSemigroup_194 -> T_IsSemigroup_194
forall a b. a -> b
coe T_IsSemigroup_194
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_86 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_94 (T_IsMagma_86 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86
v4))
                    AgdaAny
v5))))
-- Algebra.Bundles.Semilattice._.setoid
d_setoid_446 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Semilattice_402 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_446 :: () -> () -> T_Semilattice_402 -> T_Setoid_44
d_setoid_446 ~()
v0 ~()
v1 T_Semilattice_402
v2 = T_Semilattice_402 -> T_Setoid_44
du_setoid_446 T_Semilattice_402
v2
du_setoid_446 ::
  T_Semilattice_402 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_446 :: T_Semilattice_402 -> T_Setoid_44
du_setoid_446 T_Semilattice_402
v0
  = let v1 :: T_IsSemilattice_312
v1 = T_Semilattice_402 -> T_IsSemilattice_312
d_isSemilattice_422 (T_Semilattice_402 -> T_Semilattice_402
forall a b. a -> b
coe T_Semilattice_402
v0) in
    AgdaAny -> T_Setoid_44
forall a b. a -> b
coe
      (let v2 :: T_IsBand_230
v2 = T_IsSemilattice_312 -> T_IsBand_230
MAlonzo.Code.Algebra.Structures.d_isBand_320 (T_IsSemilattice_312 -> T_IsSemilattice_312
forall a b. a -> b
coe T_IsSemilattice_312
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_194
v3
                = T_IsBand_230 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_238 (T_IsBand_230 -> T_IsBand_230
forall a b. a -> b
coe T_IsBand_230
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsMagma_86 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMagma_86 -> T_Setoid_44
MAlonzo.Code.Algebra.Structures.du_setoid_110
               ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202 (T_IsSemigroup_194 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194
v3)))))
-- Algebra.Bundles.Semilattice._.sym
d_sym_448 ::
  T_Semilattice_402 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_448 :: T_Semilattice_402 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_448 T_Semilattice_402
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_86 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_86 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_94
         ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202
            ((T_IsBand_230 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsBand_230 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_238
               ((T_IsSemilattice_312 -> T_IsBand_230) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsSemilattice_312 -> T_IsBand_230
MAlonzo.Code.Algebra.Structures.d_isBand_320
                  ((T_Semilattice_402 -> T_IsSemilattice_312) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semilattice_402 -> T_IsSemilattice_312
d_isSemilattice_422 (T_Semilattice_402 -> AgdaAny
forall a b. a -> b
coe T_Semilattice_402
v0))))))
-- Algebra.Bundles.Semilattice._.trans
d_trans_450 ::
  T_Semilattice_402 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_450 :: T_Semilattice_402
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_450 T_Semilattice_402
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_86 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_86 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_94
         ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202
            ((T_IsBand_230 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsBand_230 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_238
               ((T_IsSemilattice_312 -> T_IsBand_230) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsSemilattice_312 -> T_IsBand_230
MAlonzo.Code.Algebra.Structures.d_isBand_320
                  ((T_Semilattice_402 -> T_IsSemilattice_312) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semilattice_402 -> T_IsSemilattice_312
d_isSemilattice_422 (T_Semilattice_402 -> AgdaAny
forall a b. a -> b
coe T_Semilattice_402
v0))))))
-- Algebra.Bundles.Semilattice._.∙-cong
d_'8729''45'cong_452 ::
  T_Semilattice_402 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_452 :: T_Semilattice_402
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_452 T_Semilattice_402
v0
  = (T_IsMagma_86
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsMagma_86
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_96
      ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202
         ((T_IsBand_230 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsBand_230 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_238
            ((T_IsSemilattice_312 -> T_IsBand_230) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemilattice_312 -> T_IsBand_230
MAlonzo.Code.Algebra.Structures.d_isBand_320
               ((T_Semilattice_402 -> T_IsSemilattice_312) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semilattice_402 -> T_IsSemilattice_312
d_isSemilattice_422 (T_Semilattice_402 -> AgdaAny
forall a b. a -> b
coe T_Semilattice_402
v0)))))
-- Algebra.Bundles.Semilattice._.∙-congʳ
d_'8729''45'cong'691'_454 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Semilattice_402 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_454 :: ()
-> ()
-> T_Semilattice_402
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_454 ~()
v0 ~()
v1 T_Semilattice_402
v2
  = T_Semilattice_402
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_454 T_Semilattice_402
v2
du_'8729''45'cong'691'_454 ::
  T_Semilattice_402 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_454 :: T_Semilattice_402
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_454 T_Semilattice_402
v0
  = let v1 :: T_IsSemilattice_312
v1 = T_Semilattice_402 -> T_IsSemilattice_312
d_isSemilattice_422 (T_Semilattice_402 -> T_Semilattice_402
forall a b. a -> b
coe T_Semilattice_402
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsBand_230
v2 = T_IsSemilattice_312 -> T_IsBand_230
MAlonzo.Code.Algebra.Structures.d_isBand_320 (T_IsSemilattice_312 -> T_IsSemilattice_312
forall a b. a -> b
coe T_IsSemilattice_312
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_194
v3
                = T_IsBand_230 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_238 (T_IsBand_230 -> T_IsBand_230
forall a b. a -> b
coe T_IsBand_230
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsMagma_86
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMagma_86 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'691'_116
               ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202 (T_IsSemigroup_194 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194
v3)))))
-- Algebra.Bundles.Semilattice._.∙-congˡ
d_'8729''45'cong'737'_456 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Semilattice_402 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_456 :: ()
-> ()
-> T_Semilattice_402
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_456 ~()
v0 ~()
v1 T_Semilattice_402
v2
  = T_Semilattice_402
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_456 T_Semilattice_402
v2
du_'8729''45'cong'737'_456 ::
  T_Semilattice_402 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_456 :: T_Semilattice_402
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_456 T_Semilattice_402
v0
  = let v1 :: T_IsSemilattice_312
v1 = T_Semilattice_402 -> T_IsSemilattice_312
d_isSemilattice_422 (T_Semilattice_402 -> T_Semilattice_402
forall a b. a -> b
coe T_Semilattice_402
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsBand_230
v2 = T_IsSemilattice_312 -> T_IsBand_230
MAlonzo.Code.Algebra.Structures.d_isBand_320 (T_IsSemilattice_312 -> T_IsSemilattice_312
forall a b. a -> b
coe T_IsSemilattice_312
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_194
v3
                = T_IsBand_230 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_238 (T_IsBand_230 -> T_IsBand_230
forall a b. a -> b
coe T_IsBand_230
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsMagma_86
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMagma_86 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'737'_112
               ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202 (T_IsSemigroup_194 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194
v3)))))
-- Algebra.Bundles.Semilattice.band
d_band_458 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Semilattice_402 -> T_Band_266
d_band_458 :: () -> () -> T_Semilattice_402 -> T_Band_266
d_band_458 ~()
v0 ~()
v1 T_Semilattice_402
v2 = T_Semilattice_402 -> T_Band_266
du_band_458 T_Semilattice_402
v2
du_band_458 :: T_Semilattice_402 -> T_Band_266
du_band_458 :: T_Semilattice_402 -> T_Band_266
du_band_458 T_Semilattice_402
v0
  = ((AgdaAny -> AgdaAny -> AgdaAny) -> T_IsBand_230 -> T_Band_266)
-> (AgdaAny -> AgdaAny -> AgdaAny) -> T_IsBand_230 -> T_Band_266
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny) -> T_IsBand_230 -> T_Band_266
C_Band'46'constructor_4745 (T_Semilattice_402 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8743'__420 (T_Semilattice_402 -> T_Semilattice_402
forall a b. a -> b
coe T_Semilattice_402
v0))
      (T_IsSemilattice_312 -> T_IsBand_230
MAlonzo.Code.Algebra.Structures.d_isBand_320
         ((T_Semilattice_402 -> T_IsSemilattice_312)
-> AgdaAny -> T_IsSemilattice_312
forall a b. a -> b
coe T_Semilattice_402 -> T_IsSemilattice_312
d_isSemilattice_422 (T_Semilattice_402 -> AgdaAny
forall a b. a -> b
coe T_Semilattice_402
v0)))
-- Algebra.Bundles.Semilattice._._≉_
d__'8777'__462 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Semilattice_402 -> AgdaAny -> AgdaAny -> ()
d__'8777'__462 :: () -> () -> T_Semilattice_402 -> AgdaAny -> AgdaAny -> ()
d__'8777'__462 = () -> () -> T_Semilattice_402 -> AgdaAny -> AgdaAny -> ()
forall a. a
erased
-- Algebra.Bundles.Semilattice._.magma
d_magma_464 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Semilattice_402 -> T_Magma_36
d_magma_464 :: () -> () -> T_Semilattice_402 -> T_Magma_36
d_magma_464 ~()
v0 ~()
v1 T_Semilattice_402
v2 = T_Semilattice_402 -> T_Magma_36
du_magma_464 T_Semilattice_402
v2
du_magma_464 :: T_Semilattice_402 -> T_Magma_36
du_magma_464 :: T_Semilattice_402 -> T_Magma_36
du_magma_464 T_Semilattice_402
v0
  = let v1 :: t
v1 = (T_Semilattice_402 -> T_Band_266) -> AgdaAny -> t
forall a b. a -> b
coe T_Semilattice_402 -> T_Band_266
du_band_458 (T_Semilattice_402 -> AgdaAny
forall a b. a -> b
coe T_Semilattice_402
v0) in
    AgdaAny -> T_Magma_36
forall a b. a -> b
coe ((T_Semigroup_206 -> T_Magma_36) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semigroup_206 -> T_Magma_36
du_magma_254 ((T_Band_266 -> T_Semigroup_206) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Band_266 -> T_Semigroup_206
du_semigroup_318 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1)))
-- Algebra.Bundles.Semilattice._.rawMagma
d_rawMagma_466 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Semilattice_402 -> T_RawMagma_8
d_rawMagma_466 :: () -> () -> T_Semilattice_402 -> T_RawMagma_8
d_rawMagma_466 ~()
v0 ~()
v1 T_Semilattice_402
v2 = T_Semilattice_402 -> T_RawMagma_8
du_rawMagma_466 T_Semilattice_402
v2
du_rawMagma_466 :: T_Semilattice_402 -> T_RawMagma_8
du_rawMagma_466 :: T_Semilattice_402 -> T_RawMagma_8
du_rawMagma_466 T_Semilattice_402
v0
  = let v1 :: t
v1 = (T_Semilattice_402 -> T_Band_266) -> AgdaAny -> t
forall a b. a -> b
coe T_Semilattice_402 -> T_Band_266
du_band_458 (T_Semilattice_402 -> AgdaAny
forall a b. a -> b
coe T_Semilattice_402
v0) in
    AgdaAny -> T_RawMagma_8
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_Band_266 -> T_Semigroup_206) -> AgdaAny -> t
forall a b. a -> b
coe T_Band_266 -> T_Semigroup_206
du_semigroup_318 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_Magma_36 -> T_RawMagma_8) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Magma_36 -> T_RawMagma_8
du_rawMagma_80 ((T_Semigroup_206 -> T_Magma_36) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semigroup_206 -> T_Magma_36
du_magma_254 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2))))
-- Algebra.Bundles.Semilattice._.semigroup
d_semigroup_468 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Semilattice_402 -> T_Semigroup_206
d_semigroup_468 :: () -> () -> T_Semilattice_402 -> T_Semigroup_206
d_semigroup_468 ~()
v0 ~()
v1 T_Semilattice_402
v2 = T_Semilattice_402 -> T_Semigroup_206
du_semigroup_468 T_Semilattice_402
v2
du_semigroup_468 :: T_Semilattice_402 -> T_Semigroup_206
du_semigroup_468 :: T_Semilattice_402 -> T_Semigroup_206
du_semigroup_468 T_Semilattice_402
v0
  = (T_Band_266 -> T_Semigroup_206) -> AgdaAny -> T_Semigroup_206
forall a b. a -> b
coe T_Band_266 -> T_Semigroup_206
du_semigroup_318 ((T_Semilattice_402 -> T_Band_266) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semilattice_402 -> T_Band_266
du_band_458 (T_Semilattice_402 -> AgdaAny
forall a b. a -> b
coe T_Semilattice_402
v0))
-- Algebra.Bundles.RawMonoid
d_RawMonoid_474 :: p -> p -> ()
d_RawMonoid_474 p
a0 p
a1 = ()
data T_RawMonoid_474
  = C_RawMonoid'46'constructor_8313 (AgdaAny -> AgdaAny -> AgdaAny)
                                    AgdaAny
-- Algebra.Bundles.RawMonoid.Carrier
d_Carrier_488 :: T_RawMonoid_474 -> ()
d_Carrier_488 :: T_RawMonoid_474 -> ()
d_Carrier_488 = T_RawMonoid_474 -> ()
forall a. a
erased
-- Algebra.Bundles.RawMonoid._≈_
d__'8776'__490 :: T_RawMonoid_474 -> AgdaAny -> AgdaAny -> ()
d__'8776'__490 :: T_RawMonoid_474 -> AgdaAny -> AgdaAny -> ()
d__'8776'__490 = T_RawMonoid_474 -> AgdaAny -> AgdaAny -> ()
forall a. a
erased
-- Algebra.Bundles.RawMonoid._∙_
d__'8729'__492 :: T_RawMonoid_474 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__492 :: T_RawMonoid_474 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__492 T_RawMonoid_474
v0
  = case T_RawMonoid_474 -> T_RawMonoid_474
forall a b. a -> b
coe T_RawMonoid_474
v0 of
      C_RawMonoid'46'constructor_8313 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny
v4 -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v3
      T_RawMonoid_474
_ -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.RawMonoid.ε
d_ε_494 :: T_RawMonoid_474 -> AgdaAny
d_ε_494 :: T_RawMonoid_474 -> AgdaAny
d_ε_494 T_RawMonoid_474
v0
  = case T_RawMonoid_474 -> T_RawMonoid_474
forall a b. a -> b
coe T_RawMonoid_474
v0 of
      C_RawMonoid'46'constructor_8313 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny
v4 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v4
      T_RawMonoid_474
_ -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.RawMonoid.rawMagma
d_rawMagma_496 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_RawMonoid_474 -> T_RawMagma_8
d_rawMagma_496 :: () -> () -> T_RawMonoid_474 -> T_RawMagma_8
d_rawMagma_496 ~()
v0 ~()
v1 T_RawMonoid_474
v2 = T_RawMonoid_474 -> T_RawMagma_8
du_rawMagma_496 T_RawMonoid_474
v2
du_rawMagma_496 :: T_RawMonoid_474 -> T_RawMagma_8
du_rawMagma_496 :: T_RawMonoid_474 -> T_RawMagma_8
du_rawMagma_496 T_RawMonoid_474
v0
  = ((AgdaAny -> AgdaAny -> AgdaAny) -> T_RawMagma_8)
-> (AgdaAny -> AgdaAny -> AgdaAny) -> T_RawMagma_8
forall a b. a -> b
coe (AgdaAny -> AgdaAny -> AgdaAny) -> T_RawMagma_8
C_RawMagma'46'constructor_79 (T_RawMonoid_474 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__492 (T_RawMonoid_474 -> T_RawMonoid_474
forall a b. a -> b
coe T_RawMonoid_474
v0))
-- Algebra.Bundles.RawMonoid._._≉_
d__'8777'__500 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_RawMonoid_474 -> AgdaAny -> AgdaAny -> ()
d__'8777'__500 :: () -> () -> T_RawMonoid_474 -> AgdaAny -> AgdaAny -> ()
d__'8777'__500 = () -> () -> T_RawMonoid_474 -> AgdaAny -> AgdaAny -> ()
forall a. a
erased
-- Algebra.Bundles.Monoid
d_Monoid_506 :: p -> p -> ()
d_Monoid_506 p
a0 p
a1 = ()
data T_Monoid_506
  = C_Monoid'46'constructor_8851 (AgdaAny -> AgdaAny -> AgdaAny)
                                 AgdaAny MAlonzo.Code.Algebra.Structures.T_IsMonoid_358
-- Algebra.Bundles.Monoid.Carrier
d_Carrier_522 :: T_Monoid_506 -> ()
d_Carrier_522 :: T_Monoid_506 -> ()
d_Carrier_522 = T_Monoid_506 -> ()
forall a. a
erased
-- Algebra.Bundles.Monoid._≈_
d__'8776'__524 :: T_Monoid_506 -> AgdaAny -> AgdaAny -> ()
d__'8776'__524 :: T_Monoid_506 -> AgdaAny -> AgdaAny -> ()
d__'8776'__524 = T_Monoid_506 -> AgdaAny -> AgdaAny -> ()
forall a. a
erased
-- Algebra.Bundles.Monoid._∙_
d__'8729'__526 :: T_Monoid_506 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__526 :: T_Monoid_506 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__526 T_Monoid_506
v0
  = case T_Monoid_506 -> T_Monoid_506
forall a b. a -> b
coe T_Monoid_506
v0 of
      C_Monoid'46'constructor_8851 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny
v4 T_IsMonoid_358
v5 -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v3
      T_Monoid_506
_ -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.Monoid.ε
d_ε_528 :: T_Monoid_506 -> AgdaAny
d_ε_528 :: T_Monoid_506 -> AgdaAny
d_ε_528 T_Monoid_506
v0
  = case T_Monoid_506 -> T_Monoid_506
forall a b. a -> b
coe T_Monoid_506
v0 of
      C_Monoid'46'constructor_8851 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny
v4 T_IsMonoid_358
v5 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v4
      T_Monoid_506
_ -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.Monoid.isMonoid
d_isMonoid_530 ::
  T_Monoid_506 -> MAlonzo.Code.Algebra.Structures.T_IsMonoid_358
d_isMonoid_530 :: T_Monoid_506 -> T_IsMonoid_358
d_isMonoid_530 T_Monoid_506
v0
  = case T_Monoid_506 -> T_Monoid_506
forall a b. a -> b
coe T_Monoid_506
v0 of
      C_Monoid'46'constructor_8851 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny
v4 T_IsMonoid_358
v5 -> T_IsMonoid_358 -> T_IsMonoid_358
forall a b. a -> b
coe T_IsMonoid_358
v5
      T_Monoid_506
_ -> T_IsMonoid_358
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.Monoid._.assoc
d_assoc_534 ::
  T_Monoid_506 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_534 :: T_Monoid_506 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_534 T_Monoid_506
v0
  = (T_IsSemigroup_194 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsSemigroup_194 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_assoc_204
      ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368
         ((T_Monoid_506 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Monoid_506 -> T_IsMonoid_358
d_isMonoid_530 (T_Monoid_506 -> AgdaAny
forall a b. a -> b
coe T_Monoid_506
v0)))
-- Algebra.Bundles.Monoid._.identity
d_identity_536 ::
  T_Monoid_506 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_identity_536 :: T_Monoid_506 -> T_Σ_14
d_identity_536 T_Monoid_506
v0
  = (T_IsMonoid_358 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsMonoid_358 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_identity_370
      ((T_Monoid_506 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Monoid_506 -> T_IsMonoid_358
d_isMonoid_530 (T_Monoid_506 -> AgdaAny
forall a b. a -> b
coe T_Monoid_506
v0))
-- Algebra.Bundles.Monoid._.identityʳ
d_identity'691'_538 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Monoid_506 -> AgdaAny -> AgdaAny
d_identity'691'_538 :: () -> () -> T_Monoid_506 -> AgdaAny -> AgdaAny
d_identity'691'_538 ~()
v0 ~()
v1 T_Monoid_506
v2 = T_Monoid_506 -> AgdaAny -> AgdaAny
du_identity'691'_538 T_Monoid_506
v2
du_identity'691'_538 :: T_Monoid_506 -> AgdaAny -> AgdaAny
du_identity'691'_538 :: T_Monoid_506 -> AgdaAny -> AgdaAny
du_identity'691'_538 T_Monoid_506
v0
  = (T_IsMonoid_358 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsMonoid_358 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_identity'691'_400
      ((T_Monoid_506 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Monoid_506 -> T_IsMonoid_358
d_isMonoid_530 (T_Monoid_506 -> AgdaAny
forall a b. a -> b
coe T_Monoid_506
v0))
-- Algebra.Bundles.Monoid._.identityˡ
d_identity'737'_540 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Monoid_506 -> AgdaAny -> AgdaAny
d_identity'737'_540 :: () -> () -> T_Monoid_506 -> AgdaAny -> AgdaAny
d_identity'737'_540 ~()
v0 ~()
v1 T_Monoid_506
v2 = T_Monoid_506 -> AgdaAny -> AgdaAny
du_identity'737'_540 T_Monoid_506
v2
du_identity'737'_540 :: T_Monoid_506 -> AgdaAny -> AgdaAny
du_identity'737'_540 :: T_Monoid_506 -> AgdaAny -> AgdaAny
du_identity'737'_540 T_Monoid_506
v0
  = (T_IsMonoid_358 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsMonoid_358 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_identity'737'_398
      ((T_Monoid_506 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Monoid_506 -> T_IsMonoid_358
d_isMonoid_530 (T_Monoid_506 -> AgdaAny
forall a b. a -> b
coe T_Monoid_506
v0))
-- Algebra.Bundles.Monoid._.isEquivalence
d_isEquivalence_542 ::
  T_Monoid_506 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_542 :: T_Monoid_506 -> T_IsEquivalence_26
d_isEquivalence_542 T_Monoid_506
v0
  = (T_IsMagma_86 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      T_IsMagma_86 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_94
      ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202
         ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368
            ((T_Monoid_506 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Monoid_506 -> T_IsMonoid_358
d_isMonoid_530 (T_Monoid_506 -> AgdaAny
forall a b. a -> b
coe T_Monoid_506
v0))))
-- Algebra.Bundles.Monoid._.isMagma
d_isMagma_544 ::
  T_Monoid_506 -> MAlonzo.Code.Algebra.Structures.T_IsMagma_86
d_isMagma_544 :: T_Monoid_506 -> T_IsMagma_86
d_isMagma_544 T_Monoid_506
v0
  = (T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> T_IsMagma_86
forall a b. a -> b
coe
      T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202
      ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368
         ((T_Monoid_506 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Monoid_506 -> T_IsMonoid_358
d_isMonoid_530 (T_Monoid_506 -> AgdaAny
forall a b. a -> b
coe T_Monoid_506
v0)))
-- Algebra.Bundles.Monoid._.isPartialEquivalence
d_isPartialEquivalence_546 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Monoid_506 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_546 :: () -> () -> T_Monoid_506 -> T_IsPartialEquivalence_16
d_isPartialEquivalence_546 ~()
v0 ~()
v1 T_Monoid_506
v2
  = T_Monoid_506 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_546 T_Monoid_506
v2
du_isPartialEquivalence_546 ::
  T_Monoid_506 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_546 :: T_Monoid_506 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_546 T_Monoid_506
v0
  = let v1 :: T_IsMonoid_358
v1 = T_Monoid_506 -> T_IsMonoid_358
d_isMonoid_530 (T_Monoid_506 -> T_Monoid_506
forall a b. a -> b
coe T_Monoid_506
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsSemigroup_194
v2
             = T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368 (T_IsMonoid_358 -> T_IsMonoid_358
forall a b. a -> b
coe T_IsMonoid_358
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsMagma_86
v3 = T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202 (T_IsSemigroup_194 -> T_IsSemigroup_194
forall a b. a -> b
coe T_IsSemigroup_194
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_86 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsMagma_86 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_94 (T_IsMagma_86 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86
v3)))))
-- Algebra.Bundles.Monoid._.isSemigroup
d_isSemigroup_548 ::
  T_Monoid_506 -> MAlonzo.Code.Algebra.Structures.T_IsSemigroup_194
d_isSemigroup_548 :: T_Monoid_506 -> T_IsSemigroup_194
d_isSemigroup_548 T_Monoid_506
v0
  = (T_IsMonoid_358 -> T_IsSemigroup_194)
-> AgdaAny -> T_IsSemigroup_194
forall a b. a -> b
coe
      T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368
      ((T_Monoid_506 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Monoid_506 -> T_IsMonoid_358
d_isMonoid_530 (T_Monoid_506 -> AgdaAny
forall a b. a -> b
coe T_Monoid_506
v0))
-- Algebra.Bundles.Monoid._.refl
d_refl_550 :: T_Monoid_506 -> AgdaAny -> AgdaAny
d_refl_550 :: T_Monoid_506 -> AgdaAny -> AgdaAny
d_refl_550 T_Monoid_506
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_86 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_86 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_94
         ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202
            ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368
               ((T_Monoid_506 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Monoid_506 -> T_IsMonoid_358
d_isMonoid_530 (T_Monoid_506 -> AgdaAny
forall a b. a -> b
coe T_Monoid_506
v0)))))
-- Algebra.Bundles.Monoid._.reflexive
d_reflexive_552 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Monoid_506 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_552 :: ()
-> ()
-> T_Monoid_506
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_552 ~()
v0 ~()
v1 T_Monoid_506
v2 = T_Monoid_506 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_552 T_Monoid_506
v2
du_reflexive_552 ::
  T_Monoid_506 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_552 :: T_Monoid_506 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_552 T_Monoid_506
v0
  = let v1 :: T_IsMonoid_358
v1 = T_Monoid_506 -> T_IsMonoid_358
d_isMonoid_530 (T_Monoid_506 -> T_Monoid_506
forall a b. a -> b
coe T_Monoid_506
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemigroup_194
v2
             = T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368 (T_IsMonoid_358 -> T_IsMonoid_358
forall a b. a -> b
coe T_IsMonoid_358
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsMagma_86
v3 = T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202 (T_IsSemigroup_194 -> T_IsSemigroup_194
forall a b. a -> b
coe T_IsSemigroup_194
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_86 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_94 (T_IsMagma_86 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86
v3))
                 AgdaAny
v4)))
-- Algebra.Bundles.Monoid._.setoid
d_setoid_554 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Monoid_506 -> MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_554 :: () -> () -> T_Monoid_506 -> T_Setoid_44
d_setoid_554 ~()
v0 ~()
v1 T_Monoid_506
v2 = T_Monoid_506 -> T_Setoid_44
du_setoid_554 T_Monoid_506
v2
du_setoid_554 ::
  T_Monoid_506 -> MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_554 :: T_Monoid_506 -> T_Setoid_44
du_setoid_554 T_Monoid_506
v0
  = let v1 :: T_IsMonoid_358
v1 = T_Monoid_506 -> T_IsMonoid_358
d_isMonoid_530 (T_Monoid_506 -> T_Monoid_506
forall a b. a -> b
coe T_Monoid_506
v0) in
    AgdaAny -> T_Setoid_44
forall a b. a -> b
coe
      (let v2 :: T_IsSemigroup_194
v2
             = T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368 (T_IsMonoid_358 -> T_IsMonoid_358
forall a b. a -> b
coe T_IsMonoid_358
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsMagma_86 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMagma_86 -> T_Setoid_44
MAlonzo.Code.Algebra.Structures.du_setoid_110
            ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202 (T_IsSemigroup_194 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194
v2))))
-- Algebra.Bundles.Monoid._.sym
d_sym_556 ::
  T_Monoid_506 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_556 :: T_Monoid_506 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_556 T_Monoid_506
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_86 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_86 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_94
         ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202
            ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368
               ((T_Monoid_506 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Monoid_506 -> T_IsMonoid_358
d_isMonoid_530 (T_Monoid_506 -> AgdaAny
forall a b. a -> b
coe T_Monoid_506
v0)))))
-- Algebra.Bundles.Monoid._.trans
d_trans_558 ::
  T_Monoid_506 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_558 :: T_Monoid_506
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_558 T_Monoid_506
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_86 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_86 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_94
         ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202
            ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368
               ((T_Monoid_506 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Monoid_506 -> T_IsMonoid_358
d_isMonoid_530 (T_Monoid_506 -> AgdaAny
forall a b. a -> b
coe T_Monoid_506
v0)))))
-- Algebra.Bundles.Monoid._.∙-cong
d_'8729''45'cong_560 ::
  T_Monoid_506 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_560 :: T_Monoid_506
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_560 T_Monoid_506
v0
  = (T_IsMagma_86
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsMagma_86
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_96
      ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202
         ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368
            ((T_Monoid_506 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Monoid_506 -> T_IsMonoid_358
d_isMonoid_530 (T_Monoid_506 -> AgdaAny
forall a b. a -> b
coe T_Monoid_506
v0))))
-- Algebra.Bundles.Monoid._.∙-congʳ
d_'8729''45'cong'691'_562 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Monoid_506 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_562 :: ()
-> ()
-> T_Monoid_506
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_562 ~()
v0 ~()
v1 T_Monoid_506
v2
  = T_Monoid_506 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_562 T_Monoid_506
v2
du_'8729''45'cong'691'_562 ::
  T_Monoid_506 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_562 :: T_Monoid_506 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_562 T_Monoid_506
v0
  = let v1 :: T_IsMonoid_358
v1 = T_Monoid_506 -> T_IsMonoid_358
d_isMonoid_530 (T_Monoid_506 -> T_Monoid_506
forall a b. a -> b
coe T_Monoid_506
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemigroup_194
v2
             = T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368 (T_IsMonoid_358 -> T_IsMonoid_358
forall a b. a -> b
coe T_IsMonoid_358
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsMagma_86
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMagma_86 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'691'_116
            ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202 (T_IsSemigroup_194 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194
v2))))
-- Algebra.Bundles.Monoid._.∙-congˡ
d_'8729''45'cong'737'_564 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Monoid_506 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_564 :: ()
-> ()
-> T_Monoid_506
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_564 ~()
v0 ~()
v1 T_Monoid_506
v2
  = T_Monoid_506 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_564 T_Monoid_506
v2
du_'8729''45'cong'737'_564 ::
  T_Monoid_506 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_564 :: T_Monoid_506 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_564 T_Monoid_506
v0
  = let v1 :: T_IsMonoid_358
v1 = T_Monoid_506 -> T_IsMonoid_358
d_isMonoid_530 (T_Monoid_506 -> T_Monoid_506
forall a b. a -> b
coe T_Monoid_506
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemigroup_194
v2
             = T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368 (T_IsMonoid_358 -> T_IsMonoid_358
forall a b. a -> b
coe T_IsMonoid_358
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsMagma_86
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMagma_86 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'737'_112
            ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202 (T_IsSemigroup_194 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194
v2))))
-- Algebra.Bundles.Monoid.semigroup
d_semigroup_566 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Monoid_506 -> T_Semigroup_206
d_semigroup_566 :: () -> () -> T_Monoid_506 -> T_Semigroup_206
d_semigroup_566 ~()
v0 ~()
v1 T_Monoid_506
v2 = T_Monoid_506 -> T_Semigroup_206
du_semigroup_566 T_Monoid_506
v2
du_semigroup_566 :: T_Monoid_506 -> T_Semigroup_206
du_semigroup_566 :: T_Monoid_506 -> T_Semigroup_206
du_semigroup_566 T_Monoid_506
v0
  = ((AgdaAny -> AgdaAny -> AgdaAny)
 -> T_IsSemigroup_194 -> T_Semigroup_206)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsSemigroup_194
-> T_Semigroup_206
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsSemigroup_194 -> T_Semigroup_206
C_Semigroup'46'constructor_3669 (T_Monoid_506 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__526 (T_Monoid_506 -> T_Monoid_506
forall a b. a -> b
coe T_Monoid_506
v0))
      (T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368
         ((T_Monoid_506 -> T_IsMonoid_358) -> AgdaAny -> T_IsMonoid_358
forall a b. a -> b
coe T_Monoid_506 -> T_IsMonoid_358
d_isMonoid_530 (T_Monoid_506 -> AgdaAny
forall a b. a -> b
coe T_Monoid_506
v0)))
-- Algebra.Bundles.Monoid._._≉_
d__'8777'__570 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Monoid_506 -> AgdaAny -> AgdaAny -> ()
d__'8777'__570 :: () -> () -> T_Monoid_506 -> AgdaAny -> AgdaAny -> ()
d__'8777'__570 = () -> () -> T_Monoid_506 -> AgdaAny -> AgdaAny -> ()
forall a. a
erased
-- Algebra.Bundles.Monoid._.magma
d_magma_572 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Monoid_506 -> T_Magma_36
d_magma_572 :: () -> () -> T_Monoid_506 -> T_Magma_36
d_magma_572 ~()
v0 ~()
v1 T_Monoid_506
v2 = T_Monoid_506 -> T_Magma_36
du_magma_572 T_Monoid_506
v2
du_magma_572 :: T_Monoid_506 -> T_Magma_36
du_magma_572 :: T_Monoid_506 -> T_Magma_36
du_magma_572 T_Monoid_506
v0 = (T_Semigroup_206 -> T_Magma_36) -> AgdaAny -> T_Magma_36
forall a b. a -> b
coe T_Semigroup_206 -> T_Magma_36
du_magma_254 ((T_Monoid_506 -> T_Semigroup_206) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Monoid_506 -> T_Semigroup_206
du_semigroup_566 (T_Monoid_506 -> AgdaAny
forall a b. a -> b
coe T_Monoid_506
v0))
-- Algebra.Bundles.Monoid._.rawMagma
d_rawMagma_574 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Monoid_506 -> T_RawMagma_8
d_rawMagma_574 :: () -> () -> T_Monoid_506 -> T_RawMagma_8
d_rawMagma_574 ~()
v0 ~()
v1 T_Monoid_506
v2 = T_Monoid_506 -> T_RawMagma_8
du_rawMagma_574 T_Monoid_506
v2
du_rawMagma_574 :: T_Monoid_506 -> T_RawMagma_8
du_rawMagma_574 :: T_Monoid_506 -> T_RawMagma_8
du_rawMagma_574 T_Monoid_506
v0
  = let v1 :: t
v1 = (T_Monoid_506 -> T_Semigroup_206) -> AgdaAny -> t
forall a b. a -> b
coe T_Monoid_506 -> T_Semigroup_206
du_semigroup_566 (T_Monoid_506 -> AgdaAny
forall a b. a -> b
coe T_Monoid_506
v0) in
    AgdaAny -> T_RawMagma_8
forall a b. a -> b
coe ((T_Magma_36 -> T_RawMagma_8) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Magma_36 -> T_RawMagma_8
du_rawMagma_80 ((T_Semigroup_206 -> T_Magma_36) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semigroup_206 -> T_Magma_36
du_magma_254 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1)))
-- Algebra.Bundles.Monoid.rawMonoid
d_rawMonoid_576 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Monoid_506 -> T_RawMonoid_474
d_rawMonoid_576 :: () -> () -> T_Monoid_506 -> T_RawMonoid_474
d_rawMonoid_576 ~()
v0 ~()
v1 T_Monoid_506
v2 = T_Monoid_506 -> T_RawMonoid_474
du_rawMonoid_576 T_Monoid_506
v2
du_rawMonoid_576 :: T_Monoid_506 -> T_RawMonoid_474
du_rawMonoid_576 :: T_Monoid_506 -> T_RawMonoid_474
du_rawMonoid_576 T_Monoid_506
v0
  = ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> T_RawMonoid_474)
-> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> T_RawMonoid_474
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> T_RawMonoid_474
C_RawMonoid'46'constructor_8313 (T_Monoid_506 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__526 (T_Monoid_506 -> T_Monoid_506
forall a b. a -> b
coe T_Monoid_506
v0))
      (T_Monoid_506 -> AgdaAny
d_ε_528 (T_Monoid_506 -> T_Monoid_506
forall a b. a -> b
coe T_Monoid_506
v0))
-- Algebra.Bundles.CommutativeMonoid
d_CommutativeMonoid_582 :: p -> p -> ()
d_CommutativeMonoid_582 p
a0 p
a1 = ()
data T_CommutativeMonoid_582
  = C_CommutativeMonoid'46'constructor_10343 (AgdaAny ->
                                              AgdaAny -> AgdaAny)
                                             AgdaAny
                                             MAlonzo.Code.Algebra.Structures.T_IsCommutativeMonoid_406
-- Algebra.Bundles.CommutativeMonoid.Carrier
d_Carrier_598 :: T_CommutativeMonoid_582 -> ()
d_Carrier_598 :: T_CommutativeMonoid_582 -> ()
d_Carrier_598 = T_CommutativeMonoid_582 -> ()
forall a. a
erased
-- Algebra.Bundles.CommutativeMonoid._≈_
d__'8776'__600 ::
  T_CommutativeMonoid_582 -> AgdaAny -> AgdaAny -> ()
d__'8776'__600 :: T_CommutativeMonoid_582 -> AgdaAny -> AgdaAny -> ()
d__'8776'__600 = T_CommutativeMonoid_582 -> AgdaAny -> AgdaAny -> ()
forall a. a
erased
-- Algebra.Bundles.CommutativeMonoid._∙_
d__'8729'__602 ::
  T_CommutativeMonoid_582 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__602 :: T_CommutativeMonoid_582 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__602 T_CommutativeMonoid_582
v0
  = case T_CommutativeMonoid_582 -> T_CommutativeMonoid_582
forall a b. a -> b
coe T_CommutativeMonoid_582
v0 of
      C_CommutativeMonoid'46'constructor_10343 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny
v4 T_IsCommutativeMonoid_406
v5 -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v3
      T_CommutativeMonoid_582
_ -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.CommutativeMonoid.ε
d_ε_604 :: T_CommutativeMonoid_582 -> AgdaAny
d_ε_604 :: T_CommutativeMonoid_582 -> AgdaAny
d_ε_604 T_CommutativeMonoid_582
v0
  = case T_CommutativeMonoid_582 -> T_CommutativeMonoid_582
forall a b. a -> b
coe T_CommutativeMonoid_582
v0 of
      C_CommutativeMonoid'46'constructor_10343 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny
v4 T_IsCommutativeMonoid_406
v5 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v4
      T_CommutativeMonoid_582
_ -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.CommutativeMonoid.isCommutativeMonoid
d_isCommutativeMonoid_606 ::
  T_CommutativeMonoid_582 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMonoid_406
d_isCommutativeMonoid_606 :: T_CommutativeMonoid_582 -> T_IsCommutativeMonoid_406
d_isCommutativeMonoid_606 T_CommutativeMonoid_582
v0
  = case T_CommutativeMonoid_582 -> T_CommutativeMonoid_582
forall a b. a -> b
coe T_CommutativeMonoid_582
v0 of
      C_CommutativeMonoid'46'constructor_10343 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny
v4 T_IsCommutativeMonoid_406
v5 -> T_IsCommutativeMonoid_406 -> T_IsCommutativeMonoid_406
forall a b. a -> b
coe T_IsCommutativeMonoid_406
v5
      T_CommutativeMonoid_582
_ -> T_IsCommutativeMonoid_406
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.CommutativeMonoid._.assoc
d_assoc_610 ::
  T_CommutativeMonoid_582 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_610 :: T_CommutativeMonoid_582 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_610 T_CommutativeMonoid_582
v0
  = (T_IsSemigroup_194 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsSemigroup_194 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_assoc_204
      ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368
         ((T_IsCommutativeMonoid_406 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCommutativeMonoid_406 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_416
            ((T_CommutativeMonoid_582 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeMonoid_582 -> T_IsCommutativeMonoid_406
d_isCommutativeMonoid_606 (T_CommutativeMonoid_582 -> AgdaAny
forall a b. a -> b
coe T_CommutativeMonoid_582
v0))))
-- Algebra.Bundles.CommutativeMonoid._.comm
d_comm_612 ::
  T_CommutativeMonoid_582 -> AgdaAny -> AgdaAny -> AgdaAny
d_comm_612 :: T_CommutativeMonoid_582 -> AgdaAny -> AgdaAny -> AgdaAny
d_comm_612 T_CommutativeMonoid_582
v0
  = (T_IsCommutativeMonoid_406 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsCommutativeMonoid_406 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_comm_418
      ((T_CommutativeMonoid_582 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeMonoid_582 -> T_IsCommutativeMonoid_406
d_isCommutativeMonoid_606 (T_CommutativeMonoid_582 -> AgdaAny
forall a b. a -> b
coe T_CommutativeMonoid_582
v0))
-- Algebra.Bundles.CommutativeMonoid._.identity
d_identity_614 ::
  T_CommutativeMonoid_582 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_identity_614 :: T_CommutativeMonoid_582 -> T_Σ_14
d_identity_614 T_CommutativeMonoid_582
v0
  = (T_IsMonoid_358 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsMonoid_358 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_identity_370
      ((T_IsCommutativeMonoid_406 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCommutativeMonoid_406 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_416
         ((T_CommutativeMonoid_582 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeMonoid_582 -> T_IsCommutativeMonoid_406
d_isCommutativeMonoid_606 (T_CommutativeMonoid_582 -> AgdaAny
forall a b. a -> b
coe T_CommutativeMonoid_582
v0)))
-- Algebra.Bundles.CommutativeMonoid._.identityʳ
d_identity'691'_616 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeMonoid_582 -> AgdaAny -> AgdaAny
d_identity'691'_616 :: () -> () -> T_CommutativeMonoid_582 -> AgdaAny -> AgdaAny
d_identity'691'_616 ~()
v0 ~()
v1 T_CommutativeMonoid_582
v2 = T_CommutativeMonoid_582 -> AgdaAny -> AgdaAny
du_identity'691'_616 T_CommutativeMonoid_582
v2
du_identity'691'_616 ::
  T_CommutativeMonoid_582 -> AgdaAny -> AgdaAny
du_identity'691'_616 :: T_CommutativeMonoid_582 -> AgdaAny -> AgdaAny
du_identity'691'_616 T_CommutativeMonoid_582
v0
  = let v1 :: T_IsCommutativeMonoid_406
v1 = T_CommutativeMonoid_582 -> T_IsCommutativeMonoid_406
d_isCommutativeMonoid_606 (T_CommutativeMonoid_582 -> T_CommutativeMonoid_582
forall a b. a -> b
coe T_CommutativeMonoid_582
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsMonoid_358 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoid_358 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_identity'691'_400
         ((T_IsCommutativeMonoid_406 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_406 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_416 (T_IsCommutativeMonoid_406 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_406
v1)))
-- Algebra.Bundles.CommutativeMonoid._.identityˡ
d_identity'737'_618 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeMonoid_582 -> AgdaAny -> AgdaAny
d_identity'737'_618 :: () -> () -> T_CommutativeMonoid_582 -> AgdaAny -> AgdaAny
d_identity'737'_618 ~()
v0 ~()
v1 T_CommutativeMonoid_582
v2 = T_CommutativeMonoid_582 -> AgdaAny -> AgdaAny
du_identity'737'_618 T_CommutativeMonoid_582
v2
du_identity'737'_618 ::
  T_CommutativeMonoid_582 -> AgdaAny -> AgdaAny
du_identity'737'_618 :: T_CommutativeMonoid_582 -> AgdaAny -> AgdaAny
du_identity'737'_618 T_CommutativeMonoid_582
v0
  = let v1 :: T_IsCommutativeMonoid_406
v1 = T_CommutativeMonoid_582 -> T_IsCommutativeMonoid_406
d_isCommutativeMonoid_606 (T_CommutativeMonoid_582 -> T_CommutativeMonoid_582
forall a b. a -> b
coe T_CommutativeMonoid_582
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsMonoid_358 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoid_358 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_identity'737'_398
         ((T_IsCommutativeMonoid_406 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_406 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_416 (T_IsCommutativeMonoid_406 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_406
v1)))
-- Algebra.Bundles.CommutativeMonoid._.isCommutativeMagma
d_isCommutativeMagma_620 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeMonoid_582 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMagma_122
d_isCommutativeMagma_620 :: () -> () -> T_CommutativeMonoid_582 -> T_IsCommutativeMagma_122
d_isCommutativeMagma_620 ~()
v0 ~()
v1 T_CommutativeMonoid_582
v2 = T_CommutativeMonoid_582 -> T_IsCommutativeMagma_122
du_isCommutativeMagma_620 T_CommutativeMonoid_582
v2
du_isCommutativeMagma_620 ::
  T_CommutativeMonoid_582 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMagma_122
du_isCommutativeMagma_620 :: T_CommutativeMonoid_582 -> T_IsCommutativeMagma_122
du_isCommutativeMagma_620 T_CommutativeMonoid_582
v0
  = let v1 :: T_IsCommutativeMonoid_406
v1 = T_CommutativeMonoid_582 -> T_IsCommutativeMonoid_406
d_isCommutativeMonoid_606 (T_CommutativeMonoid_582 -> T_CommutativeMonoid_582
forall a b. a -> b
coe T_CommutativeMonoid_582
v0) in
    AgdaAny -> T_IsCommutativeMagma_122
forall a b. a -> b
coe
      ((T_IsCommutativeSemigroup_270 -> T_IsCommutativeMagma_122)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCommutativeSemigroup_270 -> T_IsCommutativeMagma_122
MAlonzo.Code.Algebra.Structures.du_isCommutativeMagma_308
         ((T_IsCommutativeMonoid_406 -> T_IsCommutativeSemigroup_270)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCommutativeMonoid_406 -> T_IsCommutativeSemigroup_270
MAlonzo.Code.Algebra.Structures.du_isCommutativeSemigroup_454
            (T_IsCommutativeMonoid_406 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_406
v1)))
-- Algebra.Bundles.CommutativeMonoid._.isCommutativeSemigroup
d_isCommutativeSemigroup_622 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeMonoid_582 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_270
d_isCommutativeSemigroup_622 :: () -> () -> T_CommutativeMonoid_582 -> T_IsCommutativeSemigroup_270
d_isCommutativeSemigroup_622 ~()
v0 ~()
v1 T_CommutativeMonoid_582
v2
  = T_CommutativeMonoid_582 -> T_IsCommutativeSemigroup_270
du_isCommutativeSemigroup_622 T_CommutativeMonoid_582
v2
du_isCommutativeSemigroup_622 ::
  T_CommutativeMonoid_582 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_270
du_isCommutativeSemigroup_622 :: T_CommutativeMonoid_582 -> T_IsCommutativeSemigroup_270
du_isCommutativeSemigroup_622 T_CommutativeMonoid_582
v0
  = (T_IsCommutativeMonoid_406 -> T_IsCommutativeSemigroup_270)
-> AgdaAny -> T_IsCommutativeSemigroup_270
forall a b. a -> b
coe
      T_IsCommutativeMonoid_406 -> T_IsCommutativeSemigroup_270
MAlonzo.Code.Algebra.Structures.du_isCommutativeSemigroup_454
      ((T_CommutativeMonoid_582 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeMonoid_582 -> T_IsCommutativeMonoid_406
d_isCommutativeMonoid_606 (T_CommutativeMonoid_582 -> AgdaAny
forall a b. a -> b
coe T_CommutativeMonoid_582
v0))
-- Algebra.Bundles.CommutativeMonoid._.isEquivalence
d_isEquivalence_624 ::
  T_CommutativeMonoid_582 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_624 :: T_CommutativeMonoid_582 -> T_IsEquivalence_26
d_isEquivalence_624 T_CommutativeMonoid_582
v0
  = (T_IsMagma_86 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      T_IsMagma_86 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_94
      ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202
         ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368
            ((T_IsCommutativeMonoid_406 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsCommutativeMonoid_406 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_416
               ((T_CommutativeMonoid_582 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeMonoid_582 -> T_IsCommutativeMonoid_406
d_isCommutativeMonoid_606 (T_CommutativeMonoid_582 -> AgdaAny
forall a b. a -> b
coe T_CommutativeMonoid_582
v0)))))
-- Algebra.Bundles.CommutativeMonoid._.isMagma
d_isMagma_626 ::
  T_CommutativeMonoid_582 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_86
d_isMagma_626 :: T_CommutativeMonoid_582 -> T_IsMagma_86
d_isMagma_626 T_CommutativeMonoid_582
v0
  = (T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> T_IsMagma_86
forall a b. a -> b
coe
      T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202
      ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368
         ((T_IsCommutativeMonoid_406 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCommutativeMonoid_406 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_416
            ((T_CommutativeMonoid_582 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeMonoid_582 -> T_IsCommutativeMonoid_406
d_isCommutativeMonoid_606 (T_CommutativeMonoid_582 -> AgdaAny
forall a b. a -> b
coe T_CommutativeMonoid_582
v0))))
-- Algebra.Bundles.CommutativeMonoid._.isMonoid
d_isMonoid_628 ::
  T_CommutativeMonoid_582 ->
  MAlonzo.Code.Algebra.Structures.T_IsMonoid_358
d_isMonoid_628 :: T_CommutativeMonoid_582 -> T_IsMonoid_358
d_isMonoid_628 T_CommutativeMonoid_582
v0
  = (T_IsCommutativeMonoid_406 -> T_IsMonoid_358)
-> AgdaAny -> T_IsMonoid_358
forall a b. a -> b
coe
      T_IsCommutativeMonoid_406 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_416
      ((T_CommutativeMonoid_582 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeMonoid_582 -> T_IsCommutativeMonoid_406
d_isCommutativeMonoid_606 (T_CommutativeMonoid_582 -> AgdaAny
forall a b. a -> b
coe T_CommutativeMonoid_582
v0))
-- Algebra.Bundles.CommutativeMonoid._.isPartialEquivalence
d_isPartialEquivalence_630 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeMonoid_582 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_630 :: () -> () -> T_CommutativeMonoid_582 -> T_IsPartialEquivalence_16
d_isPartialEquivalence_630 ~()
v0 ~()
v1 T_CommutativeMonoid_582
v2
  = T_CommutativeMonoid_582 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_630 T_CommutativeMonoid_582
v2
du_isPartialEquivalence_630 ::
  T_CommutativeMonoid_582 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_630 :: T_CommutativeMonoid_582 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_630 T_CommutativeMonoid_582
v0
  = let v1 :: T_IsCommutativeMonoid_406
v1 = T_CommutativeMonoid_582 -> T_IsCommutativeMonoid_406
d_isCommutativeMonoid_606 (T_CommutativeMonoid_582 -> T_CommutativeMonoid_582
forall a b. a -> b
coe T_CommutativeMonoid_582
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsMonoid_358
v2
             = T_IsCommutativeMonoid_406 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_416 (T_IsCommutativeMonoid_406 -> T_IsCommutativeMonoid_406
forall a b. a -> b
coe T_IsCommutativeMonoid_406
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_194
v3
                = T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368 (T_IsMonoid_358 -> T_IsMonoid_358
forall a b. a -> b
coe T_IsMonoid_358
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsMagma_86
v4 = T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202 (T_IsSemigroup_194 -> T_IsSemigroup_194
forall a b. a -> b
coe T_IsSemigroup_194
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_86 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsMagma_86 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_94 (T_IsMagma_86 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86
v4))))))
-- Algebra.Bundles.CommutativeMonoid._.isSemigroup
d_isSemigroup_632 ::
  T_CommutativeMonoid_582 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_194
d_isSemigroup_632 :: T_CommutativeMonoid_582 -> T_IsSemigroup_194
d_isSemigroup_632 T_CommutativeMonoid_582
v0
  = (T_IsMonoid_358 -> T_IsSemigroup_194)
-> AgdaAny -> T_IsSemigroup_194
forall a b. a -> b
coe
      T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368
      ((T_IsCommutativeMonoid_406 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCommutativeMonoid_406 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_416
         ((T_CommutativeMonoid_582 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeMonoid_582 -> T_IsCommutativeMonoid_406
d_isCommutativeMonoid_606 (T_CommutativeMonoid_582 -> AgdaAny
forall a b. a -> b
coe T_CommutativeMonoid_582
v0)))
-- Algebra.Bundles.CommutativeMonoid._.refl
d_refl_634 :: T_CommutativeMonoid_582 -> AgdaAny -> AgdaAny
d_refl_634 :: T_CommutativeMonoid_582 -> AgdaAny -> AgdaAny
d_refl_634 T_CommutativeMonoid_582
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_86 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_86 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_94
         ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202
            ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368
               ((T_IsCommutativeMonoid_406 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsCommutativeMonoid_406 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_416
                  ((T_CommutativeMonoid_582 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeMonoid_582 -> T_IsCommutativeMonoid_406
d_isCommutativeMonoid_606 (T_CommutativeMonoid_582 -> AgdaAny
forall a b. a -> b
coe T_CommutativeMonoid_582
v0))))))
-- Algebra.Bundles.CommutativeMonoid._.reflexive
d_reflexive_636 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeMonoid_582 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_636 :: ()
-> ()
-> T_CommutativeMonoid_582
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_636 ~()
v0 ~()
v1 T_CommutativeMonoid_582
v2 = T_CommutativeMonoid_582
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_636 T_CommutativeMonoid_582
v2
du_reflexive_636 ::
  T_CommutativeMonoid_582 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_636 :: T_CommutativeMonoid_582
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_636 T_CommutativeMonoid_582
v0
  = let v1 :: T_IsCommutativeMonoid_406
v1 = T_CommutativeMonoid_582 -> T_IsCommutativeMonoid_406
d_isCommutativeMonoid_606 (T_CommutativeMonoid_582 -> T_CommutativeMonoid_582
forall a b. a -> b
coe T_CommutativeMonoid_582
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsMonoid_358
v2
             = T_IsCommutativeMonoid_406 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_416 (T_IsCommutativeMonoid_406 -> T_IsCommutativeMonoid_406
forall a b. a -> b
coe T_IsCommutativeMonoid_406
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_194
v3
                = T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368 (T_IsMonoid_358 -> T_IsMonoid_358
forall a b. a -> b
coe T_IsMonoid_358
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsMagma_86
v4 = T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202 (T_IsSemigroup_194 -> T_IsSemigroup_194
forall a b. a -> b
coe T_IsSemigroup_194
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_86 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_94 (T_IsMagma_86 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86
v4))
                    AgdaAny
v5))))
-- Algebra.Bundles.CommutativeMonoid._.setoid
d_setoid_638 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeMonoid_582 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_638 :: () -> () -> T_CommutativeMonoid_582 -> T_Setoid_44
d_setoid_638 ~()
v0 ~()
v1 T_CommutativeMonoid_582
v2 = T_CommutativeMonoid_582 -> T_Setoid_44
du_setoid_638 T_CommutativeMonoid_582
v2
du_setoid_638 ::
  T_CommutativeMonoid_582 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_638 :: T_CommutativeMonoid_582 -> T_Setoid_44
du_setoid_638 T_CommutativeMonoid_582
v0
  = let v1 :: T_IsCommutativeMonoid_406
v1 = T_CommutativeMonoid_582 -> T_IsCommutativeMonoid_406
d_isCommutativeMonoid_606 (T_CommutativeMonoid_582 -> T_CommutativeMonoid_582
forall a b. a -> b
coe T_CommutativeMonoid_582
v0) in
    AgdaAny -> T_Setoid_44
forall a b. a -> b
coe
      (let v2 :: T_IsMonoid_358
v2
             = T_IsCommutativeMonoid_406 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_416 (T_IsCommutativeMonoid_406 -> T_IsCommutativeMonoid_406
forall a b. a -> b
coe T_IsCommutativeMonoid_406
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_194
v3
                = T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368 (T_IsMonoid_358 -> T_IsMonoid_358
forall a b. a -> b
coe T_IsMonoid_358
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsMagma_86 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMagma_86 -> T_Setoid_44
MAlonzo.Code.Algebra.Structures.du_setoid_110
               ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202 (T_IsSemigroup_194 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194
v3)))))
-- Algebra.Bundles.CommutativeMonoid._.sym
d_sym_640 ::
  T_CommutativeMonoid_582 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_640 :: T_CommutativeMonoid_582 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_640 T_CommutativeMonoid_582
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_86 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_86 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_94
         ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202
            ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368
               ((T_IsCommutativeMonoid_406 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsCommutativeMonoid_406 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_416
                  ((T_CommutativeMonoid_582 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeMonoid_582 -> T_IsCommutativeMonoid_406
d_isCommutativeMonoid_606 (T_CommutativeMonoid_582 -> AgdaAny
forall a b. a -> b
coe T_CommutativeMonoid_582
v0))))))
-- Algebra.Bundles.CommutativeMonoid._.trans
d_trans_642 ::
  T_CommutativeMonoid_582 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_642 :: T_CommutativeMonoid_582
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_642 T_CommutativeMonoid_582
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_86 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_86 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_94
         ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202
            ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368
               ((T_IsCommutativeMonoid_406 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsCommutativeMonoid_406 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_416
                  ((T_CommutativeMonoid_582 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeMonoid_582 -> T_IsCommutativeMonoid_406
d_isCommutativeMonoid_606 (T_CommutativeMonoid_582 -> AgdaAny
forall a b. a -> b
coe T_CommutativeMonoid_582
v0))))))
-- Algebra.Bundles.CommutativeMonoid._.∙-cong
d_'8729''45'cong_644 ::
  T_CommutativeMonoid_582 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_644 :: T_CommutativeMonoid_582
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_644 T_CommutativeMonoid_582
v0
  = (T_IsMagma_86
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsMagma_86
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_96
      ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202
         ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368
            ((T_IsCommutativeMonoid_406 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsCommutativeMonoid_406 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_416
               ((T_CommutativeMonoid_582 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeMonoid_582 -> T_IsCommutativeMonoid_406
d_isCommutativeMonoid_606 (T_CommutativeMonoid_582 -> AgdaAny
forall a b. a -> b
coe T_CommutativeMonoid_582
v0)))))
-- Algebra.Bundles.CommutativeMonoid._.∙-congʳ
d_'8729''45'cong'691'_646 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeMonoid_582 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_646 :: ()
-> ()
-> T_CommutativeMonoid_582
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_646 ~()
v0 ~()
v1 T_CommutativeMonoid_582
v2
  = T_CommutativeMonoid_582
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_646 T_CommutativeMonoid_582
v2
du_'8729''45'cong'691'_646 ::
  T_CommutativeMonoid_582 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_646 :: T_CommutativeMonoid_582
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_646 T_CommutativeMonoid_582
v0
  = let v1 :: T_IsCommutativeMonoid_406
v1 = T_CommutativeMonoid_582 -> T_IsCommutativeMonoid_406
d_isCommutativeMonoid_606 (T_CommutativeMonoid_582 -> T_CommutativeMonoid_582
forall a b. a -> b
coe T_CommutativeMonoid_582
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsMonoid_358
v2
             = T_IsCommutativeMonoid_406 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_416 (T_IsCommutativeMonoid_406 -> T_IsCommutativeMonoid_406
forall a b. a -> b
coe T_IsCommutativeMonoid_406
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_194
v3
                = T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368 (T_IsMonoid_358 -> T_IsMonoid_358
forall a b. a -> b
coe T_IsMonoid_358
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsMagma_86
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMagma_86 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'691'_116
               ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202 (T_IsSemigroup_194 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194
v3)))))
-- Algebra.Bundles.CommutativeMonoid._.∙-congˡ
d_'8729''45'cong'737'_648 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeMonoid_582 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_648 :: ()
-> ()
-> T_CommutativeMonoid_582
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_648 ~()
v0 ~()
v1 T_CommutativeMonoid_582
v2
  = T_CommutativeMonoid_582
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_648 T_CommutativeMonoid_582
v2
du_'8729''45'cong'737'_648 ::
  T_CommutativeMonoid_582 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_648 :: T_CommutativeMonoid_582
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_648 T_CommutativeMonoid_582
v0
  = let v1 :: T_IsCommutativeMonoid_406
v1 = T_CommutativeMonoid_582 -> T_IsCommutativeMonoid_406
d_isCommutativeMonoid_606 (T_CommutativeMonoid_582 -> T_CommutativeMonoid_582
forall a b. a -> b
coe T_CommutativeMonoid_582
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsMonoid_358
v2
             = T_IsCommutativeMonoid_406 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_416 (T_IsCommutativeMonoid_406 -> T_IsCommutativeMonoid_406
forall a b. a -> b
coe T_IsCommutativeMonoid_406
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_194
v3
                = T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368 (T_IsMonoid_358 -> T_IsMonoid_358
forall a b. a -> b
coe T_IsMonoid_358
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsMagma_86
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMagma_86 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'737'_112
               ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202 (T_IsSemigroup_194 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194
v3)))))
-- Algebra.Bundles.CommutativeMonoid.monoid
d_monoid_650 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeMonoid_582 -> T_Monoid_506
d_monoid_650 :: () -> () -> T_CommutativeMonoid_582 -> T_Monoid_506
d_monoid_650 ~()
v0 ~()
v1 T_CommutativeMonoid_582
v2 = T_CommutativeMonoid_582 -> T_Monoid_506
du_monoid_650 T_CommutativeMonoid_582
v2
du_monoid_650 :: T_CommutativeMonoid_582 -> T_Monoid_506
du_monoid_650 :: T_CommutativeMonoid_582 -> T_Monoid_506
du_monoid_650 T_CommutativeMonoid_582
v0
  = ((AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny -> T_IsMonoid_358 -> T_Monoid_506)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsMonoid_358
-> T_Monoid_506
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> T_IsMonoid_358 -> T_Monoid_506
C_Monoid'46'constructor_8851 (T_CommutativeMonoid_582 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__602 (T_CommutativeMonoid_582 -> T_CommutativeMonoid_582
forall a b. a -> b
coe T_CommutativeMonoid_582
v0))
      (T_CommutativeMonoid_582 -> AgdaAny
d_ε_604 (T_CommutativeMonoid_582 -> T_CommutativeMonoid_582
forall a b. a -> b
coe T_CommutativeMonoid_582
v0))
      (T_IsCommutativeMonoid_406 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_416
         ((T_CommutativeMonoid_582 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> T_IsCommutativeMonoid_406
forall a b. a -> b
coe T_CommutativeMonoid_582 -> T_IsCommutativeMonoid_406
d_isCommutativeMonoid_606 (T_CommutativeMonoid_582 -> AgdaAny
forall a b. a -> b
coe T_CommutativeMonoid_582
v0)))
-- Algebra.Bundles.CommutativeMonoid._._≉_
d__'8777'__654 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeMonoid_582 -> AgdaAny -> AgdaAny -> ()
d__'8777'__654 :: () -> () -> T_CommutativeMonoid_582 -> AgdaAny -> AgdaAny -> ()
d__'8777'__654 = () -> () -> T_CommutativeMonoid_582 -> AgdaAny -> AgdaAny -> ()
forall a. a
erased
-- Algebra.Bundles.CommutativeMonoid._.magma
d_magma_656 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeMonoid_582 -> T_Magma_36
d_magma_656 :: () -> () -> T_CommutativeMonoid_582 -> T_Magma_36
d_magma_656 ~()
v0 ~()
v1 T_CommutativeMonoid_582
v2 = T_CommutativeMonoid_582 -> T_Magma_36
du_magma_656 T_CommutativeMonoid_582
v2
du_magma_656 :: T_CommutativeMonoid_582 -> T_Magma_36
du_magma_656 :: T_CommutativeMonoid_582 -> T_Magma_36
du_magma_656 T_CommutativeMonoid_582
v0
  = let v1 :: t
v1 = (T_CommutativeMonoid_582 -> T_Monoid_506) -> AgdaAny -> t
forall a b. a -> b
coe T_CommutativeMonoid_582 -> T_Monoid_506
du_monoid_650 (T_CommutativeMonoid_582 -> AgdaAny
forall a b. a -> b
coe T_CommutativeMonoid_582
v0) in
    AgdaAny -> T_Magma_36
forall a b. a -> b
coe ((T_Semigroup_206 -> T_Magma_36) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semigroup_206 -> T_Magma_36
du_magma_254 ((T_Monoid_506 -> T_Semigroup_206) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Monoid_506 -> T_Semigroup_206
du_semigroup_566 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1)))
-- Algebra.Bundles.CommutativeMonoid._.rawMagma
d_rawMagma_658 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeMonoid_582 -> T_RawMagma_8
d_rawMagma_658 :: () -> () -> T_CommutativeMonoid_582 -> T_RawMagma_8
d_rawMagma_658 ~()
v0 ~()
v1 T_CommutativeMonoid_582
v2 = T_CommutativeMonoid_582 -> T_RawMagma_8
du_rawMagma_658 T_CommutativeMonoid_582
v2
du_rawMagma_658 :: T_CommutativeMonoid_582 -> T_RawMagma_8
du_rawMagma_658 :: T_CommutativeMonoid_582 -> T_RawMagma_8
du_rawMagma_658 T_CommutativeMonoid_582
v0
  = let v1 :: t
v1 = (T_CommutativeMonoid_582 -> T_Monoid_506) -> AgdaAny -> t
forall a b. a -> b
coe T_CommutativeMonoid_582 -> T_Monoid_506
du_monoid_650 (T_CommutativeMonoid_582 -> AgdaAny
forall a b. a -> b
coe T_CommutativeMonoid_582
v0) in
    AgdaAny -> T_RawMagma_8
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_Monoid_506 -> T_Semigroup_206) -> AgdaAny -> t
forall a b. a -> b
coe T_Monoid_506 -> T_Semigroup_206
du_semigroup_566 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_Magma_36 -> T_RawMagma_8) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Magma_36 -> T_RawMagma_8
du_rawMagma_80 ((T_Semigroup_206 -> T_Magma_36) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semigroup_206 -> T_Magma_36
du_magma_254 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2))))
-- Algebra.Bundles.CommutativeMonoid._.rawMonoid
d_rawMonoid_660 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeMonoid_582 -> T_RawMonoid_474
d_rawMonoid_660 :: () -> () -> T_CommutativeMonoid_582 -> T_RawMonoid_474
d_rawMonoid_660 ~()
v0 ~()
v1 T_CommutativeMonoid_582
v2 = T_CommutativeMonoid_582 -> T_RawMonoid_474
du_rawMonoid_660 T_CommutativeMonoid_582
v2
du_rawMonoid_660 :: T_CommutativeMonoid_582 -> T_RawMonoid_474
du_rawMonoid_660 :: T_CommutativeMonoid_582 -> T_RawMonoid_474
du_rawMonoid_660 T_CommutativeMonoid_582
v0
  = (T_Monoid_506 -> T_RawMonoid_474) -> AgdaAny -> T_RawMonoid_474
forall a b. a -> b
coe T_Monoid_506 -> T_RawMonoid_474
du_rawMonoid_576 ((T_CommutativeMonoid_582 -> T_Monoid_506) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeMonoid_582 -> T_Monoid_506
du_monoid_650 (T_CommutativeMonoid_582 -> AgdaAny
forall a b. a -> b
coe T_CommutativeMonoid_582
v0))
-- Algebra.Bundles.CommutativeMonoid._.semigroup
d_semigroup_662 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeMonoid_582 -> T_Semigroup_206
d_semigroup_662 :: () -> () -> T_CommutativeMonoid_582 -> T_Semigroup_206
d_semigroup_662 ~()
v0 ~()
v1 T_CommutativeMonoid_582
v2 = T_CommutativeMonoid_582 -> T_Semigroup_206
du_semigroup_662 T_CommutativeMonoid_582
v2
du_semigroup_662 :: T_CommutativeMonoid_582 -> T_Semigroup_206
du_semigroup_662 :: T_CommutativeMonoid_582 -> T_Semigroup_206
du_semigroup_662 T_CommutativeMonoid_582
v0
  = (T_Monoid_506 -> T_Semigroup_206) -> AgdaAny -> T_Semigroup_206
forall a b. a -> b
coe T_Monoid_506 -> T_Semigroup_206
du_semigroup_566 ((T_CommutativeMonoid_582 -> T_Monoid_506) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeMonoid_582 -> T_Monoid_506
du_monoid_650 (T_CommutativeMonoid_582 -> AgdaAny
forall a b. a -> b
coe T_CommutativeMonoid_582
v0))
-- Algebra.Bundles.CommutativeMonoid.commutativeSemigroup
d_commutativeSemigroup_664 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeMonoid_582 -> T_CommutativeSemigroup_332
d_commutativeSemigroup_664 :: () -> () -> T_CommutativeMonoid_582 -> T_CommutativeSemigroup_332
d_commutativeSemigroup_664 ~()
v0 ~()
v1 T_CommutativeMonoid_582
v2
  = T_CommutativeMonoid_582 -> T_CommutativeSemigroup_332
du_commutativeSemigroup_664 T_CommutativeMonoid_582
v2
du_commutativeSemigroup_664 ::
  T_CommutativeMonoid_582 -> T_CommutativeSemigroup_332
du_commutativeSemigroup_664 :: T_CommutativeMonoid_582 -> T_CommutativeSemigroup_332
du_commutativeSemigroup_664 T_CommutativeMonoid_582
v0
  = ((AgdaAny -> AgdaAny -> AgdaAny)
 -> T_IsCommutativeSemigroup_270 -> T_CommutativeSemigroup_332)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_CommutativeSemigroup_332
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsCommutativeSemigroup_270 -> T_CommutativeSemigroup_332
C_CommutativeSemigroup'46'constructor_5887
      (T_CommutativeMonoid_582 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__602 (T_CommutativeMonoid_582 -> T_CommutativeMonoid_582
forall a b. a -> b
coe T_CommutativeMonoid_582
v0))
      ((T_IsCommutativeMonoid_406 -> T_IsCommutativeSemigroup_270)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCommutativeMonoid_406 -> T_IsCommutativeSemigroup_270
MAlonzo.Code.Algebra.Structures.du_isCommutativeSemigroup_454
         ((T_CommutativeMonoid_582 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeMonoid_582 -> T_IsCommutativeMonoid_406
d_isCommutativeMonoid_606 (T_CommutativeMonoid_582 -> AgdaAny
forall a b. a -> b
coe T_CommutativeMonoid_582
v0)))
-- Algebra.Bundles.CommutativeMonoid._.commutativeMagma
d_commutativeMagma_668 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeMonoid_582 -> T_CommutativeMagma_148
d_commutativeMagma_668 :: () -> () -> T_CommutativeMonoid_582 -> T_CommutativeMagma_148
d_commutativeMagma_668 ~()
v0 ~()
v1 T_CommutativeMonoid_582
v2 = T_CommutativeMonoid_582 -> T_CommutativeMagma_148
du_commutativeMagma_668 T_CommutativeMonoid_582
v2
du_commutativeMagma_668 ::
  T_CommutativeMonoid_582 -> T_CommutativeMagma_148
du_commutativeMagma_668 :: T_CommutativeMonoid_582 -> T_CommutativeMagma_148
du_commutativeMagma_668 T_CommutativeMonoid_582
v0
  = (T_CommutativeSemigroup_332 -> T_CommutativeMagma_148)
-> AgdaAny -> T_CommutativeMagma_148
forall a b. a -> b
coe
      T_CommutativeSemigroup_332 -> T_CommutativeMagma_148
du_commutativeMagma_396 ((T_CommutativeMonoid_582 -> T_CommutativeSemigroup_332)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeMonoid_582 -> T_CommutativeSemigroup_332
du_commutativeSemigroup_664 (T_CommutativeMonoid_582 -> AgdaAny
forall a b. a -> b
coe T_CommutativeMonoid_582
v0))
-- Algebra.Bundles.IdempotentCommutativeMonoid
d_IdempotentCommutativeMonoid_674 :: p -> p -> ()
d_IdempotentCommutativeMonoid_674 p
a0 p
a1 = ()
data T_IdempotentCommutativeMonoid_674
  = C_IdempotentCommutativeMonoid'46'constructor_12109 (AgdaAny ->
                                                        AgdaAny -> AgdaAny)
                                                       AgdaAny
                                                       MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_464
-- Algebra.Bundles.IdempotentCommutativeMonoid.Carrier
d_Carrier_690 :: T_IdempotentCommutativeMonoid_674 -> ()
d_Carrier_690 :: T_IdempotentCommutativeMonoid_674 -> ()
d_Carrier_690 = T_IdempotentCommutativeMonoid_674 -> ()
forall a. a
erased
-- Algebra.Bundles.IdempotentCommutativeMonoid._≈_
d__'8776'__692 ::
  T_IdempotentCommutativeMonoid_674 -> AgdaAny -> AgdaAny -> ()
d__'8776'__692 :: T_IdempotentCommutativeMonoid_674 -> AgdaAny -> AgdaAny -> ()
d__'8776'__692 = T_IdempotentCommutativeMonoid_674 -> AgdaAny -> AgdaAny -> ()
forall a. a
erased
-- Algebra.Bundles.IdempotentCommutativeMonoid._∙_
d__'8729'__694 ::
  T_IdempotentCommutativeMonoid_674 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__694 :: T_IdempotentCommutativeMonoid_674 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__694 T_IdempotentCommutativeMonoid_674
v0
  = case T_IdempotentCommutativeMonoid_674
-> T_IdempotentCommutativeMonoid_674
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_674
v0 of
      C_IdempotentCommutativeMonoid'46'constructor_12109 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny
v4 T_IsIdempotentCommutativeMonoid_464
v5
        -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v3
      T_IdempotentCommutativeMonoid_674
_ -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.IdempotentCommutativeMonoid.ε
d_ε_696 :: T_IdempotentCommutativeMonoid_674 -> AgdaAny
d_ε_696 :: T_IdempotentCommutativeMonoid_674 -> AgdaAny
d_ε_696 T_IdempotentCommutativeMonoid_674
v0
  = case T_IdempotentCommutativeMonoid_674
-> T_IdempotentCommutativeMonoid_674
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_674
v0 of
      C_IdempotentCommutativeMonoid'46'constructor_12109 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny
v4 T_IsIdempotentCommutativeMonoid_464
v5
        -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v4
      T_IdempotentCommutativeMonoid_674
_ -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.IdempotentCommutativeMonoid.isIdempotentCommutativeMonoid
d_isIdempotentCommutativeMonoid_698 ::
  T_IdempotentCommutativeMonoid_674 ->
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_464
d_isIdempotentCommutativeMonoid_698 :: T_IdempotentCommutativeMonoid_674
-> T_IsIdempotentCommutativeMonoid_464
d_isIdempotentCommutativeMonoid_698 T_IdempotentCommutativeMonoid_674
v0
  = case T_IdempotentCommutativeMonoid_674
-> T_IdempotentCommutativeMonoid_674
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_674
v0 of
      C_IdempotentCommutativeMonoid'46'constructor_12109 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny
v4 T_IsIdempotentCommutativeMonoid_464
v5
        -> T_IsIdempotentCommutativeMonoid_464
-> T_IsIdempotentCommutativeMonoid_464
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_464
v5
      T_IdempotentCommutativeMonoid_674
_ -> T_IsIdempotentCommutativeMonoid_464
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.IdempotentCommutativeMonoid._.assoc
d_assoc_702 ::
  T_IdempotentCommutativeMonoid_674 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_702 :: T_IdempotentCommutativeMonoid_674
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_702 T_IdempotentCommutativeMonoid_674
v0
  = (T_IsSemigroup_194 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsSemigroup_194 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_assoc_204
      ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368
         ((T_IsCommutativeMonoid_406 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCommutativeMonoid_406 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_416
            ((T_IsIdempotentCommutativeMonoid_464 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsIdempotentCommutativeMonoid_464 -> T_IsCommutativeMonoid_406
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_474
               ((T_IdempotentCommutativeMonoid_674
 -> T_IsIdempotentCommutativeMonoid_464)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_674
-> T_IsIdempotentCommutativeMonoid_464
d_isIdempotentCommutativeMonoid_698 (T_IdempotentCommutativeMonoid_674 -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_674
v0)))))
-- Algebra.Bundles.IdempotentCommutativeMonoid._.comm
d_comm_704 ::
  T_IdempotentCommutativeMonoid_674 -> AgdaAny -> AgdaAny -> AgdaAny
d_comm_704 :: T_IdempotentCommutativeMonoid_674 -> AgdaAny -> AgdaAny -> AgdaAny
d_comm_704 T_IdempotentCommutativeMonoid_674
v0
  = (T_IsCommutativeMonoid_406 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsCommutativeMonoid_406 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_comm_418
      ((T_IsIdempotentCommutativeMonoid_464 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsIdempotentCommutativeMonoid_464 -> T_IsCommutativeMonoid_406
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_474
         ((T_IdempotentCommutativeMonoid_674
 -> T_IsIdempotentCommutativeMonoid_464)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_674
-> T_IsIdempotentCommutativeMonoid_464
d_isIdempotentCommutativeMonoid_698 (T_IdempotentCommutativeMonoid_674 -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_674
v0)))
-- Algebra.Bundles.IdempotentCommutativeMonoid._.idem
d_idem_706 ::
  T_IdempotentCommutativeMonoid_674 -> AgdaAny -> AgdaAny
d_idem_706 :: T_IdempotentCommutativeMonoid_674 -> AgdaAny -> AgdaAny
d_idem_706 T_IdempotentCommutativeMonoid_674
v0
  = (T_IsIdempotentCommutativeMonoid_464 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsIdempotentCommutativeMonoid_464 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_idem_476
      ((T_IdempotentCommutativeMonoid_674
 -> T_IsIdempotentCommutativeMonoid_464)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_674
-> T_IsIdempotentCommutativeMonoid_464
d_isIdempotentCommutativeMonoid_698 (T_IdempotentCommutativeMonoid_674 -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_674
v0))
-- Algebra.Bundles.IdempotentCommutativeMonoid._.identity
d_identity_708 ::
  T_IdempotentCommutativeMonoid_674 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_identity_708 :: T_IdempotentCommutativeMonoid_674 -> T_Σ_14
d_identity_708 T_IdempotentCommutativeMonoid_674
v0
  = (T_IsMonoid_358 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsMonoid_358 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_identity_370
      ((T_IsCommutativeMonoid_406 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCommutativeMonoid_406 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_416
         ((T_IsIdempotentCommutativeMonoid_464 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsIdempotentCommutativeMonoid_464 -> T_IsCommutativeMonoid_406
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_474
            ((T_IdempotentCommutativeMonoid_674
 -> T_IsIdempotentCommutativeMonoid_464)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_674
-> T_IsIdempotentCommutativeMonoid_464
d_isIdempotentCommutativeMonoid_698 (T_IdempotentCommutativeMonoid_674 -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_674
v0))))
-- Algebra.Bundles.IdempotentCommutativeMonoid._.identityʳ
d_identity'691'_710 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentCommutativeMonoid_674 -> AgdaAny -> AgdaAny
d_identity'691'_710 :: () -> () -> T_IdempotentCommutativeMonoid_674 -> AgdaAny -> AgdaAny
d_identity'691'_710 ~()
v0 ~()
v1 T_IdempotentCommutativeMonoid_674
v2 = T_IdempotentCommutativeMonoid_674 -> AgdaAny -> AgdaAny
du_identity'691'_710 T_IdempotentCommutativeMonoid_674
v2
du_identity'691'_710 ::
  T_IdempotentCommutativeMonoid_674 -> AgdaAny -> AgdaAny
du_identity'691'_710 :: T_IdempotentCommutativeMonoid_674 -> AgdaAny -> AgdaAny
du_identity'691'_710 T_IdempotentCommutativeMonoid_674
v0
  = let v1 :: T_IsIdempotentCommutativeMonoid_464
v1 = T_IdempotentCommutativeMonoid_674
-> T_IsIdempotentCommutativeMonoid_464
d_isIdempotentCommutativeMonoid_698 (T_IdempotentCommutativeMonoid_674
-> T_IdempotentCommutativeMonoid_674
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_674
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsCommutativeMonoid_406
v2
             = T_IsIdempotentCommutativeMonoid_464 -> T_IsCommutativeMonoid_406
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_474
                 (T_IsIdempotentCommutativeMonoid_464
-> T_IsIdempotentCommutativeMonoid_464
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_464
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsMonoid_358 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoid_358 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_identity'691'_400
            ((T_IsCommutativeMonoid_406 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_406 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_416 (T_IsCommutativeMonoid_406 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_406
v2))))
-- Algebra.Bundles.IdempotentCommutativeMonoid._.identityˡ
d_identity'737'_712 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentCommutativeMonoid_674 -> AgdaAny -> AgdaAny
d_identity'737'_712 :: () -> () -> T_IdempotentCommutativeMonoid_674 -> AgdaAny -> AgdaAny
d_identity'737'_712 ~()
v0 ~()
v1 T_IdempotentCommutativeMonoid_674
v2 = T_IdempotentCommutativeMonoid_674 -> AgdaAny -> AgdaAny
du_identity'737'_712 T_IdempotentCommutativeMonoid_674
v2
du_identity'737'_712 ::
  T_IdempotentCommutativeMonoid_674 -> AgdaAny -> AgdaAny
du_identity'737'_712 :: T_IdempotentCommutativeMonoid_674 -> AgdaAny -> AgdaAny
du_identity'737'_712 T_IdempotentCommutativeMonoid_674
v0
  = let v1 :: T_IsIdempotentCommutativeMonoid_464
v1 = T_IdempotentCommutativeMonoid_674
-> T_IsIdempotentCommutativeMonoid_464
d_isIdempotentCommutativeMonoid_698 (T_IdempotentCommutativeMonoid_674
-> T_IdempotentCommutativeMonoid_674
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_674
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsCommutativeMonoid_406
v2
             = T_IsIdempotentCommutativeMonoid_464 -> T_IsCommutativeMonoid_406
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_474
                 (T_IsIdempotentCommutativeMonoid_464
-> T_IsIdempotentCommutativeMonoid_464
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_464
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsMonoid_358 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoid_358 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_identity'737'_398
            ((T_IsCommutativeMonoid_406 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_406 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_416 (T_IsCommutativeMonoid_406 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_406
v2))))
-- Algebra.Bundles.IdempotentCommutativeMonoid._.isCommutativeMagma
d_isCommutativeMagma_714 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentCommutativeMonoid_674 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMagma_122
d_isCommutativeMagma_714 :: ()
-> ()
-> T_IdempotentCommutativeMonoid_674
-> T_IsCommutativeMagma_122
d_isCommutativeMagma_714 ~()
v0 ~()
v1 T_IdempotentCommutativeMonoid_674
v2 = T_IdempotentCommutativeMonoid_674 -> T_IsCommutativeMagma_122
du_isCommutativeMagma_714 T_IdempotentCommutativeMonoid_674
v2
du_isCommutativeMagma_714 ::
  T_IdempotentCommutativeMonoid_674 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMagma_122
du_isCommutativeMagma_714 :: T_IdempotentCommutativeMonoid_674 -> T_IsCommutativeMagma_122
du_isCommutativeMagma_714 T_IdempotentCommutativeMonoid_674
v0
  = let v1 :: T_IsIdempotentCommutativeMonoid_464
v1 = T_IdempotentCommutativeMonoid_674
-> T_IsIdempotentCommutativeMonoid_464
d_isIdempotentCommutativeMonoid_698 (T_IdempotentCommutativeMonoid_674
-> T_IdempotentCommutativeMonoid_674
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_674
v0) in
    AgdaAny -> T_IsCommutativeMagma_122
forall a b. a -> b
coe
      (let v2 :: T_IsCommutativeMonoid_406
v2
             = T_IsIdempotentCommutativeMonoid_464 -> T_IsCommutativeMonoid_406
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_474
                 (T_IsIdempotentCommutativeMonoid_464
-> T_IsIdempotentCommutativeMonoid_464
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_464
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsCommutativeSemigroup_270 -> T_IsCommutativeMagma_122)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCommutativeSemigroup_270 -> T_IsCommutativeMagma_122
MAlonzo.Code.Algebra.Structures.du_isCommutativeMagma_308
            ((T_IsCommutativeMonoid_406 -> T_IsCommutativeSemigroup_270)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsCommutativeMonoid_406 -> T_IsCommutativeSemigroup_270
MAlonzo.Code.Algebra.Structures.du_isCommutativeSemigroup_454
               (T_IsCommutativeMonoid_406 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_406
v2))))
-- Algebra.Bundles.IdempotentCommutativeMonoid._.isCommutativeMonoid
d_isCommutativeMonoid_716 ::
  T_IdempotentCommutativeMonoid_674 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMonoid_406
d_isCommutativeMonoid_716 :: T_IdempotentCommutativeMonoid_674 -> T_IsCommutativeMonoid_406
d_isCommutativeMonoid_716 T_IdempotentCommutativeMonoid_674
v0
  = (T_IsIdempotentCommutativeMonoid_464 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> T_IsCommutativeMonoid_406
forall a b. a -> b
coe
      T_IsIdempotentCommutativeMonoid_464 -> T_IsCommutativeMonoid_406
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_474
      ((T_IdempotentCommutativeMonoid_674
 -> T_IsIdempotentCommutativeMonoid_464)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_674
-> T_IsIdempotentCommutativeMonoid_464
d_isIdempotentCommutativeMonoid_698 (T_IdempotentCommutativeMonoid_674 -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_674
v0))
-- Algebra.Bundles.IdempotentCommutativeMonoid._.isCommutativeSemigroup
d_isCommutativeSemigroup_718 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentCommutativeMonoid_674 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_270
d_isCommutativeSemigroup_718 :: ()
-> ()
-> T_IdempotentCommutativeMonoid_674
-> T_IsCommutativeSemigroup_270
d_isCommutativeSemigroup_718 ~()
v0 ~()
v1 T_IdempotentCommutativeMonoid_674
v2
  = T_IdempotentCommutativeMonoid_674 -> T_IsCommutativeSemigroup_270
du_isCommutativeSemigroup_718 T_IdempotentCommutativeMonoid_674
v2
du_isCommutativeSemigroup_718 ::
  T_IdempotentCommutativeMonoid_674 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_270
du_isCommutativeSemigroup_718 :: T_IdempotentCommutativeMonoid_674 -> T_IsCommutativeSemigroup_270
du_isCommutativeSemigroup_718 T_IdempotentCommutativeMonoid_674
v0
  = let v1 :: T_IsIdempotentCommutativeMonoid_464
v1 = T_IdempotentCommutativeMonoid_674
-> T_IsIdempotentCommutativeMonoid_464
d_isIdempotentCommutativeMonoid_698 (T_IdempotentCommutativeMonoid_674
-> T_IdempotentCommutativeMonoid_674
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_674
v0) in
    AgdaAny -> T_IsCommutativeSemigroup_270
forall a b. a -> b
coe
      ((T_IsCommutativeMonoid_406 -> T_IsCommutativeSemigroup_270)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCommutativeMonoid_406 -> T_IsCommutativeSemigroup_270
MAlonzo.Code.Algebra.Structures.du_isCommutativeSemigroup_454
         ((T_IsIdempotentCommutativeMonoid_464 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsIdempotentCommutativeMonoid_464 -> T_IsCommutativeMonoid_406
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_474
            (T_IsIdempotentCommutativeMonoid_464 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_464
v1)))
-- Algebra.Bundles.IdempotentCommutativeMonoid._.isEquivalence
d_isEquivalence_720 ::
  T_IdempotentCommutativeMonoid_674 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_720 :: T_IdempotentCommutativeMonoid_674 -> T_IsEquivalence_26
d_isEquivalence_720 T_IdempotentCommutativeMonoid_674
v0
  = (T_IsMagma_86 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      T_IsMagma_86 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_94
      ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202
         ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368
            ((T_IsCommutativeMonoid_406 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsCommutativeMonoid_406 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_416
               ((T_IsIdempotentCommutativeMonoid_464 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsIdempotentCommutativeMonoid_464 -> T_IsCommutativeMonoid_406
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_474
                  ((T_IdempotentCommutativeMonoid_674
 -> T_IsIdempotentCommutativeMonoid_464)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_674
-> T_IsIdempotentCommutativeMonoid_464
d_isIdempotentCommutativeMonoid_698 (T_IdempotentCommutativeMonoid_674 -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_674
v0))))))
-- Algebra.Bundles.IdempotentCommutativeMonoid._.isMagma
d_isMagma_722 ::
  T_IdempotentCommutativeMonoid_674 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_86
d_isMagma_722 :: T_IdempotentCommutativeMonoid_674 -> T_IsMagma_86
d_isMagma_722 T_IdempotentCommutativeMonoid_674
v0
  = (T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> T_IsMagma_86
forall a b. a -> b
coe
      T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202
      ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368
         ((T_IsCommutativeMonoid_406 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCommutativeMonoid_406 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_416
            ((T_IsIdempotentCommutativeMonoid_464 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsIdempotentCommutativeMonoid_464 -> T_IsCommutativeMonoid_406
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_474
               ((T_IdempotentCommutativeMonoid_674
 -> T_IsIdempotentCommutativeMonoid_464)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_674
-> T_IsIdempotentCommutativeMonoid_464
d_isIdempotentCommutativeMonoid_698 (T_IdempotentCommutativeMonoid_674 -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_674
v0)))))
-- Algebra.Bundles.IdempotentCommutativeMonoid._.isMonoid
d_isMonoid_724 ::
  T_IdempotentCommutativeMonoid_674 ->
  MAlonzo.Code.Algebra.Structures.T_IsMonoid_358
d_isMonoid_724 :: T_IdempotentCommutativeMonoid_674 -> T_IsMonoid_358
d_isMonoid_724 T_IdempotentCommutativeMonoid_674
v0
  = (T_IsCommutativeMonoid_406 -> T_IsMonoid_358)
-> AgdaAny -> T_IsMonoid_358
forall a b. a -> b
coe
      T_IsCommutativeMonoid_406 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_416
      ((T_IsIdempotentCommutativeMonoid_464 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsIdempotentCommutativeMonoid_464 -> T_IsCommutativeMonoid_406
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_474
         ((T_IdempotentCommutativeMonoid_674
 -> T_IsIdempotentCommutativeMonoid_464)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_674
-> T_IsIdempotentCommutativeMonoid_464
d_isIdempotentCommutativeMonoid_698 (T_IdempotentCommutativeMonoid_674 -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_674
v0)))
-- Algebra.Bundles.IdempotentCommutativeMonoid._.isPartialEquivalence
d_isPartialEquivalence_726 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentCommutativeMonoid_674 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_726 :: ()
-> ()
-> T_IdempotentCommutativeMonoid_674
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_726 ~()
v0 ~()
v1 T_IdempotentCommutativeMonoid_674
v2
  = T_IdempotentCommutativeMonoid_674 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_726 T_IdempotentCommutativeMonoid_674
v2
du_isPartialEquivalence_726 ::
  T_IdempotentCommutativeMonoid_674 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_726 :: T_IdempotentCommutativeMonoid_674 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_726 T_IdempotentCommutativeMonoid_674
v0
  = let v1 :: T_IsIdempotentCommutativeMonoid_464
v1 = T_IdempotentCommutativeMonoid_674
-> T_IsIdempotentCommutativeMonoid_464
d_isIdempotentCommutativeMonoid_698 (T_IdempotentCommutativeMonoid_674
-> T_IdempotentCommutativeMonoid_674
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_674
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsCommutativeMonoid_406
v2
             = T_IsIdempotentCommutativeMonoid_464 -> T_IsCommutativeMonoid_406
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_474
                 (T_IsIdempotentCommutativeMonoid_464
-> T_IsIdempotentCommutativeMonoid_464
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_464
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsMonoid_358
v3
                = T_IsCommutativeMonoid_406 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_416 (T_IsCommutativeMonoid_406 -> T_IsCommutativeMonoid_406
forall a b. a -> b
coe T_IsCommutativeMonoid_406
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsSemigroup_194
v4
                   = T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368 (T_IsMonoid_358 -> T_IsMonoid_358
forall a b. a -> b
coe T_IsMonoid_358
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsMagma_86
v5 = T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202 (T_IsSemigroup_194 -> T_IsSemigroup_194
forall a b. a -> b
coe T_IsSemigroup_194
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_86 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsMagma_86 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_94 (T_IsMagma_86 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86
v5)))))))
-- Algebra.Bundles.IdempotentCommutativeMonoid._.isSemigroup
d_isSemigroup_728 ::
  T_IdempotentCommutativeMonoid_674 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_194
d_isSemigroup_728 :: T_IdempotentCommutativeMonoid_674 -> T_IsSemigroup_194
d_isSemigroup_728 T_IdempotentCommutativeMonoid_674
v0
  = (T_IsMonoid_358 -> T_IsSemigroup_194)
-> AgdaAny -> T_IsSemigroup_194
forall a b. a -> b
coe
      T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368
      ((T_IsCommutativeMonoid_406 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCommutativeMonoid_406 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_416
         ((T_IsIdempotentCommutativeMonoid_464 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsIdempotentCommutativeMonoid_464 -> T_IsCommutativeMonoid_406
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_474
            ((T_IdempotentCommutativeMonoid_674
 -> T_IsIdempotentCommutativeMonoid_464)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_674
-> T_IsIdempotentCommutativeMonoid_464
d_isIdempotentCommutativeMonoid_698 (T_IdempotentCommutativeMonoid_674 -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_674
v0))))
-- Algebra.Bundles.IdempotentCommutativeMonoid._.refl
d_refl_730 ::
  T_IdempotentCommutativeMonoid_674 -> AgdaAny -> AgdaAny
d_refl_730 :: T_IdempotentCommutativeMonoid_674 -> AgdaAny -> AgdaAny
d_refl_730 T_IdempotentCommutativeMonoid_674
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_86 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_86 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_94
         ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202
            ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368
               ((T_IsCommutativeMonoid_406 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsCommutativeMonoid_406 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_416
                  ((T_IsIdempotentCommutativeMonoid_464 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsIdempotentCommutativeMonoid_464 -> T_IsCommutativeMonoid_406
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_474
                     ((T_IdempotentCommutativeMonoid_674
 -> T_IsIdempotentCommutativeMonoid_464)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_674
-> T_IsIdempotentCommutativeMonoid_464
d_isIdempotentCommutativeMonoid_698 (T_IdempotentCommutativeMonoid_674 -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_674
v0)))))))
-- Algebra.Bundles.IdempotentCommutativeMonoid._.reflexive
d_reflexive_732 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentCommutativeMonoid_674 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_732 :: ()
-> ()
-> T_IdempotentCommutativeMonoid_674
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_732 ~()
v0 ~()
v1 T_IdempotentCommutativeMonoid_674
v2 = T_IdempotentCommutativeMonoid_674
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_732 T_IdempotentCommutativeMonoid_674
v2
du_reflexive_732 ::
  T_IdempotentCommutativeMonoid_674 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_732 :: T_IdempotentCommutativeMonoid_674
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_732 T_IdempotentCommutativeMonoid_674
v0
  = let v1 :: T_IsIdempotentCommutativeMonoid_464
v1 = T_IdempotentCommutativeMonoid_674
-> T_IsIdempotentCommutativeMonoid_464
d_isIdempotentCommutativeMonoid_698 (T_IdempotentCommutativeMonoid_674
-> T_IdempotentCommutativeMonoid_674
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_674
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsCommutativeMonoid_406
v2
             = T_IsIdempotentCommutativeMonoid_464 -> T_IsCommutativeMonoid_406
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_474
                 (T_IsIdempotentCommutativeMonoid_464
-> T_IsIdempotentCommutativeMonoid_464
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_464
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsMonoid_358
v3
                = T_IsCommutativeMonoid_406 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_416 (T_IsCommutativeMonoid_406 -> T_IsCommutativeMonoid_406
forall a b. a -> b
coe T_IsCommutativeMonoid_406
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsSemigroup_194
v4
                   = T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368 (T_IsMonoid_358 -> T_IsMonoid_358
forall a b. a -> b
coe T_IsMonoid_358
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsMagma_86
v5 = T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202 (T_IsSemigroup_194 -> T_IsSemigroup_194
forall a b. a -> b
coe T_IsSemigroup_194
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_86 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_94 (T_IsMagma_86 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86
v5))
                       AgdaAny
v6)))))
-- Algebra.Bundles.IdempotentCommutativeMonoid._.setoid
d_setoid_734 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentCommutativeMonoid_674 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_734 :: () -> () -> T_IdempotentCommutativeMonoid_674 -> T_Setoid_44
d_setoid_734 ~()
v0 ~()
v1 T_IdempotentCommutativeMonoid_674
v2 = T_IdempotentCommutativeMonoid_674 -> T_Setoid_44
du_setoid_734 T_IdempotentCommutativeMonoid_674
v2
du_setoid_734 ::
  T_IdempotentCommutativeMonoid_674 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_734 :: T_IdempotentCommutativeMonoid_674 -> T_Setoid_44
du_setoid_734 T_IdempotentCommutativeMonoid_674
v0
  = let v1 :: T_IsIdempotentCommutativeMonoid_464
v1 = T_IdempotentCommutativeMonoid_674
-> T_IsIdempotentCommutativeMonoid_464
d_isIdempotentCommutativeMonoid_698 (T_IdempotentCommutativeMonoid_674
-> T_IdempotentCommutativeMonoid_674
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_674
v0) in
    AgdaAny -> T_Setoid_44
forall a b. a -> b
coe
      (let v2 :: T_IsCommutativeMonoid_406
v2
             = T_IsIdempotentCommutativeMonoid_464 -> T_IsCommutativeMonoid_406
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_474
                 (T_IsIdempotentCommutativeMonoid_464
-> T_IsIdempotentCommutativeMonoid_464
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_464
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsMonoid_358
v3
                = T_IsCommutativeMonoid_406 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_416 (T_IsCommutativeMonoid_406 -> T_IsCommutativeMonoid_406
forall a b. a -> b
coe T_IsCommutativeMonoid_406
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsSemigroup_194
v4
                   = T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368 (T_IsMonoid_358 -> T_IsMonoid_358
forall a b. a -> b
coe T_IsMonoid_358
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               ((T_IsMagma_86 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsMagma_86 -> T_Setoid_44
MAlonzo.Code.Algebra.Structures.du_setoid_110
                  ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202 (T_IsSemigroup_194 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194
v4))))))
-- Algebra.Bundles.IdempotentCommutativeMonoid._.sym
d_sym_736 ::
  T_IdempotentCommutativeMonoid_674 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_736 :: T_IdempotentCommutativeMonoid_674
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_736 T_IdempotentCommutativeMonoid_674
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_86 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_86 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_94
         ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202
            ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368
               ((T_IsCommutativeMonoid_406 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsCommutativeMonoid_406 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_416
                  ((T_IsIdempotentCommutativeMonoid_464 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsIdempotentCommutativeMonoid_464 -> T_IsCommutativeMonoid_406
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_474
                     ((T_IdempotentCommutativeMonoid_674
 -> T_IsIdempotentCommutativeMonoid_464)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_674
-> T_IsIdempotentCommutativeMonoid_464
d_isIdempotentCommutativeMonoid_698 (T_IdempotentCommutativeMonoid_674 -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_674
v0)))))))
-- Algebra.Bundles.IdempotentCommutativeMonoid._.trans
d_trans_738 ::
  T_IdempotentCommutativeMonoid_674 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_738 :: T_IdempotentCommutativeMonoid_674
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_738 T_IdempotentCommutativeMonoid_674
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_86 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_86 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_94
         ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202
            ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368
               ((T_IsCommutativeMonoid_406 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsCommutativeMonoid_406 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_416
                  ((T_IsIdempotentCommutativeMonoid_464 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsIdempotentCommutativeMonoid_464 -> T_IsCommutativeMonoid_406
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_474
                     ((T_IdempotentCommutativeMonoid_674
 -> T_IsIdempotentCommutativeMonoid_464)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_674
-> T_IsIdempotentCommutativeMonoid_464
d_isIdempotentCommutativeMonoid_698 (T_IdempotentCommutativeMonoid_674 -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_674
v0)))))))
-- Algebra.Bundles.IdempotentCommutativeMonoid._.∙-cong
d_'8729''45'cong_740 ::
  T_IdempotentCommutativeMonoid_674 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_740 :: T_IdempotentCommutativeMonoid_674
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_740 T_IdempotentCommutativeMonoid_674
v0
  = (T_IsMagma_86
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsMagma_86
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_96
      ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202
         ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368
            ((T_IsCommutativeMonoid_406 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsCommutativeMonoid_406 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_416
               ((T_IsIdempotentCommutativeMonoid_464 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsIdempotentCommutativeMonoid_464 -> T_IsCommutativeMonoid_406
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_474
                  ((T_IdempotentCommutativeMonoid_674
 -> T_IsIdempotentCommutativeMonoid_464)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_674
-> T_IsIdempotentCommutativeMonoid_464
d_isIdempotentCommutativeMonoid_698 (T_IdempotentCommutativeMonoid_674 -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_674
v0))))))
-- Algebra.Bundles.IdempotentCommutativeMonoid._.∙-congʳ
d_'8729''45'cong'691'_742 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentCommutativeMonoid_674 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_742 :: ()
-> ()
-> T_IdempotentCommutativeMonoid_674
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_742 ~()
v0 ~()
v1 T_IdempotentCommutativeMonoid_674
v2
  = T_IdempotentCommutativeMonoid_674
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_742 T_IdempotentCommutativeMonoid_674
v2
du_'8729''45'cong'691'_742 ::
  T_IdempotentCommutativeMonoid_674 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_742 :: T_IdempotentCommutativeMonoid_674
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_742 T_IdempotentCommutativeMonoid_674
v0
  = let v1 :: T_IsIdempotentCommutativeMonoid_464
v1 = T_IdempotentCommutativeMonoid_674
-> T_IsIdempotentCommutativeMonoid_464
d_isIdempotentCommutativeMonoid_698 (T_IdempotentCommutativeMonoid_674
-> T_IdempotentCommutativeMonoid_674
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_674
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsCommutativeMonoid_406
v2
             = T_IsIdempotentCommutativeMonoid_464 -> T_IsCommutativeMonoid_406
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_474
                 (T_IsIdempotentCommutativeMonoid_464
-> T_IsIdempotentCommutativeMonoid_464
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_464
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsMonoid_358
v3
                = T_IsCommutativeMonoid_406 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_416 (T_IsCommutativeMonoid_406 -> T_IsCommutativeMonoid_406
forall a b. a -> b
coe T_IsCommutativeMonoid_406
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsSemigroup_194
v4
                   = T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368 (T_IsMonoid_358 -> T_IsMonoid_358
forall a b. a -> b
coe T_IsMonoid_358
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               ((T_IsMagma_86
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsMagma_86 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'691'_116
                  ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202 (T_IsSemigroup_194 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194
v4))))))
-- Algebra.Bundles.IdempotentCommutativeMonoid._.∙-congˡ
d_'8729''45'cong'737'_744 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentCommutativeMonoid_674 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_744 :: ()
-> ()
-> T_IdempotentCommutativeMonoid_674
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_744 ~()
v0 ~()
v1 T_IdempotentCommutativeMonoid_674
v2
  = T_IdempotentCommutativeMonoid_674
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_744 T_IdempotentCommutativeMonoid_674
v2
du_'8729''45'cong'737'_744 ::
  T_IdempotentCommutativeMonoid_674 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_744 :: T_IdempotentCommutativeMonoid_674
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_744 T_IdempotentCommutativeMonoid_674
v0
  = let v1 :: T_IsIdempotentCommutativeMonoid_464
v1 = T_IdempotentCommutativeMonoid_674
-> T_IsIdempotentCommutativeMonoid_464
d_isIdempotentCommutativeMonoid_698 (T_IdempotentCommutativeMonoid_674
-> T_IdempotentCommutativeMonoid_674
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_674
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsCommutativeMonoid_406
v2
             = T_IsIdempotentCommutativeMonoid_464 -> T_IsCommutativeMonoid_406
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_474
                 (T_IsIdempotentCommutativeMonoid_464
-> T_IsIdempotentCommutativeMonoid_464
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_464
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsMonoid_358
v3
                = T_IsCommutativeMonoid_406 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_416 (T_IsCommutativeMonoid_406 -> T_IsCommutativeMonoid_406
forall a b. a -> b
coe T_IsCommutativeMonoid_406
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsSemigroup_194
v4
                   = T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368 (T_IsMonoid_358 -> T_IsMonoid_358
forall a b. a -> b
coe T_IsMonoid_358
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               ((T_IsMagma_86
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsMagma_86 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'737'_112
                  ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202 (T_IsSemigroup_194 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194
v4))))))
-- Algebra.Bundles.IdempotentCommutativeMonoid.commutativeMonoid
d_commutativeMonoid_746 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentCommutativeMonoid_674 -> T_CommutativeMonoid_582
d_commutativeMonoid_746 :: ()
-> ()
-> T_IdempotentCommutativeMonoid_674
-> T_CommutativeMonoid_582
d_commutativeMonoid_746 ~()
v0 ~()
v1 T_IdempotentCommutativeMonoid_674
v2 = T_IdempotentCommutativeMonoid_674 -> T_CommutativeMonoid_582
du_commutativeMonoid_746 T_IdempotentCommutativeMonoid_674
v2
du_commutativeMonoid_746 ::
  T_IdempotentCommutativeMonoid_674 -> T_CommutativeMonoid_582
du_commutativeMonoid_746 :: T_IdempotentCommutativeMonoid_674 -> T_CommutativeMonoid_582
du_commutativeMonoid_746 T_IdempotentCommutativeMonoid_674
v0
  = ((AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny -> T_IsCommutativeMonoid_406 -> T_CommutativeMonoid_582)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsCommutativeMonoid_406
-> T_CommutativeMonoid_582
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> T_IsCommutativeMonoid_406 -> T_CommutativeMonoid_582
C_CommutativeMonoid'46'constructor_10343 (T_IdempotentCommutativeMonoid_674 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__694 (T_IdempotentCommutativeMonoid_674
-> T_IdempotentCommutativeMonoid_674
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_674
v0))
      (T_IdempotentCommutativeMonoid_674 -> AgdaAny
d_ε_696 (T_IdempotentCommutativeMonoid_674
-> T_IdempotentCommutativeMonoid_674
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_674
v0))
      (T_IsIdempotentCommutativeMonoid_464 -> T_IsCommutativeMonoid_406
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_474
         ((T_IdempotentCommutativeMonoid_674
 -> T_IsIdempotentCommutativeMonoid_464)
-> AgdaAny -> T_IsIdempotentCommutativeMonoid_464
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_674
-> T_IsIdempotentCommutativeMonoid_464
d_isIdempotentCommutativeMonoid_698 (T_IdempotentCommutativeMonoid_674 -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_674
v0)))
-- Algebra.Bundles.IdempotentCommutativeMonoid._._≉_
d__'8777'__750 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentCommutativeMonoid_674 -> AgdaAny -> AgdaAny -> ()
d__'8777'__750 :: ()
-> ()
-> T_IdempotentCommutativeMonoid_674
-> AgdaAny
-> AgdaAny
-> ()
d__'8777'__750 = ()
-> ()
-> T_IdempotentCommutativeMonoid_674
-> AgdaAny
-> AgdaAny
-> ()
forall a. a
erased
-- Algebra.Bundles.IdempotentCommutativeMonoid._.commutativeMagma
d_commutativeMagma_752 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentCommutativeMonoid_674 -> T_CommutativeMagma_148
d_commutativeMagma_752 :: ()
-> ()
-> T_IdempotentCommutativeMonoid_674
-> T_CommutativeMagma_148
d_commutativeMagma_752 ~()
v0 ~()
v1 T_IdempotentCommutativeMonoid_674
v2 = T_IdempotentCommutativeMonoid_674 -> T_CommutativeMagma_148
du_commutativeMagma_752 T_IdempotentCommutativeMonoid_674
v2
du_commutativeMagma_752 ::
  T_IdempotentCommutativeMonoid_674 -> T_CommutativeMagma_148
du_commutativeMagma_752 :: T_IdempotentCommutativeMonoid_674 -> T_CommutativeMagma_148
du_commutativeMagma_752 T_IdempotentCommutativeMonoid_674
v0
  = let v1 :: t
v1 = (T_IdempotentCommutativeMonoid_674 -> T_CommutativeMonoid_582)
-> AgdaAny -> t
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_674 -> T_CommutativeMonoid_582
du_commutativeMonoid_746 (T_IdempotentCommutativeMonoid_674 -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_674
v0) in
    AgdaAny -> T_CommutativeMagma_148
forall a b. a -> b
coe
      ((T_CommutativeSemigroup_332 -> T_CommutativeMagma_148)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_CommutativeSemigroup_332 -> T_CommutativeMagma_148
du_commutativeMagma_396 ((T_CommutativeMonoid_582 -> T_CommutativeSemigroup_332)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeMonoid_582 -> T_CommutativeSemigroup_332
du_commutativeSemigroup_664 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1)))
-- Algebra.Bundles.IdempotentCommutativeMonoid._.commutativeSemigroup
d_commutativeSemigroup_754 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentCommutativeMonoid_674 -> T_CommutativeSemigroup_332
d_commutativeSemigroup_754 :: ()
-> ()
-> T_IdempotentCommutativeMonoid_674
-> T_CommutativeSemigroup_332
d_commutativeSemigroup_754 ~()
v0 ~()
v1 T_IdempotentCommutativeMonoid_674
v2
  = T_IdempotentCommutativeMonoid_674 -> T_CommutativeSemigroup_332
du_commutativeSemigroup_754 T_IdempotentCommutativeMonoid_674
v2
du_commutativeSemigroup_754 ::
  T_IdempotentCommutativeMonoid_674 -> T_CommutativeSemigroup_332
du_commutativeSemigroup_754 :: T_IdempotentCommutativeMonoid_674 -> T_CommutativeSemigroup_332
du_commutativeSemigroup_754 T_IdempotentCommutativeMonoid_674
v0
  = (T_CommutativeMonoid_582 -> T_CommutativeSemigroup_332)
-> AgdaAny -> T_CommutativeSemigroup_332
forall a b. a -> b
coe
      T_CommutativeMonoid_582 -> T_CommutativeSemigroup_332
du_commutativeSemigroup_664 ((T_IdempotentCommutativeMonoid_674 -> T_CommutativeMonoid_582)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_674 -> T_CommutativeMonoid_582
du_commutativeMonoid_746 (T_IdempotentCommutativeMonoid_674 -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_674
v0))
-- Algebra.Bundles.IdempotentCommutativeMonoid._.magma
d_magma_756 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentCommutativeMonoid_674 -> T_Magma_36
d_magma_756 :: () -> () -> T_IdempotentCommutativeMonoid_674 -> T_Magma_36
d_magma_756 ~()
v0 ~()
v1 T_IdempotentCommutativeMonoid_674
v2 = T_IdempotentCommutativeMonoid_674 -> T_Magma_36
du_magma_756 T_IdempotentCommutativeMonoid_674
v2
du_magma_756 :: T_IdempotentCommutativeMonoid_674 -> T_Magma_36
du_magma_756 :: T_IdempotentCommutativeMonoid_674 -> T_Magma_36
du_magma_756 T_IdempotentCommutativeMonoid_674
v0
  = let v1 :: t
v1 = (T_IdempotentCommutativeMonoid_674 -> T_CommutativeMonoid_582)
-> AgdaAny -> t
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_674 -> T_CommutativeMonoid_582
du_commutativeMonoid_746 (T_IdempotentCommutativeMonoid_674 -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_674
v0) in
    AgdaAny -> T_Magma_36
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_CommutativeMonoid_582 -> T_Monoid_506) -> AgdaAny -> t
forall a b. a -> b
coe T_CommutativeMonoid_582 -> T_Monoid_506
du_monoid_650 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_Semigroup_206 -> T_Magma_36) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semigroup_206 -> T_Magma_36
du_magma_254 ((T_Monoid_506 -> T_Semigroup_206) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Monoid_506 -> T_Semigroup_206
du_semigroup_566 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2))))
-- Algebra.Bundles.IdempotentCommutativeMonoid._.monoid
d_monoid_758 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentCommutativeMonoid_674 -> T_Monoid_506
d_monoid_758 :: () -> () -> T_IdempotentCommutativeMonoid_674 -> T_Monoid_506
d_monoid_758 ~()
v0 ~()
v1 T_IdempotentCommutativeMonoid_674
v2 = T_IdempotentCommutativeMonoid_674 -> T_Monoid_506
du_monoid_758 T_IdempotentCommutativeMonoid_674
v2
du_monoid_758 :: T_IdempotentCommutativeMonoid_674 -> T_Monoid_506
du_monoid_758 :: T_IdempotentCommutativeMonoid_674 -> T_Monoid_506
du_monoid_758 T_IdempotentCommutativeMonoid_674
v0
  = (T_CommutativeMonoid_582 -> T_Monoid_506)
-> AgdaAny -> T_Monoid_506
forall a b. a -> b
coe T_CommutativeMonoid_582 -> T_Monoid_506
du_monoid_650 ((T_IdempotentCommutativeMonoid_674 -> T_CommutativeMonoid_582)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_674 -> T_CommutativeMonoid_582
du_commutativeMonoid_746 (T_IdempotentCommutativeMonoid_674 -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_674
v0))
-- Algebra.Bundles.IdempotentCommutativeMonoid._.rawMagma
d_rawMagma_760 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentCommutativeMonoid_674 -> T_RawMagma_8
d_rawMagma_760 :: () -> () -> T_IdempotentCommutativeMonoid_674 -> T_RawMagma_8
d_rawMagma_760 ~()
v0 ~()
v1 T_IdempotentCommutativeMonoid_674
v2 = T_IdempotentCommutativeMonoid_674 -> T_RawMagma_8
du_rawMagma_760 T_IdempotentCommutativeMonoid_674
v2
du_rawMagma_760 ::
  T_IdempotentCommutativeMonoid_674 -> T_RawMagma_8
du_rawMagma_760 :: T_IdempotentCommutativeMonoid_674 -> T_RawMagma_8
du_rawMagma_760 T_IdempotentCommutativeMonoid_674
v0
  = let v1 :: t
v1 = (T_IdempotentCommutativeMonoid_674 -> T_CommutativeMonoid_582)
-> AgdaAny -> t
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_674 -> T_CommutativeMonoid_582
du_commutativeMonoid_746 (T_IdempotentCommutativeMonoid_674 -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_674
v0) in
    AgdaAny -> T_RawMagma_8
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_CommutativeMonoid_582 -> T_Monoid_506) -> AgdaAny -> t
forall a b. a -> b
coe T_CommutativeMonoid_582 -> T_Monoid_506
du_monoid_650 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: t
v3 = (T_Monoid_506 -> T_Semigroup_206) -> AgdaAny -> t
forall a b. a -> b
coe T_Monoid_506 -> T_Semigroup_206
du_semigroup_566 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_Magma_36 -> T_RawMagma_8) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Magma_36 -> T_RawMagma_8
du_rawMagma_80 ((T_Semigroup_206 -> T_Magma_36) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semigroup_206 -> T_Magma_36
du_magma_254 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3)))))
-- Algebra.Bundles.IdempotentCommutativeMonoid._.rawMonoid
d_rawMonoid_762 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentCommutativeMonoid_674 -> T_RawMonoid_474
d_rawMonoid_762 :: () -> () -> T_IdempotentCommutativeMonoid_674 -> T_RawMonoid_474
d_rawMonoid_762 ~()
v0 ~()
v1 T_IdempotentCommutativeMonoid_674
v2 = T_IdempotentCommutativeMonoid_674 -> T_RawMonoid_474
du_rawMonoid_762 T_IdempotentCommutativeMonoid_674
v2
du_rawMonoid_762 ::
  T_IdempotentCommutativeMonoid_674 -> T_RawMonoid_474
du_rawMonoid_762 :: T_IdempotentCommutativeMonoid_674 -> T_RawMonoid_474
du_rawMonoid_762 T_IdempotentCommutativeMonoid_674
v0
  = let v1 :: t
v1 = (T_IdempotentCommutativeMonoid_674 -> T_CommutativeMonoid_582)
-> AgdaAny -> t
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_674 -> T_CommutativeMonoid_582
du_commutativeMonoid_746 (T_IdempotentCommutativeMonoid_674 -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_674
v0) in
    AgdaAny -> T_RawMonoid_474
forall a b. a -> b
coe ((T_Monoid_506 -> T_RawMonoid_474) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Monoid_506 -> T_RawMonoid_474
du_rawMonoid_576 ((T_CommutativeMonoid_582 -> T_Monoid_506) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeMonoid_582 -> T_Monoid_506
du_monoid_650 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1)))
-- Algebra.Bundles.IdempotentCommutativeMonoid._.semigroup
d_semigroup_764 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentCommutativeMonoid_674 -> T_Semigroup_206
d_semigroup_764 :: () -> () -> T_IdempotentCommutativeMonoid_674 -> T_Semigroup_206
d_semigroup_764 ~()
v0 ~()
v1 T_IdempotentCommutativeMonoid_674
v2 = T_IdempotentCommutativeMonoid_674 -> T_Semigroup_206
du_semigroup_764 T_IdempotentCommutativeMonoid_674
v2
du_semigroup_764 ::
  T_IdempotentCommutativeMonoid_674 -> T_Semigroup_206
du_semigroup_764 :: T_IdempotentCommutativeMonoid_674 -> T_Semigroup_206
du_semigroup_764 T_IdempotentCommutativeMonoid_674
v0
  = let v1 :: t
v1 = (T_IdempotentCommutativeMonoid_674 -> T_CommutativeMonoid_582)
-> AgdaAny -> t
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_674 -> T_CommutativeMonoid_582
du_commutativeMonoid_746 (T_IdempotentCommutativeMonoid_674 -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_674
v0) in
    AgdaAny -> T_Semigroup_206
forall a b. a -> b
coe ((T_Monoid_506 -> T_Semigroup_206) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Monoid_506 -> T_Semigroup_206
du_semigroup_566 ((T_CommutativeMonoid_582 -> T_Monoid_506) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeMonoid_582 -> T_Monoid_506
du_monoid_650 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1)))
-- Algebra.Bundles.BoundedLattice
d_BoundedLattice_766 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 -> ()
d_BoundedLattice_766 :: () -> () -> ()
d_BoundedLattice_766 = () -> () -> ()
forall a. a
erased
-- Algebra.Bundles.BoundedLattice._∙_
d__'8729'__776 ::
  T_IdempotentCommutativeMonoid_674 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__776 :: T_IdempotentCommutativeMonoid_674 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__776 T_IdempotentCommutativeMonoid_674
v0 = (T_IdempotentCommutativeMonoid_674
 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_674 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__694 (T_IdempotentCommutativeMonoid_674 -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_674
v0)
-- Algebra.Bundles.BoundedLattice._≈_
d__'8776'__778 ::
  T_IdempotentCommutativeMonoid_674 -> AgdaAny -> AgdaAny -> ()
d__'8776'__778 :: T_IdempotentCommutativeMonoid_674 -> AgdaAny -> AgdaAny -> ()
d__'8776'__778 = T_IdempotentCommutativeMonoid_674 -> AgdaAny -> AgdaAny -> ()
forall a. a
erased
-- Algebra.Bundles.BoundedLattice._≉_
d__'8777'__780 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentCommutativeMonoid_674 -> AgdaAny -> AgdaAny -> ()
d__'8777'__780 :: ()
-> ()
-> T_IdempotentCommutativeMonoid_674
-> AgdaAny
-> AgdaAny
-> ()
d__'8777'__780 = ()
-> ()
-> T_IdempotentCommutativeMonoid_674
-> AgdaAny
-> AgdaAny
-> ()
forall a. a
erased
-- Algebra.Bundles.BoundedLattice.Carrier
d_Carrier_782 :: T_IdempotentCommutativeMonoid_674 -> ()
d_Carrier_782 :: T_IdempotentCommutativeMonoid_674 -> ()
d_Carrier_782 = T_IdempotentCommutativeMonoid_674 -> ()
forall a. a
erased
-- Algebra.Bundles.BoundedLattice.assoc
d_assoc_784 ::
  T_IdempotentCommutativeMonoid_674 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_784 :: T_IdempotentCommutativeMonoid_674
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_784 T_IdempotentCommutativeMonoid_674
v0
  = (T_IsSemigroup_194 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsSemigroup_194 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_assoc_204
      ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368
         ((T_IsCommutativeMonoid_406 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCommutativeMonoid_406 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_416
            ((T_IsIdempotentCommutativeMonoid_464 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsIdempotentCommutativeMonoid_464 -> T_IsCommutativeMonoid_406
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_474
               ((T_IdempotentCommutativeMonoid_674
 -> T_IsIdempotentCommutativeMonoid_464)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_674
-> T_IsIdempotentCommutativeMonoid_464
d_isIdempotentCommutativeMonoid_698 (T_IdempotentCommutativeMonoid_674 -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_674
v0)))))
-- Algebra.Bundles.BoundedLattice.comm
d_comm_786 ::
  T_IdempotentCommutativeMonoid_674 -> AgdaAny -> AgdaAny -> AgdaAny
d_comm_786 :: T_IdempotentCommutativeMonoid_674 -> AgdaAny -> AgdaAny -> AgdaAny
d_comm_786 T_IdempotentCommutativeMonoid_674
v0
  = (T_IsCommutativeMonoid_406 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsCommutativeMonoid_406 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_comm_418
      ((T_IsIdempotentCommutativeMonoid_464 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsIdempotentCommutativeMonoid_464 -> T_IsCommutativeMonoid_406
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_474
         ((T_IdempotentCommutativeMonoid_674
 -> T_IsIdempotentCommutativeMonoid_464)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_674
-> T_IsIdempotentCommutativeMonoid_464
d_isIdempotentCommutativeMonoid_698 (T_IdempotentCommutativeMonoid_674 -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_674
v0)))
-- Algebra.Bundles.BoundedLattice.commutativeMagma
d_commutativeMagma_788 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentCommutativeMonoid_674 -> T_CommutativeMagma_148
d_commutativeMagma_788 :: ()
-> ()
-> T_IdempotentCommutativeMonoid_674
-> T_CommutativeMagma_148
d_commutativeMagma_788 ~()
v0 ~()
v1 T_IdempotentCommutativeMonoid_674
v2 = T_IdempotentCommutativeMonoid_674 -> T_CommutativeMagma_148
du_commutativeMagma_788 T_IdempotentCommutativeMonoid_674
v2
du_commutativeMagma_788 ::
  T_IdempotentCommutativeMonoid_674 -> T_CommutativeMagma_148
du_commutativeMagma_788 :: T_IdempotentCommutativeMonoid_674 -> T_CommutativeMagma_148
du_commutativeMagma_788 T_IdempotentCommutativeMonoid_674
v0
  = let v1 :: t
v1 = (T_IdempotentCommutativeMonoid_674 -> T_CommutativeMonoid_582)
-> AgdaAny -> t
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_674 -> T_CommutativeMonoid_582
du_commutativeMonoid_746 (T_IdempotentCommutativeMonoid_674 -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_674
v0) in
    AgdaAny -> T_CommutativeMagma_148
forall a b. a -> b
coe
      ((T_CommutativeSemigroup_332 -> T_CommutativeMagma_148)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_CommutativeSemigroup_332 -> T_CommutativeMagma_148
du_commutativeMagma_396 ((T_CommutativeMonoid_582 -> T_CommutativeSemigroup_332)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeMonoid_582 -> T_CommutativeSemigroup_332
du_commutativeSemigroup_664 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1)))
-- Algebra.Bundles.BoundedLattice.commutativeMonoid
d_commutativeMonoid_790 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentCommutativeMonoid_674 -> T_CommutativeMonoid_582
d_commutativeMonoid_790 :: ()
-> ()
-> T_IdempotentCommutativeMonoid_674
-> T_CommutativeMonoid_582
d_commutativeMonoid_790 ~()
v0 ~()
v1 T_IdempotentCommutativeMonoid_674
v2 = T_IdempotentCommutativeMonoid_674 -> T_CommutativeMonoid_582
du_commutativeMonoid_790 T_IdempotentCommutativeMonoid_674
v2
du_commutativeMonoid_790 ::
  T_IdempotentCommutativeMonoid_674 -> T_CommutativeMonoid_582
du_commutativeMonoid_790 :: T_IdempotentCommutativeMonoid_674 -> T_CommutativeMonoid_582
du_commutativeMonoid_790 T_IdempotentCommutativeMonoid_674
v0 = (T_IdempotentCommutativeMonoid_674 -> T_CommutativeMonoid_582)
-> AgdaAny -> T_CommutativeMonoid_582
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_674 -> T_CommutativeMonoid_582
du_commutativeMonoid_746 (T_IdempotentCommutativeMonoid_674 -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_674
v0)
-- Algebra.Bundles.BoundedLattice.commutativeSemigroup
d_commutativeSemigroup_792 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentCommutativeMonoid_674 -> T_CommutativeSemigroup_332
d_commutativeSemigroup_792 :: ()
-> ()
-> T_IdempotentCommutativeMonoid_674
-> T_CommutativeSemigroup_332
d_commutativeSemigroup_792 ~()
v0 ~()
v1 T_IdempotentCommutativeMonoid_674
v2
  = T_IdempotentCommutativeMonoid_674 -> T_CommutativeSemigroup_332
du_commutativeSemigroup_792 T_IdempotentCommutativeMonoid_674
v2
du_commutativeSemigroup_792 ::
  T_IdempotentCommutativeMonoid_674 -> T_CommutativeSemigroup_332
du_commutativeSemigroup_792 :: T_IdempotentCommutativeMonoid_674 -> T_CommutativeSemigroup_332
du_commutativeSemigroup_792 T_IdempotentCommutativeMonoid_674
v0
  = (T_CommutativeMonoid_582 -> T_CommutativeSemigroup_332)
-> AgdaAny -> T_CommutativeSemigroup_332
forall a b. a -> b
coe
      T_CommutativeMonoid_582 -> T_CommutativeSemigroup_332
du_commutativeSemigroup_664 ((T_IdempotentCommutativeMonoid_674 -> T_CommutativeMonoid_582)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_674 -> T_CommutativeMonoid_582
du_commutativeMonoid_746 (T_IdempotentCommutativeMonoid_674 -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_674
v0))
-- Algebra.Bundles.BoundedLattice.idem
d_idem_794 ::
  T_IdempotentCommutativeMonoid_674 -> AgdaAny -> AgdaAny
d_idem_794 :: T_IdempotentCommutativeMonoid_674 -> AgdaAny -> AgdaAny
d_idem_794 T_IdempotentCommutativeMonoid_674
v0
  = (T_IsIdempotentCommutativeMonoid_464 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsIdempotentCommutativeMonoid_464 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_idem_476
      ((T_IdempotentCommutativeMonoid_674
 -> T_IsIdempotentCommutativeMonoid_464)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_674
-> T_IsIdempotentCommutativeMonoid_464
d_isIdempotentCommutativeMonoid_698 (T_IdempotentCommutativeMonoid_674 -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_674
v0))
-- Algebra.Bundles.BoundedLattice.identity
d_identity_796 ::
  T_IdempotentCommutativeMonoid_674 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_identity_796 :: T_IdempotentCommutativeMonoid_674 -> T_Σ_14
d_identity_796 T_IdempotentCommutativeMonoid_674
v0
  = (T_IsMonoid_358 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsMonoid_358 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_identity_370
      ((T_IsCommutativeMonoid_406 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCommutativeMonoid_406 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_416
         ((T_IsIdempotentCommutativeMonoid_464 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsIdempotentCommutativeMonoid_464 -> T_IsCommutativeMonoid_406
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_474
            ((T_IdempotentCommutativeMonoid_674
 -> T_IsIdempotentCommutativeMonoid_464)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_674
-> T_IsIdempotentCommutativeMonoid_464
d_isIdempotentCommutativeMonoid_698 (T_IdempotentCommutativeMonoid_674 -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_674
v0))))
-- Algebra.Bundles.BoundedLattice.identityʳ
d_identity'691'_798 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentCommutativeMonoid_674 -> AgdaAny -> AgdaAny
d_identity'691'_798 :: () -> () -> T_IdempotentCommutativeMonoid_674 -> AgdaAny -> AgdaAny
d_identity'691'_798 ~()
v0 ~()
v1 T_IdempotentCommutativeMonoid_674
v2 = T_IdempotentCommutativeMonoid_674 -> AgdaAny -> AgdaAny
du_identity'691'_798 T_IdempotentCommutativeMonoid_674
v2
du_identity'691'_798 ::
  T_IdempotentCommutativeMonoid_674 -> AgdaAny -> AgdaAny
du_identity'691'_798 :: T_IdempotentCommutativeMonoid_674 -> AgdaAny -> AgdaAny
du_identity'691'_798 T_IdempotentCommutativeMonoid_674
v0
  = let v1 :: T_IsIdempotentCommutativeMonoid_464
v1 = T_IdempotentCommutativeMonoid_674
-> T_IsIdempotentCommutativeMonoid_464
d_isIdempotentCommutativeMonoid_698 (T_IdempotentCommutativeMonoid_674
-> T_IdempotentCommutativeMonoid_674
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_674
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsCommutativeMonoid_406
v2
             = T_IsIdempotentCommutativeMonoid_464 -> T_IsCommutativeMonoid_406
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_474
                 (T_IsIdempotentCommutativeMonoid_464
-> T_IsIdempotentCommutativeMonoid_464
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_464
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsMonoid_358 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoid_358 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_identity'691'_400
            ((T_IsCommutativeMonoid_406 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_406 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_416 (T_IsCommutativeMonoid_406 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_406
v2))))
-- Algebra.Bundles.BoundedLattice.identityˡ
d_identity'737'_800 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentCommutativeMonoid_674 -> AgdaAny -> AgdaAny
d_identity'737'_800 :: () -> () -> T_IdempotentCommutativeMonoid_674 -> AgdaAny -> AgdaAny
d_identity'737'_800 ~()
v0 ~()
v1 T_IdempotentCommutativeMonoid_674
v2 = T_IdempotentCommutativeMonoid_674 -> AgdaAny -> AgdaAny
du_identity'737'_800 T_IdempotentCommutativeMonoid_674
v2
du_identity'737'_800 ::
  T_IdempotentCommutativeMonoid_674 -> AgdaAny -> AgdaAny
du_identity'737'_800 :: T_IdempotentCommutativeMonoid_674 -> AgdaAny -> AgdaAny
du_identity'737'_800 T_IdempotentCommutativeMonoid_674
v0
  = let v1 :: T_IsIdempotentCommutativeMonoid_464
v1 = T_IdempotentCommutativeMonoid_674
-> T_IsIdempotentCommutativeMonoid_464
d_isIdempotentCommutativeMonoid_698 (T_IdempotentCommutativeMonoid_674
-> T_IdempotentCommutativeMonoid_674
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_674
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsCommutativeMonoid_406
v2
             = T_IsIdempotentCommutativeMonoid_464 -> T_IsCommutativeMonoid_406
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_474
                 (T_IsIdempotentCommutativeMonoid_464
-> T_IsIdempotentCommutativeMonoid_464
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_464
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsMonoid_358 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoid_358 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_identity'737'_398
            ((T_IsCommutativeMonoid_406 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_406 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_416 (T_IsCommutativeMonoid_406 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_406
v2))))
-- Algebra.Bundles.BoundedLattice.isCommutativeMagma
d_isCommutativeMagma_802 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentCommutativeMonoid_674 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMagma_122
d_isCommutativeMagma_802 :: ()
-> ()
-> T_IdempotentCommutativeMonoid_674
-> T_IsCommutativeMagma_122
d_isCommutativeMagma_802 ~()
v0 ~()
v1 T_IdempotentCommutativeMonoid_674
v2 = T_IdempotentCommutativeMonoid_674 -> T_IsCommutativeMagma_122
du_isCommutativeMagma_802 T_IdempotentCommutativeMonoid_674
v2
du_isCommutativeMagma_802 ::
  T_IdempotentCommutativeMonoid_674 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMagma_122
du_isCommutativeMagma_802 :: T_IdempotentCommutativeMonoid_674 -> T_IsCommutativeMagma_122
du_isCommutativeMagma_802 T_IdempotentCommutativeMonoid_674
v0
  = let v1 :: T_IsIdempotentCommutativeMonoid_464
v1 = T_IdempotentCommutativeMonoid_674
-> T_IsIdempotentCommutativeMonoid_464
d_isIdempotentCommutativeMonoid_698 (T_IdempotentCommutativeMonoid_674
-> T_IdempotentCommutativeMonoid_674
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_674
v0) in
    AgdaAny -> T_IsCommutativeMagma_122
forall a b. a -> b
coe
      (let v2 :: T_IsCommutativeMonoid_406
v2
             = T_IsIdempotentCommutativeMonoid_464 -> T_IsCommutativeMonoid_406
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_474
                 (T_IsIdempotentCommutativeMonoid_464
-> T_IsIdempotentCommutativeMonoid_464
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_464
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsCommutativeSemigroup_270 -> T_IsCommutativeMagma_122)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCommutativeSemigroup_270 -> T_IsCommutativeMagma_122
MAlonzo.Code.Algebra.Structures.du_isCommutativeMagma_308
            ((T_IsCommutativeMonoid_406 -> T_IsCommutativeSemigroup_270)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsCommutativeMonoid_406 -> T_IsCommutativeSemigroup_270
MAlonzo.Code.Algebra.Structures.du_isCommutativeSemigroup_454
               (T_IsCommutativeMonoid_406 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_406
v2))))
-- Algebra.Bundles.BoundedLattice.isCommutativeMonoid
d_isCommutativeMonoid_804 ::
  T_IdempotentCommutativeMonoid_674 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMonoid_406
d_isCommutativeMonoid_804 :: T_IdempotentCommutativeMonoid_674 -> T_IsCommutativeMonoid_406
d_isCommutativeMonoid_804 T_IdempotentCommutativeMonoid_674
v0
  = (T_IsIdempotentCommutativeMonoid_464 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> T_IsCommutativeMonoid_406
forall a b. a -> b
coe
      T_IsIdempotentCommutativeMonoid_464 -> T_IsCommutativeMonoid_406
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_474
      ((T_IdempotentCommutativeMonoid_674
 -> T_IsIdempotentCommutativeMonoid_464)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_674
-> T_IsIdempotentCommutativeMonoid_464
d_isIdempotentCommutativeMonoid_698 (T_IdempotentCommutativeMonoid_674 -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_674
v0))
-- Algebra.Bundles.BoundedLattice.isCommutativeSemigroup
d_isCommutativeSemigroup_806 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentCommutativeMonoid_674 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_270
d_isCommutativeSemigroup_806 :: ()
-> ()
-> T_IdempotentCommutativeMonoid_674
-> T_IsCommutativeSemigroup_270
d_isCommutativeSemigroup_806 ~()
v0 ~()
v1 T_IdempotentCommutativeMonoid_674
v2
  = T_IdempotentCommutativeMonoid_674 -> T_IsCommutativeSemigroup_270
du_isCommutativeSemigroup_806 T_IdempotentCommutativeMonoid_674
v2
du_isCommutativeSemigroup_806 ::
  T_IdempotentCommutativeMonoid_674 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_270
du_isCommutativeSemigroup_806 :: T_IdempotentCommutativeMonoid_674 -> T_IsCommutativeSemigroup_270
du_isCommutativeSemigroup_806 T_IdempotentCommutativeMonoid_674
v0
  = let v1 :: T_IsIdempotentCommutativeMonoid_464
v1 = T_IdempotentCommutativeMonoid_674
-> T_IsIdempotentCommutativeMonoid_464
d_isIdempotentCommutativeMonoid_698 (T_IdempotentCommutativeMonoid_674
-> T_IdempotentCommutativeMonoid_674
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_674
v0) in
    AgdaAny -> T_IsCommutativeSemigroup_270
forall a b. a -> b
coe
      ((T_IsCommutativeMonoid_406 -> T_IsCommutativeSemigroup_270)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCommutativeMonoid_406 -> T_IsCommutativeSemigroup_270
MAlonzo.Code.Algebra.Structures.du_isCommutativeSemigroup_454
         ((T_IsIdempotentCommutativeMonoid_464 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsIdempotentCommutativeMonoid_464 -> T_IsCommutativeMonoid_406
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_474
            (T_IsIdempotentCommutativeMonoid_464 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_464
v1)))
-- Algebra.Bundles.BoundedLattice.isEquivalence
d_isEquivalence_808 ::
  T_IdempotentCommutativeMonoid_674 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_808 :: T_IdempotentCommutativeMonoid_674 -> T_IsEquivalence_26
d_isEquivalence_808 T_IdempotentCommutativeMonoid_674
v0
  = (T_IsMagma_86 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      T_IsMagma_86 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_94
      ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202
         ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368
            ((T_IsCommutativeMonoid_406 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsCommutativeMonoid_406 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_416
               ((T_IsIdempotentCommutativeMonoid_464 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsIdempotentCommutativeMonoid_464 -> T_IsCommutativeMonoid_406
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_474
                  ((T_IdempotentCommutativeMonoid_674
 -> T_IsIdempotentCommutativeMonoid_464)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_674
-> T_IsIdempotentCommutativeMonoid_464
d_isIdempotentCommutativeMonoid_698 (T_IdempotentCommutativeMonoid_674 -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_674
v0))))))
-- Algebra.Bundles.BoundedLattice.isIdempotentCommutativeMonoid
d_isIdempotentCommutativeMonoid_810 ::
  T_IdempotentCommutativeMonoid_674 ->
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_464
d_isIdempotentCommutativeMonoid_810 :: T_IdempotentCommutativeMonoid_674
-> T_IsIdempotentCommutativeMonoid_464
d_isIdempotentCommutativeMonoid_810 T_IdempotentCommutativeMonoid_674
v0
  = (T_IdempotentCommutativeMonoid_674
 -> T_IsIdempotentCommutativeMonoid_464)
-> AgdaAny -> T_IsIdempotentCommutativeMonoid_464
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_674
-> T_IsIdempotentCommutativeMonoid_464
d_isIdempotentCommutativeMonoid_698 (T_IdempotentCommutativeMonoid_674 -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_674
v0)
-- Algebra.Bundles.BoundedLattice.isMagma
d_isMagma_812 ::
  T_IdempotentCommutativeMonoid_674 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_86
d_isMagma_812 :: T_IdempotentCommutativeMonoid_674 -> T_IsMagma_86
d_isMagma_812 T_IdempotentCommutativeMonoid_674
v0
  = (T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> T_IsMagma_86
forall a b. a -> b
coe
      T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202
      ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368
         ((T_IsCommutativeMonoid_406 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCommutativeMonoid_406 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_416
            ((T_IsIdempotentCommutativeMonoid_464 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsIdempotentCommutativeMonoid_464 -> T_IsCommutativeMonoid_406
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_474
               ((T_IdempotentCommutativeMonoid_674
 -> T_IsIdempotentCommutativeMonoid_464)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_674
-> T_IsIdempotentCommutativeMonoid_464
d_isIdempotentCommutativeMonoid_698 (T_IdempotentCommutativeMonoid_674 -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_674
v0)))))
-- Algebra.Bundles.BoundedLattice.isMonoid
d_isMonoid_814 ::
  T_IdempotentCommutativeMonoid_674 ->
  MAlonzo.Code.Algebra.Structures.T_IsMonoid_358
d_isMonoid_814 :: T_IdempotentCommutativeMonoid_674 -> T_IsMonoid_358
d_isMonoid_814 T_IdempotentCommutativeMonoid_674
v0
  = (T_IsCommutativeMonoid_406 -> T_IsMonoid_358)
-> AgdaAny -> T_IsMonoid_358
forall a b. a -> b
coe
      T_IsCommutativeMonoid_406 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_416
      ((T_IsIdempotentCommutativeMonoid_464 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsIdempotentCommutativeMonoid_464 -> T_IsCommutativeMonoid_406
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_474
         ((T_IdempotentCommutativeMonoid_674
 -> T_IsIdempotentCommutativeMonoid_464)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_674
-> T_IsIdempotentCommutativeMonoid_464
d_isIdempotentCommutativeMonoid_698 (T_IdempotentCommutativeMonoid_674 -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_674
v0)))
-- Algebra.Bundles.BoundedLattice.isPartialEquivalence
d_isPartialEquivalence_816 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentCommutativeMonoid_674 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_816 :: ()
-> ()
-> T_IdempotentCommutativeMonoid_674
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_816 ~()
v0 ~()
v1 T_IdempotentCommutativeMonoid_674
v2
  = T_IdempotentCommutativeMonoid_674 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_816 T_IdempotentCommutativeMonoid_674
v2
du_isPartialEquivalence_816 ::
  T_IdempotentCommutativeMonoid_674 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_816 :: T_IdempotentCommutativeMonoid_674 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_816 T_IdempotentCommutativeMonoid_674
v0
  = let v1 :: T_IsIdempotentCommutativeMonoid_464
v1 = T_IdempotentCommutativeMonoid_674
-> T_IsIdempotentCommutativeMonoid_464
d_isIdempotentCommutativeMonoid_698 (T_IdempotentCommutativeMonoid_674
-> T_IdempotentCommutativeMonoid_674
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_674
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsCommutativeMonoid_406
v2
             = T_IsIdempotentCommutativeMonoid_464 -> T_IsCommutativeMonoid_406
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_474
                 (T_IsIdempotentCommutativeMonoid_464
-> T_IsIdempotentCommutativeMonoid_464
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_464
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsMonoid_358
v3
                = T_IsCommutativeMonoid_406 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_416 (T_IsCommutativeMonoid_406 -> T_IsCommutativeMonoid_406
forall a b. a -> b
coe T_IsCommutativeMonoid_406
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsSemigroup_194
v4
                   = T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368 (T_IsMonoid_358 -> T_IsMonoid_358
forall a b. a -> b
coe T_IsMonoid_358
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsMagma_86
v5 = T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202 (T_IsSemigroup_194 -> T_IsSemigroup_194
forall a b. a -> b
coe T_IsSemigroup_194
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_86 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsMagma_86 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_94 (T_IsMagma_86 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86
v5)))))))
-- Algebra.Bundles.BoundedLattice.isSemigroup
d_isSemigroup_818 ::
  T_IdempotentCommutativeMonoid_674 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_194
d_isSemigroup_818 :: T_IdempotentCommutativeMonoid_674 -> T_IsSemigroup_194
d_isSemigroup_818 T_IdempotentCommutativeMonoid_674
v0
  = (T_IsMonoid_358 -> T_IsSemigroup_194)
-> AgdaAny -> T_IsSemigroup_194
forall a b. a -> b
coe
      T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368
      ((T_IsCommutativeMonoid_406 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCommutativeMonoid_406 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_416
         ((T_IsIdempotentCommutativeMonoid_464 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsIdempotentCommutativeMonoid_464 -> T_IsCommutativeMonoid_406
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_474
            ((T_IdempotentCommutativeMonoid_674
 -> T_IsIdempotentCommutativeMonoid_464)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_674
-> T_IsIdempotentCommutativeMonoid_464
d_isIdempotentCommutativeMonoid_698 (T_IdempotentCommutativeMonoid_674 -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_674
v0))))
-- Algebra.Bundles.BoundedLattice.magma
d_magma_820 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentCommutativeMonoid_674 -> T_Magma_36
d_magma_820 :: () -> () -> T_IdempotentCommutativeMonoid_674 -> T_Magma_36
d_magma_820 ~()
v0 ~()
v1 T_IdempotentCommutativeMonoid_674
v2 = T_IdempotentCommutativeMonoid_674 -> T_Magma_36
du_magma_820 T_IdempotentCommutativeMonoid_674
v2
du_magma_820 :: T_IdempotentCommutativeMonoid_674 -> T_Magma_36
du_magma_820 :: T_IdempotentCommutativeMonoid_674 -> T_Magma_36
du_magma_820 T_IdempotentCommutativeMonoid_674
v0
  = let v1 :: t
v1 = (T_IdempotentCommutativeMonoid_674 -> T_CommutativeMonoid_582)
-> AgdaAny -> t
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_674 -> T_CommutativeMonoid_582
du_commutativeMonoid_746 (T_IdempotentCommutativeMonoid_674 -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_674
v0) in
    AgdaAny -> T_Magma_36
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_CommutativeMonoid_582 -> T_Monoid_506) -> AgdaAny -> t
forall a b. a -> b
coe T_CommutativeMonoid_582 -> T_Monoid_506
du_monoid_650 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_Semigroup_206 -> T_Magma_36) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semigroup_206 -> T_Magma_36
du_magma_254 ((T_Monoid_506 -> T_Semigroup_206) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Monoid_506 -> T_Semigroup_206
du_semigroup_566 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2))))
-- Algebra.Bundles.BoundedLattice.monoid
d_monoid_822 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentCommutativeMonoid_674 -> T_Monoid_506
d_monoid_822 :: () -> () -> T_IdempotentCommutativeMonoid_674 -> T_Monoid_506
d_monoid_822 ~()
v0 ~()
v1 T_IdempotentCommutativeMonoid_674
v2 = T_IdempotentCommutativeMonoid_674 -> T_Monoid_506
du_monoid_822 T_IdempotentCommutativeMonoid_674
v2
du_monoid_822 :: T_IdempotentCommutativeMonoid_674 -> T_Monoid_506
du_monoid_822 :: T_IdempotentCommutativeMonoid_674 -> T_Monoid_506
du_monoid_822 T_IdempotentCommutativeMonoid_674
v0
  = (T_CommutativeMonoid_582 -> T_Monoid_506)
-> AgdaAny -> T_Monoid_506
forall a b. a -> b
coe T_CommutativeMonoid_582 -> T_Monoid_506
du_monoid_650 ((T_IdempotentCommutativeMonoid_674 -> T_CommutativeMonoid_582)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_674 -> T_CommutativeMonoid_582
du_commutativeMonoid_746 (T_IdempotentCommutativeMonoid_674 -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_674
v0))
-- Algebra.Bundles.BoundedLattice.rawMagma
d_rawMagma_824 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentCommutativeMonoid_674 -> T_RawMagma_8
d_rawMagma_824 :: () -> () -> T_IdempotentCommutativeMonoid_674 -> T_RawMagma_8
d_rawMagma_824 ~()
v0 ~()
v1 T_IdempotentCommutativeMonoid_674
v2 = T_IdempotentCommutativeMonoid_674 -> T_RawMagma_8
du_rawMagma_824 T_IdempotentCommutativeMonoid_674
v2
du_rawMagma_824 ::
  T_IdempotentCommutativeMonoid_674 -> T_RawMagma_8
du_rawMagma_824 :: T_IdempotentCommutativeMonoid_674 -> T_RawMagma_8
du_rawMagma_824 T_IdempotentCommutativeMonoid_674
v0
  = let v1 :: t
v1 = (T_IdempotentCommutativeMonoid_674 -> T_CommutativeMonoid_582)
-> AgdaAny -> t
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_674 -> T_CommutativeMonoid_582
du_commutativeMonoid_746 (T_IdempotentCommutativeMonoid_674 -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_674
v0) in
    AgdaAny -> T_RawMagma_8
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_CommutativeMonoid_582 -> T_Monoid_506) -> AgdaAny -> t
forall a b. a -> b
coe T_CommutativeMonoid_582 -> T_Monoid_506
du_monoid_650 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: t
v3 = (T_Monoid_506 -> T_Semigroup_206) -> AgdaAny -> t
forall a b. a -> b
coe T_Monoid_506 -> T_Semigroup_206
du_semigroup_566 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_Magma_36 -> T_RawMagma_8) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Magma_36 -> T_RawMagma_8
du_rawMagma_80 ((T_Semigroup_206 -> T_Magma_36) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semigroup_206 -> T_Magma_36
du_magma_254 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3)))))
-- Algebra.Bundles.BoundedLattice.rawMonoid
d_rawMonoid_826 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentCommutativeMonoid_674 -> T_RawMonoid_474
d_rawMonoid_826 :: () -> () -> T_IdempotentCommutativeMonoid_674 -> T_RawMonoid_474
d_rawMonoid_826 ~()
v0 ~()
v1 T_IdempotentCommutativeMonoid_674
v2 = T_IdempotentCommutativeMonoid_674 -> T_RawMonoid_474
du_rawMonoid_826 T_IdempotentCommutativeMonoid_674
v2
du_rawMonoid_826 ::
  T_IdempotentCommutativeMonoid_674 -> T_RawMonoid_474
du_rawMonoid_826 :: T_IdempotentCommutativeMonoid_674 -> T_RawMonoid_474
du_rawMonoid_826 T_IdempotentCommutativeMonoid_674
v0
  = let v1 :: t
v1 = (T_IdempotentCommutativeMonoid_674 -> T_CommutativeMonoid_582)
-> AgdaAny -> t
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_674 -> T_CommutativeMonoid_582
du_commutativeMonoid_746 (T_IdempotentCommutativeMonoid_674 -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_674
v0) in
    AgdaAny -> T_RawMonoid_474
forall a b. a -> b
coe ((T_Monoid_506 -> T_RawMonoid_474) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Monoid_506 -> T_RawMonoid_474
du_rawMonoid_576 ((T_CommutativeMonoid_582 -> T_Monoid_506) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeMonoid_582 -> T_Monoid_506
du_monoid_650 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1)))
-- Algebra.Bundles.BoundedLattice.refl
d_refl_828 ::
  T_IdempotentCommutativeMonoid_674 -> AgdaAny -> AgdaAny
d_refl_828 :: T_IdempotentCommutativeMonoid_674 -> AgdaAny -> AgdaAny
d_refl_828 T_IdempotentCommutativeMonoid_674
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_86 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_86 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_94
         ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202
            ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368
               ((T_IsCommutativeMonoid_406 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsCommutativeMonoid_406 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_416
                  ((T_IsIdempotentCommutativeMonoid_464 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsIdempotentCommutativeMonoid_464 -> T_IsCommutativeMonoid_406
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_474
                     ((T_IdempotentCommutativeMonoid_674
 -> T_IsIdempotentCommutativeMonoid_464)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_674
-> T_IsIdempotentCommutativeMonoid_464
d_isIdempotentCommutativeMonoid_698 (T_IdempotentCommutativeMonoid_674 -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_674
v0)))))))
-- Algebra.Bundles.BoundedLattice.reflexive
d_reflexive_830 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentCommutativeMonoid_674 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_830 :: ()
-> ()
-> T_IdempotentCommutativeMonoid_674
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_830 ~()
v0 ~()
v1 T_IdempotentCommutativeMonoid_674
v2 = T_IdempotentCommutativeMonoid_674
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_830 T_IdempotentCommutativeMonoid_674
v2
du_reflexive_830 ::
  T_IdempotentCommutativeMonoid_674 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_830 :: T_IdempotentCommutativeMonoid_674
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_830 T_IdempotentCommutativeMonoid_674
v0
  = let v1 :: T_IsIdempotentCommutativeMonoid_464
v1 = T_IdempotentCommutativeMonoid_674
-> T_IsIdempotentCommutativeMonoid_464
d_isIdempotentCommutativeMonoid_698 (T_IdempotentCommutativeMonoid_674
-> T_IdempotentCommutativeMonoid_674
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_674
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsCommutativeMonoid_406
v2
             = T_IsIdempotentCommutativeMonoid_464 -> T_IsCommutativeMonoid_406
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_474
                 (T_IsIdempotentCommutativeMonoid_464
-> T_IsIdempotentCommutativeMonoid_464
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_464
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsMonoid_358
v3
                = T_IsCommutativeMonoid_406 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_416 (T_IsCommutativeMonoid_406 -> T_IsCommutativeMonoid_406
forall a b. a -> b
coe T_IsCommutativeMonoid_406
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsSemigroup_194
v4
                   = T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368 (T_IsMonoid_358 -> T_IsMonoid_358
forall a b. a -> b
coe T_IsMonoid_358
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsMagma_86
v5 = T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202 (T_IsSemigroup_194 -> T_IsSemigroup_194
forall a b. a -> b
coe T_IsSemigroup_194
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_86 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_94 (T_IsMagma_86 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86
v5))
                       AgdaAny
v6)))))
-- Algebra.Bundles.BoundedLattice.semigroup
d_semigroup_832 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentCommutativeMonoid_674 -> T_Semigroup_206
d_semigroup_832 :: () -> () -> T_IdempotentCommutativeMonoid_674 -> T_Semigroup_206
d_semigroup_832 ~()
v0 ~()
v1 T_IdempotentCommutativeMonoid_674
v2 = T_IdempotentCommutativeMonoid_674 -> T_Semigroup_206
du_semigroup_832 T_IdempotentCommutativeMonoid_674
v2
du_semigroup_832 ::
  T_IdempotentCommutativeMonoid_674 -> T_Semigroup_206
du_semigroup_832 :: T_IdempotentCommutativeMonoid_674 -> T_Semigroup_206
du_semigroup_832 T_IdempotentCommutativeMonoid_674
v0
  = let v1 :: t
v1 = (T_IdempotentCommutativeMonoid_674 -> T_CommutativeMonoid_582)
-> AgdaAny -> t
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_674 -> T_CommutativeMonoid_582
du_commutativeMonoid_746 (T_IdempotentCommutativeMonoid_674 -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_674
v0) in
    AgdaAny -> T_Semigroup_206
forall a b. a -> b
coe ((T_Monoid_506 -> T_Semigroup_206) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Monoid_506 -> T_Semigroup_206
du_semigroup_566 ((T_CommutativeMonoid_582 -> T_Monoid_506) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeMonoid_582 -> T_Monoid_506
du_monoid_650 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1)))
-- Algebra.Bundles.BoundedLattice.setoid
d_setoid_834 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentCommutativeMonoid_674 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_834 :: () -> () -> T_IdempotentCommutativeMonoid_674 -> T_Setoid_44
d_setoid_834 ~()
v0 ~()
v1 T_IdempotentCommutativeMonoid_674
v2 = T_IdempotentCommutativeMonoid_674 -> T_Setoid_44
du_setoid_834 T_IdempotentCommutativeMonoid_674
v2
du_setoid_834 ::
  T_IdempotentCommutativeMonoid_674 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_834 :: T_IdempotentCommutativeMonoid_674 -> T_Setoid_44
du_setoid_834 T_IdempotentCommutativeMonoid_674
v0
  = let v1 :: T_IsIdempotentCommutativeMonoid_464
v1 = T_IdempotentCommutativeMonoid_674
-> T_IsIdempotentCommutativeMonoid_464
d_isIdempotentCommutativeMonoid_698 (T_IdempotentCommutativeMonoid_674
-> T_IdempotentCommutativeMonoid_674
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_674
v0) in
    AgdaAny -> T_Setoid_44
forall a b. a -> b
coe
      (let v2 :: T_IsCommutativeMonoid_406
v2
             = T_IsIdempotentCommutativeMonoid_464 -> T_IsCommutativeMonoid_406
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_474
                 (T_IsIdempotentCommutativeMonoid_464
-> T_IsIdempotentCommutativeMonoid_464
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_464
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsMonoid_358
v3
                = T_IsCommutativeMonoid_406 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_416 (T_IsCommutativeMonoid_406 -> T_IsCommutativeMonoid_406
forall a b. a -> b
coe T_IsCommutativeMonoid_406
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsSemigroup_194
v4
                   = T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368 (T_IsMonoid_358 -> T_IsMonoid_358
forall a b. a -> b
coe T_IsMonoid_358
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               ((T_IsMagma_86 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsMagma_86 -> T_Setoid_44
MAlonzo.Code.Algebra.Structures.du_setoid_110
                  ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202 (T_IsSemigroup_194 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194
v4))))))
-- Algebra.Bundles.BoundedLattice.sym
d_sym_836 ::
  T_IdempotentCommutativeMonoid_674 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_836 :: T_IdempotentCommutativeMonoid_674
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_836 T_IdempotentCommutativeMonoid_674
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_86 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_86 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_94
         ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202
            ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368
               ((T_IsCommutativeMonoid_406 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsCommutativeMonoid_406 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_416
