{-# 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.Data.Bool.Properties 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.Bool
import qualified MAlonzo.Code.Agda.Builtin.Equality
import qualified MAlonzo.Code.Agda.Builtin.Sigma
import qualified MAlonzo.Code.Agda.Builtin.Unit
import qualified MAlonzo.Code.Agda.Primitive
import qualified MAlonzo.Code.Algebra.Bundles
import qualified MAlonzo.Code.Algebra.Lattice.Bundles
import qualified MAlonzo.Code.Algebra.Lattice.Properties.BooleanAlgebra
import qualified MAlonzo.Code.Algebra.Lattice.Structures
import qualified MAlonzo.Code.Algebra.Structures
import qualified MAlonzo.Code.Data.Bool.Base
import qualified MAlonzo.Code.Data.Irrelevant
import qualified MAlonzo.Code.Data.Sum.Base
import qualified MAlonzo.Code.Function.Bundles
import qualified MAlonzo.Code.Induction.WellFounded
import qualified MAlonzo.Code.Relation.Binary.Bundles
import qualified MAlonzo.Code.Relation.Binary.Definitions
import qualified MAlonzo.Code.Relation.Binary.PropositionalEquality.Properties
import qualified MAlonzo.Code.Relation.Binary.Structures
import qualified MAlonzo.Code.Relation.Nullary.Decidable.Core
import qualified MAlonzo.Code.Relation.Nullary.Reflects

-- Data.Bool.Properties._._Absorbs_
d__Absorbs__8 ::
  (Bool -> Bool -> Bool) -> (Bool -> Bool -> Bool) -> ()
d__Absorbs__8 :: (Bool -> Bool -> Bool) -> (Bool -> Bool -> Bool) -> ()
d__Absorbs__8 = (Bool -> Bool -> Bool) -> (Bool -> Bool -> Bool) -> ()
forall a. a
erased
-- Data.Bool.Properties._._DistributesOver_
d__DistributesOver__10 ::
  (Bool -> Bool -> Bool) -> (Bool -> Bool -> Bool) -> ()
d__DistributesOver__10 :: (Bool -> Bool -> Bool) -> (Bool -> Bool -> Bool) -> ()
d__DistributesOver__10 = (Bool -> Bool -> Bool) -> (Bool -> Bool -> Bool) -> ()
forall a. a
erased
-- Data.Bool.Properties._._DistributesOverʳ_
d__DistributesOver'691'__12 ::
  (Bool -> Bool -> Bool) -> (Bool -> Bool -> Bool) -> ()
d__DistributesOver'691'__12 :: (Bool -> Bool -> Bool) -> (Bool -> Bool -> Bool) -> ()
d__DistributesOver'691'__12 = (Bool -> Bool -> Bool) -> (Bool -> Bool -> Bool) -> ()
forall a. a
erased
-- Data.Bool.Properties._._DistributesOverˡ_
d__DistributesOver'737'__14 ::
  (Bool -> Bool -> Bool) -> (Bool -> Bool -> Bool) -> ()
d__DistributesOver'737'__14 :: (Bool -> Bool -> Bool) -> (Bool -> Bool -> Bool) -> ()
d__DistributesOver'737'__14 = (Bool -> Bool -> Bool) -> (Bool -> Bool -> Bool) -> ()
forall a. a
erased
-- Data.Bool.Properties._._IdempotentOn_
d__IdempotentOn__16 :: (Bool -> Bool -> Bool) -> Bool -> ()
d__IdempotentOn__16 :: (Bool -> Bool -> Bool) -> Bool -> ()
d__IdempotentOn__16 = (Bool -> Bool -> Bool) -> Bool -> ()
forall a. a
erased
-- Data.Bool.Properties._._MiddleFourExchange_
d__MiddleFourExchange__18 ::
  (Bool -> Bool -> Bool) -> (Bool -> Bool -> Bool) -> ()
d__MiddleFourExchange__18 :: (Bool -> Bool -> Bool) -> (Bool -> Bool -> Bool) -> ()
d__MiddleFourExchange__18 = (Bool -> Bool -> Bool) -> (Bool -> Bool -> Bool) -> ()
forall a. a
erased
-- Data.Bool.Properties._.Absorptive
d_Absorptive_20 ::
  (Bool -> Bool -> Bool) -> (Bool -> Bool -> Bool) -> ()
d_Absorptive_20 :: (Bool -> Bool -> Bool) -> (Bool -> Bool -> Bool) -> ()
d_Absorptive_20 = (Bool -> Bool -> Bool) -> (Bool -> Bool -> Bool) -> ()
forall a. a
erased
-- Data.Bool.Properties._.AlmostCancellative
d_AlmostCancellative_22 :: Bool -> (Bool -> Bool -> Bool) -> ()
d_AlmostCancellative_22 :: Bool -> (Bool -> Bool -> Bool) -> ()
d_AlmostCancellative_22 = Bool -> (Bool -> Bool -> Bool) -> ()
forall a. a
erased
-- Data.Bool.Properties._.AlmostLeftCancellative
d_AlmostLeftCancellative_24 :: Bool -> (Bool -> Bool -> Bool) -> ()
d_AlmostLeftCancellative_24 :: Bool -> (Bool -> Bool -> Bool) -> ()
d_AlmostLeftCancellative_24 = Bool -> (Bool -> Bool -> Bool) -> ()
forall a. a
erased
-- Data.Bool.Properties._.AlmostRightCancellative
d_AlmostRightCancellative_26 ::
  Bool -> (Bool -> Bool -> Bool) -> ()
d_AlmostRightCancellative_26 :: Bool -> (Bool -> Bool -> Bool) -> ()
d_AlmostRightCancellative_26 = Bool -> (Bool -> Bool -> Bool) -> ()
forall a. a
erased
-- Data.Bool.Properties._.Alternative
d_Alternative_28 :: (Bool -> Bool -> Bool) -> ()
d_Alternative_28 :: (Bool -> Bool -> Bool) -> ()
d_Alternative_28 = (Bool -> Bool -> Bool) -> ()
forall a. a
erased
-- Data.Bool.Properties._.Associative
d_Associative_30 :: (Bool -> Bool -> Bool) -> ()
d_Associative_30 :: (Bool -> Bool -> Bool) -> ()
d_Associative_30 = (Bool -> Bool -> Bool) -> ()
forall a. a
erased
-- Data.Bool.Properties._.Cancellative
d_Cancellative_32 :: (Bool -> Bool -> Bool) -> ()
d_Cancellative_32 :: (Bool -> Bool -> Bool) -> ()
d_Cancellative_32 = (Bool -> Bool -> Bool) -> ()
forall a. a
erased
-- Data.Bool.Properties._.Commutative
d_Commutative_34 :: (Bool -> Bool -> Bool) -> ()
d_Commutative_34 :: (Bool -> Bool -> Bool) -> ()
d_Commutative_34 = (Bool -> Bool -> Bool) -> ()
forall a. a
erased
-- Data.Bool.Properties._.Congruent₁
d_Congruent'8321'_36 :: (Bool -> Bool) -> ()
d_Congruent'8321'_36 :: (Bool -> Bool) -> ()
d_Congruent'8321'_36 = (Bool -> Bool) -> ()
forall a. a
erased
-- Data.Bool.Properties._.Congruent₂
d_Congruent'8322'_38 :: (Bool -> Bool -> Bool) -> ()
d_Congruent'8322'_38 :: (Bool -> Bool -> Bool) -> ()
d_Congruent'8322'_38 = (Bool -> Bool -> Bool) -> ()
forall a. a
erased
-- Data.Bool.Properties._.Conical
d_Conical_40 :: Bool -> (Bool -> Bool -> Bool) -> ()
d_Conical_40 :: Bool -> (Bool -> Bool -> Bool) -> ()
d_Conical_40 = Bool -> (Bool -> Bool -> Bool) -> ()
forall a. a
erased
-- Data.Bool.Properties._.Flexible
d_Flexible_42 :: (Bool -> Bool -> Bool) -> ()
d_Flexible_42 :: (Bool -> Bool -> Bool) -> ()
d_Flexible_42 = (Bool -> Bool -> Bool) -> ()
forall a. a
erased
-- Data.Bool.Properties._.Idempotent
d_Idempotent_44 :: (Bool -> Bool -> Bool) -> ()
d_Idempotent_44 :: (Bool -> Bool -> Bool) -> ()
d_Idempotent_44 = (Bool -> Bool -> Bool) -> ()
forall a. a
erased
-- Data.Bool.Properties._.IdempotentFun
d_IdempotentFun_46 :: (Bool -> Bool) -> ()
d_IdempotentFun_46 :: (Bool -> Bool) -> ()
d_IdempotentFun_46 = (Bool -> Bool) -> ()
forall a. a
erased
-- Data.Bool.Properties._.Identical
d_Identical_48 :: (Bool -> Bool -> Bool) -> ()
d_Identical_48 :: (Bool -> Bool -> Bool) -> ()
d_Identical_48 = (Bool -> Bool -> Bool) -> ()
forall a. a
erased
-- Data.Bool.Properties._.Identity
d_Identity_50 :: Bool -> (Bool -> Bool -> Bool) -> ()
d_Identity_50 :: Bool -> (Bool -> Bool -> Bool) -> ()
d_Identity_50 = Bool -> (Bool -> Bool -> Bool) -> ()
forall a. a
erased
-- Data.Bool.Properties._.Interchangable
d_Interchangable_52 ::
  (Bool -> Bool -> Bool) -> (Bool -> Bool -> Bool) -> ()
d_Interchangable_52 :: (Bool -> Bool -> Bool) -> (Bool -> Bool -> Bool) -> ()
d_Interchangable_52 = (Bool -> Bool -> Bool) -> (Bool -> Bool -> Bool) -> ()
forall a. a
erased
-- Data.Bool.Properties._.Inverse
d_Inverse_54 ::
  Bool -> (Bool -> Bool) -> (Bool -> Bool -> Bool) -> ()
d_Inverse_54 :: Bool -> (Bool -> Bool) -> (Bool -> Bool -> Bool) -> ()
d_Inverse_54 = Bool -> (Bool -> Bool) -> (Bool -> Bool -> Bool) -> ()
forall a. a
erased
-- Data.Bool.Properties._.Invertible
d_Invertible_56 :: Bool -> (Bool -> Bool -> Bool) -> Bool -> ()
d_Invertible_56 :: Bool -> (Bool -> Bool -> Bool) -> Bool -> ()
d_Invertible_56 = Bool -> (Bool -> Bool -> Bool) -> Bool -> ()
forall a. a
erased
-- Data.Bool.Properties._.Involutive
d_Involutive_58 :: (Bool -> Bool) -> ()
d_Involutive_58 :: (Bool -> Bool) -> ()
d_Involutive_58 = (Bool -> Bool) -> ()
forall a. a
erased
-- Data.Bool.Properties._.LeftAlternative
d_LeftAlternative_60 :: (Bool -> Bool -> Bool) -> ()
d_LeftAlternative_60 :: (Bool -> Bool -> Bool) -> ()
d_LeftAlternative_60 = (Bool -> Bool -> Bool) -> ()
forall a. a
erased
-- Data.Bool.Properties._.LeftBol
d_LeftBol_62 :: (Bool -> Bool -> Bool) -> ()
d_LeftBol_62 :: (Bool -> Bool -> Bool) -> ()
d_LeftBol_62 = (Bool -> Bool -> Bool) -> ()
forall a. a
erased
-- Data.Bool.Properties._.LeftCancellative
d_LeftCancellative_64 :: (Bool -> Bool -> Bool) -> ()
d_LeftCancellative_64 :: (Bool -> Bool -> Bool) -> ()
d_LeftCancellative_64 = (Bool -> Bool -> Bool) -> ()
forall a. a
erased
-- Data.Bool.Properties._.LeftCongruent
d_LeftCongruent_66 :: (Bool -> Bool -> Bool) -> ()
d_LeftCongruent_66 :: (Bool -> Bool -> Bool) -> ()
d_LeftCongruent_66 = (Bool -> Bool -> Bool) -> ()
forall a. a
erased
-- Data.Bool.Properties._.LeftConical
d_LeftConical_68 :: Bool -> (Bool -> Bool -> Bool) -> ()
d_LeftConical_68 :: Bool -> (Bool -> Bool -> Bool) -> ()
d_LeftConical_68 = Bool -> (Bool -> Bool -> Bool) -> ()
forall a. a
erased
-- Data.Bool.Properties._.LeftDivides
d_LeftDivides_70 ::
  (Bool -> Bool -> Bool) -> (Bool -> Bool -> Bool) -> ()
d_LeftDivides_70 :: (Bool -> Bool -> Bool) -> (Bool -> Bool -> Bool) -> ()
d_LeftDivides_70 = (Bool -> Bool -> Bool) -> (Bool -> Bool -> Bool) -> ()
forall a. a
erased
-- Data.Bool.Properties._.LeftDividesʳ
d_LeftDivides'691'_72 ::
  (Bool -> Bool -> Bool) -> (Bool -> Bool -> Bool) -> ()
d_LeftDivides'691'_72 :: (Bool -> Bool -> Bool) -> (Bool -> Bool -> Bool) -> ()
d_LeftDivides'691'_72 = (Bool -> Bool -> Bool) -> (Bool -> Bool -> Bool) -> ()
forall a. a
erased
-- Data.Bool.Properties._.LeftDividesˡ
d_LeftDivides'737'_74 ::
  (Bool -> Bool -> Bool) -> (Bool -> Bool -> Bool) -> ()
d_LeftDivides'737'_74 :: (Bool -> Bool -> Bool) -> (Bool -> Bool -> Bool) -> ()
d_LeftDivides'737'_74 = (Bool -> Bool -> Bool) -> (Bool -> Bool -> Bool) -> ()
forall a. a
erased
-- Data.Bool.Properties._.LeftIdentity
d_LeftIdentity_76 :: Bool -> (Bool -> Bool -> Bool) -> ()
d_LeftIdentity_76 :: Bool -> (Bool -> Bool -> Bool) -> ()
d_LeftIdentity_76 = Bool -> (Bool -> Bool -> Bool) -> ()
forall a. a
erased
-- Data.Bool.Properties._.LeftInverse
d_LeftInverse_78 ::
  Bool -> (Bool -> Bool) -> (Bool -> Bool -> Bool) -> ()
d_LeftInverse_78 :: Bool -> (Bool -> Bool) -> (Bool -> Bool -> Bool) -> ()
d_LeftInverse_78 = Bool -> (Bool -> Bool) -> (Bool -> Bool -> Bool) -> ()
forall a. a
erased
-- Data.Bool.Properties._.LeftInvertible
d_LeftInvertible_80 :: Bool -> (Bool -> Bool -> Bool) -> Bool -> ()
d_LeftInvertible_80 :: Bool -> (Bool -> Bool -> Bool) -> Bool -> ()
d_LeftInvertible_80 = Bool -> (Bool -> Bool -> Bool) -> Bool -> ()
forall a. a
erased
-- Data.Bool.Properties._.LeftSemimedial
d_LeftSemimedial_82 :: (Bool -> Bool -> Bool) -> ()
d_LeftSemimedial_82 :: (Bool -> Bool -> Bool) -> ()
d_LeftSemimedial_82 = (Bool -> Bool -> Bool) -> ()
forall a. a
erased
-- Data.Bool.Properties._.LeftZero
d_LeftZero_84 :: Bool -> (Bool -> Bool -> Bool) -> ()
d_LeftZero_84 :: Bool -> (Bool -> Bool -> Bool) -> ()
d_LeftZero_84 = Bool -> (Bool -> Bool -> Bool) -> ()
forall a. a
erased
-- Data.Bool.Properties._.Medial
d_Medial_86 :: (Bool -> Bool -> Bool) -> ()
d_Medial_86 :: (Bool -> Bool -> Bool) -> ()
d_Medial_86 = (Bool -> Bool -> Bool) -> ()
forall a. a
erased
-- Data.Bool.Properties._.MiddleBol
d_MiddleBol_88 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) -> (Bool -> Bool -> Bool) -> ()
d_MiddleBol_88 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool) -> (Bool -> Bool -> Bool) -> ()
d_MiddleBol_88 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool) -> (Bool -> Bool -> Bool) -> ()
forall a. a
erased
-- Data.Bool.Properties._.RightAlternative
d_RightAlternative_90 :: (Bool -> Bool -> Bool) -> ()
d_RightAlternative_90 :: (Bool -> Bool -> Bool) -> ()
d_RightAlternative_90 = (Bool -> Bool -> Bool) -> ()
forall a. a
erased
-- Data.Bool.Properties._.RightBol
d_RightBol_92 :: (Bool -> Bool -> Bool) -> ()
d_RightBol_92 :: (Bool -> Bool -> Bool) -> ()
d_RightBol_92 = (Bool -> Bool -> Bool) -> ()
forall a. a
erased
-- Data.Bool.Properties._.RightCancellative
d_RightCancellative_94 :: (Bool -> Bool -> Bool) -> ()
d_RightCancellative_94 :: (Bool -> Bool -> Bool) -> ()
d_RightCancellative_94 = (Bool -> Bool -> Bool) -> ()
forall a. a
erased
-- Data.Bool.Properties._.RightCongruent
d_RightCongruent_96 :: (Bool -> Bool -> Bool) -> ()
d_RightCongruent_96 :: (Bool -> Bool -> Bool) -> ()
d_RightCongruent_96 = (Bool -> Bool -> Bool) -> ()
forall a. a
erased
-- Data.Bool.Properties._.RightConical
d_RightConical_98 :: Bool -> (Bool -> Bool -> Bool) -> ()
d_RightConical_98 :: Bool -> (Bool -> Bool -> Bool) -> ()
d_RightConical_98 = Bool -> (Bool -> Bool -> Bool) -> ()
forall a. a
erased
-- Data.Bool.Properties._.RightDivides
d_RightDivides_100 ::
  (Bool -> Bool -> Bool) -> (Bool -> Bool -> Bool) -> ()
d_RightDivides_100 :: (Bool -> Bool -> Bool) -> (Bool -> Bool -> Bool) -> ()
d_RightDivides_100 = (Bool -> Bool -> Bool) -> (Bool -> Bool -> Bool) -> ()
forall a. a
erased
-- Data.Bool.Properties._.RightDividesʳ
d_RightDivides'691'_102 ::
  (Bool -> Bool -> Bool) -> (Bool -> Bool -> Bool) -> ()
d_RightDivides'691'_102 :: (Bool -> Bool -> Bool) -> (Bool -> Bool -> Bool) -> ()
d_RightDivides'691'_102 = (Bool -> Bool -> Bool) -> (Bool -> Bool -> Bool) -> ()
forall a. a
erased
-- Data.Bool.Properties._.RightDividesˡ
d_RightDivides'737'_104 ::
  (Bool -> Bool -> Bool) -> (Bool -> Bool -> Bool) -> ()
d_RightDivides'737'_104 :: (Bool -> Bool -> Bool) -> (Bool -> Bool -> Bool) -> ()
d_RightDivides'737'_104 = (Bool -> Bool -> Bool) -> (Bool -> Bool -> Bool) -> ()
forall a. a
erased
-- Data.Bool.Properties._.RightIdentity
d_RightIdentity_106 :: Bool -> (Bool -> Bool -> Bool) -> ()
d_RightIdentity_106 :: Bool -> (Bool -> Bool -> Bool) -> ()
d_RightIdentity_106 = Bool -> (Bool -> Bool -> Bool) -> ()
forall a. a
erased
-- Data.Bool.Properties._.RightInverse
d_RightInverse_108 ::
  Bool -> (Bool -> Bool) -> (Bool -> Bool -> Bool) -> ()
d_RightInverse_108 :: Bool -> (Bool -> Bool) -> (Bool -> Bool -> Bool) -> ()
d_RightInverse_108 = Bool -> (Bool -> Bool) -> (Bool -> Bool -> Bool) -> ()
forall a. a
erased
-- Data.Bool.Properties._.RightInvertible
d_RightInvertible_110 ::
  Bool -> (Bool -> Bool -> Bool) -> Bool -> ()
d_RightInvertible_110 :: Bool -> (Bool -> Bool -> Bool) -> Bool -> ()
d_RightInvertible_110 = Bool -> (Bool -> Bool -> Bool) -> Bool -> ()
forall a. a
erased
-- Data.Bool.Properties._.RightSemimedial
d_RightSemimedial_112 :: (Bool -> Bool -> Bool) -> ()
d_RightSemimedial_112 :: (Bool -> Bool -> Bool) -> ()
d_RightSemimedial_112 = (Bool -> Bool -> Bool) -> ()
forall a. a
erased
-- Data.Bool.Properties._.RightZero
d_RightZero_114 :: Bool -> (Bool -> Bool -> Bool) -> ()
d_RightZero_114 :: Bool -> (Bool -> Bool -> Bool) -> ()
d_RightZero_114 = Bool -> (Bool -> Bool -> Bool) -> ()
forall a. a
erased
-- Data.Bool.Properties._.Selective
d_Selective_116 :: (Bool -> Bool -> Bool) -> ()
d_Selective_116 :: (Bool -> Bool -> Bool) -> ()
d_Selective_116 = (Bool -> Bool -> Bool) -> ()
forall a. a
erased
-- Data.Bool.Properties._.SelfInverse
d_SelfInverse_118 :: (Bool -> Bool) -> ()
d_SelfInverse_118 :: (Bool -> Bool) -> ()
d_SelfInverse_118 = (Bool -> Bool) -> ()
forall a. a
erased
-- Data.Bool.Properties._.Semimedial
d_Semimedial_120 :: (Bool -> Bool -> Bool) -> ()
d_Semimedial_120 :: (Bool -> Bool -> Bool) -> ()
d_Semimedial_120 = (Bool -> Bool -> Bool) -> ()
forall a. a
erased
-- Data.Bool.Properties._.StarDestructive
d_StarDestructive_122 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) -> (Bool -> Bool) -> ()
d_StarDestructive_122 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool) -> (Bool -> Bool) -> ()
d_StarDestructive_122 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool) -> (Bool -> Bool) -> ()
forall a. a
erased
-- Data.Bool.Properties._.StarExpansive
d_StarExpansive_124 ::
  Bool ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) -> (Bool -> Bool) -> ()
d_StarExpansive_124 :: Bool
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> ()
d_StarExpansive_124 = Bool
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> ()
forall a. a
erased
-- Data.Bool.Properties._.StarLeftDestructive
d_StarLeftDestructive_126 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) -> (Bool -> Bool) -> ()
d_StarLeftDestructive_126 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool) -> (Bool -> Bool) -> ()
d_StarLeftDestructive_126 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool) -> (Bool -> Bool) -> ()
forall a. a
erased
-- Data.Bool.Properties._.StarLeftExpansive
d_StarLeftExpansive_128 ::
  Bool ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) -> (Bool -> Bool) -> ()
d_StarLeftExpansive_128 :: Bool
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> ()
d_StarLeftExpansive_128 = Bool
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> ()
forall a. a
erased
-- Data.Bool.Properties._.StarRightDestructive
d_StarRightDestructive_130 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) -> (Bool -> Bool) -> ()
d_StarRightDestructive_130 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool) -> (Bool -> Bool) -> ()
d_StarRightDestructive_130 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool) -> (Bool -> Bool) -> ()
forall a. a
erased
-- Data.Bool.Properties._.StarRightExpansive
d_StarRightExpansive_132 ::
  Bool ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) -> (Bool -> Bool) -> ()
d_StarRightExpansive_132 :: Bool
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> ()
d_StarRightExpansive_132 = Bool
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> ()
forall a. a
erased
-- Data.Bool.Properties._.Zero
d_Zero_134 :: Bool -> (Bool -> Bool -> Bool) -> ()
d_Zero_134 :: Bool -> (Bool -> Bool -> Bool) -> ()
d_Zero_134 = Bool -> (Bool -> Bool -> Bool) -> ()
forall a. a
erased
-- Data.Bool.Properties._.IsAbelianGroup
d_IsAbelianGroup_138 :: p -> p -> p -> ()
d_IsAbelianGroup_138 p
a0 p
a1 p
a2 = ()
-- Data.Bool.Properties._.IsAlternativeMagma
d_IsAlternativeMagma_142 :: p -> ()
d_IsAlternativeMagma_142 p
a0 = ()
-- Data.Bool.Properties._.IsBand
d_IsBand_146 :: p -> ()
d_IsBand_146 p
a0 = ()
-- Data.Bool.Properties._.IsCancellativeCommutativeSemiring
d_IsCancellativeCommutativeSemiring_150 :: p -> p -> p -> p -> ()
d_IsCancellativeCommutativeSemiring_150 p
a0 p
a1 p
a2 p
a3 = ()
-- Data.Bool.Properties._.IsCommutativeBand
d_IsCommutativeBand_154 :: p -> ()
d_IsCommutativeBand_154 p
a0 = ()
-- Data.Bool.Properties._.IsCommutativeMagma
d_IsCommutativeMagma_158 :: p -> ()
d_IsCommutativeMagma_158 p
a0 = ()
-- Data.Bool.Properties._.IsCommutativeMonoid
d_IsCommutativeMonoid_162 :: p -> p -> ()
d_IsCommutativeMonoid_162 p
a0 p
a1 = ()
-- Data.Bool.Properties._.IsCommutativeRing
d_IsCommutativeRing_166 :: p -> p -> p -> p -> p -> ()
d_IsCommutativeRing_166 p
a0 p
a1 p
a2 p
a3 p
a4 = ()
-- Data.Bool.Properties._.IsCommutativeSemigroup
d_IsCommutativeSemigroup_170 :: p -> ()
d_IsCommutativeSemigroup_170 p
a0 = ()
-- Data.Bool.Properties._.IsCommutativeSemiring
d_IsCommutativeSemiring_174 :: p -> p -> p -> p -> ()
d_IsCommutativeSemiring_174 p
a0 p
a1 p
a2 p
a3 = ()
-- Data.Bool.Properties._.IsCommutativeSemiringWithoutOne
d_IsCommutativeSemiringWithoutOne_178 :: p -> p -> p -> ()
d_IsCommutativeSemiringWithoutOne_178 p
a0 p
a1 p
a2 = ()
-- Data.Bool.Properties._.IsFlexibleMagma
d_IsFlexibleMagma_182 :: p -> ()
d_IsFlexibleMagma_182 p
a0 = ()
-- Data.Bool.Properties._.IsGroup
d_IsGroup_186 :: p -> p -> p -> ()
d_IsGroup_186 p
a0 p
a1 p
a2 = ()
-- Data.Bool.Properties._.IsIdempotentCommutativeMonoid
d_IsIdempotentCommutativeMonoid_190 :: p -> p -> ()
d_IsIdempotentCommutativeMonoid_190 p
a0 p
a1 = ()
-- Data.Bool.Properties._.IsIdempotentMagma
d_IsIdempotentMagma_194 :: p -> ()
d_IsIdempotentMagma_194 p
a0 = ()
-- Data.Bool.Properties._.IsIdempotentMonoid
d_IsIdempotentMonoid_198 :: p -> p -> ()
d_IsIdempotentMonoid_198 p
a0 p
a1 = ()
-- Data.Bool.Properties._.IsIdempotentSemiring
d_IsIdempotentSemiring_202 :: p -> p -> p -> p -> ()
d_IsIdempotentSemiring_202 p
a0 p
a1 p
a2 p
a3 = ()
-- Data.Bool.Properties._.IsInvertibleMagma
d_IsInvertibleMagma_206 :: p -> p -> p -> ()
d_IsInvertibleMagma_206 p
a0 p
a1 p
a2 = ()
-- Data.Bool.Properties._.IsInvertibleUnitalMagma
d_IsInvertibleUnitalMagma_210 :: p -> p -> p -> ()
d_IsInvertibleUnitalMagma_210 p
a0 p
a1 p
a2 = ()
-- Data.Bool.Properties._.IsKleeneAlgebra
d_IsKleeneAlgebra_214 :: p -> p -> p -> p -> p -> ()
d_IsKleeneAlgebra_214 p
a0 p
a1 p
a2 p
a3 p
a4 = ()
-- Data.Bool.Properties._.IsLeftBolLoop
d_IsLeftBolLoop_218 :: p -> p -> p -> p -> ()
d_IsLeftBolLoop_218 p
a0 p
a1 p
a2 p
a3 = ()
-- Data.Bool.Properties._.IsLoop
d_IsLoop_222 :: p -> p -> p -> p -> ()
d_IsLoop_222 p
a0 p
a1 p
a2 p
a3 = ()
-- Data.Bool.Properties._.IsMagma
d_IsMagma_226 :: p -> ()
d_IsMagma_226 p
a0 = ()
-- Data.Bool.Properties._.IsMedialMagma
d_IsMedialMagma_230 :: p -> ()
d_IsMedialMagma_230 p
a0 = ()
-- Data.Bool.Properties._.IsMiddleBolLoop
d_IsMiddleBolLoop_234 :: p -> p -> p -> p -> ()
d_IsMiddleBolLoop_234 p
a0 p
a1 p
a2 p
a3 = ()
-- Data.Bool.Properties._.IsMonoid
d_IsMonoid_238 :: p -> p -> ()
d_IsMonoid_238 p
a0 p
a1 = ()
-- Data.Bool.Properties._.IsMoufangLoop
d_IsMoufangLoop_242 :: p -> p -> p -> p -> ()
d_IsMoufangLoop_242 p
a0 p
a1 p
a2 p
a3 = ()
-- Data.Bool.Properties._.IsNearSemiring
d_IsNearSemiring_246 :: p -> p -> p -> ()
d_IsNearSemiring_246 p
a0 p
a1 p
a2 = ()
-- Data.Bool.Properties._.IsNearring
d_IsNearring_250 :: p -> p -> p -> p -> p -> ()
d_IsNearring_250 p
a0 p
a1 p
a2 p
a3 p
a4 = ()
-- Data.Bool.Properties._.IsNonAssociativeRing
d_IsNonAssociativeRing_254 :: p -> p -> p -> p -> p -> ()
d_IsNonAssociativeRing_254 p
a0 p
a1 p
a2 p
a3 p
a4 = ()
-- Data.Bool.Properties._.IsQuasigroup
d_IsQuasigroup_258 :: p -> p -> p -> ()
d_IsQuasigroup_258 p
a0 p
a1 p
a2 = ()
-- Data.Bool.Properties._.IsQuasiring
d_IsQuasiring_262 :: p -> p -> p -> p -> ()
d_IsQuasiring_262 p
a0 p
a1 p
a2 p
a3 = ()
-- Data.Bool.Properties._.IsRightBolLoop
d_IsRightBolLoop_266 :: p -> p -> p -> p -> ()
d_IsRightBolLoop_266 p
a0 p
a1 p
a2 p
a3 = ()
-- Data.Bool.Properties._.IsRing
d_IsRing_270 :: p -> p -> p -> p -> p -> ()
d_IsRing_270 p
a0 p
a1 p
a2 p
a3 p
a4 = ()
-- Data.Bool.Properties._.IsRingWithoutOne
d_IsRingWithoutOne_274 :: p -> p -> p -> p -> ()
d_IsRingWithoutOne_274 p
a0 p
a1 p
a2 p
a3 = ()
-- Data.Bool.Properties._.IsSelectiveMagma
d_IsSelectiveMagma_278 :: p -> ()
d_IsSelectiveMagma_278 p
a0 = ()
-- Data.Bool.Properties._.IsSemigroup
d_IsSemigroup_282 :: p -> ()
d_IsSemigroup_282 p
a0 = ()
-- Data.Bool.Properties._.IsSemimedialMagma
d_IsSemimedialMagma_286 :: p -> ()
d_IsSemimedialMagma_286 p
a0 = ()
-- Data.Bool.Properties._.IsSemiring
d_IsSemiring_290 :: p -> p -> p -> p -> ()
d_IsSemiring_290 p
a0 p
a1 p
a2 p
a3 = ()
-- Data.Bool.Properties._.IsSemiringWithoutAnnihilatingZero
d_IsSemiringWithoutAnnihilatingZero_294 :: p -> p -> p -> p -> ()
d_IsSemiringWithoutAnnihilatingZero_294 p
a0 p
a1 p
a2 p
a3 = ()
-- Data.Bool.Properties._.IsSemiringWithoutOne
d_IsSemiringWithoutOne_298 :: p -> p -> p -> ()
d_IsSemiringWithoutOne_298 p
a0 p
a1 p
a2 = ()
-- Data.Bool.Properties._.IsSuccessorSet
d_IsSuccessorSet_302 :: p -> p -> ()
d_IsSuccessorSet_302 p
a0 p
a1 = ()
-- Data.Bool.Properties._.IsUnitalMagma
d_IsUnitalMagma_306 :: p -> p -> ()
d_IsUnitalMagma_306 p
a0 p
a1 = ()
-- Data.Bool.Properties._.IsAbelianGroup._//_
d__'47''47'__312 ::
  (Bool -> Bool -> Bool) ->
  Bool ->
  (Bool -> Bool) ->
  MAlonzo.Code.Algebra.Structures.T_IsAbelianGroup_1172 ->
  Bool -> Bool -> Bool
d__'47''47'__312 :: (Bool -> Bool -> Bool)
-> Bool
-> (Bool -> Bool)
-> T_IsAbelianGroup_1172
-> Bool
-> Bool
-> Bool
d__'47''47'__312 Bool -> Bool -> Bool
v0 ~Bool
v1 Bool -> Bool
v2 ~T_IsAbelianGroup_1172
v3 = (Bool -> Bool -> Bool) -> (Bool -> Bool) -> Bool -> Bool -> Bool
du__'47''47'__312 Bool -> Bool -> Bool
v0 Bool -> Bool
v2
du__'47''47'__312 ::
  (Bool -> Bool -> Bool) -> (Bool -> Bool) -> Bool -> Bool -> Bool
du__'47''47'__312 :: (Bool -> Bool -> Bool) -> (Bool -> Bool) -> Bool -> Bool -> Bool
du__'47''47'__312 Bool -> Bool -> Bool
v0 Bool -> Bool
v1
  = ((Any -> Any -> Any) -> (Any -> Any) -> Any -> Any -> Any)
-> Any -> Any -> Bool -> Bool -> Bool
forall a b. a -> b
coe
      (Any -> Any -> Any) -> (Any -> Any) -> Any -> Any -> Any
MAlonzo.Code.Algebra.Structures.du__'47''47'__1136 ((Bool -> Bool -> Bool) -> Any
forall a b. a -> b
coe Bool -> Bool -> Bool
v0)
      ((Bool -> Bool) -> Any
forall a b. a -> b
coe Bool -> Bool
v1)
-- Data.Bool.Properties._.IsAbelianGroup.assoc
d_assoc_314 ::
  MAlonzo.Code.Algebra.Structures.T_IsAbelianGroup_1172 ->
  Bool ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_assoc_314 :: T_IsAbelianGroup_1172 -> Bool -> Bool -> Bool -> T__'8801'__12
d_assoc_314 = T_IsAbelianGroup_1172 -> Bool -> Bool -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsAbelianGroup.comm
d_comm_316 ::
  MAlonzo.Code.Algebra.Structures.T_IsAbelianGroup_1172 ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_comm_316 :: T_IsAbelianGroup_1172 -> Bool -> Bool -> T__'8801'__12
d_comm_316 = T_IsAbelianGroup_1172 -> Bool -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsAbelianGroup.identity
d_identity_318 ::
  MAlonzo.Code.Algebra.Structures.T_IsAbelianGroup_1172 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_identity_318 :: T_IsAbelianGroup_1172 -> T_Σ_14
d_identity_318 T_IsAbelianGroup_1172
v0
  = (T_IsMonoid_712 -> T_Σ_14) -> Any -> T_Σ_14
forall a b. a -> b
coe
      T_IsMonoid_712 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_identity_724
      ((T_IsGroup_1074 -> T_IsMonoid_712) -> Any -> Any
forall a b. a -> b
coe
         T_IsGroup_1074 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_1088
         ((T_IsAbelianGroup_1172 -> T_IsGroup_1074) -> Any -> Any
forall a b. a -> b
coe T_IsAbelianGroup_1172 -> T_IsGroup_1074
MAlonzo.Code.Algebra.Structures.d_isGroup_1184 (T_IsAbelianGroup_1172 -> Any
forall a b. a -> b
coe T_IsAbelianGroup_1172
v0)))
-- Data.Bool.Properties._.IsAbelianGroup.identityʳ
d_identity'691'_320 ::
  (Bool -> Bool -> Bool) ->
  Bool ->
  (Bool -> Bool) ->
  MAlonzo.Code.Algebra.Structures.T_IsAbelianGroup_1172 ->
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_identity'691'_320 :: (Bool -> Bool -> Bool)
-> Bool
-> (Bool -> Bool)
-> T_IsAbelianGroup_1172
-> Bool
-> T__'8801'__12
d_identity'691'_320 = (Bool -> Bool -> Bool)
-> Bool
-> (Bool -> Bool)
-> T_IsAbelianGroup_1172
-> Bool
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsAbelianGroup.identityˡ
d_identity'737'_322 ::
  (Bool -> Bool -> Bool) ->
  Bool ->
  (Bool -> Bool) ->
  MAlonzo.Code.Algebra.Structures.T_IsAbelianGroup_1172 ->
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_identity'737'_322 :: (Bool -> Bool -> Bool)
-> Bool
-> (Bool -> Bool)
-> T_IsAbelianGroup_1172
-> Bool
-> T__'8801'__12
d_identity'737'_322 = (Bool -> Bool -> Bool)
-> Bool
-> (Bool -> Bool)
-> T_IsAbelianGroup_1172
-> Bool
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsAbelianGroup.inverse
d_inverse_324 ::
  MAlonzo.Code.Algebra.Structures.T_IsAbelianGroup_1172 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_inverse_324 :: T_IsAbelianGroup_1172 -> T_Σ_14
d_inverse_324 T_IsAbelianGroup_1172
v0
  = (T_IsGroup_1074 -> T_Σ_14) -> Any -> T_Σ_14
forall a b. a -> b
coe
      T_IsGroup_1074 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_inverse_1090
      ((T_IsAbelianGroup_1172 -> T_IsGroup_1074) -> Any -> Any
forall a b. a -> b
coe T_IsAbelianGroup_1172 -> T_IsGroup_1074
MAlonzo.Code.Algebra.Structures.d_isGroup_1184 (T_IsAbelianGroup_1172 -> Any
forall a b. a -> b
coe T_IsAbelianGroup_1172
v0))
-- Data.Bool.Properties._.IsAbelianGroup.inverseʳ
d_inverse'691'_326 ::
  (Bool -> Bool -> Bool) ->
  Bool ->
  (Bool -> Bool) ->
  MAlonzo.Code.Algebra.Structures.T_IsAbelianGroup_1172 ->
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_inverse'691'_326 :: (Bool -> Bool -> Bool)
-> Bool
-> (Bool -> Bool)
-> T_IsAbelianGroup_1172
-> Bool
-> T__'8801'__12
d_inverse'691'_326 = (Bool -> Bool -> Bool)
-> Bool
-> (Bool -> Bool)
-> T_IsAbelianGroup_1172
-> Bool
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsAbelianGroup.inverseˡ
d_inverse'737'_328 ::
  (Bool -> Bool -> Bool) ->
  Bool ->
  (Bool -> Bool) ->
  MAlonzo.Code.Algebra.Structures.T_IsAbelianGroup_1172 ->
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_inverse'737'_328 :: (Bool -> Bool -> Bool)
-> Bool
-> (Bool -> Bool)
-> T_IsAbelianGroup_1172
-> Bool
-> T__'8801'__12
d_inverse'737'_328 = (Bool -> Bool -> Bool)
-> Bool
-> (Bool -> Bool)
-> T_IsAbelianGroup_1172
-> Bool
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsAbelianGroup.isCommutativeMagma
d_isCommutativeMagma_330 ::
  (Bool -> Bool -> Bool) ->
  Bool ->
  (Bool -> Bool) ->
  MAlonzo.Code.Algebra.Structures.T_IsAbelianGroup_1172 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMagma_214
d_isCommutativeMagma_330 :: (Bool -> Bool -> Bool)
-> Bool
-> (Bool -> Bool)
-> T_IsAbelianGroup_1172
-> T_IsCommutativeMagma_214
d_isCommutativeMagma_330 ~Bool -> Bool -> Bool
v0 ~Bool
v1 ~Bool -> Bool
v2 T_IsAbelianGroup_1172
v3
  = T_IsAbelianGroup_1172 -> T_IsCommutativeMagma_214
du_isCommutativeMagma_330 T_IsAbelianGroup_1172
v3
du_isCommutativeMagma_330 ::
  MAlonzo.Code.Algebra.Structures.T_IsAbelianGroup_1172 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMagma_214
du_isCommutativeMagma_330 :: T_IsAbelianGroup_1172 -> T_IsCommutativeMagma_214
du_isCommutativeMagma_330 T_IsAbelianGroup_1172
v0
  = let v1 :: Any
v1
          = (T_IsAbelianGroup_1172 -> T_IsCommutativeMonoid_764) -> Any -> Any
forall a b. a -> b
coe
              T_IsAbelianGroup_1172 -> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.du_isCommutativeMonoid_1244
              (T_IsAbelianGroup_1172 -> Any
forall a b. a -> b
coe T_IsAbelianGroup_1172
v0) in
    Any -> T_IsCommutativeMagma_214
forall a b. a -> b
coe
      ((T_IsCommutativeSemigroup_568 -> T_IsCommutativeMagma_214)
-> Any -> Any
forall a b. a -> b
coe
         T_IsCommutativeSemigroup_568 -> T_IsCommutativeMagma_214
MAlonzo.Code.Algebra.Structures.du_isCommutativeMagma_606
         ((T_IsCommutativeMonoid_764 -> T_IsCommutativeSemigroup_568)
-> Any -> Any
forall a b. a -> b
coe
            T_IsCommutativeMonoid_764 -> T_IsCommutativeSemigroup_568
MAlonzo.Code.Algebra.Structures.du_isCommutativeSemigroup_814
            (Any -> Any
forall a b. a -> b
coe Any
v1)))
-- Data.Bool.Properties._.IsAbelianGroup.isCommutativeMonoid
d_isCommutativeMonoid_332 ::
  (Bool -> Bool -> Bool) ->
  Bool ->
  (Bool -> Bool) ->
  MAlonzo.Code.Algebra.Structures.T_IsAbelianGroup_1172 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMonoid_764
d_isCommutativeMonoid_332 :: (Bool -> Bool -> Bool)
-> Bool
-> (Bool -> Bool)
-> T_IsAbelianGroup_1172
-> T_IsCommutativeMonoid_764
d_isCommutativeMonoid_332 Bool -> Bool -> Bool
v0 Bool
v1 Bool -> Bool
v2 T_IsAbelianGroup_1172
v3
  = (T_IsAbelianGroup_1172 -> T_IsCommutativeMonoid_764)
-> T_IsAbelianGroup_1172 -> T_IsCommutativeMonoid_764
forall a b. a -> b
coe
      T_IsAbelianGroup_1172 -> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.du_isCommutativeMonoid_1244 T_IsAbelianGroup_1172
v3
-- Data.Bool.Properties._.IsAbelianGroup.isCommutativeSemigroup
d_isCommutativeSemigroup_334 ::
  (Bool -> Bool -> Bool) ->
  Bool ->
  (Bool -> Bool) ->
  MAlonzo.Code.Algebra.Structures.T_IsAbelianGroup_1172 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_568
d_isCommutativeSemigroup_334 :: (Bool -> Bool -> Bool)
-> Bool
-> (Bool -> Bool)
-> T_IsAbelianGroup_1172
-> T_IsCommutativeSemigroup_568
d_isCommutativeSemigroup_334 ~Bool -> Bool -> Bool
v0 ~Bool
v1 ~Bool -> Bool
v2 T_IsAbelianGroup_1172
v3
  = T_IsAbelianGroup_1172 -> T_IsCommutativeSemigroup_568
du_isCommutativeSemigroup_334 T_IsAbelianGroup_1172
v3
du_isCommutativeSemigroup_334 ::
  MAlonzo.Code.Algebra.Structures.T_IsAbelianGroup_1172 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_568
du_isCommutativeSemigroup_334 :: T_IsAbelianGroup_1172 -> T_IsCommutativeSemigroup_568
du_isCommutativeSemigroup_334 T_IsAbelianGroup_1172
v0
  = (T_IsCommutativeMonoid_764 -> T_IsCommutativeSemigroup_568)
-> Any -> T_IsCommutativeSemigroup_568
forall a b. a -> b
coe
      T_IsCommutativeMonoid_764 -> T_IsCommutativeSemigroup_568
MAlonzo.Code.Algebra.Structures.du_isCommutativeSemigroup_814
      ((T_IsAbelianGroup_1172 -> T_IsCommutativeMonoid_764) -> Any -> Any
forall a b. a -> b
coe
         T_IsAbelianGroup_1172 -> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.du_isCommutativeMonoid_1244
         (T_IsAbelianGroup_1172 -> Any
forall a b. a -> b
coe T_IsAbelianGroup_1172
v0))
-- Data.Bool.Properties._.IsAbelianGroup.isEquivalence
d_isEquivalence_336 ::
  MAlonzo.Code.Algebra.Structures.T_IsAbelianGroup_1172 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
d_isEquivalence_336 :: T_IsAbelianGroup_1172 -> T_IsEquivalence_28
d_isEquivalence_336 T_IsAbelianGroup_1172
v0
  = (T_IsMagma_178 -> T_IsEquivalence_28) -> Any -> T_IsEquivalence_28
forall a b. a -> b
coe
      T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186
      ((T_IsSemigroup_488 -> T_IsMagma_178) -> Any -> Any
forall a b. a -> b
coe
         T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496
         ((T_IsMonoid_712 -> T_IsSemigroup_488) -> Any -> Any
forall a b. a -> b
coe
            T_IsMonoid_712 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_722
            ((T_IsGroup_1074 -> T_IsMonoid_712) -> Any -> Any
forall a b. a -> b
coe
               T_IsGroup_1074 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_1088
               ((T_IsAbelianGroup_1172 -> T_IsGroup_1074) -> Any -> Any
forall a b. a -> b
coe T_IsAbelianGroup_1172 -> T_IsGroup_1074
MAlonzo.Code.Algebra.Structures.d_isGroup_1184 (T_IsAbelianGroup_1172 -> Any
forall a b. a -> b
coe T_IsAbelianGroup_1172
v0)))))
-- Data.Bool.Properties._.IsAbelianGroup.isGroup
d_isGroup_338 ::
  MAlonzo.Code.Algebra.Structures.T_IsAbelianGroup_1172 ->
  MAlonzo.Code.Algebra.Structures.T_IsGroup_1074
d_isGroup_338 :: T_IsAbelianGroup_1172 -> T_IsGroup_1074
d_isGroup_338 T_IsAbelianGroup_1172
v0
  = (T_IsAbelianGroup_1172 -> T_IsGroup_1074) -> Any -> T_IsGroup_1074
forall a b. a -> b
coe T_IsAbelianGroup_1172 -> T_IsGroup_1074
MAlonzo.Code.Algebra.Structures.d_isGroup_1184 (T_IsAbelianGroup_1172 -> Any
forall a b. a -> b
coe T_IsAbelianGroup_1172
v0)
-- Data.Bool.Properties._.IsAbelianGroup.isInvertibleMagma
d_isInvertibleMagma_340 ::
  (Bool -> Bool -> Bool) ->
  Bool ->
  (Bool -> Bool) ->
  MAlonzo.Code.Algebra.Structures.T_IsAbelianGroup_1172 ->
  MAlonzo.Code.Algebra.Structures.T_IsInvertibleMagma_958
d_isInvertibleMagma_340 :: (Bool -> Bool -> Bool)
-> Bool
-> (Bool -> Bool)
-> T_IsAbelianGroup_1172
-> T_IsInvertibleMagma_958
d_isInvertibleMagma_340 ~Bool -> Bool -> Bool
v0 ~Bool
v1 ~Bool -> Bool
v2 T_IsAbelianGroup_1172
v3
  = T_IsAbelianGroup_1172 -> T_IsInvertibleMagma_958
du_isInvertibleMagma_340 T_IsAbelianGroup_1172
v3
du_isInvertibleMagma_340 ::
  MAlonzo.Code.Algebra.Structures.T_IsAbelianGroup_1172 ->
  MAlonzo.Code.Algebra.Structures.T_IsInvertibleMagma_958
du_isInvertibleMagma_340 :: T_IsAbelianGroup_1172 -> T_IsInvertibleMagma_958
du_isInvertibleMagma_340 T_IsAbelianGroup_1172
v0
  = (T_IsGroup_1074 -> T_IsInvertibleMagma_958)
-> Any -> T_IsInvertibleMagma_958
forall a b. a -> b
coe
      T_IsGroup_1074 -> T_IsInvertibleMagma_958
MAlonzo.Code.Algebra.Structures.du_isInvertibleMagma_1160
      ((T_IsAbelianGroup_1172 -> T_IsGroup_1074) -> Any -> Any
forall a b. a -> b
coe T_IsAbelianGroup_1172 -> T_IsGroup_1074
MAlonzo.Code.Algebra.Structures.d_isGroup_1184 (T_IsAbelianGroup_1172 -> Any
forall a b. a -> b
coe T_IsAbelianGroup_1172
v0))
-- Data.Bool.Properties._.IsAbelianGroup.isInvertibleUnitalMagma
d_isInvertibleUnitalMagma_342 ::
  (Bool -> Bool -> Bool) ->
  Bool ->
  (Bool -> Bool) ->
  MAlonzo.Code.Algebra.Structures.T_IsAbelianGroup_1172 ->
  MAlonzo.Code.Algebra.Structures.T_IsInvertibleUnitalMagma_1012
d_isInvertibleUnitalMagma_342 :: (Bool -> Bool -> Bool)
-> Bool
-> (Bool -> Bool)
-> T_IsAbelianGroup_1172
-> T_IsInvertibleUnitalMagma_1012
d_isInvertibleUnitalMagma_342 ~Bool -> Bool -> Bool
v0 ~Bool
v1 ~Bool -> Bool
v2 T_IsAbelianGroup_1172
v3
  = T_IsAbelianGroup_1172 -> T_IsInvertibleUnitalMagma_1012
du_isInvertibleUnitalMagma_342 T_IsAbelianGroup_1172
v3
du_isInvertibleUnitalMagma_342 ::
  MAlonzo.Code.Algebra.Structures.T_IsAbelianGroup_1172 ->
  MAlonzo.Code.Algebra.Structures.T_IsInvertibleUnitalMagma_1012
du_isInvertibleUnitalMagma_342 :: T_IsAbelianGroup_1172 -> T_IsInvertibleUnitalMagma_1012
du_isInvertibleUnitalMagma_342 T_IsAbelianGroup_1172
v0
  = (T_IsGroup_1074 -> T_IsInvertibleUnitalMagma_1012)
-> Any -> T_IsInvertibleUnitalMagma_1012
forall a b. a -> b
coe
      T_IsGroup_1074 -> T_IsInvertibleUnitalMagma_1012
MAlonzo.Code.Algebra.Structures.du_isInvertibleUnitalMagma_1162
      ((T_IsAbelianGroup_1172 -> T_IsGroup_1074) -> Any -> Any
forall a b. a -> b
coe T_IsAbelianGroup_1172 -> T_IsGroup_1074
MAlonzo.Code.Algebra.Structures.d_isGroup_1184 (T_IsAbelianGroup_1172 -> Any
forall a b. a -> b
coe T_IsAbelianGroup_1172
v0))
-- Data.Bool.Properties._.IsAbelianGroup.isMagma
d_isMagma_344 ::
  MAlonzo.Code.Algebra.Structures.T_IsAbelianGroup_1172 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_178
d_isMagma_344 :: T_IsAbelianGroup_1172 -> T_IsMagma_178
d_isMagma_344 T_IsAbelianGroup_1172
v0
  = (T_IsSemigroup_488 -> T_IsMagma_178) -> Any -> T_IsMagma_178
forall a b. a -> b
coe
      T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496
      ((T_IsMonoid_712 -> T_IsSemigroup_488) -> Any -> Any
forall a b. a -> b
coe
         T_IsMonoid_712 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_722
         ((T_IsGroup_1074 -> T_IsMonoid_712) -> Any -> Any
forall a b. a -> b
coe
            T_IsGroup_1074 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_1088
            ((T_IsAbelianGroup_1172 -> T_IsGroup_1074) -> Any -> Any
forall a b. a -> b
coe T_IsAbelianGroup_1172 -> T_IsGroup_1074
MAlonzo.Code.Algebra.Structures.d_isGroup_1184 (T_IsAbelianGroup_1172 -> Any
forall a b. a -> b
coe T_IsAbelianGroup_1172
v0))))
-- Data.Bool.Properties._.IsAbelianGroup.isMonoid
d_isMonoid_346 ::
  MAlonzo.Code.Algebra.Structures.T_IsAbelianGroup_1172 ->
  MAlonzo.Code.Algebra.Structures.T_IsMonoid_712
d_isMonoid_346 :: T_IsAbelianGroup_1172 -> T_IsMonoid_712
d_isMonoid_346 T_IsAbelianGroup_1172
v0
  = (T_IsGroup_1074 -> T_IsMonoid_712) -> Any -> T_IsMonoid_712
forall a b. a -> b
coe
      T_IsGroup_1074 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_1088
      ((T_IsAbelianGroup_1172 -> T_IsGroup_1074) -> Any -> Any
forall a b. a -> b
coe T_IsAbelianGroup_1172 -> T_IsGroup_1074
MAlonzo.Code.Algebra.Structures.d_isGroup_1184 (T_IsAbelianGroup_1172 -> Any
forall a b. a -> b
coe T_IsAbelianGroup_1172
v0))
-- Data.Bool.Properties._.IsAbelianGroup.isPartialEquivalence
d_isPartialEquivalence_348 ::
  (Bool -> Bool -> Bool) ->
  Bool ->
  (Bool -> Bool) ->
  MAlonzo.Code.Algebra.Structures.T_IsAbelianGroup_1172 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_348 :: (Bool -> Bool -> Bool)
-> Bool
-> (Bool -> Bool)
-> T_IsAbelianGroup_1172
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_348 ~Bool -> Bool -> Bool
v0 ~Bool
v1 ~Bool -> Bool
v2 T_IsAbelianGroup_1172
v3
  = T_IsAbelianGroup_1172 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_348 T_IsAbelianGroup_1172
v3
du_isPartialEquivalence_348 ::
  MAlonzo.Code.Algebra.Structures.T_IsAbelianGroup_1172 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_348 :: T_IsAbelianGroup_1172 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_348 T_IsAbelianGroup_1172
v0
  = let v1 :: T_IsGroup_1074
v1
          = T_IsAbelianGroup_1172 -> T_IsGroup_1074
MAlonzo.Code.Algebra.Structures.d_isGroup_1184 (T_IsAbelianGroup_1172 -> T_IsAbelianGroup_1172
forall a b. a -> b
coe T_IsAbelianGroup_1172
v0) in
    Any -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsMonoid_712
v2
             = T_IsGroup_1074 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_1088 (T_IsGroup_1074 -> T_IsGroup_1074
forall a b. a -> b
coe T_IsGroup_1074
v1) in
       Any -> Any
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_488
v3
                = T_IsMonoid_712 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_722 (T_IsMonoid_712 -> T_IsMonoid_712
forall a b. a -> b
coe T_IsMonoid_712
v2) in
          Any -> Any
forall a b. a -> b
coe
            (let v4 :: T_IsMagma_178
v4 = T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496 (T_IsSemigroup_488 -> T_IsSemigroup_488
forall a b. a -> b
coe T_IsSemigroup_488
v3) in
             Any -> Any
forall a b. a -> b
coe
               ((T_IsEquivalence_28 -> T_IsPartialEquivalence_16) -> Any -> Any
forall a b. a -> b
coe
                  T_IsEquivalence_28 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_44
                  ((T_IsMagma_178 -> T_IsEquivalence_28) -> Any -> Any
forall a b. a -> b
coe
                     T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186 (T_IsMagma_178 -> Any
forall a b. a -> b
coe T_IsMagma_178
v4))))))
-- Data.Bool.Properties._.IsAbelianGroup.isSemigroup
d_isSemigroup_350 ::
  MAlonzo.Code.Algebra.Structures.T_IsAbelianGroup_1172 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_488
d_isSemigroup_350 :: T_IsAbelianGroup_1172 -> T_IsSemigroup_488
d_isSemigroup_350 T_IsAbelianGroup_1172
v0
  = (T_IsMonoid_712 -> T_IsSemigroup_488) -> Any -> T_IsSemigroup_488
forall a b. a -> b
coe
      T_IsMonoid_712 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_722
      ((T_IsGroup_1074 -> T_IsMonoid_712) -> Any -> Any
forall a b. a -> b
coe
         T_IsGroup_1074 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_1088
         ((T_IsAbelianGroup_1172 -> T_IsGroup_1074) -> Any -> Any
forall a b. a -> b
coe T_IsAbelianGroup_1172 -> T_IsGroup_1074
MAlonzo.Code.Algebra.Structures.d_isGroup_1184 (T_IsAbelianGroup_1172 -> Any
forall a b. a -> b
coe T_IsAbelianGroup_1172
v0)))
-- Data.Bool.Properties._.IsAbelianGroup.isUnitalMagma
d_isUnitalMagma_352 ::
  (Bool -> Bool -> Bool) ->
  Bool ->
  (Bool -> Bool) ->
  MAlonzo.Code.Algebra.Structures.T_IsAbelianGroup_1172 ->
  MAlonzo.Code.Algebra.Structures.T_IsUnitalMagma_666
d_isUnitalMagma_352 :: (Bool -> Bool -> Bool)
-> Bool
-> (Bool -> Bool)
-> T_IsAbelianGroup_1172
-> T_IsUnitalMagma_666
d_isUnitalMagma_352 ~Bool -> Bool -> Bool
v0 ~Bool
v1 ~Bool -> Bool
v2 T_IsAbelianGroup_1172
v3 = T_IsAbelianGroup_1172 -> T_IsUnitalMagma_666
du_isUnitalMagma_352 T_IsAbelianGroup_1172
v3
du_isUnitalMagma_352 ::
  MAlonzo.Code.Algebra.Structures.T_IsAbelianGroup_1172 ->
  MAlonzo.Code.Algebra.Structures.T_IsUnitalMagma_666
du_isUnitalMagma_352 :: T_IsAbelianGroup_1172 -> T_IsUnitalMagma_666
du_isUnitalMagma_352 T_IsAbelianGroup_1172
v0
  = let v1 :: T_IsGroup_1074
v1
          = T_IsAbelianGroup_1172 -> T_IsGroup_1074
MAlonzo.Code.Algebra.Structures.d_isGroup_1184 (T_IsAbelianGroup_1172 -> T_IsAbelianGroup_1172
forall a b. a -> b
coe T_IsAbelianGroup_1172
v0) in
    Any -> T_IsUnitalMagma_666
forall a b. a -> b
coe
      ((T_IsMonoid_712 -> T_IsUnitalMagma_666) -> Any -> Any
forall a b. a -> b
coe
         T_IsMonoid_712 -> T_IsUnitalMagma_666
MAlonzo.Code.Algebra.Structures.du_isUnitalMagma_756
         ((T_IsGroup_1074 -> T_IsMonoid_712) -> Any -> Any
forall a b. a -> b
coe T_IsGroup_1074 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_1088 (T_IsGroup_1074 -> Any
forall a b. a -> b
coe T_IsGroup_1074
v1)))
-- Data.Bool.Properties._.IsAbelianGroup.refl
d_refl_354 ::
  MAlonzo.Code.Algebra.Structures.T_IsAbelianGroup_1172 ->
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_refl_354 :: T_IsAbelianGroup_1172 -> Bool -> T__'8801'__12
d_refl_354 = T_IsAbelianGroup_1172 -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsAbelianGroup.reflexive
d_reflexive_356 ::
  (Bool -> Bool -> Bool) ->
  Bool ->
  (Bool -> Bool) ->
  MAlonzo.Code.Algebra.Structures.T_IsAbelianGroup_1172 ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_reflexive_356 :: (Bool -> Bool -> Bool)
-> Bool
-> (Bool -> Bool)
-> T_IsAbelianGroup_1172
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_reflexive_356 = (Bool -> Bool -> Bool)
-> Bool
-> (Bool -> Bool)
-> T_IsAbelianGroup_1172
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsAbelianGroup.setoid
d_setoid_358 ::
  (Bool -> Bool -> Bool) ->
  Bool ->
  (Bool -> Bool) ->
  MAlonzo.Code.Algebra.Structures.T_IsAbelianGroup_1172 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
d_setoid_358 :: (Bool -> Bool -> Bool)
-> Bool -> (Bool -> Bool) -> T_IsAbelianGroup_1172 -> T_Setoid_46
d_setoid_358 ~Bool -> Bool -> Bool
v0 ~Bool
v1 ~Bool -> Bool
v2 T_IsAbelianGroup_1172
v3 = T_IsAbelianGroup_1172 -> T_Setoid_46
du_setoid_358 T_IsAbelianGroup_1172
v3
du_setoid_358 ::
  MAlonzo.Code.Algebra.Structures.T_IsAbelianGroup_1172 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
du_setoid_358 :: T_IsAbelianGroup_1172 -> T_Setoid_46
du_setoid_358 T_IsAbelianGroup_1172
v0
  = let v1 :: T_IsGroup_1074
v1
          = T_IsAbelianGroup_1172 -> T_IsGroup_1074
MAlonzo.Code.Algebra.Structures.d_isGroup_1184 (T_IsAbelianGroup_1172 -> T_IsAbelianGroup_1172
forall a b. a -> b
coe T_IsAbelianGroup_1172
v0) in
    Any -> T_Setoid_46
forall a b. a -> b
coe
      (let v2 :: T_IsMonoid_712
v2
             = T_IsGroup_1074 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_1088 (T_IsGroup_1074 -> T_IsGroup_1074
forall a b. a -> b
coe T_IsGroup_1074
v1) in
       Any -> Any
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_488
v3
                = T_IsMonoid_712 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_722 (T_IsMonoid_712 -> T_IsMonoid_712
forall a b. a -> b
coe T_IsMonoid_712
v2) in
          Any -> Any
forall a b. a -> b
coe
            ((T_IsMagma_178 -> T_Setoid_46) -> Any -> Any
forall a b. a -> b
coe
               T_IsMagma_178 -> T_Setoid_46
MAlonzo.Code.Algebra.Structures.du_setoid_202
               ((T_IsSemigroup_488 -> T_IsMagma_178) -> Any -> Any
forall a b. a -> b
coe T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496 (T_IsSemigroup_488 -> Any
forall a b. a -> b
coe T_IsSemigroup_488
v3)))))
-- Data.Bool.Properties._.IsAbelianGroup.sym
d_sym_360 ::
  MAlonzo.Code.Algebra.Structures.T_IsAbelianGroup_1172 ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_sym_360 :: T_IsAbelianGroup_1172
-> Bool -> Bool -> T__'8801'__12 -> T__'8801'__12
d_sym_360 = T_IsAbelianGroup_1172
-> Bool -> Bool -> T__'8801'__12 -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsAbelianGroup.trans
d_trans_362 ::
  MAlonzo.Code.Algebra.Structures.T_IsAbelianGroup_1172 ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_trans_362 :: T_IsAbelianGroup_1172
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
d_trans_362 = T_IsAbelianGroup_1172
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsAbelianGroup.uniqueʳ-⁻¹
d_unique'691''45''8315''185'_364 ::
  (Bool -> Bool -> Bool) ->
  Bool ->
  (Bool -> Bool) ->
  MAlonzo.Code.Algebra.Structures.T_IsAbelianGroup_1172 ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_unique'691''45''8315''185'_364 :: (Bool -> Bool -> Bool)
-> Bool
-> (Bool -> Bool)
-> T_IsAbelianGroup_1172
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_unique'691''45''8315''185'_364 = (Bool -> Bool -> Bool)
-> Bool
-> (Bool -> Bool)
-> T_IsAbelianGroup_1172
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsAbelianGroup.uniqueˡ-⁻¹
d_unique'737''45''8315''185'_366 ::
  (Bool -> Bool -> Bool) ->
  Bool ->
  (Bool -> Bool) ->
  MAlonzo.Code.Algebra.Structures.T_IsAbelianGroup_1172 ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_unique'737''45''8315''185'_366 :: (Bool -> Bool -> Bool)
-> Bool
-> (Bool -> Bool)
-> T_IsAbelianGroup_1172
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_unique'737''45''8315''185'_366 = (Bool -> Bool -> Bool)
-> Bool
-> (Bool -> Bool)
-> T_IsAbelianGroup_1172
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsAbelianGroup.⁻¹-cong
d_'8315''185''45'cong_368 ::
  MAlonzo.Code.Algebra.Structures.T_IsAbelianGroup_1172 ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8315''185''45'cong_368 :: T_IsAbelianGroup_1172
-> Bool -> Bool -> T__'8801'__12 -> T__'8801'__12
d_'8315''185''45'cong_368 = T_IsAbelianGroup_1172
-> Bool -> Bool -> T__'8801'__12 -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsAbelianGroup.∙-cong
d_'8729''45'cong_370 ::
  MAlonzo.Code.Algebra.Structures.T_IsAbelianGroup_1172 ->
  Bool ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8729''45'cong_370 :: T_IsAbelianGroup_1172
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong_370 = T_IsAbelianGroup_1172
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsAbelianGroup.∙-congʳ
d_'8729''45'cong'691'_372 ::
  (Bool -> Bool -> Bool) ->
  Bool ->
  (Bool -> Bool) ->
  MAlonzo.Code.Algebra.Structures.T_IsAbelianGroup_1172 ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8729''45'cong'691'_372 :: (Bool -> Bool -> Bool)
-> Bool
-> (Bool -> Bool)
-> T_IsAbelianGroup_1172
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong'691'_372 = (Bool -> Bool -> Bool)
-> Bool
-> (Bool -> Bool)
-> T_IsAbelianGroup_1172
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsAbelianGroup.∙-congˡ
d_'8729''45'cong'737'_374 ::
  (Bool -> Bool -> Bool) ->
  Bool ->
  (Bool -> Bool) ->
  MAlonzo.Code.Algebra.Structures.T_IsAbelianGroup_1172 ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8729''45'cong'737'_374 :: (Bool -> Bool -> Bool)
-> Bool
-> (Bool -> Bool)
-> T_IsAbelianGroup_1172
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong'737'_374 = (Bool -> Bool -> Bool)
-> Bool
-> (Bool -> Bool)
-> T_IsAbelianGroup_1172
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsAlternativeMagma.alter
d_alter_378 ::
  MAlonzo.Code.Algebra.Structures.T_IsAlternativeMagma_290 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_alter_378 :: T_IsAlternativeMagma_290 -> T_Σ_14
d_alter_378 T_IsAlternativeMagma_290
v0
  = (T_IsAlternativeMagma_290 -> T_Σ_14) -> Any -> T_Σ_14
forall a b. a -> b
coe T_IsAlternativeMagma_290 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_alter_300 (T_IsAlternativeMagma_290 -> Any
forall a b. a -> b
coe T_IsAlternativeMagma_290
v0)
-- Data.Bool.Properties._.IsAlternativeMagma.alternativeʳ
d_alternative'691'_380 ::
  (Bool -> Bool -> Bool) ->
  MAlonzo.Code.Algebra.Structures.T_IsAlternativeMagma_290 ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_alternative'691'_380 :: (Bool -> Bool -> Bool)
-> T_IsAlternativeMagma_290 -> Bool -> Bool -> T__'8801'__12
d_alternative'691'_380 = (Bool -> Bool -> Bool)
-> T_IsAlternativeMagma_290 -> Bool -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsAlternativeMagma.alternativeˡ
d_alternative'737'_382 ::
  (Bool -> Bool -> Bool) ->
  MAlonzo.Code.Algebra.Structures.T_IsAlternativeMagma_290 ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_alternative'737'_382 :: (Bool -> Bool -> Bool)
-> T_IsAlternativeMagma_290 -> Bool -> Bool -> T__'8801'__12
d_alternative'737'_382 = (Bool -> Bool -> Bool)
-> T_IsAlternativeMagma_290 -> Bool -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsAlternativeMagma.isEquivalence
d_isEquivalence_384 ::
  MAlonzo.Code.Algebra.Structures.T_IsAlternativeMagma_290 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
d_isEquivalence_384 :: T_IsAlternativeMagma_290 -> T_IsEquivalence_28
d_isEquivalence_384 T_IsAlternativeMagma_290
v0
  = (T_IsMagma_178 -> T_IsEquivalence_28) -> Any -> T_IsEquivalence_28
forall a b. a -> b
coe
      T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186
      ((T_IsAlternativeMagma_290 -> T_IsMagma_178) -> Any -> Any
forall a b. a -> b
coe T_IsAlternativeMagma_290 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_298 (T_IsAlternativeMagma_290 -> Any
forall a b. a -> b
coe T_IsAlternativeMagma_290
v0))
-- Data.Bool.Properties._.IsAlternativeMagma.isMagma
d_isMagma_386 ::
  MAlonzo.Code.Algebra.Structures.T_IsAlternativeMagma_290 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_178
d_isMagma_386 :: T_IsAlternativeMagma_290 -> T_IsMagma_178
d_isMagma_386 T_IsAlternativeMagma_290
v0
  = (T_IsAlternativeMagma_290 -> T_IsMagma_178) -> Any -> T_IsMagma_178
forall a b. a -> b
coe T_IsAlternativeMagma_290 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_298 (T_IsAlternativeMagma_290 -> Any
forall a b. a -> b
coe T_IsAlternativeMagma_290
v0)
-- Data.Bool.Properties._.IsAlternativeMagma.isPartialEquivalence
d_isPartialEquivalence_388 ::
  (Bool -> Bool -> Bool) ->
  MAlonzo.Code.Algebra.Structures.T_IsAlternativeMagma_290 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_388 :: (Bool -> Bool -> Bool)
-> T_IsAlternativeMagma_290 -> T_IsPartialEquivalence_16
d_isPartialEquivalence_388 ~Bool -> Bool -> Bool
v0 T_IsAlternativeMagma_290
v1 = T_IsAlternativeMagma_290 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_388 T_IsAlternativeMagma_290
v1
du_isPartialEquivalence_388 ::
  MAlonzo.Code.Algebra.Structures.T_IsAlternativeMagma_290 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_388 :: T_IsAlternativeMagma_290 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_388 T_IsAlternativeMagma_290
v0
  = let v1 :: T_IsMagma_178
v1
          = T_IsAlternativeMagma_290 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_298 (T_IsAlternativeMagma_290 -> T_IsAlternativeMagma_290
forall a b. a -> b
coe T_IsAlternativeMagma_290
v0) in
    Any -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      ((T_IsEquivalence_28 -> T_IsPartialEquivalence_16) -> Any -> Any
forall a b. a -> b
coe
         T_IsEquivalence_28 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_44
         ((T_IsMagma_178 -> T_IsEquivalence_28) -> Any -> Any
forall a b. a -> b
coe T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186 (T_IsMagma_178 -> Any
forall a b. a -> b
coe T_IsMagma_178
v1)))
-- Data.Bool.Properties._.IsAlternativeMagma.refl
d_refl_390 ::
  MAlonzo.Code.Algebra.Structures.T_IsAlternativeMagma_290 ->
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_refl_390 :: T_IsAlternativeMagma_290 -> Bool -> T__'8801'__12
d_refl_390 = T_IsAlternativeMagma_290 -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsAlternativeMagma.reflexive
d_reflexive_392 ::
  (Bool -> Bool -> Bool) ->
  MAlonzo.Code.Algebra.Structures.T_IsAlternativeMagma_290 ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_reflexive_392 :: (Bool -> Bool -> Bool)