                  ((T_IsIdempotentCommutativeMonoid_464 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsIdempotentCommutativeMonoid_464 -> T_IsCommutativeMonoid_406
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_474
                     ((T_IdempotentCommutativeMonoid_674
 -> T_IsIdempotentCommutativeMonoid_464)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_674
-> T_IsIdempotentCommutativeMonoid_464
d_isIdempotentCommutativeMonoid_698 (T_IdempotentCommutativeMonoid_674 -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_674
v0)))))))
-- Algebra.Bundles.BoundedLattice.trans
d_trans_838 ::
  T_IdempotentCommutativeMonoid_674 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_838 :: T_IdempotentCommutativeMonoid_674
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_838 T_IdempotentCommutativeMonoid_674
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_86 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_86 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_94
         ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202
            ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368
               ((T_IsCommutativeMonoid_406 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsCommutativeMonoid_406 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_416
                  ((T_IsIdempotentCommutativeMonoid_464 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsIdempotentCommutativeMonoid_464 -> T_IsCommutativeMonoid_406
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_474
                     ((T_IdempotentCommutativeMonoid_674
 -> T_IsIdempotentCommutativeMonoid_464)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_674
-> T_IsIdempotentCommutativeMonoid_464
d_isIdempotentCommutativeMonoid_698 (T_IdempotentCommutativeMonoid_674 -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_674
v0)))))))
-- Algebra.Bundles.BoundedLattice.ε
d_ε_840 :: T_IdempotentCommutativeMonoid_674 -> AgdaAny
d_ε_840 :: T_IdempotentCommutativeMonoid_674 -> AgdaAny
d_ε_840 T_IdempotentCommutativeMonoid_674
v0 = (T_IdempotentCommutativeMonoid_674 -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_674 -> AgdaAny
d_ε_696 (T_IdempotentCommutativeMonoid_674 -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_674
v0)
-- Algebra.Bundles.BoundedLattice.∙-cong
d_'8729''45'cong_842 ::
  T_IdempotentCommutativeMonoid_674 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_842 :: T_IdempotentCommutativeMonoid_674
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_842 T_IdempotentCommutativeMonoid_674
v0
  = (T_IsMagma_86
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsMagma_86
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_96
      ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202
         ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368
            ((T_IsCommutativeMonoid_406 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsCommutativeMonoid_406 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_416
               ((T_IsIdempotentCommutativeMonoid_464 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsIdempotentCommutativeMonoid_464 -> T_IsCommutativeMonoid_406
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_474
                  ((T_IdempotentCommutativeMonoid_674
 -> T_IsIdempotentCommutativeMonoid_464)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_674
-> T_IsIdempotentCommutativeMonoid_464
d_isIdempotentCommutativeMonoid_698 (T_IdempotentCommutativeMonoid_674 -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_674
v0))))))
-- Algebra.Bundles.BoundedLattice.∙-congʳ
d_'8729''45'cong'691'_844 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentCommutativeMonoid_674 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_844 :: ()
-> ()
-> T_IdempotentCommutativeMonoid_674
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_844 ~()
v0 ~()
v1 T_IdempotentCommutativeMonoid_674
v2
  = T_IdempotentCommutativeMonoid_674
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_844 T_IdempotentCommutativeMonoid_674
v2
du_'8729''45'cong'691'_844 ::
  T_IdempotentCommutativeMonoid_674 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_844 :: T_IdempotentCommutativeMonoid_674
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_844 T_IdempotentCommutativeMonoid_674
v0
  = let v1 :: T_IsIdempotentCommutativeMonoid_464
v1 = T_IdempotentCommutativeMonoid_674
-> T_IsIdempotentCommutativeMonoid_464
d_isIdempotentCommutativeMonoid_698 (T_IdempotentCommutativeMonoid_674
-> T_IdempotentCommutativeMonoid_674
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_674
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsCommutativeMonoid_406
v2
             = T_IsIdempotentCommutativeMonoid_464 -> T_IsCommutativeMonoid_406
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_474
                 (T_IsIdempotentCommutativeMonoid_464
-> T_IsIdempotentCommutativeMonoid_464
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_464
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsMonoid_358
v3
                = T_IsCommutativeMonoid_406 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_416 (T_IsCommutativeMonoid_406 -> T_IsCommutativeMonoid_406
forall a b. a -> b
coe T_IsCommutativeMonoid_406
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsSemigroup_194
v4
                   = T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368 (T_IsMonoid_358 -> T_IsMonoid_358
forall a b. a -> b
coe T_IsMonoid_358
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               ((T_IsMagma_86
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsMagma_86 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'691'_116
                  ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202 (T_IsSemigroup_194 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194
v4))))))
-- Algebra.Bundles.BoundedLattice.∙-congˡ
d_'8729''45'cong'737'_846 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentCommutativeMonoid_674 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_846 :: ()
-> ()
-> T_IdempotentCommutativeMonoid_674
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_846 ~()
v0 ~()
v1 T_IdempotentCommutativeMonoid_674
v2
  = T_IdempotentCommutativeMonoid_674
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_846 T_IdempotentCommutativeMonoid_674
v2
du_'8729''45'cong'737'_846 ::
  T_IdempotentCommutativeMonoid_674 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_846 :: T_IdempotentCommutativeMonoid_674
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_846 T_IdempotentCommutativeMonoid_674
v0
  = let v1 :: T_IsIdempotentCommutativeMonoid_464
v1 = T_IdempotentCommutativeMonoid_674
-> T_IsIdempotentCommutativeMonoid_464
d_isIdempotentCommutativeMonoid_698 (T_IdempotentCommutativeMonoid_674
-> T_IdempotentCommutativeMonoid_674
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_674
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsCommutativeMonoid_406
v2
             = T_IsIdempotentCommutativeMonoid_464 -> T_IsCommutativeMonoid_406
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_474
                 (T_IsIdempotentCommutativeMonoid_464
-> T_IsIdempotentCommutativeMonoid_464
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_464
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsMonoid_358
v3
                = T_IsCommutativeMonoid_406 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_416 (T_IsCommutativeMonoid_406 -> T_IsCommutativeMonoid_406
forall a b. a -> b
coe T_IsCommutativeMonoid_406
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsSemigroup_194
v4
                   = T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368 (T_IsMonoid_358 -> T_IsMonoid_358
forall a b. a -> b
coe T_IsMonoid_358
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               ((T_IsMagma_86
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsMagma_86 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'737'_112
                  ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202 (T_IsSemigroup_194 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194
v4))))))
-- Algebra.Bundles.RawGroup
d_RawGroup_852 :: p -> p -> ()
d_RawGroup_852 p
a0 p
a1 = ()
data T_RawGroup_852
  = C_RawGroup'46'constructor_13903 (AgdaAny -> AgdaAny -> AgdaAny)
                                    AgdaAny (AgdaAny -> AgdaAny)
-- Algebra.Bundles.RawGroup.Carrier
d_Carrier_868 :: T_RawGroup_852 -> ()
d_Carrier_868 :: T_RawGroup_852 -> ()
d_Carrier_868 = T_RawGroup_852 -> ()
forall a. a
erased
-- Algebra.Bundles.RawGroup._≈_
d__'8776'__870 :: T_RawGroup_852 -> AgdaAny -> AgdaAny -> ()
d__'8776'__870 :: T_RawGroup_852 -> AgdaAny -> AgdaAny -> ()
d__'8776'__870 = T_RawGroup_852 -> AgdaAny -> AgdaAny -> ()
forall a. a
erased
-- Algebra.Bundles.RawGroup._∙_
d__'8729'__872 :: T_RawGroup_852 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__872 :: T_RawGroup_852 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__872 T_RawGroup_852
v0
  = case T_RawGroup_852 -> T_RawGroup_852
forall a b. a -> b
coe T_RawGroup_852
v0 of
      C_RawGroup'46'constructor_13903 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny
v4 AgdaAny -> AgdaAny
v5 -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v3
      T_RawGroup_852
_ -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.RawGroup.ε
d_ε_874 :: T_RawGroup_852 -> AgdaAny
d_ε_874 :: T_RawGroup_852 -> AgdaAny
d_ε_874 T_RawGroup_852
v0
  = case T_RawGroup_852 -> T_RawGroup_852
forall a b. a -> b
coe T_RawGroup_852
v0 of
      C_RawGroup'46'constructor_13903 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny
v4 AgdaAny -> AgdaAny
v5 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v4
      T_RawGroup_852
_ -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.RawGroup._⁻¹
d__'8315''185'_876 :: T_RawGroup_852 -> AgdaAny -> AgdaAny
d__'8315''185'_876 :: T_RawGroup_852 -> AgdaAny -> AgdaAny
d__'8315''185'_876 T_RawGroup_852
v0
  = case T_RawGroup_852 -> T_RawGroup_852
forall a b. a -> b
coe T_RawGroup_852
v0 of
      C_RawGroup'46'constructor_13903 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny
v4 AgdaAny -> AgdaAny
v5 -> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v5
      T_RawGroup_852
_ -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.RawGroup.rawMonoid
d_rawMonoid_878 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_RawGroup_852 -> T_RawMonoid_474
d_rawMonoid_878 :: () -> () -> T_RawGroup_852 -> T_RawMonoid_474
d_rawMonoid_878 ~()
v0 ~()
v1 T_RawGroup_852
v2 = T_RawGroup_852 -> T_RawMonoid_474
du_rawMonoid_878 T_RawGroup_852
v2
du_rawMonoid_878 :: T_RawGroup_852 -> T_RawMonoid_474
du_rawMonoid_878 :: T_RawGroup_852 -> T_RawMonoid_474
du_rawMonoid_878 T_RawGroup_852
v0
  = ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> T_RawMonoid_474)
-> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> T_RawMonoid_474
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> T_RawMonoid_474
C_RawMonoid'46'constructor_8313 (T_RawGroup_852 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__872 (T_RawGroup_852 -> T_RawGroup_852
forall a b. a -> b
coe T_RawGroup_852
v0))
      (T_RawGroup_852 -> AgdaAny
d_ε_874 (T_RawGroup_852 -> T_RawGroup_852
forall a b. a -> b
coe T_RawGroup_852
v0))
-- Algebra.Bundles.RawGroup._._≉_
d__'8777'__882 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_RawGroup_852 -> AgdaAny -> AgdaAny -> ()
d__'8777'__882 :: () -> () -> T_RawGroup_852 -> AgdaAny -> AgdaAny -> ()
d__'8777'__882 = () -> () -> T_RawGroup_852 -> AgdaAny -> AgdaAny -> ()
forall a. a
erased
-- Algebra.Bundles.RawGroup._.rawMagma
d_rawMagma_884 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_RawGroup_852 -> T_RawMagma_8
d_rawMagma_884 :: () -> () -> T_RawGroup_852 -> T_RawMagma_8
d_rawMagma_884 ~()
v0 ~()
v1 T_RawGroup_852
v2 = T_RawGroup_852 -> T_RawMagma_8
du_rawMagma_884 T_RawGroup_852
v2
du_rawMagma_884 :: T_RawGroup_852 -> T_RawMagma_8
du_rawMagma_884 :: T_RawGroup_852 -> T_RawMagma_8
du_rawMagma_884 T_RawGroup_852
v0
  = (T_RawMonoid_474 -> T_RawMagma_8) -> AgdaAny -> T_RawMagma_8
forall a b. a -> b
coe T_RawMonoid_474 -> T_RawMagma_8
du_rawMagma_496 ((T_RawGroup_852 -> T_RawMonoid_474) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_RawGroup_852 -> T_RawMonoid_474
du_rawMonoid_878 (T_RawGroup_852 -> AgdaAny
forall a b. a -> b
coe T_RawGroup_852
v0))
-- Algebra.Bundles.Group
d_Group_890 :: p -> p -> ()
d_Group_890 p
a0 p
a1 = ()
data T_Group_890
  = C_Group'46'constructor_14575 (AgdaAny -> AgdaAny -> AgdaAny)
                                 AgdaAny (AgdaAny -> AgdaAny)
                                 MAlonzo.Code.Algebra.Structures.T_IsGroup_580
-- Algebra.Bundles.Group.Carrier
d_Carrier_908 :: T_Group_890 -> ()
d_Carrier_908 :: T_Group_890 -> ()
d_Carrier_908 = T_Group_890 -> ()
forall a. a
erased
-- Algebra.Bundles.Group._≈_
d__'8776'__910 :: T_Group_890 -> AgdaAny -> AgdaAny -> ()
d__'8776'__910 :: T_Group_890 -> AgdaAny -> AgdaAny -> ()
d__'8776'__910 = T_Group_890 -> AgdaAny -> AgdaAny -> ()
forall a. a
erased
-- Algebra.Bundles.Group._∙_
d__'8729'__912 :: T_Group_890 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__912 :: T_Group_890 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__912 T_Group_890
v0
  = case T_Group_890 -> T_Group_890
forall a b. a -> b
coe T_Group_890
v0 of
      C_Group'46'constructor_14575 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny
v4 AgdaAny -> AgdaAny
v5 T_IsGroup_580
v6 -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v3
      T_Group_890
_ -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.Group.ε
d_ε_914 :: T_Group_890 -> AgdaAny
d_ε_914 :: T_Group_890 -> AgdaAny
d_ε_914 T_Group_890
v0
  = case T_Group_890 -> T_Group_890
forall a b. a -> b
coe T_Group_890
v0 of
      C_Group'46'constructor_14575 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny
v4 AgdaAny -> AgdaAny
v5 T_IsGroup_580
v6 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v4
      T_Group_890
_ -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.Group._⁻¹
d__'8315''185'_916 :: T_Group_890 -> AgdaAny -> AgdaAny
d__'8315''185'_916 :: T_Group_890 -> AgdaAny -> AgdaAny
d__'8315''185'_916 T_Group_890
v0
  = case T_Group_890 -> T_Group_890
forall a b. a -> b
coe T_Group_890
v0 of
      C_Group'46'constructor_14575 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny
v4 AgdaAny -> AgdaAny
v5 T_IsGroup_580
v6 -> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v5
      T_Group_890
_ -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.Group.isGroup
d_isGroup_918 ::
  T_Group_890 -> MAlonzo.Code.Algebra.Structures.T_IsGroup_580
d_isGroup_918 :: T_Group_890 -> T_IsGroup_580
d_isGroup_918 T_Group_890
v0
  = case T_Group_890 -> T_Group_890
forall a b. a -> b
coe T_Group_890
v0 of
      C_Group'46'constructor_14575 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny
v4 AgdaAny -> AgdaAny
v5 T_IsGroup_580
v6 -> T_IsGroup_580 -> T_IsGroup_580
forall a b. a -> b
coe T_IsGroup_580
v6
      T_Group_890
_ -> T_IsGroup_580
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.Group._._-_
d__'45'__922 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Group_890 -> AgdaAny -> AgdaAny -> AgdaAny
d__'45'__922 :: () -> () -> T_Group_890 -> AgdaAny -> AgdaAny -> AgdaAny
d__'45'__922 ~()
v0 ~()
v1 T_Group_890
v2 = T_Group_890 -> AgdaAny -> AgdaAny -> AgdaAny
du__'45'__922 T_Group_890
v2
du__'45'__922 :: T_Group_890 -> AgdaAny -> AgdaAny -> AgdaAny
du__'45'__922 :: T_Group_890 -> AgdaAny -> AgdaAny -> AgdaAny
du__'45'__922 T_Group_890
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'__634
      ((T_Group_890 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Group_890 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__912 (T_Group_890 -> AgdaAny
forall a b. a -> b
coe T_Group_890
v0)) ((T_Group_890 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Group_890 -> AgdaAny -> AgdaAny
d__'8315''185'_916 (T_Group_890 -> AgdaAny
forall a b. a -> b
coe T_Group_890
v0))
-- Algebra.Bundles.Group._.assoc
d_assoc_924 ::
  T_Group_890 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_924 :: T_Group_890 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_924 T_Group_890
v0
  = (T_IsSemigroup_194 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsSemigroup_194 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_assoc_204
      ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368
         ((T_IsGroup_580 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsGroup_580 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_594
            ((T_Group_890 -> T_IsGroup_580) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Group_890 -> T_IsGroup_580
d_isGroup_918 (T_Group_890 -> AgdaAny
forall a b. a -> b
coe T_Group_890
v0))))
-- Algebra.Bundles.Group._.identity
d_identity_926 ::
  T_Group_890 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_identity_926 :: T_Group_890 -> T_Σ_14
d_identity_926 T_Group_890
v0
  = (T_IsMonoid_358 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsMonoid_358 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_identity_370
      ((T_IsGroup_580 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsGroup_580 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_594
         ((T_Group_890 -> T_IsGroup_580) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Group_890 -> T_IsGroup_580
d_isGroup_918 (T_Group_890 -> AgdaAny
forall a b. a -> b
coe T_Group_890
v0)))
-- Algebra.Bundles.Group._.identityʳ
d_identity'691'_928 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Group_890 -> AgdaAny -> AgdaAny
d_identity'691'_928 :: () -> () -> T_Group_890 -> AgdaAny -> AgdaAny
d_identity'691'_928 ~()
v0 ~()
v1 T_Group_890
v2 = T_Group_890 -> AgdaAny -> AgdaAny
du_identity'691'_928 T_Group_890
v2
du_identity'691'_928 :: T_Group_890 -> AgdaAny -> AgdaAny
du_identity'691'_928 :: T_Group_890 -> AgdaAny -> AgdaAny
du_identity'691'_928 T_Group_890
v0
  = let v1 :: T_IsGroup_580
v1 = T_Group_890 -> T_IsGroup_580
d_isGroup_918 (T_Group_890 -> T_Group_890
forall a b. a -> b
coe T_Group_890
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsMonoid_358 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoid_358 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_identity'691'_400
         ((T_IsGroup_580 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_580 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_594 (T_IsGroup_580 -> AgdaAny
forall a b. a -> b
coe T_IsGroup_580
v1)))
-- Algebra.Bundles.Group._.identityˡ
d_identity'737'_930 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Group_890 -> AgdaAny -> AgdaAny
d_identity'737'_930 :: () -> () -> T_Group_890 -> AgdaAny -> AgdaAny
d_identity'737'_930 ~()
v0 ~()
v1 T_Group_890
v2 = T_Group_890 -> AgdaAny -> AgdaAny
du_identity'737'_930 T_Group_890
v2
du_identity'737'_930 :: T_Group_890 -> AgdaAny -> AgdaAny
du_identity'737'_930 :: T_Group_890 -> AgdaAny -> AgdaAny
du_identity'737'_930 T_Group_890
v0
  = let v1 :: T_IsGroup_580
v1 = T_Group_890 -> T_IsGroup_580
d_isGroup_918 (T_Group_890 -> T_Group_890
forall a b. a -> b
coe T_Group_890
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsMonoid_358 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoid_358 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_identity'737'_398
         ((T_IsGroup_580 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_580 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_594 (T_IsGroup_580 -> AgdaAny
forall a b. a -> b
coe T_IsGroup_580
v1)))
-- Algebra.Bundles.Group._.inverse
d_inverse_932 ::
  T_Group_890 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_inverse_932 :: T_Group_890 -> T_Σ_14
d_inverse_932 T_Group_890
v0
  = (T_IsGroup_580 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsGroup_580 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_inverse_596
      ((T_Group_890 -> T_IsGroup_580) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Group_890 -> T_IsGroup_580
d_isGroup_918 (T_Group_890 -> AgdaAny
forall a b. a -> b
coe T_Group_890
v0))
-- Algebra.Bundles.Group._.inverseʳ
d_inverse'691'_934 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Group_890 -> AgdaAny -> AgdaAny
d_inverse'691'_934 :: () -> () -> T_Group_890 -> AgdaAny -> AgdaAny
d_inverse'691'_934 ~()
v0 ~()
v1 T_Group_890
v2 = T_Group_890 -> AgdaAny -> AgdaAny
du_inverse'691'_934 T_Group_890
v2
du_inverse'691'_934 :: T_Group_890 -> AgdaAny -> AgdaAny
du_inverse'691'_934 :: T_Group_890 -> AgdaAny -> AgdaAny
du_inverse'691'_934 T_Group_890
v0
  = (T_IsGroup_580 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsGroup_580 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_inverse'691'_642
      ((T_Group_890 -> T_IsGroup_580) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Group_890 -> T_IsGroup_580
d_isGroup_918 (T_Group_890 -> AgdaAny
forall a b. a -> b
coe T_Group_890
v0))
-- Algebra.Bundles.Group._.inverseˡ
d_inverse'737'_936 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Group_890 -> AgdaAny -> AgdaAny
d_inverse'737'_936 :: () -> () -> T_Group_890 -> AgdaAny -> AgdaAny
d_inverse'737'_936 ~()
v0 ~()
v1 T_Group_890
v2 = T_Group_890 -> AgdaAny -> AgdaAny
du_inverse'737'_936 T_Group_890
v2
du_inverse'737'_936 :: T_Group_890 -> AgdaAny -> AgdaAny
du_inverse'737'_936 :: T_Group_890 -> AgdaAny -> AgdaAny
du_inverse'737'_936 T_Group_890
v0
  = (T_IsGroup_580 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsGroup_580 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_inverse'737'_640
      ((T_Group_890 -> T_IsGroup_580) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Group_890 -> T_IsGroup_580
d_isGroup_918 (T_Group_890 -> AgdaAny
forall a b. a -> b
coe T_Group_890
v0))
-- Algebra.Bundles.Group._.isEquivalence
d_isEquivalence_938 ::
  T_Group_890 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_938 :: T_Group_890 -> T_IsEquivalence_26
d_isEquivalence_938 T_Group_890
v0
  = (T_IsMagma_86 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      T_IsMagma_86 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_94
      ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202
         ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368
            ((T_IsGroup_580 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsGroup_580 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_594
               ((T_Group_890 -> T_IsGroup_580) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Group_890 -> T_IsGroup_580
d_isGroup_918 (T_Group_890 -> AgdaAny
forall a b. a -> b
coe T_Group_890
v0)))))
-- Algebra.Bundles.Group._.isMagma
d_isMagma_940 ::
  T_Group_890 -> MAlonzo.Code.Algebra.Structures.T_IsMagma_86
d_isMagma_940 :: T_Group_890 -> T_IsMagma_86
d_isMagma_940 T_Group_890
v0
  = (T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> T_IsMagma_86
forall a b. a -> b
coe
      T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202
      ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368
         ((T_IsGroup_580 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsGroup_580 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_594
            ((T_Group_890 -> T_IsGroup_580) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Group_890 -> T_IsGroup_580
d_isGroup_918 (T_Group_890 -> AgdaAny
forall a b. a -> b
coe T_Group_890
v0))))
-- Algebra.Bundles.Group._.isMonoid
d_isMonoid_942 ::
  T_Group_890 -> MAlonzo.Code.Algebra.Structures.T_IsMonoid_358
d_isMonoid_942 :: T_Group_890 -> T_IsMonoid_358
d_isMonoid_942 T_Group_890
v0
  = (T_IsGroup_580 -> T_IsMonoid_358) -> AgdaAny -> T_IsMonoid_358
forall a b. a -> b
coe
      T_IsGroup_580 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_594
      ((T_Group_890 -> T_IsGroup_580) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Group_890 -> T_IsGroup_580
d_isGroup_918 (T_Group_890 -> AgdaAny
forall a b. a -> b
coe T_Group_890
v0))
-- Algebra.Bundles.Group._.isPartialEquivalence
d_isPartialEquivalence_944 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Group_890 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_944 :: () -> () -> T_Group_890 -> T_IsPartialEquivalence_16
d_isPartialEquivalence_944 ~()
v0 ~()
v1 T_Group_890
v2
  = T_Group_890 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_944 T_Group_890
v2
du_isPartialEquivalence_944 ::
  T_Group_890 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_944 :: T_Group_890 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_944 T_Group_890
v0
  = let v1 :: T_IsGroup_580
v1 = T_Group_890 -> T_IsGroup_580
d_isGroup_918 (T_Group_890 -> T_Group_890
forall a b. a -> b
coe T_Group_890
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsMonoid_358
v2
             = T_IsGroup_580 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_594 (T_IsGroup_580 -> T_IsGroup_580
forall a b. a -> b
coe T_IsGroup_580
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_194
v3
                = T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368 (T_IsMonoid_358 -> T_IsMonoid_358
forall a b. a -> b
coe T_IsMonoid_358
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsMagma_86
v4 = T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202 (T_IsSemigroup_194 -> T_IsSemigroup_194
forall a b. a -> b
coe T_IsSemigroup_194
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_86 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsMagma_86 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_94 (T_IsMagma_86 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86
v4))))))
-- Algebra.Bundles.Group._.isSemigroup
d_isSemigroup_946 ::
  T_Group_890 -> MAlonzo.Code.Algebra.Structures.T_IsSemigroup_194
d_isSemigroup_946 :: T_Group_890 -> T_IsSemigroup_194
d_isSemigroup_946 T_Group_890
v0
  = (T_IsMonoid_358 -> T_IsSemigroup_194)
-> AgdaAny -> T_IsSemigroup_194
forall a b. a -> b
coe
      T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368
      ((T_IsGroup_580 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsGroup_580 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_594
         ((T_Group_890 -> T_IsGroup_580) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Group_890 -> T_IsGroup_580
d_isGroup_918 (T_Group_890 -> AgdaAny
forall a b. a -> b
coe T_Group_890
v0)))
-- Algebra.Bundles.Group._.refl
d_refl_948 :: T_Group_890 -> AgdaAny -> AgdaAny
d_refl_948 :: T_Group_890 -> AgdaAny -> AgdaAny
d_refl_948 T_Group_890
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_86 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_86 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_94
         ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202
            ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368
               ((T_IsGroup_580 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsGroup_580 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_594
                  ((T_Group_890 -> T_IsGroup_580) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Group_890 -> T_IsGroup_580
d_isGroup_918 (T_Group_890 -> AgdaAny
forall a b. a -> b
coe T_Group_890
v0))))))
-- Algebra.Bundles.Group._.reflexive
d_reflexive_950 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Group_890 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_950 :: ()
-> ()
-> T_Group_890
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_950 ~()
v0 ~()
v1 T_Group_890
v2 = T_Group_890 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_950 T_Group_890
v2
du_reflexive_950 ::
  T_Group_890 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_950 :: T_Group_890 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_950 T_Group_890
v0
  = let v1 :: T_IsGroup_580
v1 = T_Group_890 -> T_IsGroup_580
d_isGroup_918 (T_Group_890 -> T_Group_890
forall a b. a -> b
coe T_Group_890
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsMonoid_358
v2
             = T_IsGroup_580 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_594 (T_IsGroup_580 -> T_IsGroup_580
forall a b. a -> b
coe T_IsGroup_580
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_194
v3
                = T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368 (T_IsMonoid_358 -> T_IsMonoid_358
forall a b. a -> b
coe T_IsMonoid_358
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsMagma_86
v4 = T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202 (T_IsSemigroup_194 -> T_IsSemigroup_194
forall a b. a -> b
coe T_IsSemigroup_194
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_86 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_94 (T_IsMagma_86 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86
v4))
                    AgdaAny
v5))))
-- Algebra.Bundles.Group._.setoid
d_setoid_952 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Group_890 -> MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_952 :: () -> () -> T_Group_890 -> T_Setoid_44
d_setoid_952 ~()
v0 ~()
v1 T_Group_890
v2 = T_Group_890 -> T_Setoid_44
du_setoid_952 T_Group_890
v2
du_setoid_952 ::
  T_Group_890 -> MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_952 :: T_Group_890 -> T_Setoid_44
du_setoid_952 T_Group_890
v0
  = let v1 :: T_IsGroup_580
v1 = T_Group_890 -> T_IsGroup_580
d_isGroup_918 (T_Group_890 -> T_Group_890
forall a b. a -> b
coe T_Group_890
v0) in
    AgdaAny -> T_Setoid_44
forall a b. a -> b
coe
      (let v2 :: T_IsMonoid_358
v2
             = T_IsGroup_580 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_594 (T_IsGroup_580 -> T_IsGroup_580
forall a b. a -> b
coe T_IsGroup_580
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_194
v3
                = T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368 (T_IsMonoid_358 -> T_IsMonoid_358
forall a b. a -> b
coe T_IsMonoid_358
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsMagma_86 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMagma_86 -> T_Setoid_44
MAlonzo.Code.Algebra.Structures.du_setoid_110
               ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202 (T_IsSemigroup_194 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194
v3)))))
-- Algebra.Bundles.Group._.sym
d_sym_954 ::
  T_Group_890 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_954 :: T_Group_890 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_954 T_Group_890
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_86 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_86 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_94
         ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202
            ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368
               ((T_IsGroup_580 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsGroup_580 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_594
                  ((T_Group_890 -> T_IsGroup_580) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Group_890 -> T_IsGroup_580
d_isGroup_918 (T_Group_890 -> AgdaAny
forall a b. a -> b
coe T_Group_890
v0))))))
-- Algebra.Bundles.Group._.trans
d_trans_956 ::
  T_Group_890 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_956 :: T_Group_890
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_956 T_Group_890
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_86 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_86 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_94
         ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202
            ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368
               ((T_IsGroup_580 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsGroup_580 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_594
                  ((T_Group_890 -> T_IsGroup_580) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Group_890 -> T_IsGroup_580
d_isGroup_918 (T_Group_890 -> AgdaAny
forall a b. a -> b
coe T_Group_890
v0))))))
-- Algebra.Bundles.Group._.uniqueʳ-⁻¹
d_unique'691''45''8315''185'_958 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Group_890 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_unique'691''45''8315''185'_958 :: () -> () -> T_Group_890 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_unique'691''45''8315''185'_958 ~()
v0 ~()
v1 T_Group_890
v2
  = T_Group_890 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_unique'691''45''8315''185'_958 T_Group_890
v2
du_unique'691''45''8315''185'_958 ::
  T_Group_890 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_unique'691''45''8315''185'_958 :: T_Group_890 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_unique'691''45''8315''185'_958 T_Group_890
v0
  = ((AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> (AgdaAny -> AgdaAny)
 -> T_IsGroup_580
 -> 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_580
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.du_unique'691''45''8315''185'_654
      ((T_Group_890 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Group_890 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__912 (T_Group_890 -> AgdaAny
forall a b. a -> b
coe T_Group_890
v0)) ((T_Group_890 -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Group_890 -> AgdaAny
d_ε_914 (T_Group_890 -> AgdaAny
forall a b. a -> b
coe T_Group_890
v0))
      ((T_Group_890 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Group_890 -> AgdaAny -> AgdaAny
d__'8315''185'_916 (T_Group_890 -> AgdaAny
forall a b. a -> b
coe T_Group_890
v0)) ((T_Group_890 -> T_IsGroup_580) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Group_890 -> T_IsGroup_580
d_isGroup_918 (T_Group_890 -> AgdaAny
forall a b. a -> b
coe T_Group_890
v0))
-- Algebra.Bundles.Group._.uniqueˡ-⁻¹
d_unique'737''45''8315''185'_960 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Group_890 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_unique'737''45''8315''185'_960 :: () -> () -> T_Group_890 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_unique'737''45''8315''185'_960 ~()
v0 ~()
v1 T_Group_890
v2
  = T_Group_890 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_unique'737''45''8315''185'_960 T_Group_890
v2
du_unique'737''45''8315''185'_960 ::
  T_Group_890 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_unique'737''45''8315''185'_960 :: T_Group_890 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_unique'737''45''8315''185'_960 T_Group_890
v0
  = ((AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> (AgdaAny -> AgdaAny)
 -> T_IsGroup_580
 -> 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_580
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.du_unique'737''45''8315''185'_648
      ((T_Group_890 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Group_890 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__912 (T_Group_890 -> AgdaAny
forall a b. a -> b
coe T_Group_890
v0)) ((T_Group_890 -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Group_890 -> AgdaAny
d_ε_914 (T_Group_890 -> AgdaAny
forall a b. a -> b
coe T_Group_890
v0))
      ((T_Group_890 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Group_890 -> AgdaAny -> AgdaAny
d__'8315''185'_916 (T_Group_890 -> AgdaAny
forall a b. a -> b
coe T_Group_890
v0)) ((T_Group_890 -> T_IsGroup_580) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Group_890 -> T_IsGroup_580
d_isGroup_918 (T_Group_890 -> AgdaAny
forall a b. a -> b
coe T_Group_890
v0))
-- Algebra.Bundles.Group._.⁻¹-cong
d_'8315''185''45'cong_962 ::
  T_Group_890 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8315''185''45'cong_962 :: T_Group_890 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8315''185''45'cong_962 T_Group_890
v0
  = (T_IsGroup_580 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsGroup_580 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8315''185''45'cong_598
      ((T_Group_890 -> T_IsGroup_580) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Group_890 -> T_IsGroup_580
d_isGroup_918 (T_Group_890 -> AgdaAny
forall a b. a -> b
coe T_Group_890
v0))
-- Algebra.Bundles.Group._.∙-cong
d_'8729''45'cong_964 ::
  T_Group_890 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_964 :: T_Group_890
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_964 T_Group_890
v0
  = (T_IsMagma_86
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsMagma_86
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_96
      ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202
         ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368
            ((T_IsGroup_580 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsGroup_580 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_594
               ((T_Group_890 -> T_IsGroup_580) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Group_890 -> T_IsGroup_580
d_isGroup_918 (T_Group_890 -> AgdaAny
forall a b. a -> b
coe T_Group_890
v0)))))
-- Algebra.Bundles.Group._.∙-congʳ
d_'8729''45'cong'691'_966 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Group_890 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_966 :: ()
-> ()
-> T_Group_890
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_966 ~()
v0 ~()
v1 T_Group_890
v2
  = T_Group_890 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_966 T_Group_890
v2
du_'8729''45'cong'691'_966 ::
  T_Group_890 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_966 :: T_Group_890 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_966 T_Group_890
v0
  = let v1 :: T_IsGroup_580
v1 = T_Group_890 -> T_IsGroup_580
d_isGroup_918 (T_Group_890 -> T_Group_890
forall a b. a -> b
coe T_Group_890
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsMonoid_358
v2
             = T_IsGroup_580 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_594 (T_IsGroup_580 -> T_IsGroup_580
forall a b. a -> b
coe T_IsGroup_580
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_194
v3
                = T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368 (T_IsMonoid_358 -> T_IsMonoid_358
forall a b. a -> b
coe T_IsMonoid_358
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsMagma_86
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMagma_86 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'691'_116
               ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202 (T_IsSemigroup_194 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194
v3)))))
-- Algebra.Bundles.Group._.∙-congˡ
d_'8729''45'cong'737'_968 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Group_890 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_968 :: ()
-> ()
-> T_Group_890
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_968 ~()
v0 ~()
v1 T_Group_890
v2
  = T_Group_890 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_968 T_Group_890
v2
du_'8729''45'cong'737'_968 ::
  T_Group_890 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_968 :: T_Group_890 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_968 T_Group_890
v0
  = let v1 :: T_IsGroup_580
v1 = T_Group_890 -> T_IsGroup_580
d_isGroup_918 (T_Group_890 -> T_Group_890
forall a b. a -> b
coe T_Group_890
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsMonoid_358
v2
             = T_IsGroup_580 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_594 (T_IsGroup_580 -> T_IsGroup_580
forall a b. a -> b
coe T_IsGroup_580
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_194
v3
                = T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368 (T_IsMonoid_358 -> T_IsMonoid_358
forall a b. a -> b
coe T_IsMonoid_358
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsMagma_86
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMagma_86 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'737'_112
               ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202 (T_IsSemigroup_194 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194
v3)))))
-- Algebra.Bundles.Group.rawGroup
d_rawGroup_970 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Group_890 -> T_RawGroup_852
d_rawGroup_970 :: () -> () -> T_Group_890 -> T_RawGroup_852
d_rawGroup_970 ~()
v0 ~()
v1 T_Group_890
v2 = T_Group_890 -> T_RawGroup_852
du_rawGroup_970 T_Group_890
v2
du_rawGroup_970 :: T_Group_890 -> T_RawGroup_852
du_rawGroup_970 :: T_Group_890 -> T_RawGroup_852
du_rawGroup_970 T_Group_890
v0
  = ((AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny -> (AgdaAny -> AgdaAny) -> T_RawGroup_852)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_RawGroup_852
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> (AgdaAny -> AgdaAny) -> T_RawGroup_852
C_RawGroup'46'constructor_13903 (T_Group_890 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__912 (T_Group_890 -> T_Group_890
forall a b. a -> b
coe T_Group_890
v0))
      (T_Group_890 -> AgdaAny
d_ε_914 (T_Group_890 -> T_Group_890
forall a b. a -> b
coe T_Group_890
v0)) (T_Group_890 -> AgdaAny -> AgdaAny
d__'8315''185'_916 (T_Group_890 -> T_Group_890
forall a b. a -> b
coe T_Group_890
v0))
-- Algebra.Bundles.Group.monoid
d_monoid_972 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Group_890 -> T_Monoid_506
d_monoid_972 :: () -> () -> T_Group_890 -> T_Monoid_506
d_monoid_972 ~()
v0 ~()
v1 T_Group_890
v2 = T_Group_890 -> T_Monoid_506
du_monoid_972 T_Group_890
v2
du_monoid_972 :: T_Group_890 -> T_Monoid_506
du_monoid_972 :: T_Group_890 -> T_Monoid_506
du_monoid_972 T_Group_890
v0
  = ((AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny -> T_IsMonoid_358 -> T_Monoid_506)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsMonoid_358
-> T_Monoid_506
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> T_IsMonoid_358 -> T_Monoid_506
C_Monoid'46'constructor_8851 (T_Group_890 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__912 (T_Group_890 -> T_Group_890
forall a b. a -> b
coe T_Group_890
v0))
      (T_Group_890 -> AgdaAny
d_ε_914 (T_Group_890 -> T_Group_890
forall a b. a -> b
coe T_Group_890
v0))
      (T_IsGroup_580 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_594
         ((T_Group_890 -> T_IsGroup_580) -> AgdaAny -> T_IsGroup_580
forall a b. a -> b
coe T_Group_890 -> T_IsGroup_580
d_isGroup_918 (T_Group_890 -> AgdaAny
forall a b. a -> b
coe T_Group_890
v0)))
-- Algebra.Bundles.Group._._≉_
d__'8777'__976 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Group_890 -> AgdaAny -> AgdaAny -> ()
d__'8777'__976 :: () -> () -> T_Group_890 -> AgdaAny -> AgdaAny -> ()
d__'8777'__976 = () -> () -> T_Group_890 -> AgdaAny -> AgdaAny -> ()
forall a. a
erased
-- Algebra.Bundles.Group._.magma
d_magma_978 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 -> T_Group_890 -> T_Magma_36
d_magma_978 :: () -> () -> T_Group_890 -> T_Magma_36
d_magma_978 ~()
v0 ~()
v1 T_Group_890
v2 = T_Group_890 -> T_Magma_36
du_magma_978 T_Group_890
v2
du_magma_978 :: T_Group_890 -> T_Magma_36
du_magma_978 :: T_Group_890 -> T_Magma_36
du_magma_978 T_Group_890
v0
  = let v1 :: t
v1 = (T_Group_890 -> T_Monoid_506) -> AgdaAny -> t
forall a b. a -> b
coe T_Group_890 -> T_Monoid_506
du_monoid_972 (T_Group_890 -> AgdaAny
forall a b. a -> b
coe T_Group_890
v0) in
    AgdaAny -> T_Magma_36
forall a b. a -> b
coe ((T_Semigroup_206 -> T_Magma_36) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semigroup_206 -> T_Magma_36
du_magma_254 ((T_Monoid_506 -> T_Semigroup_206) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Monoid_506 -> T_Semigroup_206
du_semigroup_566 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1)))
-- Algebra.Bundles.Group._.rawMagma
d_rawMagma_980 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Group_890 -> T_RawMagma_8
d_rawMagma_980 :: () -> () -> T_Group_890 -> T_RawMagma_8
d_rawMagma_980 ~()
v0 ~()
v1 T_Group_890
v2 = T_Group_890 -> T_RawMagma_8
du_rawMagma_980 T_Group_890
v2
du_rawMagma_980 :: T_Group_890 -> T_RawMagma_8
du_rawMagma_980 :: T_Group_890 -> T_RawMagma_8
du_rawMagma_980 T_Group_890
v0
  = let v1 :: t
v1 = (T_Group_890 -> T_Monoid_506) -> AgdaAny -> t
forall a b. a -> b
coe T_Group_890 -> T_Monoid_506
du_monoid_972 (T_Group_890 -> AgdaAny
forall a b. a -> b
coe T_Group_890
v0) in
    AgdaAny -> T_RawMagma_8
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_Monoid_506 -> T_Semigroup_206) -> AgdaAny -> t
forall a b. a -> b
coe T_Monoid_506 -> T_Semigroup_206
du_semigroup_566 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_Magma_36 -> T_RawMagma_8) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Magma_36 -> T_RawMagma_8
du_rawMagma_80 ((T_Semigroup_206 -> T_Magma_36) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semigroup_206 -> T_Magma_36
du_magma_254 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2))))
-- Algebra.Bundles.Group._.rawMonoid
d_rawMonoid_982 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Group_890 -> T_RawMonoid_474
d_rawMonoid_982 :: () -> () -> T_Group_890 -> T_RawMonoid_474
d_rawMonoid_982 ~()
v0 ~()
v1 T_Group_890
v2 = T_Group_890 -> T_RawMonoid_474
du_rawMonoid_982 T_Group_890
v2
du_rawMonoid_982 :: T_Group_890 -> T_RawMonoid_474
du_rawMonoid_982 :: T_Group_890 -> T_RawMonoid_474
du_rawMonoid_982 T_Group_890
v0
  = (T_Monoid_506 -> T_RawMonoid_474) -> AgdaAny -> T_RawMonoid_474
forall a b. a -> b
coe T_Monoid_506 -> T_RawMonoid_474
du_rawMonoid_576 ((T_Group_890 -> T_Monoid_506) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Group_890 -> T_Monoid_506
du_monoid_972 (T_Group_890 -> AgdaAny
forall a b. a -> b
coe T_Group_890
v0))
-- Algebra.Bundles.Group._.semigroup
d_semigroup_984 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Group_890 -> T_Semigroup_206
d_semigroup_984 :: () -> () -> T_Group_890 -> T_Semigroup_206
d_semigroup_984 ~()
v0 ~()
v1 T_Group_890
v2 = T_Group_890 -> T_Semigroup_206
du_semigroup_984 T_Group_890
v2
du_semigroup_984 :: T_Group_890 -> T_Semigroup_206
du_semigroup_984 :: T_Group_890 -> T_Semigroup_206
du_semigroup_984 T_Group_890
v0
  = (T_Monoid_506 -> T_Semigroup_206) -> AgdaAny -> T_Semigroup_206
forall a b. a -> b
coe T_Monoid_506 -> T_Semigroup_206
du_semigroup_566 ((T_Group_890 -> T_Monoid_506) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Group_890 -> T_Monoid_506
du_monoid_972 (T_Group_890 -> AgdaAny
forall a b. a -> b
coe T_Group_890
v0))
-- Algebra.Bundles.AbelianGroup
d_AbelianGroup_990 :: p -> p -> ()
d_AbelianGroup_990 p
a0 p
a1 = ()
data T_AbelianGroup_990
  = C_AbelianGroup'46'constructor_16529 (AgdaAny ->
                                         AgdaAny -> AgdaAny)
                                        AgdaAny (AgdaAny -> AgdaAny)
                                        MAlonzo.Code.Algebra.Structures.T_IsAbelianGroup_662
-- Algebra.Bundles.AbelianGroup.Carrier
d_Carrier_1008 :: T_AbelianGroup_990 -> ()
d_Carrier_1008 :: T_AbelianGroup_990 -> ()
d_Carrier_1008 = T_AbelianGroup_990 -> ()
forall a. a
erased
-- Algebra.Bundles.AbelianGroup._≈_
d__'8776'__1010 :: T_AbelianGroup_990 -> AgdaAny -> AgdaAny -> ()
d__'8776'__1010 :: T_AbelianGroup_990 -> AgdaAny -> AgdaAny -> ()
d__'8776'__1010 = T_AbelianGroup_990 -> AgdaAny -> AgdaAny -> ()
forall a. a
erased
-- Algebra.Bundles.AbelianGroup._∙_
d__'8729'__1012 ::
  T_AbelianGroup_990 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__1012 :: T_AbelianGroup_990 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__1012 T_AbelianGroup_990
v0
  = case T_AbelianGroup_990 -> T_AbelianGroup_990
forall a b. a -> b
coe T_AbelianGroup_990
v0 of
      C_AbelianGroup'46'constructor_16529 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny
v4 AgdaAny -> AgdaAny
v5 T_IsAbelianGroup_662
v6 -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v3
      T_AbelianGroup_990
_ -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.AbelianGroup.ε
d_ε_1014 :: T_AbelianGroup_990 -> AgdaAny
d_ε_1014 :: T_AbelianGroup_990 -> AgdaAny
d_ε_1014 T_AbelianGroup_990
v0
  = case T_AbelianGroup_990 -> T_AbelianGroup_990
forall a b. a -> b
coe T_AbelianGroup_990
v0 of
      C_AbelianGroup'46'constructor_16529 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny
v4 AgdaAny -> AgdaAny
v5 T_IsAbelianGroup_662
v6 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v4
      T_AbelianGroup_990
_ -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.AbelianGroup._⁻¹
d__'8315''185'_1016 :: T_AbelianGroup_990 -> AgdaAny -> AgdaAny
d__'8315''185'_1016 :: T_AbelianGroup_990 -> AgdaAny -> AgdaAny
d__'8315''185'_1016 T_AbelianGroup_990
v0
  = case T_AbelianGroup_990 -> T_AbelianGroup_990
forall a b. a -> b
coe T_AbelianGroup_990
v0 of
      C_AbelianGroup'46'constructor_16529 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny
v4 AgdaAny -> AgdaAny
v5 T_IsAbelianGroup_662
v6 -> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v5
      T_AbelianGroup_990
_ -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.AbelianGroup.isAbelianGroup
d_isAbelianGroup_1018 ::
  T_AbelianGroup_990 ->
  MAlonzo.Code.Algebra.Structures.T_IsAbelianGroup_662
d_isAbelianGroup_1018 :: T_AbelianGroup_990 -> T_IsAbelianGroup_662
d_isAbelianGroup_1018 T_AbelianGroup_990
v0
  = case T_AbelianGroup_990 -> T_AbelianGroup_990
forall a b. a -> b
coe T_AbelianGroup_990
v0 of
      C_AbelianGroup'46'constructor_16529 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny
v4 AgdaAny -> AgdaAny
v5 T_IsAbelianGroup_662
v6 -> T_IsAbelianGroup_662 -> T_IsAbelianGroup_662
forall a b. a -> b
coe T_IsAbelianGroup_662
v6
      T_AbelianGroup_990
_ -> T_IsAbelianGroup_662
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.AbelianGroup._._-_
d__'45'__1022 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_AbelianGroup_990 -> AgdaAny -> AgdaAny -> AgdaAny
d__'45'__1022 :: () -> () -> T_AbelianGroup_990 -> AgdaAny -> AgdaAny -> AgdaAny
d__'45'__1022 ~()
v0 ~()
v1 T_AbelianGroup_990
v2 = T_AbelianGroup_990 -> AgdaAny -> AgdaAny -> AgdaAny
du__'45'__1022 T_AbelianGroup_990
v2
du__'45'__1022 ::
  T_AbelianGroup_990 -> AgdaAny -> AgdaAny -> AgdaAny
du__'45'__1022 :: T_AbelianGroup_990 -> AgdaAny -> AgdaAny -> AgdaAny
du__'45'__1022 T_AbelianGroup_990
v0
  = let v1 :: AgdaAny -> AgdaAny -> AgdaAny
v1 = T_AbelianGroup_990 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__1012 (T_AbelianGroup_990 -> T_AbelianGroup_990
forall a b. a -> b
coe T_AbelianGroup_990
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: AgdaAny -> AgdaAny
v2 = T_AbelianGroup_990 -> AgdaAny -> AgdaAny
d__'8315''185'_1016 (T_AbelianGroup_990 -> T_AbelianGroup_990
forall a b. a -> b
coe T_AbelianGroup_990
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__'45'__634 ((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_1024 ::
  T_AbelianGroup_990 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_1024 :: T_AbelianGroup_990 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_1024 T_AbelianGroup_990
v0
  = (T_IsSemigroup_194 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsSemigroup_194 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_assoc_204
      ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368
         ((T_IsGroup_580 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsGroup_580 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_594
            ((T_IsAbelianGroup_662 -> T_IsGroup_580) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsAbelianGroup_662 -> T_IsGroup_580
MAlonzo.Code.Algebra.Structures.d_isGroup_674
               ((T_AbelianGroup_990 -> T_IsAbelianGroup_662) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_AbelianGroup_990 -> T_IsAbelianGroup_662
d_isAbelianGroup_1018 (T_AbelianGroup_990 -> AgdaAny
forall a b. a -> b
coe T_AbelianGroup_990
v0)))))
-- Algebra.Bundles.AbelianGroup._.comm
d_comm_1026 :: T_AbelianGroup_990 -> AgdaAny -> AgdaAny -> AgdaAny
d_comm_1026 :: T_AbelianGroup_990 -> AgdaAny -> AgdaAny -> AgdaAny
d_comm_1026 T_AbelianGroup_990
v0
  = (T_IsAbelianGroup_662 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsAbelianGroup_662 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_comm_676
      ((T_AbelianGroup_990 -> T_IsAbelianGroup_662) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_AbelianGroup_990 -> T_IsAbelianGroup_662
d_isAbelianGroup_1018 (T_AbelianGroup_990 -> AgdaAny
forall a b. a -> b
coe T_AbelianGroup_990
v0))
-- Algebra.Bundles.AbelianGroup._.identity
d_identity_1028 ::
  T_AbelianGroup_990 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_identity_1028 :: T_AbelianGroup_990 -> T_Σ_14
d_identity_1028 T_AbelianGroup_990
v0
  = (T_IsMonoid_358 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsMonoid_358 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_identity_370
      ((T_IsGroup_580 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsGroup_580 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_594
         ((T_IsAbelianGroup_662 -> T_IsGroup_580) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsAbelianGroup_662 -> T_IsGroup_580
MAlonzo.Code.Algebra.Structures.d_isGroup_674
            ((T_AbelianGroup_990 -> T_IsAbelianGroup_662) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_AbelianGroup_990 -> T_IsAbelianGroup_662
d_isAbelianGroup_1018 (T_AbelianGroup_990 -> AgdaAny
forall a b. a -> b
coe T_AbelianGroup_990
v0))))
-- Algebra.Bundles.AbelianGroup._.identityʳ
d_identity'691'_1030 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_AbelianGroup_990 -> AgdaAny -> AgdaAny
d_identity'691'_1030 :: () -> () -> T_AbelianGroup_990 -> AgdaAny -> AgdaAny
d_identity'691'_1030 ~()
v0 ~()
v1 T_AbelianGroup_990
v2 = T_AbelianGroup_990 -> AgdaAny -> AgdaAny
du_identity'691'_1030 T_AbelianGroup_990
v2
du_identity'691'_1030 :: T_AbelianGroup_990 -> AgdaAny -> AgdaAny
du_identity'691'_1030 :: T_AbelianGroup_990 -> AgdaAny -> AgdaAny
du_identity'691'_1030 T_AbelianGroup_990
v0
  = let v1 :: T_IsAbelianGroup_662
v1 = T_AbelianGroup_990 -> T_IsAbelianGroup_662
d_isAbelianGroup_1018 (T_AbelianGroup_990 -> T_AbelianGroup_990
forall a b. a -> b
coe T_AbelianGroup_990
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsGroup_580
v2 = T_IsAbelianGroup_662 -> T_IsGroup_580
MAlonzo.Code.Algebra.Structures.d_isGroup_674 (T_IsAbelianGroup_662 -> T_IsAbelianGroup_662
forall a b. a -> b
coe T_IsAbelianGroup_662
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsMonoid_358 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoid_358 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_identity'691'_400
            ((T_IsGroup_580 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_580 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_594 (T_IsGroup_580 -> AgdaAny
forall a b. a -> b
coe T_IsGroup_580
v2))))
-- Algebra.Bundles.AbelianGroup._.identityˡ
d_identity'737'_1032 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_AbelianGroup_990 -> AgdaAny -> AgdaAny
d_identity'737'_1032 :: () -> () -> T_AbelianGroup_990 -> AgdaAny -> AgdaAny
d_identity'737'_1032 ~()
v0 ~()
v1 T_AbelianGroup_990
v2 = T_AbelianGroup_990 -> AgdaAny -> AgdaAny
du_identity'737'_1032 T_AbelianGroup_990
v2
du_identity'737'_1032 :: T_AbelianGroup_990 -> AgdaAny -> AgdaAny
du_identity'737'_1032 :: T_AbelianGroup_990 -> AgdaAny -> AgdaAny
du_identity'737'_1032 T_AbelianGroup_990
v0
  = let v1 :: T_IsAbelianGroup_662
v1 = T_AbelianGroup_990 -> T_IsAbelianGroup_662
d_isAbelianGroup_1018 (T_AbelianGroup_990 -> T_AbelianGroup_990
forall a b. a -> b
coe T_AbelianGroup_990
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsGroup_580
v2 = T_IsAbelianGroup_662 -> T_IsGroup_580
MAlonzo.Code.Algebra.Structures.d_isGroup_674 (T_IsAbelianGroup_662 -> T_IsAbelianGroup_662
forall a b. a -> b
coe T_IsAbelianGroup_662
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsMonoid_358 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoid_358 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_identity'737'_398
            ((T_IsGroup_580 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_580 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_594 (T_IsGroup_580 -> AgdaAny
forall a b. a -> b
coe T_IsGroup_580
v2))))
-- Algebra.Bundles.AbelianGroup._.inverse
d_inverse_1034 ::
  T_AbelianGroup_990 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_inverse_1034 :: T_AbelianGroup_990 -> T_Σ_14
d_inverse_1034 T_AbelianGroup_990
v0
  = (T_IsGroup_580 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsGroup_580 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_inverse_596
      ((T_IsAbelianGroup_662 -> T_IsGroup_580) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsAbelianGroup_662 -> T_IsGroup_580
MAlonzo.Code.Algebra.Structures.d_isGroup_674
         ((T_AbelianGroup_990 -> T_IsAbelianGroup_662) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_AbelianGroup_990 -> T_IsAbelianGroup_662
d_isAbelianGroup_1018 (T_AbelianGroup_990 -> AgdaAny
forall a b. a -> b
coe T_AbelianGroup_990
v0)))
-- Algebra.Bundles.AbelianGroup._.inverseʳ
d_inverse'691'_1036 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_AbelianGroup_990 -> AgdaAny -> AgdaAny
d_inverse'691'_1036 :: () -> () -> T_AbelianGroup_990 -> AgdaAny -> AgdaAny
d_inverse'691'_1036 ~()
v0 ~()
v1 T_AbelianGroup_990
v2 = T_AbelianGroup_990 -> AgdaAny -> AgdaAny
du_inverse'691'_1036 T_AbelianGroup_990
v2
du_inverse'691'_1036 :: T_AbelianGroup_990 -> AgdaAny -> AgdaAny
du_inverse'691'_1036 :: T_AbelianGroup_990 -> AgdaAny -> AgdaAny
du_inverse'691'_1036 T_AbelianGroup_990
v0
  = let v1 :: T_IsAbelianGroup_662
v1 = T_AbelianGroup_990 -> T_IsAbelianGroup_662
d_isAbelianGroup_1018 (T_AbelianGroup_990 -> T_AbelianGroup_990
forall a b. a -> b
coe T_AbelianGroup_990
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsGroup_580 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsGroup_580 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_inverse'691'_642
         ((T_IsAbelianGroup_662 -> T_IsGroup_580) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_662 -> T_IsGroup_580
MAlonzo.Code.Algebra.Structures.d_isGroup_674 (T_IsAbelianGroup_662 -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_662
v1)))
-- Algebra.Bundles.AbelianGroup._.inverseˡ
d_inverse'737'_1038 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_AbelianGroup_990 -> AgdaAny -> AgdaAny
d_inverse'737'_1038 :: () -> () -> T_AbelianGroup_990 -> AgdaAny -> AgdaAny
d_inverse'737'_1038 ~()
v0 ~()
v1 T_AbelianGroup_990
v2 = T_AbelianGroup_990 -> AgdaAny -> AgdaAny
du_inverse'737'_1038 T_AbelianGroup_990
v2
du_inverse'737'_1038 :: T_AbelianGroup_990 -> AgdaAny -> AgdaAny
du_inverse'737'_1038 :: T_AbelianGroup_990 -> AgdaAny -> AgdaAny
du_inverse'737'_1038 T_AbelianGroup_990
v0
  = let v1 :: T_IsAbelianGroup_662
v1 = T_AbelianGroup_990 -> T_IsAbelianGroup_662
d_isAbelianGroup_1018 (T_AbelianGroup_990 -> T_AbelianGroup_990
forall a b. a -> b
coe T_AbelianGroup_990
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsGroup_580 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsGroup_580 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_inverse'737'_640
         ((T_IsAbelianGroup_662 -> T_IsGroup_580) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_662 -> T_IsGroup_580
MAlonzo.Code.Algebra.Structures.d_isGroup_674 (T_IsAbelianGroup_662 -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_662
v1)))
-- Algebra.Bundles.AbelianGroup._.isCommutativeMagma
d_isCommutativeMagma_1040 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_AbelianGroup_990 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMagma_122
d_isCommutativeMagma_1040 :: () -> () -> T_AbelianGroup_990 -> T_IsCommutativeMagma_122
d_isCommutativeMagma_1040 ~()
v0 ~()
v1 T_AbelianGroup_990
v2
  = T_AbelianGroup_990 -> T_IsCommutativeMagma_122
du_isCommutativeMagma_1040 T_AbelianGroup_990
v2
du_isCommutativeMagma_1040 ::
  T_AbelianGroup_990 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMagma_122
du_isCommutativeMagma_1040 :: T_AbelianGroup_990 -> T_IsCommutativeMagma_122
du_isCommutativeMagma_1040 T_AbelianGroup_990
v0
  = let v1 :: T_IsAbelianGroup_662
v1 = T_AbelianGroup_990 -> T_IsAbelianGroup_662
d_isAbelianGroup_1018 (T_AbelianGroup_990 -> T_AbelianGroup_990
forall a b. a -> b
coe T_AbelianGroup_990
v0) in
    AgdaAny -> T_IsCommutativeMagma_122
forall a b. a -> b
coe
      (let v2 :: t
v2
             = (T_IsAbelianGroup_662 -> T_IsCommutativeMonoid_406) -> AgdaAny -> t
forall a b. a -> b
coe
                 T_IsAbelianGroup_662 -> T_IsCommutativeMonoid_406
MAlonzo.Code.Algebra.Structures.du_isCommutativeMonoid_728
                 (T_IsAbelianGroup_662 -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_662
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsCommutativeSemigroup_270 -> T_IsCommutativeMagma_122)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCommutativeSemigroup_270 -> T_IsCommutativeMagma_122
MAlonzo.Code.Algebra.Structures.du_isCommutativeMagma_308
            ((T_IsCommutativeMonoid_406 -> T_IsCommutativeSemigroup_270)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsCommutativeMonoid_406 -> T_IsCommutativeSemigroup_270
MAlonzo.Code.Algebra.Structures.du_isCommutativeSemigroup_454
               (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2))))
-- Algebra.Bundles.AbelianGroup._.isCommutativeMonoid
d_isCommutativeMonoid_1042 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_AbelianGroup_990 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMonoid_406
d_isCommutativeMonoid_1042 :: () -> () -> T_AbelianGroup_990 -> T_IsCommutativeMonoid_406
d_isCommutativeMonoid_1042 ~()
v0 ~()
v1 T_AbelianGroup_990
v2
  = T_AbelianGroup_990 -> T_IsCommutativeMonoid_406
du_isCommutativeMonoid_1042 T_AbelianGroup_990
v2
du_isCommutativeMonoid_1042 ::
  T_AbelianGroup_990 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMonoid_406
du_isCommutativeMonoid_1042 :: T_AbelianGroup_990 -> T_IsCommutativeMonoid_406
du_isCommutativeMonoid_1042 T_AbelianGroup_990
v0
  = (T_IsAbelianGroup_662 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> T_IsCommutativeMonoid_406
forall a b. a -> b
coe
      T_IsAbelianGroup_662 -> T_IsCommutativeMonoid_406
MAlonzo.Code.Algebra.Structures.du_isCommutativeMonoid_728
      ((T_AbelianGroup_990 -> T_IsAbelianGroup_662) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_AbelianGroup_990 -> T_IsAbelianGroup_662
d_isAbelianGroup_1018 (T_AbelianGroup_990 -> AgdaAny
forall a b. a -> b
coe T_AbelianGroup_990
v0))
-- Algebra.Bundles.AbelianGroup._.isCommutativeSemigroup
d_isCommutativeSemigroup_1044 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_AbelianGroup_990 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_270
d_isCommutativeSemigroup_1044 :: () -> () -> T_AbelianGroup_990 -> T_IsCommutativeSemigroup_270
d_isCommutativeSemigroup_1044 ~()
v0 ~()
v1 T_AbelianGroup_990
v2
  = T_AbelianGroup_990 -> T_IsCommutativeSemigroup_270
du_isCommutativeSemigroup_1044 T_AbelianGroup_990
v2
du_isCommutativeSemigroup_1044 ::
  T_AbelianGroup_990 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_270
du_isCommutativeSemigroup_1044 :: T_AbelianGroup_990 -> T_IsCommutativeSemigroup_270
du_isCommutativeSemigroup_1044 T_AbelianGroup_990
v0
  = let v1 :: T_IsAbelianGroup_662
v1 = T_AbelianGroup_990 -> T_IsAbelianGroup_662
d_isAbelianGroup_1018 (T_AbelianGroup_990 -> T_AbelianGroup_990
forall a b. a -> b
coe T_AbelianGroup_990
v0) in
    AgdaAny -> T_IsCommutativeSemigroup_270
forall a b. a -> b
coe
      ((T_IsCommutativeMonoid_406 -> T_IsCommutativeSemigroup_270)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCommutativeMonoid_406 -> T_IsCommutativeSemigroup_270
MAlonzo.Code.Algebra.Structures.du_isCommutativeSemigroup_454
         ((T_IsAbelianGroup_662 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsAbelianGroup_662 -> T_IsCommutativeMonoid_406
MAlonzo.Code.Algebra.Structures.du_isCommutativeMonoid_728
            (T_IsAbelianGroup_662 -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_662
v1)))
-- Algebra.Bundles.AbelianGroup._.isEquivalence
d_isEquivalence_1046 ::
  T_AbelianGroup_990 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_1046 :: T_AbelianGroup_990 -> T_IsEquivalence_26
d_isEquivalence_1046 T_AbelianGroup_990
v0
  = (T_IsMagma_86 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      T_IsMagma_86 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_94
      ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202
         ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368
            ((T_IsGroup_580 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsGroup_580 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_594
               ((T_IsAbelianGroup_662 -> T_IsGroup_580) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsAbelianGroup_662 -> T_IsGroup_580
MAlonzo.Code.Algebra.Structures.d_isGroup_674
                  ((T_AbelianGroup_990 -> T_IsAbelianGroup_662) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_AbelianGroup_990 -> T_IsAbelianGroup_662
d_isAbelianGroup_1018 (T_AbelianGroup_990 -> AgdaAny
forall a b. a -> b
coe T_AbelianGroup_990
v0))))))
-- Algebra.Bundles.AbelianGroup._.isGroup
d_isGroup_1048 ::
  T_AbelianGroup_990 -> MAlonzo.Code.Algebra.Structures.T_IsGroup_580
d_isGroup_1048 :: T_AbelianGroup_990 -> T_IsGroup_580
d_isGroup_1048 T_AbelianGroup_990
v0
  = (T_IsAbelianGroup_662 -> T_IsGroup_580) -> AgdaAny -> T_IsGroup_580
forall a b. a -> b
coe
      T_IsAbelianGroup_662 -> T_IsGroup_580
MAlonzo.Code.Algebra.Structures.d_isGroup_674
      ((T_AbelianGroup_990 -> T_IsAbelianGroup_662) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_AbelianGroup_990 -> T_IsAbelianGroup_662
d_isAbelianGroup_1018 (T_AbelianGroup_990 -> AgdaAny
forall a b. a -> b
coe T_AbelianGroup_990
v0))
-- Algebra.Bundles.AbelianGroup._.isMagma
d_isMagma_1050 ::
  T_AbelianGroup_990 -> MAlonzo.Code.Algebra.Structures.T_IsMagma_86
d_isMagma_1050 :: T_AbelianGroup_990 -> T_IsMagma_86
d_isMagma_1050 T_AbelianGroup_990
v0
  = (T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> T_IsMagma_86
forall a b. a -> b
coe
      T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202
      ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368
         ((T_IsGroup_580 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsGroup_580 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_594
            ((T_IsAbelianGroup_662 -> T_IsGroup_580) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsAbelianGroup_662 -> T_IsGroup_580
MAlonzo.Code.Algebra.Structures.d_isGroup_674
               ((T_AbelianGroup_990 -> T_IsAbelianGroup_662) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_AbelianGroup_990 -> T_IsAbelianGroup_662
d_isAbelianGroup_1018 (T_AbelianGroup_990 -> AgdaAny
forall a b. a -> b
coe T_AbelianGroup_990
v0)))))
-- Algebra.Bundles.AbelianGroup._.isMonoid
d_isMonoid_1052 ::
  T_AbelianGroup_990 ->
  MAlonzo.Code.Algebra.Structures.T_IsMonoid_358
d_isMonoid_1052 :: T_AbelianGroup_990 -> T_IsMonoid_358
d_isMonoid_1052 T_AbelianGroup_990
v0
  = (T_IsGroup_580 -> T_IsMonoid_358) -> AgdaAny -> T_IsMonoid_358
forall a b. a -> b
coe
      T_IsGroup_580 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_594
      ((T_IsAbelianGroup_662 -> T_IsGroup_580) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsAbelianGroup_662 -> T_IsGroup_580
MAlonzo.Code.Algebra.Structures.d_isGroup_674
         ((T_AbelianGroup_990 -> T_IsAbelianGroup_662) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_AbelianGroup_990 -> T_IsAbelianGroup_662
d_isAbelianGroup_1018 (T_AbelianGroup_990 -> AgdaAny
forall a b. a -> b
coe T_AbelianGroup_990
v0)))
-- Algebra.Bundles.AbelianGroup._.isPartialEquivalence
d_isPartialEquivalence_1054 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_AbelianGroup_990 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_1054 :: () -> () -> T_AbelianGroup_990 -> T_IsPartialEquivalence_16
d_isPartialEquivalence_1054 ~()
v0 ~()
v1 T_AbelianGroup_990
v2
  = T_AbelianGroup_990 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_1054 T_AbelianGroup_990
v2
du_isPartialEquivalence_1054 ::
  T_AbelianGroup_990 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_1054 :: T_AbelianGroup_990 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_1054 T_AbelianGroup_990
v0
  = let v1 :: T_IsAbelianGroup_662
v1 = T_AbelianGroup_990 -> T_IsAbelianGroup_662
d_isAbelianGroup_1018 (T_AbelianGroup_990 -> T_AbelianGroup_990
forall a b. a -> b
coe T_AbelianGroup_990
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsGroup_580
v2 = T_IsAbelianGroup_662 -> T_IsGroup_580
MAlonzo.Code.Algebra.Structures.d_isGroup_674 (T_IsAbelianGroup_662 -> T_IsAbelianGroup_662
forall a b. a -> b
coe T_IsAbelianGroup_662
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsMonoid_358
v3
                = T_IsGroup_580 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_594 (T_IsGroup_580 -> T_IsGroup_580
forall a b. a -> b
coe T_IsGroup_580
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsSemigroup_194
v4
                   = T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368 (T_IsMonoid_358 -> T_IsMonoid_358
forall a b. a -> b
coe T_IsMonoid_358
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsMagma_86
v5 = T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202 (T_IsSemigroup_194 -> T_IsSemigroup_194
forall a b. a -> b
coe T_IsSemigroup_194
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_86 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsMagma_86 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_94 (T_IsMagma_86 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86
v5)))))))
-- Algebra.Bundles.AbelianGroup._.isSemigroup
d_isSemigroup_1056 ::
  T_AbelianGroup_990 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_194
d_isSemigroup_1056 :: T_AbelianGroup_990 -> T_IsSemigroup_194
d_isSemigroup_1056 T_AbelianGroup_990
v0
  = (T_IsMonoid_358 -> T_IsSemigroup_194)
-> AgdaAny -> T_IsSemigroup_194
forall a b. a -> b
coe
      T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368
      ((T_IsGroup_580 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsGroup_580 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_594
         ((T_IsAbelianGroup_662 -> T_IsGroup_580) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsAbelianGroup_662 -> T_IsGroup_580
MAlonzo.Code.Algebra.Structures.d_isGroup_674
            ((T_AbelianGroup_990 -> T_IsAbelianGroup_662) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_AbelianGroup_990 -> T_IsAbelianGroup_662
d_isAbelianGroup_1018 (T_AbelianGroup_990 -> AgdaAny
forall a b. a -> b
coe T_AbelianGroup_990
v0))))
-- Algebra.Bundles.AbelianGroup._.refl
d_refl_1058 :: T_AbelianGroup_990 -> AgdaAny -> AgdaAny
d_refl_1058 :: T_AbelianGroup_990 -> AgdaAny -> AgdaAny
d_refl_1058 T_AbelianGroup_990
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_86 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_86 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_94
         ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202
            ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368
               ((T_IsGroup_580 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsGroup_580 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_594
                  ((T_IsAbelianGroup_662 -> T_IsGroup_580) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsAbelianGroup_662 -> T_IsGroup_580
MAlonzo.Code.Algebra.Structures.d_isGroup_674
                     ((T_AbelianGroup_990 -> T_IsAbelianGroup_662) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_AbelianGroup_990 -> T_IsAbelianGroup_662
d_isAbelianGroup_1018 (T_AbelianGroup_990 -> AgdaAny
forall a b. a -> b
coe T_AbelianGroup_990
v0)))))))
-- Algebra.Bundles.AbelianGroup._.reflexive
d_reflexive_1060 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_AbelianGroup_990 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_1060 :: ()
-> ()
-> T_AbelianGroup_990
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_1060 ~()
v0 ~()
v1 T_AbelianGroup_990
v2 = T_AbelianGroup_990
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_1060 T_AbelianGroup_990
v2
du_reflexive_1060 ::
  T_AbelianGroup_990 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_1060 :: T_AbelianGroup_990
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_1060 T_AbelianGroup_990
v0
  = let v1 :: T_IsAbelianGroup_662
v1 = T_AbelianGroup_990 -> T_IsAbelianGroup_662
d_isAbelianGroup_1018 (T_AbelianGroup_990 -> T_AbelianGroup_990
forall a b. a -> b
coe T_AbelianGroup_990
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsGroup_580
v2 = T_IsAbelianGroup_662 -> T_IsGroup_580
MAlonzo.Code.Algebra.Structures.d_isGroup_674 (T_IsAbelianGroup_662 -> T_IsAbelianGroup_662
forall a b. a -> b
coe T_IsAbelianGroup_662
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsMonoid_358
v3
                = T_IsGroup_580 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_594 (T_IsGroup_580 -> T_IsGroup_580
forall a b. a -> b
coe T_IsGroup_580
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsSemigroup_194
v4
                   = T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368 (T_IsMonoid_358 -> T_IsMonoid_358
forall a b. a -> b
coe T_IsMonoid_358
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsMagma_86
v5 = T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202 (T_IsSemigroup_194 -> T_IsSemigroup_194
forall a b. a -> b
coe T_IsSemigroup_194
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_86 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_94 (T_IsMagma_86 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86
v5))
                       AgdaAny
v6)))))
-- Algebra.Bundles.AbelianGroup._.setoid
d_setoid_1062 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_AbelianGroup_990 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_1062 :: () -> () -> T_AbelianGroup_990 -> T_Setoid_44
d_setoid_1062 ~()
v0 ~()
v1 T_AbelianGroup_990
v2 = T_AbelianGroup_990 -> T_Setoid_44
du_setoid_1062 T_AbelianGroup_990
v2
du_setoid_1062 ::
  T_AbelianGroup_990 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_1062 :: T_AbelianGroup_990 -> T_Setoid_44
du_setoid_1062 T_AbelianGroup_990
v0
  = let v1 :: T_IsAbelianGroup_662
v1 = T_AbelianGroup_990 -> T_IsAbelianGroup_662
d_isAbelianGroup_1018 (T_AbelianGroup_990 -> T_AbelianGroup_990
forall a b. a -> b
coe T_AbelianGroup_990
v0) in
    AgdaAny -> T_Setoid_44
forall a b. a -> b
coe
      (let v2 :: T_IsGroup_580
v2 = T_IsAbelianGroup_662 -> T_IsGroup_580
MAlonzo.Code.Algebra.Structures.d_isGroup_674 (T_IsAbelianGroup_662 -> T_IsAbelianGroup_662
forall a b. a -> b
coe T_IsAbelianGroup_662
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsMonoid_358
v3
                = T_IsGroup_580 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_594 (T_IsGroup_580 -> T_IsGroup_580
forall a b. a -> b
coe T_IsGroup_580
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsSemigroup_194
v4
                   = T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368 (T_IsMonoid_358 -> T_IsMonoid_358
forall a b. a -> b
coe T_IsMonoid_358
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               ((T_IsMagma_86 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsMagma_86 -> T_Setoid_44
MAlonzo.Code.Algebra.Structures.du_setoid_110
                  ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202 (T_IsSemigroup_194 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194
v4))))))
-- Algebra.Bundles.AbelianGroup._.sym
d_sym_1064 ::
  T_AbelianGroup_990 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_1064 :: T_AbelianGroup_990 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_1064 T_AbelianGroup_990
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_86 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_86 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_94
         ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202
            ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368
               ((T_IsGroup_580 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsGroup_580 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_594
                  ((T_IsAbelianGroup_662 -> T_IsGroup_580) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsAbelianGroup_662 -> T_IsGroup_580
MAlonzo.Code.Algebra.Structures.d_isGroup_674
                     ((T_AbelianGroup_990 -> T_IsAbelianGroup_662) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_AbelianGroup_990 -> T_IsAbelianGroup_662
d_isAbelianGroup_1018 (T_AbelianGroup_990 -> AgdaAny
forall a b. a -> b
coe T_AbelianGroup_990
v0)))))))
-- Algebra.Bundles.AbelianGroup._.trans
d_trans_1066 ::
  T_AbelianGroup_990 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_1066 :: T_AbelianGroup_990
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_1066 T_AbelianGroup_990
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_86 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_86 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_94
         ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202
            ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368
               ((T_IsGroup_580 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsGroup_580 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_594
                  ((T_IsAbelianGroup_662 -> T_IsGroup_580) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsAbelianGroup_662 -> T_IsGroup_580
MAlonzo.Code.Algebra.Structures.d_isGroup_674
                     ((T_AbelianGroup_990 -> T_IsAbelianGroup_662) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_AbelianGroup_990 -> T_IsAbelianGroup_662
d_isAbelianGroup_1018 (T_AbelianGroup_990 -> AgdaAny
forall a b. a -> b
coe T_AbelianGroup_990
v0)))))))
-- Algebra.Bundles.AbelianGroup._.uniqueʳ-⁻¹
d_unique'691''45''8315''185'_1068 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_AbelianGroup_990 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_unique'691''45''8315''185'_1068 :: ()
-> ()
-> T_AbelianGroup_990
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_unique'691''45''8315''185'_1068 ~()
v0 ~()
v1 T_AbelianGroup_990
v2
  = T_AbelianGroup_990 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_unique'691''45''8315''185'_1068 T_AbelianGroup_990
v2
du_unique'691''45''8315''185'_1068 ::
  T_AbelianGroup_990 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_unique'691''45''8315''185'_1068 :: T_AbelianGroup_990 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_unique'691''45''8315''185'_1068 T_AbelianGroup_990
v0
  = let v1 :: AgdaAny -> AgdaAny -> AgdaAny
v1 = T_AbelianGroup_990 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__1012 (T_AbelianGroup_990 -> T_AbelianGroup_990
forall a b. a -> b
coe T_AbelianGroup_990
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: AgdaAny
v2 = T_AbelianGroup_990 -> AgdaAny
d_ε_1014 (T_AbelianGroup_990 -> T_AbelianGroup_990
forall a b. a -> b
coe T_AbelianGroup_990
v0) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: AgdaAny -> AgdaAny
v3 = T_AbelianGroup_990 -> AgdaAny -> AgdaAny
d__'8315''185'_1016 (T_AbelianGroup_990 -> T_AbelianGroup_990
forall a b. a -> b
coe T_AbelianGroup_990
v0) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsAbelianGroup_662
v4 = T_AbelianGroup_990 -> T_IsAbelianGroup_662
d_isAbelianGroup_1018 (T_AbelianGroup_990 -> T_AbelianGroup_990
forall a b. a -> b
coe T_AbelianGroup_990
v0) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (((AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> (AgdaAny -> AgdaAny)
 -> T_IsGroup_580
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsGroup_580
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.du_unique'691''45''8315''185'_654
                  ((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_662 -> T_IsGroup_580) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_662 -> T_IsGroup_580
MAlonzo.Code.Algebra.Structures.d_isGroup_674 (T_IsAbelianGroup_662 -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_662
v4))))))
-- Algebra.Bundles.AbelianGroup._.uniqueˡ-⁻¹
d_unique'737''45''8315''185'_1070 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_AbelianGroup_990 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_unique'737''45''8315''185'_1070 :: ()
-> ()
-> T_AbelianGroup_990
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_unique'737''45''8315''185'_1070 ~()
v0 ~()
v1 T_AbelianGroup_990
v2
  = T_AbelianGroup_990 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_unique'737''45''8315''185'_1070 T_AbelianGroup_990
v2
du_unique'737''45''8315''185'_1070 ::
  T_AbelianGroup_990 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_unique'737''45''8315''185'_1070 :: T_AbelianGroup_990 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_unique'737''45''8315''185'_1070 T_AbelianGroup_990
v0
  = let v1 :: AgdaAny -> AgdaAny -> AgdaAny
v1 = T_AbelianGroup_990 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__1012 (T_AbelianGroup_990 -> T_AbelianGroup_990
forall a b. a -> b
coe T_AbelianGroup_990
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: AgdaAny
v2 = T_AbelianGroup_990 -> AgdaAny
d_ε_1014 (T_AbelianGroup_990 -> T_AbelianGroup_990
forall a b. a -> b
coe T_AbelianGroup_990
v0) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: AgdaAny -> AgdaAny
v3 = T_AbelianGroup_990 -> AgdaAny -> AgdaAny
d__'8315''185'_1016 (T_AbelianGroup_990 -> T_AbelianGroup_990
forall a b. a -> b
coe T_AbelianGroup_990
v0) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsAbelianGroup_662
v4 = T_AbelianGroup_990 -> T_IsAbelianGroup_662
d_isAbelianGroup_1018 (T_AbelianGroup_990 -> T_AbelianGroup_990
forall a b. a -> b
coe T_AbelianGroup_990
v0) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (((AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> (AgdaAny -> AgdaAny)
 -> T_IsGroup_580
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsGroup_580
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.du_unique'737''45''8315''185'_648
                  ((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_662 -> T_IsGroup_580) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_662 -> T_IsGroup_580
MAlonzo.Code.Algebra.Structures.d_isGroup_674 (T_IsAbelianGroup_662 -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_662
v4))))))
-- Algebra.Bundles.AbelianGroup._.⁻¹-cong
d_'8315''185''45'cong_1072 ::
  T_AbelianGroup_990 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8315''185''45'cong_1072 :: T_AbelianGroup_990 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8315''185''45'cong_1072 T_AbelianGroup_990
v0
  = (T_IsGroup_580 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsGroup_580 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8315''185''45'cong_598
      ((T_IsAbelianGroup_662 -> T_IsGroup_580) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsAbelianGroup_662 -> T_IsGroup_580
MAlonzo.Code.Algebra.Structures.d_isGroup_674
         ((T_AbelianGroup_990 -> T_IsAbelianGroup_662) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_AbelianGroup_990 -> T_IsAbelianGroup_662
d_isAbelianGroup_1018 (T_AbelianGroup_990 -> AgdaAny
forall a b. a -> b
coe T_AbelianGroup_990
v0)))
-- Algebra.Bundles.AbelianGroup._.∙-cong
d_'8729''45'cong_1074 ::
  T_AbelianGroup_990 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_1074 :: T_AbelianGroup_990
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_1074 T_AbelianGroup_990
v0
  = (T_IsMagma_86
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsMagma_86
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_96
      ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202
         ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368
            ((T_IsGroup_580 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsGroup_580 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_594
               ((T_IsAbelianGroup_662 -> T_IsGroup_580) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsAbelianGroup_662 -> T_IsGroup_580
MAlonzo.Code.Algebra.Structures.d_isGroup_674
                  ((T_AbelianGroup_990 -> T_IsAbelianGroup_662) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_AbelianGroup_990 -> T_IsAbelianGroup_662
d_isAbelianGroup_1018 (T_AbelianGroup_990 -> AgdaAny
forall a b. a -> b
coe T_AbelianGroup_990
v0))))))
-- Algebra.Bundles.AbelianGroup._.∙-congʳ
d_'8729''45'cong'691'_1076 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_AbelianGroup_990 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_1076 :: ()
-> ()
-> T_AbelianGroup_990
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_1076 ~()
v0 ~()
v1 T_AbelianGroup_990
v2
  = T_AbelianGroup_990
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1076 T_AbelianGroup_990
v2
du_'8729''45'cong'691'_1076 ::
  T_AbelianGroup_990 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1076 :: T_AbelianGroup_990
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1076 T_AbelianGroup_990
v0
  = let v1 :: T_IsAbelianGroup_662
v1 = T_AbelianGroup_990 -> T_IsAbelianGroup_662
d_isAbelianGroup_1018 (T_AbelianGroup_990 -> T_AbelianGroup_990
forall a b. a -> b
coe T_AbelianGroup_990
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsGroup_580
v2 = T_IsAbelianGroup_662 -> T_IsGroup_580
MAlonzo.Code.Algebra.Structures.d_isGroup_674 (T_IsAbelianGroup_662 -> T_IsAbelianGroup_662
forall a b. a -> b
coe T_IsAbelianGroup_662
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsMonoid_358
v3
                = T_IsGroup_580 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_594 (T_IsGroup_580 -> T_IsGroup_580
forall a b. a -> b
coe T_IsGroup_580
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsSemigroup_194
v4
                   = T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368 (T_IsMonoid_358 -> T_IsMonoid_358
forall a b. a -> b
coe T_IsMonoid_358
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               ((T_IsMagma_86
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsMagma_86 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'691'_116
                  ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202 (T_IsSemigroup_194 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194
v4))))))
-- Algebra.Bundles.AbelianGroup._.∙-congˡ
d_'8729''45'cong'737'_1078 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_AbelianGroup_990 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_1078 :: ()
-> ()
-> T_AbelianGroup_990
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_1078 ~()
v0 ~()
v1 T_AbelianGroup_990
v2
  = T_AbelianGroup_990
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1078 T_AbelianGroup_990
v2
du_'8729''45'cong'737'_1078 ::
  T_AbelianGroup_990 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1078 :: T_AbelianGroup_990
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1078 T_AbelianGroup_990
v0
  = let v1 :: T_IsAbelianGroup_662
v1 = T_AbelianGroup_990 -> T_IsAbelianGroup_662
d_isAbelianGroup_1018 (T_AbelianGroup_990 -> T_AbelianGroup_990
forall a b. a -> b
coe T_AbelianGroup_990
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsGroup_580
v2 = T_IsAbelianGroup_662 -> T_IsGroup_580
MAlonzo.Code.Algebra.Structures.d_isGroup_674 (T_IsAbelianGroup_662 -> T_IsAbelianGroup_662
forall a b. a -> b
coe T_IsAbelianGroup_662
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsMonoid_358
v3
                = T_IsGroup_580 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_594 (T_IsGroup_580 -> T_IsGroup_580
forall a b. a -> b
coe T_IsGroup_580
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsSemigroup_194
v4
                   = T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368 (T_IsMonoid_358 -> T_IsMonoid_358
forall a b. a -> b
coe T_IsMonoid_358
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               ((T_IsMagma_86
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsMagma_86 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'737'_112
                  ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202 (T_IsSemigroup_194 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194
v4))))))
-- Algebra.Bundles.AbelianGroup.group
d_group_1080 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_AbelianGroup_990 -> T_Group_890
d_group_1080 :: () -> () -> T_AbelianGroup_990 -> T_Group_890
d_group_1080 ~()
v0 ~()
v1 T_AbelianGroup_990
v2 = T_AbelianGroup_990 -> T_Group_890
du_group_1080 T_AbelianGroup_990
v2
du_group_1080 :: T_AbelianGroup_990 -> T_Group_890
du_group_1080 :: T_AbelianGroup_990 -> T_Group_890
du_group_1080 T_AbelianGroup_990
v0
  = ((AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny -> (AgdaAny -> AgdaAny) -> T_IsGroup_580 -> T_Group_890)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsGroup_580
-> T_Group_890
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> (AgdaAny -> AgdaAny) -> T_IsGroup_580 -> T_Group_890
C_Group'46'constructor_14575 (T_AbelianGroup_990 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__1012 (T_AbelianGroup_990 -> T_AbelianGroup_990
forall a b. a -> b
coe T_AbelianGroup_990
v0))
      (T_AbelianGroup_990 -> AgdaAny
d_ε_1014 (T_AbelianGroup_990 -> T_AbelianGroup_990
forall a b. a -> b
coe T_AbelianGroup_990
v0)) (T_AbelianGroup_990 -> AgdaAny -> AgdaAny
d__'8315''185'_1016 (T_AbelianGroup_990 -> T_AbelianGroup_990
forall a b. a -> b
coe T_AbelianGroup_990
v0))
      (T_IsAbelianGroup_662 -> T_IsGroup_580
MAlonzo.Code.Algebra.Structures.d_isGroup_674
         ((T_AbelianGroup_990 -> T_IsAbelianGroup_662)
-> AgdaAny -> T_IsAbelianGroup_662
forall a b. a -> b
coe T_AbelianGroup_990 -> T_IsAbelianGroup_662
d_isAbelianGroup_1018 (T_AbelianGroup_990 -> AgdaAny
forall a b. a -> b
coe T_AbelianGroup_990
v0)))
-- Algebra.Bundles.AbelianGroup._._≉_
d__'8777'__1084 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_AbelianGroup_990 -> AgdaAny -> AgdaAny -> ()
d__'8777'__1084 :: () -> () -> T_AbelianGroup_990 -> AgdaAny -> AgdaAny -> ()
d__'8777'__1084 = () -> () -> T_AbelianGroup_990 -> AgdaAny -> AgdaAny -> ()
forall a. a
erased
-- Algebra.Bundles.AbelianGroup._.magma
d_magma_1086 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_AbelianGroup_990 -> T_Magma_36
d_magma_1086 :: () -> () -> T_AbelianGroup_990 -> T_Magma_36
d_magma_1086 ~()
v0 ~()
v1 T_AbelianGroup_990
v2 = T_AbelianGroup_990 -> T_Magma_36
du_magma_1086 T_AbelianGroup_990
v2
du_magma_1086 :: T_AbelianGroup_990 -> T_Magma_36
du_magma_1086 :: T_AbelianGroup_990 -> T_Magma_36
du_magma_1086 T_AbelianGroup_990
v0
  = let v1 :: t
v1 = (T_AbelianGroup_990 -> T_Group_890) -> AgdaAny -> t
forall a b. a -> b
coe T_AbelianGroup_990 -> T_Group_890
du_group_1080 (T_AbelianGroup_990 -> AgdaAny
forall a b. a -> b
coe T_AbelianGroup_990
v0) in
    AgdaAny -> T_Magma_36
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_Group_890 -> T_Monoid_506) -> AgdaAny -> t
forall a b. a -> b
coe T_Group_890 -> T_Monoid_506
du_monoid_972 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_Semigroup_206 -> T_Magma_36) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semigroup_206 -> T_Magma_36
du_magma_254 ((T_Monoid_506 -> T_Semigroup_206) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Monoid_506 -> T_Semigroup_206
du_semigroup_566 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2))))
-- Algebra.Bundles.AbelianGroup._.monoid
d_monoid_1088 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_AbelianGroup_990 -> T_Monoid_506
d_monoid_1088 :: () -> () -> T_AbelianGroup_990 -> T_Monoid_506
d_monoid_1088 ~()
v0 ~()
v1 T_AbelianGroup_990
v2 = T_AbelianGroup_990 -> T_Monoid_506
du_monoid_1088 T_AbelianGroup_990
v2
du_monoid_1088 :: T_AbelianGroup_990 -> T_Monoid_506
du_monoid_1088 :: T_AbelianGroup_990 -> T_Monoid_506
du_monoid_1088 T_AbelianGroup_990
v0 = (T_Group_890 -> T_Monoid_506) -> AgdaAny -> T_Monoid_506
forall a b. a -> b
coe T_Group_890 -> T_Monoid_506
du_monoid_972 ((T_AbelianGroup_990 -> T_Group_890) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_AbelianGroup_990 -> T_Group_890
du_group_1080 (T_AbelianGroup_990 -> AgdaAny
forall a b. a -> b
coe T_AbelianGroup_990
v0))
-- Algebra.Bundles.AbelianGroup._.rawGroup
d_rawGroup_1090 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_AbelianGroup_990 -> T_RawGroup_852
d_rawGroup_1090 :: () -> () -> T_AbelianGroup_990 -> T_RawGroup_852
d_rawGroup_1090 ~()
v0 ~()
v1 T_AbelianGroup_990
v2 = T_AbelianGroup_990 -> T_RawGroup_852
du_rawGroup_1090 T_AbelianGroup_990
v2
du_rawGroup_1090 :: T_AbelianGroup_990 -> T_RawGroup_852
du_rawGroup_1090 :: T_AbelianGroup_990 -> T_RawGroup_852
du_rawGroup_1090 T_AbelianGroup_990
v0
  = (T_Group_890 -> T_RawGroup_852) -> AgdaAny -> T_RawGroup_852
forall a b. a -> b
coe T_Group_890 -> T_RawGroup_852
du_rawGroup_970 ((T_AbelianGroup_990 -> T_Group_890) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_AbelianGroup_990 -> T_Group_890
du_group_1080 (T_AbelianGroup_990 -> AgdaAny
forall a b. a -> b
coe T_AbelianGroup_990
v0))
-- Algebra.Bundles.AbelianGroup._.rawMagma
d_rawMagma_1092 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_AbelianGroup_990 -> T_RawMagma_8
d_rawMagma_1092 :: () -> () -> T_AbelianGroup_990 -> T_RawMagma_8
d_rawMagma_1092 ~()
v0 ~()
v1 T_AbelianGroup_990
v2 = T_AbelianGroup_990 -> T_RawMagma_8
du_rawMagma_1092 T_AbelianGroup_990
v2
du_rawMagma_1092 :: T_AbelianGroup_990 -> T_RawMagma_8
du_rawMagma_1092 :: T_AbelianGroup_990 -> T_RawMagma_8
du_rawMagma_1092 T_AbelianGroup_990
v0
  = let v1 :: t
v1 = (T_AbelianGroup_990 -> T_Group_890) -> AgdaAny -> t
forall a b. a -> b
coe T_AbelianGroup_990 -> T_Group_890
du_group_1080 (T_AbelianGroup_990 -> AgdaAny
forall a b. a -> b
coe T_AbelianGroup_990
v0) in
    AgdaAny -> T_RawMagma_8
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_Group_890 -> T_Monoid_506) -> AgdaAny -> t
forall a b. a -> b
coe T_Group_890 -> T_Monoid_506
du_monoid_972 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: t
v3 = (T_Monoid_506 -> T_Semigroup_206) -> AgdaAny -> t
forall a b. a -> b
coe T_Monoid_506 -> T_Semigroup_206
du_semigroup_566 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_Magma_36 -> T_RawMagma_8) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Magma_36 -> T_RawMagma_8
du_rawMagma_80 ((T_Semigroup_206 -> T_Magma_36) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semigroup_206 -> T_Magma_36
du_magma_254 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3)))))
-- Algebra.Bundles.AbelianGroup._.rawMonoid
d_rawMonoid_1094 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_AbelianGroup_990 -> T_RawMonoid_474
d_rawMonoid_1094 :: () -> () -> T_AbelianGroup_990 -> T_RawMonoid_474
d_rawMonoid_1094 ~()
v0 ~()
v1 T_AbelianGroup_990
v2 = T_AbelianGroup_990 -> T_RawMonoid_474
du_rawMonoid_1094 T_AbelianGroup_990
v2
du_rawMonoid_1094 :: T_AbelianGroup_990 -> T_RawMonoid_474
du_rawMonoid_1094 :: T_AbelianGroup_990 -> T_RawMonoid_474
du_rawMonoid_1094 T_AbelianGroup_990
v0
  = let v1 :: t
v1 = (T_AbelianGroup_990 -> T_Group_890) -> AgdaAny -> t
forall a b. a -> b
coe T_AbelianGroup_990 -> T_Group_890
du_group_1080 (T_AbelianGroup_990 -> AgdaAny
forall a b. a -> b
coe T_AbelianGroup_990
v0) in
    AgdaAny -> T_RawMonoid_474
forall a b. a -> b
coe ((T_Monoid_506 -> T_RawMonoid_474) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Monoid_506 -> T_RawMonoid_474
du_rawMonoid_576 ((T_Group_890 -> T_Monoid_506) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Group_890 -> T_Monoid_506
du_monoid_972 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1)))
-- Algebra.Bundles.AbelianGroup._.semigroup
d_semigroup_1096 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_AbelianGroup_990 -> T_Semigroup_206
d_semigroup_1096 :: () -> () -> T_AbelianGroup_990 -> T_Semigroup_206
d_semigroup_1096 ~()
v0 ~()
v1 T_AbelianGroup_990
v2 = T_AbelianGroup_990 -> T_Semigroup_206
du_semigroup_1096 T_AbelianGroup_990
v2
du_semigroup_1096 :: T_AbelianGroup_990 -> T_Semigroup_206
du_semigroup_1096 :: T_AbelianGroup_990 -> T_Semigroup_206
du_semigroup_1096 T_AbelianGroup_990
v0
  = let v1 :: t
v1 = (T_AbelianGroup_990 -> T_Group_890) -> AgdaAny -> t
forall a b. a -> b
coe T_AbelianGroup_990 -> T_Group_890
du_group_1080 (T_AbelianGroup_990 -> AgdaAny
forall a b. a -> b
coe T_AbelianGroup_990
v0) in
    AgdaAny -> T_Semigroup_206
forall a b. a -> b
coe ((T_Monoid_506 -> T_Semigroup_206) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Monoid_506 -> T_Semigroup_206
du_semigroup_566 ((T_Group_890 -> T_Monoid_506) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Group_890 -> T_Monoid_506
du_monoid_972 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1)))
-- Algebra.Bundles.AbelianGroup.commutativeMonoid
d_commutativeMonoid_1098 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_AbelianGroup_990 -> T_CommutativeMonoid_582
d_commutativeMonoid_1098 :: () -> () -> T_AbelianGroup_990 -> T_CommutativeMonoid_582
d_commutativeMonoid_1098 ~()
v0 ~()
v1 T_AbelianGroup_990
v2 = T_AbelianGroup_990 -> T_CommutativeMonoid_582
du_commutativeMonoid_1098 T_AbelianGroup_990
v2
du_commutativeMonoid_1098 ::
  T_AbelianGroup_990 -> T_CommutativeMonoid_582
du_commutativeMonoid_1098 :: T_AbelianGroup_990 -> T_CommutativeMonoid_582
du_commutativeMonoid_1098 T_AbelianGroup_990
v0
  = ((AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny -> T_IsCommutativeMonoid_406 -> T_CommutativeMonoid_582)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_CommutativeMonoid_582
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> T_IsCommutativeMonoid_406 -> T_CommutativeMonoid_582
C_CommutativeMonoid'46'constructor_10343 (T_AbelianGroup_990 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__1012 (T_AbelianGroup_990 -> T_AbelianGroup_990
forall a b. a -> b
coe T_AbelianGroup_990
v0))
      (T_AbelianGroup_990 -> AgdaAny
d_ε_1014 (T_AbelianGroup_990 -> T_AbelianGroup_990
forall a b. a -> b
coe T_AbelianGroup_990
v0))
      ((T_IsAbelianGroup_662 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsAbelianGroup_662 -> T_IsCommutativeMonoid_406
MAlonzo.Code.Algebra.Structures.du_isCommutativeMonoid_728
         ((T_AbelianGroup_990 -> T_IsAbelianGroup_662) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_AbelianGroup_990 -> T_IsAbelianGroup_662
d_isAbelianGroup_1018 (T_AbelianGroup_990 -> AgdaAny
forall a b. a -> b
coe T_AbelianGroup_990
v0)))
-- Algebra.Bundles.AbelianGroup._.commutativeMagma
d_commutativeMagma_1102 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_AbelianGroup_990 -> T_CommutativeMagma_148
d_commutativeMagma_1102 :: () -> () -> T_AbelianGroup_990 -> T_CommutativeMagma_148
d_commutativeMagma_1102 ~()
v0 ~()
v1 T_AbelianGroup_990
v2 = T_AbelianGroup_990 -> T_CommutativeMagma_148
du_commutativeMagma_1102 T_AbelianGroup_990
v2
du_commutativeMagma_1102 ::
  T_AbelianGroup_990 -> T_CommutativeMagma_148
du_commutativeMagma_1102 :: T_AbelianGroup_990 -> T_CommutativeMagma_148
du_commutativeMagma_1102 T_AbelianGroup_990
v0
  = let v1 :: t
v1 = (T_AbelianGroup_990 -> T_CommutativeMonoid_582) -> AgdaAny -> t
forall a b. a -> b
coe T_AbelianGroup_990 -> T_CommutativeMonoid_582
du_commutativeMonoid_1098 (T_AbelianGroup_990 -> AgdaAny
forall a b. a -> b
coe T_AbelianGroup_990
v0) in
    AgdaAny -> T_CommutativeMagma_148
forall a b. a -> b
coe
      ((T_CommutativeSemigroup_332 -> T_CommutativeMagma_148)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_CommutativeSemigroup_332 -> T_CommutativeMagma_148
du_commutativeMagma_396 ((T_CommutativeMonoid_582 -> T_CommutativeSemigroup_332)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeMonoid_582 -> T_CommutativeSemigroup_332
du_commutativeSemigroup_664 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1)))
-- Algebra.Bundles.AbelianGroup._.commutativeSemigroup
d_commutativeSemigroup_1104 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_AbelianGroup_990 -> T_CommutativeSemigroup_332
d_commutativeSemigroup_1104 :: () -> () -> T_AbelianGroup_990 -> T_CommutativeSemigroup_332
d_commutativeSemigroup_1104 ~()
v0 ~()
v1 T_AbelianGroup_990
v2
  = T_AbelianGroup_990 -> T_CommutativeSemigroup_332
du_commutativeSemigroup_1104 T_AbelianGroup_990
v2
du_commutativeSemigroup_1104 ::
  T_AbelianGroup_990 -> T_CommutativeSemigroup_332
du_commutativeSemigroup_1104 :: T_AbelianGroup_990 -> T_CommutativeSemigroup_332
du_commutativeSemigroup_1104 T_AbelianGroup_990
v0
  = (T_CommutativeMonoid_582 -> T_CommutativeSemigroup_332)
-> AgdaAny -> T_CommutativeSemigroup_332
forall a b. a -> b
coe
      T_CommutativeMonoid_582 -> T_CommutativeSemigroup_332
du_commutativeSemigroup_664
      ((T_AbelianGroup_990 -> T_CommutativeMonoid_582)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_AbelianGroup_990 -> T_CommutativeMonoid_582
du_commutativeMonoid_1098 (T_AbelianGroup_990 -> AgdaAny
forall a b. a -> b
coe T_AbelianGroup_990
v0))
-- Algebra.Bundles.RawLattice
d_RawLattice_1110 :: p -> p -> ()
d_RawLattice_1110 p
a0 p
a1 = ()
data T_RawLattice_1110
  = C_RawLattice'46'constructor_18647 (AgdaAny -> AgdaAny -> AgdaAny)
                                      (AgdaAny -> AgdaAny -> AgdaAny)
-- Algebra.Bundles.RawLattice.Carrier
d_Carrier_1124 :: T_RawLattice_1110 -> ()
d_Carrier_1124 :: T_RawLattice_1110 -> ()
d_Carrier_1124 = T_RawLattice_1110 -> ()
forall a. a
erased
-- Algebra.Bundles.RawLattice._≈_
d__'8776'__1126 :: T_RawLattice_1110 -> AgdaAny -> AgdaAny -> ()
d__'8776'__1126 :: T_RawLattice_1110 -> AgdaAny -> AgdaAny -> ()
d__'8776'__1126 = T_RawLattice_1110 -> AgdaAny -> AgdaAny -> ()
forall a. a
erased
-- Algebra.Bundles.RawLattice._∧_
d__'8743'__1128 ::
  T_RawLattice_1110 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8743'__1128 :: T_RawLattice_1110 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8743'__1128 T_RawLattice_1110
v0
  = case T_RawLattice_1110 -> T_RawLattice_1110
forall a b. a -> b
coe T_RawLattice_1110
v0 of
      C_RawLattice'46'constructor_18647 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v3
      T_RawLattice_1110
_ -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.RawLattice._∨_
d__'8744'__1130 ::
  T_RawLattice_1110 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8744'__1130 :: T_RawLattice_1110 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8744'__1130 T_RawLattice_1110
v0
  = case T_RawLattice_1110 -> T_RawLattice_1110
forall a b. a -> b
coe T_RawLattice_1110
v0 of
      C_RawLattice'46'constructor_18647 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v4
      T_RawLattice_1110
_ -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.RawLattice.∨-rawMagma
d_'8744''45'rawMagma_1132 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_RawLattice_1110 -> T_RawMagma_8
d_'8744''45'rawMagma_1132 :: () -> () -> T_RawLattice_1110 -> T_RawMagma_8
d_'8744''45'rawMagma_1132 ~()
v0 ~()
v1 T_RawLattice_1110
v2
  = T_RawLattice_1110 -> T_RawMagma_8
du_'8744''45'rawMagma_1132 T_RawLattice_1110
v2
du_'8744''45'rawMagma_1132 :: T_RawLattice_1110 -> T_RawMagma_8
du_'8744''45'rawMagma_1132 :: T_RawLattice_1110 -> T_RawMagma_8
du_'8744''45'rawMagma_1132 T_RawLattice_1110
v0
  = ((AgdaAny -> AgdaAny -> AgdaAny) -> T_RawMagma_8)
-> (AgdaAny -> AgdaAny -> AgdaAny) -> T_RawMagma_8
forall a b. a -> b
coe (AgdaAny -> AgdaAny -> AgdaAny) -> T_RawMagma_8
C_RawMagma'46'constructor_79 (T_RawLattice_1110 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8744'__1130 (T_RawLattice_1110 -> T_RawLattice_1110
forall a b. a -> b
coe T_RawLattice_1110
v0))
-- Algebra.Bundles.RawLattice.∧-rawMagma
d_'8743''45'rawMagma_1134 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_RawLattice_1110 -> T_RawMagma_8
d_'8743''45'rawMagma_1134 :: () -> () -> T_RawLattice_1110 -> T_RawMagma_8
d_'8743''45'rawMagma_1134 ~()
v0 ~()
v1 T_RawLattice_1110
v2
  = T_RawLattice_1110 -> T_RawMagma_8
du_'8743''45'rawMagma_1134 T_RawLattice_1110
v2
du_'8743''45'rawMagma_1134 :: T_RawLattice_1110 -> T_RawMagma_8
du_'8743''45'rawMagma_1134 :: T_RawLattice_1110 -> T_RawMagma_8
du_'8743''45'rawMagma_1134 T_RawLattice_1110
v0
  = ((AgdaAny -> AgdaAny -> AgdaAny) -> T_RawMagma_8)
-> (AgdaAny -> AgdaAny -> AgdaAny) -> T_RawMagma_8
forall a b. a -> b
coe (AgdaAny -> AgdaAny -> AgdaAny) -> T_RawMagma_8
C_RawMagma'46'constructor_79 (T_RawLattice_1110 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8743'__1128 (T_RawLattice_1110 -> T_RawLattice_1110
forall a b. a -> b
coe T_RawLattice_1110
v0))
-- Algebra.Bundles.RawLattice._._≉_
d__'8777'__1138 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_RawLattice_1110 -> AgdaAny -> AgdaAny -> ()
d__'8777'__1138 :: () -> () -> T_RawLattice_1110 -> AgdaAny -> AgdaAny -> ()
d__'8777'__1138 = () -> () -> T_RawLattice_1110 -> AgdaAny -> AgdaAny -> ()
forall a. a
erased
-- Algebra.Bundles.Lattice
d_Lattice_1144 :: p -> p -> ()
d_Lattice_1144 p
a0 p
a1 = ()
data T_Lattice_1144
  = C_Lattice'46'constructor_19309 (AgdaAny -> AgdaAny -> AgdaAny)
                                   (AgdaAny -> AgdaAny -> AgdaAny)
                                   MAlonzo.Code.Algebra.Structures.T_IsLattice_740
-- Algebra.Bundles.Lattice.Carrier
d_Carrier_1160 :: T_Lattice_1144 -> ()
d_Carrier_1160 :: T_Lattice_1144 -> ()
d_Carrier_1160 = T_Lattice_1144 -> ()
forall a. a
erased
-- Algebra.Bundles.Lattice._≈_
d__'8776'__1162 :: T_Lattice_1144 -> AgdaAny -> AgdaAny -> ()
d__'8776'__1162 :: T_Lattice_1144 -> AgdaAny -> AgdaAny -> ()
d__'8776'__1162 = T_Lattice_1144 -> AgdaAny -> AgdaAny -> ()
forall a. a
erased
-- Algebra.Bundles.Lattice._∨_
d__'8744'__1164 :: T_Lattice_1144 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8744'__1164 :: T_Lattice_1144 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8744'__1164 T_Lattice_1144
v0
  = case T_Lattice_1144 -> T_Lattice_1144
forall a b. a -> b
coe T_Lattice_1144
v0 of
      C_Lattice'46'constructor_19309 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsLattice_740
v5 -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v3
      T_Lattice_1144
_ -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.Lattice._∧_
d__'8743'__1166 :: T_Lattice_1144 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8743'__1166 :: T_Lattice_1144 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8743'__1166 T_Lattice_1144
v0
  = case T_Lattice_1144 -> T_Lattice_1144
forall a b. a -> b
coe T_Lattice_1144
v0 of
      C_Lattice'46'constructor_19309 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsLattice_740
v5 -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v4
      T_Lattice_1144
_ -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.Lattice.isLattice
d_isLattice_1168 ::
  T_Lattice_1144 -> MAlonzo.Code.Algebra.Structures.T_IsLattice_740
d_isLattice_1168 :: T_Lattice_1144 -> T_IsLattice_740
d_isLattice_1168 T_Lattice_1144
v0
  = case T_Lattice_1144 -> T_Lattice_1144
forall a b. a -> b
coe T_Lattice_1144
v0 of
      C_Lattice'46'constructor_19309 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsLattice_740
v5 -> T_IsLattice_740 -> T_IsLattice_740
forall a b. a -> b
coe T_IsLattice_740
v5
      T_Lattice_1144
_ -> T_IsLattice_740
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.Lattice._.absorptive
d_absorptive_1172 ::
  T_Lattice_1144 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_absorptive_1172 :: T_Lattice_1144 -> T_Σ_14
d_absorptive_1172 T_Lattice_1144
v0
  = (T_IsLattice_740 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsLattice_740 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_absorptive_776
      ((T_Lattice_1144 -> T_IsLattice_740) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Lattice_1144 -> T_IsLattice_740
d_isLattice_1168 (T_Lattice_1144 -> AgdaAny
forall a b. a -> b
coe T_Lattice_1144
v0))
-- Algebra.Bundles.Lattice._.isEquivalence
d_isEquivalence_1174 ::
  T_Lattice_1144 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_1174 :: T_Lattice_1144 -> T_IsEquivalence_26
d_isEquivalence_1174 T_Lattice_1144
v0
  = (T_IsLattice_740 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      T_IsLattice_740 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_762
      ((T_Lattice_1144 -> T_IsLattice_740) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Lattice_1144 -> T_IsLattice_740
d_isLattice_1168 (T_Lattice_1144 -> AgdaAny
forall a b. a -> b
coe T_Lattice_1144
v0))
-- Algebra.Bundles.Lattice._.isPartialEquivalence
d_isPartialEquivalence_1176 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Lattice_1144 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_1176 :: () -> () -> T_Lattice_1144 -> T_IsPartialEquivalence_16
d_isPartialEquivalence_1176 ~()
v0 ~()
v1 T_Lattice_1144
v2
  = T_Lattice_1144 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_1176 T_Lattice_1144
v2
du_isPartialEquivalence_1176 ::
  T_Lattice_1144 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_1176 :: T_Lattice_1144 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_1176 T_Lattice_1144
v0
  = let v1 :: T_IsLattice_740
v1 = T_Lattice_1144 -> T_IsLattice_740
d_isLattice_1168 (T_Lattice_1144 -> T_Lattice_1144
forall a b. a -> b
coe T_Lattice_1144
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_IsLattice_740 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_740 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_762 (T_IsLattice_740 -> AgdaAny
forall a b. a -> b
coe T_IsLattice_740
v1)))
-- Algebra.Bundles.Lattice._.refl
d_refl_1178 :: T_Lattice_1144 -> AgdaAny -> AgdaAny
d_refl_1178 :: T_Lattice_1144 -> AgdaAny -> AgdaAny
d_refl_1178 T_Lattice_1144
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_IsLattice_740 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsLattice_740 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_762
         ((T_Lattice_1144 -> T_IsLattice_740) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Lattice_1144 -> T_IsLattice_740
d_isLattice_1168 (T_Lattice_1144 -> AgdaAny
forall a b. a -> b
coe T_Lattice_1144
v0)))
-- Algebra.Bundles.Lattice._.reflexive
d_reflexive_1180 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Lattice_1144 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_1180 :: ()
-> ()
-> T_Lattice_1144
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_1180 ~()
v0 ~()
v1 T_Lattice_1144
v2 = T_Lattice_1144 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_1180 T_Lattice_1144
v2
du_reflexive_1180 ::
  T_Lattice_1144 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_1180 :: T_Lattice_1144 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_1180 T_Lattice_1144
v0
  = let v1 :: T_IsLattice_740
v1 = T_Lattice_1144 -> T_IsLattice_740
d_isLattice_1168 (T_Lattice_1144 -> T_Lattice_1144
forall a b. a -> b
coe T_Lattice_1144
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_IsLattice_740 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_740 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_762 (T_IsLattice_740 -> AgdaAny
forall a b. a -> b
coe T_IsLattice_740
v1))
           AgdaAny
v2)
-- Algebra.Bundles.Lattice._.sym
d_sym_1182 ::
  T_Lattice_1144 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_1182 :: T_Lattice_1144 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_1182 T_Lattice_1144
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_IsLattice_740 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsLattice_740 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_762
         ((T_Lattice_1144 -> T_IsLattice_740) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Lattice_1144 -> T_IsLattice_740
d_isLattice_1168 (T_Lattice_1144 -> AgdaAny
forall a b. a -> b
coe T_Lattice_1144
v0)))
-- Algebra.Bundles.Lattice._.trans
d_trans_1184 ::
  T_Lattice_1144 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_1184 :: T_Lattice_1144
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_1184 T_Lattice_1144
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_IsLattice_740 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsLattice_740 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_762
         ((T_Lattice_1144 -> T_IsLattice_740) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Lattice_1144 -> T_IsLattice_740
d_isLattice_1168 (T_Lattice_1144 -> AgdaAny
forall a b. a -> b
coe T_Lattice_1144
v0)))
-- Algebra.Bundles.Lattice._.∧-absorbs-∨
d_'8743''45'absorbs'45''8744'_1186 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Lattice_1144 -> AgdaAny -> AgdaAny -> AgdaAny
d_'8743''45'absorbs'45''8744'_1186 :: () -> () -> T_Lattice_1144 -> AgdaAny -> AgdaAny -> AgdaAny
d_'8743''45'absorbs'45''8744'_1186 ~()
v0 ~()
v1 T_Lattice_1144
v2
  = T_Lattice_1144 -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'absorbs'45''8744'_1186 T_Lattice_1144
v2
du_'8743''45'absorbs'45''8744'_1186 ::
  T_Lattice_1144 -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'absorbs'45''8744'_1186 :: T_Lattice_1144 -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'absorbs'45''8744'_1186 T_Lattice_1144
v0
  = (T_IsLattice_740 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsLattice_740 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'8743''45'absorbs'45''8744'_792
      ((T_Lattice_1144 -> T_IsLattice_740) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Lattice_1144 -> T_IsLattice_740
d_isLattice_1168 (T_Lattice_1144 -> AgdaAny
forall a b. a -> b
coe T_Lattice_1144
v0))
-- Algebra.Bundles.Lattice._.∧-assoc
d_'8743''45'assoc_1188 ::
  T_Lattice_1144 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8743''45'assoc_1188 :: T_Lattice_1144 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8743''45'assoc_1188 T_Lattice_1144
v0
  = (T_IsLattice_740 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsLattice_740 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8743''45'assoc_772
      ((T_Lattice_1144 -> T_IsLattice_740) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Lattice_1144 -> T_IsLattice_740
d_isLattice_1168 (T_Lattice_1144 -> AgdaAny
forall a b. a -> b
coe T_Lattice_1144
v0))
-- Algebra.Bundles.Lattice._.∧-comm
d_'8743''45'comm_1190 ::
  T_Lattice_1144 -> AgdaAny -> AgdaAny -> AgdaAny
d_'8743''45'comm_1190 :: T_Lattice_1144 -> AgdaAny -> AgdaAny -> AgdaAny
d_'8743''45'comm_1190 T_Lattice_1144
v0
  = (T_IsLattice_740 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsLattice_740 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8743''45'comm_770
      ((T_Lattice_1144 -> T_IsLattice_740) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Lattice_1144 -> T_IsLattice_740
d_isLattice_1168 (T_Lattice_1144 -> AgdaAny
forall a b. a -> b
coe T_Lattice_1144
v0))
-- Algebra.Bundles.Lattice._.∧-cong
d_'8743''45'cong_1192 ::
  T_Lattice_1144 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8743''45'cong_1192 :: T_Lattice_1144
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8743''45'cong_1192 T_Lattice_1144
v0
  = (T_IsLattice_740
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsLattice_740
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8743''45'cong_774
      ((T_Lattice_1144 -> T_IsLattice_740) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Lattice_1144 -> T_IsLattice_740
d_isLattice_1168 (T_Lattice_1144 -> AgdaAny
forall a b. a -> b
coe T_Lattice_1144
v0))
-- Algebra.Bundles.Lattice._.∧-congʳ
d_'8743''45'cong'691'_1194 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Lattice_1144 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8743''45'cong'691'_1194 :: ()
-> ()
-> T_Lattice_1144
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8743''45'cong'691'_1194 ~()
v0 ~()
v1 T_Lattice_1144
v2
  = T_Lattice_1144
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'cong'691'_1194 T_Lattice_1144
v2
du_'8743''45'cong'691'_1194 ::
  T_Lattice_1144 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'cong'691'_1194 :: T_Lattice_1144
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'cong'691'_1194 T_Lattice_1144
v0
  = (T_IsLattice_740
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsLattice_740
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'8743''45'cong'691'_798
      ((T_Lattice_1144 -> T_IsLattice_740) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Lattice_1144 -> T_IsLattice_740
d_isLattice_1168 (T_Lattice_1144 -> AgdaAny
forall a b. a -> b
coe T_Lattice_1144
v0))
-- Algebra.Bundles.Lattice._.∧-congˡ
d_'8743''45'cong'737'_1196 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Lattice_1144 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8743''45'cong'737'_1196 :: ()
-> ()
-> T_Lattice_1144
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8743''45'cong'737'_1196 ~()
v0 ~()
v1 T_Lattice_1144
v2
  = T_Lattice_1144
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'cong'737'_1196 T_Lattice_1144
v2
du_'8743''45'cong'737'_1196 ::
  T_Lattice_1144 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'cong'737'_1196 :: T_Lattice_1144
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'cong'737'_1196 T_Lattice_1144
v0
  = (T_IsLattice_740
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsLattice_740
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'8743''45'cong'737'_794
      ((T_Lattice_1144 -> T_IsLattice_740) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Lattice_1144 -> T_IsLattice_740
d_isLattice_1168 (T_Lattice_1144 -> AgdaAny
forall a b. a -> b
coe T_Lattice_1144
v0))
-- Algebra.Bundles.Lattice._.∨-absorbs-∧
d_'8744''45'absorbs'45''8743'_1198 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Lattice_1144 -> AgdaAny -> AgdaAny -> AgdaAny
d_'8744''45'absorbs'45''8743'_1198 :: () -> () -> T_Lattice_1144 -> AgdaAny -> AgdaAny -> AgdaAny
d_'8744''45'absorbs'45''8743'_1198 ~()
v0 ~()
v1 T_Lattice_1144
v2
  = T_Lattice_1144 -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'absorbs'45''8743'_1198 T_Lattice_1144
v2
du_'8744''45'absorbs'45''8743'_1198 ::
  T_Lattice_1144 -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'absorbs'45''8743'_1198 :: T_Lattice_1144 -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'absorbs'45''8743'_1198 T_Lattice_1144
v0
  = (T_IsLattice_740 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsLattice_740 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'8744''45'absorbs'45''8743'_790
      ((T_Lattice_1144 -> T_IsLattice_740) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Lattice_1144 -> T_IsLattice_740
d_isLattice_1168 (T_Lattice_1144 -> AgdaAny
forall a b. a -> b
coe T_Lattice_1144
v0))
-- Algebra.Bundles.Lattice._.∨-assoc
d_'8744''45'assoc_1200 ::
  T_Lattice_1144 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8744''45'assoc_1200 :: T_Lattice_1144 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8744''45'assoc_1200 T_Lattice_1144
v0
  = (T_IsLattice_740 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsLattice_740 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8744''45'assoc_766
      ((T_Lattice_1144 -> T_IsLattice_740) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Lattice_1144 -> T_IsLattice_740
d_isLattice_1168 (T_Lattice_1144 -> AgdaAny
forall a b. a -> b
coe T_Lattice_1144
v0))
-- Algebra.Bundles.Lattice._.∨-comm
d_'8744''45'comm_1202 ::
  T_Lattice_1144 -> AgdaAny -> AgdaAny -> AgdaAny
d_'8744''45'comm_1202 :: T_Lattice_1144 -> AgdaAny -> AgdaAny -> AgdaAny
d_'8744''45'comm_1202 T_Lattice_1144
v0
  = (T_IsLattice_740 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsLattice_740 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8744''45'comm_764
      ((T_Lattice_1144 -> T_IsLattice_740) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Lattice_1144 -> T_IsLattice_740
d_isLattice_1168 (T_Lattice_1144 -> AgdaAny
forall a b. a -> b
coe T_Lattice_1144
v0))
-- Algebra.Bundles.Lattice._.∨-cong
d_'8744''45'cong_1204 ::
  T_Lattice_1144 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8744''45'cong_1204 :: T_Lattice_1144
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8744''45'cong_1204 T_Lattice_1144
v0
  = (T_IsLattice_740
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsLattice_740
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8744''45'cong_768
      ((T_Lattice_1144 -> T_IsLattice_740) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Lattice_1144 -> T_IsLattice_740
d_isLattice_1168 (T_Lattice_1144 -> AgdaAny
forall a b. a -> b
coe T_Lattice_1144
v0))
-- Algebra.Bundles.Lattice._.∨-congʳ
d_'8744''45'cong'691'_1206 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Lattice_1144 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8744''45'cong'691'_1206 :: ()
-> ()
-> T_Lattice_1144
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8744''45'cong'691'_1206 ~()
v0 ~()
v1 T_Lattice_1144
v2
  = T_Lattice_1144
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'cong'691'_1206 T_Lattice_1144
v2
du_'8744''45'cong'691'_1206 ::
  T_Lattice_1144 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'cong'691'_1206 :: T_Lattice_1144
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'cong'691'_1206 T_Lattice_1144
v0
  = (T_IsLattice_740
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsLattice_740
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'8744''45'cong'691'_806
      ((T_Lattice_1144 -> T_IsLattice_740) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Lattice_1144 -> T_IsLattice_740
d_isLattice_1168 (T_Lattice_1144 -> AgdaAny
forall a b. a -> b
coe T_Lattice_1144
v0))
-- Algebra.Bundles.Lattice._.∨-congˡ
d_'8744''45'cong'737'_1208 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Lattice_1144 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8744''45'cong'737'_1208 :: ()
-> ()
-> T_Lattice_1144
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8744''45'cong'737'_1208 ~()
v0 ~()
v1 T_Lattice_1144
v2
  = T_Lattice_1144
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'cong'737'_1208 T_Lattice_1144
v2
du_'8744''45'cong'737'_1208 ::
  T_Lattice_1144 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'cong'737'_1208 :: T_Lattice_1144
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'cong'737'_1208 T_Lattice_1144
v0
  = (T_IsLattice_740
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsLattice_740
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'8744''45'cong'737'_802
      ((T_Lattice_1144 -> T_IsLattice_740) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Lattice_1144 -> T_IsLattice_740
d_isLattice_1168 (T_Lattice_1144 -> AgdaAny
forall a b. a -> b
coe T_Lattice_1144
v0))
-- Algebra.Bundles.Lattice.rawLattice
d_rawLattice_1210 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Lattice_1144 -> T_RawLattice_1110
d_rawLattice_1210 :: () -> () -> T_Lattice_1144 -> T_RawLattice_1110
d_rawLattice_1210 ~()
v0 ~()
v1 T_Lattice_1144
v2 = T_Lattice_1144 -> T_RawLattice_1110
du_rawLattice_1210 T_Lattice_1144
v2
du_rawLattice_1210 :: T_Lattice_1144 -> T_RawLattice_1110
du_rawLattice_1210 :: T_Lattice_1144 -> T_RawLattice_1110
du_rawLattice_1210 T_Lattice_1144
v0
  = ((AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny) -> T_RawLattice_1110)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_RawLattice_1110
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny) -> T_RawLattice_1110
C_RawLattice'46'constructor_18647 (T_Lattice_1144 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8743'__1166 (T_Lattice_1144 -> T_Lattice_1144
forall a b. a -> b
coe T_Lattice_1144
v0))
      (T_Lattice_1144 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8744'__1164 (T_Lattice_1144 -> T_Lattice_1144
forall a b. a -> b
coe T_Lattice_1144
v0))
-- Algebra.Bundles.Lattice._.∧-rawMagma
d_'8743''45'rawMagma_1214 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Lattice_1144 -> T_RawMagma_8
d_'8743''45'rawMagma_1214 :: () -> () -> T_Lattice_1144 -> T_RawMagma_8
d_'8743''45'rawMagma_1214 ~()
v0 ~()
v1 T_Lattice_1144
v2
  = T_Lattice_1144 -> T_RawMagma_8
du_'8743''45'rawMagma_1214 T_Lattice_1144
v2
du_'8743''45'rawMagma_1214 :: T_Lattice_1144 -> T_RawMagma_8
du_'8743''45'rawMagma_1214 :: T_Lattice_1144 -> T_RawMagma_8
du_'8743''45'rawMagma_1214 T_Lattice_1144
v0
  = (T_RawLattice_1110 -> T_RawMagma_8) -> AgdaAny -> T_RawMagma_8
forall a b. a -> b
coe T_RawLattice_1110 -> T_RawMagma_8
du_'8743''45'rawMagma_1134 ((T_Lattice_1144 -> T_RawLattice_1110) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Lattice_1144 -> T_RawLattice_1110
du_rawLattice_1210 (T_Lattice_1144 -> AgdaAny
forall a b. a -> b
coe T_Lattice_1144
v0))
-- Algebra.Bundles.Lattice._.∨-rawMagma
d_'8744''45'rawMagma_1216 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Lattice_1144 -> T_RawMagma_8
d_'8744''45'rawMagma_1216 :: () -> () -> T_Lattice_1144 -> T_RawMagma_8
d_'8744''45'rawMagma_1216 ~()
v0 ~()
v1 T_Lattice_1144
v2
  = T_Lattice_1144 -> T_RawMagma_8
du_'8744''45'rawMagma_1216 T_Lattice_1144
v2
du_'8744''45'rawMagma_1216 :: T_Lattice_1144 -> T_RawMagma_8
du_'8744''45'rawMagma_1216 :: T_Lattice_1144 -> T_RawMagma_8
du_'8744''45'rawMagma_1216 T_Lattice_1144
v0
  = (T_RawLattice_1110 -> T_RawMagma_8) -> AgdaAny -> T_RawMagma_8
forall a b. a -> b
coe T_RawLattice_1110 -> T_RawMagma_8
du_'8744''45'rawMagma_1132 ((T_Lattice_1144 -> T_RawLattice_1110) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Lattice_1144 -> T_RawLattice_1110
du_rawLattice_1210 (T_Lattice_1144 -> AgdaAny
forall a b. a -> b
coe T_Lattice_1144
v0))
-- Algebra.Bundles.Lattice.setoid
d_setoid_1218 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Lattice_1144 -> MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_1218 :: () -> () -> T_Lattice_1144 -> T_Setoid_44
d_setoid_1218 ~()
v0 ~()
v1 T_Lattice_1144
v2 = T_Lattice_1144 -> T_Setoid_44
du_setoid_1218 T_Lattice_1144
v2
du_setoid_1218 ::
  T_Lattice_1144 -> MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_1218 :: T_Lattice_1144 -> T_Setoid_44
du_setoid_1218 T_Lattice_1144
v0
  = (T_IsEquivalence_26 -> T_Setoid_44)
-> T_IsEquivalence_26 -> T_Setoid_44
forall a b. a -> b
coe
      T_IsEquivalence_26 -> T_Setoid_44
MAlonzo.Code.Relation.Binary.Bundles.C_Setoid'46'constructor_727
      (T_IsLattice_740 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_762
         ((T_Lattice_1144 -> T_IsLattice_740) -> AgdaAny -> T_IsLattice_740
forall a b. a -> b
coe T_Lattice_1144 -> T_IsLattice_740
d_isLattice_1168 (T_Lattice_1144 -> AgdaAny
forall a b. a -> b
coe T_Lattice_1144
v0)))
-- Algebra.Bundles.Lattice._._≉_
d__'8777'__1222 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Lattice_1144 -> AgdaAny -> AgdaAny -> ()
d__'8777'__1222 :: () -> () -> T_Lattice_1144 -> AgdaAny -> AgdaAny -> ()
d__'8777'__1222 = () -> () -> T_Lattice_1144 -> AgdaAny -> AgdaAny -> ()
forall a. a
erased
-- Algebra.Bundles.DistributiveLattice
d_DistributiveLattice_1228 :: p -> p -> ()
d_DistributiveLattice_1228 p
a0 p
a1 = ()
data T_DistributiveLattice_1228
  = C_DistributiveLattice'46'constructor_20939 (AgdaAny ->
                                                AgdaAny -> AgdaAny)
                                               (AgdaAny -> AgdaAny -> AgdaAny)
                                               MAlonzo.Code.Algebra.Structures.T_IsDistributiveLattice_814
-- Algebra.Bundles.DistributiveLattice.Carrier
d_Carrier_1244 :: T_DistributiveLattice_1228 -> ()
d_Carrier_1244 :: T_DistributiveLattice_1228 -> ()
d_Carrier_1244 = T_DistributiveLattice_1228 -> ()
forall a. a
erased
-- Algebra.Bundles.DistributiveLattice._≈_
d__'8776'__1246 ::
  T_DistributiveLattice_1228 -> AgdaAny -> AgdaAny -> ()
d__'8776'__1246 :: T_DistributiveLattice_1228 -> AgdaAny -> AgdaAny -> ()
d__'8776'__1246 = T_DistributiveLattice_1228 -> AgdaAny -> AgdaAny -> ()
forall a. a
erased
-- Algebra.Bundles.DistributiveLattice._∨_
d__'8744'__1248 ::
  T_DistributiveLattice_1228 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8744'__1248 :: T_DistributiveLattice_1228 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8744'__1248 T_DistributiveLattice_1228
v0
  = case T_DistributiveLattice_1228 -> T_DistributiveLattice_1228
forall a b. a -> b
coe T_DistributiveLattice_1228
v0 of
      C_DistributiveLattice'46'constructor_20939 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsDistributiveLattice_814
v5 -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v3
      T_DistributiveLattice_1228
_ -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.DistributiveLattice._∧_
d__'8743'__1250 ::
  T_DistributiveLattice_1228 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8743'__1250 :: T_DistributiveLattice_1228 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8743'__1250 T_DistributiveLattice_1228
v0
  = case T_DistributiveLattice_1228 -> T_DistributiveLattice_1228
forall a b. a -> b
coe T_DistributiveLattice_1228
v0 of
      C_DistributiveLattice'46'constructor_20939 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsDistributiveLattice_814
v5 -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v4
      T_DistributiveLattice_1228
_ -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.DistributiveLattice.isDistributiveLattice
d_isDistributiveLattice_1252 ::
  T_DistributiveLattice_1228 ->
  MAlonzo.Code.Algebra.Structures.T_IsDistributiveLattice_814
d_isDistributiveLattice_1252 :: T_DistributiveLattice_1228 -> T_IsDistributiveLattice_814
d_isDistributiveLattice_1252 T_DistributiveLattice_1228
v0
  = case T_DistributiveLattice_1228 -> T_DistributiveLattice_1228
forall a b. a -> b
coe T_DistributiveLattice_1228
v0 of
      C_DistributiveLattice'46'constructor_20939 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsDistributiveLattice_814
v5 -> T_IsDistributiveLattice_814 -> T_IsDistributiveLattice_814
forall a b. a -> b
coe T_IsDistributiveLattice_814
v5
      T_DistributiveLattice_1228
_ -> T_IsDistributiveLattice_814
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.DistributiveLattice._.absorptive
d_absorptive_1256 ::
  T_DistributiveLattice_1228 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_absorptive_1256 :: T_DistributiveLattice_1228 -> T_Σ_14
d_absorptive_1256 T_DistributiveLattice_1228
v0
  = (T_IsLattice_740 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsLattice_740 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_absorptive_776
      ((T_IsDistributiveLattice_814 -> T_IsLattice_740)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsDistributiveLattice_814 -> T_IsLattice_740
MAlonzo.Code.Algebra.Structures.d_isLattice_824
         ((T_DistributiveLattice_1228 -> T_IsDistributiveLattice_814)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_DistributiveLattice_1228 -> T_IsDistributiveLattice_814
d_isDistributiveLattice_1252 (T_DistributiveLattice_1228 -> AgdaAny
forall a b. a -> b
coe T_DistributiveLattice_1228
v0)))
-- Algebra.Bundles.DistributiveLattice._.isEquivalence
d_isEquivalence_1258 ::
  T_DistributiveLattice_1228 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_1258 :: T_DistributiveLattice_1228 -> T_IsEquivalence_26
d_isEquivalence_1258 T_DistributiveLattice_1228
v0
  = (T_IsLattice_740 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      T_IsLattice_740 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_762
      ((T_IsDistributiveLattice_814 -> T_IsLattice_740)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsDistributiveLattice_814 -> T_IsLattice_740
MAlonzo.Code.Algebra.Structures.d_isLattice_824
         ((T_DistributiveLattice_1228 -> T_IsDistributiveLattice_814)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_DistributiveLattice_1228 -> T_IsDistributiveLattice_814
d_isDistributiveLattice_1252 (T_DistributiveLattice_1228 -> AgdaAny
forall a b. a -> b
coe T_DistributiveLattice_1228
v0)))
-- Algebra.Bundles.DistributiveLattice._.isLattice
d_isLattice_1260 ::
  T_DistributiveLattice_1228 ->
  MAlonzo.Code.Algebra.Structures.T_IsLattice_740
d_isLattice_1260 :: T_DistributiveLattice_1228 -> T_IsLattice_740
d_isLattice_1260 T_DistributiveLattice_1228
v0
  = (T_IsDistributiveLattice_814 -> T_IsLattice_740)
-> AgdaAny -> T_IsLattice_740
forall a b. a -> b
coe
      T_IsDistributiveLattice_814 -> T_IsLattice_740
MAlonzo.Code.Algebra.Structures.d_isLattice_824
      ((T_DistributiveLattice_1228 -> T_IsDistributiveLattice_814)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_DistributiveLattice_1228 -> T_IsDistributiveLattice_814
d_isDistributiveLattice_1252 (T_DistributiveLattice_1228 -> AgdaAny
forall a b. a -> b
coe T_DistributiveLattice_1228
v0))
-- Algebra.Bundles.DistributiveLattice._.isPartialEquivalence
d_isPartialEquivalence_1262 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_DistributiveLattice_1228 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_1262 :: () -> () -> T_DistributiveLattice_1228 -> T_IsPartialEquivalence_16
d_isPartialEquivalence_1262 ~()
v0 ~()
v1 T_DistributiveLattice_1228
v2
  = T_DistributiveLattice_1228 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_1262 T_DistributiveLattice_1228
v2
du_isPartialEquivalence_1262 ::
  T_DistributiveLattice_1228 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_1262 :: T_DistributiveLattice_1228 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_1262 T_DistributiveLattice_1228
v0
  = let v1 :: T_IsDistributiveLattice_814
v1 = T_DistributiveLattice_1228 -> T_IsDistributiveLattice_814
d_isDistributiveLattice_1252 (T_DistributiveLattice_1228 -> T_DistributiveLattice_1228
forall a b. a -> b
coe T_DistributiveLattice_1228
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsLattice_740
v2
             = T_IsDistributiveLattice_814 -> T_IsLattice_740
MAlonzo.Code.Algebra.Structures.d_isLattice_824 (T_IsDistributiveLattice_814 -> T_IsDistributiveLattice_814
forall a b. a -> b
coe T_IsDistributiveLattice_814
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_IsLattice_740 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsLattice_740 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_762 (T_IsLattice_740 -> AgdaAny
forall a b. a -> b
coe T_IsLattice_740
v2))))
-- Algebra.Bundles.DistributiveLattice._.refl
d_refl_1264 :: T_DistributiveLattice_1228 -> AgdaAny -> AgdaAny
d_refl_1264 :: T_DistributiveLattice_1228 -> AgdaAny -> AgdaAny
d_refl_1264 T_DistributiveLattice_1228
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_IsLattice_740 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsLattice_740 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_762
         ((T_IsDistributiveLattice_814 -> T_IsLattice_740)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsDistributiveLattice_814 -> T_IsLattice_740
MAlonzo.Code.Algebra.Structures.d_isLattice_824
            ((T_DistributiveLattice_1228 -> T_IsDistributiveLattice_814)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_DistributiveLattice_1228 -> T_IsDistributiveLattice_814
d_isDistributiveLattice_1252 (T_DistributiveLattice_1228 -> AgdaAny
forall a b. a -> b
coe T_DistributiveLattice_1228
v0))))
-- Algebra.Bundles.DistributiveLattice._.reflexive
d_reflexive_1266 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_DistributiveLattice_1228 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_1266 :: ()
-> ()
-> T_DistributiveLattice_1228
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_1266 ~()
v0 ~()
v1 T_DistributiveLattice_1228
v2 = T_DistributiveLattice_1228
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_1266 T_DistributiveLattice_1228
v2
du_reflexive_1266 ::
  T_DistributiveLattice_1228 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_1266 :: T_DistributiveLattice_1228
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_1266 T_DistributiveLattice_1228
v0
  = let v1 :: T_IsDistributiveLattice_814
v1 = T_DistributiveLattice_1228 -> T_IsDistributiveLattice_814
d_isDistributiveLattice_1252 (T_DistributiveLattice_1228 -> T_DistributiveLattice_1228
forall a b. a -> b
coe T_DistributiveLattice_1228
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsLattice_740
v2
             = T_IsDistributiveLattice_814 -> T_IsLattice_740
MAlonzo.Code.Algebra.Structures.d_isLattice_824 (T_IsDistributiveLattice_814 -> T_IsDistributiveLattice_814
forall a b. a -> b
coe T_IsDistributiveLattice_814
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_IsLattice_740 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_740 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_762 (T_IsLattice_740 -> AgdaAny
forall a b. a -> b
coe T_IsLattice_740
v2))
              AgdaAny
v3))
-- Algebra.Bundles.DistributiveLattice._.sym
d_sym_1268 ::
  T_DistributiveLattice_1228 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_1268 :: T_DistributiveLattice_1228
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_1268 T_DistributiveLattice_1228
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_IsLattice_740 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsLattice_740 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_762
         ((T_IsDistributiveLattice_814 -> T_IsLattice_740)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsDistributiveLattice_814 -> T_IsLattice_740
MAlonzo.Code.Algebra.Structures.d_isLattice_824
            ((T_DistributiveLattice_1228 -> T_IsDistributiveLattice_814)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_DistributiveLattice_1228 -> T_IsDistributiveLattice_814
d_isDistributiveLattice_1252 (T_DistributiveLattice_1228 -> AgdaAny
forall a b. a -> b
coe T_DistributiveLattice_1228
v0))))
-- Algebra.Bundles.DistributiveLattice._.trans
d_trans_1270 ::
  T_DistributiveLattice_1228 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_1270 :: T_DistributiveLattice_1228
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_1270 T_DistributiveLattice_1228
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_IsLattice_740 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsLattice_740 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_762
         ((T_IsDistributiveLattice_814 -> T_IsLattice_740)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsDistributiveLattice_814 -> T_IsLattice_740
MAlonzo.Code.Algebra.Structures.d_isLattice_824
            ((T_DistributiveLattice_1228 -> T_IsDistributiveLattice_814)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_DistributiveLattice_1228 -> T_IsDistributiveLattice_814
d_isDistributiveLattice_1252 (T_DistributiveLattice_1228 -> AgdaAny
forall a b. a -> b
coe T_DistributiveLattice_1228
v0))))
-- Algebra.Bundles.DistributiveLattice._.∧-absorbs-∨
d_'8743''45'absorbs'45''8744'_1272 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_DistributiveLattice_1228 -> AgdaAny -> AgdaAny -> AgdaAny
d_'8743''45'absorbs'45''8744'_1272 :: ()
-> ()
-> T_DistributiveLattice_1228
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8743''45'absorbs'45''8744'_1272 ~()
v0 ~()
v1 T_DistributiveLattice_1228
v2
  = T_DistributiveLattice_1228 -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'absorbs'45''8744'_1272 T_DistributiveLattice_1228
v2
du_'8743''45'absorbs'45''8744'_1272 ::
  T_DistributiveLattice_1228 -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'absorbs'45''8744'_1272 :: T_DistributiveLattice_1228 -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'absorbs'45''8744'_1272 T_DistributiveLattice_1228
v0
  = let v1 :: T_IsDistributiveLattice_814
v1 = T_DistributiveLattice_1228 -> T_IsDistributiveLattice_814
d_isDistributiveLattice_1252 (T_DistributiveLattice_1228 -> T_DistributiveLattice_1228
forall a b. a -> b
coe T_DistributiveLattice_1228
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsLattice_740 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsLattice_740 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'8743''45'absorbs'45''8744'_792
         ((T_IsDistributiveLattice_814 -> T_IsLattice_740)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_814 -> T_IsLattice_740
MAlonzo.Code.Algebra.Structures.d_isLattice_824 (T_IsDistributiveLattice_814 -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_814
v1)))
-- Algebra.Bundles.DistributiveLattice._.∧-assoc
d_'8743''45'assoc_1274 ::
  T_DistributiveLattice_1228 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8743''45'assoc_1274 :: T_DistributiveLattice_1228
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8743''45'assoc_1274 T_DistributiveLattice_1228
v0
  = (T_IsLattice_740 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsLattice_740 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8743''45'assoc_772
      ((T_IsDistributiveLattice_814 -> T_IsLattice_740)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsDistributiveLattice_814 -> T_IsLattice_740
MAlonzo.Code.Algebra.Structures.d_isLattice_824
         ((T_DistributiveLattice_1228 -> T_IsDistributiveLattice_814)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_DistributiveLattice_1228 -> T_IsDistributiveLattice_814
d_isDistributiveLattice_1252 (T_DistributiveLattice_1228 -> AgdaAny
forall a b. a -> b
coe T_DistributiveLattice_1228
v0)))
-- Algebra.Bundles.DistributiveLattice._.∧-comm
d_'8743''45'comm_1276 ::
  T_DistributiveLattice_1228 -> AgdaAny -> AgdaAny -> AgdaAny
d_'8743''45'comm_1276 :: T_DistributiveLattice_1228 -> AgdaAny -> AgdaAny -> AgdaAny
d_'8743''45'comm_1276 T_DistributiveLattice_1228
v0
  = (T_IsLattice_740 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsLattice_740 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8743''45'comm_770
      ((T_IsDistributiveLattice_814 -> T_IsLattice_740)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsDistributiveLattice_814 -> T_IsLattice_740
MAlonzo.Code.Algebra.Structures.d_isLattice_824
         ((T_DistributiveLattice_1228 -> T_IsDistributiveLattice_814)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_DistributiveLattice_1228 -> T_IsDistributiveLattice_814
d_isDistributiveLattice_1252 (T_DistributiveLattice_1228 -> AgdaAny
forall a b. a -> b
coe T_DistributiveLattice_1228
v0)))
-- Algebra.Bundles.DistributiveLattice._.∧-cong
d_'8743''45'cong_1278 ::
  T_DistributiveLattice_1228 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8743''45'cong_1278 :: T_DistributiveLattice_1228
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8743''45'cong_1278 T_DistributiveLattice_1228
v0
  = (T_IsLattice_740
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsLattice_740
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8743''45'cong_774
      ((T_IsDistributiveLattice_814 -> T_IsLattice_740)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsDistributiveLattice_814 -> T_IsLattice_740
MAlonzo.Code.Algebra.Structures.d_isLattice_824
         ((T_DistributiveLattice_1228 -> T_IsDistributiveLattice_814)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_DistributiveLattice_1228 -> T_IsDistributiveLattice_814
d_isDistributiveLattice_1252 (T_DistributiveLattice_1228 -> AgdaAny
forall a b. a -> b
coe T_DistributiveLattice_1228
v0)))
-- Algebra.Bundles.DistributiveLattice._.∧-congʳ
d_'8743''45'cong'691'_1280 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_DistributiveLattice_1228 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8743''45'cong'691'_1280 :: ()
-> ()
-> T_DistributiveLattice_1228
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8743''45'cong'691'_1280 ~()
v0 ~()
v1 T_DistributiveLattice_1228
v2
  = T_DistributiveLattice_1228
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'cong'691'_1280 T_DistributiveLattice_1228
v2
du_'8743''45'cong'691'_1280 ::
  T_DistributiveLattice_1228 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'cong'691'_1280 :: T_DistributiveLattice_1228
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'cong'691'_1280 T_DistributiveLattice_1228
v0
  = let v1 :: T_IsDistributiveLattice_814
v1 = T_DistributiveLattice_1228 -> T_IsDistributiveLattice_814
d_isDistributiveLattice_1252 (T_DistributiveLattice_1228 -> T_DistributiveLattice_1228
forall a b. a -> b
coe T_DistributiveLattice_1228
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsLattice_740
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsLattice_740
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'8743''45'cong'691'_798
         ((T_IsDistributiveLattice_814 -> T_IsLattice_740)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_814 -> T_IsLattice_740
MAlonzo.Code.Algebra.Structures.d_isLattice_824 (T_IsDistributiveLattice_814 -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_814
v1)))
-- Algebra.Bundles.DistributiveLattice._.∧-congˡ
d_'8743''45'cong'737'_1282 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_DistributiveLattice_1228 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8743''45'cong'737'_1282 :: ()
-> ()
-> T_DistributiveLattice_1228
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8743''45'cong'737'_1282 ~()
v0 ~()
v1 T_DistributiveLattice_1228
v2
  = T_DistributiveLattice_1228
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'cong'737'_1282 T_DistributiveLattice_1228
v2
du_'8743''45'cong'737'_1282 ::
  T_DistributiveLattice_1228 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'cong'737'_1282 :: T_DistributiveLattice_1228
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'cong'737'_1282 T_DistributiveLattice_1228
v0
  = let v1 :: T_IsDistributiveLattice_814
v1 = T_DistributiveLattice_1228 -> T_IsDistributiveLattice_814
d_isDistributiveLattice_1252 (T_DistributiveLattice_1228 -> T_DistributiveLattice_1228
forall a b. a -> b
coe T_DistributiveLattice_1228
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsLattice_740
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsLattice_740
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'8743''45'cong'737'_794
         ((T_IsDistributiveLattice_814 -> T_IsLattice_740)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_814 -> T_IsLattice_740
MAlonzo.Code.Algebra.Structures.d_isLattice_824 (T_IsDistributiveLattice_814 -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_814
v1)))
-- Algebra.Bundles.DistributiveLattice._.∨-absorbs-∧
d_'8744''45'absorbs'45''8743'_1284 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_DistributiveLattice_1228 -> AgdaAny -> AgdaAny -> AgdaAny
d_'8744''45'absorbs'45''8743'_1284 :: ()
-> ()
-> T_DistributiveLattice_1228
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8744''45'absorbs'45''8743'_1284 ~()
v0 ~()
v1 T_DistributiveLattice_1228
v2
  = T_DistributiveLattice_1228 -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'absorbs'45''8743'_1284 T_DistributiveLattice_1228
v2
du_'8744''45'absorbs'45''8743'_1284 ::
  T_DistributiveLattice_1228 -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'absorbs'45''8743'_1284 :: T_DistributiveLattice_1228 -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'absorbs'45''8743'_1284 T_DistributiveLattice_1228
v0
  = let v1 :: T_IsDistributiveLattice_814
v1 = T_DistributiveLattice_1228 -> T_IsDistributiveLattice_814
d_isDistributiveLattice_1252 (T_DistributiveLattice_1228 -> T_DistributiveLattice_1228
forall a b. a -> b
coe T_DistributiveLattice_1228
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsLattice_740 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsLattice_740 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'8744''45'absorbs'45''8743'_790
         ((T_IsDistributiveLattice_814 -> T_IsLattice_740)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_814 -> T_IsLattice_740
MAlonzo.Code.Algebra.Structures.d_isLattice_824 (T_IsDistributiveLattice_814 -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_814
v1)))
-- Algebra.Bundles.DistributiveLattice._.∨-assoc
d_'8744''45'assoc_1286 ::
  T_DistributiveLattice_1228 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8744''45'assoc_1286 :: T_DistributiveLattice_1228
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8744''45'assoc_1286 T_DistributiveLattice_1228
v0
  = (T_IsLattice_740 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsLattice_740 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8744''45'assoc_766
      ((T_IsDistributiveLattice_814 -> T_IsLattice_740)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsDistributiveLattice_814 -> T_IsLattice_740
MAlonzo.Code.Algebra.Structures.d_isLattice_824
         ((T_DistributiveLattice_1228 -> T_IsDistributiveLattice_814)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_DistributiveLattice_1228 -> T_IsDistributiveLattice_814
d_isDistributiveLattice_1252 (T_DistributiveLattice_1228 -> AgdaAny
forall a b. a -> b
coe T_DistributiveLattice_1228
v0)))
-- Algebra.Bundles.DistributiveLattice._.∨-comm
d_'8744''45'comm_1288 ::
  T_DistributiveLattice_1228 -> AgdaAny -> AgdaAny -> AgdaAny
d_'8744''45'comm_1288 :: T_DistributiveLattice_1228 -> AgdaAny -> AgdaAny -> AgdaAny
d_'8744''45'comm_1288 T_DistributiveLattice_1228
v0
  = (T_IsLattice_740 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsLattice_740 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8744''45'comm_764
      ((T_IsDistributiveLattice_814 -> T_IsLattice_740)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsDistributiveLattice_814 -> T_IsLattice_740
MAlonzo.Code.Algebra.Structures.d_isLattice_824
         ((T_DistributiveLattice_1228 -> T_IsDistributiveLattice_814)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_DistributiveLattice_1228 -> T_IsDistributiveLattice_814
d_isDistributiveLattice_1252 (T_DistributiveLattice_1228 -> AgdaAny
forall a b. a -> b
coe T_DistributiveLattice_1228
v0)))
-- Algebra.Bundles.DistributiveLattice._.∨-cong
d_'8744''45'cong_1290 ::
  T_DistributiveLattice_1228 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8744''45'cong_1290 :: T_DistributiveLattice_1228
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8744''45'cong_1290 T_DistributiveLattice_1228
v0
  = (T_IsLattice_740
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsLattice_740
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8744''45'cong_768
      ((T_IsDistributiveLattice_814 -> T_IsLattice_740)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsDistributiveLattice_814 -> T_IsLattice_740
MAlonzo.Code.Algebra.Structures.d_isLattice_824
         ((T_DistributiveLattice_1228 -> T_IsDistributiveLattice_814)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_DistributiveLattice_1228 -> T_IsDistributiveLattice_814
d_isDistributiveLattice_1252 (T_DistributiveLattice_1228 -> AgdaAny
forall a b. a -> b
coe T_DistributiveLattice_1228
v0)))
-- Algebra.Bundles.DistributiveLattice._.∨-congʳ
d_'8744''45'cong'691'_1292 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_DistributiveLattice_1228 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8744''45'cong'691'_1292 :: ()
-> ()
-> T_DistributiveLattice_1228
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8744''45'cong'691'_1292 ~()
v0 ~()
v1 T_DistributiveLattice_1228
v2
  = T_DistributiveLattice_1228
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'cong'691'_1292 T_DistributiveLattice_1228
v2
du_'8744''45'cong'691'_1292 ::
  T_DistributiveLattice_1228 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'cong'691'_1292 :: T_DistributiveLattice_1228
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'cong'691'_1292 T_DistributiveLattice_1228
v0
  = let v1 :: T_IsDistributiveLattice_814
v1 = T_DistributiveLattice_1228 -> T_IsDistributiveLattice_814
d_isDistributiveLattice_1252 (T_DistributiveLattice_1228 -> T_DistributiveLattice_1228
forall a b. a -> b
coe T_DistributiveLattice_1228
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsLattice_740
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsLattice_740
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'8744''45'cong'691'_806
         ((T_IsDistributiveLattice_814 -> T_IsLattice_740)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_814 -> T_IsLattice_740
MAlonzo.Code.Algebra.Structures.d_isLattice_824 (T_IsDistributiveLattice_814 -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_814
v1)))
-- Algebra.Bundles.DistributiveLattice._.∨-congˡ
d_'8744''45'cong'737'_1294 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_DistributiveLattice_1228 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8744''45'cong'737'_1294 :: ()
-> ()
-> T_DistributiveLattice_1228
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8744''45'cong'737'_1294 ~()
v0 ~()
v1 T_DistributiveLattice_1228
v2
  = T_DistributiveLattice_1228
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'cong'737'_1294 T_DistributiveLattice_1228
v2
du_'8744''45'cong'737'_1294 ::
  T_DistributiveLattice_1228 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'cong'737'_1294 :: T_DistributiveLattice_1228
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'cong'737'_1294 T_DistributiveLattice_1228
v0
  = let v1 :: T_IsDistributiveLattice_814
v1 = T_DistributiveLattice_1228 -> T_IsDistributiveLattice_814
d_isDistributiveLattice_1252 (T_DistributiveLattice_1228 -> T_DistributiveLattice_1228
forall a b. a -> b
coe T_DistributiveLattice_1228
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsLattice_740
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsLattice_740
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'8744''45'cong'737'_802
         ((T_IsDistributiveLattice_814 -> T_IsLattice_740)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_814 -> T_IsLattice_740
MAlonzo.Code.Algebra.Structures.d_isLattice_824 (T_IsDistributiveLattice_814 -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_814
v1)))
-- Algebra.Bundles.DistributiveLattice._.∨-distribʳ-∧
d_'8744''45'distrib'691''45''8743'_1296 ::
  T_DistributiveLattice_1228 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8744''45'distrib'691''45''8743'_1296 :: T_DistributiveLattice_1228
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8744''45'distrib'691''45''8743'_1296 T_DistributiveLattice_1228
v0
  = (T_IsDistributiveLattice_814
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsDistributiveLattice_814
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8744''45'distrib'691''45''8743'_826
      ((T_DistributiveLattice_1228 -> T_IsDistributiveLattice_814)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_DistributiveLattice_1228 -> T_IsDistributiveLattice_814
d_isDistributiveLattice_1252 (T_DistributiveLattice_1228 -> AgdaAny
forall a b. a -> b
coe T_DistributiveLattice_1228
v0))
-- Algebra.Bundles.DistributiveLattice._.∨-∧-distribʳ
d_'8744''45''8743''45'distrib'691'_1298 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_DistributiveLattice_1228 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8744''45''8743''45'distrib'691'_1298 :: ()
-> ()
-> T_DistributiveLattice_1228
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8744''45''8743''45'distrib'691'_1298 ~()
v0 ~()
v1 T_DistributiveLattice_1228
v2
  = T_DistributiveLattice_1228
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45''8743''45'distrib'691'_1298 T_DistributiveLattice_1228
v2
du_'8744''45''8743''45'distrib'691'_1298 ::
  T_DistributiveLattice_1228 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45''8743''45'distrib'691'_1298 :: T_DistributiveLattice_1228
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45''8743''45'distrib'691'_1298 T_DistributiveLattice_1228
v0
  = (T_IsDistributiveLattice_814
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsDistributiveLattice_814
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'8744''45''8743''45'distrib'691'_868
      ((T_DistributiveLattice_1228 -> T_IsDistributiveLattice_814)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_DistributiveLattice_1228 -> T_IsDistributiveLattice_814
d_isDistributiveLattice_1252 (T_DistributiveLattice_1228 -> AgdaAny
forall a b. a -> b
coe T_DistributiveLattice_1228
v0))
-- Algebra.Bundles.DistributiveLattice.lattice
d_lattice_1300 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_DistributiveLattice_1228 -> T_Lattice_1144
d_lattice_1300 :: () -> () -> T_DistributiveLattice_1228 -> T_Lattice_1144
d_lattice_1300 ~()
v0 ~()
v1 T_DistributiveLattice_1228
v2 = T_DistributiveLattice_1228 -> T_Lattice_1144
du_lattice_1300 T_DistributiveLattice_1228
v2
du_lattice_1300 :: T_DistributiveLattice_1228 -> T_Lattice_1144
du_lattice_1300 :: T_DistributiveLattice_1228 -> T_Lattice_1144
du_lattice_1300 T_DistributiveLattice_1228
v0
  = ((AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> T_IsLattice_740
 -> T_Lattice_1144)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsLattice_740
-> T_Lattice_1144
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsLattice_740
-> T_Lattice_1144
C_Lattice'46'constructor_19309 (T_DistributiveLattice_1228 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8744'__1248 (T_DistributiveLattice_1228 -> T_DistributiveLattice_1228
forall a b. a -> b
coe T_DistributiveLattice_1228
v0))
      (T_DistributiveLattice_1228 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8743'__1250 (T_DistributiveLattice_1228 -> T_DistributiveLattice_1228
forall a b. a -> b
coe T_DistributiveLattice_1228
v0))
      (T_IsDistributiveLattice_814 -> T_IsLattice_740
MAlonzo.Code.Algebra.Structures.d_isLattice_824
         ((T_DistributiveLattice_1228 -> T_IsDistributiveLattice_814)
-> AgdaAny -> T_IsDistributiveLattice_814
forall a b. a -> b
coe T_DistributiveLattice_1228 -> T_IsDistributiveLattice_814
d_isDistributiveLattice_1252 (T_DistributiveLattice_1228 -> AgdaAny
forall a b. a -> b
coe T_DistributiveLattice_1228
v0)))
-- Algebra.Bundles.DistributiveLattice._._≉_
d__'8777'__1304 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_DistributiveLattice_1228 -> AgdaAny -> AgdaAny -> ()
d__'8777'__1304 :: () -> () -> T_DistributiveLattice_1228 -> AgdaAny -> AgdaAny -> ()
d__'8777'__1304 = () -> () -> T_DistributiveLattice_1228 -> AgdaAny -> AgdaAny -> ()
forall a. a
erased
-- Algebra.Bundles.DistributiveLattice._.rawLattice
d_rawLattice_1306 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_DistributiveLattice_1228 -> T_RawLattice_1110
d_rawLattice_1306 :: () -> () -> T_DistributiveLattice_1228 -> T_RawLattice_1110
d_rawLattice_1306 ~()
v0 ~()
v1 T_DistributiveLattice_1228
v2 = T_DistributiveLattice_1228 -> T_RawLattice_1110
du_rawLattice_1306 T_DistributiveLattice_1228
v2
du_rawLattice_1306 ::
  T_DistributiveLattice_1228 -> T_RawLattice_1110
du_rawLattice_1306 :: T_DistributiveLattice_1228 -> T_RawLattice_1110
du_rawLattice_1306 T_DistributiveLattice_1228
v0
  = (T_Lattice_1144 -> T_RawLattice_1110)
-> AgdaAny -> T_RawLattice_1110
forall a b. a -> b
coe T_Lattice_1144 -> T_RawLattice_1110
du_rawLattice_1210 ((T_DistributiveLattice_1228 -> T_Lattice_1144)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_DistributiveLattice_1228 -> T_Lattice_1144
du_lattice_1300 (T_DistributiveLattice_1228 -> AgdaAny
forall a b. a -> b
coe T_DistributiveLattice_1228
v0))
-- Algebra.Bundles.DistributiveLattice._.setoid
d_setoid_1308 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_DistributiveLattice_1228 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_1308 :: () -> () -> T_DistributiveLattice_1228 -> T_Setoid_44
d_setoid_1308 ~()
v0 ~()
v1 T_DistributiveLattice_1228
v2 = T_DistributiveLattice_1228 -> T_Setoid_44
du_setoid_1308 T_DistributiveLattice_1228
v2
du_setoid_1308 ::
  T_DistributiveLattice_1228 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_1308 :: T_DistributiveLattice_1228 -> T_Setoid_44
du_setoid_1308 T_DistributiveLattice_1228
v0
  = (T_Lattice_1144 -> T_Setoid_44) -> AgdaAny -> T_Setoid_44
forall a b. a -> b
coe T_Lattice_1144 -> T_Setoid_44
du_setoid_1218 ((T_DistributiveLattice_1228 -> T_Lattice_1144)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_DistributiveLattice_1228 -> T_Lattice_1144
du_lattice_1300 (T_DistributiveLattice_1228 -> AgdaAny
forall a b. a -> b
coe T_DistributiveLattice_1228
v0))
-- Algebra.Bundles.RawNearSemiring
d_RawNearSemiring_1314 :: p -> p -> ()
d_RawNearSemiring_1314 p
a0 p
a1 = ()
data T_RawNearSemiring_1314
  = C_RawNearSemiring'46'constructor_22495 (AgdaAny ->
                                            AgdaAny -> AgdaAny)
                                           (AgdaAny -> AgdaAny -> AgdaAny) AgdaAny
-- Algebra.Bundles.RawNearSemiring.Carrier
d_Carrier_1330 :: T_RawNearSemiring_1314 -> ()
d_Carrier_1330 :: T_RawNearSemiring_1314 -> ()
d_Carrier_1330 = T_RawNearSemiring_1314 -> ()
forall a. a
erased
-- Algebra.Bundles.RawNearSemiring._≈_
d__'8776'__1332 ::
  T_RawNearSemiring_1314 -> AgdaAny -> AgdaAny -> ()
d__'8776'__1332 :: T_RawNearSemiring_1314 -> AgdaAny -> AgdaAny -> ()
d__'8776'__1332 = T_RawNearSemiring_1314 -> AgdaAny -> AgdaAny -> ()
forall a. a
erased
-- Algebra.Bundles.RawNearSemiring._+_
d__'43'__1334 ::
  T_RawNearSemiring_1314 -> AgdaAny -> AgdaAny -> AgdaAny
d__'43'__1334 :: T_RawNearSemiring_1314 -> AgdaAny -> AgdaAny -> AgdaAny
d__'43'__1334 T_RawNearSemiring_1314
v0
  = case T_RawNearSemiring_1314 -> T_RawNearSemiring_1314
forall a b. a -> b
coe T_RawNearSemiring_1314
v0 of
      C_RawNearSemiring'46'constructor_22495 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny
v5 -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v3
      T_RawNearSemiring_1314
_ -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.RawNearSemiring._*_
d__'42'__1336 ::
  T_RawNearSemiring_1314 -> AgdaAny -> AgdaAny -> AgdaAny
d__'42'__1336 :: T_RawNearSemiring_1314 -> AgdaAny -> AgdaAny -> AgdaAny
d__'42'__1336 T_RawNearSemiring_1314
v0
  = case T_RawNearSemiring_1314 -> T_RawNearSemiring_1314
forall a b. a -> b
coe T_RawNearSemiring_1314
v0 of
      C_RawNearSemiring'46'constructor_22495 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny
v5 -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v4
      T_RawNearSemiring_1314
_ -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.RawNearSemiring.0#
d_0'35'_1338 :: T_RawNearSemiring_1314 -> AgdaAny
d_0'35'_1338 :: T_RawNearSemiring_1314 -> AgdaAny
d_0'35'_1338 T_RawNearSemiring_1314
v0
  = case T_RawNearSemiring_1314 -> T_RawNearSemiring_1314
forall a b. a -> b
coe T_RawNearSemiring_1314
v0 of
      C_RawNearSemiring'46'constructor_22495 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny
v5 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v5
      T_RawNearSemiring_1314
_ -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.RawNearSemiring.+-rawMonoid
d_'43''45'rawMonoid_1340 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_RawNearSemiring_1314 -> T_RawMonoid_474
d_'43''45'rawMonoid_1340 :: () -> () -> T_RawNearSemiring_1314 -> T_RawMonoid_474
d_'43''45'rawMonoid_1340 ~()
v0 ~()
v1 T_RawNearSemiring_1314
v2 = T_RawNearSemiring_1314 -> T_RawMonoid_474
du_'43''45'rawMonoid_1340 T_RawNearSemiring_1314
v2
du_'43''45'rawMonoid_1340 ::
  T_RawNearSemiring_1314 -> T_RawMonoid_474
du_'43''45'rawMonoid_1340 :: T_RawNearSemiring_1314 -> T_RawMonoid_474
du_'43''45'rawMonoid_1340 T_RawNearSemiring_1314
v0
  = ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> T_RawMonoid_474)
-> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> T_RawMonoid_474
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> T_RawMonoid_474
C_RawMonoid'46'constructor_8313 (T_RawNearSemiring_1314 -> AgdaAny -> AgdaAny -> AgdaAny
d__'43'__1334 (T_RawNearSemiring_1314 -> T_RawNearSemiring_1314
forall a b. a -> b
coe T_RawNearSemiring_1314
v0))
      (T_RawNearSemiring_1314 -> AgdaAny
d_0'35'_1338 (T_RawNearSemiring_1314 -> T_RawNearSemiring_1314
forall a b. a -> b
coe T_RawNearSemiring_1314
v0))
-- Algebra.Bundles.RawNearSemiring._._≉_
d__'8777'__1344 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_RawNearSemiring_1314 -> AgdaAny -> AgdaAny -> ()
d__'8777'__1344 :: () -> () -> T_RawNearSemiring_1314 -> AgdaAny -> AgdaAny -> ()
d__'8777'__1344 = () -> () -> T_RawNearSemiring_1314 -> AgdaAny -> AgdaAny -> ()
forall a. a
erased
-- Algebra.Bundles.RawNearSemiring._.rawMagma
d_rawMagma_1346 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_RawNearSemiring_1314 -> T_RawMagma_8
d_rawMagma_1346 :: () -> () -> T_RawNearSemiring_1314 -> T_RawMagma_8
d_rawMagma_1346 ~()
v0 ~()
v1 T_RawNearSemiring_1314
v2 = T_RawNearSemiring_1314 -> T_RawMagma_8
du_rawMagma_1346 T_RawNearSemiring_1314
v2
du_rawMagma_1346 :: T_RawNearSemiring_1314 -> T_RawMagma_8
du_rawMagma_1346 :: T_RawNearSemiring_1314 -> T_RawMagma_8
du_rawMagma_1346 T_RawNearSemiring_1314
v0
  = (T_RawMonoid_474 -> T_RawMagma_8) -> AgdaAny -> T_RawMagma_8
forall a b. a -> b
coe T_RawMonoid_474 -> T_RawMagma_8
du_rawMagma_496 ((T_RawNearSemiring_1314 -> T_RawMonoid_474) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_RawNearSemiring_1314 -> T_RawMonoid_474
du_'43''45'rawMonoid_1340 (T_RawNearSemiring_1314 -> AgdaAny
forall a b. a -> b
coe T_RawNearSemiring_1314
v0))
-- Algebra.Bundles.RawNearSemiring.*-rawMagma
d_'42''45'rawMagma_1348 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_RawNearSemiring_1314 -> T_RawMagma_8
d_'42''45'rawMagma_1348 :: () -> () -> T_RawNearSemiring_1314 -> T_RawMagma_8
d_'42''45'rawMagma_1348 ~()
v0 ~()
v1 T_RawNearSemiring_1314
v2 = T_RawNearSemiring_1314 -> T_RawMagma_8
du_'42''45'rawMagma_1348 T_RawNearSemiring_1314
v2
du_'42''45'rawMagma_1348 :: T_RawNearSemiring_1314 -> T_RawMagma_8
du_'42''45'rawMagma_1348 :: T_RawNearSemiring_1314 -> T_RawMagma_8
du_'42''45'rawMagma_1348 T_RawNearSemiring_1314
v0
  = ((AgdaAny -> AgdaAny -> AgdaAny) -> T_RawMagma_8)
-> (AgdaAny -> AgdaAny -> AgdaAny) -> T_RawMagma_8
forall a b. a -> b
coe (AgdaAny -> AgdaAny -> AgdaAny) -> T_RawMagma_8
C_RawMagma'46'constructor_79 (T_RawNearSemiring_1314 -> AgdaAny -> AgdaAny -> AgdaAny
d__'42'__1336 (T_RawNearSemiring_1314 -> T_RawNearSemiring_1314
forall a b. a -> b
coe T_RawNearSemiring_1314
v0))
-- Algebra.Bundles.NearSemiring
d_NearSemiring_1354 :: p -> p -> ()
d_NearSemiring_1354 p
a0 p
a1 = ()
data T_NearSemiring_1354
  = C_NearSemiring'46'constructor_23249 (AgdaAny ->
                                         AgdaAny -> AgdaAny)
                                        (AgdaAny -> AgdaAny -> AgdaAny) AgdaAny
                                        MAlonzo.Code.Algebra.Structures.T_IsNearSemiring_876
-- Algebra.Bundles.NearSemiring.Carrier
d_Carrier_1372 :: T_NearSemiring_1354 -> ()
d_Carrier_1372 :: T_NearSemiring_1354 -> ()
d_Carrier_1372 = T_NearSemiring_1354 -> ()
forall a. a
erased
-- Algebra.Bundles.NearSemiring._≈_
d__'8776'__1374 :: T_NearSemiring_1354 -> AgdaAny -> AgdaAny -> ()
d__'8776'__1374 :: T_NearSemiring_1354 -> AgdaAny -> AgdaAny -> ()
d__'8776'__1374 = T_NearSemiring_1354 -> AgdaAny -> AgdaAny -> ()
forall a. a
erased
-- Algebra.Bundles.NearSemiring._+_
d__'43'__1376 ::
  T_NearSemiring_1354 -> AgdaAny -> AgdaAny -> AgdaAny
d__'43'__1376 :: T_NearSemiring_1354 -> AgdaAny -> AgdaAny -> AgdaAny
d__'43'__1376 T_NearSemiring_1354
v0
  = case T_NearSemiring_1354 -> T_NearSemiring_1354
forall a b. a -> b
coe T_NearSemiring_1354
v0 of
      C_NearSemiring'46'constructor_23249 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny
v5 T_IsNearSemiring_876
v6 -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v3
      T_NearSemiring_1354
_ -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.NearSemiring._*_
d__'42'__1378 ::
  T_NearSemiring_1354 -> AgdaAny -> AgdaAny -> AgdaAny
d__'42'__1378 :: T_NearSemiring_1354 -> AgdaAny -> AgdaAny -> AgdaAny
d__'42'__1378 T_NearSemiring_1354
v0
  = case T_NearSemiring_1354 -> T_NearSemiring_1354
forall a b. a -> b
coe T_NearSemiring_1354
v0 of
      C_NearSemiring'46'constructor_23249 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny
v5 T_IsNearSemiring_876
v6 -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v4
      T_NearSemiring_1354
_ -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.NearSemiring.0#
d_0'35'_1380 :: T_NearSemiring_1354 -> AgdaAny
d_0'35'_1380 :: T_NearSemiring_1354 -> AgdaAny
d_0'35'_1380 T_NearSemiring_1354
v0
  = case T_NearSemiring_1354 -> T_NearSemiring_1354
forall a b. a -> b
coe T_NearSemiring_1354
v0 of
      C_NearSemiring'46'constructor_23249 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny
v5 T_IsNearSemiring_876
v6 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v5
      T_NearSemiring_1354
_ -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.NearSemiring.isNearSemiring
d_isNearSemiring_1382 ::
  T_NearSemiring_1354 ->
  MAlonzo.Code.Algebra.Structures.T_IsNearSemiring_876
d_isNearSemiring_1382 :: T_NearSemiring_1354 -> T_IsNearSemiring_876
d_isNearSemiring_1382 T_NearSemiring_1354
v0
  = case T_NearSemiring_1354 -> T_NearSemiring_1354
forall a b. a -> b
coe T_NearSemiring_1354
v0 of
      C_NearSemiring'46'constructor_23249 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny
v5 T_IsNearSemiring_876
v6 -> T_IsNearSemiring_876 -> T_IsNearSemiring_876
forall a b. a -> b
coe T_IsNearSemiring_876
v6
      T_NearSemiring_1354
_ -> T_IsNearSemiring_876
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.NearSemiring._.assoc
d_assoc_1386 ::
  T_NearSemiring_1354 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_1386 :: T_NearSemiring_1354 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_1386 T_NearSemiring_1354
v0
  = (T_IsSemigroup_194 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsSemigroup_194 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_assoc_204
      ((T_IsNearSemiring_876 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsNearSemiring_876 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_'42''45'isSemigroup_894
         ((T_NearSemiring_1354 -> T_IsNearSemiring_876) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_NearSemiring_1354 -> T_IsNearSemiring_876
d_isNearSemiring_1382 (T_NearSemiring_1354 -> AgdaAny
forall a b. a -> b
coe T_NearSemiring_1354
v0)))
-- Algebra.Bundles.NearSemiring._.∙-cong
d_'8729''45'cong_1388 ::
  T_NearSemiring_1354 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_1388 :: T_NearSemiring_1354
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_1388 T_NearSemiring_1354
v0
  = (T_IsMagma_86
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsMagma_86
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_96
      ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202
         ((T_IsNearSemiring_876 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsNearSemiring_876 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_'42''45'isSemigroup_894
            ((T_NearSemiring_1354 -> T_IsNearSemiring_876) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_NearSemiring_1354 -> T_IsNearSemiring_876
d_isNearSemiring_1382 (T_NearSemiring_1354 -> AgdaAny
forall a b. a -> b
coe T_NearSemiring_1354
v0))))
-- Algebra.Bundles.NearSemiring._.∙-congʳ
d_'8729''45'cong'691'_1390 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_NearSemiring_1354 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_1390 :: ()
-> ()
-> T_NearSemiring_1354
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_1390 ~()
v0 ~()
v1 T_NearSemiring_1354
v2
  = T_NearSemiring_1354
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1390 T_NearSemiring_1354
v2
du_'8729''45'cong'691'_1390 ::
  T_NearSemiring_1354 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1390 :: T_NearSemiring_1354
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1390 T_NearSemiring_1354
v0
  = let v1 :: T_IsNearSemiring_876
v1 = T_NearSemiring_1354 -> T_IsNearSemiring_876
d_isNearSemiring_1382 (T_NearSemiring_1354 -> T_NearSemiring_1354
forall a b. a -> b
coe T_NearSemiring_1354
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemigroup_194
v2
             = T_IsNearSemiring_876 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_'42''45'isSemigroup_894
                 (T_IsNearSemiring_876 -> T_IsNearSemiring_876
forall a b. a -> b
coe T_IsNearSemiring_876
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsMagma_86
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMagma_86 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'691'_116
            ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202 (T_IsSemigroup_194 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194
v2))))
-- Algebra.Bundles.NearSemiring._.∙-congˡ
d_'8729''45'cong'737'_1392 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_NearSemiring_1354 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_1392 :: ()
-> ()
-> T_NearSemiring_1354
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_1392 ~()
v0 ~()
v1 T_NearSemiring_1354
v2
  = T_NearSemiring_1354
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1392 T_NearSemiring_1354
v2
du_'8729''45'cong'737'_1392 ::
  T_NearSemiring_1354 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1392 :: T_NearSemiring_1354
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1392 T_NearSemiring_1354
v0
  = let v1 :: T_IsNearSemiring_876
v1 = T_NearSemiring_1354 -> T_IsNearSemiring_876
d_isNearSemiring_1382 (T_NearSemiring_1354 -> T_NearSemiring_1354
forall a b. a -> b
coe T_NearSemiring_1354
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemigroup_194
v2
             = T_IsNearSemiring_876 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_'42''45'isSemigroup_894
                 (T_IsNearSemiring_876 -> T_IsNearSemiring_876
forall a b. a -> b
coe T_IsNearSemiring_876
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsMagma_86
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMagma_86 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'737'_112
            ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202 (T_IsSemigroup_194 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194
v2))))
-- Algebra.Bundles.NearSemiring._.isMagma
d_isMagma_1394 ::
  T_NearSemiring_1354 -> MAlonzo.Code.Algebra.Structures.T_IsMagma_86
d_isMagma_1394 :: T_NearSemiring_1354 -> T_IsMagma_86
d_isMagma_1394 T_NearSemiring_1354
v0
  = (T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> T_IsMagma_86
forall a b. a -> b
coe
      T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202
      ((T_IsNearSemiring_876 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsNearSemiring_876 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_'42''45'isSemigroup_894
         ((T_NearSemiring_1354 -> T_IsNearSemiring_876) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_NearSemiring_1354 -> T_IsNearSemiring_876
d_isNearSemiring_1382 (T_NearSemiring_1354 -> AgdaAny
forall a b. a -> b
coe T_NearSemiring_1354
v0)))
-- Algebra.Bundles.NearSemiring._.*-isSemigroup
d_'42''45'isSemigroup_1396 ::
  T_NearSemiring_1354 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_194
d_'42''45'isSemigroup_1396 :: T_NearSemiring_1354 -> T_IsSemigroup_194
d_'42''45'isSemigroup_1396 T_NearSemiring_1354
v0
  = (T_IsNearSemiring_876 -> T_IsSemigroup_194)
-> AgdaAny -> T_IsSemigroup_194
forall a b. a -> b
coe
      T_IsNearSemiring_876 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_'42''45'isSemigroup_894
      ((T_NearSemiring_1354 -> T_IsNearSemiring_876) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_NearSemiring_1354 -> T_IsNearSemiring_876
d_isNearSemiring_1382 (T_NearSemiring_1354 -> AgdaAny
forall a b. a -> b
coe T_NearSemiring_1354
v0))
-- Algebra.Bundles.NearSemiring._.assoc
d_assoc_1398 ::
  T_NearSemiring_1354 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_1398 :: T_NearSemiring_1354 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_1398 T_NearSemiring_1354
v0
  = (T_IsSemigroup_194 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsSemigroup_194 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_assoc_204
      ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368
         ((T_IsNearSemiring_876 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsNearSemiring_876 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_'43''45'isMonoid_892
            ((T_NearSemiring_1354 -> T_IsNearSemiring_876) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_NearSemiring_1354 -> T_IsNearSemiring_876
d_isNearSemiring_1382 (T_NearSemiring_1354 -> AgdaAny
forall a b. a -> b
coe T_NearSemiring_1354
v0))))
-- Algebra.Bundles.NearSemiring._.∙-cong
d_'8729''45'cong_1400 ::
  T_NearSemiring_1354 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_1400 :: T_NearSemiring_1354
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_1400 T_NearSemiring_1354
v0
  = (T_IsMagma_86
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsMagma_86
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_96
      ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202
         ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368
            ((T_IsNearSemiring_876 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsNearSemiring_876 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_'43''45'isMonoid_892
               ((T_NearSemiring_1354 -> T_IsNearSemiring_876) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_NearSemiring_1354 -> T_IsNearSemiring_876
d_isNearSemiring_1382 (T_NearSemiring_1354 -> AgdaAny
forall a b. a -> b
coe T_NearSemiring_1354
v0)))))
-- Algebra.Bundles.NearSemiring._.∙-congʳ
d_'8729''45'cong'691'_1402 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_NearSemiring_1354 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_1402 :: ()
-> ()
-> T_NearSemiring_1354
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_1402 ~()
v0 ~()
v1 T_NearSemiring_1354
v2
  = T_NearSemiring_1354
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1402 T_NearSemiring_1354
v2
du_'8729''45'cong'691'_1402 ::
  T_NearSemiring_1354 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1402 :: T_NearSemiring_1354
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1402 T_NearSemiring_1354
v0
  = let v1 :: T_IsNearSemiring_876
v1 = T_NearSemiring_1354 -> T_IsNearSemiring_876
d_isNearSemiring_1382 (T_NearSemiring_1354 -> T_NearSemiring_1354
forall a b. a -> b
coe T_NearSemiring_1354
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsMonoid_358
v2
             = T_IsNearSemiring_876 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_'43''45'isMonoid_892
                 (T_IsNearSemiring_876 -> T_IsNearSemiring_876
forall a b. a -> b
coe T_IsNearSemiring_876
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_194
v3
                = T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368 (T_IsMonoid_358 -> T_IsMonoid_358
forall a b. a -> b
coe T_IsMonoid_358
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsMagma_86
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMagma_86 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'691'_116
               ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202 (T_IsSemigroup_194 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194
v3)))))
-- Algebra.Bundles.NearSemiring._.∙-congˡ
d_'8729''45'cong'737'_1404 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_NearSemiring_1354 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_1404 :: ()
-> ()
-> T_NearSemiring_1354
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_1404 ~()
v0 ~()
v1 T_NearSemiring_1354
v2
  = T_NearSemiring_1354
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1404 T_NearSemiring_1354
v2
du_'8729''45'cong'737'_1404 ::
  T_NearSemiring_1354 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1404 :: T_NearSemiring_1354
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1404 T_NearSemiring_1354
v0
  = let v1 :: T_IsNearSemiring_876
v1 = T_NearSemiring_1354 -> T_IsNearSemiring_876
d_isNearSemiring_1382 (T_NearSemiring_1354 -> T_NearSemiring_1354
forall a b. a -> b
coe T_NearSemiring_1354
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsMonoid_358
v2
             = T_IsNearSemiring_876 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_'43''45'isMonoid_892
                 (T_IsNearSemiring_876 -> T_IsNearSemiring_876
forall a b. a -> b
coe T_IsNearSemiring_876
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_194
v3
                = T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368 (T_IsMonoid_358 -> T_IsMonoid_358
forall a b. a -> b
coe T_IsMonoid_358
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsMagma_86
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMagma_86 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'737'_112
               ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202 (T_IsSemigroup_194 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194
v3)))))
-- Algebra.Bundles.NearSemiring._.identity
d_identity_1406 ::
  T_NearSemiring_1354 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_identity_1406 :: T_NearSemiring_1354 -> T_Σ_14
d_identity_1406 T_NearSemiring_1354
v0
  = (T_IsMonoid_358 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsMonoid_358 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_identity_370
      ((T_IsNearSemiring_876 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsNearSemiring_876 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_'43''45'isMonoid_892
         ((T_NearSemiring_1354 -> T_IsNearSemiring_876) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_NearSemiring_1354 -> T_IsNearSemiring_876
d_isNearSemiring_1382 (T_NearSemiring_1354 -> AgdaAny
forall a b. a -> b
coe T_NearSemiring_1354
v0)))
-- Algebra.Bundles.NearSemiring._.identityʳ
d_identity'691'_1408 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_NearSemiring_1354 -> AgdaAny -> AgdaAny
d_identity'691'_1408 :: () -> () -> T_NearSemiring_1354 -> AgdaAny -> AgdaAny
d_identity'691'_1408 ~()
v0 ~()
v1 T_NearSemiring_1354
v2 = T_NearSemiring_1354 -> AgdaAny -> AgdaAny
du_identity'691'_1408 T_NearSemiring_1354
v2
du_identity'691'_1408 :: T_NearSemiring_1354 -> AgdaAny -> AgdaAny
du_identity'691'_1408 :: T_NearSemiring_1354 -> AgdaAny -> AgdaAny
du_identity'691'_1408 T_NearSemiring_1354
v0
  = let v1 :: T_IsNearSemiring_876
v1 = T_NearSemiring_1354 -> T_IsNearSemiring_876
d_isNearSemiring_1382 (T_NearSemiring_1354 -> T_NearSemiring_1354
forall a b. a -> b
coe T_NearSemiring_1354
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsMonoid_358 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoid_358 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_identity'691'_400
         ((T_IsNearSemiring_876 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsNearSemiring_876 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_'43''45'isMonoid_892 (T_IsNearSemiring_876 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiring_876
v1)))
-- Algebra.Bundles.NearSemiring._.identityˡ
d_identity'737'_1410 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_NearSemiring_1354 -> AgdaAny -> AgdaAny
d_identity'737'_1410 :: () -> () -> T_NearSemiring_1354 -> AgdaAny -> AgdaAny
d_identity'737'_1410 ~()
v0 ~()
v1 T_NearSemiring_1354
v2 = T_NearSemiring_1354 -> AgdaAny -> AgdaAny
du_identity'737'_1410 T_NearSemiring_1354
v2
du_identity'737'_1410 :: T_NearSemiring_1354 -> AgdaAny -> AgdaAny
du_identity'737'_1410 :: T_NearSemiring_1354 -> AgdaAny -> AgdaAny
du_identity'737'_1410 T_NearSemiring_1354
v0
  = let v1 :: T_IsNearSemiring_876
v1 = T_NearSemiring_1354 -> T_IsNearSemiring_876
d_isNearSemiring_1382 (T_NearSemiring_1354 -> T_NearSemiring_1354
forall a b. a -> b
coe T_NearSemiring_1354
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsMonoid_358 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoid_358 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_identity'737'_398
         ((T_IsNearSemiring_876 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsNearSemiring_876 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_'43''45'isMonoid_892 (T_IsNearSemiring_876 -> AgdaAny
forall a b. a -> b
coe T_IsNearSemiring_876
v1)))
-- Algebra.Bundles.NearSemiring._.isMagma
d_isMagma_1412 ::
  T_NearSemiring_1354 -> MAlonzo.Code.Algebra.Structures.T_IsMagma_86
d_isMagma_1412 :: T_NearSemiring_1354 -> T_IsMagma_86
d_isMagma_1412 T_NearSemiring_1354
v0
  = (T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> T_IsMagma_86
forall a b. a -> b
coe
      T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202
      ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368
         ((T_IsNearSemiring_876 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsNearSemiring_876 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_'43''45'isMonoid_892
            ((T_NearSemiring_1354 -> T_IsNearSemiring_876) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_NearSemiring_1354 -> T_IsNearSemiring_876
d_isNearSemiring_1382 (T_NearSemiring_1354 -> AgdaAny
forall a b. a -> b
coe T_NearSemiring_1354
v0))))
-- Algebra.Bundles.NearSemiring._.+-isMonoid
d_'43''45'isMonoid_1414 ::
  T_NearSemiring_1354 ->
  MAlonzo.Code.Algebra.Structures.T_IsMonoid_358
d_'43''45'isMonoid_1414 :: T_NearSemiring_1354 -> T_IsMonoid_358
d_'43''45'isMonoid_1414 T_NearSemiring_1354
v0
  = (T_IsNearSemiring_876 -> T_IsMonoid_358)
-> AgdaAny -> T_IsMonoid_358
forall a b. a -> b
coe
      T_IsNearSemiring_876 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_'43''45'isMonoid_892
      ((T_NearSemiring_1354 -> T_IsNearSemiring_876) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_NearSemiring_1354 -> T_IsNearSemiring_876
d_isNearSemiring_1382 (T_NearSemiring_1354 -> AgdaAny
forall a b. a -> b
coe T_NearSemiring_1354
v0))
-- Algebra.Bundles.NearSemiring._.isSemigroup
d_isSemigroup_1416 ::
  T_NearSemiring_1354 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_194
d_isSemigroup_1416 :: T_NearSemiring_1354 -> T_IsSemigroup_194
d_isSemigroup_1416 T_NearSemiring_1354
v0
  = (T_IsMonoid_358 -> T_IsSemigroup_194)
-> AgdaAny -> T_IsSemigroup_194
forall a b. a -> b
coe
      T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368
      ((T_IsNearSemiring_876 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsNearSemiring_876 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_'43''45'isMonoid_892
         ((T_NearSemiring_1354 -> T_IsNearSemiring_876) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_NearSemiring_1354 -> T_IsNearSemiring_876
d_isNearSemiring_1382 (T_NearSemiring_1354 -> AgdaAny
forall a b. a -> b
coe T_NearSemiring_1354
v0)))
-- Algebra.Bundles.NearSemiring._.distribʳ
d_distrib'691'_1418 ::
  T_NearSemiring_1354 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_distrib'691'_1418 :: T_NearSemiring_1354 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_distrib'691'_1418 T_NearSemiring_1354
v0
  = (T_IsNearSemiring_876 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsNearSemiring_876 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_distrib'691'_896
      ((T_NearSemiring_1354 -> T_IsNearSemiring_876) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_NearSemiring_1354 -> T_IsNearSemiring_876
d_isNearSemiring_1382 (T_NearSemiring_1354 -> AgdaAny
forall a b. a -> b
coe T_NearSemiring_1354
v0))
-- Algebra.Bundles.NearSemiring._.isEquivalence
d_isEquivalence_1420 ::
  T_NearSemiring_1354 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_1420 :: T_NearSemiring_1354 -> T_IsEquivalence_26
d_isEquivalence_1420 T_NearSemiring_1354
v0
  = (T_IsMagma_86 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      T_IsMagma_86 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_94
      ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202
         ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368
            ((T_IsNearSemiring_876 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsNearSemiring_876 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_'43''45'isMonoid_892
               ((T_NearSemiring_1354 -> T_IsNearSemiring_876) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_NearSemiring_1354 -> T_IsNearSemiring_876
d_isNearSemiring_1382 (T_NearSemiring_1354 -> AgdaAny
forall a b. a -> b
coe T_NearSemiring_1354
v0)))))
-- Algebra.Bundles.NearSemiring._.isPartialEquivalence
d_isPartialEquivalence_1422 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_NearSemiring_1354 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_1422 :: () -> () -> T_NearSemiring_1354 -> T_IsPartialEquivalence_16
d_isPartialEquivalence_1422 ~()
v0 ~()
v1 T_NearSemiring_1354
v2
  = T_NearSemiring_1354 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_1422 T_NearSemiring_1354
v2
du_isPartialEquivalence_1422 ::
  T_NearSemiring_1354 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_1422 :: T_NearSemiring_1354 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_1422 T_NearSemiring_1354
v0
  = let v1 :: T_IsNearSemiring_876
v1 = T_NearSemiring_1354 -> T_IsNearSemiring_876
d_isNearSemiring_1382 (T_NearSemiring_1354 -> T_NearSemiring_1354
forall a b. a -> b
coe T_NearSemiring_1354
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsMonoid_358
v2
             = T_IsNearSemiring_876 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_'43''45'isMonoid_892
                 (T_IsNearSemiring_876 -> T_IsNearSemiring_876
forall a b. a -> b
coe T_IsNearSemiring_876
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_194
v3
                = T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368 (T_IsMonoid_358 -> T_IsMonoid_358
forall a b. a -> b
coe T_IsMonoid_358
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsMagma_86
v4 = T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202 (T_IsSemigroup_194 -> T_IsSemigroup_194
forall a b. a -> b
coe T_IsSemigroup_194
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_86 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsMagma_86 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_94 (T_IsMagma_86 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86
v4))))))
-- Algebra.Bundles.NearSemiring._.refl
d_refl_1424 :: T_NearSemiring_1354 -> AgdaAny -> AgdaAny
d_refl_1424 :: T_NearSemiring_1354 -> AgdaAny -> AgdaAny
d_refl_1424 T_NearSemiring_1354
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_86 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_86 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_94
         ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202
            ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368
               ((T_IsNearSemiring_876 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsNearSemiring_876 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_'43''45'isMonoid_892
                  ((T_NearSemiring_1354 -> T_IsNearSemiring_876) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_NearSemiring_1354 -> T_IsNearSemiring_876
d_isNearSemiring_1382 (T_NearSemiring_1354 -> AgdaAny
forall a b. a -> b
coe T_NearSemiring_1354
v0))))))
-- Algebra.Bundles.NearSemiring._.reflexive
d_reflexive_1426 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_NearSemiring_1354 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_1426 :: ()
-> ()
-> T_NearSemiring_1354
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_1426 ~()
v0 ~()
v1 T_NearSemiring_1354
v2 = T_NearSemiring_1354
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_1426 T_NearSemiring_1354
v2
du_reflexive_1426 ::
  T_NearSemiring_1354 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_1426 :: T_NearSemiring_1354
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_1426 T_NearSemiring_1354
v0
  = let v1 :: T_IsNearSemiring_876
v1 = T_NearSemiring_1354 -> T_IsNearSemiring_876
d_isNearSemiring_1382 (T_NearSemiring_1354 -> T_NearSemiring_1354
forall a b. a -> b
coe T_NearSemiring_1354
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsMonoid_358
v2
             = T_IsNearSemiring_876 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_'43''45'isMonoid_892
                 (T_IsNearSemiring_876 -> T_IsNearSemiring_876
forall a b. a -> b
coe T_IsNearSemiring_876
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_194
v3
                = T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368 (T_IsMonoid_358 -> T_IsMonoid_358
forall a b. a -> b
coe T_IsMonoid_358
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsMagma_86
v4 = T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202 (T_IsSemigroup_194 -> T_IsSemigroup_194
forall a b. a -> b
coe T_IsSemigroup_194
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_86 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_94 (T_IsMagma_86 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86
v4))
                    AgdaAny
v5))))
-- Algebra.Bundles.NearSemiring._.setoid
d_setoid_1428 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_NearSemiring_1354 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_1428 :: () -> () -> T_NearSemiring_1354 -> T_Setoid_44
d_setoid_1428 ~()
v0 ~()
v1 T_NearSemiring_1354
v2 = T_NearSemiring_1354 -> T_Setoid_44
du_setoid_1428 T_NearSemiring_1354
v2
du_setoid_1428 ::
  T_NearSemiring_1354 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_1428 :: T_NearSemiring_1354 -> T_Setoid_44
du_setoid_1428 T_NearSemiring_1354
v0
  = let v1 :: T_IsNearSemiring_876
v1 = T_NearSemiring_1354 -> T_IsNearSemiring_876
d_isNearSemiring_1382 (T_NearSemiring_1354 -> T_NearSemiring_1354
forall a b. a -> b
coe T_NearSemiring_1354
v0) in
    AgdaAny -> T_Setoid_44
forall a b. a -> b
coe
      (let v2 :: T_IsMonoid_358
v2
             = T_IsNearSemiring_876 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_'43''45'isMonoid_892
                 (T_IsNearSemiring_876 -> T_IsNearSemiring_876
forall a b. a -> b
coe T_IsNearSemiring_876
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_194
v3
                = T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368 (T_IsMonoid_358 -> T_IsMonoid_358
forall a b. a -> b
coe T_IsMonoid_358
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsMagma_86 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMagma_86 -> T_Setoid_44
MAlonzo.Code.Algebra.Structures.du_setoid_110
               ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202 (T_IsSemigroup_194 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194
v3)))))
-- Algebra.Bundles.NearSemiring._.sym
d_sym_1430 ::
  T_NearSemiring_1354 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_1430 :: T_NearSemiring_1354 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_1430 T_NearSemiring_1354
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_86 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_86 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_94
         ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202
            ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368
               ((T_IsNearSemiring_876 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsNearSemiring_876 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_'43''45'isMonoid_892
                  ((T_NearSemiring_1354 -> T_IsNearSemiring_876) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_NearSemiring_1354 -> T_IsNearSemiring_876
d_isNearSemiring_1382 (T_NearSemiring_1354 -> AgdaAny
forall a b. a -> b
coe T_NearSemiring_1354
v0))))))
-- Algebra.Bundles.NearSemiring._.trans
d_trans_1432 ::
  T_NearSemiring_1354 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_1432 :: T_NearSemiring_1354
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_1432 T_NearSemiring_1354
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_86 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_86 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_94
         ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202
            ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368
               ((T_IsNearSemiring_876 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsNearSemiring_876 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_'43''45'isMonoid_892
                  ((T_NearSemiring_1354 -> T_IsNearSemiring_876) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_NearSemiring_1354 -> T_IsNearSemiring_876
d_isNearSemiring_1382 (T_NearSemiring_1354 -> AgdaAny
forall a b. a -> b
coe T_NearSemiring_1354
v0))))))
-- Algebra.Bundles.NearSemiring._.zeroˡ
d_zero'737'_1434 :: T_NearSemiring_1354 -> AgdaAny -> AgdaAny
d_zero'737'_1434 :: T_NearSemiring_1354 -> AgdaAny -> AgdaAny
d_zero'737'_1434 T_NearSemiring_1354
v0
  = (T_IsNearSemiring_876 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsNearSemiring_876 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_zero'737'_898
      ((T_NearSemiring_1354 -> T_IsNearSemiring_876) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_NearSemiring_1354 -> T_IsNearSemiring_876
d_isNearSemiring_1382 (T_NearSemiring_1354 -> AgdaAny
forall a b. a -> b
coe T_NearSemiring_1354
v0))
-- Algebra.Bundles.NearSemiring.rawNearSemiring
d_rawNearSemiring_1436 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_NearSemiring_1354 -> T_RawNearSemiring_1314
d_rawNearSemiring_1436 :: () -> () -> T_NearSemiring_1354 -> T_RawNearSemiring_1314
d_rawNearSemiring_1436 ~()
v0 ~()
v1 T_NearSemiring_1354
v2 = T_NearSemiring_1354 -> T_RawNearSemiring_1314
du_rawNearSemiring_1436 T_NearSemiring_1354
v2
du_rawNearSemiring_1436 ::
  T_NearSemiring_1354 -> T_RawNearSemiring_1314
du_rawNearSemiring_1436 :: T_NearSemiring_1354 -> T_RawNearSemiring_1314
du_rawNearSemiring_1436 T_NearSemiring_1354
v0
  = ((AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> T_RawNearSemiring_1314)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_RawNearSemiring_1314
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_RawNearSemiring_1314
C_RawNearSemiring'46'constructor_22495 (T_NearSemiring_1354 -> AgdaAny -> AgdaAny -> AgdaAny
d__'43'__1376 (T_NearSemiring_1354 -> T_NearSemiring_1354
forall a b. a -> b
coe T_NearSemiring_1354
v0))
      (T_NearSemiring_1354 -> AgdaAny -> AgdaAny -> AgdaAny
d__'42'__1378 (T_NearSemiring_1354 -> T_NearSemiring_1354
forall a b. a -> b
coe T_NearSemiring_1354
v0)) (T_NearSemiring_1354 -> AgdaAny
d_0'35'_1380 (T_NearSemiring_1354 -> T_NearSemiring_1354
forall a b. a -> b
coe T_NearSemiring_1354
v0))
-- Algebra.Bundles.NearSemiring.+-monoid
d_'43''45'monoid_1438 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_NearSemiring_1354 -> T_Monoid_506
d_'43''45'monoid_1438 :: () -> () -> T_NearSemiring_1354 -> T_Monoid_506
d_'43''45'monoid_1438 ~()
v0 ~()
v1 T_NearSemiring_1354
v2 = T_NearSemiring_1354 -> T_Monoid_506
du_'43''45'monoid_1438 T_NearSemiring_1354
v2
du_'43''45'monoid_1438 :: T_NearSemiring_1354 -> T_Monoid_506
du_'43''45'monoid_1438 :: T_NearSemiring_1354 -> T_Monoid_506
du_'43''45'monoid_1438 T_NearSemiring_1354
v0
  = ((AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny -> T_IsMonoid_358 -> T_Monoid_506)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsMonoid_358
-> T_Monoid_506
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> T_IsMonoid_358 -> T_Monoid_506
C_Monoid'46'constructor_8851 (T_NearSemiring_1354 -> AgdaAny -> AgdaAny -> AgdaAny
d__'43'__1376 (T_NearSemiring_1354 -> T_NearSemiring_1354
forall a b. a -> b
coe T_NearSemiring_1354
v0))
      (T_NearSemiring_1354 -> AgdaAny
d_0'35'_1380 (T_NearSemiring_1354 -> T_NearSemiring_1354
forall a b. a -> b
coe T_NearSemiring_1354
v0))
      (T_IsNearSemiring_876 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_'43''45'isMonoid_892
         ((T_NearSemiring_1354 -> T_IsNearSemiring_876)
-> AgdaAny -> T_IsNearSemiring_876
forall a b. a -> b
coe T_NearSemiring_1354 -> T_IsNearSemiring_876
d_isNearSemiring_1382 (T_NearSemiring_1354 -> AgdaAny
forall a b. a -> b
coe T_NearSemiring_1354
v0)))
-- Algebra.Bundles.NearSemiring._._≉_
d__'8777'__1442 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_NearSemiring_1354 -> AgdaAny -> AgdaAny -> ()
d__'8777'__1442 :: () -> () -> T_NearSemiring_1354 -> AgdaAny -> AgdaAny -> ()
d__'8777'__1442 = () -> () -> T_NearSemiring_1354 -> AgdaAny -> AgdaAny -> ()
forall a. a
erased
-- Algebra.Bundles.NearSemiring._.magma
d_magma_1444 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_NearSemiring_1354 -> T_Magma_36
d_magma_1444 :: () -> () -> T_NearSemiring_1354 -> T_Magma_36
d_magma_1444 ~()
v0 ~()
v1 T_NearSemiring_1354
v2 = T_NearSemiring_1354 -> T_Magma_36
du_magma_1444 T_NearSemiring_1354
v2
du_magma_1444 :: T_NearSemiring_1354 -> T_Magma_36
du_magma_1444 :: T_NearSemiring_1354 -> T_Magma_36
du_magma_1444 T_NearSemiring_1354
v0
  = let v1 :: t
v1 = (T_NearSemiring_1354 -> T_Monoid_506) -> AgdaAny -> t
forall a b. a -> b
coe T_NearSemiring_1354 -> T_Monoid_506
du_'43''45'monoid_1438 (T_NearSemiring_1354 -> AgdaAny
forall a b. a -> b
coe T_NearSemiring_1354
v0) in
    AgdaAny -> T_Magma_36
forall a b. a -> b
coe ((T_Semigroup_206 -> T_Magma_36) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semigroup_206 -> T_Magma_36
du_magma_254 ((T_Monoid_506 -> T_Semigroup_206) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Monoid_506 -> T_Semigroup_206
du_semigroup_566 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1)))
-- Algebra.Bundles.NearSemiring._.rawMagma
d_rawMagma_1446 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_NearSemiring_1354 -> T_RawMagma_8
d_rawMagma_1446 :: () -> () -> T_NearSemiring_1354 -> T_RawMagma_8
d_rawMagma_1446 ~()
v0 ~()
v1 T_NearSemiring_1354
v2 = T_NearSemiring_1354 -> T_RawMagma_8
du_rawMagma_1446 T_NearSemiring_1354
v2
du_rawMagma_1446 :: T_NearSemiring_1354 -> T_RawMagma_8
du_rawMagma_1446 :: T_NearSemiring_1354 -> T_RawMagma_8
du_rawMagma_1446 T_NearSemiring_1354
v0
  = let v1 :: t
v1 = (T_NearSemiring_1354 -> T_Monoid_506) -> AgdaAny -> t
forall a b. a -> b
coe T_NearSemiring_1354 -> T_Monoid_506
du_'43''45'monoid_1438 (T_NearSemiring_1354 -> AgdaAny
forall a b. a -> b
coe T_NearSemiring_1354
v0) in
    AgdaAny -> T_RawMagma_8
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_Monoid_506 -> T_Semigroup_206) -> AgdaAny -> t
forall a b. a -> b
coe T_Monoid_506 -> T_Semigroup_206
du_semigroup_566 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_Magma_36 -> T_RawMagma_8) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Magma_36 -> T_RawMagma_8
du_rawMagma_80 ((T_Semigroup_206 -> T_Magma_36) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semigroup_206 -> T_Magma_36
du_magma_254 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2))))
-- Algebra.Bundles.NearSemiring._.rawMonoid
d_rawMonoid_1448 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_NearSemiring_1354 -> T_RawMonoid_474
d_rawMonoid_1448 :: () -> () -> T_NearSemiring_1354 -> T_RawMonoid_474
d_rawMonoid_1448 ~()
v0 ~()
v1 T_NearSemiring_1354
v2 = T_NearSemiring_1354 -> T_RawMonoid_474
du_rawMonoid_1448 T_NearSemiring_1354
v2
du_rawMonoid_1448 :: T_NearSemiring_1354 -> T_RawMonoid_474
du_rawMonoid_1448 :: T_NearSemiring_1354 -> T_RawMonoid_474
du_rawMonoid_1448 T_NearSemiring_1354
v0
  = (T_Monoid_506 -> T_RawMonoid_474) -> AgdaAny -> T_RawMonoid_474
forall a b. a -> b
coe T_Monoid_506 -> T_RawMonoid_474
du_rawMonoid_576 ((T_NearSemiring_1354 -> T_Monoid_506) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_NearSemiring_1354 -> T_Monoid_506
du_'43''45'monoid_1438 (T_NearSemiring_1354 -> AgdaAny
forall a b. a -> b
coe T_NearSemiring_1354
v0))
-- Algebra.Bundles.NearSemiring._.semigroup
d_semigroup_1450 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_NearSemiring_1354 -> T_Semigroup_206
d_semigroup_1450 :: () -> () -> T_NearSemiring_1354 -> T_Semigroup_206
d_semigroup_1450 ~()
v0 ~()
v1 T_NearSemiring_1354
v2 = T_NearSemiring_1354 -> T_Semigroup_206
du_semigroup_1450 T_NearSemiring_1354
v2
du_semigroup_1450 :: T_NearSemiring_1354 -> T_Semigroup_206
du_semigroup_1450 :: T_NearSemiring_1354 -> T_Semigroup_206
du_semigroup_1450 T_NearSemiring_1354
v0
  = (T_Monoid_506 -> T_Semigroup_206) -> AgdaAny -> T_Semigroup_206
forall a b. a -> b
coe T_Monoid_506 -> T_Semigroup_206
du_semigroup_566 ((T_NearSemiring_1354 -> T_Monoid_506) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_NearSemiring_1354 -> T_Monoid_506
du_'43''45'monoid_1438 (T_NearSemiring_1354 -> AgdaAny
forall a b. a -> b
coe T_NearSemiring_1354
v0))
-- Algebra.Bundles.NearSemiring.*-semigroup
d_'42''45'semigroup_1452 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_NearSemiring_1354 -> T_Semigroup_206
d_'42''45'semigroup_1452 :: () -> () -> T_NearSemiring_1354 -> T_Semigroup_206
d_'42''45'semigroup_1452 ~()
v0 ~()
v1 T_NearSemiring_1354
v2 = T_NearSemiring_1354 -> T_Semigroup_206
du_'42''45'semigroup_1452 T_NearSemiring_1354
v2
du_'42''45'semigroup_1452 :: T_NearSemiring_1354 -> T_Semigroup_206
du_'42''45'semigroup_1452 :: T_NearSemiring_1354 -> T_Semigroup_206
du_'42''45'semigroup_1452 T_NearSemiring_1354
v0
  = ((AgdaAny -> AgdaAny -> AgdaAny)
 -> T_IsSemigroup_194 -> T_Semigroup_206)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsSemigroup_194
-> T_Semigroup_206
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsSemigroup_194 -> T_Semigroup_206
C_Semigroup'46'constructor_3669 (T_NearSemiring_1354 -> AgdaAny -> AgdaAny -> AgdaAny
d__'42'__1378 (T_NearSemiring_1354 -> T_NearSemiring_1354
forall a b. a -> b
coe T_NearSemiring_1354
v0))
      (T_IsNearSemiring_876 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_'42''45'isSemigroup_894
         ((T_NearSemiring_1354 -> T_IsNearSemiring_876)
-> AgdaAny -> T_IsNearSemiring_876
forall a b. a -> b
coe T_NearSemiring_1354 -> T_IsNearSemiring_876
d_isNearSemiring_1382 (T_NearSemiring_1354 -> AgdaAny
forall a b. a -> b
coe T_NearSemiring_1354
v0)))
-- Algebra.Bundles.NearSemiring._.magma
d_magma_1456 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_NearSemiring_1354 -> T_Magma_36
d_magma_1456 :: () -> () -> T_NearSemiring_1354 -> T_Magma_36
d_magma_1456 ~()
v0 ~()
v1 T_NearSemiring_1354
v2 = T_NearSemiring_1354 -> T_Magma_36
du_magma_1456 T_NearSemiring_1354
v2
du_magma_1456 :: T_NearSemiring_1354 -> T_Magma_36
du_magma_1456 :: T_NearSemiring_1354 -> T_Magma_36
du_magma_1456 T_NearSemiring_1354
v0
  = (T_Semigroup_206 -> T_Magma_36) -> AgdaAny -> T_Magma_36
forall a b. a -> b
coe T_Semigroup_206 -> T_Magma_36
du_magma_254 ((T_NearSemiring_1354 -> T_Semigroup_206) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_NearSemiring_1354 -> T_Semigroup_206
du_'42''45'semigroup_1452 (T_NearSemiring_1354 -> AgdaAny
forall a b. a -> b
coe T_NearSemiring_1354
v0))
-- Algebra.Bundles.NearSemiring._.rawMagma
d_rawMagma_1458 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_NearSemiring_1354 -> T_RawMagma_8
d_rawMagma_1458 :: () -> () -> T_NearSemiring_1354 -> T_RawMagma_8
d_rawMagma_1458 ~()
v0 ~()
v1 T_NearSemiring_1354
v2 = T_NearSemiring_1354 -> T_RawMagma_8
du_rawMagma_1458 T_NearSemiring_1354
v2
du_rawMagma_1458 :: T_NearSemiring_1354 -> T_RawMagma_8
du_rawMagma_1458 :: T_NearSemiring_1354 -> T_RawMagma_8
du_rawMagma_1458 T_NearSemiring_1354
v0
  = let v1 :: t
v1 = (T_NearSemiring_1354 -> T_Semigroup_206) -> AgdaAny -> t
forall a b. a -> b
coe T_NearSemiring_1354 -> T_Semigroup_206
du_'42''45'semigroup_1452 (T_NearSemiring_1354 -> AgdaAny
forall a b. a -> b
coe T_NearSemiring_1354
v0) in
    AgdaAny -> T_RawMagma_8
forall a b. a -> b
coe ((T_Magma_36 -> T_RawMagma_8) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Magma_36 -> T_RawMagma_8
du_rawMagma_80 ((T_Semigroup_206 -> T_Magma_36) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semigroup_206 -> T_Magma_36
du_magma_254 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1)))
-- Algebra.Bundles.SemiringWithoutOne
d_SemiringWithoutOne_1464 :: p -> p -> ()
d_SemiringWithoutOne_1464 p
a0 p
a1 = ()
data T_SemiringWithoutOne_1464
  = C_SemiringWithoutOne'46'constructor_25531 (AgdaAny ->
                                               AgdaAny -> AgdaAny)
                                              (AgdaAny -> AgdaAny -> AgdaAny) AgdaAny
                                              MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutOne_952
-- Algebra.Bundles.SemiringWithoutOne.Carrier
d_Carrier_1482 :: T_SemiringWithoutOne_1464 -> ()
d_Carrier_1482 :: T_SemiringWithoutOne_1464 -> ()
d_Carrier_1482 = T_SemiringWithoutOne_1464 -> ()
forall a. a
erased
-- Algebra.Bundles.SemiringWithoutOne._≈_
d__'8776'__1484 ::
  T_SemiringWithoutOne_1464 -> AgdaAny -> AgdaAny -> ()
d__'8776'__1484 :: T_SemiringWithoutOne_1464 -> AgdaAny -> AgdaAny -> ()
d__'8776'__1484 = T_SemiringWithoutOne_1464 -> AgdaAny -> AgdaAny -> ()
forall a. a
erased
-- Algebra.Bundles.SemiringWithoutOne._+_
d__'43'__1486 ::
  T_SemiringWithoutOne_1464 -> AgdaAny -> AgdaAny -> AgdaAny
d__'43'__1486 :: T_SemiringWithoutOne_1464 -> AgdaAny -> AgdaAny -> AgdaAny
d__'43'__1486 T_SemiringWithoutOne_1464
v0
  = case T_SemiringWithoutOne_1464 -> T_SemiringWithoutOne_1464
forall a b. a -> b
coe T_SemiringWithoutOne_1464
v0 of
      C_SemiringWithoutOne'46'constructor_25531 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny
v5 T_IsSemiringWithoutOne_952
v6 -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v3
      T_SemiringWithoutOne_1464
_ -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.SemiringWithoutOne._*_
d__'42'__1488 ::
  T_SemiringWithoutOne_1464 -> AgdaAny -> AgdaAny -> AgdaAny
d__'42'__1488 :: T_SemiringWithoutOne_1464 -> AgdaAny -> AgdaAny -> AgdaAny
d__'42'__1488 T_SemiringWithoutOne_1464
v0
  = case T_SemiringWithoutOne_1464 -> T_SemiringWithoutOne_1464
forall a b. a -> b
coe T_SemiringWithoutOne_1464
v0 of
      C_SemiringWithoutOne'46'constructor_25531 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny
v5 T_IsSemiringWithoutOne_952
v6 -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v4
      T_SemiringWithoutOne_1464
_ -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.SemiringWithoutOne.0#
d_0'35'_1490 :: T_SemiringWithoutOne_1464 -> AgdaAny
d_0'35'_1490 :: T_SemiringWithoutOne_1464 -> AgdaAny
d_0'35'_1490 T_SemiringWithoutOne_1464
v0
  = case T_SemiringWithoutOne_1464 -> T_SemiringWithoutOne_1464
forall a b. a -> b
coe T_SemiringWithoutOne_1464
v0 of
      C_SemiringWithoutOne'46'constructor_25531 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny
v5 T_IsSemiringWithoutOne_952
v6 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v5
      T_SemiringWithoutOne_1464
_ -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.SemiringWithoutOne.isSemiringWithoutOne
d_isSemiringWithoutOne_1492 ::
  T_SemiringWithoutOne_1464 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutOne_952
d_isSemiringWithoutOne_1492 :: T_SemiringWithoutOne_1464 -> T_IsSemiringWithoutOne_952
d_isSemiringWithoutOne_1492 T_SemiringWithoutOne_1464
v0
  = case T_SemiringWithoutOne_1464 -> T_SemiringWithoutOne_1464
forall a b. a -> b
coe T_SemiringWithoutOne_1464
v0 of
      C_SemiringWithoutOne'46'constructor_25531 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny
v5 T_IsSemiringWithoutOne_952
v6 -> T_IsSemiringWithoutOne_952 -> T_IsSemiringWithoutOne_952
forall a b. a -> b
coe T_IsSemiringWithoutOne_952
v6
      T_SemiringWithoutOne_1464
_ -> T_IsSemiringWithoutOne_952
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.SemiringWithoutOne._.assoc
d_assoc_1496 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SemiringWithoutOne_1464 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_1496 :: ()
-> ()
-> T_SemiringWithoutOne_1464
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_assoc_1496 ~()
v0 ~()
v1 T_SemiringWithoutOne_1464
v2 = T_SemiringWithoutOne_1464
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_assoc_1496 T_SemiringWithoutOne_1464
v2
du_assoc_1496 ::
  T_SemiringWithoutOne_1464 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_assoc_1496 :: T_SemiringWithoutOne_1464
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_assoc_1496 T_SemiringWithoutOne_1464
v0
  = let v1 :: T_IsSemiringWithoutOne_952
v1 = T_SemiringWithoutOne_1464 -> T_IsSemiringWithoutOne_952
d_isSemiringWithoutOne_1492 (T_SemiringWithoutOne_1464 -> T_SemiringWithoutOne_1464
forall a b. a -> b
coe T_SemiringWithoutOne_1464
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsSemigroup_194 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_194 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_assoc_204
         ((T_IsSemiringWithoutOne_952 -> T_IsSemigroup_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemiringWithoutOne_952 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_'42''45'isSemigroup_970
            (T_IsSemiringWithoutOne_952 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_952
v1)))
-- Algebra.Bundles.SemiringWithoutOne._.∙-cong
d_'8729''45'cong_1498 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SemiringWithoutOne_1464 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_1498 :: ()
-> ()
-> T_SemiringWithoutOne_1464
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_1498 ~()
v0 ~()
v1 T_SemiringWithoutOne_1464
v2 = T_SemiringWithoutOne_1464
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_'8729''45'cong_1498 T_SemiringWithoutOne_1464
v2
du_'8729''45'cong_1498 ::
  T_SemiringWithoutOne_1464 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong_1498 :: T_SemiringWithoutOne_1464
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_'8729''45'cong_1498 T_SemiringWithoutOne_1464
v0
  = let v1 :: T_IsSemiringWithoutOne_952
v1 = T_SemiringWithoutOne_1464 -> T_IsSemiringWithoutOne_952
d_isSemiringWithoutOne_1492 (T_SemiringWithoutOne_1464 -> T_SemiringWithoutOne_1464
forall a b. a -> b
coe T_SemiringWithoutOne_1464
v0) in
    AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      ((T_IsMagma_86
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_86
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_96
         ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202
            ((T_IsSemiringWithoutOne_952 -> T_IsSemigroup_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemiringWithoutOne_952 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_'42''45'isSemigroup_970
               (T_IsSemiringWithoutOne_952 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_952
v1))))
-- Algebra.Bundles.SemiringWithoutOne._.∙-congʳ
d_'8729''45'cong'691'_1500 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SemiringWithoutOne_1464 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_1500 :: ()
-> ()
-> T_SemiringWithoutOne_1464
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_1500 ~()
v0 ~()
v1 T_SemiringWithoutOne_1464
v2
  = T_SemiringWithoutOne_1464
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1500 T_SemiringWithoutOne_1464
v2
du_'8729''45'cong'691'_1500 ::
  T_SemiringWithoutOne_1464 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1500 :: T_SemiringWithoutOne_1464
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1500 T_SemiringWithoutOne_1464
v0
  = let v1 :: T_IsSemiringWithoutOne_952
v1 = T_SemiringWithoutOne_1464 -> T_IsSemiringWithoutOne_952
d_isSemiringWithoutOne_1492 (T_SemiringWithoutOne_1464 -> T_SemiringWithoutOne_1464
forall a b. a -> b
coe T_SemiringWithoutOne_1464
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: t
v2
             = (T_IsSemiringWithoutOne_952 -> T_IsNearSemiring_876)
-> AgdaAny -> t
forall a b. a -> b
coe
                 T_IsSemiringWithoutOne_952 -> T_IsNearSemiring_876
MAlonzo.Code.Algebra.Structures.du_isNearSemiring_990 (T_IsSemiringWithoutOne_952 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_952
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_194
v3
                = T_IsNearSemiring_876 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_'42''45'isSemigroup_894
                    (AgdaAny -> T_IsNearSemiring_876
forall a b. a -> b
coe AgdaAny
forall a. a
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsMagma_86
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMagma_86 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'691'_116
               ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202 (T_IsSemigroup_194 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194
v3)))))
-- Algebra.Bundles.SemiringWithoutOne._.∙-congˡ
d_'8729''45'cong'737'_1502 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SemiringWithoutOne_1464 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_1502 :: ()
-> ()
-> T_SemiringWithoutOne_1464
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_1502 ~()
v0 ~()
v1 T_SemiringWithoutOne_1464
v2
  = T_SemiringWithoutOne_1464
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1502 T_SemiringWithoutOne_1464
v2
du_'8729''45'cong'737'_1502 ::
  T_SemiringWithoutOne_1464 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1502 :: T_SemiringWithoutOne_1464
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1502 T_SemiringWithoutOne_1464
v0
  = let v1 :: T_IsSemiringWithoutOne_952
v1 = T_SemiringWithoutOne_1464 -> T_IsSemiringWithoutOne_952
d_isSemiringWithoutOne_1492 (T_SemiringWithoutOne_1464 -> T_SemiringWithoutOne_1464
forall a b. a -> b
coe T_SemiringWithoutOne_1464
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: t
v2
             = (T_IsSemiringWithoutOne_952 -> T_IsNearSemiring_876)
-> AgdaAny -> t
forall a b. a -> b
coe
                 T_IsSemiringWithoutOne_952 -> T_IsNearSemiring_876
MAlonzo.Code.Algebra.Structures.du_isNearSemiring_990 (T_IsSemiringWithoutOne_952 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_952
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_194
v3
                = T_IsNearSemiring_876 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_'42''45'isSemigroup_894
                    (AgdaAny -> T_IsNearSemiring_876
forall a b. a -> b
coe AgdaAny
forall a. a
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsMagma_86
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMagma_86 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'737'_112
               ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202 (T_IsSemigroup_194 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194
v3)))))
-- Algebra.Bundles.SemiringWithoutOne._.isMagma
d_isMagma_1504 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SemiringWithoutOne_1464 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_86
d_isMagma_1504 :: () -> () -> T_SemiringWithoutOne_1464 -> T_IsMagma_86
d_isMagma_1504 ~()
v0 ~()
v1 T_SemiringWithoutOne_1464
v2 = T_SemiringWithoutOne_1464 -> T_IsMagma_86
du_isMagma_1504 T_SemiringWithoutOne_1464
v2
du_isMagma_1504 ::
  T_SemiringWithoutOne_1464 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_86
du_isMagma_1504 :: T_SemiringWithoutOne_1464 -> T_IsMagma_86
du_isMagma_1504 T_SemiringWithoutOne_1464
v0
  = let v1 :: T_IsSemiringWithoutOne_952
v1 = T_SemiringWithoutOne_1464 -> T_IsSemiringWithoutOne_952
d_isSemiringWithoutOne_1492 (T_SemiringWithoutOne_1464 -> T_SemiringWithoutOne_1464
forall a b. a -> b
coe T_SemiringWithoutOne_1464
v0) in
    AgdaAny -> T_IsMagma_86
forall a b. a -> b
coe
      ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202
         ((T_IsSemiringWithoutOne_952 -> T_IsSemigroup_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemiringWithoutOne_952 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_'42''45'isSemigroup_970
            (T_IsSemiringWithoutOne_952 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_952
v1)))
-- Algebra.Bundles.SemiringWithoutOne._.*-isSemigroup
d_'42''45'isSemigroup_1506 ::
  T_SemiringWithoutOne_1464 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_194
d_'42''45'isSemigroup_1506 :: T_SemiringWithoutOne_1464 -> T_IsSemigroup_194
d_'42''45'isSemigroup_1506 T_SemiringWithoutOne_1464
v0
  = (T_IsSemiringWithoutOne_952 -> T_IsSemigroup_194)
-> AgdaAny -> T_IsSemigroup_194
forall a b. a -> b
coe
      T_IsSemiringWithoutOne_952 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_'42''45'isSemigroup_970
      ((T_SemiringWithoutOne_1464 -> T_IsSemiringWithoutOne_952)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutOne_1464 -> T_IsSemiringWithoutOne_952
d_isSemiringWithoutOne_1492 (T_SemiringWithoutOne_1464 -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutOne_1464
v0))
-- Algebra.Bundles.SemiringWithoutOne._.assoc
d_assoc_1508 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SemiringWithoutOne_1464 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_1508 :: ()
-> ()
-> T_SemiringWithoutOne_1464
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_assoc_1508 ~()
v0 ~()
v1 T_SemiringWithoutOne_1464
v2 = T_SemiringWithoutOne_1464
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_assoc_1508 T_SemiringWithoutOne_1464
v2
du_assoc_1508 ::
  T_SemiringWithoutOne_1464 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_assoc_1508 :: T_SemiringWithoutOne_1464
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_assoc_1508 T_SemiringWithoutOne_1464
v0
  = let v1 :: T_IsSemiringWithoutOne_952
v1 = T_SemiringWithoutOne_1464 -> T_IsSemiringWithoutOne_952
d_isSemiringWithoutOne_1492 (T_SemiringWithoutOne_1464 -> T_SemiringWithoutOne_1464
forall a b. a -> b
coe T_SemiringWithoutOne_1464
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsSemigroup_194 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_194 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_assoc_204
         ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368
            ((T_IsCommutativeMonoid_406 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsCommutativeMonoid_406 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_416
               ((T_IsSemiringWithoutOne_952 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsSemiringWithoutOne_952 -> T_IsCommutativeMonoid_406
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_968
                  (T_IsSemiringWithoutOne_952 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_952
v1)))))
-- Algebra.Bundles.SemiringWithoutOne._.comm
d_comm_1510 ::
  T_SemiringWithoutOne_1464 -> AgdaAny -> AgdaAny -> AgdaAny
d_comm_1510 :: T_SemiringWithoutOne_1464 -> AgdaAny -> AgdaAny -> AgdaAny
d_comm_1510 T_SemiringWithoutOne_1464
v0
  = (T_IsCommutativeMonoid_406 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsCommutativeMonoid_406 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_comm_418
      ((T_IsSemiringWithoutOne_952 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiringWithoutOne_952 -> T_IsCommutativeMonoid_406
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_968
         ((T_SemiringWithoutOne_1464 -> T_IsSemiringWithoutOne_952)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutOne_1464 -> T_IsSemiringWithoutOne_952
d_isSemiringWithoutOne_1492 (T_SemiringWithoutOne_1464 -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutOne_1464
v0)))
-- Algebra.Bundles.SemiringWithoutOne._.∙-cong
d_'8729''45'cong_1512 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SemiringWithoutOne_1464 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_1512 :: ()
-> ()
-> T_SemiringWithoutOne_1464
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_1512 ~()
v0 ~()
v1 T_SemiringWithoutOne_1464
v2 = T_SemiringWithoutOne_1464
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_'8729''45'cong_1512 T_SemiringWithoutOne_1464
v2
du_'8729''45'cong_1512 ::
  T_SemiringWithoutOne_1464 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong_1512 :: T_SemiringWithoutOne_1464
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_'8729''45'cong_1512 T_SemiringWithoutOne_1464
v0
  = let v1 :: T_IsSemiringWithoutOne_952
v1 = T_SemiringWithoutOne_1464 -> T_IsSemiringWithoutOne_952
d_isSemiringWithoutOne_1492 (T_SemiringWithoutOne_1464 -> T_SemiringWithoutOne_1464
forall a b. a -> b
coe T_SemiringWithoutOne_1464
v0) in
    AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      ((T_IsMagma_86
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_86
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_96
         ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202
            ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368
               ((T_IsCommutativeMonoid_406 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsCommutativeMonoid_406 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_416
                  ((T_IsSemiringWithoutOne_952 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsSemiringWithoutOne_952 -> T_IsCommutativeMonoid_406
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_968
                     (T_IsSemiringWithoutOne_952 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_952
v1))))))
-- Algebra.Bundles.SemiringWithoutOne._.∙-congʳ
d_'8729''45'cong'691'_1514 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SemiringWithoutOne_1464 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_1514 :: ()
-> ()
-> T_SemiringWithoutOne_1464
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_1514 ~()
v0 ~()
v1 T_SemiringWithoutOne_1464
v2
  = T_SemiringWithoutOne_1464
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1514 T_SemiringWithoutOne_1464
v2
du_'8729''45'cong'691'_1514 ::
  T_SemiringWithoutOne_1464 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1514 :: T_SemiringWithoutOne_1464
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1514 T_SemiringWithoutOne_1464
v0
  = let v1 :: T_IsSemiringWithoutOne_952
v1 = T_SemiringWithoutOne_1464 -> T_IsSemiringWithoutOne_952
d_isSemiringWithoutOne_1492 (T_SemiringWithoutOne_1464 -> T_SemiringWithoutOne_1464
forall a b. a -> b
coe T_SemiringWithoutOne_1464
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: t
v2
             = (T_IsSemiringWithoutOne_952 -> T_IsNearSemiring_876)
-> AgdaAny -> t
forall a b. a -> b
coe
                 T_IsSemiringWithoutOne_952 -> T_IsNearSemiring_876
MAlonzo.Code.Algebra.Structures.du_isNearSemiring_990 (T_IsSemiringWithoutOne_952 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_952
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsMonoid_358
v3
                = T_IsNearSemiring_876 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_'43''45'isMonoid_892
                    (AgdaAny -> T_IsNearSemiring_876
forall a b. a -> b
coe AgdaAny
forall a. a
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsSemigroup_194
v4
                   = T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368 (T_IsMonoid_358 -> T_IsMonoid_358
forall a b. a -> b
coe T_IsMonoid_358
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               ((T_IsMagma_86
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsMagma_86 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'691'_116
                  ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202 (T_IsSemigroup_194 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194
v4))))))
-- Algebra.Bundles.SemiringWithoutOne._.∙-congˡ
d_'8729''45'cong'737'_1516 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SemiringWithoutOne_1464 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_1516 :: ()
-> ()
-> T_SemiringWithoutOne_1464
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_1516 ~()
v0 ~()
v1 T_SemiringWithoutOne_1464
v2
  = T_SemiringWithoutOne_1464
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1516 T_SemiringWithoutOne_1464
v2
du_'8729''45'cong'737'_1516 ::
  T_SemiringWithoutOne_1464 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1516 :: T_SemiringWithoutOne_1464
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1516 T_SemiringWithoutOne_1464
v0
  = let v1 :: T_IsSemiringWithoutOne_952
v1 = T_SemiringWithoutOne_1464 -> T_IsSemiringWithoutOne_952
d_isSemiringWithoutOne_1492 (T_SemiringWithoutOne_1464 -> T_SemiringWithoutOne_1464
forall a b. a -> b
coe T_SemiringWithoutOne_1464
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: t
v2
             = (T_IsSemiringWithoutOne_952 -> T_IsNearSemiring_876)
-> AgdaAny -> t
forall a b. a -> b
coe
                 T_IsSemiringWithoutOne_952 -> T_IsNearSemiring_876
MAlonzo.Code.Algebra.Structures.du_isNearSemiring_990 (T_IsSemiringWithoutOne_952 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_952
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsMonoid_358
v3
                = T_IsNearSemiring_876 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_'43''45'isMonoid_892
                    (AgdaAny -> T_IsNearSemiring_876
forall a b. a -> b
coe AgdaAny
forall a. a
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsSemigroup_194
v4
                   = T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368 (T_IsMonoid_358 -> T_IsMonoid_358
forall a b. a -> b
coe T_IsMonoid_358
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               ((T_IsMagma_86
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsMagma_86 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'737'_112
                  ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202 (T_IsSemigroup_194 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194
v4))))))
-- Algebra.Bundles.SemiringWithoutOne._.identity
d_identity_1518 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SemiringWithoutOne_1464 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_identity_1518 :: () -> () -> T_SemiringWithoutOne_1464 -> T_Σ_14
d_identity_1518 ~()
v0 ~()
v1 T_SemiringWithoutOne_1464
v2 = T_SemiringWithoutOne_1464 -> T_Σ_14
du_identity_1518 T_SemiringWithoutOne_1464
v2
du_identity_1518 ::
  T_SemiringWithoutOne_1464 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
du_identity_1518 :: T_SemiringWithoutOne_1464 -> T_Σ_14
du_identity_1518 T_SemiringWithoutOne_1464
v0
  = let v1 :: T_IsSemiringWithoutOne_952
v1 = T_SemiringWithoutOne_1464 -> T_IsSemiringWithoutOne_952
d_isSemiringWithoutOne_1492 (T_SemiringWithoutOne_1464 -> T_SemiringWithoutOne_1464
forall a b. a -> b
coe T_SemiringWithoutOne_1464
v0) in
    AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      ((T_IsMonoid_358 -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoid_358 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_identity_370
         ((T_IsCommutativeMonoid_406 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCommutativeMonoid_406 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_416
            ((T_IsSemiringWithoutOne_952 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemiringWithoutOne_952 -> T_IsCommutativeMonoid_406
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_968
               (T_IsSemiringWithoutOne_952 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_952
v1))))
-- Algebra.Bundles.SemiringWithoutOne._.identityʳ
d_identity'691'_1520 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SemiringWithoutOne_1464 -> AgdaAny -> AgdaAny
d_identity'691'_1520 :: () -> () -> T_SemiringWithoutOne_1464 -> AgdaAny -> AgdaAny
d_identity'691'_1520 ~()
v0 ~()
v1 T_SemiringWithoutOne_1464
v2 = T_SemiringWithoutOne_1464 -> AgdaAny -> AgdaAny
du_identity'691'_1520 T_SemiringWithoutOne_1464
v2
du_identity'691'_1520 ::
  T_SemiringWithoutOne_1464 -> AgdaAny -> AgdaAny
du_identity'691'_1520 :: T_SemiringWithoutOne_1464 -> AgdaAny -> AgdaAny
du_identity'691'_1520 T_SemiringWithoutOne_1464
v0
  = let v1 :: T_IsSemiringWithoutOne_952
v1 = T_SemiringWithoutOne_1464 -> T_IsSemiringWithoutOne_952
d_isSemiringWithoutOne_1492 (T_SemiringWithoutOne_1464 -> T_SemiringWithoutOne_1464
forall a b. a -> b
coe T_SemiringWithoutOne_1464
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: t
v2
             = (T_IsSemiringWithoutOne_952 -> T_IsNearSemiring_876)
-> AgdaAny -> t
forall a b. a -> b
coe
                 T_IsSemiringWithoutOne_952 -> T_IsNearSemiring_876
MAlonzo.Code.Algebra.Structures.du_isNearSemiring_990 (T_IsSemiringWithoutOne_952 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_952
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsMonoid_358 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoid_358 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_identity'691'_400
            ((T_IsNearSemiring_876 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsNearSemiring_876 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_'43''45'isMonoid_892 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2))))
-- Algebra.Bundles.SemiringWithoutOne._.identityˡ
d_identity'737'_1522 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SemiringWithoutOne_1464 -> AgdaAny -> AgdaAny
d_identity'737'_1522 :: () -> () -> T_SemiringWithoutOne_1464 -> AgdaAny -> AgdaAny
d_identity'737'_1522 ~()
v0 ~()
v1 T_SemiringWithoutOne_1464
v2 = T_SemiringWithoutOne_1464 -> AgdaAny -> AgdaAny
du_identity'737'_1522 T_SemiringWithoutOne_1464
v2
du_identity'737'_1522 ::
  T_SemiringWithoutOne_1464 -> AgdaAny -> AgdaAny
du_identity'737'_1522 :: T_SemiringWithoutOne_1464 -> AgdaAny -> AgdaAny
du_identity'737'_1522 T_SemiringWithoutOne_1464
v0
  = let v1 :: T_IsSemiringWithoutOne_952
v1 = T_SemiringWithoutOne_1464 -> T_IsSemiringWithoutOne_952
d_isSemiringWithoutOne_1492 (T_SemiringWithoutOne_1464 -> T_SemiringWithoutOne_1464
forall a b. a -> b
coe T_SemiringWithoutOne_1464
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: t
v2
             = (T_IsSemiringWithoutOne_952 -> T_IsNearSemiring_876)
-> AgdaAny -> t
forall a b. a -> b
coe
                 T_IsSemiringWithoutOne_952 -> T_IsNearSemiring_876
MAlonzo.Code.Algebra.Structures.du_isNearSemiring_990 (T_IsSemiringWithoutOne_952 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_952
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsMonoid_358 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoid_358 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_identity'737'_398
            ((T_IsNearSemiring_876 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsNearSemiring_876 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_'43''45'isMonoid_892 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2))))
-- Algebra.Bundles.SemiringWithoutOne._.isCommutativeMagma
d_isCommutativeMagma_1524 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SemiringWithoutOne_1464 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMagma_122
d_isCommutativeMagma_1524 :: () -> () -> T_SemiringWithoutOne_1464 -> T_IsCommutativeMagma_122
d_isCommutativeMagma_1524 ~()
v0 ~()
v1 T_SemiringWithoutOne_1464
v2
  = T_SemiringWithoutOne_1464 -> T_IsCommutativeMagma_122
du_isCommutativeMagma_1524 T_SemiringWithoutOne_1464
v2
du_isCommutativeMagma_1524 ::
  T_SemiringWithoutOne_1464 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMagma_122
du_isCommutativeMagma_1524 :: T_SemiringWithoutOne_1464 -> T_IsCommutativeMagma_122
du_isCommutativeMagma_1524 T_SemiringWithoutOne_1464
v0
  = let v1 :: T_IsSemiringWithoutOne_952
v1 = T_SemiringWithoutOne_1464 -> T_IsSemiringWithoutOne_952
d_isSemiringWithoutOne_1492 (T_SemiringWithoutOne_1464 -> T_SemiringWithoutOne_1464
forall a b. a -> b
coe T_SemiringWithoutOne_1464
v0) in
    AgdaAny -> T_IsCommutativeMagma_122
forall a b. a -> b
coe
      (let v2 :: T_IsCommutativeMonoid_406
v2
             = T_IsSemiringWithoutOne_952 -> T_IsCommutativeMonoid_406
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_968
                 (T_IsSemiringWithoutOne_952 -> T_IsSemiringWithoutOne_952
forall a b. a -> b
coe T_IsSemiringWithoutOne_952
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsCommutativeSemigroup_270 -> T_IsCommutativeMagma_122)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCommutativeSemigroup_270 -> T_IsCommutativeMagma_122
MAlonzo.Code.Algebra.Structures.du_isCommutativeMagma_308
            ((T_IsCommutativeMonoid_406 -> T_IsCommutativeSemigroup_270)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsCommutativeMonoid_406 -> T_IsCommutativeSemigroup_270
MAlonzo.Code.Algebra.Structures.du_isCommutativeSemigroup_454
               (T_IsCommutativeMonoid_406 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_406
v2))))
-- Algebra.Bundles.SemiringWithoutOne._.+-isCommutativeMonoid
d_'43''45'isCommutativeMonoid_1526 ::
  T_SemiringWithoutOne_1464 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMonoid_406
d_'43''45'isCommutativeMonoid_1526 :: T_SemiringWithoutOne_1464 -> T_IsCommutativeMonoid_406
d_'43''45'isCommutativeMonoid_1526 T_SemiringWithoutOne_1464
v0
  = (T_IsSemiringWithoutOne_952 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> T_IsCommutativeMonoid_406
forall a b. a -> b
coe
      T_IsSemiringWithoutOne_952 -> T_IsCommutativeMonoid_406
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_968
      ((T_SemiringWithoutOne_1464 -> T_IsSemiringWithoutOne_952)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutOne_1464 -> T_IsSemiringWithoutOne_952
d_isSemiringWithoutOne_1492 (T_SemiringWithoutOne_1464 -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutOne_1464
v0))
-- Algebra.Bundles.SemiringWithoutOne._.isCommutativeSemigroup
d_isCommutativeSemigroup_1528 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SemiringWithoutOne_1464 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_270
d_isCommutativeSemigroup_1528 :: ()
-> () -> T_SemiringWithoutOne_1464 -> T_IsCommutativeSemigroup_270
d_isCommutativeSemigroup_1528 ~()
v0 ~()
v1 T_SemiringWithoutOne_1464
v2
  = T_SemiringWithoutOne_1464 -> T_IsCommutativeSemigroup_270
du_isCommutativeSemigroup_1528 T_SemiringWithoutOne_1464
v2
du_isCommutativeSemigroup_1528 ::
  T_SemiringWithoutOne_1464 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_270
du_isCommutativeSemigroup_1528 :: T_SemiringWithoutOne_1464 -> T_IsCommutativeSemigroup_270
du_isCommutativeSemigroup_1528 T_SemiringWithoutOne_1464
v0
  = let v1 :: T_IsSemiringWithoutOne_952
v1 = T_SemiringWithoutOne_1464 -> T_IsSemiringWithoutOne_952
d_isSemiringWithoutOne_1492 (T_SemiringWithoutOne_1464 -> T_SemiringWithoutOne_1464
forall a b. a -> b
coe T_SemiringWithoutOne_1464
v0) in
    AgdaAny -> T_IsCommutativeSemigroup_270
forall a b. a -> b
coe
      ((T_IsCommutativeMonoid_406 -> T_IsCommutativeSemigroup_270)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCommutativeMonoid_406 -> T_IsCommutativeSemigroup_270
MAlonzo.Code.Algebra.Structures.du_isCommutativeSemigroup_454
         ((T_IsSemiringWithoutOne_952 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemiringWithoutOne_952 -> T_IsCommutativeMonoid_406
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_968
            (T_IsSemiringWithoutOne_952 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_952
v1)))
-- Algebra.Bundles.SemiringWithoutOne._.isMagma
d_isMagma_1530 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SemiringWithoutOne_1464 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_86
d_isMagma_1530 :: () -> () -> T_SemiringWithoutOne_1464 -> T_IsMagma_86
d_isMagma_1530 ~()
v0 ~()
v1 T_SemiringWithoutOne_1464
v2 = T_SemiringWithoutOne_1464 -> T_IsMagma_86
du_isMagma_1530 T_SemiringWithoutOne_1464
v2
du_isMagma_1530 ::
  T_SemiringWithoutOne_1464 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_86
du_isMagma_1530 :: T_SemiringWithoutOne_1464 -> T_IsMagma_86
du_isMagma_1530 T_SemiringWithoutOne_1464
v0
  = let v1 :: T_IsSemiringWithoutOne_952
v1 = T_SemiringWithoutOne_1464 -> T_IsSemiringWithoutOne_952
d_isSemiringWithoutOne_1492 (T_SemiringWithoutOne_1464 -> T_SemiringWithoutOne_1464
forall a b. a -> b
coe T_SemiringWithoutOne_1464
v0) in
    AgdaAny -> T_IsMagma_86
forall a b. a -> b
coe
      ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202
         ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368
            ((T_IsCommutativeMonoid_406 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsCommutativeMonoid_406 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_416
               ((T_IsSemiringWithoutOne_952 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsSemiringWithoutOne_952 -> T_IsCommutativeMonoid_406
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_968
                  (T_IsSemiringWithoutOne_952 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_952
v1)))))
-- Algebra.Bundles.SemiringWithoutOne._.isMonoid
d_isMonoid_1532 ::
  T_SemiringWithoutOne_1464 ->
  MAlonzo.Code.Algebra.Structures.T_IsMonoid_358
d_isMonoid_1532 :: T_SemiringWithoutOne_1464 -> T_IsMonoid_358
d_isMonoid_1532 T_SemiringWithoutOne_1464
v0
  = (T_IsCommutativeMonoid_406 -> T_IsMonoid_358)
-> AgdaAny -> T_IsMonoid_358
forall a b. a -> b
coe
      T_IsCommutativeMonoid_406 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_416
      ((T_IsSemiringWithoutOne_952 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiringWithoutOne_952 -> T_IsCommutativeMonoid_406
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_968
         ((T_SemiringWithoutOne_1464 -> T_IsSemiringWithoutOne_952)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutOne_1464 -> T_IsSemiringWithoutOne_952
d_isSemiringWithoutOne_1492 (T_SemiringWithoutOne_1464 -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutOne_1464
v0)))
-- Algebra.Bundles.SemiringWithoutOne._.isSemigroup
d_isSemigroup_1534 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SemiringWithoutOne_1464 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_194
d_isSemigroup_1534 :: () -> () -> T_SemiringWithoutOne_1464 -> T_IsSemigroup_194
d_isSemigroup_1534 ~()
v0 ~()
v1 T_SemiringWithoutOne_1464
v2 = T_SemiringWithoutOne_1464 -> T_IsSemigroup_194
du_isSemigroup_1534 T_SemiringWithoutOne_1464
v2
du_isSemigroup_1534 ::
  T_SemiringWithoutOne_1464 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_194
du_isSemigroup_1534 :: T_SemiringWithoutOne_1464 -> T_IsSemigroup_194
du_isSemigroup_1534 T_SemiringWithoutOne_1464
v0
  = let v1 :: T_IsSemiringWithoutOne_952
v1 = T_SemiringWithoutOne_1464 -> T_IsSemiringWithoutOne_952
d_isSemiringWithoutOne_1492 (T_SemiringWithoutOne_1464 -> T_SemiringWithoutOne_1464
forall a b. a -> b
coe T_SemiringWithoutOne_1464
v0) in
    AgdaAny -> T_IsSemigroup_194
forall a b. a -> b
coe
      ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368
         ((T_IsCommutativeMonoid_406 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCommutativeMonoid_406 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_416
            ((T_IsSemiringWithoutOne_952 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemiringWithoutOne_952 -> T_IsCommutativeMonoid_406
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_968
               (T_IsSemiringWithoutOne_952 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_952
v1))))
-- Algebra.Bundles.SemiringWithoutOne._.distrib
d_distrib_1536 ::
  T_SemiringWithoutOne_1464 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_distrib_1536 :: T_SemiringWithoutOne_1464 -> T_Σ_14
d_distrib_1536 T_SemiringWithoutOne_1464
v0
  = (T_IsSemiringWithoutOne_952 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsSemiringWithoutOne_952 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_distrib_972
      ((T_SemiringWithoutOne_1464 -> T_IsSemiringWithoutOne_952)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutOne_1464 -> T_IsSemiringWithoutOne_952
d_isSemiringWithoutOne_1492 (T_SemiringWithoutOne_1464 -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutOne_1464
v0))
-- Algebra.Bundles.SemiringWithoutOne._.distribʳ
d_distrib'691'_1538 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SemiringWithoutOne_1464 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_distrib'691'_1538 :: ()
-> ()
-> T_SemiringWithoutOne_1464
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_distrib'691'_1538 ~()
v0 ~()
v1 T_SemiringWithoutOne_1464
v2 = T_SemiringWithoutOne_1464
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'691'_1538 T_SemiringWithoutOne_1464
v2
du_distrib'691'_1538 ::
  T_SemiringWithoutOne_1464 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'691'_1538 :: T_SemiringWithoutOne_1464
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'691'_1538 T_SemiringWithoutOne_1464
v0
  = let v1 :: T_IsSemiringWithoutOne_952
v1 = T_SemiringWithoutOne_1464 -> T_IsSemiringWithoutOne_952
d_isSemiringWithoutOne_1492 (T_SemiringWithoutOne_1464 -> T_SemiringWithoutOne_1464
forall a b. a -> b
coe T_SemiringWithoutOne_1464
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_Σ_14 -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_Σ_14 -> AgdaAny
MAlonzo.Code.Agda.Builtin.Sigma.d_snd_30
         ((T_IsSemiringWithoutOne_952 -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_952 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_distrib_972 (T_IsSemiringWithoutOne_952 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_952
v1)))
-- Algebra.Bundles.SemiringWithoutOne._.isEquivalence
d_isEquivalence_1540 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SemiringWithoutOne_1464 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_1540 :: () -> () -> T_SemiringWithoutOne_1464 -> T_IsEquivalence_26
d_isEquivalence_1540 ~()
v0 ~()
v1 T_SemiringWithoutOne_1464
v2 = T_SemiringWithoutOne_1464 -> T_IsEquivalence_26
du_isEquivalence_1540 T_SemiringWithoutOne_1464
v2
du_isEquivalence_1540 ::
  T_SemiringWithoutOne_1464 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
du_isEquivalence_1540 :: T_SemiringWithoutOne_1464 -> T_IsEquivalence_26
du_isEquivalence_1540 T_SemiringWithoutOne_1464
v0
  = let v1 :: T_IsSemiringWithoutOne_952
v1 = T_SemiringWithoutOne_1464 -> T_IsSemiringWithoutOne_952
d_isSemiringWithoutOne_1492 (T_SemiringWithoutOne_1464 -> T_SemiringWithoutOne_1464
forall a b. a -> b
coe T_SemiringWithoutOne_1464
v0) in
    AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      ((T_IsMagma_86 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_86 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_94
         ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202
            ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368
               ((T_IsCommutativeMonoid_406 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsCommutativeMonoid_406 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_416
                  ((T_IsSemiringWithoutOne_952 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsSemiringWithoutOne_952 -> T_IsCommutativeMonoid_406
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_968
                     (T_IsSemiringWithoutOne_952 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_952
v1))))))
-- Algebra.Bundles.SemiringWithoutOne._.isNearSemiring
d_isNearSemiring_1542 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SemiringWithoutOne_1464 ->
  MAlonzo.Code.Algebra.Structures.T_IsNearSemiring_876
d_isNearSemiring_1542 :: () -> () -> T_SemiringWithoutOne_1464 -> T_IsNearSemiring_876
d_isNearSemiring_1542 ~()
v0 ~()
v1 T_SemiringWithoutOne_1464
v2 = T_SemiringWithoutOne_1464 -> T_IsNearSemiring_876
du_isNearSemiring_1542 T_SemiringWithoutOne_1464
v2
du_isNearSemiring_1542 ::
  T_SemiringWithoutOne_1464 ->
  MAlonzo.Code.Algebra.Structures.T_IsNearSemiring_876
du_isNearSemiring_1542 :: T_SemiringWithoutOne_1464 -> T_IsNearSemiring_876
du_isNearSemiring_1542 T_SemiringWithoutOne_1464
v0
  = (T_IsSemiringWithoutOne_952 -> T_IsNearSemiring_876)
-> AgdaAny -> T_IsNearSemiring_876
forall a b. a -> b
coe
      T_IsSemiringWithoutOne_952 -> T_IsNearSemiring_876
MAlonzo.Code.Algebra.Structures.du_isNearSemiring_990
      ((T_SemiringWithoutOne_1464 -> T_IsSemiringWithoutOne_952)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutOne_1464 -> T_IsSemiringWithoutOne_952
d_isSemiringWithoutOne_1492 (T_SemiringWithoutOne_1464 -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutOne_1464
v0))
-- Algebra.Bundles.SemiringWithoutOne._.isPartialEquivalence
d_isPartialEquivalence_1544 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SemiringWithoutOne_1464 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_1544 :: () -> () -> T_SemiringWithoutOne_1464 -> T_IsPartialEquivalence_16
d_isPartialEquivalence_1544 ~()
v0 ~()
v1 T_SemiringWithoutOne_1464
v2
  = T_SemiringWithoutOne_1464 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_1544 T_SemiringWithoutOne_1464
v2
du_isPartialEquivalence_1544 ::
  T_SemiringWithoutOne_1464 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_1544 :: T_SemiringWithoutOne_1464 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_1544 T_SemiringWithoutOne_1464
v0
  = let v1 :: T_IsSemiringWithoutOne_952
v1 = T_SemiringWithoutOne_1464 -> T_IsSemiringWithoutOne_952
d_isSemiringWithoutOne_1492 (T_SemiringWithoutOne_1464 -> T_SemiringWithoutOne_1464
forall a b. a -> b
coe T_SemiringWithoutOne_1464
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: t
v2
             = (T_IsSemiringWithoutOne_952 -> T_IsNearSemiring_876)
-> AgdaAny -> t
forall a b. a -> b
coe
                 T_IsSemiringWithoutOne_952 -> T_IsNearSemiring_876
MAlonzo.Code.Algebra.Structures.du_isNearSemiring_990 (T_IsSemiringWithoutOne_952 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_952
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsMonoid_358
v3
                = T_IsNearSemiring_876 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_'43''45'isMonoid_892
                    (AgdaAny -> T_IsNearSemiring_876
forall a b. a -> b
coe AgdaAny
forall a. a
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsSemigroup_194
v4
                   = T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368 (T_IsMonoid_358 -> T_IsMonoid_358
forall a b. a -> b
coe T_IsMonoid_358
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsMagma_86
v5 = T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202 (T_IsSemigroup_194 -> T_IsSemigroup_194
forall a b. a -> b
coe T_IsSemigroup_194
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_86 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsMagma_86 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_94 (T_IsMagma_86 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86
v5)))))))
-- Algebra.Bundles.SemiringWithoutOne._.refl
d_refl_1546 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SemiringWithoutOne_1464 -> AgdaAny -> AgdaAny
d_refl_1546 :: () -> () -> T_SemiringWithoutOne_1464 -> AgdaAny -> AgdaAny
d_refl_1546 ~()
v0 ~()
v1 T_SemiringWithoutOne_1464
v2 = T_SemiringWithoutOne_1464 -> AgdaAny -> AgdaAny
du_refl_1546 T_SemiringWithoutOne_1464
v2
du_refl_1546 :: T_SemiringWithoutOne_1464 -> AgdaAny -> AgdaAny
du_refl_1546 :: T_SemiringWithoutOne_1464 -> AgdaAny -> AgdaAny
du_refl_1546 T_SemiringWithoutOne_1464
v0
  = let v1 :: T_IsSemiringWithoutOne_952
v1 = T_SemiringWithoutOne_1464 -> T_IsSemiringWithoutOne_952
d_isSemiringWithoutOne_1492 (T_SemiringWithoutOne_1464 -> T_SemiringWithoutOne_1464
forall a b. a -> b
coe T_SemiringWithoutOne_1464
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsEquivalence_26 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_34
         ((T_IsMagma_86 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMagma_86 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_94
            ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202
               ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368
                  ((T_IsCommutativeMonoid_406 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsCommutativeMonoid_406 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_416
                     ((T_IsSemiringWithoutOne_952 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsSemiringWithoutOne_952 -> T_IsCommutativeMonoid_406
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_968
                        (T_IsSemiringWithoutOne_952 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_952
v1)))))))
-- Algebra.Bundles.SemiringWithoutOne._.reflexive
d_reflexive_1548 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SemiringWithoutOne_1464 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_1548 :: ()
-> ()
-> T_SemiringWithoutOne_1464
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_1548 ~()
v0 ~()
v1 T_SemiringWithoutOne_1464
v2 = T_SemiringWithoutOne_1464
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_1548 T_SemiringWithoutOne_1464
v2
du_reflexive_1548 ::
  T_SemiringWithoutOne_1464 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_1548 :: T_SemiringWithoutOne_1464
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_1548 T_SemiringWithoutOne_1464
v0
  = let v1 :: T_IsSemiringWithoutOne_952
v1 = T_SemiringWithoutOne_1464 -> T_IsSemiringWithoutOne_952
d_isSemiringWithoutOne_1492 (T_SemiringWithoutOne_1464 -> T_SemiringWithoutOne_1464
forall a b. a -> b
coe T_SemiringWithoutOne_1464
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: t
v2
             = (T_IsSemiringWithoutOne_952 -> T_IsNearSemiring_876)
-> AgdaAny -> t
forall a b. a -> b
coe
                 T_IsSemiringWithoutOne_952 -> T_IsNearSemiring_876
MAlonzo.Code.Algebra.Structures.du_isNearSemiring_990 (T_IsSemiringWithoutOne_952 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_952
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsMonoid_358
v3
                = T_IsNearSemiring_876 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_'43''45'isMonoid_892
                    (AgdaAny -> T_IsNearSemiring_876
forall a b. a -> b
coe AgdaAny
forall a. a
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsSemigroup_194
v4
                   = T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368 (T_IsMonoid_358 -> T_IsMonoid_358
forall a b. a -> b
coe T_IsMonoid_358
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsMagma_86
v5 = T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202 (T_IsSemigroup_194 -> T_IsSemigroup_194
forall a b. a -> b
coe T_IsSemigroup_194
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_86 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_94 (T_IsMagma_86 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86
v5))
                       AgdaAny
v6)))))
-- Algebra.Bundles.SemiringWithoutOne._.setoid
d_setoid_1550 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SemiringWithoutOne_1464 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_1550 :: () -> () -> T_SemiringWithoutOne_1464 -> T_Setoid_44
d_setoid_1550 ~()
v0 ~()
v1 T_SemiringWithoutOne_1464
v2 = T_SemiringWithoutOne_1464 -> T_Setoid_44
du_setoid_1550 T_SemiringWithoutOne_1464
v2
du_setoid_1550 ::
  T_SemiringWithoutOne_1464 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_1550 :: T_SemiringWithoutOne_1464 -> T_Setoid_44
du_setoid_1550 T_SemiringWithoutOne_1464
v0
  = let v1 :: T_IsSemiringWithoutOne_952
v1 = T_SemiringWithoutOne_1464 -> T_IsSemiringWithoutOne_952
d_isSemiringWithoutOne_1492 (T_SemiringWithoutOne_1464 -> T_SemiringWithoutOne_1464
forall a b. a -> b
coe T_SemiringWithoutOne_1464
v0) in
    AgdaAny -> T_Setoid_44
forall a b. a -> b
coe
      (let v2 :: t
v2
             = (T_IsSemiringWithoutOne_952 -> T_IsNearSemiring_876)
-> AgdaAny -> t
forall a b. a -> b
coe
                 T_IsSemiringWithoutOne_952 -> T_IsNearSemiring_876
MAlonzo.Code.Algebra.Structures.du_isNearSemiring_990 (T_IsSemiringWithoutOne_952 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_952
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsMonoid_358
v3
                = T_IsNearSemiring_876 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_'43''45'isMonoid_892
                    (AgdaAny -> T_IsNearSemiring_876
forall a b. a -> b
coe AgdaAny
forall a. a
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsSemigroup_194
v4
                   = T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368 (T_IsMonoid_358 -> T_IsMonoid_358
forall a b. a -> b
coe T_IsMonoid_358
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               ((T_IsMagma_86 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsMagma_86 -> T_Setoid_44
MAlonzo.Code.Algebra.Structures.du_setoid_110
                  ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202 (T_IsSemigroup_194 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194
v4))))))
-- Algebra.Bundles.SemiringWithoutOne._.sym
d_sym_1552 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SemiringWithoutOne_1464 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_1552 :: ()
-> ()
-> T_SemiringWithoutOne_1464
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_sym_1552 ~()
v0 ~()
v1 T_SemiringWithoutOne_1464
v2 = T_SemiringWithoutOne_1464
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_1552 T_SemiringWithoutOne_1464
v2
du_sym_1552 ::
  T_SemiringWithoutOne_1464 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_1552 :: T_SemiringWithoutOne_1464
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_1552 T_SemiringWithoutOne_1464
v0
  = let v1 :: T_IsSemiringWithoutOne_952
v1 = T_SemiringWithoutOne_1464 -> T_IsSemiringWithoutOne_952
d_isSemiringWithoutOne_1492 (T_SemiringWithoutOne_1464 -> T_SemiringWithoutOne_1464
forall a b. a -> b
coe T_SemiringWithoutOne_1464
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_36
         ((T_IsMagma_86 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMagma_86 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_94
            ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202
               ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368
                  ((T_IsCommutativeMonoid_406 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsCommutativeMonoid_406 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_416
                     ((T_IsSemiringWithoutOne_952 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsSemiringWithoutOne_952 -> T_IsCommutativeMonoid_406
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_968
                        (T_IsSemiringWithoutOne_952 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_952
v1)))))))
-- Algebra.Bundles.SemiringWithoutOne._.trans
d_trans_1554 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SemiringWithoutOne_1464 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_1554 :: ()
-> ()
-> T_SemiringWithoutOne_1464
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_trans_1554 ~()
v0 ~()
v1 T_SemiringWithoutOne_1464
v2 = T_SemiringWithoutOne_1464
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_1554 T_SemiringWithoutOne_1464
v2
du_trans_1554 ::
  T_SemiringWithoutOne_1464 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_1554 :: T_SemiringWithoutOne_1464
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_1554 T_SemiringWithoutOne_1464
v0
  = let v1 :: T_IsSemiringWithoutOne_952
v1 = T_SemiringWithoutOne_1464 -> T_IsSemiringWithoutOne_952
d_isSemiringWithoutOne_1492 (T_SemiringWithoutOne_1464 -> T_SemiringWithoutOne_1464
forall a b. a -> b
coe T_SemiringWithoutOne_1464
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsEquivalence_26
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsEquivalence_26
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_38
         ((T_IsMagma_86 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMagma_86 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_94
            ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202
               ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368
                  ((T_IsCommutativeMonoid_406 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsCommutativeMonoid_406 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_416
                     ((T_IsSemiringWithoutOne_952 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsSemiringWithoutOne_952 -> T_IsCommutativeMonoid_406
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_968
                        (T_IsSemiringWithoutOne_952 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_952
v1)))))))
-- Algebra.Bundles.SemiringWithoutOne._.zero
d_zero_1556 ::
  T_SemiringWithoutOne_1464 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_zero_1556 :: T_SemiringWithoutOne_1464 -> T_Σ_14
d_zero_1556 T_SemiringWithoutOne_1464
v0
  = (T_IsSemiringWithoutOne_952 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsSemiringWithoutOne_952 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_zero_974
      ((T_SemiringWithoutOne_1464 -> T_IsSemiringWithoutOne_952)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutOne_1464 -> T_IsSemiringWithoutOne_952
d_isSemiringWithoutOne_1492 (T_SemiringWithoutOne_1464 -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutOne_1464
v0))
-- Algebra.Bundles.SemiringWithoutOne._.zeroʳ
d_zero'691'_1558 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SemiringWithoutOne_1464 -> AgdaAny -> AgdaAny
d_zero'691'_1558 :: () -> () -> T_SemiringWithoutOne_1464 -> AgdaAny -> AgdaAny
d_zero'691'_1558 ~()
v0 ~()
v1 T_SemiringWithoutOne_1464
v2 = T_SemiringWithoutOne_1464 -> AgdaAny -> AgdaAny
du_zero'691'_1558 T_SemiringWithoutOne_1464
v2
du_zero'691'_1558 ::
  T_SemiringWithoutOne_1464 -> AgdaAny -> AgdaAny
du_zero'691'_1558 :: T_SemiringWithoutOne_1464 -> AgdaAny -> AgdaAny
du_zero'691'_1558 T_SemiringWithoutOne_1464
v0
  = (T_IsSemiringWithoutOne_952 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsSemiringWithoutOne_952 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_zero'691'_988
      ((T_SemiringWithoutOne_1464 -> T_IsSemiringWithoutOne_952)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutOne_1464 -> T_IsSemiringWithoutOne_952
d_isSemiringWithoutOne_1492 (T_SemiringWithoutOne_1464 -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutOne_1464
v0))
-- Algebra.Bundles.SemiringWithoutOne._.zeroˡ
d_zero'737'_1560 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SemiringWithoutOne_1464 -> AgdaAny -> AgdaAny
d_zero'737'_1560 :: () -> () -> T_SemiringWithoutOne_1464 -> AgdaAny -> AgdaAny
d_zero'737'_1560 ~()
v0 ~()
v1 T_SemiringWithoutOne_1464
v2 = T_SemiringWithoutOne_1464 -> AgdaAny -> AgdaAny
du_zero'737'_1560 T_SemiringWithoutOne_1464
v2
du_zero'737'_1560 ::
  T_SemiringWithoutOne_1464 -> AgdaAny -> AgdaAny
du_zero'737'_1560 :: T_SemiringWithoutOne_1464 -> AgdaAny -> AgdaAny
du_zero'737'_1560 T_SemiringWithoutOne_1464
v0
  = (T_IsSemiringWithoutOne_952 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsSemiringWithoutOne_952 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_zero'737'_986
      ((T_SemiringWithoutOne_1464 -> T_IsSemiringWithoutOne_952)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutOne_1464 -> T_IsSemiringWithoutOne_952
d_isSemiringWithoutOne_1492 (T_SemiringWithoutOne_1464 -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutOne_1464
v0))
-- Algebra.Bundles.SemiringWithoutOne.nearSemiring
d_nearSemiring_1562 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SemiringWithoutOne_1464 -> T_NearSemiring_1354
d_nearSemiring_1562 :: () -> () -> T_SemiringWithoutOne_1464 -> T_NearSemiring_1354
d_nearSemiring_1562 ~()
v0 ~()
v1 T_SemiringWithoutOne_1464
v2 = T_SemiringWithoutOne_1464 -> T_NearSemiring_1354
du_nearSemiring_1562 T_SemiringWithoutOne_1464
v2
du_nearSemiring_1562 ::
  T_SemiringWithoutOne_1464 -> T_NearSemiring_1354
du_nearSemiring_1562 :: T_SemiringWithoutOne_1464 -> T_NearSemiring_1354
du_nearSemiring_1562 T_SemiringWithoutOne_1464
v0
  = ((AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> T_IsNearSemiring_876
 -> T_NearSemiring_1354)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_NearSemiring_1354
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsNearSemiring_876
-> T_NearSemiring_1354
C_NearSemiring'46'constructor_23249 (T_SemiringWithoutOne_1464 -> AgdaAny -> AgdaAny -> AgdaAny
d__'43'__1486 (T_SemiringWithoutOne_1464 -> T_SemiringWithoutOne_1464
forall a b. a -> b
coe T_SemiringWithoutOne_1464
v0))
      (T_SemiringWithoutOne_1464 -> AgdaAny -> AgdaAny -> AgdaAny
d__'42'__1488 (T_SemiringWithoutOne_1464 -> T_SemiringWithoutOne_1464
forall a b. a -> b
coe T_SemiringWithoutOne_1464
v0)) (T_SemiringWithoutOne_1464 -> AgdaAny
d_0'35'_1490 (T_SemiringWithoutOne_1464 -> T_SemiringWithoutOne_1464
forall a b. a -> b
coe T_SemiringWithoutOne_1464
v0))
      ((T_IsSemiringWithoutOne_952 -> T_IsNearSemiring_876)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiringWithoutOne_952 -> T_IsNearSemiring_876
MAlonzo.Code.Algebra.Structures.du_isNearSemiring_990
         ((T_SemiringWithoutOne_1464 -> T_IsSemiringWithoutOne_952)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutOne_1464 -> T_IsSemiringWithoutOne_952
d_isSemiringWithoutOne_1492 (T_SemiringWithoutOne_1464 -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutOne_1464
v0)))
-- Algebra.Bundles.SemiringWithoutOne._._≉_
d__'8777'__1566 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SemiringWithoutOne_1464 -> AgdaAny -> AgdaAny -> ()
d__'8777'__1566 :: () -> () -> T_SemiringWithoutOne_1464 -> AgdaAny -> AgdaAny -> ()
d__'8777'__1566 = () -> () -> T_SemiringWithoutOne_1464 -> AgdaAny -> AgdaAny -> ()
forall a. a
erased
-- Algebra.Bundles.SemiringWithoutOne._.magma
d_magma_1568 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SemiringWithoutOne_1464 -> T_Magma_36
d_magma_1568 :: () -> () -> T_SemiringWithoutOne_1464 -> T_Magma_36
d_magma_1568 ~()
v0 ~()
v1 T_SemiringWithoutOne_1464
v2 = T_SemiringWithoutOne_1464 -> T_Magma_36
du_magma_1568 T_SemiringWithoutOne_1464
v2
du_magma_1568 :: T_SemiringWithoutOne_1464 -> T_Magma_36
du_magma_1568 :: T_SemiringWithoutOne_1464 -> T_Magma_36
du_magma_1568 T_SemiringWithoutOne_1464
v0
  = let v1 :: t
v1 = (T_SemiringWithoutOne_1464 -> T_NearSemiring_1354) -> AgdaAny -> t
forall a b. a -> b
coe T_SemiringWithoutOne_1464 -> T_NearSemiring_1354
du_nearSemiring_1562 (T_SemiringWithoutOne_1464 -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutOne_1464
v0) in
    AgdaAny -> T_Magma_36
forall a b. a -> b
coe ((T_Semigroup_206 -> T_Magma_36) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semigroup_206 -> T_Magma_36
du_magma_254 ((T_NearSemiring_1354 -> T_Semigroup_206) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_NearSemiring_1354 -> T_Semigroup_206
du_'42''45'semigroup_1452 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1)))
-- Algebra.Bundles.SemiringWithoutOne._.rawMagma
d_rawMagma_1570 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SemiringWithoutOne_1464 -> T_RawMagma_8
d_rawMagma_1570 :: () -> () -> T_SemiringWithoutOne_1464 -> T_RawMagma_8
d_rawMagma_1570 ~()
v0 ~()
v1 T_SemiringWithoutOne_1464
v2 = T_SemiringWithoutOne_1464 -> T_RawMagma_8
du_rawMagma_1570 T_SemiringWithoutOne_1464
v2
du_rawMagma_1570 :: T_SemiringWithoutOne_1464 -> T_RawMagma_8
du_rawMagma_1570 :: T_SemiringWithoutOne_1464 -> T_RawMagma_8
du_rawMagma_1570 T_SemiringWithoutOne_1464
v0
  = let v1 :: t
v1 = (T_SemiringWithoutOne_1464 -> T_NearSemiring_1354) -> AgdaAny -> t
forall a b. a -> b
coe T_SemiringWithoutOne_1464 -> T_NearSemiring_1354
du_nearSemiring_1562 (T_SemiringWithoutOne_1464 -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutOne_1464
v0) in
    AgdaAny -> T_RawMagma_8
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_NearSemiring_1354 -> T_Semigroup_206) -> AgdaAny -> t
forall a b. a -> b
coe T_NearSemiring_1354 -> T_Semigroup_206
du_'42''45'semigroup_1452 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_Magma_36 -> T_RawMagma_8) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Magma_36 -> T_RawMagma_8
du_rawMagma_80 ((T_Semigroup_206 -> T_Magma_36) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semigroup_206 -> T_Magma_36
du_magma_254 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2))))
-- Algebra.Bundles.SemiringWithoutOne._.*-semigroup
d_'42''45'semigroup_1572 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SemiringWithoutOne_1464 -> T_Semigroup_206
d_'42''45'semigroup_1572 :: () -> () -> T_SemiringWithoutOne_1464 -> T_Semigroup_206
d_'42''45'semigroup_1572 ~()
v0 ~()
v1 T_SemiringWithoutOne_1464
v2 = T_SemiringWithoutOne_1464 -> T_Semigroup_206
du_'42''45'semigroup_1572 T_SemiringWithoutOne_1464
v2
du_'42''45'semigroup_1572 ::
  T_SemiringWithoutOne_1464 -> T_Semigroup_206
du_'42''45'semigroup_1572 :: T_SemiringWithoutOne_1464 -> T_Semigroup_206
du_'42''45'semigroup_1572 T_SemiringWithoutOne_1464
v0
  = (T_NearSemiring_1354 -> T_Semigroup_206)
-> AgdaAny -> T_Semigroup_206
forall a b. a -> b
coe T_NearSemiring_1354 -> T_Semigroup_206
du_'42''45'semigroup_1452 ((T_SemiringWithoutOne_1464 -> T_NearSemiring_1354)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutOne_1464 -> T_NearSemiring_1354
du_nearSemiring_1562 (T_SemiringWithoutOne_1464 -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutOne_1464
v0))
-- Algebra.Bundles.SemiringWithoutOne._.magma
d_magma_1574 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SemiringWithoutOne_1464 -> T_Magma_36
d_magma_1574 :: () -> () -> T_SemiringWithoutOne_1464 -> T_Magma_36
d_magma_1574 ~()
v0 ~()
v1 T_SemiringWithoutOne_1464
v2 = T_SemiringWithoutOne_1464 -> T_Magma_36
du_magma_1574 T_SemiringWithoutOne_1464
v2
du_magma_1574 :: T_SemiringWithoutOne_1464 -> T_Magma_36
du_magma_1574 :: T_SemiringWithoutOne_1464 -> T_Magma_36
du_magma_1574 T_SemiringWithoutOne_1464
v0
  = let v1 :: t
v1 = (T_SemiringWithoutOne_1464 -> T_NearSemiring_1354) -> AgdaAny -> t
forall a b. a -> b
coe T_SemiringWithoutOne_1464 -> T_NearSemiring_1354
du_nearSemiring_1562 (T_SemiringWithoutOne_1464 -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutOne_1464
v0) in
    AgdaAny -> T_Magma_36
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_NearSemiring_1354 -> T_Monoid_506) -> AgdaAny -> t
forall a b. a -> b
coe T_NearSemiring_1354 -> T_Monoid_506
du_'43''45'monoid_1438 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_Semigroup_206 -> T_Magma_36) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semigroup_206 -> T_Magma_36
du_magma_254 ((T_Monoid_506 -> T_Semigroup_206) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Monoid_506 -> T_Semigroup_206
du_semigroup_566 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2))))
-- Algebra.Bundles.SemiringWithoutOne._.+-monoid
d_'43''45'monoid_1576 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SemiringWithoutOne_1464 -> T_Monoid_506
d_'43''45'monoid_1576 :: () -> () -> T_SemiringWithoutOne_1464 -> T_Monoid_506
d_'43''45'monoid_1576 ~()
v0 ~()
v1 T_SemiringWithoutOne_1464
v2 = T_SemiringWithoutOne_1464 -> T_Monoid_506
du_'43''45'monoid_1576 T_SemiringWithoutOne_1464
v2
du_'43''45'monoid_1576 :: T_SemiringWithoutOne_1464 -> T_Monoid_506
du_'43''45'monoid_1576 :: T_SemiringWithoutOne_1464 -> T_Monoid_506
du_'43''45'monoid_1576 T_SemiringWithoutOne_1464
v0
  = (T_NearSemiring_1354 -> T_Monoid_506) -> AgdaAny -> T_Monoid_506
forall a b. a -> b
coe T_NearSemiring_1354 -> T_Monoid_506
du_'43''45'monoid_1438 ((T_SemiringWithoutOne_1464 -> T_NearSemiring_1354)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutOne_1464 -> T_NearSemiring_1354
du_nearSemiring_1562 (T_SemiringWithoutOne_1464 -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutOne_1464
v0))
-- Algebra.Bundles.SemiringWithoutOne._.rawMagma
d_rawMagma_1578 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SemiringWithoutOne_1464 -> T_RawMagma_8
d_rawMagma_1578 :: () -> () -> T_SemiringWithoutOne_1464 -> T_RawMagma_8
d_rawMagma_1578 ~()
v0 ~()
v1 T_SemiringWithoutOne_1464
v2 = T_SemiringWithoutOne_1464 -> T_RawMagma_8
du_rawMagma_1578 T_SemiringWithoutOne_1464
v2
du_rawMagma_1578 :: T_SemiringWithoutOne_1464 -> T_RawMagma_8
du_rawMagma_1578 :: T_SemiringWithoutOne_1464 -> T_RawMagma_8
du_rawMagma_1578 T_SemiringWithoutOne_1464
v0
  = let v1 :: t
v1 = (T_SemiringWithoutOne_1464 -> T_NearSemiring_1354) -> AgdaAny -> t
forall a b. a -> b
coe T_SemiringWithoutOne_1464 -> T_NearSemiring_1354
du_nearSemiring_1562 (T_SemiringWithoutOne_1464 -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutOne_1464
v0) in
    AgdaAny -> T_RawMagma_8
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_NearSemiring_1354 -> T_Monoid_506) -> AgdaAny -> t
forall a b. a -> b
coe T_NearSemiring_1354 -> T_Monoid_506
du_'43''45'monoid_1438 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: t
v3 = (T_Monoid_506 -> T_Semigroup_206) -> AgdaAny -> t
forall a b. a -> b
coe T_Monoid_506 -> T_Semigroup_206
du_semigroup_566 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_Magma_36 -> T_RawMagma_8) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Magma_36 -> T_RawMagma_8
du_rawMagma_80 ((T_Semigroup_206 -> T_Magma_36) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semigroup_206 -> T_Magma_36
du_magma_254 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3)))))
-- Algebra.Bundles.SemiringWithoutOne._.rawMonoid
d_rawMonoid_1580 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SemiringWithoutOne_1464 -> T_RawMonoid_474
d_rawMonoid_1580 :: () -> () -> T_SemiringWithoutOne_1464 -> T_RawMonoid_474
d_rawMonoid_1580 ~()
v0 ~()
v1 T_SemiringWithoutOne_1464
v2 = T_SemiringWithoutOne_1464 -> T_RawMonoid_474
du_rawMonoid_1580 T_SemiringWithoutOne_1464
v2
du_rawMonoid_1580 :: T_SemiringWithoutOne_1464 -> T_RawMonoid_474
du_rawMonoid_1580 :: T_SemiringWithoutOne_1464 -> T_RawMonoid_474
du_rawMonoid_1580 T_SemiringWithoutOne_1464
v0
  = let v1 :: t
v1 = (T_SemiringWithoutOne_1464 -> T_NearSemiring_1354) -> AgdaAny -> t
forall a b. a -> b
coe T_SemiringWithoutOne_1464 -> T_NearSemiring_1354
du_nearSemiring_1562 (T_SemiringWithoutOne_1464 -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutOne_1464
v0) in
    AgdaAny -> T_RawMonoid_474
forall a b. a -> b
coe ((T_Monoid_506 -> T_RawMonoid_474) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Monoid_506 -> T_RawMonoid_474
du_rawMonoid_576 ((T_NearSemiring_1354 -> T_Monoid_506) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_NearSemiring_1354 -> T_Monoid_506
du_'43''45'monoid_1438 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1)))
-- Algebra.Bundles.SemiringWithoutOne._.semigroup
d_semigroup_1582 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SemiringWithoutOne_1464 -> T_Semigroup_206
d_semigroup_1582 :: () -> () -> T_SemiringWithoutOne_1464 -> T_Semigroup_206
d_semigroup_1582 ~()
v0 ~()
v1 T_SemiringWithoutOne_1464
v2 = T_SemiringWithoutOne_1464 -> T_Semigroup_206
du_semigroup_1582 T_SemiringWithoutOne_1464
v2
du_semigroup_1582 :: T_SemiringWithoutOne_1464 -> T_Semigroup_206
du_semigroup_1582 :: T_SemiringWithoutOne_1464 -> T_Semigroup_206
du_semigroup_1582 T_SemiringWithoutOne_1464
v0
  = let v1 :: t
v1 = (T_SemiringWithoutOne_1464 -> T_NearSemiring_1354) -> AgdaAny -> t
forall a b. a -> b
coe T_SemiringWithoutOne_1464 -> T_NearSemiring_1354
du_nearSemiring_1562 (T_SemiringWithoutOne_1464 -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutOne_1464
v0) in
    AgdaAny -> T_Semigroup_206
forall a b. a -> b
coe ((T_Monoid_506 -> T_Semigroup_206) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Monoid_506 -> T_Semigroup_206
du_semigroup_566 ((T_NearSemiring_1354 -> T_Monoid_506) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_NearSemiring_1354 -> T_Monoid_506
du_'43''45'monoid_1438 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1)))
-- Algebra.Bundles.SemiringWithoutOne._.rawNearSemiring
d_rawNearSemiring_1584 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SemiringWithoutOne_1464 -> T_RawNearSemiring_1314
d_rawNearSemiring_1584 :: () -> () -> T_SemiringWithoutOne_1464 -> T_RawNearSemiring_1314
d_rawNearSemiring_1584 ~()
v0 ~()
v1 T_SemiringWithoutOne_1464
v2 = T_SemiringWithoutOne_1464 -> T_RawNearSemiring_1314
du_rawNearSemiring_1584 T_SemiringWithoutOne_1464
v2
du_rawNearSemiring_1584 ::
  T_SemiringWithoutOne_1464 -> T_RawNearSemiring_1314
du_rawNearSemiring_1584 :: T_SemiringWithoutOne_1464 -> T_RawNearSemiring_1314
du_rawNearSemiring_1584 T_SemiringWithoutOne_1464
v0
  = (T_NearSemiring_1354 -> T_RawNearSemiring_1314)
-> AgdaAny -> T_RawNearSemiring_1314
forall a b. a -> b
coe T_NearSemiring_1354 -> T_RawNearSemiring_1314
du_rawNearSemiring_1436 ((T_SemiringWithoutOne_1464 -> T_NearSemiring_1354)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutOne_1464 -> T_NearSemiring_1354
du_nearSemiring_1562 (T_SemiringWithoutOne_1464 -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutOne_1464
v0))
-- Algebra.Bundles.SemiringWithoutOne.+-commutativeMonoid
d_'43''45'commutativeMonoid_1586 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SemiringWithoutOne_1464 -> T_CommutativeMonoid_582
d_'43''45'commutativeMonoid_1586 :: () -> () -> T_SemiringWithoutOne_1464 -> T_CommutativeMonoid_582
d_'43''45'commutativeMonoid_1586 ~()
v0 ~()
v1 T_SemiringWithoutOne_1464
v2
  = T_SemiringWithoutOne_1464 -> T_CommutativeMonoid_582
du_'43''45'commutativeMonoid_1586 T_SemiringWithoutOne_1464
v2
du_'43''45'commutativeMonoid_1586 ::
  T_SemiringWithoutOne_1464 -> T_CommutativeMonoid_582
du_'43''45'commutativeMonoid_1586 :: T_SemiringWithoutOne_1464 -> T_CommutativeMonoid_582
du_'43''45'commutativeMonoid_1586 T_SemiringWithoutOne_1464
v0
  = ((AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny -> T_IsCommutativeMonoid_406 -> T_CommutativeMonoid_582)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsCommutativeMonoid_406
-> T_CommutativeMonoid_582
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> T_IsCommutativeMonoid_406 -> T_CommutativeMonoid_582
C_CommutativeMonoid'46'constructor_10343 (T_SemiringWithoutOne_1464 -> AgdaAny -> AgdaAny -> AgdaAny
d__'43'__1486 (T_SemiringWithoutOne_1464 -> T_SemiringWithoutOne_1464
forall a b. a -> b
coe T_SemiringWithoutOne_1464
v0))
      (T_SemiringWithoutOne_1464 -> AgdaAny
d_0'35'_1490 (T_SemiringWithoutOne_1464 -> T_SemiringWithoutOne_1464
forall a b. a -> b
coe T_SemiringWithoutOne_1464
v0))
      (T_IsSemiringWithoutOne_952 -> T_IsCommutativeMonoid_406
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_968
         ((T_SemiringWithoutOne_1464 -> T_IsSemiringWithoutOne_952)
-> AgdaAny -> T_IsSemiringWithoutOne_952
forall a b. a -> b
coe T_SemiringWithoutOne_1464 -> T_IsSemiringWithoutOne_952
d_isSemiringWithoutOne_1492 (T_SemiringWithoutOne_1464 -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutOne_1464
v0)))
-- Algebra.Bundles.SemiringWithoutOne._.commutativeMagma
d_commutativeMagma_1590 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SemiringWithoutOne_1464 -> T_CommutativeMagma_148
d_commutativeMagma_1590 :: () -> () -> T_SemiringWithoutOne_1464 -> T_CommutativeMagma_148
d_commutativeMagma_1590 ~()
v0 ~()
v1 T_SemiringWithoutOne_1464
v2 = T_SemiringWithoutOne_1464 -> T_CommutativeMagma_148
du_commutativeMagma_1590 T_SemiringWithoutOne_1464
v2
du_commutativeMagma_1590 ::
  T_SemiringWithoutOne_1464 -> T_CommutativeMagma_148
du_commutativeMagma_1590 :: T_SemiringWithoutOne_1464 -> T_CommutativeMagma_148
du_commutativeMagma_1590 T_SemiringWithoutOne_1464
v0
  = let v1 :: t
v1 = (T_SemiringWithoutOne_1464 -> T_CommutativeMonoid_582)
-> AgdaAny -> t
forall a b. a -> b
coe T_SemiringWithoutOne_1464 -> T_CommutativeMonoid_582
du_'43''45'commutativeMonoid_1586 (T_SemiringWithoutOne_1464 -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutOne_1464
v0) in
    AgdaAny -> T_CommutativeMagma_148
forall a b. a -> b
coe
      ((T_CommutativeSemigroup_332 -> T_CommutativeMagma_148)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_CommutativeSemigroup_332 -> T_CommutativeMagma_148
du_commutativeMagma_396 ((T_CommutativeMonoid_582 -> T_CommutativeSemigroup_332)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeMonoid_582 -> T_CommutativeSemigroup_332
du_commutativeSemigroup_664 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1)))
-- Algebra.Bundles.SemiringWithoutOne._.commutativeSemigroup
d_commutativeSemigroup_1592 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SemiringWithoutOne_1464 -> T_CommutativeSemigroup_332
d_commutativeSemigroup_1592 :: () -> () -> T_SemiringWithoutOne_1464 -> T_CommutativeSemigroup_332
d_commutativeSemigroup_1592 ~()
v0 ~()
v1 T_SemiringWithoutOne_1464
v2
  = T_SemiringWithoutOne_1464 -> T_CommutativeSemigroup_332
du_commutativeSemigroup_1592 T_SemiringWithoutOne_1464
v2
du_commutativeSemigroup_1592 ::
  T_SemiringWithoutOne_1464 -> T_CommutativeSemigroup_332
du_commutativeSemigroup_1592 :: T_SemiringWithoutOne_1464 -> T_CommutativeSemigroup_332
du_commutativeSemigroup_1592 T_SemiringWithoutOne_1464
v0
  = (T_CommutativeMonoid_582 -> T_CommutativeSemigroup_332)
-> AgdaAny -> T_CommutativeSemigroup_332
forall a b. a -> b
coe
      T_CommutativeMonoid_582 -> T_CommutativeSemigroup_332
du_commutativeSemigroup_664
      ((T_SemiringWithoutOne_1464 -> T_CommutativeMonoid_582)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutOne_1464 -> T_CommutativeMonoid_582
du_'43''45'commutativeMonoid_1586 (T_SemiringWithoutOne_1464 -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutOne_1464
v0))
-- Algebra.Bundles.CommutativeSemiringWithoutOne
d_CommutativeSemiringWithoutOne_1598 :: p -> p -> ()
d_CommutativeSemiringWithoutOne_1598 p
a0 p
a1 = ()
data T_CommutativeSemiringWithoutOne_1598
  = C_CommutativeSemiringWithoutOne'46'constructor_27945 (AgdaAny ->
                                                          AgdaAny -> AgdaAny)
                                                         (AgdaAny -> AgdaAny -> AgdaAny) AgdaAny
                                                         MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiringWithoutOne_1044
-- Algebra.Bundles.CommutativeSemiringWithoutOne.Carrier
d_Carrier_1616 :: T_CommutativeSemiringWithoutOne_1598 -> ()
d_Carrier_1616 :: T_CommutativeSemiringWithoutOne_1598 -> ()
d_Carrier_1616 = T_CommutativeSemiringWithoutOne_1598 -> ()
forall a. a
erased
-- Algebra.Bundles.CommutativeSemiringWithoutOne._≈_
d__'8776'__1618 ::
  T_CommutativeSemiringWithoutOne_1598 -> AgdaAny -> AgdaAny -> ()
d__'8776'__1618 :: T_CommutativeSemiringWithoutOne_1598 -> AgdaAny -> AgdaAny -> ()
d__'8776'__1618 = T_CommutativeSemiringWithoutOne_1598 -> AgdaAny -> AgdaAny -> ()
forall a. a
erased
-- Algebra.Bundles.CommutativeSemiringWithoutOne._+_
d__'43'__1620 ::
  T_CommutativeSemiringWithoutOne_1598 ->
  AgdaAny -> AgdaAny -> AgdaAny
d__'43'__1620 :: T_CommutativeSemiringWithoutOne_1598
-> AgdaAny -> AgdaAny -> AgdaAny
d__'43'__1620 T_CommutativeSemiringWithoutOne_1598
v0
  = case T_CommutativeSemiringWithoutOne_1598
-> T_CommutativeSemiringWithoutOne_1598
forall a b. a -> b
coe T_CommutativeSemiringWithoutOne_1598
v0 of
      C_CommutativeSemiringWithoutOne'46'constructor_27945 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny
v5 T_IsCommutativeSemiringWithoutOne_1044
v6
        -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v3
      T_CommutativeSemiringWithoutOne_1598
_ -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.CommutativeSemiringWithoutOne._*_
d__'42'__1622 ::
  T_CommutativeSemiringWithoutOne_1598 ->
  AgdaAny -> AgdaAny -> AgdaAny
d__'42'__1622 :: T_CommutativeSemiringWithoutOne_1598
-> AgdaAny -> AgdaAny -> AgdaAny
d__'42'__1622 T_CommutativeSemiringWithoutOne_1598
v0
  = case T_CommutativeSemiringWithoutOne_1598
-> T_CommutativeSemiringWithoutOne_1598
forall a b. a -> b
coe T_CommutativeSemiringWithoutOne_1598
v0 of
      C_CommutativeSemiringWithoutOne'46'constructor_27945 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny
v5 T_IsCommutativeSemiringWithoutOne_1044
v6
        -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v4
      T_CommutativeSemiringWithoutOne_1598
_ -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.CommutativeSemiringWithoutOne.0#
d_0'35'_1624 :: T_CommutativeSemiringWithoutOne_1598 -> AgdaAny
d_0'35'_1624 :: T_CommutativeSemiringWithoutOne_1598 -> AgdaAny
d_0'35'_1624 T_CommutativeSemiringWithoutOne_1598
v0
  = case T_CommutativeSemiringWithoutOne_1598
-> T_CommutativeSemiringWithoutOne_1598
forall a b. a -> b
coe T_CommutativeSemiringWithoutOne_1598
v0 of
      C_CommutativeSemiringWithoutOne'46'constructor_27945 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny
v5 T_IsCommutativeSemiringWithoutOne_1044
v6
        -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v5
      T_CommutativeSemiringWithoutOne_1598
_ -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.CommutativeSemiringWithoutOne.isCommutativeSemiringWithoutOne
d_isCommutativeSemiringWithoutOne_1626 ::
  T_CommutativeSemiringWithoutOne_1598 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiringWithoutOne_1044
d_isCommutativeSemiringWithoutOne_1626 :: T_CommutativeSemiringWithoutOne_1598
-> T_IsCommutativeSemiringWithoutOne_1044
d_isCommutativeSemiringWithoutOne_1626 T_CommutativeSemiringWithoutOne_1598
v0
  = case T_CommutativeSemiringWithoutOne_1598
-> T_CommutativeSemiringWithoutOne_1598
forall a b. a -> b
coe T_CommutativeSemiringWithoutOne_1598
v0 of
      C_CommutativeSemiringWithoutOne'46'constructor_27945 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny
v5 T_IsCommutativeSemiringWithoutOne_1044
v6
        -> T_IsCommutativeSemiringWithoutOne_1044
-> T_IsCommutativeSemiringWithoutOne_1044
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1044
v6
      T_CommutativeSemiringWithoutOne_1598
_ -> T_IsCommutativeSemiringWithoutOne_1044
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.CommutativeSemiringWithoutOne._.assoc
d_assoc_1630 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeSemiringWithoutOne_1598 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_1630 :: ()
-> ()
-> T_CommutativeSemiringWithoutOne_1598
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_assoc_1630 ~()
v0 ~()
v1 T_CommutativeSemiringWithoutOne_1598
v2 = T_CommutativeSemiringWithoutOne_1598
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_assoc_1630 T_CommutativeSemiringWithoutOne_1598
v2
du_assoc_1630 ::
  T_CommutativeSemiringWithoutOne_1598 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_assoc_1630 :: T_CommutativeSemiringWithoutOne_1598
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_assoc_1630 T_CommutativeSemiringWithoutOne_1598
v0
  = let v1 :: T_IsCommutativeSemiringWithoutOne_1044
v1 = T_CommutativeSemiringWithoutOne_1598
-> T_IsCommutativeSemiringWithoutOne_1044
d_isCommutativeSemiringWithoutOne_1626 (T_CommutativeSemiringWithoutOne_1598
-> T_CommutativeSemiringWithoutOne_1598
forall a b. a -> b
coe T_CommutativeSemiringWithoutOne_1598
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemiringWithoutOne_952
v2
             = T_IsCommutativeSemiringWithoutOne_1044
-> T_IsSemiringWithoutOne_952
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutOne_1056
                 (T_IsCommutativeSemiringWithoutOne_1044
-> T_IsCommutativeSemiringWithoutOne_1044
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1044
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsSemigroup_194 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_194 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_assoc_204
            ((T_IsSemiringWithoutOne_952 -> T_IsSemigroup_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemiringWithoutOne_952 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_'42''45'isSemigroup_970
               (T_IsSemiringWithoutOne_952 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_952
v2))))
-- Algebra.Bundles.CommutativeSemiringWithoutOne._.*-comm
d_'42''45'comm_1632 ::
  T_CommutativeSemiringWithoutOne_1598 ->
  AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'comm_1632 :: T_CommutativeSemiringWithoutOne_1598
-> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'comm_1632 T_CommutativeSemiringWithoutOne_1598
v0
  = (T_IsCommutativeSemiringWithoutOne_1044
 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsCommutativeSemiringWithoutOne_1044
-> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'42''45'comm_1058
      ((T_CommutativeSemiringWithoutOne_1598
 -> T_IsCommutativeSemiringWithoutOne_1044)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemiringWithoutOne_1598
-> T_IsCommutativeSemiringWithoutOne_1044
d_isCommutativeSemiringWithoutOne_1626 (T_CommutativeSemiringWithoutOne_1598 -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemiringWithoutOne_1598
v0))
-- Algebra.Bundles.CommutativeSemiringWithoutOne._.∙-cong
d_'8729''45'cong_1634 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeSemiringWithoutOne_1598 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_1634 :: ()
-> ()
-> T_CommutativeSemiringWithoutOne_1598
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_1634 ~()
v0 ~()
v1 T_CommutativeSemiringWithoutOne_1598
v2 = T_CommutativeSemiringWithoutOne_1598
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_'8729''45'cong_1634 T_CommutativeSemiringWithoutOne_1598
v2
du_'8729''45'cong_1634 ::
  T_CommutativeSemiringWithoutOne_1598 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong_1634 :: T_CommutativeSemiringWithoutOne_1598
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_'8729''45'cong_1634 T_CommutativeSemiringWithoutOne_1598
v0
  = let v1 :: T_IsCommutativeSemiringWithoutOne_1044
v1 = T_CommutativeSemiringWithoutOne_1598
-> T_IsCommutativeSemiringWithoutOne_1044
d_isCommutativeSemiringWithoutOne_1626 (T_CommutativeSemiringWithoutOne_1598
-> T_CommutativeSemiringWithoutOne_1598
forall a b. a -> b
coe T_CommutativeSemiringWithoutOne_1598
v0) in
    AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemiringWithoutOne_952
v2
             = T_IsCommutativeSemiringWithoutOne_1044
-> T_IsSemiringWithoutOne_952
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutOne_1056
                 (T_IsCommutativeSemiringWithoutOne_1044
-> T_IsCommutativeSemiringWithoutOne_1044
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1044
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsMagma_86
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMagma_86
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_96
            ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202
               ((T_IsSemiringWithoutOne_952 -> T_IsSemigroup_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsSemiringWithoutOne_952 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_'42''45'isSemigroup_970
                  (T_IsSemiringWithoutOne_952 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_952
v2)))))
-- Algebra.Bundles.CommutativeSemiringWithoutOne._.∙-congʳ
d_'8729''45'cong'691'_1636 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeSemiringWithoutOne_1598 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_1636 :: ()
-> ()
-> T_CommutativeSemiringWithoutOne_1598
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_1636 ~()
v0 ~()
v1 T_CommutativeSemiringWithoutOne_1598
v2
  = T_CommutativeSemiringWithoutOne_1598
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1636 T_CommutativeSemiringWithoutOne_1598
v2
du_'8729''45'cong'691'_1636 ::
  T_CommutativeSemiringWithoutOne_1598 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1636 :: T_CommutativeSemiringWithoutOne_1598
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1636 T_CommutativeSemiringWithoutOne_1598
v0
  = let v1 :: T_IsCommutativeSemiringWithoutOne_1044
v1 = T_CommutativeSemiringWithoutOne_1598
-> T_IsCommutativeSemiringWithoutOne_1044
d_isCommutativeSemiringWithoutOne_1626 (T_CommutativeSemiringWithoutOne_1598
-> T_CommutativeSemiringWithoutOne_1598
forall a b. a -> b
coe T_CommutativeSemiringWithoutOne_1598
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemiringWithoutOne_952
v2
             = T_IsCommutativeSemiringWithoutOne_1044
-> T_IsSemiringWithoutOne_952
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutOne_1056
                 (T_IsCommutativeSemiringWithoutOne_1044
-> T_IsCommutativeSemiringWithoutOne_1044
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1044
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: t
v3
                = (T_IsSemiringWithoutOne_952 -> T_IsNearSemiring_876)
-> AgdaAny -> t
forall a b. a -> b
coe
                    T_IsSemiringWithoutOne_952 -> T_IsNearSemiring_876
MAlonzo.Code.Algebra.Structures.du_isNearSemiring_990 (T_IsSemiringWithoutOne_952 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_952
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsSemigroup_194
v4
                   = T_IsNearSemiring_876 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_'42''45'isSemigroup_894
                       (AgdaAny -> T_IsNearSemiring_876
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               ((T_IsMagma_86
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsMagma_86 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'691'_116
                  ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202 (T_IsSemigroup_194 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194
v4))))))
-- Algebra.Bundles.CommutativeSemiringWithoutOne._.∙-congˡ
d_'8729''45'cong'737'_1638 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeSemiringWithoutOne_1598 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_1638 :: ()
-> ()
-> T_CommutativeSemiringWithoutOne_1598
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_1638 ~()
v0 ~()
v1 T_CommutativeSemiringWithoutOne_1598
v2
  = T_CommutativeSemiringWithoutOne_1598
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1638 T_CommutativeSemiringWithoutOne_1598
v2
du_'8729''45'cong'737'_1638 ::
  T_CommutativeSemiringWithoutOne_1598 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1638 :: T_CommutativeSemiringWithoutOne_1598
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1638 T_CommutativeSemiringWithoutOne_1598
v0
  = let v1 :: T_IsCommutativeSemiringWithoutOne_1044
v1 = T_CommutativeSemiringWithoutOne_1598
-> T_IsCommutativeSemiringWithoutOne_1044
d_isCommutativeSemiringWithoutOne_1626 (T_CommutativeSemiringWithoutOne_1598
-> T_CommutativeSemiringWithoutOne_1598
forall a b. a -> b
coe T_CommutativeSemiringWithoutOne_1598
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemiringWithoutOne_952
v2
             = T_IsCommutativeSemiringWithoutOne_1044
-> T_IsSemiringWithoutOne_952
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutOne_1056
                 (T_IsCommutativeSemiringWithoutOne_1044
-> T_IsCommutativeSemiringWithoutOne_1044
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1044
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: t
v3
                = (T_IsSemiringWithoutOne_952 -> T_IsNearSemiring_876)
-> AgdaAny -> t
forall a b. a -> b
coe
                    T_IsSemiringWithoutOne_952 -> T_IsNearSemiring_876
MAlonzo.Code.Algebra.Structures.du_isNearSemiring_990 (T_IsSemiringWithoutOne_952 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_952
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsSemigroup_194
v4
                   = T_IsNearSemiring_876 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_'42''45'isSemigroup_894
                       (AgdaAny -> T_IsNearSemiring_876
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               ((T_IsMagma_86
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsMagma_86 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'737'_112
                  ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202 (T_IsSemigroup_194 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194
v4))))))
-- Algebra.Bundles.CommutativeSemiringWithoutOne._.isCommutativeMagma
d_isCommutativeMagma_1640 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeSemiringWithoutOne_1598 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMagma_122
d_isCommutativeMagma_1640 :: ()
-> ()
-> T_CommutativeSemiringWithoutOne_1598
-> T_IsCommutativeMagma_122
d_isCommutativeMagma_1640 ~()
v0 ~()
v1 T_CommutativeSemiringWithoutOne_1598
v2
  = T_CommutativeSemiringWithoutOne_1598 -> T_IsCommutativeMagma_122
du_isCommutativeMagma_1640 T_CommutativeSemiringWithoutOne_1598
v2
du_isCommutativeMagma_1640 ::
  T_CommutativeSemiringWithoutOne_1598 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMagma_122
du_isCommutativeMagma_1640 :: T_CommutativeSemiringWithoutOne_1598 -> T_IsCommutativeMagma_122
du_isCommutativeMagma_1640 T_CommutativeSemiringWithoutOne_1598
v0
  = let v1 :: T_IsCommutativeSemiringWithoutOne_1044
v1 = T_CommutativeSemiringWithoutOne_1598
-> T_IsCommutativeSemiringWithoutOne_1044
d_isCommutativeSemiringWithoutOne_1626 (T_CommutativeSemiringWithoutOne_1598
-> T_CommutativeSemiringWithoutOne_1598
forall a b. a -> b
coe T_CommutativeSemiringWithoutOne_1598
v0) in
    AgdaAny -> T_IsCommutativeMagma_122
forall a b. a -> b
coe
      ((T_IsCommutativeSemigroup_270 -> T_IsCommutativeMagma_122)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCommutativeSemigroup_270 -> T_IsCommutativeMagma_122
MAlonzo.Code.Algebra.Structures.du_isCommutativeMagma_308
         ((T_IsCommutativeSemiringWithoutOne_1044
 -> T_IsCommutativeSemigroup_270)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCommutativeSemiringWithoutOne_1044
-> T_IsCommutativeSemigroup_270
MAlonzo.Code.Algebra.Structures.du_'42''45'isCommutativeSemigroup_1128
            (T_IsCommutativeSemiringWithoutOne_1044 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1044
v1)))
-- Algebra.Bundles.CommutativeSemiringWithoutOne._.*-isCommutativeSemigroup
d_'42''45'isCommutativeSemigroup_1642 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeSemiringWithoutOne_1598 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_270
d_'42''45'isCommutativeSemigroup_1642 :: ()
-> ()
-> T_CommutativeSemiringWithoutOne_1598
-> T_IsCommutativeSemigroup_270
d_'42''45'isCommutativeSemigroup_1642 ~()
v0 ~()
v1 T_CommutativeSemiringWithoutOne_1598
v2
  = T_CommutativeSemiringWithoutOne_1598
-> T_IsCommutativeSemigroup_270
du_'42''45'isCommutativeSemigroup_1642 T_CommutativeSemiringWithoutOne_1598
v2
du_'42''45'isCommutativeSemigroup_1642 ::
  T_CommutativeSemiringWithoutOne_1598 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_270
du_'42''45'isCommutativeSemigroup_1642 :: T_CommutativeSemiringWithoutOne_1598
-> T_IsCommutativeSemigroup_270
du_'42''45'isCommutativeSemigroup_1642 T_CommutativeSemiringWithoutOne_1598
v0
  = (T_IsCommutativeSemiringWithoutOne_1044
 -> T_IsCommutativeSemigroup_270)
-> AgdaAny -> T_IsCommutativeSemigroup_270
forall a b. a -> b
coe
      T_IsCommutativeSemiringWithoutOne_1044
-> T_IsCommutativeSemigroup_270
MAlonzo.Code.Algebra.Structures.du_'42''45'isCommutativeSemigroup_1128
      ((T_CommutativeSemiringWithoutOne_1598
 -> T_IsCommutativeSemiringWithoutOne_1044)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemiringWithoutOne_1598
-> T_IsCommutativeSemiringWithoutOne_1044
d_isCommutativeSemiringWithoutOne_1626 (T_CommutativeSemiringWithoutOne_1598 -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemiringWithoutOne_1598
v0))
-- Algebra.Bundles.CommutativeSemiringWithoutOne._.isMagma
d_isMagma_1644 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeSemiringWithoutOne_1598 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_86
d_isMagma_1644 :: () -> () -> T_CommutativeSemiringWithoutOne_1598 -> T_IsMagma_86
d_isMagma_1644 ~()
v0 ~()
v1 T_CommutativeSemiringWithoutOne_1598
v2 = T_CommutativeSemiringWithoutOne_1598 -> T_IsMagma_86
du_isMagma_1644 T_CommutativeSemiringWithoutOne_1598
v2
du_isMagma_1644 ::
  T_CommutativeSemiringWithoutOne_1598 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_86
du_isMagma_1644 :: T_CommutativeSemiringWithoutOne_1598 -> T_IsMagma_86
du_isMagma_1644 T_CommutativeSemiringWithoutOne_1598
v0
  = let v1 :: T_IsCommutativeSemiringWithoutOne_1044
v1 = T_CommutativeSemiringWithoutOne_1598
-> T_IsCommutativeSemiringWithoutOne_1044
d_isCommutativeSemiringWithoutOne_1626 (T_CommutativeSemiringWithoutOne_1598
-> T_CommutativeSemiringWithoutOne_1598
forall a b. a -> b
coe T_CommutativeSemiringWithoutOne_1598
v0) in
    AgdaAny -> T_IsMagma_86
forall a b. a -> b
coe
      (let v2 :: T_IsSemiringWithoutOne_952
v2
             = T_IsCommutativeSemiringWithoutOne_1044
-> T_IsSemiringWithoutOne_952
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutOne_1056
                 (T_IsCommutativeSemiringWithoutOne_1044
-> T_IsCommutativeSemiringWithoutOne_1044
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1044
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202
            ((T_IsSemiringWithoutOne_952 -> T_IsSemigroup_194)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemiringWithoutOne_952 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_'42''45'isSemigroup_970
               (T_IsSemiringWithoutOne_952 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_952
v2))))
-- Algebra.Bundles.CommutativeSemiringWithoutOne._.*-isSemigroup
d_'42''45'isSemigroup_1646 ::
  T_CommutativeSemiringWithoutOne_1598 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_194
d_'42''45'isSemigroup_1646 :: T_CommutativeSemiringWithoutOne_1598 -> T_IsSemigroup_194
d_'42''45'isSemigroup_1646 T_CommutativeSemiringWithoutOne_1598
v0
  = (T_IsSemiringWithoutOne_952 -> T_IsSemigroup_194)
-> AgdaAny -> T_IsSemigroup_194
forall a b. a -> b
coe
      T_IsSemiringWithoutOne_952 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_'42''45'isSemigroup_970
      ((T_IsCommutativeSemiringWithoutOne_1044
 -> T_IsSemiringWithoutOne_952)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCommutativeSemiringWithoutOne_1044
-> T_IsSemiringWithoutOne_952
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutOne_1056
         ((T_CommutativeSemiringWithoutOne_1598
 -> T_IsCommutativeSemiringWithoutOne_1044)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemiringWithoutOne_1598
-> T_IsCommutativeSemiringWithoutOne_1044
d_isCommutativeSemiringWithoutOne_1626 (T_CommutativeSemiringWithoutOne_1598 -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemiringWithoutOne_1598
v0)))
-- Algebra.Bundles.CommutativeSemiringWithoutOne._.assoc
d_assoc_1648 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeSemiringWithoutOne_1598 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_1648 :: ()
-> ()
-> T_CommutativeSemiringWithoutOne_1598
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_assoc_1648 ~()
v0 ~()
v1 T_CommutativeSemiringWithoutOne_1598
v2 = T_CommutativeSemiringWithoutOne_1598
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_assoc_1648 T_CommutativeSemiringWithoutOne_1598
v2
du_assoc_1648 ::
  T_CommutativeSemiringWithoutOne_1598 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_assoc_1648 :: T_CommutativeSemiringWithoutOne_1598
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_assoc_1648 T_CommutativeSemiringWithoutOne_1598
v0
  = let v1 :: T_IsCommutativeSemiringWithoutOne_1044
v1 = T_CommutativeSemiringWithoutOne_1598
-> T_IsCommutativeSemiringWithoutOne_1044
d_isCommutativeSemiringWithoutOne_1626 (T_CommutativeSemiringWithoutOne_1598
-> T_CommutativeSemiringWithoutOne_1598
forall a b. a -> b
coe T_CommutativeSemiringWithoutOne_1598
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemiringWithoutOne_952
v2
             = T_IsCommutativeSemiringWithoutOne_1044
-> T_IsSemiringWithoutOne_952
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutOne_1056
                 (T_IsCommutativeSemiringWithoutOne_1044
-> T_IsCommutativeSemiringWithoutOne_1044
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1044
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsSemigroup_194 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_194 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_assoc_204
            ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368
               ((T_IsCommutativeMonoid_406 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsCommutativeMonoid_406 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_416
                  ((T_IsSemiringWithoutOne_952 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsSemiringWithoutOne_952 -> T_IsCommutativeMonoid_406
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_968
                     (T_IsSemiringWithoutOne_952 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_952
v2))))))
-- Algebra.Bundles.CommutativeSemiringWithoutOne._.comm
d_comm_1650 ::
  T_CommutativeSemiringWithoutOne_1598 ->
  AgdaAny -> AgdaAny -> AgdaAny
d_comm_1650 :: T_CommutativeSemiringWithoutOne_1598
-> AgdaAny -> AgdaAny -> AgdaAny
d_comm_1650 T_CommutativeSemiringWithoutOne_1598
v0
  = (T_IsCommutativeMonoid_406 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsCommutativeMonoid_406 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_comm_418
      ((T_IsSemiringWithoutOne_952 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiringWithoutOne_952 -> T_IsCommutativeMonoid_406
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_968
         ((T_IsCommutativeSemiringWithoutOne_1044
 -> T_IsSemiringWithoutOne_952)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCommutativeSemiringWithoutOne_1044
-> T_IsSemiringWithoutOne_952
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutOne_1056
            ((T_CommutativeSemiringWithoutOne_1598
 -> T_IsCommutativeSemiringWithoutOne_1044)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemiringWithoutOne_1598
-> T_IsCommutativeSemiringWithoutOne_1044
d_isCommutativeSemiringWithoutOne_1626 (T_CommutativeSemiringWithoutOne_1598 -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemiringWithoutOne_1598
v0))))
-- Algebra.Bundles.CommutativeSemiringWithoutOne._.∙-cong
d_'8729''45'cong_1652 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeSemiringWithoutOne_1598 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_1652 :: ()
-> ()
-> T_CommutativeSemiringWithoutOne_1598
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_1652 ~()
v0 ~()
v1 T_CommutativeSemiringWithoutOne_1598
v2 = T_CommutativeSemiringWithoutOne_1598
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_'8729''45'cong_1652 T_CommutativeSemiringWithoutOne_1598
v2
du_'8729''45'cong_1652 ::
  T_CommutativeSemiringWithoutOne_1598 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong_1652 :: T_CommutativeSemiringWithoutOne_1598
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_'8729''45'cong_1652 T_CommutativeSemiringWithoutOne_1598
v0
  = let v1 :: T_IsCommutativeSemiringWithoutOne_1044
v1 = T_CommutativeSemiringWithoutOne_1598
-> T_IsCommutativeSemiringWithoutOne_1044
d_isCommutativeSemiringWithoutOne_1626 (T_CommutativeSemiringWithoutOne_1598
-> T_CommutativeSemiringWithoutOne_1598
forall a b. a -> b
coe T_CommutativeSemiringWithoutOne_1598
v0) in
    AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemiringWithoutOne_952
v2
             = T_IsCommutativeSemiringWithoutOne_1044
-> T_IsSemiringWithoutOne_952
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutOne_1056
                 (T_IsCommutativeSemiringWithoutOne_1044
-> T_IsCommutativeSemiringWithoutOne_1044
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1044
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsMagma_86
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMagma_86
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_96
            ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202
               ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368
                  ((T_IsCommutativeMonoid_406 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsCommutativeMonoid_406 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_416
                     ((T_IsSemiringWithoutOne_952 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsSemiringWithoutOne_952 -> T_IsCommutativeMonoid_406
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_968
                        (T_IsSemiringWithoutOne_952 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_952
v2)))))))
-- Algebra.Bundles.CommutativeSemiringWithoutOne._.∙-congʳ
d_'8729''45'cong'691'_1654 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeSemiringWithoutOne_1598 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_1654 :: ()
-> ()
-> T_CommutativeSemiringWithoutOne_1598
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_1654 ~()
v0 ~()
v1 T_CommutativeSemiringWithoutOne_1598
v2
  = T_CommutativeSemiringWithoutOne_1598
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1654 T_CommutativeSemiringWithoutOne_1598
v2
du_'8729''45'cong'691'_1654 ::
  T_CommutativeSemiringWithoutOne_1598 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1654 :: T_CommutativeSemiringWithoutOne_1598
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1654 T_CommutativeSemiringWithoutOne_1598
v0
  = let v1 :: T_IsCommutativeSemiringWithoutOne_1044
v1 = T_CommutativeSemiringWithoutOne_1598
-> T_IsCommutativeSemiringWithoutOne_1044
d_isCommutativeSemiringWithoutOne_1626 (T_CommutativeSemiringWithoutOne_1598
-> T_CommutativeSemiringWithoutOne_1598
forall a b. a -> b
coe T_CommutativeSemiringWithoutOne_1598
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemiringWithoutOne_952
v2
             = T_IsCommutativeSemiringWithoutOne_1044
-> T_IsSemiringWithoutOne_952
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutOne_1056
                 (T_IsCommutativeSemiringWithoutOne_1044
-> T_IsCommutativeSemiringWithoutOne_1044
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1044
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: t
v3
                = (T_IsSemiringWithoutOne_952 -> T_IsNearSemiring_876)
-> AgdaAny -> t
forall a b. a -> b
coe
                    T_IsSemiringWithoutOne_952 -> T_IsNearSemiring_876
MAlonzo.Code.Algebra.Structures.du_isNearSemiring_990 (T_IsSemiringWithoutOne_952 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_952
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsMonoid_358
v4
                   = T_IsNearSemiring_876 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_'43''45'isMonoid_892
                       (AgdaAny -> T_IsNearSemiring_876
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsSemigroup_194
v5
                      = T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368 (T_IsMonoid_358 -> T_IsMonoid_358
forall a b. a -> b
coe T_IsMonoid_358
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  ((T_IsMagma_86
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsMagma_86 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'691'_116
                     ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202 (T_IsSemigroup_194 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194
v5)))))))
-- Algebra.Bundles.CommutativeSemiringWithoutOne._.∙-congˡ
d_'8729''45'cong'737'_1656 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeSemiringWithoutOne_1598 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_1656 :: ()
-> ()
-> T_CommutativeSemiringWithoutOne_1598
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_1656 ~()
v0 ~()
v1 T_CommutativeSemiringWithoutOne_1598
v2
  = T_CommutativeSemiringWithoutOne_1598
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1656 T_CommutativeSemiringWithoutOne_1598
v2
du_'8729''45'cong'737'_1656 ::
  T_CommutativeSemiringWithoutOne_1598 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1656 :: T_CommutativeSemiringWithoutOne_1598
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1656 T_CommutativeSemiringWithoutOne_1598
v0
  = let v1 :: T_IsCommutativeSemiringWithoutOne_1044
v1 = T_CommutativeSemiringWithoutOne_1598
-> T_IsCommutativeSemiringWithoutOne_1044
d_isCommutativeSemiringWithoutOne_1626 (T_CommutativeSemiringWithoutOne_1598
-> T_CommutativeSemiringWithoutOne_1598
forall a b. a -> b
coe T_CommutativeSemiringWithoutOne_1598
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemiringWithoutOne_952
v2
             = T_IsCommutativeSemiringWithoutOne_1044
-> T_IsSemiringWithoutOne_952
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutOne_1056
                 (T_IsCommutativeSemiringWithoutOne_1044
-> T_IsCommutativeSemiringWithoutOne_1044
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1044
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: t
v3
                = (T_IsSemiringWithoutOne_952 -> T_IsNearSemiring_876)
-> AgdaAny -> t
forall a b. a -> b
coe
                    T_IsSemiringWithoutOne_952 -> T_IsNearSemiring_876
MAlonzo.Code.Algebra.Structures.du_isNearSemiring_990 (T_IsSemiringWithoutOne_952 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_952
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsMonoid_358
v4
                   = T_IsNearSemiring_876 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_'43''45'isMonoid_892
                       (AgdaAny -> T_IsNearSemiring_876
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsSemigroup_194
v5
                      = T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368 (T_IsMonoid_358 -> T_IsMonoid_358
forall a b. a -> b
coe T_IsMonoid_358
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  ((T_IsMagma_86
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsMagma_86 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'737'_112
                     ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202 (T_IsSemigroup_194 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194
v5)))))))
-- Algebra.Bundles.CommutativeSemiringWithoutOne._.identity
d_identity_1658 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeSemiringWithoutOne_1598 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_identity_1658 :: () -> () -> T_CommutativeSemiringWithoutOne_1598 -> T_Σ_14
d_identity_1658 ~()
v0 ~()
v1 T_CommutativeSemiringWithoutOne_1598
v2 = T_CommutativeSemiringWithoutOne_1598 -> T_Σ_14
du_identity_1658 T_CommutativeSemiringWithoutOne_1598
v2
du_identity_1658 ::
  T_CommutativeSemiringWithoutOne_1598 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
du_identity_1658 :: T_CommutativeSemiringWithoutOne_1598 -> T_Σ_14
du_identity_1658 T_CommutativeSemiringWithoutOne_1598
v0
  = let v1 :: T_IsCommutativeSemiringWithoutOne_1044
v1 = T_CommutativeSemiringWithoutOne_1598
-> T_IsCommutativeSemiringWithoutOne_1044
d_isCommutativeSemiringWithoutOne_1626 (T_CommutativeSemiringWithoutOne_1598
-> T_CommutativeSemiringWithoutOne_1598
forall a b. a -> b
coe T_CommutativeSemiringWithoutOne_1598
v0) in
    AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      (let v2 :: T_IsSemiringWithoutOne_952
v2
             = T_IsCommutativeSemiringWithoutOne_1044
-> T_IsSemiringWithoutOne_952
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutOne_1056
                 (T_IsCommutativeSemiringWithoutOne_1044
-> T_IsCommutativeSemiringWithoutOne_1044
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1044
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsMonoid_358 -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoid_358 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_identity_370
            ((T_IsCommutativeMonoid_406 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsCommutativeMonoid_406 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_416
               ((T_IsSemiringWithoutOne_952 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsSemiringWithoutOne_952 -> T_IsCommutativeMonoid_406
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_968
                  (T_IsSemiringWithoutOne_952 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_952
v2)))))
-- Algebra.Bundles.CommutativeSemiringWithoutOne._.identityʳ
d_identity'691'_1660 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeSemiringWithoutOne_1598 -> AgdaAny -> AgdaAny
d_identity'691'_1660 :: ()
-> () -> T_CommutativeSemiringWithoutOne_1598 -> AgdaAny -> AgdaAny
d_identity'691'_1660 ~()
v0 ~()
v1 T_CommutativeSemiringWithoutOne_1598
v2 = T_CommutativeSemiringWithoutOne_1598 -> AgdaAny -> AgdaAny
du_identity'691'_1660 T_CommutativeSemiringWithoutOne_1598
v2
du_identity'691'_1660 ::
  T_CommutativeSemiringWithoutOne_1598 -> AgdaAny -> AgdaAny
du_identity'691'_1660 :: T_CommutativeSemiringWithoutOne_1598 -> AgdaAny -> AgdaAny
du_identity'691'_1660 T_CommutativeSemiringWithoutOne_1598
v0
  = let v1 :: T_IsCommutativeSemiringWithoutOne_1044
v1 = T_CommutativeSemiringWithoutOne_1598
-> T_IsCommutativeSemiringWithoutOne_1044
d_isCommutativeSemiringWithoutOne_1626 (T_CommutativeSemiringWithoutOne_1598
-> T_CommutativeSemiringWithoutOne_1598
forall a b. a -> b
coe T_CommutativeSemiringWithoutOne_1598
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemiringWithoutOne_952
v2
             = T_IsCommutativeSemiringWithoutOne_1044
-> T_IsSemiringWithoutOne_952
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutOne_1056
                 (T_IsCommutativeSemiringWithoutOne_1044
-> T_IsCommutativeSemiringWithoutOne_1044
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1044
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: t
v3
                = (T_IsSemiringWithoutOne_952 -> T_IsNearSemiring_876)
-> AgdaAny -> t
forall a b. a -> b
coe
                    T_IsSemiringWithoutOne_952 -> T_IsNearSemiring_876
MAlonzo.Code.Algebra.Structures.du_isNearSemiring_990 (T_IsSemiringWithoutOne_952 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_952
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsMonoid_358 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_358 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_identity'691'_400
               ((T_IsNearSemiring_876 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsNearSemiring_876 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_'43''45'isMonoid_892 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3)))))
-- Algebra.Bundles.CommutativeSemiringWithoutOne._.identityˡ
d_identity'737'_1662 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeSemiringWithoutOne_1598 -> AgdaAny -> AgdaAny
d_identity'737'_1662 :: ()
-> () -> T_CommutativeSemiringWithoutOne_1598 -> AgdaAny -> AgdaAny
d_identity'737'_1662 ~()
v0 ~()
v1 T_CommutativeSemiringWithoutOne_1598
v2 = T_CommutativeSemiringWithoutOne_1598 -> AgdaAny -> AgdaAny
du_identity'737'_1662 T_CommutativeSemiringWithoutOne_1598
v2
du_identity'737'_1662 ::
  T_CommutativeSemiringWithoutOne_1598 -> AgdaAny -> AgdaAny
du_identity'737'_1662 :: T_CommutativeSemiringWithoutOne_1598 -> AgdaAny -> AgdaAny
du_identity'737'_1662 T_CommutativeSemiringWithoutOne_1598
v0
  = let v1 :: T_IsCommutativeSemiringWithoutOne_1044
v1 = T_CommutativeSemiringWithoutOne_1598
-> T_IsCommutativeSemiringWithoutOne_1044
d_isCommutativeSemiringWithoutOne_1626 (T_CommutativeSemiringWithoutOne_1598
-> T_CommutativeSemiringWithoutOne_1598
forall a b. a -> b
coe T_CommutativeSemiringWithoutOne_1598
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemiringWithoutOne_952
v2
             = T_IsCommutativeSemiringWithoutOne_1044
-> T_IsSemiringWithoutOne_952
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutOne_1056
                 (T_IsCommutativeSemiringWithoutOne_1044
-> T_IsCommutativeSemiringWithoutOne_1044
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1044
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: t
v3
                = (T_IsSemiringWithoutOne_952 -> T_IsNearSemiring_876)
-> AgdaAny -> t
forall a b. a -> b
coe
                    T_IsSemiringWithoutOne_952 -> T_IsNearSemiring_876
MAlonzo.Code.Algebra.Structures.du_isNearSemiring_990 (T_IsSemiringWithoutOne_952 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_952
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsMonoid_358 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_358 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_identity'737'_398
               ((T_IsNearSemiring_876 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsNearSemiring_876 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_'43''45'isMonoid_892 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3)))))
-- Algebra.Bundles.CommutativeSemiringWithoutOne._.isCommutativeMagma
d_isCommutativeMagma_1664 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeSemiringWithoutOne_1598 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMagma_122
d_isCommutativeMagma_1664 :: ()
-> ()
-> T_CommutativeSemiringWithoutOne_1598
-> T_IsCommutativeMagma_122
d_isCommutativeMagma_1664 ~()
v0 ~()
v1 T_CommutativeSemiringWithoutOne_1598
v2
  = T_CommutativeSemiringWithoutOne_1598 -> T_IsCommutativeMagma_122
du_isCommutativeMagma_1664 T_CommutativeSemiringWithoutOne_1598
v2
du_isCommutativeMagma_1664 ::
  T_CommutativeSemiringWithoutOne_1598 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMagma_122
du_isCommutativeMagma_1664 :: T_CommutativeSemiringWithoutOne_1598 -> T_IsCommutativeMagma_122
du_isCommutativeMagma_1664 T_CommutativeSemiringWithoutOne_1598
v0
  = let v1 :: T_IsCommutativeSemiringWithoutOne_1044
v1 = T_CommutativeSemiringWithoutOne_1598
-> T_IsCommutativeSemiringWithoutOne_1044
d_isCommutativeSemiringWithoutOne_1626 (T_CommutativeSemiringWithoutOne_1598
-> T_CommutativeSemiringWithoutOne_1598
forall a b. a -> b
coe T_CommutativeSemiringWithoutOne_1598
v0) in
    AgdaAny -> T_IsCommutativeMagma_122
forall a b. a -> b
coe
      (let v2 :: T_IsSemiringWithoutOne_952
v2
             = T_IsCommutativeSemiringWithoutOne_1044
-> T_IsSemiringWithoutOne_952
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutOne_1056
                 (T_IsCommutativeSemiringWithoutOne_1044
-> T_IsCommutativeSemiringWithoutOne_1044
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1044
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsCommutativeMonoid_406
v3
                = T_IsSemiringWithoutOne_952 -> T_IsCommutativeMonoid_406