-> T_IsAlternativeMagma_290
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_reflexive_392 = (Bool -> Bool -> Bool)
-> T_IsAlternativeMagma_290
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsAlternativeMagma.setoid
d_setoid_394 ::
  (Bool -> Bool -> Bool) ->
  MAlonzo.Code.Algebra.Structures.T_IsAlternativeMagma_290 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
d_setoid_394 :: (Bool -> Bool -> Bool) -> T_IsAlternativeMagma_290 -> T_Setoid_46
d_setoid_394 ~Bool -> Bool -> Bool
v0 T_IsAlternativeMagma_290
v1 = T_IsAlternativeMagma_290 -> T_Setoid_46
du_setoid_394 T_IsAlternativeMagma_290
v1
du_setoid_394 ::
  MAlonzo.Code.Algebra.Structures.T_IsAlternativeMagma_290 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
du_setoid_394 :: T_IsAlternativeMagma_290 -> T_Setoid_46
du_setoid_394 T_IsAlternativeMagma_290
v0
  = (T_IsMagma_178 -> T_Setoid_46) -> Any -> T_Setoid_46
forall a b. a -> b
coe
      T_IsMagma_178 -> T_Setoid_46
MAlonzo.Code.Algebra.Structures.du_setoid_202
      ((T_IsAlternativeMagma_290 -> T_IsMagma_178) -> Any -> Any
forall a b. a -> b
coe T_IsAlternativeMagma_290 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_298 (T_IsAlternativeMagma_290 -> Any
forall a b. a -> b
coe T_IsAlternativeMagma_290
v0))
-- Data.Bool.Properties._.IsAlternativeMagma.sym
d_sym_396 ::
  MAlonzo.Code.Algebra.Structures.T_IsAlternativeMagma_290 ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_sym_396 :: T_IsAlternativeMagma_290
-> Bool -> Bool -> T__'8801'__12 -> T__'8801'__12
d_sym_396 = T_IsAlternativeMagma_290
-> Bool -> Bool -> T__'8801'__12 -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsAlternativeMagma.trans
d_trans_398 ::
  MAlonzo.Code.Algebra.Structures.T_IsAlternativeMagma_290 ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_trans_398 :: T_IsAlternativeMagma_290
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
d_trans_398 = T_IsAlternativeMagma_290
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsAlternativeMagma.∙-cong
d_'8729''45'cong_400 ::
  MAlonzo.Code.Algebra.Structures.T_IsAlternativeMagma_290 ->
  Bool ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8729''45'cong_400 :: T_IsAlternativeMagma_290
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong_400 = T_IsAlternativeMagma_290
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsAlternativeMagma.∙-congʳ
d_'8729''45'cong'691'_402 ::
  (Bool -> Bool -> Bool) ->
  MAlonzo.Code.Algebra.Structures.T_IsAlternativeMagma_290 ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8729''45'cong'691'_402 :: (Bool -> Bool -> Bool)
-> T_IsAlternativeMagma_290
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong'691'_402 = (Bool -> Bool -> Bool)
-> T_IsAlternativeMagma_290
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsAlternativeMagma.∙-congˡ
d_'8729''45'cong'737'_404 ::
  (Bool -> Bool -> Bool) ->
  MAlonzo.Code.Algebra.Structures.T_IsAlternativeMagma_290 ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8729''45'cong'737'_404 :: (Bool -> Bool -> Bool)
-> T_IsAlternativeMagma_290
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong'737'_404 = (Bool -> Bool -> Bool)
-> T_IsAlternativeMagma_290
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsBand.assoc
d_assoc_408 ::
  MAlonzo.Code.Algebra.Structures.T_IsBand_526 ->
  Bool ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_assoc_408 :: T_IsBand_526 -> Bool -> Bool -> Bool -> T__'8801'__12
d_assoc_408 = T_IsBand_526 -> Bool -> Bool -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsBand.idem
d_idem_410 ::
  MAlonzo.Code.Algebra.Structures.T_IsBand_526 ->
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_idem_410 :: T_IsBand_526 -> Bool -> T__'8801'__12
d_idem_410 = T_IsBand_526 -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsBand.isEquivalence
d_isEquivalence_412 ::
  MAlonzo.Code.Algebra.Structures.T_IsBand_526 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
d_isEquivalence_412 :: T_IsBand_526 -> T_IsEquivalence_28
d_isEquivalence_412 T_IsBand_526
v0
  = (T_IsMagma_178 -> T_IsEquivalence_28) -> Any -> T_IsEquivalence_28
forall a b. a -> b
coe
      T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186
      ((T_IsSemigroup_488 -> T_IsMagma_178) -> Any -> Any
forall a b. a -> b
coe
         T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496
         ((T_IsBand_526 -> T_IsSemigroup_488) -> Any -> Any
forall a b. a -> b
coe T_IsBand_526 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_534 (T_IsBand_526 -> Any
forall a b. a -> b
coe T_IsBand_526
v0)))
-- Data.Bool.Properties._.IsBand.isMagma
d_isMagma_414 ::
  MAlonzo.Code.Algebra.Structures.T_IsBand_526 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_178
d_isMagma_414 :: T_IsBand_526 -> T_IsMagma_178
d_isMagma_414 T_IsBand_526
v0
  = (T_IsSemigroup_488 -> T_IsMagma_178) -> Any -> T_IsMagma_178
forall a b. a -> b
coe
      T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496
      ((T_IsBand_526 -> T_IsSemigroup_488) -> Any -> Any
forall a b. a -> b
coe T_IsBand_526 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_534 (T_IsBand_526 -> Any
forall a b. a -> b
coe T_IsBand_526
v0))
-- Data.Bool.Properties._.IsBand.isPartialEquivalence
d_isPartialEquivalence_416 ::
  (Bool -> Bool -> Bool) ->
  MAlonzo.Code.Algebra.Structures.T_IsBand_526 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_416 :: (Bool -> Bool -> Bool) -> T_IsBand_526 -> T_IsPartialEquivalence_16
d_isPartialEquivalence_416 ~Bool -> Bool -> Bool
v0 T_IsBand_526
v1 = T_IsBand_526 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_416 T_IsBand_526
v1
du_isPartialEquivalence_416 ::
  MAlonzo.Code.Algebra.Structures.T_IsBand_526 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_416 :: T_IsBand_526 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_416 T_IsBand_526
v0
  = let v1 :: T_IsSemigroup_488
v1
          = T_IsBand_526 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_534 (T_IsBand_526 -> T_IsBand_526
forall a b. a -> b
coe T_IsBand_526
v0) in
    Any -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsMagma_178
v2 = T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496 (T_IsSemigroup_488 -> T_IsSemigroup_488
forall a b. a -> b
coe T_IsSemigroup_488
v1) in
       Any -> Any
forall a b. a -> b
coe
         ((T_IsEquivalence_28 -> T_IsPartialEquivalence_16) -> Any -> Any
forall a b. a -> b
coe
            T_IsEquivalence_28 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_44
            ((T_IsMagma_178 -> T_IsEquivalence_28) -> Any -> Any
forall a b. a -> b
coe
               T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186 (T_IsMagma_178 -> Any
forall a b. a -> b
coe T_IsMagma_178
v2))))
-- Data.Bool.Properties._.IsBand.isSemigroup
d_isSemigroup_418 ::
  MAlonzo.Code.Algebra.Structures.T_IsBand_526 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_488
d_isSemigroup_418 :: T_IsBand_526 -> T_IsSemigroup_488
d_isSemigroup_418 T_IsBand_526
v0
  = (T_IsBand_526 -> T_IsSemigroup_488) -> Any -> T_IsSemigroup_488
forall a b. a -> b
coe T_IsBand_526 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_534 (T_IsBand_526 -> Any
forall a b. a -> b
coe T_IsBand_526
v0)
-- Data.Bool.Properties._.IsBand.refl
d_refl_420 ::
  MAlonzo.Code.Algebra.Structures.T_IsBand_526 ->
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_refl_420 :: T_IsBand_526 -> Bool -> T__'8801'__12
d_refl_420 = T_IsBand_526 -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsBand.reflexive
d_reflexive_422 ::
  (Bool -> Bool -> Bool) ->
  MAlonzo.Code.Algebra.Structures.T_IsBand_526 ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_reflexive_422 :: (Bool -> Bool -> Bool)
-> T_IsBand_526 -> Bool -> Bool -> T__'8801'__12 -> T__'8801'__12
d_reflexive_422 = (Bool -> Bool -> Bool)
-> T_IsBand_526 -> Bool -> Bool -> T__'8801'__12 -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsBand.setoid
d_setoid_424 ::
  (Bool -> Bool -> Bool) ->
  MAlonzo.Code.Algebra.Structures.T_IsBand_526 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
d_setoid_424 :: (Bool -> Bool -> Bool) -> T_IsBand_526 -> T_Setoid_46
d_setoid_424 ~Bool -> Bool -> Bool
v0 T_IsBand_526
v1 = T_IsBand_526 -> T_Setoid_46
du_setoid_424 T_IsBand_526
v1
du_setoid_424 ::
  MAlonzo.Code.Algebra.Structures.T_IsBand_526 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
du_setoid_424 :: T_IsBand_526 -> T_Setoid_46
du_setoid_424 T_IsBand_526
v0
  = let v1 :: T_IsSemigroup_488
v1
          = T_IsBand_526 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_534 (T_IsBand_526 -> T_IsBand_526
forall a b. a -> b
coe T_IsBand_526
v0) in
    Any -> T_Setoid_46
forall a b. a -> b
coe
      ((T_IsMagma_178 -> T_Setoid_46) -> Any -> Any
forall a b. a -> b
coe
         T_IsMagma_178 -> T_Setoid_46
MAlonzo.Code.Algebra.Structures.du_setoid_202
         ((T_IsSemigroup_488 -> T_IsMagma_178) -> Any -> Any
forall a b. a -> b
coe T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496 (T_IsSemigroup_488 -> Any
forall a b. a -> b
coe T_IsSemigroup_488
v1)))
-- Data.Bool.Properties._.IsBand.sym
d_sym_426 ::
  MAlonzo.Code.Algebra.Structures.T_IsBand_526 ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_sym_426 :: T_IsBand_526 -> Bool -> Bool -> T__'8801'__12 -> T__'8801'__12
d_sym_426 = T_IsBand_526 -> Bool -> Bool -> T__'8801'__12 -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsBand.trans
d_trans_428 ::
  MAlonzo.Code.Algebra.Structures.T_IsBand_526 ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_trans_428 :: T_IsBand_526
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
d_trans_428 = T_IsBand_526
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsBand.∙-cong
d_'8729''45'cong_430 ::
  MAlonzo.Code.Algebra.Structures.T_IsBand_526 ->
  Bool ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8729''45'cong_430 :: T_IsBand_526
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong_430 = T_IsBand_526
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsBand.∙-congʳ
d_'8729''45'cong'691'_432 ::
  (Bool -> Bool -> Bool) ->
  MAlonzo.Code.Algebra.Structures.T_IsBand_526 ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8729''45'cong'691'_432 :: (Bool -> Bool -> Bool)
-> T_IsBand_526
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong'691'_432 = (Bool -> Bool -> Bool)
-> T_IsBand_526
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsBand.∙-congˡ
d_'8729''45'cong'737'_434 ::
  (Bool -> Bool -> Bool) ->
  MAlonzo.Code.Algebra.Structures.T_IsBand_526 ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8729''45'cong'737'_434 :: (Bool -> Bool -> Bool)
-> T_IsBand_526
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong'737'_434 = (Bool -> Bool -> Bool)
-> T_IsBand_526
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsCancellativeCommutativeSemiring.*-assoc
d_'42''45'assoc_438 ::
  MAlonzo.Code.Algebra.Structures.T_IsCancellativeCommutativeSemiring_1872 ->
  Bool ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'42''45'assoc_438 :: T_IsCancellativeCommutativeSemiring_1872
-> Bool -> Bool -> Bool -> T__'8801'__12
d_'42''45'assoc_438 = T_IsCancellativeCommutativeSemiring_1872
-> Bool -> Bool -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsCancellativeCommutativeSemiring.*-cancelʳ-nonZero
d_'42''45'cancel'691''45'nonZero_440 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsCancellativeCommutativeSemiring_1872 ->
  Bool ->
  Bool ->
  Bool ->
  (MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
   MAlonzo.Code.Data.Irrelevant.T_Irrelevant_20) ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'42''45'cancel'691''45'nonZero_440 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> T_IsCancellativeCommutativeSemiring_1872
-> Bool
-> Bool
-> Bool
-> (T__'8801'__12 -> T_Irrelevant_20)
-> T__'8801'__12
-> T__'8801'__12
d_'42''45'cancel'691''45'nonZero_440 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> T_IsCancellativeCommutativeSemiring_1872
-> Bool
-> Bool
-> Bool
-> (T__'8801'__12 -> T_Irrelevant_20)
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsCancellativeCommutativeSemiring.*-cancelˡ-nonZero
d_'42''45'cancel'737''45'nonZero_442 ::
  MAlonzo.Code.Algebra.Structures.T_IsCancellativeCommutativeSemiring_1872 ->
  Bool ->
  Bool ->
  Bool ->
  (MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
   MAlonzo.Code.Data.Irrelevant.T_Irrelevant_20) ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'42''45'cancel'737''45'nonZero_442 :: T_IsCancellativeCommutativeSemiring_1872
-> Bool
-> Bool
-> Bool
-> (T__'8801'__12 -> T_Irrelevant_20)
-> T__'8801'__12
-> T__'8801'__12
d_'42''45'cancel'737''45'nonZero_442 = T_IsCancellativeCommutativeSemiring_1872
-> Bool
-> Bool
-> Bool
-> (T__'8801'__12 -> T_Irrelevant_20)
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsCancellativeCommutativeSemiring.*-comm
d_'42''45'comm_444 ::
  MAlonzo.Code.Algebra.Structures.T_IsCancellativeCommutativeSemiring_1872 ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'42''45'comm_444 :: T_IsCancellativeCommutativeSemiring_1872
-> Bool -> Bool -> T__'8801'__12
d_'42''45'comm_444 = T_IsCancellativeCommutativeSemiring_1872
-> Bool -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsCancellativeCommutativeSemiring.*-cong
d_'42''45'cong_446 ::
  MAlonzo.Code.Algebra.Structures.T_IsCancellativeCommutativeSemiring_1872 ->
  Bool ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'42''45'cong_446 :: T_IsCancellativeCommutativeSemiring_1872
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
d_'42''45'cong_446 = T_IsCancellativeCommutativeSemiring_1872
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsCancellativeCommutativeSemiring.∙-congʳ
d_'8729''45'cong'691'_448 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsCancellativeCommutativeSemiring_1872 ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8729''45'cong'691'_448 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> T_IsCancellativeCommutativeSemiring_1872
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong'691'_448 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> T_IsCancellativeCommutativeSemiring_1872
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsCancellativeCommutativeSemiring.∙-congˡ
d_'8729''45'cong'737'_450 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsCancellativeCommutativeSemiring_1872 ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8729''45'cong'737'_450 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> T_IsCancellativeCommutativeSemiring_1872
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong'737'_450 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> T_IsCancellativeCommutativeSemiring_1872
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsCancellativeCommutativeSemiring.*-identity
d_'42''45'identity_452 ::
  MAlonzo.Code.Algebra.Structures.T_IsCancellativeCommutativeSemiring_1872 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'42''45'identity_452 :: T_IsCancellativeCommutativeSemiring_1872 -> T_Σ_14
d_'42''45'identity_452 T_IsCancellativeCommutativeSemiring_1872
v0
  = (T_IsSemiringWithoutAnnihilatingZero_1536 -> T_Σ_14)
-> Any -> T_Σ_14
forall a b. a -> b
coe
      T_IsSemiringWithoutAnnihilatingZero_1536 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_'42''45'identity_1562
      ((T_IsSemiring_1640 -> T_IsSemiringWithoutAnnihilatingZero_1536)
-> Any -> Any
forall a b. a -> b
coe
         T_IsSemiring_1640 -> T_IsSemiringWithoutAnnihilatingZero_1536
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1654
         ((T_IsCommutativeSemiring_1750 -> T_IsSemiring_1640) -> Any -> Any
forall a b. a -> b
coe
            T_IsCommutativeSemiring_1750 -> T_IsSemiring_1640
MAlonzo.Code.Algebra.Structures.d_isSemiring_1764
            ((T_IsCancellativeCommutativeSemiring_1872
 -> T_IsCommutativeSemiring_1750)
-> Any -> Any
forall a b. a -> b
coe
               T_IsCancellativeCommutativeSemiring_1872
-> T_IsCommutativeSemiring_1750
MAlonzo.Code.Algebra.Structures.d_isCommutativeSemiring_1886
               (T_IsCancellativeCommutativeSemiring_1872 -> Any
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1872
v0))))
-- Data.Bool.Properties._.IsCancellativeCommutativeSemiring.identityʳ
d_identity'691'_454 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsCancellativeCommutativeSemiring_1872 ->
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_identity'691'_454 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> T_IsCancellativeCommutativeSemiring_1872
-> Bool
-> T__'8801'__12
d_identity'691'_454 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> T_IsCancellativeCommutativeSemiring_1872
-> Bool
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsCancellativeCommutativeSemiring.identityˡ
d_identity'737'_456 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsCancellativeCommutativeSemiring_1872 ->
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_identity'737'_456 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> T_IsCancellativeCommutativeSemiring_1872
-> Bool
-> T__'8801'__12
d_identity'737'_456 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> T_IsCancellativeCommutativeSemiring_1872
-> Bool
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsCancellativeCommutativeSemiring.isCommutativeMagma
d_isCommutativeMagma_458 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsCancellativeCommutativeSemiring_1872 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMagma_214
d_isCommutativeMagma_458 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> T_IsCancellativeCommutativeSemiring_1872
-> T_IsCommutativeMagma_214
d_isCommutativeMagma_458 ~Bool -> Bool -> Bool
v0 ~Bool -> Bool -> Bool
v1 ~Bool
v2 ~Bool
v3 T_IsCancellativeCommutativeSemiring_1872
v4
  = T_IsCancellativeCommutativeSemiring_1872
-> T_IsCommutativeMagma_214
du_isCommutativeMagma_458 T_IsCancellativeCommutativeSemiring_1872
v4
du_isCommutativeMagma_458 ::
  MAlonzo.Code.Algebra.Structures.T_IsCancellativeCommutativeSemiring_1872 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMagma_214
du_isCommutativeMagma_458 :: T_IsCancellativeCommutativeSemiring_1872
-> T_IsCommutativeMagma_214
du_isCommutativeMagma_458 T_IsCancellativeCommutativeSemiring_1872
v0
  = let v1 :: T_IsCommutativeSemiring_1750
v1
          = T_IsCancellativeCommutativeSemiring_1872
-> T_IsCommutativeSemiring_1750
MAlonzo.Code.Algebra.Structures.d_isCommutativeSemiring_1886
              (T_IsCancellativeCommutativeSemiring_1872
-> T_IsCancellativeCommutativeSemiring_1872
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1872
v0) in
    Any -> T_IsCommutativeMagma_214
forall a b. a -> b
coe
      (let v2 :: Any
v2
             = (T_IsCommutativeSemiring_1750
 -> T_IsCommutativeSemiringWithoutOne_1438)
-> Any -> Any
forall a b. a -> b
coe
                 T_IsCommutativeSemiring_1750
-> T_IsCommutativeSemiringWithoutOne_1438
MAlonzo.Code.Algebra.Structures.du_isCommutativeSemiringWithoutOne_1852
                 (T_IsCommutativeSemiring_1750 -> Any
forall a b. a -> b
coe T_IsCommutativeSemiring_1750
v1) in
       Any -> Any
forall a b. a -> b
coe
         ((T_IsCommutativeSemigroup_568 -> T_IsCommutativeMagma_214)
-> Any -> Any
forall a b. a -> b
coe
            T_IsCommutativeSemigroup_568 -> T_IsCommutativeMagma_214
MAlonzo.Code.Algebra.Structures.du_isCommutativeMagma_606
            ((T_IsCommutativeSemiringWithoutOne_1438
 -> T_IsCommutativeSemigroup_568)
-> Any -> Any
forall a b. a -> b
coe
               T_IsCommutativeSemiringWithoutOne_1438
-> T_IsCommutativeSemigroup_568
MAlonzo.Code.Algebra.Structures.du_'42''45'isCommutativeSemigroup_1520
               (Any -> Any
forall a b. a -> b
coe Any
v2))))
-- Data.Bool.Properties._.IsCancellativeCommutativeSemiring.*-isCommutativeMonoid
d_'42''45'isCommutativeMonoid_460 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsCancellativeCommutativeSemiring_1872 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMonoid_764
d_'42''45'isCommutativeMonoid_460 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> T_IsCancellativeCommutativeSemiring_1872
-> T_IsCommutativeMonoid_764
d_'42''45'isCommutativeMonoid_460 ~Bool -> Bool -> Bool
v0 ~Bool -> Bool -> Bool
v1 ~Bool
v2 ~Bool
v3 T_IsCancellativeCommutativeSemiring_1872
v4
  = T_IsCancellativeCommutativeSemiring_1872
-> T_IsCommutativeMonoid_764
du_'42''45'isCommutativeMonoid_460 T_IsCancellativeCommutativeSemiring_1872
v4
du_'42''45'isCommutativeMonoid_460 ::
  MAlonzo.Code.Algebra.Structures.T_IsCancellativeCommutativeSemiring_1872 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMonoid_764
du_'42''45'isCommutativeMonoid_460 :: T_IsCancellativeCommutativeSemiring_1872
-> T_IsCommutativeMonoid_764
du_'42''45'isCommutativeMonoid_460 T_IsCancellativeCommutativeSemiring_1872
v0
  = (T_IsCommutativeSemiring_1750 -> T_IsCommutativeMonoid_764)
-> Any -> T_IsCommutativeMonoid_764
forall a b. a -> b
coe
      T_IsCommutativeSemiring_1750 -> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.du_'42''45'isCommutativeMonoid_1860
      ((T_IsCancellativeCommutativeSemiring_1872
 -> T_IsCommutativeSemiring_1750)
-> Any -> Any
forall a b. a -> b
coe
         T_IsCancellativeCommutativeSemiring_1872
-> T_IsCommutativeSemiring_1750
MAlonzo.Code.Algebra.Structures.d_isCommutativeSemiring_1886
         (T_IsCancellativeCommutativeSemiring_1872 -> Any
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1872
v0))
-- Data.Bool.Properties._.IsCancellativeCommutativeSemiring.*-isCommutativeSemigroup
d_'42''45'isCommutativeSemigroup_462 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsCancellativeCommutativeSemiring_1872 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_568
d_'42''45'isCommutativeSemigroup_462 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> T_IsCancellativeCommutativeSemiring_1872
-> T_IsCommutativeSemigroup_568
d_'42''45'isCommutativeSemigroup_462 ~Bool -> Bool -> Bool
v0 ~Bool -> Bool -> Bool
v1 ~Bool
v2 ~Bool
v3 T_IsCancellativeCommutativeSemiring_1872
v4
  = T_IsCancellativeCommutativeSemiring_1872
-> T_IsCommutativeSemigroup_568
du_'42''45'isCommutativeSemigroup_462 T_IsCancellativeCommutativeSemiring_1872
v4
du_'42''45'isCommutativeSemigroup_462 ::
  MAlonzo.Code.Algebra.Structures.T_IsCancellativeCommutativeSemiring_1872 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_568
du_'42''45'isCommutativeSemigroup_462 :: T_IsCancellativeCommutativeSemiring_1872
-> T_IsCommutativeSemigroup_568
du_'42''45'isCommutativeSemigroup_462 T_IsCancellativeCommutativeSemiring_1872
v0
  = let v1 :: T_IsCommutativeSemiring_1750
v1
          = T_IsCancellativeCommutativeSemiring_1872
-> T_IsCommutativeSemiring_1750
MAlonzo.Code.Algebra.Structures.d_isCommutativeSemiring_1886
              (T_IsCancellativeCommutativeSemiring_1872
-> T_IsCancellativeCommutativeSemiring_1872
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1872
v0) in
    Any -> T_IsCommutativeSemigroup_568
forall a b. a -> b
coe
      ((T_IsCommutativeSemiringWithoutOne_1438
 -> T_IsCommutativeSemigroup_568)
-> Any -> Any
forall a b. a -> b
coe
         T_IsCommutativeSemiringWithoutOne_1438
-> T_IsCommutativeSemigroup_568
MAlonzo.Code.Algebra.Structures.du_'42''45'isCommutativeSemigroup_1520
         ((T_IsCommutativeSemiring_1750
 -> T_IsCommutativeSemiringWithoutOne_1438)
-> Any -> Any
forall a b. a -> b
coe
            T_IsCommutativeSemiring_1750
-> T_IsCommutativeSemiringWithoutOne_1438
MAlonzo.Code.Algebra.Structures.du_isCommutativeSemiringWithoutOne_1852
            (T_IsCommutativeSemiring_1750 -> Any
forall a b. a -> b
coe T_IsCommutativeSemiring_1750
v1)))
-- Data.Bool.Properties._.IsCancellativeCommutativeSemiring.*-isMagma
d_'42''45'isMagma_464 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsCancellativeCommutativeSemiring_1872 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_178
d_'42''45'isMagma_464 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> T_IsCancellativeCommutativeSemiring_1872
-> T_IsMagma_178
d_'42''45'isMagma_464 ~Bool -> Bool -> Bool
v0 ~Bool -> Bool -> Bool
v1 ~Bool
v2 ~Bool
v3 T_IsCancellativeCommutativeSemiring_1872
v4
  = T_IsCancellativeCommutativeSemiring_1872 -> T_IsMagma_178
du_'42''45'isMagma_464 T_IsCancellativeCommutativeSemiring_1872
v4
du_'42''45'isMagma_464 ::
  MAlonzo.Code.Algebra.Structures.T_IsCancellativeCommutativeSemiring_1872 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_178
du_'42''45'isMagma_464 :: T_IsCancellativeCommutativeSemiring_1872 -> T_IsMagma_178
du_'42''45'isMagma_464 T_IsCancellativeCommutativeSemiring_1872
v0
  = let v1 :: T_IsCommutativeSemiring_1750
v1
          = T_IsCancellativeCommutativeSemiring_1872
-> T_IsCommutativeSemiring_1750
MAlonzo.Code.Algebra.Structures.d_isCommutativeSemiring_1886
              (T_IsCancellativeCommutativeSemiring_1872
-> T_IsCancellativeCommutativeSemiring_1872
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1872
v0) in
    Any -> T_IsMagma_178
forall a b. a -> b
coe
      (let v2 :: T_IsSemiring_1640
v2
             = T_IsCommutativeSemiring_1750 -> T_IsSemiring_1640
MAlonzo.Code.Algebra.Structures.d_isSemiring_1764 (T_IsCommutativeSemiring_1750 -> T_IsCommutativeSemiring_1750
forall a b. a -> b
coe T_IsCommutativeSemiring_1750
v1) in
       Any -> Any
forall a b. a -> b
coe
         ((T_IsSemiringWithoutAnnihilatingZero_1536 -> T_IsMagma_178)
-> Any -> Any
forall a b. a -> b
coe
            T_IsSemiringWithoutAnnihilatingZero_1536 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.du_'42''45'isMagma_1614
            ((T_IsSemiring_1640 -> T_IsSemiringWithoutAnnihilatingZero_1536)
-> Any -> Any
forall a b. a -> b
coe
               T_IsSemiring_1640 -> T_IsSemiringWithoutAnnihilatingZero_1536
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1654
               (T_IsSemiring_1640 -> Any
forall a b. a -> b
coe T_IsSemiring_1640
v2))))
-- Data.Bool.Properties._.IsCancellativeCommutativeSemiring.*-isMonoid
d_'42''45'isMonoid_466 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsCancellativeCommutativeSemiring_1872 ->
  MAlonzo.Code.Algebra.Structures.T_IsMonoid_712
d_'42''45'isMonoid_466 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> T_IsCancellativeCommutativeSemiring_1872
-> T_IsMonoid_712
d_'42''45'isMonoid_466 ~Bool -> Bool -> Bool
v0 ~Bool -> Bool -> Bool
v1 ~Bool
v2 ~Bool
v3 T_IsCancellativeCommutativeSemiring_1872
v4
  = T_IsCancellativeCommutativeSemiring_1872 -> T_IsMonoid_712
du_'42''45'isMonoid_466 T_IsCancellativeCommutativeSemiring_1872
v4
du_'42''45'isMonoid_466 ::
  MAlonzo.Code.Algebra.Structures.T_IsCancellativeCommutativeSemiring_1872 ->
  MAlonzo.Code.Algebra.Structures.T_IsMonoid_712
du_'42''45'isMonoid_466 :: T_IsCancellativeCommutativeSemiring_1872 -> T_IsMonoid_712
du_'42''45'isMonoid_466 T_IsCancellativeCommutativeSemiring_1872
v0
  = let v1 :: T_IsCommutativeSemiring_1750
v1
          = T_IsCancellativeCommutativeSemiring_1872
-> T_IsCommutativeSemiring_1750
MAlonzo.Code.Algebra.Structures.d_isCommutativeSemiring_1886
              (T_IsCancellativeCommutativeSemiring_1872
-> T_IsCancellativeCommutativeSemiring_1872
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1872
v0) in
    Any -> T_IsMonoid_712
forall a b. a -> b
coe
      (let v2 :: T_IsSemiring_1640
v2
             = T_IsCommutativeSemiring_1750 -> T_IsSemiring_1640
MAlonzo.Code.Algebra.Structures.d_isSemiring_1764 (T_IsCommutativeSemiring_1750 -> T_IsCommutativeSemiring_1750
forall a b. a -> b
coe T_IsCommutativeSemiring_1750
v1) in
       Any -> Any
forall a b. a -> b
coe
         ((T_IsSemiringWithoutAnnihilatingZero_1536 -> T_IsMonoid_712)
-> Any -> Any
forall a b. a -> b
coe
            T_IsSemiringWithoutAnnihilatingZero_1536 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.du_'42''45'isMonoid_1618
            ((T_IsSemiring_1640 -> T_IsSemiringWithoutAnnihilatingZero_1536)
-> Any -> Any
forall a b. a -> b
coe
               T_IsSemiring_1640 -> T_IsSemiringWithoutAnnihilatingZero_1536
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1654
               (T_IsSemiring_1640 -> Any
forall a b. a -> b
coe T_IsSemiring_1640
v2))))
-- Data.Bool.Properties._.IsCancellativeCommutativeSemiring.*-isSemigroup
d_'42''45'isSemigroup_468 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsCancellativeCommutativeSemiring_1872 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_488
d_'42''45'isSemigroup_468 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> T_IsCancellativeCommutativeSemiring_1872
-> T_IsSemigroup_488
d_'42''45'isSemigroup_468 ~Bool -> Bool -> Bool
v0 ~Bool -> Bool -> Bool
v1 ~Bool
v2 ~Bool
v3 T_IsCancellativeCommutativeSemiring_1872
v4
  = T_IsCancellativeCommutativeSemiring_1872 -> T_IsSemigroup_488
du_'42''45'isSemigroup_468 T_IsCancellativeCommutativeSemiring_1872
v4
du_'42''45'isSemigroup_468 ::
  MAlonzo.Code.Algebra.Structures.T_IsCancellativeCommutativeSemiring_1872 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_488
du_'42''45'isSemigroup_468 :: T_IsCancellativeCommutativeSemiring_1872 -> T_IsSemigroup_488
du_'42''45'isSemigroup_468 T_IsCancellativeCommutativeSemiring_1872
v0
  = let v1 :: T_IsCommutativeSemiring_1750
v1
          = T_IsCancellativeCommutativeSemiring_1872
-> T_IsCommutativeSemiring_1750
MAlonzo.Code.Algebra.Structures.d_isCommutativeSemiring_1886
              (T_IsCancellativeCommutativeSemiring_1872
-> T_IsCancellativeCommutativeSemiring_1872
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1872
v0) in
    Any -> T_IsSemigroup_488
forall a b. a -> b
coe
      (let v2 :: T_IsSemiring_1640
v2
             = T_IsCommutativeSemiring_1750 -> T_IsSemiring_1640
MAlonzo.Code.Algebra.Structures.d_isSemiring_1764 (T_IsCommutativeSemiring_1750 -> T_IsCommutativeSemiring_1750
forall a b. a -> b
coe T_IsCommutativeSemiring_1750
v1) in
       Any -> Any
forall a b. a -> b
coe
         ((T_IsSemiringWithoutAnnihilatingZero_1536 -> T_IsSemigroup_488)
-> Any -> Any
forall a b. a -> b
coe
            T_IsSemiringWithoutAnnihilatingZero_1536 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.du_'42''45'isSemigroup_1616
            ((T_IsSemiring_1640 -> T_IsSemiringWithoutAnnihilatingZero_1536)
-> Any -> Any
forall a b. a -> b
coe
               T_IsSemiring_1640 -> T_IsSemiringWithoutAnnihilatingZero_1536
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1654
               (T_IsSemiring_1640 -> Any
forall a b. a -> b
coe T_IsSemiring_1640
v2))))
-- Data.Bool.Properties._.IsCancellativeCommutativeSemiring.assoc
d_assoc_470 ::
  MAlonzo.Code.Algebra.Structures.T_IsCancellativeCommutativeSemiring_1872 ->
  Bool ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_assoc_470 :: T_IsCancellativeCommutativeSemiring_1872
-> Bool -> Bool -> Bool -> T__'8801'__12
d_assoc_470 = T_IsCancellativeCommutativeSemiring_1872
-> Bool -> Bool -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsCancellativeCommutativeSemiring.comm
d_comm_472 ::
  MAlonzo.Code.Algebra.Structures.T_IsCancellativeCommutativeSemiring_1872 ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_comm_472 :: T_IsCancellativeCommutativeSemiring_1872
-> Bool -> Bool -> T__'8801'__12
d_comm_472 = T_IsCancellativeCommutativeSemiring_1872
-> Bool -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsCancellativeCommutativeSemiring.∙-cong
d_'8729''45'cong_474 ::
  MAlonzo.Code.Algebra.Structures.T_IsCancellativeCommutativeSemiring_1872 ->
  Bool ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8729''45'cong_474 :: T_IsCancellativeCommutativeSemiring_1872
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong_474 = T_IsCancellativeCommutativeSemiring_1872
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsCancellativeCommutativeSemiring.∙-congʳ
d_'8729''45'cong'691'_476 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsCancellativeCommutativeSemiring_1872 ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8729''45'cong'691'_476 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> T_IsCancellativeCommutativeSemiring_1872
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong'691'_476 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> T_IsCancellativeCommutativeSemiring_1872
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsCancellativeCommutativeSemiring.∙-congˡ
d_'8729''45'cong'737'_478 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsCancellativeCommutativeSemiring_1872 ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8729''45'cong'737'_478 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> T_IsCancellativeCommutativeSemiring_1872
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong'737'_478 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> T_IsCancellativeCommutativeSemiring_1872
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsCancellativeCommutativeSemiring.identity
d_identity_480 ::
  MAlonzo.Code.Algebra.Structures.T_IsCancellativeCommutativeSemiring_1872 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_identity_480 :: T_IsCancellativeCommutativeSemiring_1872 -> T_Σ_14
d_identity_480 T_IsCancellativeCommutativeSemiring_1872
v0
  = (T_IsMonoid_712 -> T_Σ_14) -> Any -> T_Σ_14
forall a b. a -> b
coe
      T_IsMonoid_712 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_identity_724
      ((T_IsCommutativeMonoid_764 -> T_IsMonoid_712) -> Any -> Any
forall a b. a -> b
coe
         T_IsCommutativeMonoid_764 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_774
         ((T_IsSemiringWithoutAnnihilatingZero_1536
 -> T_IsCommutativeMonoid_764)
-> Any -> Any
forall a b. a -> b
coe
            T_IsSemiringWithoutAnnihilatingZero_1536
-> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1556
            ((T_IsSemiring_1640 -> T_IsSemiringWithoutAnnihilatingZero_1536)
-> Any -> Any
forall a b. a -> b
coe
               T_IsSemiring_1640 -> T_IsSemiringWithoutAnnihilatingZero_1536
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1654
               ((T_IsCommutativeSemiring_1750 -> T_IsSemiring_1640) -> Any -> Any
forall a b. a -> b
coe
                  T_IsCommutativeSemiring_1750 -> T_IsSemiring_1640
MAlonzo.Code.Algebra.Structures.d_isSemiring_1764
                  ((T_IsCancellativeCommutativeSemiring_1872
 -> T_IsCommutativeSemiring_1750)
-> Any -> Any
forall a b. a -> b
coe
                     T_IsCancellativeCommutativeSemiring_1872
-> T_IsCommutativeSemiring_1750
MAlonzo.Code.Algebra.Structures.d_isCommutativeSemiring_1886
                     (T_IsCancellativeCommutativeSemiring_1872 -> Any
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1872
v0))))))
-- Data.Bool.Properties._.IsCancellativeCommutativeSemiring.identityʳ
d_identity'691'_482 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsCancellativeCommutativeSemiring_1872 ->
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_identity'691'_482 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> T_IsCancellativeCommutativeSemiring_1872
-> Bool
-> T__'8801'__12
d_identity'691'_482 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> T_IsCancellativeCommutativeSemiring_1872
-> Bool
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsCancellativeCommutativeSemiring.identityˡ
d_identity'737'_484 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsCancellativeCommutativeSemiring_1872 ->
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_identity'737'_484 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> T_IsCancellativeCommutativeSemiring_1872
-> Bool
-> T__'8801'__12
d_identity'737'_484 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> T_IsCancellativeCommutativeSemiring_1872
-> Bool
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsCancellativeCommutativeSemiring.isCommutativeMagma
d_isCommutativeMagma_486 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsCancellativeCommutativeSemiring_1872 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMagma_214
d_isCommutativeMagma_486 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> T_IsCancellativeCommutativeSemiring_1872
-> T_IsCommutativeMagma_214
d_isCommutativeMagma_486 ~Bool -> Bool -> Bool
v0 ~Bool -> Bool -> Bool
v1 ~Bool
v2 ~Bool
v3 T_IsCancellativeCommutativeSemiring_1872
v4
  = T_IsCancellativeCommutativeSemiring_1872
-> T_IsCommutativeMagma_214
du_isCommutativeMagma_486 T_IsCancellativeCommutativeSemiring_1872
v4
du_isCommutativeMagma_486 ::
  MAlonzo.Code.Algebra.Structures.T_IsCancellativeCommutativeSemiring_1872 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMagma_214
du_isCommutativeMagma_486 :: T_IsCancellativeCommutativeSemiring_1872
-> T_IsCommutativeMagma_214
du_isCommutativeMagma_486 T_IsCancellativeCommutativeSemiring_1872
v0
  = let v1 :: T_IsCommutativeSemiring_1750
v1
          = T_IsCancellativeCommutativeSemiring_1872
-> T_IsCommutativeSemiring_1750
MAlonzo.Code.Algebra.Structures.d_isCommutativeSemiring_1886
              (T_IsCancellativeCommutativeSemiring_1872
-> T_IsCancellativeCommutativeSemiring_1872
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1872
v0) in
    Any -> T_IsCommutativeMagma_214
forall a b. a -> b
coe
      (let v2 :: T_IsSemiring_1640
v2
             = T_IsCommutativeSemiring_1750 -> T_IsSemiring_1640
MAlonzo.Code.Algebra.Structures.d_isSemiring_1764 (T_IsCommutativeSemiring_1750 -> T_IsCommutativeSemiring_1750
forall a b. a -> b
coe T_IsCommutativeSemiring_1750
v1) in
       Any -> Any
forall a b. a -> b
coe
         (let v3 :: T_IsSemiringWithoutAnnihilatingZero_1536
v3
                = T_IsSemiring_1640 -> T_IsSemiringWithoutAnnihilatingZero_1536
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1654
                    (T_IsSemiring_1640 -> T_IsSemiring_1640
forall a b. a -> b
coe T_IsSemiring_1640
v2) in
          Any -> Any
forall a b. a -> b
coe
            (let v4 :: T_IsCommutativeMonoid_764
v4
                   = T_IsSemiringWithoutAnnihilatingZero_1536
-> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1556
                       (T_IsSemiringWithoutAnnihilatingZero_1536
-> T_IsSemiringWithoutAnnihilatingZero_1536
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1536
v3) in
             Any -> Any
forall a b. a -> b
coe
               ((T_IsCommutativeSemigroup_568 -> T_IsCommutativeMagma_214)
-> Any -> Any
forall a b. a -> b
coe
                  T_IsCommutativeSemigroup_568 -> T_IsCommutativeMagma_214
MAlonzo.Code.Algebra.Structures.du_isCommutativeMagma_606
                  ((T_IsCommutativeMonoid_764 -> T_IsCommutativeSemigroup_568)
-> Any -> Any
forall a b. a -> b
coe
                     T_IsCommutativeMonoid_764 -> T_IsCommutativeSemigroup_568
MAlonzo.Code.Algebra.Structures.du_isCommutativeSemigroup_814
                     (T_IsCommutativeMonoid_764 -> Any
forall a b. a -> b
coe T_IsCommutativeMonoid_764
v4))))))
-- Data.Bool.Properties._.IsCancellativeCommutativeSemiring.+-isCommutativeMonoid
d_'43''45'isCommutativeMonoid_488 ::
  MAlonzo.Code.Algebra.Structures.T_IsCancellativeCommutativeSemiring_1872 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMonoid_764
d_'43''45'isCommutativeMonoid_488 :: T_IsCancellativeCommutativeSemiring_1872
-> T_IsCommutativeMonoid_764
d_'43''45'isCommutativeMonoid_488 T_IsCancellativeCommutativeSemiring_1872
v0
  = (T_IsSemiringWithoutAnnihilatingZero_1536
 -> T_IsCommutativeMonoid_764)
-> Any -> T_IsCommutativeMonoid_764
forall a b. a -> b
coe
      T_IsSemiringWithoutAnnihilatingZero_1536
-> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1556
      ((T_IsSemiring_1640 -> T_IsSemiringWithoutAnnihilatingZero_1536)
-> Any -> Any
forall a b. a -> b
coe
         T_IsSemiring_1640 -> T_IsSemiringWithoutAnnihilatingZero_1536
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1654
         ((T_IsCommutativeSemiring_1750 -> T_IsSemiring_1640) -> Any -> Any
forall a b. a -> b
coe
            T_IsCommutativeSemiring_1750 -> T_IsSemiring_1640
MAlonzo.Code.Algebra.Structures.d_isSemiring_1764
            ((T_IsCancellativeCommutativeSemiring_1872
 -> T_IsCommutativeSemiring_1750)
-> Any -> Any
forall a b. a -> b
coe
               T_IsCancellativeCommutativeSemiring_1872
-> T_IsCommutativeSemiring_1750
MAlonzo.Code.Algebra.Structures.d_isCommutativeSemiring_1886
               (T_IsCancellativeCommutativeSemiring_1872 -> Any
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1872
v0))))
-- Data.Bool.Properties._.IsCancellativeCommutativeSemiring.isCommutativeSemigroup
d_isCommutativeSemigroup_490 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsCancellativeCommutativeSemiring_1872 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_568
d_isCommutativeSemigroup_490 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> T_IsCancellativeCommutativeSemiring_1872
-> T_IsCommutativeSemigroup_568
d_isCommutativeSemigroup_490 ~Bool -> Bool -> Bool
v0 ~Bool -> Bool -> Bool
v1 ~Bool
v2 ~Bool
v3 T_IsCancellativeCommutativeSemiring_1872
v4
  = T_IsCancellativeCommutativeSemiring_1872
-> T_IsCommutativeSemigroup_568
du_isCommutativeSemigroup_490 T_IsCancellativeCommutativeSemiring_1872
v4
du_isCommutativeSemigroup_490 ::
  MAlonzo.Code.Algebra.Structures.T_IsCancellativeCommutativeSemiring_1872 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_568
du_isCommutativeSemigroup_490 :: T_IsCancellativeCommutativeSemiring_1872
-> T_IsCommutativeSemigroup_568
du_isCommutativeSemigroup_490 T_IsCancellativeCommutativeSemiring_1872
v0
  = let v1 :: T_IsCommutativeSemiring_1750
v1
          = T_IsCancellativeCommutativeSemiring_1872
-> T_IsCommutativeSemiring_1750
MAlonzo.Code.Algebra.Structures.d_isCommutativeSemiring_1886
              (T_IsCancellativeCommutativeSemiring_1872
-> T_IsCancellativeCommutativeSemiring_1872
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1872
v0) in
    Any -> T_IsCommutativeSemigroup_568
forall a b. a -> b
coe
      (let v2 :: T_IsSemiring_1640
v2
             = T_IsCommutativeSemiring_1750 -> T_IsSemiring_1640
MAlonzo.Code.Algebra.Structures.d_isSemiring_1764 (T_IsCommutativeSemiring_1750 -> T_IsCommutativeSemiring_1750
forall a b. a -> b
coe T_IsCommutativeSemiring_1750
v1) in
       Any -> Any
forall a b. a -> b
coe
         (let v3 :: T_IsSemiringWithoutAnnihilatingZero_1536
v3
                = T_IsSemiring_1640 -> T_IsSemiringWithoutAnnihilatingZero_1536
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1654
                    (T_IsSemiring_1640 -> T_IsSemiring_1640
forall a b. a -> b
coe T_IsSemiring_1640
v2) in
          Any -> Any
forall a b. a -> b
coe
            ((T_IsCommutativeMonoid_764 -> T_IsCommutativeSemigroup_568)
-> Any -> Any
forall a b. a -> b
coe
               T_IsCommutativeMonoid_764 -> T_IsCommutativeSemigroup_568
MAlonzo.Code.Algebra.Structures.du_isCommutativeSemigroup_814
               ((T_IsSemiringWithoutAnnihilatingZero_1536
 -> T_IsCommutativeMonoid_764)
-> Any -> Any
forall a b. a -> b
coe
                  T_IsSemiringWithoutAnnihilatingZero_1536
-> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1556
                  (T_IsSemiringWithoutAnnihilatingZero_1536 -> Any
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1536
v3)))))
-- Data.Bool.Properties._.IsCancellativeCommutativeSemiring.isMagma
d_isMagma_492 ::
  MAlonzo.Code.Algebra.Structures.T_IsCancellativeCommutativeSemiring_1872 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_178
d_isMagma_492 :: T_IsCancellativeCommutativeSemiring_1872 -> T_IsMagma_178
d_isMagma_492 T_IsCancellativeCommutativeSemiring_1872
v0
  = (T_IsSemigroup_488 -> T_IsMagma_178) -> Any -> T_IsMagma_178
forall a b. a -> b
coe
      T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496
      ((T_IsMonoid_712 -> T_IsSemigroup_488) -> Any -> Any
forall a b. a -> b
coe
         T_IsMonoid_712 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_722
         ((T_IsCommutativeMonoid_764 -> T_IsMonoid_712) -> Any -> Any
forall a b. a -> b
coe
            T_IsCommutativeMonoid_764 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_774
            ((T_IsSemiringWithoutAnnihilatingZero_1536
 -> T_IsCommutativeMonoid_764)
-> Any -> Any
forall a b. a -> b
coe
               T_IsSemiringWithoutAnnihilatingZero_1536
-> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1556
               ((T_IsSemiring_1640 -> T_IsSemiringWithoutAnnihilatingZero_1536)
-> Any -> Any
forall a b. a -> b
coe
                  T_IsSemiring_1640 -> T_IsSemiringWithoutAnnihilatingZero_1536
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1654
                  ((T_IsCommutativeSemiring_1750 -> T_IsSemiring_1640) -> Any -> Any
forall a b. a -> b
coe
                     T_IsCommutativeSemiring_1750 -> T_IsSemiring_1640
MAlonzo.Code.Algebra.Structures.d_isSemiring_1764
                     ((T_IsCancellativeCommutativeSemiring_1872
 -> T_IsCommutativeSemiring_1750)
-> Any -> Any
forall a b. a -> b
coe
                        T_IsCancellativeCommutativeSemiring_1872
-> T_IsCommutativeSemiring_1750
MAlonzo.Code.Algebra.Structures.d_isCommutativeSemiring_1886
                        (T_IsCancellativeCommutativeSemiring_1872 -> Any
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1872
v0)))))))
-- Data.Bool.Properties._.IsCancellativeCommutativeSemiring.isMonoid
d_isMonoid_494 ::
  MAlonzo.Code.Algebra.Structures.T_IsCancellativeCommutativeSemiring_1872 ->
  MAlonzo.Code.Algebra.Structures.T_IsMonoid_712
d_isMonoid_494 :: T_IsCancellativeCommutativeSemiring_1872 -> T_IsMonoid_712
d_isMonoid_494 T_IsCancellativeCommutativeSemiring_1872
v0
  = (T_IsCommutativeMonoid_764 -> T_IsMonoid_712)
-> Any -> T_IsMonoid_712
forall a b. a -> b
coe
      T_IsCommutativeMonoid_764 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_774
      ((T_IsSemiringWithoutAnnihilatingZero_1536
 -> T_IsCommutativeMonoid_764)
-> Any -> Any
forall a b. a -> b
coe
         T_IsSemiringWithoutAnnihilatingZero_1536
-> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1556
         ((T_IsSemiring_1640 -> T_IsSemiringWithoutAnnihilatingZero_1536)
-> Any -> Any
forall a b. a -> b
coe
            T_IsSemiring_1640 -> T_IsSemiringWithoutAnnihilatingZero_1536
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1654
            ((T_IsCommutativeSemiring_1750 -> T_IsSemiring_1640) -> Any -> Any
forall a b. a -> b
coe
               T_IsCommutativeSemiring_1750 -> T_IsSemiring_1640
MAlonzo.Code.Algebra.Structures.d_isSemiring_1764
               ((T_IsCancellativeCommutativeSemiring_1872
 -> T_IsCommutativeSemiring_1750)
-> Any -> Any
forall a b. a -> b
coe
                  T_IsCancellativeCommutativeSemiring_1872
-> T_IsCommutativeSemiring_1750
MAlonzo.Code.Algebra.Structures.d_isCommutativeSemiring_1886
                  (T_IsCancellativeCommutativeSemiring_1872 -> Any
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1872
v0)))))
-- Data.Bool.Properties._.IsCancellativeCommutativeSemiring.isSemigroup
d_isSemigroup_496 ::
  MAlonzo.Code.Algebra.Structures.T_IsCancellativeCommutativeSemiring_1872 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_488
d_isSemigroup_496 :: T_IsCancellativeCommutativeSemiring_1872 -> T_IsSemigroup_488
d_isSemigroup_496 T_IsCancellativeCommutativeSemiring_1872
v0
  = (T_IsMonoid_712 -> T_IsSemigroup_488) -> Any -> T_IsSemigroup_488
forall a b. a -> b
coe
      T_IsMonoid_712 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_722
      ((T_IsCommutativeMonoid_764 -> T_IsMonoid_712) -> Any -> Any
forall a b. a -> b
coe
         T_IsCommutativeMonoid_764 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_774
         ((T_IsSemiringWithoutAnnihilatingZero_1536
 -> T_IsCommutativeMonoid_764)
-> Any -> Any
forall a b. a -> b
coe
            T_IsSemiringWithoutAnnihilatingZero_1536
-> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1556
            ((T_IsSemiring_1640 -> T_IsSemiringWithoutAnnihilatingZero_1536)
-> Any -> Any
forall a b. a -> b
coe
               T_IsSemiring_1640 -> T_IsSemiringWithoutAnnihilatingZero_1536
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1654
               ((T_IsCommutativeSemiring_1750 -> T_IsSemiring_1640) -> Any -> Any
forall a b. a -> b
coe
                  T_IsCommutativeSemiring_1750 -> T_IsSemiring_1640
MAlonzo.Code.Algebra.Structures.d_isSemiring_1764
                  ((T_IsCancellativeCommutativeSemiring_1872
 -> T_IsCommutativeSemiring_1750)
-> Any -> Any
forall a b. a -> b
coe
                     T_IsCancellativeCommutativeSemiring_1872
-> T_IsCommutativeSemiring_1750
MAlonzo.Code.Algebra.Structures.d_isCommutativeSemiring_1886
                     (T_IsCancellativeCommutativeSemiring_1872 -> Any
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1872
v0))))))
-- Data.Bool.Properties._.IsCancellativeCommutativeSemiring.isUnitalMagma
d_isUnitalMagma_498 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsCancellativeCommutativeSemiring_1872 ->
  MAlonzo.Code.Algebra.Structures.T_IsUnitalMagma_666
d_isUnitalMagma_498 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> T_IsCancellativeCommutativeSemiring_1872
-> T_IsUnitalMagma_666
d_isUnitalMagma_498 ~Bool -> Bool -> Bool
v0 ~Bool -> Bool -> Bool
v1 ~Bool
v2 ~Bool
v3 T_IsCancellativeCommutativeSemiring_1872
v4 = T_IsCancellativeCommutativeSemiring_1872 -> T_IsUnitalMagma_666
du_isUnitalMagma_498 T_IsCancellativeCommutativeSemiring_1872
v4
du_isUnitalMagma_498 ::
  MAlonzo.Code.Algebra.Structures.T_IsCancellativeCommutativeSemiring_1872 ->
  MAlonzo.Code.Algebra.Structures.T_IsUnitalMagma_666
du_isUnitalMagma_498 :: T_IsCancellativeCommutativeSemiring_1872 -> T_IsUnitalMagma_666
du_isUnitalMagma_498 T_IsCancellativeCommutativeSemiring_1872
v0
  = let v1 :: T_IsCommutativeSemiring_1750
v1
          = T_IsCancellativeCommutativeSemiring_1872
-> T_IsCommutativeSemiring_1750
MAlonzo.Code.Algebra.Structures.d_isCommutativeSemiring_1886
              (T_IsCancellativeCommutativeSemiring_1872
-> T_IsCancellativeCommutativeSemiring_1872
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1872
v0) in
    Any -> T_IsUnitalMagma_666
forall a b. a -> b
coe
      (let v2 :: T_IsSemiring_1640
v2
             = T_IsCommutativeSemiring_1750 -> T_IsSemiring_1640
MAlonzo.Code.Algebra.Structures.d_isSemiring_1764 (T_IsCommutativeSemiring_1750 -> T_IsCommutativeSemiring_1750
forall a b. a -> b
coe T_IsCommutativeSemiring_1750
v1) in
       Any -> Any
forall a b. a -> b
coe
         (let v3 :: T_IsSemiringWithoutAnnihilatingZero_1536
v3
                = T_IsSemiring_1640 -> T_IsSemiringWithoutAnnihilatingZero_1536
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1654
                    (T_IsSemiring_1640 -> T_IsSemiring_1640
forall a b. a -> b
coe T_IsSemiring_1640
v2) in
          Any -> Any
forall a b. a -> b
coe
            (let v4 :: T_IsCommutativeMonoid_764
v4
                   = T_IsSemiringWithoutAnnihilatingZero_1536
-> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1556
                       (T_IsSemiringWithoutAnnihilatingZero_1536
-> T_IsSemiringWithoutAnnihilatingZero_1536
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1536
v3) in
             Any -> Any
forall a b. a -> b
coe
               ((T_IsMonoid_712 -> T_IsUnitalMagma_666) -> Any -> Any
forall a b. a -> b
coe
                  T_IsMonoid_712 -> T_IsUnitalMagma_666
MAlonzo.Code.Algebra.Structures.du_isUnitalMagma_756
                  ((T_IsCommutativeMonoid_764 -> T_IsMonoid_712) -> Any -> Any
forall a b. a -> b
coe T_IsCommutativeMonoid_764 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_774 (T_IsCommutativeMonoid_764 -> Any
forall a b. a -> b
coe T_IsCommutativeMonoid_764
v4))))))
-- Data.Bool.Properties._.IsCancellativeCommutativeSemiring.distrib
d_distrib_500 ::
  MAlonzo.Code.Algebra.Structures.T_IsCancellativeCommutativeSemiring_1872 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_distrib_500 :: T_IsCancellativeCommutativeSemiring_1872 -> T_Σ_14
d_distrib_500 T_IsCancellativeCommutativeSemiring_1872
v0
  = (T_IsSemiringWithoutAnnihilatingZero_1536 -> T_Σ_14)
-> Any -> T_Σ_14
forall a b. a -> b
coe
      T_IsSemiringWithoutAnnihilatingZero_1536 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_distrib_1564
      ((T_IsSemiring_1640 -> T_IsSemiringWithoutAnnihilatingZero_1536)
-> Any -> Any
forall a b. a -> b
coe
         T_IsSemiring_1640 -> T_IsSemiringWithoutAnnihilatingZero_1536
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1654
         ((T_IsCommutativeSemiring_1750 -> T_IsSemiring_1640) -> Any -> Any
forall a b. a -> b
coe
            T_IsCommutativeSemiring_1750 -> T_IsSemiring_1640
MAlonzo.Code.Algebra.Structures.d_isSemiring_1764
            ((T_IsCancellativeCommutativeSemiring_1872
 -> T_IsCommutativeSemiring_1750)
-> Any -> Any
forall a b. a -> b
coe
               T_IsCancellativeCommutativeSemiring_1872
-> T_IsCommutativeSemiring_1750
MAlonzo.Code.Algebra.Structures.d_isCommutativeSemiring_1886
               (T_IsCancellativeCommutativeSemiring_1872 -> Any
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1872
v0))))
-- Data.Bool.Properties._.IsCancellativeCommutativeSemiring.distribʳ
d_distrib'691'_502 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsCancellativeCommutativeSemiring_1872 ->
  Bool ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_distrib'691'_502 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> T_IsCancellativeCommutativeSemiring_1872
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
d_distrib'691'_502 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> T_IsCancellativeCommutativeSemiring_1872
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsCancellativeCommutativeSemiring.distribˡ
d_distrib'737'_504 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsCancellativeCommutativeSemiring_1872 ->
  Bool ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_distrib'737'_504 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> T_IsCancellativeCommutativeSemiring_1872
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
d_distrib'737'_504 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> T_IsCancellativeCommutativeSemiring_1872
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsCancellativeCommutativeSemiring.isCommutativeSemiring
d_isCommutativeSemiring_506 ::
  MAlonzo.Code.Algebra.Structures.T_IsCancellativeCommutativeSemiring_1872 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiring_1750
d_isCommutativeSemiring_506 :: T_IsCancellativeCommutativeSemiring_1872
-> T_IsCommutativeSemiring_1750
d_isCommutativeSemiring_506 T_IsCancellativeCommutativeSemiring_1872
v0
  = (T_IsCancellativeCommutativeSemiring_1872
 -> T_IsCommutativeSemiring_1750)
-> Any -> T_IsCommutativeSemiring_1750
forall a b. a -> b
coe
      T_IsCancellativeCommutativeSemiring_1872
-> T_IsCommutativeSemiring_1750
MAlonzo.Code.Algebra.Structures.d_isCommutativeSemiring_1886
      (T_IsCancellativeCommutativeSemiring_1872 -> Any
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1872
v0)
-- Data.Bool.Properties._.IsCancellativeCommutativeSemiring.isCommutativeSemiringWithoutOne
d_isCommutativeSemiringWithoutOne_508 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsCancellativeCommutativeSemiring_1872 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiringWithoutOne_1438
d_isCommutativeSemiringWithoutOne_508 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> T_IsCancellativeCommutativeSemiring_1872
-> T_IsCommutativeSemiringWithoutOne_1438
d_isCommutativeSemiringWithoutOne_508 ~Bool -> Bool -> Bool
v0 ~Bool -> Bool -> Bool
v1 ~Bool
v2 ~Bool
v3 T_IsCancellativeCommutativeSemiring_1872
v4
  = T_IsCancellativeCommutativeSemiring_1872
-> T_IsCommutativeSemiringWithoutOne_1438
du_isCommutativeSemiringWithoutOne_508 T_IsCancellativeCommutativeSemiring_1872
v4
du_isCommutativeSemiringWithoutOne_508 ::
  MAlonzo.Code.Algebra.Structures.T_IsCancellativeCommutativeSemiring_1872 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiringWithoutOne_1438
du_isCommutativeSemiringWithoutOne_508 :: T_IsCancellativeCommutativeSemiring_1872
-> T_IsCommutativeSemiringWithoutOne_1438
du_isCommutativeSemiringWithoutOne_508 T_IsCancellativeCommutativeSemiring_1872
v0
  = (T_IsCommutativeSemiring_1750
 -> T_IsCommutativeSemiringWithoutOne_1438)
-> Any -> T_IsCommutativeSemiringWithoutOne_1438
forall a b. a -> b
coe
      T_IsCommutativeSemiring_1750
-> T_IsCommutativeSemiringWithoutOne_1438
MAlonzo.Code.Algebra.Structures.du_isCommutativeSemiringWithoutOne_1852
      ((T_IsCancellativeCommutativeSemiring_1872
 -> T_IsCommutativeSemiring_1750)
-> Any -> Any
forall a b. a -> b
coe
         T_IsCancellativeCommutativeSemiring_1872
-> T_IsCommutativeSemiring_1750
MAlonzo.Code.Algebra.Structures.d_isCommutativeSemiring_1886
         (T_IsCancellativeCommutativeSemiring_1872 -> Any
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1872
v0))
-- Data.Bool.Properties._.IsCancellativeCommutativeSemiring.isEquivalence
d_isEquivalence_510 ::
  MAlonzo.Code.Algebra.Structures.T_IsCancellativeCommutativeSemiring_1872 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
d_isEquivalence_510 :: T_IsCancellativeCommutativeSemiring_1872 -> T_IsEquivalence_28
d_isEquivalence_510 T_IsCancellativeCommutativeSemiring_1872
v0
  = (T_IsMagma_178 -> T_IsEquivalence_28) -> Any -> T_IsEquivalence_28
forall a b. a -> b
coe
      T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186
      ((T_IsSemigroup_488 -> T_IsMagma_178) -> Any -> Any
forall a b. a -> b
coe
         T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496
         ((T_IsMonoid_712 -> T_IsSemigroup_488) -> Any -> Any
forall a b. a -> b
coe
            T_IsMonoid_712 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_722
            ((T_IsCommutativeMonoid_764 -> T_IsMonoid_712) -> Any -> Any
forall a b. a -> b
coe
               T_IsCommutativeMonoid_764 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_774
               ((T_IsSemiringWithoutAnnihilatingZero_1536
 -> T_IsCommutativeMonoid_764)
-> Any -> Any
forall a b. a -> b
coe
                  T_IsSemiringWithoutAnnihilatingZero_1536
-> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1556
                  ((T_IsSemiring_1640 -> T_IsSemiringWithoutAnnihilatingZero_1536)
-> Any -> Any
forall a b. a -> b
coe
                     T_IsSemiring_1640 -> T_IsSemiringWithoutAnnihilatingZero_1536
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1654
                     ((T_IsCommutativeSemiring_1750 -> T_IsSemiring_1640) -> Any -> Any
forall a b. a -> b
coe
                        T_IsCommutativeSemiring_1750 -> T_IsSemiring_1640
MAlonzo.Code.Algebra.Structures.d_isSemiring_1764
                        ((T_IsCancellativeCommutativeSemiring_1872
 -> T_IsCommutativeSemiring_1750)
-> Any -> Any
forall a b. a -> b
coe
                           T_IsCancellativeCommutativeSemiring_1872
-> T_IsCommutativeSemiring_1750
MAlonzo.Code.Algebra.Structures.d_isCommutativeSemiring_1886
                           (T_IsCancellativeCommutativeSemiring_1872 -> Any
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1872
v0))))))))
-- Data.Bool.Properties._.IsCancellativeCommutativeSemiring.isNearSemiring
d_isNearSemiring_512 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsCancellativeCommutativeSemiring_1872 ->
  MAlonzo.Code.Algebra.Structures.T_IsNearSemiring_1260
d_isNearSemiring_512 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> T_IsCancellativeCommutativeSemiring_1872
-> T_IsNearSemiring_1260
d_isNearSemiring_512 ~Bool -> Bool -> Bool
v0 ~Bool -> Bool -> Bool
v1 ~Bool
v2 ~Bool
v3 T_IsCancellativeCommutativeSemiring_1872
v4 = T_IsCancellativeCommutativeSemiring_1872 -> T_IsNearSemiring_1260
du_isNearSemiring_512 T_IsCancellativeCommutativeSemiring_1872
v4
du_isNearSemiring_512 ::
  MAlonzo.Code.Algebra.Structures.T_IsCancellativeCommutativeSemiring_1872 ->
  MAlonzo.Code.Algebra.Structures.T_IsNearSemiring_1260
du_isNearSemiring_512 :: T_IsCancellativeCommutativeSemiring_1872 -> T_IsNearSemiring_1260
du_isNearSemiring_512 T_IsCancellativeCommutativeSemiring_1872
v0
  = let v1 :: T_IsCommutativeSemiring_1750
v1
          = T_IsCancellativeCommutativeSemiring_1872
-> T_IsCommutativeSemiring_1750
MAlonzo.Code.Algebra.Structures.d_isCommutativeSemiring_1886
              (T_IsCancellativeCommutativeSemiring_1872
-> T_IsCancellativeCommutativeSemiring_1872
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1872
v0) in
    Any -> T_IsNearSemiring_1260
forall a b. a -> b
coe
      (let v2 :: T_IsSemiring_1640
v2
             = T_IsCommutativeSemiring_1750 -> T_IsSemiring_1640
MAlonzo.Code.Algebra.Structures.d_isSemiring_1764 (T_IsCommutativeSemiring_1750 -> T_IsCommutativeSemiring_1750
forall a b. a -> b
coe T_IsCommutativeSemiring_1750
v1) in
       Any -> Any
forall a b. a -> b
coe
         ((T_IsSemiringWithoutOne_1342 -> T_IsNearSemiring_1260)
-> Any -> Any
forall a b. a -> b
coe
            T_IsSemiringWithoutOne_1342 -> T_IsNearSemiring_1260
MAlonzo.Code.Algebra.Structures.du_isNearSemiring_1428
            ((T_IsSemiring_1640 -> T_IsSemiringWithoutOne_1342) -> Any -> Any
forall a b. a -> b
coe
               T_IsSemiring_1640 -> T_IsSemiringWithoutOne_1342
MAlonzo.Code.Algebra.Structures.du_isSemiringWithoutOne_1730
               (T_IsSemiring_1640 -> Any
forall a b. a -> b
coe T_IsSemiring_1640
v2))))
-- Data.Bool.Properties._.IsCancellativeCommutativeSemiring.isPartialEquivalence
d_isPartialEquivalence_514 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsCancellativeCommutativeSemiring_1872 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_514 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> T_IsCancellativeCommutativeSemiring_1872
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_514 ~Bool -> Bool -> Bool
v0 ~Bool -> Bool -> Bool
v1 ~Bool
v2 ~Bool
v3 T_IsCancellativeCommutativeSemiring_1872
v4
  = T_IsCancellativeCommutativeSemiring_1872
-> T_IsPartialEquivalence_16
du_isPartialEquivalence_514 T_IsCancellativeCommutativeSemiring_1872
v4
du_isPartialEquivalence_514 ::
  MAlonzo.Code.Algebra.Structures.T_IsCancellativeCommutativeSemiring_1872 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_514 :: T_IsCancellativeCommutativeSemiring_1872
-> T_IsPartialEquivalence_16
du_isPartialEquivalence_514 T_IsCancellativeCommutativeSemiring_1872
v0
  = let v1 :: T_IsCommutativeSemiring_1750
v1
          = T_IsCancellativeCommutativeSemiring_1872
-> T_IsCommutativeSemiring_1750
MAlonzo.Code.Algebra.Structures.d_isCommutativeSemiring_1886
              (T_IsCancellativeCommutativeSemiring_1872
-> T_IsCancellativeCommutativeSemiring_1872
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1872
v0) in
    Any -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsSemiring_1640
v2
             = T_IsCommutativeSemiring_1750 -> T_IsSemiring_1640
MAlonzo.Code.Algebra.Structures.d_isSemiring_1764 (T_IsCommutativeSemiring_1750 -> T_IsCommutativeSemiring_1750
forall a b. a -> b
coe T_IsCommutativeSemiring_1750
v1) in
       Any -> Any
forall a b. a -> b
coe
         (let v3 :: T_IsSemiringWithoutAnnihilatingZero_1536
v3
                = T_IsSemiring_1640 -> T_IsSemiringWithoutAnnihilatingZero_1536
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1654
                    (T_IsSemiring_1640 -> T_IsSemiring_1640
forall a b. a -> b
coe T_IsSemiring_1640
v2) in
          Any -> Any
forall a b. a -> b
coe
            (let v4 :: T_IsCommutativeMonoid_764
v4
                   = T_IsSemiringWithoutAnnihilatingZero_1536
-> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1556
                       (T_IsSemiringWithoutAnnihilatingZero_1536
-> T_IsSemiringWithoutAnnihilatingZero_1536
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1536
v3) in
             Any -> Any
forall a b. a -> b
coe
               (let v5 :: T_IsMonoid_712
v5
                      = T_IsCommutativeMonoid_764 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_774 (T_IsCommutativeMonoid_764 -> T_IsCommutativeMonoid_764
forall a b. a -> b
coe T_IsCommutativeMonoid_764
v4) in
                Any -> Any
forall a b. a -> b
coe
                  (let v6 :: T_IsSemigroup_488
v6
                         = T_IsMonoid_712 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_722 (T_IsMonoid_712 -> T_IsMonoid_712
forall a b. a -> b
coe T_IsMonoid_712
v5) in
                   Any -> Any
forall a b. a -> b
coe
                     (let v7 :: T_IsMagma_178
v7 = T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496 (T_IsSemigroup_488 -> T_IsSemigroup_488
forall a b. a -> b
coe T_IsSemigroup_488
v6) in
                      Any -> Any
forall a b. a -> b
coe
                        ((T_IsEquivalence_28 -> T_IsPartialEquivalence_16) -> Any -> Any
forall a b. a -> b
coe
                           T_IsEquivalence_28 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_44
                           ((T_IsMagma_178 -> T_IsEquivalence_28) -> Any -> Any
forall a b. a -> b
coe
                              T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186
                              (T_IsMagma_178 -> Any
forall a b. a -> b
coe T_IsMagma_178
v7)))))))))
-- Data.Bool.Properties._.IsCancellativeCommutativeSemiring.isSemiring
d_isSemiring_516 ::
  MAlonzo.Code.Algebra.Structures.T_IsCancellativeCommutativeSemiring_1872 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemiring_1640
d_isSemiring_516 :: T_IsCancellativeCommutativeSemiring_1872 -> T_IsSemiring_1640
d_isSemiring_516 T_IsCancellativeCommutativeSemiring_1872
v0
  = (T_IsCommutativeSemiring_1750 -> T_IsSemiring_1640)
-> Any -> T_IsSemiring_1640
forall a b. a -> b
coe
      T_IsCommutativeSemiring_1750 -> T_IsSemiring_1640
MAlonzo.Code.Algebra.Structures.d_isSemiring_1764
      ((T_IsCancellativeCommutativeSemiring_1872
 -> T_IsCommutativeSemiring_1750)
-> Any -> Any
forall a b. a -> b
coe
         T_IsCancellativeCommutativeSemiring_1872
-> T_IsCommutativeSemiring_1750
MAlonzo.Code.Algebra.Structures.d_isCommutativeSemiring_1886
         (T_IsCancellativeCommutativeSemiring_1872 -> Any
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1872
v0))
-- Data.Bool.Properties._.IsCancellativeCommutativeSemiring.isSemiringWithoutAnnihilatingZero
d_isSemiringWithoutAnnihilatingZero_518 ::
  MAlonzo.Code.Algebra.Structures.T_IsCancellativeCommutativeSemiring_1872 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutAnnihilatingZero_1536
d_isSemiringWithoutAnnihilatingZero_518 :: T_IsCancellativeCommutativeSemiring_1872
-> T_IsSemiringWithoutAnnihilatingZero_1536
d_isSemiringWithoutAnnihilatingZero_518 T_IsCancellativeCommutativeSemiring_1872
v0
  = (T_IsSemiring_1640 -> T_IsSemiringWithoutAnnihilatingZero_1536)
-> Any -> T_IsSemiringWithoutAnnihilatingZero_1536
forall a b. a -> b
coe
      T_IsSemiring_1640 -> T_IsSemiringWithoutAnnihilatingZero_1536
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1654
      ((T_IsCommutativeSemiring_1750 -> T_IsSemiring_1640) -> Any -> Any
forall a b. a -> b
coe
         T_IsCommutativeSemiring_1750 -> T_IsSemiring_1640
MAlonzo.Code.Algebra.Structures.d_isSemiring_1764
         ((T_IsCancellativeCommutativeSemiring_1872
 -> T_IsCommutativeSemiring_1750)
-> Any -> Any
forall a b. a -> b
coe
            T_IsCancellativeCommutativeSemiring_1872
-> T_IsCommutativeSemiring_1750
MAlonzo.Code.Algebra.Structures.d_isCommutativeSemiring_1886
            (T_IsCancellativeCommutativeSemiring_1872 -> Any
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1872
v0)))
-- Data.Bool.Properties._.IsCancellativeCommutativeSemiring.isSemiringWithoutOne
d_isSemiringWithoutOne_520 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsCancellativeCommutativeSemiring_1872 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutOne_1342
d_isSemiringWithoutOne_520 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> T_IsCancellativeCommutativeSemiring_1872
-> T_IsSemiringWithoutOne_1342
d_isSemiringWithoutOne_520 ~Bool -> Bool -> Bool
v0 ~Bool -> Bool -> Bool
v1 ~Bool
v2 ~Bool
v3 T_IsCancellativeCommutativeSemiring_1872
v4
  = T_IsCancellativeCommutativeSemiring_1872
-> T_IsSemiringWithoutOne_1342
du_isSemiringWithoutOne_520 T_IsCancellativeCommutativeSemiring_1872
v4
du_isSemiringWithoutOne_520 ::
  MAlonzo.Code.Algebra.Structures.T_IsCancellativeCommutativeSemiring_1872 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutOne_1342
du_isSemiringWithoutOne_520 :: T_IsCancellativeCommutativeSemiring_1872
-> T_IsSemiringWithoutOne_1342
du_isSemiringWithoutOne_520 T_IsCancellativeCommutativeSemiring_1872
v0
  = let v1 :: T_IsCommutativeSemiring_1750
v1
          = T_IsCancellativeCommutativeSemiring_1872
-> T_IsCommutativeSemiring_1750
MAlonzo.Code.Algebra.Structures.d_isCommutativeSemiring_1886
              (T_IsCancellativeCommutativeSemiring_1872
-> T_IsCancellativeCommutativeSemiring_1872
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1872
v0) in
    Any -> T_IsSemiringWithoutOne_1342
forall a b. a -> b
coe
      ((T_IsSemiring_1640 -> T_IsSemiringWithoutOne_1342) -> Any -> Any
forall a b. a -> b
coe
         T_IsSemiring_1640 -> T_IsSemiringWithoutOne_1342
MAlonzo.Code.Algebra.Structures.du_isSemiringWithoutOne_1730
         ((T_IsCommutativeSemiring_1750 -> T_IsSemiring_1640) -> Any -> Any
forall a b. a -> b
coe T_IsCommutativeSemiring_1750 -> T_IsSemiring_1640
MAlonzo.Code.Algebra.Structures.d_isSemiring_1764 (T_IsCommutativeSemiring_1750 -> Any
forall a b. a -> b
coe T_IsCommutativeSemiring_1750
v1)))
-- Data.Bool.Properties._.IsCancellativeCommutativeSemiring.refl
d_refl_522 ::
  MAlonzo.Code.Algebra.Structures.T_IsCancellativeCommutativeSemiring_1872 ->
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_refl_522 :: T_IsCancellativeCommutativeSemiring_1872 -> Bool -> T__'8801'__12
d_refl_522 = T_IsCancellativeCommutativeSemiring_1872 -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsCancellativeCommutativeSemiring.reflexive
d_reflexive_524 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsCancellativeCommutativeSemiring_1872 ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_reflexive_524 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> T_IsCancellativeCommutativeSemiring_1872
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_reflexive_524 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> T_IsCancellativeCommutativeSemiring_1872
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsCancellativeCommutativeSemiring.setoid
d_setoid_526 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsCancellativeCommutativeSemiring_1872 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
d_setoid_526 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> T_IsCancellativeCommutativeSemiring_1872
-> T_Setoid_46
d_setoid_526 ~Bool -> Bool -> Bool
v0 ~Bool -> Bool -> Bool
v1 ~Bool
v2 ~Bool
v3 T_IsCancellativeCommutativeSemiring_1872
v4 = T_IsCancellativeCommutativeSemiring_1872 -> T_Setoid_46
du_setoid_526 T_IsCancellativeCommutativeSemiring_1872
v4
du_setoid_526 ::
  MAlonzo.Code.Algebra.Structures.T_IsCancellativeCommutativeSemiring_1872 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
du_setoid_526 :: T_IsCancellativeCommutativeSemiring_1872 -> T_Setoid_46
du_setoid_526 T_IsCancellativeCommutativeSemiring_1872
v0
  = let v1 :: T_IsCommutativeSemiring_1750
v1
          = T_IsCancellativeCommutativeSemiring_1872
-> T_IsCommutativeSemiring_1750
MAlonzo.Code.Algebra.Structures.d_isCommutativeSemiring_1886
              (T_IsCancellativeCommutativeSemiring_1872
-> T_IsCancellativeCommutativeSemiring_1872
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1872
v0) in
    Any -> T_Setoid_46
forall a b. a -> b
coe
      (let v2 :: T_IsSemiring_1640
v2
             = T_IsCommutativeSemiring_1750 -> T_IsSemiring_1640
MAlonzo.Code.Algebra.Structures.d_isSemiring_1764 (T_IsCommutativeSemiring_1750 -> T_IsCommutativeSemiring_1750
forall a b. a -> b
coe T_IsCommutativeSemiring_1750
v1) in
       Any -> Any
forall a b. a -> b
coe
         (let v3 :: T_IsSemiringWithoutAnnihilatingZero_1536
v3
                = T_IsSemiring_1640 -> T_IsSemiringWithoutAnnihilatingZero_1536
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1654
                    (T_IsSemiring_1640 -> T_IsSemiring_1640
forall a b. a -> b
coe T_IsSemiring_1640
v2) in
          Any -> Any
forall a b. a -> b
coe
            (let v4 :: T_IsCommutativeMonoid_764
v4
                   = T_IsSemiringWithoutAnnihilatingZero_1536
-> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1556
                       (T_IsSemiringWithoutAnnihilatingZero_1536
-> T_IsSemiringWithoutAnnihilatingZero_1536
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1536
v3) in
             Any -> Any
forall a b. a -> b
coe
               (let v5 :: T_IsMonoid_712
v5
                      = T_IsCommutativeMonoid_764 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_774 (T_IsCommutativeMonoid_764 -> T_IsCommutativeMonoid_764
forall a b. a -> b
coe T_IsCommutativeMonoid_764
v4) in
                Any -> Any
forall a b. a -> b
coe
                  (let v6 :: T_IsSemigroup_488
v6
                         = T_IsMonoid_712 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_722 (T_IsMonoid_712 -> T_IsMonoid_712
forall a b. a -> b
coe T_IsMonoid_712
v5) in
                   Any -> Any
forall a b. a -> b
coe
                     ((T_IsMagma_178 -> T_Setoid_46) -> Any -> Any
forall a b. a -> b
coe
                        T_IsMagma_178 -> T_Setoid_46
MAlonzo.Code.Algebra.Structures.du_setoid_202
                        ((T_IsSemigroup_488 -> T_IsMagma_178) -> Any -> Any
forall a b. a -> b
coe T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496 (T_IsSemigroup_488 -> Any
forall a b. a -> b
coe T_IsSemigroup_488
v6))))))))
-- Data.Bool.Properties._.IsCancellativeCommutativeSemiring.sym
d_sym_528 ::
  MAlonzo.Code.Algebra.Structures.T_IsCancellativeCommutativeSemiring_1872 ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_sym_528 :: T_IsCancellativeCommutativeSemiring_1872
-> Bool -> Bool -> T__'8801'__12 -> T__'8801'__12
d_sym_528 = T_IsCancellativeCommutativeSemiring_1872
-> Bool -> Bool -> T__'8801'__12 -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsCancellativeCommutativeSemiring.trans
d_trans_530 ::
  MAlonzo.Code.Algebra.Structures.T_IsCancellativeCommutativeSemiring_1872 ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_trans_530 :: T_IsCancellativeCommutativeSemiring_1872
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
d_trans_530 = T_IsCancellativeCommutativeSemiring_1872
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsCancellativeCommutativeSemiring.zero
d_zero_532 ::
  MAlonzo.Code.Algebra.Structures.T_IsCancellativeCommutativeSemiring_1872 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_zero_532 :: T_IsCancellativeCommutativeSemiring_1872 -> T_Σ_14
d_zero_532 T_IsCancellativeCommutativeSemiring_1872
v0
  = (T_IsSemiring_1640 -> T_Σ_14) -> Any -> T_Σ_14
forall a b. a -> b
coe
      T_IsSemiring_1640 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_zero_1656
      ((T_IsCommutativeSemiring_1750 -> T_IsSemiring_1640) -> Any -> Any
forall a b. a -> b
coe
         T_IsCommutativeSemiring_1750 -> T_IsSemiring_1640
MAlonzo.Code.Algebra.Structures.d_isSemiring_1764
         ((T_IsCancellativeCommutativeSemiring_1872
 -> T_IsCommutativeSemiring_1750)
-> Any -> Any
forall a b. a -> b
coe
            T_IsCancellativeCommutativeSemiring_1872
-> T_IsCommutativeSemiring_1750
MAlonzo.Code.Algebra.Structures.d_isCommutativeSemiring_1886
            (T_IsCancellativeCommutativeSemiring_1872 -> Any
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1872
v0)))
-- Data.Bool.Properties._.IsCancellativeCommutativeSemiring.zeroʳ
d_zero'691'_534 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsCancellativeCommutativeSemiring_1872 ->
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_zero'691'_534 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> T_IsCancellativeCommutativeSemiring_1872
-> Bool
-> T__'8801'__12
d_zero'691'_534 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> T_IsCancellativeCommutativeSemiring_1872
-> Bool
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsCancellativeCommutativeSemiring.zeroˡ
d_zero'737'_536 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsCancellativeCommutativeSemiring_1872 ->
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_zero'737'_536 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> T_IsCancellativeCommutativeSemiring_1872
-> Bool
-> T__'8801'__12
d_zero'737'_536 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> T_IsCancellativeCommutativeSemiring_1872
-> Bool
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsCommutativeBand.assoc
d_assoc_540 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_612 ->
  Bool ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_assoc_540 :: T_IsCommutativeBand_612 -> Bool -> Bool -> Bool -> T__'8801'__12
d_assoc_540 = T_IsCommutativeBand_612 -> Bool -> Bool -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsCommutativeBand.comm
d_comm_542 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_612 ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_comm_542 :: T_IsCommutativeBand_612 -> Bool -> Bool -> T__'8801'__12
d_comm_542 = T_IsCommutativeBand_612 -> Bool -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsCommutativeBand.idem
d_idem_544 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_612 ->
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_idem_544 :: T_IsCommutativeBand_612 -> Bool -> T__'8801'__12
d_idem_544 = T_IsCommutativeBand_612 -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsCommutativeBand.isBand
d_isBand_546 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_612 ->
  MAlonzo.Code.Algebra.Structures.T_IsBand_526
d_isBand_546 :: T_IsCommutativeBand_612 -> T_IsBand_526
d_isBand_546 T_IsCommutativeBand_612
v0
  = (T_IsCommutativeBand_612 -> T_IsBand_526) -> Any -> T_IsBand_526
forall a b. a -> b
coe T_IsCommutativeBand_612 -> T_IsBand_526
MAlonzo.Code.Algebra.Structures.d_isBand_620 (T_IsCommutativeBand_612 -> Any
forall a b. a -> b
coe T_IsCommutativeBand_612
v0)
-- Data.Bool.Properties._.IsCommutativeBand.isCommutativeMagma
d_isCommutativeMagma_548 ::
  (Bool -> Bool -> Bool) ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_612 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMagma_214
d_isCommutativeMagma_548 :: (Bool -> Bool -> Bool)
-> T_IsCommutativeBand_612 -> T_IsCommutativeMagma_214
d_isCommutativeMagma_548 ~Bool -> Bool -> Bool
v0 T_IsCommutativeBand_612
v1 = T_IsCommutativeBand_612 -> T_IsCommutativeMagma_214
du_isCommutativeMagma_548 T_IsCommutativeBand_612
v1
du_isCommutativeMagma_548 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_612 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMagma_214
du_isCommutativeMagma_548 :: T_IsCommutativeBand_612 -> T_IsCommutativeMagma_214
du_isCommutativeMagma_548 T_IsCommutativeBand_612
v0
  = (T_IsCommutativeSemigroup_568 -> T_IsCommutativeMagma_214)
-> Any -> T_IsCommutativeMagma_214
forall a b. a -> b
coe
      T_IsCommutativeSemigroup_568 -> T_IsCommutativeMagma_214
MAlonzo.Code.Algebra.Structures.du_isCommutativeMagma_606
      ((T_IsCommutativeBand_612 -> T_IsCommutativeSemigroup_568)
-> Any -> Any
forall a b. a -> b
coe
         T_IsCommutativeBand_612 -> T_IsCommutativeSemigroup_568
MAlonzo.Code.Algebra.Structures.du_isCommutativeSemigroup_654
         (T_IsCommutativeBand_612 -> Any
forall a b. a -> b
coe T_IsCommutativeBand_612
v0))
-- Data.Bool.Properties._.IsCommutativeBand.isCommutativeSemigroup
d_isCommutativeSemigroup_550 ::
  (Bool -> Bool -> Bool) ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_612 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_568
d_isCommutativeSemigroup_550 :: (Bool -> Bool -> Bool)
-> T_IsCommutativeBand_612 -> T_IsCommutativeSemigroup_568
d_isCommutativeSemigroup_550 Bool -> Bool -> Bool
v0 T_IsCommutativeBand_612
v1
  = (T_IsCommutativeBand_612 -> T_IsCommutativeSemigroup_568)
-> T_IsCommutativeBand_612 -> T_IsCommutativeSemigroup_568
forall a b. a -> b
coe
      T_IsCommutativeBand_612 -> T_IsCommutativeSemigroup_568
MAlonzo.Code.Algebra.Structures.du_isCommutativeSemigroup_654 T_IsCommutativeBand_612
v1
-- Data.Bool.Properties._.IsCommutativeBand.isEquivalence
d_isEquivalence_552 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_612 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
d_isEquivalence_552 :: T_IsCommutativeBand_612 -> T_IsEquivalence_28
d_isEquivalence_552 T_IsCommutativeBand_612
v0
  = (T_IsMagma_178 -> T_IsEquivalence_28) -> Any -> T_IsEquivalence_28
forall a b. a -> b
coe
      T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186
      ((T_IsSemigroup_488 -> T_IsMagma_178) -> Any -> Any
forall a b. a -> b
coe
         T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496
         ((T_IsBand_526 -> T_IsSemigroup_488) -> Any -> Any
forall a b. a -> b
coe
            T_IsBand_526 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_534
            ((T_IsCommutativeBand_612 -> T_IsBand_526) -> Any -> Any
forall a b. a -> b
coe T_IsCommutativeBand_612 -> T_IsBand_526
MAlonzo.Code.Algebra.Structures.d_isBand_620 (T_IsCommutativeBand_612 -> Any
forall a b. a -> b
coe T_IsCommutativeBand_612
v0))))
-- Data.Bool.Properties._.IsCommutativeBand.isMagma
d_isMagma_554 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_612 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_178
d_isMagma_554 :: T_IsCommutativeBand_612 -> T_IsMagma_178
d_isMagma_554 T_IsCommutativeBand_612
v0
  = (T_IsSemigroup_488 -> T_IsMagma_178) -> Any -> T_IsMagma_178
forall a b. a -> b
coe
      T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496
      ((T_IsBand_526 -> T_IsSemigroup_488) -> Any -> Any
forall a b. a -> b
coe
         T_IsBand_526 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_534
         ((T_IsCommutativeBand_612 -> T_IsBand_526) -> Any -> Any
forall a b. a -> b
coe T_IsCommutativeBand_612 -> T_IsBand_526
MAlonzo.Code.Algebra.Structures.d_isBand_620 (T_IsCommutativeBand_612 -> Any
forall a b. a -> b
coe T_IsCommutativeBand_612
v0)))
-- Data.Bool.Properties._.IsCommutativeBand.isPartialEquivalence
d_isPartialEquivalence_556 ::
  (Bool -> Bool -> Bool) ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_612 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_556 :: (Bool -> Bool -> Bool)
-> T_IsCommutativeBand_612 -> T_IsPartialEquivalence_16
d_isPartialEquivalence_556 ~Bool -> Bool -> Bool
v0 T_IsCommutativeBand_612
v1 = T_IsCommutativeBand_612 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_556 T_IsCommutativeBand_612
v1
du_isPartialEquivalence_556 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_612 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_556 :: T_IsCommutativeBand_612 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_556 T_IsCommutativeBand_612
v0
  = let v1 :: T_IsBand_526
v1 = T_IsCommutativeBand_612 -> T_IsBand_526
MAlonzo.Code.Algebra.Structures.d_isBand_620 (T_IsCommutativeBand_612 -> T_IsCommutativeBand_612
forall a b. a -> b
coe T_IsCommutativeBand_612
v0) in
    Any -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsSemigroup_488
v2
             = T_IsBand_526 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_534 (T_IsBand_526 -> T_IsBand_526
forall a b. a -> b
coe T_IsBand_526
v1) in
       Any -> Any
forall a b. a -> b
coe
         (let v3 :: T_IsMagma_178
v3 = T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496 (T_IsSemigroup_488 -> T_IsSemigroup_488
forall a b. a -> b
coe T_IsSemigroup_488
v2) in
          Any -> Any
forall a b. a -> b
coe
            ((T_IsEquivalence_28 -> T_IsPartialEquivalence_16) -> Any -> Any
forall a b. a -> b
coe
               T_IsEquivalence_28 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_44
               ((T_IsMagma_178 -> T_IsEquivalence_28) -> Any -> Any
forall a b. a -> b
coe
                  T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186 (T_IsMagma_178 -> Any
forall a b. a -> b
coe T_IsMagma_178
v3)))))
-- Data.Bool.Properties._.IsCommutativeBand.isSemigroup
d_isSemigroup_558 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_612 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_488
d_isSemigroup_558 :: T_IsCommutativeBand_612 -> T_IsSemigroup_488
d_isSemigroup_558 T_IsCommutativeBand_612
v0
  = (T_IsBand_526 -> T_IsSemigroup_488) -> Any -> T_IsSemigroup_488
forall a b. a -> b
coe
      T_IsBand_526 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_534
      ((T_IsCommutativeBand_612 -> T_IsBand_526) -> Any -> Any
forall a b. a -> b
coe T_IsCommutativeBand_612 -> T_IsBand_526
MAlonzo.Code.Algebra.Structures.d_isBand_620 (T_IsCommutativeBand_612 -> Any
forall a b. a -> b
coe T_IsCommutativeBand_612
v0))
-- Data.Bool.Properties._.IsCommutativeBand.refl
d_refl_560 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_612 ->
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_refl_560 :: T_IsCommutativeBand_612 -> Bool -> T__'8801'__12
d_refl_560 = T_IsCommutativeBand_612 -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsCommutativeBand.reflexive
d_reflexive_562 ::
  (Bool -> Bool -> Bool) ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_612 ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_reflexive_562 :: (Bool -> Bool -> Bool)
-> T_IsCommutativeBand_612
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_reflexive_562 = (Bool -> Bool -> Bool)
-> T_IsCommutativeBand_612
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsCommutativeBand.setoid
d_setoid_564 ::
  (Bool -> Bool -> Bool) ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_612 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
d_setoid_564 :: (Bool -> Bool -> Bool) -> T_IsCommutativeBand_612 -> T_Setoid_46
d_setoid_564 ~Bool -> Bool -> Bool
v0 T_IsCommutativeBand_612
v1 = T_IsCommutativeBand_612 -> T_Setoid_46
du_setoid_564 T_IsCommutativeBand_612
v1
du_setoid_564 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_612 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
du_setoid_564 :: T_IsCommutativeBand_612 -> T_Setoid_46
du_setoid_564 T_IsCommutativeBand_612
v0
  = let v1 :: T_IsBand_526
v1 = T_IsCommutativeBand_612 -> T_IsBand_526
MAlonzo.Code.Algebra.Structures.d_isBand_620 (T_IsCommutativeBand_612 -> T_IsCommutativeBand_612
forall a b. a -> b
coe T_IsCommutativeBand_612
v0) in
    Any -> T_Setoid_46
forall a b. a -> b
coe
      (let v2 :: T_IsSemigroup_488
v2
             = T_IsBand_526 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_534 (T_IsBand_526 -> T_IsBand_526
forall a b. a -> b
coe T_IsBand_526
v1) in
       Any -> Any
forall a b. a -> b
coe
         ((T_IsMagma_178 -> T_Setoid_46) -> Any -> Any
forall a b. a -> b
coe
            T_IsMagma_178 -> T_Setoid_46
MAlonzo.Code.Algebra.Structures.du_setoid_202
            ((T_IsSemigroup_488 -> T_IsMagma_178) -> Any -> Any
forall a b. a -> b
coe T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496 (T_IsSemigroup_488 -> Any
forall a b. a -> b
coe T_IsSemigroup_488
v2))))
-- Data.Bool.Properties._.IsCommutativeBand.sym
d_sym_566 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_612 ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_sym_566 :: T_IsCommutativeBand_612
-> Bool -> Bool -> T__'8801'__12 -> T__'8801'__12
d_sym_566 = T_IsCommutativeBand_612
-> Bool -> Bool -> T__'8801'__12 -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsCommutativeBand.trans
d_trans_568 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_612 ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_trans_568 :: T_IsCommutativeBand_612
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
d_trans_568 = T_IsCommutativeBand_612
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsCommutativeBand.∙-cong
d_'8729''45'cong_570 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_612 ->
  Bool ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8729''45'cong_570 :: T_IsCommutativeBand_612
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong_570 = T_IsCommutativeBand_612
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsCommutativeBand.∙-congʳ
d_'8729''45'cong'691'_572 ::
  (Bool -> Bool -> Bool) ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_612 ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8729''45'cong'691'_572 :: (Bool -> Bool -> Bool)
-> T_IsCommutativeBand_612
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong'691'_572 = (Bool -> Bool -> Bool)
-> T_IsCommutativeBand_612
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsCommutativeBand.∙-congˡ
d_'8729''45'cong'737'_574 ::
  (Bool -> Bool -> Bool) ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_612 ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8729''45'cong'737'_574 :: (Bool -> Bool -> Bool)
-> T_IsCommutativeBand_612
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong'737'_574 = (Bool -> Bool -> Bool)
-> T_IsCommutativeBand_612
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsCommutativeMagma.comm
d_comm_578 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMagma_214 ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_comm_578 :: T_IsCommutativeMagma_214 -> Bool -> Bool -> T__'8801'__12
d_comm_578 = T_IsCommutativeMagma_214 -> Bool -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsCommutativeMagma.isEquivalence
d_isEquivalence_580 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMagma_214 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
d_isEquivalence_580 :: T_IsCommutativeMagma_214 -> T_IsEquivalence_28
d_isEquivalence_580 T_IsCommutativeMagma_214
v0
  = (T_IsMagma_178 -> T_IsEquivalence_28) -> Any -> T_IsEquivalence_28
forall a b. a -> b
coe
      T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186
      ((T_IsCommutativeMagma_214 -> T_IsMagma_178) -> Any -> Any
forall a b. a -> b
coe T_IsCommutativeMagma_214 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_222 (T_IsCommutativeMagma_214 -> Any
forall a b. a -> b
coe T_IsCommutativeMagma_214
v0))
-- Data.Bool.Properties._.IsCommutativeMagma.isMagma
d_isMagma_582 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMagma_214 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_178
d_isMagma_582 :: T_IsCommutativeMagma_214 -> T_IsMagma_178
d_isMagma_582 T_IsCommutativeMagma_214
v0
  = (T_IsCommutativeMagma_214 -> T_IsMagma_178) -> Any -> T_IsMagma_178
forall a b. a -> b
coe T_IsCommutativeMagma_214 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_222 (T_IsCommutativeMagma_214 -> Any
forall a b. a -> b
coe T_IsCommutativeMagma_214
v0)
-- Data.Bool.Properties._.IsCommutativeMagma.isPartialEquivalence
d_isPartialEquivalence_584 ::
  (Bool -> Bool -> Bool) ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMagma_214 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_584 :: (Bool -> Bool -> Bool)
-> T_IsCommutativeMagma_214 -> T_IsPartialEquivalence_16
d_isPartialEquivalence_584 ~Bool -> Bool -> Bool
v0 T_IsCommutativeMagma_214
v1 = T_IsCommutativeMagma_214 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_584 T_IsCommutativeMagma_214
v1
du_isPartialEquivalence_584 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMagma_214 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_584 :: T_IsCommutativeMagma_214 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_584 T_IsCommutativeMagma_214
v0
  = let v1 :: T_IsMagma_178
v1
          = T_IsCommutativeMagma_214 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_222 (T_IsCommutativeMagma_214 -> T_IsCommutativeMagma_214
forall a b. a -> b
coe T_IsCommutativeMagma_214
v0) in
    Any -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      ((T_IsEquivalence_28 -> T_IsPartialEquivalence_16) -> Any -> Any
forall a b. a -> b
coe
         T_IsEquivalence_28 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_44
         ((T_IsMagma_178 -> T_IsEquivalence_28) -> Any -> Any
forall a b. a -> b
coe T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186 (T_IsMagma_178 -> Any
forall a b. a -> b
coe T_IsMagma_178
v1)))
-- Data.Bool.Properties._.IsCommutativeMagma.refl
d_refl_586 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMagma_214 ->
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_refl_586 :: T_IsCommutativeMagma_214 -> Bool -> T__'8801'__12
d_refl_586 = T_IsCommutativeMagma_214 -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsCommutativeMagma.reflexive
d_reflexive_588 ::
  (Bool -> Bool -> Bool) ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMagma_214 ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_reflexive_588 :: (Bool -> Bool -> Bool)
-> T_IsCommutativeMagma_214
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_reflexive_588 = (Bool -> Bool -> Bool)
-> T_IsCommutativeMagma_214
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsCommutativeMagma.setoid
d_setoid_590 ::
  (Bool -> Bool -> Bool) ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMagma_214 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
d_setoid_590 :: (Bool -> Bool -> Bool) -> T_IsCommutativeMagma_214 -> T_Setoid_46
d_setoid_590 ~Bool -> Bool -> Bool
v0 T_IsCommutativeMagma_214
v1 = T_IsCommutativeMagma_214 -> T_Setoid_46
du_setoid_590 T_IsCommutativeMagma_214
v1
du_setoid_590 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMagma_214 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
du_setoid_590 :: T_IsCommutativeMagma_214 -> T_Setoid_46
du_setoid_590 T_IsCommutativeMagma_214
v0
  = (T_IsMagma_178 -> T_Setoid_46) -> Any -> T_Setoid_46
forall a b. a -> b
coe
      T_IsMagma_178 -> T_Setoid_46
MAlonzo.Code.Algebra.Structures.du_setoid_202
      ((T_IsCommutativeMagma_214 -> T_IsMagma_178) -> Any -> Any
forall a b. a -> b
coe T_IsCommutativeMagma_214 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_222 (T_IsCommutativeMagma_214 -> Any
forall a b. a -> b
coe T_IsCommutativeMagma_214
v0))
-- Data.Bool.Properties._.IsCommutativeMagma.sym
d_sym_592 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMagma_214 ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_sym_592 :: T_IsCommutativeMagma_214
-> Bool -> Bool -> T__'8801'__12 -> T__'8801'__12
d_sym_592 = T_IsCommutativeMagma_214
-> Bool -> Bool -> T__'8801'__12 -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsCommutativeMagma.trans
d_trans_594 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMagma_214 ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_trans_594 :: T_IsCommutativeMagma_214
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
d_trans_594 = T_IsCommutativeMagma_214
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsCommutativeMagma.∙-cong
d_'8729''45'cong_596 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMagma_214 ->
  Bool ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8729''45'cong_596 :: T_IsCommutativeMagma_214
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong_596 = T_IsCommutativeMagma_214
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsCommutativeMagma.∙-congʳ
d_'8729''45'cong'691'_598 ::
  (Bool -> Bool -> Bool) ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMagma_214 ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8729''45'cong'691'_598 :: (Bool -> Bool -> Bool)
-> T_IsCommutativeMagma_214
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong'691'_598 = (Bool -> Bool -> Bool)
-> T_IsCommutativeMagma_214
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsCommutativeMagma.∙-congˡ
d_'8729''45'cong'737'_600 ::
  (Bool -> Bool -> Bool) ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMagma_214 ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8729''45'cong'737'_600 :: (Bool -> Bool -> Bool)
-> T_IsCommutativeMagma_214
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong'737'_600 = (Bool -> Bool -> Bool)
-> T_IsCommutativeMagma_214
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsCommutativeMonoid.assoc
d_assoc_604 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMonoid_764 ->
  Bool ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_assoc_604 :: T_IsCommutativeMonoid_764 -> Bool -> Bool -> Bool -> T__'8801'__12
d_assoc_604 = T_IsCommutativeMonoid_764 -> Bool -> Bool -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsCommutativeMonoid.comm
d_comm_606 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMonoid_764 ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_comm_606 :: T_IsCommutativeMonoid_764 -> Bool -> Bool -> T__'8801'__12
d_comm_606 = T_IsCommutativeMonoid_764 -> Bool -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsCommutativeMonoid.identity
d_identity_608 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMonoid_764 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_identity_608 :: T_IsCommutativeMonoid_764 -> T_Σ_14
d_identity_608 T_IsCommutativeMonoid_764
v0
  = (T_IsMonoid_712 -> T_Σ_14) -> Any -> T_Σ_14
forall a b. a -> b
coe
      T_IsMonoid_712 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_identity_724
      ((T_IsCommutativeMonoid_764 -> T_IsMonoid_712) -> Any -> Any
forall a b. a -> b
coe T_IsCommutativeMonoid_764 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_774 (T_IsCommutativeMonoid_764 -> Any
forall a b. a -> b
coe T_IsCommutativeMonoid_764
v0))
-- Data.Bool.Properties._.IsCommutativeMonoid.identityʳ
d_identity'691'_610 ::
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMonoid_764 ->
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_identity'691'_610 :: (Bool -> Bool -> Bool)
-> Bool -> T_IsCommutativeMonoid_764 -> Bool -> T__'8801'__12
d_identity'691'_610 = (Bool -> Bool -> Bool)
-> Bool -> T_IsCommutativeMonoid_764 -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsCommutativeMonoid.identityˡ
d_identity'737'_612 ::
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMonoid_764 ->
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_identity'737'_612 :: (Bool -> Bool -> Bool)
-> Bool -> T_IsCommutativeMonoid_764 -> Bool -> T__'8801'__12
d_identity'737'_612 = (Bool -> Bool -> Bool)
-> Bool -> T_IsCommutativeMonoid_764 -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsCommutativeMonoid.isCommutativeMagma
d_isCommutativeMagma_614 ::
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMonoid_764 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMagma_214
d_isCommutativeMagma_614 :: (Bool -> Bool -> Bool)
-> Bool -> T_IsCommutativeMonoid_764 -> T_IsCommutativeMagma_214
d_isCommutativeMagma_614 ~Bool -> Bool -> Bool
v0 ~Bool
v1 T_IsCommutativeMonoid_764
v2 = T_IsCommutativeMonoid_764 -> T_IsCommutativeMagma_214
du_isCommutativeMagma_614 T_IsCommutativeMonoid_764
v2
du_isCommutativeMagma_614 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMonoid_764 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMagma_214
du_isCommutativeMagma_614 :: T_IsCommutativeMonoid_764 -> T_IsCommutativeMagma_214
du_isCommutativeMagma_614 T_IsCommutativeMonoid_764
v0
  = (T_IsCommutativeSemigroup_568 -> T_IsCommutativeMagma_214)
-> Any -> T_IsCommutativeMagma_214
forall a b. a -> b
coe
      T_IsCommutativeSemigroup_568 -> T_IsCommutativeMagma_214
MAlonzo.Code.Algebra.Structures.du_isCommutativeMagma_606
      ((T_IsCommutativeMonoid_764 -> T_IsCommutativeSemigroup_568)
-> Any -> Any
forall a b. a -> b
coe
         T_IsCommutativeMonoid_764 -> T_IsCommutativeSemigroup_568
MAlonzo.Code.Algebra.Structures.du_isCommutativeSemigroup_814
         (T_IsCommutativeMonoid_764 -> Any
forall a b. a -> b
coe T_IsCommutativeMonoid_764
v0))
-- Data.Bool.Properties._.IsCommutativeMonoid.isCommutativeSemigroup
d_isCommutativeSemigroup_616 ::
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMonoid_764 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_568
d_isCommutativeSemigroup_616 :: (Bool -> Bool -> Bool)
-> Bool
-> T_IsCommutativeMonoid_764
-> T_IsCommutativeSemigroup_568
d_isCommutativeSemigroup_616 Bool -> Bool -> Bool
v0 Bool
v1 T_IsCommutativeMonoid_764
v2
  = (T_IsCommutativeMonoid_764 -> T_IsCommutativeSemigroup_568)
-> T_IsCommutativeMonoid_764 -> T_IsCommutativeSemigroup_568
forall a b. a -> b
coe
      T_IsCommutativeMonoid_764 -> T_IsCommutativeSemigroup_568
MAlonzo.Code.Algebra.Structures.du_isCommutativeSemigroup_814 T_IsCommutativeMonoid_764
v2
-- Data.Bool.Properties._.IsCommutativeMonoid.isEquivalence
d_isEquivalence_618 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMonoid_764 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
d_isEquivalence_618 :: T_IsCommutativeMonoid_764 -> T_IsEquivalence_28
d_isEquivalence_618 T_IsCommutativeMonoid_764
v0
  = (T_IsMagma_178 -> T_IsEquivalence_28) -> Any -> T_IsEquivalence_28
forall a b. a -> b
coe
      T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186
      ((T_IsSemigroup_488 -> T_IsMagma_178) -> Any -> Any
forall a b. a -> b
coe
         T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496
         ((T_IsMonoid_712 -> T_IsSemigroup_488) -> Any -> Any
forall a b. a -> b
coe
            T_IsMonoid_712 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_722
            ((T_IsCommutativeMonoid_764 -> T_IsMonoid_712) -> Any -> Any
forall a b. a -> b
coe T_IsCommutativeMonoid_764 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_774 (T_IsCommutativeMonoid_764 -> Any
forall a b. a -> b
coe T_IsCommutativeMonoid_764
v0))))
-- Data.Bool.Properties._.IsCommutativeMonoid.isMagma
d_isMagma_620 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMonoid_764 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_178
d_isMagma_620 :: T_IsCommutativeMonoid_764 -> T_IsMagma_178
d_isMagma_620 T_IsCommutativeMonoid_764
v0
  = (T_IsSemigroup_488 -> T_IsMagma_178) -> Any -> T_IsMagma_178
forall a b. a -> b
coe
      T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496
      ((T_IsMonoid_712 -> T_IsSemigroup_488) -> Any -> Any
forall a b. a -> b
coe
         T_IsMonoid_712 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_722
         ((T_IsCommutativeMonoid_764 -> T_IsMonoid_712) -> Any -> Any
forall a b. a -> b
coe T_IsCommutativeMonoid_764 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_774 (T_IsCommutativeMonoid_764 -> Any
forall a b. a -> b
coe T_IsCommutativeMonoid_764
v0)))
-- Data.Bool.Properties._.IsCommutativeMonoid.isMonoid
d_isMonoid_622 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMonoid_764 ->
  MAlonzo.Code.Algebra.Structures.T_IsMonoid_712
d_isMonoid_622 :: T_IsCommutativeMonoid_764 -> T_IsMonoid_712
d_isMonoid_622 T_IsCommutativeMonoid_764
v0
  = (T_IsCommutativeMonoid_764 -> T_IsMonoid_712)
-> Any -> T_IsMonoid_712
forall a b. a -> b
coe T_IsCommutativeMonoid_764 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_774 (T_IsCommutativeMonoid_764 -> Any
forall a b. a -> b
coe T_IsCommutativeMonoid_764
v0)
-- Data.Bool.Properties._.IsCommutativeMonoid.isPartialEquivalence
d_isPartialEquivalence_624 ::
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMonoid_764 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_624 :: (Bool -> Bool -> Bool)
-> Bool -> T_IsCommutativeMonoid_764 -> T_IsPartialEquivalence_16
d_isPartialEquivalence_624 ~Bool -> Bool -> Bool
v0 ~Bool
v1 T_IsCommutativeMonoid_764
v2
  = T_IsCommutativeMonoid_764 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_624 T_IsCommutativeMonoid_764
v2
du_isPartialEquivalence_624 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMonoid_764 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_624 :: T_IsCommutativeMonoid_764 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_624 T_IsCommutativeMonoid_764
v0
  = let v1 :: T_IsMonoid_712
v1
          = T_IsCommutativeMonoid_764 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_774 (T_IsCommutativeMonoid_764 -> T_IsCommutativeMonoid_764
forall a b. a -> b
coe T_IsCommutativeMonoid_764
v0) in
    Any -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsSemigroup_488
v2
             = T_IsMonoid_712 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_722 (T_IsMonoid_712 -> T_IsMonoid_712
forall a b. a -> b
coe T_IsMonoid_712
v1) in
       Any -> Any
forall a b. a -> b
coe
         (let v3 :: T_IsMagma_178
v3 = T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496 (T_IsSemigroup_488 -> T_IsSemigroup_488
forall a b. a -> b
coe T_IsSemigroup_488
v2) in
          Any -> Any
forall a b. a -> b
coe
            ((T_IsEquivalence_28 -> T_IsPartialEquivalence_16) -> Any -> Any
forall a b. a -> b
coe
               T_IsEquivalence_28 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_44
               ((T_IsMagma_178 -> T_IsEquivalence_28) -> Any -> Any
forall a b. a -> b
coe
                  T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186 (T_IsMagma_178 -> Any
forall a b. a -> b
coe T_IsMagma_178
v3)))))
-- Data.Bool.Properties._.IsCommutativeMonoid.isSemigroup
d_isSemigroup_626 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMonoid_764 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_488
d_isSemigroup_626 :: T_IsCommutativeMonoid_764 -> T_IsSemigroup_488
d_isSemigroup_626 T_IsCommutativeMonoid_764
v0
  = (T_IsMonoid_712 -> T_IsSemigroup_488) -> Any -> T_IsSemigroup_488
forall a b. a -> b
coe
      T_IsMonoid_712 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_722
      ((T_IsCommutativeMonoid_764 -> T_IsMonoid_712) -> Any -> Any
forall a b. a -> b
coe T_IsCommutativeMonoid_764 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_774 (T_IsCommutativeMonoid_764 -> Any
forall a b. a -> b
coe T_IsCommutativeMonoid_764
v0))
-- Data.Bool.Properties._.IsCommutativeMonoid.isUnitalMagma
d_isUnitalMagma_628 ::
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMonoid_764 ->
  MAlonzo.Code.Algebra.Structures.T_IsUnitalMagma_666
d_isUnitalMagma_628 :: (Bool -> Bool -> Bool)
-> Bool -> T_IsCommutativeMonoid_764 -> T_IsUnitalMagma_666
d_isUnitalMagma_628 ~Bool -> Bool -> Bool
v0 ~Bool
v1 T_IsCommutativeMonoid_764
v2 = T_IsCommutativeMonoid_764 -> T_IsUnitalMagma_666
du_isUnitalMagma_628 T_IsCommutativeMonoid_764
v2
du_isUnitalMagma_628 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMonoid_764 ->
  MAlonzo.Code.Algebra.Structures.T_IsUnitalMagma_666
du_isUnitalMagma_628 :: T_IsCommutativeMonoid_764 -> T_IsUnitalMagma_666
du_isUnitalMagma_628 T_IsCommutativeMonoid_764
v0
  = (T_IsMonoid_712 -> T_IsUnitalMagma_666)
-> Any -> T_IsUnitalMagma_666
forall a b. a -> b
coe
      T_IsMonoid_712 -> T_IsUnitalMagma_666
MAlonzo.Code.Algebra.Structures.du_isUnitalMagma_756
      ((T_IsCommutativeMonoid_764 -> T_IsMonoid_712) -> Any -> Any
forall a b. a -> b
coe T_IsCommutativeMonoid_764 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_774 (T_IsCommutativeMonoid_764 -> Any
forall a b. a -> b
coe T_IsCommutativeMonoid_764
v0))
-- Data.Bool.Properties._.IsCommutativeMonoid.refl
d_refl_630 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMonoid_764 ->
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_refl_630 :: T_IsCommutativeMonoid_764 -> Bool -> T__'8801'__12
d_refl_630 = T_IsCommutativeMonoid_764 -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsCommutativeMonoid.reflexive
d_reflexive_632 ::
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMonoid_764 ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_reflexive_632 :: (Bool -> Bool -> Bool)
-> Bool
-> T_IsCommutativeMonoid_764
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_reflexive_632 = (Bool -> Bool -> Bool)
-> Bool
-> T_IsCommutativeMonoid_764
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsCommutativeMonoid.setoid
d_setoid_634 ::
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMonoid_764 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
d_setoid_634 :: (Bool -> Bool -> Bool)
-> Bool -> T_IsCommutativeMonoid_764 -> T_Setoid_46
d_setoid_634 ~Bool -> Bool -> Bool
v0 ~Bool
v1 T_IsCommutativeMonoid_764
v2 = T_IsCommutativeMonoid_764 -> T_Setoid_46
du_setoid_634 T_IsCommutativeMonoid_764
v2
du_setoid_634 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMonoid_764 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
du_setoid_634 :: T_IsCommutativeMonoid_764 -> T_Setoid_46
du_setoid_634 T_IsCommutativeMonoid_764
v0
  = let v1 :: T_IsMonoid_712
v1
          = T_IsCommutativeMonoid_764 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_774 (T_IsCommutativeMonoid_764 -> T_IsCommutativeMonoid_764
forall a b. a -> b
coe T_IsCommutativeMonoid_764
v0) in
    Any -> T_Setoid_46
forall a b. a -> b
coe