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_968
                    (T_IsSemiringWithoutOne_952 -> T_IsSemiringWithoutOne_952
forall a b. a -> b
coe T_IsSemiringWithoutOne_952
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsCommutativeSemigroup_270 -> T_IsCommutativeMagma_122)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsCommutativeSemigroup_270 -> T_IsCommutativeMagma_122
MAlonzo.Code.Algebra.Structures.du_isCommutativeMagma_308
               ((T_IsCommutativeMonoid_406 -> T_IsCommutativeSemigroup_270)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsCommutativeMonoid_406 -> T_IsCommutativeSemigroup_270
MAlonzo.Code.Algebra.Structures.du_isCommutativeSemigroup_454
                  (T_IsCommutativeMonoid_406 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_406
v3)))))
-- Algebra.Bundles.CommutativeSemiringWithoutOne._.+-isCommutativeMonoid
d_'43''45'isCommutativeMonoid_1666 ::
  T_CommutativeSemiringWithoutOne_1598 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMonoid_406
d_'43''45'isCommutativeMonoid_1666 :: T_CommutativeSemiringWithoutOne_1598 -> T_IsCommutativeMonoid_406
d_'43''45'isCommutativeMonoid_1666 T_CommutativeSemiringWithoutOne_1598
v0
  = (T_IsSemiringWithoutOne_952 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> T_IsCommutativeMonoid_406
forall a b. a -> b
coe
      T_IsSemiringWithoutOne_952 -> T_IsCommutativeMonoid_406
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_968
      ((T_IsCommutativeSemiringWithoutOne_1044
 -> T_IsSemiringWithoutOne_952)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCommutativeSemiringWithoutOne_1044
-> T_IsSemiringWithoutOne_952
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutOne_1056
         ((T_CommutativeSemiringWithoutOne_1598
 -> T_IsCommutativeSemiringWithoutOne_1044)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemiringWithoutOne_1598
-> T_IsCommutativeSemiringWithoutOne_1044
d_isCommutativeSemiringWithoutOne_1626 (T_CommutativeSemiringWithoutOne_1598 -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemiringWithoutOne_1598
v0)))
-- Algebra.Bundles.CommutativeSemiringWithoutOne._.isCommutativeSemigroup
d_isCommutativeSemigroup_1668 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeSemiringWithoutOne_1598 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_270
d_isCommutativeSemigroup_1668 :: ()
-> ()
-> T_CommutativeSemiringWithoutOne_1598
-> T_IsCommutativeSemigroup_270
d_isCommutativeSemigroup_1668 ~()
v0 ~()
v1 T_CommutativeSemiringWithoutOne_1598
v2
  = T_CommutativeSemiringWithoutOne_1598
-> T_IsCommutativeSemigroup_270
du_isCommutativeSemigroup_1668 T_CommutativeSemiringWithoutOne_1598
v2
du_isCommutativeSemigroup_1668 ::
  T_CommutativeSemiringWithoutOne_1598 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_270
du_isCommutativeSemigroup_1668 :: T_CommutativeSemiringWithoutOne_1598
-> T_IsCommutativeSemigroup_270
du_isCommutativeSemigroup_1668 T_CommutativeSemiringWithoutOne_1598
v0
  = let v1 :: T_IsCommutativeSemiringWithoutOne_1044
v1 = T_CommutativeSemiringWithoutOne_1598
-> T_IsCommutativeSemiringWithoutOne_1044
d_isCommutativeSemiringWithoutOne_1626 (T_CommutativeSemiringWithoutOne_1598
-> T_CommutativeSemiringWithoutOne_1598
forall a b. a -> b
coe T_CommutativeSemiringWithoutOne_1598
v0) in
    AgdaAny -> T_IsCommutativeSemigroup_270
forall a b. a -> b
coe
      (let v2 :: T_IsSemiringWithoutOne_952
v2
             = T_IsCommutativeSemiringWithoutOne_1044
-> T_IsSemiringWithoutOne_952
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutOne_1056
                 (T_IsCommutativeSemiringWithoutOne_1044
-> T_IsCommutativeSemiringWithoutOne_1044
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1044
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsCommutativeMonoid_406 -> T_IsCommutativeSemigroup_270)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCommutativeMonoid_406 -> T_IsCommutativeSemigroup_270
MAlonzo.Code.Algebra.Structures.du_isCommutativeSemigroup_454
            ((T_IsSemiringWithoutOne_952 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemiringWithoutOne_952 -> T_IsCommutativeMonoid_406
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_968
               (T_IsSemiringWithoutOne_952 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_952
v2))))
-- Algebra.Bundles.CommutativeSemiringWithoutOne._.isMagma
d_isMagma_1670 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeSemiringWithoutOne_1598 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_86
d_isMagma_1670 :: () -> () -> T_CommutativeSemiringWithoutOne_1598 -> T_IsMagma_86
d_isMagma_1670 ~()
v0 ~()
v1 T_CommutativeSemiringWithoutOne_1598
v2 = T_CommutativeSemiringWithoutOne_1598 -> T_IsMagma_86
du_isMagma_1670 T_CommutativeSemiringWithoutOne_1598
v2
du_isMagma_1670 ::
  T_CommutativeSemiringWithoutOne_1598 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_86
du_isMagma_1670 :: T_CommutativeSemiringWithoutOne_1598 -> T_IsMagma_86
du_isMagma_1670 T_CommutativeSemiringWithoutOne_1598
v0
  = let v1 :: T_IsCommutativeSemiringWithoutOne_1044
v1 = T_CommutativeSemiringWithoutOne_1598
-> T_IsCommutativeSemiringWithoutOne_1044
d_isCommutativeSemiringWithoutOne_1626 (T_CommutativeSemiringWithoutOne_1598
-> T_CommutativeSemiringWithoutOne_1598
forall a b. a -> b
coe T_CommutativeSemiringWithoutOne_1598
v0) in
    AgdaAny -> T_IsMagma_86
forall a b. a -> b
coe
      (let v2 :: T_IsSemiringWithoutOne_952
v2
             = T_IsCommutativeSemiringWithoutOne_1044
-> T_IsSemiringWithoutOne_952
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutOne_1056
                 (T_IsCommutativeSemiringWithoutOne_1044
-> T_IsCommutativeSemiringWithoutOne_1044
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1044
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202
            ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368
               ((T_IsCommutativeMonoid_406 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsCommutativeMonoid_406 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_416
                  ((T_IsSemiringWithoutOne_952 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsSemiringWithoutOne_952 -> T_IsCommutativeMonoid_406
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_968
                     (T_IsSemiringWithoutOne_952 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_952
v2))))))
-- Algebra.Bundles.CommutativeSemiringWithoutOne._.isMonoid
d_isMonoid_1672 ::
  T_CommutativeSemiringWithoutOne_1598 ->
  MAlonzo.Code.Algebra.Structures.T_IsMonoid_358
d_isMonoid_1672 :: T_CommutativeSemiringWithoutOne_1598 -> T_IsMonoid_358
d_isMonoid_1672 T_CommutativeSemiringWithoutOne_1598
v0
  = (T_IsCommutativeMonoid_406 -> T_IsMonoid_358)
-> AgdaAny -> T_IsMonoid_358
forall a b. a -> b
coe
      T_IsCommutativeMonoid_406 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_416
      ((T_IsSemiringWithoutOne_952 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiringWithoutOne_952 -> T_IsCommutativeMonoid_406
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_968
         ((T_IsCommutativeSemiringWithoutOne_1044
 -> T_IsSemiringWithoutOne_952)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCommutativeSemiringWithoutOne_1044
-> T_IsSemiringWithoutOne_952
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutOne_1056
            ((T_CommutativeSemiringWithoutOne_1598
 -> T_IsCommutativeSemiringWithoutOne_1044)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemiringWithoutOne_1598
-> T_IsCommutativeSemiringWithoutOne_1044
d_isCommutativeSemiringWithoutOne_1626 (T_CommutativeSemiringWithoutOne_1598 -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemiringWithoutOne_1598
v0))))
-- Algebra.Bundles.CommutativeSemiringWithoutOne._.isSemigroup
d_isSemigroup_1674 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeSemiringWithoutOne_1598 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_194
d_isSemigroup_1674 :: ()
-> () -> T_CommutativeSemiringWithoutOne_1598 -> T_IsSemigroup_194
d_isSemigroup_1674 ~()
v0 ~()
v1 T_CommutativeSemiringWithoutOne_1598
v2 = T_CommutativeSemiringWithoutOne_1598 -> T_IsSemigroup_194
du_isSemigroup_1674 T_CommutativeSemiringWithoutOne_1598
v2
du_isSemigroup_1674 ::
  T_CommutativeSemiringWithoutOne_1598 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_194
du_isSemigroup_1674 :: T_CommutativeSemiringWithoutOne_1598 -> T_IsSemigroup_194
du_isSemigroup_1674 T_CommutativeSemiringWithoutOne_1598
v0
  = let v1 :: T_IsCommutativeSemiringWithoutOne_1044
v1 = T_CommutativeSemiringWithoutOne_1598
-> T_IsCommutativeSemiringWithoutOne_1044
d_isCommutativeSemiringWithoutOne_1626 (T_CommutativeSemiringWithoutOne_1598
-> T_CommutativeSemiringWithoutOne_1598
forall a b. a -> b
coe T_CommutativeSemiringWithoutOne_1598
v0) in
    AgdaAny -> T_IsSemigroup_194
forall a b. a -> b
coe
      (let v2 :: T_IsSemiringWithoutOne_952
v2
             = T_IsCommutativeSemiringWithoutOne_1044
-> T_IsSemiringWithoutOne_952
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutOne_1056
                 (T_IsCommutativeSemiringWithoutOne_1044
-> T_IsCommutativeSemiringWithoutOne_1044
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1044
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368
            ((T_IsCommutativeMonoid_406 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsCommutativeMonoid_406 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_416
               ((T_IsSemiringWithoutOne_952 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsSemiringWithoutOne_952 -> T_IsCommutativeMonoid_406
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_968
                  (T_IsSemiringWithoutOne_952 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_952
v2)))))
-- Algebra.Bundles.CommutativeSemiringWithoutOne._.distrib
d_distrib_1676 ::
  T_CommutativeSemiringWithoutOne_1598 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_distrib_1676 :: T_CommutativeSemiringWithoutOne_1598 -> T_Σ_14
d_distrib_1676 T_CommutativeSemiringWithoutOne_1598
v0
  = (T_IsSemiringWithoutOne_952 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsSemiringWithoutOne_952 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_distrib_972
      ((T_IsCommutativeSemiringWithoutOne_1044
 -> T_IsSemiringWithoutOne_952)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCommutativeSemiringWithoutOne_1044
-> T_IsSemiringWithoutOne_952
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutOne_1056
         ((T_CommutativeSemiringWithoutOne_1598
 -> T_IsCommutativeSemiringWithoutOne_1044)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemiringWithoutOne_1598
-> T_IsCommutativeSemiringWithoutOne_1044
d_isCommutativeSemiringWithoutOne_1626 (T_CommutativeSemiringWithoutOne_1598 -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemiringWithoutOne_1598
v0)))
-- Algebra.Bundles.CommutativeSemiringWithoutOne._.distribʳ
d_distrib'691'_1678 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeSemiringWithoutOne_1598 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_distrib'691'_1678 :: ()
-> ()
-> T_CommutativeSemiringWithoutOne_1598
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_distrib'691'_1678 ~()
v0 ~()
v1 T_CommutativeSemiringWithoutOne_1598
v2 = T_CommutativeSemiringWithoutOne_1598
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'691'_1678 T_CommutativeSemiringWithoutOne_1598
v2
du_distrib'691'_1678 ::
  T_CommutativeSemiringWithoutOne_1598 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'691'_1678 :: T_CommutativeSemiringWithoutOne_1598
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'691'_1678 T_CommutativeSemiringWithoutOne_1598
v0
  = let v1 :: T_IsCommutativeSemiringWithoutOne_1044
v1 = T_CommutativeSemiringWithoutOne_1598
-> T_IsCommutativeSemiringWithoutOne_1044
d_isCommutativeSemiringWithoutOne_1626 (T_CommutativeSemiringWithoutOne_1598
-> T_CommutativeSemiringWithoutOne_1598
forall a b. a -> b
coe T_CommutativeSemiringWithoutOne_1598
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemiringWithoutOne_952
v2
             = T_IsCommutativeSemiringWithoutOne_1044
-> T_IsSemiringWithoutOne_952
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutOne_1056
                 (T_IsCommutativeSemiringWithoutOne_1044
-> T_IsCommutativeSemiringWithoutOne_1044
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1044
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_Σ_14 -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_Σ_14 -> AgdaAny
MAlonzo.Code.Agda.Builtin.Sigma.d_snd_30
            ((T_IsSemiringWithoutOne_952 -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_952 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_distrib_972 (T_IsSemiringWithoutOne_952 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_952
v2))))
-- Algebra.Bundles.CommutativeSemiringWithoutOne._.isEquivalence
d_isEquivalence_1680 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeSemiringWithoutOne_1598 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_1680 :: ()
-> () -> T_CommutativeSemiringWithoutOne_1598 -> T_IsEquivalence_26
d_isEquivalence_1680 ~()
v0 ~()
v1 T_CommutativeSemiringWithoutOne_1598
v2 = T_CommutativeSemiringWithoutOne_1598 -> T_IsEquivalence_26
du_isEquivalence_1680 T_CommutativeSemiringWithoutOne_1598
v2
du_isEquivalence_1680 ::
  T_CommutativeSemiringWithoutOne_1598 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
du_isEquivalence_1680 :: T_CommutativeSemiringWithoutOne_1598 -> T_IsEquivalence_26
du_isEquivalence_1680 T_CommutativeSemiringWithoutOne_1598
v0
  = let v1 :: T_IsCommutativeSemiringWithoutOne_1044
v1 = T_CommutativeSemiringWithoutOne_1598
-> T_IsCommutativeSemiringWithoutOne_1044
d_isCommutativeSemiringWithoutOne_1626 (T_CommutativeSemiringWithoutOne_1598
-> T_CommutativeSemiringWithoutOne_1598
forall a b. a -> b
coe T_CommutativeSemiringWithoutOne_1598
v0) in
    AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      (let v2 :: T_IsSemiringWithoutOne_952
v2
             = T_IsCommutativeSemiringWithoutOne_1044
-> T_IsSemiringWithoutOne_952
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutOne_1056
                 (T_IsCommutativeSemiringWithoutOne_1044
-> T_IsCommutativeSemiringWithoutOne_1044
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1044
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsMagma_86 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMagma_86 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_94
            ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202
               ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368
                  ((T_IsCommutativeMonoid_406 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsCommutativeMonoid_406 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_416
                     ((T_IsSemiringWithoutOne_952 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsSemiringWithoutOne_952 -> T_IsCommutativeMonoid_406
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_968
                        (T_IsSemiringWithoutOne_952 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_952
v2)))))))
-- Algebra.Bundles.CommutativeSemiringWithoutOne._.isNearSemiring
d_isNearSemiring_1682 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeSemiringWithoutOne_1598 ->
  MAlonzo.Code.Algebra.Structures.T_IsNearSemiring_876
d_isNearSemiring_1682 :: ()
-> ()
-> T_CommutativeSemiringWithoutOne_1598
-> T_IsNearSemiring_876
d_isNearSemiring_1682 ~()
v0 ~()
v1 T_CommutativeSemiringWithoutOne_1598
v2 = T_CommutativeSemiringWithoutOne_1598 -> T_IsNearSemiring_876
du_isNearSemiring_1682 T_CommutativeSemiringWithoutOne_1598
v2
du_isNearSemiring_1682 ::
  T_CommutativeSemiringWithoutOne_1598 ->
  MAlonzo.Code.Algebra.Structures.T_IsNearSemiring_876
du_isNearSemiring_1682 :: T_CommutativeSemiringWithoutOne_1598 -> T_IsNearSemiring_876
du_isNearSemiring_1682 T_CommutativeSemiringWithoutOne_1598
v0
  = let v1 :: T_IsCommutativeSemiringWithoutOne_1044
v1 = T_CommutativeSemiringWithoutOne_1598
-> T_IsCommutativeSemiringWithoutOne_1044
d_isCommutativeSemiringWithoutOne_1626 (T_CommutativeSemiringWithoutOne_1598
-> T_CommutativeSemiringWithoutOne_1598
forall a b. a -> b
coe T_CommutativeSemiringWithoutOne_1598
v0) in
    AgdaAny -> T_IsNearSemiring_876
forall a b. a -> b
coe
      ((T_IsSemiringWithoutOne_952 -> T_IsNearSemiring_876)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiringWithoutOne_952 -> T_IsNearSemiring_876
MAlonzo.Code.Algebra.Structures.du_isNearSemiring_990
         ((T_IsCommutativeSemiringWithoutOne_1044
 -> T_IsSemiringWithoutOne_952)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCommutativeSemiringWithoutOne_1044
-> T_IsSemiringWithoutOne_952
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutOne_1056
            (T_IsCommutativeSemiringWithoutOne_1044 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1044
v1)))
-- Algebra.Bundles.CommutativeSemiringWithoutOne._.isPartialEquivalence
d_isPartialEquivalence_1684 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeSemiringWithoutOne_1598 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_1684 :: ()
-> ()
-> T_CommutativeSemiringWithoutOne_1598
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_1684 ~()
v0 ~()
v1 T_CommutativeSemiringWithoutOne_1598
v2
  = T_CommutativeSemiringWithoutOne_1598 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_1684 T_CommutativeSemiringWithoutOne_1598
v2
du_isPartialEquivalence_1684 ::
  T_CommutativeSemiringWithoutOne_1598 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_1684 :: T_CommutativeSemiringWithoutOne_1598 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_1684 T_CommutativeSemiringWithoutOne_1598
v0
  = let v1 :: T_IsCommutativeSemiringWithoutOne_1044
v1 = T_CommutativeSemiringWithoutOne_1598
-> T_IsCommutativeSemiringWithoutOne_1044
d_isCommutativeSemiringWithoutOne_1626 (T_CommutativeSemiringWithoutOne_1598
-> T_CommutativeSemiringWithoutOne_1598
forall a b. a -> b
coe T_CommutativeSemiringWithoutOne_1598
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsSemiringWithoutOne_952
v2
             = T_IsCommutativeSemiringWithoutOne_1044
-> T_IsSemiringWithoutOne_952
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutOne_1056
                 (T_IsCommutativeSemiringWithoutOne_1044
-> T_IsCommutativeSemiringWithoutOne_1044
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1044
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: t
v3
                = (T_IsSemiringWithoutOne_952 -> T_IsNearSemiring_876)
-> AgdaAny -> t
forall a b. a -> b
coe
                    T_IsSemiringWithoutOne_952 -> T_IsNearSemiring_876
MAlonzo.Code.Algebra.Structures.du_isNearSemiring_990 (T_IsSemiringWithoutOne_952 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_952
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsMonoid_358
v4
                   = T_IsNearSemiring_876 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_'43''45'isMonoid_892
                       (AgdaAny -> T_IsNearSemiring_876
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsSemigroup_194
v5
                      = T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368 (T_IsMonoid_358 -> T_IsMonoid_358
forall a b. a -> b
coe T_IsMonoid_358
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (let v6 :: T_IsMagma_86
v6 = T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202 (T_IsSemigroup_194 -> T_IsSemigroup_194
forall a b. a -> b
coe T_IsSemigroup_194
v5) in
                   AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     ((T_IsEquivalence_26 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsEquivalence_26 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
                        ((T_IsMagma_86 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_IsMagma_86 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_94 (T_IsMagma_86 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86
v6))))))))
-- Algebra.Bundles.CommutativeSemiringWithoutOne._.isSemiringWithoutOne
d_isSemiringWithoutOne_1686 ::
  T_CommutativeSemiringWithoutOne_1598 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutOne_952
d_isSemiringWithoutOne_1686 :: T_CommutativeSemiringWithoutOne_1598 -> T_IsSemiringWithoutOne_952
d_isSemiringWithoutOne_1686 T_CommutativeSemiringWithoutOne_1598
v0
  = (T_IsCommutativeSemiringWithoutOne_1044
 -> T_IsSemiringWithoutOne_952)
-> AgdaAny -> T_IsSemiringWithoutOne_952
forall a b. a -> b
coe
      T_IsCommutativeSemiringWithoutOne_1044
-> T_IsSemiringWithoutOne_952
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutOne_1056
      ((T_CommutativeSemiringWithoutOne_1598
 -> T_IsCommutativeSemiringWithoutOne_1044)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemiringWithoutOne_1598
-> T_IsCommutativeSemiringWithoutOne_1044
d_isCommutativeSemiringWithoutOne_1626 (T_CommutativeSemiringWithoutOne_1598 -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemiringWithoutOne_1598
v0))
-- Algebra.Bundles.CommutativeSemiringWithoutOne._.refl
d_refl_1688 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeSemiringWithoutOne_1598 -> AgdaAny -> AgdaAny
d_refl_1688 :: ()
-> () -> T_CommutativeSemiringWithoutOne_1598 -> AgdaAny -> AgdaAny
d_refl_1688 ~()
v0 ~()
v1 T_CommutativeSemiringWithoutOne_1598
v2 = T_CommutativeSemiringWithoutOne_1598 -> AgdaAny -> AgdaAny
du_refl_1688 T_CommutativeSemiringWithoutOne_1598
v2
du_refl_1688 ::
  T_CommutativeSemiringWithoutOne_1598 -> AgdaAny -> AgdaAny
du_refl_1688 :: T_CommutativeSemiringWithoutOne_1598 -> AgdaAny -> AgdaAny
du_refl_1688 T_CommutativeSemiringWithoutOne_1598
v0
  = let v1 :: T_IsCommutativeSemiringWithoutOne_1044
v1 = T_CommutativeSemiringWithoutOne_1598
-> T_IsCommutativeSemiringWithoutOne_1044
d_isCommutativeSemiringWithoutOne_1626 (T_CommutativeSemiringWithoutOne_1598
-> T_CommutativeSemiringWithoutOne_1598
forall a b. a -> b
coe T_CommutativeSemiringWithoutOne_1598
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemiringWithoutOne_952
v2
             = T_IsCommutativeSemiringWithoutOne_1044
-> T_IsSemiringWithoutOne_952
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutOne_1056
                 (T_IsCommutativeSemiringWithoutOne_1044
-> T_IsCommutativeSemiringWithoutOne_1044
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1044
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsEquivalence_26 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_34
            ((T_IsMagma_86 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMagma_86 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_94
               ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202
                  ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368
                     ((T_IsCommutativeMonoid_406 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsCommutativeMonoid_406 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_416
                        ((T_IsSemiringWithoutOne_952 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_IsSemiringWithoutOne_952 -> T_IsCommutativeMonoid_406
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_968
                           (T_IsSemiringWithoutOne_952 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_952
v2))))))))
-- Algebra.Bundles.CommutativeSemiringWithoutOne._.reflexive
d_reflexive_1690 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeSemiringWithoutOne_1598 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_1690 :: ()
-> ()
-> T_CommutativeSemiringWithoutOne_1598
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_1690 ~()
v0 ~()
v1 T_CommutativeSemiringWithoutOne_1598
v2 = T_CommutativeSemiringWithoutOne_1598
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_1690 T_CommutativeSemiringWithoutOne_1598
v2
du_reflexive_1690 ::
  T_CommutativeSemiringWithoutOne_1598 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_1690 :: T_CommutativeSemiringWithoutOne_1598
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_1690 T_CommutativeSemiringWithoutOne_1598
v0
  = let v1 :: T_IsCommutativeSemiringWithoutOne_1044
v1 = T_CommutativeSemiringWithoutOne_1598
-> T_IsCommutativeSemiringWithoutOne_1044
d_isCommutativeSemiringWithoutOne_1626 (T_CommutativeSemiringWithoutOne_1598
-> T_CommutativeSemiringWithoutOne_1598
forall a b. a -> b
coe T_CommutativeSemiringWithoutOne_1598
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemiringWithoutOne_952
v2
             = T_IsCommutativeSemiringWithoutOne_1044
-> T_IsSemiringWithoutOne_952
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutOne_1056
                 (T_IsCommutativeSemiringWithoutOne_1044
-> T_IsCommutativeSemiringWithoutOne_1044
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1044
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: t
v3
                = (T_IsSemiringWithoutOne_952 -> T_IsNearSemiring_876)
-> AgdaAny -> t
forall a b. a -> b
coe
                    T_IsSemiringWithoutOne_952 -> T_IsNearSemiring_876
MAlonzo.Code.Algebra.Structures.du_isNearSemiring_990 (T_IsSemiringWithoutOne_952 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_952
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsMonoid_358
v4
                   = T_IsNearSemiring_876 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_'43''45'isMonoid_892
                       (AgdaAny -> T_IsNearSemiring_876
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsSemigroup_194
v5
                      = T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368 (T_IsMonoid_358 -> T_IsMonoid_358
forall a b. a -> b
coe T_IsMonoid_358
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (let v6 :: T_IsMagma_86
v6 = T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202 (T_IsSemigroup_194 -> T_IsSemigroup_194
forall a b. a -> b
coe T_IsSemigroup_194
v5) in
                   (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
                     (\ AgdaAny
v7 AgdaAny
v8 AgdaAny
v9 ->
                        (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                          T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
                          ((T_IsMagma_86 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_94 (T_IsMagma_86 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86
v6))
                          AgdaAny
v7))))))
-- Algebra.Bundles.CommutativeSemiringWithoutOne._.setoid
d_setoid_1692 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeSemiringWithoutOne_1598 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_1692 :: () -> () -> T_CommutativeSemiringWithoutOne_1598 -> T_Setoid_44
d_setoid_1692 ~()
v0 ~()
v1 T_CommutativeSemiringWithoutOne_1598
v2 = T_CommutativeSemiringWithoutOne_1598 -> T_Setoid_44
du_setoid_1692 T_CommutativeSemiringWithoutOne_1598
v2
du_setoid_1692 ::
  T_CommutativeSemiringWithoutOne_1598 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_1692 :: T_CommutativeSemiringWithoutOne_1598 -> T_Setoid_44
du_setoid_1692 T_CommutativeSemiringWithoutOne_1598
v0
  = let v1 :: T_IsCommutativeSemiringWithoutOne_1044
v1 = T_CommutativeSemiringWithoutOne_1598
-> T_IsCommutativeSemiringWithoutOne_1044
d_isCommutativeSemiringWithoutOne_1626 (T_CommutativeSemiringWithoutOne_1598
-> T_CommutativeSemiringWithoutOne_1598
forall a b. a -> b
coe T_CommutativeSemiringWithoutOne_1598
v0) in
    AgdaAny -> T_Setoid_44
forall a b. a -> b
coe
      (let v2 :: T_IsSemiringWithoutOne_952
v2
             = T_IsCommutativeSemiringWithoutOne_1044
-> T_IsSemiringWithoutOne_952
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutOne_1056
                 (T_IsCommutativeSemiringWithoutOne_1044
-> T_IsCommutativeSemiringWithoutOne_1044
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1044
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: t
v3
                = (T_IsSemiringWithoutOne_952 -> T_IsNearSemiring_876)
-> AgdaAny -> t
forall a b. a -> b
coe
                    T_IsSemiringWithoutOne_952 -> T_IsNearSemiring_876
MAlonzo.Code.Algebra.Structures.du_isNearSemiring_990 (T_IsSemiringWithoutOne_952 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_952
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsMonoid_358
v4
                   = T_IsNearSemiring_876 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_'43''45'isMonoid_892
                       (AgdaAny -> T_IsNearSemiring_876
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsSemigroup_194
v5
                      = T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368 (T_IsMonoid_358 -> T_IsMonoid_358
forall a b. a -> b
coe T_IsMonoid_358
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  ((T_IsMagma_86 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsMagma_86 -> T_Setoid_44
MAlonzo.Code.Algebra.Structures.du_setoid_110
                     ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202 (T_IsSemigroup_194 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194
v5)))))))
-- Algebra.Bundles.CommutativeSemiringWithoutOne._.sym
d_sym_1694 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeSemiringWithoutOne_1598 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_1694 :: ()
-> ()
-> T_CommutativeSemiringWithoutOne_1598
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_sym_1694 ~()
v0 ~()
v1 T_CommutativeSemiringWithoutOne_1598
v2 = T_CommutativeSemiringWithoutOne_1598
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_1694 T_CommutativeSemiringWithoutOne_1598
v2
du_sym_1694 ::
  T_CommutativeSemiringWithoutOne_1598 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_1694 :: T_CommutativeSemiringWithoutOne_1598
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_1694 T_CommutativeSemiringWithoutOne_1598
v0
  = let v1 :: T_IsCommutativeSemiringWithoutOne_1044
v1 = T_CommutativeSemiringWithoutOne_1598
-> T_IsCommutativeSemiringWithoutOne_1044
d_isCommutativeSemiringWithoutOne_1626 (T_CommutativeSemiringWithoutOne_1598
-> T_CommutativeSemiringWithoutOne_1598
forall a b. a -> b
coe T_CommutativeSemiringWithoutOne_1598
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemiringWithoutOne_952
v2
             = T_IsCommutativeSemiringWithoutOne_1044
-> T_IsSemiringWithoutOne_952
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutOne_1056
                 (T_IsCommutativeSemiringWithoutOne_1044
-> T_IsCommutativeSemiringWithoutOne_1044
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1044
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_36
            ((T_IsMagma_86 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMagma_86 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_94
               ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202
                  ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368
                     ((T_IsCommutativeMonoid_406 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsCommutativeMonoid_406 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_416
                        ((T_IsSemiringWithoutOne_952 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_IsSemiringWithoutOne_952 -> T_IsCommutativeMonoid_406
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_968
                           (T_IsSemiringWithoutOne_952 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_952
v2))))))))
-- Algebra.Bundles.CommutativeSemiringWithoutOne._.trans
d_trans_1696 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeSemiringWithoutOne_1598 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_1696 :: ()
-> ()
-> T_CommutativeSemiringWithoutOne_1598
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_trans_1696 ~()
v0 ~()
v1 T_CommutativeSemiringWithoutOne_1598
v2 = T_CommutativeSemiringWithoutOne_1598
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_1696 T_CommutativeSemiringWithoutOne_1598
v2
du_trans_1696 ::
  T_CommutativeSemiringWithoutOne_1598 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_1696 :: T_CommutativeSemiringWithoutOne_1598
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_1696 T_CommutativeSemiringWithoutOne_1598
v0
  = let v1 :: T_IsCommutativeSemiringWithoutOne_1044
v1 = T_CommutativeSemiringWithoutOne_1598
-> T_IsCommutativeSemiringWithoutOne_1044
d_isCommutativeSemiringWithoutOne_1626 (T_CommutativeSemiringWithoutOne_1598
-> T_CommutativeSemiringWithoutOne_1598
forall a b. a -> b
coe T_CommutativeSemiringWithoutOne_1598
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemiringWithoutOne_952
v2
             = T_IsCommutativeSemiringWithoutOne_1044
-> T_IsSemiringWithoutOne_952
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutOne_1056
                 (T_IsCommutativeSemiringWithoutOne_1044
-> T_IsCommutativeSemiringWithoutOne_1044
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1044
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsEquivalence_26
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsEquivalence_26
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_38
            ((T_IsMagma_86 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMagma_86 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_94
               ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202
                  ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368
                     ((T_IsCommutativeMonoid_406 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsCommutativeMonoid_406 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_416
                        ((T_IsSemiringWithoutOne_952 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_IsSemiringWithoutOne_952 -> T_IsCommutativeMonoid_406
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_968
                           (T_IsSemiringWithoutOne_952 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutOne_952
v2))))))))
-- Algebra.Bundles.CommutativeSemiringWithoutOne._.zero
d_zero_1698 ::
  T_CommutativeSemiringWithoutOne_1598 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_zero_1698 :: T_CommutativeSemiringWithoutOne_1598 -> T_Σ_14
d_zero_1698 T_CommutativeSemiringWithoutOne_1598
v0
  = (T_IsSemiringWithoutOne_952 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsSemiringWithoutOne_952 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_zero_974
      ((T_IsCommutativeSemiringWithoutOne_1044
 -> T_IsSemiringWithoutOne_952)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCommutativeSemiringWithoutOne_1044
-> T_IsSemiringWithoutOne_952
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutOne_1056
         ((T_CommutativeSemiringWithoutOne_1598
 -> T_IsCommutativeSemiringWithoutOne_1044)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemiringWithoutOne_1598
-> T_IsCommutativeSemiringWithoutOne_1044
d_isCommutativeSemiringWithoutOne_1626 (T_CommutativeSemiringWithoutOne_1598 -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemiringWithoutOne_1598
v0)))
-- Algebra.Bundles.CommutativeSemiringWithoutOne._.zeroʳ
d_zero'691'_1700 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeSemiringWithoutOne_1598 -> AgdaAny -> AgdaAny
d_zero'691'_1700 :: ()
-> () -> T_CommutativeSemiringWithoutOne_1598 -> AgdaAny -> AgdaAny
d_zero'691'_1700 ~()
v0 ~()
v1 T_CommutativeSemiringWithoutOne_1598
v2 = T_CommutativeSemiringWithoutOne_1598 -> AgdaAny -> AgdaAny
du_zero'691'_1700 T_CommutativeSemiringWithoutOne_1598
v2
du_zero'691'_1700 ::
  T_CommutativeSemiringWithoutOne_1598 -> AgdaAny -> AgdaAny
du_zero'691'_1700 :: T_CommutativeSemiringWithoutOne_1598 -> AgdaAny -> AgdaAny
du_zero'691'_1700 T_CommutativeSemiringWithoutOne_1598
v0
  = let v1 :: T_IsCommutativeSemiringWithoutOne_1044
v1 = T_CommutativeSemiringWithoutOne_1598
-> T_IsCommutativeSemiringWithoutOne_1044
d_isCommutativeSemiringWithoutOne_1626 (T_CommutativeSemiringWithoutOne_1598
-> T_CommutativeSemiringWithoutOne_1598
forall a b. a -> b
coe T_CommutativeSemiringWithoutOne_1598
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsSemiringWithoutOne_952 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiringWithoutOne_952 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_zero'691'_988
         ((T_IsCommutativeSemiringWithoutOne_1044
 -> T_IsSemiringWithoutOne_952)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCommutativeSemiringWithoutOne_1044
-> T_IsSemiringWithoutOne_952
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutOne_1056
            (T_IsCommutativeSemiringWithoutOne_1044 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1044
v1)))
-- Algebra.Bundles.CommutativeSemiringWithoutOne._.zeroˡ
d_zero'737'_1702 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeSemiringWithoutOne_1598 -> AgdaAny -> AgdaAny
d_zero'737'_1702 :: ()
-> () -> T_CommutativeSemiringWithoutOne_1598 -> AgdaAny -> AgdaAny
d_zero'737'_1702 ~()
v0 ~()
v1 T_CommutativeSemiringWithoutOne_1598
v2 = T_CommutativeSemiringWithoutOne_1598 -> AgdaAny -> AgdaAny
du_zero'737'_1702 T_CommutativeSemiringWithoutOne_1598
v2
du_zero'737'_1702 ::
  T_CommutativeSemiringWithoutOne_1598 -> AgdaAny -> AgdaAny
du_zero'737'_1702 :: T_CommutativeSemiringWithoutOne_1598 -> AgdaAny -> AgdaAny
du_zero'737'_1702 T_CommutativeSemiringWithoutOne_1598
v0
  = let v1 :: T_IsCommutativeSemiringWithoutOne_1044
v1 = T_CommutativeSemiringWithoutOne_1598
-> T_IsCommutativeSemiringWithoutOne_1044
d_isCommutativeSemiringWithoutOne_1626 (T_CommutativeSemiringWithoutOne_1598
-> T_CommutativeSemiringWithoutOne_1598
forall a b. a -> b
coe T_CommutativeSemiringWithoutOne_1598
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsSemiringWithoutOne_952 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiringWithoutOne_952 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_zero'737'_986
         ((T_IsCommutativeSemiringWithoutOne_1044
 -> T_IsSemiringWithoutOne_952)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCommutativeSemiringWithoutOne_1044
-> T_IsSemiringWithoutOne_952
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutOne_1056
            (T_IsCommutativeSemiringWithoutOne_1044 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1044
v1)))
-- Algebra.Bundles.CommutativeSemiringWithoutOne.semiringWithoutOne
d_semiringWithoutOne_1704 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeSemiringWithoutOne_1598 -> T_SemiringWithoutOne_1464
d_semiringWithoutOne_1704 :: ()
-> ()
-> T_CommutativeSemiringWithoutOne_1598
-> T_SemiringWithoutOne_1464
d_semiringWithoutOne_1704 ~()
v0 ~()
v1 T_CommutativeSemiringWithoutOne_1598
v2
  = T_CommutativeSemiringWithoutOne_1598 -> T_SemiringWithoutOne_1464
du_semiringWithoutOne_1704 T_CommutativeSemiringWithoutOne_1598
v2
du_semiringWithoutOne_1704 ::
  T_CommutativeSemiringWithoutOne_1598 -> T_SemiringWithoutOne_1464
du_semiringWithoutOne_1704 :: T_CommutativeSemiringWithoutOne_1598 -> T_SemiringWithoutOne_1464
du_semiringWithoutOne_1704 T_CommutativeSemiringWithoutOne_1598
v0
  = ((AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> T_IsSemiringWithoutOne_952
 -> T_SemiringWithoutOne_1464)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsSemiringWithoutOne_952
-> T_SemiringWithoutOne_1464
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsSemiringWithoutOne_952
-> T_SemiringWithoutOne_1464
C_SemiringWithoutOne'46'constructor_25531 (T_CommutativeSemiringWithoutOne_1598
-> AgdaAny -> AgdaAny -> AgdaAny
d__'43'__1620 (T_CommutativeSemiringWithoutOne_1598
-> T_CommutativeSemiringWithoutOne_1598
forall a b. a -> b
coe T_CommutativeSemiringWithoutOne_1598
v0))
      (T_CommutativeSemiringWithoutOne_1598
-> AgdaAny -> AgdaAny -> AgdaAny
d__'42'__1622 (T_CommutativeSemiringWithoutOne_1598
-> T_CommutativeSemiringWithoutOne_1598
forall a b. a -> b
coe T_CommutativeSemiringWithoutOne_1598
v0)) (T_CommutativeSemiringWithoutOne_1598 -> AgdaAny
d_0'35'_1624 (T_CommutativeSemiringWithoutOne_1598
-> T_CommutativeSemiringWithoutOne_1598
forall a b. a -> b
coe T_CommutativeSemiringWithoutOne_1598
v0))
      (T_IsCommutativeSemiringWithoutOne_1044
-> T_IsSemiringWithoutOne_952
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutOne_1056
         ((T_CommutativeSemiringWithoutOne_1598
 -> T_IsCommutativeSemiringWithoutOne_1044)
-> AgdaAny -> T_IsCommutativeSemiringWithoutOne_1044
forall a b. a -> b
coe T_CommutativeSemiringWithoutOne_1598
-> T_IsCommutativeSemiringWithoutOne_1044
d_isCommutativeSemiringWithoutOne_1626 (T_CommutativeSemiringWithoutOne_1598 -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemiringWithoutOne_1598
v0)))
-- Algebra.Bundles.CommutativeSemiringWithoutOne._._≉_
d__'8777'__1708 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeSemiringWithoutOne_1598 -> AgdaAny -> AgdaAny -> ()
d__'8777'__1708 :: ()
-> ()
-> T_CommutativeSemiringWithoutOne_1598
-> AgdaAny
-> AgdaAny
-> ()
d__'8777'__1708 = ()
-> ()
-> T_CommutativeSemiringWithoutOne_1598
-> AgdaAny
-> AgdaAny
-> ()
forall a. a
erased
-- Algebra.Bundles.CommutativeSemiringWithoutOne._.magma
d_magma_1710 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeSemiringWithoutOne_1598 -> T_Magma_36
d_magma_1710 :: () -> () -> T_CommutativeSemiringWithoutOne_1598 -> T_Magma_36
d_magma_1710 ~()
v0 ~()
v1 T_CommutativeSemiringWithoutOne_1598
v2 = T_CommutativeSemiringWithoutOne_1598 -> T_Magma_36
du_magma_1710 T_CommutativeSemiringWithoutOne_1598
v2
du_magma_1710 :: T_CommutativeSemiringWithoutOne_1598 -> T_Magma_36
du_magma_1710 :: T_CommutativeSemiringWithoutOne_1598 -> T_Magma_36
du_magma_1710 T_CommutativeSemiringWithoutOne_1598
v0
  = let v1 :: t
v1 = (T_CommutativeSemiringWithoutOne_1598 -> T_SemiringWithoutOne_1464)
-> AgdaAny -> t
forall a b. a -> b
coe T_CommutativeSemiringWithoutOne_1598 -> T_SemiringWithoutOne_1464
du_semiringWithoutOne_1704 (T_CommutativeSemiringWithoutOne_1598 -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemiringWithoutOne_1598
v0) in
    AgdaAny -> T_Magma_36
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_SemiringWithoutOne_1464 -> T_NearSemiring_1354) -> AgdaAny -> t
forall a b. a -> b
coe T_SemiringWithoutOne_1464 -> T_NearSemiring_1354
du_nearSemiring_1562 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_Semigroup_206 -> T_Magma_36) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semigroup_206 -> T_Magma_36
du_magma_254 ((T_NearSemiring_1354 -> T_Semigroup_206) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_NearSemiring_1354 -> T_Semigroup_206
du_'42''45'semigroup_1452 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2))))
-- Algebra.Bundles.CommutativeSemiringWithoutOne._.rawMagma
d_rawMagma_1712 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeSemiringWithoutOne_1598 -> T_RawMagma_8
d_rawMagma_1712 :: () -> () -> T_CommutativeSemiringWithoutOne_1598 -> T_RawMagma_8
d_rawMagma_1712 ~()
v0 ~()
v1 T_CommutativeSemiringWithoutOne_1598
v2 = T_CommutativeSemiringWithoutOne_1598 -> T_RawMagma_8
du_rawMagma_1712 T_CommutativeSemiringWithoutOne_1598
v2
du_rawMagma_1712 ::
  T_CommutativeSemiringWithoutOne_1598 -> T_RawMagma_8
du_rawMagma_1712 :: T_CommutativeSemiringWithoutOne_1598 -> T_RawMagma_8
du_rawMagma_1712 T_CommutativeSemiringWithoutOne_1598
v0
  = let v1 :: t
v1 = (T_CommutativeSemiringWithoutOne_1598 -> T_SemiringWithoutOne_1464)
-> AgdaAny -> t
forall a b. a -> b
coe T_CommutativeSemiringWithoutOne_1598 -> T_SemiringWithoutOne_1464
du_semiringWithoutOne_1704 (T_CommutativeSemiringWithoutOne_1598 -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemiringWithoutOne_1598
v0) in
    AgdaAny -> T_RawMagma_8
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_SemiringWithoutOne_1464 -> T_NearSemiring_1354) -> AgdaAny -> t
forall a b. a -> b
coe T_SemiringWithoutOne_1464 -> T_NearSemiring_1354
du_nearSemiring_1562 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: t
v3 = (T_NearSemiring_1354 -> T_Semigroup_206) -> AgdaAny -> t
forall a b. a -> b
coe T_NearSemiring_1354 -> T_Semigroup_206
du_'42''45'semigroup_1452 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_Magma_36 -> T_RawMagma_8) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Magma_36 -> T_RawMagma_8
du_rawMagma_80 ((T_Semigroup_206 -> T_Magma_36) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semigroup_206 -> T_Magma_36
du_magma_254 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3)))))
-- Algebra.Bundles.CommutativeSemiringWithoutOne._.*-semigroup
d_'42''45'semigroup_1714 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeSemiringWithoutOne_1598 -> T_Semigroup_206
d_'42''45'semigroup_1714 :: () -> () -> T_CommutativeSemiringWithoutOne_1598 -> T_Semigroup_206
d_'42''45'semigroup_1714 ~()
v0 ~()
v1 T_CommutativeSemiringWithoutOne_1598
v2 = T_CommutativeSemiringWithoutOne_1598 -> T_Semigroup_206
du_'42''45'semigroup_1714 T_CommutativeSemiringWithoutOne_1598
v2
du_'42''45'semigroup_1714 ::
  T_CommutativeSemiringWithoutOne_1598 -> T_Semigroup_206
du_'42''45'semigroup_1714 :: T_CommutativeSemiringWithoutOne_1598 -> T_Semigroup_206
du_'42''45'semigroup_1714 T_CommutativeSemiringWithoutOne_1598
v0
  = let v1 :: t
v1 = (T_CommutativeSemiringWithoutOne_1598 -> T_SemiringWithoutOne_1464)
-> AgdaAny -> t
forall a b. a -> b
coe T_CommutativeSemiringWithoutOne_1598 -> T_SemiringWithoutOne_1464
du_semiringWithoutOne_1704 (T_CommutativeSemiringWithoutOne_1598 -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemiringWithoutOne_1598
v0) in
    AgdaAny -> T_Semigroup_206
forall a b. a -> b
coe
      ((T_NearSemiring_1354 -> T_Semigroup_206) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_NearSemiring_1354 -> T_Semigroup_206
du_'42''45'semigroup_1452 ((T_SemiringWithoutOne_1464 -> T_NearSemiring_1354)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutOne_1464 -> T_NearSemiring_1354
du_nearSemiring_1562 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1)))
-- Algebra.Bundles.CommutativeSemiringWithoutOne._.+-commutativeMonoid
d_'43''45'commutativeMonoid_1716 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeSemiringWithoutOne_1598 -> T_CommutativeMonoid_582
d_'43''45'commutativeMonoid_1716 :: ()
-> ()
-> T_CommutativeSemiringWithoutOne_1598
-> T_CommutativeMonoid_582
d_'43''45'commutativeMonoid_1716 ~()
v0 ~()
v1 T_CommutativeSemiringWithoutOne_1598
v2
  = T_CommutativeSemiringWithoutOne_1598 -> T_CommutativeMonoid_582
du_'43''45'commutativeMonoid_1716 T_CommutativeSemiringWithoutOne_1598
v2
du_'43''45'commutativeMonoid_1716 ::
  T_CommutativeSemiringWithoutOne_1598 -> T_CommutativeMonoid_582
du_'43''45'commutativeMonoid_1716 :: T_CommutativeSemiringWithoutOne_1598 -> T_CommutativeMonoid_582
du_'43''45'commutativeMonoid_1716 T_CommutativeSemiringWithoutOne_1598
v0
  = (T_SemiringWithoutOne_1464 -> T_CommutativeMonoid_582)
-> AgdaAny -> T_CommutativeMonoid_582
forall a b. a -> b
coe
      T_SemiringWithoutOne_1464 -> T_CommutativeMonoid_582
du_'43''45'commutativeMonoid_1586
      ((T_CommutativeSemiringWithoutOne_1598 -> T_SemiringWithoutOne_1464)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemiringWithoutOne_1598 -> T_SemiringWithoutOne_1464
du_semiringWithoutOne_1704 (T_CommutativeSemiringWithoutOne_1598 -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemiringWithoutOne_1598
v0))
-- Algebra.Bundles.CommutativeSemiringWithoutOne._.commutativeSemigroup
d_commutativeSemigroup_1718 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeSemiringWithoutOne_1598 -> T_CommutativeSemigroup_332
d_commutativeSemigroup_1718 :: ()
-> ()
-> T_CommutativeSemiringWithoutOne_1598
-> T_CommutativeSemigroup_332
d_commutativeSemigroup_1718 ~()
v0 ~()
v1 T_CommutativeSemiringWithoutOne_1598
v2
  = T_CommutativeSemiringWithoutOne_1598 -> T_CommutativeSemigroup_332
du_commutativeSemigroup_1718 T_CommutativeSemiringWithoutOne_1598
v2
du_commutativeSemigroup_1718 ::
  T_CommutativeSemiringWithoutOne_1598 -> T_CommutativeSemigroup_332
du_commutativeSemigroup_1718 :: T_CommutativeSemiringWithoutOne_1598 -> T_CommutativeSemigroup_332
du_commutativeSemigroup_1718 T_CommutativeSemiringWithoutOne_1598
v0
  = let v1 :: t
v1 = (T_CommutativeSemiringWithoutOne_1598 -> T_SemiringWithoutOne_1464)
-> AgdaAny -> t
forall a b. a -> b
coe T_CommutativeSemiringWithoutOne_1598 -> T_SemiringWithoutOne_1464
du_semiringWithoutOne_1704 (T_CommutativeSemiringWithoutOne_1598 -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemiringWithoutOne_1598
v0) in
    AgdaAny -> T_CommutativeSemigroup_332
forall a b. a -> b
coe
      ((T_CommutativeMonoid_582 -> T_CommutativeSemigroup_332)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_CommutativeMonoid_582 -> T_CommutativeSemigroup_332
du_commutativeSemigroup_664
         ((T_SemiringWithoutOne_1464 -> T_CommutativeMonoid_582)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutOne_1464 -> T_CommutativeMonoid_582
du_'43''45'commutativeMonoid_1586 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1)))
-- Algebra.Bundles.CommutativeSemiringWithoutOne._.magma
d_magma_1720 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeSemiringWithoutOne_1598 -> T_Magma_36
d_magma_1720 :: () -> () -> T_CommutativeSemiringWithoutOne_1598 -> T_Magma_36
d_magma_1720 ~()
v0 ~()
v1 T_CommutativeSemiringWithoutOne_1598
v2 = T_CommutativeSemiringWithoutOne_1598 -> T_Magma_36
du_magma_1720 T_CommutativeSemiringWithoutOne_1598
v2
du_magma_1720 :: T_CommutativeSemiringWithoutOne_1598 -> T_Magma_36
du_magma_1720 :: T_CommutativeSemiringWithoutOne_1598 -> T_Magma_36
du_magma_1720 T_CommutativeSemiringWithoutOne_1598
v0
  = let v1 :: t
v1 = (T_CommutativeSemiringWithoutOne_1598 -> T_SemiringWithoutOne_1464)
-> AgdaAny -> t
forall a b. a -> b
coe T_CommutativeSemiringWithoutOne_1598 -> T_SemiringWithoutOne_1464
du_semiringWithoutOne_1704 (T_CommutativeSemiringWithoutOne_1598 -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemiringWithoutOne_1598
v0) in
    AgdaAny -> T_Magma_36
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_SemiringWithoutOne_1464 -> T_NearSemiring_1354) -> AgdaAny -> t
forall a b. a -> b
coe T_SemiringWithoutOne_1464 -> T_NearSemiring_1354
du_nearSemiring_1562 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: t
v3 = (T_NearSemiring_1354 -> T_Monoid_506) -> AgdaAny -> t
forall a b. a -> b
coe T_NearSemiring_1354 -> T_Monoid_506
du_'43''45'monoid_1438 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_Semigroup_206 -> T_Magma_36) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semigroup_206 -> T_Magma_36
du_magma_254 ((T_Monoid_506 -> T_Semigroup_206) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Monoid_506 -> T_Semigroup_206
du_semigroup_566 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3)))))
-- Algebra.Bundles.CommutativeSemiringWithoutOne._.+-monoid
d_'43''45'monoid_1722 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeSemiringWithoutOne_1598 -> T_Monoid_506
d_'43''45'monoid_1722 :: () -> () -> T_CommutativeSemiringWithoutOne_1598 -> T_Monoid_506
d_'43''45'monoid_1722 ~()
v0 ~()
v1 T_CommutativeSemiringWithoutOne_1598
v2 = T_CommutativeSemiringWithoutOne_1598 -> T_Monoid_506
du_'43''45'monoid_1722 T_CommutativeSemiringWithoutOne_1598
v2
du_'43''45'monoid_1722 ::
  T_CommutativeSemiringWithoutOne_1598 -> T_Monoid_506
du_'43''45'monoid_1722 :: T_CommutativeSemiringWithoutOne_1598 -> T_Monoid_506
du_'43''45'monoid_1722 T_CommutativeSemiringWithoutOne_1598
v0
  = let v1 :: t
v1 = (T_CommutativeSemiringWithoutOne_1598 -> T_SemiringWithoutOne_1464)
-> AgdaAny -> t
forall a b. a -> b
coe T_CommutativeSemiringWithoutOne_1598 -> T_SemiringWithoutOne_1464
du_semiringWithoutOne_1704 (T_CommutativeSemiringWithoutOne_1598 -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemiringWithoutOne_1598
v0) in
    AgdaAny -> T_Monoid_506
forall a b. a -> b
coe
      ((T_NearSemiring_1354 -> T_Monoid_506) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_NearSemiring_1354 -> T_Monoid_506
du_'43''45'monoid_1438 ((T_SemiringWithoutOne_1464 -> T_NearSemiring_1354)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutOne_1464 -> T_NearSemiring_1354
du_nearSemiring_1562 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1)))
-- Algebra.Bundles.CommutativeSemiringWithoutOne._.rawMagma
d_rawMagma_1724 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeSemiringWithoutOne_1598 -> T_RawMagma_8
d_rawMagma_1724 :: () -> () -> T_CommutativeSemiringWithoutOne_1598 -> T_RawMagma_8
d_rawMagma_1724 ~()
v0 ~()
v1 T_CommutativeSemiringWithoutOne_1598
v2 = T_CommutativeSemiringWithoutOne_1598 -> T_RawMagma_8
du_rawMagma_1724 T_CommutativeSemiringWithoutOne_1598
v2
du_rawMagma_1724 ::
  T_CommutativeSemiringWithoutOne_1598 -> T_RawMagma_8
du_rawMagma_1724 :: T_CommutativeSemiringWithoutOne_1598 -> T_RawMagma_8
du_rawMagma_1724 T_CommutativeSemiringWithoutOne_1598
v0
  = let v1 :: t
v1 = (T_CommutativeSemiringWithoutOne_1598 -> T_SemiringWithoutOne_1464)
-> AgdaAny -> t
forall a b. a -> b
coe T_CommutativeSemiringWithoutOne_1598 -> T_SemiringWithoutOne_1464
du_semiringWithoutOne_1704 (T_CommutativeSemiringWithoutOne_1598 -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemiringWithoutOne_1598
v0) in
    AgdaAny -> T_RawMagma_8
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_SemiringWithoutOne_1464 -> T_NearSemiring_1354) -> AgdaAny -> t
forall a b. a -> b
coe T_SemiringWithoutOne_1464 -> T_NearSemiring_1354
du_nearSemiring_1562 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: t
v3 = (T_NearSemiring_1354 -> T_Monoid_506) -> AgdaAny -> t
forall a b. a -> b
coe T_NearSemiring_1354 -> T_Monoid_506
du_'43''45'monoid_1438 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: t
v4 = (T_Monoid_506 -> T_Semigroup_206) -> AgdaAny -> t
forall a b. a -> b
coe T_Monoid_506 -> T_Semigroup_206
du_semigroup_566 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_Magma_36 -> T_RawMagma_8) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Magma_36 -> T_RawMagma_8
du_rawMagma_80 ((T_Semigroup_206 -> T_Magma_36) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semigroup_206 -> T_Magma_36
du_magma_254 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v4))))))
-- Algebra.Bundles.CommutativeSemiringWithoutOne._.rawMonoid
d_rawMonoid_1726 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeSemiringWithoutOne_1598 -> T_RawMonoid_474
d_rawMonoid_1726 :: () -> () -> T_CommutativeSemiringWithoutOne_1598 -> T_RawMonoid_474
d_rawMonoid_1726 ~()
v0 ~()
v1 T_CommutativeSemiringWithoutOne_1598
v2 = T_CommutativeSemiringWithoutOne_1598 -> T_RawMonoid_474
du_rawMonoid_1726 T_CommutativeSemiringWithoutOne_1598
v2
du_rawMonoid_1726 ::
  T_CommutativeSemiringWithoutOne_1598 -> T_RawMonoid_474
du_rawMonoid_1726 :: T_CommutativeSemiringWithoutOne_1598 -> T_RawMonoid_474
du_rawMonoid_1726 T_CommutativeSemiringWithoutOne_1598
v0
  = let v1 :: t
v1 = (T_CommutativeSemiringWithoutOne_1598 -> T_SemiringWithoutOne_1464)
-> AgdaAny -> t
forall a b. a -> b
coe T_CommutativeSemiringWithoutOne_1598 -> T_SemiringWithoutOne_1464
du_semiringWithoutOne_1704 (T_CommutativeSemiringWithoutOne_1598 -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemiringWithoutOne_1598
v0) in
    AgdaAny -> T_RawMonoid_474
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_SemiringWithoutOne_1464 -> T_NearSemiring_1354) -> AgdaAny -> t
forall a b. a -> b
coe T_SemiringWithoutOne_1464 -> T_NearSemiring_1354
du_nearSemiring_1562 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_Monoid_506 -> T_RawMonoid_474) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Monoid_506 -> T_RawMonoid_474
du_rawMonoid_576 ((T_NearSemiring_1354 -> T_Monoid_506) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_NearSemiring_1354 -> T_Monoid_506
du_'43''45'monoid_1438 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2))))
-- Algebra.Bundles.CommutativeSemiringWithoutOne._.semigroup
d_semigroup_1728 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeSemiringWithoutOne_1598 -> T_Semigroup_206
d_semigroup_1728 :: () -> () -> T_CommutativeSemiringWithoutOne_1598 -> T_Semigroup_206
d_semigroup_1728 ~()
v0 ~()
v1 T_CommutativeSemiringWithoutOne_1598
v2 = T_CommutativeSemiringWithoutOne_1598 -> T_Semigroup_206
du_semigroup_1728 T_CommutativeSemiringWithoutOne_1598
v2
du_semigroup_1728 ::
  T_CommutativeSemiringWithoutOne_1598 -> T_Semigroup_206
du_semigroup_1728 :: T_CommutativeSemiringWithoutOne_1598 -> T_Semigroup_206
du_semigroup_1728 T_CommutativeSemiringWithoutOne_1598
v0
  = let v1 :: t
v1 = (T_CommutativeSemiringWithoutOne_1598 -> T_SemiringWithoutOne_1464)
-> AgdaAny -> t
forall a b. a -> b
coe T_CommutativeSemiringWithoutOne_1598 -> T_SemiringWithoutOne_1464
du_semiringWithoutOne_1704 (T_CommutativeSemiringWithoutOne_1598 -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemiringWithoutOne_1598
v0) in
    AgdaAny -> T_Semigroup_206
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_SemiringWithoutOne_1464 -> T_NearSemiring_1354) -> AgdaAny -> t
forall a b. a -> b
coe T_SemiringWithoutOne_1464 -> T_NearSemiring_1354
du_nearSemiring_1562 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_Monoid_506 -> T_Semigroup_206) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Monoid_506 -> T_Semigroup_206
du_semigroup_566 ((T_NearSemiring_1354 -> T_Monoid_506) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_NearSemiring_1354 -> T_Monoid_506
du_'43''45'monoid_1438 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2))))
-- Algebra.Bundles.CommutativeSemiringWithoutOne._.nearSemiring
d_nearSemiring_1730 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeSemiringWithoutOne_1598 -> T_NearSemiring_1354
d_nearSemiring_1730 :: ()
-> ()
-> T_CommutativeSemiringWithoutOne_1598
-> T_NearSemiring_1354
d_nearSemiring_1730 ~()
v0 ~()
v1 T_CommutativeSemiringWithoutOne_1598
v2 = T_CommutativeSemiringWithoutOne_1598 -> T_NearSemiring_1354
du_nearSemiring_1730 T_CommutativeSemiringWithoutOne_1598
v2
du_nearSemiring_1730 ::
  T_CommutativeSemiringWithoutOne_1598 -> T_NearSemiring_1354
du_nearSemiring_1730 :: T_CommutativeSemiringWithoutOne_1598 -> T_NearSemiring_1354
du_nearSemiring_1730 T_CommutativeSemiringWithoutOne_1598
v0
  = (T_SemiringWithoutOne_1464 -> T_NearSemiring_1354)
-> AgdaAny -> T_NearSemiring_1354
forall a b. a -> b
coe
      T_SemiringWithoutOne_1464 -> T_NearSemiring_1354
du_nearSemiring_1562 ((T_CommutativeSemiringWithoutOne_1598 -> T_SemiringWithoutOne_1464)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemiringWithoutOne_1598 -> T_SemiringWithoutOne_1464
du_semiringWithoutOne_1704 (T_CommutativeSemiringWithoutOne_1598 -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemiringWithoutOne_1598
v0))
-- Algebra.Bundles.CommutativeSemiringWithoutOne._.rawNearSemiring
d_rawNearSemiring_1732 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeSemiringWithoutOne_1598 -> T_RawNearSemiring_1314
d_rawNearSemiring_1732 :: ()
-> ()
-> T_CommutativeSemiringWithoutOne_1598
-> T_RawNearSemiring_1314
d_rawNearSemiring_1732 ~()
v0 ~()
v1 T_CommutativeSemiringWithoutOne_1598
v2 = T_CommutativeSemiringWithoutOne_1598 -> T_RawNearSemiring_1314
du_rawNearSemiring_1732 T_CommutativeSemiringWithoutOne_1598
v2
du_rawNearSemiring_1732 ::
  T_CommutativeSemiringWithoutOne_1598 -> T_RawNearSemiring_1314
du_rawNearSemiring_1732 :: T_CommutativeSemiringWithoutOne_1598 -> T_RawNearSemiring_1314
du_rawNearSemiring_1732 T_CommutativeSemiringWithoutOne_1598
v0
  = let v1 :: t
v1 = (T_CommutativeSemiringWithoutOne_1598 -> T_SemiringWithoutOne_1464)
-> AgdaAny -> t
forall a b. a -> b
coe T_CommutativeSemiringWithoutOne_1598 -> T_SemiringWithoutOne_1464
du_semiringWithoutOne_1704 (T_CommutativeSemiringWithoutOne_1598 -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemiringWithoutOne_1598
v0) in
    AgdaAny -> T_RawNearSemiring_1314
forall a b. a -> b
coe
      ((T_NearSemiring_1354 -> T_RawNearSemiring_1314)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_NearSemiring_1354 -> T_RawNearSemiring_1314
du_rawNearSemiring_1436 ((T_SemiringWithoutOne_1464 -> T_NearSemiring_1354)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutOne_1464 -> T_NearSemiring_1354
du_nearSemiring_1562 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1)))
-- Algebra.Bundles.RawSemiring
d_RawSemiring_1738 :: p -> p -> ()
d_RawSemiring_1738 p
a0 p
a1 = ()
data T_RawSemiring_1738
  = C_RawSemiring'46'constructor_30035 (AgdaAny ->
                                        AgdaAny -> AgdaAny)
                                       (AgdaAny -> AgdaAny -> AgdaAny) AgdaAny AgdaAny
-- Algebra.Bundles.RawSemiring.Carrier
d_Carrier_1756 :: T_RawSemiring_1738 -> ()
d_Carrier_1756 :: T_RawSemiring_1738 -> ()
d_Carrier_1756 = T_RawSemiring_1738 -> ()
forall a. a
erased
-- Algebra.Bundles.RawSemiring._≈_
d__'8776'__1758 :: T_RawSemiring_1738 -> AgdaAny -> AgdaAny -> ()
d__'8776'__1758 :: T_RawSemiring_1738 -> AgdaAny -> AgdaAny -> ()
d__'8776'__1758 = T_RawSemiring_1738 -> AgdaAny -> AgdaAny -> ()
forall a. a
erased
-- Algebra.Bundles.RawSemiring._+_
d__'43'__1760 ::
  T_RawSemiring_1738 -> AgdaAny -> AgdaAny -> AgdaAny
d__'43'__1760 :: T_RawSemiring_1738 -> AgdaAny -> AgdaAny -> AgdaAny
d__'43'__1760 T_RawSemiring_1738
v0
  = case T_RawSemiring_1738 -> T_RawSemiring_1738
forall a b. a -> b
coe T_RawSemiring_1738
v0 of
      C_RawSemiring'46'constructor_30035 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny
v5 AgdaAny
v6 -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v3
      T_RawSemiring_1738
_ -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.RawSemiring._*_
d__'42'__1762 ::
  T_RawSemiring_1738 -> AgdaAny -> AgdaAny -> AgdaAny
d__'42'__1762 :: T_RawSemiring_1738 -> AgdaAny -> AgdaAny -> AgdaAny
d__'42'__1762 T_RawSemiring_1738
v0
  = case T_RawSemiring_1738 -> T_RawSemiring_1738
forall a b. a -> b
coe T_RawSemiring_1738
v0 of
      C_RawSemiring'46'constructor_30035 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny
v5 AgdaAny
v6 -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v4
      T_RawSemiring_1738
_ -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.RawSemiring.0#
d_0'35'_1764 :: T_RawSemiring_1738 -> AgdaAny
d_0'35'_1764 :: T_RawSemiring_1738 -> AgdaAny
d_0'35'_1764 T_RawSemiring_1738
v0
  = case T_RawSemiring_1738 -> T_RawSemiring_1738
forall a b. a -> b
coe T_RawSemiring_1738
v0 of
      C_RawSemiring'46'constructor_30035 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny
v5 AgdaAny
v6 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v5
      T_RawSemiring_1738
_ -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.RawSemiring.1#
d_1'35'_1766 :: T_RawSemiring_1738 -> AgdaAny
d_1'35'_1766 :: T_RawSemiring_1738 -> AgdaAny
d_1'35'_1766 T_RawSemiring_1738
v0
  = case T_RawSemiring_1738 -> T_RawSemiring_1738
forall a b. a -> b
coe T_RawSemiring_1738
v0 of
      C_RawSemiring'46'constructor_30035 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny
v5 AgdaAny
v6 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v6
      T_RawSemiring_1738
_ -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.RawSemiring.rawNearSemiring
d_rawNearSemiring_1768 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_RawSemiring_1738 -> T_RawNearSemiring_1314
d_rawNearSemiring_1768 :: () -> () -> T_RawSemiring_1738 -> T_RawNearSemiring_1314
d_rawNearSemiring_1768 ~()
v0 ~()
v1 T_RawSemiring_1738
v2 = T_RawSemiring_1738 -> T_RawNearSemiring_1314
du_rawNearSemiring_1768 T_RawSemiring_1738
v2
du_rawNearSemiring_1768 ::
  T_RawSemiring_1738 -> T_RawNearSemiring_1314
du_rawNearSemiring_1768 :: T_RawSemiring_1738 -> T_RawNearSemiring_1314
du_rawNearSemiring_1768 T_RawSemiring_1738
v0
  = ((AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> T_RawNearSemiring_1314)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_RawNearSemiring_1314
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_RawNearSemiring_1314
C_RawNearSemiring'46'constructor_22495 (T_RawSemiring_1738 -> AgdaAny -> AgdaAny -> AgdaAny
d__'43'__1760 (T_RawSemiring_1738 -> T_RawSemiring_1738
forall a b. a -> b
coe T_RawSemiring_1738
v0))
      (T_RawSemiring_1738 -> AgdaAny -> AgdaAny -> AgdaAny
d__'42'__1762 (T_RawSemiring_1738 -> T_RawSemiring_1738
forall a b. a -> b
coe T_RawSemiring_1738
v0)) (T_RawSemiring_1738 -> AgdaAny
d_0'35'_1764 (T_RawSemiring_1738 -> T_RawSemiring_1738
forall a b. a -> b
coe T_RawSemiring_1738
v0))
-- Algebra.Bundles.RawSemiring._._≉_
d__'8777'__1772 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_RawSemiring_1738 -> AgdaAny -> AgdaAny -> ()
d__'8777'__1772 :: () -> () -> T_RawSemiring_1738 -> AgdaAny -> AgdaAny -> ()
d__'8777'__1772 = () -> () -> T_RawSemiring_1738 -> AgdaAny -> AgdaAny -> ()
forall a. a
erased
-- Algebra.Bundles.RawSemiring._.*-rawMagma
d_'42''45'rawMagma_1774 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_RawSemiring_1738 -> T_RawMagma_8
d_'42''45'rawMagma_1774 :: () -> () -> T_RawSemiring_1738 -> T_RawMagma_8
d_'42''45'rawMagma_1774 ~()
v0 ~()
v1 T_RawSemiring_1738
v2 = T_RawSemiring_1738 -> T_RawMagma_8
du_'42''45'rawMagma_1774 T_RawSemiring_1738
v2
du_'42''45'rawMagma_1774 :: T_RawSemiring_1738 -> T_RawMagma_8
du_'42''45'rawMagma_1774 :: T_RawSemiring_1738 -> T_RawMagma_8
du_'42''45'rawMagma_1774 T_RawSemiring_1738
v0
  = (T_RawNearSemiring_1314 -> T_RawMagma_8) -> AgdaAny -> T_RawMagma_8
forall a b. a -> b
coe
      T_RawNearSemiring_1314 -> T_RawMagma_8
du_'42''45'rawMagma_1348 ((T_RawSemiring_1738 -> T_RawNearSemiring_1314)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_RawSemiring_1738 -> T_RawNearSemiring_1314
du_rawNearSemiring_1768 (T_RawSemiring_1738 -> AgdaAny
forall a b. a -> b
coe T_RawSemiring_1738
v0))
-- Algebra.Bundles.RawSemiring._.rawMagma
d_rawMagma_1776 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_RawSemiring_1738 -> T_RawMagma_8
d_rawMagma_1776 :: () -> () -> T_RawSemiring_1738 -> T_RawMagma_8
d_rawMagma_1776 ~()
v0 ~()
v1 T_RawSemiring_1738
v2 = T_RawSemiring_1738 -> T_RawMagma_8
du_rawMagma_1776 T_RawSemiring_1738
v2
du_rawMagma_1776 :: T_RawSemiring_1738 -> T_RawMagma_8
du_rawMagma_1776 :: T_RawSemiring_1738 -> T_RawMagma_8
du_rawMagma_1776 T_RawSemiring_1738
v0
  = let v1 :: t
v1 = (T_RawSemiring_1738 -> T_RawNearSemiring_1314) -> AgdaAny -> t
forall a b. a -> b
coe T_RawSemiring_1738 -> T_RawNearSemiring_1314
du_rawNearSemiring_1768 (T_RawSemiring_1738 -> AgdaAny
forall a b. a -> b
coe T_RawSemiring_1738
v0) in
    AgdaAny -> T_RawMagma_8
forall a b. a -> b
coe ((T_RawMonoid_474 -> T_RawMagma_8) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_RawMonoid_474 -> T_RawMagma_8
du_rawMagma_496 ((T_RawNearSemiring_1314 -> T_RawMonoid_474) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_RawNearSemiring_1314 -> T_RawMonoid_474
du_'43''45'rawMonoid_1340 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1)))
-- Algebra.Bundles.RawSemiring._.+-rawMonoid
d_'43''45'rawMonoid_1778 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_RawSemiring_1738 -> T_RawMonoid_474
d_'43''45'rawMonoid_1778 :: () -> () -> T_RawSemiring_1738 -> T_RawMonoid_474
d_'43''45'rawMonoid_1778 ~()
v0 ~()
v1 T_RawSemiring_1738
v2 = T_RawSemiring_1738 -> T_RawMonoid_474
du_'43''45'rawMonoid_1778 T_RawSemiring_1738
v2
du_'43''45'rawMonoid_1778 :: T_RawSemiring_1738 -> T_RawMonoid_474
du_'43''45'rawMonoid_1778 :: T_RawSemiring_1738 -> T_RawMonoid_474
du_'43''45'rawMonoid_1778 T_RawSemiring_1738
v0
  = (T_RawNearSemiring_1314 -> T_RawMonoid_474)
-> AgdaAny -> T_RawMonoid_474
forall a b. a -> b
coe
      T_RawNearSemiring_1314 -> T_RawMonoid_474
du_'43''45'rawMonoid_1340 ((T_RawSemiring_1738 -> T_RawNearSemiring_1314)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_RawSemiring_1738 -> T_RawNearSemiring_1314
du_rawNearSemiring_1768 (T_RawSemiring_1738 -> AgdaAny
forall a b. a -> b
coe T_RawSemiring_1738
v0))
-- Algebra.Bundles.RawSemiring.*-rawMonoid
d_'42''45'rawMonoid_1780 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_RawSemiring_1738 -> T_RawMonoid_474
d_'42''45'rawMonoid_1780 :: () -> () -> T_RawSemiring_1738 -> T_RawMonoid_474
d_'42''45'rawMonoid_1780 ~()
v0 ~()
v1 T_RawSemiring_1738
v2 = T_RawSemiring_1738 -> T_RawMonoid_474
du_'42''45'rawMonoid_1780 T_RawSemiring_1738
v2
du_'42''45'rawMonoid_1780 :: T_RawSemiring_1738 -> T_RawMonoid_474
du_'42''45'rawMonoid_1780 :: T_RawSemiring_1738 -> T_RawMonoid_474
du_'42''45'rawMonoid_1780 T_RawSemiring_1738
v0
  = ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> T_RawMonoid_474)
-> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> T_RawMonoid_474
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> T_RawMonoid_474
C_RawMonoid'46'constructor_8313 (T_RawSemiring_1738 -> AgdaAny -> AgdaAny -> AgdaAny
d__'42'__1762 (T_RawSemiring_1738 -> T_RawSemiring_1738
forall a b. a -> b
coe T_RawSemiring_1738
v0))
      (T_RawSemiring_1738 -> AgdaAny
d_1'35'_1766 (T_RawSemiring_1738 -> T_RawSemiring_1738
forall a b. a -> b
coe T_RawSemiring_1738
v0))
-- Algebra.Bundles.SemiringWithoutAnnihilatingZero
d_SemiringWithoutAnnihilatingZero_1786 :: p -> p -> ()
d_SemiringWithoutAnnihilatingZero_1786 p
a0 p
a1 = ()
data T_SemiringWithoutAnnihilatingZero_1786
  = C_SemiringWithoutAnnihilatingZero'46'constructor_30907 (AgdaAny ->
                                                            AgdaAny -> AgdaAny)
                                                           (AgdaAny -> AgdaAny -> AgdaAny) AgdaAny
                                                           AgdaAny
                                                           MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutAnnihilatingZero_1142
-- Algebra.Bundles.SemiringWithoutAnnihilatingZero.Carrier
d_Carrier_1806 :: T_SemiringWithoutAnnihilatingZero_1786 -> ()
d_Carrier_1806 :: T_SemiringWithoutAnnihilatingZero_1786 -> ()
d_Carrier_1806 = T_SemiringWithoutAnnihilatingZero_1786 -> ()
forall a. a
erased
-- Algebra.Bundles.SemiringWithoutAnnihilatingZero._≈_
d__'8776'__1808 ::
  T_SemiringWithoutAnnihilatingZero_1786 -> AgdaAny -> AgdaAny -> ()
d__'8776'__1808 :: T_SemiringWithoutAnnihilatingZero_1786 -> AgdaAny -> AgdaAny -> ()
d__'8776'__1808 = T_SemiringWithoutAnnihilatingZero_1786 -> AgdaAny -> AgdaAny -> ()
forall a. a
erased
-- Algebra.Bundles.SemiringWithoutAnnihilatingZero._+_
d__'43'__1810 ::
  T_SemiringWithoutAnnihilatingZero_1786 ->
  AgdaAny -> AgdaAny -> AgdaAny
d__'43'__1810 :: T_SemiringWithoutAnnihilatingZero_1786
-> AgdaAny -> AgdaAny -> AgdaAny
d__'43'__1810 T_SemiringWithoutAnnihilatingZero_1786
v0
  = case T_SemiringWithoutAnnihilatingZero_1786
-> T_SemiringWithoutAnnihilatingZero_1786
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_1786
v0 of
      C_SemiringWithoutAnnihilatingZero'46'constructor_30907 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny
v5 AgdaAny
v6 T_IsSemiringWithoutAnnihilatingZero_1142
v7
        -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v3
      T_SemiringWithoutAnnihilatingZero_1786
_ -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.SemiringWithoutAnnihilatingZero._*_
d__'42'__1812 ::
  T_SemiringWithoutAnnihilatingZero_1786 ->
  AgdaAny -> AgdaAny -> AgdaAny
d__'42'__1812 :: T_SemiringWithoutAnnihilatingZero_1786
-> AgdaAny -> AgdaAny -> AgdaAny
d__'42'__1812 T_SemiringWithoutAnnihilatingZero_1786
v0
  = case T_SemiringWithoutAnnihilatingZero_1786
-> T_SemiringWithoutAnnihilatingZero_1786
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_1786
v0 of
      C_SemiringWithoutAnnihilatingZero'46'constructor_30907 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny
v5 AgdaAny
v6 T_IsSemiringWithoutAnnihilatingZero_1142
v7
        -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v4
      T_SemiringWithoutAnnihilatingZero_1786
_ -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.SemiringWithoutAnnihilatingZero.0#
d_0'35'_1814 :: T_SemiringWithoutAnnihilatingZero_1786 -> AgdaAny
d_0'35'_1814 :: T_SemiringWithoutAnnihilatingZero_1786 -> AgdaAny
d_0'35'_1814 T_SemiringWithoutAnnihilatingZero_1786
v0
  = case T_SemiringWithoutAnnihilatingZero_1786
-> T_SemiringWithoutAnnihilatingZero_1786
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_1786
v0 of
      C_SemiringWithoutAnnihilatingZero'46'constructor_30907 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny
v5 AgdaAny
v6 T_IsSemiringWithoutAnnihilatingZero_1142
v7
        -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v5
      T_SemiringWithoutAnnihilatingZero_1786
_ -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.SemiringWithoutAnnihilatingZero.1#
d_1'35'_1816 :: T_SemiringWithoutAnnihilatingZero_1786 -> AgdaAny
d_1'35'_1816 :: T_SemiringWithoutAnnihilatingZero_1786 -> AgdaAny
d_1'35'_1816 T_SemiringWithoutAnnihilatingZero_1786
v0
  = case T_SemiringWithoutAnnihilatingZero_1786
-> T_SemiringWithoutAnnihilatingZero_1786
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_1786
v0 of
      C_SemiringWithoutAnnihilatingZero'46'constructor_30907 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny
v5 AgdaAny
v6 T_IsSemiringWithoutAnnihilatingZero_1142
v7
        -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v6
      T_SemiringWithoutAnnihilatingZero_1786
_ -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.SemiringWithoutAnnihilatingZero.isSemiringWithoutAnnihilatingZero
d_isSemiringWithoutAnnihilatingZero_1818 ::
  T_SemiringWithoutAnnihilatingZero_1786 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutAnnihilatingZero_1142
d_isSemiringWithoutAnnihilatingZero_1818 :: T_SemiringWithoutAnnihilatingZero_1786
-> T_IsSemiringWithoutAnnihilatingZero_1142
d_isSemiringWithoutAnnihilatingZero_1818 T_SemiringWithoutAnnihilatingZero_1786
v0
  = case T_SemiringWithoutAnnihilatingZero_1786
-> T_SemiringWithoutAnnihilatingZero_1786
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_1786
v0 of
      C_SemiringWithoutAnnihilatingZero'46'constructor_30907 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny
v5 AgdaAny
v6 T_IsSemiringWithoutAnnihilatingZero_1142
v7
        -> T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsSemiringWithoutAnnihilatingZero_1142
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1142
v7
      T_SemiringWithoutAnnihilatingZero_1786
_ -> T_IsSemiringWithoutAnnihilatingZero_1142
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.SemiringWithoutAnnihilatingZero._.assoc
d_assoc_1822 ::
  T_SemiringWithoutAnnihilatingZero_1786 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_1822 :: T_SemiringWithoutAnnihilatingZero_1786
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_1822 T_SemiringWithoutAnnihilatingZero_1786
v0
  = (T_IsSemigroup_194 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsSemigroup_194 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_assoc_204
      ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368
         ((T_IsSemiringWithoutAnnihilatingZero_1142 -> T_IsMonoid_358)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemiringWithoutAnnihilatingZero_1142 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_'42''45'isMonoid_1160
            ((T_SemiringWithoutAnnihilatingZero_1786
 -> T_IsSemiringWithoutAnnihilatingZero_1142)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_1786
-> T_IsSemiringWithoutAnnihilatingZero_1142
d_isSemiringWithoutAnnihilatingZero_1818 (T_SemiringWithoutAnnihilatingZero_1786 -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_1786
v0))))
-- Algebra.Bundles.SemiringWithoutAnnihilatingZero._.∙-cong
d_'8729''45'cong_1824 ::
  T_SemiringWithoutAnnihilatingZero_1786 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_1824 :: T_SemiringWithoutAnnihilatingZero_1786
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_1824 T_SemiringWithoutAnnihilatingZero_1786
v0
  = (T_IsMagma_86
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsMagma_86
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_96
      ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202
         ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368
            ((T_IsSemiringWithoutAnnihilatingZero_1142 -> T_IsMonoid_358)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemiringWithoutAnnihilatingZero_1142 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_'42''45'isMonoid_1160
               ((T_SemiringWithoutAnnihilatingZero_1786
 -> T_IsSemiringWithoutAnnihilatingZero_1142)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_1786
-> T_IsSemiringWithoutAnnihilatingZero_1142
d_isSemiringWithoutAnnihilatingZero_1818 (T_SemiringWithoutAnnihilatingZero_1786 -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_1786
v0)))))
-- Algebra.Bundles.SemiringWithoutAnnihilatingZero._.∙-congʳ
d_'8729''45'cong'691'_1826 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SemiringWithoutAnnihilatingZero_1786 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_1826 :: ()
-> ()
-> T_SemiringWithoutAnnihilatingZero_1786
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_1826 ~()
v0 ~()
v1 T_SemiringWithoutAnnihilatingZero_1786
v2
  = T_SemiringWithoutAnnihilatingZero_1786
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1826 T_SemiringWithoutAnnihilatingZero_1786
v2
du_'8729''45'cong'691'_1826 ::
  T_SemiringWithoutAnnihilatingZero_1786 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1826 :: T_SemiringWithoutAnnihilatingZero_1786
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1826 T_SemiringWithoutAnnihilatingZero_1786
v0
  = let v1 :: T_IsSemiringWithoutAnnihilatingZero_1142
v1 = T_SemiringWithoutAnnihilatingZero_1786
-> T_IsSemiringWithoutAnnihilatingZero_1142
d_isSemiringWithoutAnnihilatingZero_1818 (T_SemiringWithoutAnnihilatingZero_1786
-> T_SemiringWithoutAnnihilatingZero_1786
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_1786
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsMonoid_358
v2
             = T_IsSemiringWithoutAnnihilatingZero_1142 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_'42''45'isMonoid_1160
                 (T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsSemiringWithoutAnnihilatingZero_1142
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1142
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_194
v3
                = T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368 (T_IsMonoid_358 -> T_IsMonoid_358
forall a b. a -> b
coe T_IsMonoid_358
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsMagma_86
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMagma_86 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'691'_116
               ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202 (T_IsSemigroup_194 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194
v3)))))
-- Algebra.Bundles.SemiringWithoutAnnihilatingZero._.∙-congˡ
d_'8729''45'cong'737'_1828 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SemiringWithoutAnnihilatingZero_1786 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_1828 :: ()
-> ()
-> T_SemiringWithoutAnnihilatingZero_1786
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_1828 ~()
v0 ~()
v1 T_SemiringWithoutAnnihilatingZero_1786
v2
  = T_SemiringWithoutAnnihilatingZero_1786
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1828 T_SemiringWithoutAnnihilatingZero_1786
v2
du_'8729''45'cong'737'_1828 ::
  T_SemiringWithoutAnnihilatingZero_1786 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1828 :: T_SemiringWithoutAnnihilatingZero_1786
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1828 T_SemiringWithoutAnnihilatingZero_1786
v0
  = let v1 :: T_IsSemiringWithoutAnnihilatingZero_1142
v1 = T_SemiringWithoutAnnihilatingZero_1786
-> T_IsSemiringWithoutAnnihilatingZero_1142
d_isSemiringWithoutAnnihilatingZero_1818 (T_SemiringWithoutAnnihilatingZero_1786
-> T_SemiringWithoutAnnihilatingZero_1786
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_1786
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsMonoid_358
v2
             = T_IsSemiringWithoutAnnihilatingZero_1142 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_'42''45'isMonoid_1160
                 (T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsSemiringWithoutAnnihilatingZero_1142
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1142
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_194
v3
                = T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368 (T_IsMonoid_358 -> T_IsMonoid_358
forall a b. a -> b
coe T_IsMonoid_358
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsMagma_86
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMagma_86 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'737'_112
               ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202 (T_IsSemigroup_194 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194
v3)))))
-- Algebra.Bundles.SemiringWithoutAnnihilatingZero._.identity
d_identity_1830 ::
  T_SemiringWithoutAnnihilatingZero_1786 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_identity_1830 :: T_SemiringWithoutAnnihilatingZero_1786 -> T_Σ_14
d_identity_1830 T_SemiringWithoutAnnihilatingZero_1786
v0
  = (T_IsMonoid_358 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsMonoid_358 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_identity_370
      ((T_IsSemiringWithoutAnnihilatingZero_1142 -> T_IsMonoid_358)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiringWithoutAnnihilatingZero_1142 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_'42''45'isMonoid_1160
         ((T_SemiringWithoutAnnihilatingZero_1786
 -> T_IsSemiringWithoutAnnihilatingZero_1142)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_1786
-> T_IsSemiringWithoutAnnihilatingZero_1142
d_isSemiringWithoutAnnihilatingZero_1818 (T_SemiringWithoutAnnihilatingZero_1786 -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_1786
v0)))
-- Algebra.Bundles.SemiringWithoutAnnihilatingZero._.identityʳ
d_identity'691'_1832 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SemiringWithoutAnnihilatingZero_1786 -> AgdaAny -> AgdaAny
d_identity'691'_1832 :: ()
-> ()
-> T_SemiringWithoutAnnihilatingZero_1786
-> AgdaAny
-> AgdaAny
d_identity'691'_1832 ~()
v0 ~()
v1 T_SemiringWithoutAnnihilatingZero_1786
v2 = T_SemiringWithoutAnnihilatingZero_1786 -> AgdaAny -> AgdaAny
du_identity'691'_1832 T_SemiringWithoutAnnihilatingZero_1786
v2
du_identity'691'_1832 ::
  T_SemiringWithoutAnnihilatingZero_1786 -> AgdaAny -> AgdaAny
du_identity'691'_1832 :: T_SemiringWithoutAnnihilatingZero_1786 -> AgdaAny -> AgdaAny
du_identity'691'_1832 T_SemiringWithoutAnnihilatingZero_1786
v0
  = let v1 :: T_IsSemiringWithoutAnnihilatingZero_1142
v1 = T_SemiringWithoutAnnihilatingZero_1786
-> T_IsSemiringWithoutAnnihilatingZero_1142
d_isSemiringWithoutAnnihilatingZero_1818 (T_SemiringWithoutAnnihilatingZero_1786
-> T_SemiringWithoutAnnihilatingZero_1786
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_1786
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsMonoid_358 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoid_358 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_identity'691'_400
         ((T_IsSemiringWithoutAnnihilatingZero_1142 -> T_IsMonoid_358)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemiringWithoutAnnihilatingZero_1142 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_'42''45'isMonoid_1160 (T_IsSemiringWithoutAnnihilatingZero_1142 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1142
v1)))
-- Algebra.Bundles.SemiringWithoutAnnihilatingZero._.identityˡ
d_identity'737'_1834 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SemiringWithoutAnnihilatingZero_1786 -> AgdaAny -> AgdaAny
d_identity'737'_1834 :: ()
-> ()
-> T_SemiringWithoutAnnihilatingZero_1786
-> AgdaAny
-> AgdaAny
d_identity'737'_1834 ~()
v0 ~()
v1 T_SemiringWithoutAnnihilatingZero_1786
v2 = T_SemiringWithoutAnnihilatingZero_1786 -> AgdaAny -> AgdaAny
du_identity'737'_1834 T_SemiringWithoutAnnihilatingZero_1786
v2
du_identity'737'_1834 ::
  T_SemiringWithoutAnnihilatingZero_1786 -> AgdaAny -> AgdaAny
du_identity'737'_1834 :: T_SemiringWithoutAnnihilatingZero_1786 -> AgdaAny -> AgdaAny
du_identity'737'_1834 T_SemiringWithoutAnnihilatingZero_1786
v0
  = let v1 :: T_IsSemiringWithoutAnnihilatingZero_1142
v1 = T_SemiringWithoutAnnihilatingZero_1786
-> T_IsSemiringWithoutAnnihilatingZero_1142
d_isSemiringWithoutAnnihilatingZero_1818 (T_SemiringWithoutAnnihilatingZero_1786
-> T_SemiringWithoutAnnihilatingZero_1786
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_1786
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsMonoid_358 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoid_358 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_identity'737'_398
         ((T_IsSemiringWithoutAnnihilatingZero_1142 -> T_IsMonoid_358)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemiringWithoutAnnihilatingZero_1142 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_'42''45'isMonoid_1160 (T_IsSemiringWithoutAnnihilatingZero_1142 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1142
v1)))
-- Algebra.Bundles.SemiringWithoutAnnihilatingZero._.isMagma
d_isMagma_1836 ::
  T_SemiringWithoutAnnihilatingZero_1786 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_86
d_isMagma_1836 :: T_SemiringWithoutAnnihilatingZero_1786 -> T_IsMagma_86
d_isMagma_1836 T_SemiringWithoutAnnihilatingZero_1786
v0
  = (T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> T_IsMagma_86
forall a b. a -> b
coe
      T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202
      ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368
         ((T_IsSemiringWithoutAnnihilatingZero_1142 -> T_IsMonoid_358)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemiringWithoutAnnihilatingZero_1142 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_'42''45'isMonoid_1160
            ((T_SemiringWithoutAnnihilatingZero_1786
 -> T_IsSemiringWithoutAnnihilatingZero_1142)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_1786
-> T_IsSemiringWithoutAnnihilatingZero_1142
d_isSemiringWithoutAnnihilatingZero_1818 (T_SemiringWithoutAnnihilatingZero_1786 -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_1786
v0))))
-- Algebra.Bundles.SemiringWithoutAnnihilatingZero._.*-isMonoid
d_'42''45'isMonoid_1838 ::
  T_SemiringWithoutAnnihilatingZero_1786 ->
  MAlonzo.Code.Algebra.Structures.T_IsMonoid_358
d_'42''45'isMonoid_1838 :: T_SemiringWithoutAnnihilatingZero_1786 -> T_IsMonoid_358
d_'42''45'isMonoid_1838 T_SemiringWithoutAnnihilatingZero_1786
v0
  = (T_IsSemiringWithoutAnnihilatingZero_1142 -> T_IsMonoid_358)
-> AgdaAny -> T_IsMonoid_358
forall a b. a -> b
coe
      T_IsSemiringWithoutAnnihilatingZero_1142 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_'42''45'isMonoid_1160
      ((T_SemiringWithoutAnnihilatingZero_1786
 -> T_IsSemiringWithoutAnnihilatingZero_1142)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_1786
-> T_IsSemiringWithoutAnnihilatingZero_1142
d_isSemiringWithoutAnnihilatingZero_1818 (T_SemiringWithoutAnnihilatingZero_1786 -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_1786
v0))
-- Algebra.Bundles.SemiringWithoutAnnihilatingZero._.isSemigroup
d_isSemigroup_1840 ::
  T_SemiringWithoutAnnihilatingZero_1786 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_194
d_isSemigroup_1840 :: T_SemiringWithoutAnnihilatingZero_1786 -> T_IsSemigroup_194
d_isSemigroup_1840 T_SemiringWithoutAnnihilatingZero_1786
v0
  = (T_IsMonoid_358 -> T_IsSemigroup_194)
-> AgdaAny -> T_IsSemigroup_194
forall a b. a -> b
coe
      T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368
      ((T_IsSemiringWithoutAnnihilatingZero_1142 -> T_IsMonoid_358)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiringWithoutAnnihilatingZero_1142 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_'42''45'isMonoid_1160
         ((T_SemiringWithoutAnnihilatingZero_1786
 -> T_IsSemiringWithoutAnnihilatingZero_1142)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_1786
-> T_IsSemiringWithoutAnnihilatingZero_1142
d_isSemiringWithoutAnnihilatingZero_1818 (T_SemiringWithoutAnnihilatingZero_1786 -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_1786
v0)))
-- Algebra.Bundles.SemiringWithoutAnnihilatingZero._.assoc
d_assoc_1842 ::
  T_SemiringWithoutAnnihilatingZero_1786 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_1842 :: T_SemiringWithoutAnnihilatingZero_1786
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_1842 T_SemiringWithoutAnnihilatingZero_1786
v0
  = (T_IsSemigroup_194 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsSemigroup_194 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_assoc_204
      ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368
         ((T_IsCommutativeMonoid_406 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCommutativeMonoid_406 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_416
            ((T_IsSemiringWithoutAnnihilatingZero_1142
 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsCommutativeMonoid_406
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1158
               ((T_SemiringWithoutAnnihilatingZero_1786
 -> T_IsSemiringWithoutAnnihilatingZero_1142)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_1786
-> T_IsSemiringWithoutAnnihilatingZero_1142
d_isSemiringWithoutAnnihilatingZero_1818 (T_SemiringWithoutAnnihilatingZero_1786 -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_1786
v0)))))
-- Algebra.Bundles.SemiringWithoutAnnihilatingZero._.comm
d_comm_1844 ::
  T_SemiringWithoutAnnihilatingZero_1786 ->
  AgdaAny -> AgdaAny -> AgdaAny
d_comm_1844 :: T_SemiringWithoutAnnihilatingZero_1786
-> AgdaAny -> AgdaAny -> AgdaAny
d_comm_1844 T_SemiringWithoutAnnihilatingZero_1786
v0
  = (T_IsCommutativeMonoid_406 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsCommutativeMonoid_406 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_comm_418
      ((T_IsSemiringWithoutAnnihilatingZero_1142
 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsCommutativeMonoid_406
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1158
         ((T_SemiringWithoutAnnihilatingZero_1786
 -> T_IsSemiringWithoutAnnihilatingZero_1142)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_1786
-> T_IsSemiringWithoutAnnihilatingZero_1142
d_isSemiringWithoutAnnihilatingZero_1818 (T_SemiringWithoutAnnihilatingZero_1786 -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_1786
v0)))
-- Algebra.Bundles.SemiringWithoutAnnihilatingZero._.∙-cong
d_'8729''45'cong_1846 ::
  T_SemiringWithoutAnnihilatingZero_1786 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_1846 :: T_SemiringWithoutAnnihilatingZero_1786
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_1846 T_SemiringWithoutAnnihilatingZero_1786
v0
  = (T_IsMagma_86
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsMagma_86
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_96
      ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202
         ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368
            ((T_IsCommutativeMonoid_406 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsCommutativeMonoid_406 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_416
               ((T_IsSemiringWithoutAnnihilatingZero_1142
 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsCommutativeMonoid_406
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1158
                  ((T_SemiringWithoutAnnihilatingZero_1786
 -> T_IsSemiringWithoutAnnihilatingZero_1142)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_1786
-> T_IsSemiringWithoutAnnihilatingZero_1142
d_isSemiringWithoutAnnihilatingZero_1818 (T_SemiringWithoutAnnihilatingZero_1786 -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_1786
v0))))))
-- Algebra.Bundles.SemiringWithoutAnnihilatingZero._.∙-congʳ
d_'8729''45'cong'691'_1848 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SemiringWithoutAnnihilatingZero_1786 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_1848 :: ()
-> ()
-> T_SemiringWithoutAnnihilatingZero_1786
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_1848 ~()
v0 ~()
v1 T_SemiringWithoutAnnihilatingZero_1786
v2
  = T_SemiringWithoutAnnihilatingZero_1786
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1848 T_SemiringWithoutAnnihilatingZero_1786
v2
du_'8729''45'cong'691'_1848 ::
  T_SemiringWithoutAnnihilatingZero_1786 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1848 :: T_SemiringWithoutAnnihilatingZero_1786
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1848 T_SemiringWithoutAnnihilatingZero_1786
v0
  = let v1 :: T_IsSemiringWithoutAnnihilatingZero_1142
v1 = T_SemiringWithoutAnnihilatingZero_1786
-> T_IsSemiringWithoutAnnihilatingZero_1142
d_isSemiringWithoutAnnihilatingZero_1818 (T_SemiringWithoutAnnihilatingZero_1786
-> T_SemiringWithoutAnnihilatingZero_1786
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_1786
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsCommutativeMonoid_406
v2
             = T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsCommutativeMonoid_406
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1158
                 (T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsSemiringWithoutAnnihilatingZero_1142
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1142
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsMonoid_358
v3
                = T_IsCommutativeMonoid_406 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_416 (T_IsCommutativeMonoid_406 -> T_IsCommutativeMonoid_406
forall a b. a -> b
coe T_IsCommutativeMonoid_406
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsSemigroup_194
v4
                   = T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368 (T_IsMonoid_358 -> T_IsMonoid_358
forall a b. a -> b
coe T_IsMonoid_358
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               ((T_IsMagma_86
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsMagma_86 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'691'_116
                  ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202 (T_IsSemigroup_194 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194
v4))))))
-- Algebra.Bundles.SemiringWithoutAnnihilatingZero._.∙-congˡ
d_'8729''45'cong'737'_1850 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SemiringWithoutAnnihilatingZero_1786 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_1850 :: ()
-> ()
-> T_SemiringWithoutAnnihilatingZero_1786
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_1850 ~()
v0 ~()
v1 T_SemiringWithoutAnnihilatingZero_1786
v2
  = T_SemiringWithoutAnnihilatingZero_1786
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1850 T_SemiringWithoutAnnihilatingZero_1786
v2
du_'8729''45'cong'737'_1850 ::
  T_SemiringWithoutAnnihilatingZero_1786 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1850 :: T_SemiringWithoutAnnihilatingZero_1786
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1850 T_SemiringWithoutAnnihilatingZero_1786
v0
  = let v1 :: T_IsSemiringWithoutAnnihilatingZero_1142
v1 = T_SemiringWithoutAnnihilatingZero_1786
-> T_IsSemiringWithoutAnnihilatingZero_1142
d_isSemiringWithoutAnnihilatingZero_1818 (T_SemiringWithoutAnnihilatingZero_1786
-> T_SemiringWithoutAnnihilatingZero_1786
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_1786
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsCommutativeMonoid_406
v2
             = T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsCommutativeMonoid_406
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1158
                 (T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsSemiringWithoutAnnihilatingZero_1142
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1142
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsMonoid_358
v3
                = T_IsCommutativeMonoid_406 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_416 (T_IsCommutativeMonoid_406 -> T_IsCommutativeMonoid_406
forall a b. a -> b
coe T_IsCommutativeMonoid_406
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsSemigroup_194
v4
                   = T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368 (T_IsMonoid_358 -> T_IsMonoid_358
forall a b. a -> b
coe T_IsMonoid_358
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               ((T_IsMagma_86
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsMagma_86 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'737'_112
                  ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202 (T_IsSemigroup_194 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194
v4))))))
-- Algebra.Bundles.SemiringWithoutAnnihilatingZero._.identity
d_identity_1852 ::
  T_SemiringWithoutAnnihilatingZero_1786 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_identity_1852 :: T_SemiringWithoutAnnihilatingZero_1786 -> T_Σ_14
d_identity_1852 T_SemiringWithoutAnnihilatingZero_1786
v0
  = (T_IsMonoid_358 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsMonoid_358 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_identity_370
      ((T_IsCommutativeMonoid_406 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCommutativeMonoid_406 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_416
         ((T_IsSemiringWithoutAnnihilatingZero_1142
 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsCommutativeMonoid_406
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1158
            ((T_SemiringWithoutAnnihilatingZero_1786
 -> T_IsSemiringWithoutAnnihilatingZero_1142)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_1786
-> T_IsSemiringWithoutAnnihilatingZero_1142
d_isSemiringWithoutAnnihilatingZero_1818 (T_SemiringWithoutAnnihilatingZero_1786 -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_1786
v0))))
-- Algebra.Bundles.SemiringWithoutAnnihilatingZero._.identityʳ
d_identity'691'_1854 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SemiringWithoutAnnihilatingZero_1786 -> AgdaAny -> AgdaAny
d_identity'691'_1854 :: ()
-> ()
-> T_SemiringWithoutAnnihilatingZero_1786
-> AgdaAny
-> AgdaAny
d_identity'691'_1854 ~()
v0 ~()
v1 T_SemiringWithoutAnnihilatingZero_1786
v2 = T_SemiringWithoutAnnihilatingZero_1786 -> AgdaAny -> AgdaAny
du_identity'691'_1854 T_SemiringWithoutAnnihilatingZero_1786
v2
du_identity'691'_1854 ::
  T_SemiringWithoutAnnihilatingZero_1786 -> AgdaAny -> AgdaAny
du_identity'691'_1854 :: T_SemiringWithoutAnnihilatingZero_1786 -> AgdaAny -> AgdaAny
du_identity'691'_1854 T_SemiringWithoutAnnihilatingZero_1786
v0
  = let v1 :: T_IsSemiringWithoutAnnihilatingZero_1142
v1 = T_SemiringWithoutAnnihilatingZero_1786
-> T_IsSemiringWithoutAnnihilatingZero_1142
d_isSemiringWithoutAnnihilatingZero_1818 (T_SemiringWithoutAnnihilatingZero_1786
-> T_SemiringWithoutAnnihilatingZero_1786
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_1786
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsCommutativeMonoid_406
v2
             = T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsCommutativeMonoid_406
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1158
                 (T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsSemiringWithoutAnnihilatingZero_1142
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1142
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsMonoid_358 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoid_358 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_identity'691'_400
            ((T_IsCommutativeMonoid_406 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_406 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_416 (T_IsCommutativeMonoid_406 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_406
v2))))
-- Algebra.Bundles.SemiringWithoutAnnihilatingZero._.identityˡ
d_identity'737'_1856 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SemiringWithoutAnnihilatingZero_1786 -> AgdaAny -> AgdaAny
d_identity'737'_1856 :: ()
-> ()
-> T_SemiringWithoutAnnihilatingZero_1786
-> AgdaAny
-> AgdaAny
d_identity'737'_1856 ~()
v0 ~()
v1 T_SemiringWithoutAnnihilatingZero_1786
v2 = T_SemiringWithoutAnnihilatingZero_1786 -> AgdaAny -> AgdaAny
du_identity'737'_1856 T_SemiringWithoutAnnihilatingZero_1786
v2
du_identity'737'_1856 ::
  T_SemiringWithoutAnnihilatingZero_1786 -> AgdaAny -> AgdaAny
du_identity'737'_1856 :: T_SemiringWithoutAnnihilatingZero_1786 -> AgdaAny -> AgdaAny
du_identity'737'_1856 T_SemiringWithoutAnnihilatingZero_1786
v0
  = let v1 :: T_IsSemiringWithoutAnnihilatingZero_1142
v1 = T_SemiringWithoutAnnihilatingZero_1786
-> T_IsSemiringWithoutAnnihilatingZero_1142
d_isSemiringWithoutAnnihilatingZero_1818 (T_SemiringWithoutAnnihilatingZero_1786
-> T_SemiringWithoutAnnihilatingZero_1786
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_1786
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsCommutativeMonoid_406
v2
             = T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsCommutativeMonoid_406
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1158
                 (T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsSemiringWithoutAnnihilatingZero_1142
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1142
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsMonoid_358 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoid_358 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_identity'737'_398
            ((T_IsCommutativeMonoid_406 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_406 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_416 (T_IsCommutativeMonoid_406 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_406
v2))))
-- Algebra.Bundles.SemiringWithoutAnnihilatingZero._.isCommutativeMagma
d_isCommutativeMagma_1858 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SemiringWithoutAnnihilatingZero_1786 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMagma_122
d_isCommutativeMagma_1858 :: ()
-> ()
-> T_SemiringWithoutAnnihilatingZero_1786
-> T_IsCommutativeMagma_122
d_isCommutativeMagma_1858 ~()
v0 ~()
v1 T_SemiringWithoutAnnihilatingZero_1786
v2
  = T_SemiringWithoutAnnihilatingZero_1786 -> T_IsCommutativeMagma_122
du_isCommutativeMagma_1858 T_SemiringWithoutAnnihilatingZero_1786
v2
du_isCommutativeMagma_1858 ::
  T_SemiringWithoutAnnihilatingZero_1786 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMagma_122
du_isCommutativeMagma_1858 :: T_SemiringWithoutAnnihilatingZero_1786 -> T_IsCommutativeMagma_122
du_isCommutativeMagma_1858 T_SemiringWithoutAnnihilatingZero_1786
v0
  = let v1 :: T_IsSemiringWithoutAnnihilatingZero_1142
v1 = T_SemiringWithoutAnnihilatingZero_1786
-> T_IsSemiringWithoutAnnihilatingZero_1142
d_isSemiringWithoutAnnihilatingZero_1818 (T_SemiringWithoutAnnihilatingZero_1786
-> T_SemiringWithoutAnnihilatingZero_1786
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_1786
v0) in
    AgdaAny -> T_IsCommutativeMagma_122
forall a b. a -> b
coe
      (let v2 :: T_IsCommutativeMonoid_406
v2
             = T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsCommutativeMonoid_406
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1158
                 (T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsSemiringWithoutAnnihilatingZero_1142
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1142
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsCommutativeSemigroup_270 -> T_IsCommutativeMagma_122)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCommutativeSemigroup_270 -> T_IsCommutativeMagma_122
MAlonzo.Code.Algebra.Structures.du_isCommutativeMagma_308
            ((T_IsCommutativeMonoid_406 -> T_IsCommutativeSemigroup_270)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsCommutativeMonoid_406 -> T_IsCommutativeSemigroup_270
MAlonzo.Code.Algebra.Structures.du_isCommutativeSemigroup_454
               (T_IsCommutativeMonoid_406 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_406
v2))))
-- Algebra.Bundles.SemiringWithoutAnnihilatingZero._.+-isCommutativeMonoid
d_'43''45'isCommutativeMonoid_1860 ::
  T_SemiringWithoutAnnihilatingZero_1786 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMonoid_406
d_'43''45'isCommutativeMonoid_1860 :: T_SemiringWithoutAnnihilatingZero_1786 -> T_IsCommutativeMonoid_406
d_'43''45'isCommutativeMonoid_1860 T_SemiringWithoutAnnihilatingZero_1786
v0
  = (T_IsSemiringWithoutAnnihilatingZero_1142
 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> T_IsCommutativeMonoid_406
forall a b. a -> b
coe
      T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsCommutativeMonoid_406
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1158
      ((T_SemiringWithoutAnnihilatingZero_1786
 -> T_IsSemiringWithoutAnnihilatingZero_1142)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_1786
-> T_IsSemiringWithoutAnnihilatingZero_1142
d_isSemiringWithoutAnnihilatingZero_1818 (T_SemiringWithoutAnnihilatingZero_1786 -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_1786
v0))
-- Algebra.Bundles.SemiringWithoutAnnihilatingZero._.isCommutativeSemigroup
d_isCommutativeSemigroup_1862 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SemiringWithoutAnnihilatingZero_1786 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_270
d_isCommutativeSemigroup_1862 :: ()
-> ()
-> T_SemiringWithoutAnnihilatingZero_1786
-> T_IsCommutativeSemigroup_270
d_isCommutativeSemigroup_1862 ~()
v0 ~()
v1 T_SemiringWithoutAnnihilatingZero_1786
v2
  = T_SemiringWithoutAnnihilatingZero_1786
-> T_IsCommutativeSemigroup_270
du_isCommutativeSemigroup_1862 T_SemiringWithoutAnnihilatingZero_1786
v2
du_isCommutativeSemigroup_1862 ::
  T_SemiringWithoutAnnihilatingZero_1786 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_270
du_isCommutativeSemigroup_1862 :: T_SemiringWithoutAnnihilatingZero_1786
-> T_IsCommutativeSemigroup_270
du_isCommutativeSemigroup_1862 T_SemiringWithoutAnnihilatingZero_1786
v0
  = let v1 :: T_IsSemiringWithoutAnnihilatingZero_1142
v1 = T_SemiringWithoutAnnihilatingZero_1786
-> T_IsSemiringWithoutAnnihilatingZero_1142
d_isSemiringWithoutAnnihilatingZero_1818 (T_SemiringWithoutAnnihilatingZero_1786
-> T_SemiringWithoutAnnihilatingZero_1786
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_1786
v0) in
    AgdaAny -> T_IsCommutativeSemigroup_270
forall a b. a -> b
coe
      ((T_IsCommutativeMonoid_406 -> T_IsCommutativeSemigroup_270)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCommutativeMonoid_406 -> T_IsCommutativeSemigroup_270
MAlonzo.Code.Algebra.Structures.du_isCommutativeSemigroup_454
         ((T_IsSemiringWithoutAnnihilatingZero_1142
 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsCommutativeMonoid_406
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1158
            (T_IsSemiringWithoutAnnihilatingZero_1142 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1142
v1)))
-- Algebra.Bundles.SemiringWithoutAnnihilatingZero._.isMagma
d_isMagma_1864 ::
  T_SemiringWithoutAnnihilatingZero_1786 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_86
d_isMagma_1864 :: T_SemiringWithoutAnnihilatingZero_1786 -> T_IsMagma_86
d_isMagma_1864 T_SemiringWithoutAnnihilatingZero_1786
v0
  = (T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> T_IsMagma_86
forall a b. a -> b
coe
      T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202
      ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368
         ((T_IsCommutativeMonoid_406 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCommutativeMonoid_406 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_416
            ((T_IsSemiringWithoutAnnihilatingZero_1142
 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsCommutativeMonoid_406
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1158
               ((T_SemiringWithoutAnnihilatingZero_1786
 -> T_IsSemiringWithoutAnnihilatingZero_1142)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_1786
-> T_IsSemiringWithoutAnnihilatingZero_1142
d_isSemiringWithoutAnnihilatingZero_1818 (T_SemiringWithoutAnnihilatingZero_1786 -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_1786
v0)))))
-- Algebra.Bundles.SemiringWithoutAnnihilatingZero._.isMonoid
d_isMonoid_1866 ::
  T_SemiringWithoutAnnihilatingZero_1786 ->
  MAlonzo.Code.Algebra.Structures.T_IsMonoid_358
d_isMonoid_1866 :: T_SemiringWithoutAnnihilatingZero_1786 -> T_IsMonoid_358
d_isMonoid_1866 T_SemiringWithoutAnnihilatingZero_1786
v0
  = (T_IsCommutativeMonoid_406 -> T_IsMonoid_358)
-> AgdaAny -> T_IsMonoid_358
forall a b. a -> b
coe
      T_IsCommutativeMonoid_406 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_416
      ((T_IsSemiringWithoutAnnihilatingZero_1142
 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsCommutativeMonoid_406
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1158
         ((T_SemiringWithoutAnnihilatingZero_1786
 -> T_IsSemiringWithoutAnnihilatingZero_1142)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_1786
-> T_IsSemiringWithoutAnnihilatingZero_1142
d_isSemiringWithoutAnnihilatingZero_1818 (T_SemiringWithoutAnnihilatingZero_1786 -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_1786
v0)))
-- Algebra.Bundles.SemiringWithoutAnnihilatingZero._.isSemigroup
d_isSemigroup_1868 ::
  T_SemiringWithoutAnnihilatingZero_1786 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_194
d_isSemigroup_1868 :: T_SemiringWithoutAnnihilatingZero_1786 -> T_IsSemigroup_194
d_isSemigroup_1868 T_SemiringWithoutAnnihilatingZero_1786
v0
  = (T_IsMonoid_358 -> T_IsSemigroup_194)
-> AgdaAny -> T_IsSemigroup_194
forall a b. a -> b
coe
      T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368
      ((T_IsCommutativeMonoid_406 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCommutativeMonoid_406 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_416
         ((T_IsSemiringWithoutAnnihilatingZero_1142
 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsCommutativeMonoid_406
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1158
            ((T_SemiringWithoutAnnihilatingZero_1786
 -> T_IsSemiringWithoutAnnihilatingZero_1142)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_1786
-> T_IsSemiringWithoutAnnihilatingZero_1142
d_isSemiringWithoutAnnihilatingZero_1818 (T_SemiringWithoutAnnihilatingZero_1786 -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_1786
v0))))
-- Algebra.Bundles.SemiringWithoutAnnihilatingZero._.distrib
d_distrib_1870 ::
  T_SemiringWithoutAnnihilatingZero_1786 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_distrib_1870 :: T_SemiringWithoutAnnihilatingZero_1786 -> T_Σ_14
d_distrib_1870 T_SemiringWithoutAnnihilatingZero_1786
v0
  = (T_IsSemiringWithoutAnnihilatingZero_1142 -> T_Σ_14)
-> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsSemiringWithoutAnnihilatingZero_1142 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_distrib_1162
      ((T_SemiringWithoutAnnihilatingZero_1786
 -> T_IsSemiringWithoutAnnihilatingZero_1142)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_1786
-> T_IsSemiringWithoutAnnihilatingZero_1142
d_isSemiringWithoutAnnihilatingZero_1818 (T_SemiringWithoutAnnihilatingZero_1786 -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_1786
v0))
-- Algebra.Bundles.SemiringWithoutAnnihilatingZero._.distribʳ
d_distrib'691'_1872 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SemiringWithoutAnnihilatingZero_1786 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_distrib'691'_1872 :: ()
-> ()
-> T_SemiringWithoutAnnihilatingZero_1786
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_distrib'691'_1872 ~()
v0 ~()
v1 T_SemiringWithoutAnnihilatingZero_1786
v2 = T_SemiringWithoutAnnihilatingZero_1786
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'691'_1872 T_SemiringWithoutAnnihilatingZero_1786
v2
du_distrib'691'_1872 ::
  T_SemiringWithoutAnnihilatingZero_1786 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'691'_1872 :: T_SemiringWithoutAnnihilatingZero_1786
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'691'_1872 T_SemiringWithoutAnnihilatingZero_1786
v0
  = (T_IsSemiringWithoutAnnihilatingZero_1142
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsSemiringWithoutAnnihilatingZero_1142
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_distrib'691'_1166
      ((T_SemiringWithoutAnnihilatingZero_1786
 -> T_IsSemiringWithoutAnnihilatingZero_1142)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_1786
-> T_IsSemiringWithoutAnnihilatingZero_1142
d_isSemiringWithoutAnnihilatingZero_1818 (T_SemiringWithoutAnnihilatingZero_1786 -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_1786
v0))
-- Algebra.Bundles.SemiringWithoutAnnihilatingZero._.distribˡ
d_distrib'737'_1874 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SemiringWithoutAnnihilatingZero_1786 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_distrib'737'_1874 :: ()
-> ()
-> T_SemiringWithoutAnnihilatingZero_1786
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_distrib'737'_1874 ~()
v0 ~()
v1 T_SemiringWithoutAnnihilatingZero_1786
v2 = T_SemiringWithoutAnnihilatingZero_1786
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'737'_1874 T_SemiringWithoutAnnihilatingZero_1786
v2
du_distrib'737'_1874 ::
  T_SemiringWithoutAnnihilatingZero_1786 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'737'_1874 :: T_SemiringWithoutAnnihilatingZero_1786
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'737'_1874 T_SemiringWithoutAnnihilatingZero_1786
v0
  = (T_IsSemiringWithoutAnnihilatingZero_1142
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsSemiringWithoutAnnihilatingZero_1142
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_distrib'737'_1164
      ((T_SemiringWithoutAnnihilatingZero_1786
 -> T_IsSemiringWithoutAnnihilatingZero_1142)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_1786
-> T_IsSemiringWithoutAnnihilatingZero_1142
d_isSemiringWithoutAnnihilatingZero_1818 (T_SemiringWithoutAnnihilatingZero_1786 -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_1786
v0))
-- Algebra.Bundles.SemiringWithoutAnnihilatingZero._.isEquivalence
d_isEquivalence_1876 ::
  T_SemiringWithoutAnnihilatingZero_1786 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_1876 :: T_SemiringWithoutAnnihilatingZero_1786 -> T_IsEquivalence_26
d_isEquivalence_1876 T_SemiringWithoutAnnihilatingZero_1786
v0
  = (T_IsMagma_86 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      T_IsMagma_86 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_94
      ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202
         ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368
            ((T_IsCommutativeMonoid_406 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsCommutativeMonoid_406 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_416
               ((T_IsSemiringWithoutAnnihilatingZero_1142
 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsCommutativeMonoid_406
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1158
                  ((T_SemiringWithoutAnnihilatingZero_1786
 -> T_IsSemiringWithoutAnnihilatingZero_1142)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_1786
-> T_IsSemiringWithoutAnnihilatingZero_1142
d_isSemiringWithoutAnnihilatingZero_1818 (T_SemiringWithoutAnnihilatingZero_1786 -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_1786
v0))))))
-- Algebra.Bundles.SemiringWithoutAnnihilatingZero._.isPartialEquivalence
d_isPartialEquivalence_1878 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SemiringWithoutAnnihilatingZero_1786 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_1878 :: ()
-> ()
-> T_SemiringWithoutAnnihilatingZero_1786
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_1878 ~()
v0 ~()
v1 T_SemiringWithoutAnnihilatingZero_1786
v2
  = T_SemiringWithoutAnnihilatingZero_1786 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_1878 T_SemiringWithoutAnnihilatingZero_1786
v2
du_isPartialEquivalence_1878 ::
  T_SemiringWithoutAnnihilatingZero_1786 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_1878 :: T_SemiringWithoutAnnihilatingZero_1786 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_1878 T_SemiringWithoutAnnihilatingZero_1786
v0
  = let v1 :: T_IsSemiringWithoutAnnihilatingZero_1142
v1 = T_SemiringWithoutAnnihilatingZero_1786
-> T_IsSemiringWithoutAnnihilatingZero_1142
d_isSemiringWithoutAnnihilatingZero_1818 (T_SemiringWithoutAnnihilatingZero_1786
-> T_SemiringWithoutAnnihilatingZero_1786
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_1786
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsCommutativeMonoid_406
v2
             = T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsCommutativeMonoid_406
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1158
                 (T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsSemiringWithoutAnnihilatingZero_1142
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1142
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsMonoid_358
v3
                = T_IsCommutativeMonoid_406 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_416 (T_IsCommutativeMonoid_406 -> T_IsCommutativeMonoid_406
forall a b. a -> b
coe T_IsCommutativeMonoid_406
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsSemigroup_194
v4
                   = T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368 (T_IsMonoid_358 -> T_IsMonoid_358
forall a b. a -> b
coe T_IsMonoid_358
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsMagma_86
v5 = T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202 (T_IsSemigroup_194 -> T_IsSemigroup_194
forall a b. a -> b
coe T_IsSemigroup_194
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_86 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsMagma_86 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_94 (T_IsMagma_86 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86
v5)))))))
-- Algebra.Bundles.SemiringWithoutAnnihilatingZero._.refl
d_refl_1880 ::
  T_SemiringWithoutAnnihilatingZero_1786 -> AgdaAny -> AgdaAny
d_refl_1880 :: T_SemiringWithoutAnnihilatingZero_1786 -> AgdaAny -> AgdaAny
d_refl_1880 T_SemiringWithoutAnnihilatingZero_1786
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_86 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_86 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_94
         ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202
            ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368
               ((T_IsCommutativeMonoid_406 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsCommutativeMonoid_406 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_416
                  ((T_IsSemiringWithoutAnnihilatingZero_1142
 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsCommutativeMonoid_406
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1158
                     ((T_SemiringWithoutAnnihilatingZero_1786
 -> T_IsSemiringWithoutAnnihilatingZero_1142)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_1786
-> T_IsSemiringWithoutAnnihilatingZero_1142
d_isSemiringWithoutAnnihilatingZero_1818 (T_SemiringWithoutAnnihilatingZero_1786 -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_1786
v0)))))))
-- Algebra.Bundles.SemiringWithoutAnnihilatingZero._.reflexive
d_reflexive_1882 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SemiringWithoutAnnihilatingZero_1786 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_1882 :: ()
-> ()
-> T_SemiringWithoutAnnihilatingZero_1786
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_1882 ~()
v0 ~()
v1 T_SemiringWithoutAnnihilatingZero_1786
v2 = T_SemiringWithoutAnnihilatingZero_1786
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_1882 T_SemiringWithoutAnnihilatingZero_1786
v2
du_reflexive_1882 ::
  T_SemiringWithoutAnnihilatingZero_1786 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_1882 :: T_SemiringWithoutAnnihilatingZero_1786
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_1882 T_SemiringWithoutAnnihilatingZero_1786
v0
  = let v1 :: T_IsSemiringWithoutAnnihilatingZero_1142
v1 = T_SemiringWithoutAnnihilatingZero_1786
-> T_IsSemiringWithoutAnnihilatingZero_1142
d_isSemiringWithoutAnnihilatingZero_1818 (T_SemiringWithoutAnnihilatingZero_1786
-> T_SemiringWithoutAnnihilatingZero_1786
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_1786
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsCommutativeMonoid_406
v2
             = T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsCommutativeMonoid_406
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1158
                 (T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsSemiringWithoutAnnihilatingZero_1142
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1142
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsMonoid_358
v3
                = T_IsCommutativeMonoid_406 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_416 (T_IsCommutativeMonoid_406 -> T_IsCommutativeMonoid_406
forall a b. a -> b
coe T_IsCommutativeMonoid_406
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsSemigroup_194
v4
                   = T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368 (T_IsMonoid_358 -> T_IsMonoid_358
forall a b. a -> b
coe T_IsMonoid_358
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsMagma_86
v5 = T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202 (T_IsSemigroup_194 -> T_IsSemigroup_194
forall a b. a -> b
coe T_IsSemigroup_194
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_86 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_94 (T_IsMagma_86 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86
v5))
                       AgdaAny
v6)))))
-- Algebra.Bundles.SemiringWithoutAnnihilatingZero._.setoid
d_setoid_1884 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SemiringWithoutAnnihilatingZero_1786 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_1884 :: () -> () -> T_SemiringWithoutAnnihilatingZero_1786 -> T_Setoid_44
d_setoid_1884 ~()
v0 ~()
v1 T_SemiringWithoutAnnihilatingZero_1786
v2 = T_SemiringWithoutAnnihilatingZero_1786 -> T_Setoid_44
du_setoid_1884 T_SemiringWithoutAnnihilatingZero_1786
v2
du_setoid_1884 ::
  T_SemiringWithoutAnnihilatingZero_1786 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_1884 :: T_SemiringWithoutAnnihilatingZero_1786 -> T_Setoid_44
du_setoid_1884 T_SemiringWithoutAnnihilatingZero_1786
v0
  = let v1 :: T_IsSemiringWithoutAnnihilatingZero_1142
v1 = T_SemiringWithoutAnnihilatingZero_1786
-> T_IsSemiringWithoutAnnihilatingZero_1142
d_isSemiringWithoutAnnihilatingZero_1818 (T_SemiringWithoutAnnihilatingZero_1786
-> T_SemiringWithoutAnnihilatingZero_1786
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_1786
v0) in
    AgdaAny -> T_Setoid_44
forall a b. a -> b
coe
      (let v2 :: T_IsCommutativeMonoid_406
v2
             = T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsCommutativeMonoid_406
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1158
                 (T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsSemiringWithoutAnnihilatingZero_1142
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1142
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsMonoid_358
v3
                = T_IsCommutativeMonoid_406 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_416 (T_IsCommutativeMonoid_406 -> T_IsCommutativeMonoid_406
forall a b. a -> b
coe T_IsCommutativeMonoid_406
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsSemigroup_194
v4
                   = T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368 (T_IsMonoid_358 -> T_IsMonoid_358
forall a b. a -> b
coe T_IsMonoid_358
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               ((T_IsMagma_86 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsMagma_86 -> T_Setoid_44
MAlonzo.Code.Algebra.Structures.du_setoid_110
                  ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202 (T_IsSemigroup_194 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194
v4))))))
-- Algebra.Bundles.SemiringWithoutAnnihilatingZero._.sym
d_sym_1886 ::
  T_SemiringWithoutAnnihilatingZero_1786 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_1886 :: T_SemiringWithoutAnnihilatingZero_1786
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_1886 T_SemiringWithoutAnnihilatingZero_1786
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_86 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_86 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_94
         ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202
            ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368
               ((T_IsCommutativeMonoid_406 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsCommutativeMonoid_406 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_416
                  ((T_IsSemiringWithoutAnnihilatingZero_1142
 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsCommutativeMonoid_406
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1158
                     ((T_SemiringWithoutAnnihilatingZero_1786
 -> T_IsSemiringWithoutAnnihilatingZero_1142)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_1786
-> T_IsSemiringWithoutAnnihilatingZero_1142
d_isSemiringWithoutAnnihilatingZero_1818 (T_SemiringWithoutAnnihilatingZero_1786 -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_1786
v0)))))))
-- Algebra.Bundles.SemiringWithoutAnnihilatingZero._.trans
d_trans_1888 ::
  T_SemiringWithoutAnnihilatingZero_1786 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_1888 :: T_SemiringWithoutAnnihilatingZero_1786
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_1888 T_SemiringWithoutAnnihilatingZero_1786
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_86 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_86 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_94
         ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202
            ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368
               ((T_IsCommutativeMonoid_406 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsCommutativeMonoid_406 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_416
                  ((T_IsSemiringWithoutAnnihilatingZero_1142
 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsCommutativeMonoid_406
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1158
                     ((T_SemiringWithoutAnnihilatingZero_1786
 -> T_IsSemiringWithoutAnnihilatingZero_1142)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_1786
-> T_IsSemiringWithoutAnnihilatingZero_1142
d_isSemiringWithoutAnnihilatingZero_1818 (T_SemiringWithoutAnnihilatingZero_1786 -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_1786
v0)))))))
-- Algebra.Bundles.SemiringWithoutAnnihilatingZero.rawSemiring
d_rawSemiring_1890 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SemiringWithoutAnnihilatingZero_1786 -> T_RawSemiring_1738
d_rawSemiring_1890 :: ()
-> ()
-> T_SemiringWithoutAnnihilatingZero_1786
-> T_RawSemiring_1738
d_rawSemiring_1890 ~()
v0 ~()
v1 T_SemiringWithoutAnnihilatingZero_1786
v2 = T_SemiringWithoutAnnihilatingZero_1786 -> T_RawSemiring_1738
du_rawSemiring_1890 T_SemiringWithoutAnnihilatingZero_1786
v2
du_rawSemiring_1890 ::
  T_SemiringWithoutAnnihilatingZero_1786 -> T_RawSemiring_1738
du_rawSemiring_1890 :: T_SemiringWithoutAnnihilatingZero_1786 -> T_RawSemiring_1738
du_rawSemiring_1890 T_SemiringWithoutAnnihilatingZero_1786
v0
  = ((AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> AgdaAny
 -> T_RawSemiring_1738)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_RawSemiring_1738
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_RawSemiring_1738
C_RawSemiring'46'constructor_30035 (T_SemiringWithoutAnnihilatingZero_1786
-> AgdaAny -> AgdaAny -> AgdaAny
d__'43'__1810 (T_SemiringWithoutAnnihilatingZero_1786
-> T_SemiringWithoutAnnihilatingZero_1786
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_1786
v0))
      (T_SemiringWithoutAnnihilatingZero_1786
-> AgdaAny -> AgdaAny -> AgdaAny
d__'42'__1812 (T_SemiringWithoutAnnihilatingZero_1786
-> T_SemiringWithoutAnnihilatingZero_1786
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_1786
v0)) (T_SemiringWithoutAnnihilatingZero_1786 -> AgdaAny
d_0'35'_1814 (T_SemiringWithoutAnnihilatingZero_1786
-> T_SemiringWithoutAnnihilatingZero_1786
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_1786
v0))
      (T_SemiringWithoutAnnihilatingZero_1786 -> AgdaAny
d_1'35'_1816 (T_SemiringWithoutAnnihilatingZero_1786
-> T_SemiringWithoutAnnihilatingZero_1786
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_1786
v0))
-- Algebra.Bundles.SemiringWithoutAnnihilatingZero._.rawNearSemiring
d_rawNearSemiring_1894 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SemiringWithoutAnnihilatingZero_1786 -> T_RawNearSemiring_1314
d_rawNearSemiring_1894 :: ()
-> ()
-> T_SemiringWithoutAnnihilatingZero_1786
-> T_RawNearSemiring_1314
d_rawNearSemiring_1894 ~()
v0 ~()
v1 T_SemiringWithoutAnnihilatingZero_1786
v2 = T_SemiringWithoutAnnihilatingZero_1786 -> T_RawNearSemiring_1314
du_rawNearSemiring_1894 T_SemiringWithoutAnnihilatingZero_1786
v2
du_rawNearSemiring_1894 ::
  T_SemiringWithoutAnnihilatingZero_1786 -> T_RawNearSemiring_1314
du_rawNearSemiring_1894 :: T_SemiringWithoutAnnihilatingZero_1786 -> T_RawNearSemiring_1314
du_rawNearSemiring_1894 T_SemiringWithoutAnnihilatingZero_1786
v0
  = (T_RawSemiring_1738 -> T_RawNearSemiring_1314)
-> AgdaAny -> T_RawNearSemiring_1314
forall a b. a -> b
coe T_RawSemiring_1738 -> T_RawNearSemiring_1314
du_rawNearSemiring_1768 ((T_SemiringWithoutAnnihilatingZero_1786 -> T_RawSemiring_1738)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_1786 -> T_RawSemiring_1738
du_rawSemiring_1890 (T_SemiringWithoutAnnihilatingZero_1786 -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_1786
v0))
-- Algebra.Bundles.SemiringWithoutAnnihilatingZero.+-commutativeMonoid
d_'43''45'commutativeMonoid_1896 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SemiringWithoutAnnihilatingZero_1786 -> T_CommutativeMonoid_582
d_'43''45'commutativeMonoid_1896 :: ()
-> ()
-> T_SemiringWithoutAnnihilatingZero_1786
-> T_CommutativeMonoid_582
d_'43''45'commutativeMonoid_1896 ~()
v0 ~()
v1 T_SemiringWithoutAnnihilatingZero_1786
v2
  = T_SemiringWithoutAnnihilatingZero_1786 -> T_CommutativeMonoid_582
du_'43''45'commutativeMonoid_1896 T_SemiringWithoutAnnihilatingZero_1786
v2
du_'43''45'commutativeMonoid_1896 ::
  T_SemiringWithoutAnnihilatingZero_1786 -> T_CommutativeMonoid_582
du_'43''45'commutativeMonoid_1896 :: T_SemiringWithoutAnnihilatingZero_1786 -> T_CommutativeMonoid_582
du_'43''45'commutativeMonoid_1896 T_SemiringWithoutAnnihilatingZero_1786
v0
  = ((AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny -> T_IsCommutativeMonoid_406 -> T_CommutativeMonoid_582)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsCommutativeMonoid_406
-> T_CommutativeMonoid_582
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> T_IsCommutativeMonoid_406 -> T_CommutativeMonoid_582
C_CommutativeMonoid'46'constructor_10343 (T_SemiringWithoutAnnihilatingZero_1786
-> AgdaAny -> AgdaAny -> AgdaAny
d__'43'__1810 (T_SemiringWithoutAnnihilatingZero_1786
-> T_SemiringWithoutAnnihilatingZero_1786
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_1786
v0))
      (T_SemiringWithoutAnnihilatingZero_1786 -> AgdaAny
d_0'35'_1814 (T_SemiringWithoutAnnihilatingZero_1786
-> T_SemiringWithoutAnnihilatingZero_1786
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_1786
v0))
      (T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsCommutativeMonoid_406
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1158
         ((T_SemiringWithoutAnnihilatingZero_1786
 -> T_IsSemiringWithoutAnnihilatingZero_1142)
-> AgdaAny -> T_IsSemiringWithoutAnnihilatingZero_1142
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_1786
-> T_IsSemiringWithoutAnnihilatingZero_1142
d_isSemiringWithoutAnnihilatingZero_1818 (T_SemiringWithoutAnnihilatingZero_1786 -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_1786
v0)))
-- Algebra.Bundles.SemiringWithoutAnnihilatingZero._._≉_
d__'8777'__1900 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SemiringWithoutAnnihilatingZero_1786 -> AgdaAny -> AgdaAny -> ()
d__'8777'__1900 :: ()
-> ()
-> T_SemiringWithoutAnnihilatingZero_1786
-> AgdaAny
-> AgdaAny
-> ()
d__'8777'__1900 = ()
-> ()
-> T_SemiringWithoutAnnihilatingZero_1786
-> AgdaAny
-> AgdaAny
-> ()
forall a. a
erased
-- Algebra.Bundles.SemiringWithoutAnnihilatingZero._.commutativeMagma
d_commutativeMagma_1902 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SemiringWithoutAnnihilatingZero_1786 -> T_CommutativeMagma_148
d_commutativeMagma_1902 :: ()
-> ()
-> T_SemiringWithoutAnnihilatingZero_1786
-> T_CommutativeMagma_148
d_commutativeMagma_1902 ~()
v0 ~()
v1 T_SemiringWithoutAnnihilatingZero_1786
v2 = T_SemiringWithoutAnnihilatingZero_1786 -> T_CommutativeMagma_148
du_commutativeMagma_1902 T_SemiringWithoutAnnihilatingZero_1786
v2
du_commutativeMagma_1902 ::
  T_SemiringWithoutAnnihilatingZero_1786 -> T_CommutativeMagma_148
du_commutativeMagma_1902 :: T_SemiringWithoutAnnihilatingZero_1786 -> T_CommutativeMagma_148
du_commutativeMagma_1902 T_SemiringWithoutAnnihilatingZero_1786
v0
  = let v1 :: t
v1 = (T_SemiringWithoutAnnihilatingZero_1786 -> T_CommutativeMonoid_582)
-> AgdaAny -> t
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_1786 -> T_CommutativeMonoid_582
du_'43''45'commutativeMonoid_1896 (T_SemiringWithoutAnnihilatingZero_1786 -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_1786
v0) in
    AgdaAny -> T_CommutativeMagma_148
forall a b. a -> b
coe
      ((T_CommutativeSemigroup_332 -> T_CommutativeMagma_148)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_CommutativeSemigroup_332 -> T_CommutativeMagma_148
du_commutativeMagma_396 ((T_CommutativeMonoid_582 -> T_CommutativeSemigroup_332)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeMonoid_582 -> T_CommutativeSemigroup_332
du_commutativeSemigroup_664 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1)))
-- Algebra.Bundles.SemiringWithoutAnnihilatingZero._.commutativeSemigroup
d_commutativeSemigroup_1904 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SemiringWithoutAnnihilatingZero_1786 ->
  T_CommutativeSemigroup_332
d_commutativeSemigroup_1904 :: ()
-> ()
-> T_SemiringWithoutAnnihilatingZero_1786
-> T_CommutativeSemigroup_332
d_commutativeSemigroup_1904 ~()
v0 ~()
v1 T_SemiringWithoutAnnihilatingZero_1786
v2
  = T_SemiringWithoutAnnihilatingZero_1786
-> T_CommutativeSemigroup_332
du_commutativeSemigroup_1904 T_SemiringWithoutAnnihilatingZero_1786
v2
du_commutativeSemigroup_1904 ::
  T_SemiringWithoutAnnihilatingZero_1786 ->
  T_CommutativeSemigroup_332
du_commutativeSemigroup_1904 :: T_SemiringWithoutAnnihilatingZero_1786
-> T_CommutativeSemigroup_332
du_commutativeSemigroup_1904 T_SemiringWithoutAnnihilatingZero_1786
v0
  = (T_CommutativeMonoid_582 -> T_CommutativeSemigroup_332)
-> AgdaAny -> T_CommutativeSemigroup_332
forall a b. a -> b
coe
      T_CommutativeMonoid_582 -> T_CommutativeSemigroup_332
du_commutativeSemigroup_664
      ((T_SemiringWithoutAnnihilatingZero_1786 -> T_CommutativeMonoid_582)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_1786 -> T_CommutativeMonoid_582
du_'43''45'commutativeMonoid_1896 (T_SemiringWithoutAnnihilatingZero_1786 -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_1786
v0))
-- Algebra.Bundles.SemiringWithoutAnnihilatingZero._.magma
d_magma_1906 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SemiringWithoutAnnihilatingZero_1786 -> T_Magma_36
d_magma_1906 :: () -> () -> T_SemiringWithoutAnnihilatingZero_1786 -> T_Magma_36
d_magma_1906 ~()
v0 ~()
v1 T_SemiringWithoutAnnihilatingZero_1786
v2 = T_SemiringWithoutAnnihilatingZero_1786 -> T_Magma_36
du_magma_1906 T_SemiringWithoutAnnihilatingZero_1786
v2
du_magma_1906 ::
  T_SemiringWithoutAnnihilatingZero_1786 -> T_Magma_36
du_magma_1906 :: T_SemiringWithoutAnnihilatingZero_1786 -> T_Magma_36
du_magma_1906 T_SemiringWithoutAnnihilatingZero_1786
v0
  = let v1 :: t
v1 = (T_SemiringWithoutAnnihilatingZero_1786 -> T_CommutativeMonoid_582)
-> AgdaAny -> t
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_1786 -> T_CommutativeMonoid_582
du_'43''45'commutativeMonoid_1896 (T_SemiringWithoutAnnihilatingZero_1786 -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_1786
v0) in
    AgdaAny -> T_Magma_36
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_CommutativeMonoid_582 -> T_Monoid_506) -> AgdaAny -> t
forall a b. a -> b
coe T_CommutativeMonoid_582 -> T_Monoid_506
du_monoid_650 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_Semigroup_206 -> T_Magma_36) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semigroup_206 -> T_Magma_36
du_magma_254 ((T_Monoid_506 -> T_Semigroup_206) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Monoid_506 -> T_Semigroup_206
du_semigroup_566 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2))))
-- Algebra.Bundles.SemiringWithoutAnnihilatingZero._.monoid
d_monoid_1908 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SemiringWithoutAnnihilatingZero_1786 -> T_Monoid_506
d_monoid_1908 :: () -> () -> T_SemiringWithoutAnnihilatingZero_1786 -> T_Monoid_506
d_monoid_1908 ~()
v0 ~()
v1 T_SemiringWithoutAnnihilatingZero_1786
v2 = T_SemiringWithoutAnnihilatingZero_1786 -> T_Monoid_506
du_monoid_1908 T_SemiringWithoutAnnihilatingZero_1786
v2
du_monoid_1908 ::
  T_SemiringWithoutAnnihilatingZero_1786 -> T_Monoid_506
du_monoid_1908 :: T_SemiringWithoutAnnihilatingZero_1786 -> T_Monoid_506
du_monoid_1908 T_SemiringWithoutAnnihilatingZero_1786
v0
  = (T_CommutativeMonoid_582 -> T_Monoid_506)
-> AgdaAny -> T_Monoid_506
forall a b. a -> b
coe
      T_CommutativeMonoid_582 -> T_Monoid_506
du_monoid_650 ((T_SemiringWithoutAnnihilatingZero_1786 -> T_CommutativeMonoid_582)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_1786 -> T_CommutativeMonoid_582
du_'43''45'commutativeMonoid_1896 (T_SemiringWithoutAnnihilatingZero_1786 -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_1786
v0))
-- Algebra.Bundles.SemiringWithoutAnnihilatingZero._.rawMagma
d_rawMagma_1910 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SemiringWithoutAnnihilatingZero_1786 -> T_RawMagma_8
d_rawMagma_1910 :: () -> () -> T_SemiringWithoutAnnihilatingZero_1786 -> T_RawMagma_8
d_rawMagma_1910 ~()
v0 ~()
v1 T_SemiringWithoutAnnihilatingZero_1786
v2 = T_SemiringWithoutAnnihilatingZero_1786 -> T_RawMagma_8
du_rawMagma_1910 T_SemiringWithoutAnnihilatingZero_1786
v2
du_rawMagma_1910 ::
  T_SemiringWithoutAnnihilatingZero_1786 -> T_RawMagma_8
du_rawMagma_1910 :: T_SemiringWithoutAnnihilatingZero_1786 -> T_RawMagma_8
du_rawMagma_1910 T_SemiringWithoutAnnihilatingZero_1786
v0
  = let v1 :: t
v1 = (T_SemiringWithoutAnnihilatingZero_1786 -> T_CommutativeMonoid_582)
-> AgdaAny -> t
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_1786 -> T_CommutativeMonoid_582
du_'43''45'commutativeMonoid_1896 (T_SemiringWithoutAnnihilatingZero_1786 -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_1786
v0) in
    AgdaAny -> T_RawMagma_8
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_CommutativeMonoid_582 -> T_Monoid_506) -> AgdaAny -> t
forall a b. a -> b
coe T_CommutativeMonoid_582 -> T_Monoid_506
du_monoid_650 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: t
v3 = (T_Monoid_506 -> T_Semigroup_206) -> AgdaAny -> t
forall a b. a -> b
coe T_Monoid_506 -> T_Semigroup_206
du_semigroup_566 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_Magma_36 -> T_RawMagma_8) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Magma_36 -> T_RawMagma_8
du_rawMagma_80 ((T_Semigroup_206 -> T_Magma_36) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semigroup_206 -> T_Magma_36
du_magma_254 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3)))))
-- Algebra.Bundles.SemiringWithoutAnnihilatingZero._.rawMonoid
d_rawMonoid_1912 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SemiringWithoutAnnihilatingZero_1786 -> T_RawMonoid_474
d_rawMonoid_1912 :: ()
-> () -> T_SemiringWithoutAnnihilatingZero_1786 -> T_RawMonoid_474
d_rawMonoid_1912 ~()
v0 ~()
v1 T_SemiringWithoutAnnihilatingZero_1786
v2 = T_SemiringWithoutAnnihilatingZero_1786 -> T_RawMonoid_474
du_rawMonoid_1912 T_SemiringWithoutAnnihilatingZero_1786
v2
du_rawMonoid_1912 ::
  T_SemiringWithoutAnnihilatingZero_1786 -> T_RawMonoid_474
du_rawMonoid_1912 :: T_SemiringWithoutAnnihilatingZero_1786 -> T_RawMonoid_474
du_rawMonoid_1912 T_SemiringWithoutAnnihilatingZero_1786
v0
  = let v1 :: t
v1 = (T_SemiringWithoutAnnihilatingZero_1786 -> T_CommutativeMonoid_582)
-> AgdaAny -> t
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_1786 -> T_CommutativeMonoid_582
du_'43''45'commutativeMonoid_1896 (T_SemiringWithoutAnnihilatingZero_1786 -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_1786
v0) in
    AgdaAny -> T_RawMonoid_474
forall a b. a -> b
coe ((T_Monoid_506 -> T_RawMonoid_474) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Monoid_506 -> T_RawMonoid_474
du_rawMonoid_576 ((T_CommutativeMonoid_582 -> T_Monoid_506) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeMonoid_582 -> T_Monoid_506
du_monoid_650 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1)))
-- Algebra.Bundles.SemiringWithoutAnnihilatingZero._.semigroup
d_semigroup_1914 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SemiringWithoutAnnihilatingZero_1786 -> T_Semigroup_206
d_semigroup_1914 :: ()
-> () -> T_SemiringWithoutAnnihilatingZero_1786 -> T_Semigroup_206
d_semigroup_1914 ~()
v0 ~()
v1 T_SemiringWithoutAnnihilatingZero_1786
v2 = T_SemiringWithoutAnnihilatingZero_1786 -> T_Semigroup_206
du_semigroup_1914 T_SemiringWithoutAnnihilatingZero_1786
v2
du_semigroup_1914 ::
  T_SemiringWithoutAnnihilatingZero_1786 -> T_Semigroup_206
du_semigroup_1914 :: T_SemiringWithoutAnnihilatingZero_1786 -> T_Semigroup_206
du_semigroup_1914 T_SemiringWithoutAnnihilatingZero_1786
v0
  = let v1 :: t
v1 = (T_SemiringWithoutAnnihilatingZero_1786 -> T_CommutativeMonoid_582)
-> AgdaAny -> t
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_1786 -> T_CommutativeMonoid_582
du_'43''45'commutativeMonoid_1896 (T_SemiringWithoutAnnihilatingZero_1786 -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_1786
v0) in
    AgdaAny -> T_Semigroup_206
forall a b. a -> b
coe ((T_Monoid_506 -> T_Semigroup_206) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Monoid_506 -> T_Semigroup_206
du_semigroup_566 ((T_CommutativeMonoid_582 -> T_Monoid_506) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeMonoid_582 -> T_Monoid_506
du_monoid_650 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1)))
-- Algebra.Bundles.SemiringWithoutAnnihilatingZero.*-monoid
d_'42''45'monoid_1916 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SemiringWithoutAnnihilatingZero_1786 -> T_Monoid_506
d_'42''45'monoid_1916 :: () -> () -> T_SemiringWithoutAnnihilatingZero_1786 -> T_Monoid_506
d_'42''45'monoid_1916 ~()
v0 ~()
v1 T_SemiringWithoutAnnihilatingZero_1786
v2 = T_SemiringWithoutAnnihilatingZero_1786 -> T_Monoid_506
du_'42''45'monoid_1916 T_SemiringWithoutAnnihilatingZero_1786
v2
du_'42''45'monoid_1916 ::
  T_SemiringWithoutAnnihilatingZero_1786 -> T_Monoid_506
du_'42''45'monoid_1916 :: T_SemiringWithoutAnnihilatingZero_1786 -> T_Monoid_506
du_'42''45'monoid_1916 T_SemiringWithoutAnnihilatingZero_1786
v0
  = ((AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny -> T_IsMonoid_358 -> T_Monoid_506)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsMonoid_358
-> T_Monoid_506
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> T_IsMonoid_358 -> T_Monoid_506
C_Monoid'46'constructor_8851 (T_SemiringWithoutAnnihilatingZero_1786
-> AgdaAny -> AgdaAny -> AgdaAny
d__'42'__1812 (T_SemiringWithoutAnnihilatingZero_1786
-> T_SemiringWithoutAnnihilatingZero_1786
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_1786
v0))
      (T_SemiringWithoutAnnihilatingZero_1786 -> AgdaAny
d_1'35'_1816 (T_SemiringWithoutAnnihilatingZero_1786
-> T_SemiringWithoutAnnihilatingZero_1786
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_1786
v0))
      (T_IsSemiringWithoutAnnihilatingZero_1142 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_'42''45'isMonoid_1160
         ((T_SemiringWithoutAnnihilatingZero_1786
 -> T_IsSemiringWithoutAnnihilatingZero_1142)
-> AgdaAny -> T_IsSemiringWithoutAnnihilatingZero_1142
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_1786
-> T_IsSemiringWithoutAnnihilatingZero_1142
d_isSemiringWithoutAnnihilatingZero_1818 (T_SemiringWithoutAnnihilatingZero_1786 -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_1786
v0)))
-- Algebra.Bundles.SemiringWithoutAnnihilatingZero._.magma
d_magma_1920 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SemiringWithoutAnnihilatingZero_1786 -> T_Magma_36
d_magma_1920 :: () -> () -> T_SemiringWithoutAnnihilatingZero_1786 -> T_Magma_36
d_magma_1920 ~()
v0 ~()
v1 T_SemiringWithoutAnnihilatingZero_1786
v2 = T_SemiringWithoutAnnihilatingZero_1786 -> T_Magma_36
du_magma_1920 T_SemiringWithoutAnnihilatingZero_1786
v2
du_magma_1920 ::
  T_SemiringWithoutAnnihilatingZero_1786 -> T_Magma_36
du_magma_1920 :: T_SemiringWithoutAnnihilatingZero_1786 -> T_Magma_36
du_magma_1920 T_SemiringWithoutAnnihilatingZero_1786
v0
  = let v1 :: t
v1 = (T_SemiringWithoutAnnihilatingZero_1786 -> T_Monoid_506)
-> AgdaAny -> t
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_1786 -> T_Monoid_506
du_'42''45'monoid_1916 (T_SemiringWithoutAnnihilatingZero_1786 -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_1786
v0) in
    AgdaAny -> T_Magma_36
forall a b. a -> b
coe ((T_Semigroup_206 -> T_Magma_36) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semigroup_206 -> T_Magma_36
du_magma_254 ((T_Monoid_506 -> T_Semigroup_206) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Monoid_506 -> T_Semigroup_206
du_semigroup_566 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1)))
-- Algebra.Bundles.SemiringWithoutAnnihilatingZero._.rawMagma
d_rawMagma_1922 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SemiringWithoutAnnihilatingZero_1786 -> T_RawMagma_8
d_rawMagma_1922 :: () -> () -> T_SemiringWithoutAnnihilatingZero_1786 -> T_RawMagma_8
d_rawMagma_1922 ~()
v0 ~()
v1 T_SemiringWithoutAnnihilatingZero_1786
v2 = T_SemiringWithoutAnnihilatingZero_1786 -> T_RawMagma_8
du_rawMagma_1922 T_SemiringWithoutAnnihilatingZero_1786
v2
du_rawMagma_1922 ::
  T_SemiringWithoutAnnihilatingZero_1786 -> T_RawMagma_8
du_rawMagma_1922 :: T_SemiringWithoutAnnihilatingZero_1786 -> T_RawMagma_8
du_rawMagma_1922 T_SemiringWithoutAnnihilatingZero_1786
v0
  = let v1 :: t
v1 = (T_SemiringWithoutAnnihilatingZero_1786 -> T_Monoid_506)
-> AgdaAny -> t
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_1786 -> T_Monoid_506
du_'42''45'monoid_1916 (T_SemiringWithoutAnnihilatingZero_1786 -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_1786
v0) in
    AgdaAny -> T_RawMagma_8
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_Monoid_506 -> T_Semigroup_206) -> AgdaAny -> t
forall a b. a -> b
coe T_Monoid_506 -> T_Semigroup_206
du_semigroup_566 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_Magma_36 -> T_RawMagma_8) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Magma_36 -> T_RawMagma_8
du_rawMagma_80 ((T_Semigroup_206 -> T_Magma_36) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semigroup_206 -> T_Magma_36
du_magma_254 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2))))
-- Algebra.Bundles.SemiringWithoutAnnihilatingZero._.rawMonoid
d_rawMonoid_1924 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SemiringWithoutAnnihilatingZero_1786 -> T_RawMonoid_474
d_rawMonoid_1924 :: ()
-> () -> T_SemiringWithoutAnnihilatingZero_1786 -> T_RawMonoid_474
d_rawMonoid_1924 ~()
v0 ~()
v1 T_SemiringWithoutAnnihilatingZero_1786
v2 = T_SemiringWithoutAnnihilatingZero_1786 -> T_RawMonoid_474
du_rawMonoid_1924 T_SemiringWithoutAnnihilatingZero_1786
v2
du_rawMonoid_1924 ::
  T_SemiringWithoutAnnihilatingZero_1786 -> T_RawMonoid_474
du_rawMonoid_1924 :: T_SemiringWithoutAnnihilatingZero_1786 -> T_RawMonoid_474
du_rawMonoid_1924 T_SemiringWithoutAnnihilatingZero_1786
v0
  = (T_Monoid_506 -> T_RawMonoid_474) -> AgdaAny -> T_RawMonoid_474
forall a b. a -> b
coe T_Monoid_506 -> T_RawMonoid_474
du_rawMonoid_576 ((T_SemiringWithoutAnnihilatingZero_1786 -> T_Monoid_506)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_1786 -> T_Monoid_506
du_'42''45'monoid_1916 (T_SemiringWithoutAnnihilatingZero_1786 -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_1786
v0))
-- Algebra.Bundles.SemiringWithoutAnnihilatingZero._.semigroup
d_semigroup_1926 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SemiringWithoutAnnihilatingZero_1786 -> T_Semigroup_206
d_semigroup_1926 :: ()
-> () -> T_SemiringWithoutAnnihilatingZero_1786 -> T_Semigroup_206
d_semigroup_1926 ~()
v0 ~()
v1 T_SemiringWithoutAnnihilatingZero_1786
v2 = T_SemiringWithoutAnnihilatingZero_1786 -> T_Semigroup_206
du_semigroup_1926 T_SemiringWithoutAnnihilatingZero_1786
v2
du_semigroup_1926 ::
  T_SemiringWithoutAnnihilatingZero_1786 -> T_Semigroup_206
du_semigroup_1926 :: T_SemiringWithoutAnnihilatingZero_1786 -> T_Semigroup_206
du_semigroup_1926 T_SemiringWithoutAnnihilatingZero_1786
v0
  = (T_Monoid_506 -> T_Semigroup_206) -> AgdaAny -> T_Semigroup_206
forall a b. a -> b
coe T_Monoid_506 -> T_Semigroup_206
du_semigroup_566 ((T_SemiringWithoutAnnihilatingZero_1786 -> T_Monoid_506)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_1786 -> T_Monoid_506
du_'42''45'monoid_1916 (T_SemiringWithoutAnnihilatingZero_1786 -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_1786
v0))
-- Algebra.Bundles.Semiring
d_Semiring_1932 :: p -> p -> ()
d_Semiring_1932 p
a0 p
a1 = ()
data T_Semiring_1932
  = C_Semiring'46'constructor_33613 (AgdaAny -> AgdaAny -> AgdaAny)
                                    (AgdaAny -> AgdaAny -> AgdaAny) AgdaAny AgdaAny
                                    MAlonzo.Code.Algebra.Structures.T_IsSemiring_1238
-- Algebra.Bundles.Semiring.Carrier
d_Carrier_1952 :: T_Semiring_1932 -> ()
d_Carrier_1952 :: T_Semiring_1932 -> ()
d_Carrier_1952 = T_Semiring_1932 -> ()
forall a. a
erased
-- Algebra.Bundles.Semiring._≈_
d__'8776'__1954 :: T_Semiring_1932 -> AgdaAny -> AgdaAny -> ()
d__'8776'__1954 :: T_Semiring_1932 -> AgdaAny -> AgdaAny -> ()
d__'8776'__1954 = T_Semiring_1932 -> AgdaAny -> AgdaAny -> ()
forall a. a
erased
-- Algebra.Bundles.Semiring._+_
d__'43'__1956 :: T_Semiring_1932 -> AgdaAny -> AgdaAny -> AgdaAny
d__'43'__1956 :: T_Semiring_1932 -> AgdaAny -> AgdaAny -> AgdaAny
d__'43'__1956 T_Semiring_1932
v0
  = case T_Semiring_1932 -> T_Semiring_1932
forall a b. a -> b
coe T_Semiring_1932
v0 of
      C_Semiring'46'constructor_33613 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny
v5 AgdaAny
v6 T_IsSemiring_1238
v7 -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v3
      T_Semiring_1932
_ -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.Semiring._*_
d__'42'__1958 :: T_Semiring_1932 -> AgdaAny -> AgdaAny -> AgdaAny
d__'42'__1958 :: T_Semiring_1932 -> AgdaAny -> AgdaAny -> AgdaAny
d__'42'__1958 T_Semiring_1932
v0
  = case T_Semiring_1932 -> T_Semiring_1932
forall a b. a -> b
coe T_Semiring_1932
v0 of
      C_Semiring'46'constructor_33613 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny
v5 AgdaAny
v6 T_IsSemiring_1238
v7 -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v4
      T_Semiring_1932
_ -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.Semiring.0#
d_0'35'_1960 :: T_Semiring_1932 -> AgdaAny
d_0'35'_1960 :: T_Semiring_1932 -> AgdaAny
d_0'35'_1960 T_Semiring_1932
v0
  = case T_Semiring_1932 -> T_Semiring_1932
forall a b. a -> b
coe T_Semiring_1932
v0 of
      C_Semiring'46'constructor_33613 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny
v5 AgdaAny
v6 T_IsSemiring_1238
v7 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v5
      T_Semiring_1932
_ -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.Semiring.1#
d_1'35'_1962 :: T_Semiring_1932 -> AgdaAny
d_1'35'_1962 :: T_Semiring_1932 -> AgdaAny
d_1'35'_1962 T_Semiring_1932
v0
  = case T_Semiring_1932 -> T_Semiring_1932
forall a b. a -> b
coe T_Semiring_1932
v0 of
      C_Semiring'46'constructor_33613 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny
v5 AgdaAny
v6 T_IsSemiring_1238
v7 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v6
      T_Semiring_1932
_ -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.Semiring.isSemiring
d_isSemiring_1964 ::
  T_Semiring_1932 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemiring_1238
d_isSemiring_1964 :: T_Semiring_1932 -> T_IsSemiring_1238
d_isSemiring_1964 T_Semiring_1932
v0
  = case T_Semiring_1932 -> T_Semiring_1932
forall a b. a -> b
coe T_Semiring_1932
v0 of
      C_Semiring'46'constructor_33613 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny
v5 AgdaAny
v6 T_IsSemiring_1238
v7 -> T_IsSemiring_1238 -> T_IsSemiring_1238
forall a b. a -> b
coe T_IsSemiring_1238
v7
      T_Semiring_1932
_ -> T_IsSemiring_1238
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.Semiring._.assoc
d_assoc_1968 ::
  T_Semiring_1932 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_1968 :: T_Semiring_1932 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_1968 T_Semiring_1932
v0
  = (T_IsSemigroup_194 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsSemigroup_194 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_assoc_204
      ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368
         ((T_IsSemiringWithoutAnnihilatingZero_1142 -> T_IsMonoid_358)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemiringWithoutAnnihilatingZero_1142 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_'42''45'isMonoid_1160
            ((T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1252
               ((T_Semiring_1932 -> T_IsSemiring_1238) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semiring_1932 -> T_IsSemiring_1238
d_isSemiring_1964 (T_Semiring_1932 -> AgdaAny
forall a b. a -> b
coe T_Semiring_1932
v0)))))
-- Algebra.Bundles.Semiring._.∙-cong
d_'8729''45'cong_1970 ::
  T_Semiring_1932 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_1970 :: T_Semiring_1932
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_1970 T_Semiring_1932
v0
  = (T_IsMagma_86
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsMagma_86
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_96
      ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202
         ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368
            ((T_IsSemiringWithoutAnnihilatingZero_1142 -> T_IsMonoid_358)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemiringWithoutAnnihilatingZero_1142 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_'42''45'isMonoid_1160
               ((T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1252
                  ((T_Semiring_1932 -> T_IsSemiring_1238) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semiring_1932 -> T_IsSemiring_1238
d_isSemiring_1964 (T_Semiring_1932 -> AgdaAny
forall a b. a -> b
coe T_Semiring_1932
v0))))))
-- Algebra.Bundles.Semiring._.∙-congʳ
d_'8729''45'cong'691'_1972 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Semiring_1932 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_1972 :: ()
-> ()
-> T_Semiring_1932
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_1972 ~()
v0 ~()
v1 T_Semiring_1932
v2
  = T_Semiring_1932
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1972 T_Semiring_1932
v2
du_'8729''45'cong'691'_1972 ::
  T_Semiring_1932 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1972 :: T_Semiring_1932
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1972 T_Semiring_1932
v0
  = let v1 :: T_IsSemiring_1238
v1 = T_Semiring_1932 -> T_IsSemiring_1238
d_isSemiring_1964 (T_Semiring_1932 -> T_Semiring_1932
forall a b. a -> b
coe T_Semiring_1932
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemiringWithoutAnnihilatingZero_1142
v2
             = T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1252
                 (T_IsSemiring_1238 -> T_IsSemiring_1238
forall a b. a -> b
coe T_IsSemiring_1238
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsMonoid_358
v3
                = T_IsSemiringWithoutAnnihilatingZero_1142 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_'42''45'isMonoid_1160
                    (T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsSemiringWithoutAnnihilatingZero_1142
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1142
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsSemigroup_194
v4
                   = T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368 (T_IsMonoid_358 -> T_IsMonoid_358
forall a b. a -> b
coe T_IsMonoid_358
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               ((T_IsMagma_86
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsMagma_86 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'691'_116
                  ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202 (T_IsSemigroup_194 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194
v4))))))
-- Algebra.Bundles.Semiring._.∙-congˡ
d_'8729''45'cong'737'_1974 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Semiring_1932 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_1974 :: ()
-> ()
-> T_Semiring_1932
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_1974 ~()
v0 ~()
v1 T_Semiring_1932
v2
  = T_Semiring_1932
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1974 T_Semiring_1932
v2
du_'8729''45'cong'737'_1974 ::
  T_Semiring_1932 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1974 :: T_Semiring_1932
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1974 T_Semiring_1932
v0
  = let v1 :: T_IsSemiring_1238
v1 = T_Semiring_1932 -> T_IsSemiring_1238
d_isSemiring_1964 (T_Semiring_1932 -> T_Semiring_1932
forall a b. a -> b
coe T_Semiring_1932
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemiringWithoutAnnihilatingZero_1142
v2
             = T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1252
                 (T_IsSemiring_1238 -> T_IsSemiring_1238
forall a b. a -> b
coe T_IsSemiring_1238
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsMonoid_358
v3
                = T_IsSemiringWithoutAnnihilatingZero_1142 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_'42''45'isMonoid_1160
                    (T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsSemiringWithoutAnnihilatingZero_1142
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1142
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsSemigroup_194
v4
                   = T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368 (T_IsMonoid_358 -> T_IsMonoid_358
forall a b. a -> b
coe T_IsMonoid_358
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               ((T_IsMagma_86
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsMagma_86 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'737'_112
                  ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202 (T_IsSemigroup_194 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194
v4))))))
-- Algebra.Bundles.Semiring._.identity
d_identity_1976 ::
  T_Semiring_1932 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_identity_1976 :: T_Semiring_1932 -> T_Σ_14
d_identity_1976 T_Semiring_1932
v0
  = (T_IsMonoid_358 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsMonoid_358 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_identity_370
      ((T_IsSemiringWithoutAnnihilatingZero_1142 -> T_IsMonoid_358)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiringWithoutAnnihilatingZero_1142 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_'42''45'isMonoid_1160
         ((T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1252
            ((T_Semiring_1932 -> T_IsSemiring_1238) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semiring_1932 -> T_IsSemiring_1238
d_isSemiring_1964 (T_Semiring_1932 -> AgdaAny
forall a b. a -> b
coe T_Semiring_1932
v0))))
-- Algebra.Bundles.Semiring._.identityʳ
d_identity'691'_1978 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Semiring_1932 -> AgdaAny -> AgdaAny
d_identity'691'_1978 :: () -> () -> T_Semiring_1932 -> AgdaAny -> AgdaAny