      (let v2 :: T_IsSemigroup_488
v2
             = T_IsMonoid_712 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_722 (T_IsMonoid_712 -> T_IsMonoid_712
forall a b. a -> b
coe T_IsMonoid_712
v1) in
       Any -> Any
forall a b. a -> b
coe
         ((T_IsMagma_178 -> T_Setoid_46) -> Any -> Any
forall a b. a -> b
coe
            T_IsMagma_178 -> T_Setoid_46
MAlonzo.Code.Algebra.Structures.du_setoid_202
            ((T_IsSemigroup_488 -> T_IsMagma_178) -> Any -> Any
forall a b. a -> b
coe T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496 (T_IsSemigroup_488 -> Any
forall a b. a -> b
coe T_IsSemigroup_488
v2))))
-- Data.Bool.Properties._.IsCommutativeMonoid.sym
d_sym_636 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMonoid_764 ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_sym_636 :: T_IsCommutativeMonoid_764
-> Bool -> Bool -> T__'8801'__12 -> T__'8801'__12
d_sym_636 = T_IsCommutativeMonoid_764
-> Bool -> Bool -> T__'8801'__12 -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsCommutativeMonoid.trans
d_trans_638 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMonoid_764 ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_trans_638 :: T_IsCommutativeMonoid_764
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
d_trans_638 = T_IsCommutativeMonoid_764
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsCommutativeMonoid.∙-cong
d_'8729''45'cong_640 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMonoid_764 ->
  Bool ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8729''45'cong_640 :: T_IsCommutativeMonoid_764
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong_640 = T_IsCommutativeMonoid_764
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsCommutativeMonoid.∙-congʳ
d_'8729''45'cong'691'_642 ::
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMonoid_764 ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8729''45'cong'691'_642 :: (Bool -> Bool -> Bool)
-> Bool
-> T_IsCommutativeMonoid_764
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong'691'_642 = (Bool -> Bool -> Bool)
-> Bool
-> T_IsCommutativeMonoid_764
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsCommutativeMonoid.∙-congˡ
d_'8729''45'cong'737'_644 ::
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMonoid_764 ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8729''45'cong'737'_644 :: (Bool -> Bool -> Bool)
-> Bool
-> T_IsCommutativeMonoid_764
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong'737'_644 = (Bool -> Bool -> Bool)
-> Bool
-> T_IsCommutativeMonoid_764
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsCommutativeRing._//_
d__'47''47'__648 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeRing_2888 ->
  Bool -> Bool -> Bool
d__'47''47'__648 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsCommutativeRing_2888
-> Bool
-> Bool
-> Bool
d__'47''47'__648 Bool -> Bool -> Bool
v0 ~Bool -> Bool -> Bool
v1 Bool -> Bool
v2 ~Bool
v3 ~Bool
v4 ~T_IsCommutativeRing_2888
v5 = (Bool -> Bool -> Bool) -> (Bool -> Bool) -> Bool -> Bool -> Bool
du__'47''47'__648 Bool -> Bool -> Bool
v0 Bool -> Bool
v2
du__'47''47'__648 ::
  (Bool -> Bool -> Bool) -> (Bool -> Bool) -> Bool -> Bool -> Bool
du__'47''47'__648 :: (Bool -> Bool -> Bool) -> (Bool -> Bool) -> Bool -> Bool -> Bool
du__'47''47'__648 Bool -> Bool -> Bool
v0 Bool -> Bool
v1
  = ((Any -> Any -> Any) -> (Any -> Any) -> Any -> Any -> Any)
-> Any -> Any -> Bool -> Bool -> Bool
forall a b. a -> b
coe
      (Any -> Any -> Any) -> (Any -> Any) -> Any -> Any -> Any
MAlonzo.Code.Algebra.Structures.du__'47''47'__1136 ((Bool -> Bool -> Bool) -> Any
forall a b. a -> b
coe Bool -> Bool -> Bool
v0)
      ((Bool -> Bool) -> Any
forall a b. a -> b
coe Bool -> Bool
v1)
-- Data.Bool.Properties._.IsCommutativeRing.*-assoc
d_'42''45'assoc_650 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeRing_2888 ->
  Bool ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'42''45'assoc_650 :: T_IsCommutativeRing_2888 -> Bool -> Bool -> Bool -> T__'8801'__12
d_'42''45'assoc_650 = T_IsCommutativeRing_2888 -> Bool -> Bool -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsCommutativeRing.*-comm
d_'42''45'comm_652 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeRing_2888 ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'42''45'comm_652 :: T_IsCommutativeRing_2888 -> Bool -> Bool -> T__'8801'__12
d_'42''45'comm_652 = T_IsCommutativeRing_2888 -> Bool -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsCommutativeRing.*-cong
d_'42''45'cong_654 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeRing_2888 ->
  Bool ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'42''45'cong_654 :: T_IsCommutativeRing_2888
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
d_'42''45'cong_654 = T_IsCommutativeRing_2888
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsCommutativeRing.∙-congʳ
d_'8729''45'cong'691'_656 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeRing_2888 ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8729''45'cong'691'_656 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsCommutativeRing_2888
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong'691'_656 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsCommutativeRing_2888
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsCommutativeRing.∙-congˡ
d_'8729''45'cong'737'_658 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeRing_2888 ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8729''45'cong'737'_658 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsCommutativeRing_2888
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong'737'_658 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsCommutativeRing_2888
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsCommutativeRing.*-identity
d_'42''45'identity_660 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeRing_2888 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'42''45'identity_660 :: T_IsCommutativeRing_2888 -> T_Σ_14
d_'42''45'identity_660 T_IsCommutativeRing_2888
v0
  = (T_IsRing_2740 -> T_Σ_14) -> Any -> T_Σ_14
forall a b. a -> b
coe
      T_IsRing_2740 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_'42''45'identity_2768
      ((T_IsCommutativeRing_2888 -> T_IsRing_2740) -> Any -> Any
forall a b. a -> b
coe T_IsCommutativeRing_2888 -> T_IsRing_2740
MAlonzo.Code.Algebra.Structures.d_isRing_2904 (T_IsCommutativeRing_2888 -> Any
forall a b. a -> b
coe T_IsCommutativeRing_2888
v0))
-- Data.Bool.Properties._.IsCommutativeRing.identityʳ
d_identity'691'_662 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeRing_2888 ->
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_identity'691'_662 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsCommutativeRing_2888
-> Bool
-> T__'8801'__12
d_identity'691'_662 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsCommutativeRing_2888
-> Bool
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsCommutativeRing.identityˡ
d_identity'737'_664 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeRing_2888 ->
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_identity'737'_664 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsCommutativeRing_2888
-> Bool
-> T__'8801'__12
d_identity'737'_664 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsCommutativeRing_2888
-> Bool
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsCommutativeRing.isCommutativeMagma
d_isCommutativeMagma_666 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeRing_2888 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMagma_214
d_isCommutativeMagma_666 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsCommutativeRing_2888
-> T_IsCommutativeMagma_214
d_isCommutativeMagma_666 Bool -> Bool -> Bool
v0 Bool -> Bool -> Bool
v1 Bool -> Bool
v2 Bool
v3 ~Bool
v4 T_IsCommutativeRing_2888
v5
  = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> T_IsCommutativeRing_2888
-> T_IsCommutativeMagma_214
du_isCommutativeMagma_666 Bool -> Bool -> Bool
v0 Bool -> Bool -> Bool
v1 Bool -> Bool
v2 Bool
v3 T_IsCommutativeRing_2888
v5
du_isCommutativeMagma_666 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeRing_2888 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMagma_214
du_isCommutativeMagma_666 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> T_IsCommutativeRing_2888
-> T_IsCommutativeMagma_214
du_isCommutativeMagma_666 Bool -> Bool -> Bool
v0 Bool -> Bool -> Bool
v1 Bool -> Bool
v2 Bool
v3 T_IsCommutativeRing_2888
v4
  = let v5 :: Any
v5
          = ((Any -> Any -> Any)
 -> (Any -> Any -> Any)
 -> (Any -> Any)
 -> Any
 -> T_IsCommutativeRing_2888
 -> T_IsCommutativeSemiring_1750)
-> Any -> Any -> Any -> Any -> Any -> Any
forall a b. a -> b
coe
              (Any -> Any -> Any)
-> (Any -> Any -> Any)
-> (Any -> Any)
-> Any
-> T_IsCommutativeRing_2888
-> T_IsCommutativeSemiring_1750
MAlonzo.Code.Algebra.Structures.du_isCommutativeSemiring_3018
              ((Bool -> Bool -> Bool) -> Any
forall a b. a -> b
coe Bool -> Bool -> Bool
v0) ((Bool -> Bool -> Bool) -> Any
forall a b. a -> b
coe Bool -> Bool -> Bool
v1) ((Bool -> Bool) -> Any
forall a b. a -> b
coe Bool -> Bool
v2) (Bool -> Any
forall a b. a -> b
coe Bool
v3) (T_IsCommutativeRing_2888 -> Any
forall a b. a -> b
coe T_IsCommutativeRing_2888
v4) in
    Any -> T_IsCommutativeMagma_214
forall a b. a -> b
coe
      (let v6 :: Any
v6
             = (T_IsCommutativeSemiring_1750
 -> T_IsCommutativeSemiringWithoutOne_1438)
-> Any -> Any
forall a b. a -> b
coe
                 T_IsCommutativeSemiring_1750
-> T_IsCommutativeSemiringWithoutOne_1438
MAlonzo.Code.Algebra.Structures.du_isCommutativeSemiringWithoutOne_1852
                 (Any -> Any
forall a b. a -> b
coe Any
v5) in
       Any -> Any
forall a b. a -> b
coe
         ((T_IsCommutativeSemigroup_568 -> T_IsCommutativeMagma_214)
-> Any -> Any
forall a b. a -> b
coe
            T_IsCommutativeSemigroup_568 -> T_IsCommutativeMagma_214
MAlonzo.Code.Algebra.Structures.du_isCommutativeMagma_606
            ((T_IsCommutativeSemiringWithoutOne_1438
 -> T_IsCommutativeSemigroup_568)
-> Any -> Any
forall a b. a -> b
coe
               T_IsCommutativeSemiringWithoutOne_1438
-> T_IsCommutativeSemigroup_568
MAlonzo.Code.Algebra.Structures.du_'42''45'isCommutativeSemigroup_1520
               (Any -> Any
forall a b. a -> b
coe Any
v6))))
-- Data.Bool.Properties._.IsCommutativeRing.*-isCommutativeMonoid
d_'42''45'isCommutativeMonoid_668 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeRing_2888 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMonoid_764
d_'42''45'isCommutativeMonoid_668 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsCommutativeRing_2888
-> T_IsCommutativeMonoid_764
d_'42''45'isCommutativeMonoid_668 Bool -> Bool -> Bool
v0 Bool -> Bool -> Bool
v1 Bool -> Bool
v2 Bool
v3 ~Bool
v4 T_IsCommutativeRing_2888
v5
  = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> T_IsCommutativeRing_2888
-> T_IsCommutativeMonoid_764
du_'42''45'isCommutativeMonoid_668 Bool -> Bool -> Bool
v0 Bool -> Bool -> Bool
v1 Bool -> Bool
v2 Bool
v3 T_IsCommutativeRing_2888
v5
du_'42''45'isCommutativeMonoid_668 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeRing_2888 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMonoid_764
du_'42''45'isCommutativeMonoid_668 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> T_IsCommutativeRing_2888
-> T_IsCommutativeMonoid_764
du_'42''45'isCommutativeMonoid_668 Bool -> Bool -> Bool
v0 Bool -> Bool -> Bool
v1 Bool -> Bool
v2 Bool
v3 T_IsCommutativeRing_2888
v4
  = (T_IsCommutativeSemiring_1750 -> T_IsCommutativeMonoid_764)
-> Any -> T_IsCommutativeMonoid_764
forall a b. a -> b
coe
      T_IsCommutativeSemiring_1750 -> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.du_'42''45'isCommutativeMonoid_1860
      (((Any -> Any -> Any)
 -> (Any -> Any -> Any)
 -> (Any -> Any)
 -> Any
 -> T_IsCommutativeRing_2888
 -> T_IsCommutativeSemiring_1750)
-> Any -> Any -> Any -> Any -> Any -> Any
forall a b. a -> b
coe
         (Any -> Any -> Any)
-> (Any -> Any -> Any)
-> (Any -> Any)
-> Any
-> T_IsCommutativeRing_2888
-> T_IsCommutativeSemiring_1750
MAlonzo.Code.Algebra.Structures.du_isCommutativeSemiring_3018
         ((Bool -> Bool -> Bool) -> Any
forall a b. a -> b
coe Bool -> Bool -> Bool
v0) ((Bool -> Bool -> Bool) -> Any
forall a b. a -> b
coe Bool -> Bool -> Bool
v1) ((Bool -> Bool) -> Any
forall a b. a -> b
coe Bool -> Bool
v2) (Bool -> Any
forall a b. a -> b
coe Bool
v3) (T_IsCommutativeRing_2888 -> Any
forall a b. a -> b
coe T_IsCommutativeRing_2888
v4))
-- Data.Bool.Properties._.IsCommutativeRing.*-isCommutativeSemigroup
d_'42''45'isCommutativeSemigroup_670 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeRing_2888 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_568
d_'42''45'isCommutativeSemigroup_670 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsCommutativeRing_2888
-> T_IsCommutativeSemigroup_568
d_'42''45'isCommutativeSemigroup_670 Bool -> Bool -> Bool
v0 Bool -> Bool -> Bool
v1 Bool -> Bool
v2 Bool
v3 ~Bool
v4 T_IsCommutativeRing_2888
v5
  = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> T_IsCommutativeRing_2888
-> T_IsCommutativeSemigroup_568
du_'42''45'isCommutativeSemigroup_670 Bool -> Bool -> Bool
v0 Bool -> Bool -> Bool
v1 Bool -> Bool
v2 Bool
v3 T_IsCommutativeRing_2888
v5
du_'42''45'isCommutativeSemigroup_670 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeRing_2888 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_568
du_'42''45'isCommutativeSemigroup_670 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> T_IsCommutativeRing_2888
-> T_IsCommutativeSemigroup_568
du_'42''45'isCommutativeSemigroup_670 Bool -> Bool -> Bool
v0 Bool -> Bool -> Bool
v1 Bool -> Bool
v2 Bool
v3 T_IsCommutativeRing_2888
v4
  = let v5 :: Any
v5
          = ((Any -> Any -> Any)
 -> (Any -> Any -> Any)
 -> (Any -> Any)
 -> Any
 -> T_IsCommutativeRing_2888
 -> T_IsCommutativeSemiring_1750)
-> Any -> Any -> Any -> Any -> Any -> Any
forall a b. a -> b
coe
              (Any -> Any -> Any)
-> (Any -> Any -> Any)
-> (Any -> Any)
-> Any
-> T_IsCommutativeRing_2888
-> T_IsCommutativeSemiring_1750
MAlonzo.Code.Algebra.Structures.du_isCommutativeSemiring_3018
              ((Bool -> Bool -> Bool) -> Any
forall a b. a -> b
coe Bool -> Bool -> Bool
v0) ((Bool -> Bool -> Bool) -> Any
forall a b. a -> b
coe Bool -> Bool -> Bool
v1) ((Bool -> Bool) -> Any
forall a b. a -> b
coe Bool -> Bool
v2) (Bool -> Any
forall a b. a -> b
coe Bool
v3) (T_IsCommutativeRing_2888 -> Any
forall a b. a -> b
coe T_IsCommutativeRing_2888
v4) in
    Any -> T_IsCommutativeSemigroup_568
forall a b. a -> b
coe
      ((T_IsCommutativeSemiringWithoutOne_1438
 -> T_IsCommutativeSemigroup_568)
-> Any -> Any
forall a b. a -> b
coe
         T_IsCommutativeSemiringWithoutOne_1438
-> T_IsCommutativeSemigroup_568
MAlonzo.Code.Algebra.Structures.du_'42''45'isCommutativeSemigroup_1520
         ((T_IsCommutativeSemiring_1750
 -> T_IsCommutativeSemiringWithoutOne_1438)
-> Any -> Any
forall a b. a -> b
coe
            T_IsCommutativeSemiring_1750
-> T_IsCommutativeSemiringWithoutOne_1438
MAlonzo.Code.Algebra.Structures.du_isCommutativeSemiringWithoutOne_1852
            (Any -> Any
forall a b. a -> b
coe Any
v5)))
-- Data.Bool.Properties._.IsCommutativeRing.*-isMagma
d_'42''45'isMagma_672 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeRing_2888 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_178
d_'42''45'isMagma_672 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsCommutativeRing_2888
-> T_IsMagma_178
d_'42''45'isMagma_672 Bool -> Bool -> Bool
v0 Bool -> Bool -> Bool
v1 Bool -> Bool
v2 Bool
v3 ~Bool
v4 T_IsCommutativeRing_2888
v5
  = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> T_IsCommutativeRing_2888
-> T_IsMagma_178
du_'42''45'isMagma_672 Bool -> Bool -> Bool
v0 Bool -> Bool -> Bool
v1 Bool -> Bool
v2 Bool
v3 T_IsCommutativeRing_2888
v5
du_'42''45'isMagma_672 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeRing_2888 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_178
du_'42''45'isMagma_672 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> T_IsCommutativeRing_2888
-> T_IsMagma_178
du_'42''45'isMagma_672 Bool -> Bool -> Bool
v0 Bool -> Bool -> Bool
v1 Bool -> Bool
v2 Bool
v3 T_IsCommutativeRing_2888
v4
  = let v5 :: T_IsRing_2740
v5
          = T_IsCommutativeRing_2888 -> T_IsRing_2740
MAlonzo.Code.Algebra.Structures.d_isRing_2904 (T_IsCommutativeRing_2888 -> T_IsCommutativeRing_2888
forall a b. a -> b
coe T_IsCommutativeRing_2888
v4) in
    Any -> T_IsMagma_178
forall a b. a -> b
coe
      (let v6 :: Any
v6
             = (T_IsRing_2740 -> T_IsRingWithoutOne_2368) -> Any -> Any
forall a b. a -> b
coe
                 T_IsRing_2740 -> T_IsRingWithoutOne_2368
MAlonzo.Code.Algebra.Structures.du_isRingWithoutOne_2772
                 (T_IsRing_2740 -> Any
forall a b. a -> b
coe T_IsRing_2740
v5) in
       Any -> Any
forall a b. a -> b
coe
         ((T_IsNearSemiring_1260 -> T_IsMagma_178) -> Any -> Any
forall a b. a -> b
coe
            T_IsNearSemiring_1260 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.du_'42''45'isMagma_1324
            (((Any -> Any -> Any)
 -> (Any -> Any -> Any)
 -> (Any -> Any)
 -> Any
 -> T_IsRingWithoutOne_2368
 -> T_IsNearSemiring_1260)
-> Any -> Any -> Any -> Any -> Any -> Any
forall a b. a -> b
coe
               (Any -> Any -> Any)
-> (Any -> Any -> Any)
-> (Any -> Any)
-> Any
-> T_IsRingWithoutOne_2368
-> T_IsNearSemiring_1260
MAlonzo.Code.Algebra.Structures.du_isNearSemiring_2470 ((Bool -> Bool -> Bool) -> Any
forall a b. a -> b
coe Bool -> Bool -> Bool
v0)
               ((Bool -> Bool -> Bool) -> Any
forall a b. a -> b
coe Bool -> Bool -> Bool
v1) ((Bool -> Bool) -> Any
forall a b. a -> b
coe Bool -> Bool
v2) (Bool -> Any
forall a b. a -> b
coe Bool
v3) (Any -> Any
forall a b. a -> b
coe Any
v6))))
-- Data.Bool.Properties._.IsCommutativeRing.*-isMonoid
d_'42''45'isMonoid_674 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeRing_2888 ->
  MAlonzo.Code.Algebra.Structures.T_IsMonoid_712
d_'42''45'isMonoid_674 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsCommutativeRing_2888
-> T_IsMonoid_712
d_'42''45'isMonoid_674 Bool -> Bool -> Bool
v0 Bool -> Bool -> Bool
v1 Bool -> Bool
v2 Bool
v3 ~Bool
v4 T_IsCommutativeRing_2888
v5
  = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> T_IsCommutativeRing_2888
-> T_IsMonoid_712
du_'42''45'isMonoid_674 Bool -> Bool -> Bool
v0 Bool -> Bool -> Bool
v1 Bool -> Bool
v2 Bool
v3 T_IsCommutativeRing_2888
v5
du_'42''45'isMonoid_674 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeRing_2888 ->
  MAlonzo.Code.Algebra.Structures.T_IsMonoid_712
du_'42''45'isMonoid_674 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> T_IsCommutativeRing_2888
-> T_IsMonoid_712
du_'42''45'isMonoid_674 Bool -> Bool -> Bool
v0 Bool -> Bool -> Bool
v1 Bool -> Bool
v2 Bool
v3 T_IsCommutativeRing_2888
v4
  = ((Any -> Any -> Any)
 -> (Any -> Any -> Any)
 -> (Any -> Any)
 -> Any
 -> T_IsRing_2740
 -> T_IsMonoid_712)
-> Any -> Any -> Any -> Any -> Any -> T_IsMonoid_712
forall a b. a -> b
coe
      (Any -> Any -> Any)
-> (Any -> Any -> Any)
-> (Any -> Any)
-> Any
-> T_IsRing_2740
-> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.du_'42''45'isMonoid_2860 ((Bool -> Bool -> Bool) -> Any
forall a b. a -> b
coe Bool -> Bool -> Bool
v0)
      ((Bool -> Bool -> Bool) -> Any
forall a b. a -> b
coe Bool -> Bool -> Bool
v1) ((Bool -> Bool) -> Any
forall a b. a -> b
coe Bool -> Bool
v2) (Bool -> Any
forall a b. a -> b
coe Bool
v3)
      ((T_IsCommutativeRing_2888 -> T_IsRing_2740) -> Any -> Any
forall a b. a -> b
coe T_IsCommutativeRing_2888 -> T_IsRing_2740
MAlonzo.Code.Algebra.Structures.d_isRing_2904 (T_IsCommutativeRing_2888 -> Any
forall a b. a -> b
coe T_IsCommutativeRing_2888
v4))
-- Data.Bool.Properties._.IsCommutativeRing.*-isSemigroup
d_'42''45'isSemigroup_676 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeRing_2888 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_488
d_'42''45'isSemigroup_676 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsCommutativeRing_2888
-> T_IsSemigroup_488
d_'42''45'isSemigroup_676 Bool -> Bool -> Bool
v0 Bool -> Bool -> Bool
v1 Bool -> Bool
v2 Bool
v3 ~Bool
v4 T_IsCommutativeRing_2888
v5
  = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> T_IsCommutativeRing_2888
-> T_IsSemigroup_488
du_'42''45'isSemigroup_676 Bool -> Bool -> Bool
v0 Bool -> Bool -> Bool
v1 Bool -> Bool
v2 Bool
v3 T_IsCommutativeRing_2888
v5
du_'42''45'isSemigroup_676 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeRing_2888 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_488
du_'42''45'isSemigroup_676 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> T_IsCommutativeRing_2888
-> T_IsSemigroup_488
du_'42''45'isSemigroup_676 Bool -> Bool -> Bool
v0 Bool -> Bool -> Bool
v1 Bool -> Bool
v2 Bool
v3 T_IsCommutativeRing_2888
v4
  = let v5 :: T_IsRing_2740
v5
          = T_IsCommutativeRing_2888 -> T_IsRing_2740
MAlonzo.Code.Algebra.Structures.d_isRing_2904 (T_IsCommutativeRing_2888 -> T_IsCommutativeRing_2888
forall a b. a -> b
coe T_IsCommutativeRing_2888
v4) in
    Any -> T_IsSemigroup_488
forall a b. a -> b
coe
      (let v6 :: Any
v6
             = (T_IsRing_2740 -> T_IsRingWithoutOne_2368) -> Any -> Any
forall a b. a -> b
coe
                 T_IsRing_2740 -> T_IsRingWithoutOne_2368
MAlonzo.Code.Algebra.Structures.du_isRingWithoutOne_2772
                 (T_IsRing_2740 -> Any
forall a b. a -> b
coe T_IsRing_2740
v5) in
       Any -> Any
forall a b. a -> b
coe
         ((T_IsNearSemiring_1260 -> T_IsSemigroup_488) -> Any -> Any
forall a b. a -> b
coe
            T_IsNearSemiring_1260 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.du_'42''45'isSemigroup_1326
            (((Any -> Any -> Any)
 -> (Any -> Any -> Any)
 -> (Any -> Any)
 -> Any
 -> T_IsRingWithoutOne_2368
 -> T_IsNearSemiring_1260)
-> Any -> Any -> Any -> Any -> Any -> Any
forall a b. a -> b
coe
               (Any -> Any -> Any)
-> (Any -> Any -> Any)
-> (Any -> Any)
-> Any
-> T_IsRingWithoutOne_2368
-> T_IsNearSemiring_1260
MAlonzo.Code.Algebra.Structures.du_isNearSemiring_2470 ((Bool -> Bool -> Bool) -> Any
forall a b. a -> b
coe Bool -> Bool -> Bool
v0)
               ((Bool -> Bool -> Bool) -> Any
forall a b. a -> b
coe Bool -> Bool -> Bool
v1) ((Bool -> Bool) -> Any
forall a b. a -> b
coe Bool -> Bool
v2) (Bool -> Any
forall a b. a -> b
coe Bool
v3) (Any -> Any
forall a b. a -> b
coe Any
v6))))
-- Data.Bool.Properties._.IsCommutativeRing.assoc
d_assoc_678 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeRing_2888 ->
  Bool ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_assoc_678 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsCommutativeRing_2888
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
d_assoc_678 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsCommutativeRing_2888
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsCommutativeRing.comm
d_comm_680 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeRing_2888 ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_comm_680 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsCommutativeRing_2888
-> Bool
-> Bool
-> T__'8801'__12
d_comm_680 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsCommutativeRing_2888
-> Bool
-> Bool
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsCommutativeRing.∙-cong
d_'8729''45'cong_682 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeRing_2888 ->
  Bool ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8729''45'cong_682 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsCommutativeRing_2888
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong_682 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsCommutativeRing_2888
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsCommutativeRing.∙-congʳ
d_'8729''45'cong'691'_684 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeRing_2888 ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8729''45'cong'691'_684 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsCommutativeRing_2888
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong'691'_684 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsCommutativeRing_2888
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsCommutativeRing.∙-congˡ
d_'8729''45'cong'737'_686 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeRing_2888 ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8729''45'cong'737'_686 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsCommutativeRing_2888
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong'737'_686 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsCommutativeRing_2888
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsCommutativeRing.identity
d_identity_688 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeRing_2888 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_identity_688 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsCommutativeRing_2888
-> T_Σ_14
d_identity_688 ~Bool -> Bool -> Bool
v0 ~Bool -> Bool -> Bool
v1 ~Bool -> Bool
v2 ~Bool
v3 ~Bool
v4 T_IsCommutativeRing_2888
v5 = T_IsCommutativeRing_2888 -> T_Σ_14
du_identity_688 T_IsCommutativeRing_2888
v5
du_identity_688 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeRing_2888 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
du_identity_688 :: T_IsCommutativeRing_2888 -> T_Σ_14
du_identity_688 T_IsCommutativeRing_2888
v0
  = let v1 :: T_IsRing_2740
v1
          = T_IsCommutativeRing_2888 -> T_IsRing_2740
MAlonzo.Code.Algebra.Structures.d_isRing_2904 (T_IsCommutativeRing_2888 -> T_IsCommutativeRing_2888
forall a b. a -> b
coe T_IsCommutativeRing_2888
v0) in
    Any -> T_Σ_14
forall a b. a -> b
coe
      ((T_IsMonoid_712 -> T_Σ_14) -> Any -> Any
forall a b. a -> b
coe
         T_IsMonoid_712 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_identity_724
         ((T_IsGroup_1074 -> T_IsMonoid_712) -> Any -> Any
forall a b. a -> b
coe
            T_IsGroup_1074 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_1088
            ((T_IsAbelianGroup_1172 -> T_IsGroup_1074) -> Any -> Any
forall a b. a -> b
coe
               T_IsAbelianGroup_1172 -> T_IsGroup_1074
MAlonzo.Code.Algebra.Structures.d_isGroup_1184
               ((T_IsRing_2740 -> T_IsAbelianGroup_1172) -> Any -> Any
forall a b. a -> b
coe
                  T_IsRing_2740 -> T_IsAbelianGroup_1172
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2762
                  (T_IsRing_2740 -> Any
forall a b. a -> b
coe T_IsRing_2740
v1)))))
-- Data.Bool.Properties._.IsCommutativeRing.identityʳ
d_identity'691'_690 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeRing_2888 ->
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_identity'691'_690 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsCommutativeRing_2888
-> Bool
-> T__'8801'__12
d_identity'691'_690 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsCommutativeRing_2888
-> Bool
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsCommutativeRing.identityˡ
d_identity'737'_692 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeRing_2888 ->
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_identity'737'_692 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsCommutativeRing_2888
-> Bool
-> T__'8801'__12
d_identity'737'_692 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsCommutativeRing_2888
-> Bool
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsCommutativeRing.+-isAbelianGroup
d_'43''45'isAbelianGroup_694 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeRing_2888 ->
  MAlonzo.Code.Algebra.Structures.T_IsAbelianGroup_1172
d_'43''45'isAbelianGroup_694 :: T_IsCommutativeRing_2888 -> T_IsAbelianGroup_1172
d_'43''45'isAbelianGroup_694 T_IsCommutativeRing_2888
v0
  = (T_IsRing_2740 -> T_IsAbelianGroup_1172)
-> Any -> T_IsAbelianGroup_1172
forall a b. a -> b
coe
      T_IsRing_2740 -> T_IsAbelianGroup_1172
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2762
      ((T_IsCommutativeRing_2888 -> T_IsRing_2740) -> Any -> Any
forall a b. a -> b
coe T_IsCommutativeRing_2888 -> T_IsRing_2740
MAlonzo.Code.Algebra.Structures.d_isRing_2904 (T_IsCommutativeRing_2888 -> Any
forall a b. a -> b
coe T_IsCommutativeRing_2888
v0))
-- Data.Bool.Properties._.IsCommutativeRing.isCommutativeMagma
d_isCommutativeMagma_696 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeRing_2888 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMagma_214
d_isCommutativeMagma_696 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsCommutativeRing_2888
-> T_IsCommutativeMagma_214
d_isCommutativeMagma_696 ~Bool -> Bool -> Bool
v0 ~Bool -> Bool -> Bool
v1 ~Bool -> Bool
v2 ~Bool
v3 ~Bool
v4 T_IsCommutativeRing_2888
v5
  = T_IsCommutativeRing_2888 -> T_IsCommutativeMagma_214
du_isCommutativeMagma_696 T_IsCommutativeRing_2888
v5
du_isCommutativeMagma_696 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeRing_2888 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMagma_214
du_isCommutativeMagma_696 :: T_IsCommutativeRing_2888 -> T_IsCommutativeMagma_214
du_isCommutativeMagma_696 T_IsCommutativeRing_2888
v0
  = let v1 :: T_IsRing_2740
v1
          = T_IsCommutativeRing_2888 -> T_IsRing_2740
MAlonzo.Code.Algebra.Structures.d_isRing_2904 (T_IsCommutativeRing_2888 -> T_IsCommutativeRing_2888
forall a b. a -> b
coe T_IsCommutativeRing_2888
v0) in
    Any -> T_IsCommutativeMagma_214
forall a b. a -> b
coe
      (let v2 :: Any
v2
             = (T_IsRing_2740 -> T_IsRingWithoutOne_2368) -> Any -> Any
forall a b. a -> b
coe
                 T_IsRing_2740 -> T_IsRingWithoutOne_2368
MAlonzo.Code.Algebra.Structures.du_isRingWithoutOne_2772
                 (T_IsRing_2740 -> Any
forall a b. a -> b
coe T_IsRing_2740
v1) in
       Any -> Any
forall a b. a -> b
coe
         (let v3 :: T_IsAbelianGroup_1172
v3
                = T_IsRingWithoutOne_2368 -> T_IsAbelianGroup_1172
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2386
                    (Any -> T_IsRingWithoutOne_2368
forall a b. a -> b
coe Any
v2) in
          Any -> Any
forall a b. a -> b
coe
            (let v4 :: Any
v4
                   = (T_IsAbelianGroup_1172 -> T_IsCommutativeMonoid_764) -> Any -> Any
forall a b. a -> b
coe
                       T_IsAbelianGroup_1172 -> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.du_isCommutativeMonoid_1244
                       (T_IsAbelianGroup_1172 -> Any
forall a b. a -> b
coe T_IsAbelianGroup_1172
v3) in
             Any -> Any
forall a b. a -> b
coe
               ((T_IsCommutativeSemigroup_568 -> T_IsCommutativeMagma_214)
-> Any -> Any
forall a b. a -> b
coe
                  T_IsCommutativeSemigroup_568 -> T_IsCommutativeMagma_214
MAlonzo.Code.Algebra.Structures.du_isCommutativeMagma_606
                  ((T_IsCommutativeMonoid_764 -> T_IsCommutativeSemigroup_568)
-> Any -> Any
forall a b. a -> b
coe
                     T_IsCommutativeMonoid_764 -> T_IsCommutativeSemigroup_568
MAlonzo.Code.Algebra.Structures.du_isCommutativeSemigroup_814
                     (Any -> Any
forall a b. a -> b
coe Any
v4))))))
-- Data.Bool.Properties._.IsCommutativeRing.isCommutativeMonoid
d_isCommutativeMonoid_698 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeRing_2888 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMonoid_764
d_isCommutativeMonoid_698 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsCommutativeRing_2888
-> T_IsCommutativeMonoid_764
d_isCommutativeMonoid_698 ~Bool -> Bool -> Bool
v0 ~Bool -> Bool -> Bool
v1 ~Bool -> Bool
v2 ~Bool
v3 ~Bool
v4 T_IsCommutativeRing_2888
v5
  = T_IsCommutativeRing_2888 -> T_IsCommutativeMonoid_764
du_isCommutativeMonoid_698 T_IsCommutativeRing_2888
v5
du_isCommutativeMonoid_698 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeRing_2888 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMonoid_764
du_isCommutativeMonoid_698 :: T_IsCommutativeRing_2888 -> T_IsCommutativeMonoid_764
du_isCommutativeMonoid_698 T_IsCommutativeRing_2888
v0
  = let v1 :: T_IsRing_2740
v1
          = T_IsCommutativeRing_2888 -> T_IsRing_2740
MAlonzo.Code.Algebra.Structures.d_isRing_2904 (T_IsCommutativeRing_2888 -> T_IsCommutativeRing_2888
forall a b. a -> b
coe T_IsCommutativeRing_2888
v0) in
    Any -> T_IsCommutativeMonoid_764
forall a b. a -> b
coe
      (let v2 :: Any
v2
             = (T_IsRing_2740 -> T_IsRingWithoutOne_2368) -> Any -> Any
forall a b. a -> b
coe
                 T_IsRing_2740 -> T_IsRingWithoutOne_2368
MAlonzo.Code.Algebra.Structures.du_isRingWithoutOne_2772
                 (T_IsRing_2740 -> Any
forall a b. a -> b
coe T_IsRing_2740
v1) in
       Any -> Any
forall a b. a -> b
coe
         ((T_IsAbelianGroup_1172 -> T_IsCommutativeMonoid_764) -> Any -> Any
forall a b. a -> b
coe
            T_IsAbelianGroup_1172 -> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.du_isCommutativeMonoid_1244
            ((T_IsRingWithoutOne_2368 -> T_IsAbelianGroup_1172) -> Any -> Any
forall a b. a -> b
coe
               T_IsRingWithoutOne_2368 -> T_IsAbelianGroup_1172
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2386
               (Any -> Any
forall a b. a -> b
coe Any
v2))))
-- Data.Bool.Properties._.IsCommutativeRing.isCommutativeSemigroup
d_isCommutativeSemigroup_700 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeRing_2888 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_568
d_isCommutativeSemigroup_700 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsCommutativeRing_2888
-> T_IsCommutativeSemigroup_568
d_isCommutativeSemigroup_700 ~Bool -> Bool -> Bool
v0 ~Bool -> Bool -> Bool
v1 ~Bool -> Bool
v2 ~Bool
v3 ~Bool
v4 T_IsCommutativeRing_2888
v5
  = T_IsCommutativeRing_2888 -> T_IsCommutativeSemigroup_568
du_isCommutativeSemigroup_700 T_IsCommutativeRing_2888
v5
du_isCommutativeSemigroup_700 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeRing_2888 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_568
du_isCommutativeSemigroup_700 :: T_IsCommutativeRing_2888 -> T_IsCommutativeSemigroup_568
du_isCommutativeSemigroup_700 T_IsCommutativeRing_2888
v0
  = let v1 :: T_IsRing_2740
v1
          = T_IsCommutativeRing_2888 -> T_IsRing_2740
MAlonzo.Code.Algebra.Structures.d_isRing_2904 (T_IsCommutativeRing_2888 -> T_IsCommutativeRing_2888
forall a b. a -> b
coe T_IsCommutativeRing_2888
v0) in
    Any -> T_IsCommutativeSemigroup_568
forall a b. a -> b
coe
      (let v2 :: Any
v2
             = (T_IsRing_2740 -> T_IsRingWithoutOne_2368) -> Any -> Any
forall a b. a -> b
coe
                 T_IsRing_2740 -> T_IsRingWithoutOne_2368
MAlonzo.Code.Algebra.Structures.du_isRingWithoutOne_2772
                 (T_IsRing_2740 -> Any
forall a b. a -> b
coe T_IsRing_2740
v1) in
       Any -> Any
forall a b. a -> b
coe
         (let v3 :: T_IsAbelianGroup_1172
v3
                = T_IsRingWithoutOne_2368 -> T_IsAbelianGroup_1172
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2386
                    (Any -> T_IsRingWithoutOne_2368
forall a b. a -> b
coe Any
v2) in
          Any -> Any
forall a b. a -> b
coe
            ((T_IsCommutativeMonoid_764 -> T_IsCommutativeSemigroup_568)
-> Any -> Any
forall a b. a -> b
coe
               T_IsCommutativeMonoid_764 -> T_IsCommutativeSemigroup_568
MAlonzo.Code.Algebra.Structures.du_isCommutativeSemigroup_814
               ((T_IsAbelianGroup_1172 -> T_IsCommutativeMonoid_764) -> Any -> Any
forall a b. a -> b
coe
                  T_IsAbelianGroup_1172 -> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.du_isCommutativeMonoid_1244
                  (T_IsAbelianGroup_1172 -> Any
forall a b. a -> b
coe T_IsAbelianGroup_1172
v3)))))
-- Data.Bool.Properties._.IsCommutativeRing.isGroup
d_isGroup_702 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeRing_2888 ->
  MAlonzo.Code.Algebra.Structures.T_IsGroup_1074
d_isGroup_702 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsCommutativeRing_2888
-> T_IsGroup_1074
d_isGroup_702 ~Bool -> Bool -> Bool
v0 ~Bool -> Bool -> Bool
v1 ~Bool -> Bool
v2 ~Bool
v3 ~Bool
v4 T_IsCommutativeRing_2888
v5 = T_IsCommutativeRing_2888 -> T_IsGroup_1074
du_isGroup_702 T_IsCommutativeRing_2888
v5
du_isGroup_702 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeRing_2888 ->
  MAlonzo.Code.Algebra.Structures.T_IsGroup_1074
du_isGroup_702 :: T_IsCommutativeRing_2888 -> T_IsGroup_1074
du_isGroup_702 T_IsCommutativeRing_2888
v0
  = let v1 :: T_IsRing_2740
v1
          = T_IsCommutativeRing_2888 -> T_IsRing_2740
MAlonzo.Code.Algebra.Structures.d_isRing_2904 (T_IsCommutativeRing_2888 -> T_IsCommutativeRing_2888
forall a b. a -> b
coe T_IsCommutativeRing_2888
v0) in
    Any -> T_IsGroup_1074
forall a b. a -> b
coe
      ((T_IsAbelianGroup_1172 -> T_IsGroup_1074) -> Any -> Any
forall a b. a -> b
coe
         T_IsAbelianGroup_1172 -> T_IsGroup_1074
MAlonzo.Code.Algebra.Structures.d_isGroup_1184
         ((T_IsRing_2740 -> T_IsAbelianGroup_1172) -> Any -> Any
forall a b. a -> b
coe
            T_IsRing_2740 -> T_IsAbelianGroup_1172
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2762
            (T_IsRing_2740 -> Any
forall a b. a -> b
coe T_IsRing_2740
v1)))
-- Data.Bool.Properties._.IsCommutativeRing.isInvertibleMagma
d_isInvertibleMagma_704 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeRing_2888 ->
  MAlonzo.Code.Algebra.Structures.T_IsInvertibleMagma_958
d_isInvertibleMagma_704 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsCommutativeRing_2888
-> T_IsInvertibleMagma_958
d_isInvertibleMagma_704 ~Bool -> Bool -> Bool
v0 ~Bool -> Bool -> Bool
v1 ~Bool -> Bool
v2 ~Bool
v3 ~Bool
v4 T_IsCommutativeRing_2888
v5
  = T_IsCommutativeRing_2888 -> T_IsInvertibleMagma_958
du_isInvertibleMagma_704 T_IsCommutativeRing_2888
v5
du_isInvertibleMagma_704 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeRing_2888 ->
  MAlonzo.Code.Algebra.Structures.T_IsInvertibleMagma_958
du_isInvertibleMagma_704 :: T_IsCommutativeRing_2888 -> T_IsInvertibleMagma_958
du_isInvertibleMagma_704 T_IsCommutativeRing_2888
v0
  = let v1 :: T_IsRing_2740
v1
          = T_IsCommutativeRing_2888 -> T_IsRing_2740
MAlonzo.Code.Algebra.Structures.d_isRing_2904 (T_IsCommutativeRing_2888 -> T_IsCommutativeRing_2888
forall a b. a -> b
coe T_IsCommutativeRing_2888
v0) in
    Any -> T_IsInvertibleMagma_958
forall a b. a -> b
coe
      (let v2 :: Any
v2
             = (T_IsRing_2740 -> T_IsRingWithoutOne_2368) -> Any -> Any
forall a b. a -> b
coe
                 T_IsRing_2740 -> T_IsRingWithoutOne_2368
MAlonzo.Code.Algebra.Structures.du_isRingWithoutOne_2772
                 (T_IsRing_2740 -> Any
forall a b. a -> b
coe T_IsRing_2740
v1) in
       Any -> Any
forall a b. a -> b
coe
         (let v3 :: T_IsAbelianGroup_1172
v3
                = T_IsRingWithoutOne_2368 -> T_IsAbelianGroup_1172
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2386
                    (Any -> T_IsRingWithoutOne_2368
forall a b. a -> b
coe Any
v2) in
          Any -> Any
forall a b. a -> b
coe
            ((T_IsGroup_1074 -> T_IsInvertibleMagma_958) -> Any -> Any
forall a b. a -> b
coe
               T_IsGroup_1074 -> T_IsInvertibleMagma_958
MAlonzo.Code.Algebra.Structures.du_isInvertibleMagma_1160
               ((T_IsAbelianGroup_1172 -> T_IsGroup_1074) -> Any -> Any
forall a b. a -> b
coe T_IsAbelianGroup_1172 -> T_IsGroup_1074
MAlonzo.Code.Algebra.Structures.d_isGroup_1184 (T_IsAbelianGroup_1172 -> Any
forall a b. a -> b
coe T_IsAbelianGroup_1172
v3)))))
-- Data.Bool.Properties._.IsCommutativeRing.isInvertibleUnitalMagma
d_isInvertibleUnitalMagma_706 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeRing_2888 ->
  MAlonzo.Code.Algebra.Structures.T_IsInvertibleUnitalMagma_1012
d_isInvertibleUnitalMagma_706 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsCommutativeRing_2888
-> T_IsInvertibleUnitalMagma_1012
d_isInvertibleUnitalMagma_706 ~Bool -> Bool -> Bool
v0 ~Bool -> Bool -> Bool
v1 ~Bool -> Bool
v2 ~Bool
v3 ~Bool
v4 T_IsCommutativeRing_2888
v5
  = T_IsCommutativeRing_2888 -> T_IsInvertibleUnitalMagma_1012
du_isInvertibleUnitalMagma_706 T_IsCommutativeRing_2888
v5
du_isInvertibleUnitalMagma_706 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeRing_2888 ->
  MAlonzo.Code.Algebra.Structures.T_IsInvertibleUnitalMagma_1012
du_isInvertibleUnitalMagma_706 :: T_IsCommutativeRing_2888 -> T_IsInvertibleUnitalMagma_1012
du_isInvertibleUnitalMagma_706 T_IsCommutativeRing_2888
v0
  = let v1 :: T_IsRing_2740
v1
          = T_IsCommutativeRing_2888 -> T_IsRing_2740
MAlonzo.Code.Algebra.Structures.d_isRing_2904 (T_IsCommutativeRing_2888 -> T_IsCommutativeRing_2888
forall a b. a -> b
coe T_IsCommutativeRing_2888
v0) in
    Any -> T_IsInvertibleUnitalMagma_1012
forall a b. a -> b
coe
      (let v2 :: Any
v2
             = (T_IsRing_2740 -> T_IsRingWithoutOne_2368) -> Any -> Any
forall a b. a -> b
coe
                 T_IsRing_2740 -> T_IsRingWithoutOne_2368
MAlonzo.Code.Algebra.Structures.du_isRingWithoutOne_2772
                 (T_IsRing_2740 -> Any
forall a b. a -> b
coe T_IsRing_2740
v1) in
       Any -> Any
forall a b. a -> b
coe
         (let v3 :: T_IsAbelianGroup_1172
v3
                = T_IsRingWithoutOne_2368 -> T_IsAbelianGroup_1172
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2386
                    (Any -> T_IsRingWithoutOne_2368
forall a b. a -> b
coe Any
v2) in
          Any -> Any
forall a b. a -> b
coe
            ((T_IsGroup_1074 -> T_IsInvertibleUnitalMagma_1012) -> Any -> Any
forall a b. a -> b
coe
               T_IsGroup_1074 -> T_IsInvertibleUnitalMagma_1012
MAlonzo.Code.Algebra.Structures.du_isInvertibleUnitalMagma_1162
               ((T_IsAbelianGroup_1172 -> T_IsGroup_1074) -> Any -> Any
forall a b. a -> b
coe T_IsAbelianGroup_1172 -> T_IsGroup_1074
MAlonzo.Code.Algebra.Structures.d_isGroup_1184 (T_IsAbelianGroup_1172 -> Any
forall a b. a -> b
coe T_IsAbelianGroup_1172
v3)))))
-- Data.Bool.Properties._.IsCommutativeRing.isMagma
d_isMagma_708 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeRing_2888 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_178
d_isMagma_708 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsCommutativeRing_2888
-> T_IsMagma_178
d_isMagma_708 ~Bool -> Bool -> Bool
v0 ~Bool -> Bool -> Bool
v1 ~Bool -> Bool
v2 ~Bool
v3 ~Bool
v4 T_IsCommutativeRing_2888
v5 = T_IsCommutativeRing_2888 -> T_IsMagma_178
du_isMagma_708 T_IsCommutativeRing_2888
v5
du_isMagma_708 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeRing_2888 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_178
du_isMagma_708 :: T_IsCommutativeRing_2888 -> T_IsMagma_178
du_isMagma_708 T_IsCommutativeRing_2888
v0
  = let v1 :: T_IsRing_2740
v1
          = T_IsCommutativeRing_2888 -> T_IsRing_2740
MAlonzo.Code.Algebra.Structures.d_isRing_2904 (T_IsCommutativeRing_2888 -> T_IsCommutativeRing_2888
forall a b. a -> b
coe T_IsCommutativeRing_2888
v0) in
    Any -> T_IsMagma_178
forall a b. a -> b
coe
      ((T_IsSemigroup_488 -> T_IsMagma_178) -> Any -> Any
forall a b. a -> b
coe
         T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496
         ((T_IsMonoid_712 -> T_IsSemigroup_488) -> Any -> Any
forall a b. a -> b
coe
            T_IsMonoid_712 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_722
            ((T_IsGroup_1074 -> T_IsMonoid_712) -> Any -> Any
forall a b. a -> b
coe
               T_IsGroup_1074 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_1088
               ((T_IsAbelianGroup_1172 -> T_IsGroup_1074) -> Any -> Any
forall a b. a -> b
coe
                  T_IsAbelianGroup_1172 -> T_IsGroup_1074
MAlonzo.Code.Algebra.Structures.d_isGroup_1184
                  ((T_IsRing_2740 -> T_IsAbelianGroup_1172) -> Any -> Any
forall a b. a -> b
coe
                     T_IsRing_2740 -> T_IsAbelianGroup_1172
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2762
                     (T_IsRing_2740 -> Any
forall a b. a -> b
coe T_IsRing_2740
v1))))))
-- Data.Bool.Properties._.IsCommutativeRing.isMonoid
d_isMonoid_710 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeRing_2888 ->
  MAlonzo.Code.Algebra.Structures.T_IsMonoid_712
d_isMonoid_710 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsCommutativeRing_2888
-> T_IsMonoid_712
d_isMonoid_710 ~Bool -> Bool -> Bool
v0 ~Bool -> Bool -> Bool
v1 ~Bool -> Bool
v2 ~Bool
v3 ~Bool
v4 T_IsCommutativeRing_2888
v5 = T_IsCommutativeRing_2888 -> T_IsMonoid_712
du_isMonoid_710 T_IsCommutativeRing_2888
v5
du_isMonoid_710 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeRing_2888 ->
  MAlonzo.Code.Algebra.Structures.T_IsMonoid_712
du_isMonoid_710 :: T_IsCommutativeRing_2888 -> T_IsMonoid_712
du_isMonoid_710 T_IsCommutativeRing_2888
v0
  = let v1 :: T_IsRing_2740
v1
          = T_IsCommutativeRing_2888 -> T_IsRing_2740
MAlonzo.Code.Algebra.Structures.d_isRing_2904 (T_IsCommutativeRing_2888 -> T_IsCommutativeRing_2888
forall a b. a -> b
coe T_IsCommutativeRing_2888
v0) in
    Any -> T_IsMonoid_712
forall a b. a -> b
coe
      ((T_IsGroup_1074 -> T_IsMonoid_712) -> Any -> Any
forall a b. a -> b
coe
         T_IsGroup_1074 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_1088
         ((T_IsAbelianGroup_1172 -> T_IsGroup_1074) -> Any -> Any
forall a b. a -> b
coe
            T_IsAbelianGroup_1172 -> T_IsGroup_1074
MAlonzo.Code.Algebra.Structures.d_isGroup_1184
            ((T_IsRing_2740 -> T_IsAbelianGroup_1172) -> Any -> Any
forall a b. a -> b
coe
               T_IsRing_2740 -> T_IsAbelianGroup_1172
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2762
               (T_IsRing_2740 -> Any
forall a b. a -> b
coe T_IsRing_2740
v1))))
-- Data.Bool.Properties._.IsCommutativeRing.isSemigroup
d_isSemigroup_712 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeRing_2888 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_488
d_isSemigroup_712 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsCommutativeRing_2888
-> T_IsSemigroup_488
d_isSemigroup_712 ~Bool -> Bool -> Bool
v0 ~Bool -> Bool -> Bool
v1 ~Bool -> Bool
v2 ~Bool
v3 ~Bool
v4 T_IsCommutativeRing_2888
v5 = T_IsCommutativeRing_2888 -> T_IsSemigroup_488
du_isSemigroup_712 T_IsCommutativeRing_2888
v5
du_isSemigroup_712 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeRing_2888 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_488
du_isSemigroup_712 :: T_IsCommutativeRing_2888 -> T_IsSemigroup_488
du_isSemigroup_712 T_IsCommutativeRing_2888
v0
  = let v1 :: T_IsRing_2740
v1
          = T_IsCommutativeRing_2888 -> T_IsRing_2740
MAlonzo.Code.Algebra.Structures.d_isRing_2904 (T_IsCommutativeRing_2888 -> T_IsCommutativeRing_2888
forall a b. a -> b
coe T_IsCommutativeRing_2888
v0) in
    Any -> T_IsSemigroup_488
forall a b. a -> b
coe
      ((T_IsMonoid_712 -> T_IsSemigroup_488) -> Any -> Any
forall a b. a -> b
coe
         T_IsMonoid_712 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_722
         ((T_IsGroup_1074 -> T_IsMonoid_712) -> Any -> Any
forall a b. a -> b
coe
            T_IsGroup_1074 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_1088
            ((T_IsAbelianGroup_1172 -> T_IsGroup_1074) -> Any -> Any
forall a b. a -> b
coe
               T_IsAbelianGroup_1172 -> T_IsGroup_1074
MAlonzo.Code.Algebra.Structures.d_isGroup_1184
               ((T_IsRing_2740 -> T_IsAbelianGroup_1172) -> Any -> Any
forall a b. a -> b
coe
                  T_IsRing_2740 -> T_IsAbelianGroup_1172
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2762
                  (T_IsRing_2740 -> Any
forall a b. a -> b
coe T_IsRing_2740
v1)))))
-- Data.Bool.Properties._.IsCommutativeRing.isUnitalMagma
d_isUnitalMagma_714 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeRing_2888 ->
  MAlonzo.Code.Algebra.Structures.T_IsUnitalMagma_666
d_isUnitalMagma_714 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsCommutativeRing_2888
-> T_IsUnitalMagma_666
d_isUnitalMagma_714 ~Bool -> Bool -> Bool
v0 ~Bool -> Bool -> Bool
v1 ~Bool -> Bool
v2 ~Bool
v3 ~Bool
v4 T_IsCommutativeRing_2888
v5
  = T_IsCommutativeRing_2888 -> T_IsUnitalMagma_666
du_isUnitalMagma_714 T_IsCommutativeRing_2888
v5
du_isUnitalMagma_714 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeRing_2888 ->
  MAlonzo.Code.Algebra.Structures.T_IsUnitalMagma_666
du_isUnitalMagma_714 :: T_IsCommutativeRing_2888 -> T_IsUnitalMagma_666
du_isUnitalMagma_714 T_IsCommutativeRing_2888
v0
  = let v1 :: T_IsRing_2740
v1
          = T_IsCommutativeRing_2888 -> T_IsRing_2740
MAlonzo.Code.Algebra.Structures.d_isRing_2904 (T_IsCommutativeRing_2888 -> T_IsCommutativeRing_2888
forall a b. a -> b
coe T_IsCommutativeRing_2888
v0) in
    Any -> T_IsUnitalMagma_666
forall a b. a -> b
coe
      (let v2 :: Any
v2
             = (T_IsRing_2740 -> T_IsRingWithoutOne_2368) -> Any -> Any
forall a b. a -> b
coe
                 T_IsRing_2740 -> T_IsRingWithoutOne_2368
MAlonzo.Code.Algebra.Structures.du_isRingWithoutOne_2772
                 (T_IsRing_2740 -> Any
forall a b. a -> b
coe T_IsRing_2740
v1) in
       Any -> Any
forall a b. a -> b
coe
         (let v3 :: T_IsAbelianGroup_1172
v3
                = T_IsRingWithoutOne_2368 -> T_IsAbelianGroup_1172
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2386
                    (Any -> T_IsRingWithoutOne_2368
forall a b. a -> b
coe Any
v2) in
          Any -> Any
forall a b. a -> b
coe
            (let v4 :: T_IsGroup_1074
v4
                   = T_IsAbelianGroup_1172 -> T_IsGroup_1074
MAlonzo.Code.Algebra.Structures.d_isGroup_1184 (T_IsAbelianGroup_1172 -> T_IsAbelianGroup_1172
forall a b. a -> b
coe T_IsAbelianGroup_1172
v3) in
             Any -> Any
forall a b. a -> b
coe
               ((T_IsMonoid_712 -> T_IsUnitalMagma_666) -> Any -> Any
forall a b. a -> b
coe
                  T_IsMonoid_712 -> T_IsUnitalMagma_666
MAlonzo.Code.Algebra.Structures.du_isUnitalMagma_756
                  ((T_IsGroup_1074 -> T_IsMonoid_712) -> Any -> Any
forall a b. a -> b
coe T_IsGroup_1074 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_1088 (T_IsGroup_1074 -> Any
forall a b. a -> b
coe T_IsGroup_1074
v4))))))
-- Data.Bool.Properties._.IsCommutativeRing.⁻¹-cong
d_'8315''185''45'cong_716 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeRing_2888 ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8315''185''45'cong_716 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsCommutativeRing_2888
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_'8315''185''45'cong_716 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsCommutativeRing_2888
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsCommutativeRing.inverse
d_inverse_718 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeRing_2888 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_inverse_718 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsCommutativeRing_2888
-> T_Σ_14
d_inverse_718 ~Bool -> Bool -> Bool
v0 ~Bool -> Bool -> Bool
v1 ~Bool -> Bool
v2 ~Bool
v3 ~Bool
v4 T_IsCommutativeRing_2888
v5 = T_IsCommutativeRing_2888 -> T_Σ_14
du_inverse_718 T_IsCommutativeRing_2888
v5
du_inverse_718 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeRing_2888 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
du_inverse_718 :: T_IsCommutativeRing_2888 -> T_Σ_14
du_inverse_718 T_IsCommutativeRing_2888
v0
  = let v1 :: T_IsRing_2740
v1
          = T_IsCommutativeRing_2888 -> T_IsRing_2740
MAlonzo.Code.Algebra.Structures.d_isRing_2904 (T_IsCommutativeRing_2888 -> T_IsCommutativeRing_2888
forall a b. a -> b
coe T_IsCommutativeRing_2888
v0) in
    Any -> T_Σ_14
forall a b. a -> b
coe
      ((T_IsGroup_1074 -> T_Σ_14) -> Any -> Any
forall a b. a -> b
coe
         T_IsGroup_1074 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_inverse_1090
         ((T_IsAbelianGroup_1172 -> T_IsGroup_1074) -> Any -> Any
forall a b. a -> b
coe
            T_IsAbelianGroup_1172 -> T_IsGroup_1074
MAlonzo.Code.Algebra.Structures.d_isGroup_1184
            ((T_IsRing_2740 -> T_IsAbelianGroup_1172) -> Any -> Any
forall a b. a -> b
coe
               T_IsRing_2740 -> T_IsAbelianGroup_1172
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2762
               (T_IsRing_2740 -> Any
forall a b. a -> b
coe T_IsRing_2740
v1))))
-- Data.Bool.Properties._.IsCommutativeRing.inverseʳ
d_inverse'691'_720 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeRing_2888 ->
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_inverse'691'_720 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsCommutativeRing_2888
-> Bool
-> T__'8801'__12
d_inverse'691'_720 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsCommutativeRing_2888
-> Bool
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsCommutativeRing.inverseˡ
d_inverse'737'_722 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeRing_2888 ->
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_inverse'737'_722 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsCommutativeRing_2888
-> Bool
-> T__'8801'__12
d_inverse'737'_722 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsCommutativeRing_2888
-> Bool
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsCommutativeRing.distrib
d_distrib_724 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeRing_2888 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_distrib_724 :: T_IsCommutativeRing_2888 -> T_Σ_14
d_distrib_724 T_IsCommutativeRing_2888
v0
  = (T_IsRing_2740 -> T_Σ_14) -> Any -> T_Σ_14
forall a b. a -> b
coe
      T_IsRing_2740 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_distrib_2770
      ((T_IsCommutativeRing_2888 -> T_IsRing_2740) -> Any -> Any
forall a b. a -> b
coe T_IsCommutativeRing_2888 -> T_IsRing_2740
MAlonzo.Code.Algebra.Structures.d_isRing_2904 (T_IsCommutativeRing_2888 -> Any
forall a b. a -> b
coe T_IsCommutativeRing_2888
v0))
-- Data.Bool.Properties._.IsCommutativeRing.distribʳ
d_distrib'691'_726 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeRing_2888 ->
  Bool ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_distrib'691'_726 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsCommutativeRing_2888
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
d_distrib'691'_726 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsCommutativeRing_2888
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsCommutativeRing.distribˡ
d_distrib'737'_728 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeRing_2888 ->
  Bool ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_distrib'737'_728 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsCommutativeRing_2888
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
d_distrib'737'_728 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsCommutativeRing_2888
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsCommutativeRing.isCommutativeSemiring
d_isCommutativeSemiring_730 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeRing_2888 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiring_1750
d_isCommutativeSemiring_730 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsCommutativeRing_2888
-> T_IsCommutativeSemiring_1750
d_isCommutativeSemiring_730 Bool -> Bool -> Bool
v0 Bool -> Bool -> Bool
v1 Bool -> Bool
v2 Bool
v3 Bool
v4 T_IsCommutativeRing_2888
v5
  = ((Any -> Any -> Any)
 -> (Any -> Any -> Any)
 -> (Any -> Any)
 -> Any
 -> T_IsCommutativeRing_2888
 -> T_IsCommutativeSemiring_1750)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> T_IsCommutativeRing_2888
-> T_IsCommutativeSemiring_1750
forall a b. a -> b
coe
      (Any -> Any -> Any)
-> (Any -> Any -> Any)
-> (Any -> Any)
-> Any
-> T_IsCommutativeRing_2888
-> T_IsCommutativeSemiring_1750
MAlonzo.Code.Algebra.Structures.du_isCommutativeSemiring_3018 Bool -> Bool -> Bool
v0 Bool -> Bool -> Bool
v1
      Bool -> Bool
v2 Bool
v3 T_IsCommutativeRing_2888
v5
-- Data.Bool.Properties._.IsCommutativeRing.isCommutativeSemiringWithoutOne
d_isCommutativeSemiringWithoutOne_732 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeRing_2888 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiringWithoutOne_1438
d_isCommutativeSemiringWithoutOne_732 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsCommutativeRing_2888
-> T_IsCommutativeSemiringWithoutOne_1438
d_isCommutativeSemiringWithoutOne_732 Bool -> Bool -> Bool
v0 Bool -> Bool -> Bool
v1 Bool -> Bool
v2 Bool
v3 ~Bool
v4 T_IsCommutativeRing_2888
v5
  = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> T_IsCommutativeRing_2888
-> T_IsCommutativeSemiringWithoutOne_1438
du_isCommutativeSemiringWithoutOne_732 Bool -> Bool -> Bool
v0 Bool -> Bool -> Bool
v1 Bool -> Bool
v2 Bool
v3 T_IsCommutativeRing_2888
v5
du_isCommutativeSemiringWithoutOne_732 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeRing_2888 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiringWithoutOne_1438
du_isCommutativeSemiringWithoutOne_732 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> T_IsCommutativeRing_2888
-> T_IsCommutativeSemiringWithoutOne_1438
du_isCommutativeSemiringWithoutOne_732 Bool -> Bool -> Bool
v0 Bool -> Bool -> Bool
v1 Bool -> Bool
v2 Bool
v3 T_IsCommutativeRing_2888
v4
  = (T_IsCommutativeSemiring_1750
 -> T_IsCommutativeSemiringWithoutOne_1438)
-> Any -> T_IsCommutativeSemiringWithoutOne_1438
forall a b. a -> b
coe
      T_IsCommutativeSemiring_1750
-> T_IsCommutativeSemiringWithoutOne_1438
MAlonzo.Code.Algebra.Structures.du_isCommutativeSemiringWithoutOne_1852
      (((Any -> Any -> Any)
 -> (Any -> Any -> Any)
 -> (Any -> Any)
 -> Any
 -> T_IsCommutativeRing_2888
 -> T_IsCommutativeSemiring_1750)
-> Any -> Any -> Any -> Any -> Any -> Any
forall a b. a -> b
coe
         (Any -> Any -> Any)
-> (Any -> Any -> Any)
-> (Any -> Any)
-> Any
-> T_IsCommutativeRing_2888
-> T_IsCommutativeSemiring_1750
MAlonzo.Code.Algebra.Structures.du_isCommutativeSemiring_3018
         ((Bool -> Bool -> Bool) -> Any
forall a b. a -> b
coe Bool -> Bool -> Bool
v0) ((Bool -> Bool -> Bool) -> Any
forall a b. a -> b
coe Bool -> Bool -> Bool
v1) ((Bool -> Bool) -> Any
forall a b. a -> b
coe Bool -> Bool
v2) (Bool -> Any
forall a b. a -> b
coe Bool
v3) (T_IsCommutativeRing_2888 -> Any
forall a b. a -> b
coe T_IsCommutativeRing_2888
v4))
-- Data.Bool.Properties._.IsCommutativeRing.isEquivalence
d_isEquivalence_734 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeRing_2888 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
d_isEquivalence_734 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsCommutativeRing_2888
-> T_IsEquivalence_28
d_isEquivalence_734 ~Bool -> Bool -> Bool
v0 ~Bool -> Bool -> Bool
v1 ~Bool -> Bool
v2 ~Bool
v3 ~Bool
v4 T_IsCommutativeRing_2888
v5
  = T_IsCommutativeRing_2888 -> T_IsEquivalence_28
du_isEquivalence_734 T_IsCommutativeRing_2888
v5
du_isEquivalence_734 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeRing_2888 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
du_isEquivalence_734 :: T_IsCommutativeRing_2888 -> T_IsEquivalence_28
du_isEquivalence_734 T_IsCommutativeRing_2888
v0
  = let v1 :: T_IsRing_2740
v1
          = T_IsCommutativeRing_2888 -> T_IsRing_2740
MAlonzo.Code.Algebra.Structures.d_isRing_2904 (T_IsCommutativeRing_2888 -> T_IsCommutativeRing_2888
forall a b. a -> b
coe T_IsCommutativeRing_2888
v0) in
    Any -> T_IsEquivalence_28
forall a b. a -> b
coe
      ((T_IsMagma_178 -> T_IsEquivalence_28) -> Any -> Any
forall a b. a -> b
coe
         T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186
         ((T_IsSemigroup_488 -> T_IsMagma_178) -> Any -> Any
forall a b. a -> b
coe
            T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496
            ((T_IsMonoid_712 -> T_IsSemigroup_488) -> Any -> Any
forall a b. a -> b
coe
               T_IsMonoid_712 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_722
               ((T_IsGroup_1074 -> T_IsMonoid_712) -> Any -> Any
forall a b. a -> b
coe
                  T_IsGroup_1074 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_1088
                  ((T_IsAbelianGroup_1172 -> T_IsGroup_1074) -> Any -> Any
forall a b. a -> b
coe
                     T_IsAbelianGroup_1172 -> T_IsGroup_1074
MAlonzo.Code.Algebra.Structures.d_isGroup_1184
                     ((T_IsRing_2740 -> T_IsAbelianGroup_1172) -> Any -> Any
forall a b. a -> b
coe
                        T_IsRing_2740 -> T_IsAbelianGroup_1172
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2762
                        (T_IsRing_2740 -> Any
forall a b. a -> b
coe T_IsRing_2740
v1)))))))
-- Data.Bool.Properties._.IsCommutativeRing.isNearSemiring
d_isNearSemiring_736 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeRing_2888 ->
  MAlonzo.Code.Algebra.Structures.T_IsNearSemiring_1260
d_isNearSemiring_736 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsCommutativeRing_2888
-> T_IsNearSemiring_1260
d_isNearSemiring_736 Bool -> Bool -> Bool
v0 Bool -> Bool -> Bool
v1 Bool -> Bool
v2 Bool
v3 ~Bool
v4 T_IsCommutativeRing_2888
v5
  = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> T_IsCommutativeRing_2888
-> T_IsNearSemiring_1260
du_isNearSemiring_736 Bool -> Bool -> Bool
v0 Bool -> Bool -> Bool
v1 Bool -> Bool
v2 Bool
v3 T_IsCommutativeRing_2888
v5
du_isNearSemiring_736 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeRing_2888 ->
  MAlonzo.Code.Algebra.Structures.T_IsNearSemiring_1260
du_isNearSemiring_736 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> T_IsCommutativeRing_2888
-> T_IsNearSemiring_1260
du_isNearSemiring_736 Bool -> Bool -> Bool
v0 Bool -> Bool -> Bool
v1 Bool -> Bool
v2 Bool
v3 T_IsCommutativeRing_2888
v4
  = let v5 :: T_IsRing_2740
v5
          = T_IsCommutativeRing_2888 -> T_IsRing_2740
MAlonzo.Code.Algebra.Structures.d_isRing_2904 (T_IsCommutativeRing_2888 -> T_IsCommutativeRing_2888
forall a b. a -> b
coe T_IsCommutativeRing_2888
v4) in
    Any -> T_IsNearSemiring_1260
forall a b. a -> b
coe
      (((Any -> Any -> Any)
 -> (Any -> Any -> Any)
 -> (Any -> Any)
 -> Any
 -> T_IsRingWithoutOne_2368
 -> T_IsNearSemiring_1260)
-> Any -> Any -> Any -> Any -> Any -> Any
forall a b. a -> b
coe
         (Any -> Any -> Any)
-> (Any -> Any -> Any)
-> (Any -> Any)
-> Any
-> T_IsRingWithoutOne_2368
-> T_IsNearSemiring_1260
MAlonzo.Code.Algebra.Structures.du_isNearSemiring_2470 ((Bool -> Bool -> Bool) -> Any
forall a b. a -> b
coe Bool -> Bool -> Bool
v0)
         ((Bool -> Bool -> Bool) -> Any
forall a b. a -> b
coe Bool -> Bool -> Bool
v1) ((Bool -> Bool) -> Any
forall a b. a -> b
coe Bool -> Bool
v2) (Bool -> Any
forall a b. a -> b
coe Bool
v3)
         ((T_IsRing_2740 -> T_IsRingWithoutOne_2368) -> Any -> Any
forall a b. a -> b
coe
            T_IsRing_2740 -> T_IsRingWithoutOne_2368
MAlonzo.Code.Algebra.Structures.du_isRingWithoutOne_2772 (T_IsRing_2740 -> Any
forall a b. a -> b
coe T_IsRing_2740
v5)))
-- Data.Bool.Properties._.IsCommutativeRing.isPartialEquivalence
d_isPartialEquivalence_738 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeRing_2888 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_738 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsCommutativeRing_2888
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_738 ~Bool -> Bool -> Bool
v0 ~Bool -> Bool -> Bool
v1 ~Bool -> Bool
v2 ~Bool
v3 ~Bool
v4 T_IsCommutativeRing_2888
v5
  = T_IsCommutativeRing_2888 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_738 T_IsCommutativeRing_2888
v5
du_isPartialEquivalence_738 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeRing_2888 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_738 :: T_IsCommutativeRing_2888 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_738 T_IsCommutativeRing_2888
v0
  = let v1 :: T_IsRing_2740
v1
          = T_IsCommutativeRing_2888 -> T_IsRing_2740
MAlonzo.Code.Algebra.Structures.d_isRing_2904 (T_IsCommutativeRing_2888 -> T_IsCommutativeRing_2888
forall a b. a -> b
coe T_IsCommutativeRing_2888
v0) in
    Any -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: Any
v2
             = (T_IsRing_2740 -> T_IsRingWithoutOne_2368) -> Any -> Any
forall a b. a -> b
coe
                 T_IsRing_2740 -> T_IsRingWithoutOne_2368
MAlonzo.Code.Algebra.Structures.du_isRingWithoutOne_2772
                 (T_IsRing_2740 -> Any
forall a b. a -> b
coe T_IsRing_2740
v1) in
       Any -> Any
forall a b. a -> b
coe
         (let v3 :: T_IsAbelianGroup_1172
v3
                = T_IsRingWithoutOne_2368 -> T_IsAbelianGroup_1172
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2386
                    (Any -> T_IsRingWithoutOne_2368
forall a b. a -> b
coe Any
v2) in
          Any -> Any
forall a b. a -> b
coe
            (let v4 :: T_IsGroup_1074
v4
                   = T_IsAbelianGroup_1172 -> T_IsGroup_1074
MAlonzo.Code.Algebra.Structures.d_isGroup_1184 (T_IsAbelianGroup_1172 -> T_IsAbelianGroup_1172
forall a b. a -> b
coe T_IsAbelianGroup_1172
v3) in
             Any -> Any
forall a b. a -> b
coe
               (let v5 :: T_IsMonoid_712
v5
                      = T_IsGroup_1074 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_1088 (T_IsGroup_1074 -> T_IsGroup_1074
forall a b. a -> b
coe T_IsGroup_1074
v4) in
                Any -> Any
forall a b. a -> b
coe
                  (let v6 :: T_IsSemigroup_488
v6
                         = T_IsMonoid_712 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_722 (T_IsMonoid_712 -> T_IsMonoid_712
forall a b. a -> b
coe T_IsMonoid_712
v5) in
                   Any -> Any
forall a b. a -> b
coe
                     (let v7 :: T_IsMagma_178
v7 = T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496 (T_IsSemigroup_488 -> T_IsSemigroup_488
forall a b. a -> b
coe T_IsSemigroup_488
v6) in
                      Any -> Any
forall a b. a -> b
coe
                        ((T_IsEquivalence_28 -> T_IsPartialEquivalence_16) -> Any -> Any
forall a b. a -> b
coe
                           T_IsEquivalence_28 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_44
                           ((T_IsMagma_178 -> T_IsEquivalence_28) -> Any -> Any
forall a b. a -> b
coe
                              T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186
                              (T_IsMagma_178 -> Any
forall a b. a -> b
coe T_IsMagma_178
v7)))))))))
-- Data.Bool.Properties._.IsCommutativeRing.isRing
d_isRing_740 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeRing_2888 ->
  MAlonzo.Code.Algebra.Structures.T_IsRing_2740
d_isRing_740 :: T_IsCommutativeRing_2888 -> T_IsRing_2740
d_isRing_740 T_IsCommutativeRing_2888
v0
  = (T_IsCommutativeRing_2888 -> T_IsRing_2740) -> Any -> T_IsRing_2740
forall a b. a -> b
coe T_IsCommutativeRing_2888 -> T_IsRing_2740
MAlonzo.Code.Algebra.Structures.d_isRing_2904 (T_IsCommutativeRing_2888 -> Any
forall a b. a -> b
coe T_IsCommutativeRing_2888
v0)
-- Data.Bool.Properties._.IsCommutativeRing.isRingWithoutOne
d_isRingWithoutOne_742 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeRing_2888 ->
  MAlonzo.Code.Algebra.Structures.T_IsRingWithoutOne_2368
d_isRingWithoutOne_742 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsCommutativeRing_2888
-> T_IsRingWithoutOne_2368
d_isRingWithoutOne_742 ~Bool -> Bool -> Bool
v0 ~Bool -> Bool -> Bool
v1 ~Bool -> Bool
v2 ~Bool
v3 ~Bool
v4 T_IsCommutativeRing_2888
v5
  = T_IsCommutativeRing_2888 -> T_IsRingWithoutOne_2368
du_isRingWithoutOne_742 T_IsCommutativeRing_2888
v5
du_isRingWithoutOne_742 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeRing_2888 ->
  MAlonzo.Code.Algebra.Structures.T_IsRingWithoutOne_2368
du_isRingWithoutOne_742 :: T_IsCommutativeRing_2888 -> T_IsRingWithoutOne_2368
du_isRingWithoutOne_742 T_IsCommutativeRing_2888
v0
  = (T_IsRing_2740 -> T_IsRingWithoutOne_2368)
-> Any -> T_IsRingWithoutOne_2368
forall a b. a -> b
coe
      T_IsRing_2740 -> T_IsRingWithoutOne_2368
MAlonzo.Code.Algebra.Structures.du_isRingWithoutOne_2772
      ((T_IsCommutativeRing_2888 -> T_IsRing_2740) -> Any -> Any
forall a b. a -> b
coe T_IsCommutativeRing_2888 -> T_IsRing_2740
MAlonzo.Code.Algebra.Structures.d_isRing_2904 (T_IsCommutativeRing_2888 -> Any
forall a b. a -> b
coe T_IsCommutativeRing_2888
v0))
-- Data.Bool.Properties._.IsCommutativeRing.isSemiring
d_isSemiring_744 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeRing_2888 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemiring_1640
d_isSemiring_744 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsCommutativeRing_2888
-> T_IsSemiring_1640
d_isSemiring_744 Bool -> Bool -> Bool
v0 Bool -> Bool -> Bool
v1 Bool -> Bool
v2 Bool
v3 ~Bool
v4 T_IsCommutativeRing_2888
v5
  = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> T_IsCommutativeRing_2888
-> T_IsSemiring_1640
du_isSemiring_744 Bool -> Bool -> Bool
v0 Bool -> Bool -> Bool
v1 Bool -> Bool
v2 Bool
v3 T_IsCommutativeRing_2888
v5
du_isSemiring_744 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeRing_2888 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemiring_1640
du_isSemiring_744 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> T_IsCommutativeRing_2888
-> T_IsSemiring_1640
du_isSemiring_744 Bool -> Bool -> Bool
v0 Bool -> Bool -> Bool
v1 Bool -> Bool
v2 Bool
v3 T_IsCommutativeRing_2888
v4
  = ((Any -> Any -> Any)
 -> (Any -> Any -> Any)
 -> (Any -> Any)
 -> Any
 -> T_IsRing_2740
 -> T_IsSemiring_1640)
-> Any -> Any -> Any -> Any -> Any -> T_IsSemiring_1640
forall a b. a -> b
coe
      (Any -> Any -> Any)
-> (Any -> Any -> Any)
-> (Any -> Any)
-> Any
-> T_IsRing_2740
-> T_IsSemiring_1640
MAlonzo.Code.Algebra.Structures.du_isSemiring_2870 ((Bool -> Bool -> Bool) -> Any
forall a b. a -> b
coe Bool -> Bool -> Bool
v0)
      ((Bool -> Bool -> Bool) -> Any
forall a b. a -> b
coe Bool -> Bool -> Bool
v1) ((Bool -> Bool) -> Any
forall a b. a -> b
coe Bool -> Bool
v2) (Bool -> Any
forall a b. a -> b
coe Bool
v3)
      ((T_IsCommutativeRing_2888 -> T_IsRing_2740) -> Any -> Any
forall a b. a -> b
coe T_IsCommutativeRing_2888 -> T_IsRing_2740
MAlonzo.Code.Algebra.Structures.d_isRing_2904 (T_IsCommutativeRing_2888 -> Any
forall a b. a -> b
coe T_IsCommutativeRing_2888
v4))
-- Data.Bool.Properties._.IsCommutativeRing.isSemiringWithoutAnnihilatingZero
d_isSemiringWithoutAnnihilatingZero_746 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeRing_2888 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutAnnihilatingZero_1536
d_isSemiringWithoutAnnihilatingZero_746 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsCommutativeRing_2888
-> T_IsSemiringWithoutAnnihilatingZero_1536
d_isSemiringWithoutAnnihilatingZero_746 ~Bool -> Bool -> Bool
v0 ~Bool -> Bool -> Bool
v1 ~Bool -> Bool
v2 ~Bool
v3 ~Bool
v4 T_IsCommutativeRing_2888
v5
  = T_IsCommutativeRing_2888
-> T_IsSemiringWithoutAnnihilatingZero_1536
du_isSemiringWithoutAnnihilatingZero_746 T_IsCommutativeRing_2888
v5
du_isSemiringWithoutAnnihilatingZero_746 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeRing_2888 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutAnnihilatingZero_1536
du_isSemiringWithoutAnnihilatingZero_746 :: T_IsCommutativeRing_2888
-> T_IsSemiringWithoutAnnihilatingZero_1536
du_isSemiringWithoutAnnihilatingZero_746 T_IsCommutativeRing_2888
v0
  = (T_IsRing_2740 -> T_IsSemiringWithoutAnnihilatingZero_1536)
-> Any -> T_IsSemiringWithoutAnnihilatingZero_1536
forall a b. a -> b
coe
      T_IsRing_2740 -> T_IsSemiringWithoutAnnihilatingZero_1536
MAlonzo.Code.Algebra.Structures.du_isSemiringWithoutAnnihilatingZero_2868
      ((T_IsCommutativeRing_2888 -> T_IsRing_2740) -> Any -> Any
forall a b. a -> b
coe T_IsCommutativeRing_2888 -> T_IsRing_2740
MAlonzo.Code.Algebra.Structures.d_isRing_2904 (T_IsCommutativeRing_2888 -> Any
forall a b. a -> b
coe T_IsCommutativeRing_2888
v0))
-- Data.Bool.Properties._.IsCommutativeRing.isSemiringWithoutOne
d_isSemiringWithoutOne_748 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeRing_2888 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutOne_1342
d_isSemiringWithoutOne_748 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsCommutativeRing_2888
-> T_IsSemiringWithoutOne_1342
d_isSemiringWithoutOne_748 Bool -> Bool -> Bool
v0 Bool -> Bool -> Bool
v1 Bool -> Bool
v2 Bool
v3 ~Bool
v4 T_IsCommutativeRing_2888
v5
  = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> T_IsCommutativeRing_2888
-> T_IsSemiringWithoutOne_1342
du_isSemiringWithoutOne_748 Bool -> Bool -> Bool
v0 Bool -> Bool -> Bool
v1 Bool -> Bool
v2 Bool
v3 T_IsCommutativeRing_2888
v5
du_isSemiringWithoutOne_748 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeRing_2888 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutOne_1342
du_isSemiringWithoutOne_748 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> T_IsCommutativeRing_2888
-> T_IsSemiringWithoutOne_1342
du_isSemiringWithoutOne_748 Bool -> Bool -> Bool
v0 Bool -> Bool -> Bool
v1 Bool -> Bool
v2 Bool
v3 T_IsCommutativeRing_2888
v4
  = let v5 :: T_IsRing_2740
v5
          = T_IsCommutativeRing_2888 -> T_IsRing_2740
MAlonzo.Code.Algebra.Structures.d_isRing_2904 (T_IsCommutativeRing_2888 -> T_IsCommutativeRing_2888
forall a b. a -> b
coe T_IsCommutativeRing_2888
v4) in
    Any -> T_IsSemiringWithoutOne_1342
forall a b. a -> b
coe
      ((T_IsSemiring_1640 -> T_IsSemiringWithoutOne_1342) -> Any -> Any
forall a b. a -> b
coe
         T_IsSemiring_1640 -> T_IsSemiringWithoutOne_1342
MAlonzo.Code.Algebra.Structures.du_isSemiringWithoutOne_1730
         (((Any -> Any -> Any)
 -> (Any -> Any -> Any)
 -> (Any -> Any)
 -> Any
 -> T_IsRing_2740
 -> T_IsSemiring_1640)
-> Any -> Any -> Any -> Any -> Any -> Any
forall a b. a -> b
coe
            (Any -> Any -> Any)
-> (Any -> Any -> Any)
-> (Any -> Any)
-> Any
-> T_IsRing_2740
-> T_IsSemiring_1640
MAlonzo.Code.Algebra.Structures.du_isSemiring_2870 ((Bool -> Bool -> Bool) -> Any
forall a b. a -> b
coe Bool -> Bool -> Bool
v0)
            ((Bool -> Bool -> Bool) -> Any
forall a b. a -> b
coe Bool -> Bool -> Bool
v1) ((Bool -> Bool) -> Any
forall a b. a -> b
coe Bool -> Bool
v2) (Bool -> Any
forall a b. a -> b
coe Bool
v3) (T_IsRing_2740 -> Any
forall a b. a -> b
coe T_IsRing_2740
v5)))
-- Data.Bool.Properties._.IsCommutativeRing.refl
d_refl_750 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeRing_2888 ->
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_refl_750 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsCommutativeRing_2888
-> Bool
-> T__'8801'__12
d_refl_750 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsCommutativeRing_2888
-> Bool
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsCommutativeRing.reflexive
d_reflexive_752 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeRing_2888 ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_reflexive_752 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsCommutativeRing_2888
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_reflexive_752 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsCommutativeRing_2888
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsCommutativeRing.setoid
d_setoid_754 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeRing_2888 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
d_setoid_754 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsCommutativeRing_2888
-> T_Setoid_46
d_setoid_754 ~Bool -> Bool -> Bool
v0 ~Bool -> Bool -> Bool
v1 ~Bool -> Bool
v2 ~Bool
v3 ~Bool
v4 T_IsCommutativeRing_2888
v5 = T_IsCommutativeRing_2888 -> T_Setoid_46
du_setoid_754 T_IsCommutativeRing_2888
v5
du_setoid_754 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeRing_2888 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
du_setoid_754 :: T_IsCommutativeRing_2888 -> T_Setoid_46
du_setoid_754 T_IsCommutativeRing_2888
v0
  = let v1 :: T_IsRing_2740
v1
          = T_IsCommutativeRing_2888 -> T_IsRing_2740
MAlonzo.Code.Algebra.Structures.d_isRing_2904 (T_IsCommutativeRing_2888 -> T_IsCommutativeRing_2888
forall a b. a -> b
coe T_IsCommutativeRing_2888
v0) in
    Any -> T_Setoid_46
forall a b. a -> b
coe
      (let v2 :: Any
v2
             = (T_IsRing_2740 -> T_IsRingWithoutOne_2368) -> Any -> Any
forall a b. a -> b
coe
                 T_IsRing_2740 -> T_IsRingWithoutOne_2368
MAlonzo.Code.Algebra.Structures.du_isRingWithoutOne_2772
                 (T_IsRing_2740 -> Any
forall a b. a -> b
coe T_IsRing_2740
v1) in
       Any -> Any
forall a b. a -> b
coe
         (let v3 :: T_IsAbelianGroup_1172
v3
                = T_IsRingWithoutOne_2368 -> T_IsAbelianGroup_1172
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2386
                    (Any -> T_IsRingWithoutOne_2368
forall a b. a -> b
coe Any
v2) in
          Any -> Any
forall a b. a -> b
coe
            (let v4 :: T_IsGroup_1074
v4
                   = T_IsAbelianGroup_1172 -> T_IsGroup_1074
MAlonzo.Code.Algebra.Structures.d_isGroup_1184 (T_IsAbelianGroup_1172 -> T_IsAbelianGroup_1172
forall a b. a -> b
coe T_IsAbelianGroup_1172
v3) in
             Any -> Any
forall a b. a -> b
coe
               (let v5 :: T_IsMonoid_712
v5
                      = T_IsGroup_1074 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_1088 (T_IsGroup_1074 -> T_IsGroup_1074
forall a b. a -> b
coe T_IsGroup_1074
v4) in
                Any -> Any
forall a b. a -> b
coe
                  (let v6 :: T_IsSemigroup_488
v6
                         = T_IsMonoid_712 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_722 (T_IsMonoid_712 -> T_IsMonoid_712
forall a b. a -> b
coe T_IsMonoid_712
v5) in
                   Any -> Any
forall a b. a -> b
coe
                     ((T_IsMagma_178 -> T_Setoid_46) -> Any -> Any
forall a b. a -> b
coe
                        T_IsMagma_178 -> T_Setoid_46
MAlonzo.Code.Algebra.Structures.du_setoid_202
                        ((T_IsSemigroup_488 -> T_IsMagma_178) -> Any -> Any
forall a b. a -> b
coe T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496 (T_IsSemigroup_488 -> Any
forall a b. a -> b
coe T_IsSemigroup_488
v6))))))))
-- Data.Bool.Properties._.IsCommutativeRing.sym
d_sym_756 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeRing_2888 ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_sym_756 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsCommutativeRing_2888
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_sym_756 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsCommutativeRing_2888
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsCommutativeRing.trans
d_trans_758 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeRing_2888 ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_trans_758 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsCommutativeRing_2888
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
d_trans_758 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsCommutativeRing_2888
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsCommutativeRing.uniqueʳ-⁻¹
d_unique'691''45''8315''185'_760 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeRing_2888 ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_unique'691''45''8315''185'_760 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsCommutativeRing_2888
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_unique'691''45''8315''185'_760 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsCommutativeRing_2888
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsCommutativeRing.uniqueˡ-⁻¹
d_unique'737''45''8315''185'_762 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeRing_2888 ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_unique'737''45''8315''185'_762 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsCommutativeRing_2888
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_unique'737''45''8315''185'_762 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsCommutativeRing_2888
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsCommutativeRing.zero
d_zero_764 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeRing_2888 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_zero_764 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsCommutativeRing_2888
-> T_Σ_14
d_zero_764 Bool -> Bool -> Bool
v0 Bool -> Bool -> Bool
v1 Bool -> Bool
v2 Bool
v3 ~Bool
v4 T_IsCommutativeRing_2888
v5 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> T_IsCommutativeRing_2888
-> T_Σ_14
du_zero_764 Bool -> Bool -> Bool
v0 Bool -> Bool -> Bool
v1 Bool -> Bool
v2 Bool
v3 T_IsCommutativeRing_2888
v5
du_zero_764 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeRing_2888 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
du_zero_764 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> T_IsCommutativeRing_2888
-> T_Σ_14
du_zero_764 Bool -> Bool -> Bool
v0 Bool -> Bool -> Bool
v1 Bool -> Bool
v2 Bool
v3 T_IsCommutativeRing_2888
v4
  = let v5 :: T_IsRing_2740
v5
          = T_IsCommutativeRing_2888 -> T_IsRing_2740
MAlonzo.Code.Algebra.Structures.d_isRing_2904 (T_IsCommutativeRing_2888 -> T_IsCommutativeRing_2888
forall a b. a -> b
coe T_IsCommutativeRing_2888
v4) in
    Any -> T_Σ_14
forall a b. a -> b
coe
      (((Any -> Any -> Any)
 -> (Any -> Any -> Any)
 -> (Any -> Any)
 -> Any
 -> T_IsRingWithoutOne_2368
 -> T_Σ_14)
-> Any -> Any -> Any -> Any -> Any -> Any
forall a b. a -> b
coe
         (Any -> Any -> Any)
-> (Any -> Any -> Any)
-> (Any -> Any)
-> Any
-> T_IsRingWithoutOne_2368
-> T_Σ_14
MAlonzo.Code.Algebra.Structures.du_zero_2468 ((Bool -> Bool -> Bool) -> Any
forall a b. a -> b
coe Bool -> Bool -> Bool
v0) ((Bool -> Bool -> Bool) -> Any
forall a b. a -> b
coe Bool -> Bool -> Bool
v1)
         ((Bool -> Bool) -> Any
forall a b. a -> b
coe Bool -> Bool
v2) (Bool -> Any
forall a b. a -> b
coe Bool
v3)
         ((T_IsRing_2740 -> T_IsRingWithoutOne_2368) -> Any -> Any
forall a b. a -> b
coe
            T_IsRing_2740 -> T_IsRingWithoutOne_2368
MAlonzo.Code.Algebra.Structures.du_isRingWithoutOne_2772 (T_IsRing_2740 -> Any
forall a b. a -> b
coe T_IsRing_2740
v5)))
-- Data.Bool.Properties._.IsCommutativeRing.zeroʳ
d_zero'691'_766 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeRing_2888 ->
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_zero'691'_766 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsCommutativeRing_2888
-> Bool
-> T__'8801'__12
d_zero'691'_766 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsCommutativeRing_2888
-> Bool
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsCommutativeRing.zeroˡ
d_zero'737'_768 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeRing_2888 ->
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_zero'737'_768 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsCommutativeRing_2888
-> Bool
-> T__'8801'__12
d_zero'737'_768 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsCommutativeRing_2888
-> Bool
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsCommutativeSemigroup.assoc
d_assoc_772 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_568 ->
  Bool ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_assoc_772 :: T_IsCommutativeSemigroup_568
-> Bool -> Bool -> Bool -> T__'8801'__12
d_assoc_772 = T_IsCommutativeSemigroup_568
-> Bool -> Bool -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsCommutativeSemigroup.comm
d_comm_774 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_568 ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_comm_774 :: T_IsCommutativeSemigroup_568 -> Bool -> Bool -> T__'8801'__12
d_comm_774 = T_IsCommutativeSemigroup_568 -> Bool -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsCommutativeSemigroup.isCommutativeMagma
d_isCommutativeMagma_776 ::
  (Bool -> Bool -> Bool) ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_568 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMagma_214
d_isCommutativeMagma_776 :: (Bool -> Bool -> Bool)
-> T_IsCommutativeSemigroup_568 -> T_IsCommutativeMagma_214
d_isCommutativeMagma_776 Bool -> Bool -> Bool
v0 T_IsCommutativeSemigroup_568
v1
  = (T_IsCommutativeSemigroup_568 -> T_IsCommutativeMagma_214)
-> T_IsCommutativeSemigroup_568 -> T_IsCommutativeMagma_214
forall a b. a -> b
coe T_IsCommutativeSemigroup_568 -> T_IsCommutativeMagma_214
MAlonzo.Code.Algebra.Structures.du_isCommutativeMagma_606 T_IsCommutativeSemigroup_568
v1
-- Data.Bool.Properties._.IsCommutativeSemigroup.isEquivalence
d_isEquivalence_778 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_568 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
d_isEquivalence_778 :: T_IsCommutativeSemigroup_568 -> T_IsEquivalence_28
d_isEquivalence_778 T_IsCommutativeSemigroup_568
v0
  = (T_IsMagma_178 -> T_IsEquivalence_28) -> Any -> T_IsEquivalence_28
forall a b. a -> b
coe
      T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186
      ((T_IsSemigroup_488 -> T_IsMagma_178) -> Any -> Any
forall a b. a -> b
coe
         T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496
         ((T_IsCommutativeSemigroup_568 -> T_IsSemigroup_488) -> Any -> Any
forall a b. a -> b
coe T_IsCommutativeSemigroup_568 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_576 (T_IsCommutativeSemigroup_568 -> Any
forall a b. a -> b
coe T_IsCommutativeSemigroup_568
v0)))
-- Data.Bool.Properties._.IsCommutativeSemigroup.isMagma
d_isMagma_780 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_568 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_178
d_isMagma_780 :: T_IsCommutativeSemigroup_568 -> T_IsMagma_178
d_isMagma_780 T_IsCommutativeSemigroup_568
v0
  = (T_IsSemigroup_488 -> T_IsMagma_178) -> Any -> T_IsMagma_178
forall a b. a -> b
coe
      T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496
      ((T_IsCommutativeSemigroup_568 -> T_IsSemigroup_488) -> Any -> Any
forall a b. a -> b
coe T_IsCommutativeSemigroup_568 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_576 (T_IsCommutativeSemigroup_568 -> Any
forall a b. a -> b
coe T_IsCommutativeSemigroup_568
v0))
-- Data.Bool.Properties._.IsCommutativeSemigroup.isPartialEquivalence
d_isPartialEquivalence_782 ::
  (Bool -> Bool -> Bool) ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_568 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_782 :: (Bool -> Bool -> Bool)
-> T_IsCommutativeSemigroup_568 -> T_IsPartialEquivalence_16
d_isPartialEquivalence_782 ~Bool -> Bool -> Bool
v0 T_IsCommutativeSemigroup_568
v1 = T_IsCommutativeSemigroup_568 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_782 T_IsCommutativeSemigroup_568
v1
du_isPartialEquivalence_782 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_568 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_782 :: T_IsCommutativeSemigroup_568 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_782 T_IsCommutativeSemigroup_568
v0
  = let v1 :: T_IsSemigroup_488
v1
          = T_IsCommutativeSemigroup_568 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_576 (T_IsCommutativeSemigroup_568 -> T_IsCommutativeSemigroup_568
forall a b. a -> b
coe T_IsCommutativeSemigroup_568
v0) in
    Any -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsMagma_178
v2 = T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496 (T_IsSemigroup_488 -> T_IsSemigroup_488
forall a b. a -> b
coe T_IsSemigroup_488
v1) in
       Any -> Any
forall a b. a -> b
coe
         ((T_IsEquivalence_28 -> T_IsPartialEquivalence_16) -> Any -> Any
forall a b. a -> b
coe
            T_IsEquivalence_28 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_44
            ((T_IsMagma_178 -> T_IsEquivalence_28) -> Any -> Any
forall a b. a -> b
coe
               T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186 (T_IsMagma_178 -> Any
forall a b. a -> b
coe T_IsMagma_178
v2))))
-- Data.Bool.Properties._.IsCommutativeSemigroup.isSemigroup
d_isSemigroup_784 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_568 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_488
d_isSemigroup_784 :: T_IsCommutativeSemigroup_568 -> T_IsSemigroup_488
d_isSemigroup_784 T_IsCommutativeSemigroup_568
v0
  = (T_IsCommutativeSemigroup_568 -> T_IsSemigroup_488)
-> Any -> T_IsSemigroup_488
forall a b. a -> b
coe T_IsCommutativeSemigroup_568 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_576 (T_IsCommutativeSemigroup_568 -> Any
forall a b. a -> b
coe T_IsCommutativeSemigroup_568
v0)
-- Data.Bool.Properties._.IsCommutativeSemigroup.refl
d_refl_786 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_568 ->
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_refl_786 :: T_IsCommutativeSemigroup_568 -> Bool -> T__'8801'__12
d_refl_786 = T_IsCommutativeSemigroup_568 -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsCommutativeSemigroup.reflexive
d_reflexive_788 ::
  (Bool -> Bool -> Bool) ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_568 ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_reflexive_788 :: (Bool -> Bool -> Bool)
-> T_IsCommutativeSemigroup_568
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_reflexive_788 = (Bool -> Bool -> Bool)
-> T_IsCommutativeSemigroup_568
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsCommutativeSemigroup.setoid
d_setoid_790 ::
  (Bool -> Bool -> Bool) ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_568 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
d_setoid_790 :: (Bool -> Bool -> Bool)
-> T_IsCommutativeSemigroup_568 -> T_Setoid_46
d_setoid_790 ~Bool -> Bool -> Bool
v0 T_IsCommutativeSemigroup_568
v1 = T_IsCommutativeSemigroup_568 -> T_Setoid_46
du_setoid_790 T_IsCommutativeSemigroup_568
v1
du_setoid_790 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_568 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
du_setoid_790 :: T_IsCommutativeSemigroup_568 -> T_Setoid_46
du_setoid_790 T_IsCommutativeSemigroup_568
v0
  = let v1 :: T_IsSemigroup_488
v1
          = T_IsCommutativeSemigroup_568 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_576 (T_IsCommutativeSemigroup_568 -> T_IsCommutativeSemigroup_568
forall a b. a -> b
coe T_IsCommutativeSemigroup_568
v0) in
    Any -> T_Setoid_46
forall a b. a -> b
coe
      ((T_IsMagma_178 -> T_Setoid_46) -> Any -> Any
forall a b. a -> b
coe
         T_IsMagma_178 -> T_Setoid_46
MAlonzo.Code.Algebra.Structures.du_setoid_202
         ((T_IsSemigroup_488 -> T_IsMagma_178) -> Any -> Any
forall a b. a -> b
coe T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496 (T_IsSemigroup_488 -> Any
forall a b. a -> b
coe T_IsSemigroup_488
v1)))
-- Data.Bool.Properties._.IsCommutativeSemigroup.sym
d_sym_792 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_568 ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_sym_792 :: T_IsCommutativeSemigroup_568
-> Bool -> Bool -> T__'8801'__12 -> T__'8801'__12
d_sym_792 = T_IsCommutativeSemigroup_568
-> Bool -> Bool -> T__'8801'__12 -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsCommutativeSemigroup.trans
d_trans_794 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_568 ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_trans_794 :: T_IsCommutativeSemigroup_568
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
d_trans_794 = T_IsCommutativeSemigroup_568
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsCommutativeSemigroup.∙-cong
d_'8729''45'cong_796 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_568 ->
  Bool ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8729''45'cong_796 :: T_IsCommutativeSemigroup_568
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong_796 = T_IsCommutativeSemigroup_568
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsCommutativeSemigroup.∙-congʳ
d_'8729''45'cong'691'_798 ::
  (Bool -> Bool -> Bool) ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_568 ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8729''45'cong'691'_798 :: (Bool -> Bool -> Bool)
-> T_IsCommutativeSemigroup_568
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong'691'_798 = (Bool -> Bool -> Bool)
-> T_IsCommutativeSemigroup_568
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsCommutativeSemigroup.∙-congˡ
d_'8729''45'cong'737'_800 ::
  (Bool -> Bool -> Bool) ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_568 ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8729''45'cong'737'_800 :: (Bool -> Bool -> Bool)
-> T_IsCommutativeSemigroup_568
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong'737'_800 = (Bool -> Bool -> Bool)
-> T_IsCommutativeSemigroup_568
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsCommutativeSemiring.*-assoc
d_'42''45'assoc_804 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiring_1750 ->
  Bool ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'42''45'assoc_804 :: T_IsCommutativeSemiring_1750
-> Bool -> Bool -> Bool -> T__'8801'__12
d_'42''45'assoc_804 = T_IsCommutativeSemiring_1750
-> Bool -> Bool -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsCommutativeSemiring.*-comm
d_'42''45'comm_806 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiring_1750 ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'42''45'comm_806 :: T_IsCommutativeSemiring_1750 -> Bool -> Bool -> T__'8801'__12
d_'42''45'comm_806 = T_IsCommutativeSemiring_1750 -> Bool -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsCommutativeSemiring.*-cong
d_'42''45'cong_808 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiring_1750 ->
  Bool ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'42''45'cong_808 :: T_IsCommutativeSemiring_1750
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
d_'42''45'cong_808 = T_IsCommutativeSemiring_1750
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsCommutativeSemiring.∙-congʳ
d_'8729''45'cong'691'_810 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiring_1750 ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8729''45'cong'691'_810 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> T_IsCommutativeSemiring_1750
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong'691'_810 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> T_IsCommutativeSemiring_1750
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsCommutativeSemiring.∙-congˡ
d_'8729''45'cong'737'_812 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiring_1750 ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8729''45'cong'737'_812 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> T_IsCommutativeSemiring_1750
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong'737'_812 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> T_IsCommutativeSemiring_1750
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsCommutativeSemiring.*-identity
d_'42''45'identity_814 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiring_1750 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'42''45'identity_814 :: T_IsCommutativeSemiring_1750 -> T_Σ_14
d_'42''45'identity_814 T_IsCommutativeSemiring_1750
v0
  = (T_IsSemiringWithoutAnnihilatingZero_1536 -> T_Σ_14)
-> Any -> T_Σ_14
forall a b. a -> b
coe
      T_IsSemiringWithoutAnnihilatingZero_1536 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_'42''45'identity_1562
      ((T_IsSemiring_1640 -> T_IsSemiringWithoutAnnihilatingZero_1536)
-> Any -> Any
forall a b. a -> b
coe
         T_IsSemiring_1640 -> T_IsSemiringWithoutAnnihilatingZero_1536
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1654
         ((T_IsCommutativeSemiring_1750 -> T_IsSemiring_1640) -> Any -> Any
forall a b. a -> b
coe T_IsCommutativeSemiring_1750 -> T_IsSemiring_1640
MAlonzo.Code.Algebra.Structures.d_isSemiring_1764 (T_IsCommutativeSemiring_1750 -> Any
forall a b. a -> b
coe T_IsCommutativeSemiring_1750
v0)))
-- Data.Bool.Properties._.IsCommutativeSemiring.identityʳ
d_identity'691'_816 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiring_1750 ->
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_identity'691'_816 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> T_IsCommutativeSemiring_1750
-> Bool
-> T__'8801'__12
d_identity'691'_816 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> T_IsCommutativeSemiring_1750
-> Bool
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsCommutativeSemiring.identityˡ
d_identity'737'_818 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiring_1750 ->
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_identity'737'_818 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> T_IsCommutativeSemiring_1750
-> Bool
-> T__'8801'__12
d_identity'737'_818 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> T_IsCommutativeSemiring_1750
-> Bool
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsCommutativeSemiring.isCommutativeMagma
d_isCommutativeMagma_820 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiring_1750 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMagma_214
d_isCommutativeMagma_820 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> T_IsCommutativeSemiring_1750
-> T_IsCommutativeMagma_214
d_isCommutativeMagma_820 ~Bool -> Bool -> Bool
v0 ~Bool -> Bool -> Bool
v1 ~Bool
v2 ~Bool
v3 T_IsCommutativeSemiring_1750
v4
  = T_IsCommutativeSemiring_1750 -> T_IsCommutativeMagma_214
du_isCommutativeMagma_820 T_IsCommutativeSemiring_1750
v4
du_isCommutativeMagma_820 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiring_1750 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMagma_214
du_isCommutativeMagma_820 :: T_IsCommutativeSemiring_1750 -> T_IsCommutativeMagma_214
du_isCommutativeMagma_820 T_IsCommutativeSemiring_1750
v0
  = let v1 :: Any
v1
          = (T_IsCommutativeSemiring_1750
 -> T_IsCommutativeSemiringWithoutOne_1438)
-> Any -> Any
forall a b. a -> b
coe
              T_IsCommutativeSemiring_1750
-> T_IsCommutativeSemiringWithoutOne_1438
MAlonzo.Code.Algebra.Structures.du_isCommutativeSemiringWithoutOne_1852
              (T_IsCommutativeSemiring_1750 -> Any
forall a b. a -> b
coe T_IsCommutativeSemiring_1750
v0) in
    Any -> T_IsCommutativeMagma_214
forall a b. a -> b
coe
      ((T_IsCommutativeSemigroup_568 -> T_IsCommutativeMagma_214)
-> Any -> Any
forall a b. a -> b
coe
         T_IsCommutativeSemigroup_568 -> T_IsCommutativeMagma_214
MAlonzo.Code.Algebra.Structures.du_isCommutativeMagma_606
         ((T_IsCommutativeSemiringWithoutOne_1438
 -> T_IsCommutativeSemigroup_568)
-> Any -> Any
forall a b. a -> b
coe
            T_IsCommutativeSemiringWithoutOne_1438
-> T_IsCommutativeSemigroup_568
MAlonzo.Code.Algebra.Structures.du_'42''45'isCommutativeSemigroup_1520
            (Any -> Any
forall a b. a -> b
coe Any
v1)))
-- Data.Bool.Properties._.IsCommutativeSemiring.*-isCommutativeMonoid
d_'42''45'isCommutativeMonoid_822 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiring_1750 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMonoid_764
d_'42''45'isCommutativeMonoid_822 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> T_IsCommutativeSemiring_1750
-> T_IsCommutativeMonoid_764
d_'42''45'isCommutativeMonoid_822 Bool -> Bool -> Bool
v0 Bool -> Bool -> Bool
v1 Bool
v2 Bool
v3 T_IsCommutativeSemiring_1750
v4
  = (T_IsCommutativeSemiring_1750 -> T_IsCommutativeMonoid_764)
-> T_IsCommutativeSemiring_1750 -> T_IsCommutativeMonoid_764
forall a b. a -> b
coe
      T_IsCommutativeSemiring_1750 -> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.du_'42''45'isCommutativeMonoid_1860
      T_IsCommutativeSemiring_1750
v4
-- Data.Bool.Properties._.IsCommutativeSemiring.*-isCommutativeSemigroup
d_'42''45'isCommutativeSemigroup_824 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiring_1750 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_568
d_'42''45'isCommutativeSemigroup_824 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> T_IsCommutativeSemiring_1750
-> T_IsCommutativeSemigroup_568
d_'42''45'isCommutativeSemigroup_824 ~Bool -> Bool -> Bool
v0 ~Bool -> Bool -> Bool
v1 ~Bool
v2 ~Bool
v3 T_IsCommutativeSemiring_1750
v4
  = T_IsCommutativeSemiring_1750 -> T_IsCommutativeSemigroup_568
du_'42''45'isCommutativeSemigroup_824 T_IsCommutativeSemiring_1750
v4
du_'42''45'isCommutativeSemigroup_824 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiring_1750 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_568
du_'42''45'isCommutativeSemigroup_824 :: T_IsCommutativeSemiring_1750 -> T_IsCommutativeSemigroup_568
du_'42''45'isCommutativeSemigroup_824 T_IsCommutativeSemiring_1750
v0
  = (T_IsCommutativeSemiringWithoutOne_1438
 -> T_IsCommutativeSemigroup_568)
-> Any -> T_IsCommutativeSemigroup_568
forall a b. a -> b
coe
      T_IsCommutativeSemiringWithoutOne_1438
-> T_IsCommutativeSemigroup_568
MAlonzo.Code.Algebra.Structures.du_'42''45'isCommutativeSemigroup_1520
      ((T_IsCommutativeSemiring_1750
 -> T_IsCommutativeSemiringWithoutOne_1438)
-> Any -> Any
forall a b. a -> b
coe
         T_IsCommutativeSemiring_1750
-> T_IsCommutativeSemiringWithoutOne_1438
MAlonzo.Code.Algebra.Structures.du_isCommutativeSemiringWithoutOne_1852
         (T_IsCommutativeSemiring_1750 -> Any
forall a b. a -> b
coe T_IsCommutativeSemiring_1750
v0))
-- Data.Bool.Properties._.IsCommutativeSemiring.*-isMagma
d_'42''45'isMagma_826 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiring_1750 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_178
d_'42''45'isMagma_826 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> T_IsCommutativeSemiring_1750
-> T_IsMagma_178
d_'42''45'isMagma_826 ~Bool -> Bool -> Bool
v0 ~Bool -> Bool -> Bool
v1 ~Bool
v2 ~Bool
v3 T_IsCommutativeSemiring_1750
v4
  = T_IsCommutativeSemiring_1750 -> T_IsMagma_178
du_'42''45'isMagma_826 T_IsCommutativeSemiring_1750
v4
du_'42''45'isMagma_826 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiring_1750 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_178
du_'42''45'isMagma_826 :: T_IsCommutativeSemiring_1750 -> T_IsMagma_178
du_'42''45'isMagma_826 T_IsCommutativeSemiring_1750
v0
  = let v1 :: T_IsSemiring_1640
v1
          = T_IsCommutativeSemiring_1750 -> T_IsSemiring_1640
MAlonzo.Code.Algebra.Structures.d_isSemiring_1764 (T_IsCommutativeSemiring_1750 -> T_IsCommutativeSemiring_1750
forall a b. a -> b
coe T_IsCommutativeSemiring_1750
v0) in
    Any -> T_IsMagma_178
forall a b. a -> b
coe
      ((T_IsSemiringWithoutAnnihilatingZero_1536 -> T_IsMagma_178)
-> Any -> Any
forall a b. a -> b
coe
         T_IsSemiringWithoutAnnihilatingZero_1536 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.du_'42''45'isMagma_1614
         ((T_IsSemiring_1640 -> T_IsSemiringWithoutAnnihilatingZero_1536)
-> Any -> Any
forall a b. a -> b
coe
            T_IsSemiring_1640 -> T_IsSemiringWithoutAnnihilatingZero_1536
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1654
            (T_IsSemiring_1640 -> Any
forall a b. a -> b
coe T_IsSemiring_1640
v1)))
-- Data.Bool.Properties._.IsCommutativeSemiring.*-isMonoid
d_'42''45'isMonoid_828 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiring_1750 ->
  MAlonzo.Code.Algebra.Structures.T_IsMonoid_712
d_'42''45'isMonoid_828 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> T_IsCommutativeSemiring_1750
-> T_IsMonoid_712
d_'42''45'isMonoid_828 ~Bool -> Bool -> Bool
v0 ~Bool -> Bool -> Bool
v1 ~Bool
v2 ~Bool
v3 T_IsCommutativeSemiring_1750
v4
  = T_IsCommutativeSemiring_1750 -> T_IsMonoid_712
du_'42''45'isMonoid_828 T_IsCommutativeSemiring_1750
v4
du_'42''45'isMonoid_828 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiring_1750 ->
  MAlonzo.Code.Algebra.Structures.T_IsMonoid_712
du_'42''45'isMonoid_828 :: T_IsCommutativeSemiring_1750 -> T_IsMonoid_712
du_'42''45'isMonoid_828 T_IsCommutativeSemiring_1750
v0
  = let v1 :: T_IsSemiring_1640
v1
          = T_IsCommutativeSemiring_1750 -> T_IsSemiring_1640
MAlonzo.Code.Algebra.Structures.d_isSemiring_1764 (T_IsCommutativeSemiring_1750 -> T_IsCommutativeSemiring_1750
forall a b. a -> b
coe T_IsCommutativeSemiring_1750
v0) in
    Any -> T_IsMonoid_712
forall a b. a -> b
coe
      ((T_IsSemiringWithoutAnnihilatingZero_1536 -> T_IsMonoid_712)
-> Any -> Any
forall a b. a -> b
coe
         T_IsSemiringWithoutAnnihilatingZero_1536 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.du_'42''45'isMonoid_1618
         ((T_IsSemiring_1640 -> T_IsSemiringWithoutAnnihilatingZero_1536)
-> Any -> Any
forall a b. a -> b
coe
            T_IsSemiring_1640 -> T_IsSemiringWithoutAnnihilatingZero_1536
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1654
            (T_IsSemiring_1640 -> Any
forall a b. a -> b
coe T_IsSemiring_1640
v1)))
-- Data.Bool.Properties._.IsCommutativeSemiring.*-isSemigroup
d_'42''45'isSemigroup_830 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiring_1750 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_488
d_'42''45'isSemigroup_830 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> T_IsCommutativeSemiring_1750
-> T_IsSemigroup_488
d_'42''45'isSemigroup_830 ~Bool -> Bool -> Bool
v0 ~Bool -> Bool -> Bool
v1 ~Bool
v2 ~Bool
v3 T_IsCommutativeSemiring_1750
v4
  = T_IsCommutativeSemiring_1750 -> T_IsSemigroup_488
du_'42''45'isSemigroup_830 T_IsCommutativeSemiring_1750
v4
du_'42''45'isSemigroup_830 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiring_1750 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_488
du_'42''45'isSemigroup_830 :: T_IsCommutativeSemiring_1750 -> T_IsSemigroup_488
du_'42''45'isSemigroup_830 T_IsCommutativeSemiring_1750
v0
  = let v1 :: T_IsSemiring_1640
v1
          = T_IsCommutativeSemiring_1750 -> T_IsSemiring_1640
MAlonzo.Code.Algebra.Structures.d_isSemiring_1764 (T_IsCommutativeSemiring_1750 -> T_IsCommutativeSemiring_1750
forall a b. a -> b
coe T_IsCommutativeSemiring_1750
v0) in
    Any -> T_IsSemigroup_488
forall a b. a -> b
coe
      ((T_IsSemiringWithoutAnnihilatingZero_1536 -> T_IsSemigroup_488)
-> Any -> Any
forall a b. a -> b
coe
         T_IsSemiringWithoutAnnihilatingZero_1536 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.du_'42''45'isSemigroup_1616
         ((T_IsSemiring_1640 -> T_IsSemiringWithoutAnnihilatingZero_1536)
-> Any -> Any
forall a b. a -> b
coe
            T_IsSemiring_1640 -> T_IsSemiringWithoutAnnihilatingZero_1536
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1654
            (T_IsSemiring_1640 -> Any
forall a b. a -> b
coe T_IsSemiring_1640
v1)))
-- Data.Bool.Properties._.IsCommutativeSemiring.assoc
d_assoc_832 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiring_1750 ->
  Bool ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_assoc_832 :: T_IsCommutativeSemiring_1750
-> Bool -> Bool -> Bool -> T__'8801'__12
d_assoc_832 = T_IsCommutativeSemiring_1750
-> Bool -> Bool -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsCommutativeSemiring.comm
d_comm_834 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiring_1750 ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_comm_834 :: T_IsCommutativeSemiring_1750 -> Bool -> Bool -> T__'8801'__12
d_comm_834 = T_IsCommutativeSemiring_1750 -> Bool -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsCommutativeSemiring.∙-cong
d_'8729''45'cong_836 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiring_1750 ->
  Bool ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8729''45'cong_836 :: T_IsCommutativeSemiring_1750
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong_836 = T_IsCommutativeSemiring_1750
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsCommutativeSemiring.∙-congʳ
d_'8729''45'cong'691'_838 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiring_1750 ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8729''45'cong'691'_838 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> T_IsCommutativeSemiring_1750
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong'691'_838 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> T_IsCommutativeSemiring_1750
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsCommutativeSemiring.∙-congˡ
d_'8729''45'cong'737'_840 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiring_1750 ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8729''45'cong'737'_840 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> T_IsCommutativeSemiring_1750
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong'737'_840 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> T_IsCommutativeSemiring_1750
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsCommutativeSemiring.identity
d_identity_842 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiring_1750 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_identity_842 :: T_IsCommutativeSemiring_1750 -> T_Σ_14
d_identity_842 T_IsCommutativeSemiring_1750
v0
  = (T_IsMonoid_712 -> T_Σ_14) -> Any -> T_Σ_14
forall a b. a -> b
coe
      T_IsMonoid_712 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_identity_724
      ((T_IsCommutativeMonoid_764 -> T_IsMonoid_712) -> Any -> Any
forall a b. a -> b
coe
         T_IsCommutativeMonoid_764 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_774