d_identity'691'_1978 ~()
v0 ~()
v1 T_Semiring_1932
v2 = T_Semiring_1932 -> AgdaAny -> AgdaAny
du_identity'691'_1978 T_Semiring_1932
v2
du_identity'691'_1978 :: T_Semiring_1932 -> AgdaAny -> AgdaAny
du_identity'691'_1978 :: T_Semiring_1932 -> AgdaAny -> AgdaAny
du_identity'691'_1978 T_Semiring_1932
v0
  = let v1 :: T_IsSemiring_1238
v1 = T_Semiring_1932 -> T_IsSemiring_1238
d_isSemiring_1964 (T_Semiring_1932 -> T_Semiring_1932
forall a b. a -> b
coe T_Semiring_1932
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemiringWithoutAnnihilatingZero_1142
v2
             = T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1252
                 (T_IsSemiring_1238 -> T_IsSemiring_1238
forall a b. a -> b
coe T_IsSemiring_1238
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsMonoid_358 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoid_358 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_identity'691'_400
            ((T_IsSemiringWithoutAnnihilatingZero_1142 -> T_IsMonoid_358)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemiringWithoutAnnihilatingZero_1142 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_'42''45'isMonoid_1160 (T_IsSemiringWithoutAnnihilatingZero_1142 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1142
v2))))
-- Algebra.Bundles.Semiring._.identityˡ
d_identity'737'_1980 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Semiring_1932 -> AgdaAny -> AgdaAny
d_identity'737'_1980 :: () -> () -> T_Semiring_1932 -> AgdaAny -> AgdaAny
d_identity'737'_1980 ~()
v0 ~()
v1 T_Semiring_1932
v2 = T_Semiring_1932 -> AgdaAny -> AgdaAny
du_identity'737'_1980 T_Semiring_1932
v2
du_identity'737'_1980 :: T_Semiring_1932 -> AgdaAny -> AgdaAny
du_identity'737'_1980 :: T_Semiring_1932 -> AgdaAny -> AgdaAny
du_identity'737'_1980 T_Semiring_1932
v0
  = let v1 :: T_IsSemiring_1238
v1 = T_Semiring_1932 -> T_IsSemiring_1238
d_isSemiring_1964 (T_Semiring_1932 -> T_Semiring_1932
forall a b. a -> b
coe T_Semiring_1932
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemiringWithoutAnnihilatingZero_1142
v2
             = T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1252
                 (T_IsSemiring_1238 -> T_IsSemiring_1238
forall a b. a -> b
coe T_IsSemiring_1238
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsMonoid_358 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoid_358 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_identity'737'_398
            ((T_IsSemiringWithoutAnnihilatingZero_1142 -> T_IsMonoid_358)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemiringWithoutAnnihilatingZero_1142 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_'42''45'isMonoid_1160 (T_IsSemiringWithoutAnnihilatingZero_1142 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1142
v2))))
-- Algebra.Bundles.Semiring._.isMagma
d_isMagma_1982 ::
  T_Semiring_1932 -> MAlonzo.Code.Algebra.Structures.T_IsMagma_86
d_isMagma_1982 :: T_Semiring_1932 -> T_IsMagma_86
d_isMagma_1982 T_Semiring_1932
v0
  = (T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> T_IsMagma_86
forall a b. a -> b
coe
      T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202
      ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368
         ((T_IsSemiringWithoutAnnihilatingZero_1142 -> T_IsMonoid_358)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemiringWithoutAnnihilatingZero_1142 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_'42''45'isMonoid_1160
            ((T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1252
               ((T_Semiring_1932 -> T_IsSemiring_1238) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semiring_1932 -> T_IsSemiring_1238
d_isSemiring_1964 (T_Semiring_1932 -> AgdaAny
forall a b. a -> b
coe T_Semiring_1932
v0)))))
-- Algebra.Bundles.Semiring._.*-isMonoid
d_'42''45'isMonoid_1984 ::
  T_Semiring_1932 -> MAlonzo.Code.Algebra.Structures.T_IsMonoid_358
d_'42''45'isMonoid_1984 :: T_Semiring_1932 -> T_IsMonoid_358
d_'42''45'isMonoid_1984 T_Semiring_1932
v0
  = (T_IsSemiringWithoutAnnihilatingZero_1142 -> T_IsMonoid_358)
-> AgdaAny -> T_IsMonoid_358
forall a b. a -> b
coe
      T_IsSemiringWithoutAnnihilatingZero_1142 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_'42''45'isMonoid_1160
      ((T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1252
         ((T_Semiring_1932 -> T_IsSemiring_1238) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semiring_1932 -> T_IsSemiring_1238
d_isSemiring_1964 (T_Semiring_1932 -> AgdaAny
forall a b. a -> b
coe T_Semiring_1932
v0)))
-- Algebra.Bundles.Semiring._.isSemigroup
d_isSemigroup_1986 ::
  T_Semiring_1932 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_194
d_isSemigroup_1986 :: T_Semiring_1932 -> T_IsSemigroup_194
d_isSemigroup_1986 T_Semiring_1932
v0
  = (T_IsMonoid_358 -> T_IsSemigroup_194)
-> AgdaAny -> T_IsSemigroup_194
forall a b. a -> b
coe
      T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368
      ((T_IsSemiringWithoutAnnihilatingZero_1142 -> T_IsMonoid_358)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiringWithoutAnnihilatingZero_1142 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_'42''45'isMonoid_1160
         ((T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1252
            ((T_Semiring_1932 -> T_IsSemiring_1238) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semiring_1932 -> T_IsSemiring_1238
d_isSemiring_1964 (T_Semiring_1932 -> AgdaAny
forall a b. a -> b
coe T_Semiring_1932
v0))))
-- Algebra.Bundles.Semiring._.assoc
d_assoc_1988 ::
  T_Semiring_1932 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_1988 :: T_Semiring_1932 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_1988 T_Semiring_1932
v0
  = (T_IsSemigroup_194 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsSemigroup_194 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_assoc_204
      ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368
         ((T_IsCommutativeMonoid_406 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCommutativeMonoid_406 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_416
            ((T_IsSemiringWithoutAnnihilatingZero_1142
 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsCommutativeMonoid_406
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1158
               ((T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1252
                  ((T_Semiring_1932 -> T_IsSemiring_1238) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semiring_1932 -> T_IsSemiring_1238
d_isSemiring_1964 (T_Semiring_1932 -> AgdaAny
forall a b. a -> b
coe T_Semiring_1932
v0))))))
-- Algebra.Bundles.Semiring._.comm
d_comm_1990 :: T_Semiring_1932 -> AgdaAny -> AgdaAny -> AgdaAny
d_comm_1990 :: T_Semiring_1932 -> AgdaAny -> AgdaAny -> AgdaAny
d_comm_1990 T_Semiring_1932
v0
  = (T_IsCommutativeMonoid_406 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsCommutativeMonoid_406 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_comm_418
      ((T_IsSemiringWithoutAnnihilatingZero_1142
 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsCommutativeMonoid_406
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1158
         ((T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1252
            ((T_Semiring_1932 -> T_IsSemiring_1238) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semiring_1932 -> T_IsSemiring_1238
d_isSemiring_1964 (T_Semiring_1932 -> AgdaAny
forall a b. a -> b
coe T_Semiring_1932
v0))))
-- Algebra.Bundles.Semiring._.∙-cong
d_'8729''45'cong_1992 ::
  T_Semiring_1932 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_1992 :: T_Semiring_1932
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_1992 T_Semiring_1932
v0
  = (T_IsMagma_86
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsMagma_86
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_96
      ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202
         ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368
            ((T_IsCommutativeMonoid_406 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsCommutativeMonoid_406 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_416
               ((T_IsSemiringWithoutAnnihilatingZero_1142
 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsCommutativeMonoid_406
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1158
                  ((T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1252
                     ((T_Semiring_1932 -> T_IsSemiring_1238) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semiring_1932 -> T_IsSemiring_1238
d_isSemiring_1964 (T_Semiring_1932 -> AgdaAny
forall a b. a -> b
coe T_Semiring_1932
v0)))))))
-- Algebra.Bundles.Semiring._.∙-congʳ
d_'8729''45'cong'691'_1994 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Semiring_1932 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_1994 :: ()
-> ()
-> T_Semiring_1932
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_1994 ~()
v0 ~()
v1 T_Semiring_1932
v2
  = T_Semiring_1932
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1994 T_Semiring_1932
v2
du_'8729''45'cong'691'_1994 ::
  T_Semiring_1932 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1994 :: T_Semiring_1932
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1994 T_Semiring_1932
v0
  = let v1 :: T_IsSemiring_1238
v1 = T_Semiring_1932 -> T_IsSemiring_1238
d_isSemiring_1964 (T_Semiring_1932 -> T_Semiring_1932
forall a b. a -> b
coe T_Semiring_1932
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemiringWithoutAnnihilatingZero_1142
v2
             = T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1252
                 (T_IsSemiring_1238 -> T_IsSemiring_1238
forall a b. a -> b
coe T_IsSemiring_1238
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsCommutativeMonoid_406
v3
                = T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsCommutativeMonoid_406
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1158
                    (T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsSemiringWithoutAnnihilatingZero_1142
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1142
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsMonoid_358
v4
                   = T_IsCommutativeMonoid_406 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_416 (T_IsCommutativeMonoid_406 -> T_IsCommutativeMonoid_406
forall a b. a -> b
coe T_IsCommutativeMonoid_406
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsSemigroup_194
v5
                      = T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368 (T_IsMonoid_358 -> T_IsMonoid_358
forall a b. a -> b
coe T_IsMonoid_358
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  ((T_IsMagma_86
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsMagma_86 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'691'_116
                     ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202 (T_IsSemigroup_194 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194
v5)))))))
-- Algebra.Bundles.Semiring._.∙-congˡ
d_'8729''45'cong'737'_1996 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Semiring_1932 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_1996 :: ()
-> ()
-> T_Semiring_1932
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_1996 ~()
v0 ~()
v1 T_Semiring_1932
v2
  = T_Semiring_1932
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1996 T_Semiring_1932
v2
du_'8729''45'cong'737'_1996 ::
  T_Semiring_1932 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1996 :: T_Semiring_1932
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1996 T_Semiring_1932
v0
  = let v1 :: T_IsSemiring_1238
v1 = T_Semiring_1932 -> T_IsSemiring_1238
d_isSemiring_1964 (T_Semiring_1932 -> T_Semiring_1932
forall a b. a -> b
coe T_Semiring_1932
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemiringWithoutAnnihilatingZero_1142
v2
             = T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1252
                 (T_IsSemiring_1238 -> T_IsSemiring_1238
forall a b. a -> b
coe T_IsSemiring_1238
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsCommutativeMonoid_406
v3
                = T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsCommutativeMonoid_406
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1158
                    (T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsSemiringWithoutAnnihilatingZero_1142
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1142
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsMonoid_358
v4
                   = T_IsCommutativeMonoid_406 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_416 (T_IsCommutativeMonoid_406 -> T_IsCommutativeMonoid_406
forall a b. a -> b
coe T_IsCommutativeMonoid_406
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsSemigroup_194
v5
                      = T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368 (T_IsMonoid_358 -> T_IsMonoid_358
forall a b. a -> b
coe T_IsMonoid_358
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  ((T_IsMagma_86
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsMagma_86 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'737'_112
                     ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202 (T_IsSemigroup_194 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194
v5)))))))
-- Algebra.Bundles.Semiring._.identity
d_identity_1998 ::
  T_Semiring_1932 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_identity_1998 :: T_Semiring_1932 -> T_Σ_14
d_identity_1998 T_Semiring_1932
v0
  = (T_IsMonoid_358 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsMonoid_358 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_identity_370
      ((T_IsCommutativeMonoid_406 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCommutativeMonoid_406 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_416
         ((T_IsSemiringWithoutAnnihilatingZero_1142
 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsCommutativeMonoid_406
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1158
            ((T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1252
               ((T_Semiring_1932 -> T_IsSemiring_1238) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semiring_1932 -> T_IsSemiring_1238
d_isSemiring_1964 (T_Semiring_1932 -> AgdaAny
forall a b. a -> b
coe T_Semiring_1932
v0)))))
-- Algebra.Bundles.Semiring._.identityʳ
d_identity'691'_2000 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Semiring_1932 -> AgdaAny -> AgdaAny
d_identity'691'_2000 :: () -> () -> T_Semiring_1932 -> AgdaAny -> AgdaAny
d_identity'691'_2000 ~()
v0 ~()
v1 T_Semiring_1932
v2 = T_Semiring_1932 -> AgdaAny -> AgdaAny
du_identity'691'_2000 T_Semiring_1932
v2
du_identity'691'_2000 :: T_Semiring_1932 -> AgdaAny -> AgdaAny
du_identity'691'_2000 :: T_Semiring_1932 -> AgdaAny -> AgdaAny
du_identity'691'_2000 T_Semiring_1932
v0
  = let v1 :: T_IsSemiring_1238
v1 = T_Semiring_1932 -> T_IsSemiring_1238
d_isSemiring_1964 (T_Semiring_1932 -> T_Semiring_1932
forall a b. a -> b
coe T_Semiring_1932
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemiringWithoutAnnihilatingZero_1142
v2
             = T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1252
                 (T_IsSemiring_1238 -> T_IsSemiring_1238
forall a b. a -> b
coe T_IsSemiring_1238
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsCommutativeMonoid_406
v3
                = T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsCommutativeMonoid_406
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1158
                    (T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsSemiringWithoutAnnihilatingZero_1142
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1142
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsMonoid_358 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_358 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_identity'691'_400
               ((T_IsCommutativeMonoid_406 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_406 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_416 (T_IsCommutativeMonoid_406 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_406
v3)))))
-- Algebra.Bundles.Semiring._.identityˡ
d_identity'737'_2002 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Semiring_1932 -> AgdaAny -> AgdaAny
d_identity'737'_2002 :: () -> () -> T_Semiring_1932 -> AgdaAny -> AgdaAny
d_identity'737'_2002 ~()
v0 ~()
v1 T_Semiring_1932
v2 = T_Semiring_1932 -> AgdaAny -> AgdaAny
du_identity'737'_2002 T_Semiring_1932
v2
du_identity'737'_2002 :: T_Semiring_1932 -> AgdaAny -> AgdaAny
du_identity'737'_2002 :: T_Semiring_1932 -> AgdaAny -> AgdaAny
du_identity'737'_2002 T_Semiring_1932
v0
  = let v1 :: T_IsSemiring_1238
v1 = T_Semiring_1932 -> T_IsSemiring_1238
d_isSemiring_1964 (T_Semiring_1932 -> T_Semiring_1932
forall a b. a -> b
coe T_Semiring_1932
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemiringWithoutAnnihilatingZero_1142
v2
             = T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1252
                 (T_IsSemiring_1238 -> T_IsSemiring_1238
forall a b. a -> b
coe T_IsSemiring_1238
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsCommutativeMonoid_406
v3
                = T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsCommutativeMonoid_406
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1158
                    (T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsSemiringWithoutAnnihilatingZero_1142
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1142
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsMonoid_358 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_358 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_identity'737'_398
               ((T_IsCommutativeMonoid_406 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_406 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_416 (T_IsCommutativeMonoid_406 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_406
v3)))))
-- Algebra.Bundles.Semiring._.isCommutativeMagma
d_isCommutativeMagma_2004 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Semiring_1932 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMagma_122
d_isCommutativeMagma_2004 :: () -> () -> T_Semiring_1932 -> T_IsCommutativeMagma_122
d_isCommutativeMagma_2004 ~()
v0 ~()
v1 T_Semiring_1932
v2
  = T_Semiring_1932 -> T_IsCommutativeMagma_122
du_isCommutativeMagma_2004 T_Semiring_1932
v2
du_isCommutativeMagma_2004 ::
  T_Semiring_1932 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMagma_122
du_isCommutativeMagma_2004 :: T_Semiring_1932 -> T_IsCommutativeMagma_122
du_isCommutativeMagma_2004 T_Semiring_1932
v0
  = let v1 :: T_IsSemiring_1238
v1 = T_Semiring_1932 -> T_IsSemiring_1238
d_isSemiring_1964 (T_Semiring_1932 -> T_Semiring_1932
forall a b. a -> b
coe T_Semiring_1932
v0) in
    AgdaAny -> T_IsCommutativeMagma_122
forall a b. a -> b
coe
      (let v2 :: T_IsSemiringWithoutAnnihilatingZero_1142
v2
             = T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1252
                 (T_IsSemiring_1238 -> T_IsSemiring_1238
forall a b. a -> b
coe T_IsSemiring_1238
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsCommutativeMonoid_406
v3
                = T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsCommutativeMonoid_406
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1158
                    (T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsSemiringWithoutAnnihilatingZero_1142
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1142
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsCommutativeSemigroup_270 -> T_IsCommutativeMagma_122)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsCommutativeSemigroup_270 -> T_IsCommutativeMagma_122
MAlonzo.Code.Algebra.Structures.du_isCommutativeMagma_308
               ((T_IsCommutativeMonoid_406 -> T_IsCommutativeSemigroup_270)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsCommutativeMonoid_406 -> T_IsCommutativeSemigroup_270
MAlonzo.Code.Algebra.Structures.du_isCommutativeSemigroup_454
                  (T_IsCommutativeMonoid_406 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_406
v3)))))
-- Algebra.Bundles.Semiring._.+-isCommutativeMonoid
d_'43''45'isCommutativeMonoid_2006 ::
  T_Semiring_1932 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMonoid_406
d_'43''45'isCommutativeMonoid_2006 :: T_Semiring_1932 -> T_IsCommutativeMonoid_406
d_'43''45'isCommutativeMonoid_2006 T_Semiring_1932
v0
  = (T_IsSemiringWithoutAnnihilatingZero_1142
 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> T_IsCommutativeMonoid_406
forall a b. a -> b
coe
      T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsCommutativeMonoid_406
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1158
      ((T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1252
         ((T_Semiring_1932 -> T_IsSemiring_1238) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semiring_1932 -> T_IsSemiring_1238
d_isSemiring_1964 (T_Semiring_1932 -> AgdaAny
forall a b. a -> b
coe T_Semiring_1932
v0)))
-- Algebra.Bundles.Semiring._.isCommutativeSemigroup
d_isCommutativeSemigroup_2008 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Semiring_1932 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_270
d_isCommutativeSemigroup_2008 :: () -> () -> T_Semiring_1932 -> T_IsCommutativeSemigroup_270
d_isCommutativeSemigroup_2008 ~()
v0 ~()
v1 T_Semiring_1932
v2
  = T_Semiring_1932 -> T_IsCommutativeSemigroup_270
du_isCommutativeSemigroup_2008 T_Semiring_1932
v2
du_isCommutativeSemigroup_2008 ::
  T_Semiring_1932 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_270
du_isCommutativeSemigroup_2008 :: T_Semiring_1932 -> T_IsCommutativeSemigroup_270
du_isCommutativeSemigroup_2008 T_Semiring_1932
v0
  = let v1 :: T_IsSemiring_1238
v1 = T_Semiring_1932 -> T_IsSemiring_1238
d_isSemiring_1964 (T_Semiring_1932 -> T_Semiring_1932
forall a b. a -> b
coe T_Semiring_1932
v0) in
    AgdaAny -> T_IsCommutativeSemigroup_270
forall a b. a -> b
coe
      (let v2 :: T_IsSemiringWithoutAnnihilatingZero_1142
v2
             = T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1252
                 (T_IsSemiring_1238 -> T_IsSemiring_1238
forall a b. a -> b
coe T_IsSemiring_1238
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsCommutativeMonoid_406 -> T_IsCommutativeSemigroup_270)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCommutativeMonoid_406 -> T_IsCommutativeSemigroup_270
MAlonzo.Code.Algebra.Structures.du_isCommutativeSemigroup_454
            ((T_IsSemiringWithoutAnnihilatingZero_1142
 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsCommutativeMonoid_406
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1158
               (T_IsSemiringWithoutAnnihilatingZero_1142 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1142
v2))))
-- Algebra.Bundles.Semiring._.isMagma
d_isMagma_2010 ::
  T_Semiring_1932 -> MAlonzo.Code.Algebra.Structures.T_IsMagma_86
d_isMagma_2010 :: T_Semiring_1932 -> T_IsMagma_86
d_isMagma_2010 T_Semiring_1932
v0
  = (T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> T_IsMagma_86
forall a b. a -> b
coe
      T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202
      ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368
         ((T_IsCommutativeMonoid_406 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCommutativeMonoid_406 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_416
            ((T_IsSemiringWithoutAnnihilatingZero_1142
 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsCommutativeMonoid_406
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1158
               ((T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1252
                  ((T_Semiring_1932 -> T_IsSemiring_1238) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semiring_1932 -> T_IsSemiring_1238
d_isSemiring_1964 (T_Semiring_1932 -> AgdaAny
forall a b. a -> b
coe T_Semiring_1932
v0))))))
-- Algebra.Bundles.Semiring._.isMonoid
d_isMonoid_2012 ::
  T_Semiring_1932 -> MAlonzo.Code.Algebra.Structures.T_IsMonoid_358
d_isMonoid_2012 :: T_Semiring_1932 -> T_IsMonoid_358
d_isMonoid_2012 T_Semiring_1932
v0
  = (T_IsCommutativeMonoid_406 -> T_IsMonoid_358)
-> AgdaAny -> T_IsMonoid_358
forall a b. a -> b
coe
      T_IsCommutativeMonoid_406 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_416
      ((T_IsSemiringWithoutAnnihilatingZero_1142
 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsCommutativeMonoid_406
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1158
         ((T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1252
            ((T_Semiring_1932 -> T_IsSemiring_1238) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semiring_1932 -> T_IsSemiring_1238
d_isSemiring_1964 (T_Semiring_1932 -> AgdaAny
forall a b. a -> b
coe T_Semiring_1932
v0))))
-- Algebra.Bundles.Semiring._.isSemigroup
d_isSemigroup_2014 ::
  T_Semiring_1932 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_194
d_isSemigroup_2014 :: T_Semiring_1932 -> T_IsSemigroup_194
d_isSemigroup_2014 T_Semiring_1932
v0
  = (T_IsMonoid_358 -> T_IsSemigroup_194)
-> AgdaAny -> T_IsSemigroup_194
forall a b. a -> b
coe
      T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368
      ((T_IsCommutativeMonoid_406 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCommutativeMonoid_406 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_416
         ((T_IsSemiringWithoutAnnihilatingZero_1142
 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsCommutativeMonoid_406
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1158
            ((T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1252
               ((T_Semiring_1932 -> T_IsSemiring_1238) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semiring_1932 -> T_IsSemiring_1238
d_isSemiring_1964 (T_Semiring_1932 -> AgdaAny
forall a b. a -> b
coe T_Semiring_1932
v0)))))
-- Algebra.Bundles.Semiring._.distrib
d_distrib_2016 ::
  T_Semiring_1932 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_distrib_2016 :: T_Semiring_1932 -> T_Σ_14
d_distrib_2016 T_Semiring_1932
v0
  = (T_IsSemiringWithoutAnnihilatingZero_1142 -> T_Σ_14)
-> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsSemiringWithoutAnnihilatingZero_1142 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_distrib_1162
      ((T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1252
         ((T_Semiring_1932 -> T_IsSemiring_1238) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semiring_1932 -> T_IsSemiring_1238
d_isSemiring_1964 (T_Semiring_1932 -> AgdaAny
forall a b. a -> b
coe T_Semiring_1932
v0)))
-- Algebra.Bundles.Semiring._.distribʳ
d_distrib'691'_2018 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Semiring_1932 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_distrib'691'_2018 :: ()
-> ()
-> T_Semiring_1932
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_distrib'691'_2018 ~()
v0 ~()
v1 T_Semiring_1932
v2 = T_Semiring_1932 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'691'_2018 T_Semiring_1932
v2
du_distrib'691'_2018 ::
  T_Semiring_1932 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'691'_2018 :: T_Semiring_1932 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'691'_2018 T_Semiring_1932
v0
  = let v1 :: T_IsSemiring_1238
v1 = T_Semiring_1932 -> T_IsSemiring_1238
d_isSemiring_1964 (T_Semiring_1932 -> T_Semiring_1932
forall a b. a -> b
coe T_Semiring_1932
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsSemiringWithoutAnnihilatingZero_1142
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiringWithoutAnnihilatingZero_1142
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_distrib'691'_1166
         ((T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1252
            (T_IsSemiring_1238 -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1238
v1)))
-- Algebra.Bundles.Semiring._.distribˡ
d_distrib'737'_2020 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Semiring_1932 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_distrib'737'_2020 :: ()
-> ()
-> T_Semiring_1932
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_distrib'737'_2020 ~()
v0 ~()
v1 T_Semiring_1932
v2 = T_Semiring_1932 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'737'_2020 T_Semiring_1932
v2
du_distrib'737'_2020 ::
  T_Semiring_1932 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'737'_2020 :: T_Semiring_1932 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'737'_2020 T_Semiring_1932
v0
  = let v1 :: T_IsSemiring_1238
v1 = T_Semiring_1932 -> T_IsSemiring_1238
d_isSemiring_1964 (T_Semiring_1932 -> T_Semiring_1932
forall a b. a -> b
coe T_Semiring_1932
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsSemiringWithoutAnnihilatingZero_1142
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiringWithoutAnnihilatingZero_1142
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_distrib'737'_1164
         ((T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1252
            (T_IsSemiring_1238 -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1238
v1)))
-- Algebra.Bundles.Semiring._.isEquivalence
d_isEquivalence_2022 ::
  T_Semiring_1932 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_2022 :: T_Semiring_1932 -> T_IsEquivalence_26
d_isEquivalence_2022 T_Semiring_1932
v0
  = (T_IsMagma_86 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      T_IsMagma_86 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_94
      ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202
         ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368
            ((T_IsCommutativeMonoid_406 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsCommutativeMonoid_406 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_416
               ((T_IsSemiringWithoutAnnihilatingZero_1142
 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsCommutativeMonoid_406
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1158
                  ((T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1252
                     ((T_Semiring_1932 -> T_IsSemiring_1238) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semiring_1932 -> T_IsSemiring_1238
d_isSemiring_1964 (T_Semiring_1932 -> AgdaAny
forall a b. a -> b
coe T_Semiring_1932
v0)))))))
-- Algebra.Bundles.Semiring._.isNearSemiring
d_isNearSemiring_2024 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Semiring_1932 ->
  MAlonzo.Code.Algebra.Structures.T_IsNearSemiring_876
d_isNearSemiring_2024 :: () -> () -> T_Semiring_1932 -> T_IsNearSemiring_876
d_isNearSemiring_2024 ~()
v0 ~()
v1 T_Semiring_1932
v2 = T_Semiring_1932 -> T_IsNearSemiring_876
du_isNearSemiring_2024 T_Semiring_1932
v2
du_isNearSemiring_2024 ::
  T_Semiring_1932 ->
  MAlonzo.Code.Algebra.Structures.T_IsNearSemiring_876
du_isNearSemiring_2024 :: T_Semiring_1932 -> T_IsNearSemiring_876
du_isNearSemiring_2024 T_Semiring_1932
v0
  = let v1 :: T_IsSemiring_1238
v1 = T_Semiring_1932 -> T_IsSemiring_1238
d_isSemiring_1964 (T_Semiring_1932 -> T_Semiring_1932
forall a b. a -> b
coe T_Semiring_1932
v0) in
    AgdaAny -> T_IsNearSemiring_876
forall a b. a -> b
coe
      ((T_IsSemiringWithoutOne_952 -> T_IsNearSemiring_876)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiringWithoutOne_952 -> T_IsNearSemiring_876
MAlonzo.Code.Algebra.Structures.du_isNearSemiring_990
         ((T_IsSemiring_1238 -> T_IsSemiringWithoutOne_952)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemiring_1238 -> T_IsSemiringWithoutOne_952
MAlonzo.Code.Algebra.Structures.du_isSemiringWithoutOne_1326
            (T_IsSemiring_1238 -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1238
v1)))
-- Algebra.Bundles.Semiring._.isPartialEquivalence
d_isPartialEquivalence_2026 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Semiring_1932 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_2026 :: () -> () -> T_Semiring_1932 -> T_IsPartialEquivalence_16
d_isPartialEquivalence_2026 ~()
v0 ~()
v1 T_Semiring_1932
v2
  = T_Semiring_1932 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_2026 T_Semiring_1932
v2
du_isPartialEquivalence_2026 ::
  T_Semiring_1932 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_2026 :: T_Semiring_1932 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_2026 T_Semiring_1932
v0
  = let v1 :: T_IsSemiring_1238
v1 = T_Semiring_1932 -> T_IsSemiring_1238
d_isSemiring_1964 (T_Semiring_1932 -> T_Semiring_1932
forall a b. a -> b
coe T_Semiring_1932
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsSemiringWithoutAnnihilatingZero_1142
v2
             = T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1252
                 (T_IsSemiring_1238 -> T_IsSemiring_1238
forall a b. a -> b
coe T_IsSemiring_1238
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsCommutativeMonoid_406
v3
                = T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsCommutativeMonoid_406
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1158
                    (T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsSemiringWithoutAnnihilatingZero_1142
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1142
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsMonoid_358
v4
                   = T_IsCommutativeMonoid_406 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_416 (T_IsCommutativeMonoid_406 -> T_IsCommutativeMonoid_406
forall a b. a -> b
coe T_IsCommutativeMonoid_406
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsSemigroup_194
v5
                      = T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368 (T_IsMonoid_358 -> T_IsMonoid_358
forall a b. a -> b
coe T_IsMonoid_358
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (let v6 :: T_IsMagma_86
v6 = T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202 (T_IsSemigroup_194 -> T_IsSemigroup_194
forall a b. a -> b
coe T_IsSemigroup_194
v5) in
                   AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     ((T_IsEquivalence_26 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsEquivalence_26 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
                        ((T_IsMagma_86 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_IsMagma_86 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_94 (T_IsMagma_86 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86
v6))))))))
-- Algebra.Bundles.Semiring._.isSemiringWithoutAnnihilatingZero
d_isSemiringWithoutAnnihilatingZero_2028 ::
  T_Semiring_1932 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutAnnihilatingZero_1142
d_isSemiringWithoutAnnihilatingZero_2028 :: T_Semiring_1932 -> T_IsSemiringWithoutAnnihilatingZero_1142
d_isSemiringWithoutAnnihilatingZero_2028 T_Semiring_1932
v0
  = (T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142)
-> AgdaAny -> T_IsSemiringWithoutAnnihilatingZero_1142
forall a b. a -> b
coe
      T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1252
      ((T_Semiring_1932 -> T_IsSemiring_1238) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semiring_1932 -> T_IsSemiring_1238
d_isSemiring_1964 (T_Semiring_1932 -> AgdaAny
forall a b. a -> b
coe T_Semiring_1932
v0))
-- Algebra.Bundles.Semiring._.isSemiringWithoutOne
d_isSemiringWithoutOne_2030 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Semiring_1932 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutOne_952
d_isSemiringWithoutOne_2030 :: () -> () -> T_Semiring_1932 -> T_IsSemiringWithoutOne_952
d_isSemiringWithoutOne_2030 ~()
v0 ~()
v1 T_Semiring_1932
v2
  = T_Semiring_1932 -> T_IsSemiringWithoutOne_952
du_isSemiringWithoutOne_2030 T_Semiring_1932
v2
du_isSemiringWithoutOne_2030 ::
  T_Semiring_1932 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutOne_952
du_isSemiringWithoutOne_2030 :: T_Semiring_1932 -> T_IsSemiringWithoutOne_952
du_isSemiringWithoutOne_2030 T_Semiring_1932
v0
  = (T_IsSemiring_1238 -> T_IsSemiringWithoutOne_952)
-> AgdaAny -> T_IsSemiringWithoutOne_952
forall a b. a -> b
coe
      T_IsSemiring_1238 -> T_IsSemiringWithoutOne_952
MAlonzo.Code.Algebra.Structures.du_isSemiringWithoutOne_1326
      ((T_Semiring_1932 -> T_IsSemiring_1238) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semiring_1932 -> T_IsSemiring_1238
d_isSemiring_1964 (T_Semiring_1932 -> AgdaAny
forall a b. a -> b
coe T_Semiring_1932
v0))
-- Algebra.Bundles.Semiring._.refl
d_refl_2032 :: T_Semiring_1932 -> AgdaAny -> AgdaAny
d_refl_2032 :: T_Semiring_1932 -> AgdaAny -> AgdaAny
d_refl_2032 T_Semiring_1932
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_86 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_86 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_94
         ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202
            ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368
               ((T_IsCommutativeMonoid_406 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsCommutativeMonoid_406 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_416
                  ((T_IsSemiringWithoutAnnihilatingZero_1142
 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsCommutativeMonoid_406
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1158
                     ((T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1252
                        ((T_Semiring_1932 -> T_IsSemiring_1238) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semiring_1932 -> T_IsSemiring_1238
d_isSemiring_1964 (T_Semiring_1932 -> AgdaAny
forall a b. a -> b
coe T_Semiring_1932
v0))))))))
-- Algebra.Bundles.Semiring._.reflexive
d_reflexive_2034 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Semiring_1932 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_2034 :: ()
-> ()
-> T_Semiring_1932
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_2034 ~()
v0 ~()
v1 T_Semiring_1932
v2 = T_Semiring_1932 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_2034 T_Semiring_1932
v2
du_reflexive_2034 ::
  T_Semiring_1932 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_2034 :: T_Semiring_1932 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_2034 T_Semiring_1932
v0
  = let v1 :: T_IsSemiring_1238
v1 = T_Semiring_1932 -> T_IsSemiring_1238
d_isSemiring_1964 (T_Semiring_1932 -> T_Semiring_1932
forall a b. a -> b
coe T_Semiring_1932
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemiringWithoutAnnihilatingZero_1142
v2
             = T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1252
                 (T_IsSemiring_1238 -> T_IsSemiring_1238
forall a b. a -> b
coe T_IsSemiring_1238
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsCommutativeMonoid_406
v3
                = T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsCommutativeMonoid_406
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1158
                    (T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsSemiringWithoutAnnihilatingZero_1142
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1142
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsMonoid_358
v4
                   = T_IsCommutativeMonoid_406 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_416 (T_IsCommutativeMonoid_406 -> T_IsCommutativeMonoid_406
forall a b. a -> b
coe T_IsCommutativeMonoid_406
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsSemigroup_194
v5
                      = T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368 (T_IsMonoid_358 -> T_IsMonoid_358
forall a b. a -> b
coe T_IsMonoid_358
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (let v6 :: T_IsMagma_86
v6 = T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202 (T_IsSemigroup_194 -> T_IsSemigroup_194
forall a b. a -> b
coe T_IsSemigroup_194
v5) in
                   (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
                     (\ AgdaAny
v7 AgdaAny
v8 AgdaAny
v9 ->
                        (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                          T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
                          ((T_IsMagma_86 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_94 (T_IsMagma_86 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86
v6))
                          AgdaAny
v7))))))
-- Algebra.Bundles.Semiring._.setoid
d_setoid_2036 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Semiring_1932 -> MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_2036 :: () -> () -> T_Semiring_1932 -> T_Setoid_44
d_setoid_2036 ~()
v0 ~()
v1 T_Semiring_1932
v2 = T_Semiring_1932 -> T_Setoid_44
du_setoid_2036 T_Semiring_1932
v2
du_setoid_2036 ::
  T_Semiring_1932 -> MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_2036 :: T_Semiring_1932 -> T_Setoid_44
du_setoid_2036 T_Semiring_1932
v0
  = let v1 :: T_IsSemiring_1238
v1 = T_Semiring_1932 -> T_IsSemiring_1238
d_isSemiring_1964 (T_Semiring_1932 -> T_Semiring_1932
forall a b. a -> b
coe T_Semiring_1932
v0) in
    AgdaAny -> T_Setoid_44
forall a b. a -> b
coe
      (let v2 :: T_IsSemiringWithoutAnnihilatingZero_1142
v2
             = T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1252
                 (T_IsSemiring_1238 -> T_IsSemiring_1238
forall a b. a -> b
coe T_IsSemiring_1238
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsCommutativeMonoid_406
v3
                = T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsCommutativeMonoid_406
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1158
                    (T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsSemiringWithoutAnnihilatingZero_1142
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1142
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsMonoid_358
v4
                   = T_IsCommutativeMonoid_406 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_416 (T_IsCommutativeMonoid_406 -> T_IsCommutativeMonoid_406
forall a b. a -> b
coe T_IsCommutativeMonoid_406
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsSemigroup_194
v5
                      = T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368 (T_IsMonoid_358 -> T_IsMonoid_358
forall a b. a -> b
coe T_IsMonoid_358
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  ((T_IsMagma_86 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsMagma_86 -> T_Setoid_44
MAlonzo.Code.Algebra.Structures.du_setoid_110
                     ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202 (T_IsSemigroup_194 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194
v5)))))))
-- Algebra.Bundles.Semiring._.sym
d_sym_2038 ::
  T_Semiring_1932 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_2038 :: T_Semiring_1932 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_2038 T_Semiring_1932
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_86 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_86 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_94
         ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202
            ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368
               ((T_IsCommutativeMonoid_406 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsCommutativeMonoid_406 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_416
                  ((T_IsSemiringWithoutAnnihilatingZero_1142
 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsCommutativeMonoid_406
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1158
                     ((T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1252
                        ((T_Semiring_1932 -> T_IsSemiring_1238) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semiring_1932 -> T_IsSemiring_1238
d_isSemiring_1964 (T_Semiring_1932 -> AgdaAny
forall a b. a -> b
coe T_Semiring_1932
v0))))))))
-- Algebra.Bundles.Semiring._.trans
d_trans_2040 ::
  T_Semiring_1932 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_2040 :: T_Semiring_1932
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_2040 T_Semiring_1932
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_86 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_86 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_94
         ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202
            ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368
               ((T_IsCommutativeMonoid_406 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsCommutativeMonoid_406 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_416
                  ((T_IsSemiringWithoutAnnihilatingZero_1142
 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsCommutativeMonoid_406
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1158
                     ((T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1252
                        ((T_Semiring_1932 -> T_IsSemiring_1238) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semiring_1932 -> T_IsSemiring_1238
d_isSemiring_1964 (T_Semiring_1932 -> AgdaAny
forall a b. a -> b
coe T_Semiring_1932
v0))))))))
-- Algebra.Bundles.Semiring._.zero
d_zero_2042 ::
  T_Semiring_1932 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_zero_2042 :: T_Semiring_1932 -> T_Σ_14
d_zero_2042 T_Semiring_1932
v0
  = (T_IsSemiring_1238 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsSemiring_1238 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_zero_1254
      ((T_Semiring_1932 -> T_IsSemiring_1238) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semiring_1932 -> T_IsSemiring_1238
d_isSemiring_1964 (T_Semiring_1932 -> AgdaAny
forall a b. a -> b
coe T_Semiring_1932
v0))
-- Algebra.Bundles.Semiring._.zeroʳ
d_zero'691'_2044 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Semiring_1932 -> AgdaAny -> AgdaAny
d_zero'691'_2044 :: () -> () -> T_Semiring_1932 -> AgdaAny -> AgdaAny
d_zero'691'_2044 ~()
v0 ~()
v1 T_Semiring_1932
v2 = T_Semiring_1932 -> AgdaAny -> AgdaAny
du_zero'691'_2044 T_Semiring_1932
v2
du_zero'691'_2044 :: T_Semiring_1932 -> AgdaAny -> AgdaAny
du_zero'691'_2044 :: T_Semiring_1932 -> AgdaAny -> AgdaAny
du_zero'691'_2044 T_Semiring_1932
v0
  = let v1 :: T_IsSemiring_1238
v1 = T_Semiring_1932 -> T_IsSemiring_1238
d_isSemiring_1964 (T_Semiring_1932 -> T_Semiring_1932
forall a b. a -> b
coe T_Semiring_1932
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsSemiringWithoutOne_952 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiringWithoutOne_952 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_zero'691'_988
         ((T_IsSemiring_1238 -> T_IsSemiringWithoutOne_952)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemiring_1238 -> T_IsSemiringWithoutOne_952
MAlonzo.Code.Algebra.Structures.du_isSemiringWithoutOne_1326
            (T_IsSemiring_1238 -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1238
v1)))
-- Algebra.Bundles.Semiring._.zeroˡ
d_zero'737'_2046 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Semiring_1932 -> AgdaAny -> AgdaAny
d_zero'737'_2046 :: () -> () -> T_Semiring_1932 -> AgdaAny -> AgdaAny
d_zero'737'_2046 ~()
v0 ~()
v1 T_Semiring_1932
v2 = T_Semiring_1932 -> AgdaAny -> AgdaAny
du_zero'737'_2046 T_Semiring_1932
v2
du_zero'737'_2046 :: T_Semiring_1932 -> AgdaAny -> AgdaAny
du_zero'737'_2046 :: T_Semiring_1932 -> AgdaAny -> AgdaAny
du_zero'737'_2046 T_Semiring_1932
v0
  = let v1 :: T_IsSemiring_1238
v1 = T_Semiring_1932 -> T_IsSemiring_1238
d_isSemiring_1964 (T_Semiring_1932 -> T_Semiring_1932
forall a b. a -> b
coe T_Semiring_1932
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsSemiringWithoutOne_952 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiringWithoutOne_952 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_zero'737'_986
         ((T_IsSemiring_1238 -> T_IsSemiringWithoutOne_952)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemiring_1238 -> T_IsSemiringWithoutOne_952
MAlonzo.Code.Algebra.Structures.du_isSemiringWithoutOne_1326
            (T_IsSemiring_1238 -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1238
v1)))
-- Algebra.Bundles.Semiring.semiringWithoutAnnihilatingZero
d_semiringWithoutAnnihilatingZero_2048 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Semiring_1932 -> T_SemiringWithoutAnnihilatingZero_1786
d_semiringWithoutAnnihilatingZero_2048 :: ()
-> () -> T_Semiring_1932 -> T_SemiringWithoutAnnihilatingZero_1786
d_semiringWithoutAnnihilatingZero_2048 ~()
v0 ~()
v1 T_Semiring_1932
v2
  = T_Semiring_1932 -> T_SemiringWithoutAnnihilatingZero_1786
du_semiringWithoutAnnihilatingZero_2048 T_Semiring_1932
v2
du_semiringWithoutAnnihilatingZero_2048 ::
  T_Semiring_1932 -> T_SemiringWithoutAnnihilatingZero_1786
du_semiringWithoutAnnihilatingZero_2048 :: T_Semiring_1932 -> T_SemiringWithoutAnnihilatingZero_1786
du_semiringWithoutAnnihilatingZero_2048 T_Semiring_1932
v0
  = ((AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> AgdaAny
 -> T_IsSemiringWithoutAnnihilatingZero_1142
 -> T_SemiringWithoutAnnihilatingZero_1786)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsSemiringWithoutAnnihilatingZero_1142
-> T_SemiringWithoutAnnihilatingZero_1786
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsSemiringWithoutAnnihilatingZero_1142
-> T_SemiringWithoutAnnihilatingZero_1786
C_SemiringWithoutAnnihilatingZero'46'constructor_30907
      (T_Semiring_1932 -> AgdaAny -> AgdaAny -> AgdaAny
d__'43'__1956 (T_Semiring_1932 -> T_Semiring_1932
forall a b. a -> b
coe T_Semiring_1932
v0)) (T_Semiring_1932 -> AgdaAny -> AgdaAny -> AgdaAny
d__'42'__1958 (T_Semiring_1932 -> T_Semiring_1932
forall a b. a -> b
coe T_Semiring_1932
v0))
      (T_Semiring_1932 -> AgdaAny
d_0'35'_1960 (T_Semiring_1932 -> T_Semiring_1932
forall a b. a -> b
coe T_Semiring_1932
v0)) (T_Semiring_1932 -> AgdaAny
d_1'35'_1962 (T_Semiring_1932 -> T_Semiring_1932
forall a b. a -> b
coe T_Semiring_1932
v0))
      (T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1252
         ((T_Semiring_1932 -> T_IsSemiring_1238)
-> AgdaAny -> T_IsSemiring_1238
forall a b. a -> b
coe T_Semiring_1932 -> T_IsSemiring_1238
d_isSemiring_1964 (T_Semiring_1932 -> AgdaAny
forall a b. a -> b
coe T_Semiring_1932
v0)))
-- Algebra.Bundles.Semiring._._≉_
d__'8777'__2052 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Semiring_1932 -> AgdaAny -> AgdaAny -> ()
d__'8777'__2052 :: () -> () -> T_Semiring_1932 -> AgdaAny -> AgdaAny -> ()
d__'8777'__2052 = () -> () -> T_Semiring_1932 -> AgdaAny -> AgdaAny -> ()
forall a. a
erased
-- Algebra.Bundles.Semiring._.magma
d_magma_2054 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Semiring_1932 -> T_Magma_36
d_magma_2054 :: () -> () -> T_Semiring_1932 -> T_Magma_36
d_magma_2054 ~()
v0 ~()
v1 T_Semiring_1932
v2 = T_Semiring_1932 -> T_Magma_36
du_magma_2054 T_Semiring_1932
v2
du_magma_2054 :: T_Semiring_1932 -> T_Magma_36
du_magma_2054 :: T_Semiring_1932 -> T_Magma_36
du_magma_2054 T_Semiring_1932
v0
  = let v1 :: t
v1 = (T_Semiring_1932 -> T_SemiringWithoutAnnihilatingZero_1786)
-> AgdaAny -> t
forall a b. a -> b
coe T_Semiring_1932 -> T_SemiringWithoutAnnihilatingZero_1786
du_semiringWithoutAnnihilatingZero_2048 (T_Semiring_1932 -> AgdaAny
forall a b. a -> b
coe T_Semiring_1932
v0) in
    AgdaAny -> T_Magma_36
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_SemiringWithoutAnnihilatingZero_1786 -> T_Monoid_506)
-> AgdaAny -> t
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_1786 -> T_Monoid_506
du_'42''45'monoid_1916 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_Semigroup_206 -> T_Magma_36) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semigroup_206 -> T_Magma_36
du_magma_254 ((T_Monoid_506 -> T_Semigroup_206) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Monoid_506 -> T_Semigroup_206
du_semigroup_566 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2))))
-- Algebra.Bundles.Semiring._.*-monoid
d_'42''45'monoid_2056 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Semiring_1932 -> T_Monoid_506
d_'42''45'monoid_2056 :: () -> () -> T_Semiring_1932 -> T_Monoid_506
d_'42''45'monoid_2056 ~()
v0 ~()
v1 T_Semiring_1932
v2 = T_Semiring_1932 -> T_Monoid_506
du_'42''45'monoid_2056 T_Semiring_1932
v2
du_'42''45'monoid_2056 :: T_Semiring_1932 -> T_Monoid_506
du_'42''45'monoid_2056 :: T_Semiring_1932 -> T_Monoid_506
du_'42''45'monoid_2056 T_Semiring_1932
v0
  = (T_SemiringWithoutAnnihilatingZero_1786 -> T_Monoid_506)
-> AgdaAny -> T_Monoid_506
forall a b. a -> b
coe
      T_SemiringWithoutAnnihilatingZero_1786 -> T_Monoid_506
du_'42''45'monoid_1916
      ((T_Semiring_1932 -> T_SemiringWithoutAnnihilatingZero_1786)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semiring_1932 -> T_SemiringWithoutAnnihilatingZero_1786
du_semiringWithoutAnnihilatingZero_2048 (T_Semiring_1932 -> AgdaAny
forall a b. a -> b
coe T_Semiring_1932
v0))
-- Algebra.Bundles.Semiring._.rawMagma
d_rawMagma_2058 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Semiring_1932 -> T_RawMagma_8
d_rawMagma_2058 :: () -> () -> T_Semiring_1932 -> T_RawMagma_8
d_rawMagma_2058 ~()
v0 ~()
v1 T_Semiring_1932
v2 = T_Semiring_1932 -> T_RawMagma_8
du_rawMagma_2058 T_Semiring_1932
v2
du_rawMagma_2058 :: T_Semiring_1932 -> T_RawMagma_8
du_rawMagma_2058 :: T_Semiring_1932 -> T_RawMagma_8
du_rawMagma_2058 T_Semiring_1932
v0
  = let v1 :: t
v1 = (T_Semiring_1932 -> T_SemiringWithoutAnnihilatingZero_1786)
-> AgdaAny -> t
forall a b. a -> b
coe T_Semiring_1932 -> T_SemiringWithoutAnnihilatingZero_1786
du_semiringWithoutAnnihilatingZero_2048 (T_Semiring_1932 -> AgdaAny
forall a b. a -> b
coe T_Semiring_1932
v0) in
    AgdaAny -> T_RawMagma_8
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_SemiringWithoutAnnihilatingZero_1786 -> T_Monoid_506)
-> AgdaAny -> t
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_1786 -> T_Monoid_506
du_'42''45'monoid_1916 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: t
v3 = (T_Monoid_506 -> T_Semigroup_206) -> AgdaAny -> t
forall a b. a -> b
coe T_Monoid_506 -> T_Semigroup_206
du_semigroup_566 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_Magma_36 -> T_RawMagma_8) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Magma_36 -> T_RawMagma_8
du_rawMagma_80 ((T_Semigroup_206 -> T_Magma_36) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semigroup_206 -> T_Magma_36
du_magma_254 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3)))))
-- Algebra.Bundles.Semiring._.rawMonoid
d_rawMonoid_2060 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Semiring_1932 -> T_RawMonoid_474
d_rawMonoid_2060 :: () -> () -> T_Semiring_1932 -> T_RawMonoid_474
d_rawMonoid_2060 ~()
v0 ~()
v1 T_Semiring_1932
v2 = T_Semiring_1932 -> T_RawMonoid_474
du_rawMonoid_2060 T_Semiring_1932
v2
du_rawMonoid_2060 :: T_Semiring_1932 -> T_RawMonoid_474
du_rawMonoid_2060 :: T_Semiring_1932 -> T_RawMonoid_474
du_rawMonoid_2060 T_Semiring_1932
v0
  = let v1 :: t
v1 = (T_Semiring_1932 -> T_SemiringWithoutAnnihilatingZero_1786)
-> AgdaAny -> t
forall a b. a -> b
coe T_Semiring_1932 -> T_SemiringWithoutAnnihilatingZero_1786
du_semiringWithoutAnnihilatingZero_2048 (T_Semiring_1932 -> AgdaAny
forall a b. a -> b
coe T_Semiring_1932
v0) in
    AgdaAny -> T_RawMonoid_474
forall a b. a -> b
coe ((T_Monoid_506 -> T_RawMonoid_474) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Monoid_506 -> T_RawMonoid_474
du_rawMonoid_576 ((T_SemiringWithoutAnnihilatingZero_1786 -> T_Monoid_506)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_1786 -> T_Monoid_506
du_'42''45'monoid_1916 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1)))
-- Algebra.Bundles.Semiring._.semigroup
d_semigroup_2062 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Semiring_1932 -> T_Semigroup_206
d_semigroup_2062 :: () -> () -> T_Semiring_1932 -> T_Semigroup_206
d_semigroup_2062 ~()
v0 ~()
v1 T_Semiring_1932
v2 = T_Semiring_1932 -> T_Semigroup_206
du_semigroup_2062 T_Semiring_1932
v2
du_semigroup_2062 :: T_Semiring_1932 -> T_Semigroup_206
du_semigroup_2062 :: T_Semiring_1932 -> T_Semigroup_206
du_semigroup_2062 T_Semiring_1932
v0
  = let v1 :: t
v1 = (T_Semiring_1932 -> T_SemiringWithoutAnnihilatingZero_1786)
-> AgdaAny -> t
forall a b. a -> b
coe T_Semiring_1932 -> T_SemiringWithoutAnnihilatingZero_1786
du_semiringWithoutAnnihilatingZero_2048 (T_Semiring_1932 -> AgdaAny
forall a b. a -> b
coe T_Semiring_1932
v0) in
    AgdaAny -> T_Semigroup_206
forall a b. a -> b
coe ((T_Monoid_506 -> T_Semigroup_206) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Monoid_506 -> T_Semigroup_206
du_semigroup_566 ((T_SemiringWithoutAnnihilatingZero_1786 -> T_Monoid_506)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_1786 -> T_Monoid_506
du_'42''45'monoid_1916 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1)))
-- Algebra.Bundles.Semiring._.commutativeMagma
d_commutativeMagma_2064 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Semiring_1932 -> T_CommutativeMagma_148
d_commutativeMagma_2064 :: () -> () -> T_Semiring_1932 -> T_CommutativeMagma_148
d_commutativeMagma_2064 ~()
v0 ~()
v1 T_Semiring_1932
v2 = T_Semiring_1932 -> T_CommutativeMagma_148
du_commutativeMagma_2064 T_Semiring_1932
v2
du_commutativeMagma_2064 ::
  T_Semiring_1932 -> T_CommutativeMagma_148
du_commutativeMagma_2064 :: T_Semiring_1932 -> T_CommutativeMagma_148
du_commutativeMagma_2064 T_Semiring_1932
v0
  = let v1 :: t
v1 = (T_Semiring_1932 -> T_SemiringWithoutAnnihilatingZero_1786)
-> AgdaAny -> t
forall a b. a -> b
coe T_Semiring_1932 -> T_SemiringWithoutAnnihilatingZero_1786
du_semiringWithoutAnnihilatingZero_2048 (T_Semiring_1932 -> AgdaAny
forall a b. a -> b
coe T_Semiring_1932
v0) in
    AgdaAny -> T_CommutativeMagma_148
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_SemiringWithoutAnnihilatingZero_1786 -> T_CommutativeMonoid_582)
-> AgdaAny -> t
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_1786 -> T_CommutativeMonoid_582
du_'43''45'commutativeMonoid_1896 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_CommutativeSemigroup_332 -> T_CommutativeMagma_148)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_CommutativeSemigroup_332 -> T_CommutativeMagma_148
du_commutativeMagma_396
            ((T_CommutativeMonoid_582 -> T_CommutativeSemigroup_332)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeMonoid_582 -> T_CommutativeSemigroup_332
du_commutativeSemigroup_664 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2))))
-- Algebra.Bundles.Semiring._.+-commutativeMonoid
d_'43''45'commutativeMonoid_2066 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Semiring_1932 -> T_CommutativeMonoid_582
d_'43''45'commutativeMonoid_2066 :: () -> () -> T_Semiring_1932 -> T_CommutativeMonoid_582
d_'43''45'commutativeMonoid_2066 ~()
v0 ~()
v1 T_Semiring_1932
v2
  = T_Semiring_1932 -> T_CommutativeMonoid_582
du_'43''45'commutativeMonoid_2066 T_Semiring_1932
v2
du_'43''45'commutativeMonoid_2066 ::
  T_Semiring_1932 -> T_CommutativeMonoid_582
du_'43''45'commutativeMonoid_2066 :: T_Semiring_1932 -> T_CommutativeMonoid_582
du_'43''45'commutativeMonoid_2066 T_Semiring_1932
v0
  = (T_SemiringWithoutAnnihilatingZero_1786 -> T_CommutativeMonoid_582)
-> AgdaAny -> T_CommutativeMonoid_582
forall a b. a -> b
coe
      T_SemiringWithoutAnnihilatingZero_1786 -> T_CommutativeMonoid_582
du_'43''45'commutativeMonoid_1896
      ((T_Semiring_1932 -> T_SemiringWithoutAnnihilatingZero_1786)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semiring_1932 -> T_SemiringWithoutAnnihilatingZero_1786
du_semiringWithoutAnnihilatingZero_2048 (T_Semiring_1932 -> AgdaAny
forall a b. a -> b
coe T_Semiring_1932
v0))
-- Algebra.Bundles.Semiring._.commutativeSemigroup
d_commutativeSemigroup_2068 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Semiring_1932 -> T_CommutativeSemigroup_332
d_commutativeSemigroup_2068 :: () -> () -> T_Semiring_1932 -> T_CommutativeSemigroup_332
d_commutativeSemigroup_2068 ~()
v0 ~()
v1 T_Semiring_1932
v2
  = T_Semiring_1932 -> T_CommutativeSemigroup_332
du_commutativeSemigroup_2068 T_Semiring_1932
v2
du_commutativeSemigroup_2068 ::
  T_Semiring_1932 -> T_CommutativeSemigroup_332
du_commutativeSemigroup_2068 :: T_Semiring_1932 -> T_CommutativeSemigroup_332
du_commutativeSemigroup_2068 T_Semiring_1932
v0
  = let v1 :: t
v1 = (T_Semiring_1932 -> T_SemiringWithoutAnnihilatingZero_1786)
-> AgdaAny -> t
forall a b. a -> b
coe T_Semiring_1932 -> T_SemiringWithoutAnnihilatingZero_1786
du_semiringWithoutAnnihilatingZero_2048 (T_Semiring_1932 -> AgdaAny
forall a b. a -> b
coe T_Semiring_1932
v0) in
    AgdaAny -> T_CommutativeSemigroup_332
forall a b. a -> b
coe
      ((T_CommutativeMonoid_582 -> T_CommutativeSemigroup_332)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_CommutativeMonoid_582 -> T_CommutativeSemigroup_332
du_commutativeSemigroup_664
         ((T_SemiringWithoutAnnihilatingZero_1786 -> T_CommutativeMonoid_582)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_1786 -> T_CommutativeMonoid_582
du_'43''45'commutativeMonoid_1896 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1)))
-- Algebra.Bundles.Semiring._.magma
d_magma_2070 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Semiring_1932 -> T_Magma_36
d_magma_2070 :: () -> () -> T_Semiring_1932 -> T_Magma_36
d_magma_2070 ~()
v0 ~()
v1 T_Semiring_1932
v2 = T_Semiring_1932 -> T_Magma_36
du_magma_2070 T_Semiring_1932
v2
du_magma_2070 :: T_Semiring_1932 -> T_Magma_36
du_magma_2070 :: T_Semiring_1932 -> T_Magma_36
du_magma_2070 T_Semiring_1932
v0
  = let v1 :: t
v1 = (T_Semiring_1932 -> T_SemiringWithoutAnnihilatingZero_1786)
-> AgdaAny -> t
forall a b. a -> b
coe T_Semiring_1932 -> T_SemiringWithoutAnnihilatingZero_1786
du_semiringWithoutAnnihilatingZero_2048 (T_Semiring_1932 -> AgdaAny
forall a b. a -> b
coe T_Semiring_1932
v0) in
    AgdaAny -> T_Magma_36
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_SemiringWithoutAnnihilatingZero_1786 -> T_CommutativeMonoid_582)
-> AgdaAny -> t
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_1786 -> T_CommutativeMonoid_582
du_'43''45'commutativeMonoid_1896 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: t
v3 = (T_CommutativeMonoid_582 -> T_Monoid_506) -> AgdaAny -> t
forall a b. a -> b
coe T_CommutativeMonoid_582 -> T_Monoid_506
du_monoid_650 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_Semigroup_206 -> T_Magma_36) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semigroup_206 -> T_Magma_36
du_magma_254 ((T_Monoid_506 -> T_Semigroup_206) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Monoid_506 -> T_Semigroup_206
du_semigroup_566 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3)))))
-- Algebra.Bundles.Semiring._.monoid
d_monoid_2072 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Semiring_1932 -> T_Monoid_506
d_monoid_2072 :: () -> () -> T_Semiring_1932 -> T_Monoid_506
d_monoid_2072 ~()
v0 ~()
v1 T_Semiring_1932
v2 = T_Semiring_1932 -> T_Monoid_506
du_monoid_2072 T_Semiring_1932
v2
du_monoid_2072 :: T_Semiring_1932 -> T_Monoid_506
du_monoid_2072 :: T_Semiring_1932 -> T_Monoid_506
du_monoid_2072 T_Semiring_1932
v0
  = let v1 :: t
v1 = (T_Semiring_1932 -> T_SemiringWithoutAnnihilatingZero_1786)
-> AgdaAny -> t
forall a b. a -> b
coe T_Semiring_1932 -> T_SemiringWithoutAnnihilatingZero_1786
du_semiringWithoutAnnihilatingZero_2048 (T_Semiring_1932 -> AgdaAny
forall a b. a -> b
coe T_Semiring_1932
v0) in
    AgdaAny -> T_Monoid_506
forall a b. a -> b
coe
      ((T_CommutativeMonoid_582 -> T_Monoid_506) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_CommutativeMonoid_582 -> T_Monoid_506
du_monoid_650 ((T_SemiringWithoutAnnihilatingZero_1786 -> T_CommutativeMonoid_582)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_1786 -> T_CommutativeMonoid_582
du_'43''45'commutativeMonoid_1896 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1)))
-- Algebra.Bundles.Semiring._.rawMagma
d_rawMagma_2074 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Semiring_1932 -> T_RawMagma_8
d_rawMagma_2074 :: () -> () -> T_Semiring_1932 -> T_RawMagma_8
d_rawMagma_2074 ~()
v0 ~()
v1 T_Semiring_1932
v2 = T_Semiring_1932 -> T_RawMagma_8
du_rawMagma_2074 T_Semiring_1932
v2
du_rawMagma_2074 :: T_Semiring_1932 -> T_RawMagma_8
du_rawMagma_2074 :: T_Semiring_1932 -> T_RawMagma_8
du_rawMagma_2074 T_Semiring_1932
v0
  = let v1 :: t
v1 = (T_Semiring_1932 -> T_SemiringWithoutAnnihilatingZero_1786)
-> AgdaAny -> t
forall a b. a -> b
coe T_Semiring_1932 -> T_SemiringWithoutAnnihilatingZero_1786
du_semiringWithoutAnnihilatingZero_2048 (T_Semiring_1932 -> AgdaAny
forall a b. a -> b
coe T_Semiring_1932
v0) in
    AgdaAny -> T_RawMagma_8
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_SemiringWithoutAnnihilatingZero_1786 -> T_CommutativeMonoid_582)
-> AgdaAny -> t
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_1786 -> T_CommutativeMonoid_582
du_'43''45'commutativeMonoid_1896 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: t
v3 = (T_CommutativeMonoid_582 -> T_Monoid_506) -> AgdaAny -> t
forall a b. a -> b
coe T_CommutativeMonoid_582 -> T_Monoid_506
du_monoid_650 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: t
v4 = (T_Monoid_506 -> T_Semigroup_206) -> AgdaAny -> t
forall a b. a -> b
coe T_Monoid_506 -> T_Semigroup_206
du_semigroup_566 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_Magma_36 -> T_RawMagma_8) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Magma_36 -> T_RawMagma_8
du_rawMagma_80 ((T_Semigroup_206 -> T_Magma_36) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semigroup_206 -> T_Magma_36
du_magma_254 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v4))))))
-- Algebra.Bundles.Semiring._.rawMonoid
d_rawMonoid_2076 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Semiring_1932 -> T_RawMonoid_474
d_rawMonoid_2076 :: () -> () -> T_Semiring_1932 -> T_RawMonoid_474
d_rawMonoid_2076 ~()
v0 ~()
v1 T_Semiring_1932
v2 = T_Semiring_1932 -> T_RawMonoid_474
du_rawMonoid_2076 T_Semiring_1932
v2
du_rawMonoid_2076 :: T_Semiring_1932 -> T_RawMonoid_474
du_rawMonoid_2076 :: T_Semiring_1932 -> T_RawMonoid_474
du_rawMonoid_2076 T_Semiring_1932
v0
  = let v1 :: t
v1 = (T_Semiring_1932 -> T_SemiringWithoutAnnihilatingZero_1786)
-> AgdaAny -> t
forall a b. a -> b
coe T_Semiring_1932 -> T_SemiringWithoutAnnihilatingZero_1786
du_semiringWithoutAnnihilatingZero_2048 (T_Semiring_1932 -> AgdaAny
forall a b. a -> b
coe T_Semiring_1932
v0) in
    AgdaAny -> T_RawMonoid_474
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_SemiringWithoutAnnihilatingZero_1786 -> T_CommutativeMonoid_582)
-> AgdaAny -> t
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_1786 -> T_CommutativeMonoid_582
du_'43''45'commutativeMonoid_1896 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_Monoid_506 -> T_RawMonoid_474) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Monoid_506 -> T_RawMonoid_474
du_rawMonoid_576 ((T_CommutativeMonoid_582 -> T_Monoid_506) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeMonoid_582 -> T_Monoid_506
du_monoid_650 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2))))
-- Algebra.Bundles.Semiring._.semigroup
d_semigroup_2078 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Semiring_1932 -> T_Semigroup_206
d_semigroup_2078 :: () -> () -> T_Semiring_1932 -> T_Semigroup_206
d_semigroup_2078 ~()
v0 ~()
v1 T_Semiring_1932
v2 = T_Semiring_1932 -> T_Semigroup_206
du_semigroup_2078 T_Semiring_1932
v2
du_semigroup_2078 :: T_Semiring_1932 -> T_Semigroup_206
du_semigroup_2078 :: T_Semiring_1932 -> T_Semigroup_206
du_semigroup_2078 T_Semiring_1932
v0
  = let v1 :: t
v1 = (T_Semiring_1932 -> T_SemiringWithoutAnnihilatingZero_1786)
-> AgdaAny -> t
forall a b. a -> b
coe T_Semiring_1932 -> T_SemiringWithoutAnnihilatingZero_1786
du_semiringWithoutAnnihilatingZero_2048 (T_Semiring_1932 -> AgdaAny
forall a b. a -> b
coe T_Semiring_1932
v0) in
    AgdaAny -> T_Semigroup_206
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_SemiringWithoutAnnihilatingZero_1786 -> T_CommutativeMonoid_582)
-> AgdaAny -> t
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_1786 -> T_CommutativeMonoid_582
du_'43''45'commutativeMonoid_1896 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_Monoid_506 -> T_Semigroup_206) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Monoid_506 -> T_Semigroup_206
du_semigroup_566 ((T_CommutativeMonoid_582 -> T_Monoid_506) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeMonoid_582 -> T_Monoid_506
du_monoid_650 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2))))
-- Algebra.Bundles.Semiring._.rawNearSemiring
d_rawNearSemiring_2080 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Semiring_1932 -> T_RawNearSemiring_1314
d_rawNearSemiring_2080 :: () -> () -> T_Semiring_1932 -> T_RawNearSemiring_1314
d_rawNearSemiring_2080 ~()
v0 ~()
v1 T_Semiring_1932
v2 = T_Semiring_1932 -> T_RawNearSemiring_1314
du_rawNearSemiring_2080 T_Semiring_1932
v2
du_rawNearSemiring_2080 ::
  T_Semiring_1932 -> T_RawNearSemiring_1314
du_rawNearSemiring_2080 :: T_Semiring_1932 -> T_RawNearSemiring_1314
du_rawNearSemiring_2080 T_Semiring_1932
v0
  = let v1 :: t
v1 = (T_Semiring_1932 -> T_SemiringWithoutAnnihilatingZero_1786)
-> AgdaAny -> t
forall a b. a -> b
coe T_Semiring_1932 -> T_SemiringWithoutAnnihilatingZero_1786
du_semiringWithoutAnnihilatingZero_2048 (T_Semiring_1932 -> AgdaAny
forall a b. a -> b
coe T_Semiring_1932
v0) in
    AgdaAny -> T_RawNearSemiring_1314
forall a b. a -> b
coe
      ((T_RawSemiring_1738 -> T_RawNearSemiring_1314)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_RawSemiring_1738 -> T_RawNearSemiring_1314
du_rawNearSemiring_1768 ((T_SemiringWithoutAnnihilatingZero_1786 -> T_RawSemiring_1738)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_1786 -> T_RawSemiring_1738
du_rawSemiring_1890 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1)))
-- Algebra.Bundles.Semiring._.rawSemiring
d_rawSemiring_2082 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Semiring_1932 -> T_RawSemiring_1738
d_rawSemiring_2082 :: () -> () -> T_Semiring_1932 -> T_RawSemiring_1738
d_rawSemiring_2082 ~()
v0 ~()
v1 T_Semiring_1932
v2 = T_Semiring_1932 -> T_RawSemiring_1738
du_rawSemiring_2082 T_Semiring_1932
v2
du_rawSemiring_2082 :: T_Semiring_1932 -> T_RawSemiring_1738
du_rawSemiring_2082 :: T_Semiring_1932 -> T_RawSemiring_1738
du_rawSemiring_2082 T_Semiring_1932
v0
  = (T_SemiringWithoutAnnihilatingZero_1786 -> T_RawSemiring_1738)
-> AgdaAny -> T_RawSemiring_1738
forall a b. a -> b
coe
      T_SemiringWithoutAnnihilatingZero_1786 -> T_RawSemiring_1738
du_rawSemiring_1890
      ((T_Semiring_1932 -> T_SemiringWithoutAnnihilatingZero_1786)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semiring_1932 -> T_SemiringWithoutAnnihilatingZero_1786
du_semiringWithoutAnnihilatingZero_2048 (T_Semiring_1932 -> AgdaAny
forall a b. a -> b
coe T_Semiring_1932
v0))
-- Algebra.Bundles.Semiring.semiringWithoutOne
d_semiringWithoutOne_2084 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Semiring_1932 -> T_SemiringWithoutOne_1464
d_semiringWithoutOne_2084 :: () -> () -> T_Semiring_1932 -> T_SemiringWithoutOne_1464
d_semiringWithoutOne_2084 ~()
v0 ~()
v1 T_Semiring_1932
v2
  = T_Semiring_1932 -> T_SemiringWithoutOne_1464
du_semiringWithoutOne_2084 T_Semiring_1932
v2
du_semiringWithoutOne_2084 ::
  T_Semiring_1932 -> T_SemiringWithoutOne_1464
du_semiringWithoutOne_2084 :: T_Semiring_1932 -> T_SemiringWithoutOne_1464
du_semiringWithoutOne_2084 T_Semiring_1932
v0
  = ((AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> T_IsSemiringWithoutOne_952
 -> T_SemiringWithoutOne_1464)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_SemiringWithoutOne_1464
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsSemiringWithoutOne_952
-> T_SemiringWithoutOne_1464
C_SemiringWithoutOne'46'constructor_25531 (T_Semiring_1932 -> AgdaAny -> AgdaAny -> AgdaAny
d__'43'__1956 (T_Semiring_1932 -> T_Semiring_1932
forall a b. a -> b
coe T_Semiring_1932
v0))
      (T_Semiring_1932 -> AgdaAny -> AgdaAny -> AgdaAny
d__'42'__1958 (T_Semiring_1932 -> T_Semiring_1932
forall a b. a -> b
coe T_Semiring_1932
v0)) (T_Semiring_1932 -> AgdaAny
d_0'35'_1960 (T_Semiring_1932 -> T_Semiring_1932
forall a b. a -> b
coe T_Semiring_1932
v0))
      ((T_IsSemiring_1238 -> T_IsSemiringWithoutOne_952)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiring_1238 -> T_IsSemiringWithoutOne_952
MAlonzo.Code.Algebra.Structures.du_isSemiringWithoutOne_1326
         ((T_Semiring_1932 -> T_IsSemiring_1238) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semiring_1932 -> T_IsSemiring_1238
d_isSemiring_1964 (T_Semiring_1932 -> AgdaAny
forall a b. a -> b
coe T_Semiring_1932
v0)))
-- Algebra.Bundles.Semiring._.nearSemiring
d_nearSemiring_2088 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Semiring_1932 -> T_NearSemiring_1354
d_nearSemiring_2088 :: () -> () -> T_Semiring_1932 -> T_NearSemiring_1354
d_nearSemiring_2088 ~()
v0 ~()
v1 T_Semiring_1932
v2 = T_Semiring_1932 -> T_NearSemiring_1354
du_nearSemiring_2088 T_Semiring_1932
v2
du_nearSemiring_2088 :: T_Semiring_1932 -> T_NearSemiring_1354
du_nearSemiring_2088 :: T_Semiring_1932 -> T_NearSemiring_1354
du_nearSemiring_2088 T_Semiring_1932
v0
  = (T_SemiringWithoutOne_1464 -> T_NearSemiring_1354)
-> AgdaAny -> T_NearSemiring_1354
forall a b. a -> b
coe
      T_SemiringWithoutOne_1464 -> T_NearSemiring_1354
du_nearSemiring_1562 ((T_Semiring_1932 -> T_SemiringWithoutOne_1464)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semiring_1932 -> T_SemiringWithoutOne_1464
du_semiringWithoutOne_2084 (T_Semiring_1932 -> AgdaAny
forall a b. a -> b
coe T_Semiring_1932
v0))
-- Algebra.Bundles.CommutativeSemiring
d_CommutativeSemiring_2094 :: p -> p -> ()
d_CommutativeSemiring_2094 p
a0 p
a1 = ()
data T_CommutativeSemiring_2094
  = C_CommutativeSemiring'46'constructor_36513 (AgdaAny ->
                                                AgdaAny -> AgdaAny)
                                               (AgdaAny -> AgdaAny -> AgdaAny) AgdaAny AgdaAny
                                               MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiring_1344
-- Algebra.Bundles.CommutativeSemiring.Carrier
d_Carrier_2114 :: T_CommutativeSemiring_2094 -> ()
d_Carrier_2114 :: T_CommutativeSemiring_2094 -> ()
d_Carrier_2114 = T_CommutativeSemiring_2094 -> ()
forall a. a
erased
-- Algebra.Bundles.CommutativeSemiring._≈_
d__'8776'__2116 ::
  T_CommutativeSemiring_2094 -> AgdaAny -> AgdaAny -> ()
d__'8776'__2116 :: T_CommutativeSemiring_2094 -> AgdaAny -> AgdaAny -> ()
d__'8776'__2116 = T_CommutativeSemiring_2094 -> AgdaAny -> AgdaAny -> ()
forall a. a
erased
-- Algebra.Bundles.CommutativeSemiring._+_
d__'43'__2118 ::
  T_CommutativeSemiring_2094 -> AgdaAny -> AgdaAny -> AgdaAny
d__'43'__2118 :: T_CommutativeSemiring_2094 -> AgdaAny -> AgdaAny -> AgdaAny
d__'43'__2118 T_CommutativeSemiring_2094
v0
  = case T_CommutativeSemiring_2094 -> T_CommutativeSemiring_2094
forall a b. a -> b
coe T_CommutativeSemiring_2094
v0 of
      C_CommutativeSemiring'46'constructor_36513 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny
v5 AgdaAny
v6 T_IsCommutativeSemiring_1344
v7 -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v3
      T_CommutativeSemiring_2094
_ -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.CommutativeSemiring._*_
d__'42'__2120 ::
  T_CommutativeSemiring_2094 -> AgdaAny -> AgdaAny -> AgdaAny
d__'42'__2120 :: T_CommutativeSemiring_2094 -> AgdaAny -> AgdaAny -> AgdaAny
d__'42'__2120 T_CommutativeSemiring_2094
v0
  = case T_CommutativeSemiring_2094 -> T_CommutativeSemiring_2094
forall a b. a -> b
coe T_CommutativeSemiring_2094
v0 of
      C_CommutativeSemiring'46'constructor_36513 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny
v5 AgdaAny
v6 T_IsCommutativeSemiring_1344
v7 -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v4
      T_CommutativeSemiring_2094
_ -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.CommutativeSemiring.0#
d_0'35'_2122 :: T_CommutativeSemiring_2094 -> AgdaAny
d_0'35'_2122 :: T_CommutativeSemiring_2094 -> AgdaAny
d_0'35'_2122 T_CommutativeSemiring_2094
v0
  = case T_CommutativeSemiring_2094 -> T_CommutativeSemiring_2094
forall a b. a -> b
coe T_CommutativeSemiring_2094
v0 of
      C_CommutativeSemiring'46'constructor_36513 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny
v5 AgdaAny
v6 T_IsCommutativeSemiring_1344
v7 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v5
      T_CommutativeSemiring_2094
_ -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.CommutativeSemiring.1#
d_1'35'_2124 :: T_CommutativeSemiring_2094 -> AgdaAny
d_1'35'_2124 :: T_CommutativeSemiring_2094 -> AgdaAny
d_1'35'_2124 T_CommutativeSemiring_2094
v0
  = case T_CommutativeSemiring_2094 -> T_CommutativeSemiring_2094
forall a b. a -> b
coe T_CommutativeSemiring_2094
v0 of
      C_CommutativeSemiring'46'constructor_36513 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny
v5 AgdaAny
v6 T_IsCommutativeSemiring_1344
v7 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v6
      T_CommutativeSemiring_2094
_ -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.CommutativeSemiring.isCommutativeSemiring
d_isCommutativeSemiring_2126 ::
  T_CommutativeSemiring_2094 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiring_1344
d_isCommutativeSemiring_2126 :: T_CommutativeSemiring_2094 -> T_IsCommutativeSemiring_1344
d_isCommutativeSemiring_2126 T_CommutativeSemiring_2094
v0
  = case T_CommutativeSemiring_2094 -> T_CommutativeSemiring_2094
forall a b. a -> b
coe T_CommutativeSemiring_2094
v0 of
      C_CommutativeSemiring'46'constructor_36513 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny
v5 AgdaAny
v6 T_IsCommutativeSemiring_1344
v7 -> T_IsCommutativeSemiring_1344 -> T_IsCommutativeSemiring_1344
forall a b. a -> b
coe T_IsCommutativeSemiring_1344
v7
      T_CommutativeSemiring_2094
_ -> T_IsCommutativeSemiring_1344
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.CommutativeSemiring._.assoc
d_assoc_2130 ::
  T_CommutativeSemiring_2094 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_2130 :: T_CommutativeSemiring_2094
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_2130 T_CommutativeSemiring_2094
v0
  = (T_IsSemigroup_194 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsSemigroup_194 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_assoc_204
      ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368
         ((T_IsSemiringWithoutAnnihilatingZero_1142 -> T_IsMonoid_358)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemiringWithoutAnnihilatingZero_1142 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_'42''45'isMonoid_1160
            ((T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1252
               ((T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238
MAlonzo.Code.Algebra.Structures.d_isSemiring_1358
                  ((T_CommutativeSemiring_2094 -> T_IsCommutativeSemiring_1344)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemiring_2094 -> T_IsCommutativeSemiring_1344
d_isCommutativeSemiring_2126 (T_CommutativeSemiring_2094 -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemiring_2094
v0))))))
-- Algebra.Bundles.CommutativeSemiring._.*-comm
d_'42''45'comm_2132 ::
  T_CommutativeSemiring_2094 -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'comm_2132 :: T_CommutativeSemiring_2094 -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'comm_2132 T_CommutativeSemiring_2094
v0
  = (T_IsCommutativeSemiring_1344 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsCommutativeSemiring_1344 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'42''45'comm_1360
      ((T_CommutativeSemiring_2094 -> T_IsCommutativeSemiring_1344)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemiring_2094 -> T_IsCommutativeSemiring_1344
d_isCommutativeSemiring_2126 (T_CommutativeSemiring_2094 -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemiring_2094
v0))
-- Algebra.Bundles.CommutativeSemiring._.∙-cong
d_'8729''45'cong_2134 ::
  T_CommutativeSemiring_2094 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_2134 :: T_CommutativeSemiring_2094
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_2134 T_CommutativeSemiring_2094
v0
  = (T_IsMagma_86
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsMagma_86
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_96
      ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202
         ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368
            ((T_IsSemiringWithoutAnnihilatingZero_1142 -> T_IsMonoid_358)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemiringWithoutAnnihilatingZero_1142 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_'42''45'isMonoid_1160
               ((T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1252
                  ((T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238
MAlonzo.Code.Algebra.Structures.d_isSemiring_1358
                     ((T_CommutativeSemiring_2094 -> T_IsCommutativeSemiring_1344)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemiring_2094 -> T_IsCommutativeSemiring_1344
d_isCommutativeSemiring_2126 (T_CommutativeSemiring_2094 -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemiring_2094
v0)))))))
-- Algebra.Bundles.CommutativeSemiring._.∙-congʳ
d_'8729''45'cong'691'_2136 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeSemiring_2094 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_2136 :: ()
-> ()
-> T_CommutativeSemiring_2094
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_2136 ~()
v0 ~()
v1 T_CommutativeSemiring_2094
v2
  = T_CommutativeSemiring_2094
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_2136 T_CommutativeSemiring_2094
v2
du_'8729''45'cong'691'_2136 ::
  T_CommutativeSemiring_2094 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_2136 :: T_CommutativeSemiring_2094
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_2136 T_CommutativeSemiring_2094
v0
  = let v1 :: T_IsCommutativeSemiring_1344
v1 = T_CommutativeSemiring_2094 -> T_IsCommutativeSemiring_1344
d_isCommutativeSemiring_2126 (T_CommutativeSemiring_2094 -> T_CommutativeSemiring_2094
forall a b. a -> b
coe T_CommutativeSemiring_2094
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemiring_1238
v2
             = T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238
MAlonzo.Code.Algebra.Structures.d_isSemiring_1358 (T_IsCommutativeSemiring_1344 -> T_IsCommutativeSemiring_1344
forall a b. a -> b
coe T_IsCommutativeSemiring_1344
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemiringWithoutAnnihilatingZero_1142
v3
                = T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1252
                    (T_IsSemiring_1238 -> T_IsSemiring_1238
forall a b. a -> b
coe T_IsSemiring_1238
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsMonoid_358
v4
                   = T_IsSemiringWithoutAnnihilatingZero_1142 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_'42''45'isMonoid_1160
                       (T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsSemiringWithoutAnnihilatingZero_1142
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1142
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsSemigroup_194
v5
                      = T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368 (T_IsMonoid_358 -> T_IsMonoid_358
forall a b. a -> b
coe T_IsMonoid_358
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  ((T_IsMagma_86
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsMagma_86 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'691'_116
                     ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202 (T_IsSemigroup_194 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194
v5)))))))
-- Algebra.Bundles.CommutativeSemiring._.∙-congˡ
d_'8729''45'cong'737'_2138 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeSemiring_2094 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_2138 :: ()
-> ()
-> T_CommutativeSemiring_2094
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_2138 ~()
v0 ~()
v1 T_CommutativeSemiring_2094
v2
  = T_CommutativeSemiring_2094
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_2138 T_CommutativeSemiring_2094
v2
du_'8729''45'cong'737'_2138 ::
  T_CommutativeSemiring_2094 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_2138 :: T_CommutativeSemiring_2094
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_2138 T_CommutativeSemiring_2094
v0
  = let v1 :: T_IsCommutativeSemiring_1344
v1 = T_CommutativeSemiring_2094 -> T_IsCommutativeSemiring_1344
d_isCommutativeSemiring_2126 (T_CommutativeSemiring_2094 -> T_CommutativeSemiring_2094
forall a b. a -> b
coe T_CommutativeSemiring_2094
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemiring_1238
v2
             = T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238
MAlonzo.Code.Algebra.Structures.d_isSemiring_1358 (T_IsCommutativeSemiring_1344 -> T_IsCommutativeSemiring_1344
forall a b. a -> b
coe T_IsCommutativeSemiring_1344
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemiringWithoutAnnihilatingZero_1142
v3
                = T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1252
                    (T_IsSemiring_1238 -> T_IsSemiring_1238
forall a b. a -> b
coe T_IsSemiring_1238
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsMonoid_358
v4
                   = T_IsSemiringWithoutAnnihilatingZero_1142 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_'42''45'isMonoid_1160
                       (T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsSemiringWithoutAnnihilatingZero_1142
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1142
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsSemigroup_194
v5
                      = T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368 (T_IsMonoid_358 -> T_IsMonoid_358
forall a b. a -> b
coe T_IsMonoid_358
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  ((T_IsMagma_86
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsMagma_86 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'737'_112
                     ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202 (T_IsSemigroup_194 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194
v5)))))))
-- Algebra.Bundles.CommutativeSemiring._.identity
d_identity_2140 ::
  T_CommutativeSemiring_2094 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_identity_2140 :: T_CommutativeSemiring_2094 -> T_Σ_14
d_identity_2140 T_CommutativeSemiring_2094
v0
  = (T_IsMonoid_358 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsMonoid_358 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_identity_370
      ((T_IsSemiringWithoutAnnihilatingZero_1142 -> T_IsMonoid_358)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiringWithoutAnnihilatingZero_1142 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_'42''45'isMonoid_1160
         ((T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1252
            ((T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238
MAlonzo.Code.Algebra.Structures.d_isSemiring_1358
               ((T_CommutativeSemiring_2094 -> T_IsCommutativeSemiring_1344)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemiring_2094 -> T_IsCommutativeSemiring_1344
d_isCommutativeSemiring_2126 (T_CommutativeSemiring_2094 -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemiring_2094
v0)))))
-- Algebra.Bundles.CommutativeSemiring._.identityʳ
d_identity'691'_2142 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeSemiring_2094 -> AgdaAny -> AgdaAny
d_identity'691'_2142 :: () -> () -> T_CommutativeSemiring_2094 -> AgdaAny -> AgdaAny
d_identity'691'_2142 ~()
v0 ~()
v1 T_CommutativeSemiring_2094
v2 = T_CommutativeSemiring_2094 -> AgdaAny -> AgdaAny
du_identity'691'_2142 T_CommutativeSemiring_2094
v2
du_identity'691'_2142 ::
  T_CommutativeSemiring_2094 -> AgdaAny -> AgdaAny
du_identity'691'_2142 :: T_CommutativeSemiring_2094 -> AgdaAny -> AgdaAny
du_identity'691'_2142 T_CommutativeSemiring_2094
v0
  = let v1 :: T_IsCommutativeSemiring_1344
v1 = T_CommutativeSemiring_2094 -> T_IsCommutativeSemiring_1344
d_isCommutativeSemiring_2126 (T_CommutativeSemiring_2094 -> T_CommutativeSemiring_2094
forall a b. a -> b
coe T_CommutativeSemiring_2094
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemiring_1238
v2
             = T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238
MAlonzo.Code.Algebra.Structures.d_isSemiring_1358 (T_IsCommutativeSemiring_1344 -> T_IsCommutativeSemiring_1344
forall a b. a -> b
coe T_IsCommutativeSemiring_1344
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemiringWithoutAnnihilatingZero_1142
v3
                = T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1252
                    (T_IsSemiring_1238 -> T_IsSemiring_1238
forall a b. a -> b
coe T_IsSemiring_1238
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsMonoid_358 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_358 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_identity'691'_400
               ((T_IsSemiringWithoutAnnihilatingZero_1142 -> T_IsMonoid_358)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsSemiringWithoutAnnihilatingZero_1142 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_'42''45'isMonoid_1160
                  (T_IsSemiringWithoutAnnihilatingZero_1142 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1142
v3)))))
-- Algebra.Bundles.CommutativeSemiring._.identityˡ
d_identity'737'_2144 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeSemiring_2094 -> AgdaAny -> AgdaAny
d_identity'737'_2144 :: () -> () -> T_CommutativeSemiring_2094 -> AgdaAny -> AgdaAny
d_identity'737'_2144 ~()
v0 ~()
v1 T_CommutativeSemiring_2094
v2 = T_CommutativeSemiring_2094 -> AgdaAny -> AgdaAny
du_identity'737'_2144 T_CommutativeSemiring_2094
v2
du_identity'737'_2144 ::
  T_CommutativeSemiring_2094 -> AgdaAny -> AgdaAny
du_identity'737'_2144 :: T_CommutativeSemiring_2094 -> AgdaAny -> AgdaAny
du_identity'737'_2144 T_CommutativeSemiring_2094
v0
  = let v1 :: T_IsCommutativeSemiring_1344
v1 = T_CommutativeSemiring_2094 -> T_IsCommutativeSemiring_1344
d_isCommutativeSemiring_2126 (T_CommutativeSemiring_2094 -> T_CommutativeSemiring_2094
forall a b. a -> b
coe T_CommutativeSemiring_2094
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemiring_1238
v2
             = T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238
MAlonzo.Code.Algebra.Structures.d_isSemiring_1358 (T_IsCommutativeSemiring_1344 -> T_IsCommutativeSemiring_1344
forall a b. a -> b
coe T_IsCommutativeSemiring_1344
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemiringWithoutAnnihilatingZero_1142
v3
                = T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1252
                    (T_IsSemiring_1238 -> T_IsSemiring_1238
forall a b. a -> b
coe T_IsSemiring_1238
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsMonoid_358 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_358 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_identity'737'_398
               ((T_IsSemiringWithoutAnnihilatingZero_1142 -> T_IsMonoid_358)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsSemiringWithoutAnnihilatingZero_1142 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_'42''45'isMonoid_1160
                  (T_IsSemiringWithoutAnnihilatingZero_1142 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1142
v3)))))
-- Algebra.Bundles.CommutativeSemiring._.isCommutativeMagma
d_isCommutativeMagma_2146 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeSemiring_2094 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMagma_122
d_isCommutativeMagma_2146 :: () -> () -> T_CommutativeSemiring_2094 -> T_IsCommutativeMagma_122
d_isCommutativeMagma_2146 ~()
v0 ~()
v1 T_CommutativeSemiring_2094
v2
  = T_CommutativeSemiring_2094 -> T_IsCommutativeMagma_122
du_isCommutativeMagma_2146 T_CommutativeSemiring_2094
v2
du_isCommutativeMagma_2146 ::
  T_CommutativeSemiring_2094 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMagma_122
du_isCommutativeMagma_2146 :: T_CommutativeSemiring_2094 -> T_IsCommutativeMagma_122
du_isCommutativeMagma_2146 T_CommutativeSemiring_2094
v0
  = let v1 :: T_IsCommutativeSemiring_1344
v1 = T_CommutativeSemiring_2094 -> T_IsCommutativeSemiring_1344
d_isCommutativeSemiring_2126 (T_CommutativeSemiring_2094 -> T_CommutativeSemiring_2094
forall a b. a -> b
coe T_CommutativeSemiring_2094
v0) in
    AgdaAny -> T_IsCommutativeMagma_122
forall a b. a -> b
coe
      (let v2 :: t
v2
             = (T_IsCommutativeSemiring_1344
 -> T_IsCommutativeSemiringWithoutOne_1044)
-> AgdaAny -> t
forall a b. a -> b
coe
                 T_IsCommutativeSemiring_1344
-> T_IsCommutativeSemiringWithoutOne_1044
MAlonzo.Code.Algebra.Structures.du_isCommutativeSemiringWithoutOne_1444
                 (T_IsCommutativeSemiring_1344 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiring_1344
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsCommutativeSemigroup_270 -> T_IsCommutativeMagma_122)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCommutativeSemigroup_270 -> T_IsCommutativeMagma_122
MAlonzo.Code.Algebra.Structures.du_isCommutativeMagma_308
            ((T_IsCommutativeSemiringWithoutOne_1044
 -> T_IsCommutativeSemigroup_270)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsCommutativeSemiringWithoutOne_1044
-> T_IsCommutativeSemigroup_270
MAlonzo.Code.Algebra.Structures.du_'42''45'isCommutativeSemigroup_1128
               (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2))))
-- Algebra.Bundles.CommutativeSemiring._.*-isCommutativeMonoid
d_'42''45'isCommutativeMonoid_2148 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeSemiring_2094 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMonoid_406
d_'42''45'isCommutativeMonoid_2148 :: () -> () -> T_CommutativeSemiring_2094 -> T_IsCommutativeMonoid_406
d_'42''45'isCommutativeMonoid_2148 ~()
v0 ~()
v1 T_CommutativeSemiring_2094
v2
  = T_CommutativeSemiring_2094 -> T_IsCommutativeMonoid_406
du_'42''45'isCommutativeMonoid_2148 T_CommutativeSemiring_2094
v2
du_'42''45'isCommutativeMonoid_2148 ::
  T_CommutativeSemiring_2094 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMonoid_406
du_'42''45'isCommutativeMonoid_2148 :: T_CommutativeSemiring_2094 -> T_IsCommutativeMonoid_406
du_'42''45'isCommutativeMonoid_2148 T_CommutativeSemiring_2094
v0
  = (T_IsCommutativeSemiring_1344 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> T_IsCommutativeMonoid_406
forall a b. a -> b
coe
      T_IsCommutativeSemiring_1344 -> T_IsCommutativeMonoid_406
MAlonzo.Code.Algebra.Structures.du_'42''45'isCommutativeMonoid_1452
      ((T_CommutativeSemiring_2094 -> T_IsCommutativeSemiring_1344)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemiring_2094 -> T_IsCommutativeSemiring_1344
d_isCommutativeSemiring_2126 (T_CommutativeSemiring_2094 -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemiring_2094
v0))
-- Algebra.Bundles.CommutativeSemiring._.*-isCommutativeSemigroup
d_'42''45'isCommutativeSemigroup_2150 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeSemiring_2094 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_270
d_'42''45'isCommutativeSemigroup_2150 :: ()
-> () -> T_CommutativeSemiring_2094 -> T_IsCommutativeSemigroup_270
d_'42''45'isCommutativeSemigroup_2150 ~()
v0 ~()
v1 T_CommutativeSemiring_2094
v2
  = T_CommutativeSemiring_2094 -> T_IsCommutativeSemigroup_270
du_'42''45'isCommutativeSemigroup_2150 T_CommutativeSemiring_2094
v2
du_'42''45'isCommutativeSemigroup_2150 ::
  T_CommutativeSemiring_2094 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_270
du_'42''45'isCommutativeSemigroup_2150 :: T_CommutativeSemiring_2094 -> T_IsCommutativeSemigroup_270
du_'42''45'isCommutativeSemigroup_2150 T_CommutativeSemiring_2094
v0
  = let v1 :: T_IsCommutativeSemiring_1344
v1 = T_CommutativeSemiring_2094 -> T_IsCommutativeSemiring_1344
d_isCommutativeSemiring_2126 (T_CommutativeSemiring_2094 -> T_CommutativeSemiring_2094
forall a b. a -> b
coe T_CommutativeSemiring_2094
v0) in
    AgdaAny -> T_IsCommutativeSemigroup_270
forall a b. a -> b
coe
      ((T_IsCommutativeSemiringWithoutOne_1044
 -> T_IsCommutativeSemigroup_270)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCommutativeSemiringWithoutOne_1044
-> T_IsCommutativeSemigroup_270
MAlonzo.Code.Algebra.Structures.du_'42''45'isCommutativeSemigroup_1128
         ((T_IsCommutativeSemiring_1344
 -> T_IsCommutativeSemiringWithoutOne_1044)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCommutativeSemiring_1344
-> T_IsCommutativeSemiringWithoutOne_1044
MAlonzo.Code.Algebra.Structures.du_isCommutativeSemiringWithoutOne_1444
            (T_IsCommutativeSemiring_1344 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiring_1344
v1)))
-- Algebra.Bundles.CommutativeSemiring._.isMagma
d_isMagma_2152 ::
  T_CommutativeSemiring_2094 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_86
d_isMagma_2152 :: T_CommutativeSemiring_2094 -> T_IsMagma_86
d_isMagma_2152 T_CommutativeSemiring_2094
v0
  = (T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> T_IsMagma_86
forall a b. a -> b
coe
      T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202
      ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368
         ((T_IsSemiringWithoutAnnihilatingZero_1142 -> T_IsMonoid_358)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemiringWithoutAnnihilatingZero_1142 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_'42''45'isMonoid_1160
            ((T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1252
               ((T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238
MAlonzo.Code.Algebra.Structures.d_isSemiring_1358
                  ((T_CommutativeSemiring_2094 -> T_IsCommutativeSemiring_1344)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemiring_2094 -> T_IsCommutativeSemiring_1344
d_isCommutativeSemiring_2126 (T_CommutativeSemiring_2094 -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemiring_2094
v0))))))
-- Algebra.Bundles.CommutativeSemiring._.*-isMonoid
d_'42''45'isMonoid_2154 ::
  T_CommutativeSemiring_2094 ->
  MAlonzo.Code.Algebra.Structures.T_IsMonoid_358
d_'42''45'isMonoid_2154 :: T_CommutativeSemiring_2094 -> T_IsMonoid_358
d_'42''45'isMonoid_2154 T_CommutativeSemiring_2094
v0
  = (T_IsSemiringWithoutAnnihilatingZero_1142 -> T_IsMonoid_358)
-> AgdaAny -> T_IsMonoid_358
forall a b. a -> b
coe
      T_IsSemiringWithoutAnnihilatingZero_1142 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_'42''45'isMonoid_1160
      ((T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1252
         ((T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238
MAlonzo.Code.Algebra.Structures.d_isSemiring_1358
            ((T_CommutativeSemiring_2094 -> T_IsCommutativeSemiring_1344)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemiring_2094 -> T_IsCommutativeSemiring_1344
d_isCommutativeSemiring_2126 (T_CommutativeSemiring_2094 -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemiring_2094
v0))))
-- Algebra.Bundles.CommutativeSemiring._.isSemigroup
d_isSemigroup_2156 ::
  T_CommutativeSemiring_2094 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_194
d_isSemigroup_2156 :: T_CommutativeSemiring_2094 -> T_IsSemigroup_194
d_isSemigroup_2156 T_CommutativeSemiring_2094
v0
  = (T_IsMonoid_358 -> T_IsSemigroup_194)
-> AgdaAny -> T_IsSemigroup_194
forall a b. a -> b
coe
      T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368
      ((T_IsSemiringWithoutAnnihilatingZero_1142 -> T_IsMonoid_358)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiringWithoutAnnihilatingZero_1142 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_'42''45'isMonoid_1160
         ((T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1252
            ((T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238
MAlonzo.Code.Algebra.Structures.d_isSemiring_1358
               ((T_CommutativeSemiring_2094 -> T_IsCommutativeSemiring_1344)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemiring_2094 -> T_IsCommutativeSemiring_1344
d_isCommutativeSemiring_2126 (T_CommutativeSemiring_2094 -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemiring_2094
v0)))))
-- Algebra.Bundles.CommutativeSemiring._.assoc
d_assoc_2158 ::
  T_CommutativeSemiring_2094 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_2158 :: T_CommutativeSemiring_2094
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_2158 T_CommutativeSemiring_2094
v0
  = (T_IsSemigroup_194 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsSemigroup_194 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_assoc_204
      ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368
         ((T_IsCommutativeMonoid_406 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCommutativeMonoid_406 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_416
            ((T_IsSemiringWithoutAnnihilatingZero_1142
 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsCommutativeMonoid_406
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1158
               ((T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1252
                  ((T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238
MAlonzo.Code.Algebra.Structures.d_isSemiring_1358
                     ((T_CommutativeSemiring_2094 -> T_IsCommutativeSemiring_1344)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemiring_2094 -> T_IsCommutativeSemiring_1344
d_isCommutativeSemiring_2126 (T_CommutativeSemiring_2094 -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemiring_2094
v0)))))))
-- Algebra.Bundles.CommutativeSemiring._.comm
d_comm_2160 ::
  T_CommutativeSemiring_2094 -> AgdaAny -> AgdaAny -> AgdaAny
d_comm_2160 :: T_CommutativeSemiring_2094 -> AgdaAny -> AgdaAny -> AgdaAny
d_comm_2160 T_CommutativeSemiring_2094
v0
  = (T_IsCommutativeMonoid_406 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsCommutativeMonoid_406 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_comm_418
      ((T_IsSemiringWithoutAnnihilatingZero_1142
 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsCommutativeMonoid_406
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1158
         ((T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1252
            ((T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238
MAlonzo.Code.Algebra.Structures.d_isSemiring_1358
               ((T_CommutativeSemiring_2094 -> T_IsCommutativeSemiring_1344)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemiring_2094 -> T_IsCommutativeSemiring_1344
d_isCommutativeSemiring_2126 (T_CommutativeSemiring_2094 -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemiring_2094
v0)))))
-- Algebra.Bundles.CommutativeSemiring._.∙-cong
d_'8729''45'cong_2162 ::
  T_CommutativeSemiring_2094 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_2162 :: T_CommutativeSemiring_2094
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_2162 T_CommutativeSemiring_2094
v0
  = (T_IsMagma_86
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsMagma_86
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_96
      ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202
         ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368
            ((T_IsCommutativeMonoid_406 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsCommutativeMonoid_406 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_416
               ((T_IsSemiringWithoutAnnihilatingZero_1142
 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsCommutativeMonoid_406
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1158
                  ((T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1252
                     ((T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238
MAlonzo.Code.Algebra.Structures.d_isSemiring_1358
                        ((T_CommutativeSemiring_2094 -> T_IsCommutativeSemiring_1344)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemiring_2094 -> T_IsCommutativeSemiring_1344
d_isCommutativeSemiring_2126 (T_CommutativeSemiring_2094 -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemiring_2094
v0))))))))
-- Algebra.Bundles.CommutativeSemiring._.∙-congʳ
d_'8729''45'cong'691'_2164 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeSemiring_2094 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_2164 :: ()
-> ()
-> T_CommutativeSemiring_2094
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_2164 ~()
v0 ~()
v1 T_CommutativeSemiring_2094
v2
  = T_CommutativeSemiring_2094
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_2164 T_CommutativeSemiring_2094
v2
du_'8729''45'cong'691'_2164 ::
  T_CommutativeSemiring_2094 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_2164 :: T_CommutativeSemiring_2094
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_2164 T_CommutativeSemiring_2094
v0
  = let v1 :: T_IsCommutativeSemiring_1344
v1 = T_CommutativeSemiring_2094 -> T_IsCommutativeSemiring_1344
d_isCommutativeSemiring_2126 (T_CommutativeSemiring_2094 -> T_CommutativeSemiring_2094
forall a b. a -> b
coe T_CommutativeSemiring_2094
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemiring_1238
v2
             = T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238
MAlonzo.Code.Algebra.Structures.d_isSemiring_1358 (T_IsCommutativeSemiring_1344 -> T_IsCommutativeSemiring_1344
forall a b. a -> b
coe T_IsCommutativeSemiring_1344
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemiringWithoutAnnihilatingZero_1142
v3
                = T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1252
                    (T_IsSemiring_1238 -> T_IsSemiring_1238
forall a b. a -> b
coe T_IsSemiring_1238
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsCommutativeMonoid_406
v4
                   = T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsCommutativeMonoid_406
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1158
                       (T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsSemiringWithoutAnnihilatingZero_1142
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1142
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsMonoid_358
v5
                      = T_IsCommutativeMonoid_406 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_416 (T_IsCommutativeMonoid_406 -> T_IsCommutativeMonoid_406
forall a b. a -> b
coe T_IsCommutativeMonoid_406
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (let v6 :: T_IsSemigroup_194
v6
                         = T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368 (T_IsMonoid_358 -> T_IsMonoid_358
forall a b. a -> b
coe T_IsMonoid_358
v5) in
                   AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     ((T_IsMagma_86
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsMagma_86 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'691'_116
                        ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202 (T_IsSemigroup_194 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194
v6))))))))
-- Algebra.Bundles.CommutativeSemiring._.∙-congˡ
d_'8729''45'cong'737'_2166 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeSemiring_2094 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_2166 :: ()
-> ()
-> T_CommutativeSemiring_2094
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_2166 ~()
v0 ~()
v1 T_CommutativeSemiring_2094
v2
  = T_CommutativeSemiring_2094
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_2166 T_CommutativeSemiring_2094
v2
du_'8729''45'cong'737'_2166 ::
  T_CommutativeSemiring_2094 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_2166 :: T_CommutativeSemiring_2094
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_2166 T_CommutativeSemiring_2094
v0
  = let v1 :: T_IsCommutativeSemiring_1344
v1 = T_CommutativeSemiring_2094 -> T_IsCommutativeSemiring_1344
d_isCommutativeSemiring_2126 (T_CommutativeSemiring_2094 -> T_CommutativeSemiring_2094
forall a b. a -> b
coe T_CommutativeSemiring_2094
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemiring_1238
v2
             = T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238
MAlonzo.Code.Algebra.Structures.d_isSemiring_1358 (T_IsCommutativeSemiring_1344 -> T_IsCommutativeSemiring_1344
forall a b. a -> b
coe T_IsCommutativeSemiring_1344
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemiringWithoutAnnihilatingZero_1142
v3
                = T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1252
                    (T_IsSemiring_1238 -> T_IsSemiring_1238
forall a b. a -> b
coe T_IsSemiring_1238
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsCommutativeMonoid_406
v4
                   = T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsCommutativeMonoid_406
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1158
                       (T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsSemiringWithoutAnnihilatingZero_1142
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1142
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsMonoid_358
v5
                      = T_IsCommutativeMonoid_406 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_416 (T_IsCommutativeMonoid_406 -> T_IsCommutativeMonoid_406
forall a b. a -> b
coe T_IsCommutativeMonoid_406
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (let v6 :: T_IsSemigroup_194
v6
                         = T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368 (T_IsMonoid_358 -> T_IsMonoid_358
forall a b. a -> b
coe T_IsMonoid_358
v5) in
                   AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     ((T_IsMagma_86
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsMagma_86 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'737'_112
                        ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202 (T_IsSemigroup_194 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194
v6))))))))
-- Algebra.Bundles.CommutativeSemiring._.identity
d_identity_2168 ::
  T_CommutativeSemiring_2094 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_identity_2168 :: T_CommutativeSemiring_2094 -> T_Σ_14
d_identity_2168 T_CommutativeSemiring_2094
v0
  = (T_IsMonoid_358 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsMonoid_358 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_identity_370
      ((T_IsCommutativeMonoid_406 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCommutativeMonoid_406 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_416
         ((T_IsSemiringWithoutAnnihilatingZero_1142
 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsCommutativeMonoid_406
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1158
            ((T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1252
               ((T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238
MAlonzo.Code.Algebra.Structures.d_isSemiring_1358
                  ((T_CommutativeSemiring_2094 -> T_IsCommutativeSemiring_1344)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemiring_2094 -> T_IsCommutativeSemiring_1344
d_isCommutativeSemiring_2126 (T_CommutativeSemiring_2094 -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemiring_2094
v0))))))
-- Algebra.Bundles.CommutativeSemiring._.identityʳ
d_identity'691'_2170 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeSemiring_2094 -> AgdaAny -> AgdaAny
d_identity'691'_2170 :: () -> () -> T_CommutativeSemiring_2094 -> AgdaAny -> AgdaAny
d_identity'691'_2170 ~()
v0 ~()
v1 T_CommutativeSemiring_2094
v2 = T_CommutativeSemiring_2094 -> AgdaAny -> AgdaAny
du_identity'691'_2170 T_CommutativeSemiring_2094
v2
du_identity'691'_2170 ::
  T_CommutativeSemiring_2094 -> AgdaAny -> AgdaAny
du_identity'691'_2170 :: T_CommutativeSemiring_2094 -> AgdaAny -> AgdaAny
du_identity'691'_2170 T_CommutativeSemiring_2094
v0
  = let v1 :: T_IsCommutativeSemiring_1344
v1 = T_CommutativeSemiring_2094 -> T_IsCommutativeSemiring_1344
d_isCommutativeSemiring_2126 (T_CommutativeSemiring_2094 -> T_CommutativeSemiring_2094
forall a b. a -> b
coe T_CommutativeSemiring_2094
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemiring_1238
v2
             = T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238
MAlonzo.Code.Algebra.Structures.d_isSemiring_1358 (T_IsCommutativeSemiring_1344 -> T_IsCommutativeSemiring_1344
forall a b. a -> b
coe T_IsCommutativeSemiring_1344
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemiringWithoutAnnihilatingZero_1142
v3
                = T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1252
                    (T_IsSemiring_1238 -> T_IsSemiring_1238
forall a b. a -> b
coe T_IsSemiring_1238
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsCommutativeMonoid_406
v4
                   = T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsCommutativeMonoid_406
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1158
                       (T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsSemiringWithoutAnnihilatingZero_1142
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1142
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               ((T_IsMonoid_358 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsMonoid_358 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_identity'691'_400
                  ((T_IsCommutativeMonoid_406 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_406 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_416 (T_IsCommutativeMonoid_406 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_406
v4))))))
-- Algebra.Bundles.CommutativeSemiring._.identityˡ
d_identity'737'_2172 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeSemiring_2094 -> AgdaAny -> AgdaAny
d_identity'737'_2172 :: () -> () -> T_CommutativeSemiring_2094 -> AgdaAny -> AgdaAny
d_identity'737'_2172 ~()
v0 ~()
v1 T_CommutativeSemiring_2094
v2 = T_CommutativeSemiring_2094 -> AgdaAny -> AgdaAny
du_identity'737'_2172 T_CommutativeSemiring_2094
v2
du_identity'737'_2172 ::
  T_CommutativeSemiring_2094 -> AgdaAny -> AgdaAny
du_identity'737'_2172 :: T_CommutativeSemiring_2094 -> AgdaAny -> AgdaAny
du_identity'737'_2172 T_CommutativeSemiring_2094
v0
  = let v1 :: T_IsCommutativeSemiring_1344
v1 = T_CommutativeSemiring_2094 -> T_IsCommutativeSemiring_1344
d_isCommutativeSemiring_2126 (T_CommutativeSemiring_2094 -> T_CommutativeSemiring_2094
forall a b. a -> b
coe T_CommutativeSemiring_2094
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemiring_1238
v2
             = T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238
MAlonzo.Code.Algebra.Structures.d_isSemiring_1358 (T_IsCommutativeSemiring_1344 -> T_IsCommutativeSemiring_1344
forall a b. a -> b
coe T_IsCommutativeSemiring_1344
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemiringWithoutAnnihilatingZero_1142
v3
                = T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1252
                    (T_IsSemiring_1238 -> T_IsSemiring_1238
forall a b. a -> b
coe T_IsSemiring_1238
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsCommutativeMonoid_406
v4
                   = T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsCommutativeMonoid_406
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1158
                       (T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsSemiringWithoutAnnihilatingZero_1142
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1142
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               ((T_IsMonoid_358 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsMonoid_358 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_identity'737'_398
                  ((T_IsCommutativeMonoid_406 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_406 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_416 (T_IsCommutativeMonoid_406 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_406
v4))))))
-- Algebra.Bundles.CommutativeSemiring._.isCommutativeMagma
d_isCommutativeMagma_2174 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeSemiring_2094 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMagma_122
d_isCommutativeMagma_2174 :: () -> () -> T_CommutativeSemiring_2094 -> T_IsCommutativeMagma_122
d_isCommutativeMagma_2174 ~()
v0 ~()
v1 T_CommutativeSemiring_2094
v2
  = T_CommutativeSemiring_2094 -> T_IsCommutativeMagma_122
du_isCommutativeMagma_2174 T_CommutativeSemiring_2094
v2
du_isCommutativeMagma_2174 ::
  T_CommutativeSemiring_2094 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMagma_122
du_isCommutativeMagma_2174 :: T_CommutativeSemiring_2094 -> T_IsCommutativeMagma_122
du_isCommutativeMagma_2174 T_CommutativeSemiring_2094
v0
  = let v1 :: T_IsCommutativeSemiring_1344
v1 = T_CommutativeSemiring_2094 -> T_IsCommutativeSemiring_1344
d_isCommutativeSemiring_2126 (T_CommutativeSemiring_2094 -> T_CommutativeSemiring_2094
forall a b. a -> b
coe T_CommutativeSemiring_2094
v0) in
    AgdaAny -> T_IsCommutativeMagma_122
forall a b. a -> b
coe
      (let v2 :: T_IsSemiring_1238
v2
             = T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238
MAlonzo.Code.Algebra.Structures.d_isSemiring_1358 (T_IsCommutativeSemiring_1344 -> T_IsCommutativeSemiring_1344
forall a b. a -> b
coe T_IsCommutativeSemiring_1344
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemiringWithoutAnnihilatingZero_1142
v3
                = T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1252
                    (T_IsSemiring_1238 -> T_IsSemiring_1238
forall a b. a -> b
coe T_IsSemiring_1238
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsCommutativeMonoid_406
v4
                   = T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsCommutativeMonoid_406
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1158
                       (T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsSemiringWithoutAnnihilatingZero_1142
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1142
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               ((T_IsCommutativeSemigroup_270 -> T_IsCommutativeMagma_122)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsCommutativeSemigroup_270 -> T_IsCommutativeMagma_122
MAlonzo.Code.Algebra.Structures.du_isCommutativeMagma_308
                  ((T_IsCommutativeMonoid_406 -> T_IsCommutativeSemigroup_270)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsCommutativeMonoid_406 -> T_IsCommutativeSemigroup_270
MAlonzo.Code.Algebra.Structures.du_isCommutativeSemigroup_454
                     (T_IsCommutativeMonoid_406 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_406
v4))))))
-- Algebra.Bundles.CommutativeSemiring._.+-isCommutativeMonoid
d_'43''45'isCommutativeMonoid_2176 ::
  T_CommutativeSemiring_2094 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMonoid_406
d_'43''45'isCommutativeMonoid_2176 :: T_CommutativeSemiring_2094 -> T_IsCommutativeMonoid_406
d_'43''45'isCommutativeMonoid_2176 T_CommutativeSemiring_2094
v0
  = (T_IsSemiringWithoutAnnihilatingZero_1142
 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> T_IsCommutativeMonoid_406
forall a b. a -> b
coe
      T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsCommutativeMonoid_406
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1158
      ((T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1252
         ((T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238
MAlonzo.Code.Algebra.Structures.d_isSemiring_1358
            ((T_CommutativeSemiring_2094 -> T_IsCommutativeSemiring_1344)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemiring_2094 -> T_IsCommutativeSemiring_1344
d_isCommutativeSemiring_2126 (T_CommutativeSemiring_2094 -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemiring_2094
v0))))
-- Algebra.Bundles.CommutativeSemiring._.isCommutativeSemigroup
d_isCommutativeSemigroup_2178 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeSemiring_2094 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_270
d_isCommutativeSemigroup_2178 :: ()
-> () -> T_CommutativeSemiring_2094 -> T_IsCommutativeSemigroup_270
d_isCommutativeSemigroup_2178 ~()
v0 ~()
v1 T_CommutativeSemiring_2094
v2
  = T_CommutativeSemiring_2094 -> T_IsCommutativeSemigroup_270
du_isCommutativeSemigroup_2178 T_CommutativeSemiring_2094
v2
du_isCommutativeSemigroup_2178 ::
  T_CommutativeSemiring_2094 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_270
du_isCommutativeSemigroup_2178 :: T_CommutativeSemiring_2094 -> T_IsCommutativeSemigroup_270
du_isCommutativeSemigroup_2178 T_CommutativeSemiring_2094
v0
  = let v1 :: T_IsCommutativeSemiring_1344
v1 = T_CommutativeSemiring_2094 -> T_IsCommutativeSemiring_1344
d_isCommutativeSemiring_2126 (T_CommutativeSemiring_2094 -> T_CommutativeSemiring_2094
forall a b. a -> b
coe T_CommutativeSemiring_2094
v0) in
    AgdaAny -> T_IsCommutativeSemigroup_270
forall a b. a -> b
coe
      (let v2 :: T_IsSemiring_1238
v2
             = T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238
MAlonzo.Code.Algebra.Structures.d_isSemiring_1358 (T_IsCommutativeSemiring_1344 -> T_IsCommutativeSemiring_1344
forall a b. a -> b
coe T_IsCommutativeSemiring_1344
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemiringWithoutAnnihilatingZero_1142
v3
                = T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1252
                    (T_IsSemiring_1238 -> T_IsSemiring_1238
forall a b. a -> b
coe T_IsSemiring_1238
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsCommutativeMonoid_406 -> T_IsCommutativeSemigroup_270)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsCommutativeMonoid_406 -> T_IsCommutativeSemigroup_270
MAlonzo.Code.Algebra.Structures.du_isCommutativeSemigroup_454
               ((T_IsSemiringWithoutAnnihilatingZero_1142
 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsCommutativeMonoid_406
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1158
                  (T_IsSemiringWithoutAnnihilatingZero_1142 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1142
v3)))))
-- Algebra.Bundles.CommutativeSemiring._.isMagma
d_isMagma_2180 ::
  T_CommutativeSemiring_2094 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_86
d_isMagma_2180 :: T_CommutativeSemiring_2094 -> T_IsMagma_86
d_isMagma_2180 T_CommutativeSemiring_2094
v0
  = (T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> T_IsMagma_86
forall a b. a -> b
coe
      T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202
      ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368
         ((T_IsCommutativeMonoid_406 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCommutativeMonoid_406 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_416
            ((T_IsSemiringWithoutAnnihilatingZero_1142
 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsCommutativeMonoid_406
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1158
               ((T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1252
                  ((T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238
MAlonzo.Code.Algebra.Structures.d_isSemiring_1358
                     ((T_CommutativeSemiring_2094 -> T_IsCommutativeSemiring_1344)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemiring_2094 -> T_IsCommutativeSemiring_1344
d_isCommutativeSemiring_2126 (T_CommutativeSemiring_2094 -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemiring_2094
v0)))))))
-- Algebra.Bundles.CommutativeSemiring._.isMonoid
d_isMonoid_2182 ::
  T_CommutativeSemiring_2094 ->
  MAlonzo.Code.Algebra.Structures.T_IsMonoid_358
d_isMonoid_2182 :: T_CommutativeSemiring_2094 -> T_IsMonoid_358
d_isMonoid_2182 T_CommutativeSemiring_2094
v0
  = (T_IsCommutativeMonoid_406 -> T_IsMonoid_358)
-> AgdaAny -> T_IsMonoid_358
forall a b. a -> b
coe
      T_IsCommutativeMonoid_406 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_416
      ((T_IsSemiringWithoutAnnihilatingZero_1142
 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsCommutativeMonoid_406
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1158
         ((T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1252
            ((T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238
MAlonzo.Code.Algebra.Structures.d_isSemiring_1358
               ((T_CommutativeSemiring_2094 -> T_IsCommutativeSemiring_1344)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemiring_2094 -> T_IsCommutativeSemiring_1344
d_isCommutativeSemiring_2126 (T_CommutativeSemiring_2094 -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemiring_2094
v0)))))
-- Algebra.Bundles.CommutativeSemiring._.isSemigroup
d_isSemigroup_2184 ::
  T_CommutativeSemiring_2094 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_194
d_isSemigroup_2184 :: T_CommutativeSemiring_2094 -> T_IsSemigroup_194
d_isSemigroup_2184 T_CommutativeSemiring_2094
v0
  = (T_IsMonoid_358 -> T_IsSemigroup_194)
-> AgdaAny -> T_IsSemigroup_194
forall a b. a -> b
coe
      T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368
      ((T_IsCommutativeMonoid_406 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCommutativeMonoid_406 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_416
         ((T_IsSemiringWithoutAnnihilatingZero_1142
 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsCommutativeMonoid_406
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1158
            ((T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1252
               ((T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238
MAlonzo.Code.Algebra.Structures.d_isSemiring_1358
                  ((T_CommutativeSemiring_2094 -> T_IsCommutativeSemiring_1344)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemiring_2094 -> T_IsCommutativeSemiring_1344
d_isCommutativeSemiring_2126 (T_CommutativeSemiring_2094 -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemiring_2094
v0))))))
-- Algebra.Bundles.CommutativeSemiring._.distrib
d_distrib_2186 ::
  T_CommutativeSemiring_2094 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_distrib_2186 :: T_CommutativeSemiring_2094 -> T_Σ_14
d_distrib_2186 T_CommutativeSemiring_2094
v0
  = (T_IsSemiringWithoutAnnihilatingZero_1142 -> T_Σ_14)
-> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsSemiringWithoutAnnihilatingZero_1142 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_distrib_1162
      ((T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1252
         ((T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238
MAlonzo.Code.Algebra.Structures.d_isSemiring_1358
            ((T_CommutativeSemiring_2094 -> T_IsCommutativeSemiring_1344)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemiring_2094 -> T_IsCommutativeSemiring_1344
d_isCommutativeSemiring_2126 (T_CommutativeSemiring_2094 -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemiring_2094
v0))))
-- Algebra.Bundles.CommutativeSemiring._.distribʳ
d_distrib'691'_2188 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeSemiring_2094 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_distrib'691'_2188 :: ()
-> ()
-> T_CommutativeSemiring_2094
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_distrib'691'_2188 ~()
v0 ~()
v1 T_CommutativeSemiring_2094
v2 = T_CommutativeSemiring_2094
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'691'_2188 T_CommutativeSemiring_2094
v2
du_distrib'691'_2188 ::
  T_CommutativeSemiring_2094 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'691'_2188 :: T_CommutativeSemiring_2094
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'691'_2188 T_CommutativeSemiring_2094
v0
  = let v1 :: T_IsCommutativeSemiring_1344
v1 = T_CommutativeSemiring_2094 -> T_IsCommutativeSemiring_1344
d_isCommutativeSemiring_2126 (T_CommutativeSemiring_2094 -> T_CommutativeSemiring_2094
forall a b. a -> b
coe T_CommutativeSemiring_2094
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemiring_1238
v2
             = T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238
MAlonzo.Code.Algebra.Structures.d_isSemiring_1358 (T_IsCommutativeSemiring_1344 -> T_IsCommutativeSemiring_1344
forall a b. a -> b
coe T_IsCommutativeSemiring_1344
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsSemiringWithoutAnnihilatingZero_1142
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemiringWithoutAnnihilatingZero_1142
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_distrib'691'_1166
            ((T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1252
               (T_IsSemiring_1238 -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1238
v2))))
-- Algebra.Bundles.CommutativeSemiring._.distribˡ
d_distrib'737'_2190 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeSemiring_2094 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_distrib'737'_2190 :: ()
-> ()
-> T_CommutativeSemiring_2094
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_distrib'737'_2190 ~()
v0 ~()
v1 T_CommutativeSemiring_2094
v2 = T_CommutativeSemiring_2094
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'737'_2190 T_CommutativeSemiring_2094
v2
du_distrib'737'_2190 ::
  T_CommutativeSemiring_2094 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'737'_2190 :: T_CommutativeSemiring_2094
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'737'_2190 T_CommutativeSemiring_2094
v0
  = let v1 :: T_IsCommutativeSemiring_1344
v1 = T_CommutativeSemiring_2094 -> T_IsCommutativeSemiring_1344
d_isCommutativeSemiring_2126 (T_CommutativeSemiring_2094 -> T_CommutativeSemiring_2094
forall a b. a -> b
coe T_CommutativeSemiring_2094
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemiring_1238
v2
             = T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238
MAlonzo.Code.Algebra.Structures.d_isSemiring_1358 (T_IsCommutativeSemiring_1344 -> T_IsCommutativeSemiring_1344
forall a b. a -> b
coe T_IsCommutativeSemiring_1344
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsSemiringWithoutAnnihilatingZero_1142
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemiringWithoutAnnihilatingZero_1142
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_distrib'737'_1164
            ((T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1252
               (T_IsSemiring_1238 -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1238
v2))))
-- Algebra.Bundles.CommutativeSemiring._.isCommutativeSemiringWithoutOne
d_isCommutativeSemiringWithoutOne_2192 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeSemiring_2094 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiringWithoutOne_1044
d_isCommutativeSemiringWithoutOne_2192 :: ()
-> ()
-> T_CommutativeSemiring_2094
-> T_IsCommutativeSemiringWithoutOne_1044
d_isCommutativeSemiringWithoutOne_2192 ~()
v0 ~()
v1 T_CommutativeSemiring_2094
v2
  = T_CommutativeSemiring_2094
-> T_IsCommutativeSemiringWithoutOne_1044
du_isCommutativeSemiringWithoutOne_2192 T_CommutativeSemiring_2094
v2
du_isCommutativeSemiringWithoutOne_2192 ::
  T_CommutativeSemiring_2094 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiringWithoutOne_1044
du_isCommutativeSemiringWithoutOne_2192 :: T_CommutativeSemiring_2094
-> T_IsCommutativeSemiringWithoutOne_1044
du_isCommutativeSemiringWithoutOne_2192 T_CommutativeSemiring_2094
v0
  = (T_IsCommutativeSemiring_1344
 -> T_IsCommutativeSemiringWithoutOne_1044)
-> AgdaAny -> T_IsCommutativeSemiringWithoutOne_1044
forall a b. a -> b
coe
      T_IsCommutativeSemiring_1344
-> T_IsCommutativeSemiringWithoutOne_1044
MAlonzo.Code.Algebra.Structures.du_isCommutativeSemiringWithoutOne_1444
      ((T_CommutativeSemiring_2094 -> T_IsCommutativeSemiring_1344)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemiring_2094 -> T_IsCommutativeSemiring_1344
d_isCommutativeSemiring_2126 (T_CommutativeSemiring_2094 -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemiring_2094
v0))
-- Algebra.Bundles.CommutativeSemiring._.isEquivalence
d_isEquivalence_2194 ::
  T_CommutativeSemiring_2094 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_2194 :: T_CommutativeSemiring_2094 -> T_IsEquivalence_26
d_isEquivalence_2194 T_CommutativeSemiring_2094
v0
  = (T_IsMagma_86 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      T_IsMagma_86 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_94
      ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202
         ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368
            ((T_IsCommutativeMonoid_406 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsCommutativeMonoid_406 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_416
               ((T_IsSemiringWithoutAnnihilatingZero_1142
 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsCommutativeMonoid_406
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1158
                  ((T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1252
                     ((T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238
MAlonzo.Code.Algebra.Structures.d_isSemiring_1358
                        ((T_CommutativeSemiring_2094 -> T_IsCommutativeSemiring_1344)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemiring_2094 -> T_IsCommutativeSemiring_1344
d_isCommutativeSemiring_2126 (T_CommutativeSemiring_2094 -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemiring_2094
v0))))))))
-- Algebra.Bundles.CommutativeSemiring._.isNearSemiring
d_isNearSemiring_2196 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeSemiring_2094 ->
  MAlonzo.Code.Algebra.Structures.T_IsNearSemiring_876
d_isNearSemiring_2196 :: () -> () -> T_CommutativeSemiring_2094 -> T_IsNearSemiring_876
d_isNearSemiring_2196 ~()
v0 ~()
v1 T_CommutativeSemiring_2094
v2 = T_CommutativeSemiring_2094 -> T_IsNearSemiring_876
du_isNearSemiring_2196 T_CommutativeSemiring_2094
v2
du_isNearSemiring_2196 ::
  T_CommutativeSemiring_2094 ->
  MAlonzo.Code.Algebra.Structures.T_IsNearSemiring_876
du_isNearSemiring_2196 :: T_CommutativeSemiring_2094 -> T_IsNearSemiring_876
du_isNearSemiring_2196 T_CommutativeSemiring_2094
v0
  = let v1 :: T_IsCommutativeSemiring_1344
v1 = T_CommutativeSemiring_2094 -> T_IsCommutativeSemiring_1344
d_isCommutativeSemiring_2126 (T_CommutativeSemiring_2094 -> T_CommutativeSemiring_2094
forall a b. a -> b
coe T_CommutativeSemiring_2094
v0) in
    AgdaAny -> T_IsNearSemiring_876
forall a b. a -> b
coe
      (let v2 :: T_IsSemiring_1238
v2
             = T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238
MAlonzo.Code.Algebra.Structures.d_isSemiring_1358 (T_IsCommutativeSemiring_1344 -> T_IsCommutativeSemiring_1344
forall a b. a -> b
coe T_IsCommutativeSemiring_1344
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsSemiringWithoutOne_952 -> T_IsNearSemiring_876)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemiringWithoutOne_952 -> T_IsNearSemiring_876
MAlonzo.Code.Algebra.Structures.du_isNearSemiring_990
            ((T_IsSemiring_1238 -> T_IsSemiringWithoutOne_952)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemiring_1238 -> T_IsSemiringWithoutOne_952
MAlonzo.Code.Algebra.Structures.du_isSemiringWithoutOne_1326
               (T_IsSemiring_1238 -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1238
v2))))
-- Algebra.Bundles.CommutativeSemiring._.isPartialEquivalence
d_isPartialEquivalence_2198 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeSemiring_2094 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_2198 :: () -> () -> T_CommutativeSemiring_2094 -> T_IsPartialEquivalence_16
d_isPartialEquivalence_2198 ~()
v0 ~()
v1 T_CommutativeSemiring_2094
v2
  = T_CommutativeSemiring_2094 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_2198 T_CommutativeSemiring_2094
v2
du_isPartialEquivalence_2198 ::
  T_CommutativeSemiring_2094 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_2198 :: T_CommutativeSemiring_2094 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_2198 T_CommutativeSemiring_2094
v0
  = let v1 :: T_IsCommutativeSemiring_1344
v1 = T_CommutativeSemiring_2094 -> T_IsCommutativeSemiring_1344
d_isCommutativeSemiring_2126 (T_CommutativeSemiring_2094 -> T_CommutativeSemiring_2094
forall a b. a -> b
coe T_CommutativeSemiring_2094
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsSemiring_1238
v2
             = T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238
MAlonzo.Code.Algebra.Structures.d_isSemiring_1358 (T_IsCommutativeSemiring_1344 -> T_IsCommutativeSemiring_1344
forall a b. a -> b
coe T_IsCommutativeSemiring_1344
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemiringWithoutAnnihilatingZero_1142
v3
                = T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1252
                    (T_IsSemiring_1238 -> T_IsSemiring_1238
forall a b. a -> b
coe T_IsSemiring_1238
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsCommutativeMonoid_406
v4
                   = T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsCommutativeMonoid_406
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1158
                       (T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsSemiringWithoutAnnihilatingZero_1142
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1142
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsMonoid_358
v5
                      = T_IsCommutativeMonoid_406 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_416 (T_IsCommutativeMonoid_406 -> T_IsCommutativeMonoid_406
forall a b. a -> b
coe T_IsCommutativeMonoid_406
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (let v6 :: T_IsSemigroup_194
v6
                         = T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368 (T_IsMonoid_358 -> T_IsMonoid_358
forall a b. a -> b
coe T_IsMonoid_358
v5) in
                   AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     (let v7 :: T_IsMagma_86
v7 = T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202 (T_IsSemigroup_194 -> T_IsSemigroup_194
forall a b. a -> b
coe T_IsSemigroup_194
v6) in
                      AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        ((T_IsEquivalence_26 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_IsEquivalence_26 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
                           ((T_IsMagma_86 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                              T_IsMagma_86 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_94 (T_IsMagma_86 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86
v7)))))))))
-- Algebra.Bundles.CommutativeSemiring._.isSemiring
d_isSemiring_2200 ::
  T_CommutativeSemiring_2094 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemiring_1238
d_isSemiring_2200 :: T_CommutativeSemiring_2094 -> T_IsSemiring_1238
d_isSemiring_2200 T_CommutativeSemiring_2094
v0
  = (T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238)
-> AgdaAny -> T_IsSemiring_1238
forall a b. a -> b
coe
      T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238
MAlonzo.Code.Algebra.Structures.d_isSemiring_1358
      ((T_CommutativeSemiring_2094 -> T_IsCommutativeSemiring_1344)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemiring_2094 -> T_IsCommutativeSemiring_1344
d_isCommutativeSemiring_2126 (T_CommutativeSemiring_2094 -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemiring_2094
v0))
-- Algebra.Bundles.CommutativeSemiring._.isSemiringWithoutAnnihilatingZero
d_isSemiringWithoutAnnihilatingZero_2202 ::
  T_CommutativeSemiring_2094 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutAnnihilatingZero_1142
d_isSemiringWithoutAnnihilatingZero_2202 :: T_CommutativeSemiring_2094
-> T_IsSemiringWithoutAnnihilatingZero_1142
d_isSemiringWithoutAnnihilatingZero_2202 T_CommutativeSemiring_2094
v0
  = (T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142)
-> AgdaAny -> T_IsSemiringWithoutAnnihilatingZero_1142
forall a b. a -> b
coe
      T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1252
      ((T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238
MAlonzo.Code.Algebra.Structures.d_isSemiring_1358
         ((T_CommutativeSemiring_2094 -> T_IsCommutativeSemiring_1344)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemiring_2094 -> T_IsCommutativeSemiring_1344
d_isCommutativeSemiring_2126 (T_CommutativeSemiring_2094 -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemiring_2094
v0)))
-- Algebra.Bundles.CommutativeSemiring._.isSemiringWithoutOne
d_isSemiringWithoutOne_2204 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeSemiring_2094 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutOne_952
d_isSemiringWithoutOne_2204 :: ()
-> () -> T_CommutativeSemiring_2094 -> T_IsSemiringWithoutOne_952
d_isSemiringWithoutOne_2204 ~()
v0 ~()
v1 T_CommutativeSemiring_2094
v2
  = T_CommutativeSemiring_2094 -> T_IsSemiringWithoutOne_952
du_isSemiringWithoutOne_2204 T_CommutativeSemiring_2094
v2
du_isSemiringWithoutOne_2204 ::
  T_CommutativeSemiring_2094 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutOne_952
du_isSemiringWithoutOne_2204 :: T_CommutativeSemiring_2094 -> T_IsSemiringWithoutOne_952
du_isSemiringWithoutOne_2204 T_CommutativeSemiring_2094
v0
  = let v1 :: T_IsCommutativeSemiring_1344
v1 = T_CommutativeSemiring_2094 -> T_IsCommutativeSemiring_1344
d_isCommutativeSemiring_2126 (T_CommutativeSemiring_2094 -> T_CommutativeSemiring_2094
forall a b. a -> b
coe T_CommutativeSemiring_2094
v0) in
    AgdaAny -> T_IsSemiringWithoutOne_952
forall a b. a -> b
coe
      ((T_IsSemiring_1238 -> T_IsSemiringWithoutOne_952)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiring_1238 -> T_IsSemiringWithoutOne_952
MAlonzo.Code.Algebra.Structures.du_isSemiringWithoutOne_1326
         ((T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238
MAlonzo.Code.Algebra.Structures.d_isSemiring_1358 (T_IsCommutativeSemiring_1344 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiring_1344
v1)))
-- Algebra.Bundles.CommutativeSemiring._.refl
d_refl_2206 :: T_CommutativeSemiring_2094 -> AgdaAny -> AgdaAny
d_refl_2206 :: T_CommutativeSemiring_2094 -> AgdaAny -> AgdaAny
d_refl_2206 T_CommutativeSemiring_2094
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_86 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_86 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_94
         ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202
            ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368
               ((T_IsCommutativeMonoid_406 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsCommutativeMonoid_406 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_416
                  ((T_IsSemiringWithoutAnnihilatingZero_1142
 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsCommutativeMonoid_406
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1158
                     ((T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1252
                        ((T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238
MAlonzo.Code.Algebra.Structures.d_isSemiring_1358
                           ((T_CommutativeSemiring_2094 -> T_IsCommutativeSemiring_1344)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemiring_2094 -> T_IsCommutativeSemiring_1344
d_isCommutativeSemiring_2126 (T_CommutativeSemiring_2094 -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemiring_2094
v0)))))))))
-- Algebra.Bundles.CommutativeSemiring._.reflexive
d_reflexive_2208 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeSemiring_2094 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_2208 :: ()
-> ()
-> T_CommutativeSemiring_2094
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_2208 ~()
v0 ~()
v1 T_CommutativeSemiring_2094
v2 = T_CommutativeSemiring_2094
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_2208 T_CommutativeSemiring_2094
v2
du_reflexive_2208 ::
  T_CommutativeSemiring_2094 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_2208 :: T_CommutativeSemiring_2094
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_2208 T_CommutativeSemiring_2094
v0
  = let v1 :: T_IsCommutativeSemiring_1344
v1 = T_CommutativeSemiring_2094 -> T_IsCommutativeSemiring_1344
d_isCommutativeSemiring_2126 (T_CommutativeSemiring_2094 -> T_CommutativeSemiring_2094
forall a b. a -> b
coe T_CommutativeSemiring_2094
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemiring_1238
v2
             = T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238
MAlonzo.Code.Algebra.Structures.d_isSemiring_1358 (T_IsCommutativeSemiring_1344 -> T_IsCommutativeSemiring_1344
forall a b. a -> b
coe T_IsCommutativeSemiring_1344
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemiringWithoutAnnihilatingZero_1142
v3
                = T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1252
                    (T_IsSemiring_1238 -> T_IsSemiring_1238
forall a b. a -> b
coe T_IsSemiring_1238
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsCommutativeMonoid_406
v4
                   = T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsCommutativeMonoid_406
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1158
                       (T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsSemiringWithoutAnnihilatingZero_1142
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1142
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsMonoid_358
v5
                      = T_IsCommutativeMonoid_406 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_416 (T_IsCommutativeMonoid_406 -> T_IsCommutativeMonoid_406
forall a b. a -> b
coe T_IsCommutativeMonoid_406
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (let v6 :: T_IsSemigroup_194
v6
                         = T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368 (T_IsMonoid_358 -> T_IsMonoid_358
forall a b. a -> b
coe T_IsMonoid_358
v5) in
                   AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     (let v7 :: T_IsMagma_86
v7 = T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202 (T_IsSemigroup_194 -> T_IsSemigroup_194
forall a b. a -> b
coe T_IsSemigroup_194
v6) in
                      (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
                        (\ AgdaAny
v8 AgdaAny
v9 AgdaAny
v10 ->
                           (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                             T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
                             ((T_IsMagma_86 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_94 (T_IsMagma_86 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86
v7))
                             AgdaAny
v8)))))))
-- Algebra.Bundles.CommutativeSemiring._.setoid
d_setoid_2210 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeSemiring_2094 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_2210 :: () -> () -> T_CommutativeSemiring_2094 -> T_Setoid_44
d_setoid_2210 ~()
v0 ~()
v1 T_CommutativeSemiring_2094
v2 = T_CommutativeSemiring_2094 -> T_Setoid_44
du_setoid_2210 T_CommutativeSemiring_2094
v2
du_setoid_2210 ::
  T_CommutativeSemiring_2094 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_2210 :: T_CommutativeSemiring_2094 -> T_Setoid_44
du_setoid_2210 T_CommutativeSemiring_2094
v0
  = let v1 :: T_IsCommutativeSemiring_1344
v1 = T_CommutativeSemiring_2094 -> T_IsCommutativeSemiring_1344
d_isCommutativeSemiring_2126 (T_CommutativeSemiring_2094 -> T_CommutativeSemiring_2094
forall a b. a -> b
coe T_CommutativeSemiring_2094
v0) in
    AgdaAny -> T_Setoid_44
forall a b. a -> b
coe
      (let v2 :: T_IsSemiring_1238
v2
             = T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238
MAlonzo.Code.Algebra.Structures.d_isSemiring_1358 (T_IsCommutativeSemiring_1344 -> T_IsCommutativeSemiring_1344
forall a b. a -> b
coe T_IsCommutativeSemiring_1344
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemiringWithoutAnnihilatingZero_1142
v3
                = T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1252
                    (T_IsSemiring_1238 -> T_IsSemiring_1238
forall a b. a -> b
coe T_IsSemiring_1238
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsCommutativeMonoid_406
v4
                   = T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsCommutativeMonoid_406
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1158
                       (T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsSemiringWithoutAnnihilatingZero_1142
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1142
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsMonoid_358
v5
                      = T_IsCommutativeMonoid_406 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_416 (T_IsCommutativeMonoid_406 -> T_IsCommutativeMonoid_406
forall a b. a -> b
coe T_IsCommutativeMonoid_406
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (let v6 :: T_IsSemigroup_194
v6
                         = T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368 (T_IsMonoid_358 -> T_IsMonoid_358
forall a b. a -> b
coe T_IsMonoid_358
v5) in
                   AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     ((T_IsMagma_86 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsMagma_86 -> T_Setoid_44
MAlonzo.Code.Algebra.Structures.du_setoid_110
                        ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202 (T_IsSemigroup_194 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194
v6))))))))
-- Algebra.Bundles.CommutativeSemiring._.sym
d_sym_2212 ::
  T_CommutativeSemiring_2094 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_2212 :: T_CommutativeSemiring_2094
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_2212 T_CommutativeSemiring_2094
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_86 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_86 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_94
         ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202
            ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368
               ((T_IsCommutativeMonoid_406 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsCommutativeMonoid_406 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_416
                  ((T_IsSemiringWithoutAnnihilatingZero_1142
 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsCommutativeMonoid_406
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1158
                     ((T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1252
                        ((T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238
MAlonzo.Code.Algebra.Structures.d_isSemiring_1358
                           ((T_CommutativeSemiring_2094 -> T_IsCommutativeSemiring_1344)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemiring_2094 -> T_IsCommutativeSemiring_1344
d_isCommutativeSemiring_2126 (T_CommutativeSemiring_2094 -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemiring_2094
v0)))))))))
-- Algebra.Bundles.CommutativeSemiring._.trans
d_trans_2214 ::
  T_CommutativeSemiring_2094 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_2214 :: T_CommutativeSemiring_2094
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_2214 T_CommutativeSemiring_2094
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_86 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_86 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_94
         ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202
            ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368
               ((T_IsCommutativeMonoid_406 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsCommutativeMonoid_406 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_416
                  ((T_IsSemiringWithoutAnnihilatingZero_1142
 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsCommutativeMonoid_406
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1158
                     ((T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1252
                        ((T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238
MAlonzo.Code.Algebra.Structures.d_isSemiring_1358
                           ((T_CommutativeSemiring_2094 -> T_IsCommutativeSemiring_1344)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemiring_2094 -> T_IsCommutativeSemiring_1344
d_isCommutativeSemiring_2126 (T_CommutativeSemiring_2094 -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemiring_2094
v0)))))))))
-- Algebra.Bundles.CommutativeSemiring._.zero
d_zero_2216 ::
  T_CommutativeSemiring_2094 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_zero_2216 :: T_CommutativeSemiring_2094 -> T_Σ_14
d_zero_2216 T_CommutativeSemiring_2094
v0
  = (T_IsSemiring_1238 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsSemiring_1238 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_zero_1254
      ((T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238
MAlonzo.Code.Algebra.Structures.d_isSemiring_1358
         ((T_CommutativeSemiring_2094 -> T_IsCommutativeSemiring_1344)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemiring_2094 -> T_IsCommutativeSemiring_1344
d_isCommutativeSemiring_2126 (T_CommutativeSemiring_2094 -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemiring_2094
v0)))
-- Algebra.Bundles.CommutativeSemiring._.zeroʳ
d_zero'691'_2218 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeSemiring_2094 -> AgdaAny -> AgdaAny
d_zero'691'_2218 :: () -> () -> T_CommutativeSemiring_2094 -> AgdaAny -> AgdaAny
d_zero'691'_2218 ~()
v0 ~()
v1 T_CommutativeSemiring_2094
v2 = T_CommutativeSemiring_2094 -> AgdaAny -> AgdaAny
du_zero'691'_2218 T_CommutativeSemiring_2094
v2
du_zero'691'_2218 ::
  T_CommutativeSemiring_2094 -> AgdaAny -> AgdaAny
du_zero'691'_2218 :: T_CommutativeSemiring_2094 -> AgdaAny -> AgdaAny
du_zero'691'_2218 T_CommutativeSemiring_2094
v0
  = let v1 :: T_IsCommutativeSemiring_1344
v1 = T_CommutativeSemiring_2094 -> T_IsCommutativeSemiring_1344
d_isCommutativeSemiring_2126 (T_CommutativeSemiring_2094 -> T_CommutativeSemiring_2094
forall a b. a -> b
coe T_CommutativeSemiring_2094
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemiring_1238
v2
             = T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238
MAlonzo.Code.Algebra.Structures.d_isSemiring_1358 (T_IsCommutativeSemiring_1344 -> T_IsCommutativeSemiring_1344
forall a b. a -> b
coe T_IsCommutativeSemiring_1344
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsSemiringWithoutOne_952 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemiringWithoutOne_952 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_zero'691'_988
            ((T_IsSemiring_1238 -> T_IsSemiringWithoutOne_952)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemiring_1238 -> T_IsSemiringWithoutOne_952
MAlonzo.Code.Algebra.Structures.du_isSemiringWithoutOne_1326
               (T_IsSemiring_1238 -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1238
v2))))
-- Algebra.Bundles.CommutativeSemiring._.zeroˡ
d_zero'737'_2220 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeSemiring_2094 -> AgdaAny -> AgdaAny
d_zero'737'_2220 :: () -> () -> T_CommutativeSemiring_2094 -> AgdaAny -> AgdaAny
d_zero'737'_2220 ~()
v0 ~()
v1 T_CommutativeSemiring_2094
v2 = T_CommutativeSemiring_2094 -> AgdaAny -> AgdaAny
du_zero'737'_2220 T_CommutativeSemiring_2094
v2
du_zero'737'_2220 ::
  T_CommutativeSemiring_2094 -> AgdaAny -> AgdaAny
du_zero'737'_2220 :: T_CommutativeSemiring_2094 -> AgdaAny -> AgdaAny
du_zero'737'_2220 T_CommutativeSemiring_2094
v0
  = let v1 :: T_IsCommutativeSemiring_1344
v1 = T_CommutativeSemiring_2094 -> T_IsCommutativeSemiring_1344
d_isCommutativeSemiring_2126 (T_CommutativeSemiring_2094 -> T_CommutativeSemiring_2094
forall a b. a -> b
coe T_CommutativeSemiring_2094
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemiring_1238
v2
             = T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238
MAlonzo.Code.Algebra.Structures.d_isSemiring_1358 (T_IsCommutativeSemiring_1344 -> T_IsCommutativeSemiring_1344
forall a b. a -> b
coe T_IsCommutativeSemiring_1344
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsSemiringWithoutOne_952 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemiringWithoutOne_952 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_zero'737'_986
            ((T_IsSemiring_1238 -> T_IsSemiringWithoutOne_952)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemiring_1238 -> T_IsSemiringWithoutOne_952
MAlonzo.Code.Algebra.Structures.du_isSemiringWithoutOne_1326
               (T_IsSemiring_1238 -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1238
v2))))
-- Algebra.Bundles.CommutativeSemiring.semiring
d_semiring_2222 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeSemiring_2094 -> T_Semiring_1932
d_semiring_2222 :: () -> () -> T_CommutativeSemiring_2094 -> T_Semiring_1932
d_semiring_2222 ~()
v0 ~()
v1 T_CommutativeSemiring_2094
v2 = T_CommutativeSemiring_2094 -> T_Semiring_1932
du_semiring_2222 T_CommutativeSemiring_2094
v2
du_semiring_2222 :: T_CommutativeSemiring_2094 -> T_Semiring_1932
du_semiring_2222 :: T_CommutativeSemiring_2094 -> T_Semiring_1932
du_semiring_2222 T_CommutativeSemiring_2094
v0
  = ((AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> AgdaAny
 -> T_IsSemiring_1238
 -> T_Semiring_1932)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsSemiring_1238
-> T_Semiring_1932
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsSemiring_1238
-> T_Semiring_1932
C_Semiring'46'constructor_33613 (T_CommutativeSemiring_2094 -> AgdaAny -> AgdaAny -> AgdaAny
d__'43'__2118 (T_CommutativeSemiring_2094 -> T_CommutativeSemiring_2094
forall a b. a -> b
coe T_CommutativeSemiring_2094
v0))
      (T_CommutativeSemiring_2094 -> AgdaAny -> AgdaAny -> AgdaAny
d__'42'__2120 (T_CommutativeSemiring_2094 -> T_CommutativeSemiring_2094
forall a b. a -> b
coe T_CommutativeSemiring_2094
v0)) (T_CommutativeSemiring_2094 -> AgdaAny
d_0'35'_2122 (T_CommutativeSemiring_2094 -> T_CommutativeSemiring_2094
forall a b. a -> b
coe T_CommutativeSemiring_2094
v0))
      (T_CommutativeSemiring_2094 -> AgdaAny
d_1'35'_2124 (T_CommutativeSemiring_2094 -> T_CommutativeSemiring_2094
forall a b. a -> b
coe T_CommutativeSemiring_2094
v0))
      (T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238
MAlonzo.Code.Algebra.Structures.d_isSemiring_1358
         ((T_CommutativeSemiring_2094 -> T_IsCommutativeSemiring_1344)
-> AgdaAny -> T_IsCommutativeSemiring_1344
forall a b. a -> b
coe T_CommutativeSemiring_2094 -> T_IsCommutativeSemiring_1344
d_isCommutativeSemiring_2126 (T_CommutativeSemiring_2094 -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemiring_2094
v0)))
-- Algebra.Bundles.CommutativeSemiring._._≉_
d__'8777'__2226 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeSemiring_2094 -> AgdaAny -> AgdaAny -> ()
d__'8777'__2226 :: () -> () -> T_CommutativeSemiring_2094 -> AgdaAny -> AgdaAny -> ()
d__'8777'__2226 = () -> () -> T_CommutativeSemiring_2094 -> AgdaAny -> AgdaAny -> ()
forall a. a
erased
-- Algebra.Bundles.CommutativeSemiring._.magma
d_magma_2228 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeSemiring_2094 -> T_Magma_36
d_magma_2228 :: () -> () -> T_CommutativeSemiring_2094 -> T_Magma_36
d_magma_2228 ~()
v0 ~()
v1 T_CommutativeSemiring_2094
v2 = T_CommutativeSemiring_2094 -> T_Magma_36
du_magma_2228 T_CommutativeSemiring_2094
v2
du_magma_2228 :: T_CommutativeSemiring_2094 -> T_Magma_36
du_magma_2228 :: T_CommutativeSemiring_2094 -> T_Magma_36
du_magma_2228 T_CommutativeSemiring_2094
v0
  = let v1 :: t
v1 = (T_CommutativeSemiring_2094 -> T_Semiring_1932) -> AgdaAny -> t
forall a b. a -> b
coe T_CommutativeSemiring_2094 -> T_Semiring_1932
du_semiring_2222 (T_CommutativeSemiring_2094 -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemiring_2094
v0) in
    AgdaAny -> T_Magma_36
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_Semiring_1932 -> T_SemiringWithoutAnnihilatingZero_1786)
-> AgdaAny -> t
forall a b. a -> b
coe T_Semiring_1932 -> T_SemiringWithoutAnnihilatingZero_1786
du_semiringWithoutAnnihilatingZero_2048 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: t
v3 = (T_SemiringWithoutAnnihilatingZero_1786 -> T_Monoid_506)
-> AgdaAny -> t
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_1786 -> T_Monoid_506
du_'42''45'monoid_1916 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_Semigroup_206 -> T_Magma_36) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semigroup_206 -> T_Magma_36
du_magma_254 ((T_Monoid_506 -> T_Semigroup_206) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Monoid_506 -> T_Semigroup_206
du_semigroup_566 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3)))))
-- Algebra.Bundles.CommutativeSemiring._.*-monoid