         ((T_IsSemiringWithoutAnnihilatingZero_1536
 -> T_IsCommutativeMonoid_764)
-> Any -> Any
forall a b. a -> b
coe
            T_IsSemiringWithoutAnnihilatingZero_1536
-> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1556
            ((T_IsSemiring_1640 -> T_IsSemiringWithoutAnnihilatingZero_1536)
-> Any -> Any
forall a b. a -> b
coe
               T_IsSemiring_1640 -> T_IsSemiringWithoutAnnihilatingZero_1536
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1654
               ((T_IsCommutativeSemiring_1750 -> T_IsSemiring_1640) -> Any -> Any
forall a b. a -> b
coe T_IsCommutativeSemiring_1750 -> T_IsSemiring_1640
MAlonzo.Code.Algebra.Structures.d_isSemiring_1764 (T_IsCommutativeSemiring_1750 -> Any
forall a b. a -> b
coe T_IsCommutativeSemiring_1750
v0)))))
-- Data.Bool.Properties._.IsCommutativeSemiring.identityʳ
d_identity'691'_844 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiring_1750 ->
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_identity'691'_844 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> T_IsCommutativeSemiring_1750
-> Bool
-> T__'8801'__12
d_identity'691'_844 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> T_IsCommutativeSemiring_1750
-> Bool
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsCommutativeSemiring.identityˡ
d_identity'737'_846 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiring_1750 ->
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_identity'737'_846 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> T_IsCommutativeSemiring_1750
-> Bool
-> T__'8801'__12
d_identity'737'_846 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> T_IsCommutativeSemiring_1750
-> Bool
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsCommutativeSemiring.isCommutativeMagma
d_isCommutativeMagma_848 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiring_1750 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMagma_214
d_isCommutativeMagma_848 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> T_IsCommutativeSemiring_1750
-> T_IsCommutativeMagma_214
d_isCommutativeMagma_848 ~Bool -> Bool -> Bool
v0 ~Bool -> Bool -> Bool
v1 ~Bool
v2 ~Bool
v3 T_IsCommutativeSemiring_1750
v4
  = T_IsCommutativeSemiring_1750 -> T_IsCommutativeMagma_214
du_isCommutativeMagma_848 T_IsCommutativeSemiring_1750
v4
du_isCommutativeMagma_848 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiring_1750 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMagma_214
du_isCommutativeMagma_848 :: T_IsCommutativeSemiring_1750 -> T_IsCommutativeMagma_214
du_isCommutativeMagma_848 T_IsCommutativeSemiring_1750
v0
  = let v1 :: T_IsSemiring_1640
v1
          = T_IsCommutativeSemiring_1750 -> T_IsSemiring_1640
MAlonzo.Code.Algebra.Structures.d_isSemiring_1764 (T_IsCommutativeSemiring_1750 -> T_IsCommutativeSemiring_1750
forall a b. a -> b
coe T_IsCommutativeSemiring_1750
v0) in
    Any -> T_IsCommutativeMagma_214
forall a b. a -> b
coe
      (let v2 :: T_IsSemiringWithoutAnnihilatingZero_1536
v2
             = T_IsSemiring_1640 -> T_IsSemiringWithoutAnnihilatingZero_1536
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1654
                 (T_IsSemiring_1640 -> T_IsSemiring_1640
forall a b. a -> b
coe T_IsSemiring_1640
v1) in
       Any -> Any
forall a b. a -> b
coe
         (let v3 :: T_IsCommutativeMonoid_764
v3
                = T_IsSemiringWithoutAnnihilatingZero_1536
-> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1556
                    (T_IsSemiringWithoutAnnihilatingZero_1536
-> T_IsSemiringWithoutAnnihilatingZero_1536
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1536
v2) in
          Any -> Any
forall a b. a -> b
coe
            ((T_IsCommutativeSemigroup_568 -> T_IsCommutativeMagma_214)
-> Any -> Any
forall a b. a -> b
coe
               T_IsCommutativeSemigroup_568 -> T_IsCommutativeMagma_214
MAlonzo.Code.Algebra.Structures.du_isCommutativeMagma_606
               ((T_IsCommutativeMonoid_764 -> T_IsCommutativeSemigroup_568)
-> Any -> Any
forall a b. a -> b
coe
                  T_IsCommutativeMonoid_764 -> T_IsCommutativeSemigroup_568
MAlonzo.Code.Algebra.Structures.du_isCommutativeSemigroup_814
                  (T_IsCommutativeMonoid_764 -> Any
forall a b. a -> b
coe T_IsCommutativeMonoid_764
v3)))))
-- Data.Bool.Properties._.IsCommutativeSemiring.+-isCommutativeMonoid
d_'43''45'isCommutativeMonoid_850 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiring_1750 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMonoid_764
d_'43''45'isCommutativeMonoid_850 :: T_IsCommutativeSemiring_1750 -> T_IsCommutativeMonoid_764
d_'43''45'isCommutativeMonoid_850 T_IsCommutativeSemiring_1750
v0
  = (T_IsSemiringWithoutAnnihilatingZero_1536
 -> T_IsCommutativeMonoid_764)
-> Any -> T_IsCommutativeMonoid_764
forall a b. a -> b
coe
      T_IsSemiringWithoutAnnihilatingZero_1536
-> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1556
      ((T_IsSemiring_1640 -> T_IsSemiringWithoutAnnihilatingZero_1536)
-> Any -> Any
forall a b. a -> b
coe
         T_IsSemiring_1640 -> T_IsSemiringWithoutAnnihilatingZero_1536
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1654
         ((T_IsCommutativeSemiring_1750 -> T_IsSemiring_1640) -> Any -> Any
forall a b. a -> b
coe T_IsCommutativeSemiring_1750 -> T_IsSemiring_1640
MAlonzo.Code.Algebra.Structures.d_isSemiring_1764 (T_IsCommutativeSemiring_1750 -> Any
forall a b. a -> b
coe T_IsCommutativeSemiring_1750
v0)))
-- Data.Bool.Properties._.IsCommutativeSemiring.isCommutativeSemigroup
d_isCommutativeSemigroup_852 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiring_1750 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_568
d_isCommutativeSemigroup_852 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> T_IsCommutativeSemiring_1750
-> T_IsCommutativeSemigroup_568
d_isCommutativeSemigroup_852 ~Bool -> Bool -> Bool
v0 ~Bool -> Bool -> Bool
v1 ~Bool
v2 ~Bool
v3 T_IsCommutativeSemiring_1750
v4
  = T_IsCommutativeSemiring_1750 -> T_IsCommutativeSemigroup_568
du_isCommutativeSemigroup_852 T_IsCommutativeSemiring_1750
v4
du_isCommutativeSemigroup_852 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiring_1750 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_568
du_isCommutativeSemigroup_852 :: T_IsCommutativeSemiring_1750 -> T_IsCommutativeSemigroup_568
du_isCommutativeSemigroup_852 T_IsCommutativeSemiring_1750
v0
  = let v1 :: T_IsSemiring_1640
v1
          = T_IsCommutativeSemiring_1750 -> T_IsSemiring_1640
MAlonzo.Code.Algebra.Structures.d_isSemiring_1764 (T_IsCommutativeSemiring_1750 -> T_IsCommutativeSemiring_1750
forall a b. a -> b
coe T_IsCommutativeSemiring_1750
v0) in
    Any -> T_IsCommutativeSemigroup_568
forall a b. a -> b
coe
      (let v2 :: T_IsSemiringWithoutAnnihilatingZero_1536
v2
             = T_IsSemiring_1640 -> T_IsSemiringWithoutAnnihilatingZero_1536
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1654
                 (T_IsSemiring_1640 -> T_IsSemiring_1640
forall a b. a -> b
coe T_IsSemiring_1640
v1) in
       Any -> Any
forall a b. a -> b
coe
         ((T_IsCommutativeMonoid_764 -> T_IsCommutativeSemigroup_568)
-> Any -> Any
forall a b. a -> b
coe
            T_IsCommutativeMonoid_764 -> T_IsCommutativeSemigroup_568
MAlonzo.Code.Algebra.Structures.du_isCommutativeSemigroup_814
            ((T_IsSemiringWithoutAnnihilatingZero_1536
 -> T_IsCommutativeMonoid_764)
-> Any -> Any
forall a b. a -> b
coe
               T_IsSemiringWithoutAnnihilatingZero_1536
-> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1556
               (T_IsSemiringWithoutAnnihilatingZero_1536 -> Any
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1536
v2))))
-- Data.Bool.Properties._.IsCommutativeSemiring.isMagma
d_isMagma_854 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiring_1750 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_178
d_isMagma_854 :: T_IsCommutativeSemiring_1750 -> T_IsMagma_178
d_isMagma_854 T_IsCommutativeSemiring_1750
v0
  = (T_IsSemigroup_488 -> T_IsMagma_178) -> Any -> T_IsMagma_178
forall a b. a -> b
coe
      T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496
      ((T_IsMonoid_712 -> T_IsSemigroup_488) -> Any -> Any
forall a b. a -> b
coe
         T_IsMonoid_712 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_722
         ((T_IsCommutativeMonoid_764 -> T_IsMonoid_712) -> Any -> Any
forall a b. a -> b
coe
            T_IsCommutativeMonoid_764 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_774
            ((T_IsSemiringWithoutAnnihilatingZero_1536
 -> T_IsCommutativeMonoid_764)
-> Any -> Any
forall a b. a -> b
coe
               T_IsSemiringWithoutAnnihilatingZero_1536
-> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1556
               ((T_IsSemiring_1640 -> T_IsSemiringWithoutAnnihilatingZero_1536)
-> Any -> Any
forall a b. a -> b
coe
                  T_IsSemiring_1640 -> T_IsSemiringWithoutAnnihilatingZero_1536
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1654
                  ((T_IsCommutativeSemiring_1750 -> T_IsSemiring_1640) -> Any -> Any
forall a b. a -> b
coe
                     T_IsCommutativeSemiring_1750 -> T_IsSemiring_1640
MAlonzo.Code.Algebra.Structures.d_isSemiring_1764 (T_IsCommutativeSemiring_1750 -> Any
forall a b. a -> b
coe T_IsCommutativeSemiring_1750
v0))))))
-- Data.Bool.Properties._.IsCommutativeSemiring.isMonoid
d_isMonoid_856 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiring_1750 ->
  MAlonzo.Code.Algebra.Structures.T_IsMonoid_712
d_isMonoid_856 :: T_IsCommutativeSemiring_1750 -> T_IsMonoid_712
d_isMonoid_856 T_IsCommutativeSemiring_1750
v0
  = (T_IsCommutativeMonoid_764 -> T_IsMonoid_712)
-> Any -> T_IsMonoid_712
forall a b. a -> b
coe
      T_IsCommutativeMonoid_764 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_774
      ((T_IsSemiringWithoutAnnihilatingZero_1536
 -> T_IsCommutativeMonoid_764)
-> Any -> Any
forall a b. a -> b
coe
         T_IsSemiringWithoutAnnihilatingZero_1536
-> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1556
         ((T_IsSemiring_1640 -> T_IsSemiringWithoutAnnihilatingZero_1536)
-> Any -> Any
forall a b. a -> b
coe
            T_IsSemiring_1640 -> T_IsSemiringWithoutAnnihilatingZero_1536
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1654
            ((T_IsCommutativeSemiring_1750 -> T_IsSemiring_1640) -> Any -> Any
forall a b. a -> b
coe T_IsCommutativeSemiring_1750 -> T_IsSemiring_1640
MAlonzo.Code.Algebra.Structures.d_isSemiring_1764 (T_IsCommutativeSemiring_1750 -> Any
forall a b. a -> b
coe T_IsCommutativeSemiring_1750
v0))))
-- Data.Bool.Properties._.IsCommutativeSemiring.isSemigroup
d_isSemigroup_858 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiring_1750 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_488
d_isSemigroup_858 :: T_IsCommutativeSemiring_1750 -> T_IsSemigroup_488
d_isSemigroup_858 T_IsCommutativeSemiring_1750
v0
  = (T_IsMonoid_712 -> T_IsSemigroup_488) -> Any -> T_IsSemigroup_488
forall a b. a -> b
coe
      T_IsMonoid_712 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_722
      ((T_IsCommutativeMonoid_764 -> T_IsMonoid_712) -> Any -> Any
forall a b. a -> b
coe
         T_IsCommutativeMonoid_764 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_774
         ((T_IsSemiringWithoutAnnihilatingZero_1536
 -> T_IsCommutativeMonoid_764)
-> Any -> Any
forall a b. a -> b
coe
            T_IsSemiringWithoutAnnihilatingZero_1536
-> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1556
            ((T_IsSemiring_1640 -> T_IsSemiringWithoutAnnihilatingZero_1536)
-> Any -> Any
forall a b. a -> b
coe
               T_IsSemiring_1640 -> T_IsSemiringWithoutAnnihilatingZero_1536
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1654
               ((T_IsCommutativeSemiring_1750 -> T_IsSemiring_1640) -> Any -> Any
forall a b. a -> b
coe T_IsCommutativeSemiring_1750 -> T_IsSemiring_1640
MAlonzo.Code.Algebra.Structures.d_isSemiring_1764 (T_IsCommutativeSemiring_1750 -> Any
forall a b. a -> b
coe T_IsCommutativeSemiring_1750
v0)))))
-- Data.Bool.Properties._.IsCommutativeSemiring.isUnitalMagma
d_isUnitalMagma_860 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiring_1750 ->
  MAlonzo.Code.Algebra.Structures.T_IsUnitalMagma_666
d_isUnitalMagma_860 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> T_IsCommutativeSemiring_1750
-> T_IsUnitalMagma_666
d_isUnitalMagma_860 ~Bool -> Bool -> Bool
v0 ~Bool -> Bool -> Bool
v1 ~Bool
v2 ~Bool
v3 T_IsCommutativeSemiring_1750
v4 = T_IsCommutativeSemiring_1750 -> T_IsUnitalMagma_666
du_isUnitalMagma_860 T_IsCommutativeSemiring_1750
v4
du_isUnitalMagma_860 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiring_1750 ->
  MAlonzo.Code.Algebra.Structures.T_IsUnitalMagma_666
du_isUnitalMagma_860 :: T_IsCommutativeSemiring_1750 -> T_IsUnitalMagma_666
du_isUnitalMagma_860 T_IsCommutativeSemiring_1750
v0
  = let v1 :: T_IsSemiring_1640
v1
          = T_IsCommutativeSemiring_1750 -> T_IsSemiring_1640
MAlonzo.Code.Algebra.Structures.d_isSemiring_1764 (T_IsCommutativeSemiring_1750 -> T_IsCommutativeSemiring_1750
forall a b. a -> b
coe T_IsCommutativeSemiring_1750
v0) in
    Any -> T_IsUnitalMagma_666
forall a b. a -> b
coe
      (let v2 :: T_IsSemiringWithoutAnnihilatingZero_1536
v2
             = T_IsSemiring_1640 -> T_IsSemiringWithoutAnnihilatingZero_1536
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1654
                 (T_IsSemiring_1640 -> T_IsSemiring_1640
forall a b. a -> b
coe T_IsSemiring_1640
v1) in
       Any -> Any
forall a b. a -> b
coe
         (let v3 :: T_IsCommutativeMonoid_764
v3
                = T_IsSemiringWithoutAnnihilatingZero_1536
-> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1556
                    (T_IsSemiringWithoutAnnihilatingZero_1536
-> T_IsSemiringWithoutAnnihilatingZero_1536
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1536
v2) in
          Any -> Any
forall a b. a -> b
coe
            ((T_IsMonoid_712 -> T_IsUnitalMagma_666) -> Any -> Any
forall a b. a -> b
coe
               T_IsMonoid_712 -> T_IsUnitalMagma_666
MAlonzo.Code.Algebra.Structures.du_isUnitalMagma_756
               ((T_IsCommutativeMonoid_764 -> T_IsMonoid_712) -> Any -> Any
forall a b. a -> b
coe T_IsCommutativeMonoid_764 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_774 (T_IsCommutativeMonoid_764 -> Any
forall a b. a -> b
coe T_IsCommutativeMonoid_764
v3)))))
-- Data.Bool.Properties._.IsCommutativeSemiring.distrib
d_distrib_862 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiring_1750 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_distrib_862 :: T_IsCommutativeSemiring_1750 -> T_Σ_14
d_distrib_862 T_IsCommutativeSemiring_1750
v0
  = (T_IsSemiringWithoutAnnihilatingZero_1536 -> T_Σ_14)
-> Any -> T_Σ_14
forall a b. a -> b
coe
      T_IsSemiringWithoutAnnihilatingZero_1536 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_distrib_1564
      ((T_IsSemiring_1640 -> T_IsSemiringWithoutAnnihilatingZero_1536)
-> Any -> Any
forall a b. a -> b
coe
         T_IsSemiring_1640 -> T_IsSemiringWithoutAnnihilatingZero_1536
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1654
         ((T_IsCommutativeSemiring_1750 -> T_IsSemiring_1640) -> Any -> Any
forall a b. a -> b
coe T_IsCommutativeSemiring_1750 -> T_IsSemiring_1640
MAlonzo.Code.Algebra.Structures.d_isSemiring_1764 (T_IsCommutativeSemiring_1750 -> Any
forall a b. a -> b
coe T_IsCommutativeSemiring_1750
v0)))
-- Data.Bool.Properties._.IsCommutativeSemiring.distribʳ
d_distrib'691'_864 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiring_1750 ->
  Bool ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_distrib'691'_864 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> T_IsCommutativeSemiring_1750
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
d_distrib'691'_864 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> T_IsCommutativeSemiring_1750
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsCommutativeSemiring.distribˡ
d_distrib'737'_866 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiring_1750 ->
  Bool ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_distrib'737'_866 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> T_IsCommutativeSemiring_1750
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
d_distrib'737'_866 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> T_IsCommutativeSemiring_1750
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsCommutativeSemiring.isCommutativeSemiringWithoutOne
d_isCommutativeSemiringWithoutOne_868 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiring_1750 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiringWithoutOne_1438
d_isCommutativeSemiringWithoutOne_868 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> T_IsCommutativeSemiring_1750
-> T_IsCommutativeSemiringWithoutOne_1438
d_isCommutativeSemiringWithoutOne_868 Bool -> Bool -> Bool
v0 Bool -> Bool -> Bool
v1 Bool
v2 Bool
v3 T_IsCommutativeSemiring_1750
v4
  = (T_IsCommutativeSemiring_1750
 -> T_IsCommutativeSemiringWithoutOne_1438)
-> T_IsCommutativeSemiring_1750
-> T_IsCommutativeSemiringWithoutOne_1438
forall a b. a -> b
coe
      T_IsCommutativeSemiring_1750
-> T_IsCommutativeSemiringWithoutOne_1438
MAlonzo.Code.Algebra.Structures.du_isCommutativeSemiringWithoutOne_1852
      T_IsCommutativeSemiring_1750
v4
-- Data.Bool.Properties._.IsCommutativeSemiring.isEquivalence
d_isEquivalence_870 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiring_1750 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
d_isEquivalence_870 :: T_IsCommutativeSemiring_1750 -> T_IsEquivalence_28
d_isEquivalence_870 T_IsCommutativeSemiring_1750
v0
  = (T_IsMagma_178 -> T_IsEquivalence_28) -> Any -> T_IsEquivalence_28
forall a b. a -> b
coe
      T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186
      ((T_IsSemigroup_488 -> T_IsMagma_178) -> Any -> Any
forall a b. a -> b
coe
         T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496
         ((T_IsMonoid_712 -> T_IsSemigroup_488) -> Any -> Any
forall a b. a -> b
coe
            T_IsMonoid_712 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_722
            ((T_IsCommutativeMonoid_764 -> T_IsMonoid_712) -> Any -> Any
forall a b. a -> b
coe
               T_IsCommutativeMonoid_764 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_774
               ((T_IsSemiringWithoutAnnihilatingZero_1536
 -> T_IsCommutativeMonoid_764)
-> Any -> Any
forall a b. a -> b
coe
                  T_IsSemiringWithoutAnnihilatingZero_1536
-> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1556
                  ((T_IsSemiring_1640 -> T_IsSemiringWithoutAnnihilatingZero_1536)
-> Any -> Any
forall a b. a -> b
coe
                     T_IsSemiring_1640 -> T_IsSemiringWithoutAnnihilatingZero_1536
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1654
                     ((T_IsCommutativeSemiring_1750 -> T_IsSemiring_1640) -> Any -> Any
forall a b. a -> b
coe
                        T_IsCommutativeSemiring_1750 -> T_IsSemiring_1640
MAlonzo.Code.Algebra.Structures.d_isSemiring_1764 (T_IsCommutativeSemiring_1750 -> Any
forall a b. a -> b
coe T_IsCommutativeSemiring_1750
v0)))))))
-- Data.Bool.Properties._.IsCommutativeSemiring.isNearSemiring
d_isNearSemiring_872 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiring_1750 ->
  MAlonzo.Code.Algebra.Structures.T_IsNearSemiring_1260
d_isNearSemiring_872 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> T_IsCommutativeSemiring_1750
-> T_IsNearSemiring_1260
d_isNearSemiring_872 ~Bool -> Bool -> Bool
v0 ~Bool -> Bool -> Bool
v1 ~Bool
v2 ~Bool
v3 T_IsCommutativeSemiring_1750
v4 = T_IsCommutativeSemiring_1750 -> T_IsNearSemiring_1260
du_isNearSemiring_872 T_IsCommutativeSemiring_1750
v4
du_isNearSemiring_872 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiring_1750 ->
  MAlonzo.Code.Algebra.Structures.T_IsNearSemiring_1260
du_isNearSemiring_872 :: T_IsCommutativeSemiring_1750 -> T_IsNearSemiring_1260
du_isNearSemiring_872 T_IsCommutativeSemiring_1750
v0
  = let v1 :: T_IsSemiring_1640
v1
          = T_IsCommutativeSemiring_1750 -> T_IsSemiring_1640
MAlonzo.Code.Algebra.Structures.d_isSemiring_1764 (T_IsCommutativeSemiring_1750 -> T_IsCommutativeSemiring_1750
forall a b. a -> b
coe T_IsCommutativeSemiring_1750
v0) in
    Any -> T_IsNearSemiring_1260
forall a b. a -> b
coe
      ((T_IsSemiringWithoutOne_1342 -> T_IsNearSemiring_1260)
-> Any -> Any
forall a b. a -> b
coe
         T_IsSemiringWithoutOne_1342 -> T_IsNearSemiring_1260
MAlonzo.Code.Algebra.Structures.du_isNearSemiring_1428
         ((T_IsSemiring_1640 -> T_IsSemiringWithoutOne_1342) -> Any -> Any
forall a b. a -> b
coe
            T_IsSemiring_1640 -> T_IsSemiringWithoutOne_1342
MAlonzo.Code.Algebra.Structures.du_isSemiringWithoutOne_1730
            (T_IsSemiring_1640 -> Any
forall a b. a -> b
coe T_IsSemiring_1640
v1)))
-- Data.Bool.Properties._.IsCommutativeSemiring.isPartialEquivalence
d_isPartialEquivalence_874 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiring_1750 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_874 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> T_IsCommutativeSemiring_1750
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_874 ~Bool -> Bool -> Bool
v0 ~Bool -> Bool -> Bool
v1 ~Bool
v2 ~Bool
v3 T_IsCommutativeSemiring_1750
v4
  = T_IsCommutativeSemiring_1750 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_874 T_IsCommutativeSemiring_1750
v4
du_isPartialEquivalence_874 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiring_1750 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_874 :: T_IsCommutativeSemiring_1750 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_874 T_IsCommutativeSemiring_1750
v0
  = let v1 :: T_IsSemiring_1640
v1
          = T_IsCommutativeSemiring_1750 -> T_IsSemiring_1640
MAlonzo.Code.Algebra.Structures.d_isSemiring_1764 (T_IsCommutativeSemiring_1750 -> T_IsCommutativeSemiring_1750
forall a b. a -> b
coe T_IsCommutativeSemiring_1750
v0) in
    Any -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsSemiringWithoutAnnihilatingZero_1536
v2
             = T_IsSemiring_1640 -> T_IsSemiringWithoutAnnihilatingZero_1536
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1654
                 (T_IsSemiring_1640 -> T_IsSemiring_1640
forall a b. a -> b
coe T_IsSemiring_1640
v1) in
       Any -> Any
forall a b. a -> b
coe
         (let v3 :: T_IsCommutativeMonoid_764
v3
                = T_IsSemiringWithoutAnnihilatingZero_1536
-> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1556
                    (T_IsSemiringWithoutAnnihilatingZero_1536
-> T_IsSemiringWithoutAnnihilatingZero_1536
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1536
v2) in
          Any -> Any
forall a b. a -> b
coe
            (let v4 :: T_IsMonoid_712
v4
                   = T_IsCommutativeMonoid_764 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_774 (T_IsCommutativeMonoid_764 -> T_IsCommutativeMonoid_764
forall a b. a -> b
coe T_IsCommutativeMonoid_764
v3) in
             Any -> Any
forall a b. a -> b
coe
               (let v5 :: T_IsSemigroup_488
v5
                      = T_IsMonoid_712 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_722 (T_IsMonoid_712 -> T_IsMonoid_712
forall a b. a -> b
coe T_IsMonoid_712
v4) in
                Any -> Any
forall a b. a -> b
coe
                  (let v6 :: T_IsMagma_178
v6 = T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496 (T_IsSemigroup_488 -> T_IsSemigroup_488
forall a b. a -> b
coe T_IsSemigroup_488
v5) in
                   Any -> Any
forall a b. a -> b
coe
                     ((T_IsEquivalence_28 -> T_IsPartialEquivalence_16) -> Any -> Any
forall a b. a -> b
coe
                        T_IsEquivalence_28 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_44
                        ((T_IsMagma_178 -> T_IsEquivalence_28) -> Any -> Any
forall a b. a -> b
coe
                           T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186 (T_IsMagma_178 -> Any
forall a b. a -> b
coe T_IsMagma_178
v6))))))))
-- Data.Bool.Properties._.IsCommutativeSemiring.isSemiring
d_isSemiring_876 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiring_1750 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemiring_1640
d_isSemiring_876 :: T_IsCommutativeSemiring_1750 -> T_IsSemiring_1640
d_isSemiring_876 T_IsCommutativeSemiring_1750
v0
  = (T_IsCommutativeSemiring_1750 -> T_IsSemiring_1640)
-> Any -> T_IsSemiring_1640
forall a b. a -> b
coe T_IsCommutativeSemiring_1750 -> T_IsSemiring_1640
MAlonzo.Code.Algebra.Structures.d_isSemiring_1764 (T_IsCommutativeSemiring_1750 -> Any
forall a b. a -> b
coe T_IsCommutativeSemiring_1750
v0)
-- Data.Bool.Properties._.IsCommutativeSemiring.isSemiringWithoutAnnihilatingZero
d_isSemiringWithoutAnnihilatingZero_878 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiring_1750 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutAnnihilatingZero_1536
d_isSemiringWithoutAnnihilatingZero_878 :: T_IsCommutativeSemiring_1750
-> T_IsSemiringWithoutAnnihilatingZero_1536
d_isSemiringWithoutAnnihilatingZero_878 T_IsCommutativeSemiring_1750
v0
  = (T_IsSemiring_1640 -> T_IsSemiringWithoutAnnihilatingZero_1536)
-> Any -> T_IsSemiringWithoutAnnihilatingZero_1536
forall a b. a -> b
coe
      T_IsSemiring_1640 -> T_IsSemiringWithoutAnnihilatingZero_1536
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1654
      ((T_IsCommutativeSemiring_1750 -> T_IsSemiring_1640) -> Any -> Any
forall a b. a -> b
coe T_IsCommutativeSemiring_1750 -> T_IsSemiring_1640
MAlonzo.Code.Algebra.Structures.d_isSemiring_1764 (T_IsCommutativeSemiring_1750 -> Any
forall a b. a -> b
coe T_IsCommutativeSemiring_1750
v0))
-- Data.Bool.Properties._.IsCommutativeSemiring.isSemiringWithoutOne
d_isSemiringWithoutOne_880 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiring_1750 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutOne_1342
d_isSemiringWithoutOne_880 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> T_IsCommutativeSemiring_1750
-> T_IsSemiringWithoutOne_1342
d_isSemiringWithoutOne_880 ~Bool -> Bool -> Bool
v0 ~Bool -> Bool -> Bool
v1 ~Bool
v2 ~Bool
v3 T_IsCommutativeSemiring_1750
v4
  = T_IsCommutativeSemiring_1750 -> T_IsSemiringWithoutOne_1342
du_isSemiringWithoutOne_880 T_IsCommutativeSemiring_1750
v4
du_isSemiringWithoutOne_880 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiring_1750 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutOne_1342
du_isSemiringWithoutOne_880 :: T_IsCommutativeSemiring_1750 -> T_IsSemiringWithoutOne_1342
du_isSemiringWithoutOne_880 T_IsCommutativeSemiring_1750
v0
  = (T_IsSemiring_1640 -> T_IsSemiringWithoutOne_1342)
-> Any -> T_IsSemiringWithoutOne_1342
forall a b. a -> b
coe
      T_IsSemiring_1640 -> T_IsSemiringWithoutOne_1342
MAlonzo.Code.Algebra.Structures.du_isSemiringWithoutOne_1730
      ((T_IsCommutativeSemiring_1750 -> T_IsSemiring_1640) -> Any -> Any
forall a b. a -> b
coe T_IsCommutativeSemiring_1750 -> T_IsSemiring_1640
MAlonzo.Code.Algebra.Structures.d_isSemiring_1764 (T_IsCommutativeSemiring_1750 -> Any
forall a b. a -> b
coe T_IsCommutativeSemiring_1750
v0))
-- Data.Bool.Properties._.IsCommutativeSemiring.refl
d_refl_882 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiring_1750 ->
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_refl_882 :: T_IsCommutativeSemiring_1750 -> Bool -> T__'8801'__12
d_refl_882 = T_IsCommutativeSemiring_1750 -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsCommutativeSemiring.reflexive
d_reflexive_884 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiring_1750 ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_reflexive_884 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> T_IsCommutativeSemiring_1750
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_reflexive_884 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> T_IsCommutativeSemiring_1750
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsCommutativeSemiring.setoid
d_setoid_886 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiring_1750 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
d_setoid_886 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> T_IsCommutativeSemiring_1750
-> T_Setoid_46
d_setoid_886 ~Bool -> Bool -> Bool
v0 ~Bool -> Bool -> Bool
v1 ~Bool
v2 ~Bool
v3 T_IsCommutativeSemiring_1750
v4 = T_IsCommutativeSemiring_1750 -> T_Setoid_46
du_setoid_886 T_IsCommutativeSemiring_1750
v4
du_setoid_886 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiring_1750 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
du_setoid_886 :: T_IsCommutativeSemiring_1750 -> T_Setoid_46
du_setoid_886 T_IsCommutativeSemiring_1750
v0
  = let v1 :: T_IsSemiring_1640
v1
          = T_IsCommutativeSemiring_1750 -> T_IsSemiring_1640
MAlonzo.Code.Algebra.Structures.d_isSemiring_1764 (T_IsCommutativeSemiring_1750 -> T_IsCommutativeSemiring_1750
forall a b. a -> b
coe T_IsCommutativeSemiring_1750
v0) in
    Any -> T_Setoid_46
forall a b. a -> b
coe
      (let v2 :: T_IsSemiringWithoutAnnihilatingZero_1536
v2
             = T_IsSemiring_1640 -> T_IsSemiringWithoutAnnihilatingZero_1536
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1654
                 (T_IsSemiring_1640 -> T_IsSemiring_1640
forall a b. a -> b
coe T_IsSemiring_1640
v1) in
       Any -> Any
forall a b. a -> b
coe
         (let v3 :: T_IsCommutativeMonoid_764
v3
                = T_IsSemiringWithoutAnnihilatingZero_1536
-> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1556
                    (T_IsSemiringWithoutAnnihilatingZero_1536
-> T_IsSemiringWithoutAnnihilatingZero_1536
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1536
v2) in
          Any -> Any
forall a b. a -> b
coe
            (let v4 :: T_IsMonoid_712
v4
                   = T_IsCommutativeMonoid_764 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_774 (T_IsCommutativeMonoid_764 -> T_IsCommutativeMonoid_764
forall a b. a -> b
coe T_IsCommutativeMonoid_764
v3) in
             Any -> Any
forall a b. a -> b
coe
               (let v5 :: T_IsSemigroup_488
v5
                      = T_IsMonoid_712 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_722 (T_IsMonoid_712 -> T_IsMonoid_712
forall a b. a -> b
coe T_IsMonoid_712
v4) in
                Any -> Any
forall a b. a -> b
coe
                  ((T_IsMagma_178 -> T_Setoid_46) -> Any -> Any
forall a b. a -> b
coe
                     T_IsMagma_178 -> T_Setoid_46
MAlonzo.Code.Algebra.Structures.du_setoid_202
                     ((T_IsSemigroup_488 -> T_IsMagma_178) -> Any -> Any
forall a b. a -> b
coe T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496 (T_IsSemigroup_488 -> Any
forall a b. a -> b
coe T_IsSemigroup_488
v5)))))))
-- Data.Bool.Properties._.IsCommutativeSemiring.sym
d_sym_888 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiring_1750 ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_sym_888 :: T_IsCommutativeSemiring_1750
-> Bool -> Bool -> T__'8801'__12 -> T__'8801'__12
d_sym_888 = T_IsCommutativeSemiring_1750
-> Bool -> Bool -> T__'8801'__12 -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsCommutativeSemiring.trans
d_trans_890 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiring_1750 ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_trans_890 :: T_IsCommutativeSemiring_1750
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
d_trans_890 = T_IsCommutativeSemiring_1750
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsCommutativeSemiring.zero
d_zero_892 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiring_1750 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_zero_892 :: T_IsCommutativeSemiring_1750 -> T_Σ_14
d_zero_892 T_IsCommutativeSemiring_1750
v0
  = (T_IsSemiring_1640 -> T_Σ_14) -> Any -> T_Σ_14
forall a b. a -> b
coe
      T_IsSemiring_1640 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_zero_1656
      ((T_IsCommutativeSemiring_1750 -> T_IsSemiring_1640) -> Any -> Any
forall a b. a -> b
coe T_IsCommutativeSemiring_1750 -> T_IsSemiring_1640
MAlonzo.Code.Algebra.Structures.d_isSemiring_1764 (T_IsCommutativeSemiring_1750 -> Any
forall a b. a -> b
coe T_IsCommutativeSemiring_1750
v0))
-- Data.Bool.Properties._.IsCommutativeSemiring.zeroʳ
d_zero'691'_894 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiring_1750 ->
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_zero'691'_894 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> T_IsCommutativeSemiring_1750
-> Bool
-> T__'8801'__12
d_zero'691'_894 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> T_IsCommutativeSemiring_1750
-> Bool
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsCommutativeSemiring.zeroˡ
d_zero'737'_896 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiring_1750 ->
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_zero'737'_896 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> T_IsCommutativeSemiring_1750
-> Bool
-> T__'8801'__12
d_zero'737'_896 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> T_IsCommutativeSemiring_1750
-> Bool
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsCommutativeSemiringWithoutOne.*-assoc
d_'42''45'assoc_900 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiringWithoutOne_1438 ->
  Bool ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'42''45'assoc_900 :: T_IsCommutativeSemiringWithoutOne_1438
-> Bool -> Bool -> Bool -> T__'8801'__12
d_'42''45'assoc_900 = T_IsCommutativeSemiringWithoutOne_1438
-> Bool -> Bool -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsCommutativeSemiringWithoutOne.*-comm
d_'42''45'comm_902 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiringWithoutOne_1438 ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'42''45'comm_902 :: T_IsCommutativeSemiringWithoutOne_1438
-> Bool -> Bool -> T__'8801'__12
d_'42''45'comm_902 = T_IsCommutativeSemiringWithoutOne_1438
-> Bool -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsCommutativeSemiringWithoutOne.*-cong
d_'42''45'cong_904 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiringWithoutOne_1438 ->
  Bool ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'42''45'cong_904 :: T_IsCommutativeSemiringWithoutOne_1438
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
d_'42''45'cong_904 = T_IsCommutativeSemiringWithoutOne_1438
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsCommutativeSemiringWithoutOne.∙-congʳ
d_'8729''45'cong'691'_906 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiringWithoutOne_1438 ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8729''45'cong'691'_906 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsCommutativeSemiringWithoutOne_1438
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong'691'_906 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsCommutativeSemiringWithoutOne_1438
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsCommutativeSemiringWithoutOne.∙-congˡ
d_'8729''45'cong'737'_908 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiringWithoutOne_1438 ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8729''45'cong'737'_908 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsCommutativeSemiringWithoutOne_1438
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong'737'_908 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsCommutativeSemiringWithoutOne_1438
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsCommutativeSemiringWithoutOne.isCommutativeMagma
d_isCommutativeMagma_910 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiringWithoutOne_1438 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMagma_214
d_isCommutativeMagma_910 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsCommutativeSemiringWithoutOne_1438
-> T_IsCommutativeMagma_214
d_isCommutativeMagma_910 ~Bool -> Bool -> Bool
v0 ~Bool -> Bool -> Bool
v1 ~Bool
v2 T_IsCommutativeSemiringWithoutOne_1438
v3
  = T_IsCommutativeSemiringWithoutOne_1438 -> T_IsCommutativeMagma_214
du_isCommutativeMagma_910 T_IsCommutativeSemiringWithoutOne_1438
v3
du_isCommutativeMagma_910 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiringWithoutOne_1438 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMagma_214
du_isCommutativeMagma_910 :: T_IsCommutativeSemiringWithoutOne_1438 -> T_IsCommutativeMagma_214
du_isCommutativeMagma_910 T_IsCommutativeSemiringWithoutOne_1438
v0
  = (T_IsCommutativeSemigroup_568 -> T_IsCommutativeMagma_214)
-> Any -> T_IsCommutativeMagma_214
forall a b. a -> b
coe
      T_IsCommutativeSemigroup_568 -> T_IsCommutativeMagma_214
MAlonzo.Code.Algebra.Structures.du_isCommutativeMagma_606
      ((T_IsCommutativeSemiringWithoutOne_1438
 -> T_IsCommutativeSemigroup_568)
-> Any -> Any
forall a b. a -> b
coe
         T_IsCommutativeSemiringWithoutOne_1438
-> T_IsCommutativeSemigroup_568
MAlonzo.Code.Algebra.Structures.du_'42''45'isCommutativeSemigroup_1520
         (T_IsCommutativeSemiringWithoutOne_1438 -> Any
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1438
v0))
-- Data.Bool.Properties._.IsCommutativeSemiringWithoutOne.*-isCommutativeSemigroup
d_'42''45'isCommutativeSemigroup_912 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiringWithoutOne_1438 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_568
d_'42''45'isCommutativeSemigroup_912 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsCommutativeSemiringWithoutOne_1438
-> T_IsCommutativeSemigroup_568
d_'42''45'isCommutativeSemigroup_912 Bool -> Bool -> Bool
v0 Bool -> Bool -> Bool
v1 Bool
v2 T_IsCommutativeSemiringWithoutOne_1438
v3
  = (T_IsCommutativeSemiringWithoutOne_1438
 -> T_IsCommutativeSemigroup_568)
-> T_IsCommutativeSemiringWithoutOne_1438
-> T_IsCommutativeSemigroup_568
forall a b. a -> b
coe
      T_IsCommutativeSemiringWithoutOne_1438
-> T_IsCommutativeSemigroup_568
MAlonzo.Code.Algebra.Structures.du_'42''45'isCommutativeSemigroup_1520
      T_IsCommutativeSemiringWithoutOne_1438
v3
-- Data.Bool.Properties._.IsCommutativeSemiringWithoutOne.*-isMagma
d_'42''45'isMagma_914 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiringWithoutOne_1438 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_178
d_'42''45'isMagma_914 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsCommutativeSemiringWithoutOne_1438
-> T_IsMagma_178
d_'42''45'isMagma_914 ~Bool -> Bool -> Bool
v0 ~Bool -> Bool -> Bool
v1 ~Bool
v2 T_IsCommutativeSemiringWithoutOne_1438
v3 = T_IsCommutativeSemiringWithoutOne_1438 -> T_IsMagma_178
du_'42''45'isMagma_914 T_IsCommutativeSemiringWithoutOne_1438
v3
du_'42''45'isMagma_914 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiringWithoutOne_1438 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_178
du_'42''45'isMagma_914 :: T_IsCommutativeSemiringWithoutOne_1438 -> T_IsMagma_178
du_'42''45'isMagma_914 T_IsCommutativeSemiringWithoutOne_1438
v0
  = (T_IsSemiringWithoutOne_1342 -> T_IsMagma_178)
-> Any -> T_IsMagma_178
forall a b. a -> b
coe
      T_IsSemiringWithoutOne_1342 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.du_'42''45'isMagma_1410
      ((T_IsCommutativeSemiringWithoutOne_1438
 -> T_IsSemiringWithoutOne_1342)
-> Any -> Any
forall a b. a -> b
coe
         T_IsCommutativeSemiringWithoutOne_1438
-> T_IsSemiringWithoutOne_1342
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutOne_1450
         (T_IsCommutativeSemiringWithoutOne_1438 -> Any
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1438
v0))
-- Data.Bool.Properties._.IsCommutativeSemiringWithoutOne.*-isSemigroup
d_'42''45'isSemigroup_916 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiringWithoutOne_1438 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_488
d_'42''45'isSemigroup_916 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsCommutativeSemiringWithoutOne_1438
-> T_IsSemigroup_488
d_'42''45'isSemigroup_916 ~Bool -> Bool -> Bool
v0 ~Bool -> Bool -> Bool
v1 ~Bool
v2 T_IsCommutativeSemiringWithoutOne_1438
v3
  = T_IsCommutativeSemiringWithoutOne_1438 -> T_IsSemigroup_488
du_'42''45'isSemigroup_916 T_IsCommutativeSemiringWithoutOne_1438
v3
du_'42''45'isSemigroup_916 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiringWithoutOne_1438 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_488
du_'42''45'isSemigroup_916 :: T_IsCommutativeSemiringWithoutOne_1438 -> T_IsSemigroup_488
du_'42''45'isSemigroup_916 T_IsCommutativeSemiringWithoutOne_1438
v0
  = (T_IsSemiringWithoutOne_1342 -> T_IsSemigroup_488)
-> Any -> T_IsSemigroup_488
forall a b. a -> b
coe
      T_IsSemiringWithoutOne_1342 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.du_'42''45'isSemigroup_1412
      ((T_IsCommutativeSemiringWithoutOne_1438
 -> T_IsSemiringWithoutOne_1342)
-> Any -> Any
forall a b. a -> b
coe
         T_IsCommutativeSemiringWithoutOne_1438
-> T_IsSemiringWithoutOne_1342
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutOne_1450
         (T_IsCommutativeSemiringWithoutOne_1438 -> Any
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1438
v0))
-- Data.Bool.Properties._.IsCommutativeSemiringWithoutOne.assoc
d_assoc_918 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiringWithoutOne_1438 ->
  Bool ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_assoc_918 :: T_IsCommutativeSemiringWithoutOne_1438
-> Bool -> Bool -> Bool -> T__'8801'__12
d_assoc_918 = T_IsCommutativeSemiringWithoutOne_1438
-> Bool -> Bool -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsCommutativeSemiringWithoutOne.comm
d_comm_920 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiringWithoutOne_1438 ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_comm_920 :: T_IsCommutativeSemiringWithoutOne_1438
-> Bool -> Bool -> T__'8801'__12
d_comm_920 = T_IsCommutativeSemiringWithoutOne_1438
-> Bool -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsCommutativeSemiringWithoutOne.∙-cong
d_'8729''45'cong_922 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiringWithoutOne_1438 ->
  Bool ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8729''45'cong_922 :: T_IsCommutativeSemiringWithoutOne_1438
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong_922 = T_IsCommutativeSemiringWithoutOne_1438
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsCommutativeSemiringWithoutOne.∙-congʳ
d_'8729''45'cong'691'_924 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiringWithoutOne_1438 ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8729''45'cong'691'_924 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsCommutativeSemiringWithoutOne_1438
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong'691'_924 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsCommutativeSemiringWithoutOne_1438
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsCommutativeSemiringWithoutOne.∙-congˡ
d_'8729''45'cong'737'_926 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiringWithoutOne_1438 ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8729''45'cong'737'_926 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsCommutativeSemiringWithoutOne_1438
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong'737'_926 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsCommutativeSemiringWithoutOne_1438
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsCommutativeSemiringWithoutOne.identity
d_identity_928 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiringWithoutOne_1438 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_identity_928 :: T_IsCommutativeSemiringWithoutOne_1438 -> T_Σ_14
d_identity_928 T_IsCommutativeSemiringWithoutOne_1438
v0
  = (T_IsMonoid_712 -> T_Σ_14) -> Any -> T_Σ_14
forall a b. a -> b
coe
      T_IsMonoid_712 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_identity_724
      ((T_IsCommutativeMonoid_764 -> T_IsMonoid_712) -> Any -> Any
forall a b. a -> b
coe
         T_IsCommutativeMonoid_764 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_774
         ((T_IsSemiringWithoutOne_1342 -> T_IsCommutativeMonoid_764)
-> Any -> Any
forall a b. a -> b
coe
            T_IsSemiringWithoutOne_1342 -> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1360
            ((T_IsCommutativeSemiringWithoutOne_1438
 -> T_IsSemiringWithoutOne_1342)
-> Any -> Any
forall a b. a -> b
coe
               T_IsCommutativeSemiringWithoutOne_1438
-> T_IsSemiringWithoutOne_1342
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutOne_1450
               (T_IsCommutativeSemiringWithoutOne_1438 -> Any
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1438
v0))))
-- Data.Bool.Properties._.IsCommutativeSemiringWithoutOne.identityʳ
d_identity'691'_930 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiringWithoutOne_1438 ->
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_identity'691'_930 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsCommutativeSemiringWithoutOne_1438
-> Bool
-> T__'8801'__12
d_identity'691'_930 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsCommutativeSemiringWithoutOne_1438
-> Bool
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsCommutativeSemiringWithoutOne.identityˡ
d_identity'737'_932 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiringWithoutOne_1438 ->
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_identity'737'_932 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsCommutativeSemiringWithoutOne_1438
-> Bool
-> T__'8801'__12
d_identity'737'_932 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsCommutativeSemiringWithoutOne_1438
-> Bool
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsCommutativeSemiringWithoutOne.isCommutativeMagma
d_isCommutativeMagma_934 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiringWithoutOne_1438 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMagma_214
d_isCommutativeMagma_934 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsCommutativeSemiringWithoutOne_1438
-> T_IsCommutativeMagma_214
d_isCommutativeMagma_934 ~Bool -> Bool -> Bool
v0 ~Bool -> Bool -> Bool
v1 ~Bool
v2 T_IsCommutativeSemiringWithoutOne_1438
v3
  = T_IsCommutativeSemiringWithoutOne_1438 -> T_IsCommutativeMagma_214
du_isCommutativeMagma_934 T_IsCommutativeSemiringWithoutOne_1438
v3
du_isCommutativeMagma_934 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiringWithoutOne_1438 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMagma_214
du_isCommutativeMagma_934 :: T_IsCommutativeSemiringWithoutOne_1438 -> T_IsCommutativeMagma_214
du_isCommutativeMagma_934 T_IsCommutativeSemiringWithoutOne_1438
v0
  = let v1 :: T_IsSemiringWithoutOne_1342
v1
          = T_IsCommutativeSemiringWithoutOne_1438
-> T_IsSemiringWithoutOne_1342
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutOne_1450
              (T_IsCommutativeSemiringWithoutOne_1438
-> T_IsCommutativeSemiringWithoutOne_1438
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1438
v0) in
    Any -> T_IsCommutativeMagma_214
forall a b. a -> b
coe
      (let v2 :: T_IsCommutativeMonoid_764
v2
             = T_IsSemiringWithoutOne_1342 -> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1360
                 (T_IsSemiringWithoutOne_1342 -> T_IsSemiringWithoutOne_1342
forall a b. a -> b
coe T_IsSemiringWithoutOne_1342
v1) in
       Any -> Any
forall a b. a -> b
coe
         ((T_IsCommutativeSemigroup_568 -> T_IsCommutativeMagma_214)
-> Any -> Any
forall a b. a -> b
coe
            T_IsCommutativeSemigroup_568 -> T_IsCommutativeMagma_214
MAlonzo.Code.Algebra.Structures.du_isCommutativeMagma_606
            ((T_IsCommutativeMonoid_764 -> T_IsCommutativeSemigroup_568)
-> Any -> Any
forall a b. a -> b
coe
               T_IsCommutativeMonoid_764 -> T_IsCommutativeSemigroup_568
MAlonzo.Code.Algebra.Structures.du_isCommutativeSemigroup_814
               (T_IsCommutativeMonoid_764 -> Any
forall a b. a -> b
coe T_IsCommutativeMonoid_764
v2))))
-- Data.Bool.Properties._.IsCommutativeSemiringWithoutOne.+-isCommutativeMonoid
d_'43''45'isCommutativeMonoid_936 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiringWithoutOne_1438 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMonoid_764
d_'43''45'isCommutativeMonoid_936 :: T_IsCommutativeSemiringWithoutOne_1438 -> T_IsCommutativeMonoid_764
d_'43''45'isCommutativeMonoid_936 T_IsCommutativeSemiringWithoutOne_1438
v0
  = (T_IsSemiringWithoutOne_1342 -> T_IsCommutativeMonoid_764)
-> Any -> T_IsCommutativeMonoid_764
forall a b. a -> b
coe
      T_IsSemiringWithoutOne_1342 -> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1360
      ((T_IsCommutativeSemiringWithoutOne_1438
 -> T_IsSemiringWithoutOne_1342)
-> Any -> Any
forall a b. a -> b
coe
         T_IsCommutativeSemiringWithoutOne_1438
-> T_IsSemiringWithoutOne_1342
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutOne_1450
         (T_IsCommutativeSemiringWithoutOne_1438 -> Any
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1438
v0))
-- Data.Bool.Properties._.IsCommutativeSemiringWithoutOne.isCommutativeSemigroup
d_isCommutativeSemigroup_938 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiringWithoutOne_1438 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_568
d_isCommutativeSemigroup_938 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsCommutativeSemiringWithoutOne_1438
-> T_IsCommutativeSemigroup_568
d_isCommutativeSemigroup_938 ~Bool -> Bool -> Bool
v0 ~Bool -> Bool -> Bool
v1 ~Bool
v2 T_IsCommutativeSemiringWithoutOne_1438
v3
  = T_IsCommutativeSemiringWithoutOne_1438
-> T_IsCommutativeSemigroup_568
du_isCommutativeSemigroup_938 T_IsCommutativeSemiringWithoutOne_1438
v3
du_isCommutativeSemigroup_938 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiringWithoutOne_1438 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_568
du_isCommutativeSemigroup_938 :: T_IsCommutativeSemiringWithoutOne_1438
-> T_IsCommutativeSemigroup_568
du_isCommutativeSemigroup_938 T_IsCommutativeSemiringWithoutOne_1438
v0
  = let v1 :: T_IsSemiringWithoutOne_1342
v1
          = T_IsCommutativeSemiringWithoutOne_1438
-> T_IsSemiringWithoutOne_1342
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutOne_1450
              (T_IsCommutativeSemiringWithoutOne_1438
-> T_IsCommutativeSemiringWithoutOne_1438
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1438
v0) in
    Any -> T_IsCommutativeSemigroup_568
forall a b. a -> b
coe
      ((T_IsCommutativeMonoid_764 -> T_IsCommutativeSemigroup_568)
-> Any -> Any
forall a b. a -> b
coe
         T_IsCommutativeMonoid_764 -> T_IsCommutativeSemigroup_568
MAlonzo.Code.Algebra.Structures.du_isCommutativeSemigroup_814
         ((T_IsSemiringWithoutOne_1342 -> T_IsCommutativeMonoid_764)
-> Any -> Any
forall a b. a -> b
coe
            T_IsSemiringWithoutOne_1342 -> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1360
            (T_IsSemiringWithoutOne_1342 -> Any
forall a b. a -> b
coe T_IsSemiringWithoutOne_1342
v1)))
-- Data.Bool.Properties._.IsCommutativeSemiringWithoutOne.isMonoid
d_isMonoid_940 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiringWithoutOne_1438 ->
  MAlonzo.Code.Algebra.Structures.T_IsMonoid_712
d_isMonoid_940 :: T_IsCommutativeSemiringWithoutOne_1438 -> T_IsMonoid_712
d_isMonoid_940 T_IsCommutativeSemiringWithoutOne_1438
v0
  = (T_IsCommutativeMonoid_764 -> T_IsMonoid_712)
-> Any -> T_IsMonoid_712
forall a b. a -> b
coe
      T_IsCommutativeMonoid_764 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_774
      ((T_IsSemiringWithoutOne_1342 -> T_IsCommutativeMonoid_764)
-> Any -> Any
forall a b. a -> b
coe
         T_IsSemiringWithoutOne_1342 -> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1360
         ((T_IsCommutativeSemiringWithoutOne_1438
 -> T_IsSemiringWithoutOne_1342)
-> Any -> Any
forall a b. a -> b
coe
            T_IsCommutativeSemiringWithoutOne_1438
-> T_IsSemiringWithoutOne_1342
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutOne_1450
            (T_IsCommutativeSemiringWithoutOne_1438 -> Any
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1438
v0)))
-- Data.Bool.Properties._.IsCommutativeSemiringWithoutOne.distrib
d_distrib_942 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiringWithoutOne_1438 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_distrib_942 :: T_IsCommutativeSemiringWithoutOne_1438 -> T_Σ_14
d_distrib_942 T_IsCommutativeSemiringWithoutOne_1438
v0
  = (T_IsSemiringWithoutOne_1342 -> T_Σ_14) -> Any -> T_Σ_14
forall a b. a -> b
coe
      T_IsSemiringWithoutOne_1342 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_distrib_1366
      ((T_IsCommutativeSemiringWithoutOne_1438
 -> T_IsSemiringWithoutOne_1342)
-> Any -> Any
forall a b. a -> b
coe
         T_IsCommutativeSemiringWithoutOne_1438
-> T_IsSemiringWithoutOne_1342
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutOne_1450
         (T_IsCommutativeSemiringWithoutOne_1438 -> Any
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1438
v0))
-- Data.Bool.Properties._.IsCommutativeSemiringWithoutOne.distribʳ
d_distrib'691'_944 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiringWithoutOne_1438 ->
  Bool ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_distrib'691'_944 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsCommutativeSemiringWithoutOne_1438
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
d_distrib'691'_944 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsCommutativeSemiringWithoutOne_1438
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsCommutativeSemiringWithoutOne.distribˡ
d_distrib'737'_946 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiringWithoutOne_1438 ->
  Bool ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_distrib'737'_946 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsCommutativeSemiringWithoutOne_1438
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
d_distrib'737'_946 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsCommutativeSemiringWithoutOne_1438
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsCommutativeSemiringWithoutOne.isEquivalence
d_isEquivalence_948 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiringWithoutOne_1438 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
d_isEquivalence_948 :: T_IsCommutativeSemiringWithoutOne_1438 -> T_IsEquivalence_28
d_isEquivalence_948 T_IsCommutativeSemiringWithoutOne_1438
v0
  = (T_IsMagma_178 -> T_IsEquivalence_28) -> Any -> T_IsEquivalence_28
forall a b. a -> b
coe
      T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186
      ((T_IsSemigroup_488 -> T_IsMagma_178) -> Any -> Any
forall a b. a -> b
coe
         T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496
         ((T_IsMonoid_712 -> T_IsSemigroup_488) -> Any -> Any
forall a b. a -> b
coe
            T_IsMonoid_712 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_722
            ((T_IsCommutativeMonoid_764 -> T_IsMonoid_712) -> Any -> Any
forall a b. a -> b
coe
               T_IsCommutativeMonoid_764 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_774
               ((T_IsSemiringWithoutOne_1342 -> T_IsCommutativeMonoid_764)
-> Any -> Any
forall a b. a -> b
coe
                  T_IsSemiringWithoutOne_1342 -> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1360
                  ((T_IsCommutativeSemiringWithoutOne_1438
 -> T_IsSemiringWithoutOne_1342)
-> Any -> Any
forall a b. a -> b
coe
                     T_IsCommutativeSemiringWithoutOne_1438
-> T_IsSemiringWithoutOne_1342
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutOne_1450
                     (T_IsCommutativeSemiringWithoutOne_1438 -> Any
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1438
v0))))))
-- Data.Bool.Properties._.IsCommutativeSemiringWithoutOne.isNearSemiring
d_isNearSemiring_950 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiringWithoutOne_1438 ->
  MAlonzo.Code.Algebra.Structures.T_IsNearSemiring_1260
d_isNearSemiring_950 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsCommutativeSemiringWithoutOne_1438
-> T_IsNearSemiring_1260
d_isNearSemiring_950 ~Bool -> Bool -> Bool
v0 ~Bool -> Bool -> Bool
v1 ~Bool
v2 T_IsCommutativeSemiringWithoutOne_1438
v3 = T_IsCommutativeSemiringWithoutOne_1438 -> T_IsNearSemiring_1260
du_isNearSemiring_950 T_IsCommutativeSemiringWithoutOne_1438
v3
du_isNearSemiring_950 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiringWithoutOne_1438 ->
  MAlonzo.Code.Algebra.Structures.T_IsNearSemiring_1260
du_isNearSemiring_950 :: T_IsCommutativeSemiringWithoutOne_1438 -> T_IsNearSemiring_1260
du_isNearSemiring_950 T_IsCommutativeSemiringWithoutOne_1438
v0
  = (T_IsSemiringWithoutOne_1342 -> T_IsNearSemiring_1260)
-> Any -> T_IsNearSemiring_1260
forall a b. a -> b
coe
      T_IsSemiringWithoutOne_1342 -> T_IsNearSemiring_1260
MAlonzo.Code.Algebra.Structures.du_isNearSemiring_1428
      ((T_IsCommutativeSemiringWithoutOne_1438
 -> T_IsSemiringWithoutOne_1342)
-> Any -> Any
forall a b. a -> b
coe
         T_IsCommutativeSemiringWithoutOne_1438
-> T_IsSemiringWithoutOne_1342
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutOne_1450
         (T_IsCommutativeSemiringWithoutOne_1438 -> Any
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1438
v0))
-- Data.Bool.Properties._.IsCommutativeSemiringWithoutOne.isPartialEquivalence
d_isPartialEquivalence_952 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiringWithoutOne_1438 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_952 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsCommutativeSemiringWithoutOne_1438
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_952 ~Bool -> Bool -> Bool
v0 ~Bool -> Bool -> Bool
v1 ~Bool
v2 T_IsCommutativeSemiringWithoutOne_1438
v3
  = T_IsCommutativeSemiringWithoutOne_1438 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_952 T_IsCommutativeSemiringWithoutOne_1438
v3
du_isPartialEquivalence_952 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiringWithoutOne_1438 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_952 :: T_IsCommutativeSemiringWithoutOne_1438 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_952 T_IsCommutativeSemiringWithoutOne_1438
v0
  = let v1 :: T_IsSemiringWithoutOne_1342
v1
          = T_IsCommutativeSemiringWithoutOne_1438
-> T_IsSemiringWithoutOne_1342
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutOne_1450
              (T_IsCommutativeSemiringWithoutOne_1438
-> T_IsCommutativeSemiringWithoutOne_1438
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1438
v0) in
    Any -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      ((T_IsEquivalence_28 -> T_IsPartialEquivalence_16) -> Any -> Any
forall a b. a -> b
coe
         T_IsEquivalence_28 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_44
         ((T_IsMagma_178 -> T_IsEquivalence_28) -> Any -> Any
forall a b. a -> b
coe
            T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186
            ((T_IsSemigroup_488 -> T_IsMagma_178) -> Any -> Any
forall a b. a -> b
coe
               T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496
               ((T_IsMonoid_712 -> T_IsSemigroup_488) -> Any -> Any
forall a b. a -> b
coe
                  T_IsMonoid_712 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_722
                  ((T_IsCommutativeMonoid_764 -> T_IsMonoid_712) -> Any -> Any
forall a b. a -> b
coe
                     T_IsCommutativeMonoid_764 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_774
                     ((T_IsSemiringWithoutOne_1342 -> T_IsCommutativeMonoid_764)
-> Any -> Any
forall a b. a -> b
coe
                        T_IsSemiringWithoutOne_1342 -> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1360
                        (T_IsSemiringWithoutOne_1342 -> Any
forall a b. a -> b
coe T_IsSemiringWithoutOne_1342
v1)))))))
-- Data.Bool.Properties._.IsCommutativeSemiringWithoutOne.isSemiringWithoutOne
d_isSemiringWithoutOne_954 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiringWithoutOne_1438 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutOne_1342
d_isSemiringWithoutOne_954 :: T_IsCommutativeSemiringWithoutOne_1438
-> T_IsSemiringWithoutOne_1342
d_isSemiringWithoutOne_954 T_IsCommutativeSemiringWithoutOne_1438
v0
  = (T_IsCommutativeSemiringWithoutOne_1438
 -> T_IsSemiringWithoutOne_1342)
-> Any -> T_IsSemiringWithoutOne_1342
forall a b. a -> b
coe
      T_IsCommutativeSemiringWithoutOne_1438
-> T_IsSemiringWithoutOne_1342
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutOne_1450
      (T_IsCommutativeSemiringWithoutOne_1438 -> Any
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1438
v0)
-- Data.Bool.Properties._.IsCommutativeSemiringWithoutOne.refl
d_refl_956 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiringWithoutOne_1438 ->
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_refl_956 :: T_IsCommutativeSemiringWithoutOne_1438 -> Bool -> T__'8801'__12
d_refl_956 = T_IsCommutativeSemiringWithoutOne_1438 -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsCommutativeSemiringWithoutOne.reflexive
d_reflexive_958 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiringWithoutOne_1438 ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_reflexive_958 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsCommutativeSemiringWithoutOne_1438
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_reflexive_958 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsCommutativeSemiringWithoutOne_1438
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsCommutativeSemiringWithoutOne.setoid
d_setoid_960 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiringWithoutOne_1438 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
d_setoid_960 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsCommutativeSemiringWithoutOne_1438
-> T_Setoid_46
d_setoid_960 ~Bool -> Bool -> Bool
v0 ~Bool -> Bool -> Bool
v1 ~Bool
v2 T_IsCommutativeSemiringWithoutOne_1438
v3 = T_IsCommutativeSemiringWithoutOne_1438 -> T_Setoid_46
du_setoid_960 T_IsCommutativeSemiringWithoutOne_1438
v3
du_setoid_960 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiringWithoutOne_1438 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
du_setoid_960 :: T_IsCommutativeSemiringWithoutOne_1438 -> T_Setoid_46
du_setoid_960 T_IsCommutativeSemiringWithoutOne_1438
v0
  = let v1 :: T_IsSemiringWithoutOne_1342
v1
          = T_IsCommutativeSemiringWithoutOne_1438
-> T_IsSemiringWithoutOne_1342
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutOne_1450
              (T_IsCommutativeSemiringWithoutOne_1438
-> T_IsCommutativeSemiringWithoutOne_1438
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1438
v0) in
    Any -> T_Setoid_46
forall a b. a -> b
coe
      (let v2 :: T_IsCommutativeMonoid_764
v2
             = T_IsSemiringWithoutOne_1342 -> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1360
                 (T_IsSemiringWithoutOne_1342 -> T_IsSemiringWithoutOne_1342
forall a b. a -> b
coe T_IsSemiringWithoutOne_1342
v1) in
       Any -> Any
forall a b. a -> b
coe
         (let v3 :: T_IsMonoid_712
v3
                = T_IsCommutativeMonoid_764 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_774 (T_IsCommutativeMonoid_764 -> T_IsCommutativeMonoid_764
forall a b. a -> b
coe T_IsCommutativeMonoid_764
v2) in
          Any -> Any
forall a b. a -> b
coe
            (let v4 :: T_IsSemigroup_488
v4
                   = T_IsMonoid_712 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_722 (T_IsMonoid_712 -> T_IsMonoid_712
forall a b. a -> b
coe T_IsMonoid_712
v3) in
             Any -> Any
forall a b. a -> b
coe
               ((T_IsMagma_178 -> T_Setoid_46) -> Any -> Any
forall a b. a -> b
coe
                  T_IsMagma_178 -> T_Setoid_46
MAlonzo.Code.Algebra.Structures.du_setoid_202
                  ((T_IsSemigroup_488 -> T_IsMagma_178) -> Any -> Any
forall a b. a -> b
coe T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496 (T_IsSemigroup_488 -> Any
forall a b. a -> b
coe T_IsSemigroup_488
v4))))))
-- Data.Bool.Properties._.IsCommutativeSemiringWithoutOne.sym
d_sym_962 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiringWithoutOne_1438 ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_sym_962 :: T_IsCommutativeSemiringWithoutOne_1438
-> Bool -> Bool -> T__'8801'__12 -> T__'8801'__12
d_sym_962 = T_IsCommutativeSemiringWithoutOne_1438
-> Bool -> Bool -> T__'8801'__12 -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsCommutativeSemiringWithoutOne.trans
d_trans_964 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiringWithoutOne_1438 ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_trans_964 :: T_IsCommutativeSemiringWithoutOne_1438
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
d_trans_964 = T_IsCommutativeSemiringWithoutOne_1438
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsCommutativeSemiringWithoutOne.zero
d_zero_966 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiringWithoutOne_1438 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_zero_966 :: T_IsCommutativeSemiringWithoutOne_1438 -> T_Σ_14
d_zero_966 T_IsCommutativeSemiringWithoutOne_1438
v0
  = (T_IsSemiringWithoutOne_1342 -> T_Σ_14) -> Any -> T_Σ_14
forall a b. a -> b
coe
      T_IsSemiringWithoutOne_1342 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_zero_1368
      ((T_IsCommutativeSemiringWithoutOne_1438
 -> T_IsSemiringWithoutOne_1342)
-> Any -> Any
forall a b. a -> b
coe
         T_IsCommutativeSemiringWithoutOne_1438
-> T_IsSemiringWithoutOne_1342
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutOne_1450
         (T_IsCommutativeSemiringWithoutOne_1438 -> Any
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1438
v0))
-- Data.Bool.Properties._.IsCommutativeSemiringWithoutOne.zeroʳ
d_zero'691'_968 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiringWithoutOne_1438 ->
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_zero'691'_968 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsCommutativeSemiringWithoutOne_1438
-> Bool
-> T__'8801'__12
d_zero'691'_968 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsCommutativeSemiringWithoutOne_1438
-> Bool
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsCommutativeSemiringWithoutOne.zeroˡ
d_zero'737'_970 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiringWithoutOne_1438 ->
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_zero'737'_970 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsCommutativeSemiringWithoutOne_1438
-> Bool
-> T__'8801'__12
d_zero'737'_970 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsCommutativeSemiringWithoutOne_1438
-> Bool
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsFlexibleMagma.flex
d_flex_974 ::
  MAlonzo.Code.Algebra.Structures.T_IsFlexibleMagma_332 ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_flex_974 :: T_IsFlexibleMagma_332 -> Bool -> Bool -> T__'8801'__12
d_flex_974 = T_IsFlexibleMagma_332 -> Bool -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsFlexibleMagma.isEquivalence
d_isEquivalence_976 ::
  MAlonzo.Code.Algebra.Structures.T_IsFlexibleMagma_332 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
d_isEquivalence_976 :: T_IsFlexibleMagma_332 -> T_IsEquivalence_28
d_isEquivalence_976 T_IsFlexibleMagma_332
v0
  = (T_IsMagma_178 -> T_IsEquivalence_28) -> Any -> T_IsEquivalence_28
forall a b. a -> b
coe
      T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186
      ((T_IsFlexibleMagma_332 -> T_IsMagma_178) -> Any -> Any
forall a b. a -> b
coe T_IsFlexibleMagma_332 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_340 (T_IsFlexibleMagma_332 -> Any
forall a b. a -> b
coe T_IsFlexibleMagma_332
v0))
-- Data.Bool.Properties._.IsFlexibleMagma.isMagma
d_isMagma_978 ::
  MAlonzo.Code.Algebra.Structures.T_IsFlexibleMagma_332 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_178
d_isMagma_978 :: T_IsFlexibleMagma_332 -> T_IsMagma_178
d_isMagma_978 T_IsFlexibleMagma_332
v0
  = (T_IsFlexibleMagma_332 -> T_IsMagma_178) -> Any -> T_IsMagma_178
forall a b. a -> b
coe T_IsFlexibleMagma_332 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_340 (T_IsFlexibleMagma_332 -> Any
forall a b. a -> b
coe T_IsFlexibleMagma_332
v0)
-- Data.Bool.Properties._.IsFlexibleMagma.isPartialEquivalence
d_isPartialEquivalence_980 ::
  (Bool -> Bool -> Bool) ->
  MAlonzo.Code.Algebra.Structures.T_IsFlexibleMagma_332 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_980 :: (Bool -> Bool -> Bool)
-> T_IsFlexibleMagma_332 -> T_IsPartialEquivalence_16
d_isPartialEquivalence_980 ~Bool -> Bool -> Bool
v0 T_IsFlexibleMagma_332
v1 = T_IsFlexibleMagma_332 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_980 T_IsFlexibleMagma_332
v1
du_isPartialEquivalence_980 ::
  MAlonzo.Code.Algebra.Structures.T_IsFlexibleMagma_332 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_980 :: T_IsFlexibleMagma_332 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_980 T_IsFlexibleMagma_332
v0
  = let v1 :: T_IsMagma_178
v1
          = T_IsFlexibleMagma_332 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_340 (T_IsFlexibleMagma_332 -> T_IsFlexibleMagma_332
forall a b. a -> b
coe T_IsFlexibleMagma_332
v0) in
    Any -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      ((T_IsEquivalence_28 -> T_IsPartialEquivalence_16) -> Any -> Any
forall a b. a -> b
coe
         T_IsEquivalence_28 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_44
         ((T_IsMagma_178 -> T_IsEquivalence_28) -> Any -> Any
forall a b. a -> b
coe T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186 (T_IsMagma_178 -> Any
forall a b. a -> b
coe T_IsMagma_178
v1)))
-- Data.Bool.Properties._.IsFlexibleMagma.refl
d_refl_982 ::
  MAlonzo.Code.Algebra.Structures.T_IsFlexibleMagma_332 ->
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_refl_982 :: T_IsFlexibleMagma_332 -> Bool -> T__'8801'__12
d_refl_982 = T_IsFlexibleMagma_332 -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsFlexibleMagma.reflexive
d_reflexive_984 ::
  (Bool -> Bool -> Bool) ->
  MAlonzo.Code.Algebra.Structures.T_IsFlexibleMagma_332 ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_reflexive_984 :: (Bool -> Bool -> Bool)
-> T_IsFlexibleMagma_332
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_reflexive_984 = (Bool -> Bool -> Bool)
-> T_IsFlexibleMagma_332
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsFlexibleMagma.setoid
d_setoid_986 ::
  (Bool -> Bool -> Bool) ->
  MAlonzo.Code.Algebra.Structures.T_IsFlexibleMagma_332 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
d_setoid_986 :: (Bool -> Bool -> Bool) -> T_IsFlexibleMagma_332 -> T_Setoid_46
d_setoid_986 ~Bool -> Bool -> Bool
v0 T_IsFlexibleMagma_332
v1 = T_IsFlexibleMagma_332 -> T_Setoid_46
du_setoid_986 T_IsFlexibleMagma_332
v1
du_setoid_986 ::
  MAlonzo.Code.Algebra.Structures.T_IsFlexibleMagma_332 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
du_setoid_986 :: T_IsFlexibleMagma_332 -> T_Setoid_46
du_setoid_986 T_IsFlexibleMagma_332
v0
  = (T_IsMagma_178 -> T_Setoid_46) -> Any -> T_Setoid_46
forall a b. a -> b
coe
      T_IsMagma_178 -> T_Setoid_46
MAlonzo.Code.Algebra.Structures.du_setoid_202
      ((T_IsFlexibleMagma_332 -> T_IsMagma_178) -> Any -> Any
forall a b. a -> b
coe T_IsFlexibleMagma_332 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_340 (T_IsFlexibleMagma_332 -> Any
forall a b. a -> b
coe T_IsFlexibleMagma_332
v0))
-- Data.Bool.Properties._.IsFlexibleMagma.sym
d_sym_988 ::
  MAlonzo.Code.Algebra.Structures.T_IsFlexibleMagma_332 ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_sym_988 :: T_IsFlexibleMagma_332
-> Bool -> Bool -> T__'8801'__12 -> T__'8801'__12
d_sym_988 = T_IsFlexibleMagma_332
-> Bool -> Bool -> T__'8801'__12 -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsFlexibleMagma.trans
d_trans_990 ::
  MAlonzo.Code.Algebra.Structures.T_IsFlexibleMagma_332 ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_trans_990 :: T_IsFlexibleMagma_332
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
d_trans_990 = T_IsFlexibleMagma_332
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsFlexibleMagma.∙-cong
d_'8729''45'cong_992 ::
  MAlonzo.Code.Algebra.Structures.T_IsFlexibleMagma_332 ->
  Bool ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8729''45'cong_992 :: T_IsFlexibleMagma_332
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong_992 = T_IsFlexibleMagma_332
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsFlexibleMagma.∙-congʳ
d_'8729''45'cong'691'_994 ::
  (Bool -> Bool -> Bool) ->
  MAlonzo.Code.Algebra.Structures.T_IsFlexibleMagma_332 ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8729''45'cong'691'_994 :: (Bool -> Bool -> Bool)
-> T_IsFlexibleMagma_332
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong'691'_994 = (Bool -> Bool -> Bool)
-> T_IsFlexibleMagma_332
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsFlexibleMagma.∙-congˡ
d_'8729''45'cong'737'_996 ::
  (Bool -> Bool -> Bool) ->
  MAlonzo.Code.Algebra.Structures.T_IsFlexibleMagma_332 ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8729''45'cong'737'_996 :: (Bool -> Bool -> Bool)
-> T_IsFlexibleMagma_332
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong'737'_996 = (Bool -> Bool -> Bool)
-> T_IsFlexibleMagma_332
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsGroup._-_
d__'45'__1000 ::
  (Bool -> Bool -> Bool) ->
  Bool ->
  (Bool -> Bool) ->
  MAlonzo.Code.Algebra.Structures.T_IsGroup_1074 ->
  Bool -> Bool -> Bool
d__'45'__1000 :: (Bool -> Bool -> Bool)
-> Bool -> (Bool -> Bool) -> T_IsGroup_1074 -> Bool -> Bool -> Bool
d__'45'__1000 Bool -> Bool -> Bool
v0 Bool
v1 Bool -> Bool
v2 T_IsGroup_1074
v3
  = ((Any -> Any -> Any) -> (Any -> Any) -> Any -> Any -> Any)
-> (Bool -> Bool -> Bool) -> (Bool -> Bool) -> Bool -> Bool -> Bool
forall a b. a -> b
coe (Any -> Any -> Any) -> (Any -> Any) -> Any -> Any -> Any
MAlonzo.Code.Algebra.Structures.du__'45'__1142 Bool -> Bool -> Bool
v0 Bool -> Bool
v2
-- Data.Bool.Properties._.IsGroup._//_
d__'47''47'__1002 ::
  (Bool -> Bool -> Bool) ->
  Bool ->
  (Bool -> Bool) ->
  MAlonzo.Code.Algebra.Structures.T_IsGroup_1074 ->
  Bool -> Bool -> Bool
d__'47''47'__1002 :: (Bool -> Bool -> Bool)
-> Bool -> (Bool -> Bool) -> T_IsGroup_1074 -> Bool -> Bool -> Bool
d__'47''47'__1002 Bool -> Bool -> Bool
v0 Bool
v1 Bool -> Bool
v2 T_IsGroup_1074
v3 Bool
v4 Bool
v5
  = ((Any -> Any -> Any) -> (Any -> Any) -> Any -> Any -> Any)
-> (Bool -> Bool -> Bool) -> (Bool -> Bool) -> Bool -> Bool -> Bool
forall a b. a -> b
coe
      (Any -> Any -> Any) -> (Any -> Any) -> Any -> Any -> Any
MAlonzo.Code.Algebra.Structures.du__'47''47'__1136 Bool -> Bool -> Bool
v0 Bool -> Bool
v2 Bool
v4 Bool
v5
-- Data.Bool.Properties._.IsGroup._\\_
d__'92''92'__1004 ::
  (Bool -> Bool -> Bool) ->
  Bool ->
  (Bool -> Bool) ->
  MAlonzo.Code.Algebra.Structures.T_IsGroup_1074 ->
  Bool -> Bool -> Bool
d__'92''92'__1004 :: (Bool -> Bool -> Bool)
-> Bool -> (Bool -> Bool) -> T_IsGroup_1074 -> Bool -> Bool -> Bool
d__'92''92'__1004 Bool -> Bool -> Bool
v0 Bool
v1 Bool -> Bool
v2 T_IsGroup_1074
v3 Bool
v4 Bool
v5
  = ((Any -> Any -> Any) -> (Any -> Any) -> Any -> Any -> Any)
-> (Bool -> Bool -> Bool) -> (Bool -> Bool) -> Bool -> Bool -> Bool
forall a b. a -> b
coe
      (Any -> Any -> Any) -> (Any -> Any) -> Any -> Any -> Any
MAlonzo.Code.Algebra.Structures.du__'92''92'__1130 Bool -> Bool -> Bool
v0 Bool -> Bool
v2 Bool
v4 Bool
v5
-- Data.Bool.Properties._.IsGroup.assoc
d_assoc_1006 ::
  MAlonzo.Code.Algebra.Structures.T_IsGroup_1074 ->
  Bool ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_assoc_1006 :: T_IsGroup_1074 -> Bool -> Bool -> Bool -> T__'8801'__12
d_assoc_1006 = T_IsGroup_1074 -> Bool -> Bool -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsGroup.identity
d_identity_1008 ::
  MAlonzo.Code.Algebra.Structures.T_IsGroup_1074 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_identity_1008 :: T_IsGroup_1074 -> T_Σ_14
d_identity_1008 T_IsGroup_1074
v0
  = (T_IsMonoid_712 -> T_Σ_14) -> Any -> T_Σ_14
forall a b. a -> b
coe
      T_IsMonoid_712 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_identity_724
      ((T_IsGroup_1074 -> T_IsMonoid_712) -> Any -> Any
forall a b. a -> b
coe T_IsGroup_1074 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_1088 (T_IsGroup_1074 -> Any
forall a b. a -> b
coe T_IsGroup_1074
v0))
-- Data.Bool.Properties._.IsGroup.identityʳ
d_identity'691'_1010 ::
  (Bool -> Bool -> Bool) ->
  Bool ->
  (Bool -> Bool) ->
  MAlonzo.Code.Algebra.Structures.T_IsGroup_1074 ->
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_identity'691'_1010 :: (Bool -> Bool -> Bool)
-> Bool
-> (Bool -> Bool)
-> T_IsGroup_1074
-> Bool
-> T__'8801'__12
d_identity'691'_1010 = (Bool -> Bool -> Bool)
-> Bool
-> (Bool -> Bool)
-> T_IsGroup_1074
-> Bool
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsGroup.identityˡ
d_identity'737'_1012 ::
  (Bool -> Bool -> Bool) ->
  Bool ->
  (Bool -> Bool) ->
  MAlonzo.Code.Algebra.Structures.T_IsGroup_1074 ->
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_identity'737'_1012 :: (Bool -> Bool -> Bool)
-> Bool
-> (Bool -> Bool)
-> T_IsGroup_1074
-> Bool
-> T__'8801'__12
d_identity'737'_1012 = (Bool -> Bool -> Bool)
-> Bool
-> (Bool -> Bool)
-> T_IsGroup_1074
-> Bool
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsGroup.inverse
d_inverse_1014 ::
  MAlonzo.Code.Algebra.Structures.T_IsGroup_1074 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_inverse_1014 :: T_IsGroup_1074 -> T_Σ_14
d_inverse_1014 T_IsGroup_1074
v0
  = (T_IsGroup_1074 -> T_Σ_14) -> Any -> T_Σ_14
forall a b. a -> b
coe T_IsGroup_1074 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_inverse_1090 (T_IsGroup_1074 -> Any
forall a b. a -> b
coe T_IsGroup_1074
v0)
-- Data.Bool.Properties._.IsGroup.inverseʳ
d_inverse'691'_1016 ::
  (Bool -> Bool -> Bool) ->
  Bool ->
  (Bool -> Bool) ->
  MAlonzo.Code.Algebra.Structures.T_IsGroup_1074 ->
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_inverse'691'_1016 :: (Bool -> Bool -> Bool)
-> Bool
-> (Bool -> Bool)
-> T_IsGroup_1074
-> Bool
-> T__'8801'__12
d_inverse'691'_1016 = (Bool -> Bool -> Bool)
-> Bool
-> (Bool -> Bool)
-> T_IsGroup_1074
-> Bool
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsGroup.inverseˡ
d_inverse'737'_1018 ::
  (Bool -> Bool -> Bool) ->
  Bool ->
  (Bool -> Bool) ->
  MAlonzo.Code.Algebra.Structures.T_IsGroup_1074 ->
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_inverse'737'_1018 :: (Bool -> Bool -> Bool)
-> Bool
-> (Bool -> Bool)
-> T_IsGroup_1074
-> Bool
-> T__'8801'__12
d_inverse'737'_1018 = (Bool -> Bool -> Bool)
-> Bool
-> (Bool -> Bool)
-> T_IsGroup_1074
-> Bool
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsGroup.isEquivalence
d_isEquivalence_1020 ::
  MAlonzo.Code.Algebra.Structures.T_IsGroup_1074 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
d_isEquivalence_1020 :: T_IsGroup_1074 -> T_IsEquivalence_28
d_isEquivalence_1020 T_IsGroup_1074
v0
  = (T_IsMagma_178 -> T_IsEquivalence_28) -> Any -> T_IsEquivalence_28
forall a b. a -> b
coe
      T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186
      ((T_IsSemigroup_488 -> T_IsMagma_178) -> Any -> Any
forall a b. a -> b
coe
         T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496
         ((T_IsMonoid_712 -> T_IsSemigroup_488) -> Any -> Any
forall a b. a -> b
coe
            T_IsMonoid_712 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_722
            ((T_IsGroup_1074 -> T_IsMonoid_712) -> Any -> Any
forall a b. a -> b
coe T_IsGroup_1074 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_1088 (T_IsGroup_1074 -> Any
forall a b. a -> b
coe T_IsGroup_1074
v0))))
-- Data.Bool.Properties._.IsGroup.isInvertibleMagma
d_isInvertibleMagma_1022 ::
  (Bool -> Bool -> Bool) ->
  Bool ->
  (Bool -> Bool) ->
  MAlonzo.Code.Algebra.Structures.T_IsGroup_1074 ->
  MAlonzo.Code.Algebra.Structures.T_IsInvertibleMagma_958
d_isInvertibleMagma_1022 :: (Bool -> Bool -> Bool)
-> Bool
-> (Bool -> Bool)
-> T_IsGroup_1074
-> T_IsInvertibleMagma_958
d_isInvertibleMagma_1022 Bool -> Bool -> Bool
v0 Bool
v1 Bool -> Bool
v2 T_IsGroup_1074
v3
  = (T_IsGroup_1074 -> T_IsInvertibleMagma_958)
-> T_IsGroup_1074 -> T_IsInvertibleMagma_958
forall a b. a -> b
coe T_IsGroup_1074 -> T_IsInvertibleMagma_958
MAlonzo.Code.Algebra.Structures.du_isInvertibleMagma_1160 T_IsGroup_1074
v3
-- Data.Bool.Properties._.IsGroup.isInvertibleUnitalMagma
d_isInvertibleUnitalMagma_1024 ::
  (Bool -> Bool -> Bool) ->
  Bool ->
  (Bool -> Bool) ->
  MAlonzo.Code.Algebra.Structures.T_IsGroup_1074 ->
  MAlonzo.Code.Algebra.Structures.T_IsInvertibleUnitalMagma_1012
d_isInvertibleUnitalMagma_1024 :: (Bool -> Bool -> Bool)
-> Bool
-> (Bool -> Bool)
-> T_IsGroup_1074
-> T_IsInvertibleUnitalMagma_1012
d_isInvertibleUnitalMagma_1024 Bool -> Bool -> Bool
v0 Bool
v1 Bool -> Bool
v2 T_IsGroup_1074
v3
  = (T_IsGroup_1074 -> T_IsInvertibleUnitalMagma_1012)
-> T_IsGroup_1074 -> T_IsInvertibleUnitalMagma_1012
forall a b. a -> b
coe
      T_IsGroup_1074 -> T_IsInvertibleUnitalMagma_1012
MAlonzo.Code.Algebra.Structures.du_isInvertibleUnitalMagma_1162 T_IsGroup_1074
v3
-- Data.Bool.Properties._.IsGroup.isMagma
d_isMagma_1026 ::
  MAlonzo.Code.Algebra.Structures.T_IsGroup_1074 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_178
d_isMagma_1026 :: T_IsGroup_1074 -> T_IsMagma_178
d_isMagma_1026 T_IsGroup_1074
v0
  = (T_IsSemigroup_488 -> T_IsMagma_178) -> Any -> T_IsMagma_178
forall a b. a -> b
coe
      T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496
      ((T_IsMonoid_712 -> T_IsSemigroup_488) -> Any -> Any
forall a b. a -> b
coe
         T_IsMonoid_712 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_722
         ((T_IsGroup_1074 -> T_IsMonoid_712) -> Any -> Any
forall a b. a -> b
coe T_IsGroup_1074 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_1088 (T_IsGroup_1074 -> Any
forall a b. a -> b
coe T_IsGroup_1074
v0)))
-- Data.Bool.Properties._.IsGroup.isMonoid
d_isMonoid_1028 ::
  MAlonzo.Code.Algebra.Structures.T_IsGroup_1074 ->
  MAlonzo.Code.Algebra.Structures.T_IsMonoid_712
d_isMonoid_1028 :: T_IsGroup_1074 -> T_IsMonoid_712
d_isMonoid_1028 T_IsGroup_1074
v0
  = (T_IsGroup_1074 -> T_IsMonoid_712) -> Any -> T_IsMonoid_712
forall a b. a -> b
coe T_IsGroup_1074 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_1088 (T_IsGroup_1074 -> Any
forall a b. a -> b
coe T_IsGroup_1074
v0)
-- Data.Bool.Properties._.IsGroup.isPartialEquivalence
d_isPartialEquivalence_1030 ::
  (Bool -> Bool -> Bool) ->
  Bool ->
  (Bool -> Bool) ->
  MAlonzo.Code.Algebra.Structures.T_IsGroup_1074 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_1030 :: (Bool -> Bool -> Bool)
-> Bool
-> (Bool -> Bool)
-> T_IsGroup_1074
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_1030 ~Bool -> Bool -> Bool
v0 ~Bool
v1 ~Bool -> Bool
v2 T_IsGroup_1074
v3
  = T_IsGroup_1074 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_1030 T_IsGroup_1074
v3
du_isPartialEquivalence_1030 ::
  MAlonzo.Code.Algebra.Structures.T_IsGroup_1074 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_1030 :: T_IsGroup_1074 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_1030 T_IsGroup_1074
v0
  = let v1 :: T_IsMonoid_712
v1
          = T_IsGroup_1074 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_1088 (T_IsGroup_1074 -> T_IsGroup_1074
forall a b. a -> b
coe T_IsGroup_1074
v0) in
    Any -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsSemigroup_488
v2
             = T_IsMonoid_712 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_722 (T_IsMonoid_712 -> T_IsMonoid_712
forall a b. a -> b
coe T_IsMonoid_712
v1) in
       Any -> Any
forall a b. a -> b
coe
         (let v3 :: T_IsMagma_178
v3 = T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496 (T_IsSemigroup_488 -> T_IsSemigroup_488
forall a b. a -> b
coe T_IsSemigroup_488
v2) in
          Any -> Any
forall a b. a -> b
coe
            ((T_IsEquivalence_28 -> T_IsPartialEquivalence_16) -> Any -> Any
forall a b. a -> b
coe
               T_IsEquivalence_28 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_44
               ((T_IsMagma_178 -> T_IsEquivalence_28) -> Any -> Any
forall a b. a -> b
coe
                  T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186 (T_IsMagma_178 -> Any
forall a b. a -> b
coe T_IsMagma_178
v3)))))
-- Data.Bool.Properties._.IsGroup.isSemigroup
d_isSemigroup_1032 ::
  MAlonzo.Code.Algebra.Structures.T_IsGroup_1074 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_488
d_isSemigroup_1032 :: T_IsGroup_1074 -> T_IsSemigroup_488
d_isSemigroup_1032 T_IsGroup_1074
v0
  = (T_IsMonoid_712 -> T_IsSemigroup_488) -> Any -> T_IsSemigroup_488
forall a b. a -> b
coe
      T_IsMonoid_712 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_722
      ((T_IsGroup_1074 -> T_IsMonoid_712) -> Any -> Any
forall a b. a -> b
coe T_IsGroup_1074 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_1088 (T_IsGroup_1074 -> Any
forall a b. a -> b
coe T_IsGroup_1074
v0))
-- Data.Bool.Properties._.IsGroup.isUnitalMagma
d_isUnitalMagma_1034 ::
  (Bool -> Bool -> Bool) ->
  Bool ->
  (Bool -> Bool) ->
  MAlonzo.Code.Algebra.Structures.T_IsGroup_1074 ->
  MAlonzo.Code.Algebra.Structures.T_IsUnitalMagma_666
d_isUnitalMagma_1034 :: (Bool -> Bool -> Bool)
-> Bool -> (Bool -> Bool) -> T_IsGroup_1074 -> T_IsUnitalMagma_666
d_isUnitalMagma_1034 ~Bool -> Bool -> Bool
v0 ~Bool
v1 ~Bool -> Bool
v2 T_IsGroup_1074
v3 = T_IsGroup_1074 -> T_IsUnitalMagma_666
du_isUnitalMagma_1034 T_IsGroup_1074
v3
du_isUnitalMagma_1034 ::
  MAlonzo.Code.Algebra.Structures.T_IsGroup_1074 ->
  MAlonzo.Code.Algebra.Structures.T_IsUnitalMagma_666
du_isUnitalMagma_1034 :: T_IsGroup_1074 -> T_IsUnitalMagma_666
du_isUnitalMagma_1034 T_IsGroup_1074
v0
  = (T_IsMonoid_712 -> T_IsUnitalMagma_666)
-> Any -> T_IsUnitalMagma_666
forall a b. a -> b
coe
      T_IsMonoid_712 -> T_IsUnitalMagma_666
MAlonzo.Code.Algebra.Structures.du_isUnitalMagma_756
      ((T_IsGroup_1074 -> T_IsMonoid_712) -> Any -> Any
forall a b. a -> b
coe T_IsGroup_1074 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_1088 (T_IsGroup_1074 -> Any
forall a b. a -> b
coe T_IsGroup_1074
v0))
-- Data.Bool.Properties._.IsGroup.refl
d_refl_1036 ::
  MAlonzo.Code.Algebra.Structures.T_IsGroup_1074 ->
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_refl_1036 :: T_IsGroup_1074 -> Bool -> T__'8801'__12
d_refl_1036 = T_IsGroup_1074 -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsGroup.reflexive
d_reflexive_1038 ::
  (Bool -> Bool -> Bool) ->
  Bool ->
  (Bool -> Bool) ->
  MAlonzo.Code.Algebra.Structures.T_IsGroup_1074 ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_reflexive_1038 :: (Bool -> Bool -> Bool)
-> Bool
-> (Bool -> Bool)
-> T_IsGroup_1074
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_reflexive_1038 = (Bool -> Bool -> Bool)
-> Bool
-> (Bool -> Bool)
-> T_IsGroup_1074
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsGroup.setoid
d_setoid_1040 ::
  (Bool -> Bool -> Bool) ->
  Bool ->
  (Bool -> Bool) ->
  MAlonzo.Code.Algebra.Structures.T_IsGroup_1074 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
d_setoid_1040 :: (Bool -> Bool -> Bool)
-> Bool -> (Bool -> Bool) -> T_IsGroup_1074 -> T_Setoid_46
d_setoid_1040 ~Bool -> Bool -> Bool
v0 ~Bool
v1 ~Bool -> Bool
v2 T_IsGroup_1074
v3 = T_IsGroup_1074 -> T_Setoid_46
du_setoid_1040 T_IsGroup_1074
v3
du_setoid_1040 ::
  MAlonzo.Code.Algebra.Structures.T_IsGroup_1074 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
du_setoid_1040 :: T_IsGroup_1074 -> T_Setoid_46
du_setoid_1040 T_IsGroup_1074
v0
  = let v1 :: T_IsMonoid_712
v1
          = T_IsGroup_1074 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_1088 (T_IsGroup_1074 -> T_IsGroup_1074
forall a b. a -> b
coe T_IsGroup_1074
v0) in
    Any -> T_Setoid_46
forall a b. a -> b
coe
      (let v2 :: T_IsSemigroup_488
v2
             = T_IsMonoid_712 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_722 (T_IsMonoid_712 -> T_IsMonoid_712
forall a b. a -> b
coe T_IsMonoid_712
v1) in
       Any -> Any
forall a b. a -> b
coe
         ((T_IsMagma_178 -> T_Setoid_46) -> Any -> Any
forall a b. a -> b
coe
            T_IsMagma_178 -> T_Setoid_46
MAlonzo.Code.Algebra.Structures.du_setoid_202
            ((T_IsSemigroup_488 -> T_IsMagma_178) -> Any -> Any
forall a b. a -> b
coe T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496 (T_IsSemigroup_488 -> Any
forall a b. a -> b
coe T_IsSemigroup_488
v2))))
-- Data.Bool.Properties._.IsGroup.sym
d_sym_1042 ::
  MAlonzo.Code.Algebra.Structures.T_IsGroup_1074 ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_sym_1042 :: T_IsGroup_1074 -> Bool -> Bool -> T__'8801'__12 -> T__'8801'__12
d_sym_1042 = T_IsGroup_1074 -> Bool -> Bool -> T__'8801'__12 -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsGroup.trans
d_trans_1044 ::
  MAlonzo.Code.Algebra.Structures.T_IsGroup_1074 ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_trans_1044 :: T_IsGroup_1074
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
d_trans_1044 = T_IsGroup_1074
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsGroup.uniqueʳ-⁻¹
d_unique'691''45''8315''185'_1046 ::
  (Bool -> Bool -> Bool) ->
  Bool ->
  (Bool -> Bool) ->
  MAlonzo.Code.Algebra.Structures.T_IsGroup_1074 ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_unique'691''45''8315''185'_1046 :: (Bool -> Bool -> Bool)
-> Bool
-> (Bool -> Bool)
-> T_IsGroup_1074
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_unique'691''45''8315''185'_1046 = (Bool -> Bool -> Bool)
-> Bool
-> (Bool -> Bool)
-> T_IsGroup_1074
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsGroup.uniqueˡ-⁻¹
d_unique'737''45''8315''185'_1048 ::
  (Bool -> Bool -> Bool) ->
  Bool ->
  (Bool -> Bool) ->
  MAlonzo.Code.Algebra.Structures.T_IsGroup_1074 ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_unique'737''45''8315''185'_1048 :: (Bool -> Bool -> Bool)
-> Bool
-> (Bool -> Bool)
-> T_IsGroup_1074
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_unique'737''45''8315''185'_1048 = (Bool -> Bool -> Bool)
-> Bool
-> (Bool -> Bool)
-> T_IsGroup_1074
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsGroup.⁻¹-cong
d_'8315''185''45'cong_1050 ::
  MAlonzo.Code.Algebra.Structures.T_IsGroup_1074 ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8315''185''45'cong_1050 :: T_IsGroup_1074 -> Bool -> Bool -> T__'8801'__12 -> T__'8801'__12
d_'8315''185''45'cong_1050 = T_IsGroup_1074 -> Bool -> Bool -> T__'8801'__12 -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsGroup.∙-cong
d_'8729''45'cong_1052 ::
  MAlonzo.Code.Algebra.Structures.T_IsGroup_1074 ->
  Bool ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8729''45'cong_1052 :: T_IsGroup_1074
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong_1052 = T_IsGroup_1074
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsGroup.∙-congʳ
d_'8729''45'cong'691'_1054 ::
  (Bool -> Bool -> Bool) ->
  Bool ->
  (Bool -> Bool) ->
  MAlonzo.Code.Algebra.Structures.T_IsGroup_1074 ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8729''45'cong'691'_1054 :: (Bool -> Bool -> Bool)
-> Bool
-> (Bool -> Bool)
-> T_IsGroup_1074
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong'691'_1054 = (Bool -> Bool -> Bool)
-> Bool
-> (Bool -> Bool)
-> T_IsGroup_1074
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsGroup.∙-congˡ
d_'8729''45'cong'737'_1056 ::
  (Bool -> Bool -> Bool) ->
  Bool ->
  (Bool -> Bool) ->
  MAlonzo.Code.Algebra.Structures.T_IsGroup_1074 ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8729''45'cong'737'_1056 :: (Bool -> Bool -> Bool)
-> Bool
-> (Bool -> Bool)
-> T_IsGroup_1074
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong'737'_1056 = (Bool -> Bool -> Bool)
-> Bool
-> (Bool -> Bool)
-> T_IsGroup_1074
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsIdempotentCommutativeMonoid.assoc
d_assoc_1060 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  Bool ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_assoc_1060 :: T_IsIdempotentCommutativeMonoid_884
-> Bool -> Bool -> Bool -> T__'8801'__12
d_assoc_1060 = T_IsIdempotentCommutativeMonoid_884
-> Bool -> Bool -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsIdempotentCommutativeMonoid.comm
d_comm_1062 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_comm_1062 :: T_IsIdempotentCommutativeMonoid_884
-> Bool -> Bool -> T__'8801'__12
d_comm_1062 = T_IsIdempotentCommutativeMonoid_884
-> Bool -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsIdempotentCommutativeMonoid.idem
d_idem_1064 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_idem_1064 :: T_IsIdempotentCommutativeMonoid_884 -> Bool -> T__'8801'__12
d_idem_1064 = T_IsIdempotentCommutativeMonoid_884 -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsIdempotentCommutativeMonoid.identity
d_identity_1066 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_identity_1066 :: T_IsIdempotentCommutativeMonoid_884 -> T_Σ_14
d_identity_1066 T_IsIdempotentCommutativeMonoid_884
v0
  = (T_IsMonoid_712 -> T_Σ_14) -> Any -> T_Σ_14
forall a b. a -> b
coe
      T_IsMonoid_712 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_identity_724
      ((T_IsCommutativeMonoid_764 -> T_IsMonoid_712) -> Any -> Any
forall a b. a -> b
coe
         T_IsCommutativeMonoid_764 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_774
         ((T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764)
-> Any -> Any
forall a b. a -> b
coe
            T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_894
            (T_IsIdempotentCommutativeMonoid_884 -> Any
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884
v0)))
-- Data.Bool.Properties._.IsIdempotentCommutativeMonoid.identityʳ
d_identity'691'_1068 ::
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_identity'691'_1068 :: (Bool -> Bool -> Bool)
-> Bool
-> T_IsIdempotentCommutativeMonoid_884
-> Bool
-> T__'8801'__12
d_identity'691'_1068 = (Bool -> Bool -> Bool)
-> Bool
-> T_IsIdempotentCommutativeMonoid_884
-> Bool
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsIdempotentCommutativeMonoid.identityˡ
d_identity'737'_1070 ::
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_identity'737'_1070 :: (Bool -> Bool -> Bool)
-> Bool
-> T_IsIdempotentCommutativeMonoid_884
-> Bool
-> T__'8801'__12
d_identity'737'_1070 = (Bool -> Bool -> Bool)
-> Bool
-> T_IsIdempotentCommutativeMonoid_884
-> Bool
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsIdempotentCommutativeMonoid.isBand
d_isBand_1072 ::
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  MAlonzo.Code.Algebra.Structures.T_IsBand_526
d_isBand_1072 :: (Bool -> Bool -> Bool)
-> Bool -> T_IsIdempotentCommutativeMonoid_884 -> T_IsBand_526
d_isBand_1072 ~Bool -> Bool -> Bool
v0 ~Bool
v1 T_IsIdempotentCommutativeMonoid_884
v2 = T_IsIdempotentCommutativeMonoid_884 -> T_IsBand_526
du_isBand_1072 T_IsIdempotentCommutativeMonoid_884
v2
du_isBand_1072 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  MAlonzo.Code.Algebra.Structures.T_IsBand_526
du_isBand_1072 :: T_IsIdempotentCommutativeMonoid_884 -> T_IsBand_526
du_isBand_1072 T_IsIdempotentCommutativeMonoid_884
v0
  = (T_IsIdempotentMonoid_826 -> T_IsBand_526) -> Any -> T_IsBand_526
forall a b. a -> b
coe
      T_IsIdempotentMonoid_826 -> T_IsBand_526
MAlonzo.Code.Algebra.Structures.du_isBand_876
      ((T_IsIdempotentCommutativeMonoid_884 -> T_IsIdempotentMonoid_826)
-> Any -> Any
forall a b. a -> b
coe
         T_IsIdempotentCommutativeMonoid_884 -> T_IsIdempotentMonoid_826
MAlonzo.Code.Algebra.Structures.du_isIdempotentMonoid_942 (T_IsIdempotentCommutativeMonoid_884 -> Any
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884
v0))
-- Data.Bool.Properties._.IsIdempotentCommutativeMonoid.isCommutativeBand
d_isCommutativeBand_1074 ::
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_612
d_isCommutativeBand_1074 :: (Bool -> Bool -> Bool)
-> Bool
-> T_IsIdempotentCommutativeMonoid_884
-> T_IsCommutativeBand_612
d_isCommutativeBand_1074 Bool -> Bool -> Bool
v0 Bool
v1 T_IsIdempotentCommutativeMonoid_884
v2
  = (T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeBand_612)
-> T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeBand_612
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeBand_612
MAlonzo.Code.Algebra.Structures.du_isCommutativeBand_948 T_IsIdempotentCommutativeMonoid_884
v2
-- Data.Bool.Properties._.IsIdempotentCommutativeMonoid.isCommutativeMagma
d_isCommutativeMagma_1076 ::
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMagma_214
d_isCommutativeMagma_1076 :: (Bool -> Bool -> Bool)
-> Bool
-> T_IsIdempotentCommutativeMonoid_884
-> T_IsCommutativeMagma_214
d_isCommutativeMagma_1076 ~Bool -> Bool -> Bool
v0 ~Bool
v1 T_IsIdempotentCommutativeMonoid_884
v2
  = T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMagma_214
du_isCommutativeMagma_1076 T_IsIdempotentCommutativeMonoid_884
v2
du_isCommutativeMagma_1076 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMagma_214
du_isCommutativeMagma_1076 :: T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMagma_214
du_isCommutativeMagma_1076 T_IsIdempotentCommutativeMonoid_884
v0
  = let v1 :: T_IsCommutativeMonoid_764
v1
          = T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_894
              (T_IsIdempotentCommutativeMonoid_884
-> T_IsIdempotentCommutativeMonoid_884
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884
v0) in
    Any -> T_IsCommutativeMagma_214
forall a b. a -> b
coe
      ((T_IsCommutativeSemigroup_568 -> T_IsCommutativeMagma_214)
-> Any -> Any
forall a b. a -> b
coe
         T_IsCommutativeSemigroup_568 -> T_IsCommutativeMagma_214
MAlonzo.Code.Algebra.Structures.du_isCommutativeMagma_606
         ((T_IsCommutativeMonoid_764 -> T_IsCommutativeSemigroup_568)
-> Any -> Any
forall a b. a -> b
coe
            T_IsCommutativeMonoid_764 -> T_IsCommutativeSemigroup_568
MAlonzo.Code.Algebra.Structures.du_isCommutativeSemigroup_814
            (T_IsCommutativeMonoid_764 -> Any
forall a b. a -> b
coe T_IsCommutativeMonoid_764
v1)))
-- Data.Bool.Properties._.IsIdempotentCommutativeMonoid.isCommutativeMonoid
d_isCommutativeMonoid_1078 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMonoid_764
d_isCommutativeMonoid_1078 :: T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764
d_isCommutativeMonoid_1078 T_IsIdempotentCommutativeMonoid_884
v0
  = (T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764)
-> Any -> T_IsCommutativeMonoid_764
forall a b. a -> b
coe
      T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_894 (T_IsIdempotentCommutativeMonoid_884 -> Any
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884
v0)
-- Data.Bool.Properties._.IsIdempotentCommutativeMonoid.isCommutativeSemigroup
d_isCommutativeSemigroup_1080 ::
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_568
d_isCommutativeSemigroup_1080 :: (Bool -> Bool -> Bool)
-> Bool
-> T_IsIdempotentCommutativeMonoid_884
-> T_IsCommutativeSemigroup_568
d_isCommutativeSemigroup_1080 ~Bool -> Bool -> Bool
v0 ~Bool
v1 T_IsIdempotentCommutativeMonoid_884
v2
  = T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeSemigroup_568
du_isCommutativeSemigroup_1080 T_IsIdempotentCommutativeMonoid_884
v2
du_isCommutativeSemigroup_1080 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_568
du_isCommutativeSemigroup_1080 :: T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeSemigroup_568
du_isCommutativeSemigroup_1080 T_IsIdempotentCommutativeMonoid_884
v0
  = (T_IsCommutativeMonoid_764 -> T_IsCommutativeSemigroup_568)
-> Any -> T_IsCommutativeSemigroup_568
forall a b. a -> b
coe
      T_IsCommutativeMonoid_764 -> T_IsCommutativeSemigroup_568
MAlonzo.Code.Algebra.Structures.du_isCommutativeSemigroup_814
      ((T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764)
-> Any -> Any
forall a b. a -> b
coe
         T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_894 (T_IsIdempotentCommutativeMonoid_884 -> Any
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884
v0))
-- Data.Bool.Properties._.IsIdempotentCommutativeMonoid.isEquivalence
d_isEquivalence_1082 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
d_isEquivalence_1082 :: T_IsIdempotentCommutativeMonoid_884 -> T_IsEquivalence_28
d_isEquivalence_1082 T_IsIdempotentCommutativeMonoid_884
v0
  = (T_IsMagma_178 -> T_IsEquivalence_28) -> Any -> T_IsEquivalence_28
forall a b. a -> b
coe
      T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186
      ((T_IsSemigroup_488 -> T_IsMagma_178) -> Any -> Any
forall a b. a -> b
coe
         T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496
         ((T_IsMonoid_712 -> T_IsSemigroup_488) -> Any -> Any
forall a b. a -> b
coe
            T_IsMonoid_712 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_722
            ((T_IsCommutativeMonoid_764 -> T_IsMonoid_712) -> Any -> Any
forall a b. a -> b
coe
               T_IsCommutativeMonoid_764 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_774
               ((T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764)
-> Any -> Any
forall a b. a -> b
coe
                  T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_894
                  (T_IsIdempotentCommutativeMonoid_884 -> Any
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884
v0)))))
-- Data.Bool.Properties._.IsIdempotentCommutativeMonoid.isIdempotentMonoid
d_isIdempotentMonoid_1084 ::
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentMonoid_826
d_isIdempotentMonoid_1084 :: (Bool -> Bool -> Bool)
-> Bool
-> T_IsIdempotentCommutativeMonoid_884
-> T_IsIdempotentMonoid_826
d_isIdempotentMonoid_1084 Bool -> Bool -> Bool
v0 Bool
v1 T_IsIdempotentCommutativeMonoid_884
v2
  = (T_IsIdempotentCommutativeMonoid_884 -> T_IsIdempotentMonoid_826)
-> T_IsIdempotentCommutativeMonoid_884 -> T_IsIdempotentMonoid_826
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884 -> T_IsIdempotentMonoid_826
MAlonzo.Code.Algebra.Structures.du_isIdempotentMonoid_942 T_IsIdempotentCommutativeMonoid_884
v2
-- Data.Bool.Properties._.IsIdempotentCommutativeMonoid.isMagma
d_isMagma_1086 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_178
d_isMagma_1086 :: T_IsIdempotentCommutativeMonoid_884 -> T_IsMagma_178
d_isMagma_1086 T_IsIdempotentCommutativeMonoid_884
v0
  = (T_IsSemigroup_488 -> T_IsMagma_178) -> Any -> T_IsMagma_178
forall a b. a -> b
coe
      T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496
      ((T_IsMonoid_712 -> T_IsSemigroup_488) -> Any -> Any
forall a b. a -> b
coe
         T_IsMonoid_712 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_722
         ((T_IsCommutativeMonoid_764 -> T_IsMonoid_712) -> Any -> Any
forall a b. a -> b
coe
            T_IsCommutativeMonoid_764 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_774
            ((T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764)
-> Any -> Any
forall a b. a -> b
coe
               T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_894
               (T_IsIdempotentCommutativeMonoid_884 -> Any
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884
v0))))
-- Data.Bool.Properties._.IsIdempotentCommutativeMonoid.isMonoid
d_isMonoid_1088 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  MAlonzo.Code.Algebra.Structures.T_IsMonoid_712
d_isMonoid_1088 :: T_IsIdempotentCommutativeMonoid_884 -> T_IsMonoid_712
d_isMonoid_1088 T_IsIdempotentCommutativeMonoid_884
v0
  = (T_IsCommutativeMonoid_764 -> T_IsMonoid_712)
-> Any -> T_IsMonoid_712
forall a b. a -> b
coe
      T_IsCommutativeMonoid_764 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_774
      ((T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764)
-> Any -> Any
forall a b. a -> b
coe
         T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_894 (T_IsIdempotentCommutativeMonoid_884 -> Any
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884
v0))
-- Data.Bool.Properties._.IsIdempotentCommutativeMonoid.isPartialEquivalence
d_isPartialEquivalence_1090 ::
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_1090 :: (Bool -> Bool -> Bool)
-> Bool
-> T_IsIdempotentCommutativeMonoid_884
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_1090 ~Bool -> Bool -> Bool
v0 ~Bool
v1 T_IsIdempotentCommutativeMonoid_884
v2
  = T_IsIdempotentCommutativeMonoid_884 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_1090 T_IsIdempotentCommutativeMonoid_884
v2
du_isPartialEquivalence_1090 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_1090 :: T_IsIdempotentCommutativeMonoid_884 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_1090 T_IsIdempotentCommutativeMonoid_884
v0
  = let v1 :: T_IsCommutativeMonoid_764
v1
          = T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_894
              (T_IsIdempotentCommutativeMonoid_884
-> T_IsIdempotentCommutativeMonoid_884
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884
v0) in
    Any -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsMonoid_712
v2
             = T_IsCommutativeMonoid_764 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_774 (T_IsCommutativeMonoid_764 -> T_IsCommutativeMonoid_764
forall a b. a -> b
coe T_IsCommutativeMonoid_764
v1) in
       Any -> Any
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_488
v3
                = T_IsMonoid_712 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_722 (T_IsMonoid_712 -> T_IsMonoid_712
forall a b. a -> b
coe T_IsMonoid_712
v2) in
          Any -> Any
forall a b. a -> b
coe
            (let v4 :: T_IsMagma_178
v4 = T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496 (T_IsSemigroup_488 -> T_IsSemigroup_488
forall a b. a -> b
coe T_IsSemigroup_488
v3) in
             Any -> Any
forall a b. a -> b
coe
               ((T_IsEquivalence_28 -> T_IsPartialEquivalence_16) -> Any -> Any
forall a b. a -> b
coe
                  T_IsEquivalence_28 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_44
                  ((T_IsMagma_178 -> T_IsEquivalence_28) -> Any -> Any
forall a b. a -> b
coe
                     T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186 (T_IsMagma_178 -> Any
forall a b. a -> b
coe T_IsMagma_178
v4))))))
-- Data.Bool.Properties._.IsIdempotentCommutativeMonoid.isSemigroup
d_isSemigroup_1092 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_488
d_isSemigroup_1092 :: T_IsIdempotentCommutativeMonoid_884 -> T_IsSemigroup_488
d_isSemigroup_1092 T_IsIdempotentCommutativeMonoid_884
v0
  = (T_IsMonoid_712 -> T_IsSemigroup_488) -> Any -> T_IsSemigroup_488
forall a b. a -> b
coe
      T_IsMonoid_712 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_722
      ((T_IsCommutativeMonoid_764 -> T_IsMonoid_712) -> Any -> Any
forall a b. a -> b
coe
         T_IsCommutativeMonoid_764 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_774
         ((T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764)
-> Any -> Any
forall a b. a -> b
coe
            T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_894
            (T_IsIdempotentCommutativeMonoid_884 -> Any
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884
v0)))
-- Data.Bool.Properties._.IsIdempotentCommutativeMonoid.isUnitalMagma
d_isUnitalMagma_1094 ::
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  MAlonzo.Code.Algebra.Structures.T_IsUnitalMagma_666
d_isUnitalMagma_1094 :: (Bool -> Bool -> Bool)
-> Bool
-> T_IsIdempotentCommutativeMonoid_884
-> T_IsUnitalMagma_666
d_isUnitalMagma_1094 ~Bool -> Bool -> Bool
v0 ~Bool
v1 T_IsIdempotentCommutativeMonoid_884
v2 = T_IsIdempotentCommutativeMonoid_884 -> T_IsUnitalMagma_666
du_isUnitalMagma_1094 T_IsIdempotentCommutativeMonoid_884
v2
du_isUnitalMagma_1094 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  MAlonzo.Code.Algebra.Structures.T_IsUnitalMagma_666
du_isUnitalMagma_1094 :: T_IsIdempotentCommutativeMonoid_884 -> T_IsUnitalMagma_666
du_isUnitalMagma_1094 T_IsIdempotentCommutativeMonoid_884
v0
  = let v1 :: T_IsCommutativeMonoid_764
v1
          = T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_894
              (T_IsIdempotentCommutativeMonoid_884
-> T_IsIdempotentCommutativeMonoid_884
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884
v0) in
    Any -> T_IsUnitalMagma_666
forall a b. a -> b
coe
      ((T_IsMonoid_712 -> T_IsUnitalMagma_666) -> Any -> Any
forall a b. a -> b
coe
         T_IsMonoid_712 -> T_IsUnitalMagma_666
MAlonzo.Code.Algebra.Structures.du_isUnitalMagma_756
         ((T_IsCommutativeMonoid_764 -> T_IsMonoid_712) -> Any -> Any
forall a b. a -> b
coe T_IsCommutativeMonoid_764 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_774 (T_IsCommutativeMonoid_764 -> Any
forall a b. a -> b
coe T_IsCommutativeMonoid_764