d_'42''45'monoid_2230 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeSemiring_2094 -> T_Monoid_506
d_'42''45'monoid_2230 :: () -> () -> T_CommutativeSemiring_2094 -> T_Monoid_506
d_'42''45'monoid_2230 ~()
v0 ~()
v1 T_CommutativeSemiring_2094
v2 = T_CommutativeSemiring_2094 -> T_Monoid_506
du_'42''45'monoid_2230 T_CommutativeSemiring_2094
v2
du_'42''45'monoid_2230 ::
  T_CommutativeSemiring_2094 -> T_Monoid_506
du_'42''45'monoid_2230 :: T_CommutativeSemiring_2094 -> T_Monoid_506
du_'42''45'monoid_2230 T_CommutativeSemiring_2094
v0
  = let v1 :: t
v1 = (T_CommutativeSemiring_2094 -> T_Semiring_1932) -> AgdaAny -> t
forall a b. a -> b
coe T_CommutativeSemiring_2094 -> T_Semiring_1932
du_semiring_2222 (T_CommutativeSemiring_2094 -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemiring_2094
v0) in
    AgdaAny -> T_Monoid_506
forall a b. a -> b
coe
      ((T_SemiringWithoutAnnihilatingZero_1786 -> T_Monoid_506)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_SemiringWithoutAnnihilatingZero_1786 -> T_Monoid_506
du_'42''45'monoid_1916
         ((T_Semiring_1932 -> T_SemiringWithoutAnnihilatingZero_1786)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semiring_1932 -> T_SemiringWithoutAnnihilatingZero_1786
du_semiringWithoutAnnihilatingZero_2048 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1)))
-- Algebra.Bundles.CommutativeSemiring._.rawMagma
d_rawMagma_2232 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeSemiring_2094 -> T_RawMagma_8
d_rawMagma_2232 :: () -> () -> T_CommutativeSemiring_2094 -> T_RawMagma_8
d_rawMagma_2232 ~()
v0 ~()
v1 T_CommutativeSemiring_2094
v2 = T_CommutativeSemiring_2094 -> T_RawMagma_8
du_rawMagma_2232 T_CommutativeSemiring_2094
v2
du_rawMagma_2232 :: T_CommutativeSemiring_2094 -> T_RawMagma_8
du_rawMagma_2232 :: T_CommutativeSemiring_2094 -> T_RawMagma_8
du_rawMagma_2232 T_CommutativeSemiring_2094
v0
  = let v1 :: t
v1 = (T_CommutativeSemiring_2094 -> T_Semiring_1932) -> AgdaAny -> t
forall a b. a -> b
coe T_CommutativeSemiring_2094 -> T_Semiring_1932
du_semiring_2222 (T_CommutativeSemiring_2094 -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemiring_2094
v0) in
    AgdaAny -> T_RawMagma_8
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_Semiring_1932 -> T_SemiringWithoutAnnihilatingZero_1786)
-> AgdaAny -> t
forall a b. a -> b
coe T_Semiring_1932 -> T_SemiringWithoutAnnihilatingZero_1786
du_semiringWithoutAnnihilatingZero_2048 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: t
v3 = (T_SemiringWithoutAnnihilatingZero_1786 -> T_Monoid_506)
-> AgdaAny -> t
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_1786 -> T_Monoid_506
du_'42''45'monoid_1916 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: t
v4 = (T_Monoid_506 -> T_Semigroup_206) -> AgdaAny -> t
forall a b. a -> b
coe T_Monoid_506 -> T_Semigroup_206
du_semigroup_566 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_Magma_36 -> T_RawMagma_8) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Magma_36 -> T_RawMagma_8
du_rawMagma_80 ((T_Semigroup_206 -> T_Magma_36) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semigroup_206 -> T_Magma_36
du_magma_254 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v4))))))
-- Algebra.Bundles.CommutativeSemiring._.rawMonoid
d_rawMonoid_2234 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeSemiring_2094 -> T_RawMonoid_474
d_rawMonoid_2234 :: () -> () -> T_CommutativeSemiring_2094 -> T_RawMonoid_474
d_rawMonoid_2234 ~()
v0 ~()
v1 T_CommutativeSemiring_2094
v2 = T_CommutativeSemiring_2094 -> T_RawMonoid_474
du_rawMonoid_2234 T_CommutativeSemiring_2094
v2
du_rawMonoid_2234 :: T_CommutativeSemiring_2094 -> T_RawMonoid_474
du_rawMonoid_2234 :: T_CommutativeSemiring_2094 -> T_RawMonoid_474
du_rawMonoid_2234 T_CommutativeSemiring_2094
v0
  = let v1 :: t
v1 = (T_CommutativeSemiring_2094 -> T_Semiring_1932) -> AgdaAny -> t
forall a b. a -> b
coe T_CommutativeSemiring_2094 -> T_Semiring_1932
du_semiring_2222 (T_CommutativeSemiring_2094 -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemiring_2094
v0) in
    AgdaAny -> T_RawMonoid_474
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_Semiring_1932 -> T_SemiringWithoutAnnihilatingZero_1786)
-> AgdaAny -> t
forall a b. a -> b
coe T_Semiring_1932 -> T_SemiringWithoutAnnihilatingZero_1786
du_semiringWithoutAnnihilatingZero_2048 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_Monoid_506 -> T_RawMonoid_474) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Monoid_506 -> T_RawMonoid_474
du_rawMonoid_576 ((T_SemiringWithoutAnnihilatingZero_1786 -> T_Monoid_506)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_1786 -> T_Monoid_506
du_'42''45'monoid_1916 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2))))
-- Algebra.Bundles.CommutativeSemiring._.semigroup
d_semigroup_2236 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeSemiring_2094 -> T_Semigroup_206
d_semigroup_2236 :: () -> () -> T_CommutativeSemiring_2094 -> T_Semigroup_206
d_semigroup_2236 ~()
v0 ~()
v1 T_CommutativeSemiring_2094
v2 = T_CommutativeSemiring_2094 -> T_Semigroup_206
du_semigroup_2236 T_CommutativeSemiring_2094
v2
du_semigroup_2236 :: T_CommutativeSemiring_2094 -> T_Semigroup_206
du_semigroup_2236 :: T_CommutativeSemiring_2094 -> T_Semigroup_206
du_semigroup_2236 T_CommutativeSemiring_2094
v0
  = let v1 :: t
v1 = (T_CommutativeSemiring_2094 -> T_Semiring_1932) -> AgdaAny -> t
forall a b. a -> b
coe T_CommutativeSemiring_2094 -> T_Semiring_1932
du_semiring_2222 (T_CommutativeSemiring_2094 -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemiring_2094
v0) in
    AgdaAny -> T_Semigroup_206
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_Semiring_1932 -> T_SemiringWithoutAnnihilatingZero_1786)
-> AgdaAny -> t
forall a b. a -> b
coe T_Semiring_1932 -> T_SemiringWithoutAnnihilatingZero_1786
du_semiringWithoutAnnihilatingZero_2048 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_Monoid_506 -> T_Semigroup_206) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Monoid_506 -> T_Semigroup_206
du_semigroup_566 ((T_SemiringWithoutAnnihilatingZero_1786 -> T_Monoid_506)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_1786 -> T_Monoid_506
du_'42''45'monoid_1916 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2))))
-- Algebra.Bundles.CommutativeSemiring._.commutativeMagma
d_commutativeMagma_2238 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeSemiring_2094 -> T_CommutativeMagma_148
d_commutativeMagma_2238 :: () -> () -> T_CommutativeSemiring_2094 -> T_CommutativeMagma_148
d_commutativeMagma_2238 ~()
v0 ~()
v1 T_CommutativeSemiring_2094
v2 = T_CommutativeSemiring_2094 -> T_CommutativeMagma_148
du_commutativeMagma_2238 T_CommutativeSemiring_2094
v2
du_commutativeMagma_2238 ::
  T_CommutativeSemiring_2094 -> T_CommutativeMagma_148
du_commutativeMagma_2238 :: T_CommutativeSemiring_2094 -> T_CommutativeMagma_148
du_commutativeMagma_2238 T_CommutativeSemiring_2094
v0
  = let v1 :: t
v1 = (T_CommutativeSemiring_2094 -> T_Semiring_1932) -> AgdaAny -> t
forall a b. a -> b
coe T_CommutativeSemiring_2094 -> T_Semiring_1932
du_semiring_2222 (T_CommutativeSemiring_2094 -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemiring_2094
v0) in
    AgdaAny -> T_CommutativeMagma_148
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_Semiring_1932 -> T_SemiringWithoutAnnihilatingZero_1786)
-> AgdaAny -> t
forall a b. a -> b
coe T_Semiring_1932 -> T_SemiringWithoutAnnihilatingZero_1786
du_semiringWithoutAnnihilatingZero_2048 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: t
v3 = (T_SemiringWithoutAnnihilatingZero_1786 -> T_CommutativeMonoid_582)
-> AgdaAny -> t
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_1786 -> T_CommutativeMonoid_582
du_'43''45'commutativeMonoid_1896 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_CommutativeSemigroup_332 -> T_CommutativeMagma_148)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_CommutativeSemigroup_332 -> T_CommutativeMagma_148
du_commutativeMagma_396
               ((T_CommutativeMonoid_582 -> T_CommutativeSemigroup_332)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeMonoid_582 -> T_CommutativeSemigroup_332
du_commutativeSemigroup_664 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3)))))
-- Algebra.Bundles.CommutativeSemiring._.+-commutativeMonoid
d_'43''45'commutativeMonoid_2240 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeSemiring_2094 -> T_CommutativeMonoid_582
d_'43''45'commutativeMonoid_2240 :: () -> () -> T_CommutativeSemiring_2094 -> T_CommutativeMonoid_582
d_'43''45'commutativeMonoid_2240 ~()
v0 ~()
v1 T_CommutativeSemiring_2094
v2
  = T_CommutativeSemiring_2094 -> T_CommutativeMonoid_582
du_'43''45'commutativeMonoid_2240 T_CommutativeSemiring_2094
v2
du_'43''45'commutativeMonoid_2240 ::
  T_CommutativeSemiring_2094 -> T_CommutativeMonoid_582
du_'43''45'commutativeMonoid_2240 :: T_CommutativeSemiring_2094 -> T_CommutativeMonoid_582
du_'43''45'commutativeMonoid_2240 T_CommutativeSemiring_2094
v0
  = let v1 :: t
v1 = (T_CommutativeSemiring_2094 -> T_Semiring_1932) -> AgdaAny -> t
forall a b. a -> b
coe T_CommutativeSemiring_2094 -> T_Semiring_1932
du_semiring_2222 (T_CommutativeSemiring_2094 -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemiring_2094
v0) in
    AgdaAny -> T_CommutativeMonoid_582
forall a b. a -> b
coe
      ((T_SemiringWithoutAnnihilatingZero_1786 -> T_CommutativeMonoid_582)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_SemiringWithoutAnnihilatingZero_1786 -> T_CommutativeMonoid_582
du_'43''45'commutativeMonoid_1896
         ((T_Semiring_1932 -> T_SemiringWithoutAnnihilatingZero_1786)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semiring_1932 -> T_SemiringWithoutAnnihilatingZero_1786
du_semiringWithoutAnnihilatingZero_2048 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1)))
-- Algebra.Bundles.CommutativeSemiring._.commutativeSemigroup
d_commutativeSemigroup_2242 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeSemiring_2094 -> T_CommutativeSemigroup_332
d_commutativeSemigroup_2242 :: ()
-> () -> T_CommutativeSemiring_2094 -> T_CommutativeSemigroup_332
d_commutativeSemigroup_2242 ~()
v0 ~()
v1 T_CommutativeSemiring_2094
v2
  = T_CommutativeSemiring_2094 -> T_CommutativeSemigroup_332
du_commutativeSemigroup_2242 T_CommutativeSemiring_2094
v2
du_commutativeSemigroup_2242 ::
  T_CommutativeSemiring_2094 -> T_CommutativeSemigroup_332
du_commutativeSemigroup_2242 :: T_CommutativeSemiring_2094 -> T_CommutativeSemigroup_332
du_commutativeSemigroup_2242 T_CommutativeSemiring_2094
v0
  = let v1 :: t
v1 = (T_CommutativeSemiring_2094 -> T_Semiring_1932) -> AgdaAny -> t
forall a b. a -> b
coe T_CommutativeSemiring_2094 -> T_Semiring_1932
du_semiring_2222 (T_CommutativeSemiring_2094 -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemiring_2094
v0) in
    AgdaAny -> T_CommutativeSemigroup_332
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_Semiring_1932 -> T_SemiringWithoutAnnihilatingZero_1786)
-> AgdaAny -> t
forall a b. a -> b
coe T_Semiring_1932 -> T_SemiringWithoutAnnihilatingZero_1786
du_semiringWithoutAnnihilatingZero_2048 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_CommutativeMonoid_582 -> T_CommutativeSemigroup_332)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_CommutativeMonoid_582 -> T_CommutativeSemigroup_332
du_commutativeSemigroup_664
            ((T_SemiringWithoutAnnihilatingZero_1786 -> T_CommutativeMonoid_582)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_1786 -> T_CommutativeMonoid_582
du_'43''45'commutativeMonoid_1896 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2))))
-- Algebra.Bundles.CommutativeSemiring._.magma
d_magma_2244 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeSemiring_2094 -> T_Magma_36
d_magma_2244 :: () -> () -> T_CommutativeSemiring_2094 -> T_Magma_36
d_magma_2244 ~()
v0 ~()
v1 T_CommutativeSemiring_2094
v2 = T_CommutativeSemiring_2094 -> T_Magma_36
du_magma_2244 T_CommutativeSemiring_2094
v2
du_magma_2244 :: T_CommutativeSemiring_2094 -> T_Magma_36
du_magma_2244 :: T_CommutativeSemiring_2094 -> T_Magma_36
du_magma_2244 T_CommutativeSemiring_2094
v0
  = let v1 :: t
v1 = (T_CommutativeSemiring_2094 -> T_Semiring_1932) -> AgdaAny -> t
forall a b. a -> b
coe T_CommutativeSemiring_2094 -> T_Semiring_1932
du_semiring_2222 (T_CommutativeSemiring_2094 -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemiring_2094
v0) in
    AgdaAny -> T_Magma_36
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_Semiring_1932 -> T_SemiringWithoutAnnihilatingZero_1786)
-> AgdaAny -> t
forall a b. a -> b
coe T_Semiring_1932 -> T_SemiringWithoutAnnihilatingZero_1786
du_semiringWithoutAnnihilatingZero_2048 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: t
v3 = (T_SemiringWithoutAnnihilatingZero_1786 -> T_CommutativeMonoid_582)
-> AgdaAny -> t
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_1786 -> T_CommutativeMonoid_582
du_'43''45'commutativeMonoid_1896 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: t
v4 = (T_CommutativeMonoid_582 -> T_Monoid_506) -> AgdaAny -> t
forall a b. a -> b
coe T_CommutativeMonoid_582 -> T_Monoid_506
du_monoid_650 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_Semigroup_206 -> T_Magma_36) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semigroup_206 -> T_Magma_36
du_magma_254 ((T_Monoid_506 -> T_Semigroup_206) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Monoid_506 -> T_Semigroup_206
du_semigroup_566 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v4))))))
-- Algebra.Bundles.CommutativeSemiring._.monoid
d_monoid_2246 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeSemiring_2094 -> T_Monoid_506
d_monoid_2246 :: () -> () -> T_CommutativeSemiring_2094 -> T_Monoid_506
d_monoid_2246 ~()
v0 ~()
v1 T_CommutativeSemiring_2094
v2 = T_CommutativeSemiring_2094 -> T_Monoid_506
du_monoid_2246 T_CommutativeSemiring_2094
v2
du_monoid_2246 :: T_CommutativeSemiring_2094 -> T_Monoid_506
du_monoid_2246 :: T_CommutativeSemiring_2094 -> T_Monoid_506
du_monoid_2246 T_CommutativeSemiring_2094
v0
  = let v1 :: t
v1 = (T_CommutativeSemiring_2094 -> T_Semiring_1932) -> AgdaAny -> t
forall a b. a -> b
coe T_CommutativeSemiring_2094 -> T_Semiring_1932
du_semiring_2222 (T_CommutativeSemiring_2094 -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemiring_2094
v0) in
    AgdaAny -> T_Monoid_506
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_Semiring_1932 -> T_SemiringWithoutAnnihilatingZero_1786)
-> AgdaAny -> t
forall a b. a -> b
coe T_Semiring_1932 -> T_SemiringWithoutAnnihilatingZero_1786
du_semiringWithoutAnnihilatingZero_2048 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_CommutativeMonoid_582 -> T_Monoid_506) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_CommutativeMonoid_582 -> T_Monoid_506
du_monoid_650 ((T_SemiringWithoutAnnihilatingZero_1786 -> T_CommutativeMonoid_582)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_1786 -> T_CommutativeMonoid_582
du_'43''45'commutativeMonoid_1896 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2))))
-- Algebra.Bundles.CommutativeSemiring._.rawMagma
d_rawMagma_2248 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeSemiring_2094 -> T_RawMagma_8
d_rawMagma_2248 :: () -> () -> T_CommutativeSemiring_2094 -> T_RawMagma_8
d_rawMagma_2248 ~()
v0 ~()
v1 T_CommutativeSemiring_2094
v2 = T_CommutativeSemiring_2094 -> T_RawMagma_8
du_rawMagma_2248 T_CommutativeSemiring_2094
v2
du_rawMagma_2248 :: T_CommutativeSemiring_2094 -> T_RawMagma_8
du_rawMagma_2248 :: T_CommutativeSemiring_2094 -> T_RawMagma_8
du_rawMagma_2248 T_CommutativeSemiring_2094
v0
  = let v1 :: t
v1 = (T_CommutativeSemiring_2094 -> T_Semiring_1932) -> AgdaAny -> t
forall a b. a -> b
coe T_CommutativeSemiring_2094 -> T_Semiring_1932
du_semiring_2222 (T_CommutativeSemiring_2094 -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemiring_2094
v0) in
    AgdaAny -> T_RawMagma_8
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_Semiring_1932 -> T_SemiringWithoutAnnihilatingZero_1786)
-> AgdaAny -> t
forall a b. a -> b
coe T_Semiring_1932 -> T_SemiringWithoutAnnihilatingZero_1786
du_semiringWithoutAnnihilatingZero_2048 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: t
v3 = (T_SemiringWithoutAnnihilatingZero_1786 -> T_CommutativeMonoid_582)
-> AgdaAny -> t
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_1786 -> T_CommutativeMonoid_582
du_'43''45'commutativeMonoid_1896 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: t
v4 = (T_CommutativeMonoid_582 -> T_Monoid_506) -> AgdaAny -> t
forall a b. a -> b
coe T_CommutativeMonoid_582 -> T_Monoid_506
du_monoid_650 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: t
v5 = (T_Monoid_506 -> T_Semigroup_206) -> AgdaAny -> t
forall a b. a -> b
coe T_Monoid_506 -> T_Semigroup_206
du_semigroup_566 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_Magma_36 -> T_RawMagma_8) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Magma_36 -> T_RawMagma_8
du_rawMagma_80 ((T_Semigroup_206 -> T_Magma_36) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semigroup_206 -> T_Magma_36
du_magma_254 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v5)))))))
-- Algebra.Bundles.CommutativeSemiring._.rawMonoid
d_rawMonoid_2250 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeSemiring_2094 -> T_RawMonoid_474
d_rawMonoid_2250 :: () -> () -> T_CommutativeSemiring_2094 -> T_RawMonoid_474
d_rawMonoid_2250 ~()
v0 ~()
v1 T_CommutativeSemiring_2094
v2 = T_CommutativeSemiring_2094 -> T_RawMonoid_474
du_rawMonoid_2250 T_CommutativeSemiring_2094
v2
du_rawMonoid_2250 :: T_CommutativeSemiring_2094 -> T_RawMonoid_474
du_rawMonoid_2250 :: T_CommutativeSemiring_2094 -> T_RawMonoid_474
du_rawMonoid_2250 T_CommutativeSemiring_2094
v0
  = let v1 :: t
v1 = (T_CommutativeSemiring_2094 -> T_Semiring_1932) -> AgdaAny -> t
forall a b. a -> b
coe T_CommutativeSemiring_2094 -> T_Semiring_1932
du_semiring_2222 (T_CommutativeSemiring_2094 -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemiring_2094
v0) in
    AgdaAny -> T_RawMonoid_474
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_Semiring_1932 -> T_SemiringWithoutAnnihilatingZero_1786)
-> AgdaAny -> t
forall a b. a -> b
coe T_Semiring_1932 -> T_SemiringWithoutAnnihilatingZero_1786
du_semiringWithoutAnnihilatingZero_2048 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: t
v3 = (T_SemiringWithoutAnnihilatingZero_1786 -> T_CommutativeMonoid_582)
-> AgdaAny -> t
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_1786 -> T_CommutativeMonoid_582
du_'43''45'commutativeMonoid_1896 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_Monoid_506 -> T_RawMonoid_474) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Monoid_506 -> T_RawMonoid_474
du_rawMonoid_576 ((T_CommutativeMonoid_582 -> T_Monoid_506) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeMonoid_582 -> T_Monoid_506
du_monoid_650 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3)))))
-- Algebra.Bundles.CommutativeSemiring._.semigroup
d_semigroup_2252 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeSemiring_2094 -> T_Semigroup_206
d_semigroup_2252 :: () -> () -> T_CommutativeSemiring_2094 -> T_Semigroup_206
d_semigroup_2252 ~()
v0 ~()
v1 T_CommutativeSemiring_2094
v2 = T_CommutativeSemiring_2094 -> T_Semigroup_206
du_semigroup_2252 T_CommutativeSemiring_2094
v2
du_semigroup_2252 :: T_CommutativeSemiring_2094 -> T_Semigroup_206
du_semigroup_2252 :: T_CommutativeSemiring_2094 -> T_Semigroup_206
du_semigroup_2252 T_CommutativeSemiring_2094
v0
  = let v1 :: t
v1 = (T_CommutativeSemiring_2094 -> T_Semiring_1932) -> AgdaAny -> t
forall a b. a -> b
coe T_CommutativeSemiring_2094 -> T_Semiring_1932
du_semiring_2222 (T_CommutativeSemiring_2094 -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemiring_2094
v0) in
    AgdaAny -> T_Semigroup_206
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_Semiring_1932 -> T_SemiringWithoutAnnihilatingZero_1786)
-> AgdaAny -> t
forall a b. a -> b
coe T_Semiring_1932 -> T_SemiringWithoutAnnihilatingZero_1786
du_semiringWithoutAnnihilatingZero_2048 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: t
v3 = (T_SemiringWithoutAnnihilatingZero_1786 -> T_CommutativeMonoid_582)
-> AgdaAny -> t
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_1786 -> T_CommutativeMonoid_582
du_'43''45'commutativeMonoid_1896 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_Monoid_506 -> T_Semigroup_206) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Monoid_506 -> T_Semigroup_206
du_semigroup_566 ((T_CommutativeMonoid_582 -> T_Monoid_506) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeMonoid_582 -> T_Monoid_506
du_monoid_650 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3)))))
-- Algebra.Bundles.CommutativeSemiring._.nearSemiring
d_nearSemiring_2254 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeSemiring_2094 -> T_NearSemiring_1354
d_nearSemiring_2254 :: () -> () -> T_CommutativeSemiring_2094 -> T_NearSemiring_1354
d_nearSemiring_2254 ~()
v0 ~()
v1 T_CommutativeSemiring_2094
v2 = T_CommutativeSemiring_2094 -> T_NearSemiring_1354
du_nearSemiring_2254 T_CommutativeSemiring_2094
v2
du_nearSemiring_2254 ::
  T_CommutativeSemiring_2094 -> T_NearSemiring_1354
du_nearSemiring_2254 :: T_CommutativeSemiring_2094 -> T_NearSemiring_1354
du_nearSemiring_2254 T_CommutativeSemiring_2094
v0
  = let v1 :: t
v1 = (T_CommutativeSemiring_2094 -> T_Semiring_1932) -> AgdaAny -> t
forall a b. a -> b
coe T_CommutativeSemiring_2094 -> T_Semiring_1932
du_semiring_2222 (T_CommutativeSemiring_2094 -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemiring_2094
v0) in
    AgdaAny -> T_NearSemiring_1354
forall a b. a -> b
coe
      ((T_SemiringWithoutOne_1464 -> T_NearSemiring_1354)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_SemiringWithoutOne_1464 -> T_NearSemiring_1354
du_nearSemiring_1562 ((T_Semiring_1932 -> T_SemiringWithoutOne_1464)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semiring_1932 -> T_SemiringWithoutOne_1464
du_semiringWithoutOne_2084 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1)))
-- Algebra.Bundles.CommutativeSemiring._.rawSemiring
d_rawSemiring_2256 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeSemiring_2094 -> T_RawSemiring_1738
d_rawSemiring_2256 :: () -> () -> T_CommutativeSemiring_2094 -> T_RawSemiring_1738
d_rawSemiring_2256 ~()
v0 ~()
v1 T_CommutativeSemiring_2094
v2 = T_CommutativeSemiring_2094 -> T_RawSemiring_1738
du_rawSemiring_2256 T_CommutativeSemiring_2094
v2
du_rawSemiring_2256 ::
  T_CommutativeSemiring_2094 -> T_RawSemiring_1738
du_rawSemiring_2256 :: T_CommutativeSemiring_2094 -> T_RawSemiring_1738
du_rawSemiring_2256 T_CommutativeSemiring_2094
v0
  = let v1 :: t
v1 = (T_CommutativeSemiring_2094 -> T_Semiring_1932) -> AgdaAny -> t
forall a b. a -> b
coe T_CommutativeSemiring_2094 -> T_Semiring_1932
du_semiring_2222 (T_CommutativeSemiring_2094 -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemiring_2094
v0) in
    AgdaAny -> T_RawSemiring_1738
forall a b. a -> b
coe
      ((T_SemiringWithoutAnnihilatingZero_1786 -> T_RawSemiring_1738)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_SemiringWithoutAnnihilatingZero_1786 -> T_RawSemiring_1738
du_rawSemiring_1890
         ((T_Semiring_1932 -> T_SemiringWithoutAnnihilatingZero_1786)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semiring_1932 -> T_SemiringWithoutAnnihilatingZero_1786
du_semiringWithoutAnnihilatingZero_2048 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1)))
-- Algebra.Bundles.CommutativeSemiring._.semiringWithoutAnnihilatingZero
d_semiringWithoutAnnihilatingZero_2258 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeSemiring_2094 ->
  T_SemiringWithoutAnnihilatingZero_1786
d_semiringWithoutAnnihilatingZero_2258 :: ()
-> ()
-> T_CommutativeSemiring_2094
-> T_SemiringWithoutAnnihilatingZero_1786
d_semiringWithoutAnnihilatingZero_2258 ~()
v0 ~()
v1 T_CommutativeSemiring_2094
v2
  = T_CommutativeSemiring_2094
-> T_SemiringWithoutAnnihilatingZero_1786
du_semiringWithoutAnnihilatingZero_2258 T_CommutativeSemiring_2094
v2
du_semiringWithoutAnnihilatingZero_2258 ::
  T_CommutativeSemiring_2094 ->
  T_SemiringWithoutAnnihilatingZero_1786
du_semiringWithoutAnnihilatingZero_2258 :: T_CommutativeSemiring_2094
-> T_SemiringWithoutAnnihilatingZero_1786
du_semiringWithoutAnnihilatingZero_2258 T_CommutativeSemiring_2094
v0
  = (T_Semiring_1932 -> T_SemiringWithoutAnnihilatingZero_1786)
-> AgdaAny -> T_SemiringWithoutAnnihilatingZero_1786
forall a b. a -> b
coe
      T_Semiring_1932 -> T_SemiringWithoutAnnihilatingZero_1786
du_semiringWithoutAnnihilatingZero_2048
      ((T_CommutativeSemiring_2094 -> T_Semiring_1932)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemiring_2094 -> T_Semiring_1932
du_semiring_2222 (T_CommutativeSemiring_2094 -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemiring_2094
v0))
-- Algebra.Bundles.CommutativeSemiring._.semiringWithoutOne
d_semiringWithoutOne_2260 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeSemiring_2094 -> T_SemiringWithoutOne_1464
d_semiringWithoutOne_2260 :: () -> () -> T_CommutativeSemiring_2094 -> T_SemiringWithoutOne_1464
d_semiringWithoutOne_2260 ~()
v0 ~()
v1 T_CommutativeSemiring_2094
v2
  = T_CommutativeSemiring_2094 -> T_SemiringWithoutOne_1464
du_semiringWithoutOne_2260 T_CommutativeSemiring_2094
v2
du_semiringWithoutOne_2260 ::
  T_CommutativeSemiring_2094 -> T_SemiringWithoutOne_1464
du_semiringWithoutOne_2260 :: T_CommutativeSemiring_2094 -> T_SemiringWithoutOne_1464
du_semiringWithoutOne_2260 T_CommutativeSemiring_2094
v0
  = (T_Semiring_1932 -> T_SemiringWithoutOne_1464)
-> AgdaAny -> T_SemiringWithoutOne_1464
forall a b. a -> b
coe T_Semiring_1932 -> T_SemiringWithoutOne_1464
du_semiringWithoutOne_2084 ((T_CommutativeSemiring_2094 -> T_Semiring_1932)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemiring_2094 -> T_Semiring_1932
du_semiring_2222 (T_CommutativeSemiring_2094 -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemiring_2094
v0))
-- Algebra.Bundles.CommutativeSemiring.*-commutativeMonoid
d_'42''45'commutativeMonoid_2262 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeSemiring_2094 -> T_CommutativeMonoid_582
d_'42''45'commutativeMonoid_2262 :: () -> () -> T_CommutativeSemiring_2094 -> T_CommutativeMonoid_582
d_'42''45'commutativeMonoid_2262 ~()
v0 ~()
v1 T_CommutativeSemiring_2094
v2
  = T_CommutativeSemiring_2094 -> T_CommutativeMonoid_582
du_'42''45'commutativeMonoid_2262 T_CommutativeSemiring_2094
v2
du_'42''45'commutativeMonoid_2262 ::
  T_CommutativeSemiring_2094 -> T_CommutativeMonoid_582
du_'42''45'commutativeMonoid_2262 :: T_CommutativeSemiring_2094 -> T_CommutativeMonoid_582
du_'42''45'commutativeMonoid_2262 T_CommutativeSemiring_2094
v0
  = ((AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny -> T_IsCommutativeMonoid_406 -> T_CommutativeMonoid_582)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_CommutativeMonoid_582
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> T_IsCommutativeMonoid_406 -> T_CommutativeMonoid_582
C_CommutativeMonoid'46'constructor_10343 (T_CommutativeSemiring_2094 -> AgdaAny -> AgdaAny -> AgdaAny
d__'42'__2120 (T_CommutativeSemiring_2094 -> T_CommutativeSemiring_2094
forall a b. a -> b
coe T_CommutativeSemiring_2094
v0))
      (T_CommutativeSemiring_2094 -> AgdaAny
d_1'35'_2124 (T_CommutativeSemiring_2094 -> T_CommutativeSemiring_2094
forall a b. a -> b
coe T_CommutativeSemiring_2094
v0))
      ((T_IsCommutativeSemiring_1344 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCommutativeSemiring_1344 -> T_IsCommutativeMonoid_406
MAlonzo.Code.Algebra.Structures.du_'42''45'isCommutativeMonoid_1452
         ((T_CommutativeSemiring_2094 -> T_IsCommutativeSemiring_1344)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemiring_2094 -> T_IsCommutativeSemiring_1344
d_isCommutativeSemiring_2126 (T_CommutativeSemiring_2094 -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemiring_2094
v0)))
-- Algebra.Bundles.CommutativeSemiring._.commutativeMagma
d_commutativeMagma_2266 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeSemiring_2094 -> T_CommutativeMagma_148
d_commutativeMagma_2266 :: () -> () -> T_CommutativeSemiring_2094 -> T_CommutativeMagma_148
d_commutativeMagma_2266 ~()
v0 ~()
v1 T_CommutativeSemiring_2094
v2 = T_CommutativeSemiring_2094 -> T_CommutativeMagma_148
du_commutativeMagma_2266 T_CommutativeSemiring_2094
v2
du_commutativeMagma_2266 ::
  T_CommutativeSemiring_2094 -> T_CommutativeMagma_148
du_commutativeMagma_2266 :: T_CommutativeSemiring_2094 -> T_CommutativeMagma_148
du_commutativeMagma_2266 T_CommutativeSemiring_2094
v0
  = let v1 :: t
v1 = (T_CommutativeSemiring_2094 -> T_CommutativeMonoid_582)
-> AgdaAny -> t
forall a b. a -> b
coe T_CommutativeSemiring_2094 -> T_CommutativeMonoid_582
du_'42''45'commutativeMonoid_2262 (T_CommutativeSemiring_2094 -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemiring_2094
v0) in
    AgdaAny -> T_CommutativeMagma_148
forall a b. a -> b
coe
      ((T_CommutativeSemigroup_332 -> T_CommutativeMagma_148)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_CommutativeSemigroup_332 -> T_CommutativeMagma_148
du_commutativeMagma_396 ((T_CommutativeMonoid_582 -> T_CommutativeSemigroup_332)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeMonoid_582 -> T_CommutativeSemigroup_332
du_commutativeSemigroup_664 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1)))
-- Algebra.Bundles.CommutativeSemiring._.commutativeSemigroup
d_commutativeSemigroup_2268 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeSemiring_2094 -> T_CommutativeSemigroup_332
d_commutativeSemigroup_2268 :: ()
-> () -> T_CommutativeSemiring_2094 -> T_CommutativeSemigroup_332
d_commutativeSemigroup_2268 ~()
v0 ~()
v1 T_CommutativeSemiring_2094
v2
  = T_CommutativeSemiring_2094 -> T_CommutativeSemigroup_332
du_commutativeSemigroup_2268 T_CommutativeSemiring_2094
v2
du_commutativeSemigroup_2268 ::
  T_CommutativeSemiring_2094 -> T_CommutativeSemigroup_332
du_commutativeSemigroup_2268 :: T_CommutativeSemiring_2094 -> T_CommutativeSemigroup_332
du_commutativeSemigroup_2268 T_CommutativeSemiring_2094
v0
  = (T_CommutativeMonoid_582 -> T_CommutativeSemigroup_332)
-> AgdaAny -> T_CommutativeSemigroup_332
forall a b. a -> b
coe
      T_CommutativeMonoid_582 -> T_CommutativeSemigroup_332
du_commutativeSemigroup_664
      ((T_CommutativeSemiring_2094 -> T_CommutativeMonoid_582)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemiring_2094 -> T_CommutativeMonoid_582
du_'42''45'commutativeMonoid_2262 (T_CommutativeSemiring_2094 -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemiring_2094
v0))
-- Algebra.Bundles.CommutativeSemiring.commutativeSemiringWithoutOne
d_commutativeSemiringWithoutOne_2270 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeSemiring_2094 -> T_CommutativeSemiringWithoutOne_1598
d_commutativeSemiringWithoutOne_2270 :: ()
-> ()
-> T_CommutativeSemiring_2094
-> T_CommutativeSemiringWithoutOne_1598
d_commutativeSemiringWithoutOne_2270 ~()
v0 ~()
v1 T_CommutativeSemiring_2094
v2
  = T_CommutativeSemiring_2094 -> T_CommutativeSemiringWithoutOne_1598
du_commutativeSemiringWithoutOne_2270 T_CommutativeSemiring_2094
v2
du_commutativeSemiringWithoutOne_2270 ::
  T_CommutativeSemiring_2094 -> T_CommutativeSemiringWithoutOne_1598
du_commutativeSemiringWithoutOne_2270 :: T_CommutativeSemiring_2094 -> T_CommutativeSemiringWithoutOne_1598
du_commutativeSemiringWithoutOne_2270 T_CommutativeSemiring_2094
v0
  = ((AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> T_IsCommutativeSemiringWithoutOne_1044
 -> T_CommutativeSemiringWithoutOne_1598)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_CommutativeSemiringWithoutOne_1598
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsCommutativeSemiringWithoutOne_1044
-> T_CommutativeSemiringWithoutOne_1598
C_CommutativeSemiringWithoutOne'46'constructor_27945
      (T_CommutativeSemiring_2094 -> AgdaAny -> AgdaAny -> AgdaAny
d__'43'__2118 (T_CommutativeSemiring_2094 -> T_CommutativeSemiring_2094
forall a b. a -> b
coe T_CommutativeSemiring_2094
v0)) (T_CommutativeSemiring_2094 -> AgdaAny -> AgdaAny -> AgdaAny
d__'42'__2120 (T_CommutativeSemiring_2094 -> T_CommutativeSemiring_2094
forall a b. a -> b
coe T_CommutativeSemiring_2094
v0))
      (T_CommutativeSemiring_2094 -> AgdaAny
d_0'35'_2122 (T_CommutativeSemiring_2094 -> T_CommutativeSemiring_2094
forall a b. a -> b
coe T_CommutativeSemiring_2094
v0))
      ((T_IsCommutativeSemiring_1344
 -> T_IsCommutativeSemiringWithoutOne_1044)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCommutativeSemiring_1344
-> T_IsCommutativeSemiringWithoutOne_1044
MAlonzo.Code.Algebra.Structures.du_isCommutativeSemiringWithoutOne_1444
         ((T_CommutativeSemiring_2094 -> T_IsCommutativeSemiring_1344)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemiring_2094 -> T_IsCommutativeSemiring_1344
d_isCommutativeSemiring_2126 (T_CommutativeSemiring_2094 -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemiring_2094
v0)))
-- Algebra.Bundles.CancellativeCommutativeSemiring
d_CancellativeCommutativeSemiring_2276 :: p -> p -> ()
d_CancellativeCommutativeSemiring_2276 p
a0 p
a1 = ()
data T_CancellativeCommutativeSemiring_2276
  = C_CancellativeCommutativeSemiring'46'constructor_39835 (AgdaAny ->
                                                            AgdaAny -> AgdaAny)
                                                           (AgdaAny -> AgdaAny -> AgdaAny) AgdaAny
                                                           AgdaAny
                                                           MAlonzo.Code.Algebra.Structures.T_IsCancellativeCommutativeSemiring_1462
-- Algebra.Bundles.CancellativeCommutativeSemiring.Carrier
d_Carrier_2296 :: T_CancellativeCommutativeSemiring_2276 -> ()
d_Carrier_2296 :: T_CancellativeCommutativeSemiring_2276 -> ()
d_Carrier_2296 = T_CancellativeCommutativeSemiring_2276 -> ()
forall a. a
erased
-- Algebra.Bundles.CancellativeCommutativeSemiring._≈_
d__'8776'__2298 ::
  T_CancellativeCommutativeSemiring_2276 -> AgdaAny -> AgdaAny -> ()
d__'8776'__2298 :: T_CancellativeCommutativeSemiring_2276 -> AgdaAny -> AgdaAny -> ()
d__'8776'__2298 = T_CancellativeCommutativeSemiring_2276 -> AgdaAny -> AgdaAny -> ()
forall a. a
erased
-- Algebra.Bundles.CancellativeCommutativeSemiring._+_
d__'43'__2300 ::
  T_CancellativeCommutativeSemiring_2276 ->
  AgdaAny -> AgdaAny -> AgdaAny
d__'43'__2300 :: T_CancellativeCommutativeSemiring_2276
-> AgdaAny -> AgdaAny -> AgdaAny
d__'43'__2300 T_CancellativeCommutativeSemiring_2276
v0
  = case T_CancellativeCommutativeSemiring_2276
-> T_CancellativeCommutativeSemiring_2276
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2276
v0 of
      C_CancellativeCommutativeSemiring'46'constructor_39835 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny
v5 AgdaAny
v6 T_IsCancellativeCommutativeSemiring_1462
v7
        -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v3
      T_CancellativeCommutativeSemiring_2276
_ -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.CancellativeCommutativeSemiring._*_
d__'42'__2302 ::
  T_CancellativeCommutativeSemiring_2276 ->
  AgdaAny -> AgdaAny -> AgdaAny
d__'42'__2302 :: T_CancellativeCommutativeSemiring_2276
-> AgdaAny -> AgdaAny -> AgdaAny
d__'42'__2302 T_CancellativeCommutativeSemiring_2276
v0
  = case T_CancellativeCommutativeSemiring_2276
-> T_CancellativeCommutativeSemiring_2276
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2276
v0 of
      C_CancellativeCommutativeSemiring'46'constructor_39835 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny
v5 AgdaAny
v6 T_IsCancellativeCommutativeSemiring_1462
v7
        -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v4
      T_CancellativeCommutativeSemiring_2276
_ -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.CancellativeCommutativeSemiring.0#
d_0'35'_2304 :: T_CancellativeCommutativeSemiring_2276 -> AgdaAny
d_0'35'_2304 :: T_CancellativeCommutativeSemiring_2276 -> AgdaAny
d_0'35'_2304 T_CancellativeCommutativeSemiring_2276
v0
  = case T_CancellativeCommutativeSemiring_2276
-> T_CancellativeCommutativeSemiring_2276
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2276
v0 of
      C_CancellativeCommutativeSemiring'46'constructor_39835 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny
v5 AgdaAny
v6 T_IsCancellativeCommutativeSemiring_1462
v7
        -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v5
      T_CancellativeCommutativeSemiring_2276
_ -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.CancellativeCommutativeSemiring.1#
d_1'35'_2306 :: T_CancellativeCommutativeSemiring_2276 -> AgdaAny
d_1'35'_2306 :: T_CancellativeCommutativeSemiring_2276 -> AgdaAny
d_1'35'_2306 T_CancellativeCommutativeSemiring_2276
v0
  = case T_CancellativeCommutativeSemiring_2276
-> T_CancellativeCommutativeSemiring_2276
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2276
v0 of
      C_CancellativeCommutativeSemiring'46'constructor_39835 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny
v5 AgdaAny
v6 T_IsCancellativeCommutativeSemiring_1462
v7
        -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v6
      T_CancellativeCommutativeSemiring_2276
_ -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.CancellativeCommutativeSemiring.isCancellativeCommutativeSemiring
d_isCancellativeCommutativeSemiring_2308 ::
  T_CancellativeCommutativeSemiring_2276 ->
  MAlonzo.Code.Algebra.Structures.T_IsCancellativeCommutativeSemiring_1462
d_isCancellativeCommutativeSemiring_2308 :: T_CancellativeCommutativeSemiring_2276
-> T_IsCancellativeCommutativeSemiring_1462
d_isCancellativeCommutativeSemiring_2308 T_CancellativeCommutativeSemiring_2276
v0
  = case T_CancellativeCommutativeSemiring_2276
-> T_CancellativeCommutativeSemiring_2276
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2276
v0 of
      C_CancellativeCommutativeSemiring'46'constructor_39835 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny
v5 AgdaAny
v6 T_IsCancellativeCommutativeSemiring_1462
v7
        -> T_IsCancellativeCommutativeSemiring_1462
-> T_IsCancellativeCommutativeSemiring_1462
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1462
v7
      T_CancellativeCommutativeSemiring_2276
_ -> T_IsCancellativeCommutativeSemiring_1462
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.CancellativeCommutativeSemiring._.assoc
d_assoc_2312 ::
  T_CancellativeCommutativeSemiring_2276 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_2312 :: T_CancellativeCommutativeSemiring_2276
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_2312 T_CancellativeCommutativeSemiring_2276
v0
  = (T_IsSemigroup_194 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsSemigroup_194 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_assoc_204
      ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368
         ((T_IsSemiringWithoutAnnihilatingZero_1142 -> T_IsMonoid_358)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemiringWithoutAnnihilatingZero_1142 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_'42''45'isMonoid_1160
            ((T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1252
               ((T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238
MAlonzo.Code.Algebra.Structures.d_isSemiring_1358
                  ((T_IsCancellativeCommutativeSemiring_1462
 -> T_IsCommutativeSemiring_1344)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsCancellativeCommutativeSemiring_1462
-> T_IsCommutativeSemiring_1344
MAlonzo.Code.Algebra.Structures.d_isCommutativeSemiring_1476
                     ((T_CancellativeCommutativeSemiring_2276
 -> T_IsCancellativeCommutativeSemiring_1462)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2276
-> T_IsCancellativeCommutativeSemiring_1462
d_isCancellativeCommutativeSemiring_2308 (T_CancellativeCommutativeSemiring_2276 -> AgdaAny
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2276
v0)))))))
-- Algebra.Bundles.CancellativeCommutativeSemiring._.*-cancelˡ-nonZero
d_'42''45'cancel'737''45'nonZero_2314 ::
  T_CancellativeCommutativeSemiring_2276 ->
  AgdaAny ->
  AgdaAny ->
  AgdaAny ->
  (AgdaAny -> MAlonzo.Code.Data.Empty.T_'8869'_4) ->
  AgdaAny -> AgdaAny
d_'42''45'cancel'737''45'nonZero_2314 :: T_CancellativeCommutativeSemiring_2276
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> (AgdaAny -> T_'8869'_4)
-> AgdaAny
-> AgdaAny
d_'42''45'cancel'737''45'nonZero_2314 T_CancellativeCommutativeSemiring_2276
v0
  = (T_IsCancellativeCommutativeSemiring_1462
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> (AgdaAny -> T_'8869'_4)
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> (AgdaAny -> T_'8869'_4)
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsCancellativeCommutativeSemiring_1462
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> (AgdaAny -> T_'8869'_4)
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'42''45'cancel'737''45'nonZero_1478
      ((T_CancellativeCommutativeSemiring_2276
 -> T_IsCancellativeCommutativeSemiring_1462)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2276
-> T_IsCancellativeCommutativeSemiring_1462
d_isCancellativeCommutativeSemiring_2308 (T_CancellativeCommutativeSemiring_2276 -> AgdaAny
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2276
v0))
-- Algebra.Bundles.CancellativeCommutativeSemiring._.*-comm
d_'42''45'comm_2316 ::
  T_CancellativeCommutativeSemiring_2276 ->
  AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'comm_2316 :: T_CancellativeCommutativeSemiring_2276
-> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'comm_2316 T_CancellativeCommutativeSemiring_2276
v0
  = (T_IsCommutativeSemiring_1344 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsCommutativeSemiring_1344 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'42''45'comm_1360
      ((T_IsCancellativeCommutativeSemiring_1462
 -> T_IsCommutativeSemiring_1344)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCancellativeCommutativeSemiring_1462
-> T_IsCommutativeSemiring_1344
MAlonzo.Code.Algebra.Structures.d_isCommutativeSemiring_1476
         ((T_CancellativeCommutativeSemiring_2276
 -> T_IsCancellativeCommutativeSemiring_1462)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2276
-> T_IsCancellativeCommutativeSemiring_1462
d_isCancellativeCommutativeSemiring_2308 (T_CancellativeCommutativeSemiring_2276 -> AgdaAny
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2276
v0)))
-- Algebra.Bundles.CancellativeCommutativeSemiring._.∙-cong
d_'8729''45'cong_2318 ::
  T_CancellativeCommutativeSemiring_2276 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_2318 :: T_CancellativeCommutativeSemiring_2276
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_2318 T_CancellativeCommutativeSemiring_2276
v0
  = (T_IsMagma_86
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsMagma_86
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_96
      ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202
         ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368
            ((T_IsSemiringWithoutAnnihilatingZero_1142 -> T_IsMonoid_358)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemiringWithoutAnnihilatingZero_1142 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_'42''45'isMonoid_1160
               ((T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1252
                  ((T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238
MAlonzo.Code.Algebra.Structures.d_isSemiring_1358
                     ((T_IsCancellativeCommutativeSemiring_1462
 -> T_IsCommutativeSemiring_1344)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsCancellativeCommutativeSemiring_1462
-> T_IsCommutativeSemiring_1344
MAlonzo.Code.Algebra.Structures.d_isCommutativeSemiring_1476
                        ((T_CancellativeCommutativeSemiring_2276
 -> T_IsCancellativeCommutativeSemiring_1462)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2276
-> T_IsCancellativeCommutativeSemiring_1462
d_isCancellativeCommutativeSemiring_2308 (T_CancellativeCommutativeSemiring_2276 -> AgdaAny
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2276
v0))))))))
-- Algebra.Bundles.CancellativeCommutativeSemiring._.∙-congʳ
d_'8729''45'cong'691'_2320 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CancellativeCommutativeSemiring_2276 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_2320 :: ()
-> ()
-> T_CancellativeCommutativeSemiring_2276
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_2320 ~()
v0 ~()
v1 T_CancellativeCommutativeSemiring_2276
v2
  = T_CancellativeCommutativeSemiring_2276
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_2320 T_CancellativeCommutativeSemiring_2276
v2
du_'8729''45'cong'691'_2320 ::
  T_CancellativeCommutativeSemiring_2276 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_2320 :: T_CancellativeCommutativeSemiring_2276
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_2320 T_CancellativeCommutativeSemiring_2276
v0
  = let v1 :: T_IsCancellativeCommutativeSemiring_1462
v1 = T_CancellativeCommutativeSemiring_2276
-> T_IsCancellativeCommutativeSemiring_1462
d_isCancellativeCommutativeSemiring_2308 (T_CancellativeCommutativeSemiring_2276
-> T_CancellativeCommutativeSemiring_2276
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2276
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsCommutativeSemiring_1344
v2
             = T_IsCancellativeCommutativeSemiring_1462
-> T_IsCommutativeSemiring_1344
MAlonzo.Code.Algebra.Structures.d_isCommutativeSemiring_1476
                 (T_IsCancellativeCommutativeSemiring_1462
-> T_IsCancellativeCommutativeSemiring_1462
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1462
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemiring_1238
v3
                = T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238
MAlonzo.Code.Algebra.Structures.d_isSemiring_1358 (T_IsCommutativeSemiring_1344 -> T_IsCommutativeSemiring_1344
forall a b. a -> b
coe T_IsCommutativeSemiring_1344
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsSemiringWithoutAnnihilatingZero_1142
v4
                   = T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1252
                       (T_IsSemiring_1238 -> T_IsSemiring_1238
forall a b. a -> b
coe T_IsSemiring_1238
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsMonoid_358
v5
                      = T_IsSemiringWithoutAnnihilatingZero_1142 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_'42''45'isMonoid_1160
                          (T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsSemiringWithoutAnnihilatingZero_1142
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1142
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (let v6 :: T_IsSemigroup_194
v6
                         = T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368 (T_IsMonoid_358 -> T_IsMonoid_358
forall a b. a -> b
coe T_IsMonoid_358
v5) in
                   AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     ((T_IsMagma_86
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsMagma_86 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'691'_116
                        ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202 (T_IsSemigroup_194 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194
v6))))))))
-- Algebra.Bundles.CancellativeCommutativeSemiring._.∙-congˡ
d_'8729''45'cong'737'_2322 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CancellativeCommutativeSemiring_2276 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_2322 :: ()
-> ()
-> T_CancellativeCommutativeSemiring_2276
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_2322 ~()
v0 ~()
v1 T_CancellativeCommutativeSemiring_2276
v2
  = T_CancellativeCommutativeSemiring_2276
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_2322 T_CancellativeCommutativeSemiring_2276
v2
du_'8729''45'cong'737'_2322 ::
  T_CancellativeCommutativeSemiring_2276 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_2322 :: T_CancellativeCommutativeSemiring_2276
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_2322 T_CancellativeCommutativeSemiring_2276
v0
  = let v1 :: T_IsCancellativeCommutativeSemiring_1462
v1 = T_CancellativeCommutativeSemiring_2276
-> T_IsCancellativeCommutativeSemiring_1462
d_isCancellativeCommutativeSemiring_2308 (T_CancellativeCommutativeSemiring_2276
-> T_CancellativeCommutativeSemiring_2276
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2276
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsCommutativeSemiring_1344
v2
             = T_IsCancellativeCommutativeSemiring_1462
-> T_IsCommutativeSemiring_1344
MAlonzo.Code.Algebra.Structures.d_isCommutativeSemiring_1476
                 (T_IsCancellativeCommutativeSemiring_1462
-> T_IsCancellativeCommutativeSemiring_1462
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1462
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemiring_1238
v3
                = T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238
MAlonzo.Code.Algebra.Structures.d_isSemiring_1358 (T_IsCommutativeSemiring_1344 -> T_IsCommutativeSemiring_1344
forall a b. a -> b
coe T_IsCommutativeSemiring_1344
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsSemiringWithoutAnnihilatingZero_1142
v4
                   = T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1252
                       (T_IsSemiring_1238 -> T_IsSemiring_1238
forall a b. a -> b
coe T_IsSemiring_1238
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsMonoid_358
v5
                      = T_IsSemiringWithoutAnnihilatingZero_1142 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_'42''45'isMonoid_1160
                          (T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsSemiringWithoutAnnihilatingZero_1142
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1142
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (let v6 :: T_IsSemigroup_194
v6
                         = T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368 (T_IsMonoid_358 -> T_IsMonoid_358
forall a b. a -> b
coe T_IsMonoid_358
v5) in
                   AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     ((T_IsMagma_86
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsMagma_86 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'737'_112
                        ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202 (T_IsSemigroup_194 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194
v6))))))))
-- Algebra.Bundles.CancellativeCommutativeSemiring._.identity
d_identity_2324 ::
  T_CancellativeCommutativeSemiring_2276 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_identity_2324 :: T_CancellativeCommutativeSemiring_2276 -> T_Σ_14
d_identity_2324 T_CancellativeCommutativeSemiring_2276
v0
  = (T_IsMonoid_358 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsMonoid_358 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_identity_370
      ((T_IsSemiringWithoutAnnihilatingZero_1142 -> T_IsMonoid_358)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiringWithoutAnnihilatingZero_1142 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_'42''45'isMonoid_1160
         ((T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1252
            ((T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238
MAlonzo.Code.Algebra.Structures.d_isSemiring_1358
               ((T_IsCancellativeCommutativeSemiring_1462
 -> T_IsCommutativeSemiring_1344)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsCancellativeCommutativeSemiring_1462
-> T_IsCommutativeSemiring_1344
MAlonzo.Code.Algebra.Structures.d_isCommutativeSemiring_1476
                  ((T_CancellativeCommutativeSemiring_2276
 -> T_IsCancellativeCommutativeSemiring_1462)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2276
-> T_IsCancellativeCommutativeSemiring_1462
d_isCancellativeCommutativeSemiring_2308 (T_CancellativeCommutativeSemiring_2276 -> AgdaAny
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2276
v0))))))
-- Algebra.Bundles.CancellativeCommutativeSemiring._.identityʳ
d_identity'691'_2326 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CancellativeCommutativeSemiring_2276 -> AgdaAny -> AgdaAny
d_identity'691'_2326 :: ()
-> ()
-> T_CancellativeCommutativeSemiring_2276
-> AgdaAny
-> AgdaAny
d_identity'691'_2326 ~()
v0 ~()
v1 T_CancellativeCommutativeSemiring_2276
v2 = T_CancellativeCommutativeSemiring_2276 -> AgdaAny -> AgdaAny
du_identity'691'_2326 T_CancellativeCommutativeSemiring_2276
v2
du_identity'691'_2326 ::
  T_CancellativeCommutativeSemiring_2276 -> AgdaAny -> AgdaAny
du_identity'691'_2326 :: T_CancellativeCommutativeSemiring_2276 -> AgdaAny -> AgdaAny
du_identity'691'_2326 T_CancellativeCommutativeSemiring_2276
v0
  = let v1 :: T_IsCancellativeCommutativeSemiring_1462
v1 = T_CancellativeCommutativeSemiring_2276
-> T_IsCancellativeCommutativeSemiring_1462
d_isCancellativeCommutativeSemiring_2308 (T_CancellativeCommutativeSemiring_2276
-> T_CancellativeCommutativeSemiring_2276
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2276
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsCommutativeSemiring_1344
v2
             = T_IsCancellativeCommutativeSemiring_1462
-> T_IsCommutativeSemiring_1344
MAlonzo.Code.Algebra.Structures.d_isCommutativeSemiring_1476
                 (T_IsCancellativeCommutativeSemiring_1462
-> T_IsCancellativeCommutativeSemiring_1462
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1462
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemiring_1238
v3
                = T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238
MAlonzo.Code.Algebra.Structures.d_isSemiring_1358 (T_IsCommutativeSemiring_1344 -> T_IsCommutativeSemiring_1344
forall a b. a -> b
coe T_IsCommutativeSemiring_1344
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsSemiringWithoutAnnihilatingZero_1142
v4
                   = T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1252
                       (T_IsSemiring_1238 -> T_IsSemiring_1238
forall a b. a -> b
coe T_IsSemiring_1238
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               ((T_IsMonoid_358 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsMonoid_358 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_identity'691'_400
                  ((T_IsSemiringWithoutAnnihilatingZero_1142 -> T_IsMonoid_358)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsSemiringWithoutAnnihilatingZero_1142 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_'42''45'isMonoid_1160
                     (T_IsSemiringWithoutAnnihilatingZero_1142 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1142
v4))))))
-- Algebra.Bundles.CancellativeCommutativeSemiring._.identityˡ
d_identity'737'_2328 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CancellativeCommutativeSemiring_2276 -> AgdaAny -> AgdaAny
d_identity'737'_2328 :: ()
-> ()
-> T_CancellativeCommutativeSemiring_2276
-> AgdaAny
-> AgdaAny
d_identity'737'_2328 ~()
v0 ~()
v1 T_CancellativeCommutativeSemiring_2276
v2 = T_CancellativeCommutativeSemiring_2276 -> AgdaAny -> AgdaAny
du_identity'737'_2328 T_CancellativeCommutativeSemiring_2276
v2
du_identity'737'_2328 ::
  T_CancellativeCommutativeSemiring_2276 -> AgdaAny -> AgdaAny
du_identity'737'_2328 :: T_CancellativeCommutativeSemiring_2276 -> AgdaAny -> AgdaAny
du_identity'737'_2328 T_CancellativeCommutativeSemiring_2276
v0
  = let v1 :: T_IsCancellativeCommutativeSemiring_1462
v1 = T_CancellativeCommutativeSemiring_2276
-> T_IsCancellativeCommutativeSemiring_1462
d_isCancellativeCommutativeSemiring_2308 (T_CancellativeCommutativeSemiring_2276
-> T_CancellativeCommutativeSemiring_2276
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2276
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsCommutativeSemiring_1344
v2
             = T_IsCancellativeCommutativeSemiring_1462
-> T_IsCommutativeSemiring_1344
MAlonzo.Code.Algebra.Structures.d_isCommutativeSemiring_1476
                 (T_IsCancellativeCommutativeSemiring_1462
-> T_IsCancellativeCommutativeSemiring_1462
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1462
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemiring_1238
v3
                = T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238
MAlonzo.Code.Algebra.Structures.d_isSemiring_1358 (T_IsCommutativeSemiring_1344 -> T_IsCommutativeSemiring_1344
forall a b. a -> b
coe T_IsCommutativeSemiring_1344
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsSemiringWithoutAnnihilatingZero_1142
v4
                   = T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1252
                       (T_IsSemiring_1238 -> T_IsSemiring_1238
forall a b. a -> b
coe T_IsSemiring_1238
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               ((T_IsMonoid_358 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsMonoid_358 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_identity'737'_398
                  ((T_IsSemiringWithoutAnnihilatingZero_1142 -> T_IsMonoid_358)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsSemiringWithoutAnnihilatingZero_1142 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_'42''45'isMonoid_1160
                     (T_IsSemiringWithoutAnnihilatingZero_1142 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1142
v4))))))
-- Algebra.Bundles.CancellativeCommutativeSemiring._.isCommutativeMagma
d_isCommutativeMagma_2330 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CancellativeCommutativeSemiring_2276 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMagma_122
d_isCommutativeMagma_2330 :: ()
-> ()
-> T_CancellativeCommutativeSemiring_2276
-> T_IsCommutativeMagma_122
d_isCommutativeMagma_2330 ~()
v0 ~()
v1 T_CancellativeCommutativeSemiring_2276
v2
  = T_CancellativeCommutativeSemiring_2276 -> T_IsCommutativeMagma_122
du_isCommutativeMagma_2330 T_CancellativeCommutativeSemiring_2276
v2
du_isCommutativeMagma_2330 ::
  T_CancellativeCommutativeSemiring_2276 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMagma_122
du_isCommutativeMagma_2330 :: T_CancellativeCommutativeSemiring_2276 -> T_IsCommutativeMagma_122
du_isCommutativeMagma_2330 T_CancellativeCommutativeSemiring_2276
v0
  = let v1 :: T_IsCancellativeCommutativeSemiring_1462
v1 = T_CancellativeCommutativeSemiring_2276
-> T_IsCancellativeCommutativeSemiring_1462
d_isCancellativeCommutativeSemiring_2308 (T_CancellativeCommutativeSemiring_2276
-> T_CancellativeCommutativeSemiring_2276
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2276
v0) in
    AgdaAny -> T_IsCommutativeMagma_122
forall a b. a -> b
coe
      (let v2 :: T_IsCommutativeSemiring_1344
v2
             = T_IsCancellativeCommutativeSemiring_1462
-> T_IsCommutativeSemiring_1344
MAlonzo.Code.Algebra.Structures.d_isCommutativeSemiring_1476
                 (T_IsCancellativeCommutativeSemiring_1462
-> T_IsCancellativeCommutativeSemiring_1462
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1462
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: t
v3
                = (T_IsCommutativeSemiring_1344
 -> T_IsCommutativeSemiringWithoutOne_1044)
-> AgdaAny -> t
forall a b. a -> b
coe
                    T_IsCommutativeSemiring_1344
-> T_IsCommutativeSemiringWithoutOne_1044
MAlonzo.Code.Algebra.Structures.du_isCommutativeSemiringWithoutOne_1444
                    (T_IsCommutativeSemiring_1344 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiring_1344
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsCommutativeSemigroup_270 -> T_IsCommutativeMagma_122)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsCommutativeSemigroup_270 -> T_IsCommutativeMagma_122
MAlonzo.Code.Algebra.Structures.du_isCommutativeMagma_308
               ((T_IsCommutativeSemiringWithoutOne_1044
 -> T_IsCommutativeSemigroup_270)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsCommutativeSemiringWithoutOne_1044
-> T_IsCommutativeSemigroup_270
MAlonzo.Code.Algebra.Structures.du_'42''45'isCommutativeSemigroup_1128
                  (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3)))))
-- Algebra.Bundles.CancellativeCommutativeSemiring._.*-isCommutativeMonoid
d_'42''45'isCommutativeMonoid_2332 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CancellativeCommutativeSemiring_2276 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMonoid_406
d_'42''45'isCommutativeMonoid_2332 :: ()
-> ()
-> T_CancellativeCommutativeSemiring_2276
-> T_IsCommutativeMonoid_406
d_'42''45'isCommutativeMonoid_2332 ~()
v0 ~()
v1 T_CancellativeCommutativeSemiring_2276
v2
  = T_CancellativeCommutativeSemiring_2276 -> T_IsCommutativeMonoid_406
du_'42''45'isCommutativeMonoid_2332 T_CancellativeCommutativeSemiring_2276
v2
du_'42''45'isCommutativeMonoid_2332 ::
  T_CancellativeCommutativeSemiring_2276 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMonoid_406
du_'42''45'isCommutativeMonoid_2332 :: T_CancellativeCommutativeSemiring_2276 -> T_IsCommutativeMonoid_406
du_'42''45'isCommutativeMonoid_2332 T_CancellativeCommutativeSemiring_2276
v0
  = let v1 :: T_IsCancellativeCommutativeSemiring_1462
v1 = T_CancellativeCommutativeSemiring_2276
-> T_IsCancellativeCommutativeSemiring_1462
d_isCancellativeCommutativeSemiring_2308 (T_CancellativeCommutativeSemiring_2276
-> T_CancellativeCommutativeSemiring_2276
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2276
v0) in
    AgdaAny -> T_IsCommutativeMonoid_406
forall a b. a -> b
coe
      ((T_IsCommutativeSemiring_1344 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCommutativeSemiring_1344 -> T_IsCommutativeMonoid_406
MAlonzo.Code.Algebra.Structures.du_'42''45'isCommutativeMonoid_1452
         ((T_IsCancellativeCommutativeSemiring_1462
 -> T_IsCommutativeSemiring_1344)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCancellativeCommutativeSemiring_1462
-> T_IsCommutativeSemiring_1344
MAlonzo.Code.Algebra.Structures.d_isCommutativeSemiring_1476
            (T_IsCancellativeCommutativeSemiring_1462 -> AgdaAny
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1462
v1)))
-- Algebra.Bundles.CancellativeCommutativeSemiring._.*-isCommutativeSemigroup
d_'42''45'isCommutativeSemigroup_2334 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CancellativeCommutativeSemiring_2276 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_270
d_'42''45'isCommutativeSemigroup_2334 :: ()
-> ()
-> T_CancellativeCommutativeSemiring_2276
-> T_IsCommutativeSemigroup_270
d_'42''45'isCommutativeSemigroup_2334 ~()
v0 ~()
v1 T_CancellativeCommutativeSemiring_2276
v2
  = T_CancellativeCommutativeSemiring_2276
-> T_IsCommutativeSemigroup_270
du_'42''45'isCommutativeSemigroup_2334 T_CancellativeCommutativeSemiring_2276
v2
du_'42''45'isCommutativeSemigroup_2334 ::
  T_CancellativeCommutativeSemiring_2276 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_270
du_'42''45'isCommutativeSemigroup_2334 :: T_CancellativeCommutativeSemiring_2276
-> T_IsCommutativeSemigroup_270
du_'42''45'isCommutativeSemigroup_2334 T_CancellativeCommutativeSemiring_2276
v0
  = let v1 :: T_IsCancellativeCommutativeSemiring_1462
v1 = T_CancellativeCommutativeSemiring_2276
-> T_IsCancellativeCommutativeSemiring_1462
d_isCancellativeCommutativeSemiring_2308 (T_CancellativeCommutativeSemiring_2276
-> T_CancellativeCommutativeSemiring_2276
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2276
v0) in
    AgdaAny -> T_IsCommutativeSemigroup_270
forall a b. a -> b
coe
      (let v2 :: T_IsCommutativeSemiring_1344
v2
             = T_IsCancellativeCommutativeSemiring_1462
-> T_IsCommutativeSemiring_1344
MAlonzo.Code.Algebra.Structures.d_isCommutativeSemiring_1476
                 (T_IsCancellativeCommutativeSemiring_1462
-> T_IsCancellativeCommutativeSemiring_1462
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1462
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsCommutativeSemiringWithoutOne_1044
 -> T_IsCommutativeSemigroup_270)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCommutativeSemiringWithoutOne_1044
-> T_IsCommutativeSemigroup_270
MAlonzo.Code.Algebra.Structures.du_'42''45'isCommutativeSemigroup_1128
            ((T_IsCommutativeSemiring_1344
 -> T_IsCommutativeSemiringWithoutOne_1044)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsCommutativeSemiring_1344
-> T_IsCommutativeSemiringWithoutOne_1044
MAlonzo.Code.Algebra.Structures.du_isCommutativeSemiringWithoutOne_1444
               (T_IsCommutativeSemiring_1344 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiring_1344
v2))))
-- Algebra.Bundles.CancellativeCommutativeSemiring._.isMagma
d_isMagma_2336 ::
  T_CancellativeCommutativeSemiring_2276 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_86
d_isMagma_2336 :: T_CancellativeCommutativeSemiring_2276 -> T_IsMagma_86
d_isMagma_2336 T_CancellativeCommutativeSemiring_2276
v0
  = (T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> T_IsMagma_86
forall a b. a -> b
coe
      T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202
      ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368
         ((T_IsSemiringWithoutAnnihilatingZero_1142 -> T_IsMonoid_358)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemiringWithoutAnnihilatingZero_1142 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_'42''45'isMonoid_1160
            ((T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1252
               ((T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238
MAlonzo.Code.Algebra.Structures.d_isSemiring_1358
                  ((T_IsCancellativeCommutativeSemiring_1462
 -> T_IsCommutativeSemiring_1344)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsCancellativeCommutativeSemiring_1462
-> T_IsCommutativeSemiring_1344
MAlonzo.Code.Algebra.Structures.d_isCommutativeSemiring_1476
                     ((T_CancellativeCommutativeSemiring_2276
 -> T_IsCancellativeCommutativeSemiring_1462)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2276
-> T_IsCancellativeCommutativeSemiring_1462
d_isCancellativeCommutativeSemiring_2308 (T_CancellativeCommutativeSemiring_2276 -> AgdaAny
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2276
v0)))))))
-- Algebra.Bundles.CancellativeCommutativeSemiring._.*-isMonoid
d_'42''45'isMonoid_2338 ::
  T_CancellativeCommutativeSemiring_2276 ->
  MAlonzo.Code.Algebra.Structures.T_IsMonoid_358
d_'42''45'isMonoid_2338 :: T_CancellativeCommutativeSemiring_2276 -> T_IsMonoid_358
d_'42''45'isMonoid_2338 T_CancellativeCommutativeSemiring_2276
v0
  = (T_IsSemiringWithoutAnnihilatingZero_1142 -> T_IsMonoid_358)
-> AgdaAny -> T_IsMonoid_358
forall a b. a -> b
coe
      T_IsSemiringWithoutAnnihilatingZero_1142 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_'42''45'isMonoid_1160
      ((T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1252
         ((T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238
MAlonzo.Code.Algebra.Structures.d_isSemiring_1358
            ((T_IsCancellativeCommutativeSemiring_1462
 -> T_IsCommutativeSemiring_1344)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsCancellativeCommutativeSemiring_1462
-> T_IsCommutativeSemiring_1344
MAlonzo.Code.Algebra.Structures.d_isCommutativeSemiring_1476
               ((T_CancellativeCommutativeSemiring_2276
 -> T_IsCancellativeCommutativeSemiring_1462)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2276
-> T_IsCancellativeCommutativeSemiring_1462
d_isCancellativeCommutativeSemiring_2308 (T_CancellativeCommutativeSemiring_2276 -> AgdaAny
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2276
v0)))))
-- Algebra.Bundles.CancellativeCommutativeSemiring._.isSemigroup
d_isSemigroup_2340 ::
  T_CancellativeCommutativeSemiring_2276 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_194
d_isSemigroup_2340 :: T_CancellativeCommutativeSemiring_2276 -> T_IsSemigroup_194
d_isSemigroup_2340 T_CancellativeCommutativeSemiring_2276
v0
  = (T_IsMonoid_358 -> T_IsSemigroup_194)
-> AgdaAny -> T_IsSemigroup_194
forall a b. a -> b
coe
      T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368
      ((T_IsSemiringWithoutAnnihilatingZero_1142 -> T_IsMonoid_358)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiringWithoutAnnihilatingZero_1142 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_'42''45'isMonoid_1160
         ((T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1252
            ((T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238
MAlonzo.Code.Algebra.Structures.d_isSemiring_1358
               ((T_IsCancellativeCommutativeSemiring_1462
 -> T_IsCommutativeSemiring_1344)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsCancellativeCommutativeSemiring_1462
-> T_IsCommutativeSemiring_1344
MAlonzo.Code.Algebra.Structures.d_isCommutativeSemiring_1476
                  ((T_CancellativeCommutativeSemiring_2276
 -> T_IsCancellativeCommutativeSemiring_1462)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2276
-> T_IsCancellativeCommutativeSemiring_1462
d_isCancellativeCommutativeSemiring_2308 (T_CancellativeCommutativeSemiring_2276 -> AgdaAny
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2276
v0))))))
-- Algebra.Bundles.CancellativeCommutativeSemiring._.assoc
d_assoc_2342 ::
  T_CancellativeCommutativeSemiring_2276 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_2342 :: T_CancellativeCommutativeSemiring_2276
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_2342 T_CancellativeCommutativeSemiring_2276
v0
  = (T_IsSemigroup_194 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsSemigroup_194 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_assoc_204
      ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368
         ((T_IsCommutativeMonoid_406 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCommutativeMonoid_406 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_416
            ((T_IsSemiringWithoutAnnihilatingZero_1142
 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsCommutativeMonoid_406
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1158
               ((T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1252
                  ((T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238
MAlonzo.Code.Algebra.Structures.d_isSemiring_1358
                     ((T_IsCancellativeCommutativeSemiring_1462
 -> T_IsCommutativeSemiring_1344)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsCancellativeCommutativeSemiring_1462
-> T_IsCommutativeSemiring_1344
MAlonzo.Code.Algebra.Structures.d_isCommutativeSemiring_1476
                        ((T_CancellativeCommutativeSemiring_2276
 -> T_IsCancellativeCommutativeSemiring_1462)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2276
-> T_IsCancellativeCommutativeSemiring_1462
d_isCancellativeCommutativeSemiring_2308 (T_CancellativeCommutativeSemiring_2276 -> AgdaAny
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2276
v0))))))))
-- Algebra.Bundles.CancellativeCommutativeSemiring._.comm
d_comm_2344 ::
  T_CancellativeCommutativeSemiring_2276 ->
  AgdaAny -> AgdaAny -> AgdaAny
d_comm_2344 :: T_CancellativeCommutativeSemiring_2276
-> AgdaAny -> AgdaAny -> AgdaAny
d_comm_2344 T_CancellativeCommutativeSemiring_2276
v0
  = (T_IsCommutativeMonoid_406 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsCommutativeMonoid_406 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_comm_418
      ((T_IsSemiringWithoutAnnihilatingZero_1142
 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsCommutativeMonoid_406
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1158
         ((T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1252
            ((T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238
MAlonzo.Code.Algebra.Structures.d_isSemiring_1358
               ((T_IsCancellativeCommutativeSemiring_1462
 -> T_IsCommutativeSemiring_1344)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsCancellativeCommutativeSemiring_1462
-> T_IsCommutativeSemiring_1344
MAlonzo.Code.Algebra.Structures.d_isCommutativeSemiring_1476
                  ((T_CancellativeCommutativeSemiring_2276
 -> T_IsCancellativeCommutativeSemiring_1462)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2276
-> T_IsCancellativeCommutativeSemiring_1462
d_isCancellativeCommutativeSemiring_2308 (T_CancellativeCommutativeSemiring_2276 -> AgdaAny
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2276
v0))))))
-- Algebra.Bundles.CancellativeCommutativeSemiring._.∙-cong
d_'8729''45'cong_2346 ::
  T_CancellativeCommutativeSemiring_2276 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_2346 :: T_CancellativeCommutativeSemiring_2276
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_2346 T_CancellativeCommutativeSemiring_2276
v0
  = (T_IsMagma_86
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsMagma_86
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_96
      ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202
         ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368
            ((T_IsCommutativeMonoid_406 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsCommutativeMonoid_406 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_416
               ((T_IsSemiringWithoutAnnihilatingZero_1142
 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsCommutativeMonoid_406
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1158
                  ((T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1252
                     ((T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238
MAlonzo.Code.Algebra.Structures.d_isSemiring_1358
                        ((T_IsCancellativeCommutativeSemiring_1462
 -> T_IsCommutativeSemiring_1344)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_IsCancellativeCommutativeSemiring_1462
-> T_IsCommutativeSemiring_1344
MAlonzo.Code.Algebra.Structures.d_isCommutativeSemiring_1476
                           ((T_CancellativeCommutativeSemiring_2276
 -> T_IsCancellativeCommutativeSemiring_1462)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2276
-> T_IsCancellativeCommutativeSemiring_1462
d_isCancellativeCommutativeSemiring_2308 (T_CancellativeCommutativeSemiring_2276 -> AgdaAny
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2276
v0)))))))))
-- Algebra.Bundles.CancellativeCommutativeSemiring._.∙-congʳ
d_'8729''45'cong'691'_2348 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CancellativeCommutativeSemiring_2276 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_2348 :: ()
-> ()
-> T_CancellativeCommutativeSemiring_2276
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_2348 ~()
v0 ~()
v1 T_CancellativeCommutativeSemiring_2276
v2
  = T_CancellativeCommutativeSemiring_2276
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_2348 T_CancellativeCommutativeSemiring_2276
v2
du_'8729''45'cong'691'_2348 ::
  T_CancellativeCommutativeSemiring_2276 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_2348 :: T_CancellativeCommutativeSemiring_2276
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_2348 T_CancellativeCommutativeSemiring_2276
v0
  = let v1 :: T_IsCancellativeCommutativeSemiring_1462
v1 = T_CancellativeCommutativeSemiring_2276
-> T_IsCancellativeCommutativeSemiring_1462
d_isCancellativeCommutativeSemiring_2308 (T_CancellativeCommutativeSemiring_2276
-> T_CancellativeCommutativeSemiring_2276
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2276
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsCommutativeSemiring_1344
v2
             = T_IsCancellativeCommutativeSemiring_1462
-> T_IsCommutativeSemiring_1344
MAlonzo.Code.Algebra.Structures.d_isCommutativeSemiring_1476
                 (T_IsCancellativeCommutativeSemiring_1462
-> T_IsCancellativeCommutativeSemiring_1462
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1462
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemiring_1238
v3
                = T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238
MAlonzo.Code.Algebra.Structures.d_isSemiring_1358 (T_IsCommutativeSemiring_1344 -> T_IsCommutativeSemiring_1344
forall a b. a -> b
coe T_IsCommutativeSemiring_1344
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsSemiringWithoutAnnihilatingZero_1142
v4
                   = T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1252
                       (T_IsSemiring_1238 -> T_IsSemiring_1238
forall a b. a -> b
coe T_IsSemiring_1238
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsCommutativeMonoid_406
v5
                      = T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsCommutativeMonoid_406
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1158
                          (T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsSemiringWithoutAnnihilatingZero_1142
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1142
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (let v6 :: T_IsMonoid_358
v6
                         = T_IsCommutativeMonoid_406 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_416 (T_IsCommutativeMonoid_406 -> T_IsCommutativeMonoid_406
forall a b. a -> b
coe T_IsCommutativeMonoid_406
v5) in
                   AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     (let v7 :: T_IsSemigroup_194
v7
                            = T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368 (T_IsMonoid_358 -> T_IsMonoid_358
forall a b. a -> b
coe T_IsMonoid_358
v6) in
                      AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        ((T_IsMagma_86
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_IsMagma_86 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'691'_116
                           ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202 (T_IsSemigroup_194 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194
v7)))))))))
-- Algebra.Bundles.CancellativeCommutativeSemiring._.∙-congˡ
d_'8729''45'cong'737'_2350 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CancellativeCommutativeSemiring_2276 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_2350 :: ()
-> ()
-> T_CancellativeCommutativeSemiring_2276
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_2350 ~()
v0 ~()
v1 T_CancellativeCommutativeSemiring_2276
v2
  = T_CancellativeCommutativeSemiring_2276
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_2350 T_CancellativeCommutativeSemiring_2276
v2
du_'8729''45'cong'737'_2350 ::
  T_CancellativeCommutativeSemiring_2276 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_2350 :: T_CancellativeCommutativeSemiring_2276
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_2350 T_CancellativeCommutativeSemiring_2276
v0
  = let v1 :: T_IsCancellativeCommutativeSemiring_1462
v1 = T_CancellativeCommutativeSemiring_2276
-> T_IsCancellativeCommutativeSemiring_1462
d_isCancellativeCommutativeSemiring_2308 (T_CancellativeCommutativeSemiring_2276
-> T_CancellativeCommutativeSemiring_2276
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2276
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsCommutativeSemiring_1344
v2
             = T_IsCancellativeCommutativeSemiring_1462
-> T_IsCommutativeSemiring_1344
MAlonzo.Code.Algebra.Structures.d_isCommutativeSemiring_1476
                 (T_IsCancellativeCommutativeSemiring_1462
-> T_IsCancellativeCommutativeSemiring_1462
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1462
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemiring_1238
v3
                = T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238
MAlonzo.Code.Algebra.Structures.d_isSemiring_1358 (T_IsCommutativeSemiring_1344 -> T_IsCommutativeSemiring_1344
forall a b. a -> b
coe T_IsCommutativeSemiring_1344
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsSemiringWithoutAnnihilatingZero_1142
v4
                   = T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1252
                       (T_IsSemiring_1238 -> T_IsSemiring_1238
forall a b. a -> b
coe T_IsSemiring_1238
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsCommutativeMonoid_406
v5
                      = T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsCommutativeMonoid_406
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1158
                          (T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsSemiringWithoutAnnihilatingZero_1142
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1142
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (let v6 :: T_IsMonoid_358
v6
                         = T_IsCommutativeMonoid_406 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_416 (T_IsCommutativeMonoid_406 -> T_IsCommutativeMonoid_406
forall a b. a -> b
coe T_IsCommutativeMonoid_406
v5) in
                   AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     (let v7 :: T_IsSemigroup_194
v7
                            = T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368 (T_IsMonoid_358 -> T_IsMonoid_358
forall a b. a -> b
coe T_IsMonoid_358
v6) in
                      AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        ((T_IsMagma_86
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_IsMagma_86 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'737'_112
                           ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202 (T_IsSemigroup_194 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194
v7)))))))))
-- Algebra.Bundles.CancellativeCommutativeSemiring._.identity
d_identity_2352 ::
  T_CancellativeCommutativeSemiring_2276 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_identity_2352 :: T_CancellativeCommutativeSemiring_2276 -> T_Σ_14
d_identity_2352 T_CancellativeCommutativeSemiring_2276
v0
  = (T_IsMonoid_358 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsMonoid_358 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_identity_370
      ((T_IsCommutativeMonoid_406 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCommutativeMonoid_406 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_416
         ((T_IsSemiringWithoutAnnihilatingZero_1142
 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsCommutativeMonoid_406
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1158
            ((T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1252
               ((T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238
MAlonzo.Code.Algebra.Structures.d_isSemiring_1358
                  ((T_IsCancellativeCommutativeSemiring_1462
 -> T_IsCommutativeSemiring_1344)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsCancellativeCommutativeSemiring_1462
-> T_IsCommutativeSemiring_1344
MAlonzo.Code.Algebra.Structures.d_isCommutativeSemiring_1476
                     ((T_CancellativeCommutativeSemiring_2276
 -> T_IsCancellativeCommutativeSemiring_1462)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2276
-> T_IsCancellativeCommutativeSemiring_1462
d_isCancellativeCommutativeSemiring_2308 (T_CancellativeCommutativeSemiring_2276 -> AgdaAny
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2276
v0)))))))
-- Algebra.Bundles.CancellativeCommutativeSemiring._.identityʳ
d_identity'691'_2354 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CancellativeCommutativeSemiring_2276 -> AgdaAny -> AgdaAny
d_identity'691'_2354 :: ()
-> ()
-> T_CancellativeCommutativeSemiring_2276
-> AgdaAny
-> AgdaAny
d_identity'691'_2354 ~()
v0 ~()
v1 T_CancellativeCommutativeSemiring_2276
v2 = T_CancellativeCommutativeSemiring_2276 -> AgdaAny -> AgdaAny
du_identity'691'_2354 T_CancellativeCommutativeSemiring_2276
v2
du_identity'691'_2354 ::
  T_CancellativeCommutativeSemiring_2276 -> AgdaAny -> AgdaAny
du_identity'691'_2354 :: T_CancellativeCommutativeSemiring_2276 -> AgdaAny -> AgdaAny
du_identity'691'_2354 T_CancellativeCommutativeSemiring_2276
v0
  = let v1 :: T_IsCancellativeCommutativeSemiring_1462
v1 = T_CancellativeCommutativeSemiring_2276
-> T_IsCancellativeCommutativeSemiring_1462
d_isCancellativeCommutativeSemiring_2308 (T_CancellativeCommutativeSemiring_2276
-> T_CancellativeCommutativeSemiring_2276
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2276
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsCommutativeSemiring_1344
v2
             = T_IsCancellativeCommutativeSemiring_1462
-> T_IsCommutativeSemiring_1344
MAlonzo.Code.Algebra.Structures.d_isCommutativeSemiring_1476
                 (T_IsCancellativeCommutativeSemiring_1462
-> T_IsCancellativeCommutativeSemiring_1462
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1462
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemiring_1238
v3
                = T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238
MAlonzo.Code.Algebra.Structures.d_isSemiring_1358 (T_IsCommutativeSemiring_1344 -> T_IsCommutativeSemiring_1344
forall a b. a -> b
coe T_IsCommutativeSemiring_1344
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsSemiringWithoutAnnihilatingZero_1142
v4
                   = T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1252
                       (T_IsSemiring_1238 -> T_IsSemiring_1238
forall a b. a -> b
coe T_IsSemiring_1238
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsCommutativeMonoid_406
v5
                      = T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsCommutativeMonoid_406
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1158
                          (T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsSemiringWithoutAnnihilatingZero_1142
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1142
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  ((T_IsMonoid_358 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsMonoid_358 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_identity'691'_400
                     ((T_IsCommutativeMonoid_406 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_406 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_416 (T_IsCommutativeMonoid_406 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_406
v5)))))))
-- Algebra.Bundles.CancellativeCommutativeSemiring._.identityˡ
d_identity'737'_2356 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CancellativeCommutativeSemiring_2276 -> AgdaAny -> AgdaAny
d_identity'737'_2356 :: ()
-> ()
-> T_CancellativeCommutativeSemiring_2276
-> AgdaAny
-> AgdaAny
d_identity'737'_2356 ~()
v0 ~()
v1 T_CancellativeCommutativeSemiring_2276
v2 = T_CancellativeCommutativeSemiring_2276 -> AgdaAny -> AgdaAny
du_identity'737'_2356 T_CancellativeCommutativeSemiring_2276
v2
du_identity'737'_2356 ::
  T_CancellativeCommutativeSemiring_2276 -> AgdaAny -> AgdaAny
du_identity'737'_2356 :: T_CancellativeCommutativeSemiring_2276 -> AgdaAny -> AgdaAny
du_identity'737'_2356 T_CancellativeCommutativeSemiring_2276
v0
  = let v1 :: T_IsCancellativeCommutativeSemiring_1462
v1 = T_CancellativeCommutativeSemiring_2276
-> T_IsCancellativeCommutativeSemiring_1462
d_isCancellativeCommutativeSemiring_2308 (T_CancellativeCommutativeSemiring_2276
-> T_CancellativeCommutativeSemiring_2276
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2276
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsCommutativeSemiring_1344
v2
             = T_IsCancellativeCommutativeSemiring_1462
-> T_IsCommutativeSemiring_1344
MAlonzo.Code.Algebra.Structures.d_isCommutativeSemiring_1476
                 (T_IsCancellativeCommutativeSemiring_1462
-> T_IsCancellativeCommutativeSemiring_1462
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1462
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemiring_1238
v3
                = T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238
MAlonzo.Code.Algebra.Structures.d_isSemiring_1358 (T_IsCommutativeSemiring_1344 -> T_IsCommutativeSemiring_1344
forall a b. a -> b
coe T_IsCommutativeSemiring_1344
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsSemiringWithoutAnnihilatingZero_1142
v4
                   = T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1252
                       (T_IsSemiring_1238 -> T_IsSemiring_1238
forall a b. a -> b
coe T_IsSemiring_1238
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsCommutativeMonoid_406
v5
                      = T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsCommutativeMonoid_406
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1158
                          (T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsSemiringWithoutAnnihilatingZero_1142
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1142
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  ((T_IsMonoid_358 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsMonoid_358 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_identity'737'_398
                     ((T_IsCommutativeMonoid_406 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_406 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_416 (T_IsCommutativeMonoid_406 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_406
v5)))))))
-- Algebra.Bundles.CancellativeCommutativeSemiring._.isCommutativeMagma
d_isCommutativeMagma_2358 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CancellativeCommutativeSemiring_2276 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMagma_122
d_isCommutativeMagma_2358 :: ()
-> ()
-> T_CancellativeCommutativeSemiring_2276
-> T_IsCommutativeMagma_122
d_isCommutativeMagma_2358 ~()
v0 ~()
v1 T_CancellativeCommutativeSemiring_2276
v2
  = T_CancellativeCommutativeSemiring_2276 -> T_IsCommutativeMagma_122
du_isCommutativeMagma_2358 T_CancellativeCommutativeSemiring_2276
v2
du_isCommutativeMagma_2358 ::
  T_CancellativeCommutativeSemiring_2276 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMagma_122
du_isCommutativeMagma_2358 :: T_CancellativeCommutativeSemiring_2276 -> T_IsCommutativeMagma_122
du_isCommutativeMagma_2358 T_CancellativeCommutativeSemiring_2276
v0
  = let v1 :: T_IsCancellativeCommutativeSemiring_1462
v1 = T_CancellativeCommutativeSemiring_2276
-> T_IsCancellativeCommutativeSemiring_1462
d_isCancellativeCommutativeSemiring_2308 (T_CancellativeCommutativeSemiring_2276
-> T_CancellativeCommutativeSemiring_2276
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2276
v0) in
    AgdaAny -> T_IsCommutativeMagma_122
forall a b. a -> b
coe
      (let v2 :: T_IsCommutativeSemiring_1344
v2
             = T_IsCancellativeCommutativeSemiring_1462
-> T_IsCommutativeSemiring_1344
MAlonzo.Code.Algebra.Structures.d_isCommutativeSemiring_1476
                 (T_IsCancellativeCommutativeSemiring_1462
-> T_IsCancellativeCommutativeSemiring_1462
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1462
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemiring_1238
v3
                = T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238
MAlonzo.Code.Algebra.Structures.d_isSemiring_1358 (T_IsCommutativeSemiring_1344 -> T_IsCommutativeSemiring_1344
forall a b. a -> b
coe T_IsCommutativeSemiring_1344
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsSemiringWithoutAnnihilatingZero_1142
v4
                   = T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1252
                       (T_IsSemiring_1238 -> T_IsSemiring_1238
forall a b. a -> b
coe T_IsSemiring_1238
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsCommutativeMonoid_406
v5
                      = T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsCommutativeMonoid_406
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1158
                          (T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsSemiringWithoutAnnihilatingZero_1142
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1142
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  ((T_IsCommutativeSemigroup_270 -> T_IsCommutativeMagma_122)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsCommutativeSemigroup_270 -> T_IsCommutativeMagma_122
MAlonzo.Code.Algebra.Structures.du_isCommutativeMagma_308
                     ((T_IsCommutativeMonoid_406 -> T_IsCommutativeSemigroup_270)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsCommutativeMonoid_406 -> T_IsCommutativeSemigroup_270
MAlonzo.Code.Algebra.Structures.du_isCommutativeSemigroup_454
                        (T_IsCommutativeMonoid_406 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_406
v5)))))))
-- Algebra.Bundles.CancellativeCommutativeSemiring._.+-isCommutativeMonoid
d_'43''45'isCommutativeMonoid_2360 ::
  T_CancellativeCommutativeSemiring_2276 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMonoid_406
d_'43''45'isCommutativeMonoid_2360 :: T_CancellativeCommutativeSemiring_2276 -> T_IsCommutativeMonoid_406
d_'43''45'isCommutativeMonoid_2360 T_CancellativeCommutativeSemiring_2276
v0
  = (T_IsSemiringWithoutAnnihilatingZero_1142
 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> T_IsCommutativeMonoid_406
forall a b. a -> b
coe
      T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsCommutativeMonoid_406
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1158
      ((T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1252
         ((T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238
MAlonzo.Code.Algebra.Structures.d_isSemiring_1358
            ((T_IsCancellativeCommutativeSemiring_1462
 -> T_IsCommutativeSemiring_1344)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsCancellativeCommutativeSemiring_1462
-> T_IsCommutativeSemiring_1344
MAlonzo.Code.Algebra.Structures.d_isCommutativeSemiring_1476
               ((T_CancellativeCommutativeSemiring_2276
 -> T_IsCancellativeCommutativeSemiring_1462)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2276
-> T_IsCancellativeCommutativeSemiring_1462
d_isCancellativeCommutativeSemiring_2308 (T_CancellativeCommutativeSemiring_2276 -> AgdaAny
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2276
v0)))))
-- Algebra.Bundles.CancellativeCommutativeSemiring._.isCommutativeSemigroup
d_isCommutativeSemigroup_2362 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CancellativeCommutativeSemiring_2276 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_270
d_isCommutativeSemigroup_2362 :: ()
-> ()
-> T_CancellativeCommutativeSemiring_2276
-> T_IsCommutativeSemigroup_270
d_isCommutativeSemigroup_2362 ~()
v0 ~()
v1 T_CancellativeCommutativeSemiring_2276
v2
  = T_CancellativeCommutativeSemiring_2276
-> T_IsCommutativeSemigroup_270
du_isCommutativeSemigroup_2362 T_CancellativeCommutativeSemiring_2276
v2
du_isCommutativeSemigroup_2362 ::
  T_CancellativeCommutativeSemiring_2276 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_270
du_isCommutativeSemigroup_2362 :: T_CancellativeCommutativeSemiring_2276
-> T_IsCommutativeSemigroup_270
du_isCommutativeSemigroup_2362 T_CancellativeCommutativeSemiring_2276
v0
  = let v1 :: T_IsCancellativeCommutativeSemiring_1462
v1 = T_CancellativeCommutativeSemiring_2276
-> T_IsCancellativeCommutativeSemiring_1462
d_isCancellativeCommutativeSemiring_2308 (T_CancellativeCommutativeSemiring_2276
-> T_CancellativeCommutativeSemiring_2276
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2276
v0) in
    AgdaAny -> T_IsCommutativeSemigroup_270
forall a b. a -> b
coe
      (let v2 :: T_IsCommutativeSemiring_1344
v2
             = T_IsCancellativeCommutativeSemiring_1462
-> T_IsCommutativeSemiring_1344
MAlonzo.Code.Algebra.Structures.d_isCommutativeSemiring_1476
                 (T_IsCancellativeCommutativeSemiring_1462
-> T_IsCancellativeCommutativeSemiring_1462
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1462
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemiring_1238
v3
                = T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238
MAlonzo.Code.Algebra.Structures.d_isSemiring_1358 (T_IsCommutativeSemiring_1344 -> T_IsCommutativeSemiring_1344
forall a b. a -> b
coe T_IsCommutativeSemiring_1344
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsSemiringWithoutAnnihilatingZero_1142
v4
                   = T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1252
                       (T_IsSemiring_1238 -> T_IsSemiring_1238
forall a b. a -> b
coe T_IsSemiring_1238
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               ((T_IsCommutativeMonoid_406 -> T_IsCommutativeSemigroup_270)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsCommutativeMonoid_406 -> T_IsCommutativeSemigroup_270
MAlonzo.Code.Algebra.Structures.du_isCommutativeSemigroup_454
                  ((T_IsSemiringWithoutAnnihilatingZero_1142
 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsCommutativeMonoid_406
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1158
                     (T_IsSemiringWithoutAnnihilatingZero_1142 -> AgdaAny
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1142
v4))))))
-- Algebra.Bundles.CancellativeCommutativeSemiring._.isMagma
d_isMagma_2364 ::
  T_CancellativeCommutativeSemiring_2276 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_86
d_isMagma_2364 :: T_CancellativeCommutativeSemiring_2276 -> T_IsMagma_86
d_isMagma_2364 T_CancellativeCommutativeSemiring_2276
v0
  = (T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> T_IsMagma_86
forall a b. a -> b
coe
      T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202
      ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368
         ((T_IsCommutativeMonoid_406 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCommutativeMonoid_406 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_416
            ((T_IsSemiringWithoutAnnihilatingZero_1142
 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsCommutativeMonoid_406
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1158
               ((T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1252
                  ((T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238
MAlonzo.Code.Algebra.Structures.d_isSemiring_1358
                     ((T_IsCancellativeCommutativeSemiring_1462
 -> T_IsCommutativeSemiring_1344)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsCancellativeCommutativeSemiring_1462
-> T_IsCommutativeSemiring_1344
MAlonzo.Code.Algebra.Structures.d_isCommutativeSemiring_1476
                        ((T_CancellativeCommutativeSemiring_2276
 -> T_IsCancellativeCommutativeSemiring_1462)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2276
-> T_IsCancellativeCommutativeSemiring_1462
d_isCancellativeCommutativeSemiring_2308 (T_CancellativeCommutativeSemiring_2276 -> AgdaAny
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2276
v0))))))))
-- Algebra.Bundles.CancellativeCommutativeSemiring._.isMonoid
d_isMonoid_2366 ::
  T_CancellativeCommutativeSemiring_2276 ->
  MAlonzo.Code.Algebra.Structures.T_IsMonoid_358
d_isMonoid_2366 :: T_CancellativeCommutativeSemiring_2276 -> T_IsMonoid_358
d_isMonoid_2366 T_CancellativeCommutativeSemiring_2276
v0
  = (T_IsCommutativeMonoid_406 -> T_IsMonoid_358)
-> AgdaAny -> T_IsMonoid_358
forall a b. a -> b
coe
      T_IsCommutativeMonoid_406 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_416
      ((T_IsSemiringWithoutAnnihilatingZero_1142
 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsCommutativeMonoid_406
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1158
         ((T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1252
            ((T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238
MAlonzo.Code.Algebra.Structures.d_isSemiring_1358
               ((T_IsCancellativeCommutativeSemiring_1462
 -> T_IsCommutativeSemiring_1344)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsCancellativeCommutativeSemiring_1462
-> T_IsCommutativeSemiring_1344
MAlonzo.Code.Algebra.Structures.d_isCommutativeSemiring_1476
                  ((T_CancellativeCommutativeSemiring_2276
 -> T_IsCancellativeCommutativeSemiring_1462)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2276
-> T_IsCancellativeCommutativeSemiring_1462
d_isCancellativeCommutativeSemiring_2308 (T_CancellativeCommutativeSemiring_2276 -> AgdaAny
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2276
v0))))))
-- Algebra.Bundles.CancellativeCommutativeSemiring._.isSemigroup
d_isSemigroup_2368 ::
  T_CancellativeCommutativeSemiring_2276 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_194
d_isSemigroup_2368 :: T_CancellativeCommutativeSemiring_2276 -> T_IsSemigroup_194
d_isSemigroup_2368 T_CancellativeCommutativeSemiring_2276
v0
  = (T_IsMonoid_358 -> T_IsSemigroup_194)
-> AgdaAny -> T_IsSemigroup_194
forall a b. a -> b
coe
      T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368
      ((T_IsCommutativeMonoid_406 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCommutativeMonoid_406 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_416
         ((T_IsSemiringWithoutAnnihilatingZero_1142
 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsCommutativeMonoid_406
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1158
            ((T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1252
               ((T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238
MAlonzo.Code.Algebra.Structures.d_isSemiring_1358
                  ((T_IsCancellativeCommutativeSemiring_1462
 -> T_IsCommutativeSemiring_1344)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsCancellativeCommutativeSemiring_1462
-> T_IsCommutativeSemiring_1344
MAlonzo.Code.Algebra.Structures.d_isCommutativeSemiring_1476
                     ((T_CancellativeCommutativeSemiring_2276
 -> T_IsCancellativeCommutativeSemiring_1462)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2276
-> T_IsCancellativeCommutativeSemiring_1462
d_isCancellativeCommutativeSemiring_2308 (T_CancellativeCommutativeSemiring_2276 -> AgdaAny
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2276
v0)))))))
-- Algebra.Bundles.CancellativeCommutativeSemiring._.distrib
d_distrib_2370 ::
  T_CancellativeCommutativeSemiring_2276 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_distrib_2370 :: T_CancellativeCommutativeSemiring_2276 -> T_Σ_14
d_distrib_2370 T_CancellativeCommutativeSemiring_2276
v0
  = (T_IsSemiringWithoutAnnihilatingZero_1142 -> T_Σ_14)
-> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsSemiringWithoutAnnihilatingZero_1142 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_distrib_1162
      ((T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1252
         ((T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238
MAlonzo.Code.Algebra.Structures.d_isSemiring_1358
            ((T_IsCancellativeCommutativeSemiring_1462
 -> T_IsCommutativeSemiring_1344)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsCancellativeCommutativeSemiring_1462
-> T_IsCommutativeSemiring_1344
MAlonzo.Code.Algebra.Structures.d_isCommutativeSemiring_1476
               ((T_CancellativeCommutativeSemiring_2276
 -> T_IsCancellativeCommutativeSemiring_1462)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2276
-> T_IsCancellativeCommutativeSemiring_1462
d_isCancellativeCommutativeSemiring_2308 (T_CancellativeCommutativeSemiring_2276 -> AgdaAny
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2276
v0)))))
-- Algebra.Bundles.CancellativeCommutativeSemiring._.distribʳ
d_distrib'691'_2372 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CancellativeCommutativeSemiring_2276 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_distrib'691'_2372 :: ()
-> ()
-> T_CancellativeCommutativeSemiring_2276
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_distrib'691'_2372 ~()
v0 ~()
v1 T_CancellativeCommutativeSemiring_2276
v2 = T_CancellativeCommutativeSemiring_2276
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'691'_2372 T_CancellativeCommutativeSemiring_2276
v2
du_distrib'691'_2372 ::
  T_CancellativeCommutativeSemiring_2276 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'691'_2372 :: T_CancellativeCommutativeSemiring_2276
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'691'_2372 T_CancellativeCommutativeSemiring_2276
v0
  = let v1 :: T_IsCancellativeCommutativeSemiring_1462
v1 = T_CancellativeCommutativeSemiring_2276
-> T_IsCancellativeCommutativeSemiring_1462
d_isCancellativeCommutativeSemiring_2308 (T_CancellativeCommutativeSemiring_2276
-> T_CancellativeCommutativeSemiring_2276
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2276
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsCommutativeSemiring_1344
v2
             = T_IsCancellativeCommutativeSemiring_1462
-> T_IsCommutativeSemiring_1344
MAlonzo.Code.Algebra.Structures.d_isCommutativeSemiring_1476
                 (T_IsCancellativeCommutativeSemiring_1462
-> T_IsCancellativeCommutativeSemiring_1462
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1462
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemiring_1238
v3
                = T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238
MAlonzo.Code.Algebra.Structures.d_isSemiring_1358 (T_IsCommutativeSemiring_1344 -> T_IsCommutativeSemiring_1344
forall a b. a -> b
coe T_IsCommutativeSemiring_1344
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsSemiringWithoutAnnihilatingZero_1142
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemiringWithoutAnnihilatingZero_1142
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_distrib'691'_1166
               ((T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1252
                  (T_IsSemiring_1238 -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1238
v3)))))
-- Algebra.Bundles.CancellativeCommutativeSemiring._.distribˡ
d_distrib'737'_2374 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CancellativeCommutativeSemiring_2276 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_distrib'737'_2374 :: ()
-> ()
-> T_CancellativeCommutativeSemiring_2276
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_distrib'737'_2374 ~()
v0 ~()
v1 T_CancellativeCommutativeSemiring_2276
v2 = T_CancellativeCommutativeSemiring_2276
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'737'_2374 T_CancellativeCommutativeSemiring_2276
v2
du_distrib'737'_2374 ::
  T_CancellativeCommutativeSemiring_2276 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'737'_2374 :: T_CancellativeCommutativeSemiring_2276
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'737'_2374 T_CancellativeCommutativeSemiring_2276
v0
  = let v1 :: T_IsCancellativeCommutativeSemiring_1462
v1 = T_CancellativeCommutativeSemiring_2276
-> T_IsCancellativeCommutativeSemiring_1462
d_isCancellativeCommutativeSemiring_2308 (T_CancellativeCommutativeSemiring_2276
-> T_CancellativeCommutativeSemiring_2276
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2276
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsCommutativeSemiring_1344
v2
             = T_IsCancellativeCommutativeSemiring_1462
-> T_IsCommutativeSemiring_1344
MAlonzo.Code.Algebra.Structures.d_isCommutativeSemiring_1476
                 (T_IsCancellativeCommutativeSemiring_1462
-> T_IsCancellativeCommutativeSemiring_1462
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1462
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemiring_1238
v3
                = T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238
MAlonzo.Code.Algebra.Structures.d_isSemiring_1358 (T_IsCommutativeSemiring_1344 -> T_IsCommutativeSemiring_1344
forall a b. a -> b
coe T_IsCommutativeSemiring_1344
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsSemiringWithoutAnnihilatingZero_1142
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemiringWithoutAnnihilatingZero_1142
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_distrib'737'_1164
               ((T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1252
                  (T_IsSemiring_1238 -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1238
v3)))))
-- Algebra.Bundles.CancellativeCommutativeSemiring._.isCommutativeSemiring
d_isCommutativeSemiring_2376 ::
  T_CancellativeCommutativeSemiring_2276 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiring_1344
d_isCommutativeSemiring_2376 :: T_CancellativeCommutativeSemiring_2276
-> T_IsCommutativeSemiring_1344
d_isCommutativeSemiring_2376 T_CancellativeCommutativeSemiring_2276
v0
  = (T_IsCancellativeCommutativeSemiring_1462
 -> T_IsCommutativeSemiring_1344)
-> AgdaAny -> T_IsCommutativeSemiring_1344
forall a b. a -> b
coe
      T_IsCancellativeCommutativeSemiring_1462
-> T_IsCommutativeSemiring_1344
MAlonzo.Code.Algebra.Structures.d_isCommutativeSemiring_1476
      ((T_CancellativeCommutativeSemiring_2276
 -> T_IsCancellativeCommutativeSemiring_1462)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2276
-> T_IsCancellativeCommutativeSemiring_1462
d_isCancellativeCommutativeSemiring_2308 (T_CancellativeCommutativeSemiring_2276 -> AgdaAny
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2276
v0))
-- Algebra.Bundles.CancellativeCommutativeSemiring._.isCommutativeSemiringWithoutOne
d_isCommutativeSemiringWithoutOne_2378 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CancellativeCommutativeSemiring_2276 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiringWithoutOne_1044
d_isCommutativeSemiringWithoutOne_2378 :: ()
-> ()
-> T_CancellativeCommutativeSemiring_2276
-> T_IsCommutativeSemiringWithoutOne_1044
d_isCommutativeSemiringWithoutOne_2378 ~()
v0 ~()
v1 T_CancellativeCommutativeSemiring_2276
v2
  = T_CancellativeCommutativeSemiring_2276
-> T_IsCommutativeSemiringWithoutOne_1044
du_isCommutativeSemiringWithoutOne_2378 T_CancellativeCommutativeSemiring_2276
v2
du_isCommutativeSemiringWithoutOne_2378 ::
  T_CancellativeCommutativeSemiring_2276 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiringWithoutOne_1044
du_isCommutativeSemiringWithoutOne_2378 :: T_CancellativeCommutativeSemiring_2276
-> T_IsCommutativeSemiringWithoutOne_1044
du_isCommutativeSemiringWithoutOne_2378 T_CancellativeCommutativeSemiring_2276
v0
  = let v1 :: T_IsCancellativeCommutativeSemiring_1462
v1 = T_CancellativeCommutativeSemiring_2276
-> T_IsCancellativeCommutativeSemiring_1462
d_isCancellativeCommutativeSemiring_2308 (T_CancellativeCommutativeSemiring_2276
-> T_CancellativeCommutativeSemiring_2276
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2276
v0) in
    AgdaAny -> T_IsCommutativeSemiringWithoutOne_1044
forall a b. a -> b
coe
      ((T_IsCommutativeSemiring_1344
 -> T_IsCommutativeSemiringWithoutOne_1044)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCommutativeSemiring_1344
-> T_IsCommutativeSemiringWithoutOne_1044
MAlonzo.Code.Algebra.Structures.du_isCommutativeSemiringWithoutOne_1444
         ((T_IsCancellativeCommutativeSemiring_1462
 -> T_IsCommutativeSemiring_1344)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCancellativeCommutativeSemiring_1462
-> T_IsCommutativeSemiring_1344
MAlonzo.Code.Algebra.Structures.d_isCommutativeSemiring_1476
            (T_IsCancellativeCommutativeSemiring_1462 -> AgdaAny
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1462
v1)))
-- Algebra.Bundles.CancellativeCommutativeSemiring._.isEquivalence
d_isEquivalence_2380 ::
  T_CancellativeCommutativeSemiring_2276 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_2380 :: T_CancellativeCommutativeSemiring_2276 -> T_IsEquivalence_26
d_isEquivalence_2380 T_CancellativeCommutativeSemiring_2276
v0
  = (T_IsMagma_86 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      T_IsMagma_86 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_94
      ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202
         ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368
            ((T_IsCommutativeMonoid_406 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsCommutativeMonoid_406 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_416
               ((T_IsSemiringWithoutAnnihilatingZero_1142
 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsCommutativeMonoid_406
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1158
                  ((T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1252
                     ((T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238
MAlonzo.Code.Algebra.Structures.d_isSemiring_1358
                        ((T_IsCancellativeCommutativeSemiring_1462
 -> T_IsCommutativeSemiring_1344)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_IsCancellativeCommutativeSemiring_1462
-> T_IsCommutativeSemiring_1344
MAlonzo.Code.Algebra.Structures.d_isCommutativeSemiring_1476
                           ((T_CancellativeCommutativeSemiring_2276
 -> T_IsCancellativeCommutativeSemiring_1462)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2276
-> T_IsCancellativeCommutativeSemiring_1462
d_isCancellativeCommutativeSemiring_2308 (T_CancellativeCommutativeSemiring_2276 -> AgdaAny
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2276
v0)))))))))
-- Algebra.Bundles.CancellativeCommutativeSemiring._.isNearSemiring
d_isNearSemiring_2382 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CancellativeCommutativeSemiring_2276 ->
  MAlonzo.Code.Algebra.Structures.T_IsNearSemiring_876
d_isNearSemiring_2382 :: ()
-> ()
-> T_CancellativeCommutativeSemiring_2276
-> T_IsNearSemiring_876
d_isNearSemiring_2382 ~()
v0 ~()
v1 T_CancellativeCommutativeSemiring_2276
v2 = T_CancellativeCommutativeSemiring_2276 -> T_IsNearSemiring_876
du_isNearSemiring_2382 T_CancellativeCommutativeSemiring_2276
v2
du_isNearSemiring_2382 ::
  T_CancellativeCommutativeSemiring_2276 ->
  MAlonzo.Code.Algebra.Structures.T_IsNearSemiring_876
du_isNearSemiring_2382 :: T_CancellativeCommutativeSemiring_2276 -> T_IsNearSemiring_876
du_isNearSemiring_2382 T_CancellativeCommutativeSemiring_2276
v0
  = let v1 :: T_IsCancellativeCommutativeSemiring_1462
v1 = T_CancellativeCommutativeSemiring_2276
-> T_IsCancellativeCommutativeSemiring_1462
d_isCancellativeCommutativeSemiring_2308 (T_CancellativeCommutativeSemiring_2276
-> T_CancellativeCommutativeSemiring_2276
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2276
v0) in
    AgdaAny -> T_IsNearSemiring_876
forall a b. a -> b
coe
      (let v2 :: T_IsCommutativeSemiring_1344
v2
             = T_IsCancellativeCommutativeSemiring_1462
-> T_IsCommutativeSemiring_1344
MAlonzo.Code.Algebra.Structures.d_isCommutativeSemiring_1476
                 (T_IsCancellativeCommutativeSemiring_1462
-> T_IsCancellativeCommutativeSemiring_1462
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1462
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemiring_1238
v3
                = T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238
MAlonzo.Code.Algebra.Structures.d_isSemiring_1358 (T_IsCommutativeSemiring_1344 -> T_IsCommutativeSemiring_1344
forall a b. a -> b
coe T_IsCommutativeSemiring_1344
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsSemiringWithoutOne_952 -> T_IsNearSemiring_876)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemiringWithoutOne_952 -> T_IsNearSemiring_876
MAlonzo.Code.Algebra.Structures.du_isNearSemiring_990
               ((T_IsSemiring_1238 -> T_IsSemiringWithoutOne_952)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsSemiring_1238 -> T_IsSemiringWithoutOne_952
MAlonzo.Code.Algebra.Structures.du_isSemiringWithoutOne_1326
                  (T_IsSemiring_1238 -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1238
v3)))))
-- Algebra.Bundles.CancellativeCommutativeSemiring._.isPartialEquivalence
d_isPartialEquivalence_2384 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CancellativeCommutativeSemiring_2276 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_2384 :: ()
-> ()
-> T_CancellativeCommutativeSemiring_2276
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_2384 ~()
v0 ~()
v1 T_CancellativeCommutativeSemiring_2276
v2
  = T_CancellativeCommutativeSemiring_2276 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_2384 T_CancellativeCommutativeSemiring_2276
v2
du_isPartialEquivalence_2384 ::
  T_CancellativeCommutativeSemiring_2276 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_2384 :: T_CancellativeCommutativeSemiring_2276 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_2384 T_CancellativeCommutativeSemiring_2276
v0
  = let v1 :: T_IsCancellativeCommutativeSemiring_1462
v1 = T_CancellativeCommutativeSemiring_2276
-> T_IsCancellativeCommutativeSemiring_1462
d_isCancellativeCommutativeSemiring_2308 (T_CancellativeCommutativeSemiring_2276
-> T_CancellativeCommutativeSemiring_2276
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2276
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsCommutativeSemiring_1344
v2
             = T_IsCancellativeCommutativeSemiring_1462
-> T_IsCommutativeSemiring_1344
MAlonzo.Code.Algebra.Structures.d_isCommutativeSemiring_1476
                 (T_IsCancellativeCommutativeSemiring_1462
-> T_IsCancellativeCommutativeSemiring_1462
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1462
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemiring_1238
v3
                = T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238
MAlonzo.Code.Algebra.Structures.d_isSemiring_1358 (T_IsCommutativeSemiring_1344 -> T_IsCommutativeSemiring_1344
forall a b. a -> b
coe T_IsCommutativeSemiring_1344
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsSemiringWithoutAnnihilatingZero_1142
v4
                   = T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1252
                       (T_IsSemiring_1238 -> T_IsSemiring_1238
forall a b. a -> b
coe T_IsSemiring_1238
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsCommutativeMonoid_406
v5
                      = T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsCommutativeMonoid_406
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1158
                          (T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsSemiringWithoutAnnihilatingZero_1142
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1142
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (let v6 :: T_IsMonoid_358
v6
                         = T_IsCommutativeMonoid_406 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_416 (T_IsCommutativeMonoid_406 -> T_IsCommutativeMonoid_406
forall a b. a -> b
coe T_IsCommutativeMonoid_406
v5) in
                   AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     (let v7 :: T_IsSemigroup_194
v7
                            = T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368 (T_IsMonoid_358 -> T_IsMonoid_358
forall a b. a -> b
coe T_IsMonoid_358
v6) in
                      AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        (let v8 :: T_IsMagma_86
v8 = T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202 (T_IsSemigroup_194 -> T_IsSemigroup_194
forall a b. a -> b
coe T_IsSemigroup_194
v7) in
                         AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           ((T_IsEquivalence_26 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                              T_IsEquivalence_26 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
                              ((T_IsMagma_86 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                 T_IsMagma_86 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_94
                                 (T_IsMagma_86 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86
v8))))))))))
-- Algebra.Bundles.CancellativeCommutativeSemiring._.isSemiring
d_isSemiring_2386 ::
  T_CancellativeCommutativeSemiring_2276 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemiring_1238
d_isSemiring_2386 :: T_CancellativeCommutativeSemiring_2276 -> T_IsSemiring_1238
d_isSemiring_2386 T_CancellativeCommutativeSemiring_2276
v0
  = (T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238)
-> AgdaAny -> T_IsSemiring_1238
forall a b. a -> b
coe
      T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238
MAlonzo.Code.Algebra.Structures.d_isSemiring_1358
      ((T_IsCancellativeCommutativeSemiring_1462
 -> T_IsCommutativeSemiring_1344)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCancellativeCommutativeSemiring_1462
-> T_IsCommutativeSemiring_1344
MAlonzo.Code.Algebra.Structures.d_isCommutativeSemiring_1476
         ((T_CancellativeCommutativeSemiring_2276
 -> T_IsCancellativeCommutativeSemiring_1462)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2276
-> T_IsCancellativeCommutativeSemiring_1462
d_isCancellativeCommutativeSemiring_2308 (T_CancellativeCommutativeSemiring_2276 -> AgdaAny
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2276
v0)))
-- Algebra.Bundles.CancellativeCommutativeSemiring._.isSemiringWithoutAnnihilatingZero
d_isSemiringWithoutAnnihilatingZero_2388 ::
  T_CancellativeCommutativeSemiring_2276 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutAnnihilatingZero_1142
d_isSemiringWithoutAnnihilatingZero_2388 :: T_CancellativeCommutativeSemiring_2276
-> T_IsSemiringWithoutAnnihilatingZero_1142
d_isSemiringWithoutAnnihilatingZero_2388 T_CancellativeCommutativeSemiring_2276
v0
  = (T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142)
-> AgdaAny -> T_IsSemiringWithoutAnnihilatingZero_1142
forall a b. a -> b
coe
      T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1252
      ((T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238
MAlonzo.Code.Algebra.Structures.d_isSemiring_1358
         ((T_IsCancellativeCommutativeSemiring_1462
 -> T_IsCommutativeSemiring_1344)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCancellativeCommutativeSemiring_1462
-> T_IsCommutativeSemiring_1344
MAlonzo.Code.Algebra.Structures.d_isCommutativeSemiring_1476
            ((T_CancellativeCommutativeSemiring_2276
 -> T_IsCancellativeCommutativeSemiring_1462)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2276
-> T_IsCancellativeCommutativeSemiring_1462
d_isCancellativeCommutativeSemiring_2308 (T_CancellativeCommutativeSemiring_2276 -> AgdaAny
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2276
v0))))
-- Algebra.Bundles.CancellativeCommutativeSemiring._.isSemiringWithoutOne
d_isSemiringWithoutOne_2390 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CancellativeCommutativeSemiring_2276 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutOne_952
d_isSemiringWithoutOne_2390 :: ()
-> ()
-> T_CancellativeCommutativeSemiring_2276
-> T_IsSemiringWithoutOne_952
d_isSemiringWithoutOne_2390 ~()
v0 ~()
v1 T_CancellativeCommutativeSemiring_2276
v2
  = T_CancellativeCommutativeSemiring_2276
-> T_IsSemiringWithoutOne_952
du_isSemiringWithoutOne_2390 T_CancellativeCommutativeSemiring_2276
v2
du_isSemiringWithoutOne_2390 ::
  T_CancellativeCommutativeSemiring_2276 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutOne_952
du_isSemiringWithoutOne_2390 :: T_CancellativeCommutativeSemiring_2276
-> T_IsSemiringWithoutOne_952
du_isSemiringWithoutOne_2390 T_CancellativeCommutativeSemiring_2276
v0
  = let v1 :: T_IsCancellativeCommutativeSemiring_1462
v1 = T_CancellativeCommutativeSemiring_2276
-> T_IsCancellativeCommutativeSemiring_1462
d_isCancellativeCommutativeSemiring_2308 (T_CancellativeCommutativeSemiring_2276
-> T_CancellativeCommutativeSemiring_2276
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2276
v0) in
    AgdaAny -> T_IsSemiringWithoutOne_952
forall a b. a -> b
coe
      (let v2 :: T_IsCommutativeSemiring_1344
v2
             = T_IsCancellativeCommutativeSemiring_1462
-> T_IsCommutativeSemiring_1344
MAlonzo.Code.Algebra.Structures.d_isCommutativeSemiring_1476
                 (T_IsCancellativeCommutativeSemiring_1462
-> T_IsCancellativeCommutativeSemiring_1462
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1462
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsSemiring_1238 -> T_IsSemiringWithoutOne_952)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemiring_1238 -> T_IsSemiringWithoutOne_952
MAlonzo.Code.Algebra.Structures.du_isSemiringWithoutOne_1326
            ((T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238
MAlonzo.Code.Algebra.Structures.d_isSemiring_1358 (T_IsCommutativeSemiring_1344 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiring_1344
v2))))
-- Algebra.Bundles.CancellativeCommutativeSemiring._.refl
d_refl_2392 ::
  T_CancellativeCommutativeSemiring_2276 -> AgdaAny -> AgdaAny
d_refl_2392 :: T_CancellativeCommutativeSemiring_2276 -> AgdaAny -> AgdaAny
d_refl_2392 T_CancellativeCommutativeSemiring_2276
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_86 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_86 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_94
         ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202
            ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368
               ((T_IsCommutativeMonoid_406 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsCommutativeMonoid_406 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_416
                  ((T_IsSemiringWithoutAnnihilatingZero_1142
 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsCommutativeMonoid_406
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1158
                     ((T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1252
                        ((T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238
MAlonzo.Code.Algebra.Structures.d_isSemiring_1358
                           ((T_IsCancellativeCommutativeSemiring_1462
 -> T_IsCommutativeSemiring_1344)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                              T_IsCancellativeCommutativeSemiring_1462
-> T_IsCommutativeSemiring_1344
MAlonzo.Code.Algebra.Structures.d_isCommutativeSemiring_1476
                              ((T_CancellativeCommutativeSemiring_2276
 -> T_IsCancellativeCommutativeSemiring_1462)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2276
-> T_IsCancellativeCommutativeSemiring_1462
d_isCancellativeCommutativeSemiring_2308 (T_CancellativeCommutativeSemiring_2276 -> AgdaAny
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2276
v0))))))))))
-- Algebra.Bundles.CancellativeCommutativeSemiring._.reflexive
d_reflexive_2394 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CancellativeCommutativeSemiring_2276 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_2394 :: ()
-> ()
-> T_CancellativeCommutativeSemiring_2276
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_2394 ~()
v0 ~()
v1 T_CancellativeCommutativeSemiring_2276
v2 = T_CancellativeCommutativeSemiring_2276
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_2394 T_CancellativeCommutativeSemiring_2276
v2
du_reflexive_2394 ::
  T_CancellativeCommutativeSemiring_2276 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_2394 :: T_CancellativeCommutativeSemiring_2276
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_2394 T_CancellativeCommutativeSemiring_2276
v0
  = let v1 :: T_IsCancellativeCommutativeSemiring_1462
v1 = T_CancellativeCommutativeSemiring_2276
-> T_IsCancellativeCommutativeSemiring_1462
d_isCancellativeCommutativeSemiring_2308 (T_CancellativeCommutativeSemiring_2276
-> T_CancellativeCommutativeSemiring_2276
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2276
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsCommutativeSemiring_1344
v2
             = T_IsCancellativeCommutativeSemiring_1462
-> T_IsCommutativeSemiring_1344
MAlonzo.Code.Algebra.Structures.d_isCommutativeSemiring_1476
                 (T_IsCancellativeCommutativeSemiring_1462
-> T_IsCancellativeCommutativeSemiring_1462
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1462
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemiring_1238
v3
                = T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238
MAlonzo.Code.Algebra.Structures.d_isSemiring_1358 (T_IsCommutativeSemiring_1344 -> T_IsCommutativeSemiring_1344
forall a b. a -> b
coe T_IsCommutativeSemiring_1344
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsSemiringWithoutAnnihilatingZero_1142
v4
                   = T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1252
                       (T_IsSemiring_1238 -> T_IsSemiring_1238
forall a b. a -> b
coe T_IsSemiring_1238
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsCommutativeMonoid_406
v5
                      = T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsCommutativeMonoid_406
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1158
                          (T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsSemiringWithoutAnnihilatingZero_1142
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1142
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (let v6 :: T_IsMonoid_358
v6
                         = T_IsCommutativeMonoid_406 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_416 (T_IsCommutativeMonoid_406 -> T_IsCommutativeMonoid_406
forall a b. a -> b
coe T_IsCommutativeMonoid_406
v5) in
                   AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     (let v7 :: T_IsSemigroup_194
v7
                            = T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368 (T_IsMonoid_358 -> T_IsMonoid_358
forall a b. a -> b
coe T_IsMonoid_358
v6) in
                      AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        (let v8 :: T_IsMagma_86
v8 = T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202 (T_IsSemigroup_194 -> T_IsSemigroup_194
forall a b. a -> b
coe T_IsSemigroup_194
v7) in
                         (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
                           (\ AgdaAny
v9 AgdaAny
v10 AgdaAny
v11 ->
                              (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
                                ((T_IsMagma_86 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_94 (T_IsMagma_86 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86
v8))
                                AgdaAny
v9))))))))
-- Algebra.Bundles.CancellativeCommutativeSemiring._.setoid
d_setoid_2396 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CancellativeCommutativeSemiring_2276 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_2396 :: () -> () -> T_CancellativeCommutativeSemiring_2276 -> T_Setoid_44
d_setoid_2396 ~()
v0 ~()
v1 T_CancellativeCommutativeSemiring_2276
v2 = T_CancellativeCommutativeSemiring_2276 -> T_Setoid_44
du_setoid_2396 T_CancellativeCommutativeSemiring_2276
v2
du_setoid_2396 ::
  T_CancellativeCommutativeSemiring_2276 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_2396 :: T_CancellativeCommutativeSemiring_2276 -> T_Setoid_44
du_setoid_2396 T_CancellativeCommutativeSemiring_2276
v0
  = let v1 :: T_IsCancellativeCommutativeSemiring_1462
v1 = T_CancellativeCommutativeSemiring_2276
-> T_IsCancellativeCommutativeSemiring_1462
d_isCancellativeCommutativeSemiring_2308 (T_CancellativeCommutativeSemiring_2276
-> T_CancellativeCommutativeSemiring_2276
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2276
v0) in
    AgdaAny -> T_Setoid_44
forall a b. a -> b
coe
      (let v2 :: T_IsCommutativeSemiring_1344
v2
             = T_IsCancellativeCommutativeSemiring_1462
-> T_IsCommutativeSemiring_1344
MAlonzo.Code.Algebra.Structures.d_isCommutativeSemiring_1476
                 (T_IsCancellativeCommutativeSemiring_1462
-> T_IsCancellativeCommutativeSemiring_1462
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1462
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemiring_1238
v3
                = T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238
MAlonzo.Code.Algebra.Structures.d_isSemiring_1358 (T_IsCommutativeSemiring_1344 -> T_IsCommutativeSemiring_1344
forall a b. a -> b
coe T_IsCommutativeSemiring_1344
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsSemiringWithoutAnnihilatingZero_1142
v4
                   = T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1252
                       (T_IsSemiring_1238 -> T_IsSemiring_1238
forall a b. a -> b
coe T_IsSemiring_1238
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsCommutativeMonoid_406
v5
                      = T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsCommutativeMonoid_406
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1158
                          (T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsSemiringWithoutAnnihilatingZero_1142
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1142
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (let v6 :: T_IsMonoid_358
v6
                         = T_IsCommutativeMonoid_406 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_416 (T_IsCommutativeMonoid_406 -> T_IsCommutativeMonoid_406
forall a b. a -> b
coe T_IsCommutativeMonoid_406
v5) in
                   AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     (let v7 :: T_IsSemigroup_194
v7
                            = T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368 (T_IsMonoid_358 -> T_IsMonoid_358
forall a b. a -> b
coe T_IsMonoid_358
v6) in
                      AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        ((T_IsMagma_86 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_IsMagma_86 -> T_Setoid_44
MAlonzo.Code.Algebra.Structures.du_setoid_110
                           ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202 (T_IsSemigroup_194 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194
v7)))))))))
-- Algebra.Bundles.CancellativeCommutativeSemiring._.sym
d_sym_2398 ::
  T_CancellativeCommutativeSemiring_2276 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_2398 :: T_CancellativeCommutativeSemiring_2276
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_2398 T_CancellativeCommutativeSemiring_2276
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_86 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_86 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_94
         ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202
            ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368
               ((T_IsCommutativeMonoid_406 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsCommutativeMonoid_406 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_416
                  ((T_IsSemiringWithoutAnnihilatingZero_1142
 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsCommutativeMonoid_406
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1158
                     ((T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1252
                        ((T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238
MAlonzo.Code.Algebra.Structures.d_isSemiring_1358
                           ((T_IsCancellativeCommutativeSemiring_1462
 -> T_IsCommutativeSemiring_1344)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                              T_IsCancellativeCommutativeSemiring_1462
-> T_IsCommutativeSemiring_1344
MAlonzo.Code.Algebra.Structures.d_isCommutativeSemiring_1476
                              ((T_CancellativeCommutativeSemiring_2276
 -> T_IsCancellativeCommutativeSemiring_1462)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2276
-> T_IsCancellativeCommutativeSemiring_1462
d_isCancellativeCommutativeSemiring_2308 (T_CancellativeCommutativeSemiring_2276 -> AgdaAny
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2276
v0))))))))))
-- Algebra.Bundles.CancellativeCommutativeSemiring._.trans
d_trans_2400 ::
  T_CancellativeCommutativeSemiring_2276 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_2400 :: T_CancellativeCommutativeSemiring_2276
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_2400 T_CancellativeCommutativeSemiring_2276
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_86 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_86 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_94
         ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202
            ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368
               ((T_IsCommutativeMonoid_406 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsCommutativeMonoid_406 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_416
                  ((T_IsSemiringWithoutAnnihilatingZero_1142
 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsCommutativeMonoid_406
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1158
                     ((T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1252
                        ((T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238
MAlonzo.Code.Algebra.Structures.d_isSemiring_1358
                           ((T_IsCancellativeCommutativeSemiring_1462
 -> T_IsCommutativeSemiring_1344)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                              T_IsCancellativeCommutativeSemiring_1462
-> T_IsCommutativeSemiring_1344
MAlonzo.Code.Algebra.Structures.d_isCommutativeSemiring_1476
                              ((T_CancellativeCommutativeSemiring_2276
 -> T_IsCancellativeCommutativeSemiring_1462)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2276
-> T_IsCancellativeCommutativeSemiring_1462
d_isCancellativeCommutativeSemiring_2308 (T_CancellativeCommutativeSemiring_2276 -> AgdaAny
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2276
v0))))))))))
-- Algebra.Bundles.CancellativeCommutativeSemiring._.zero
d_zero_2402 ::
  T_CancellativeCommutativeSemiring_2276 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_zero_2402 :: T_CancellativeCommutativeSemiring_2276 -> T_Σ_14
d_zero_2402 T_CancellativeCommutativeSemiring_2276
v0
  = (T_IsSemiring_1238 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsSemiring_1238 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_zero_1254
      ((T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238
MAlonzo.Code.Algebra.Structures.d_isSemiring_1358
         ((T_IsCancellativeCommutativeSemiring_1462
 -> T_IsCommutativeSemiring_1344)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCancellativeCommutativeSemiring_1462
-> T_IsCommutativeSemiring_1344
MAlonzo.Code.Algebra.Structures.d_isCommutativeSemiring_1476
            ((T_CancellativeCommutativeSemiring_2276
 -> T_IsCancellativeCommutativeSemiring_1462)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2276
-> T_IsCancellativeCommutativeSemiring_1462
d_isCancellativeCommutativeSemiring_2308 (T_CancellativeCommutativeSemiring_2276 -> AgdaAny
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2276
v0))))
-- Algebra.Bundles.CancellativeCommutativeSemiring._.zeroʳ
d_zero'691'_2404 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CancellativeCommutativeSemiring_2276 -> AgdaAny -> AgdaAny
d_zero'691'_2404 :: ()
-> ()
-> T_CancellativeCommutativeSemiring_2276
-> AgdaAny
-> AgdaAny
d_zero'691'_2404 ~()
v0 ~()
v1 T_CancellativeCommutativeSemiring_2276
v2 = T_CancellativeCommutativeSemiring_2276 -> AgdaAny -> AgdaAny
du_zero'691'_2404 T_CancellativeCommutativeSemiring_2276
v2
du_zero'691'_2404 ::
  T_CancellativeCommutativeSemiring_2276 -> AgdaAny -> AgdaAny
du_zero'691'_2404 :: T_CancellativeCommutativeSemiring_2276 -> AgdaAny -> AgdaAny
du_zero'691'_2404 T_CancellativeCommutativeSemiring_2276
v0
  = let v1 :: T_IsCancellativeCommutativeSemiring_1462
v1 = T_CancellativeCommutativeSemiring_2276
-> T_IsCancellativeCommutativeSemiring_1462
d_isCancellativeCommutativeSemiring_2308 (T_CancellativeCommutativeSemiring_2276
-> T_CancellativeCommutativeSemiring_2276
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2276
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsCommutativeSemiring_1344
v2
             = T_IsCancellativeCommutativeSemiring_1462
-> T_IsCommutativeSemiring_1344
MAlonzo.Code.Algebra.Structures.d_isCommutativeSemiring_1476
                 (T_IsCancellativeCommutativeSemiring_1462
-> T_IsCancellativeCommutativeSemiring_1462
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1462
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemiring_1238
v3
                = T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238
MAlonzo.Code.Algebra.Structures.d_isSemiring_1358 (T_IsCommutativeSemiring_1344 -> T_IsCommutativeSemiring_1344
forall a b. a -> b
coe T_IsCommutativeSemiring_1344
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsSemiringWithoutOne_952 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemiringWithoutOne_952 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_zero'691'_988
               ((T_IsSemiring_1238 -> T_IsSemiringWithoutOne_952)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsSemiring_1238 -> T_IsSemiringWithoutOne_952
MAlonzo.Code.Algebra.Structures.du_isSemiringWithoutOne_1326
                  (T_IsSemiring_1238 -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1238
v3)))))
-- Algebra.Bundles.CancellativeCommutativeSemiring._.zeroˡ
d_zero'737'_2406 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CancellativeCommutativeSemiring_2276 -> AgdaAny -> AgdaAny
d_zero'737'_2406 :: ()
-> ()
-> T_CancellativeCommutativeSemiring_2276
-> AgdaAny
-> AgdaAny
d_zero'737'_2406 ~()
v0 ~()
v1 T_CancellativeCommutativeSemiring_2276
v2 = T_CancellativeCommutativeSemiring_2276 -> AgdaAny -> AgdaAny
du_zero'737'_2406 T_CancellativeCommutativeSemiring_2276
v2
du_zero'737'_2406 ::
  T_CancellativeCommutativeSemiring_2276 -> AgdaAny -> AgdaAny
du_zero'737'_2406 :: T_CancellativeCommutativeSemiring_2276 -> AgdaAny -> AgdaAny
du_zero'737'_2406 T_CancellativeCommutativeSemiring_2276
v0
  = let v1 :: T_IsCancellativeCommutativeSemiring_1462
v1 = T_CancellativeCommutativeSemiring_2276
-> T_IsCancellativeCommutativeSemiring_1462
d_isCancellativeCommutativeSemiring_2308 (T_CancellativeCommutativeSemiring_2276
-> T_CancellativeCommutativeSemiring_2276
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2276
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsCommutativeSemiring_1344
v2
             = T_IsCancellativeCommutativeSemiring_1462
-> T_IsCommutativeSemiring_1344
MAlonzo.Code.Algebra.Structures.d_isCommutativeSemiring_1476
                 (T_IsCancellativeCommutativeSemiring_1462
-> T_IsCancellativeCommutativeSemiring_1462
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1462
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemiring_1238
v3
                = T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238
MAlonzo.Code.Algebra.Structures.d_isSemiring_1358 (T_IsCommutativeSemiring_1344 -> T_IsCommutativeSemiring_1344
forall a b. a -> b
coe T_IsCommutativeSemiring_1344
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsSemiringWithoutOne_952 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemiringWithoutOne_952 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_zero'737'_986
               ((T_IsSemiring_1238 -> T_IsSemiringWithoutOne_952)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsSemiring_1238 -> T_IsSemiringWithoutOne_952
MAlonzo.Code.Algebra.Structures.du_isSemiringWithoutOne_1326
                  (T_IsSemiring_1238 -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1238
v3)))))
-- Algebra.Bundles.CancellativeCommutativeSemiring.commutativeSemiring
d_commutativeSemiring_2408 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CancellativeCommutativeSemiring_2276 ->
  T_CommutativeSemiring_2094
d_commutativeSemiring_2408 :: ()
-> ()
-> T_CancellativeCommutativeSemiring_2276
-> T_CommutativeSemiring_2094
d_commutativeSemiring_2408 ~()
v0 ~()
v1 T_CancellativeCommutativeSemiring_2276
v2
  = T_CancellativeCommutativeSemiring_2276
-> T_CommutativeSemiring_2094
du_commutativeSemiring_2408 T_CancellativeCommutativeSemiring_2276
v2
du_commutativeSemiring_2408 ::
  T_CancellativeCommutativeSemiring_2276 ->
  T_CommutativeSemiring_2094
du_commutativeSemiring_2408 :: T_CancellativeCommutativeSemiring_2276
-> T_CommutativeSemiring_2094
du_commutativeSemiring_2408 T_CancellativeCommutativeSemiring_2276
v0
  = ((AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> AgdaAny
 -> T_IsCommutativeSemiring_1344
 -> T_CommutativeSemiring_2094)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsCommutativeSemiring_1344
-> T_CommutativeSemiring_2094
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsCommutativeSemiring_1344
-> T_CommutativeSemiring_2094
C_CommutativeSemiring'46'constructor_36513 (T_CancellativeCommutativeSemiring_2276
-> AgdaAny -> AgdaAny -> AgdaAny
d__'43'__2300 (T_CancellativeCommutativeSemiring_2276
-> T_CancellativeCommutativeSemiring_2276
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2276
v0))
      (T_CancellativeCommutativeSemiring_2276
-> AgdaAny -> AgdaAny -> AgdaAny
d__'42'__2302 (T_CancellativeCommutativeSemiring_2276
-> T_CancellativeCommutativeSemiring_2276
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2276
v0)) (T_CancellativeCommutativeSemiring_2276 -> AgdaAny
d_0'35'_2304 (T_CancellativeCommutativeSemiring_2276
-> T_CancellativeCommutativeSemiring_2276
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2276
v0))
      (T_CancellativeCommutativeSemiring_2276 -> AgdaAny
d_1'35'_2306 (T_CancellativeCommutativeSemiring_2276
-> T_CancellativeCommutativeSemiring_2276
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2276
v0))
      (T_IsCancellativeCommutativeSemiring_1462
-> T_IsCommutativeSemiring_1344
MAlonzo.Code.Algebra.Structures.d_isCommutativeSemiring_1476
         ((T_CancellativeCommutativeSemiring_2276
 -> T_IsCancellativeCommutativeSemiring_1462)
-> AgdaAny -> T_IsCancellativeCommutativeSemiring_1462
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2276
-> T_IsCancellativeCommutativeSemiring_1462
d_isCancellativeCommutativeSemiring_2308 (T_CancellativeCommutativeSemiring_2276 -> AgdaAny
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2276
v0)))
-- Algebra.Bundles.CancellativeCommutativeSemiring._._≉_
d__'8777'__2412 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CancellativeCommutativeSemiring_2276 -> AgdaAny -> AgdaAny -> ()
d__'8777'__2412 :: ()
-> ()
-> T_CancellativeCommutativeSemiring_2276
-> AgdaAny
-> AgdaAny
-> ()
d__'8777'__2412 = ()
-> ()
-> T_CancellativeCommutativeSemiring_2276
-> AgdaAny
-> AgdaAny
-> ()
forall a. a
erased
-- Algebra.Bundles.CancellativeCommutativeSemiring._.commutativeMagma
d_commutativeMagma_2414 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CancellativeCommutativeSemiring_2276 -> T_CommutativeMagma_148
d_commutativeMagma_2414 :: ()
-> ()
-> T_CancellativeCommutativeSemiring_2276
-> T_CommutativeMagma_148
d_commutativeMagma_2414 ~()
v0 ~()
v1 T_CancellativeCommutativeSemiring_2276
v2 = T_CancellativeCommutativeSemiring_2276 -> T_CommutativeMagma_148
du_commutativeMagma_2414 T_CancellativeCommutativeSemiring_2276
v2
du_commutativeMagma_2414 ::
  T_CancellativeCommutativeSemiring_2276 -> T_CommutativeMagma_148
du_commutativeMagma_2414 :: T_CancellativeCommutativeSemiring_2276 -> T_CommutativeMagma_148
du_commutativeMagma_2414 T_CancellativeCommutativeSemiring_2276
v0
  = let v1 :: t
v1 = (T_CancellativeCommutativeSemiring_2276
 -> T_CommutativeSemiring_2094)
-> AgdaAny -> t
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2276
-> T_CommutativeSemiring_2094
du_commutativeSemiring_2408 (T_CancellativeCommutativeSemiring_2276 -> AgdaAny
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2276
v0) in
    AgdaAny -> T_CommutativeMagma_148
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_CommutativeSemiring_2094 -> T_CommutativeMonoid_582)
-> AgdaAny -> t
forall a b. a -> b
coe T_CommutativeSemiring_2094 -> T_CommutativeMonoid_582
du_'42''45'commutativeMonoid_2262 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_CommutativeSemigroup_332 -> T_CommutativeMagma_148)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_CommutativeSemigroup_332 -> T_CommutativeMagma_148
du_commutativeMagma_396
            ((T_CommutativeMonoid_582 -> T_CommutativeSemigroup_332)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeMonoid_582 -> T_CommutativeSemigroup_332
du_commutativeSemigroup_664 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2))))
-- Algebra.Bundles.CancellativeCommutativeSemiring._.*-commutativeMonoid
d_'42''45'commutativeMonoid_2416 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CancellativeCommutativeSemiring_2276 -> T_CommutativeMonoid_582
d_'42''45'commutativeMonoid_2416 :: ()
-> ()
-> T_CancellativeCommutativeSemiring_2276
-> T_CommutativeMonoid_582
d_'42''45'commutativeMonoid_2416 ~()
v0 ~()
v1 T_CancellativeCommutativeSemiring_2276
v2
  = T_CancellativeCommutativeSemiring_2276 -> T_CommutativeMonoid_582
du_'42''45'commutativeMonoid_2416 T_CancellativeCommutativeSemiring_2276
v2
du_'42''45'commutativeMonoid_2416 ::
  T_CancellativeCommutativeSemiring_2276 -> T_CommutativeMonoid_582
du_'42''45'commutativeMonoid_2416 :: T_CancellativeCommutativeSemiring_2276 -> T_CommutativeMonoid_582
du_'42''45'commutativeMonoid_2416 T_CancellativeCommutativeSemiring_2276
v0
  = (T_CommutativeSemiring_2094 -> T_CommutativeMonoid_582)
-> AgdaAny -> T_CommutativeMonoid_582
forall a b. a -> b
coe
      T_CommutativeSemiring_2094 -> T_CommutativeMonoid_582
du_'42''45'commutativeMonoid_2262
      ((T_CancellativeCommutativeSemiring_2276
 -> T_CommutativeSemiring_2094)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2276
-> T_CommutativeSemiring_2094
du_commutativeSemiring_2408 (T_CancellativeCommutativeSemiring_2276 -> AgdaAny
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2276
v0))
-- Algebra.Bundles.CancellativeCommutativeSemiring._.commutativeSemigroup
d_commutativeSemigroup_2418 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CancellativeCommutativeSemiring_2276 ->
  T_CommutativeSemigroup_332
d_commutativeSemigroup_2418 :: ()
-> ()
-> T_CancellativeCommutativeSemiring_2276
-> T_CommutativeSemigroup_332
d_commutativeSemigroup_2418 ~()
v0 ~()
v1 T_CancellativeCommutativeSemiring_2276
v2
  = T_CancellativeCommutativeSemiring_2276
-> T_CommutativeSemigroup_332
du_commutativeSemigroup_2418 T_CancellativeCommutativeSemiring_2276
v2
du_commutativeSemigroup_2418 ::
  T_CancellativeCommutativeSemiring_2276 ->
  T_CommutativeSemigroup_332
du_commutativeSemigroup_2418 :: T_CancellativeCommutativeSemiring_2276
-> T_CommutativeSemigroup_332
du_commutativeSemigroup_2418 T_CancellativeCommutativeSemiring_2276
v0
  = let v1 :: t
v1 = (T_CancellativeCommutativeSemiring_2276
 -> T_CommutativeSemiring_2094)
-> AgdaAny -> t
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2276
-> T_CommutativeSemiring_2094
du_commutativeSemiring_2408 (T_CancellativeCommutativeSemiring_2276 -> AgdaAny
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2276
v0) in
    AgdaAny -> T_CommutativeSemigroup_332
forall a b. a -> b
coe
      ((T_CommutativeMonoid_582 -> T_CommutativeSemigroup_332)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_CommutativeMonoid_582 -> T_CommutativeSemigroup_332
du_commutativeSemigroup_664
         ((T_CommutativeSemiring_2094 -> T_CommutativeMonoid_582)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemiring_2094 -> T_CommutativeMonoid_582
du_'42''45'commutativeMonoid_2262 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1)))
-- Algebra.Bundles.CancellativeCommutativeSemiring._.magma
d_magma_2420 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CancellativeCommutativeSemiring_2276 -> T_Magma_36
d_magma_2420 :: () -> () -> T_CancellativeCommutativeSemiring_2276 -> T_Magma_36
d_magma_2420 ~()
v0 ~()
v1 T_CancellativeCommutativeSemiring_2276
v2 = T_CancellativeCommutativeSemiring_2276 -> T_Magma_36
du_magma_2420 T_CancellativeCommutativeSemiring_2276
v2
du_magma_2420 ::
  T_CancellativeCommutativeSemiring_2276 -> T_Magma_36
du_magma_2420 :: T_CancellativeCommutativeSemiring_2276 -> T_Magma_36
du_magma_2420 T_CancellativeCommutativeSemiring_2276
v0
  = let v1 :: t
v1 = (T_CancellativeCommutativeSemiring_2276
 -> T_CommutativeSemiring_2094)
-> AgdaAny -> t
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2276
-> T_CommutativeSemiring_2094
du_commutativeSemiring_2408 (T_CancellativeCommutativeSemiring_2276 -> AgdaAny
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2276
v0) in
    AgdaAny -> T_Magma_36
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_CommutativeSemiring_2094 -> T_Semiring_1932) -> AgdaAny -> t
forall a b. a -> b
coe T_CommutativeSemiring_2094 -> T_Semiring_1932
du_semiring_2222 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: t
v3 = (T_Semiring_1932 -> T_SemiringWithoutAnnihilatingZero_1786)
-> AgdaAny -> t
forall a b. a -> b
coe T_Semiring_1932 -> T_SemiringWithoutAnnihilatingZero_1786
du_semiringWithoutAnnihilatingZero_2048 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: t
v4 = (T_SemiringWithoutAnnihilatingZero_1786 -> T_Monoid_506)
-> AgdaAny -> t
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_1786 -> T_Monoid_506
du_'42''45'monoid_1916 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_Semigroup_206 -> T_Magma_36) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semigroup_206 -> T_Magma_36
du_magma_254 ((T_Monoid_506 -> T_Semigroup_206) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Monoid_506 -> T_Semigroup_206
du_semigroup_566 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v4))))))
-- Algebra.Bundles.CancellativeCommutativeSemiring._.*-monoid
d_'42''45'monoid_2422 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CancellativeCommutativeSemiring_2276 -> T_Monoid_506
d_'42''45'monoid_2422 :: () -> () -> T_CancellativeCommutativeSemiring_2276 -> T_Monoid_506
d_'42''45'monoid_2422 ~()
v0 ~()
v1 T_CancellativeCommutativeSemiring_2276
v2 = T_CancellativeCommutativeSemiring_2276 -> T_Monoid_506
du_'42''45'monoid_2422 T_CancellativeCommutativeSemiring_2276
v2
du_'42''45'monoid_2422 ::
  T_CancellativeCommutativeSemiring_2276 -> T_Monoid_506
du_'42''45'monoid_2422 :: T_CancellativeCommutativeSemiring_2276 -> T_Monoid_506
du_'42''45'monoid_2422 T_CancellativeCommutativeSemiring_2276
v0
  = let v1 :: t
v1 = (T_CancellativeCommutativeSemiring_2276
 -> T_CommutativeSemiring_2094)
-> AgdaAny -> t
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2276
-> T_CommutativeSemiring_2094
du_commutativeSemiring_2408 (T_CancellativeCommutativeSemiring_2276 -> AgdaAny
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2276
v0) in
    AgdaAny -> T_Monoid_506
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_CommutativeSemiring_2094 -> T_Semiring_1932) -> AgdaAny -> t
forall a b. a -> b
coe T_CommutativeSemiring_2094 -> T_Semiring_1932
du_semiring_2222 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_SemiringWithoutAnnihilatingZero_1786 -> T_Monoid_506)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_SemiringWithoutAnnihilatingZero_1786 -> T_Monoid_506
du_'42''45'monoid_1916
            ((T_Semiring_1932 -> T_SemiringWithoutAnnihilatingZero_1786)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semiring_1932 -> T_SemiringWithoutAnnihilatingZero_1786
du_semiringWithoutAnnihilatingZero_2048 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2))))
-- Algebra.Bundles.CancellativeCommutativeSemiring._.rawMagma
d_rawMagma_2424 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CancellativeCommutativeSemiring_2276 -> T_RawMagma_8
d_rawMagma_2424 :: () -> () -> T_CancellativeCommutativeSemiring_2276 -> T_RawMagma_8
d_rawMagma_2424 ~()
v0 ~()
v1 T_CancellativeCommutativeSemiring_2276
v2 = T_CancellativeCommutativeSemiring_2276 -> T_RawMagma_8
du_rawMagma_2424 T_CancellativeCommutativeSemiring_2276
v2
du_rawMagma_2424 ::
  T_CancellativeCommutativeSemiring_2276 -> T_RawMagma_8
du_rawMagma_2424 :: T_CancellativeCommutativeSemiring_2276 -> T_RawMagma_8
du_rawMagma_2424 T_CancellativeCommutativeSemiring_2276
v0
  = let v1 :: t
v1 = (T_CancellativeCommutativeSemiring_2276
 -> T_CommutativeSemiring_2094)
-> AgdaAny -> t
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2276
-> T_CommutativeSemiring_2094
du_commutativeSemiring_2408 (T_CancellativeCommutativeSemiring_2276 -> AgdaAny
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2276
v0) in
    AgdaAny -> T_RawMagma_8
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_CommutativeSemiring_2094 -> T_Semiring_1932) -> AgdaAny -> t
forall a b. a -> b
coe T_CommutativeSemiring_2094 -> T_Semiring_1932
du_semiring_2222 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: t
v3 = (T_Semiring_1932 -> T_SemiringWithoutAnnihilatingZero_1786)
-> AgdaAny -> t
forall a b. a -> b
coe T_Semiring_1932 -> T_SemiringWithoutAnnihilatingZero_1786
du_semiringWithoutAnnihilatingZero_2048 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: t
v4 = (T_SemiringWithoutAnnihilatingZero_1786 -> T_Monoid_506)
-> AgdaAny -> t
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_1786 -> T_Monoid_506
du_'42''45'monoid_1916 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: t
v5 = (T_Monoid_506 -> T_Semigroup_206) -> AgdaAny -> t
forall a b. a -> b
coe T_Monoid_506 -> T_Semigroup_206
du_semigroup_566 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_Magma_36 -> T_RawMagma_8) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Magma_36 -> T_RawMagma_8
du_rawMagma_80 ((T_Semigroup_206 -> T_Magma_36) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semigroup_206 -> T_Magma_36
du_magma_254 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v5)))))))
-- Algebra.Bundles.CancellativeCommutativeSemiring._.rawMonoid
d_rawMonoid_2426 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CancellativeCommutativeSemiring_2276 -> T_RawMonoid_474
d_rawMonoid_2426 :: ()
-> () -> T_CancellativeCommutativeSemiring_2276 -> T_RawMonoid_474
d_rawMonoid_2426 ~()
v0 ~()
v1 T_CancellativeCommutativeSemiring_2276
v2 = T_CancellativeCommutativeSemiring_2276 -> T_RawMonoid_474
du_rawMonoid_2426 T_CancellativeCommutativeSemiring_2276
v2
du_rawMonoid_2426 ::
  T_CancellativeCommutativeSemiring_2276 -> T_RawMonoid_474
du_rawMonoid_2426 :: T_CancellativeCommutativeSemiring_2276 -> T_RawMonoid_474
du_rawMonoid_2426 T_CancellativeCommutativeSemiring_2276
v0
  = let v1 :: t
v1 = (T_CancellativeCommutativeSemiring_2276
 -> T_CommutativeSemiring_2094)
-> AgdaAny -> t
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2276
-> T_CommutativeSemiring_2094
du_commutativeSemiring_2408 (T_CancellativeCommutativeSemiring_2276 -> AgdaAny
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2276
v0) in
    AgdaAny -> T_RawMonoid_474
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_CommutativeSemiring_2094 -> T_Semiring_1932) -> AgdaAny -> t
forall a b. a -> b
coe T_CommutativeSemiring_2094 -> T_Semiring_1932
du_semiring_2222 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: t
v3 = (T_Semiring_1932 -> T_SemiringWithoutAnnihilatingZero_1786)
-> AgdaAny -> t
forall a b. a -> b
coe T_Semiring_1932 -> T_SemiringWithoutAnnihilatingZero_1786
du_semiringWithoutAnnihilatingZero_2048 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_Monoid_506 -> T_RawMonoid_474) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Monoid_506 -> T_RawMonoid_474
du_rawMonoid_576 ((T_SemiringWithoutAnnihilatingZero_1786 -> T_Monoid_506)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_1786 -> T_Monoid_506
du_'42''45'monoid_1916 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3)))))
-- Algebra.Bundles.CancellativeCommutativeSemiring._.semigroup
d_semigroup_2428 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CancellativeCommutativeSemiring_2276 -> T_Semigroup_206
d_semigroup_2428 :: ()
-> () -> T_CancellativeCommutativeSemiring_2276 -> T_Semigroup_206
d_semigroup_2428 ~()
v0 ~()
v1 T_CancellativeCommutativeSemiring_2276
v2 = T_CancellativeCommutativeSemiring_2276 -> T_Semigroup_206
du_semigroup_2428 T_CancellativeCommutativeSemiring_2276
v2
du_semigroup_2428 ::
  T_CancellativeCommutativeSemiring_2276 -> T_Semigroup_206
du_semigroup_2428 :: T_CancellativeCommutativeSemiring_2276 -> T_Semigroup_206
du_semigroup_2428 T_CancellativeCommutativeSemiring_2276
v0
  = let v1 :: t
v1 = (T_CancellativeCommutativeSemiring_2276
 -> T_CommutativeSemiring_2094)
-> AgdaAny -> t
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2276
-> T_CommutativeSemiring_2094
du_commutativeSemiring_2408 (T_CancellativeCommutativeSemiring_2276 -> AgdaAny
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2276
v0) in
    AgdaAny -> T_Semigroup_206
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_CommutativeSemiring_2094 -> T_Semiring_1932) -> AgdaAny -> t
forall a b. a -> b
coe T_CommutativeSemiring_2094 -> T_Semiring_1932
du_semiring_2222 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: t
v3 = (T_Semiring_1932 -> T_SemiringWithoutAnnihilatingZero_1786)
-> AgdaAny -> t
forall a b. a -> b
coe T_Semiring_1932 -> T_SemiringWithoutAnnihilatingZero_1786
du_semiringWithoutAnnihilatingZero_2048 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_Monoid_506 -> T_Semigroup_206) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Monoid_506 -> T_Semigroup_206
du_semigroup_566 ((T_SemiringWithoutAnnihilatingZero_1786 -> T_Monoid_506)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_1786 -> T_Monoid_506
du_'42''45'monoid_1916 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3)))))
-- Algebra.Bundles.CancellativeCommutativeSemiring._.commutativeMagma
d_commutativeMagma_2430 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CancellativeCommutativeSemiring_2276 -> T_CommutativeMagma_148
d_commutativeMagma_2430 :: ()
-> ()
-> T_CancellativeCommutativeSemiring_2276
-> T_CommutativeMagma_148
d_commutativeMagma_2430 ~()
v0 ~()
v1 T_CancellativeCommutativeSemiring_2276
v2 = T_CancellativeCommutativeSemiring_2276 -> T_CommutativeMagma_148
du_commutativeMagma_2430 T_CancellativeCommutativeSemiring_2276
v2
du_commutativeMagma_2430 ::
  T_CancellativeCommutativeSemiring_2276 -> T_CommutativeMagma_148
du_commutativeMagma_2430 :: T_CancellativeCommutativeSemiring_2276 -> T_CommutativeMagma_148
du_commutativeMagma_2430 T_CancellativeCommutativeSemiring_2276
v0
  = let v1 :: t
v1 = (T_CancellativeCommutativeSemiring_2276
 -> T_CommutativeSemiring_2094)
-> AgdaAny -> t
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2276
-> T_CommutativeSemiring_2094
du_commutativeSemiring_2408 (T_CancellativeCommutativeSemiring_2276 -> AgdaAny
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2276
v0) in
    AgdaAny -> T_CommutativeMagma_148
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_CommutativeSemiring_2094 -> T_Semiring_1932) -> AgdaAny -> t
forall a b. a -> b
coe T_CommutativeSemiring_2094 -> T_Semiring_1932
du_semiring_2222 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: t
v3 = (T_Semiring_1932 -> T_SemiringWithoutAnnihilatingZero_1786)
-> AgdaAny -> t
forall a b. a -> b
coe T_Semiring_1932 -> T_SemiringWithoutAnnihilatingZero_1786
du_semiringWithoutAnnihilatingZero_2048 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: t
v4 = (T_SemiringWithoutAnnihilatingZero_1786 -> T_CommutativeMonoid_582)
-> AgdaAny -> t
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_1786 -> T_CommutativeMonoid_582
du_'43''45'commutativeMonoid_1896 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               ((T_CommutativeSemigroup_332 -> T_CommutativeMagma_148)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_CommutativeSemigroup_332 -> T_CommutativeMagma_148
du_commutativeMagma_396
                  ((T_CommutativeMonoid_582 -> T_CommutativeSemigroup_332)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeMonoid_582 -> T_CommutativeSemigroup_332
du_commutativeSemigroup_664 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v4))))))
-- Algebra.Bundles.CancellativeCommutativeSemiring._.+-commutativeMonoid
d_'43''45'commutativeMonoid_2432 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CancellativeCommutativeSemiring_2276 -> T_CommutativeMonoid_582
d_'43''45'commutativeMonoid_2432 :: ()
-> ()
-> T_CancellativeCommutativeSemiring_2276
-> T_CommutativeMonoid_582
d_'43''45'commutativeMonoid_2432 ~()
v0 ~()
v1 T_CancellativeCommutativeSemiring_2276
v2
  = T_CancellativeCommutativeSemiring_2276 -> T_CommutativeMonoid_582
du_'43''45'commutativeMonoid_2432 T_CancellativeCommutativeSemiring_2276
v2
du_'43''45'commutativeMonoid_2432 ::
  T_CancellativeCommutativeSemiring_2276 -> T_CommutativeMonoid_582
du_'43''45'commutativeMonoid_2432 :: T_CancellativeCommutativeSemiring_2276 -> T_CommutativeMonoid_582
du_'43''45'commutativeMonoid_2432 T_CancellativeCommutativeSemiring_2276
v0
  = let v1 :: t
v1 = (T_CancellativeCommutativeSemiring_2276
 -> T_CommutativeSemiring_2094)
-> AgdaAny -> t
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2276
-> T_CommutativeSemiring_2094
du_commutativeSemiring_2408 (T_CancellativeCommutativeSemiring_2276 -> AgdaAny
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2276
v0) in
    AgdaAny -> T_CommutativeMonoid_582
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_CommutativeSemiring_2094 -> T_Semiring_1932) -> AgdaAny -> t
forall a b. a -> b
coe T_CommutativeSemiring_2094 -> T_Semiring_1932
du_semiring_2222 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_SemiringWithoutAnnihilatingZero_1786 -> T_CommutativeMonoid_582)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_SemiringWithoutAnnihilatingZero_1786 -> T_CommutativeMonoid_582
du_'43''45'commutativeMonoid_1896
            ((T_Semiring_1932 -> T_SemiringWithoutAnnihilatingZero_1786)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semiring_1932 -> T_SemiringWithoutAnnihilatingZero_1786
du_semiringWithoutAnnihilatingZero_2048 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2))))
-- Algebra.Bundles.CancellativeCommutativeSemiring._.commutativeSemigroup
d_commutativeSemigroup_2434 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CancellativeCommutativeSemiring_2276 ->
  T_CommutativeSemigroup_332
d_commutativeSemigroup_2434 :: ()
-> ()
-> T_CancellativeCommutativeSemiring_2276
-> T_CommutativeSemigroup_332
d_commutativeSemigroup_2434 ~()
v0 ~()
v1 T_CancellativeCommutativeSemiring_2276
v2
  = T_CancellativeCommutativeSemiring_2276
-> T_CommutativeSemigroup_332
du_commutativeSemigroup_2434 T_CancellativeCommutativeSemiring_2276
v2
du_commutativeSemigroup_2434 ::
  T_CancellativeCommutativeSemiring_2276 ->
  T_CommutativeSemigroup_332
du_commutativeSemigroup_2434 :: T_CancellativeCommutativeSemiring_2276
-> T_CommutativeSemigroup_332
du_commutativeSemigroup_2434 T_CancellativeCommutativeSemiring_2276
v0
  = let v1 :: t
v1 = (T_CancellativeCommutativeSemiring_2276
 -> T_CommutativeSemiring_2094)
-> AgdaAny -> t
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2276
-> T_CommutativeSemiring_2094
du_commutativeSemiring_2408 (T_CancellativeCommutativeSemiring_2276 -> AgdaAny
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2276
v0) in
    AgdaAny -> T_CommutativeSemigroup_332
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_CommutativeSemiring_2094 -> T_Semiring_1932) -> AgdaAny -> t
forall a b. a -> b
coe T_CommutativeSemiring_2094 -> T_Semiring_1932
du_semiring_2222 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: t
v3 = (T_Semiring_1932 -> T_SemiringWithoutAnnihilatingZero_1786)
-> AgdaAny -> t
forall a b. a -> b
coe T_Semiring_1932 -> T_SemiringWithoutAnnihilatingZero_1786
du_semiringWithoutAnnihilatingZero_2048 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_CommutativeMonoid_582 -> T_CommutativeSemigroup_332)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_CommutativeMonoid_582 -> T_CommutativeSemigroup_332
du_commutativeSemigroup_664
               ((T_SemiringWithoutAnnihilatingZero_1786 -> T_CommutativeMonoid_582)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_1786 -> T_CommutativeMonoid_582
du_'43''45'commutativeMonoid_1896 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3)))))
-- Algebra.Bundles.CancellativeCommutativeSemiring._.magma
d_magma_2436 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CancellativeCommutativeSemiring_2276 -> T_Magma_36
d_magma_2436 :: () -> () -> T_CancellativeCommutativeSemiring_2276 -> T_Magma_36
d_magma_2436 ~()
v0 ~()
v1 T_CancellativeCommutativeSemiring_2276
v2 = T_CancellativeCommutativeSemiring_2276 -> T_Magma_36
du_magma_2436 T_CancellativeCommutativeSemiring_2276
v2
du_magma_2436 ::
  T_CancellativeCommutativeSemiring_2276 -> T_Magma_36
du_magma_2436 :: T_CancellativeCommutativeSemiring_2276 -> T_Magma_36
du_magma_2436 T_CancellativeCommutativeSemiring_2276
v0
  = let v1 :: t
v1 = (T_CancellativeCommutativeSemiring_2276
 -> T_CommutativeSemiring_2094)
-> AgdaAny -> t
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2276
-> T_CommutativeSemiring_2094
du_commutativeSemiring_2408 (T_CancellativeCommutativeSemiring_2276 -> AgdaAny
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2276
v0) in
    AgdaAny -> T_Magma_36
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_CommutativeSemiring_2094 -> T_Semiring_1932) -> AgdaAny -> t
forall a b. a -> b
coe T_CommutativeSemiring_2094 -> T_Semiring_1932
du_semiring_2222 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: t
v3 = (T_Semiring_1932 -> T_SemiringWithoutAnnihilatingZero_1786)
-> AgdaAny -> t
forall a b. a -> b
coe T_Semiring_1932 -> T_SemiringWithoutAnnihilatingZero_1786
du_semiringWithoutAnnihilatingZero_2048 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: t
v4 = (T_SemiringWithoutAnnihilatingZero_1786 -> T_CommutativeMonoid_582)
-> AgdaAny -> t
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_1786 -> T_CommutativeMonoid_582
du_'43''45'commutativeMonoid_1896 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: t
v5 = (T_CommutativeMonoid_582 -> T_Monoid_506) -> AgdaAny -> t
forall a b. a -> b
coe T_CommutativeMonoid_582 -> T_Monoid_506
du_monoid_650 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_Semigroup_206 -> T_Magma_36) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semigroup_206 -> T_Magma_36
du_magma_254 ((T_Monoid_506 -> T_Semigroup_206) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Monoid_506 -> T_Semigroup_206
du_semigroup_566 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v5)))))))
-- Algebra.Bundles.CancellativeCommutativeSemiring._.monoid
d_monoid_2438 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CancellativeCommutativeSemiring_2276 -> T_Monoid_506
d_monoid_2438 :: () -> () -> T_CancellativeCommutativeSemiring_2276 -> T_Monoid_506
d_monoid_2438 ~()
v0 ~()
v1 T_CancellativeCommutativeSemiring_2276
v2 = T_CancellativeCommutativeSemiring_2276 -> T_Monoid_506
du_monoid_2438 T_CancellativeCommutativeSemiring_2276
v2
du_monoid_2438 ::
  T_CancellativeCommutativeSemiring_2276 -> T_Monoid_506
du_monoid_2438 :: T_CancellativeCommutativeSemiring_2276 -> T_Monoid_506
du_monoid_2438 T_CancellativeCommutativeSemiring_2276
v0
  = let v1 :: t
v1 = (T_CancellativeCommutativeSemiring_2276
 -> T_CommutativeSemiring_2094)
-> AgdaAny -> t
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2276
-> T_CommutativeSemiring_2094
du_commutativeSemiring_2408 (T_CancellativeCommutativeSemiring_2276 -> AgdaAny
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2276
v0) in
    AgdaAny -> T_Monoid_506
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_CommutativeSemiring_2094 -> T_Semiring_1932) -> AgdaAny -> t
forall a b. a -> b
coe T_CommutativeSemiring_2094 -> T_Semiring_1932
du_semiring_2222 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: t
v3 = (T_Semiring_1932 -> T_SemiringWithoutAnnihilatingZero_1786)
-> AgdaAny -> t
forall a b. a -> b
coe T_Semiring_1932 -> T_SemiringWithoutAnnihilatingZero_1786
du_semiringWithoutAnnihilatingZero_2048 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_CommutativeMonoid_582 -> T_Monoid_506) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_CommutativeMonoid_582 -> T_Monoid_506
du_monoid_650 ((T_SemiringWithoutAnnihilatingZero_1786 -> T_CommutativeMonoid_582)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_1786 -> T_CommutativeMonoid_582
du_'43''45'commutativeMonoid_1896 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3)))))
-- Algebra.Bundles.CancellativeCommutativeSemiring._.rawMagma
d_rawMagma_2440 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CancellativeCommutativeSemiring_2276 -> T_RawMagma_8
d_rawMagma_2440 :: () -> () -> T_CancellativeCommutativeSemiring_2276 -> T_RawMagma_8
d_rawMagma_2440 ~()
v0 ~()
v1 T_CancellativeCommutativeSemiring_2276
v2 = T_CancellativeCommutativeSemiring_2276 -> T_RawMagma_8
du_rawMagma_2440 T_CancellativeCommutativeSemiring_2276
v2
du_rawMagma_2440 ::
  T_CancellativeCommutativeSemiring_2276 -> T_RawMagma_8
du_rawMagma_2440 :: T_CancellativeCommutativeSemiring_2276 -> T_RawMagma_8
du_rawMagma_2440 T_CancellativeCommutativeSemiring_2276
v0
  = let v1 :: t
v1 = (T_CancellativeCommutativeSemiring_2276
 -> T_CommutativeSemiring_2094)
-> AgdaAny -> t
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2276
-> T_CommutativeSemiring_2094
du_commutativeSemiring_2408 (T_CancellativeCommutativeSemiring_2276 -> AgdaAny
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2276
v0) in
    AgdaAny -> T_RawMagma_8
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_CommutativeSemiring_2094 -> T_Semiring_1932) -> AgdaAny -> t
forall a b. a -> b
coe T_CommutativeSemiring_2094 -> T_Semiring_1932
du_semiring_2222 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: t
v3 = (T_Semiring_1932 -> T_SemiringWithoutAnnihilatingZero_1786)
-> AgdaAny -> t
forall a b. a -> b
coe T_Semiring_1932 -> T_SemiringWithoutAnnihilatingZero_1786
du_semiringWithoutAnnihilatingZero_2048 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: t
v4 = (T_SemiringWithoutAnnihilatingZero_1786 -> T_CommutativeMonoid_582)
-> AgdaAny -> t
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_1786 -> T_CommutativeMonoid_582
du_'43''45'commutativeMonoid_1896 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: t
v5 = (T_CommutativeMonoid_582 -> T_Monoid_506) -> AgdaAny -> t
forall a b. a -> b
coe T_CommutativeMonoid_582 -> T_Monoid_506
du_monoid_650 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (let v6 :: t
v6 = (T_Monoid_506 -> T_Semigroup_206) -> AgdaAny -> t
forall a b. a -> b
coe T_Monoid_506 -> T_Semigroup_206
du_semigroup_566 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v5) in
                   AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_Magma_36 -> T_RawMagma_8) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Magma_36 -> T_RawMagma_8
du_rawMagma_80 ((T_Semigroup_206 -> T_Magma_36) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semigroup_206 -> T_Magma_36
du_magma_254 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v6))))))))
-- Algebra.Bundles.CancellativeCommutativeSemiring._.rawMonoid
d_rawMonoid_2442 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CancellativeCommutativeSemiring_2276 -> T_RawMonoid_474
d_rawMonoid_2442 :: ()
-> () -> T_CancellativeCommutativeSemiring_2276 -> T_RawMonoid_474
d_rawMonoid_2442 ~()
v0 ~()
v1 T_CancellativeCommutativeSemiring_2276
v2 = T_CancellativeCommutativeSemiring_2276 -> T_RawMonoid_474
du_rawMonoid_2442 T_CancellativeCommutativeSemiring_2276
v2
du_rawMonoid_2442 ::
  T_CancellativeCommutativeSemiring_2276 -> T_RawMonoid_474
du_rawMonoid_2442 :: T_CancellativeCommutativeSemiring_2276 -> T_RawMonoid_474
du_rawMonoid_2442 T_CancellativeCommutativeSemiring_2276
v0
  = let v1 :: t
v1 = (T_CancellativeCommutativeSemiring_2276
 -> T_CommutativeSemiring_2094)
-> AgdaAny -> t
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2276
-> T_CommutativeSemiring_2094
du_commutativeSemiring_2408 (T_CancellativeCommutativeSemiring_2276 -> AgdaAny
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2276
v0) in
    AgdaAny -> T_RawMonoid_474
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_CommutativeSemiring_2094 -> T_Semiring_1932) -> AgdaAny -> t
forall a b. a -> b
coe T_CommutativeSemiring_2094 -> T_Semiring_1932
du_semiring_2222 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: t
v3 = (T_Semiring_1932 -> T_SemiringWithoutAnnihilatingZero_1786)
-> AgdaAny -> t
forall a b. a -> b
coe T_Semiring_1932 -> T_SemiringWithoutAnnihilatingZero_1786
du_semiringWithoutAnnihilatingZero_2048 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: t
v4 = (T_SemiringWithoutAnnihilatingZero_1786 -> T_CommutativeMonoid_582)
-> AgdaAny -> t
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_1786 -> T_CommutativeMonoid_582
du_'43''45'commutativeMonoid_1896 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_Monoid_506 -> T_RawMonoid_474) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Monoid_506 -> T_RawMonoid_474
du_rawMonoid_576 ((T_CommutativeMonoid_582 -> T_Monoid_506) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeMonoid_582 -> T_Monoid_506
du_monoid_650 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v4))))))
-- Algebra.Bundles.CancellativeCommutativeSemiring._.semigroup
d_semigroup_2444 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CancellativeCommutativeSemiring_2276 -> T_Semigroup_206
d_semigroup_2444 :: ()
-> () -> T_CancellativeCommutativeSemiring_2276 -> T_Semigroup_206
d_semigroup_2444 ~()
v0 ~()
v1 T_CancellativeCommutativeSemiring_2276
v2 = T_CancellativeCommutativeSemiring_2276 -> T_Semigroup_206
du_semigroup_2444 T_CancellativeCommutativeSemiring_2276
v2
du_semigroup_2444 ::
  T_CancellativeCommutativeSemiring_2276 -> T_Semigroup_206
du_semigroup_2444 :: T_CancellativeCommutativeSemiring_2276 -> T_Semigroup_206
du_semigroup_2444 T_CancellativeCommutativeSemiring_2276
v0
  = let v1 :: t
v1 = (T_CancellativeCommutativeSemiring_2276
 -> T_CommutativeSemiring_2094)
-> AgdaAny -> t
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2276
-> T_CommutativeSemiring_2094
du_commutativeSemiring_2408 (T_CancellativeCommutativeSemiring_2276 -> AgdaAny
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2276
v0) in
    AgdaAny -> T_Semigroup_206
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_CommutativeSemiring_2094 -> T_Semiring_1932) -> AgdaAny -> t
forall a b. a -> b
coe T_CommutativeSemiring_2094 -> T_Semiring_1932
du_semiring_2222 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: t
v3 = (T_Semiring_1932 -> T_SemiringWithoutAnnihilatingZero_1786)
-> AgdaAny -> t
forall a b. a -> b
coe T_Semiring_1932 -> T_SemiringWithoutAnnihilatingZero_1786
du_semiringWithoutAnnihilatingZero_2048 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: t
v4 = (T_SemiringWithoutAnnihilatingZero_1786 -> T_CommutativeMonoid_582)
-> AgdaAny -> t
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_1786 -> T_CommutativeMonoid_582
du_'43''45'commutativeMonoid_1896 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_Monoid_506 -> T_Semigroup_206) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Monoid_506 -> T_Semigroup_206
du_semigroup_566 ((T_CommutativeMonoid_582 -> T_Monoid_506) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeMonoid_582 -> T_Monoid_506
du_monoid_650 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v4))))))
-- Algebra.Bundles.CancellativeCommutativeSemiring._.nearSemiring
d_nearSemiring_2446 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CancellativeCommutativeSemiring_2276 -> T_NearSemiring_1354
d_nearSemiring_2446 :: ()
-> ()
-> T_CancellativeCommutativeSemiring_2276
-> T_NearSemiring_1354
d_nearSemiring_2446 ~()
v0 ~()
v1 T_CancellativeCommutativeSemiring_2276
v2 = T_CancellativeCommutativeSemiring_2276 -> T_NearSemiring_1354
du_nearSemiring_2446 T_CancellativeCommutativeSemiring_2276
v2
du_nearSemiring_2446 ::
  T_CancellativeCommutativeSemiring_2276 -> T_NearSemiring_1354
du_nearSemiring_2446 :: T_CancellativeCommutativeSemiring_2276 -> T_NearSemiring_1354
du_nearSemiring_2446 T_CancellativeCommutativeSemiring_2276
v0
  = let v1 :: t
v1 = (T_CancellativeCommutativeSemiring_2276
 -> T_CommutativeSemiring_2094)
-> AgdaAny -> t
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2276
-> T_CommutativeSemiring_2094
du_commutativeSemiring_2408 (T_CancellativeCommutativeSemiring_2276 -> AgdaAny
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2276
v0) in
    AgdaAny -> T_NearSemiring_1354
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_CommutativeSemiring_2094 -> T_Semiring_1932) -> AgdaAny -> t
forall a b. a -> b
coe T_CommutativeSemiring_2094 -> T_Semiring_1932
du_semiring_2222 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_SemiringWithoutOne_1464 -> T_NearSemiring_1354)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_SemiringWithoutOne_1464 -> T_NearSemiring_1354
du_nearSemiring_1562 ((T_Semiring_1932 -> T_SemiringWithoutOne_1464)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semiring_1932 -> T_SemiringWithoutOne_1464
du_semiringWithoutOne_2084 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2))))
-- Algebra.Bundles.CancellativeCommutativeSemiring._.rawSemiring
d_rawSemiring_2448 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CancellativeCommutativeSemiring_2276 -> T_RawSemiring_1738
d_rawSemiring_2448 :: ()
-> ()
-> T_CancellativeCommutativeSemiring_2276
-> T_RawSemiring_1738
d_rawSemiring_2448 ~()
v0 ~()
v1 T_CancellativeCommutativeSemiring_2276
v2 = T_CancellativeCommutativeSemiring_2276 -> T_RawSemiring_1738
du_rawSemiring_2448 T_CancellativeCommutativeSemiring_2276
v2
du_rawSemiring_2448 ::
  T_CancellativeCommutativeSemiring_2276 -> T_RawSemiring_1738
du_rawSemiring_2448 :: T_CancellativeCommutativeSemiring_2276 -> T_RawSemiring_1738
du_rawSemiring_2448 T_CancellativeCommutativeSemiring_2276
v0
  = let v1 :: t
v1 = (T_CancellativeCommutativeSemiring_2276
 -> T_CommutativeSemiring_2094)
-> AgdaAny -> t
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2276
-> T_CommutativeSemiring_2094
du_commutativeSemiring_2408 (T_CancellativeCommutativeSemiring_2276 -> AgdaAny
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2276
v0) in
    AgdaAny -> T_RawSemiring_1738
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_CommutativeSemiring_2094 -> T_Semiring_1932) -> AgdaAny -> t
forall a b. a -> b
coe T_CommutativeSemiring_2094 -> T_Semiring_1932
du_semiring_2222 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_SemiringWithoutAnnihilatingZero_1786 -> T_RawSemiring_1738)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_SemiringWithoutAnnihilatingZero_1786 -> T_RawSemiring_1738
du_rawSemiring_1890
            ((T_Semiring_1932 -> T_SemiringWithoutAnnihilatingZero_1786)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semiring_1932 -> T_SemiringWithoutAnnihilatingZero_1786
du_semiringWithoutAnnihilatingZero_2048 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2))))
-- Algebra.Bundles.CancellativeCommutativeSemiring._.semiring
d_semiring_2450 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CancellativeCommutativeSemiring_2276 -> T_Semiring_1932
d_semiring_2450 :: ()
-> () -> T_CancellativeCommutativeSemiring_2276 -> T_Semiring_1932
d_semiring_2450 ~()
v0 ~()
v1 T_CancellativeCommutativeSemiring_2276
v2 = T_CancellativeCommutativeSemiring_2276 -> T_Semiring_1932
du_semiring_2450 T_CancellativeCommutativeSemiring_2276
v2
du_semiring_2450 ::
  T_CancellativeCommutativeSemiring_2276 -> T_Semiring_1932
du_semiring_2450 :: T_CancellativeCommutativeSemiring_2276 -> T_Semiring_1932
du_semiring_2450 T_CancellativeCommutativeSemiring_2276
v0
  = (T_CommutativeSemiring_2094 -> T_Semiring_1932)
-> AgdaAny -> T_Semiring_1932
forall a b. a -> b
coe T_CommutativeSemiring_2094 -> T_Semiring_1932
du_semiring_2222 ((T_CancellativeCommutativeSemiring_2276
 -> T_CommutativeSemiring_2094)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2276
-> T_CommutativeSemiring_2094
du_commutativeSemiring_2408 (T_CancellativeCommutativeSemiring_2276 -> AgdaAny
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2276
v0))
-- Algebra.Bundles.CancellativeCommutativeSemiring._.semiringWithoutAnnihilatingZero
d_semiringWithoutAnnihilatingZero_2452 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CancellativeCommutativeSemiring_2276 ->
  T_SemiringWithoutAnnihilatingZero_1786
d_semiringWithoutAnnihilatingZero_2452 :: ()
-> ()
-> T_CancellativeCommutativeSemiring_2276
-> T_SemiringWithoutAnnihilatingZero_1786
d_semiringWithoutAnnihilatingZero_2452 ~()
v0 ~()
v1 T_CancellativeCommutativeSemiring_2276
v2
  = T_CancellativeCommutativeSemiring_2276
-> T_SemiringWithoutAnnihilatingZero_1786
du_semiringWithoutAnnihilatingZero_2452 T_CancellativeCommutativeSemiring_2276
v2
du_semiringWithoutAnnihilatingZero_2452 ::
  T_CancellativeCommutativeSemiring_2276 ->
  T_SemiringWithoutAnnihilatingZero_1786
du_semiringWithoutAnnihilatingZero_2452 :: T_CancellativeCommutativeSemiring_2276
-> T_SemiringWithoutAnnihilatingZero_1786
du_semiringWithoutAnnihilatingZero_2452 T_CancellativeCommutativeSemiring_2276
v0
  = let v1 :: t
v1 = (T_CancellativeCommutativeSemiring_2276
 -> T_CommutativeSemiring_2094)
-> AgdaAny -> t
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2276
-> T_CommutativeSemiring_2094
du_commutativeSemiring_2408 (T_CancellativeCommutativeSemiring_2276 -> AgdaAny
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2276
v0) in
    AgdaAny -> T_SemiringWithoutAnnihilatingZero_1786
forall a b. a -> b
coe
      ((T_Semiring_1932 -> T_SemiringWithoutAnnihilatingZero_1786)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_Semiring_1932 -> T_SemiringWithoutAnnihilatingZero_1786
du_semiringWithoutAnnihilatingZero_2048
         ((T_CommutativeSemiring_2094 -> T_Semiring_1932)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemiring_2094 -> T_Semiring_1932
du_semiring_2222 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1)))
-- Algebra.Bundles.CancellativeCommutativeSemiring._.semiringWithoutOne
d_semiringWithoutOne_2454 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CancellativeCommutativeSemiring_2276 -> T_SemiringWithoutOne_1464
d_semiringWithoutOne_2454 :: ()
-> ()
-> T_CancellativeCommutativeSemiring_2276
-> T_SemiringWithoutOne_1464
d_semiringWithoutOne_2454 ~()
v0 ~()
v1 T_CancellativeCommutativeSemiring_2276
v2
  = T_CancellativeCommutativeSemiring_2276 -> T_SemiringWithoutOne_1464
du_semiringWithoutOne_2454 T_CancellativeCommutativeSemiring_2276
v2
du_semiringWithoutOne_2454 ::
  T_CancellativeCommutativeSemiring_2276 -> T_SemiringWithoutOne_1464
du_semiringWithoutOne_2454 :: T_CancellativeCommutativeSemiring_2276 -> T_SemiringWithoutOne_1464
du_semiringWithoutOne_2454 T_CancellativeCommutativeSemiring_2276
v0
  = let v1 :: t
v1 = (T_CancellativeCommutativeSemiring_2276
 -> T_CommutativeSemiring_2094)
-> AgdaAny -> t
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2276
-> T_CommutativeSemiring_2094
du_commutativeSemiring_2408 (T_CancellativeCommutativeSemiring_2276 -> AgdaAny
forall a b. a -> b
coe T_CancellativeCommutativeSemiring_2276
v0) in
    AgdaAny -> T_SemiringWithoutOne_1464
forall a b. a -> b
coe
      ((T_Semiring_1932 -> T_SemiringWithoutOne_1464)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semiring_1932 -> T_SemiringWithoutOne_1464
du_semiringWithoutOne_2084 ((T_CommutativeSemiring_2094 -> T_Semiring_1932)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemiring_2094 -> T_Semiring_1932
du_semiring_2222 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1)))
-- Algebra.Bundles.RawRing
d_RawRing_2460 :: p -> p -> ()
d_RawRing_2460 p
a0 p
a1 = ()
data T_RawRing_2460
  = C_RawRing'46'constructor_42493 (AgdaAny -> AgdaAny -> AgdaAny)
                                   (AgdaAny -> AgdaAny -> AgdaAny) (AgdaAny -> AgdaAny) AgdaAny
                                   AgdaAny
-- Algebra.Bundles.RawRing.Carrier
d_Carrier_2480 :: T_RawRing_2460 -> ()
d_Carrier_2480 :: T_RawRing_2460 -> ()
d_Carrier_2480 = T_RawRing_2460 -> ()
forall a. a
erased
-- Algebra.Bundles.RawRing._≈_
d__'8776'__2482 :: T_RawRing_2460 -> AgdaAny -> AgdaAny -> ()
d__'8776'__2482 :: T_RawRing_2460 -> AgdaAny -> AgdaAny -> ()
d__'8776'__2482 = T_RawRing_2460 -> AgdaAny -> AgdaAny -> ()
forall a. a
erased
-- Algebra.Bundles.RawRing._+_
d__'43'__2484 :: T_RawRing_2460 -> AgdaAny -> AgdaAny -> AgdaAny
d__'43'__2484 :: T_RawRing_2460 -> AgdaAny -> AgdaAny -> AgdaAny
d__'43'__2484 T_RawRing_2460
v0
  = case T_RawRing_2460 -> T_RawRing_2460
forall a b. a -> b
coe T_RawRing_2460
v0 of
      C_RawRing'46'constructor_42493 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny
v5 AgdaAny
v6 AgdaAny
v7 -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v3
      T_RawRing_2460
_ -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.RawRing._*_
d__'42'__2486 :: T_RawRing_2460 -> AgdaAny -> AgdaAny -> AgdaAny
d__'42'__2486 :: T_RawRing_2460 -> AgdaAny -> AgdaAny -> AgdaAny
d__'42'__2486 T_RawRing_2460
v0
  = case T_RawRing_2460 -> T_RawRing_2460
forall a b. a -> b
coe T_RawRing_2460
v0 of
      C_RawRing'46'constructor_42493 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny
v5 AgdaAny
v6 AgdaAny
v7 -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v4
      T_RawRing_2460
_ -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.RawRing.-_
d_'45'__2488 :: T_RawRing_2460 -> AgdaAny -> AgdaAny
d_'45'__2488 :: T_RawRing_2460 -> AgdaAny -> AgdaAny
d_'45'__2488 T_RawRing_2460
v0
  = case T_RawRing_2460 -> T_RawRing_2460
forall a b. a -> b
coe T_RawRing_2460
v0 of
      C_RawRing'46'constructor_42493 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny
v5 AgdaAny
v6 AgdaAny
v7 -> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v5
      T_RawRing_2460
_ -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.RawRing.0#
d_0'35'_2490 :: T_RawRing_2460 -> AgdaAny
d_0'35'_2490 :: T_RawRing_2460 -> AgdaAny
d_0'35'_2490 T_RawRing_2460
v0
  = case T_RawRing_2460 -> T_RawRing_2460
forall a b. a -> b
coe T_RawRing_2460
v0 of
      C_RawRing'46'constructor_42493 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny
v5 AgdaAny
v6 AgdaAny
v7 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v6
      T_RawRing_2460
_ -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.RawRing.1#
d_1'35'_2492 :: T_RawRing_2460 -> AgdaAny
d_1'35'_2492 :: T_RawRing_2460 -> AgdaAny
d_1'35'_2492 T_RawRing_2460
v0
  = case T_RawRing_2460 -> T_RawRing_2460
forall a b. a -> b
coe T_RawRing_2460
v0 of
      C_RawRing'46'constructor_42493 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny
v5 AgdaAny
v6 AgdaAny
v7 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v7
      T_RawRing_2460
_ -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.RawRing.rawSemiring
d_rawSemiring_2494 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_RawRing_2460 -> T_RawSemiring_1738
d_rawSemiring_2494 :: () -> () -> T_RawRing_2460 -> T_RawSemiring_1738
d_rawSemiring_2494 ~()
v0 ~()
v1 T_RawRing_2460
v2 = T_RawRing_2460 -> T_RawSemiring_1738
du_rawSemiring_2494 T_RawRing_2460
v2
du_rawSemiring_2494 :: T_RawRing_2460 -> T_RawSemiring_1738
du_rawSemiring_2494 :: T_RawRing_2460 -> T_RawSemiring_1738
du_rawSemiring_2494 T_RawRing_2460
v0
  = ((AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> AgdaAny
 -> T_RawSemiring_1738)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_RawSemiring_1738
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_RawSemiring_1738
C_RawSemiring'46'constructor_30035 (T_RawRing_2460 -> AgdaAny -> AgdaAny -> AgdaAny
d__'43'__2484 (T_RawRing_2460 -> T_RawRing_2460
forall a b. a -> b
coe T_RawRing_2460
v0))
      (T_RawRing_2460 -> AgdaAny -> AgdaAny -> AgdaAny
d__'42'__2486 (T_RawRing_2460 -> T_RawRing_2460
forall a b. a -> b
coe T_RawRing_2460
v0)) (T_RawRing_2460 -> AgdaAny
d_0'35'_2490 (T_RawRing_2460 -> T_RawRing_2460
forall a b. a -> b
coe T_RawRing_2460
v0))
      (T_RawRing_2460 -> AgdaAny
d_1'35'_2492 (T_RawRing_2460 -> T_RawRing_2460
forall a b. a -> b
coe T_RawRing_2460
v0))
-- Algebra.Bundles.RawRing._._≉_
d__'8777'__2498 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_RawRing_2460 -> AgdaAny -> AgdaAny -> ()
d__'8777'__2498 :: () -> () -> T_RawRing_2460 -> AgdaAny -> AgdaAny -> ()
d__'8777'__2498 = () -> () -> T_RawRing_2460 -> AgdaAny -> AgdaAny -> ()
forall a. a
erased
-- Algebra.Bundles.RawRing._.*-rawMagma
d_'42''45'rawMagma_2500 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_RawRing_2460 -> T_RawMagma_8
d_'42''45'rawMagma_2500 :: () -> () -> T_RawRing_2460 -> T_RawMagma_8
d_'42''45'rawMagma_2500 ~()
v0 ~()
v1 T_RawRing_2460
v2 = T_RawRing_2460 -> T_RawMagma_8
du_'42''45'rawMagma_2500 T_RawRing_2460
v2
du_'42''45'rawMagma_2500 :: T_RawRing_2460 -> T_RawMagma_8
du_'42''45'rawMagma_2500 :: T_RawRing_2460 -> T_RawMagma_8
du_'42''45'rawMagma_2500 T_RawRing_2460
v0
  = let v1 :: t
v1 = (T_RawRing_2460 -> T_RawSemiring_1738) -> AgdaAny -> t
forall a b. a -> b
coe T_RawRing_2460 -> T_RawSemiring_1738
du_rawSemiring_2494 (T_RawRing_2460 -> AgdaAny
forall a b. a -> b
coe T_RawRing_2460
v0) in
    AgdaAny -> T_RawMagma_8
forall a b. a -> b
coe
      ((T_RawNearSemiring_1314 -> T_RawMagma_8) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_RawNearSemiring_1314 -> T_RawMagma_8
du_'42''45'rawMagma_1348 ((T_RawSemiring_1738 -> T_RawNearSemiring_1314)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_RawSemiring_1738 -> T_RawNearSemiring_1314
du_rawNearSemiring_1768 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1)))
-- Algebra.Bundles.RawRing._.*-rawMonoid
d_'42''45'rawMonoid_2502 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_RawRing_2460 -> T_RawMonoid_474
d_'42''45'rawMonoid_2502 :: () -> () -> T_RawRing_2460 -> T_RawMonoid_474
d_'42''45'rawMonoid_2502 ~()
v0 ~()
v1 T_RawRing_2460
v2 = T_RawRing_2460 -> T_RawMonoid_474
du_'42''45'rawMonoid_2502 T_RawRing_2460
v2
du_'42''45'rawMonoid_2502 :: T_RawRing_2460 -> T_RawMonoid_474
du_'42''45'rawMonoid_2502 :: T_RawRing_2460 -> T_RawMonoid_474
du_'42''45'rawMonoid_2502 T_RawRing_2460
v0
  = (T_RawSemiring_1738 -> T_RawMonoid_474)
-> AgdaAny -> T_RawMonoid_474
forall a b. a -> b
coe T_RawSemiring_1738 -> T_RawMonoid_474
du_'42''45'rawMonoid_1780 ((T_RawRing_2460 -> T_RawSemiring_1738) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_RawRing_2460 -> T_RawSemiring_1738
du_rawSemiring_2494 (T_RawRing_2460 -> AgdaAny
forall a b. a -> b
coe T_RawRing_2460
v0))
-- Algebra.Bundles.RawRing._.rawMagma
d_rawMagma_2504 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_RawRing_2460 -> T_RawMagma_8
d_rawMagma_2504 :: () -> () -> T_RawRing_2460 -> T_RawMagma_8
d_rawMagma_2504 ~()
v0 ~()
v1 T_RawRing_2460
v2 = T_RawRing_2460 -> T_RawMagma_8
du_rawMagma_2504 T_RawRing_2460
v2
du_rawMagma_2504 :: T_RawRing_2460 -> T_RawMagma_8
du_rawMagma_2504 :: T_RawRing_2460 -> T_RawMagma_8
du_rawMagma_2504 T_RawRing_2460
v0
  = let v1 :: t
v1 = (T_RawRing_2460 -> T_RawSemiring_1738) -> AgdaAny -> t
forall a b. a -> b
coe T_RawRing_2460 -> T_RawSemiring_1738
du_rawSemiring_2494 (T_RawRing_2460 -> AgdaAny
forall a b. a -> b
coe T_RawRing_2460
v0) in
    AgdaAny -> T_RawMagma_8
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_RawSemiring_1738 -> T_RawNearSemiring_1314) -> AgdaAny -> t
forall a b. a -> b
coe T_RawSemiring_1738 -> T_RawNearSemiring_1314
du_rawNearSemiring_1768 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_RawMonoid_474 -> T_RawMagma_8) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_RawMonoid_474 -> T_RawMagma_8
du_rawMagma_496 ((T_RawNearSemiring_1314 -> T_RawMonoid_474) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_RawNearSemiring_1314 -> T_RawMonoid_474
du_'43''45'rawMonoid_1340 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2))))
-- Algebra.Bundles.RawRing._.+-rawMonoid
d_'43''45'rawMonoid_2506 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_RawRing_2460 -> T_RawMonoid_474
d_'43''45'rawMonoid_2506 :: () -> () -> T_RawRing_2460 -> T_RawMonoid_474
d_'43''45'rawMonoid_2506 ~()
v0 ~()
v1 T_RawRing_2460
v2 = T_RawRing_2460 -> T_RawMonoid_474
du_'43''45'rawMonoid_2506 T_RawRing_2460
v2
du_'43''45'rawMonoid_2506 :: T_RawRing_2460 -> T_RawMonoid_474
du_'43''45'rawMonoid_2506 :: T_RawRing_2460 -> T_RawMonoid_474
du_'43''45'rawMonoid_2506 T_RawRing_2460
v0
  = let v1 :: t
v1 = (T_RawRing_2460 -> T_RawSemiring_1738) -> AgdaAny -> t
forall a b. a -> b
coe T_RawRing_2460 -> T_RawSemiring_1738
du_rawSemiring_2494 (T_RawRing_2460 -> AgdaAny
forall a b. a -> b
coe T_RawRing_2460
v0) in
    AgdaAny -> T_RawMonoid_474
forall a b. a -> b
coe
      ((T_RawNearSemiring_1314 -> T_RawMonoid_474) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_RawNearSemiring_1314 -> T_RawMonoid_474
du_'43''45'rawMonoid_1340 ((T_RawSemiring_1738 -> T_RawNearSemiring_1314)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_RawSemiring_1738 -> T_RawNearSemiring_1314
du_rawNearSemiring_1768 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1)))
-- Algebra.Bundles.RawRing.+-rawGroup
d_'43''45'rawGroup_2508 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_RawRing_2460 -> T_RawGroup_852
d_'43''45'rawGroup_2508 :: () -> () -> T_RawRing_2460 -> T_RawGroup_852
d_'43''45'rawGroup_2508 ~()
v0 ~()
v1 T_RawRing_2460
v2 = T_RawRing_2460 -> T_RawGroup_852
du_'43''45'rawGroup_2508 T_RawRing_2460
v2
du_'43''45'rawGroup_2508 :: T_RawRing_2460 -> T_RawGroup_852
du_'43''45'rawGroup_2508 :: T_RawRing_2460 -> T_RawGroup_852
du_'43''45'rawGroup_2508 T_RawRing_2460
v0
  = ((AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny -> (AgdaAny -> AgdaAny) -> T_RawGroup_852)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_RawGroup_852
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> (AgdaAny -> AgdaAny) -> T_RawGroup_852
C_RawGroup'46'constructor_13903 (T_RawRing_2460 -> AgdaAny -> AgdaAny -> AgdaAny
d__'43'__2484 (T_RawRing_2460 -> T_RawRing_2460
forall a b. a -> b
coe T_RawRing_2460
v0))
      (T_RawRing_2460 -> AgdaAny
d_0'35'_2490 (T_RawRing_2460 -> T_RawRing_2460
forall a b. a -> b
coe T_RawRing_2460
v0)) (T_RawRing_2460 -> AgdaAny -> AgdaAny
d_'45'__2488 (T_RawRing_2460 -> T_RawRing_2460
forall a b. a -> b
coe T_RawRing_2460
v0))
-- Algebra.Bundles.Ring
d_Ring_2514 :: p -> p -> ()
d_Ring_2514 p
a0 p
a1 = ()
data T_Ring_2514
  = C_Ring'46'constructor_43513 (AgdaAny -> AgdaAny -> AgdaAny)
                                (AgdaAny -> AgdaAny -> AgdaAny) (AgdaAny -> AgdaAny) AgdaAny
                                AgdaAny MAlonzo.Code.Algebra.Structures.T_IsRing_1584
-- Algebra.Bundles.Ring.Carrier
d_Carrier_2536 :: T_Ring_2514 -> ()
d_Carrier_2536 :: T_Ring_2514 -> ()
d_Carrier_2536 = T_Ring_2514 -> ()
forall a. a
erased
-- Algebra.Bundles.Ring._≈_
d__'8776'__2538 :: T_Ring_2514 -> AgdaAny -> AgdaAny -> ()
d__'8776'__2538 :: T_Ring_2514 -> AgdaAny -> AgdaAny -> ()
d__'8776'__2538 = T_Ring_2514 -> AgdaAny -> AgdaAny -> ()
forall a. a
erased
-- Algebra.Bundles.Ring._+_
d__'43'__2540 :: T_Ring_2514 -> AgdaAny -> AgdaAny -> AgdaAny
d__'43'__2540 :: T_Ring_2514 -> AgdaAny -> AgdaAny -> AgdaAny
d__'43'__2540 T_Ring_2514
v0
  = case T_Ring_2514 -> T_Ring_2514
forall a b. a -> b
coe T_Ring_2514
v0 of
      C_Ring'46'constructor_43513 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny
v5 AgdaAny
v6 AgdaAny
v7 T_IsRing_1584
v8 -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v3
      T_Ring_2514
_ -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.Ring._*_
d__'42'__2542 :: T_Ring_2514 -> AgdaAny -> AgdaAny -> AgdaAny
d__'42'__2542 :: T_Ring_2514 -> AgdaAny -> AgdaAny -> AgdaAny
d__'42'__2542 T_Ring_2514
v0
  = case T_Ring_2514 -> T_Ring_2514
forall a b. a -> b
coe T_Ring_2514
v0 of
      C_Ring'46'constructor_43513 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny
v5 AgdaAny
v6 AgdaAny
v7 T_IsRing_1584
v8 -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v4
      T_Ring_2514
_ -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.Ring.-_
d_'45'__2544 :: T_Ring_2514 -> AgdaAny -> AgdaAny
d_'45'__2544 :: T_Ring_2514 -> AgdaAny -> AgdaAny
d_'45'__2544 T_Ring_2514
v0
  = case T_Ring_2514 -> T_Ring_2514
forall a b. a -> b
coe T_Ring_2514
v0 of
      C_Ring'46'constructor_43513 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny
v5 AgdaAny
v6 AgdaAny
v7 T_IsRing_1584
v8 -> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v5
      T_Ring_2514
_ -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.Ring.0#
d_0'35'_2546 :: T_Ring_2514 -> AgdaAny
d_0'35'_2546 :: T_Ring_2514 -> AgdaAny
d_0'35'_2546 T_Ring_2514
v0
  = case T_Ring_2514 -> T_Ring_2514
forall a b. a -> b
coe T_Ring_2514
v0 of
      C_Ring'46'constructor_43513 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny
v5 AgdaAny
v6 AgdaAny
v7 T_IsRing_1584
v8 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v6
      T_Ring_2514
_ -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.Ring.1#
d_1'35'_2548 :: T_Ring_2514 -> AgdaAny
d_1'35'_2548 :: T_Ring_2514 -> AgdaAny
d_1'35'_2548 T_Ring_2514
v0
  = case T_Ring_2514 -> T_Ring_2514
forall a b. a -> b
coe T_Ring_2514
v0 of
      C_Ring'46'constructor_43513 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny
v5 AgdaAny
v6 AgdaAny
v7 T_IsRing_1584
v8 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v7
      T_Ring_2514
_ -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.Ring.isRing
d_isRing_2550 ::
  T_Ring_2514 -> MAlonzo.Code.Algebra.Structures.T_IsRing_1584
d_isRing_2550 :: T_Ring_2514 -> T_IsRing_1584
d_isRing_2550 T_Ring_2514
v0
  = case T_Ring_2514 -> T_Ring_2514
forall a b. a -> b
coe T_Ring_2514
v0 of
      C_Ring'46'constructor_43513 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny
v5 AgdaAny
v6 AgdaAny
v7 T_IsRing_1584
v8 -> T_IsRing_1584 -> T_IsRing_1584
forall a b. a -> b
coe T_IsRing_1584
v8
      T_Ring_2514
_ -> T_IsRing_1584
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.Ring._._-_
d__'45'__2554 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Ring_2514 -> AgdaAny -> AgdaAny -> AgdaAny
d__'45'__2554 :: () -> () -> T_Ring_2514 -> AgdaAny -> AgdaAny -> AgdaAny
d__'45'__2554 ~()
v0 ~()
v1 T_Ring_2514
v2 = T_Ring_2514 -> AgdaAny -> AgdaAny -> AgdaAny
du__'45'__2554 T_Ring_2514
v2
du__'45'__2554 :: T_Ring_2514 -> AgdaAny -> AgdaAny -> AgdaAny
du__'45'__2554 :: T_Ring_2514 -> AgdaAny -> AgdaAny -> AgdaAny
du__'45'__2554 T_Ring_2514
v0
  = let v1 :: AgdaAny -> AgdaAny -> AgdaAny
v1 = T_Ring_2514 -> AgdaAny -> AgdaAny -> AgdaAny
d__'43'__2540 (T_Ring_2514 -> T_Ring_2514
forall a b. a -> b
coe T_Ring_2514
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: AgdaAny -> AgdaAny
v2 = T_Ring_2514 -> AgdaAny -> AgdaAny
d_'45'__2544 (T_Ring_2514 -> T_Ring_2514
forall a b. a -> b
coe T_Ring_2514
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__'45'__634 ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v1) ((AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v2)))
-- Algebra.Bundles.Ring._.assoc
d_assoc_2556 ::
  T_Ring_2514 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_2556 :: T_Ring_2514 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_2556 T_Ring_2514
v0
  = (T_IsSemigroup_194 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsSemigroup_194 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_assoc_204
      ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368
         ((T_IsRing_1584 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsRing_1584 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_'42''45'isMonoid_1606
            ((T_Ring_2514 -> T_IsRing_1584) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Ring_2514 -> T_IsRing_1584
d_isRing_2550 (T_Ring_2514 -> AgdaAny
forall a b. a -> b
coe T_Ring_2514
v0))))
-- Algebra.Bundles.Ring._.∙-cong
d_'8729''45'cong_2558 ::
  T_Ring_2514 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_2558 :: T_Ring_2514
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_2558 T_Ring_2514
v0
  = (T_IsMagma_86
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsMagma_86
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_96
      ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202
         ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368
            ((T_IsRing_1584 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsRing_1584 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_'42''45'isMonoid_1606
               ((T_Ring_2514 -> T_IsRing_1584) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Ring_2514 -> T_IsRing_1584
d_isRing_2550 (T_Ring_2514 -> AgdaAny
forall a b. a -> b
coe T_Ring_2514
v0)))))
-- Algebra.Bundles.Ring._.∙-congʳ
d_'8729''45'cong'691'_2560 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Ring_2514 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_2560 :: ()
-> ()
-> T_Ring_2514
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_2560 ~()
v0 ~()
v1 T_Ring_2514
v2
  = T_Ring_2514 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_2560 T_Ring_2514
v2
du_'8729''45'cong'691'_2560 ::
  T_Ring_2514 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_2560 :: T_Ring_2514 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_2560 T_Ring_2514
v0
  = let v1 :: T_IsRing_1584
v1 = T_Ring_2514 -> T_IsRing_1584
d_isRing_2550 (T_Ring_2514 -> T_Ring_2514
forall a b. a -> b
coe T_Ring_2514
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsMonoid_358
v2
             = T_IsRing_1584 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_'42''45'isMonoid_1606
                 (T_IsRing_1584 -> T_IsRing_1584
forall a b. a -> b
coe T_IsRing_1584
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_194
v3
                = T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368 (T_IsMonoid_358 -> T_IsMonoid_358
forall a b. a -> b
coe T_IsMonoid_358
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsMagma_86
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMagma_86 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'691'_116
               ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202 (T_IsSemigroup_194 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194
v3)))))
-- Algebra.Bundles.Ring._.∙-congˡ
d_'8729''45'cong'737'_2562 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Ring_2514 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_2562 :: ()
-> ()
-> T_Ring_2514
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_2562 ~()
v0 ~()
v1 T_Ring_2514
v2
  = T_Ring_2514 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_2562 T_Ring_2514
v2
du_'8729''45'cong'737'_2562 ::
  T_Ring_2514 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_2562 :: T_Ring_2514 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_2562 T_Ring_2514
v0
  = let v1 :: T_IsRing_1584
v1 = T_Ring_2514 -> T_IsRing_1584
d_isRing_2550 (T_Ring_2514 -> T_Ring_2514
forall a b. a -> b
coe T_Ring_2514
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsMonoid_358
v2
             = T_IsRing_1584 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_'42''45'isMonoid_1606
                 (T_IsRing_1584 -> T_IsRing_1584
forall a b. a -> b
coe T_IsRing_1584
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_194
v3
                = T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368 (T_IsMonoid_358 -> T_IsMonoid_358
forall a b. a -> b
coe T_IsMonoid_358
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsMagma_86
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMagma_86 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'737'_112
               ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202 (T_IsSemigroup_194 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194
v3)))))
-- Algebra.Bundles.Ring._.identity
d_identity_2564 ::
  T_Ring_2514 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_identity_2564 :: T_Ring_2514 -> T_Σ_14
d_identity_2564 T_Ring_2514
v0
  = (T_IsMonoid_358 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsMonoid_358 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_identity_370
      ((T_IsRing_1584 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsRing_1584 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_'42''45'isMonoid_1606
         ((T_Ring_2514 -> T_IsRing_1584) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Ring_2514 -> T_IsRing_1584
d_isRing_2550 (T_Ring_2514 -> AgdaAny
forall a b. a -> b
coe T_Ring_2514
v0)))
-- Algebra.Bundles.Ring._.identityʳ
d_identity'691'_2566 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Ring_2514 -> AgdaAny -> AgdaAny
d_identity'691'_2566 :: () -> () -> T_Ring_2514 -> AgdaAny -> AgdaAny
d_identity'691'_2566 ~()
v0 ~()
v1 T_Ring_2514
v2 = T_Ring_2514 -> AgdaAny -> AgdaAny
du_identity'691'_2566 T_Ring_2514
v2
du_identity'691'_2566 :: T_Ring_2514 -> AgdaAny -> AgdaAny
du_identity'691'_2566 :: T_Ring_2514 -> AgdaAny -> AgdaAny
du_identity'691'_2566 T_Ring_2514
v0
  = let v1 :: T_IsRing_1584
v1 = T_Ring_2514 -> T_IsRing_1584
d_isRing_2550 (T_Ring_2514 -> T_Ring_2514
forall a b. a -> b
coe T_Ring_2514
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsMonoid_358 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoid_358 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_identity'691'_400
         ((T_IsRing_1584 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsRing_1584 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_'42''45'isMonoid_1606 (T_IsRing_1584 -> AgdaAny
forall a b. a -> b
coe T_IsRing_1584
v1)))
-- Algebra.Bundles.Ring._.identityˡ
d_identity'737'_2568 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Ring_2514 -> AgdaAny -> AgdaAny
d_identity'737'_2568 :: () -> () -> T_Ring_2514 -> AgdaAny -> AgdaAny
d_identity'737'_2568 ~()
v0 ~()
v1 T_Ring_2514
v2 = T_Ring_2514 -> AgdaAny -> AgdaAny
du_identity'737'_2568 T_Ring_2514
v2
du_identity'737'_2568 :: T_Ring_2514 -> AgdaAny -> AgdaAny
du_identity'737'_2568 :: T_Ring_2514 -> AgdaAny -> AgdaAny
du_identity'737'_2568 T_Ring_2514
v0
  = let v1 :: T_IsRing_1584
v1 = T_Ring_2514 -> T_IsRing_1584
d_isRing_2550 (T_Ring_2514 -> T_Ring_2514
forall a b. a -> b
coe T_Ring_2514
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsMonoid_358 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoid_358 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_identity'737'_398
         ((T_IsRing_1584 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsRing_1584 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_'42''45'isMonoid_1606 (T_IsRing_1584 -> AgdaAny
forall a b. a -> b
coe T_IsRing_1584
v1)))
-- Algebra.Bundles.Ring._.isMagma
d_isMagma_2570 ::
  T_Ring_2514 -> MAlonzo.Code.Algebra.Structures.T_IsMagma_86
d_isMagma_2570 :: T_Ring_2514 -> T_IsMagma_86
d_isMagma_2570 T_Ring_2514
v0
  = (T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> T_IsMagma_86
forall a b. a -> b
coe
      T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202
      ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368
         ((T_IsRing_1584 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsRing_1584 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_'42''45'isMonoid_1606
            ((T_Ring_2514 -> T_IsRing_1584) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Ring_2514 -> T_IsRing_1584
d_isRing_2550 (T_Ring_2514 -> AgdaAny
forall a b. a -> b
coe T_Ring_2514
v0))))
-- Algebra.Bundles.Ring._.*-isMonoid
d_'42''45'isMonoid_2572 ::
  T_Ring_2514 -> MAlonzo.Code.Algebra.Structures.T_IsMonoid_358
d_'42''45'isMonoid_2572 :: T_Ring_2514 -> T_IsMonoid_358
d_'42''45'isMonoid_2572 T_Ring_2514
v0
  = (T_IsRing_1584 -> T_IsMonoid_358) -> AgdaAny -> T_IsMonoid_358
forall a b. a -> b
coe
      T_IsRing_1584 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_'42''45'isMonoid_1606
      ((T_Ring_2514 -> T_IsRing_1584) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Ring_2514 -> T_IsRing_1584
d_isRing_2550 (T_Ring_2514 -> AgdaAny
forall a b. a -> b
coe T_Ring_2514
v0))
-- Algebra.Bundles.Ring._.isSemigroup
d_isSemigroup_2574 ::
  T_Ring_2514 -> MAlonzo.Code.Algebra.Structures.T_IsSemigroup_194
d_isSemigroup_2574 :: T_Ring_2514 -> T_IsSemigroup_194
d_isSemigroup_2574 T_Ring_2514
v0
  = (T_IsMonoid_358 -> T_IsSemigroup_194)
-> AgdaAny -> T_IsSemigroup_194
forall a b. a -> b
coe
      T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368
      ((T_IsRing_1584 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsRing_1584 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_'42''45'isMonoid_1606
         ((T_Ring_2514 -> T_IsRing_1584) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Ring_2514 -> T_IsRing_1584
d_isRing_2550 (T_Ring_2514 -> AgdaAny
forall a b. a -> b
coe T_Ring_2514
v0)))
-- Algebra.Bundles.Ring._.assoc
d_assoc_2576 ::
  T_Ring_2514 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_2576 :: T_Ring_2514 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_2576 T_Ring_2514
v0
  = (T_IsSemigroup_194 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsSemigroup_194 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_assoc_204
      ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368
         ((T_IsGroup_580 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsGroup_580 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_594
            ((T_IsAbelianGroup_662 -> T_IsGroup_580) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsAbelianGroup_662 -> T_IsGroup_580
MAlonzo.Code.Algebra.Structures.d_isGroup_674
               ((T_IsRing_1584 -> T_IsAbelianGroup_662) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsRing_1584 -> T_IsAbelianGroup_662
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_1604
                  ((T_Ring_2514 -> T_IsRing_1584) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Ring_2514 -> T_IsRing_1584
d_isRing_2550 (T_Ring_2514 -> AgdaAny
forall a b. a -> b
coe T_Ring_2514
v0))))))
-- Algebra.Bundles.Ring._.comm
d_comm_2578 :: T_Ring_2514 -> AgdaAny -> AgdaAny -> AgdaAny
d_comm_2578 :: T_Ring_2514 -> AgdaAny -> AgdaAny -> AgdaAny
d_comm_2578 T_Ring_2514
v0
  = (T_IsAbelianGroup_662 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsAbelianGroup_662 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_comm_676
      ((T_IsRing_1584 -> T_IsAbelianGroup_662) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsRing_1584 -> T_IsAbelianGroup_662
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_1604
         ((T_Ring_2514 -> T_IsRing_1584) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Ring_2514 -> T_IsRing_1584
d_isRing_2550 (T_Ring_2514 -> AgdaAny
forall a b. a -> b
coe T_Ring_2514
v0)))
-- Algebra.Bundles.Ring._.∙-cong
d_'8729''45'cong_2580 ::
  T_Ring_2514 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_2580 :: T_Ring_2514
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_2580 T_Ring_2514
v0
  = (T_IsMagma_86
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsMagma_86
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_96
      ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202
         ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368
            ((T_IsGroup_580 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsGroup_580 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_594
               ((T_IsAbelianGroup_662 -> T_IsGroup_580) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsAbelianGroup_662 -> T_IsGroup_580
MAlonzo.Code.Algebra.Structures.d_isGroup_674
                  ((T_IsRing_1584 -> T_IsAbelianGroup_662) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsRing_1584 -> T_IsAbelianGroup_662
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_1604
                     ((T_Ring_2514 -> T_IsRing_1584) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Ring_2514 -> T_IsRing_1584
d_isRing_2550 (T_Ring_2514 -> AgdaAny
forall a b. a -> b
coe T_Ring_2514
v0)))))))
-- Algebra.Bundles.Ring._.∙-congʳ
d_'8729''45'cong'691'_2582 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Ring_2514 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_2582 :: ()
-> ()
-> T_Ring_2514
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_2582 ~()
v0 ~()
v1 T_Ring_2514
v2
  = T_Ring_2514 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_2582 T_Ring_2514
v2
du_'8729''45'cong'691'_2582 ::
  T_Ring_2514 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_2582 :: T_Ring_2514 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_2582 T_Ring_2514
v0
  = let v1 :: T_IsRing_1584
v1 = T_Ring_2514 -> T_IsRing_1584
d_isRing_2550 (T_Ring_2514 -> T_Ring_2514
forall a b. a -> b
coe T_Ring_2514
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsAbelianGroup_662
v2
             = T_IsRing_1584 -> T_IsAbelianGroup_662
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_1604
                 (T_IsRing_1584 -> T_IsRing_1584
forall a b. a -> b
coe T_IsRing_1584
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsGroup_580
v3 = T_IsAbelianGroup_662 -> T_IsGroup_580
MAlonzo.Code.Algebra.Structures.d_isGroup_674 (T_IsAbelianGroup_662 -> T_IsAbelianGroup_662
forall a b. a -> b
coe T_IsAbelianGroup_662
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsMonoid_358
v4
                   = T_IsGroup_580 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_594 (T_IsGroup_580 -> T_IsGroup_580
forall a b. a -> b
coe T_IsGroup_580
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsSemigroup_194
v5
                      = T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368 (T_IsMonoid_358 -> T_IsMonoid_358
forall a b. a -> b
coe T_IsMonoid_358
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  ((T_IsMagma_86
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsMagma_86 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'691'_116
                     ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202 (T_IsSemigroup_194 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194
v5)))))))
-- Algebra.Bundles.Ring._.∙-congˡ
d_'8729''45'cong'737'_2584 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Ring_2514 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_2584 :: ()
-> ()
-> T_Ring_2514
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_2584 ~()
v0 ~()
v1 T_Ring_2514
v2
  = T_Ring_2514 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_2584 T_Ring_2514
v2
du_'8729''45'cong'737'_2584 ::
  T_Ring_2514 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_2584 :: T_Ring_2514 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_2584 T_Ring_2514
v0
  = let v1 :: T_IsRing_1584
v1 = T_Ring_2514 -> T_IsRing_1584
d_isRing_2550 (T_Ring_2514 -> T_Ring_2514
forall a b. a -> b
coe T_Ring_2514
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsAbelianGroup_662
v2
             = T_IsRing_1584 -> T_IsAbelianGroup_662
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_1604
                 (T_IsRing_1584 -> T_IsRing_1584
forall a b. a -> b
coe T_IsRing_1584
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsGroup_580
v3 = T_IsAbelianGroup_662 -> T_IsGroup_580
MAlonzo.Code.Algebra.Structures.d_isGroup_674 (T_IsAbelianGroup_662 -> T_IsAbelianGroup_662
forall a b. a -> b
coe T_IsAbelianGroup_662
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsMonoid_358
v4
                   = T_IsGroup_580 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_594 (T_IsGroup_580 -> T_IsGroup_580
forall a b. a -> b
coe T_IsGroup_580
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsSemigroup_194
v5
                      = T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368 (T_IsMonoid_358 -> T_IsMonoid_358
forall a b. a -> b
coe T_IsMonoid_358
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  ((T_IsMagma_86
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsMagma_86 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'737'_112
                     ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202 (T_IsSemigroup_194 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194
v5)))))))
-- Algebra.Bundles.Ring._.identity
d_identity_2586 ::
  T_Ring_2514 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_identity_2586 :: T_Ring_2514 -> T_Σ_14
d_identity_2586 T_Ring_2514
v0
  = (T_IsMonoid_358 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsMonoid_358 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_identity_370
      ((T_IsGroup_580 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsGroup_580 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_594
         ((T_IsAbelianGroup_662 -> T_IsGroup_580) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsAbelianGroup_662 -> T_IsGroup_580
MAlonzo.Code.Algebra.Structures.d_isGroup_674
            ((T_IsRing_1584 -> T_IsAbelianGroup_662) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsRing_1584 -> T_IsAbelianGroup_662
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_1604
               ((T_Ring_2514 -> T_IsRing_1584) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Ring_2514 -> T_IsRing_1584
d_isRing_2550 (T_Ring_2514 -> AgdaAny
forall a b. a -> b
coe T_Ring_2514
v0)))))
-- Algebra.Bundles.Ring._.identityʳ
d_identity'691'_2588 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Ring_2514 -> AgdaAny -> AgdaAny
d_identity'691'_2588 :: () -> () -> T_Ring_2514 -> AgdaAny -> AgdaAny
d_identity'691'_2588 ~()
v0 ~()
v1 T_Ring_2514
v2 = T_Ring_2514 -> AgdaAny -> AgdaAny
du_identity'691'_2588 T_Ring_2514
v2
du_identity'691'_2588 :: T_Ring_2514 -> AgdaAny -> AgdaAny
du_identity'691'_2588 :: T_Ring_2514 -> AgdaAny -> AgdaAny
du_identity'691'_2588 T_Ring_2514
v0
  = let v1 :: T_IsRing_1584
v1 = T_Ring_2514 -> T_IsRing_1584
d_isRing_2550 (T_Ring_2514 -> T_Ring_2514
forall a b. a -> b
coe T_Ring_2514
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsAbelianGroup_662
v2
             = T_IsRing_1584 -> T_IsAbelianGroup_662
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_1604
                 (T_IsRing_1584 -> T_IsRing_1584
forall a b. a -> b
coe T_IsRing_1584
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsGroup_580
v3 = T_IsAbelianGroup_662 -> T_IsGroup_580
MAlonzo.Code.Algebra.Structures.d_isGroup_674 (T_IsAbelianGroup_662 -> T_IsAbelianGroup_662
forall a b. a -> b
coe T_IsAbelianGroup_662
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsMonoid_358 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_358 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_identity'691'_400
               ((T_IsGroup_580 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_580 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_594 (T_IsGroup_580 -> AgdaAny
forall a b. a -> b
coe T_IsGroup_580
v3)))))
-- Algebra.Bundles.Ring._.identityˡ
d_identity'737'_2590 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Ring_2514 -> AgdaAny -> AgdaAny
d_identity'737'_2590 :: () -> () -> T_Ring_2514 -> AgdaAny -> AgdaAny
d_identity'737'_2590 ~()
v0 ~()
v1 T_Ring_2514
v2 = T_Ring_2514 -> AgdaAny -> AgdaAny
du_identity'737'_2590 T_Ring_2514
v2
du_identity'737'_2590 :: T_Ring_2514 -> AgdaAny -> AgdaAny
du_identity'737'_2590 :: T_Ring_2514 -> AgdaAny -> AgdaAny
du_identity'737'_2590 T_Ring_2514
v0
  = let v1 :: T_IsRing_1584
v1 = T_Ring_2514 -> T_IsRing_1584
d_isRing_2550 (T_Ring_2514 -> T_Ring_2514
forall a b. a -> b
coe T_Ring_2514
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsAbelianGroup_662
v2
             = T_IsRing_1584 -> T_IsAbelianGroup_662
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_1604
                 (T_IsRing_1584 -> T_IsRing_1584
forall a b. a -> b
coe T_IsRing_1584
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsGroup_580
v3 = T_IsAbelianGroup_662 -> T_IsGroup_580
MAlonzo.Code.Algebra.Structures.d_isGroup_674 (T_IsAbelianGroup_662 -> T_IsAbelianGroup_662
forall a b. a -> b
coe T_IsAbelianGroup_662
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsMonoid_358 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_358 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_identity'737'_398
               ((T_IsGroup_580 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_580 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_594 (T_IsGroup_580 -> AgdaAny
forall a b. a -> b
coe T_IsGroup_580
v3)))))
-- Algebra.Bundles.Ring._.+-isAbelianGroup
d_'43''45'isAbelianGroup_2592 ::
  T_Ring_2514 -> MAlonzo.Code.Algebra.Structures.T_IsAbelianGroup_662
d_'43''45'isAbelianGroup_2592 :: T_Ring_2514 -> T_IsAbelianGroup_662
d_'43''45'isAbelianGroup_2592 T_Ring_2514
v0
  = (T_IsRing_1584 -> T_IsAbelianGroup_662)
-> AgdaAny -> T_IsAbelianGroup_662
forall a b. a -> b
coe
      T_IsRing_1584 -> T_IsAbelianGroup_662
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_1604
      ((T_Ring_2514 -> T_IsRing_1584) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Ring_2514 -> T_IsRing_1584
d_isRing_2550 (T_Ring_2514 -> AgdaAny
forall a b. a -> b
coe T_Ring_2514
v0))
-- Algebra.Bundles.Ring._.isCommutativeMagma
d_isCommutativeMagma_2594 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Ring_2514 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMagma_122
d_isCommutativeMagma_2594 :: () -> () -> T_Ring_2514 -> T_IsCommutativeMagma_122
d_isCommutativeMagma_2594 ~()
v0 ~()
v1 T_Ring_2514
v2
  = T_Ring_2514 -> T_IsCommutativeMagma_122
du_isCommutativeMagma_2594 T_Ring_2514
v2
du_isCommutativeMagma_2594 ::
  T_Ring_2514 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMagma_122
du_isCommutativeMagma_2594 :: T_Ring_2514 -> T_IsCommutativeMagma_122
du_isCommutativeMagma_2594 T_Ring_2514
v0
  = let v1 :: T_IsRing_1584
v1 = T_Ring_2514 -> T_IsRing_1584
d_isRing_2550 (T_Ring_2514 -> T_Ring_2514
forall a b. a -> b
coe T_Ring_2514
v0) in
    AgdaAny -> T_IsCommutativeMagma_122
forall a b. a -> b
coe
      (let v2 :: T_IsAbelianGroup_662
v2
             = T_IsRing_1584 -> T_IsAbelianGroup_662
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_1604
                 (T_IsRing_1584 -> T_IsRing_1584
forall a b. a -> b
coe T_IsRing_1584
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: t
v3
                = (T_IsAbelianGroup_662 -> T_IsCommutativeMonoid_406) -> AgdaAny -> t
forall a b. a -> b
coe
                    T_IsAbelianGroup_662 -> T_IsCommutativeMonoid_406
MAlonzo.Code.Algebra.Structures.du_isCommutativeMonoid_728
                    (T_IsAbelianGroup_662 -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_662
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsCommutativeSemigroup_270 -> T_IsCommutativeMagma_122)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsCommutativeSemigroup_270 -> T_IsCommutativeMagma_122
MAlonzo.Code.Algebra.Structures.du_isCommutativeMagma_308
               ((T_IsCommutativeMonoid_406 -> T_IsCommutativeSemigroup_270)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsCommutativeMonoid_406 -> T_IsCommutativeSemigroup_270
MAlonzo.Code.Algebra.Structures.du_isCommutativeSemigroup_454
                  (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3)))))
-- Algebra.Bundles.Ring._.isCommutativeMonoid
d_isCommutativeMonoid_2596 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Ring_2514 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMonoid_406
d_isCommutativeMonoid_2596 :: () -> () -> T_Ring_2514 -> T_IsCommutativeMonoid_406
d_isCommutativeMonoid_2596 ~()
v0 ~()
v1 T_Ring_2514
v2
  = T_Ring_2514 -> T_IsCommutativeMonoid_406
du_isCommutativeMonoid_2596 T_Ring_2514
v2
du_isCommutativeMonoid_2596 ::
  T_Ring_2514 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMonoid_406
du_isCommutativeMonoid_2596 :: T_Ring_2514 -> T_IsCommutativeMonoid_406
du_isCommutativeMonoid_2596 T_Ring_2514
v0
  = let v1 :: T_IsRing_1584
v1 = T_Ring_2514 -> T_IsRing_1584
d_isRing_2550 (T_Ring_2514 -> T_Ring_2514
forall a b. a -> b
coe T_Ring_2514
v0) in
    AgdaAny -> T_IsCommutativeMonoid_406
forall a b. a -> b
coe
      ((T_IsAbelianGroup_662 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsAbelianGroup_662 -> T_IsCommutativeMonoid_406
MAlonzo.Code.Algebra.Structures.du_isCommutativeMonoid_728
         ((T_IsRing_1584 -> T_IsAbelianGroup_662) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsRing_1584 -> T_IsAbelianGroup_662
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_1604
            (T_IsRing_1584 -> AgdaAny
forall a b. a -> b
coe T_IsRing_1584
v1)))
-- Algebra.Bundles.Ring._.isCommutativeSemigroup
d_isCommutativeSemigroup_2598 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Ring_2514 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_270
d_isCommutativeSemigroup_2598 :: () -> () -> T_Ring_2514 -> T_IsCommutativeSemigroup_270
d_isCommutativeSemigroup_2598 ~()
v0 ~()
v1 T_Ring_2514
v2
  = T_Ring_2514 -> T_IsCommutativeSemigroup_270
du_isCommutativeSemigroup_2598 T_Ring_2514
v2
du_isCommutativeSemigroup_2598 ::
  T_Ring_2514 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_270
du_isCommutativeSemigroup_2598 :: T_Ring_2514 -> T_IsCommutativeSemigroup_270
du_isCommutativeSemigroup_2598 T_Ring_2514
v0
  = let v1 :: T_IsRing_1584
v1 = T_Ring_2514 -> T_IsRing_1584
d_isRing_2550 (T_Ring_2514 -> T_Ring_2514
forall a b. a -> b
coe T_Ring_2514
v0) in
    AgdaAny -> T_IsCommutativeSemigroup_270
forall a b. a -> b
coe
      (let v2 :: T_IsAbelianGroup_662
v2
             = T_IsRing_1584 -> T_IsAbelianGroup_662
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_1604
                 (T_IsRing_1584 -> T_IsRing_1584
forall a b. a -> b
coe T_IsRing_1584
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsCommutativeMonoid_406 -> T_IsCommutativeSemigroup_270)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCommutativeMonoid_406 -> T_IsCommutativeSemigroup_270
MAlonzo.Code.Algebra.Structures.du_isCommutativeSemigroup_454
            ((T_IsAbelianGroup_662 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsAbelianGroup_662 -> T_IsCommutativeMonoid_406
MAlonzo.Code.Algebra.Structures.du_isCommutativeMonoid_728
               (T_IsAbelianGroup_662 -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_662
v2))))
-- Algebra.Bundles.Ring._.isGroup
d_isGroup_2600 ::
  T_Ring_2514 -> MAlonzo.Code.Algebra.Structures.T_IsGroup_580
d_isGroup_2600 :: T_Ring_2514 -> T_IsGroup_580
d_isGroup_2600 T_Ring_2514
v0
  = (T_IsAbelianGroup_662 -> T_IsGroup_580) -> AgdaAny -> T_IsGroup_580
forall a b. a -> b
coe
      T_IsAbelianGroup_662 -> T_IsGroup_580
MAlonzo.Code.Algebra.Structures.d_isGroup_674
      ((T_IsRing_1584 -> T_IsAbelianGroup_662) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsRing_1584 -> T_IsAbelianGroup_662
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_1604
         ((T_Ring_2514 -> T_IsRing_1584) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Ring_2514 -> T_IsRing_1584
d_isRing_2550 (T_Ring_2514 -> AgdaAny
forall a b. a -> b
coe T_Ring_2514
v0)))
-- Algebra.Bundles.Ring._.isMagma
d_isMagma_2602 ::
  T_Ring_2514 -> MAlonzo.Code.Algebra.Structures.T_IsMagma_86
d_isMagma_2602 :: T_Ring_2514 -> T_IsMagma_86
d_isMagma_2602 T_Ring_2514
v0
  = (T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> T_IsMagma_86
forall a b. a -> b
coe
      T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202
      ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368
         ((T_IsGroup_580 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsGroup_580 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_594
            ((T_IsAbelianGroup_662 -> T_IsGroup_580) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsAbelianGroup_662 -> T_IsGroup_580
MAlonzo.Code.Algebra.Structures.d_isGroup_674
               ((T_IsRing_1584 -> T_IsAbelianGroup_662) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsRing_1584 -> T_IsAbelianGroup_662
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_1604
                  ((T_Ring_2514 -> T_IsRing_1584) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Ring_2514 -> T_IsRing_1584
d_isRing_2550 (T_Ring_2514 -> AgdaAny
forall a b. a -> b
coe T_Ring_2514
v0))))))
-- Algebra.Bundles.Ring._.isMonoid
d_isMonoid_2604 ::
  T_Ring_2514 -> MAlonzo.Code.Algebra.Structures.T_IsMonoid_358
d_isMonoid_2604 :: T_Ring_2514 -> T_IsMonoid_358
d_isMonoid_2604 T_Ring_2514
v0
  = (T_IsGroup_580 -> T_IsMonoid_358) -> AgdaAny -> T_IsMonoid_358
forall a b. a -> b
coe
      T_IsGroup_580 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_594
      ((T_IsAbelianGroup_662 -> T_IsGroup_580) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsAbelianGroup_662 -> T_IsGroup_580
MAlonzo.Code.Algebra.Structures.d_isGroup_674
         ((T_IsRing_1584 -> T_IsAbelianGroup_662) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsRing_1584 -> T_IsAbelianGroup_662
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_1604
            ((T_Ring_2514 -> T_IsRing_1584) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Ring_2514 -> T_IsRing_1584
d_isRing_2550 (T_Ring_2514 -> AgdaAny
forall a b. a -> b
coe T_Ring_2514
v0))))
-- Algebra.Bundles.Ring._.isSemigroup
d_isSemigroup_2606 ::
  T_Ring_2514 -> MAlonzo.Code.Algebra.Structures.T_IsSemigroup_194
d_isSemigroup_2606 :: T_Ring_2514 -> T_IsSemigroup_194
d_isSemigroup_2606 T_Ring_2514
v0
  = (T_IsMonoid_358 -> T_IsSemigroup_194)
-> AgdaAny -> T_IsSemigroup_194
forall a b. a -> b
coe
      T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368
      ((T_IsGroup_580 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsGroup_580 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_594
         ((T_IsAbelianGroup_662 -> T_IsGroup_580) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsAbelianGroup_662 -> T_IsGroup_580
MAlonzo.Code.Algebra.Structures.d_isGroup_674
            ((T_IsRing_1584 -> T_IsAbelianGroup_662) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsRing_1584 -> T_IsAbelianGroup_662
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_1604
               ((T_Ring_2514 -> T_IsRing_1584) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Ring_2514 -> T_IsRing_1584
d_isRing_2550 (T_Ring_2514 -> AgdaAny
forall a b. a -> b
coe T_Ring_2514
v0)))))
-- Algebra.Bundles.Ring._.⁻¹-cong
d_'8315''185''45'cong_2608 ::
  T_Ring_2514 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8315''185''45'cong_2608 :: T_Ring_2514 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8315''185''45'cong_2608 T_Ring_2514
v0
  = (T_IsGroup_580 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsGroup_580 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8315''185''45'cong_598
      ((T_IsAbelianGroup_662 -> T_IsGroup_580) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsAbelianGroup_662 -> T_IsGroup_580
MAlonzo.Code.Algebra.Structures.d_isGroup_674
         ((T_IsRing_1584 -> T_IsAbelianGroup_662) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsRing_1584 -> T_IsAbelianGroup_662
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_1604
            ((T_Ring_2514 -> T_IsRing_1584) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Ring_2514 -> T_IsRing_1584
d_isRing_2550 (T_Ring_2514 -> AgdaAny
forall a b. a -> b
coe T_Ring_2514
v0))))
-- Algebra.Bundles.Ring._.inverse
d_inverse_2610 ::
  T_Ring_2514 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_inverse_2610 :: T_Ring_2514 -> T_Σ_14
d_inverse_2610 T_Ring_2514
v0
  = (T_IsGroup_580 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsGroup_580 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_inverse_596
      ((T_IsAbelianGroup_662 -> T_IsGroup_580) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsAbelianGroup_662 -> T_IsGroup_580
MAlonzo.Code.Algebra.Structures.d_isGroup_674
         ((T_IsRing_1584 -> T_IsAbelianGroup_662) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsRing_1584 -> T_IsAbelianGroup_662
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_1604
            ((T_Ring_2514 -> T_IsRing_1584) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Ring_2514 -> T_IsRing_1584
d_isRing_2550 (T_Ring_2514 -> AgdaAny
forall a b. a -> b
coe T_Ring_2514
v0))))
-- Algebra.Bundles.Ring._.inverseʳ
d_inverse'691'_2612 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Ring_2514 -> AgdaAny -> AgdaAny
d_inverse'691'_2612 :: () -> () -> T_Ring_2514 -> AgdaAny -> AgdaAny
d_inverse'691'_2612 ~()
v0 ~()
v1 T_Ring_2514
v2 = T_Ring_2514 -> AgdaAny -> AgdaAny
du_inverse'691'_2612 T_Ring_2514
v2
du_inverse'691'_2612 :: T_Ring_2514 -> AgdaAny -> AgdaAny
du_inverse'691'_2612 :: T_Ring_2514 -> AgdaAny -> AgdaAny
du_inverse'691'_2612 T_Ring_2514
v0
  = let v1 :: T_IsRing_1584
v1 = T_Ring_2514 -> T_IsRing_1584
d_isRing_2550 (T_Ring_2514 -> T_Ring_2514
forall a b. a -> b
coe T_Ring_2514
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsAbelianGroup_662
v2
             = T_IsRing_1584 -> T_IsAbelianGroup_662
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_1604
                 (T_IsRing_1584 -> T_IsRing_1584
forall a b. a -> b
coe T_IsRing_1584
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsGroup_580 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsGroup_580 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_inverse'691'_642
            ((T_IsAbelianGroup_662 -> T_IsGroup_580) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_662 -> T_IsGroup_580
MAlonzo.Code.Algebra.Structures.d_isGroup_674 (T_IsAbelianGroup_662 -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_662
v2))))
-- Algebra.Bundles.Ring._.inverseˡ
d_inverse'737'_2614 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Ring_2514 -> AgdaAny -> AgdaAny
d_inverse'737'_2614 :: () -> () -> T_Ring_2514 -> AgdaAny -> AgdaAny
d_inverse'737'_2614 ~()
v0 ~()
v1 T_Ring_2514
v2 = T_Ring_2514 -> AgdaAny -> AgdaAny
du_inverse'737'_2614 T_Ring_2514
v2
du_inverse'737'_2614 :: T_Ring_2514 -> AgdaAny -> AgdaAny
du_inverse'737'_2614 :: T_Ring_2514 -> AgdaAny -> AgdaAny
du_inverse'737'_2614 T_Ring_2514
v0
  = let v1 :: T_IsRing_1584
v1 = T_Ring_2514 -> T_IsRing_1584
d_isRing_2550 (T_Ring_2514 -> T_Ring_2514
forall a b. a -> b
coe T_Ring_2514
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsAbelianGroup_662
v2
             = T_IsRing_1584 -> T_IsAbelianGroup_662
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_1604
                 (T_IsRing_1584 -> T_IsRing_1584
forall a b. a -> b
coe T_IsRing_1584
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsGroup_580 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsGroup_580 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_inverse'737'_640
            ((T_IsAbelianGroup_662 -> T_IsGroup_580) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_662 -> T_IsGroup_580
MAlonzo.Code.Algebra.Structures.d_isGroup_674 (T_IsAbelianGroup_662 -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_662
v2))))
-- Algebra.Bundles.Ring._.distrib
d_distrib_2616 ::
  T_Ring_2514 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_distrib_2616 :: T_Ring_2514 -> T_Σ_14
d_distrib_2616 T_Ring_2514
v0
  = (T_IsRing_1584 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsRing_1584 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_distrib_1608
      ((T_Ring_2514 -> T_IsRing_1584) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Ring_2514 -> T_IsRing_1584
d_isRing_2550 (T_Ring_2514 -> AgdaAny
forall a b. a -> b
coe T_Ring_2514
v0))
-- Algebra.Bundles.Ring._.distribʳ
d_distrib'691'_2618 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Ring_2514 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_distrib'691'_2618 :: () -> () -> T_Ring_2514 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_distrib'691'_2618 ~()
v0 ~()
v1 T_Ring_2514
v2 = T_Ring_2514 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'691'_2618 T_Ring_2514
v2
du_distrib'691'_2618 ::
  T_Ring_2514 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'691'_2618 :: T_Ring_2514 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'691'_2618 T_Ring_2514
v0
  = let v1 :: T_IsRing_1584
v1 = T_Ring_2514 -> T_IsRing_1584
d_isRing_2550 (T_Ring_2514 -> T_Ring_2514
forall a b. a -> b
coe T_Ring_2514
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: t
v2
             = (T_IsRing_1584 -> T_IsSemiring_1238) -> AgdaAny -> t
forall a b. a -> b
coe
                 T_IsRing_1584 -> T_IsSemiring_1238
MAlonzo.Code.Algebra.Structures.du_isSemiring_1698 (T_IsRing_1584 -> AgdaAny
forall a b. a -> b
coe T_IsRing_1584
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsSemiringWithoutAnnihilatingZero_1142
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemiringWithoutAnnihilatingZero_1142
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_distrib'691'_1166
            ((T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1252
               (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2))))
-- Algebra.Bundles.Ring._.distribˡ
d_distrib'737'_2620 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Ring_2514 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_distrib'737'_2620 :: () -> () -> T_Ring_2514 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_distrib'737'_2620 ~()
v0 ~()
v1 T_Ring_2514
v2 = T_Ring_2514 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'737'_2620 T_Ring_2514
v2
du_distrib'737'_2620 ::
  T_Ring_2514 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'737'_2620 :: T_Ring_2514 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'737'_2620 T_Ring_2514
v0
  = let v1 :: T_IsRing_1584
v1 = T_Ring_2514 -> T_IsRing_1584
d_isRing_2550 (T_Ring_2514 -> T_Ring_2514
forall a b. a -> b
coe T_Ring_2514
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: t
v2
             = (T_IsRing_1584 -> T_IsSemiring_1238) -> AgdaAny -> t
forall a b. a -> b
coe
                 T_IsRing_1584 -> T_IsSemiring_1238
MAlonzo.Code.Algebra.Structures.du_isSemiring_1698 (T_IsRing_1584 -> AgdaAny
forall a b. a -> b
coe T_IsRing_1584
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsSemiringWithoutAnnihilatingZero_1142
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemiringWithoutAnnihilatingZero_1142
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_distrib'737'_1164
            ((T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1252
               (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2))))
-- Algebra.Bundles.Ring._.isEquivalence
d_isEquivalence_2622 ::
  T_Ring_2514 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_2622 :: T_Ring_2514 -> T_IsEquivalence_26
d_isEquivalence_2622 T_Ring_2514
v0
  = (T_IsMagma_86 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      T_IsMagma_86 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_94
      ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202
         ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368
            ((T_IsGroup_580 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsGroup_580 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_594
               ((T_IsAbelianGroup_662 -> T_IsGroup_580) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsAbelianGroup_662 -> T_IsGroup_580
MAlonzo.Code.Algebra.Structures.d_isGroup_674
                  ((T_IsRing_1584 -> T_IsAbelianGroup_662) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsRing_1584 -> T_IsAbelianGroup_662
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_1604
                     ((T_Ring_2514 -> T_IsRing_1584) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Ring_2514 -> T_IsRing_1584
d_isRing_2550 (T_Ring_2514 -> AgdaAny
forall a b. a -> b
coe T_Ring_2514
v0)))))))
-- Algebra.Bundles.Ring._.isNearSemiring
d_isNearSemiring_2624 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Ring_2514 -> MAlonzo.Code.Algebra.Structures.T_IsNearSemiring_876
d_isNearSemiring_2624 :: () -> () -> T_Ring_2514 -> T_IsNearSemiring_876
d_isNearSemiring_2624 ~()
v0 ~()
v1 T_Ring_2514
v2 = T_Ring_2514 -> T_IsNearSemiring_876
du_isNearSemiring_2624 T_Ring_2514
v2
du_isNearSemiring_2624 ::
  T_Ring_2514 -> MAlonzo.Code.Algebra.Structures.T_IsNearSemiring_876
du_isNearSemiring_2624 :: T_Ring_2514 -> T_IsNearSemiring_876
du_isNearSemiring_2624 T_Ring_2514
v0
  = let v1 :: T_IsRing_1584
v1 = T_Ring_2514 -> T_IsRing_1584
d_isRing_2550 (T_Ring_2514 -> T_Ring_2514
forall a b. a -> b
coe T_Ring_2514
v0) in
    AgdaAny -> T_IsNearSemiring_876
forall a b. a -> b
coe
      (let v2 :: t
v2
             = (T_IsRing_1584 -> T_IsSemiring_1238) -> AgdaAny -> t
forall a b. a -> b
coe
                 T_IsRing_1584 -> T_IsSemiring_1238
MAlonzo.Code.Algebra.Structures.du_isSemiring_1698 (T_IsRing_1584 -> AgdaAny
forall a b. a -> b
coe T_IsRing_1584
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsSemiringWithoutOne_952 -> T_IsNearSemiring_876)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemiringWithoutOne_952 -> T_IsNearSemiring_876
MAlonzo.Code.Algebra.Structures.du_isNearSemiring_990
            ((T_IsSemiring_1238 -> T_IsSemiringWithoutOne_952)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemiring_1238 -> T_IsSemiringWithoutOne_952
MAlonzo.Code.Algebra.Structures.du_isSemiringWithoutOne_1326
               (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2))))
-- Algebra.Bundles.Ring._.isPartialEquivalence
d_isPartialEquivalence_2626 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Ring_2514 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_2626 :: () -> () -> T_Ring_2514 -> T_IsPartialEquivalence_16
d_isPartialEquivalence_2626 ~()
v0 ~()
v1 T_Ring_2514
v2
  = T_Ring_2514 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_2626 T_Ring_2514
v2
du_isPartialEquivalence_2626 ::
  T_Ring_2514 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_2626 :: T_Ring_2514 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_2626 T_Ring_2514
v0
  = let v1 :: T_IsRing_1584
v1 = T_Ring_2514 -> T_IsRing_1584
d_isRing_2550 (T_Ring_2514 -> T_Ring_2514
forall a b. a -> b
coe T_Ring_2514
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsAbelianGroup_662
v2
             = T_IsRing_1584 -> T_IsAbelianGroup_662
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_1604
                 (T_IsRing_1584 -> T_IsRing_1584
forall a b. a -> b
coe T_IsRing_1584
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsGroup_580
v3 = T_IsAbelianGroup_662 -> T_IsGroup_580
MAlonzo.Code.Algebra.Structures.d_isGroup_674 (T_IsAbelianGroup_662 -> T_IsAbelianGroup_662
forall a b. a -> b
coe T_IsAbelianGroup_662
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsMonoid_358
v4
                   = T_IsGroup_580 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_594 (T_IsGroup_580 -> T_IsGroup_580
forall a b. a -> b
coe T_IsGroup_580
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsSemigroup_194
v5
                      = T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368 (T_IsMonoid_358 -> T_IsMonoid_358
forall a b. a -> b
coe T_IsMonoid_358
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (let v6 :: T_IsMagma_86
v6 = T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202 (T_IsSemigroup_194 -> T_IsSemigroup_194
forall a b. a -> b
coe T_IsSemigroup_194
v5) in
                   AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     ((T_IsEquivalence_26 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsEquivalence_26 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
                        ((T_IsMagma_86 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_IsMagma_86 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_94 (T_IsMagma_86 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86
v6))))))))
-- Algebra.Bundles.Ring._.isSemiring
d_isSemiring_2628 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Ring_2514 -> MAlonzo.Code.Algebra.Structures.T_IsSemiring_1238
d_isSemiring_2628 :: () -> () -> T_Ring_2514 -> T_IsSemiring_1238
d_isSemiring_2628 ~()
v0 ~()
v1 T_Ring_2514
v2 = T_Ring_2514 -> T_IsSemiring_1238
du_isSemiring_2628 T_Ring_2514
v2
du_isSemiring_2628 ::
  T_Ring_2514 -> MAlonzo.Code.Algebra.Structures.T_IsSemiring_1238
du_isSemiring_2628 :: T_Ring_2514 -> T_IsSemiring_1238
du_isSemiring_2628 T_Ring_2514
v0
  = (T_IsRing_1584 -> T_IsSemiring_1238)
-> AgdaAny -> T_IsSemiring_1238
forall a b. a -> b
coe
      T_IsRing_1584 -> T_IsSemiring_1238
MAlonzo.Code.Algebra.Structures.du_isSemiring_1698
      ((T_Ring_2514 -> T_IsRing_1584) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Ring_2514 -> T_IsRing_1584
d_isRing_2550 (T_Ring_2514 -> AgdaAny
forall a b. a -> b
coe T_Ring_2514
v0))
-- Algebra.Bundles.Ring._.isSemiringWithoutAnnihilatingZero
d_isSemiringWithoutAnnihilatingZero_2630 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Ring_2514 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutAnnihilatingZero_1142
d_isSemiringWithoutAnnihilatingZero_2630 :: () -> () -> T_Ring_2514 -> T_IsSemiringWithoutAnnihilatingZero_1142
d_isSemiringWithoutAnnihilatingZero_2630 ~()
v0 ~()
v1 T_Ring_2514
v2
  = T_Ring_2514 -> T_IsSemiringWithoutAnnihilatingZero_1142
du_isSemiringWithoutAnnihilatingZero_2630 T_Ring_2514
v2
du_isSemiringWithoutAnnihilatingZero_2630 ::
  T_Ring_2514 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutAnnihilatingZero_1142
du_isSemiringWithoutAnnihilatingZero_2630 :: T_Ring_2514 -> T_IsSemiringWithoutAnnihilatingZero_1142
du_isSemiringWithoutAnnihilatingZero_2630 T_Ring_2514
v0
  = (T_IsRing_1584 -> T_IsSemiringWithoutAnnihilatingZero_1142)
-> AgdaAny -> T_IsSemiringWithoutAnnihilatingZero_1142
forall a b. a -> b
coe
      T_IsRing_1584 -> T_IsSemiringWithoutAnnihilatingZero_1142
MAlonzo.Code.Algebra.Structures.du_isSemiringWithoutAnnihilatingZero_1696
      ((T_Ring_2514 -> T_IsRing_1584) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Ring_2514 -> T_IsRing_1584
d_isRing_2550 (T_Ring_2514 -> AgdaAny
forall a b. a -> b
coe T_Ring_2514
v0))
-- Algebra.Bundles.Ring._.isSemiringWithoutOne
d_isSemiringWithoutOne_2632 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Ring_2514 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutOne_952
d_isSemiringWithoutOne_2632 :: () -> () -> T_Ring_2514 -> T_IsSemiringWithoutOne_952
d_isSemiringWithoutOne_2632 ~()
v0 ~()
v1 T_Ring_2514
v2
  = T_Ring_2514 -> T_IsSemiringWithoutOne_952
du_isSemiringWithoutOne_2632 T_Ring_2514
v2
du_isSemiringWithoutOne_2632 ::
  T_Ring_2514 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutOne_952
du_isSemiringWithoutOne_2632 :: T_Ring_2514 -> T_IsSemiringWithoutOne_952
du_isSemiringWithoutOne_2632 T_Ring_2514
v0
  = let v1 :: T_IsRing_1584
v1 = T_Ring_2514 -> T_IsRing_1584
d_isRing_2550 (T_Ring_2514 -> T_Ring_2514
forall a b. a -> b
coe T_Ring_2514
v0) in
    AgdaAny -> T_IsSemiringWithoutOne_952
forall a b. a -> b
coe
      ((T_IsSemiring_1238 -> T_IsSemiringWithoutOne_952)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemiring_1238 -> T_IsSemiringWithoutOne_952
MAlonzo.Code.Algebra.Structures.du_isSemiringWithoutOne_1326
         ((T_IsRing_1584 -> T_IsSemiring_1238) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRing_1584 -> T_IsSemiring_1238
MAlonzo.Code.Algebra.Structures.du_isSemiring_1698 (T_IsRing_1584 -> AgdaAny
forall a b. a -> b
coe T_IsRing_1584
v1)))
-- Algebra.Bundles.Ring._.refl
d_refl_2634 :: T_Ring_2514 -> AgdaAny -> AgdaAny
d_refl_2634 :: T_Ring_2514 -> AgdaAny -> AgdaAny
d_refl_2634 T_Ring_2514
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_86 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_86 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_94
         ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202
            ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368
               ((T_IsGroup_580 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsGroup_580 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_594
                  ((T_IsAbelianGroup_662 -> T_IsGroup_580) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsAbelianGroup_662 -> T_IsGroup_580
MAlonzo.Code.Algebra.Structures.d_isGroup_674
                     ((T_IsRing_1584 -> T_IsAbelianGroup_662) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsRing_1584 -> T_IsAbelianGroup_662
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_1604
                        ((T_Ring_2514 -> T_IsRing_1584) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Ring_2514 -> T_IsRing_1584
d_isRing_2550 (T_Ring_2514 -> AgdaAny
forall a b. a -> b
coe T_Ring_2514
v0))))))))
-- Algebra.Bundles.Ring._.reflexive
d_reflexive_2636 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Ring_2514 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_2636 :: ()
-> ()
-> T_Ring_2514
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_2636 ~()
v0 ~()
v1 T_Ring_2514
v2 = T_Ring_2514 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_2636 T_Ring_2514
v2
du_reflexive_2636 ::
  T_Ring_2514 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_2636 :: T_Ring_2514 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_2636 T_Ring_2514
v0
  = let v1 :: T_IsRing_1584
v1 = T_Ring_2514 -> T_IsRing_1584
d_isRing_2550 (T_Ring_2514 -> T_Ring_2514
forall a b. a -> b
coe T_Ring_2514
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsAbelianGroup_662
v2
             = T_IsRing_1584 -> T_IsAbelianGroup_662
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_1604
                 (T_IsRing_1584 -> T_IsRing_1584
forall a b. a -> b
coe T_IsRing_1584
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsGroup_580
v3 = T_IsAbelianGroup_662 -> T_IsGroup_580
MAlonzo.Code.Algebra.Structures.d_isGroup_674 (T_IsAbelianGroup_662 -> T_IsAbelianGroup_662
forall a b. a -> b
coe T_IsAbelianGroup_662
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsMonoid_358
v4
                   = T_IsGroup_580 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_594 (T_IsGroup_580 -> T_IsGroup_580
forall a b. a -> b
coe T_IsGroup_580
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsSemigroup_194
v5
                      = T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368 (T_IsMonoid_358 -> T_IsMonoid_358
forall a b. a -> b
coe T_IsMonoid_358
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (let v6 :: T_IsMagma_86
v6 = T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202 (T_IsSemigroup_194 -> T_IsSemigroup_194
forall a b. a -> b
coe T_IsSemigroup_194
v5) in
                   (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
                     (\ AgdaAny
v7 AgdaAny
v8 AgdaAny
v9 ->
                        (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                          T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
                          ((T_IsMagma_86 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_94 (T_IsMagma_86 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86
v6))
                          AgdaAny
v7))))))
-- Algebra.Bundles.Ring._.setoid
d_setoid_2638 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Ring_2514 -> MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_2638 :: () -> () -> T_Ring_2514 -> T_Setoid_44
d_setoid_2638 ~()
v0 ~()
v1 T_Ring_2514
v2 = T_Ring_2514 -> T_Setoid_44
du_setoid_2638 T_Ring_2514
v2
du_setoid_2638 ::
  T_Ring_2514 -> MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_2638 :: T_Ring_2514 -> T_Setoid_44
du_setoid_2638 T_Ring_2514
v0
  = let v1 :: T_IsRing_1584
v1 = T_Ring_2514 -> T_IsRing_1584
d_isRing_2550 (T_Ring_2514 -> T_Ring_2514
forall a b. a -> b
coe T_Ring_2514
v0) in
    AgdaAny -> T_Setoid_44
forall a b. a -> b
coe
      (let v2 :: T_IsAbelianGroup_662
v2
             = T_IsRing_1584 -> T_IsAbelianGroup_662
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_1604
                 (T_IsRing_1584 -> T_IsRing_1584
forall a b. a -> b
coe T_IsRing_1584
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsGroup_580
v3 = T_IsAbelianGroup_662 -> T_IsGroup_580
MAlonzo.Code.Algebra.Structures.d_isGroup_674 (T_IsAbelianGroup_662 -> T_IsAbelianGroup_662
forall a b. a -> b
coe T_IsAbelianGroup_662
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsMonoid_358
v4
                   = T_IsGroup_580 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_594 (T_IsGroup_580 -> T_IsGroup_580
forall a b. a -> b
coe T_IsGroup_580
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsSemigroup_194
v5
                      = T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368 (T_IsMonoid_358 -> T_IsMonoid_358
forall a b. a -> b
coe T_IsMonoid_358
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  ((T_IsMagma_86 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsMagma_86 -> T_Setoid_44
MAlonzo.Code.Algebra.Structures.du_setoid_110
                     ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202 (T_IsSemigroup_194 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194
v5)))))))
-- Algebra.Bundles.Ring._.sym
d_sym_2640 ::
  T_Ring_2514 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_2640 :: T_Ring_2514 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_2640 T_Ring_2514
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_86 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_86 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_94
         ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202
            ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368
               ((T_IsGroup_580 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsGroup_580 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_594
                  ((T_IsAbelianGroup_662 -> T_IsGroup_580) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsAbelianGroup_662 -> T_IsGroup_580
MAlonzo.Code.Algebra.Structures.d_isGroup_674
                     ((T_IsRing_1584 -> T_IsAbelianGroup_662) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsRing_1584 -> T_IsAbelianGroup_662
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_1604
                        ((T_Ring_2514 -> T_IsRing_1584) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Ring_2514 -> T_IsRing_1584
d_isRing_2550 (T_Ring_2514 -> AgdaAny
forall a b. a -> b
coe T_Ring_2514
v0))))))))
-- Algebra.Bundles.Ring._.trans
d_trans_2642 ::
  T_Ring_2514 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_2642 :: T_Ring_2514
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_2642 T_Ring_2514
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_86 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_86 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_94
         ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202
            ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368
               ((T_IsGroup_580 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsGroup_580 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_594
                  ((T_IsAbelianGroup_662 -> T_IsGroup_580) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsAbelianGroup_662 -> T_IsGroup_580
MAlonzo.Code.Algebra.Structures.d_isGroup_674
                     ((T_IsRing_1584 -> T_IsAbelianGroup_662) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsRing_1584 -> T_IsAbelianGroup_662
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_1604
                        ((T_Ring_2514 -> T_IsRing_1584) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Ring_2514 -> T_IsRing_1584
d_isRing_2550 (T_Ring_2514 -> AgdaAny
forall a b. a -> b
coe T_Ring_2514
v0))))))))
-- Algebra.Bundles.Ring._.uniqueʳ-⁻¹
d_unique'691''45''8315''185'_2644 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Ring_2514 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_unique'691''45''8315''185'_2644 :: () -> () -> T_Ring_2514 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_unique'691''45''8315''185'_2644 ~()
v0 ~()
v1 T_Ring_2514
v2
  = T_Ring_2514 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_unique'691''45''8315''185'_2644 T_Ring_2514
v2
du_unique'691''45''8315''185'_2644 ::
  T_Ring_2514 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_unique'691''45''8315''185'_2644 :: T_Ring_2514 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_unique'691''45''8315''185'_2644 T_Ring_2514
v0
  = let v1 :: AgdaAny -> AgdaAny -> AgdaAny
v1 = T_Ring_2514 -> AgdaAny -> AgdaAny -> AgdaAny
d__'43'__2540 (T_Ring_2514 -> T_Ring_2514
forall a b. a -> b
coe T_Ring_2514
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: AgdaAny -> AgdaAny
v2 = T_Ring_2514 -> AgdaAny -> AgdaAny
d_'45'__2544 (T_Ring_2514 -> T_Ring_2514
forall a b. a -> b
coe T_Ring_2514
v0) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: AgdaAny
v3 = T_Ring_2514 -> AgdaAny
d_0'35'_2546 (T_Ring_2514 -> T_Ring_2514
forall a b. a -> b
coe T_Ring_2514
v0) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsRing_1584
v4 = T_Ring_2514 -> T_IsRing_1584
d_isRing_2550 (T_Ring_2514 -> T_Ring_2514
forall a b. a -> b
coe T_Ring_2514
v0) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsAbelianGroup_662
v5
                      = T_IsRing_1584 -> T_IsAbelianGroup_662
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_1604
                          (T_IsRing_1584 -> T_IsRing_1584
forall a b. a -> b
coe T_IsRing_1584
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (((AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> (AgdaAny -> AgdaAny)
 -> T_IsGroup_580
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsGroup_580
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.du_unique'691''45''8315''185'_654
                     ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v1) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3) ((AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v2)
                     ((T_IsAbelianGroup_662 -> T_IsGroup_580) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_662 -> T_IsGroup_580
MAlonzo.Code.Algebra.Structures.d_isGroup_674 (T_IsAbelianGroup_662 -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_662
v5)))))))
-- Algebra.Bundles.Ring._.uniqueˡ-⁻¹
d_unique'737''45''8315''185'_2646 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Ring_2514 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_unique'737''45''8315''185'_2646 :: () -> () -> T_Ring_2514 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_unique'737''45''8315''185'_2646 ~()
v0 ~()
v1 T_Ring_2514
v2
  = T_Ring_2514 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_unique'737''45''8315''185'_2646 T_Ring_2514
v2
du_unique'737''45''8315''185'_2646 ::
  T_Ring_2514 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_unique'737''45''8315''185'_2646 :: T_Ring_2514 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_unique'737''45''8315''185'_2646 T_Ring_2514
v0
  = let v1 :: AgdaAny -> AgdaAny -> AgdaAny
v1 = T_Ring_2514 -> AgdaAny -> AgdaAny -> AgdaAny
d__'43'__2540 (T_Ring_2514 -> T_Ring_2514
forall a b. a -> b
coe T_Ring_2514
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: AgdaAny -> AgdaAny
v2 = T_Ring_2514 -> AgdaAny -> AgdaAny
d_'45'__2544 (T_Ring_2514 -> T_Ring_2514
forall a b. a -> b
coe T_Ring_2514
v0) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: AgdaAny
v3 = T_Ring_2514 -> AgdaAny
d_0'35'_2546 (T_Ring_2514 -> T_Ring_2514
forall a b. a -> b
coe T_Ring_2514
v0) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsRing_1584
v4 = T_Ring_2514 -> T_IsRing_1584
d_isRing_2550 (T_Ring_2514 -> T_Ring_2514
forall a b. a -> b
coe T_Ring_2514
v0) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsAbelianGroup_662
v5
                      = T_IsRing_1584 -> T_IsAbelianGroup_662
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_1604
                          (T_IsRing_1584 -> T_IsRing_1584
forall a b. a -> b
coe T_IsRing_1584
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (((AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> (AgdaAny -> AgdaAny)
 -> T_IsGroup_580
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsGroup_580
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.du_unique'737''45''8315''185'_648
                     ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v1) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3) ((AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v2)
                     ((T_IsAbelianGroup_662 -> T_IsGroup_580) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_662 -> T_IsGroup_580
MAlonzo.Code.Algebra.Structures.d_isGroup_674 (T_IsAbelianGroup_662 -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_662
v5)))))))
-- Algebra.Bundles.Ring._.zero
d_zero_2648 ::
  T_Ring_2514 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_zero_2648 :: T_Ring_2514 -> T_Σ_14
d_zero_2648 T_Ring_2514
v0
  = (T_IsRing_1584 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsRing_1584 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_zero_1610
      ((T_Ring_2514 -> T_IsRing_1584) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Ring_2514 -> T_IsRing_1584
d_isRing_2550 (T_Ring_2514 -> AgdaAny
forall a b. a -> b
coe T_Ring_2514
v0))
-- Algebra.Bundles.Ring._.zeroʳ
d_zero'691'_2650 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Ring_2514 -> AgdaAny -> AgdaAny
d_zero'691'_2650 :: () -> () -> T_Ring_2514 -> AgdaAny -> AgdaAny
d_zero'691'_2650 ~()
v0 ~()
v1 T_Ring_2514
v2 = T_Ring_2514 -> AgdaAny -> AgdaAny
du_zero'691'_2650 T_Ring_2514
v2
du_zero'691'_2650 :: T_Ring_2514 -> AgdaAny -> AgdaAny
du_zero'691'_2650 :: T_Ring_2514 -> AgdaAny -> AgdaAny
du_zero'691'_2650 T_Ring_2514
v0
  = (T_IsRing_1584 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsRing_1584 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_zero'691'_1694
      ((T_Ring_2514 -> T_IsRing_1584) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Ring_2514 -> T_IsRing_1584
d_isRing_2550 (T_Ring_2514 -> AgdaAny
forall a b. a -> b
coe T_Ring_2514
v0))
-- Algebra.Bundles.Ring._.zeroˡ
d_zero'737'_2652 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Ring_2514 -> AgdaAny -> AgdaAny
d_zero'737'_2652 :: () -> () -> T_Ring_2514 -> AgdaAny -> AgdaAny
d_zero'737'_2652 ~()
v0 ~()
v1 T_Ring_2514
v2 = T_Ring_2514 -> AgdaAny -> AgdaAny
du_zero'737'_2652 T_Ring_2514
v2
du_zero'737'_2652 :: T_Ring_2514 -> AgdaAny -> AgdaAny
du_zero'737'_2652 :: T_Ring_2514 -> AgdaAny -> AgdaAny
du_zero'737'_2652 T_Ring_2514
v0
  = (T_IsRing_1584 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsRing_1584 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_zero'737'_1692
      ((T_Ring_2514 -> T_IsRing_1584) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Ring_2514 -> T_IsRing_1584
d_isRing_2550 (T_Ring_2514 -> AgdaAny
forall a b. a -> b
coe T_Ring_2514
v0))
-- Algebra.Bundles.Ring.+-abelianGroup
d_'43''45'abelianGroup_2654 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Ring_2514 -> T_AbelianGroup_990
d_'43''45'abelianGroup_2654 :: () -> () -> T_Ring_2514 -> T_AbelianGroup_990
d_'43''45'abelianGroup_2654 ~()
v0 ~()
v1 T_Ring_2514
v2
  = T_Ring_2514 -> T_AbelianGroup_990
du_'43''45'abelianGroup_2654 T_Ring_2514
v2
du_'43''45'abelianGroup_2654 :: T_Ring_2514 -> T_AbelianGroup_990
du_'43''45'abelianGroup_2654 :: T_Ring_2514 -> T_AbelianGroup_990
du_'43''45'abelianGroup_2654 T_Ring_2514
v0
  = ((AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> (AgdaAny -> AgdaAny)
 -> T_IsAbelianGroup_662
 -> T_AbelianGroup_990)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsAbelianGroup_662
-> T_AbelianGroup_990
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsAbelianGroup_662
-> T_AbelianGroup_990
C_AbelianGroup'46'constructor_16529 (T_Ring_2514 -> AgdaAny -> AgdaAny -> AgdaAny
d__'43'__2540 (T_Ring_2514 -> T_Ring_2514
forall a b. a -> b
coe T_Ring_2514
v0))
      (T_Ring_2514 -> AgdaAny
d_0'35'_2546 (T_Ring_2514 -> T_Ring_2514
forall a b. a -> b
coe T_Ring_2514
v0)) (T_Ring_2514 -> AgdaAny -> AgdaAny
d_'45'__2544 (T_Ring_2514 -> T_Ring_2514
forall a b. a -> b
coe T_Ring_2514
v0))
      (T_IsRing_1584 -> T_IsAbelianGroup_662
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_1604
         ((T_Ring_2514 -> T_IsRing_1584) -> AgdaAny -> T_IsRing_1584
forall a b. a -> b
coe T_Ring_2514 -> T_IsRing_1584
d_isRing_2550 (T_Ring_2514 -> AgdaAny
forall a b. a -> b
coe T_Ring_2514
v0)))
-- Algebra.Bundles.Ring.semiring
d_semiring_2656 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Ring_2514 -> T_Semiring_1932
d_semiring_2656 :: () -> () -> T_Ring_2514 -> T_Semiring_1932
d_semiring_2656 ~()
v0 ~()
v1 T_Ring_2514
v2 = T_Ring_2514 -> T_Semiring_1932
du_semiring_2656 T_Ring_2514
v2
du_semiring_2656 :: T_Ring_2514 -> T_Semiring_1932
du_semiring_2656 :: T_Ring_2514 -> T_Semiring_1932
du_semiring_2656 T_Ring_2514
v0
  = ((AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> AgdaAny
 -> T_IsSemiring_1238
 -> T_Semiring_1932)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> T_Semiring_1932
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsSemiring_1238
-> T_Semiring_1932
C_Semiring'46'constructor_33613 (T_Ring_2514 -> AgdaAny -> AgdaAny -> AgdaAny
d__'43'__2540 (T_Ring_2514 -> T_Ring_2514
forall a b. a -> b
coe T_Ring_2514
v0))
      (T_Ring_2514 -> AgdaAny -> AgdaAny -> AgdaAny
d__'42'__2542 (T_Ring_2514 -> T_Ring_2514
forall a b. a -> b
coe T_Ring_2514
v0)) (T_Ring_2514 -> AgdaAny
d_0'35'_2546 (T_Ring_2514 -> T_Ring_2514
forall a b. a -> b
coe T_Ring_2514
v0))
      (T_Ring_2514 -> AgdaAny
d_1'35'_2548 (T_Ring_2514 -> T_Ring_2514
forall a b. a -> b
coe T_Ring_2514
v0))
      ((T_IsRing_1584 -> T_IsSemiring_1238) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsRing_1584 -> T_IsSemiring_1238
MAlonzo.Code.Algebra.Structures.du_isSemiring_1698
         ((T_Ring_2514 -> T_IsRing_1584) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Ring_2514 -> T_IsRing_1584
d_isRing_2550 (T_Ring_2514 -> AgdaAny
forall a b. a -> b
coe T_Ring_2514
v0)))
-- Algebra.Bundles.Ring._._≉_
d__'8777'__2660 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Ring_2514 -> AgdaAny -> AgdaAny -> ()
d__'8777'__2660 :: () -> () -> T_Ring_2514 -> AgdaAny -> AgdaAny -> ()
d__'8777'__2660 = () -> () -> T_Ring_2514 -> AgdaAny -> AgdaAny -> ()
forall a. a
erased
-- Algebra.Bundles.Ring._.magma
d_magma_2662 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 -> T_Ring_2514 -> T_Magma_36
d_magma_2662 :: () -> () -> T_Ring_2514 -> T_Magma_36
d_magma_2662 ~()
v0 ~()
v1 T_Ring_2514
v2 = T_Ring_2514 -> T_Magma_36
du_magma_2662 T_Ring_2514
v2
du_magma_2662 :: T_Ring_2514 -> T_Magma_36
du_magma_2662 :: T_Ring_2514 -> T_Magma_36
du_magma_2662 T_Ring_2514
v0
  = let v1 :: t
v1 = (T_Ring_2514 -> T_Semiring_1932) -> AgdaAny -> t
forall a b. a -> b
coe T_Ring_2514 -> T_Semiring_1932
du_semiring_2656 (T_Ring_2514 -> AgdaAny
forall a b. a -> b
coe T_Ring_2514
v0) in
    AgdaAny -> T_Magma_36
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_Semiring_1932 -> T_SemiringWithoutAnnihilatingZero_1786)
-> AgdaAny -> t
forall a b. a -> b
coe T_Semiring_1932 -> T_SemiringWithoutAnnihilatingZero_1786
du_semiringWithoutAnnihilatingZero_2048 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: t
v3 = (T_SemiringWithoutAnnihilatingZero_1786 -> T_Monoid_506)
-> AgdaAny -> t
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_1786 -> T_Monoid_506
du_'42''45'monoid_1916 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_Semigroup_206 -> T_Magma_36) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semigroup_206 -> T_Magma_36
du_magma_254 ((T_Monoid_506 -> T_Semigroup_206) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Monoid_506 -> T_Semigroup_206
du_semigroup_566 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3)))))
-- Algebra.Bundles.Ring._.*-monoid
d_'42''45'monoid_2664 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Ring_2514 -> T_Monoid_506
d_'42''45'monoid_2664 :: () -> () -> T_Ring_2514 -> T_Monoid_506
d_'42''45'monoid_2664 ~()
v0 ~()
v1 T_Ring_2514
v2 = T_Ring_2514 -> T_Monoid_506
du_'42''45'monoid_2664 T_Ring_2514
v2
du_'42''45'monoid_2664 :: T_Ring_2514 -> T_Monoid_506
du_'42''45'monoid_2664 :: T_Ring_2514 -> T_Monoid_506
du_'42''45'monoid_2664 T_Ring_2514
v0
  = let v1 :: t
v1 = (T_Ring_2514 -> T_Semiring_1932) -> AgdaAny -> t
forall a b. a -> b
coe T_Ring_2514 -> T_Semiring_1932
du_semiring_2656 (T_Ring_2514 -> AgdaAny
forall a b. a -> b
coe T_Ring_2514
v0) in
    AgdaAny -> T_Monoid_506
forall a b. a -> b
coe
      ((T_SemiringWithoutAnnihilatingZero_1786 -> T_Monoid_506)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_SemiringWithoutAnnihilatingZero_1786 -> T_Monoid_506
du_'42''45'monoid_1916
         ((T_Semiring_1932 -> T_SemiringWithoutAnnihilatingZero_1786)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semiring_1932 -> T_SemiringWithoutAnnihilatingZero_1786
du_semiringWithoutAnnihilatingZero_2048 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1)))
-- Algebra.Bundles.Ring._.rawMagma
d_rawMagma_2666 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Ring_2514 -> T_RawMagma_8
d_rawMagma_2666 :: () -> () -> T_Ring_2514 -> T_RawMagma_8
d_rawMagma_2666 ~()
v0 ~()
v1 T_Ring_2514
v2 = T_Ring_2514 -> T_RawMagma_8
du_rawMagma_2666 T_Ring_2514
v2
du_rawMagma_2666 :: T_Ring_2514 -> T_RawMagma_8
du_rawMagma_2666 :: T_Ring_2514 -> T_RawMagma_8
du_rawMagma_2666 T_Ring_2514
v0
  = let v1 :: t
v1 = (T_Ring_2514 -> T_Semiring_1932) -> AgdaAny -> t
forall a b. a -> b
coe T_Ring_2514 -> T_Semiring_1932
du_semiring_2656 (T_Ring_2514 -> AgdaAny
forall a b. a -> b
coe T_Ring_2514
v0) in
    AgdaAny -> T_RawMagma_8
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_Semiring_1932 -> T_SemiringWithoutAnnihilatingZero_1786)
-> AgdaAny -> t
forall a b. a -> b
coe T_Semiring_1932 -> T_SemiringWithoutAnnihilatingZero_1786
du_semiringWithoutAnnihilatingZero_2048 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: t
v3 = (T_SemiringWithoutAnnihilatingZero_1786 -> T_Monoid_506)
-> AgdaAny -> t
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_1786 -> T_Monoid_506
du_'42''45'monoid_1916 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: t
v4 = (T_Monoid_506 -> T_Semigroup_206) -> AgdaAny -> t
forall a b. a -> b
coe T_Monoid_506 -> T_Semigroup_206
du_semigroup_566 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_Magma_36 -> T_RawMagma_8) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Magma_36 -> T_RawMagma_8
du_rawMagma_80 ((T_Semigroup_206 -> T_Magma_36) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semigroup_206 -> T_Magma_36
du_magma_254 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v4))))))
-- Algebra.Bundles.Ring._.rawMonoid
d_rawMonoid_2668 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Ring_2514 -> T_RawMonoid_474
d_rawMonoid_2668 :: () -> () -> T_Ring_2514 -> T_RawMonoid_474
d_rawMonoid_2668 ~()
v0 ~()
v1 T_Ring_2514
v2 = T_Ring_2514 -> T_RawMonoid_474
du_rawMonoid_2668 T_Ring_2514
v2
du_rawMonoid_2668 :: T_Ring_2514 -> T_RawMonoid_474
du_rawMonoid_2668 :: T_Ring_2514 -> T_RawMonoid_474
du_rawMonoid_2668 T_Ring_2514
v0
  = let v1 :: t
v1 = (T_Ring_2514 -> T_Semiring_1932) -> AgdaAny -> t
forall a b. a -> b
coe T_Ring_2514 -> T_Semiring_1932
du_semiring_2656 (T_Ring_2514 -> AgdaAny
forall a b. a -> b
coe T_Ring_2514
v0) in
    AgdaAny -> T_RawMonoid_474
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_Semiring_1932 -> T_SemiringWithoutAnnihilatingZero_1786)
-> AgdaAny -> t
forall a b. a -> b
coe T_Semiring_1932 -> T_SemiringWithoutAnnihilatingZero_1786
du_semiringWithoutAnnihilatingZero_2048 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_Monoid_506 -> T_RawMonoid_474) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Monoid_506 -> T_RawMonoid_474
du_rawMonoid_576 ((T_SemiringWithoutAnnihilatingZero_1786 -> T_Monoid_506)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_1786 -> T_Monoid_506
du_'42''45'monoid_1916 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2))))
-- Algebra.Bundles.Ring._.semigroup
d_semigroup_2670 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Ring_2514 -> T_Semigroup_206
d_semigroup_2670 :: () -> () -> T_Ring_2514 -> T_Semigroup_206
d_semigroup_2670 ~()
v0 ~()
v1 T_Ring_2514
v2 = T_Ring_2514 -> T_Semigroup_206
du_semigroup_2670 T_Ring_2514
v2
du_semigroup_2670 :: T_Ring_2514 -> T_Semigroup_206
du_semigroup_2670 :: T_Ring_2514 -> T_Semigroup_206
du_semigroup_2670 T_Ring_2514
v0
  = let v1 :: t
v1 = (T_Ring_2514 -> T_Semiring_1932) -> AgdaAny -> t
forall a b. a -> b
coe T_Ring_2514 -> T_Semiring_1932
du_semiring_2656 (T_Ring_2514 -> AgdaAny
forall a b. a -> b
coe T_Ring_2514
v0) in
    AgdaAny -> T_Semigroup_206
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_Semiring_1932 -> T_SemiringWithoutAnnihilatingZero_1786)
-> AgdaAny -> t
forall a b. a -> b
coe T_Semiring_1932 -> T_SemiringWithoutAnnihilatingZero_1786
du_semiringWithoutAnnihilatingZero_2048 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_Monoid_506 -> T_Semigroup_206) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Monoid_506 -> T_Semigroup_206
du_semigroup_566 ((T_SemiringWithoutAnnihilatingZero_1786 -> T_Monoid_506)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_1786 -> T_Monoid_506
du_'42''45'monoid_1916 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2))))
-- Algebra.Bundles.Ring._.commutativeMagma
d_commutativeMagma_2672 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Ring_2514 -> T_CommutativeMagma_148
d_commutativeMagma_2672 :: () -> () -> T_Ring_2514 -> T_CommutativeMagma_148
d_commutativeMagma_2672 ~()
v0 ~()
v1 T_Ring_2514
v2 = T_Ring_2514 -> T_CommutativeMagma_148
du_commutativeMagma_2672 T_Ring_2514
v2
du_commutativeMagma_2672 :: T_Ring_2514 -> T_CommutativeMagma_148
du_commutativeMagma_2672 :: T_Ring_2514 -> T_CommutativeMagma_148
du_commutativeMagma_2672 T_Ring_2514
v0
  = let v1 :: t
v1 = (T_Ring_2514 -> T_Semiring_1932) -> AgdaAny -> t
forall a b. a -> b
coe T_Ring_2514 -> T_Semiring_1932
du_semiring_2656 (T_Ring_2514 -> AgdaAny
forall a b. a -> b
coe T_Ring_2514
v0) in
    AgdaAny -> T_CommutativeMagma_148
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_Semiring_1932 -> T_SemiringWithoutAnnihilatingZero_1786)
-> AgdaAny -> t
forall a b. a -> b
coe T_Semiring_1932 -> T_SemiringWithoutAnnihilatingZero_1786
du_semiringWithoutAnnihilatingZero_2048 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: t
v3 = (T_SemiringWithoutAnnihilatingZero_1786 -> T_CommutativeMonoid_582)
-> AgdaAny -> t
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_1786 -> T_CommutativeMonoid_582
du_'43''45'commutativeMonoid_1896 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_CommutativeSemigroup_332 -> T_CommutativeMagma_148)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_CommutativeSemigroup_332 -> T_CommutativeMagma_148
du_commutativeMagma_396
               ((T_CommutativeMonoid_582 -> T_CommutativeSemigroup_332)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeMonoid_582 -> T_CommutativeSemigroup_332
du_commutativeSemigroup_664 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3)))))
-- Algebra.Bundles.Ring._.+-commutativeMonoid
d_'43''45'commutativeMonoid_2674 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Ring_2514 -> T_CommutativeMonoid_582
d_'43''45'commutativeMonoid_2674 :: () -> () -> T_Ring_2514 -> T_CommutativeMonoid_582
d_'43''45'commutativeMonoid_2674 ~()
v0 ~()
v1 T_Ring_2514
v2
  = T_Ring_2514 -> T_CommutativeMonoid_582
du_'43''45'commutativeMonoid_2674 T_Ring_2514
v2
du_'43''45'commutativeMonoid_2674 ::
  T_Ring_2514 -> T_CommutativeMonoid_582
du_'43''45'commutativeMonoid_2674 :: T_Ring_2514 -> T_CommutativeMonoid_582
du_'43''45'commutativeMonoid_2674 T_Ring_2514
v0
  = let v1 :: t
v1 = (T_Ring_2514 -> T_Semiring_1932) -> AgdaAny -> t
forall a b. a -> b
coe T_Ring_2514 -> T_Semiring_1932
du_semiring_2656 (T_Ring_2514 -> AgdaAny
forall a b. a -> b
coe T_Ring_2514
v0) in
    AgdaAny -> T_CommutativeMonoid_582
forall a b. a -> b
coe
      ((T_SemiringWithoutAnnihilatingZero_1786 -> T_CommutativeMonoid_582)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_SemiringWithoutAnnihilatingZero_1786 -> T_CommutativeMonoid_582
du_'43''45'commutativeMonoid_1896
         ((T_Semiring_1932 -> T_SemiringWithoutAnnihilatingZero_1786)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semiring_1932 -> T_SemiringWithoutAnnihilatingZero_1786
du_semiringWithoutAnnihilatingZero_2048 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1)))
-- Algebra.Bundles.Ring._.commutativeSemigroup
d_commutativeSemigroup_2676 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Ring_2514 -> T_CommutativeSemigroup_332
d_commutativeSemigroup_2676 :: () -> () -> T_Ring_2514 -> T_CommutativeSemigroup_332
d_commutativeSemigroup_2676 ~()
v0 ~()
v1 T_Ring_2514
v2
  = T_Ring_2514 -> T_CommutativeSemigroup_332
du_commutativeSemigroup_2676 T_Ring_2514
v2
du_commutativeSemigroup_2676 ::
  T_Ring_2514 -> T_CommutativeSemigroup_332
du_commutativeSemigroup_2676 :: T_Ring_2514 -> T_CommutativeSemigroup_332
du_commutativeSemigroup_2676 T_Ring_2514
v0
  = let v1 :: t
v1 = (T_Ring_2514 -> T_Semiring_1932) -> AgdaAny -> t
forall a b. a -> b
coe T_Ring_2514 -> T_Semiring_1932
du_semiring_2656 (T_Ring_2514 -> AgdaAny
forall a b. a -> b
coe T_Ring_2514
v0) in
    AgdaAny -> T_CommutativeSemigroup_332
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_Semiring_1932 -> T_SemiringWithoutAnnihilatingZero_1786)
-> AgdaAny -> t
forall a b. a -> b
coe T_Semiring_1932 -> T_SemiringWithoutAnnihilatingZero_1786
du_semiringWithoutAnnihilatingZero_2048 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_CommutativeMonoid_582 -> T_CommutativeSemigroup_332)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_CommutativeMonoid_582 -> T_CommutativeSemigroup_332
du_commutativeSemigroup_664
            ((T_SemiringWithoutAnnihilatingZero_1786 -> T_CommutativeMonoid_582)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_1786 -> T_CommutativeMonoid_582
du_'43''45'commutativeMonoid_1896 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2))))
-- Algebra.Bundles.Ring._.magma
d_magma_2678 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 -> T_Ring_2514 -> T_Magma_36
d_magma_2678 :: () -> () -> T_Ring_2514 -> T_Magma_36
d_magma_2678 ~()
v0 ~()
v1 T_Ring_2514
v2 = T_Ring_2514 -> T_Magma_36
du_magma_2678 T_Ring_2514
v2
du_magma_2678 :: T_Ring_2514 -> T_Magma_36
du_magma_2678 :: T_Ring_2514 -> T_Magma_36
du_magma_2678 T_Ring_2514
v0
  = let v1 :: t
v1 = (T_Ring_2514 -> T_Semiring_1932) -> AgdaAny -> t
forall a b. a -> b
coe T_Ring_2514 -> T_Semiring_1932
du_semiring_2656 (T_Ring_2514 -> AgdaAny
forall a b. a -> b
coe T_Ring_2514
v0) in
    AgdaAny -> T_Magma_36
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_Semiring_1932 -> T_SemiringWithoutAnnihilatingZero_1786)
-> AgdaAny -> t
forall a b. a -> b
coe T_Semiring_1932 -> T_SemiringWithoutAnnihilatingZero_1786
du_semiringWithoutAnnihilatingZero_2048 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: t
v3 = (T_SemiringWithoutAnnihilatingZero_1786 -> T_CommutativeMonoid_582)
-> AgdaAny -> t
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_1786 -> T_CommutativeMonoid_582
du_'43''45'commutativeMonoid_1896 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: t
v4 = (T_CommutativeMonoid_582 -> T_Monoid_506) -> AgdaAny -> t
forall a b. a -> b
coe T_CommutativeMonoid_582 -> T_Monoid_506
du_monoid_650 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_Semigroup_206 -> T_Magma_36) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semigroup_206 -> T_Magma_36
du_magma_254 ((T_Monoid_506 -> T_Semigroup_206) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Monoid_506 -> T_Semigroup_206
du_semigroup_566 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v4))))))
-- Algebra.Bundles.Ring._.monoid
d_monoid_2680 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Ring_2514 -> T_Monoid_506
d_monoid_2680 :: () -> () -> T_Ring_2514 -> T_Monoid_506
d_monoid_2680 ~()
v0 ~()
v1 T_Ring_2514
v2 = T_Ring_2514 -> T_Monoid_506
du_monoid_2680 T_Ring_2514
v2
du_monoid_2680 :: T_Ring_2514 -> T_Monoid_506
du_monoid_2680 :: T_Ring_2514 -> T_Monoid_506
du_monoid_2680 T_Ring_2514
v0
  = let v1 :: t
v1 = (T_Ring_2514 -> T_Semiring_1932) -> AgdaAny -> t
forall a b. a -> b
coe T_Ring_2514 -> T_Semiring_1932
du_semiring_2656 (T_Ring_2514 -> AgdaAny
forall a b. a -> b
coe T_Ring_2514
v0) in
    AgdaAny -> T_Monoid_506
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_Semiring_1932 -> T_SemiringWithoutAnnihilatingZero_1786)
-> AgdaAny -> t
forall a b. a -> b
coe T_Semiring_1932 -> T_SemiringWithoutAnnihilatingZero_1786
du_semiringWithoutAnnihilatingZero_2048 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_CommutativeMonoid_582 -> T_Monoid_506) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_CommutativeMonoid_582 -> T_Monoid_506
du_monoid_650 ((T_SemiringWithoutAnnihilatingZero_1786 -> T_CommutativeMonoid_582)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_1786 -> T_CommutativeMonoid_582
du_'43''45'commutativeMonoid_1896 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2))))
-- Algebra.Bundles.Ring._.rawMagma
d_rawMagma_2682 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Ring_2514 -> T_RawMagma_8
d_rawMagma_2682 :: () -> () -> T_Ring_2514 -> T_RawMagma_8
d_rawMagma_2682 ~()
v0 ~()
v1 T_Ring_2514
v2 = T_Ring_2514 -> T_RawMagma_8
du_rawMagma_2682 T_Ring_2514
v2
du_rawMagma_2682 :: T_Ring_2514 -> T_RawMagma_8
du_rawMagma_2682 :: T_Ring_2514 -> T_RawMagma_8
du_rawMagma_2682 T_Ring_2514
v0
  = let v1 :: t
v1 = (T_Ring_2514 -> T_Semiring_1932) -> AgdaAny -> t
forall a b. a -> b
coe T_Ring_2514 -> T_Semiring_1932
du_semiring_2656 (T_Ring_2514 -> AgdaAny
forall a b. a -> b
coe T_Ring_2514
v0) in
    AgdaAny -> T_RawMagma_8
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_Semiring_1932 -> T_SemiringWithoutAnnihilatingZero_1786)
-> AgdaAny -> t
forall a b. a -> b
coe T_Semiring_1932 -> T_SemiringWithoutAnnihilatingZero_1786
du_semiringWithoutAnnihilatingZero_2048 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: t
v3 = (T_SemiringWithoutAnnihilatingZero_1786 -> T_CommutativeMonoid_582)
-> AgdaAny -> t
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_1786 -> T_CommutativeMonoid_582
du_'43''45'commutativeMonoid_1896 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: t
v4 = (T_CommutativeMonoid_582 -> T_Monoid_506) -> AgdaAny -> t
forall a b. a -> b
coe T_CommutativeMonoid_582 -> T_Monoid_506
du_monoid_650 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: t
v5 = (T_Monoid_506 -> T_Semigroup_206) -> AgdaAny -> t
forall a b. a -> b
coe T_Monoid_506 -> T_Semigroup_206
du_semigroup_566 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_Magma_36 -> T_RawMagma_8) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Magma_36 -> T_RawMagma_8
du_rawMagma_80 ((T_Semigroup_206 -> T_Magma_36) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semigroup_206 -> T_Magma_36
du_magma_254 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v5)))))))
-- Algebra.Bundles.Ring._.rawMonoid
d_rawMonoid_2684 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Ring_2514 -> T_RawMonoid_474
d_rawMonoid_2684 :: () -> () -> T_Ring_2514 -> T_RawMonoid_474
d_rawMonoid_2684 ~()
v0 ~()
v1 T_Ring_2514
v2 = T_Ring_2514 -> T_RawMonoid_474
du_rawMonoid_2684 T_Ring_2514
v2
du_rawMonoid_2684 :: T_Ring_2514 -> T_RawMonoid_474
du_rawMonoid_2684 :: T_Ring_2514 -> T_RawMonoid_474
du_rawMonoid_2684 T_Ring_2514
v0
  = let v1 :: t
v1 = (T_Ring_2514 -> T_Semiring_1932) -> AgdaAny -> t
forall a b. a -> b
coe T_Ring_2514 -> T_Semiring_1932
du_semiring_2656 (T_Ring_2514 -> AgdaAny
forall a b. a -> b
coe T_Ring_2514
v0) in
    AgdaAny -> T_RawMonoid_474
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_Semiring_1932 -> T_SemiringWithoutAnnihilatingZero_1786)
-> AgdaAny -> t
forall a b. a -> b
coe T_Semiring_1932 -> T_SemiringWithoutAnnihilatingZero_1786
du_semiringWithoutAnnihilatingZero_2048 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: t
v3 = (T_SemiringWithoutAnnihilatingZero_1786 -> T_CommutativeMonoid_582)
-> AgdaAny -> t
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_1786 -> T_CommutativeMonoid_582
du_'43''45'commutativeMonoid_1896 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_Monoid_506 -> T_RawMonoid_474) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Monoid_506 -> T_RawMonoid_474
du_rawMonoid_576 ((T_CommutativeMonoid_582 -> T_Monoid_506) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeMonoid_582 -> T_Monoid_506
du_monoid_650 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3)))))
-- Algebra.Bundles.Ring._.semigroup
d_semigroup_2686 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Ring_2514 -> T_Semigroup_206
d_semigroup_2686 :: () -> () -> T_Ring_2514 -> T_Semigroup_206
d_semigroup_2686 ~()
v0 ~()
v1 T_Ring_2514
v2 = T_Ring_2514 -> T_Semigroup_206
du_semigroup_2686 T_Ring_2514
v2
du_semigroup_2686 :: T_Ring_2514 -> T_Semigroup_206
du_semigroup_2686 :: T_Ring_2514 -> T_Semigroup_206
du_semigroup_2686 T_Ring_2514
v0
  = let v1 :: t
v1 = (T_Ring_2514 -> T_Semiring_1932) -> AgdaAny -> t
forall a b. a -> b
coe T_Ring_2514 -> T_Semiring_1932
du_semiring_2656 (T_Ring_2514 -> AgdaAny
forall a b. a -> b
coe T_Ring_2514
v0) in
    AgdaAny -> T_Semigroup_206
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_Semiring_1932 -> T_SemiringWithoutAnnihilatingZero_1786)
-> AgdaAny -> t
forall a b. a -> b
coe T_Semiring_1932 -> T_SemiringWithoutAnnihilatingZero_1786
du_semiringWithoutAnnihilatingZero_2048 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: t
v3 = (T_SemiringWithoutAnnihilatingZero_1786 -> T_CommutativeMonoid_582)
-> AgdaAny -> t
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_1786 -> T_CommutativeMonoid_582
du_'43''45'commutativeMonoid_1896 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_Monoid_506 -> T_Semigroup_206) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Monoid_506 -> T_Semigroup_206
du_semigroup_566 ((T_CommutativeMonoid_582 -> T_Monoid_506) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeMonoid_582 -> T_Monoid_506
du_monoid_650 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3)))))
-- Algebra.Bundles.Ring._.nearSemiring
d_nearSemiring_2688 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Ring_2514 -> T_NearSemiring_1354
d_nearSemiring_2688 :: () -> () -> T_Ring_2514 -> T_NearSemiring_1354
d_nearSemiring_2688 ~()
v0 ~()
v1 T_Ring_2514
v2 = T_Ring_2514 -> T_NearSemiring_1354
du_nearSemiring_2688 T_Ring_2514
v2
du_nearSemiring_2688 :: T_Ring_2514 -> T_NearSemiring_1354
du_nearSemiring_2688 :: T_Ring_2514 -> T_NearSemiring_1354
du_nearSemiring_2688 T_Ring_2514
v0
  = let v1 :: t
v1 = (T_Ring_2514 -> T_Semiring_1932) -> AgdaAny -> t
forall a b. a -> b
coe T_Ring_2514 -> T_Semiring_1932
du_semiring_2656 (T_Ring_2514 -> AgdaAny
forall a b. a -> b
coe T_Ring_2514
v0) in
    AgdaAny -> T_NearSemiring_1354
forall a b. a -> b
coe
      ((T_SemiringWithoutOne_1464 -> T_NearSemiring_1354)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_SemiringWithoutOne_1464 -> T_NearSemiring_1354
du_nearSemiring_1562 ((T_Semiring_1932 -> T_SemiringWithoutOne_1464)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semiring_1932 -> T_SemiringWithoutOne_1464
du_semiringWithoutOne_2084 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1)))
-- Algebra.Bundles.Ring._.semiringWithoutAnnihilatingZero
d_semiringWithoutAnnihilatingZero_2690 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Ring_2514 -> T_SemiringWithoutAnnihilatingZero_1786
d_semiringWithoutAnnihilatingZero_2690 :: () -> () -> T_Ring_2514 -> T_SemiringWithoutAnnihilatingZero_1786
d_semiringWithoutAnnihilatingZero_2690 ~()
v0 ~()
v1 T_Ring_2514
v2
  = T_Ring_2514 -> T_SemiringWithoutAnnihilatingZero_1786
du_semiringWithoutAnnihilatingZero_2690 T_Ring_2514
v2
du_semiringWithoutAnnihilatingZero_2690 ::
  T_Ring_2514 -> T_SemiringWithoutAnnihilatingZero_1786
du_semiringWithoutAnnihilatingZero_2690 :: T_Ring_2514 -> T_SemiringWithoutAnnihilatingZero_1786
du_semiringWithoutAnnihilatingZero_2690 T_Ring_2514
v0
  = (T_Semiring_1932 -> T_SemiringWithoutAnnihilatingZero_1786)
-> AgdaAny -> T_SemiringWithoutAnnihilatingZero_1786
forall a b. a -> b
coe
      T_Semiring_1932 -> T_SemiringWithoutAnnihilatingZero_1786
du_semiringWithoutAnnihilatingZero_2048
      ((T_Ring_2514 -> T_Semiring_1932) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Ring_2514 -> T_Semiring_1932
du_semiring_2656 (T_Ring_2514 -> AgdaAny
forall a b. a -> b
coe T_Ring_2514
v0))
-- Algebra.Bundles.Ring._.semiringWithoutOne
d_semiringWithoutOne_2692 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Ring_2514 -> T_SemiringWithoutOne_1464
d_semiringWithoutOne_2692 :: () -> () -> T_Ring_2514 -> T_SemiringWithoutOne_1464
d_semiringWithoutOne_2692 ~()
v0 ~()
v1 T_Ring_2514
v2
  = T_Ring_2514 -> T_SemiringWithoutOne_1464
du_semiringWithoutOne_2692 T_Ring_2514
v2
du_semiringWithoutOne_2692 ::
  T_Ring_2514 -> T_SemiringWithoutOne_1464
du_semiringWithoutOne_2692 :: T_Ring_2514 -> T_SemiringWithoutOne_1464
du_semiringWithoutOne_2692 T_Ring_2514
v0
  = (T_Semiring_1932 -> T_SemiringWithoutOne_1464)
-> AgdaAny -> T_SemiringWithoutOne_1464
forall a b. a -> b
coe T_Semiring_1932 -> T_SemiringWithoutOne_1464
du_semiringWithoutOne_2084 ((T_Ring_2514 -> T_Semiring_1932) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Ring_2514 -> T_Semiring_1932
du_semiring_2656 (T_Ring_2514 -> AgdaAny
forall a b. a -> b
coe T_Ring_2514
v0))
-- Algebra.Bundles.Ring._.group
d_group_2696 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Ring_2514 -> T_Group_890
d_group_2696 :: () -> () -> T_Ring_2514 -> T_Group_890
d_group_2696 ~()
v0 ~()
v1 T_Ring_2514
v2 = T_Ring_2514 -> T_Group_890
du_group_2696 T_Ring_2514
v2
du_group_2696 :: T_Ring_2514 -> T_Group_890
du_group_2696 :: T_Ring_2514 -> T_Group_890
du_group_2696 T_Ring_2514
v0
  = (T_AbelianGroup_990 -> T_Group_890) -> AgdaAny -> T_Group_890
forall a b. a -> b
coe T_AbelianGroup_990 -> T_Group_890
du_group_1080 ((T_Ring_2514 -> T_AbelianGroup_990) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Ring_2514 -> T_AbelianGroup_990
du_'43''45'abelianGroup_2654 (T_Ring_2514 -> AgdaAny
forall a b. a -> b
coe T_Ring_2514
v0))
-- Algebra.Bundles.Ring.rawRing
d_rawRing_2698 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Ring_2514 -> T_RawRing_2460
d_rawRing_2698 :: () -> () -> T_Ring_2514 -> T_RawRing_2460
d_rawRing_2698 ~()
v0 ~()
v1 T_Ring_2514
v2 = T_Ring_2514 -> T_RawRing_2460
du_rawRing_2698 T_Ring_2514
v2
du_rawRing_2698 :: T_Ring_2514 -> T_RawRing_2460
du_rawRing_2698 :: T_Ring_2514 -> T_RawRing_2460
du_rawRing_2698 T_Ring_2514
v0
  = ((AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny)
 -> AgdaAny
 -> AgdaAny
 -> T_RawRing_2460)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_RawRing_2460
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_RawRing_2460
C_RawRing'46'constructor_42493 (T_Ring_2514 -> AgdaAny -> AgdaAny -> AgdaAny
d__'43'__2540 (T_Ring_2514 -> T_Ring_2514
forall a b. a -> b
coe T_Ring_2514
v0))
      (T_Ring_2514 -> AgdaAny -> AgdaAny -> AgdaAny
d__'42'__2542 (T_Ring_2514 -> T_Ring_2514
forall a b. a -> b
coe T_Ring_2514
v0)) (T_Ring_2514 -> AgdaAny -> AgdaAny
d_'45'__2544 (T_Ring_2514 -> T_Ring_2514
forall a b. a -> b
coe T_Ring_2514
v0))
      (T_Ring_2514 -> AgdaAny
d_0'35'_2546 (T_Ring_2514 -> T_Ring_2514
forall a b. a -> b
coe T_Ring_2514
v0)) (T_Ring_2514 -> AgdaAny
d_1'35'_2548 (T_Ring_2514 -> T_Ring_2514
forall a b. a -> b
coe T_Ring_2514
v0))
-- Algebra.Bundles.CommutativeRing
d_CommutativeRing_2704 :: p -> p -> ()
d_CommutativeRing_2704 p
a0 p
a1 = ()
data T_CommutativeRing_2704
  = C_CommutativeRing'46'constructor_47013 (AgdaAny ->
                                            AgdaAny -> AgdaAny)
                                           (AgdaAny -> AgdaAny -> AgdaAny) (AgdaAny -> AgdaAny)
                                           AgdaAny AgdaAny
                                           MAlonzo.Code.Algebra.Structures.T_IsCommutativeRing_1720
-- Algebra.Bundles.CommutativeRing.Carrier
d_Carrier_2726 :: T_CommutativeRing_2704 -> ()
d_Carrier_2726 :: T_CommutativeRing_2704 -> ()
d_Carrier_2726 = T_CommutativeRing_2704 -> ()
forall a. a
erased
-- Algebra.Bundles.CommutativeRing._≈_
d__'8776'__2728 ::
  T_CommutativeRing_2704 -> AgdaAny -> AgdaAny -> ()
d__'8776'__2728 :: T_CommutativeRing_2704 -> AgdaAny -> AgdaAny -> ()
d__'8776'__2728 = T_CommutativeRing_2704 -> AgdaAny -> AgdaAny -> ()
forall a. a
erased
-- Algebra.Bundles.CommutativeRing._+_
d__'43'__2730 ::
  T_CommutativeRing_2704 -> AgdaAny -> AgdaAny -> AgdaAny
d__'43'__2730 :: T_CommutativeRing_2704 -> AgdaAny -> AgdaAny -> AgdaAny
d__'43'__2730 T_CommutativeRing_2704
v0
  = case T_CommutativeRing_2704 -> T_CommutativeRing_2704
forall a b. a -> b
coe T_CommutativeRing_2704
v0 of
      C_CommutativeRing'46'constructor_47013 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny
v5 AgdaAny
v6 AgdaAny
v7 T_IsCommutativeRing_1720
v8 -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v3
      T_CommutativeRing_2704
_ -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.CommutativeRing._*_
d__'42'__2732 ::
  T_CommutativeRing_2704 -> AgdaAny -> AgdaAny -> AgdaAny
d__'42'__2732 :: T_CommutativeRing_2704 -> AgdaAny -> AgdaAny -> AgdaAny
d__'42'__2732 T_CommutativeRing_2704
v0
  = case T_CommutativeRing_2704 -> T_CommutativeRing_2704
forall a b. a -> b
coe T_CommutativeRing_2704
v0 of
      C_CommutativeRing'46'constructor_47013 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny
v5 AgdaAny
v6 AgdaAny
v7 T_IsCommutativeRing_1720
v8 -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v4
      T_CommutativeRing_2704
_ -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.CommutativeRing.-_
d_'45'__2734 :: T_CommutativeRing_2704 -> AgdaAny -> AgdaAny
d_'45'__2734 :: T_CommutativeRing_2704 -> AgdaAny -> AgdaAny
d_'45'__2734 T_CommutativeRing_2704
v0
  = case T_CommutativeRing_2704 -> T_CommutativeRing_2704
forall a b. a -> b
coe T_CommutativeRing_2704
v0 of
      C_CommutativeRing'46'constructor_47013 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny
v5 AgdaAny
v6 AgdaAny
v7 T_IsCommutativeRing_1720
v8 -> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v5
      T_CommutativeRing_2704
_ -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.CommutativeRing.0#
d_0'35'_2736 :: T_CommutativeRing_2704 -> AgdaAny
d_0'35'_2736 :: T_CommutativeRing_2704 -> AgdaAny
d_0'35'_2736 T_CommutativeRing_2704
v0
  = case T_CommutativeRing_2704 -> T_CommutativeRing_2704
forall a b. a -> b
coe T_CommutativeRing_2704
v0 of
      C_CommutativeRing'46'constructor_47013 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny
v5 AgdaAny
v6 AgdaAny
v7 T_IsCommutativeRing_1720
v8 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v6
      T_CommutativeRing_2704
_ -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.CommutativeRing.1#
d_1'35'_2738 :: T_CommutativeRing_2704 -> AgdaAny
d_1'35'_2738 :: T_CommutativeRing_2704 -> AgdaAny
d_1'35'_2738 T_CommutativeRing_2704
v0
  = case T_CommutativeRing_2704 -> T_CommutativeRing_2704
forall a b. a -> b
coe T_CommutativeRing_2704
v0 of
      C_CommutativeRing'46'constructor_47013 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny
v5 AgdaAny
v6 AgdaAny
v7 T_IsCommutativeRing_1720
v8 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v7
      T_CommutativeRing_2704
_ -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.CommutativeRing.isCommutativeRing
d_isCommutativeRing_2740 ::
  T_CommutativeRing_2704 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeRing_1720
d_isCommutativeRing_2740 :: T_CommutativeRing_2704 -> T_IsCommutativeRing_1720
d_isCommutativeRing_2740 T_CommutativeRing_2704
v0
  = case T_CommutativeRing_2704 -> T_CommutativeRing_2704
forall a b. a -> b
coe T_CommutativeRing_2704
v0 of
      C_CommutativeRing'46'constructor_47013 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny
v5 AgdaAny
v6 AgdaAny
v7 T_IsCommutativeRing_1720
v8 -> T_IsCommutativeRing_1720 -> T_IsCommutativeRing_1720
forall a b. a -> b
coe T_IsCommutativeRing_1720
v8
      T_CommutativeRing_2704
_ -> T_IsCommutativeRing_1720
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.CommutativeRing._._-_
d__'45'__2744 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeRing_2704 -> AgdaAny -> AgdaAny -> AgdaAny
d__'45'__2744 :: () -> () -> T_CommutativeRing_2704 -> AgdaAny -> AgdaAny -> AgdaAny
d__'45'__2744 ~()
v0 ~()
v1 T_CommutativeRing_2704
v2 = T_CommutativeRing_2704 -> AgdaAny -> AgdaAny -> AgdaAny
du__'45'__2744 T_CommutativeRing_2704
v2
du__'45'__2744 ::
  T_CommutativeRing_2704 -> AgdaAny -> AgdaAny -> AgdaAny
du__'45'__2744 :: T_CommutativeRing_2704 -> AgdaAny -> AgdaAny -> AgdaAny
du__'45'__2744 T_CommutativeRing_2704
v0
  = let v1 :: AgdaAny -> AgdaAny -> AgdaAny
v1 = T_CommutativeRing_2704 -> AgdaAny -> AgdaAny -> AgdaAny
d__'43'__2730 (T_CommutativeRing_2704 -> T_CommutativeRing_2704
forall a b. a -> b
coe T_CommutativeRing_2704
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: AgdaAny -> AgdaAny
v2 = T_CommutativeRing_2704 -> AgdaAny -> AgdaAny
d_'45'__2734 (T_CommutativeRing_2704 -> T_CommutativeRing_2704
forall a b. a -> b
coe T_CommutativeRing_2704
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__'45'__634 ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v1) ((AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v2)))
-- Algebra.Bundles.CommutativeRing._.assoc
d_assoc_2746 ::
  T_CommutativeRing_2704 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_2746 :: T_CommutativeRing_2704 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_2746 T_CommutativeRing_2704
v0
  = (T_IsSemigroup_194 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsSemigroup_194 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_assoc_204
      ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368
         ((T_IsRing_1584 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsRing_1584 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_'42''45'isMonoid_1606
            ((T_IsCommutativeRing_1720 -> T_IsRing_1584) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsCommutativeRing_1720 -> T_IsRing_1584
MAlonzo.Code.Algebra.Structures.d_isRing_1736
               ((T_CommutativeRing_2704 -> T_IsCommutativeRing_1720)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeRing_2704 -> T_IsCommutativeRing_1720
d_isCommutativeRing_2740 (T_CommutativeRing_2704 -> AgdaAny
forall a b. a -> b
coe T_CommutativeRing_2704
v0)))))
-- Algebra.Bundles.CommutativeRing._.*-comm
d_'42''45'comm_2748 ::
  T_CommutativeRing_2704 -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'comm_2748 :: T_CommutativeRing_2704 -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'comm_2748 T_CommutativeRing_2704
v0
  = (T_IsCommutativeRing_1720 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsCommutativeRing_1720 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'42''45'comm_1738
      ((T_CommutativeRing_2704 -> T_IsCommutativeRing_1720)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeRing_2704 -> T_IsCommutativeRing_1720
d_isCommutativeRing_2740 (T_CommutativeRing_2704 -> AgdaAny
forall a b. a -> b
coe T_CommutativeRing_2704
v0))
-- Algebra.Bundles.CommutativeRing._.∙-cong
d_'8729''45'cong_2750 ::
  T_CommutativeRing_2704 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_2750 :: T_CommutativeRing_2704
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_2750 T_CommutativeRing_2704
v0
  = (T_IsMagma_86
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsMagma_86
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_96
      ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202
         ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368
            ((T_IsRing_1584 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsRing_1584 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_'42''45'isMonoid_1606
               ((T_IsCommutativeRing_1720 -> T_IsRing_1584) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsCommutativeRing_1720 -> T_IsRing_1584
MAlonzo.Code.Algebra.Structures.d_isRing_1736
                  ((T_CommutativeRing_2704 -> T_IsCommutativeRing_1720)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeRing_2704 -> T_IsCommutativeRing_1720
d_isCommutativeRing_2740 (T_CommutativeRing_2704 -> AgdaAny
forall a b. a -> b
coe T_CommutativeRing_2704
v0))))))
-- Algebra.Bundles.CommutativeRing._.∙-congʳ
d_'8729''45'cong'691'_2752 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeRing_2704 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_2752 :: ()
-> ()
-> T_CommutativeRing_2704
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_2752 ~()
v0 ~()
v1 T_CommutativeRing_2704
v2
  = T_CommutativeRing_2704
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_2752 T_CommutativeRing_2704
v2
du_'8729''45'cong'691'_2752 ::
  T_CommutativeRing_2704 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_2752 :: T_CommutativeRing_2704
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_2752 T_CommutativeRing_2704
v0
  = let v1 :: T_IsCommutativeRing_1720
v1 = T_CommutativeRing_2704 -> T_IsCommutativeRing_1720
d_isCommutativeRing_2740 (T_CommutativeRing_2704 -> T_CommutativeRing_2704
forall a b. a -> b
coe T_CommutativeRing_2704
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsRing_1584
v2 = T_IsCommutativeRing_1720 -> T_IsRing_1584
MAlonzo.Code.Algebra.Structures.d_isRing_1736 (T_IsCommutativeRing_1720 -> T_IsCommutativeRing_1720
forall a b. a -> b
coe T_IsCommutativeRing_1720
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsMonoid_358
v3
                = T_IsRing_1584 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_'42''45'isMonoid_1606
                    (T_IsRing_1584 -> T_IsRing_1584
forall a b. a -> b
coe T_IsRing_1584
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsSemigroup_194
v4
                   = T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368 (T_IsMonoid_358 -> T_IsMonoid_358
forall a b. a -> b
coe T_IsMonoid_358
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               ((T_IsMagma_86
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsMagma_86 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'691'_116
                  ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202 (T_IsSemigroup_194 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194
v4))))))
-- Algebra.Bundles.CommutativeRing._.∙-congˡ
d_'8729''45'cong'737'_2754 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeRing_2704 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_2754 :: ()
-> ()
-> T_CommutativeRing_2704
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_2754 ~()
v0 ~()
v1 T_CommutativeRing_2704
v2
  = T_CommutativeRing_2704
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_2754 T_CommutativeRing_2704
v2
du_'8729''45'cong'737'_2754 ::
  T_CommutativeRing_2704 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_2754 :: T_CommutativeRing_2704
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_2754 T_CommutativeRing_2704
v0
  = let v1 :: T_IsCommutativeRing_1720
v1 = T_CommutativeRing_2704 -> T_IsCommutativeRing_1720
d_isCommutativeRing_2740 (T_CommutativeRing_2704 -> T_CommutativeRing_2704
forall a b. a -> b
coe T_CommutativeRing_2704
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsRing_1584
v2 = T_IsCommutativeRing_1720 -> T_IsRing_1584
MAlonzo.Code.Algebra.Structures.d_isRing_1736 (T_IsCommutativeRing_1720 -> T_IsCommutativeRing_1720
forall a b. a -> b
coe T_IsCommutativeRing_1720
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsMonoid_358
v3
                = T_IsRing_1584 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_'42''45'isMonoid_1606
                    (T_IsRing_1584 -> T_IsRing_1584
forall a b. a -> b
coe T_IsRing_1584
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsSemigroup_194
v4
                   = T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368 (T_IsMonoid_358 -> T_IsMonoid_358
forall a b. a -> b
coe T_IsMonoid_358
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               ((T_IsMagma_86
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsMagma_86 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'737'_112
                  ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202 (T_IsSemigroup_194 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194
v4))))))
-- Algebra.Bundles.CommutativeRing._.identity
d_identity_2756 ::
  T_CommutativeRing_2704 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_identity_2756 :: T_CommutativeRing_2704 -> T_Σ_14
d_identity_2756 T_CommutativeRing_2704
v0
  = (T_IsMonoid_358 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsMonoid_358 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_identity_370
      ((T_IsRing_1584 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsRing_1584 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_'42''45'isMonoid_1606
         ((T_IsCommutativeRing_1720 -> T_IsRing_1584) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCommutativeRing_1720 -> T_IsRing_1584
MAlonzo.Code.Algebra.Structures.d_isRing_1736
            ((T_CommutativeRing_2704 -> T_IsCommutativeRing_1720)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeRing_2704 -> T_IsCommutativeRing_1720
d_isCommutativeRing_2740 (T_CommutativeRing_2704 -> AgdaAny
forall a b. a -> b
coe T_CommutativeRing_2704
v0))))
-- Algebra.Bundles.CommutativeRing._.identityʳ
d_identity'691'_2758 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeRing_2704 -> AgdaAny -> AgdaAny
d_identity'691'_2758 :: () -> () -> T_CommutativeRing_2704 -> AgdaAny -> AgdaAny
d_identity'691'_2758 ~()
v0 ~()
v1 T_CommutativeRing_2704
v2 = T_CommutativeRing_2704 -> AgdaAny -> AgdaAny
du_identity'691'_2758 T_CommutativeRing_2704
v2
du_identity'691'_2758 ::
  T_CommutativeRing_2704 -> AgdaAny -> AgdaAny
du_identity'691'_2758 :: T_CommutativeRing_2704 -> AgdaAny -> AgdaAny
du_identity'691'_2758 T_CommutativeRing_2704
v0
  = let v1 :: T_IsCommutativeRing_1720
v1 = T_CommutativeRing_2704 -> T_IsCommutativeRing_1720
d_isCommutativeRing_2740 (T_CommutativeRing_2704 -> T_CommutativeRing_2704
forall a b. a -> b
coe T_CommutativeRing_2704
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsRing_1584
v2 = T_IsCommutativeRing_1720 -> T_IsRing_1584
MAlonzo.Code.Algebra.Structures.d_isRing_1736 (T_IsCommutativeRing_1720 -> T_IsCommutativeRing_1720
forall a b. a -> b
coe T_IsCommutativeRing_1720
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsMonoid_358 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoid_358 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_identity'691'_400
            ((T_IsRing_1584 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsRing_1584 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_'42''45'isMonoid_1606 (T_IsRing_1584 -> AgdaAny
forall a b. a -> b
coe T_IsRing_1584
v2))))
-- Algebra.Bundles.CommutativeRing._.identityˡ
d_identity'737'_2760 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeRing_2704 -> AgdaAny -> AgdaAny
d_identity'737'_2760 :: () -> () -> T_CommutativeRing_2704 -> AgdaAny -> AgdaAny
d_identity'737'_2760 ~()
v0 ~()
v1 T_CommutativeRing_2704
v2 = T_CommutativeRing_2704 -> AgdaAny -> AgdaAny
du_identity'737'_2760 T_CommutativeRing_2704
v2
du_identity'737'_2760 ::
  T_CommutativeRing_2704 -> AgdaAny -> AgdaAny
du_identity'737'_2760 :: T_CommutativeRing_2704 -> AgdaAny -> AgdaAny
du_identity'737'_2760 T_CommutativeRing_2704
v0
  = let v1 :: T_IsCommutativeRing_1720
v1 = T_CommutativeRing_2704 -> T_IsCommutativeRing_1720
d_isCommutativeRing_2740 (T_CommutativeRing_2704 -> T_CommutativeRing_2704
forall a b. a -> b
coe T_CommutativeRing_2704
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsRing_1584
v2 = T_IsCommutativeRing_1720 -> T_IsRing_1584
MAlonzo.Code.Algebra.Structures.d_isRing_1736 (T_IsCommutativeRing_1720 -> T_IsCommutativeRing_1720
forall a b. a -> b
coe T_IsCommutativeRing_1720
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsMonoid_358 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoid_358 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_identity'737'_398
            ((T_IsRing_1584 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsRing_1584 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_'42''45'isMonoid_1606 (T_IsRing_1584 -> AgdaAny
forall a b. a -> b
coe T_IsRing_1584
v2))))
-- Algebra.Bundles.CommutativeRing._.isCommutativeMagma
d_isCommutativeMagma_2762 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeRing_2704 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMagma_122
d_isCommutativeMagma_2762 :: () -> () -> T_CommutativeRing_2704 -> T_IsCommutativeMagma_122
d_isCommutativeMagma_2762 ~()
v0 ~()
v1 T_CommutativeRing_2704
v2
  = T_CommutativeRing_2704 -> T_IsCommutativeMagma_122
du_isCommutativeMagma_2762 T_CommutativeRing_2704
v2
du_isCommutativeMagma_2762 ::
  T_CommutativeRing_2704 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMagma_122
du_isCommutativeMagma_2762 :: T_CommutativeRing_2704 -> T_IsCommutativeMagma_122
du_isCommutativeMagma_2762 T_CommutativeRing_2704
v0
  = let v1 :: T_IsCommutativeRing_1720
v1 = T_CommutativeRing_2704 -> T_IsCommutativeRing_1720
d_isCommutativeRing_2740 (T_CommutativeRing_2704 -> T_CommutativeRing_2704
forall a b. a -> b
coe T_CommutativeRing_2704
v0) in
    AgdaAny -> T_IsCommutativeMagma_122
forall a b. a -> b
coe
      (let v2 :: t
v2
             = (T_IsCommutativeRing_1720 -> T_IsCommutativeSemiring_1344)
-> AgdaAny -> t
forall a b. a -> b
coe
                 T_IsCommutativeRing_1720 -> T_IsCommutativeSemiring_1344
MAlonzo.Code.Algebra.Structures.du_isCommutativeSemiring_1842
                 (T_IsCommutativeRing_1720 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeRing_1720
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: t
v3
                = (T_IsCommutativeSemiring_1344
 -> T_IsCommutativeSemiringWithoutOne_1044)
-> AgdaAny -> t
forall a b. a -> b
coe
                    T_IsCommutativeSemiring_1344
-> T_IsCommutativeSemiringWithoutOne_1044
MAlonzo.Code.Algebra.Structures.du_isCommutativeSemiringWithoutOne_1444
                    (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsCommutativeSemigroup_270 -> T_IsCommutativeMagma_122)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsCommutativeSemigroup_270 -> T_IsCommutativeMagma_122
MAlonzo.Code.Algebra.Structures.du_isCommutativeMagma_308
               ((T_IsCommutativeSemiringWithoutOne_1044
 -> T_IsCommutativeSemigroup_270)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsCommutativeSemiringWithoutOne_1044
-> T_IsCommutativeSemigroup_270
MAlonzo.Code.Algebra.Structures.du_'42''45'isCommutativeSemigroup_1128
                  (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3)))))
-- Algebra.Bundles.CommutativeRing._.*-isCommutativeMonoid
d_'42''45'isCommutativeMonoid_2764 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeRing_2704 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMonoid_406
d_'42''45'isCommutativeMonoid_2764 :: () -> () -> T_CommutativeRing_2704 -> T_IsCommutativeMonoid_406
d_'42''45'isCommutativeMonoid_2764 ~()
v0 ~()
v1 T_CommutativeRing_2704
v2
  = T_CommutativeRing_2704 -> T_IsCommutativeMonoid_406
du_'42''45'isCommutativeMonoid_2764 T_CommutativeRing_2704
v2
du_'42''45'isCommutativeMonoid_2764 ::
  T_CommutativeRing_2704 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMonoid_406
du_'42''45'isCommutativeMonoid_2764 :: T_CommutativeRing_2704 -> T_IsCommutativeMonoid_406
du_'42''45'isCommutativeMonoid_2764 T_CommutativeRing_2704
v0
  = let v1 :: T_IsCommutativeRing_1720
v1 = T_CommutativeRing_2704 -> T_IsCommutativeRing_1720
d_isCommutativeRing_2740 (T_CommutativeRing_2704 -> T_CommutativeRing_2704
forall a b. a -> b
coe T_CommutativeRing_2704
v0) in
    AgdaAny -> T_IsCommutativeMonoid_406
forall a b. a -> b
coe
      ((T_IsCommutativeSemiring_1344 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCommutativeSemiring_1344 -> T_IsCommutativeMonoid_406
MAlonzo.Code.Algebra.Structures.du_'42''45'isCommutativeMonoid_1452
         ((T_IsCommutativeRing_1720 -> T_IsCommutativeSemiring_1344)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCommutativeRing_1720 -> T_IsCommutativeSemiring_1344
MAlonzo.Code.Algebra.Structures.du_isCommutativeSemiring_1842
            (T_IsCommutativeRing_1720 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeRing_1720
v1)))
-- Algebra.Bundles.CommutativeRing._.*-isCommutativeSemigroup
d_'42''45'isCommutativeSemigroup_2766 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeRing_2704 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_270
d_'42''45'isCommutativeSemigroup_2766 :: () -> () -> T_CommutativeRing_2704 -> T_IsCommutativeSemigroup_270
d_'42''45'isCommutativeSemigroup_2766 ~()
v0 ~()
v1 T_CommutativeRing_2704
v2
  = T_CommutativeRing_2704 -> T_IsCommutativeSemigroup_270
du_'42''45'isCommutativeSemigroup_2766 T_CommutativeRing_2704
v2
du_'42''45'isCommutativeSemigroup_2766 ::
  T_CommutativeRing_2704 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_270
du_'42''45'isCommutativeSemigroup_2766 :: T_CommutativeRing_2704 -> T_IsCommutativeSemigroup_270
du_'42''45'isCommutativeSemigroup_2766 T_CommutativeRing_2704
v0
  = let v1 :: T_IsCommutativeRing_1720
v1 = T_CommutativeRing_2704 -> T_IsCommutativeRing_1720
d_isCommutativeRing_2740 (T_CommutativeRing_2704 -> T_CommutativeRing_2704
forall a b. a -> b
coe T_CommutativeRing_2704
v0) in
    AgdaAny -> T_IsCommutativeSemigroup_270
forall a b. a -> b
coe
      (let v2 :: t
v2
             = (T_IsCommutativeRing_1720 -> T_IsCommutativeSemiring_1344)
-> AgdaAny -> t
forall a b. a -> b
coe
                 T_IsCommutativeRing_1720 -> T_IsCommutativeSemiring_1344
MAlonzo.Code.Algebra.Structures.du_isCommutativeSemiring_1842
                 (T_IsCommutativeRing_1720 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeRing_1720
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsCommutativeSemiringWithoutOne_1044
 -> T_IsCommutativeSemigroup_270)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCommutativeSemiringWithoutOne_1044
-> T_IsCommutativeSemigroup_270
MAlonzo.Code.Algebra.Structures.du_'42''45'isCommutativeSemigroup_1128
            ((T_IsCommutativeSemiring_1344
 -> T_IsCommutativeSemiringWithoutOne_1044)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsCommutativeSemiring_1344
-> T_IsCommutativeSemiringWithoutOne_1044
MAlonzo.Code.Algebra.Structures.du_isCommutativeSemiringWithoutOne_1444
               (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2))))
-- Algebra.Bundles.CommutativeRing._.isMagma
d_isMagma_2768 ::
  T_CommutativeRing_2704 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_86
d_isMagma_2768 :: T_CommutativeRing_2704 -> T_IsMagma_86
d_isMagma_2768 T_CommutativeRing_2704
v0
  = (T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> T_IsMagma_86
forall a b. a -> b
coe
      T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202
      ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368
         ((T_IsRing_1584 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsRing_1584 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_'42''45'isMonoid_1606
            ((T_IsCommutativeRing_1720 -> T_IsRing_1584) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsCommutativeRing_1720 -> T_IsRing_1584
MAlonzo.Code.Algebra.Structures.d_isRing_1736
               ((T_CommutativeRing_2704 -> T_IsCommutativeRing_1720)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeRing_2704 -> T_IsCommutativeRing_1720
d_isCommutativeRing_2740 (T_CommutativeRing_2704 -> AgdaAny
forall a b. a -> b
coe T_CommutativeRing_2704
v0)))))
-- Algebra.Bundles.CommutativeRing._.*-isMonoid
d_'42''45'isMonoid_2770 ::
  T_CommutativeRing_2704 ->
  MAlonzo.Code.Algebra.Structures.T_IsMonoid_358
d_'42''45'isMonoid_2770 :: T_CommutativeRing_2704 -> T_IsMonoid_358
d_'42''45'isMonoid_2770 T_CommutativeRing_2704
v0
  = (T_IsRing_1584 -> T_IsMonoid_358) -> AgdaAny -> T_IsMonoid_358
forall a b. a -> b
coe
      T_IsRing_1584 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_'42''45'isMonoid_1606
      ((T_IsCommutativeRing_1720 -> T_IsRing_1584) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCommutativeRing_1720 -> T_IsRing_1584
MAlonzo.Code.Algebra.Structures.d_isRing_1736
         ((T_CommutativeRing_2704 -> T_IsCommutativeRing_1720)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeRing_2704 -> T_IsCommutativeRing_1720
d_isCommutativeRing_2740 (T_CommutativeRing_2704 -> AgdaAny
forall a b. a -> b
coe T_CommutativeRing_2704
v0)))
-- Algebra.Bundles.CommutativeRing._.isSemigroup
d_isSemigroup_2772 ::
  T_CommutativeRing_2704 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_194
d_isSemigroup_2772 :: T_CommutativeRing_2704 -> T_IsSemigroup_194
d_isSemigroup_2772 T_CommutativeRing_2704
v0
  = (T_IsMonoid_358 -> T_IsSemigroup_194)
-> AgdaAny -> T_IsSemigroup_194
forall a b. a -> b
coe
      T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368
      ((T_IsRing_1584 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsRing_1584 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_'42''45'isMonoid_1606
         ((T_IsCommutativeRing_1720 -> T_IsRing_1584) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCommutativeRing_1720 -> T_IsRing_1584
MAlonzo.Code.Algebra.Structures.d_isRing_1736
            ((T_CommutativeRing_2704 -> T_IsCommutativeRing_1720)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeRing_2704 -> T_IsCommutativeRing_1720
d_isCommutativeRing_2740 (T_CommutativeRing_2704 -> AgdaAny
forall a b. a -> b
coe T_CommutativeRing_2704
v0))))
-- Algebra.Bundles.CommutativeRing._.assoc
d_assoc_2774 ::
  T_CommutativeRing_2704 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_2774 :: T_CommutativeRing_2704 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_2774 T_CommutativeRing_2704
v0
  = (T_IsSemigroup_194 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsSemigroup_194 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_assoc_204
      ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368
         ((T_IsGroup_580 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsGroup_580 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_594
            ((T_IsAbelianGroup_662 -> T_IsGroup_580) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsAbelianGroup_662 -> T_IsGroup_580
MAlonzo.Code.Algebra.Structures.d_isGroup_674
               ((T_IsRing_1584 -> T_IsAbelianGroup_662) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsRing_1584 -> T_IsAbelianGroup_662
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_1604
                  ((T_IsCommutativeRing_1720 -> T_IsRing_1584) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsCommutativeRing_1720 -> T_IsRing_1584
MAlonzo.Code.Algebra.Structures.d_isRing_1736
                     ((T_CommutativeRing_2704 -> T_IsCommutativeRing_1720)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeRing_2704 -> T_IsCommutativeRing_1720
d_isCommutativeRing_2740 (T_CommutativeRing_2704 -> AgdaAny
forall a b. a -> b
coe T_CommutativeRing_2704
v0)))))))
-- Algebra.Bundles.CommutativeRing._.comm
d_comm_2776 ::
  T_CommutativeRing_2704 -> AgdaAny -> AgdaAny -> AgdaAny
d_comm_2776 :: T_CommutativeRing_2704 -> AgdaAny -> AgdaAny -> AgdaAny
d_comm_2776 T_CommutativeRing_2704
v0
  = (T_IsAbelianGroup_662 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsAbelianGroup_662 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_comm_676
      ((T_IsRing_1584 -> T_IsAbelianGroup_662) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsRing_1584 -> T_IsAbelianGroup_662
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_1604
         ((T_IsCommutativeRing_1720 -> T_IsRing_1584) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCommutativeRing_1720 -> T_IsRing_1584
MAlonzo.Code.Algebra.Structures.d_isRing_1736
            ((T_CommutativeRing_2704 -> T_IsCommutativeRing_1720)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeRing_2704 -> T_IsCommutativeRing_1720
d_isCommutativeRing_2740 (T_CommutativeRing_2704 -> AgdaAny
forall a b. a -> b
coe T_CommutativeRing_2704
v0))))
-- Algebra.Bundles.CommutativeRing._.∙-cong
d_'8729''45'cong_2778 ::
  T_CommutativeRing_2704 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_2778 :: T_CommutativeRing_2704
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_2778 T_CommutativeRing_2704
v0
  = (T_IsMagma_86
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsMagma_86
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_96
      ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202
         ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368
            ((T_IsGroup_580 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsGroup_580 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_594
               ((T_IsAbelianGroup_662 -> T_IsGroup_580) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsAbelianGroup_662 -> T_IsGroup_580
MAlonzo.Code.Algebra.Structures.d_isGroup_674
                  ((T_IsRing_1584 -> T_IsAbelianGroup_662) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsRing_1584 -> T_IsAbelianGroup_662
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_1604
                     ((T_IsCommutativeRing_1720 -> T_IsRing_1584) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsCommutativeRing_1720 -> T_IsRing_1584
MAlonzo.Code.Algebra.Structures.d_isRing_1736
                        ((T_CommutativeRing_2704 -> T_IsCommutativeRing_1720)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeRing_2704 -> T_IsCommutativeRing_1720
d_isCommutativeRing_2740 (T_CommutativeRing_2704 -> AgdaAny
forall a b. a -> b
coe T_CommutativeRing_2704
v0))))))))
-- Algebra.Bundles.CommutativeRing._.∙-congʳ
d_'8729''45'cong'691'_2780 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeRing_2704 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_2780 :: ()
-> ()
-> T_CommutativeRing_2704
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_2780 ~()
v0 ~()
v1 T_CommutativeRing_2704
v2
  = T_CommutativeRing_2704
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_2780 T_CommutativeRing_2704
v2
du_'8729''45'cong'691'_2780 ::
  T_CommutativeRing_2704 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_2780 :: T_CommutativeRing_2704
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_2780 T_CommutativeRing_2704
v0
  = let v1 :: T_IsCommutativeRing_1720
v1 = T_CommutativeRing_2704 -> T_IsCommutativeRing_1720
d_isCommutativeRing_2740 (T_CommutativeRing_2704 -> T_CommutativeRing_2704
forall a b. a -> b
coe T_CommutativeRing_2704
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsRing_1584
v2 = T_IsCommutativeRing_1720 -> T_IsRing_1584
MAlonzo.Code.Algebra.Structures.d_isRing_1736 (T_IsCommutativeRing_1720 -> T_IsCommutativeRing_1720
forall a b. a -> b
coe T_IsCommutativeRing_1720
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsAbelianGroup_662
v3
                = T_IsRing_1584 -> T_IsAbelianGroup_662
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_1604
                    (T_IsRing_1584 -> T_IsRing_1584
forall a b. a -> b
coe T_IsRing_1584
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsGroup_580
v4 = T_IsAbelianGroup_662 -> T_IsGroup_580
MAlonzo.Code.Algebra.Structures.d_isGroup_674 (T_IsAbelianGroup_662 -> T_IsAbelianGroup_662
forall a b. a -> b
coe T_IsAbelianGroup_662
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsMonoid_358
v5
                      = T_IsGroup_580 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_594 (T_IsGroup_580 -> T_IsGroup_580
forall a b. a -> b
coe T_IsGroup_580
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (let v6 :: T_IsSemigroup_194
v6
                         = T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368 (T_IsMonoid_358 -> T_IsMonoid_358
forall a b. a -> b
coe T_IsMonoid_358
v5) in
                   AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     ((T_IsMagma_86
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsMagma_86 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'691'_116
                        ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202 (T_IsSemigroup_194 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194
v6))))))))
-- Algebra.Bundles.CommutativeRing._.∙-congˡ
d_'8729''45'cong'737'_2782 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeRing_2704 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_2782 :: ()
-> ()
-> T_CommutativeRing_2704
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_2782 ~()
v0 ~()
v1 T_CommutativeRing_2704
v2
  = T_CommutativeRing_2704
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_2782 T_CommutativeRing_2704
v2
du_'8729''45'cong'737'_2782 ::
  T_CommutativeRing_2704 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_2782 :: T_CommutativeRing_2704
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_2782 T_CommutativeRing_2704
v0
  = let v1 :: T_IsCommutativeRing_1720
v1 = T_CommutativeRing_2704 -> T_IsCommutativeRing_1720
d_isCommutativeRing_2740 (T_CommutativeRing_2704 -> T_CommutativeRing_2704
forall a b. a -> b
coe T_CommutativeRing_2704
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsRing_1584
v2 = T_IsCommutativeRing_1720 -> T_IsRing_1584
MAlonzo.Code.Algebra.Structures.d_isRing_1736 (T_IsCommutativeRing_1720 -> T_IsCommutativeRing_1720
forall a b. a -> b
coe T_IsCommutativeRing_1720
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsAbelianGroup_662
v3
                = T_IsRing_1584 -> T_IsAbelianGroup_662
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_1604
                    (T_IsRing_1584 -> T_IsRing_1584
forall a b. a -> b
coe T_IsRing_1584
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsGroup_580
v4 = T_IsAbelianGroup_662 -> T_IsGroup_580
MAlonzo.Code.Algebra.Structures.d_isGroup_674 (T_IsAbelianGroup_662 -> T_IsAbelianGroup_662
forall a b. a -> b
coe T_IsAbelianGroup_662
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsMonoid_358
v5
                      = T_IsGroup_580 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_594 (T_IsGroup_580 -> T_IsGroup_580
forall a b. a -> b
coe T_IsGroup_580
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (let v6 :: T_IsSemigroup_194
v6
                         = T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368 (T_IsMonoid_358 -> T_IsMonoid_358
forall a b. a -> b
coe T_IsMonoid_358
v5) in
                   AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     ((T_IsMagma_86
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsMagma_86 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'8729''45'cong'737'_112
                        ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202 (T_IsSemigroup_194 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194
v6))))))))
-- Algebra.Bundles.CommutativeRing._.identity
d_identity_2784 ::
  T_CommutativeRing_2704 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_identity_2784 :: T_CommutativeRing_2704 -> T_Σ_14
d_identity_2784 T_CommutativeRing_2704
v0
  = (T_IsMonoid_358 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsMonoid_358 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_identity_370
      ((T_IsGroup_580 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsGroup_580 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_594
         ((T_IsAbelianGroup_662 -> T_IsGroup_580) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsAbelianGroup_662 -> T_IsGroup_580
MAlonzo.Code.Algebra.Structures.d_isGroup_674
            ((T_IsRing_1584 -> T_IsAbelianGroup_662) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsRing_1584 -> T_IsAbelianGroup_662
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_1604
               ((T_IsCommutativeRing_1720 -> T_IsRing_1584) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsCommutativeRing_1720 -> T_IsRing_1584
MAlonzo.Code.Algebra.Structures.d_isRing_1736
                  ((T_CommutativeRing_2704 -> T_IsCommutativeRing_1720)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeRing_2704 -> T_IsCommutativeRing_1720
d_isCommutativeRing_2740 (T_CommutativeRing_2704 -> AgdaAny
forall a b. a -> b
coe T_CommutativeRing_2704
v0))))))
-- Algebra.Bundles.CommutativeRing._.identityʳ
d_identity'691'_2786 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeRing_2704 -> AgdaAny -> AgdaAny
d_identity'691'_2786 :: () -> () -> T_CommutativeRing_2704 -> AgdaAny -> AgdaAny
d_identity'691'_2786 ~()
v0 ~()
v1 T_CommutativeRing_2704
v2 = T_CommutativeRing_2704 -> AgdaAny -> AgdaAny
du_identity'691'_2786 T_CommutativeRing_2704
v2
du_identity'691'_2786 ::
  T_CommutativeRing_2704 -> AgdaAny -> AgdaAny
du_identity'691'_2786 :: T_CommutativeRing_2704 -> AgdaAny -> AgdaAny
du_identity'691'_2786 T_CommutativeRing_2704
v0
  = let v1 :: T_IsCommutativeRing_1720
v1 = T_CommutativeRing_2704 -> T_IsCommutativeRing_1720
d_isCommutativeRing_2740 (T_CommutativeRing_2704 -> T_CommutativeRing_2704
forall a b. a -> b
coe T_CommutativeRing_2704
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsRing_1584
v2 = T_IsCommutativeRing_1720 -> T_IsRing_1584
MAlonzo.Code.Algebra.Structures.d_isRing_1736 (T_IsCommutativeRing_1720 -> T_IsCommutativeRing_1720
forall a b. a -> b
coe T_IsCommutativeRing_1720
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsAbelianGroup_662
v3
                = T_IsRing_1584 -> T_IsAbelianGroup_662
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_1604
                    (T_IsRing_1584 -> T_IsRing_1584
forall a b. a -> b
coe T_IsRing_1584
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsGroup_580
v4 = T_IsAbelianGroup_662 -> T_IsGroup_580
MAlonzo.Code.Algebra.Structures.d_isGroup_674 (T_IsAbelianGroup_662 -> T_IsAbelianGroup_662
forall a b. a -> b
coe T_IsAbelianGroup_662
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               ((T_IsMonoid_358 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsMonoid_358 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_identity'691'_400
                  ((T_IsGroup_580 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_580 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_594 (T_IsGroup_580 -> AgdaAny
forall a b. a -> b
coe T_IsGroup_580
v4))))))
-- Algebra.Bundles.CommutativeRing._.identityˡ
d_identity'737'_2788 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeRing_2704 -> AgdaAny -> AgdaAny
d_identity'737'_2788 :: () -> () -> T_CommutativeRing_2704 -> AgdaAny -> AgdaAny
d_identity'737'_2788 ~()
v0 ~()
v1 T_CommutativeRing_2704
v2 = T_CommutativeRing_2704 -> AgdaAny -> AgdaAny
du_identity'737'_2788 T_CommutativeRing_2704
v2
du_identity'737'_2788 ::
  T_CommutativeRing_2704 -> AgdaAny -> AgdaAny
du_identity'737'_2788 :: T_CommutativeRing_2704 -> AgdaAny -> AgdaAny
du_identity'737'_2788 T_CommutativeRing_2704
v0
  = let v1 :: T_IsCommutativeRing_1720
v1 = T_CommutativeRing_2704 -> T_IsCommutativeRing_1720
d_isCommutativeRing_2740 (T_CommutativeRing_2704 -> T_CommutativeRing_2704
forall a b. a -> b
coe T_CommutativeRing_2704
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsRing_1584
v2 = T_IsCommutativeRing_1720 -> T_IsRing_1584
MAlonzo.Code.Algebra.Structures.d_isRing_1736 (T_IsCommutativeRing_1720 -> T_IsCommutativeRing_1720
forall a b. a -> b
coe T_IsCommutativeRing_1720
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsAbelianGroup_662
v3
                = T_IsRing_1584 -> T_IsAbelianGroup_662
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_1604
                    (T_IsRing_1584 -> T_IsRing_1584
forall a b. a -> b
coe T_IsRing_1584
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsGroup_580
v4 = T_IsAbelianGroup_662 -> T_IsGroup_580
MAlonzo.Code.Algebra.Structures.d_isGroup_674 (T_IsAbelianGroup_662 -> T_IsAbelianGroup_662
forall a b. a -> b
coe T_IsAbelianGroup_662
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               ((T_IsMonoid_358 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsMonoid_358 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_identity'737'_398
                  ((T_IsGroup_580 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_580 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_594 (T_IsGroup_580 -> AgdaAny
forall a b. a -> b
coe T_IsGroup_580
v4))))))
-- Algebra.Bundles.CommutativeRing._.+-isAbelianGroup
d_'43''45'isAbelianGroup_2790 ::
  T_CommutativeRing_2704 ->
  MAlonzo.Code.Algebra.Structures.T_IsAbelianGroup_662
d_'43''45'isAbelianGroup_2790 :: T_CommutativeRing_2704 -> T_IsAbelianGroup_662
d_'43''45'isAbelianGroup_2790 T_CommutativeRing_2704
v0
  = (T_IsRing_1584 -> T_IsAbelianGroup_662)
-> AgdaAny -> T_IsAbelianGroup_662
forall a b. a -> b
coe
      T_IsRing_1584 -> T_IsAbelianGroup_662
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_1604
      ((T_IsCommutativeRing_1720 -> T_IsRing_1584) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCommutativeRing_1720 -> T_IsRing_1584
MAlonzo.Code.Algebra.Structures.d_isRing_1736
         ((T_CommutativeRing_2704 -> T_IsCommutativeRing_1720)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeRing_2704 -> T_IsCommutativeRing_1720
d_isCommutativeRing_2740 (T_CommutativeRing_2704 -> AgdaAny
forall a b. a -> b
coe T_CommutativeRing_2704
v0)))
-- Algebra.Bundles.CommutativeRing._.isCommutativeMagma
d_isCommutativeMagma_2792 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeRing_2704 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMagma_122
d_isCommutativeMagma_2792 :: () -> () -> T_CommutativeRing_2704 -> T_IsCommutativeMagma_122
d_isCommutativeMagma_2792 ~()
v0 ~()
v1 T_CommutativeRing_2704
v2
  = T_CommutativeRing_2704 -> T_IsCommutativeMagma_122
du_isCommutativeMagma_2792 T_CommutativeRing_2704
v2
du_isCommutativeMagma_2792 ::
  T_CommutativeRing_2704 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMagma_122
du_isCommutativeMagma_2792 :: T_CommutativeRing_2704 -> T_IsCommutativeMagma_122
du_isCommutativeMagma_2792 T_CommutativeRing_2704
v0
  = let v1 :: T_IsCommutativeRing_1720
v1 = T_CommutativeRing_2704 -> T_IsCommutativeRing_1720
d_isCommutativeRing_2740 (T_CommutativeRing_2704 -> T_CommutativeRing_2704
forall a b. a -> b
coe T_CommutativeRing_2704
v0) in
    AgdaAny -> T_IsCommutativeMagma_122
forall a b. a -> b
coe
      (let v2 :: T_IsRing_1584
v2 = T_IsCommutativeRing_1720 -> T_IsRing_1584
MAlonzo.Code.Algebra.Structures.d_isRing_1736 (T_IsCommutativeRing_1720 -> T_IsCommutativeRing_1720
forall a b. a -> b
coe T_IsCommutativeRing_1720
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsAbelianGroup_662
v3
                = T_IsRing_1584 -> T_IsAbelianGroup_662
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_1604
                    (T_IsRing_1584 -> T_IsRing_1584
forall a b. a -> b
coe T_IsRing_1584
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: t
v4
                   = (T_IsAbelianGroup_662 -> T_IsCommutativeMonoid_406) -> AgdaAny -> t
forall a b. a -> b
coe
                       T_IsAbelianGroup_662 -> T_IsCommutativeMonoid_406
MAlonzo.Code.Algebra.Structures.du_isCommutativeMonoid_728
                       (T_IsAbelianGroup_662 -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_662
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               ((T_IsCommutativeSemigroup_270 -> T_IsCommutativeMagma_122)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsCommutativeSemigroup_270 -> T_IsCommutativeMagma_122
MAlonzo.Code.Algebra.Structures.du_isCommutativeMagma_308
                  ((T_IsCommutativeMonoid_406 -> T_IsCommutativeSemigroup_270)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsCommutativeMonoid_406 -> T_IsCommutativeSemigroup_270
MAlonzo.Code.Algebra.Structures.du_isCommutativeSemigroup_454
                     (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v4))))))
-- Algebra.Bundles.CommutativeRing._.isCommutativeMonoid
d_isCommutativeMonoid_2794 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeRing_2704 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMonoid_406
d_isCommutativeMonoid_2794 :: () -> () -> T_CommutativeRing_2704 -> T_IsCommutativeMonoid_406
d_isCommutativeMonoid_2794 ~()
v0 ~()
v1 T_CommutativeRing_2704
v2
  = T_CommutativeRing_2704 -> T_IsCommutativeMonoid_406
du_isCommutativeMonoid_2794 T_CommutativeRing_2704
v2
du_isCommutativeMonoid_2794 ::
  T_CommutativeRing_2704 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMonoid_406
du_isCommutativeMonoid_2794 :: T_CommutativeRing_2704 -> T_IsCommutativeMonoid_406
du_isCommutativeMonoid_2794 T_CommutativeRing_2704
v0
  = let v1 :: T_IsCommutativeRing_1720
v1 = T_CommutativeRing_2704 -> T_IsCommutativeRing_1720
d_isCommutativeRing_2740 (T_CommutativeRing_2704 -> T_CommutativeRing_2704
forall a b. a -> b
coe T_CommutativeRing_2704
v0) in
    AgdaAny -> T_IsCommutativeMonoid_406
forall a b. a -> b
coe
      (let v2 :: T_IsRing_1584
v2 = T_IsCommutativeRing_1720 -> T_IsRing_1584
MAlonzo.Code.Algebra.Structures.d_isRing_1736 (T_IsCommutativeRing_1720 -> T_IsCommutativeRing_1720
forall a b. a -> b
coe T_IsCommutativeRing_1720
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsAbelianGroup_662 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsAbelianGroup_662 -> T_IsCommutativeMonoid_406
MAlonzo.Code.Algebra.Structures.du_isCommutativeMonoid_728
            ((T_IsRing_1584 -> T_IsAbelianGroup_662) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsRing_1584 -> T_IsAbelianGroup_662
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_1604
               (T_IsRing_1584 -> AgdaAny
forall a b. a -> b
coe T_IsRing_1584
v2))))
-- Algebra.Bundles.CommutativeRing._.isCommutativeSemigroup
d_isCommutativeSemigroup_2796 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeRing_2704 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_270
d_isCommutativeSemigroup_2796 :: () -> () -> T_CommutativeRing_2704 -> T_IsCommutativeSemigroup_270
d_isCommutativeSemigroup_2796 ~()
v0 ~()
v1 T_CommutativeRing_2704
v2
  = T_CommutativeRing_2704 -> T_IsCommutativeSemigroup_270
du_isCommutativeSemigroup_2796 T_CommutativeRing_2704
v2
du_isCommutativeSemigroup_2796 ::
  T_CommutativeRing_2704 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_270
du_isCommutativeSemigroup_2796 :: T_CommutativeRing_2704 -> T_IsCommutativeSemigroup_270
du_isCommutativeSemigroup_2796 T_CommutativeRing_2704
v0
  = let v1 :: T_IsCommutativeRing_1720
v1 = T_CommutativeRing_2704 -> T_IsCommutativeRing_1720
d_isCommutativeRing_2740 (T_CommutativeRing_2704 -> T_CommutativeRing_2704
forall a b. a -> b
coe T_CommutativeRing_2704
v0) in
    AgdaAny -> T_IsCommutativeSemigroup_270
forall a b. a -> b
coe
      (let v2 :: T_IsRing_1584
v2 = T_IsCommutativeRing_1720 -> T_IsRing_1584
MAlonzo.Code.Algebra.Structures.d_isRing_1736 (T_IsCommutativeRing_1720 -> T_IsCommutativeRing_1720
forall a b. a -> b
coe T_IsCommutativeRing_1720
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsAbelianGroup_662
v3
                = T_IsRing_1584 -> T_IsAbelianGroup_662
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_1604
                    (T_IsRing_1584 -> T_IsRing_1584
forall a b. a -> b
coe T_IsRing_1584
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsCommutativeMonoid_406 -> T_IsCommutativeSemigroup_270)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsCommutativeMonoid_406 -> T_IsCommutativeSemigroup_270
MAlonzo.Code.Algebra.Structures.du_isCommutativeSemigroup_454
               ((T_IsAbelianGroup_662 -> T_IsCommutativeMonoid_406)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsAbelianGroup_662 -> T_IsCommutativeMonoid_406
MAlonzo.Code.Algebra.Structures.du_isCommutativeMonoid_728
                  (T_IsAbelianGroup_662 -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_662
v3)))))
-- Algebra.Bundles.CommutativeRing._.isGroup
d_isGroup_2798 ::
  T_CommutativeRing_2704 ->
  MAlonzo.Code.Algebra.Structures.T_IsGroup_580
d_isGroup_2798 :: T_CommutativeRing_2704 -> T_IsGroup_580
d_isGroup_2798 T_CommutativeRing_2704
v0
  = (T_IsAbelianGroup_662 -> T_IsGroup_580) -> AgdaAny -> T_IsGroup_580
forall a b. a -> b
coe
      T_IsAbelianGroup_662 -> T_IsGroup_580
MAlonzo.Code.Algebra.Structures.d_isGroup_674
      ((T_IsRing_1584 -> T_IsAbelianGroup_662) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsRing_1584 -> T_IsAbelianGroup_662
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_1604
         ((T_IsCommutativeRing_1720 -> T_IsRing_1584) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCommutativeRing_1720 -> T_IsRing_1584
MAlonzo.Code.Algebra.Structures.d_isRing_1736
            ((T_CommutativeRing_2704 -> T_IsCommutativeRing_1720)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeRing_2704 -> T_IsCommutativeRing_1720
d_isCommutativeRing_2740 (T_CommutativeRing_2704 -> AgdaAny
forall a b. a -> b
coe T_CommutativeRing_2704
v0))))
-- Algebra.Bundles.CommutativeRing._.isMagma
d_isMagma_2800 ::
  T_CommutativeRing_2704 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_86
d_isMagma_2800 :: T_CommutativeRing_2704 -> T_IsMagma_86
d_isMagma_2800 T_CommutativeRing_2704
v0
  = (T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> T_IsMagma_86
forall a b. a -> b
coe
      T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202
      ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368
         ((T_IsGroup_580 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsGroup_580 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_594
            ((T_IsAbelianGroup_662 -> T_IsGroup_580) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsAbelianGroup_662 -> T_IsGroup_580
MAlonzo.Code.Algebra.Structures.d_isGroup_674
               ((T_IsRing_1584 -> T_IsAbelianGroup_662) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsRing_1584 -> T_IsAbelianGroup_662
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_1604
                  ((T_IsCommutativeRing_1720 -> T_IsRing_1584) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsCommutativeRing_1720 -> T_IsRing_1584
MAlonzo.Code.Algebra.Structures.d_isRing_1736
                     ((T_CommutativeRing_2704 -> T_IsCommutativeRing_1720)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeRing_2704 -> T_IsCommutativeRing_1720
d_isCommutativeRing_2740 (T_CommutativeRing_2704 -> AgdaAny
forall a b. a -> b
coe T_CommutativeRing_2704
v0)))))))
-- Algebra.Bundles.CommutativeRing._.isMonoid
d_isMonoid_2802 ::
  T_CommutativeRing_2704 ->
  MAlonzo.Code.Algebra.Structures.T_IsMonoid_358
d_isMonoid_2802 :: T_CommutativeRing_2704 -> T_IsMonoid_358
d_isMonoid_2802 T_CommutativeRing_2704
v0
  = (T_IsGroup_580 -> T_IsMonoid_358) -> AgdaAny -> T_IsMonoid_358
forall a b. a -> b
coe
      T_IsGroup_580 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_594
      ((T_IsAbelianGroup_662 -> T_IsGroup_580) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsAbelianGroup_662 -> T_IsGroup_580
MAlonzo.Code.Algebra.Structures.d_isGroup_674
         ((T_IsRing_1584 -> T_IsAbelianGroup_662) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsRing_1584 -> T_IsAbelianGroup_662
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_1604
            ((T_IsCommutativeRing_1720 -> T_IsRing_1584) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsCommutativeRing_1720 -> T_IsRing_1584
MAlonzo.Code.Algebra.Structures.d_isRing_1736
               ((T_CommutativeRing_2704 -> T_IsCommutativeRing_1720)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeRing_2704 -> T_IsCommutativeRing_1720
d_isCommutativeRing_2740 (T_CommutativeRing_2704 -> AgdaAny
forall a b. a -> b
coe T_CommutativeRing_2704
v0)))))
-- Algebra.Bundles.CommutativeRing._.isSemigroup
d_isSemigroup_2804 ::
  T_CommutativeRing_2704 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_194
d_isSemigroup_2804 :: T_CommutativeRing_2704 -> T_IsSemigroup_194
d_isSemigroup_2804 T_CommutativeRing_2704
v0
  = (T_IsMonoid_358 -> T_IsSemigroup_194)
-> AgdaAny -> T_IsSemigroup_194
forall a b. a -> b
coe
      T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368
      ((T_IsGroup_580 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsGroup_580 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_594
         ((T_IsAbelianGroup_662 -> T_IsGroup_580) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsAbelianGroup_662 -> T_IsGroup_580
MAlonzo.Code.Algebra.Structures.d_isGroup_674
            ((T_IsRing_1584 -> T_IsAbelianGroup_662) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsRing_1584 -> T_IsAbelianGroup_662
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_1604
               ((T_IsCommutativeRing_1720 -> T_IsRing_1584) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsCommutativeRing_1720 -> T_IsRing_1584
MAlonzo.Code.Algebra.Structures.d_isRing_1736
                  ((T_CommutativeRing_2704 -> T_IsCommutativeRing_1720)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeRing_2704 -> T_IsCommutativeRing_1720
d_isCommutativeRing_2740 (T_CommutativeRing_2704 -> AgdaAny
forall a b. a -> b
coe T_CommutativeRing_2704
v0))))))
-- Algebra.Bundles.CommutativeRing._.⁻¹-cong
d_'8315''185''45'cong_2806 ::
  T_CommutativeRing_2704 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8315''185''45'cong_2806 :: T_CommutativeRing_2704 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8315''185''45'cong_2806 T_CommutativeRing_2704
v0
  = (T_IsGroup_580 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsGroup_580 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8315''185''45'cong_598
      ((T_IsAbelianGroup_662 -> T_IsGroup_580) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsAbelianGroup_662 -> T_IsGroup_580
MAlonzo.Code.Algebra.Structures.d_isGroup_674
         ((T_IsRing_1584 -> T_IsAbelianGroup_662) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsRing_1584 -> T_IsAbelianGroup_662
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_1604
            ((T_IsCommutativeRing_1720 -> T_IsRing_1584) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsCommutativeRing_1720 -> T_IsRing_1584
MAlonzo.Code.Algebra.Structures.d_isRing_1736
               ((T_CommutativeRing_2704 -> T_IsCommutativeRing_1720)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeRing_2704 -> T_IsCommutativeRing_1720
d_isCommutativeRing_2740 (T_CommutativeRing_2704 -> AgdaAny
forall a b. a -> b
coe T_CommutativeRing_2704
v0)))))
-- Algebra.Bundles.CommutativeRing._.inverse
d_inverse_2808 ::
  T_CommutativeRing_2704 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_inverse_2808 :: T_CommutativeRing_2704 -> T_Σ_14
d_inverse_2808 T_CommutativeRing_2704
v0
  = (T_IsGroup_580 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsGroup_580 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_inverse_596
      ((T_IsAbelianGroup_662 -> T_IsGroup_580) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsAbelianGroup_662 -> T_IsGroup_580
MAlonzo.Code.Algebra.Structures.d_isGroup_674
         ((T_IsRing_1584 -> T_IsAbelianGroup_662) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsRing_1584 -> T_IsAbelianGroup_662
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_1604
            ((T_IsCommutativeRing_1720 -> T_IsRing_1584) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsCommutativeRing_1720 -> T_IsRing_1584
MAlonzo.Code.Algebra.Structures.d_isRing_1736
               ((T_CommutativeRing_2704 -> T_IsCommutativeRing_1720)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeRing_2704 -> T_IsCommutativeRing_1720
d_isCommutativeRing_2740 (T_CommutativeRing_2704 -> AgdaAny
forall a b. a -> b
coe T_CommutativeRing_2704
v0)))))
-- Algebra.Bundles.CommutativeRing._.inverseʳ
d_inverse'691'_2810 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeRing_2704 -> AgdaAny -> AgdaAny
d_inverse'691'_2810 :: () -> () -> T_CommutativeRing_2704 -> AgdaAny -> AgdaAny
d_inverse'691'_2810 ~()
v0 ~()
v1 T_CommutativeRing_2704
v2 = T_CommutativeRing_2704 -> AgdaAny -> AgdaAny
du_inverse'691'_2810 T_CommutativeRing_2704
v2
du_inverse'691'_2810 ::
  T_CommutativeRing_2704 -> AgdaAny -> AgdaAny
du_inverse'691'_2810 :: T_CommutativeRing_2704 -> AgdaAny -> AgdaAny
du_inverse'691'_2810 T_CommutativeRing_2704
v0
  = let v1 :: T_IsCommutativeRing_1720
v1 = T_CommutativeRing_2704 -> T_IsCommutativeRing_1720
d_isCommutativeRing_2740 (T_CommutativeRing_2704 -> T_CommutativeRing_2704
forall a b. a -> b
coe T_CommutativeRing_2704
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsRing_1584
v2 = T_IsCommutativeRing_1720 -> T_IsRing_1584
MAlonzo.Code.Algebra.Structures.d_isRing_1736 (T_IsCommutativeRing_1720 -> T_IsCommutativeRing_1720
forall a b. a -> b
coe T_IsCommutativeRing_1720
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsAbelianGroup_662
v3
                = T_IsRing_1584 -> T_IsAbelianGroup_662
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_1604
                    (T_IsRing_1584 -> T_IsRing_1584
forall a b. a -> b
coe T_IsRing_1584
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsGroup_580 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsGroup_580 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_inverse'691'_642
               ((T_IsAbelianGroup_662 -> T_IsGroup_580) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_662 -> T_IsGroup_580
MAlonzo.Code.Algebra.Structures.d_isGroup_674 (T_IsAbelianGroup_662 -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_662
v3)))))
-- Algebra.Bundles.CommutativeRing._.inverseˡ
d_inverse'737'_2812 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeRing_2704 -> AgdaAny -> AgdaAny
d_inverse'737'_2812 :: () -> () -> T_CommutativeRing_2704 -> AgdaAny -> AgdaAny
d_inverse'737'_2812 ~()
v0 ~()
v1 T_CommutativeRing_2704
v2 = T_CommutativeRing_2704 -> AgdaAny -> AgdaAny
du_inverse'737'_2812 T_CommutativeRing_2704
v2
du_inverse'737'_2812 ::
  T_CommutativeRing_2704 -> AgdaAny -> AgdaAny
du_inverse'737'_2812 :: T_CommutativeRing_2704 -> AgdaAny -> AgdaAny
du_inverse'737'_2812 T_CommutativeRing_2704
v0
  = let v1 :: T_IsCommutativeRing_1720
v1 = T_CommutativeRing_2704 -> T_IsCommutativeRing_1720
d_isCommutativeRing_2740 (T_CommutativeRing_2704 -> T_CommutativeRing_2704
forall a b. a -> b
coe T_CommutativeRing_2704
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsRing_1584
v2 = T_IsCommutativeRing_1720 -> T_IsRing_1584
MAlonzo.Code.Algebra.Structures.d_isRing_1736 (T_IsCommutativeRing_1720 -> T_IsCommutativeRing_1720
forall a b. a -> b
coe T_IsCommutativeRing_1720
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsAbelianGroup_662
v3
                = T_IsRing_1584 -> T_IsAbelianGroup_662
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_1604
                    (T_IsRing_1584 -> T_IsRing_1584
forall a b. a -> b
coe T_IsRing_1584
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsGroup_580 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsGroup_580 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_inverse'737'_640
               ((T_IsAbelianGroup_662 -> T_IsGroup_580) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_662 -> T_IsGroup_580
MAlonzo.Code.Algebra.Structures.d_isGroup_674 (T_IsAbelianGroup_662 -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_662
v3)))))
-- Algebra.Bundles.CommutativeRing._.distrib
d_distrib_2814 ::
  T_CommutativeRing_2704 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_distrib_2814 :: T_CommutativeRing_2704 -> T_Σ_14
d_distrib_2814 T_CommutativeRing_2704
v0
  = (T_IsRing_1584 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsRing_1584 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_distrib_1608
      ((T_IsCommutativeRing_1720 -> T_IsRing_1584) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCommutativeRing_1720 -> T_IsRing_1584
MAlonzo.Code.Algebra.Structures.d_isRing_1736
         ((T_CommutativeRing_2704 -> T_IsCommutativeRing_1720)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeRing_2704 -> T_IsCommutativeRing_1720
d_isCommutativeRing_2740 (T_CommutativeRing_2704 -> AgdaAny
forall a b. a -> b
coe T_CommutativeRing_2704
v0)))
-- Algebra.Bundles.CommutativeRing._.distribʳ
d_distrib'691'_2816 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeRing_2704 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_distrib'691'_2816 :: ()
-> ()
-> T_CommutativeRing_2704
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_distrib'691'_2816 ~()
v0 ~()
v1 T_CommutativeRing_2704
v2 = T_CommutativeRing_2704 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'691'_2816 T_CommutativeRing_2704
v2
du_distrib'691'_2816 ::
  T_CommutativeRing_2704 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'691'_2816 :: T_CommutativeRing_2704 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'691'_2816 T_CommutativeRing_2704
v0
  = let v1 :: T_IsCommutativeRing_1720
v1 = T_CommutativeRing_2704 -> T_IsCommutativeRing_1720
d_isCommutativeRing_2740 (T_CommutativeRing_2704 -> T_CommutativeRing_2704
forall a b. a -> b
coe T_CommutativeRing_2704
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsRing_1584
v2 = T_IsCommutativeRing_1720 -> T_IsRing_1584
MAlonzo.Code.Algebra.Structures.d_isRing_1736 (T_IsCommutativeRing_1720 -> T_IsCommutativeRing_1720
forall a b. a -> b
coe T_IsCommutativeRing_1720
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: t
v3
                = (T_IsRing_1584 -> T_IsSemiring_1238) -> AgdaAny -> t
forall a b. a -> b
coe
                    T_IsRing_1584 -> T_IsSemiring_1238
MAlonzo.Code.Algebra.Structures.du_isSemiring_1698 (T_IsRing_1584 -> AgdaAny
forall a b. a -> b
coe T_IsRing_1584
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsSemiringWithoutAnnihilatingZero_1142
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemiringWithoutAnnihilatingZero_1142
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_distrib'691'_1166
               ((T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1252
                  (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3)))))
-- Algebra.Bundles.CommutativeRing._.distribˡ
d_distrib'737'_2818 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeRing_2704 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_distrib'737'_2818 :: ()
-> ()
-> T_CommutativeRing_2704
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_distrib'737'_2818 ~()
v0 ~()
v1 T_CommutativeRing_2704
v2 = T_CommutativeRing_2704 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'737'_2818 T_CommutativeRing_2704
v2
du_distrib'737'_2818 ::
  T_CommutativeRing_2704 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'737'_2818 :: T_CommutativeRing_2704 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_distrib'737'_2818 T_CommutativeRing_2704
v0
  = let v1 :: T_IsCommutativeRing_1720
v1 = T_CommutativeRing_2704 -> T_IsCommutativeRing_1720
d_isCommutativeRing_2740 (T_CommutativeRing_2704 -> T_CommutativeRing_2704
forall a b. a -> b
coe T_CommutativeRing_2704
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsRing_1584
v2 = T_IsCommutativeRing_1720 -> T_IsRing_1584
MAlonzo.Code.Algebra.Structures.d_isRing_1736 (T_IsCommutativeRing_1720 -> T_IsCommutativeRing_1720
forall a b. a -> b
coe T_IsCommutativeRing_1720
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: t
v3
                = (T_IsRing_1584 -> T_IsSemiring_1238) -> AgdaAny -> t
forall a b. a -> b
coe
                    T_IsRing_1584 -> T_IsSemiring_1238
MAlonzo.Code.Algebra.Structures.du_isSemiring_1698 (T_IsRing_1584 -> AgdaAny
forall a b. a -> b
coe T_IsRing_1584
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsSemiringWithoutAnnihilatingZero_1142
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemiringWithoutAnnihilatingZero_1142
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_distrib'737'_1164
               ((T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1252
                  (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3)))))
-- Algebra.Bundles.CommutativeRing._.isCommutativeSemiring
d_isCommutativeSemiring_2820 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeRing_2704 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiring_1344
d_isCommutativeSemiring_2820 :: () -> () -> T_CommutativeRing_2704 -> T_IsCommutativeSemiring_1344
d_isCommutativeSemiring_2820 ~()
v0 ~()
v1 T_CommutativeRing_2704
v2
  = T_CommutativeRing_2704 -> T_IsCommutativeSemiring_1344
du_isCommutativeSemiring_2820 T_CommutativeRing_2704
v2
du_isCommutativeSemiring_2820 ::
  T_CommutativeRing_2704 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiring_1344
du_isCommutativeSemiring_2820 :: T_CommutativeRing_2704 -> T_IsCommutativeSemiring_1344
du_isCommutativeSemiring_2820 T_CommutativeRing_2704
v0
  = (T_IsCommutativeRing_1720 -> T_IsCommutativeSemiring_1344)
-> AgdaAny -> T_IsCommutativeSemiring_1344
forall a b. a -> b
coe
      T_IsCommutativeRing_1720 -> T_IsCommutativeSemiring_1344
MAlonzo.Code.Algebra.Structures.du_isCommutativeSemiring_1842
      ((T_CommutativeRing_2704 -> T_IsCommutativeRing_1720)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeRing_2704 -> T_IsCommutativeRing_1720
d_isCommutativeRing_2740 (T_CommutativeRing_2704 -> AgdaAny
forall a b. a -> b
coe T_CommutativeRing_2704
v0))
-- Algebra.Bundles.CommutativeRing._.isCommutativeSemiringWithoutOne
d_isCommutativeSemiringWithoutOne_2822 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeRing_2704 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiringWithoutOne_1044
d_isCommutativeSemiringWithoutOne_2822 :: ()
-> ()
-> T_CommutativeRing_2704
-> T_IsCommutativeSemiringWithoutOne_1044
d_isCommutativeSemiringWithoutOne_2822 ~()
v0 ~()
v1 T_CommutativeRing_2704
v2
  = T_CommutativeRing_2704 -> T_IsCommutativeSemiringWithoutOne_1044
du_isCommutativeSemiringWithoutOne_2822 T_CommutativeRing_2704
v2
du_isCommutativeSemiringWithoutOne_2822 ::
  T_CommutativeRing_2704 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiringWithoutOne_1044
du_isCommutativeSemiringWithoutOne_2822 :: T_CommutativeRing_2704 -> T_IsCommutativeSemiringWithoutOne_1044
du_isCommutativeSemiringWithoutOne_2822 T_CommutativeRing_2704
v0
  = let v1 :: T_IsCommutativeRing_1720
v1 = T_CommutativeRing_2704 -> T_IsCommutativeRing_1720
d_isCommutativeRing_2740 (T_CommutativeRing_2704 -> T_CommutativeRing_2704
forall a b. a -> b
coe T_CommutativeRing_2704
v0) in
    AgdaAny -> T_IsCommutativeSemiringWithoutOne_1044
forall a b. a -> b
coe
      ((T_IsCommutativeSemiring_1344
 -> T_IsCommutativeSemiringWithoutOne_1044)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCommutativeSemiring_1344
-> T_IsCommutativeSemiringWithoutOne_1044
MAlonzo.Code.Algebra.Structures.du_isCommutativeSemiringWithoutOne_1444
         ((T_IsCommutativeRing_1720 -> T_IsCommutativeSemiring_1344)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCommutativeRing_1720 -> T_IsCommutativeSemiring_1344
MAlonzo.Code.Algebra.Structures.du_isCommutativeSemiring_1842
            (T_IsCommutativeRing_1720 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeRing_1720
v1)))
-- Algebra.Bundles.CommutativeRing._.isEquivalence
d_isEquivalence_2824 ::
  T_CommutativeRing_2704 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_2824 :: T_CommutativeRing_2704 -> T_IsEquivalence_26
d_isEquivalence_2824 T_CommutativeRing_2704
v0
  = (T_IsMagma_86 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      T_IsMagma_86 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_94
      ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202
         ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368
            ((T_IsGroup_580 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsGroup_580 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_594
               ((T_IsAbelianGroup_662 -> T_IsGroup_580) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsAbelianGroup_662 -> T_IsGroup_580
MAlonzo.Code.Algebra.Structures.d_isGroup_674
                  ((T_IsRing_1584 -> T_IsAbelianGroup_662) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsRing_1584 -> T_IsAbelianGroup_662
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_1604
                     ((T_IsCommutativeRing_1720 -> T_IsRing_1584) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsCommutativeRing_1720 -> T_IsRing_1584
MAlonzo.Code.Algebra.Structures.d_isRing_1736
                        ((T_CommutativeRing_2704 -> T_IsCommutativeRing_1720)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeRing_2704 -> T_IsCommutativeRing_1720
d_isCommutativeRing_2740 (T_CommutativeRing_2704 -> AgdaAny
forall a b. a -> b
coe T_CommutativeRing_2704
v0))))))))
-- Algebra.Bundles.CommutativeRing._.isNearSemiring
d_isNearSemiring_2826 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeRing_2704 ->
  MAlonzo.Code.Algebra.Structures.T_IsNearSemiring_876
d_isNearSemiring_2826 :: () -> () -> T_CommutativeRing_2704 -> T_IsNearSemiring_876
d_isNearSemiring_2826 ~()
v0 ~()
v1 T_CommutativeRing_2704
v2 = T_CommutativeRing_2704 -> T_IsNearSemiring_876
du_isNearSemiring_2826 T_CommutativeRing_2704
v2
du_isNearSemiring_2826 ::
  T_CommutativeRing_2704 ->
  MAlonzo.Code.Algebra.Structures.T_IsNearSemiring_876
du_isNearSemiring_2826 :: T_CommutativeRing_2704 -> T_IsNearSemiring_876
du_isNearSemiring_2826 T_CommutativeRing_2704
v0
  = let v1 :: T_IsCommutativeRing_1720
v1 = T_CommutativeRing_2704 -> T_IsCommutativeRing_1720
d_isCommutativeRing_2740 (T_CommutativeRing_2704 -> T_CommutativeRing_2704
forall a b. a -> b
coe T_CommutativeRing_2704
v0) in
    AgdaAny -> T_IsNearSemiring_876
forall a b. a -> b
coe
      (let v2 :: T_IsRing_1584
v2 = T_IsCommutativeRing_1720 -> T_IsRing_1584
MAlonzo.Code.Algebra.Structures.d_isRing_1736 (T_IsCommutativeRing_1720 -> T_IsCommutativeRing_1720
forall a b. a -> b
coe T_IsCommutativeRing_1720
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: t
v3
                = (T_IsRing_1584 -> T_IsSemiring_1238) -> AgdaAny -> t
forall a b. a -> b
coe
                    T_IsRing_1584 -> T_IsSemiring_1238
MAlonzo.Code.Algebra.Structures.du_isSemiring_1698 (T_IsRing_1584 -> AgdaAny
forall a b. a -> b
coe T_IsRing_1584
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsSemiringWithoutOne_952 -> T_IsNearSemiring_876)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemiringWithoutOne_952 -> T_IsNearSemiring_876
MAlonzo.Code.Algebra.Structures.du_isNearSemiring_990
               ((T_IsSemiring_1238 -> T_IsSemiringWithoutOne_952)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsSemiring_1238 -> T_IsSemiringWithoutOne_952
MAlonzo.Code.Algebra.Structures.du_isSemiringWithoutOne_1326
                  (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3)))))
-- Algebra.Bundles.CommutativeRing._.isPartialEquivalence
d_isPartialEquivalence_2828 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeRing_2704 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_2828 :: () -> () -> T_CommutativeRing_2704 -> T_IsPartialEquivalence_16
d_isPartialEquivalence_2828 ~()
v0 ~()
v1 T_CommutativeRing_2704
v2
  = T_CommutativeRing_2704 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_2828 T_CommutativeRing_2704
v2
du_isPartialEquivalence_2828 ::
  T_CommutativeRing_2704 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_2828 :: T_CommutativeRing_2704 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_2828 T_CommutativeRing_2704
v0
  = let v1 :: T_IsCommutativeRing_1720
v1 = T_CommutativeRing_2704 -> T_IsCommutativeRing_1720
d_isCommutativeRing_2740 (T_CommutativeRing_2704 -> T_CommutativeRing_2704
forall a b. a -> b
coe T_CommutativeRing_2704
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsRing_1584
v2 = T_IsCommutativeRing_1720 -> T_IsRing_1584
MAlonzo.Code.Algebra.Structures.d_isRing_1736 (T_IsCommutativeRing_1720 -> T_IsCommutativeRing_1720
forall a b. a -> b
coe T_IsCommutativeRing_1720
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsAbelianGroup_662
v3
                = T_IsRing_1584 -> T_IsAbelianGroup_662
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_1604
                    (T_IsRing_1584 -> T_IsRing_1584
forall a b. a -> b
coe T_IsRing_1584
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsGroup_580
v4 = T_IsAbelianGroup_662 -> T_IsGroup_580
MAlonzo.Code.Algebra.Structures.d_isGroup_674 (T_IsAbelianGroup_662 -> T_IsAbelianGroup_662
forall a b. a -> b
coe T_IsAbelianGroup_662
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsMonoid_358
v5
                      = T_IsGroup_580 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_594 (T_IsGroup_580 -> T_IsGroup_580
forall a b. a -> b
coe T_IsGroup_580
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (let v6 :: T_IsSemigroup_194
v6
                         = T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368 (T_IsMonoid_358 -> T_IsMonoid_358
forall a b. a -> b
coe T_IsMonoid_358
v5) in
                   AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     (let v7 :: T_IsMagma_86
v7 = T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202 (T_IsSemigroup_194 -> T_IsSemigroup_194
forall a b. a -> b
coe T_IsSemigroup_194
v6) in
                      AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        ((T_IsEquivalence_26 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_IsEquivalence_26 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
                           ((T_IsMagma_86 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                              T_IsMagma_86 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_94 (T_IsMagma_86 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86
v7)))))))))
-- Algebra.Bundles.CommutativeRing._.isRing
d_isRing_2830 ::
  T_CommutativeRing_2704 ->
  MAlonzo.Code.Algebra.Structures.T_IsRing_1584
d_isRing_2830 :: T_CommutativeRing_2704 -> T_IsRing_1584
d_isRing_2830 T_CommutativeRing_2704
v0
  = (T_IsCommutativeRing_1720 -> T_IsRing_1584)
-> AgdaAny -> T_IsRing_1584
forall a b. a -> b
coe
      T_IsCommutativeRing_1720 -> T_IsRing_1584
MAlonzo.Code.Algebra.Structures.d_isRing_1736
      ((T_CommutativeRing_2704 -> T_IsCommutativeRing_1720)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeRing_2704 -> T_IsCommutativeRing_1720
d_isCommutativeRing_2740 (T_CommutativeRing_2704 -> AgdaAny
forall a b. a -> b
coe T_CommutativeRing_2704
v0))
-- Algebra.Bundles.CommutativeRing._.isSemiring
d_isSemiring_2832 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeRing_2704 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemiring_1238
d_isSemiring_2832 :: () -> () -> T_CommutativeRing_2704 -> T_IsSemiring_1238
d_isSemiring_2832 ~()
v0 ~()
v1 T_CommutativeRing_2704
v2 = T_CommutativeRing_2704 -> T_IsSemiring_1238
du_isSemiring_2832 T_CommutativeRing_2704
v2
du_isSemiring_2832 ::
  T_CommutativeRing_2704 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemiring_1238
du_isSemiring_2832 :: T_CommutativeRing_2704 -> T_IsSemiring_1238
du_isSemiring_2832 T_CommutativeRing_2704
v0
  = let v1 :: T_IsCommutativeRing_1720
v1 = T_CommutativeRing_2704 -> T_IsCommutativeRing_1720
d_isCommutativeRing_2740 (T_CommutativeRing_2704 -> T_CommutativeRing_2704
forall a b. a -> b
coe T_CommutativeRing_2704
v0) in
    AgdaAny -> T_IsSemiring_1238
forall a b. a -> b
coe
      ((T_IsRing_1584 -> T_IsSemiring_1238) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsRing_1584 -> T_IsSemiring_1238
MAlonzo.Code.Algebra.Structures.du_isSemiring_1698
         ((T_IsCommutativeRing_1720 -> T_IsRing_1584) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeRing_1720 -> T_IsRing_1584
MAlonzo.Code.Algebra.Structures.d_isRing_1736 (T_IsCommutativeRing_1720 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeRing_1720
v1)))
-- Algebra.Bundles.CommutativeRing._.isSemiringWithoutAnnihilatingZero
d_isSemiringWithoutAnnihilatingZero_2834 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeRing_2704 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutAnnihilatingZero_1142
d_isSemiringWithoutAnnihilatingZero_2834 :: ()
-> ()
-> T_CommutativeRing_2704
-> T_IsSemiringWithoutAnnihilatingZero_1142
d_isSemiringWithoutAnnihilatingZero_2834 ~()
v0 ~()
v1 T_CommutativeRing_2704
v2
  = T_CommutativeRing_2704 -> T_IsSemiringWithoutAnnihilatingZero_1142
du_isSemiringWithoutAnnihilatingZero_2834 T_CommutativeRing_2704
v2
du_isSemiringWithoutAnnihilatingZero_2834 ::
  T_CommutativeRing_2704 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutAnnihilatingZero_1142
du_isSemiringWithoutAnnihilatingZero_2834 :: T_CommutativeRing_2704 -> T_IsSemiringWithoutAnnihilatingZero_1142
du_isSemiringWithoutAnnihilatingZero_2834 T_CommutativeRing_2704
v0
  = let v1 :: T_IsCommutativeRing_1720
v1 = T_CommutativeRing_2704 -> T_IsCommutativeRing_1720
d_isCommutativeRing_2740 (T_CommutativeRing_2704 -> T_CommutativeRing_2704
forall a b. a -> b
coe T_CommutativeRing_2704
v0) in
    AgdaAny -> T_IsSemiringWithoutAnnihilatingZero_1142
forall a b. a -> b
coe
      ((T_IsRing_1584 -> T_IsSemiringWithoutAnnihilatingZero_1142)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsRing_1584 -> T_IsSemiringWithoutAnnihilatingZero_1142
MAlonzo.Code.Algebra.Structures.du_isSemiringWithoutAnnihilatingZero_1696
         ((T_IsCommutativeRing_1720 -> T_IsRing_1584) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeRing_1720 -> T_IsRing_1584
MAlonzo.Code.Algebra.Structures.d_isRing_1736 (T_IsCommutativeRing_1720 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeRing_1720
v1)))
-- Algebra.Bundles.CommutativeRing._.isSemiringWithoutOne
d_isSemiringWithoutOne_2836 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeRing_2704 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutOne_952
d_isSemiringWithoutOne_2836 :: () -> () -> T_CommutativeRing_2704 -> T_IsSemiringWithoutOne_952
d_isSemiringWithoutOne_2836 ~()
v0 ~()
v1 T_CommutativeRing_2704
v2
  = T_CommutativeRing_2704 -> T_IsSemiringWithoutOne_952
du_isSemiringWithoutOne_2836 T_CommutativeRing_2704
v2
du_isSemiringWithoutOne_2836 ::
  T_CommutativeRing_2704 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutOne_952
du_isSemiringWithoutOne_2836 :: T_CommutativeRing_2704 -> T_IsSemiringWithoutOne_952
du_isSemiringWithoutOne_2836 T_CommutativeRing_2704
v0
  = let v1 :: T_IsCommutativeRing_1720
v1 = T_CommutativeRing_2704 -> T_IsCommutativeRing_1720
d_isCommutativeRing_2740 (T_CommutativeRing_2704 -> T_CommutativeRing_2704
forall a b. a -> b
coe T_CommutativeRing_2704
v0) in
    AgdaAny -> T_IsSemiringWithoutOne_952
forall a b. a -> b
coe
      (let v2 :: T_IsRing_1584
v2 = T_IsCommutativeRing_1720 -> T_IsRing_1584
MAlonzo.Code.Algebra.Structures.d_isRing_1736 (T_IsCommutativeRing_1720 -> T_IsCommutativeRing_1720
forall a b. a -> b
coe T_IsCommutativeRing_1720
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsSemiring_1238 -> T_IsSemiringWithoutOne_952)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemiring_1238 -> T_IsSemiringWithoutOne_952
MAlonzo.Code.Algebra.Structures.du_isSemiringWithoutOne_1326
            ((T_IsRing_1584 -> T_IsSemiring_1238) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRing_1584 -> T_IsSemiring_1238
MAlonzo.Code.Algebra.Structures.du_isSemiring_1698 (T_IsRing_1584 -> AgdaAny
forall a b. a -> b
coe T_IsRing_1584
v2))))
-- Algebra.Bundles.CommutativeRing._.refl
d_refl_2838 :: T_CommutativeRing_2704 -> AgdaAny -> AgdaAny
d_refl_2838 :: T_CommutativeRing_2704 -> AgdaAny -> AgdaAny
d_refl_2838 T_CommutativeRing_2704
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_86 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_86 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_94
         ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202
            ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368
               ((T_IsGroup_580 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsGroup_580 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_594
                  ((T_IsAbelianGroup_662 -> T_IsGroup_580) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsAbelianGroup_662 -> T_IsGroup_580
MAlonzo.Code.Algebra.Structures.d_isGroup_674
                     ((T_IsRing_1584 -> T_IsAbelianGroup_662) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsRing_1584 -> T_IsAbelianGroup_662
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_1604
                        ((T_IsCommutativeRing_1720 -> T_IsRing_1584) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_IsCommutativeRing_1720 -> T_IsRing_1584
MAlonzo.Code.Algebra.Structures.d_isRing_1736
                           ((T_CommutativeRing_2704 -> T_IsCommutativeRing_1720)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeRing_2704 -> T_IsCommutativeRing_1720
d_isCommutativeRing_2740 (T_CommutativeRing_2704 -> AgdaAny
forall a b. a -> b
coe T_CommutativeRing_2704
v0)))))))))
-- Algebra.Bundles.CommutativeRing._.reflexive
d_reflexive_2840 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeRing_2704 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_2840 :: ()
-> ()
-> T_CommutativeRing_2704
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_2840 ~()
v0 ~()
v1 T_CommutativeRing_2704
v2 = T_CommutativeRing_2704
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_2840 T_CommutativeRing_2704
v2
du_reflexive_2840 ::
  T_CommutativeRing_2704 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_2840 :: T_CommutativeRing_2704
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_2840 T_CommutativeRing_2704
v0
  = let v1 :: T_IsCommutativeRing_1720
v1 = T_CommutativeRing_2704 -> T_IsCommutativeRing_1720
d_isCommutativeRing_2740 (T_CommutativeRing_2704 -> T_CommutativeRing_2704
forall a b. a -> b
coe T_CommutativeRing_2704
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsRing_1584
v2 = T_IsCommutativeRing_1720 -> T_IsRing_1584
MAlonzo.Code.Algebra.Structures.d_isRing_1736 (T_IsCommutativeRing_1720 -> T_IsCommutativeRing_1720
forall a b. a -> b
coe T_IsCommutativeRing_1720
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsAbelianGroup_662
v3
                = T_IsRing_1584 -> T_IsAbelianGroup_662
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_1604
                    (T_IsRing_1584 -> T_IsRing_1584
forall a b. a -> b
coe T_IsRing_1584
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsGroup_580
v4 = T_IsAbelianGroup_662 -> T_IsGroup_580
MAlonzo.Code.Algebra.Structures.d_isGroup_674 (T_IsAbelianGroup_662 -> T_IsAbelianGroup_662
forall a b. a -> b
coe T_IsAbelianGroup_662
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsMonoid_358
v5
                      = T_IsGroup_580 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_594 (T_IsGroup_580 -> T_IsGroup_580
forall a b. a -> b
coe T_IsGroup_580
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (let v6 :: T_IsSemigroup_194
v6
                         = T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368 (T_IsMonoid_358 -> T_IsMonoid_358
forall a b. a -> b
coe T_IsMonoid_358
v5) in
                   AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     (let v7 :: T_IsMagma_86
v7 = T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202 (T_IsSemigroup_194 -> T_IsSemigroup_194
forall a b. a -> b
coe T_IsSemigroup_194
v6) in
                      (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
                        (\ AgdaAny
v8 AgdaAny
v9 AgdaAny
v10 ->
                           (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                             T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
                             ((T_IsMagma_86 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_94 (T_IsMagma_86 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_86
v7))
                             AgdaAny
v8)))))))
-- Algebra.Bundles.CommutativeRing._.setoid
d_setoid_2842 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeRing_2704 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_2842 :: () -> () -> T_CommutativeRing_2704 -> T_Setoid_44
d_setoid_2842 ~()
v0 ~()
v1 T_CommutativeRing_2704
v2 = T_CommutativeRing_2704 -> T_Setoid_44
du_setoid_2842 T_CommutativeRing_2704
v2
du_setoid_2842 ::
  T_CommutativeRing_2704 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_2842 :: T_CommutativeRing_2704 -> T_Setoid_44
du_setoid_2842 T_CommutativeRing_2704
v0
  = let v1 :: T_IsCommutativeRing_1720
v1 = T_CommutativeRing_2704 -> T_IsCommutativeRing_1720
d_isCommutativeRing_2740 (T_CommutativeRing_2704 -> T_CommutativeRing_2704
forall a b. a -> b
coe T_CommutativeRing_2704
v0) in
    AgdaAny -> T_Setoid_44
forall a b. a -> b
coe
      (let v2 :: T_IsRing_1584
v2 = T_IsCommutativeRing_1720 -> T_IsRing_1584
MAlonzo.Code.Algebra.Structures.d_isRing_1736 (T_IsCommutativeRing_1720 -> T_IsCommutativeRing_1720
forall a b. a -> b
coe T_IsCommutativeRing_1720
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsAbelianGroup_662
v3
                = T_IsRing_1584 -> T_IsAbelianGroup_662
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_1604
                    (T_IsRing_1584 -> T_IsRing_1584
forall a b. a -> b
coe T_IsRing_1584
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsGroup_580
v4 = T_IsAbelianGroup_662 -> T_IsGroup_580
MAlonzo.Code.Algebra.Structures.d_isGroup_674 (T_IsAbelianGroup_662 -> T_IsAbelianGroup_662
forall a b. a -> b
coe T_IsAbelianGroup_662
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsMonoid_358
v5
                      = T_IsGroup_580 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_594 (T_IsGroup_580 -> T_IsGroup_580
forall a b. a -> b
coe T_IsGroup_580
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (let v6 :: T_IsSemigroup_194
v6
                         = T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368 (T_IsMonoid_358 -> T_IsMonoid_358
forall a b. a -> b
coe T_IsMonoid_358
v5) in
                   AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     ((T_IsMagma_86 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsMagma_86 -> T_Setoid_44
MAlonzo.Code.Algebra.Structures.du_setoid_110
                        ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202 (T_IsSemigroup_194 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_194
v6))))))))
-- Algebra.Bundles.CommutativeRing._.sym
d_sym_2844 ::
  T_CommutativeRing_2704 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_2844 :: T_CommutativeRing_2704 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_2844 T_CommutativeRing_2704
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_86 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_86 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_94
         ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202
            ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368
               ((T_IsGroup_580 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsGroup_580 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_594
                  ((T_IsAbelianGroup_662 -> T_IsGroup_580) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsAbelianGroup_662 -> T_IsGroup_580
MAlonzo.Code.Algebra.Structures.d_isGroup_674
                     ((T_IsRing_1584 -> T_IsAbelianGroup_662) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsRing_1584 -> T_IsAbelianGroup_662
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_1604
                        ((T_IsCommutativeRing_1720 -> T_IsRing_1584) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_IsCommutativeRing_1720 -> T_IsRing_1584
MAlonzo.Code.Algebra.Structures.d_isRing_1736
                           ((T_CommutativeRing_2704 -> T_IsCommutativeRing_1720)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeRing_2704 -> T_IsCommutativeRing_1720
d_isCommutativeRing_2740 (T_CommutativeRing_2704 -> AgdaAny
forall a b. a -> b
coe T_CommutativeRing_2704
v0)))))))))
-- Algebra.Bundles.CommutativeRing._.trans
d_trans_2846 ::
  T_CommutativeRing_2704 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_2846 :: T_CommutativeRing_2704
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_2846 T_CommutativeRing_2704
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_86 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_86 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_94
         ((T_IsSemigroup_194 -> T_IsMagma_86) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202
            ((T_IsMonoid_358 -> T_IsSemigroup_194) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368
               ((T_IsGroup_580 -> T_IsMonoid_358) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsGroup_580 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_594
                  ((T_IsAbelianGroup_662 -> T_IsGroup_580) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsAbelianGroup_662 -> T_IsGroup_580
MAlonzo.Code.Algebra.Structures.d_isGroup_674
                     ((T_IsRing_1584 -> T_IsAbelianGroup_662) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsRing_1584 -> T_IsAbelianGroup_662
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_1604
                        ((T_IsCommutativeRing_1720 -> T_IsRing_1584) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_IsCommutativeRing_1720 -> T_IsRing_1584
MAlonzo.Code.Algebra.Structures.d_isRing_1736
                           ((T_CommutativeRing_2704 -> T_IsCommutativeRing_1720)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeRing_2704 -> T_IsCommutativeRing_1720
d_isCommutativeRing_2740 (T_CommutativeRing_2704 -> AgdaAny
forall a b. a -> b
coe T_CommutativeRing_2704
v0)))))))))
-- Algebra.Bundles.CommutativeRing._.uniqueʳ-⁻¹
d_unique'691''45''8315''185'_2848 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeRing_2704 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_unique'691''45''8315''185'_2848 :: ()
-> ()
-> T_CommutativeRing_2704
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_unique'691''45''8315''185'_2848 ~()
v0 ~()
v1 T_CommutativeRing_2704
v2
  = T_CommutativeRing_2704 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_unique'691''45''8315''185'_2848 T_CommutativeRing_2704
v2
du_unique'691''45''8315''185'_2848 ::
  T_CommutativeRing_2704 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_unique'691''45''8315''185'_2848 :: T_CommutativeRing_2704 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_unique'691''45''8315''185'_2848 T_CommutativeRing_2704
v0
  = let v1 :: AgdaAny -> AgdaAny -> AgdaAny
v1 = T_CommutativeRing_2704 -> AgdaAny -> AgdaAny -> AgdaAny
d__'43'__2730 (T_CommutativeRing_2704 -> T_CommutativeRing_2704
forall a b. a -> b
coe T_CommutativeRing_2704
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: AgdaAny -> AgdaAny
v2 = T_CommutativeRing_2704 -> AgdaAny -> AgdaAny
d_'45'__2734 (T_CommutativeRing_2704 -> T_CommutativeRing_2704
forall a b. a -> b
coe T_CommutativeRing_2704
v0) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: AgdaAny
v3 = T_CommutativeRing_2704 -> AgdaAny
d_0'35'_2736 (T_CommutativeRing_2704 -> T_CommutativeRing_2704
forall a b. a -> b
coe T_CommutativeRing_2704
v0) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsCommutativeRing_1720
v4 = T_CommutativeRing_2704 -> T_IsCommutativeRing_1720
d_isCommutativeRing_2740 (T_CommutativeRing_2704 -> T_CommutativeRing_2704
forall a b. a -> b
coe T_CommutativeRing_2704
v0) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsRing_1584
v5 = T_IsCommutativeRing_1720 -> T_IsRing_1584
MAlonzo.Code.Algebra.Structures.d_isRing_1736 (T_IsCommutativeRing_1720 -> T_IsCommutativeRing_1720
forall a b. a -> b
coe T_IsCommutativeRing_1720
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (let v6 :: T_IsAbelianGroup_662
v6
                         = T_IsRing_1584 -> T_IsAbelianGroup_662
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_1604
                             (T_IsRing_1584 -> T_IsRing_1584
forall a b. a -> b
coe T_IsRing_1584
v5) in
                   AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     (((AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> (AgdaAny -> AgdaAny)
 -> T_IsGroup_580
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsGroup_580
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.du_unique'691''45''8315''185'_654
                        ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v1) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3) ((AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v2)
                        ((T_IsAbelianGroup_662 -> T_IsGroup_580) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_662 -> T_IsGroup_580
MAlonzo.Code.Algebra.Structures.d_isGroup_674 (T_IsAbelianGroup_662 -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_662
v6))))))))
-- Algebra.Bundles.CommutativeRing._.uniqueˡ-⁻¹
d_unique'737''45''8315''185'_2850 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeRing_2704 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_unique'737''45''8315''185'_2850 :: ()
-> ()
-> T_CommutativeRing_2704
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_unique'737''45''8315''185'_2850 ~()
v0 ~()
v1 T_CommutativeRing_2704
v2
  = T_CommutativeRing_2704 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_unique'737''45''8315''185'_2850 T_CommutativeRing_2704
v2
du_unique'737''45''8315''185'_2850 ::
  T_CommutativeRing_2704 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_unique'737''45''8315''185'_2850 :: T_CommutativeRing_2704 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_unique'737''45''8315''185'_2850 T_CommutativeRing_2704
v0
  = let v1 :: AgdaAny -> AgdaAny -> AgdaAny
v1 = T_CommutativeRing_2704 -> AgdaAny -> AgdaAny -> AgdaAny
d__'43'__2730 (T_CommutativeRing_2704 -> T_CommutativeRing_2704
forall a b. a -> b
coe T_CommutativeRing_2704
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: AgdaAny -> AgdaAny
v2 = T_CommutativeRing_2704 -> AgdaAny -> AgdaAny
d_'45'__2734 (T_CommutativeRing_2704 -> T_CommutativeRing_2704
forall a b. a -> b
coe T_CommutativeRing_2704
v0) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: AgdaAny
v3 = T_CommutativeRing_2704 -> AgdaAny
d_0'35'_2736 (T_CommutativeRing_2704 -> T_CommutativeRing_2704
forall a b. a -> b
coe T_CommutativeRing_2704
v0) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsCommutativeRing_1720
v4 = T_CommutativeRing_2704 -> T_IsCommutativeRing_1720
d_isCommutativeRing_2740 (T_CommutativeRing_2704 -> T_CommutativeRing_2704
forall a b. a -> b
coe T_CommutativeRing_2704
v0) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsRing_1584
v5 = T_IsCommutativeRing_1720 -> T_IsRing_1584
MAlonzo.Code.Algebra.Structures.d_isRing_1736 (T_IsCommutativeRing_1720 -> T_IsCommutativeRing_1720
forall a b. a -> b
coe T_IsCommutativeRing_1720
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (let v6 :: T_IsAbelianGroup_662
v6
                         = T_IsRing_1584 -> T_IsAbelianGroup_662
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_1604
                             (T_IsRing_1584 -> T_IsRing_1584
forall a b. a -> b
coe T_IsRing_1584
v5) in
                   AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     (((AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> (AgdaAny -> AgdaAny)
 -> T_IsGroup_580
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsGroup_580
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.du_unique'737''45''8315''185'_648
                        ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v1) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3) ((AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v2)
                        ((T_IsAbelianGroup_662 -> T_IsGroup_580) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_662 -> T_IsGroup_580
MAlonzo.Code.Algebra.Structures.d_isGroup_674 (T_IsAbelianGroup_662 -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_662
v6))))))))
-- Algebra.Bundles.CommutativeRing._.zero
d_zero_2852 ::
  T_CommutativeRing_2704 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_zero_2852 :: T_CommutativeRing_2704 -> T_Σ_14
d_zero_2852 T_CommutativeRing_2704
v0
  = (T_IsRing_1584 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsRing_1584 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_zero_1610
      ((T_IsCommutativeRing_1720 -> T_IsRing_1584) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCommutativeRing_1720 -> T_IsRing_1584
MAlonzo.Code.Algebra.Structures.d_isRing_1736
         ((T_CommutativeRing_2704 -> T_IsCommutativeRing_1720)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeRing_2704 -> T_IsCommutativeRing_1720
d_isCommutativeRing_2740 (T_CommutativeRing_2704 -> AgdaAny
forall a b. a -> b
coe T_CommutativeRing_2704
v0)))
-- Algebra.Bundles.CommutativeRing._.zeroʳ
d_zero'691'_2854 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeRing_2704 -> AgdaAny -> AgdaAny
d_zero'691'_2854 :: () -> () -> T_CommutativeRing_2704 -> AgdaAny -> AgdaAny
d_zero'691'_2854 ~()
v0 ~()
v1 T_CommutativeRing_2704
v2 = T_CommutativeRing_2704 -> AgdaAny -> AgdaAny
du_zero'691'_2854 T_CommutativeRing_2704
v2
du_zero'691'_2854 :: T_CommutativeRing_2704 -> AgdaAny -> AgdaAny
du_zero'691'_2854 :: T_CommutativeRing_2704 -> AgdaAny -> AgdaAny
du_zero'691'_2854 T_CommutativeRing_2704
v0
  = let v1 :: T_IsCommutativeRing_1720
v1 = T_CommutativeRing_2704 -> T_IsCommutativeRing_1720
d_isCommutativeRing_2740 (T_CommutativeRing_2704 -> T_CommutativeRing_2704
forall a b. a -> b
coe T_CommutativeRing_2704
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsRing_1584 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsRing_1584 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_zero'691'_1694
         ((T_IsCommutativeRing_1720 -> T_IsRing_1584) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeRing_1720 -> T_IsRing_1584
MAlonzo.Code.Algebra.Structures.d_isRing_1736 (T_IsCommutativeRing_1720 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeRing_1720
v1)))
-- Algebra.Bundles.CommutativeRing._.zeroˡ
d_zero'737'_2856 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeRing_2704 -> AgdaAny -> AgdaAny
d_zero'737'_2856 :: () -> () -> T_CommutativeRing_2704 -> AgdaAny -> AgdaAny
d_zero'737'_2856 ~()
v0 ~()
v1 T_CommutativeRing_2704
v2 = T_CommutativeRing_2704 -> AgdaAny -> AgdaAny
du_zero'737'_2856 T_CommutativeRing_2704
v2
du_zero'737'_2856 :: T_CommutativeRing_2704 -> AgdaAny -> AgdaAny
du_zero'737'_2856 :: T_CommutativeRing_2704 -> AgdaAny -> AgdaAny
du_zero'737'_2856 T_CommutativeRing_2704
v0
  = let v1 :: T_IsCommutativeRing_1720
v1 = T_CommutativeRing_2704 -> T_IsCommutativeRing_1720
d_isCommutativeRing_2740 (T_CommutativeRing_2704 -> T_CommutativeRing_2704
forall a b. a -> b
coe T_CommutativeRing_2704
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsRing_1584 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsRing_1584 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_zero'737'_1692
         ((T_IsCommutativeRing_1720 -> T_IsRing_1584) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeRing_1720 -> T_IsRing_1584
MAlonzo.Code.Algebra.Structures.d_isRing_1736 (T_IsCommutativeRing_1720 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeRing_1720
v1)))
-- Algebra.Bundles.CommutativeRing.ring
d_ring_2858 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeRing_2704 -> T_Ring_2514
d_ring_2858 :: () -> () -> T_CommutativeRing_2704 -> T_Ring_2514
d_ring_2858 ~()
v0 ~()
v1 T_CommutativeRing_2704
v2 = T_CommutativeRing_2704 -> T_Ring_2514
du_ring_2858 T_CommutativeRing_2704
v2
du_ring_2858 :: T_CommutativeRing_2704 -> T_Ring_2514
du_ring_2858 :: T_CommutativeRing_2704 -> T_Ring_2514
du_ring_2858 T_CommutativeRing_2704
v0
  = ((AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny)
 -> AgdaAny
 -> AgdaAny
 -> T_IsRing_1584
 -> T_Ring_2514)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsRing_1584
-> T_Ring_2514
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsRing_1584
-> T_Ring_2514
C_Ring'46'constructor_43513 (T_CommutativeRing_2704 -> AgdaAny -> AgdaAny -> AgdaAny
d__'43'__2730 (T_CommutativeRing_2704 -> T_CommutativeRing_2704
forall a b. a -> b
coe T_CommutativeRing_2704
v0))
      (T_CommutativeRing_2704 -> AgdaAny -> AgdaAny -> AgdaAny
d__'42'__2732 (T_CommutativeRing_2704 -> T_CommutativeRing_2704
forall a b. a -> b
coe T_CommutativeRing_2704
v0)) (T_CommutativeRing_2704 -> AgdaAny -> AgdaAny
d_'45'__2734 (T_CommutativeRing_2704 -> T_CommutativeRing_2704
forall a b. a -> b
coe T_CommutativeRing_2704
v0))
      (T_CommutativeRing_2704 -> AgdaAny
d_0'35'_2736 (T_CommutativeRing_2704 -> T_CommutativeRing_2704
forall a b. a -> b
coe T_CommutativeRing_2704
v0)) (T_CommutativeRing_2704 -> AgdaAny
d_1'35'_2738 (T_CommutativeRing_2704 -> T_CommutativeRing_2704
forall a b. a -> b
coe T_CommutativeRing_2704
v0))
      (T_IsCommutativeRing_1720 -> T_IsRing_1584
MAlonzo.Code.Algebra.Structures.d_isRing_1736
         ((T_CommutativeRing_2704 -> T_IsCommutativeRing_1720)
-> AgdaAny -> T_IsCommutativeRing_1720
forall a b. a -> b
coe T_CommutativeRing_2704 -> T_IsCommutativeRing_1720
d_isCommutativeRing_2740 (T_CommutativeRing_2704 -> AgdaAny
forall a b. a -> b
coe T_CommutativeRing_2704
v0)))
-- Algebra.Bundles.CommutativeRing._._≉_
d__'8777'__2862 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeRing_2704 -> AgdaAny -> AgdaAny -> ()
d__'8777'__2862 :: () -> () -> T_CommutativeRing_2704 -> AgdaAny -> AgdaAny -> ()
d__'8777'__2862 = () -> () -> T_CommutativeRing_2704 -> AgdaAny -> AgdaAny -> ()
forall a. a
erased
-- Algebra.Bundles.CommutativeRing._.+-abelianGroup
d_'43''45'abelianGroup_2864 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeRing_2704 -> T_AbelianGroup_990
d_'43''45'abelianGroup_2864 :: () -> () -> T_CommutativeRing_2704 -> T_AbelianGroup_990
d_'43''45'abelianGroup_2864 ~()
v0 ~()
v1 T_CommutativeRing_2704
v2
  = T_CommutativeRing_2704 -> T_AbelianGroup_990
du_'43''45'abelianGroup_2864 T_CommutativeRing_2704
v2
du_'43''45'abelianGroup_2864 ::
  T_CommutativeRing_2704 -> T_AbelianGroup_990
du_'43''45'abelianGroup_2864 :: T_CommutativeRing_2704 -> T_AbelianGroup_990
du_'43''45'abelianGroup_2864 T_CommutativeRing_2704
v0
  = (T_Ring_2514 -> T_AbelianGroup_990)
-> AgdaAny -> T_AbelianGroup_990
forall a b. a -> b
coe T_Ring_2514 -> T_AbelianGroup_990
du_'43''45'abelianGroup_2654 ((T_CommutativeRing_2704 -> T_Ring_2514) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeRing_2704 -> T_Ring_2514
du_ring_2858 (T_CommutativeRing_2704 -> AgdaAny
forall a b. a -> b
coe T_CommutativeRing_2704
v0))
-- Algebra.Bundles.CommutativeRing._.group
d_group_2866 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeRing_2704 -> T_Group_890
d_group_2866 :: () -> () -> T_CommutativeRing_2704 -> T_Group_890
d_group_2866 ~()
v0 ~()
v1 T_CommutativeRing_2704
v2 = T_CommutativeRing_2704 -> T_Group_890
du_group_2866 T_CommutativeRing_2704
v2
du_group_2866 :: T_CommutativeRing_2704 -> T_Group_890
du_group_2866 :: T_CommutativeRing_2704 -> T_Group_890
du_group_2866 T_CommutativeRing_2704
v0
  = let v1 :: t
v1 = (T_CommutativeRing_2704 -> T_Ring_2514) -> AgdaAny -> t
forall a b. a -> b
coe T_CommutativeRing_2704 -> T_Ring_2514
du_ring_2858 (T_CommutativeRing_2704 -> AgdaAny
forall a b. a -> b
coe T_CommutativeRing_2704
v0) in
    AgdaAny -> T_Group_890
forall a b. a -> b
coe ((T_AbelianGroup_990 -> T_Group_890) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_AbelianGroup_990 -> T_Group_890
du_group_1080 ((T_Ring_2514 -> T_AbelianGroup_990) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Ring_2514 -> T_AbelianGroup_990
du_'43''45'abelianGroup_2654 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1)))
-- Algebra.Bundles.CommutativeRing._.rawRing
d_rawRing_2868 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeRing_2704 -> T_RawRing_2460
d_rawRing_2868 :: () -> () -> T_CommutativeRing_2704 -> T_RawRing_2460
d_rawRing_2868 ~()
v0 ~()
v1 T_CommutativeRing_2704
v2 = T_CommutativeRing_2704 -> T_RawRing_2460
du_rawRing_2868 T_CommutativeRing_2704
v2
du_rawRing_2868 :: T_CommutativeRing_2704 -> T_RawRing_2460
du_rawRing_2868 :: T_CommutativeRing_2704 -> T_RawRing_2460
du_rawRing_2868 T_CommutativeRing_2704
v0
  = (T_Ring_2514 -> T_RawRing_2460) -> AgdaAny -> T_RawRing_2460
forall a b. a -> b
coe T_Ring_2514 -> T_RawRing_2460
du_rawRing_2698 ((T_CommutativeRing_2704 -> T_Ring_2514) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeRing_2704 -> T_Ring_2514
du_ring_2858 (T_CommutativeRing_2704 -> AgdaAny
forall a b. a -> b
coe T_CommutativeRing_2704
v0))
-- Algebra.Bundles.CommutativeRing.commutativeSemiring
d_commutativeSemiring_2870 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeRing_2704 -> T_CommutativeSemiring_2094
d_commutativeSemiring_2870 :: () -> () -> T_CommutativeRing_2704 -> T_CommutativeSemiring_2094
d_commutativeSemiring_2870 ~()
v0 ~()
v1 T_CommutativeRing_2704
v2
  = T_CommutativeRing_2704 -> T_CommutativeSemiring_2094
du_commutativeSemiring_2870 T_CommutativeRing_2704
v2
du_commutativeSemiring_2870 ::
  T_CommutativeRing_2704 -> T_CommutativeSemiring_2094
du_commutativeSemiring_2870 :: T_CommutativeRing_2704 -> T_CommutativeSemiring_2094
du_commutativeSemiring_2870 T_CommutativeRing_2704
v0
  = ((AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> AgdaAny
 -> T_IsCommutativeSemiring_1344
 -> T_CommutativeSemiring_2094)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> T_CommutativeSemiring_2094
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsCommutativeSemiring_1344
-> T_CommutativeSemiring_2094
C_CommutativeSemiring'46'constructor_36513 (T_CommutativeRing_2704 -> AgdaAny -> AgdaAny -> AgdaAny
d__'43'__2730 (T_CommutativeRing_2704 -> T_CommutativeRing_2704
forall a b. a -> b
coe T_CommutativeRing_2704
v0))
      (T_CommutativeRing_2704 -> AgdaAny -> AgdaAny -> AgdaAny
d__'42'__2732 (T_CommutativeRing_2704 -> T_CommutativeRing_2704
forall a b. a -> b
coe T_CommutativeRing_2704
v0)) (T_CommutativeRing_2704 -> AgdaAny
d_0'35'_2736 (T_CommutativeRing_2704 -> T_CommutativeRing_2704
forall a b. a -> b
coe T_CommutativeRing_2704
v0))
      (T_CommutativeRing_2704 -> AgdaAny
d_1'35'_2738 (T_CommutativeRing_2704 -> T_CommutativeRing_2704
forall a b. a -> b
coe T_CommutativeRing_2704
v0))
      ((T_IsCommutativeRing_1720 -> T_IsCommutativeSemiring_1344)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCommutativeRing_1720 -> T_IsCommutativeSemiring_1344
MAlonzo.Code.Algebra.Structures.du_isCommutativeSemiring_1842
         ((T_CommutativeRing_2704 -> T_IsCommutativeRing_1720)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeRing_2704 -> T_IsCommutativeRing_1720
d_isCommutativeRing_2740 (T_CommutativeRing_2704 -> AgdaAny
forall a b. a -> b
coe T_CommutativeRing_2704
v0)))
-- Algebra.Bundles.CommutativeRing._.commutativeMagma
d_commutativeMagma_2874 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeRing_2704 -> T_CommutativeMagma_148
d_commutativeMagma_2874 :: () -> () -> T_CommutativeRing_2704 -> T_CommutativeMagma_148
d_commutativeMagma_2874 ~()
v0 ~()
v1 T_CommutativeRing_2704
v2 = T_CommutativeRing_2704 -> T_CommutativeMagma_148
du_commutativeMagma_2874 T_CommutativeRing_2704
v2
du_commutativeMagma_2874 ::
  T_CommutativeRing_2704 -> T_CommutativeMagma_148
du_commutativeMagma_2874 :: T_CommutativeRing_2704 -> T_CommutativeMagma_148
du_commutativeMagma_2874 T_CommutativeRing_2704
v0
  = let v1 :: t
v1 = (T_CommutativeRing_2704 -> T_CommutativeSemiring_2094)
-> AgdaAny -> t
forall a b. a -> b
coe T_CommutativeRing_2704 -> T_CommutativeSemiring_2094
du_commutativeSemiring_2870 (T_CommutativeRing_2704 -> AgdaAny
forall a b. a -> b
coe T_CommutativeRing_2704
v0) in
    AgdaAny -> T_CommutativeMagma_148
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_CommutativeSemiring_2094 -> T_CommutativeMonoid_582)
-> AgdaAny -> t
forall a b. a -> b
coe T_CommutativeSemiring_2094 -> T_CommutativeMonoid_582
du_'42''45'commutativeMonoid_2262 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_CommutativeSemigroup_332 -> T_CommutativeMagma_148)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_CommutativeSemigroup_332 -> T_CommutativeMagma_148
du_commutativeMagma_396
            ((T_CommutativeMonoid_582 -> T_CommutativeSemigroup_332)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeMonoid_582 -> T_CommutativeSemigroup_332
du_commutativeSemigroup_664 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2))))
-- Algebra.Bundles.CommutativeRing._.*-commutativeMonoid
d_'42''45'commutativeMonoid_2876 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeRing_2704 -> T_CommutativeMonoid_582
d_'42''45'commutativeMonoid_2876 :: () -> () -> T_CommutativeRing_2704 -> T_CommutativeMonoid_582
d_'42''45'commutativeMonoid_2876 ~()
v0 ~()
v1 T_CommutativeRing_2704
v2
  = T_CommutativeRing_2704 -> T_CommutativeMonoid_582
du_'42''45'commutativeMonoid_2876 T_CommutativeRing_2704
v2
du_'42''45'commutativeMonoid_2876 ::
  T_CommutativeRing_2704 -> T_CommutativeMonoid_582
du_'42''45'commutativeMonoid_2876 :: T_CommutativeRing_2704 -> T_CommutativeMonoid_582
du_'42''45'commutativeMonoid_2876 T_CommutativeRing_2704
v0
  = (T_CommutativeSemiring_2094 -> T_CommutativeMonoid_582)
-> AgdaAny -> T_CommutativeMonoid_582
forall a b. a -> b
coe
      T_CommutativeSemiring_2094 -> T_CommutativeMonoid_582
du_'42''45'commutativeMonoid_2262
      ((T_CommutativeRing_2704 -> T_CommutativeSemiring_2094)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeRing_2704 -> T_CommutativeSemiring_2094
du_commutativeSemiring_2870 (T_CommutativeRing_2704 -> AgdaAny
forall a b. a -> b
coe T_CommutativeRing_2704
v0))
-- Algebra.Bundles.CommutativeRing._.commutativeSemigroup
d_commutativeSemigroup_2878 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeRing_2704 -> T_CommutativeSemigroup_332
d_commutativeSemigroup_2878 :: () -> () -> T_CommutativeRing_2704 -> T_CommutativeSemigroup_332
d_commutativeSemigroup_2878 ~()
v0 ~()
v1 T_CommutativeRing_2704
v2
  = T_CommutativeRing_2704 -> T_CommutativeSemigroup_332
du_commutativeSemigroup_2878 T_CommutativeRing_2704
v2
du_commutativeSemigroup_2878 ::
  T_CommutativeRing_2704 -> T_CommutativeSemigroup_332
du_commutativeSemigroup_2878 :: T_CommutativeRing_2704 -> T_CommutativeSemigroup_332
du_commutativeSemigroup_2878 T_CommutativeRing_2704
v0
  = let v1 :: t
v1 = (T_CommutativeRing_2704 -> T_CommutativeSemiring_2094)
-> AgdaAny -> t
forall a b. a -> b
coe T_CommutativeRing_2704 -> T_CommutativeSemiring_2094
du_commutativeSemiring_2870 (T_CommutativeRing_2704 -> AgdaAny
forall a b. a -> b
coe T_CommutativeRing_2704
v0) in
    AgdaAny -> T_CommutativeSemigroup_332
forall a b. a -> b
coe
      ((T_CommutativeMonoid_582 -> T_CommutativeSemigroup_332)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_CommutativeMonoid_582 -> T_CommutativeSemigroup_332
du_commutativeSemigroup_664
         ((T_CommutativeSemiring_2094 -> T_CommutativeMonoid_582)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemiring_2094 -> T_CommutativeMonoid_582
du_'42''45'commutativeMonoid_2262 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1)))
-- Algebra.Bundles.CommutativeRing._.magma
d_magma_2880 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeRing_2704 -> T_Magma_36
d_magma_2880 :: () -> () -> T_CommutativeRing_2704 -> T_Magma_36
d_magma_2880 ~()
v0 ~()
v1 T_CommutativeRing_2704
v2 = T_CommutativeRing_2704 -> T_Magma_36
du_magma_2880 T_CommutativeRing_2704
v2
du_magma_2880 :: T_CommutativeRing_2704 -> T_Magma_36
du_magma_2880 :: T_CommutativeRing_2704 -> T_Magma_36
du_magma_2880 T_CommutativeRing_2704
v0
  = let v1 :: t
v1 = (T_CommutativeRing_2704 -> T_CommutativeSemiring_2094)
-> AgdaAny -> t
forall a b. a -> b
coe T_CommutativeRing_2704 -> T_CommutativeSemiring_2094
du_commutativeSemiring_2870 (T_CommutativeRing_2704 -> AgdaAny
forall a b. a -> b
coe T_CommutativeRing_2704
v0) in
    AgdaAny -> T_Magma_36
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_CommutativeSemiring_2094 -> T_Semiring_1932) -> AgdaAny -> t
forall a b. a -> b
coe T_CommutativeSemiring_2094 -> T_Semiring_1932
du_semiring_2222 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: t
v3 = (T_Semiring_1932 -> T_SemiringWithoutAnnihilatingZero_1786)
-> AgdaAny -> t
forall a b. a -> b
coe T_Semiring_1932 -> T_SemiringWithoutAnnihilatingZero_1786
du_semiringWithoutAnnihilatingZero_2048 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: t
v4 = (T_SemiringWithoutAnnihilatingZero_1786 -> T_Monoid_506)
-> AgdaAny -> t
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_1786 -> T_Monoid_506
du_'42''45'monoid_1916 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_Semigroup_206 -> T_Magma_36) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semigroup_206 -> T_Magma_36
du_magma_254 ((T_Monoid_506 -> T_Semigroup_206) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Monoid_506 -> T_Semigroup_206
du_semigroup_566 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v4))))))
-- Algebra.Bundles.CommutativeRing._.*-monoid
d_'42''45'monoid_2882 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeRing_2704 -> T_Monoid_506
d_'42''45'monoid_2882 :: () -> () -> T_CommutativeRing_2704 -> T_Monoid_506
d_'42''45'monoid_2882 ~()
v0 ~()
v1 T_CommutativeRing_2704
v2 = T_CommutativeRing_2704 -> T_Monoid_506
du_'42''45'monoid_2882 T_CommutativeRing_2704
v2
du_'42''45'monoid_2882 :: T_CommutativeRing_2704 -> T_Monoid_506
du_'42''45'monoid_2882 :: T_CommutativeRing_2704 -> T_Monoid_506
du_'42''45'monoid_2882 T_CommutativeRing_2704
v0
  = let v1 :: t
v1 = (T_CommutativeRing_2704 -> T_CommutativeSemiring_2094)
-> AgdaAny -> t
forall a b. a -> b
coe T_CommutativeRing_2704 -> T_CommutativeSemiring_2094
du_commutativeSemiring_2870 (T_CommutativeRing_2704 -> AgdaAny
forall a b. a -> b
coe T_CommutativeRing_2704
v0) in
    AgdaAny -> T_Monoid_506
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_CommutativeSemiring_2094 -> T_Semiring_1932) -> AgdaAny -> t
forall a b. a -> b
coe T_CommutativeSemiring_2094 -> T_Semiring_1932
du_semiring_2222 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_SemiringWithoutAnnihilatingZero_1786 -> T_Monoid_506)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_SemiringWithoutAnnihilatingZero_1786 -> T_Monoid_506
du_'42''45'monoid_1916
            ((T_Semiring_1932 -> T_SemiringWithoutAnnihilatingZero_1786)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semiring_1932 -> T_SemiringWithoutAnnihilatingZero_1786
du_semiringWithoutAnnihilatingZero_2048 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2))))
-- Algebra.Bundles.CommutativeRing._.rawMagma
d_rawMagma_2884 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeRing_2704 -> T_RawMagma_8
d_rawMagma_2884 :: () -> () -> T_CommutativeRing_2704 -> T_RawMagma_8
d_rawMagma_2884 ~()
v0 ~()
v1 T_CommutativeRing_2704
v2 = T_CommutativeRing_2704 -> T_RawMagma_8
du_rawMagma_2884 T_CommutativeRing_2704
v2
du_rawMagma_2884 :: T_CommutativeRing_2704 -> T_RawMagma_8
du_rawMagma_2884 :: T_CommutativeRing_2704 -> T_RawMagma_8
du_rawMagma_2884 T_CommutativeRing_2704
v0
  = let v1 :: t
v1 = (T_CommutativeRing_2704 -> T_CommutativeSemiring_2094)
-> AgdaAny -> t
forall a b. a -> b
coe T_CommutativeRing_2704 -> T_CommutativeSemiring_2094
du_commutativeSemiring_2870 (T_CommutativeRing_2704 -> AgdaAny
forall a b. a -> b
coe T_CommutativeRing_2704
v0) in
    AgdaAny -> T_RawMagma_8
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_CommutativeSemiring_2094 -> T_Semiring_1932) -> AgdaAny -> t
forall a b. a -> b
coe T_CommutativeSemiring_2094 -> T_Semiring_1932
du_semiring_2222 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: t
v3 = (T_Semiring_1932 -> T_SemiringWithoutAnnihilatingZero_1786)
-> AgdaAny -> t
forall a b. a -> b
coe T_Semiring_1932 -> T_SemiringWithoutAnnihilatingZero_1786
du_semiringWithoutAnnihilatingZero_2048 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: t
v4 = (T_SemiringWithoutAnnihilatingZero_1786 -> T_Monoid_506)
-> AgdaAny -> t
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_1786 -> T_Monoid_506
du_'42''45'monoid_1916 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: t
v5 = (T_Monoid_506 -> T_Semigroup_206) -> AgdaAny -> t
forall a b. a -> b
coe T_Monoid_506 -> T_Semigroup_206
du_semigroup_566 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_Magma_36 -> T_RawMagma_8) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Magma_36 -> T_RawMagma_8
du_rawMagma_80 ((T_Semigroup_206 -> T_Magma_36) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semigroup_206 -> T_Magma_36
du_magma_254 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v5)))))))
-- Algebra.Bundles.CommutativeRing._.rawMonoid
d_rawMonoid_2886 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeRing_2704 -> T_RawMonoid_474
d_rawMonoid_2886 :: () -> () -> T_CommutativeRing_2704 -> T_RawMonoid_474
d_rawMonoid_2886 ~()
v0 ~()
v1 T_CommutativeRing_2704
v2 = T_CommutativeRing_2704 -> T_RawMonoid_474
du_rawMonoid_2886 T_CommutativeRing_2704
v2
du_rawMonoid_2886 :: T_CommutativeRing_2704 -> T_RawMonoid_474
du_rawMonoid_2886 :: T_CommutativeRing_2704 -> T_RawMonoid_474
du_rawMonoid_2886 T_CommutativeRing_2704
v0
  = let v1 :: t
v1 = (T_CommutativeRing_2704 -> T_CommutativeSemiring_2094)
-> AgdaAny -> t
forall a b. a -> b
coe T_CommutativeRing_2704 -> T_CommutativeSemiring_2094
du_commutativeSemiring_2870 (T_CommutativeRing_2704 -> AgdaAny
forall a b. a -> b
coe T_CommutativeRing_2704
v0) in
    AgdaAny -> T_RawMonoid_474
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_CommutativeSemiring_2094 -> T_Semiring_1932) -> AgdaAny -> t
forall a b. a -> b
coe T_CommutativeSemiring_2094 -> T_Semiring_1932
du_semiring_2222 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: t
v3 = (T_Semiring_1932 -> T_SemiringWithoutAnnihilatingZero_1786)
-> AgdaAny -> t
forall a b. a -> b
coe T_Semiring_1932 -> T_SemiringWithoutAnnihilatingZero_1786
du_semiringWithoutAnnihilatingZero_2048 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_Monoid_506 -> T_RawMonoid_474) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Monoid_506 -> T_RawMonoid_474
du_rawMonoid_576 ((T_SemiringWithoutAnnihilatingZero_1786 -> T_Monoid_506)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_1786 -> T_Monoid_506
du_'42''45'monoid_1916 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3)))))
-- Algebra.Bundles.CommutativeRing._.semigroup
d_semigroup_2888 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeRing_2704 -> T_Semigroup_206
d_semigroup_2888 :: () -> () -> T_CommutativeRing_2704 -> T_Semigroup_206
d_semigroup_2888 ~()
v0 ~()
v1 T_CommutativeRing_2704
v2 = T_CommutativeRing_2704 -> T_Semigroup_206
du_semigroup_2888 T_CommutativeRing_2704
v2
du_semigroup_2888 :: T_CommutativeRing_2704 -> T_Semigroup_206
du_semigroup_2888 :: T_CommutativeRing_2704 -> T_Semigroup_206
du_semigroup_2888 T_CommutativeRing_2704
v0
  = let v1 :: t
v1 = (T_CommutativeRing_2704 -> T_CommutativeSemiring_2094)
-> AgdaAny -> t
forall a b. a -> b
coe T_CommutativeRing_2704 -> T_CommutativeSemiring_2094
du_commutativeSemiring_2870 (T_CommutativeRing_2704 -> AgdaAny
forall a b. a -> b
coe T_CommutativeRing_2704
v0) in
    AgdaAny -> T_Semigroup_206
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_CommutativeSemiring_2094 -> T_Semiring_1932) -> AgdaAny -> t
forall a b. a -> b
coe T_CommutativeSemiring_2094 -> T_Semiring_1932
du_semiring_2222 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: t
v3 = (T_Semiring_1932 -> T_SemiringWithoutAnnihilatingZero_1786)
-> AgdaAny -> t
forall a b. a -> b
coe T_Semiring_1932 -> T_SemiringWithoutAnnihilatingZero_1786
du_semiringWithoutAnnihilatingZero_2048 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_Monoid_506 -> T_Semigroup_206) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Monoid_506 -> T_Semigroup_206
du_semigroup_566 ((T_SemiringWithoutAnnihilatingZero_1786 -> T_Monoid_506)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_1786 -> T_Monoid_506
du_'42''45'monoid_1916 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3)))))
-- Algebra.Bundles.CommutativeRing._.commutativeMagma
d_commutativeMagma_2890 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeRing_2704 -> T_CommutativeMagma_148
d_commutativeMagma_2890 :: () -> () -> T_CommutativeRing_2704 -> T_CommutativeMagma_148
d_commutativeMagma_2890 ~()
v0 ~()
v1 T_CommutativeRing_2704
v2 = T_CommutativeRing_2704 -> T_CommutativeMagma_148
du_commutativeMagma_2890 T_CommutativeRing_2704
v2
du_commutativeMagma_2890 ::
  T_CommutativeRing_2704 -> T_CommutativeMagma_148
du_commutativeMagma_2890 :: T_CommutativeRing_2704 -> T_CommutativeMagma_148
du_commutativeMagma_2890 T_CommutativeRing_2704
v0
  = let v1 :: t
v1 = (T_CommutativeRing_2704 -> T_CommutativeSemiring_2094)
-> AgdaAny -> t
forall a b. a -> b
coe T_CommutativeRing_2704 -> T_CommutativeSemiring_2094
du_commutativeSemiring_2870 (T_CommutativeRing_2704 -> AgdaAny
forall a b. a -> b
coe T_CommutativeRing_2704
v0) in
    AgdaAny -> T_CommutativeMagma_148
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_CommutativeSemiring_2094 -> T_Semiring_1932) -> AgdaAny -> t
forall a b. a -> b
coe T_CommutativeSemiring_2094 -> T_Semiring_1932
du_semiring_2222 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: t
v3 = (T_Semiring_1932 -> T_SemiringWithoutAnnihilatingZero_1786)
-> AgdaAny -> t
forall a b. a -> b
coe T_Semiring_1932 -> T_SemiringWithoutAnnihilatingZero_1786
du_semiringWithoutAnnihilatingZero_2048 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: t
v4 = (T_SemiringWithoutAnnihilatingZero_1786 -> T_CommutativeMonoid_582)
-> AgdaAny -> t
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_1786 -> T_CommutativeMonoid_582
du_'43''45'commutativeMonoid_1896 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               ((T_CommutativeSemigroup_332 -> T_CommutativeMagma_148)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_CommutativeSemigroup_332 -> T_CommutativeMagma_148
du_commutativeMagma_396
                  ((T_CommutativeMonoid_582 -> T_CommutativeSemigroup_332)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeMonoid_582 -> T_CommutativeSemigroup_332
du_commutativeSemigroup_664 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v4))))))
-- Algebra.Bundles.CommutativeRing._.+-commutativeMonoid
d_'43''45'commutativeMonoid_2892 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeRing_2704 -> T_CommutativeMonoid_582
d_'43''45'commutativeMonoid_2892 :: () -> () -> T_CommutativeRing_2704 -> T_CommutativeMonoid_582
d_'43''45'commutativeMonoid_2892 ~()
v0 ~()
v1 T_CommutativeRing_2704
v2
  = T_CommutativeRing_2704 -> T_CommutativeMonoid_582
du_'43''45'commutativeMonoid_2892 T_CommutativeRing_2704
v2
du_'43''45'commutativeMonoid_2892 ::
  T_CommutativeRing_2704 -> T_CommutativeMonoid_582
du_'43''45'commutativeMonoid_2892 :: T_CommutativeRing_2704 -> T_CommutativeMonoid_582
du_'43''45'commutativeMonoid_2892 T_CommutativeRing_2704
v0
  = let v1 :: t
v1 = (T_CommutativeRing_2704 -> T_CommutativeSemiring_2094)
-> AgdaAny -> t
forall a b. a -> b
coe T_CommutativeRing_2704 -> T_CommutativeSemiring_2094
du_commutativeSemiring_2870 (T_CommutativeRing_2704 -> AgdaAny
forall a b. a -> b
coe T_CommutativeRing_2704
v0) in
    AgdaAny -> T_CommutativeMonoid_582
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_CommutativeSemiring_2094 -> T_Semiring_1932) -> AgdaAny -> t
forall a b. a -> b
coe T_CommutativeSemiring_2094 -> T_Semiring_1932
du_semiring_2222 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_SemiringWithoutAnnihilatingZero_1786 -> T_CommutativeMonoid_582)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_SemiringWithoutAnnihilatingZero_1786 -> T_CommutativeMonoid_582
du_'43''45'commutativeMonoid_1896
            ((T_Semiring_1932 -> T_SemiringWithoutAnnihilatingZero_1786)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semiring_1932 -> T_SemiringWithoutAnnihilatingZero_1786
du_semiringWithoutAnnihilatingZero_2048 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2))))
-- Algebra.Bundles.CommutativeRing._.commutativeSemigroup
d_commutativeSemigroup_2894 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeRing_2704 -> T_CommutativeSemigroup_332
d_commutativeSemigroup_2894 :: () -> () -> T_CommutativeRing_2704 -> T_CommutativeSemigroup_332
d_commutativeSemigroup_2894 ~()
v0 ~()
v1 T_CommutativeRing_2704
v2
  = T_CommutativeRing_2704 -> T_CommutativeSemigroup_332
du_commutativeSemigroup_2894 T_CommutativeRing_2704
v2
du_commutativeSemigroup_2894 ::
  T_CommutativeRing_2704 -> T_CommutativeSemigroup_332
du_commutativeSemigroup_2894 :: T_CommutativeRing_2704 -> T_CommutativeSemigroup_332
du_commutativeSemigroup_2894 T_CommutativeRing_2704
v0
  = let v1 :: t
v1 = (T_CommutativeRing_2704 -> T_CommutativeSemiring_2094)
-> AgdaAny -> t
forall a b. a -> b
coe T_CommutativeRing_2704 -> T_CommutativeSemiring_2094
du_commutativeSemiring_2870 (T_CommutativeRing_2704 -> AgdaAny
forall a b. a -> b
coe T_CommutativeRing_2704
v0) in
    AgdaAny -> T_CommutativeSemigroup_332
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_CommutativeSemiring_2094 -> T_Semiring_1932) -> AgdaAny -> t
forall a b. a -> b
coe T_CommutativeSemiring_2094 -> T_Semiring_1932
du_semiring_2222 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: t
v3 = (T_Semiring_1932 -> T_SemiringWithoutAnnihilatingZero_1786)
-> AgdaAny -> t
forall a b. a -> b
coe T_Semiring_1932 -> T_SemiringWithoutAnnihilatingZero_1786
du_semiringWithoutAnnihilatingZero_2048 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_CommutativeMonoid_582 -> T_CommutativeSemigroup_332)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_CommutativeMonoid_582 -> T_CommutativeSemigroup_332
du_commutativeSemigroup_664
               ((T_SemiringWithoutAnnihilatingZero_1786 -> T_CommutativeMonoid_582)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_1786 -> T_CommutativeMonoid_582
du_'43''45'commutativeMonoid_1896 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3)))))
-- Algebra.Bundles.CommutativeRing._.magma
d_magma_2896 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeRing_2704 -> T_Magma_36
d_magma_2896 :: () -> () -> T_CommutativeRing_2704 -> T_Magma_36
d_magma_2896 ~()
v0 ~()
v1 T_CommutativeRing_2704
v2 = T_CommutativeRing_2704 -> T_Magma_36
du_magma_2896 T_CommutativeRing_2704
v2
du_magma_2896 :: T_CommutativeRing_2704 -> T_Magma_36
du_magma_2896 :: T_CommutativeRing_2704 -> T_Magma_36
du_magma_2896 T_CommutativeRing_2704
v0
  = let v1 :: t
v1 = (T_CommutativeRing_2704 -> T_CommutativeSemiring_2094)
-> AgdaAny -> t
forall a b. a -> b
coe T_CommutativeRing_2704 -> T_CommutativeSemiring_2094
du_commutativeSemiring_2870 (T_CommutativeRing_2704 -> AgdaAny
forall a b. a -> b
coe T_CommutativeRing_2704
v0) in
    AgdaAny -> T_Magma_36
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_CommutativeSemiring_2094 -> T_Semiring_1932) -> AgdaAny -> t
forall a b. a -> b
coe T_CommutativeSemiring_2094 -> T_Semiring_1932
du_semiring_2222 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: t
v3 = (T_Semiring_1932 -> T_SemiringWithoutAnnihilatingZero_1786)
-> AgdaAny -> t
forall a b. a -> b
coe T_Semiring_1932 -> T_SemiringWithoutAnnihilatingZero_1786
du_semiringWithoutAnnihilatingZero_2048 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: t
v4 = (T_SemiringWithoutAnnihilatingZero_1786 -> T_CommutativeMonoid_582)
-> AgdaAny -> t
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_1786 -> T_CommutativeMonoid_582
du_'43''45'commutativeMonoid_1896 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: t
v5 = (T_CommutativeMonoid_582 -> T_Monoid_506) -> AgdaAny -> t
forall a b. a -> b
coe T_CommutativeMonoid_582 -> T_Monoid_506
du_monoid_650 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_Semigroup_206 -> T_Magma_36) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semigroup_206 -> T_Magma_36
du_magma_254 ((T_Monoid_506 -> T_Semigroup_206) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Monoid_506 -> T_Semigroup_206
du_semigroup_566 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v5)))))))
-- Algebra.Bundles.CommutativeRing._.monoid
d_monoid_2898 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeRing_2704 -> T_Monoid_506
d_monoid_2898 :: () -> () -> T_CommutativeRing_2704 -> T_Monoid_506
d_monoid_2898 ~()
v0 ~()
v1 T_CommutativeRing_2704
v2 = T_CommutativeRing_2704 -> T_Monoid_506
du_monoid_2898 T_CommutativeRing_2704
v2
du_monoid_2898 :: T_CommutativeRing_2704 -> T_Monoid_506
du_monoid_2898 :: T_CommutativeRing_2704 -> T_Monoid_506
du_monoid_2898 T_CommutativeRing_2704
v0
  = let v1 :: t
v1 = (T_CommutativeRing_2704 -> T_CommutativeSemiring_2094)
-> AgdaAny -> t
forall a b. a -> b
coe T_CommutativeRing_2704 -> T_CommutativeSemiring_2094
du_commutativeSemiring_2870 (T_CommutativeRing_2704 -> AgdaAny
forall a b. a -> b
coe T_CommutativeRing_2704
v0) in
    AgdaAny -> T_Monoid_506
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_CommutativeSemiring_2094 -> T_Semiring_1932) -> AgdaAny -> t
forall a b. a -> b
coe T_CommutativeSemiring_2094 -> T_Semiring_1932
du_semiring_2222 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: t
v3 = (T_Semiring_1932 -> T_SemiringWithoutAnnihilatingZero_1786)
-> AgdaAny -> t
forall a b. a -> b
coe T_Semiring_1932 -> T_SemiringWithoutAnnihilatingZero_1786
du_semiringWithoutAnnihilatingZero_2048 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_CommutativeMonoid_582 -> T_Monoid_506) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_CommutativeMonoid_582 -> T_Monoid_506
du_monoid_650 ((T_SemiringWithoutAnnihilatingZero_1786 -> T_CommutativeMonoid_582)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_1786 -> T_CommutativeMonoid_582
du_'43''45'commutativeMonoid_1896 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3)))))
-- Algebra.Bundles.CommutativeRing._.rawMagma
d_rawMagma_2900 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeRing_2704 -> T_RawMagma_8
d_rawMagma_2900 :: () -> () -> T_CommutativeRing_2704 -> T_RawMagma_8
d_rawMagma_2900 ~()
v0 ~()
v1 T_CommutativeRing_2704
v2 = T_CommutativeRing_2704 -> T_RawMagma_8
du_rawMagma_2900 T_CommutativeRing_2704
v2
du_rawMagma_2900 :: T_CommutativeRing_2704 -> T_RawMagma_8
du_rawMagma_2900 :: T_CommutativeRing_2704 -> T_RawMagma_8
du_rawMagma_2900 T_CommutativeRing_2704
v0
  = let v1 :: t
v1 = (T_CommutativeRing_2704 -> T_CommutativeSemiring_2094)
-> AgdaAny -> t
forall a b. a -> b
coe T_CommutativeRing_2704 -> T_CommutativeSemiring_2094
du_commutativeSemiring_2870 (T_CommutativeRing_2704 -> AgdaAny
forall a b. a -> b
coe T_CommutativeRing_2704
v0) in
    AgdaAny -> T_RawMagma_8
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_CommutativeSemiring_2094 -> T_Semiring_1932) -> AgdaAny -> t
forall a b. a -> b
coe T_CommutativeSemiring_2094 -> T_Semiring_1932
du_semiring_2222 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: t
v3 = (T_Semiring_1932 -> T_SemiringWithoutAnnihilatingZero_1786)
-> AgdaAny -> t
forall a b. a -> b
coe T_Semiring_1932 -> T_SemiringWithoutAnnihilatingZero_1786
du_semiringWithoutAnnihilatingZero_2048 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: t
v4 = (T_SemiringWithoutAnnihilatingZero_1786 -> T_CommutativeMonoid_582)
-> AgdaAny -> t
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_1786 -> T_CommutativeMonoid_582
du_'43''45'commutativeMonoid_1896 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: t
v5 = (T_CommutativeMonoid_582 -> T_Monoid_506) -> AgdaAny -> t
forall a b. a -> b
coe T_CommutativeMonoid_582 -> T_Monoid_506
du_monoid_650 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (let v6 :: t
v6 = (T_Monoid_506 -> T_Semigroup_206) -> AgdaAny -> t
forall a b. a -> b
coe T_Monoid_506 -> T_Semigroup_206
du_semigroup_566 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v5) in
                   AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_Magma_36 -> T_RawMagma_8) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Magma_36 -> T_RawMagma_8
du_rawMagma_80 ((T_Semigroup_206 -> T_Magma_36) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semigroup_206 -> T_Magma_36
du_magma_254 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v6))))))))
-- Algebra.Bundles.CommutativeRing._.rawMonoid
d_rawMonoid_2902 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeRing_2704 -> T_RawMonoid_474
d_rawMonoid_2902 :: () -> () -> T_CommutativeRing_2704 -> T_RawMonoid_474
d_rawMonoid_2902 ~()
v0 ~()
v1 T_CommutativeRing_2704
v2 = T_CommutativeRing_2704 -> T_RawMonoid_474
du_rawMonoid_2902 T_CommutativeRing_2704
v2
du_rawMonoid_2902 :: T_CommutativeRing_2704 -> T_RawMonoid_474
du_rawMonoid_2902 :: T_CommutativeRing_2704 -> T_RawMonoid_474
du_rawMonoid_2902 T_CommutativeRing_2704
v0
  = let v1 :: t
v1 = (T_CommutativeRing_2704 -> T_CommutativeSemiring_2094)
-> AgdaAny -> t
forall a b. a -> b
coe T_CommutativeRing_2704 -> T_CommutativeSemiring_2094
du_commutativeSemiring_2870 (T_CommutativeRing_2704 -> AgdaAny
forall a b. a -> b
coe T_CommutativeRing_2704
v0) in
    AgdaAny -> T_RawMonoid_474
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_CommutativeSemiring_2094 -> T_Semiring_1932) -> AgdaAny -> t
forall a b. a -> b
coe T_CommutativeSemiring_2094 -> T_Semiring_1932
du_semiring_2222 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: t
v3 = (T_Semiring_1932 -> T_SemiringWithoutAnnihilatingZero_1786)
-> AgdaAny -> t
forall a b. a -> b
coe T_Semiring_1932 -> T_SemiringWithoutAnnihilatingZero_1786
du_semiringWithoutAnnihilatingZero_2048 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: t
v4 = (T_SemiringWithoutAnnihilatingZero_1786 -> T_CommutativeMonoid_582)
-> AgdaAny -> t
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_1786 -> T_CommutativeMonoid_582
du_'43''45'commutativeMonoid_1896 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_Monoid_506 -> T_RawMonoid_474) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Monoid_506 -> T_RawMonoid_474
du_rawMonoid_576 ((T_CommutativeMonoid_582 -> T_Monoid_506) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeMonoid_582 -> T_Monoid_506
du_monoid_650 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v4))))))
-- Algebra.Bundles.CommutativeRing._.semigroup
d_semigroup_2904 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeRing_2704 -> T_Semigroup_206
d_semigroup_2904 :: () -> () -> T_CommutativeRing_2704 -> T_Semigroup_206
d_semigroup_2904 ~()
v0 ~()
v1 T_CommutativeRing_2704
v2 = T_CommutativeRing_2704 -> T_Semigroup_206
du_semigroup_2904 T_CommutativeRing_2704
v2
du_semigroup_2904 :: T_CommutativeRing_2704 -> T_Semigroup_206
du_semigroup_2904 :: T_CommutativeRing_2704 -> T_Semigroup_206
du_semigroup_2904 T_CommutativeRing_2704
v0
  = let v1 :: t
v1 = (T_CommutativeRing_2704 -> T_CommutativeSemiring_2094)
-> AgdaAny -> t
forall a b. a -> b
coe T_CommutativeRing_2704 -> T_CommutativeSemiring_2094
du_commutativeSemiring_2870 (T_CommutativeRing_2704 -> AgdaAny
forall a b. a -> b
coe T_CommutativeRing_2704
v0) in
    AgdaAny -> T_Semigroup_206
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_CommutativeSemiring_2094 -> T_Semiring_1932) -> AgdaAny -> t
forall a b. a -> b
coe T_CommutativeSemiring_2094 -> T_Semiring_1932
du_semiring_2222 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: t
v3 = (T_Semiring_1932 -> T_SemiringWithoutAnnihilatingZero_1786)
-> AgdaAny -> t
forall a b. a -> b
coe T_Semiring_1932 -> T_SemiringWithoutAnnihilatingZero_1786
du_semiringWithoutAnnihilatingZero_2048 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: t
v4 = (T_SemiringWithoutAnnihilatingZero_1786 -> T_CommutativeMonoid_582)
-> AgdaAny -> t
forall a b. a -> b
coe T_SemiringWithoutAnnihilatingZero_1786 -> T_CommutativeMonoid_582
du_'43''45'commutativeMonoid_1896 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_Monoid_506 -> T_Semigroup_206) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Monoid_506 -> T_Semigroup_206
du_semigroup_566 ((T_CommutativeMonoid_582 -> T_Monoid_506) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeMonoid_582 -> T_Monoid_506
du_monoid_650 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v4))))))
-- Algebra.Bundles.CommutativeRing._.commutativeSemiringWithoutOne
d_commutativeSemiringWithoutOne_2906 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeRing_2704 -> T_CommutativeSemiringWithoutOne_1598
d_commutativeSemiringWithoutOne_2906 :: ()
-> ()
-> T_CommutativeRing_2704
-> T_CommutativeSemiringWithoutOne_1598
d_commutativeSemiringWithoutOne_2906 ~()
v0 ~()
v1 T_CommutativeRing_2704
v2
  = T_CommutativeRing_2704 -> T_CommutativeSemiringWithoutOne_1598
du_commutativeSemiringWithoutOne_2906 T_CommutativeRing_2704
v2
du_commutativeSemiringWithoutOne_2906 ::
  T_CommutativeRing_2704 -> T_CommutativeSemiringWithoutOne_1598
du_commutativeSemiringWithoutOne_2906 :: T_CommutativeRing_2704 -> T_CommutativeSemiringWithoutOne_1598
du_commutativeSemiringWithoutOne_2906 T_CommutativeRing_2704
v0
  = (T_CommutativeSemiring_2094
 -> T_CommutativeSemiringWithoutOne_1598)
-> AgdaAny -> T_CommutativeSemiringWithoutOne_1598
forall a b. a -> b
coe
      T_CommutativeSemiring_2094 -> T_CommutativeSemiringWithoutOne_1598
du_commutativeSemiringWithoutOne_2270
      ((T_CommutativeRing_2704 -> T_CommutativeSemiring_2094)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeRing_2704 -> T_CommutativeSemiring_2094
du_commutativeSemiring_2870 (T_CommutativeRing_2704 -> AgdaAny
forall a b. a -> b
coe T_CommutativeRing_2704
v0))
-- Algebra.Bundles.CommutativeRing._.nearSemiring
d_nearSemiring_2908 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeRing_2704 -> T_NearSemiring_1354
d_nearSemiring_2908 :: () -> () -> T_CommutativeRing_2704 -> T_NearSemiring_1354
d_nearSemiring_2908 ~()
v0 ~()
v1 T_CommutativeRing_2704
v2 = T_CommutativeRing_2704 -> T_NearSemiring_1354
du_nearSemiring_2908 T_CommutativeRing_2704
v2
du_nearSemiring_2908 ::
  T_CommutativeRing_2704 -> T_NearSemiring_1354
du_nearSemiring_2908 :: T_CommutativeRing_2704 -> T_NearSemiring_1354
du_nearSemiring_2908 T_CommutativeRing_2704
v0
  = let v1 :: t
v1 = (T_CommutativeRing_2704 -> T_CommutativeSemiring_2094)
-> AgdaAny -> t
forall a b. a -> b
coe T_CommutativeRing_2704 -> T_CommutativeSemiring_2094
du_commutativeSemiring_2870 (T_CommutativeRing_2704 -> AgdaAny
forall a b. a -> b
coe T_CommutativeRing_2704
v0) in
    AgdaAny -> T_NearSemiring_1354
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_CommutativeSemiring_2094 -> T_Semiring_1932) -> AgdaAny -> t
forall a b. a -> b
coe T_CommutativeSemiring_2094 -> T_Semiring_1932
du_semiring_2222 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_SemiringWithoutOne_1464 -> T_NearSemiring_1354)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_SemiringWithoutOne_1464 -> T_NearSemiring_1354
du_nearSemiring_1562 ((T_Semiring_1932 -> T_SemiringWithoutOne_1464)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semiring_1932 -> T_SemiringWithoutOne_1464
du_semiringWithoutOne_2084 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2))))
-- Algebra.Bundles.CommutativeRing._.semiring
d_semiring_2910 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeRing_2704 -> T_Semiring_1932
d_semiring_2910 :: () -> () -> T_CommutativeRing_2704 -> T_Semiring_1932
d_semiring_2910 ~()
v0 ~()
v1 T_CommutativeRing_2704
v2 = T_CommutativeRing_2704 -> T_Semiring_1932
du_semiring_2910 T_CommutativeRing_2704
v2
du_semiring_2910 :: T_CommutativeRing_2704 -> T_Semiring_1932
du_semiring_2910 :: T_CommutativeRing_2704 -> T_Semiring_1932
du_semiring_2910 T_CommutativeRing_2704
v0
  = (T_CommutativeSemiring_2094 -> T_Semiring_1932)
-> AgdaAny -> T_Semiring_1932
forall a b. a -> b
coe T_CommutativeSemiring_2094 -> T_Semiring_1932
du_semiring_2222 ((T_CommutativeRing_2704 -> T_CommutativeSemiring_2094)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeRing_2704 -> T_CommutativeSemiring_2094
du_commutativeSemiring_2870 (T_CommutativeRing_2704 -> AgdaAny
forall a b. a -> b
coe T_CommutativeRing_2704
v0))
-- Algebra.Bundles.CommutativeRing._.semiringWithoutAnnihilatingZero
d_semiringWithoutAnnihilatingZero_2912 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeRing_2704 -> T_SemiringWithoutAnnihilatingZero_1786
d_semiringWithoutAnnihilatingZero_2912 :: ()
-> ()
-> T_CommutativeRing_2704
-> T_SemiringWithoutAnnihilatingZero_1786
d_semiringWithoutAnnihilatingZero_2912 ~()
v0 ~()
v1 T_CommutativeRing_2704
v2
  = T_CommutativeRing_2704 -> T_SemiringWithoutAnnihilatingZero_1786
du_semiringWithoutAnnihilatingZero_2912 T_CommutativeRing_2704
v2
du_semiringWithoutAnnihilatingZero_2912 ::
  T_CommutativeRing_2704 -> T_SemiringWithoutAnnihilatingZero_1786
du_semiringWithoutAnnihilatingZero_2912 :: T_CommutativeRing_2704 -> T_SemiringWithoutAnnihilatingZero_1786
du_semiringWithoutAnnihilatingZero_2912 T_CommutativeRing_2704
v0
  = let v1 :: t
v1 = (T_CommutativeRing_2704 -> T_CommutativeSemiring_2094)
-> AgdaAny -> t
forall a b. a -> b
coe T_CommutativeRing_2704 -> T_CommutativeSemiring_2094
du_commutativeSemiring_2870 (T_CommutativeRing_2704 -> AgdaAny
forall a b. a -> b
coe T_CommutativeRing_2704
v0) in
    AgdaAny -> T_SemiringWithoutAnnihilatingZero_1786
forall a b. a -> b
coe
      ((T_Semiring_1932 -> T_SemiringWithoutAnnihilatingZero_1786)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_Semiring_1932 -> T_SemiringWithoutAnnihilatingZero_1786
du_semiringWithoutAnnihilatingZero_2048
         ((T_CommutativeSemiring_2094 -> T_Semiring_1932)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemiring_2094 -> T_Semiring_1932
du_semiring_2222 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1)))
-- Algebra.Bundles.CommutativeRing._.semiringWithoutOne
d_semiringWithoutOne_2914 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeRing_2704 -> T_SemiringWithoutOne_1464
d_semiringWithoutOne_2914 :: () -> () -> T_CommutativeRing_2704 -> T_SemiringWithoutOne_1464
d_semiringWithoutOne_2914 ~()
v0 ~()
v1 T_CommutativeRing_2704
v2
  = T_CommutativeRing_2704 -> T_SemiringWithoutOne_1464
du_semiringWithoutOne_2914 T_CommutativeRing_2704
v2
du_semiringWithoutOne_2914 ::
  T_CommutativeRing_2704 -> T_SemiringWithoutOne_1464
du_semiringWithoutOne_2914 :: T_CommutativeRing_2704 -> T_SemiringWithoutOne_1464
du_semiringWithoutOne_2914 T_CommutativeRing_2704
v0
  = let v1 :: t
v1 = (T_CommutativeRing_2704 -> T_CommutativeSemiring_2094)
-> AgdaAny -> t
forall a b. a -> b
coe T_CommutativeRing_2704 -> T_CommutativeSemiring_2094
du_commutativeSemiring_2870 (T_CommutativeRing_2704 -> AgdaAny
forall a b. a -> b
coe T_CommutativeRing_2704
v0) in
    AgdaAny -> T_SemiringWithoutOne_1464
forall a b. a -> b
coe
      ((T_Semiring_1932 -> T_SemiringWithoutOne_1464)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semiring_1932 -> T_SemiringWithoutOne_1464
du_semiringWithoutOne_2084 ((T_CommutativeSemiring_2094 -> T_Semiring_1932)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemiring_2094 -> T_Semiring_1932
du_semiring_2222 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1)))
-- Algebra.Bundles.BooleanAlgebra
d_BooleanAlgebra_2920 :: p -> p -> ()
d_BooleanAlgebra_2920 p
a0 p
a1 = ()
data T_BooleanAlgebra_2920
  = C_BooleanAlgebra'46'constructor_50705 (AgdaAny ->
                                           AgdaAny -> AgdaAny)
                                          (AgdaAny -> AgdaAny -> AgdaAny) (AgdaAny -> AgdaAny)
                                          AgdaAny AgdaAny
                                          MAlonzo.Code.Algebra.Structures.T_IsBooleanAlgebra_1864
-- Algebra.Bundles.BooleanAlgebra.Carrier
d_Carrier_2942 :: T_BooleanAlgebra_2920 -> ()
d_Carrier_2942 :: T_BooleanAlgebra_2920 -> ()
d_Carrier_2942 = T_BooleanAlgebra_2920 -> ()
forall a. a
erased
-- Algebra.Bundles.BooleanAlgebra._≈_
d__'8776'__2944 ::
  T_BooleanAlgebra_2920 -> AgdaAny -> AgdaAny -> ()
d__'8776'__2944 :: T_BooleanAlgebra_2920 -> AgdaAny -> AgdaAny -> ()
d__'8776'__2944 = T_BooleanAlgebra_2920 -> AgdaAny -> AgdaAny -> ()
forall a. a
erased
-- Algebra.Bundles.BooleanAlgebra._∨_
d__'8744'__2946 ::
  T_BooleanAlgebra_2920 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8744'__2946 :: T_BooleanAlgebra_2920 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8744'__2946 T_BooleanAlgebra_2920
v0
  = case T_BooleanAlgebra_2920 -> T_BooleanAlgebra_2920
forall a b. a -> b
coe T_BooleanAlgebra_2920
v0 of
      C_BooleanAlgebra'46'constructor_50705 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny
v5 AgdaAny
v6 AgdaAny
v7 T_IsBooleanAlgebra_1864
v8 -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v3
      T_BooleanAlgebra_2920
_ -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.BooleanAlgebra._∧_
d__'8743'__2948 ::
  T_BooleanAlgebra_2920 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8743'__2948 :: T_BooleanAlgebra_2920 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8743'__2948 T_BooleanAlgebra_2920
v0
  = case T_BooleanAlgebra_2920 -> T_BooleanAlgebra_2920
forall a b. a -> b
coe T_BooleanAlgebra_2920
v0 of
      C_BooleanAlgebra'46'constructor_50705 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny
v5 AgdaAny
v6 AgdaAny
v7 T_IsBooleanAlgebra_1864
v8 -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v4
      T_BooleanAlgebra_2920
_ -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.BooleanAlgebra.¬_
d_'172'__2950 :: T_BooleanAlgebra_2920 -> AgdaAny -> AgdaAny
d_'172'__2950 :: T_BooleanAlgebra_2920 -> AgdaAny -> AgdaAny
d_'172'__2950 T_BooleanAlgebra_2920
v0
  = case T_BooleanAlgebra_2920 -> T_BooleanAlgebra_2920
forall a b. a -> b
coe T_BooleanAlgebra_2920
v0 of
      C_BooleanAlgebra'46'constructor_50705 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny
v5 AgdaAny
v6 AgdaAny
v7 T_IsBooleanAlgebra_1864
v8 -> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v5
      T_BooleanAlgebra_2920
_ -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.BooleanAlgebra.⊤
d_'8868'_2952 :: T_BooleanAlgebra_2920 -> AgdaAny
d_'8868'_2952 :: T_BooleanAlgebra_2920 -> AgdaAny
d_'8868'_2952 T_BooleanAlgebra_2920
v0
  = case T_BooleanAlgebra_2920 -> T_BooleanAlgebra_2920
forall a b. a -> b
coe T_BooleanAlgebra_2920
v0 of
      C_BooleanAlgebra'46'constructor_50705 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny
v5 AgdaAny
v6 AgdaAny
v7 T_IsBooleanAlgebra_1864
v8 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v6
      T_BooleanAlgebra_2920
_ -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.BooleanAlgebra.⊥
d_'8869'_2954 :: T_BooleanAlgebra_2920 -> AgdaAny
d_'8869'_2954 :: T_BooleanAlgebra_2920 -> AgdaAny
d_'8869'_2954 T_BooleanAlgebra_2920
v0
  = case T_BooleanAlgebra_2920 -> T_BooleanAlgebra_2920
forall a b. a -> b
coe T_BooleanAlgebra_2920
v0 of
      C_BooleanAlgebra'46'constructor_50705 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny
v5 AgdaAny
v6 AgdaAny
v7 T_IsBooleanAlgebra_1864
v8 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v7
      T_BooleanAlgebra_2920
_ -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.BooleanAlgebra.isBooleanAlgebra
d_isBooleanAlgebra_2956 ::
  T_BooleanAlgebra_2920 ->
  MAlonzo.Code.Algebra.Structures.T_IsBooleanAlgebra_1864
d_isBooleanAlgebra_2956 :: T_BooleanAlgebra_2920 -> T_IsBooleanAlgebra_1864
d_isBooleanAlgebra_2956 T_BooleanAlgebra_2920
v0
  = case T_BooleanAlgebra_2920 -> T_BooleanAlgebra_2920
forall a b. a -> b
coe T_BooleanAlgebra_2920
v0 of
      C_BooleanAlgebra'46'constructor_50705 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny
v5 AgdaAny
v6 AgdaAny
v7 T_IsBooleanAlgebra_1864
v8 -> T_IsBooleanAlgebra_1864 -> T_IsBooleanAlgebra_1864
forall a b. a -> b
coe T_IsBooleanAlgebra_1864
v8
      T_BooleanAlgebra_2920
_ -> T_IsBooleanAlgebra_1864
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.BooleanAlgebra._.absorptive
d_absorptive_2960 ::
  T_BooleanAlgebra_2920 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_absorptive_2960 :: T_BooleanAlgebra_2920 -> T_Σ_14
d_absorptive_2960 T_BooleanAlgebra_2920
v0
  = (T_IsLattice_740 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsLattice_740 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_absorptive_776
      ((T_IsDistributiveLattice_814 -> T_IsLattice_740)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsDistributiveLattice_814 -> T_IsLattice_740
MAlonzo.Code.Algebra.Structures.d_isLattice_824
         ((T_IsBooleanAlgebra_1864 -> T_IsDistributiveLattice_814)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsBooleanAlgebra_1864 -> T_IsDistributiveLattice_814
MAlonzo.Code.Algebra.Structures.d_isDistributiveLattice_1884
            ((T_BooleanAlgebra_2920 -> T_IsBooleanAlgebra_1864)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_2920 -> T_IsBooleanAlgebra_1864
d_isBooleanAlgebra_2956 (T_BooleanAlgebra_2920 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_2920
v0))))
-- Algebra.Bundles.BooleanAlgebra._.isDistributiveLattice
d_isDistributiveLattice_2962 ::
  T_BooleanAlgebra_2920 ->
  MAlonzo.Code.Algebra.Structures.T_IsDistributiveLattice_814
d_isDistributiveLattice_2962 :: T_BooleanAlgebra_2920 -> T_IsDistributiveLattice_814
d_isDistributiveLattice_2962 T_BooleanAlgebra_2920
v0
  = (T_IsBooleanAlgebra_1864 -> T_IsDistributiveLattice_814)
-> AgdaAny -> T_IsDistributiveLattice_814
forall a b. a -> b
coe
      T_IsBooleanAlgebra_1864 -> T_IsDistributiveLattice_814
MAlonzo.Code.Algebra.Structures.d_isDistributiveLattice_1884
      ((T_BooleanAlgebra_2920 -> T_IsBooleanAlgebra_1864)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_2920 -> T_IsBooleanAlgebra_1864
d_isBooleanAlgebra_2956 (T_BooleanAlgebra_2920 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_2920
v0))
-- Algebra.Bundles.BooleanAlgebra._.isEquivalence
d_isEquivalence_2964 ::
  T_BooleanAlgebra_2920 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_2964 :: T_BooleanAlgebra_2920 -> T_IsEquivalence_26
d_isEquivalence_2964 T_BooleanAlgebra_2920
v0
  = (T_IsLattice_740 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      T_IsLattice_740 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_762
      ((T_IsDistributiveLattice_814 -> T_IsLattice_740)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsDistributiveLattice_814 -> T_IsLattice_740
MAlonzo.Code.Algebra.Structures.d_isLattice_824
         ((T_IsBooleanAlgebra_1864 -> T_IsDistributiveLattice_814)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsBooleanAlgebra_1864 -> T_IsDistributiveLattice_814
MAlonzo.Code.Algebra.Structures.d_isDistributiveLattice_1884
            ((T_BooleanAlgebra_2920 -> T_IsBooleanAlgebra_1864)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_2920 -> T_IsBooleanAlgebra_1864
d_isBooleanAlgebra_2956 (T_BooleanAlgebra_2920 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_2920
v0))))
-- Algebra.Bundles.BooleanAlgebra._.isLattice
d_isLattice_2966 ::
  T_BooleanAlgebra_2920 ->
  MAlonzo.Code.Algebra.Structures.T_IsLattice_740
d_isLattice_2966 :: T_BooleanAlgebra_2920 -> T_IsLattice_740
d_isLattice_2966 T_BooleanAlgebra_2920
v0
  = (T_IsDistributiveLattice_814 -> T_IsLattice_740)
-> AgdaAny -> T_IsLattice_740
forall a b. a -> b
coe
      T_IsDistributiveLattice_814 -> T_IsLattice_740
MAlonzo.Code.Algebra.Structures.d_isLattice_824
      ((T_IsBooleanAlgebra_1864 -> T_IsDistributiveLattice_814)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsBooleanAlgebra_1864 -> T_IsDistributiveLattice_814
MAlonzo.Code.Algebra.Structures.d_isDistributiveLattice_1884
         ((T_BooleanAlgebra_2920 -> T_IsBooleanAlgebra_1864)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_2920 -> T_IsBooleanAlgebra_1864
d_isBooleanAlgebra_2956 (T_BooleanAlgebra_2920 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_2920
v0)))
-- Algebra.Bundles.BooleanAlgebra._.isPartialEquivalence
d_isPartialEquivalence_2968 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BooleanAlgebra_2920 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_2968 :: () -> () -> T_BooleanAlgebra_2920 -> T_IsPartialEquivalence_16
d_isPartialEquivalence_2968 ~()
v0 ~()
v1 T_BooleanAlgebra_2920
v2
  = T_BooleanAlgebra_2920 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_2968 T_BooleanAlgebra_2920
v2
du_isPartialEquivalence_2968 ::
  T_BooleanAlgebra_2920 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_2968 :: T_BooleanAlgebra_2920 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_2968 T_BooleanAlgebra_2920
v0
  = let v1 :: T_IsBooleanAlgebra_1864
v1 = T_BooleanAlgebra_2920 -> T_IsBooleanAlgebra_1864
d_isBooleanAlgebra_2956 (T_BooleanAlgebra_2920 -> T_BooleanAlgebra_2920
forall a b. a -> b
coe T_BooleanAlgebra_2920
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsDistributiveLattice_814
v2
             = T_IsBooleanAlgebra_1864 -> T_IsDistributiveLattice_814
MAlonzo.Code.Algebra.Structures.d_isDistributiveLattice_1884
                 (T_IsBooleanAlgebra_1864 -> T_IsBooleanAlgebra_1864
forall a b. a -> b
coe T_IsBooleanAlgebra_1864
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsLattice_740
v3
                = T_IsDistributiveLattice_814 -> T_IsLattice_740
MAlonzo.Code.Algebra.Structures.d_isLattice_824 (T_IsDistributiveLattice_814 -> T_IsDistributiveLattice_814
forall a b. a -> b
coe T_IsDistributiveLattice_814
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_IsLattice_740 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsLattice_740 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_762 (T_IsLattice_740 -> AgdaAny
forall a b. a -> b
coe T_IsLattice_740
v3)))))
-- Algebra.Bundles.BooleanAlgebra._.refl
d_refl_2970 :: T_BooleanAlgebra_2920 -> AgdaAny -> AgdaAny
d_refl_2970 :: T_BooleanAlgebra_2920 -> AgdaAny -> AgdaAny
d_refl_2970 T_BooleanAlgebra_2920
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_IsLattice_740 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsLattice_740 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_762
         ((T_IsDistributiveLattice_814 -> T_IsLattice_740)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsDistributiveLattice_814 -> T_IsLattice_740
MAlonzo.Code.Algebra.Structures.d_isLattice_824
            ((T_IsBooleanAlgebra_1864 -> T_IsDistributiveLattice_814)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsBooleanAlgebra_1864 -> T_IsDistributiveLattice_814
MAlonzo.Code.Algebra.Structures.d_isDistributiveLattice_1884
               ((T_BooleanAlgebra_2920 -> T_IsBooleanAlgebra_1864)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_2920 -> T_IsBooleanAlgebra_1864
d_isBooleanAlgebra_2956 (T_BooleanAlgebra_2920 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_2920
v0)))))
-- Algebra.Bundles.BooleanAlgebra._.reflexive
d_reflexive_2972 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BooleanAlgebra_2920 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_2972 :: ()
-> ()
-> T_BooleanAlgebra_2920
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_2972 ~()
v0 ~()
v1 T_BooleanAlgebra_2920
v2 = T_BooleanAlgebra_2920
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_2972 T_BooleanAlgebra_2920
v2
du_reflexive_2972 ::
  T_BooleanAlgebra_2920 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_2972 :: T_BooleanAlgebra_2920
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_2972 T_BooleanAlgebra_2920
v0
  = let v1 :: T_IsBooleanAlgebra_1864
v1 = T_BooleanAlgebra_2920 -> T_IsBooleanAlgebra_1864
d_isBooleanAlgebra_2956 (T_BooleanAlgebra_2920 -> T_BooleanAlgebra_2920
forall a b. a -> b
coe T_BooleanAlgebra_2920
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsDistributiveLattice_814
v2
             = T_IsBooleanAlgebra_1864 -> T_IsDistributiveLattice_814
MAlonzo.Code.Algebra.Structures.d_isDistributiveLattice_1884
                 (T_IsBooleanAlgebra_1864 -> T_IsBooleanAlgebra_1864
forall a b. a -> b
coe T_IsBooleanAlgebra_1864
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsLattice_740
v3
                = T_IsDistributiveLattice_814 -> T_IsLattice_740
MAlonzo.Code.Algebra.Structures.d_isLattice_824 (T_IsDistributiveLattice_814 -> T_IsDistributiveLattice_814
forall a b. a -> b
coe T_IsDistributiveLattice_814
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_IsLattice_740 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_740 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_762 (T_IsLattice_740 -> AgdaAny
forall a b. a -> b
coe T_IsLattice_740
v3))
                 AgdaAny
v4)))
-- Algebra.Bundles.BooleanAlgebra._.sym
d_sym_2974 ::
  T_BooleanAlgebra_2920 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_2974 :: T_BooleanAlgebra_2920 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_2974 T_BooleanAlgebra_2920
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_IsLattice_740 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsLattice_740 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_762
         ((T_IsDistributiveLattice_814 -> T_IsLattice_740)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsDistributiveLattice_814 -> T_IsLattice_740
MAlonzo.Code.Algebra.Structures.d_isLattice_824
            ((T_IsBooleanAlgebra_1864 -> T_IsDistributiveLattice_814)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsBooleanAlgebra_1864 -> T_IsDistributiveLattice_814
MAlonzo.Code.Algebra.Structures.d_isDistributiveLattice_1884
               ((T_BooleanAlgebra_2920 -> T_IsBooleanAlgebra_1864)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_2920 -> T_IsBooleanAlgebra_1864
d_isBooleanAlgebra_2956 (T_BooleanAlgebra_2920 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_2920
v0)))))
-- Algebra.Bundles.BooleanAlgebra._.trans
d_trans_2976 ::
  T_BooleanAlgebra_2920 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_2976 :: T_BooleanAlgebra_2920
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_2976 T_BooleanAlgebra_2920
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_IsLattice_740 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsLattice_740 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_762
         ((T_IsDistributiveLattice_814 -> T_IsLattice_740)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsDistributiveLattice_814 -> T_IsLattice_740
MAlonzo.Code.Algebra.Structures.d_isLattice_824
            ((T_IsBooleanAlgebra_1864 -> T_IsDistributiveLattice_814)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsBooleanAlgebra_1864 -> T_IsDistributiveLattice_814
MAlonzo.Code.Algebra.Structures.d_isDistributiveLattice_1884
               ((T_BooleanAlgebra_2920 -> T_IsBooleanAlgebra_1864)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_2920 -> T_IsBooleanAlgebra_1864
d_isBooleanAlgebra_2956 (T_BooleanAlgebra_2920 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_2920
v0)))))
-- Algebra.Bundles.BooleanAlgebra._.¬-cong
d_'172''45'cong_2978 ::
  T_BooleanAlgebra_2920 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'172''45'cong_2978 :: T_BooleanAlgebra_2920 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'172''45'cong_2978 T_BooleanAlgebra_2920
v0
  = (T_IsBooleanAlgebra_1864
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsBooleanAlgebra_1864 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'172''45'cong_1890
      ((T_BooleanAlgebra_2920 -> T_IsBooleanAlgebra_1864)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_2920 -> T_IsBooleanAlgebra_1864
d_isBooleanAlgebra_2956 (T_BooleanAlgebra_2920 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_2920
v0))
-- Algebra.Bundles.BooleanAlgebra._.∧-absorbs-∨
d_'8743''45'absorbs'45''8744'_2980 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BooleanAlgebra_2920 -> AgdaAny -> AgdaAny -> AgdaAny
d_'8743''45'absorbs'45''8744'_2980 :: () -> () -> T_BooleanAlgebra_2920 -> AgdaAny -> AgdaAny -> AgdaAny
d_'8743''45'absorbs'45''8744'_2980 ~()
v0 ~()
v1 T_BooleanAlgebra_2920
v2
  = T_BooleanAlgebra_2920 -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'absorbs'45''8744'_2980 T_BooleanAlgebra_2920
v2
du_'8743''45'absorbs'45''8744'_2980 ::
  T_BooleanAlgebra_2920 -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'absorbs'45''8744'_2980 :: T_BooleanAlgebra_2920 -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'absorbs'45''8744'_2980 T_BooleanAlgebra_2920
v0
  = let v1 :: T_IsBooleanAlgebra_1864
v1 = T_BooleanAlgebra_2920 -> T_IsBooleanAlgebra_1864
d_isBooleanAlgebra_2956 (T_BooleanAlgebra_2920 -> T_BooleanAlgebra_2920
forall a b. a -> b
coe T_BooleanAlgebra_2920
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsDistributiveLattice_814
v2
             = T_IsBooleanAlgebra_1864 -> T_IsDistributiveLattice_814
MAlonzo.Code.Algebra.Structures.d_isDistributiveLattice_1884
                 (T_IsBooleanAlgebra_1864 -> T_IsBooleanAlgebra_1864
forall a b. a -> b
coe T_IsBooleanAlgebra_1864
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsLattice_740 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsLattice_740 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'8743''45'absorbs'45''8744'_792
            ((T_IsDistributiveLattice_814 -> T_IsLattice_740)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_814 -> T_IsLattice_740
MAlonzo.Code.Algebra.Structures.d_isLattice_824 (T_IsDistributiveLattice_814 -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_814
v2))))
-- Algebra.Bundles.BooleanAlgebra._.∧-assoc
d_'8743''45'assoc_2982 ::
  T_BooleanAlgebra_2920 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8743''45'assoc_2982 :: T_BooleanAlgebra_2920 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8743''45'assoc_2982 T_BooleanAlgebra_2920
v0
  = (T_IsLattice_740 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsLattice_740 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8743''45'assoc_772
      ((T_IsDistributiveLattice_814 -> T_IsLattice_740)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsDistributiveLattice_814 -> T_IsLattice_740
MAlonzo.Code.Algebra.Structures.d_isLattice_824
         ((T_IsBooleanAlgebra_1864 -> T_IsDistributiveLattice_814)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsBooleanAlgebra_1864 -> T_IsDistributiveLattice_814
MAlonzo.Code.Algebra.Structures.d_isDistributiveLattice_1884
            ((T_BooleanAlgebra_2920 -> T_IsBooleanAlgebra_1864)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_2920 -> T_IsBooleanAlgebra_1864
d_isBooleanAlgebra_2956 (T_BooleanAlgebra_2920 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_2920
v0))))
-- Algebra.Bundles.BooleanAlgebra._.∧-comm
d_'8743''45'comm_2984 ::
  T_BooleanAlgebra_2920 -> AgdaAny -> AgdaAny -> AgdaAny
d_'8743''45'comm_2984 :: T_BooleanAlgebra_2920 -> AgdaAny -> AgdaAny -> AgdaAny
d_'8743''45'comm_2984 T_BooleanAlgebra_2920
v0
  = (T_IsLattice_740 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsLattice_740 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8743''45'comm_770
      ((T_IsDistributiveLattice_814 -> T_IsLattice_740)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsDistributiveLattice_814 -> T_IsLattice_740
MAlonzo.Code.Algebra.Structures.d_isLattice_824
         ((T_IsBooleanAlgebra_1864 -> T_IsDistributiveLattice_814)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsBooleanAlgebra_1864 -> T_IsDistributiveLattice_814
MAlonzo.Code.Algebra.Structures.d_isDistributiveLattice_1884
            ((T_BooleanAlgebra_2920 -> T_IsBooleanAlgebra_1864)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_2920 -> T_IsBooleanAlgebra_1864
d_isBooleanAlgebra_2956 (T_BooleanAlgebra_2920 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_2920
v0))))
-- Algebra.Bundles.BooleanAlgebra._.∧-complementʳ
d_'8743''45'complement'691'_2986 ::
  T_BooleanAlgebra_2920 -> AgdaAny -> AgdaAny
d_'8743''45'complement'691'_2986 :: T_BooleanAlgebra_2920 -> AgdaAny -> AgdaAny
d_'8743''45'complement'691'_2986 T_BooleanAlgebra_2920
v0
  = (T_IsBooleanAlgebra_1864 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsBooleanAlgebra_1864 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8743''45'complement'691'_1888
      ((T_BooleanAlgebra_2920 -> T_IsBooleanAlgebra_1864)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_2920 -> T_IsBooleanAlgebra_1864
d_isBooleanAlgebra_2956 (T_BooleanAlgebra_2920 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_2920
v0))
-- Algebra.Bundles.BooleanAlgebra._.∧-cong
d_'8743''45'cong_2988 ::
  T_BooleanAlgebra_2920 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8743''45'cong_2988 :: T_BooleanAlgebra_2920
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8743''45'cong_2988 T_BooleanAlgebra_2920
v0
  = (T_IsLattice_740
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsLattice_740
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8743''45'cong_774
      ((T_IsDistributiveLattice_814 -> T_IsLattice_740)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsDistributiveLattice_814 -> T_IsLattice_740
MAlonzo.Code.Algebra.Structures.d_isLattice_824
         ((T_IsBooleanAlgebra_1864 -> T_IsDistributiveLattice_814)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsBooleanAlgebra_1864 -> T_IsDistributiveLattice_814
MAlonzo.Code.Algebra.Structures.d_isDistributiveLattice_1884
            ((T_BooleanAlgebra_2920 -> T_IsBooleanAlgebra_1864)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_2920 -> T_IsBooleanAlgebra_1864
d_isBooleanAlgebra_2956 (T_BooleanAlgebra_2920 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_2920
v0))))
-- Algebra.Bundles.BooleanAlgebra._.∧-congʳ
d_'8743''45'cong'691'_2990 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BooleanAlgebra_2920 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8743''45'cong'691'_2990 :: ()
-> ()
-> T_BooleanAlgebra_2920
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8743''45'cong'691'_2990 ~()
v0 ~()
v1 T_BooleanAlgebra_2920
v2
  = T_BooleanAlgebra_2920
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'cong'691'_2990 T_BooleanAlgebra_2920
v2
du_'8743''45'cong'691'_2990 ::
  T_BooleanAlgebra_2920 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'cong'691'_2990 :: T_BooleanAlgebra_2920
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'cong'691'_2990 T_BooleanAlgebra_2920
v0
  = let v1 :: T_IsBooleanAlgebra_1864
v1 = T_BooleanAlgebra_2920 -> T_IsBooleanAlgebra_1864
d_isBooleanAlgebra_2956 (T_BooleanAlgebra_2920 -> T_BooleanAlgebra_2920
forall a b. a -> b
coe T_BooleanAlgebra_2920
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsDistributiveLattice_814
v2
             = T_IsBooleanAlgebra_1864 -> T_IsDistributiveLattice_814
MAlonzo.Code.Algebra.Structures.d_isDistributiveLattice_1884
                 (T_IsBooleanAlgebra_1864 -> T_IsBooleanAlgebra_1864
forall a b. a -> b
coe T_IsBooleanAlgebra_1864
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsLattice_740
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsLattice_740
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'8743''45'cong'691'_798
            ((T_IsDistributiveLattice_814 -> T_IsLattice_740)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_814 -> T_IsLattice_740
MAlonzo.Code.Algebra.Structures.d_isLattice_824 (T_IsDistributiveLattice_814 -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_814
v2))))
-- Algebra.Bundles.BooleanAlgebra._.∧-congˡ
d_'8743''45'cong'737'_2992 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BooleanAlgebra_2920 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8743''45'cong'737'_2992 :: ()
-> ()
-> T_BooleanAlgebra_2920
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8743''45'cong'737'_2992 ~()
v0 ~()
v1 T_BooleanAlgebra_2920
v2
  = T_BooleanAlgebra_2920
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'cong'737'_2992 T_BooleanAlgebra_2920
v2
du_'8743''45'cong'737'_2992 ::
  T_BooleanAlgebra_2920 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'cong'737'_2992 :: T_BooleanAlgebra_2920
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'cong'737'_2992 T_BooleanAlgebra_2920
v0
  = let v1 :: T_IsBooleanAlgebra_1864
v1 = T_BooleanAlgebra_2920 -> T_IsBooleanAlgebra_1864
d_isBooleanAlgebra_2956 (T_BooleanAlgebra_2920 -> T_BooleanAlgebra_2920
forall a b. a -> b
coe T_BooleanAlgebra_2920
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsDistributiveLattice_814
v2
             = T_IsBooleanAlgebra_1864 -> T_IsDistributiveLattice_814
MAlonzo.Code.Algebra.Structures.d_isDistributiveLattice_1884
                 (T_IsBooleanAlgebra_1864 -> T_IsBooleanAlgebra_1864
forall a b. a -> b
coe T_IsBooleanAlgebra_1864
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsLattice_740
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsLattice_740
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'8743''45'cong'737'_794
            ((T_IsDistributiveLattice_814 -> T_IsLattice_740)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_814 -> T_IsLattice_740
MAlonzo.Code.Algebra.Structures.d_isLattice_824 (T_IsDistributiveLattice_814 -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_814
v2))))
-- Algebra.Bundles.BooleanAlgebra._.∨-absorbs-∧
d_'8744''45'absorbs'45''8743'_2994 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BooleanAlgebra_2920 -> AgdaAny -> AgdaAny -> AgdaAny
d_'8744''45'absorbs'45''8743'_2994 :: () -> () -> T_BooleanAlgebra_2920 -> AgdaAny -> AgdaAny -> AgdaAny
d_'8744''45'absorbs'45''8743'_2994 ~()
v0 ~()
v1 T_BooleanAlgebra_2920
v2
  = T_BooleanAlgebra_2920 -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'absorbs'45''8743'_2994 T_BooleanAlgebra_2920
v2
du_'8744''45'absorbs'45''8743'_2994 ::
  T_BooleanAlgebra_2920 -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'absorbs'45''8743'_2994 :: T_BooleanAlgebra_2920 -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'absorbs'45''8743'_2994 T_BooleanAlgebra_2920
v0
  = let v1 :: T_IsBooleanAlgebra_1864
v1 = T_BooleanAlgebra_2920 -> T_IsBooleanAlgebra_1864
d_isBooleanAlgebra_2956 (T_BooleanAlgebra_2920 -> T_BooleanAlgebra_2920
forall a b. a -> b
coe T_BooleanAlgebra_2920
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsDistributiveLattice_814
v2
             = T_IsBooleanAlgebra_1864 -> T_IsDistributiveLattice_814
MAlonzo.Code.Algebra.Structures.d_isDistributiveLattice_1884
                 (T_IsBooleanAlgebra_1864 -> T_IsBooleanAlgebra_1864
forall a b. a -> b
coe T_IsBooleanAlgebra_1864
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsLattice_740 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsLattice_740 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'8744''45'absorbs'45''8743'_790
            ((T_IsDistributiveLattice_814 -> T_IsLattice_740)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_814 -> T_IsLattice_740
MAlonzo.Code.Algebra.Structures.d_isLattice_824 (T_IsDistributiveLattice_814 -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_814
v2))))
-- Algebra.Bundles.BooleanAlgebra._.∨-assoc
d_'8744''45'assoc_2996 ::
  T_BooleanAlgebra_2920 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8744''45'assoc_2996 :: T_BooleanAlgebra_2920 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8744''45'assoc_2996 T_BooleanAlgebra_2920
v0
  = (T_IsLattice_740 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsLattice_740 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8744''45'assoc_766
      ((T_IsDistributiveLattice_814 -> T_IsLattice_740)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsDistributiveLattice_814 -> T_IsLattice_740
MAlonzo.Code.Algebra.Structures.d_isLattice_824
         ((T_IsBooleanAlgebra_1864 -> T_IsDistributiveLattice_814)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsBooleanAlgebra_1864 -> T_IsDistributiveLattice_814
MAlonzo.Code.Algebra.Structures.d_isDistributiveLattice_1884
            ((T_BooleanAlgebra_2920 -> T_IsBooleanAlgebra_1864)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_2920 -> T_IsBooleanAlgebra_1864
d_isBooleanAlgebra_2956 (T_BooleanAlgebra_2920 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_2920
v0))))
-- Algebra.Bundles.BooleanAlgebra._.∨-comm
d_'8744''45'comm_2998 ::
  T_BooleanAlgebra_2920 -> AgdaAny -> AgdaAny -> AgdaAny
d_'8744''45'comm_2998 :: T_BooleanAlgebra_2920 -> AgdaAny -> AgdaAny -> AgdaAny
d_'8744''45'comm_2998 T_BooleanAlgebra_2920
v0
  = (T_IsLattice_740 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsLattice_740 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8744''45'comm_764
      ((T_IsDistributiveLattice_814 -> T_IsLattice_740)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsDistributiveLattice_814 -> T_IsLattice_740
MAlonzo.Code.Algebra.Structures.d_isLattice_824
         ((T_IsBooleanAlgebra_1864 -> T_IsDistributiveLattice_814)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsBooleanAlgebra_1864 -> T_IsDistributiveLattice_814
MAlonzo.Code.Algebra.Structures.d_isDistributiveLattice_1884
            ((T_BooleanAlgebra_2920 -> T_IsBooleanAlgebra_1864)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_2920 -> T_IsBooleanAlgebra_1864
d_isBooleanAlgebra_2956 (T_BooleanAlgebra_2920 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_2920
v0))))
-- Algebra.Bundles.BooleanAlgebra._.∨-complementʳ
d_'8744''45'complement'691'_3000 ::
  T_BooleanAlgebra_2920 -> AgdaAny -> AgdaAny
d_'8744''45'complement'691'_3000 :: T_BooleanAlgebra_2920 -> AgdaAny -> AgdaAny
d_'8744''45'complement'691'_3000 T_BooleanAlgebra_2920
v0
  = (T_IsBooleanAlgebra_1864 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsBooleanAlgebra_1864 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8744''45'complement'691'_1886
      ((T_BooleanAlgebra_2920 -> T_IsBooleanAlgebra_1864)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_2920 -> T_IsBooleanAlgebra_1864
d_isBooleanAlgebra_2956 (T_BooleanAlgebra_2920 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_2920
v0))
-- Algebra.Bundles.BooleanAlgebra._.∨-cong
d_'8744''45'cong_3002 ::
  T_BooleanAlgebra_2920 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8744''45'cong_3002 :: T_BooleanAlgebra_2920
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8744''45'cong_3002 T_BooleanAlgebra_2920
v0
  = (T_IsLattice_740
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsLattice_740
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8744''45'cong_768
      ((T_IsDistributiveLattice_814 -> T_IsLattice_740)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsDistributiveLattice_814 -> T_IsLattice_740
MAlonzo.Code.Algebra.Structures.d_isLattice_824
         ((T_IsBooleanAlgebra_1864 -> T_IsDistributiveLattice_814)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsBooleanAlgebra_1864 -> T_IsDistributiveLattice_814
MAlonzo.Code.Algebra.Structures.d_isDistributiveLattice_1884
            ((T_BooleanAlgebra_2920 -> T_IsBooleanAlgebra_1864)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_2920 -> T_IsBooleanAlgebra_1864
d_isBooleanAlgebra_2956 (T_BooleanAlgebra_2920 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_2920
v0))))
-- Algebra.Bundles.BooleanAlgebra._.∨-congʳ
d_'8744''45'cong'691'_3004 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BooleanAlgebra_2920 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8744''45'cong'691'_3004 :: ()
-> ()
-> T_BooleanAlgebra_2920
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8744''45'cong'691'_3004 ~()
v0 ~()
v1 T_BooleanAlgebra_2920
v2
  = T_BooleanAlgebra_2920
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'cong'691'_3004 T_BooleanAlgebra_2920
v2
du_'8744''45'cong'691'_3004 ::
  T_BooleanAlgebra_2920 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'cong'691'_3004 :: T_BooleanAlgebra_2920
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'cong'691'_3004 T_BooleanAlgebra_2920
v0
  = let v1 :: T_IsBooleanAlgebra_1864
v1 = T_BooleanAlgebra_2920 -> T_IsBooleanAlgebra_1864
d_isBooleanAlgebra_2956 (T_BooleanAlgebra_2920 -> T_BooleanAlgebra_2920
forall a b. a -> b
coe T_BooleanAlgebra_2920
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsDistributiveLattice_814
v2
             = T_IsBooleanAlgebra_1864 -> T_IsDistributiveLattice_814
MAlonzo.Code.Algebra.Structures.d_isDistributiveLattice_1884
                 (T_IsBooleanAlgebra_1864 -> T_IsBooleanAlgebra_1864
forall a b. a -> b
coe T_IsBooleanAlgebra_1864
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsLattice_740
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsLattice_740
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'8744''45'cong'691'_806
            ((T_IsDistributiveLattice_814 -> T_IsLattice_740)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_814 -> T_IsLattice_740
MAlonzo.Code.Algebra.Structures.d_isLattice_824 (T_IsDistributiveLattice_814 -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_814
v2))))
-- Algebra.Bundles.BooleanAlgebra._.∨-congˡ
d_'8744''45'cong'737'_3006 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BooleanAlgebra_2920 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8744''45'cong'737'_3006 :: ()
-> ()
-> T_BooleanAlgebra_2920
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8744''45'cong'737'_3006 ~()
v0 ~()
v1 T_BooleanAlgebra_2920
v2
  = T_BooleanAlgebra_2920
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'cong'737'_3006 T_BooleanAlgebra_2920
v2
du_'8744''45'cong'737'_3006 ::
  T_BooleanAlgebra_2920 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'cong'737'_3006 :: T_BooleanAlgebra_2920
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'cong'737'_3006 T_BooleanAlgebra_2920
v0
  = let v1 :: T_IsBooleanAlgebra_1864
v1 = T_BooleanAlgebra_2920 -> T_IsBooleanAlgebra_1864
d_isBooleanAlgebra_2956 (T_BooleanAlgebra_2920 -> T_BooleanAlgebra_2920
forall a b. a -> b
coe T_BooleanAlgebra_2920
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsDistributiveLattice_814
v2
             = T_IsBooleanAlgebra_1864 -> T_IsDistributiveLattice_814
MAlonzo.Code.Algebra.Structures.d_isDistributiveLattice_1884
                 (T_IsBooleanAlgebra_1864 -> T_IsBooleanAlgebra_1864
forall a b. a -> b
coe T_IsBooleanAlgebra_1864
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsLattice_740
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsLattice_740
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'8744''45'cong'737'_802
            ((T_IsDistributiveLattice_814 -> T_IsLattice_740)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_814 -> T_IsLattice_740
MAlonzo.Code.Algebra.Structures.d_isLattice_824 (T_IsDistributiveLattice_814 -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_814
v2))))
-- Algebra.Bundles.BooleanAlgebra._.∨-distribʳ-∧
d_'8744''45'distrib'691''45''8743'_3008 ::
  T_BooleanAlgebra_2920 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8744''45'distrib'691''45''8743'_3008 :: T_BooleanAlgebra_2920 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8744''45'distrib'691''45''8743'_3008 T_BooleanAlgebra_2920
v0
  = (T_IsDistributiveLattice_814
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsDistributiveLattice_814
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8744''45'distrib'691''45''8743'_826
      ((T_IsBooleanAlgebra_1864 -> T_IsDistributiveLattice_814)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsBooleanAlgebra_1864 -> T_IsDistributiveLattice_814
MAlonzo.Code.Algebra.Structures.d_isDistributiveLattice_1884
         ((T_BooleanAlgebra_2920 -> T_IsBooleanAlgebra_1864)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_2920 -> T_IsBooleanAlgebra_1864
d_isBooleanAlgebra_2956 (T_BooleanAlgebra_2920 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_2920
v0)))
-- Algebra.Bundles.BooleanAlgebra._.∨-∧-distribʳ
d_'8744''45''8743''45'distrib'691'_3010 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BooleanAlgebra_2920 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8744''45''8743''45'distrib'691'_3010 :: ()
-> ()
-> T_BooleanAlgebra_2920
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8744''45''8743''45'distrib'691'_3010 ~()
v0 ~()
v1 T_BooleanAlgebra_2920
v2
  = T_BooleanAlgebra_2920 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45''8743''45'distrib'691'_3010 T_BooleanAlgebra_2920
v2
du_'8744''45''8743''45'distrib'691'_3010 ::
  T_BooleanAlgebra_2920 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45''8743''45'distrib'691'_3010 :: T_BooleanAlgebra_2920 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45''8743''45'distrib'691'_3010 T_BooleanAlgebra_2920
v0
  = let v1 :: T_IsBooleanAlgebra_1864
v1 = T_BooleanAlgebra_2920 -> T_IsBooleanAlgebra_1864
d_isBooleanAlgebra_2956 (T_BooleanAlgebra_2920 -> T_BooleanAlgebra_2920
forall a b. a -> b
coe T_BooleanAlgebra_2920
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsDistributiveLattice_814
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsDistributiveLattice_814
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_'8744''45''8743''45'distrib'691'_868
         ((T_IsBooleanAlgebra_1864 -> T_IsDistributiveLattice_814)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsBooleanAlgebra_1864 -> T_IsDistributiveLattice_814
MAlonzo.Code.Algebra.Structures.d_isDistributiveLattice_1884
            (T_IsBooleanAlgebra_1864 -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_1864
v1)))
-- Algebra.Bundles.BooleanAlgebra.distributiveLattice
d_distributiveLattice_3012 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BooleanAlgebra_2920 -> T_DistributiveLattice_1228
d_distributiveLattice_3012 :: () -> () -> T_BooleanAlgebra_2920 -> T_DistributiveLattice_1228
d_distributiveLattice_3012 ~()
v0 ~()
v1 T_BooleanAlgebra_2920
v2
  = T_BooleanAlgebra_2920 -> T_DistributiveLattice_1228
du_distributiveLattice_3012 T_BooleanAlgebra_2920
v2
du_distributiveLattice_3012 ::
  T_BooleanAlgebra_2920 -> T_DistributiveLattice_1228
du_distributiveLattice_3012 :: T_BooleanAlgebra_2920 -> T_DistributiveLattice_1228
du_distributiveLattice_3012 T_BooleanAlgebra_2920
v0
  = ((AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> T_IsDistributiveLattice_814
 -> T_DistributiveLattice_1228)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsDistributiveLattice_814
-> T_DistributiveLattice_1228
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsDistributiveLattice_814
-> T_DistributiveLattice_1228
C_DistributiveLattice'46'constructor_20939
      (T_BooleanAlgebra_2920 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8744'__2946 (T_BooleanAlgebra_2920 -> T_BooleanAlgebra_2920
forall a b. a -> b
coe T_BooleanAlgebra_2920
v0)) (T_BooleanAlgebra_2920 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8743'__2948 (T_BooleanAlgebra_2920 -> T_BooleanAlgebra_2920
forall a b. a -> b
coe T_BooleanAlgebra_2920
v0))
      (T_IsBooleanAlgebra_1864 -> T_IsDistributiveLattice_814
MAlonzo.Code.Algebra.Structures.d_isDistributiveLattice_1884
         ((T_BooleanAlgebra_2920 -> T_IsBooleanAlgebra_1864)
-> AgdaAny -> T_IsBooleanAlgebra_1864
forall a b. a -> b
coe T_BooleanAlgebra_2920 -> T_IsBooleanAlgebra_1864
d_isBooleanAlgebra_2956 (T_BooleanAlgebra_2920 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_2920
v0)))
-- Algebra.Bundles.BooleanAlgebra._._≉_
d__'8777'__3016 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BooleanAlgebra_2920 -> AgdaAny -> AgdaAny -> ()
d__'8777'__3016 :: () -> () -> T_BooleanAlgebra_2920 -> AgdaAny -> AgdaAny -> ()
d__'8777'__3016 = () -> () -> T_BooleanAlgebra_2920 -> AgdaAny -> AgdaAny -> ()
forall a. a
erased
-- Algebra.Bundles.BooleanAlgebra._.lattice
d_lattice_3018 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BooleanAlgebra_2920 -> T_Lattice_1144
d_lattice_3018 :: () -> () -> T_BooleanAlgebra_2920 -> T_Lattice_1144
d_lattice_3018 ~()
v0 ~()
v1 T_BooleanAlgebra_2920
v2 = T_BooleanAlgebra_2920 -> T_Lattice_1144
du_lattice_3018 T_BooleanAlgebra_2920
v2
du_lattice_3018 :: T_BooleanAlgebra_2920 -> T_Lattice_1144
du_lattice_3018 :: T_BooleanAlgebra_2920 -> T_Lattice_1144
du_lattice_3018 T_BooleanAlgebra_2920
v0
  = (T_DistributiveLattice_1228 -> T_Lattice_1144)
-> AgdaAny -> T_Lattice_1144
forall a b. a -> b
coe T_DistributiveLattice_1228 -> T_Lattice_1144
du_lattice_1300 ((T_BooleanAlgebra_2920 -> T_DistributiveLattice_1228)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_2920 -> T_DistributiveLattice_1228
du_distributiveLattice_3012 (T_BooleanAlgebra_2920 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_2920
v0))
-- Algebra.Bundles.BooleanAlgebra._.setoid
d_setoid_3020 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BooleanAlgebra_2920 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_3020 :: () -> () -> T_BooleanAlgebra_2920 -> T_Setoid_44
d_setoid_3020 ~()
v0 ~()
v1 T_BooleanAlgebra_2920
v2 = T_BooleanAlgebra_2920 -> T_Setoid_44
du_setoid_3020 T_BooleanAlgebra_2920
v2
du_setoid_3020 ::
  T_BooleanAlgebra_2920 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_3020 :: T_BooleanAlgebra_2920 -> T_Setoid_44
du_setoid_3020 T_BooleanAlgebra_2920
v0
  = let v1 :: t
v1 = (T_BooleanAlgebra_2920 -> T_DistributiveLattice_1228)
-> AgdaAny -> t
forall a b. a -> b
coe T_BooleanAlgebra_2920 -> T_DistributiveLattice_1228
du_distributiveLattice_3012 (T_BooleanAlgebra_2920 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_2920
v0) in
    AgdaAny -> T_Setoid_44
forall a b. a -> b
coe ((T_Lattice_1144 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Lattice_1144 -> T_Setoid_44
du_setoid_1218 ((T_DistributiveLattice_1228 -> T_Lattice_1144)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_DistributiveLattice_1228 -> T_Lattice_1144
du_lattice_1300 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1)))
-- Algebra.Bundles.RawSemigroup
d_RawSemigroup_3022 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 -> ()
d_RawSemigroup_3022 :: () -> () -> ()
d_RawSemigroup_3022 = () -> () -> ()
forall a. a
erased