v1)))
-- Data.Bool.Properties._.IsIdempotentCommutativeMonoid.refl
d_refl_1096 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_refl_1096 :: T_IsIdempotentCommutativeMonoid_884 -> Bool -> T__'8801'__12
d_refl_1096 = T_IsIdempotentCommutativeMonoid_884 -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsIdempotentCommutativeMonoid.reflexive
d_reflexive_1098 ::
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_reflexive_1098 :: (Bool -> Bool -> Bool)
-> Bool
-> T_IsIdempotentCommutativeMonoid_884
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_reflexive_1098 = (Bool -> Bool -> Bool)
-> Bool
-> T_IsIdempotentCommutativeMonoid_884
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsIdempotentCommutativeMonoid.setoid
d_setoid_1100 ::
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
d_setoid_1100 :: (Bool -> Bool -> Bool)
-> Bool -> T_IsIdempotentCommutativeMonoid_884 -> T_Setoid_46
d_setoid_1100 ~Bool -> Bool -> Bool
v0 ~Bool
v1 T_IsIdempotentCommutativeMonoid_884
v2 = T_IsIdempotentCommutativeMonoid_884 -> T_Setoid_46
du_setoid_1100 T_IsIdempotentCommutativeMonoid_884
v2
du_setoid_1100 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
du_setoid_1100 :: T_IsIdempotentCommutativeMonoid_884 -> T_Setoid_46
du_setoid_1100 T_IsIdempotentCommutativeMonoid_884
v0
  = let v1 :: T_IsCommutativeMonoid_764
v1
          = T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_894
              (T_IsIdempotentCommutativeMonoid_884
-> T_IsIdempotentCommutativeMonoid_884
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884
v0) in
    Any -> T_Setoid_46
forall a b. a -> b
coe
      (let v2 :: T_IsMonoid_712
v2
             = T_IsCommutativeMonoid_764 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_774 (T_IsCommutativeMonoid_764 -> T_IsCommutativeMonoid_764
forall a b. a -> b
coe T_IsCommutativeMonoid_764
v1) in
       Any -> Any
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_488
v3
                = T_IsMonoid_712 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_722 (T_IsMonoid_712 -> T_IsMonoid_712
forall a b. a -> b
coe T_IsMonoid_712
v2) in
          Any -> Any
forall a b. a -> b
coe
            ((T_IsMagma_178 -> T_Setoid_46) -> Any -> Any
forall a b. a -> b
coe
               T_IsMagma_178 -> T_Setoid_46
MAlonzo.Code.Algebra.Structures.du_setoid_202
               ((T_IsSemigroup_488 -> T_IsMagma_178) -> Any -> Any
forall a b. a -> b
coe T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496 (T_IsSemigroup_488 -> Any
forall a b. a -> b
coe T_IsSemigroup_488
v3)))))
-- Data.Bool.Properties._.IsIdempotentCommutativeMonoid.sym
d_sym_1102 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_sym_1102 :: T_IsIdempotentCommutativeMonoid_884
-> Bool -> Bool -> T__'8801'__12 -> T__'8801'__12
d_sym_1102 = T_IsIdempotentCommutativeMonoid_884
-> Bool -> Bool -> T__'8801'__12 -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsIdempotentCommutativeMonoid.trans
d_trans_1104 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_trans_1104 :: T_IsIdempotentCommutativeMonoid_884
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
d_trans_1104 = T_IsIdempotentCommutativeMonoid_884
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsIdempotentCommutativeMonoid.∙-cong
d_'8729''45'cong_1106 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  Bool ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8729''45'cong_1106 :: T_IsIdempotentCommutativeMonoid_884
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong_1106 = T_IsIdempotentCommutativeMonoid_884
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsIdempotentCommutativeMonoid.∙-congʳ
d_'8729''45'cong'691'_1108 ::
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8729''45'cong'691'_1108 :: (Bool -> Bool -> Bool)
-> Bool
-> T_IsIdempotentCommutativeMonoid_884
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong'691'_1108 = (Bool -> Bool -> Bool)
-> Bool
-> T_IsIdempotentCommutativeMonoid_884
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsIdempotentCommutativeMonoid.∙-congˡ
d_'8729''45'cong'737'_1110 ::
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8729''45'cong'737'_1110 :: (Bool -> Bool -> Bool)
-> Bool
-> T_IsIdempotentCommutativeMonoid_884
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong'737'_1110 = (Bool -> Bool -> Bool)
-> Bool
-> T_IsIdempotentCommutativeMonoid_884
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsIdempotentMagma.idem
d_idem_1114 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentMagma_252 ->
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_idem_1114 :: T_IsIdempotentMagma_252 -> Bool -> T__'8801'__12
d_idem_1114 = T_IsIdempotentMagma_252 -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsIdempotentMagma.isEquivalence
d_isEquivalence_1116 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentMagma_252 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
d_isEquivalence_1116 :: T_IsIdempotentMagma_252 -> T_IsEquivalence_28
d_isEquivalence_1116 T_IsIdempotentMagma_252
v0
  = (T_IsMagma_178 -> T_IsEquivalence_28) -> Any -> T_IsEquivalence_28
forall a b. a -> b
coe
      T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186
      ((T_IsIdempotentMagma_252 -> T_IsMagma_178) -> Any -> Any
forall a b. a -> b
coe T_IsIdempotentMagma_252 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_260 (T_IsIdempotentMagma_252 -> Any
forall a b. a -> b
coe T_IsIdempotentMagma_252
v0))
-- Data.Bool.Properties._.IsIdempotentMagma.isMagma
d_isMagma_1118 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentMagma_252 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_178
d_isMagma_1118 :: T_IsIdempotentMagma_252 -> T_IsMagma_178
d_isMagma_1118 T_IsIdempotentMagma_252
v0
  = (T_IsIdempotentMagma_252 -> T_IsMagma_178) -> Any -> T_IsMagma_178
forall a b. a -> b
coe T_IsIdempotentMagma_252 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_260 (T_IsIdempotentMagma_252 -> Any
forall a b. a -> b
coe T_IsIdempotentMagma_252
v0)
-- Data.Bool.Properties._.IsIdempotentMagma.isPartialEquivalence
d_isPartialEquivalence_1120 ::
  (Bool -> Bool -> Bool) ->
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentMagma_252 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_1120 :: (Bool -> Bool -> Bool)
-> T_IsIdempotentMagma_252 -> T_IsPartialEquivalence_16
d_isPartialEquivalence_1120 ~Bool -> Bool -> Bool
v0 T_IsIdempotentMagma_252
v1
  = T_IsIdempotentMagma_252 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_1120 T_IsIdempotentMagma_252
v1
du_isPartialEquivalence_1120 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentMagma_252 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_1120 :: T_IsIdempotentMagma_252 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_1120 T_IsIdempotentMagma_252
v0
  = let v1 :: T_IsMagma_178
v1
          = T_IsIdempotentMagma_252 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_260 (T_IsIdempotentMagma_252 -> T_IsIdempotentMagma_252
forall a b. a -> b
coe T_IsIdempotentMagma_252
v0) in
    Any -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      ((T_IsEquivalence_28 -> T_IsPartialEquivalence_16) -> Any -> Any
forall a b. a -> b
coe
         T_IsEquivalence_28 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_44
         ((T_IsMagma_178 -> T_IsEquivalence_28) -> Any -> Any
forall a b. a -> b
coe T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186 (T_IsMagma_178 -> Any
forall a b. a -> b
coe T_IsMagma_178
v1)))
-- Data.Bool.Properties._.IsIdempotentMagma.refl
d_refl_1122 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentMagma_252 ->
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_refl_1122 :: T_IsIdempotentMagma_252 -> Bool -> T__'8801'__12
d_refl_1122 = T_IsIdempotentMagma_252 -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsIdempotentMagma.reflexive
d_reflexive_1124 ::
  (Bool -> Bool -> Bool) ->
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentMagma_252 ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_reflexive_1124 :: (Bool -> Bool -> Bool)
-> T_IsIdempotentMagma_252
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_reflexive_1124 = (Bool -> Bool -> Bool)
-> T_IsIdempotentMagma_252
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsIdempotentMagma.setoid
d_setoid_1126 ::
  (Bool -> Bool -> Bool) ->
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentMagma_252 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
d_setoid_1126 :: (Bool -> Bool -> Bool) -> T_IsIdempotentMagma_252 -> T_Setoid_46
d_setoid_1126 ~Bool -> Bool -> Bool
v0 T_IsIdempotentMagma_252
v1 = T_IsIdempotentMagma_252 -> T_Setoid_46
du_setoid_1126 T_IsIdempotentMagma_252
v1
du_setoid_1126 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentMagma_252 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
du_setoid_1126 :: T_IsIdempotentMagma_252 -> T_Setoid_46
du_setoid_1126 T_IsIdempotentMagma_252
v0
  = (T_IsMagma_178 -> T_Setoid_46) -> Any -> T_Setoid_46
forall a b. a -> b
coe
      T_IsMagma_178 -> T_Setoid_46
MAlonzo.Code.Algebra.Structures.du_setoid_202
      ((T_IsIdempotentMagma_252 -> T_IsMagma_178) -> Any -> Any
forall a b. a -> b
coe T_IsIdempotentMagma_252 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_260 (T_IsIdempotentMagma_252 -> Any
forall a b. a -> b
coe T_IsIdempotentMagma_252
v0))
-- Data.Bool.Properties._.IsIdempotentMagma.sym
d_sym_1128 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentMagma_252 ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_sym_1128 :: T_IsIdempotentMagma_252
-> Bool -> Bool -> T__'8801'__12 -> T__'8801'__12
d_sym_1128 = T_IsIdempotentMagma_252
-> Bool -> Bool -> T__'8801'__12 -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsIdempotentMagma.trans
d_trans_1130 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentMagma_252 ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_trans_1130 :: T_IsIdempotentMagma_252
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
d_trans_1130 = T_IsIdempotentMagma_252
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsIdempotentMagma.∙-cong
d_'8729''45'cong_1132 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentMagma_252 ->
  Bool ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8729''45'cong_1132 :: T_IsIdempotentMagma_252
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong_1132 = T_IsIdempotentMagma_252
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsIdempotentMagma.∙-congʳ
d_'8729''45'cong'691'_1134 ::
  (Bool -> Bool -> Bool) ->
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentMagma_252 ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8729''45'cong'691'_1134 :: (Bool -> Bool -> Bool)
-> T_IsIdempotentMagma_252
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong'691'_1134 = (Bool -> Bool -> Bool)
-> T_IsIdempotentMagma_252
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsIdempotentMagma.∙-congˡ
d_'8729''45'cong'737'_1136 ::
  (Bool -> Bool -> Bool) ->
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentMagma_252 ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8729''45'cong'737'_1136 :: (Bool -> Bool -> Bool)
-> T_IsIdempotentMagma_252
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong'737'_1136 = (Bool -> Bool -> Bool)
-> T_IsIdempotentMagma_252
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsIdempotentMonoid.assoc
d_assoc_1140 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentMonoid_826 ->
  Bool ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_assoc_1140 :: T_IsIdempotentMonoid_826 -> Bool -> Bool -> Bool -> T__'8801'__12
d_assoc_1140 = T_IsIdempotentMonoid_826 -> Bool -> Bool -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsIdempotentMonoid.idem
d_idem_1142 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentMonoid_826 ->
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_idem_1142 :: T_IsIdempotentMonoid_826 -> Bool -> T__'8801'__12
d_idem_1142 = T_IsIdempotentMonoid_826 -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsIdempotentMonoid.identity
d_identity_1144 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentMonoid_826 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_identity_1144 :: T_IsIdempotentMonoid_826 -> T_Σ_14
d_identity_1144 T_IsIdempotentMonoid_826
v0
  = (T_IsMonoid_712 -> T_Σ_14) -> Any -> T_Σ_14
forall a b. a -> b
coe
      T_IsMonoid_712 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_identity_724
      ((T_IsIdempotentMonoid_826 -> T_IsMonoid_712) -> Any -> Any
forall a b. a -> b
coe T_IsIdempotentMonoid_826 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_836 (T_IsIdempotentMonoid_826 -> Any
forall a b. a -> b
coe T_IsIdempotentMonoid_826
v0))
-- Data.Bool.Properties._.IsIdempotentMonoid.identityʳ
d_identity'691'_1146 ::
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentMonoid_826 ->
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_identity'691'_1146 :: (Bool -> Bool -> Bool)
-> Bool -> T_IsIdempotentMonoid_826 -> Bool -> T__'8801'__12
d_identity'691'_1146 = (Bool -> Bool -> Bool)
-> Bool -> T_IsIdempotentMonoid_826 -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsIdempotentMonoid.identityˡ
d_identity'737'_1148 ::
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentMonoid_826 ->
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_identity'737'_1148 :: (Bool -> Bool -> Bool)
-> Bool -> T_IsIdempotentMonoid_826 -> Bool -> T__'8801'__12
d_identity'737'_1148 = (Bool -> Bool -> Bool)
-> Bool -> T_IsIdempotentMonoid_826 -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsIdempotentMonoid.isBand
d_isBand_1150 ::
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentMonoid_826 ->
  MAlonzo.Code.Algebra.Structures.T_IsBand_526
d_isBand_1150 :: (Bool -> Bool -> Bool)
-> Bool -> T_IsIdempotentMonoid_826 -> T_IsBand_526
d_isBand_1150 Bool -> Bool -> Bool
v0 Bool
v1 T_IsIdempotentMonoid_826
v2
  = (T_IsIdempotentMonoid_826 -> T_IsBand_526)
-> T_IsIdempotentMonoid_826 -> T_IsBand_526
forall a b. a -> b
coe T_IsIdempotentMonoid_826 -> T_IsBand_526
MAlonzo.Code.Algebra.Structures.du_isBand_876 T_IsIdempotentMonoid_826
v2
-- Data.Bool.Properties._.IsIdempotentMonoid.isEquivalence
d_isEquivalence_1152 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentMonoid_826 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
d_isEquivalence_1152 :: T_IsIdempotentMonoid_826 -> T_IsEquivalence_28
d_isEquivalence_1152 T_IsIdempotentMonoid_826
v0
  = (T_IsMagma_178 -> T_IsEquivalence_28) -> Any -> T_IsEquivalence_28
forall a b. a -> b
coe
      T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186
      ((T_IsSemigroup_488 -> T_IsMagma_178) -> Any -> Any
forall a b. a -> b
coe
         T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496
         ((T_IsMonoid_712 -> T_IsSemigroup_488) -> Any -> Any
forall a b. a -> b
coe
            T_IsMonoid_712 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_722
            ((T_IsIdempotentMonoid_826 -> T_IsMonoid_712) -> Any -> Any
forall a b. a -> b
coe T_IsIdempotentMonoid_826 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_836 (T_IsIdempotentMonoid_826 -> Any
forall a b. a -> b
coe T_IsIdempotentMonoid_826
v0))))
-- Data.Bool.Properties._.IsIdempotentMonoid.isMagma
d_isMagma_1154 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentMonoid_826 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_178
d_isMagma_1154 :: T_IsIdempotentMonoid_826 -> T_IsMagma_178
d_isMagma_1154 T_IsIdempotentMonoid_826
v0
  = (T_IsSemigroup_488 -> T_IsMagma_178) -> Any -> T_IsMagma_178
forall a b. a -> b
coe
      T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496
      ((T_IsMonoid_712 -> T_IsSemigroup_488) -> Any -> Any
forall a b. a -> b
coe
         T_IsMonoid_712 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_722
         ((T_IsIdempotentMonoid_826 -> T_IsMonoid_712) -> Any -> Any
forall a b. a -> b
coe T_IsIdempotentMonoid_826 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_836 (T_IsIdempotentMonoid_826 -> Any
forall a b. a -> b
coe T_IsIdempotentMonoid_826
v0)))
-- Data.Bool.Properties._.IsIdempotentMonoid.isMonoid
d_isMonoid_1156 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentMonoid_826 ->
  MAlonzo.Code.Algebra.Structures.T_IsMonoid_712
d_isMonoid_1156 :: T_IsIdempotentMonoid_826 -> T_IsMonoid_712
d_isMonoid_1156 T_IsIdempotentMonoid_826
v0
  = (T_IsIdempotentMonoid_826 -> T_IsMonoid_712)
-> Any -> T_IsMonoid_712
forall a b. a -> b
coe T_IsIdempotentMonoid_826 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_836 (T_IsIdempotentMonoid_826 -> Any
forall a b. a -> b
coe T_IsIdempotentMonoid_826
v0)
-- Data.Bool.Properties._.IsIdempotentMonoid.isPartialEquivalence
d_isPartialEquivalence_1158 ::
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentMonoid_826 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_1158 :: (Bool -> Bool -> Bool)
-> Bool -> T_IsIdempotentMonoid_826 -> T_IsPartialEquivalence_16
d_isPartialEquivalence_1158 ~Bool -> Bool -> Bool
v0 ~Bool
v1 T_IsIdempotentMonoid_826
v2
  = T_IsIdempotentMonoid_826 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_1158 T_IsIdempotentMonoid_826
v2
du_isPartialEquivalence_1158 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentMonoid_826 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_1158 :: T_IsIdempotentMonoid_826 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_1158 T_IsIdempotentMonoid_826
v0
  = let v1 :: T_IsMonoid_712
v1
          = T_IsIdempotentMonoid_826 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_836 (T_IsIdempotentMonoid_826 -> T_IsIdempotentMonoid_826
forall a b. a -> b
coe T_IsIdempotentMonoid_826
v0) in
    Any -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsSemigroup_488
v2
             = T_IsMonoid_712 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_722 (T_IsMonoid_712 -> T_IsMonoid_712
forall a b. a -> b
coe T_IsMonoid_712
v1) in
       Any -> Any
forall a b. a -> b
coe
         (let v3 :: T_IsMagma_178
v3 = T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496 (T_IsSemigroup_488 -> T_IsSemigroup_488
forall a b. a -> b
coe T_IsSemigroup_488
v2) in
          Any -> Any
forall a b. a -> b
coe
            ((T_IsEquivalence_28 -> T_IsPartialEquivalence_16) -> Any -> Any
forall a b. a -> b
coe
               T_IsEquivalence_28 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_44
               ((T_IsMagma_178 -> T_IsEquivalence_28) -> Any -> Any
forall a b. a -> b
coe
                  T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186 (T_IsMagma_178 -> Any
forall a b. a -> b
coe T_IsMagma_178
v3)))))
-- Data.Bool.Properties._.IsIdempotentMonoid.isSemigroup
d_isSemigroup_1160 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentMonoid_826 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_488
d_isSemigroup_1160 :: T_IsIdempotentMonoid_826 -> T_IsSemigroup_488
d_isSemigroup_1160 T_IsIdempotentMonoid_826
v0
  = (T_IsMonoid_712 -> T_IsSemigroup_488) -> Any -> T_IsSemigroup_488
forall a b. a -> b
coe
      T_IsMonoid_712 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_722
      ((T_IsIdempotentMonoid_826 -> T_IsMonoid_712) -> Any -> Any
forall a b. a -> b
coe T_IsIdempotentMonoid_826 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_836 (T_IsIdempotentMonoid_826 -> Any
forall a b. a -> b
coe T_IsIdempotentMonoid_826
v0))
-- Data.Bool.Properties._.IsIdempotentMonoid.isUnitalMagma
d_isUnitalMagma_1162 ::
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentMonoid_826 ->
  MAlonzo.Code.Algebra.Structures.T_IsUnitalMagma_666
d_isUnitalMagma_1162 :: (Bool -> Bool -> Bool)
-> Bool -> T_IsIdempotentMonoid_826 -> T_IsUnitalMagma_666
d_isUnitalMagma_1162 ~Bool -> Bool -> Bool
v0 ~Bool
v1 T_IsIdempotentMonoid_826
v2 = T_IsIdempotentMonoid_826 -> T_IsUnitalMagma_666
du_isUnitalMagma_1162 T_IsIdempotentMonoid_826
v2
du_isUnitalMagma_1162 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentMonoid_826 ->
  MAlonzo.Code.Algebra.Structures.T_IsUnitalMagma_666
du_isUnitalMagma_1162 :: T_IsIdempotentMonoid_826 -> T_IsUnitalMagma_666
du_isUnitalMagma_1162 T_IsIdempotentMonoid_826
v0
  = (T_IsMonoid_712 -> T_IsUnitalMagma_666)
-> Any -> T_IsUnitalMagma_666
forall a b. a -> b
coe
      T_IsMonoid_712 -> T_IsUnitalMagma_666
MAlonzo.Code.Algebra.Structures.du_isUnitalMagma_756
      ((T_IsIdempotentMonoid_826 -> T_IsMonoid_712) -> Any -> Any
forall a b. a -> b
coe T_IsIdempotentMonoid_826 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_836 (T_IsIdempotentMonoid_826 -> Any
forall a b. a -> b
coe T_IsIdempotentMonoid_826
v0))
-- Data.Bool.Properties._.IsIdempotentMonoid.refl
d_refl_1164 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentMonoid_826 ->
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_refl_1164 :: T_IsIdempotentMonoid_826 -> Bool -> T__'8801'__12
d_refl_1164 = T_IsIdempotentMonoid_826 -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsIdempotentMonoid.reflexive
d_reflexive_1166 ::
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentMonoid_826 ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_reflexive_1166 :: (Bool -> Bool -> Bool)
-> Bool
-> T_IsIdempotentMonoid_826
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_reflexive_1166 = (Bool -> Bool -> Bool)
-> Bool
-> T_IsIdempotentMonoid_826
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsIdempotentMonoid.setoid
d_setoid_1168 ::
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentMonoid_826 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
d_setoid_1168 :: (Bool -> Bool -> Bool)
-> Bool -> T_IsIdempotentMonoid_826 -> T_Setoid_46
d_setoid_1168 ~Bool -> Bool -> Bool
v0 ~Bool
v1 T_IsIdempotentMonoid_826
v2 = T_IsIdempotentMonoid_826 -> T_Setoid_46
du_setoid_1168 T_IsIdempotentMonoid_826
v2
du_setoid_1168 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentMonoid_826 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
du_setoid_1168 :: T_IsIdempotentMonoid_826 -> T_Setoid_46
du_setoid_1168 T_IsIdempotentMonoid_826
v0
  = let v1 :: T_IsMonoid_712
v1
          = T_IsIdempotentMonoid_826 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_836 (T_IsIdempotentMonoid_826 -> T_IsIdempotentMonoid_826
forall a b. a -> b
coe T_IsIdempotentMonoid_826
v0) in
    Any -> T_Setoid_46
forall a b. a -> b
coe
      (let v2 :: T_IsSemigroup_488
v2
             = T_IsMonoid_712 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_722 (T_IsMonoid_712 -> T_IsMonoid_712
forall a b. a -> b
coe T_IsMonoid_712
v1) in
       Any -> Any
forall a b. a -> b
coe
         ((T_IsMagma_178 -> T_Setoid_46) -> Any -> Any
forall a b. a -> b
coe
            T_IsMagma_178 -> T_Setoid_46
MAlonzo.Code.Algebra.Structures.du_setoid_202
            ((T_IsSemigroup_488 -> T_IsMagma_178) -> Any -> Any
forall a b. a -> b
coe T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496 (T_IsSemigroup_488 -> Any
forall a b. a -> b
coe T_IsSemigroup_488
v2))))
-- Data.Bool.Properties._.IsIdempotentMonoid.sym
d_sym_1170 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentMonoid_826 ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_sym_1170 :: T_IsIdempotentMonoid_826
-> Bool -> Bool -> T__'8801'__12 -> T__'8801'__12
d_sym_1170 = T_IsIdempotentMonoid_826
-> Bool -> Bool -> T__'8801'__12 -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsIdempotentMonoid.trans
d_trans_1172 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentMonoid_826 ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_trans_1172 :: T_IsIdempotentMonoid_826
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
d_trans_1172 = T_IsIdempotentMonoid_826
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsIdempotentMonoid.∙-cong
d_'8729''45'cong_1174 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentMonoid_826 ->
  Bool ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8729''45'cong_1174 :: T_IsIdempotentMonoid_826
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong_1174 = T_IsIdempotentMonoid_826
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsIdempotentMonoid.∙-congʳ
d_'8729''45'cong'691'_1176 ::
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentMonoid_826 ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8729''45'cong'691'_1176 :: (Bool -> Bool -> Bool)
-> Bool
-> T_IsIdempotentMonoid_826
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong'691'_1176 = (Bool -> Bool -> Bool)
-> Bool
-> T_IsIdempotentMonoid_826
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsIdempotentMonoid.∙-congˡ
d_'8729''45'cong'737'_1178 ::
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentMonoid_826 ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8729''45'cong'737'_1178 :: (Bool -> Bool -> Bool)
-> Bool
-> T_IsIdempotentMonoid_826
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong'737'_1178 = (Bool -> Bool -> Bool)
-> Bool
-> T_IsIdempotentMonoid_826
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsIdempotentSemiring.*-assoc
d_'42''45'assoc_1182 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentSemiring_1998 ->
  Bool ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'42''45'assoc_1182 :: T_IsIdempotentSemiring_1998
-> Bool -> Bool -> Bool -> T__'8801'__12
d_'42''45'assoc_1182 = T_IsIdempotentSemiring_1998
-> Bool -> Bool -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsIdempotentSemiring.*-cong
d_'42''45'cong_1184 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentSemiring_1998 ->
  Bool ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'42''45'cong_1184 :: T_IsIdempotentSemiring_1998
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
d_'42''45'cong_1184 = T_IsIdempotentSemiring_1998
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsIdempotentSemiring.∙-congʳ
d_'8729''45'cong'691'_1186 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentSemiring_1998 ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8729''45'cong'691'_1186 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> T_IsIdempotentSemiring_1998
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong'691'_1186 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> T_IsIdempotentSemiring_1998
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsIdempotentSemiring.∙-congˡ
d_'8729''45'cong'737'_1188 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentSemiring_1998 ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8729''45'cong'737'_1188 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> T_IsIdempotentSemiring_1998
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong'737'_1188 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> T_IsIdempotentSemiring_1998
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsIdempotentSemiring.*-identity
d_'42''45'identity_1190 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentSemiring_1998 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'42''45'identity_1190 :: T_IsIdempotentSemiring_1998 -> T_Σ_14
d_'42''45'identity_1190 T_IsIdempotentSemiring_1998
v0
  = (T_IsSemiringWithoutAnnihilatingZero_1536 -> T_Σ_14)
-> Any -> T_Σ_14
forall a b. a -> b
coe
      T_IsSemiringWithoutAnnihilatingZero_1536 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_'42''45'identity_1562
      ((T_IsSemiring_1640 -> T_IsSemiringWithoutAnnihilatingZero_1536)
-> Any -> Any
forall a b. a -> b
coe
         T_IsSemiring_1640 -> T_IsSemiringWithoutAnnihilatingZero_1536
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1654
         ((T_IsIdempotentSemiring_1998 -> T_IsSemiring_1640) -> Any -> Any
forall a b. a -> b
coe T_IsIdempotentSemiring_1998 -> T_IsSemiring_1640
MAlonzo.Code.Algebra.Structures.d_isSemiring_2012 (T_IsIdempotentSemiring_1998 -> Any
forall a b. a -> b
coe T_IsIdempotentSemiring_1998
v0)))
-- Data.Bool.Properties._.IsIdempotentSemiring.identityʳ
d_identity'691'_1192 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentSemiring_1998 ->
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_identity'691'_1192 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> T_IsIdempotentSemiring_1998
-> Bool
-> T__'8801'__12
d_identity'691'_1192 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> T_IsIdempotentSemiring_1998
-> Bool
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsIdempotentSemiring.identityˡ
d_identity'737'_1194 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentSemiring_1998 ->
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_identity'737'_1194 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> T_IsIdempotentSemiring_1998
-> Bool
-> T__'8801'__12
d_identity'737'_1194 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> T_IsIdempotentSemiring_1998
-> Bool
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsIdempotentSemiring.*-isMagma
d_'42''45'isMagma_1196 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentSemiring_1998 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_178
d_'42''45'isMagma_1196 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> T_IsIdempotentSemiring_1998
-> T_IsMagma_178
d_'42''45'isMagma_1196 ~Bool -> Bool -> Bool
v0 ~Bool -> Bool -> Bool
v1 ~Bool
v2 ~Bool
v3 T_IsIdempotentSemiring_1998
v4
  = T_IsIdempotentSemiring_1998 -> T_IsMagma_178
du_'42''45'isMagma_1196 T_IsIdempotentSemiring_1998
v4
du_'42''45'isMagma_1196 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentSemiring_1998 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_178
du_'42''45'isMagma_1196 :: T_IsIdempotentSemiring_1998 -> T_IsMagma_178
du_'42''45'isMagma_1196 T_IsIdempotentSemiring_1998
v0
  = let v1 :: T_IsSemiring_1640
v1
          = T_IsIdempotentSemiring_1998 -> T_IsSemiring_1640
MAlonzo.Code.Algebra.Structures.d_isSemiring_2012 (T_IsIdempotentSemiring_1998 -> T_IsIdempotentSemiring_1998
forall a b. a -> b
coe T_IsIdempotentSemiring_1998
v0) in
    Any -> T_IsMagma_178
forall a b. a -> b
coe
      ((T_IsSemiringWithoutAnnihilatingZero_1536 -> T_IsMagma_178)
-> Any -> Any
forall a b. a -> b
coe
         T_IsSemiringWithoutAnnihilatingZero_1536 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.du_'42''45'isMagma_1614
         ((T_IsSemiring_1640 -> T_IsSemiringWithoutAnnihilatingZero_1536)
-> Any -> Any
forall a b. a -> b
coe
            T_IsSemiring_1640 -> T_IsSemiringWithoutAnnihilatingZero_1536
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1654
            (T_IsSemiring_1640 -> Any
forall a b. a -> b
coe T_IsSemiring_1640
v1)))
-- Data.Bool.Properties._.IsIdempotentSemiring.*-isMonoid
d_'42''45'isMonoid_1198 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentSemiring_1998 ->
  MAlonzo.Code.Algebra.Structures.T_IsMonoid_712
d_'42''45'isMonoid_1198 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> T_IsIdempotentSemiring_1998
-> T_IsMonoid_712
d_'42''45'isMonoid_1198 ~Bool -> Bool -> Bool
v0 ~Bool -> Bool -> Bool
v1 ~Bool
v2 ~Bool
v3 T_IsIdempotentSemiring_1998
v4
  = T_IsIdempotentSemiring_1998 -> T_IsMonoid_712
du_'42''45'isMonoid_1198 T_IsIdempotentSemiring_1998
v4
du_'42''45'isMonoid_1198 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentSemiring_1998 ->
  MAlonzo.Code.Algebra.Structures.T_IsMonoid_712
du_'42''45'isMonoid_1198 :: T_IsIdempotentSemiring_1998 -> T_IsMonoid_712
du_'42''45'isMonoid_1198 T_IsIdempotentSemiring_1998
v0
  = let v1 :: T_IsSemiring_1640
v1
          = T_IsIdempotentSemiring_1998 -> T_IsSemiring_1640
MAlonzo.Code.Algebra.Structures.d_isSemiring_2012 (T_IsIdempotentSemiring_1998 -> T_IsIdempotentSemiring_1998
forall a b. a -> b
coe T_IsIdempotentSemiring_1998
v0) in
    Any -> T_IsMonoid_712
forall a b. a -> b
coe
      ((T_IsSemiringWithoutAnnihilatingZero_1536 -> T_IsMonoid_712)
-> Any -> Any
forall a b. a -> b
coe
         T_IsSemiringWithoutAnnihilatingZero_1536 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.du_'42''45'isMonoid_1618
         ((T_IsSemiring_1640 -> T_IsSemiringWithoutAnnihilatingZero_1536)
-> Any -> Any
forall a b. a -> b
coe
            T_IsSemiring_1640 -> T_IsSemiringWithoutAnnihilatingZero_1536
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1654
            (T_IsSemiring_1640 -> Any
forall a b. a -> b
coe T_IsSemiring_1640
v1)))
-- Data.Bool.Properties._.IsIdempotentSemiring.*-isSemigroup
d_'42''45'isSemigroup_1200 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentSemiring_1998 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_488
d_'42''45'isSemigroup_1200 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> T_IsIdempotentSemiring_1998
-> T_IsSemigroup_488
d_'42''45'isSemigroup_1200 ~Bool -> Bool -> Bool
v0 ~Bool -> Bool -> Bool
v1 ~Bool
v2 ~Bool
v3 T_IsIdempotentSemiring_1998
v4
  = T_IsIdempotentSemiring_1998 -> T_IsSemigroup_488
du_'42''45'isSemigroup_1200 T_IsIdempotentSemiring_1998
v4
du_'42''45'isSemigroup_1200 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentSemiring_1998 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_488
du_'42''45'isSemigroup_1200 :: T_IsIdempotentSemiring_1998 -> T_IsSemigroup_488
du_'42''45'isSemigroup_1200 T_IsIdempotentSemiring_1998
v0
  = let v1 :: T_IsSemiring_1640
v1
          = T_IsIdempotentSemiring_1998 -> T_IsSemiring_1640
MAlonzo.Code.Algebra.Structures.d_isSemiring_2012 (T_IsIdempotentSemiring_1998 -> T_IsIdempotentSemiring_1998
forall a b. a -> b
coe T_IsIdempotentSemiring_1998
v0) in
    Any -> T_IsSemigroup_488
forall a b. a -> b
coe
      ((T_IsSemiringWithoutAnnihilatingZero_1536 -> T_IsSemigroup_488)
-> Any -> Any
forall a b. a -> b
coe
         T_IsSemiringWithoutAnnihilatingZero_1536 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.du_'42''45'isSemigroup_1616
         ((T_IsSemiring_1640 -> T_IsSemiringWithoutAnnihilatingZero_1536)
-> Any -> Any
forall a b. a -> b
coe
            T_IsSemiring_1640 -> T_IsSemiringWithoutAnnihilatingZero_1536
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1654
            (T_IsSemiring_1640 -> Any
forall a b. a -> b
coe T_IsSemiring_1640
v1)))
-- Data.Bool.Properties._.IsIdempotentSemiring.assoc
d_assoc_1202 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentSemiring_1998 ->
  Bool ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_assoc_1202 :: T_IsIdempotentSemiring_1998
-> Bool -> Bool -> Bool -> T__'8801'__12
d_assoc_1202 = T_IsIdempotentSemiring_1998
-> Bool -> Bool -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsIdempotentSemiring.comm
d_comm_1204 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentSemiring_1998 ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_comm_1204 :: T_IsIdempotentSemiring_1998 -> Bool -> Bool -> T__'8801'__12
d_comm_1204 = T_IsIdempotentSemiring_1998 -> Bool -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsIdempotentSemiring.∙-cong
d_'8729''45'cong_1206 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentSemiring_1998 ->
  Bool ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8729''45'cong_1206 :: T_IsIdempotentSemiring_1998
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong_1206 = T_IsIdempotentSemiring_1998
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsIdempotentSemiring.∙-congʳ
d_'8729''45'cong'691'_1208 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentSemiring_1998 ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8729''45'cong'691'_1208 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> T_IsIdempotentSemiring_1998
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong'691'_1208 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> T_IsIdempotentSemiring_1998
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsIdempotentSemiring.∙-congˡ
d_'8729''45'cong'737'_1210 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentSemiring_1998 ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8729''45'cong'737'_1210 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> T_IsIdempotentSemiring_1998
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong'737'_1210 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> T_IsIdempotentSemiring_1998
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsIdempotentSemiring.+-idem
d_'43''45'idem_1212 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentSemiring_1998 ->
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'43''45'idem_1212 :: T_IsIdempotentSemiring_1998 -> Bool -> T__'8801'__12
d_'43''45'idem_1212 = T_IsIdempotentSemiring_1998 -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsIdempotentSemiring.identity
d_identity_1214 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentSemiring_1998 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_identity_1214 :: T_IsIdempotentSemiring_1998 -> T_Σ_14
d_identity_1214 T_IsIdempotentSemiring_1998
v0
  = (T_IsMonoid_712 -> T_Σ_14) -> Any -> T_Σ_14
forall a b. a -> b
coe
      T_IsMonoid_712 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_identity_724
      ((T_IsCommutativeMonoid_764 -> T_IsMonoid_712) -> Any -> Any
forall a b. a -> b
coe
         T_IsCommutativeMonoid_764 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_774
         ((T_IsSemiringWithoutAnnihilatingZero_1536
 -> T_IsCommutativeMonoid_764)
-> Any -> Any
forall a b. a -> b
coe
            T_IsSemiringWithoutAnnihilatingZero_1536
-> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1556
            ((T_IsSemiring_1640 -> T_IsSemiringWithoutAnnihilatingZero_1536)
-> Any -> Any
forall a b. a -> b
coe
               T_IsSemiring_1640 -> T_IsSemiringWithoutAnnihilatingZero_1536
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1654
               ((T_IsIdempotentSemiring_1998 -> T_IsSemiring_1640) -> Any -> Any
forall a b. a -> b
coe T_IsIdempotentSemiring_1998 -> T_IsSemiring_1640
MAlonzo.Code.Algebra.Structures.d_isSemiring_2012 (T_IsIdempotentSemiring_1998 -> Any
forall a b. a -> b
coe T_IsIdempotentSemiring_1998
v0)))))
-- Data.Bool.Properties._.IsIdempotentSemiring.identityʳ
d_identity'691'_1216 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentSemiring_1998 ->
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_identity'691'_1216 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> T_IsIdempotentSemiring_1998
-> Bool
-> T__'8801'__12
d_identity'691'_1216 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> T_IsIdempotentSemiring_1998
-> Bool
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsIdempotentSemiring.identityˡ
d_identity'737'_1218 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentSemiring_1998 ->
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_identity'737'_1218 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> T_IsIdempotentSemiring_1998
-> Bool
-> T__'8801'__12
d_identity'737'_1218 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> T_IsIdempotentSemiring_1998
-> Bool
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsIdempotentSemiring.isBand
d_isBand_1220 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentSemiring_1998 ->
  MAlonzo.Code.Algebra.Structures.T_IsBand_526
d_isBand_1220 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> T_IsIdempotentSemiring_1998
-> T_IsBand_526
d_isBand_1220 ~Bool -> Bool -> Bool
v0 ~Bool -> Bool -> Bool
v1 ~Bool
v2 ~Bool
v3 T_IsIdempotentSemiring_1998
v4 = T_IsIdempotentSemiring_1998 -> T_IsBand_526
du_isBand_1220 T_IsIdempotentSemiring_1998
v4
du_isBand_1220 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentSemiring_1998 ->
  MAlonzo.Code.Algebra.Structures.T_IsBand_526
du_isBand_1220 :: T_IsIdempotentSemiring_1998 -> T_IsBand_526
du_isBand_1220 T_IsIdempotentSemiring_1998
v0
  = let v1 :: Any
v1
          = (T_IsIdempotentSemiring_1998
 -> T_IsIdempotentCommutativeMonoid_884)
-> Any -> Any
forall a b. a -> b
coe
              T_IsIdempotentSemiring_1998 -> T_IsIdempotentCommutativeMonoid_884
MAlonzo.Code.Algebra.Structures.du_'43''45'isIdempotentCommutativeMonoid_2100
              (T_IsIdempotentSemiring_1998 -> Any
forall a b. a -> b
coe T_IsIdempotentSemiring_1998
v0) in
    Any -> T_IsBand_526
forall a b. a -> b
coe
      ((T_IsIdempotentMonoid_826 -> T_IsBand_526) -> Any -> Any
forall a b. a -> b
coe
         T_IsIdempotentMonoid_826 -> T_IsBand_526
MAlonzo.Code.Algebra.Structures.du_isBand_876
         ((T_IsIdempotentCommutativeMonoid_884 -> T_IsIdempotentMonoid_826)
-> Any -> Any
forall a b. a -> b
coe
            T_IsIdempotentCommutativeMonoid_884 -> T_IsIdempotentMonoid_826
MAlonzo.Code.Algebra.Structures.du_isIdempotentMonoid_942
            (Any -> Any
forall a b. a -> b
coe Any
v1)))
-- Data.Bool.Properties._.IsIdempotentSemiring.isCommutativeBand
d_isCommutativeBand_1222 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentSemiring_1998 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_612
d_isCommutativeBand_1222 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> T_IsIdempotentSemiring_1998
-> T_IsCommutativeBand_612
d_isCommutativeBand_1222 ~Bool -> Bool -> Bool
v0 ~Bool -> Bool -> Bool
v1 ~Bool
v2 ~Bool
v3 T_IsIdempotentSemiring_1998
v4
  = T_IsIdempotentSemiring_1998 -> T_IsCommutativeBand_612
du_isCommutativeBand_1222 T_IsIdempotentSemiring_1998
v4
du_isCommutativeBand_1222 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentSemiring_1998 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_612
du_isCommutativeBand_1222 :: T_IsIdempotentSemiring_1998 -> T_IsCommutativeBand_612
du_isCommutativeBand_1222 T_IsIdempotentSemiring_1998
v0
  = (T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeBand_612)
-> Any -> T_IsCommutativeBand_612
forall a b. a -> b
coe
      T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeBand_612
MAlonzo.Code.Algebra.Structures.du_isCommutativeBand_948
      ((T_IsIdempotentSemiring_1998
 -> T_IsIdempotentCommutativeMonoid_884)
-> Any -> Any
forall a b. a -> b
coe
         T_IsIdempotentSemiring_1998 -> T_IsIdempotentCommutativeMonoid_884
MAlonzo.Code.Algebra.Structures.du_'43''45'isIdempotentCommutativeMonoid_2100
         (T_IsIdempotentSemiring_1998 -> Any
forall a b. a -> b
coe T_IsIdempotentSemiring_1998
v0))
-- Data.Bool.Properties._.IsIdempotentSemiring.isCommutativeMagma
d_isCommutativeMagma_1224 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentSemiring_1998 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMagma_214
d_isCommutativeMagma_1224 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> T_IsIdempotentSemiring_1998
-> T_IsCommutativeMagma_214
d_isCommutativeMagma_1224 ~Bool -> Bool -> Bool
v0 ~Bool -> Bool -> Bool
v1 ~Bool
v2 ~Bool
v3 T_IsIdempotentSemiring_1998
v4
  = T_IsIdempotentSemiring_1998 -> T_IsCommutativeMagma_214
du_isCommutativeMagma_1224 T_IsIdempotentSemiring_1998
v4
du_isCommutativeMagma_1224 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentSemiring_1998 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMagma_214
du_isCommutativeMagma_1224 :: T_IsIdempotentSemiring_1998 -> T_IsCommutativeMagma_214
du_isCommutativeMagma_1224 T_IsIdempotentSemiring_1998
v0
  = let v1 :: T_IsSemiring_1640
v1
          = T_IsIdempotentSemiring_1998 -> T_IsSemiring_1640
MAlonzo.Code.Algebra.Structures.d_isSemiring_2012 (T_IsIdempotentSemiring_1998 -> T_IsIdempotentSemiring_1998
forall a b. a -> b
coe T_IsIdempotentSemiring_1998
v0) in
    Any -> T_IsCommutativeMagma_214
forall a b. a -> b
coe
      (let v2 :: T_IsSemiringWithoutAnnihilatingZero_1536
v2
             = T_IsSemiring_1640 -> T_IsSemiringWithoutAnnihilatingZero_1536
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1654
                 (T_IsSemiring_1640 -> T_IsSemiring_1640
forall a b. a -> b
coe T_IsSemiring_1640
v1) in
       Any -> Any
forall a b. a -> b
coe
         (let v3 :: T_IsCommutativeMonoid_764
v3
                = T_IsSemiringWithoutAnnihilatingZero_1536
-> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1556
                    (T_IsSemiringWithoutAnnihilatingZero_1536
-> T_IsSemiringWithoutAnnihilatingZero_1536
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1536
v2) in
          Any -> Any
forall a b. a -> b
coe
            ((T_IsCommutativeSemigroup_568 -> T_IsCommutativeMagma_214)
-> Any -> Any
forall a b. a -> b
coe
               T_IsCommutativeSemigroup_568 -> T_IsCommutativeMagma_214
MAlonzo.Code.Algebra.Structures.du_isCommutativeMagma_606
               ((T_IsCommutativeMonoid_764 -> T_IsCommutativeSemigroup_568)
-> Any -> Any
forall a b. a -> b
coe
                  T_IsCommutativeMonoid_764 -> T_IsCommutativeSemigroup_568
MAlonzo.Code.Algebra.Structures.du_isCommutativeSemigroup_814
                  (T_IsCommutativeMonoid_764 -> Any
forall a b. a -> b
coe T_IsCommutativeMonoid_764
v3)))))
-- Data.Bool.Properties._.IsIdempotentSemiring.+-isCommutativeMonoid
d_'43''45'isCommutativeMonoid_1226 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentSemiring_1998 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMonoid_764
d_'43''45'isCommutativeMonoid_1226 :: T_IsIdempotentSemiring_1998 -> T_IsCommutativeMonoid_764
d_'43''45'isCommutativeMonoid_1226 T_IsIdempotentSemiring_1998
v0
  = (T_IsSemiringWithoutAnnihilatingZero_1536
 -> T_IsCommutativeMonoid_764)
-> Any -> T_IsCommutativeMonoid_764
forall a b. a -> b
coe
      T_IsSemiringWithoutAnnihilatingZero_1536
-> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1556
      ((T_IsSemiring_1640 -> T_IsSemiringWithoutAnnihilatingZero_1536)
-> Any -> Any
forall a b. a -> b
coe
         T_IsSemiring_1640 -> T_IsSemiringWithoutAnnihilatingZero_1536
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1654
         ((T_IsIdempotentSemiring_1998 -> T_IsSemiring_1640) -> Any -> Any
forall a b. a -> b
coe T_IsIdempotentSemiring_1998 -> T_IsSemiring_1640
MAlonzo.Code.Algebra.Structures.d_isSemiring_2012 (T_IsIdempotentSemiring_1998 -> Any
forall a b. a -> b
coe T_IsIdempotentSemiring_1998
v0)))
-- Data.Bool.Properties._.IsIdempotentSemiring.isCommutativeSemigroup
d_isCommutativeSemigroup_1228 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentSemiring_1998 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_568
d_isCommutativeSemigroup_1228 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> T_IsIdempotentSemiring_1998
-> T_IsCommutativeSemigroup_568
d_isCommutativeSemigroup_1228 ~Bool -> Bool -> Bool
v0 ~Bool -> Bool -> Bool
v1 ~Bool
v2 ~Bool
v3 T_IsIdempotentSemiring_1998
v4
  = T_IsIdempotentSemiring_1998 -> T_IsCommutativeSemigroup_568
du_isCommutativeSemigroup_1228 T_IsIdempotentSemiring_1998
v4
du_isCommutativeSemigroup_1228 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentSemiring_1998 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_568
du_isCommutativeSemigroup_1228 :: T_IsIdempotentSemiring_1998 -> T_IsCommutativeSemigroup_568
du_isCommutativeSemigroup_1228 T_IsIdempotentSemiring_1998
v0
  = let v1 :: T_IsSemiring_1640
v1
          = T_IsIdempotentSemiring_1998 -> T_IsSemiring_1640
MAlonzo.Code.Algebra.Structures.d_isSemiring_2012 (T_IsIdempotentSemiring_1998 -> T_IsIdempotentSemiring_1998
forall a b. a -> b
coe T_IsIdempotentSemiring_1998
v0) in
    Any -> T_IsCommutativeSemigroup_568
forall a b. a -> b
coe
      (let v2 :: T_IsSemiringWithoutAnnihilatingZero_1536
v2
             = T_IsSemiring_1640 -> T_IsSemiringWithoutAnnihilatingZero_1536
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1654
                 (T_IsSemiring_1640 -> T_IsSemiring_1640
forall a b. a -> b
coe T_IsSemiring_1640
v1) in
       Any -> Any
forall a b. a -> b
coe
         ((T_IsCommutativeMonoid_764 -> T_IsCommutativeSemigroup_568)
-> Any -> Any
forall a b. a -> b
coe
            T_IsCommutativeMonoid_764 -> T_IsCommutativeSemigroup_568
MAlonzo.Code.Algebra.Structures.du_isCommutativeSemigroup_814
            ((T_IsSemiringWithoutAnnihilatingZero_1536
 -> T_IsCommutativeMonoid_764)
-> Any -> Any
forall a b. a -> b
coe
               T_IsSemiringWithoutAnnihilatingZero_1536
-> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1556
               (T_IsSemiringWithoutAnnihilatingZero_1536 -> Any
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1536
v2))))
-- Data.Bool.Properties._.IsIdempotentSemiring.+-isIdempotentCommutativeMonoid
d_'43''45'isIdempotentCommutativeMonoid_1230 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentSemiring_1998 ->
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884
d_'43''45'isIdempotentCommutativeMonoid_1230 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> T_IsIdempotentSemiring_1998
-> T_IsIdempotentCommutativeMonoid_884
d_'43''45'isIdempotentCommutativeMonoid_1230 Bool -> Bool -> Bool
v0 Bool -> Bool -> Bool
v1 Bool
v2 Bool
v3 T_IsIdempotentSemiring_1998
v4
  = (T_IsIdempotentSemiring_1998
 -> T_IsIdempotentCommutativeMonoid_884)
-> T_IsIdempotentSemiring_1998
-> T_IsIdempotentCommutativeMonoid_884
forall a b. a -> b
coe
      T_IsIdempotentSemiring_1998 -> T_IsIdempotentCommutativeMonoid_884
MAlonzo.Code.Algebra.Structures.du_'43''45'isIdempotentCommutativeMonoid_2100
      T_IsIdempotentSemiring_1998
v4
-- Data.Bool.Properties._.IsIdempotentSemiring.isIdempotentMonoid
d_isIdempotentMonoid_1232 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentSemiring_1998 ->
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentMonoid_826
d_isIdempotentMonoid_1232 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> T_IsIdempotentSemiring_1998
-> T_IsIdempotentMonoid_826
d_isIdempotentMonoid_1232 ~Bool -> Bool -> Bool
v0 ~Bool -> Bool -> Bool
v1 ~Bool
v2 ~Bool
v3 T_IsIdempotentSemiring_1998
v4
  = T_IsIdempotentSemiring_1998 -> T_IsIdempotentMonoid_826
du_isIdempotentMonoid_1232 T_IsIdempotentSemiring_1998
v4
du_isIdempotentMonoid_1232 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentSemiring_1998 ->
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentMonoid_826
du_isIdempotentMonoid_1232 :: T_IsIdempotentSemiring_1998 -> T_IsIdempotentMonoid_826
du_isIdempotentMonoid_1232 T_IsIdempotentSemiring_1998
v0
  = (T_IsIdempotentCommutativeMonoid_884 -> T_IsIdempotentMonoid_826)
-> Any -> T_IsIdempotentMonoid_826
forall a b. a -> b
coe
      T_IsIdempotentCommutativeMonoid_884 -> T_IsIdempotentMonoid_826
MAlonzo.Code.Algebra.Structures.du_isIdempotentMonoid_942
      ((T_IsIdempotentSemiring_1998
 -> T_IsIdempotentCommutativeMonoid_884)
-> Any -> Any
forall a b. a -> b
coe
         T_IsIdempotentSemiring_1998 -> T_IsIdempotentCommutativeMonoid_884
MAlonzo.Code.Algebra.Structures.du_'43''45'isIdempotentCommutativeMonoid_2100
         (T_IsIdempotentSemiring_1998 -> Any
forall a b. a -> b
coe T_IsIdempotentSemiring_1998
v0))
-- Data.Bool.Properties._.IsIdempotentSemiring.isMagma
d_isMagma_1234 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentSemiring_1998 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_178
d_isMagma_1234 :: T_IsIdempotentSemiring_1998 -> T_IsMagma_178
d_isMagma_1234 T_IsIdempotentSemiring_1998
v0
  = (T_IsSemigroup_488 -> T_IsMagma_178) -> Any -> T_IsMagma_178
forall a b. a -> b
coe
      T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496
      ((T_IsMonoid_712 -> T_IsSemigroup_488) -> Any -> Any
forall a b. a -> b
coe
         T_IsMonoid_712 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_722
         ((T_IsCommutativeMonoid_764 -> T_IsMonoid_712) -> Any -> Any
forall a b. a -> b
coe
            T_IsCommutativeMonoid_764 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_774
            ((T_IsSemiringWithoutAnnihilatingZero_1536
 -> T_IsCommutativeMonoid_764)
-> Any -> Any
forall a b. a -> b
coe
               T_IsSemiringWithoutAnnihilatingZero_1536
-> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1556
               ((T_IsSemiring_1640 -> T_IsSemiringWithoutAnnihilatingZero_1536)
-> Any -> Any
forall a b. a -> b
coe
                  T_IsSemiring_1640 -> T_IsSemiringWithoutAnnihilatingZero_1536
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1654
                  ((T_IsIdempotentSemiring_1998 -> T_IsSemiring_1640) -> Any -> Any
forall a b. a -> b
coe
                     T_IsIdempotentSemiring_1998 -> T_IsSemiring_1640
MAlonzo.Code.Algebra.Structures.d_isSemiring_2012 (T_IsIdempotentSemiring_1998 -> Any
forall a b. a -> b
coe T_IsIdempotentSemiring_1998
v0))))))
-- Data.Bool.Properties._.IsIdempotentSemiring.isMonoid
d_isMonoid_1236 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentSemiring_1998 ->
  MAlonzo.Code.Algebra.Structures.T_IsMonoid_712
d_isMonoid_1236 :: T_IsIdempotentSemiring_1998 -> T_IsMonoid_712
d_isMonoid_1236 T_IsIdempotentSemiring_1998
v0
  = (T_IsCommutativeMonoid_764 -> T_IsMonoid_712)
-> Any -> T_IsMonoid_712
forall a b. a -> b
coe
      T_IsCommutativeMonoid_764 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_774
      ((T_IsSemiringWithoutAnnihilatingZero_1536
 -> T_IsCommutativeMonoid_764)
-> Any -> Any
forall a b. a -> b
coe
         T_IsSemiringWithoutAnnihilatingZero_1536
-> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1556
         ((T_IsSemiring_1640 -> T_IsSemiringWithoutAnnihilatingZero_1536)
-> Any -> Any
forall a b. a -> b
coe
            T_IsSemiring_1640 -> T_IsSemiringWithoutAnnihilatingZero_1536
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1654
            ((T_IsIdempotentSemiring_1998 -> T_IsSemiring_1640) -> Any -> Any
forall a b. a -> b
coe T_IsIdempotentSemiring_1998 -> T_IsSemiring_1640
MAlonzo.Code.Algebra.Structures.d_isSemiring_2012 (T_IsIdempotentSemiring_1998 -> Any
forall a b. a -> b
coe T_IsIdempotentSemiring_1998
v0))))
-- Data.Bool.Properties._.IsIdempotentSemiring.isSemigroup
d_isSemigroup_1238 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentSemiring_1998 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_488
d_isSemigroup_1238 :: T_IsIdempotentSemiring_1998 -> T_IsSemigroup_488
d_isSemigroup_1238 T_IsIdempotentSemiring_1998
v0
  = (T_IsMonoid_712 -> T_IsSemigroup_488) -> Any -> T_IsSemigroup_488
forall a b. a -> b
coe
      T_IsMonoid_712 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_722
      ((T_IsCommutativeMonoid_764 -> T_IsMonoid_712) -> Any -> Any
forall a b. a -> b
coe
         T_IsCommutativeMonoid_764 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_774
         ((T_IsSemiringWithoutAnnihilatingZero_1536
 -> T_IsCommutativeMonoid_764)
-> Any -> Any
forall a b. a -> b
coe
            T_IsSemiringWithoutAnnihilatingZero_1536
-> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1556
            ((T_IsSemiring_1640 -> T_IsSemiringWithoutAnnihilatingZero_1536)
-> Any -> Any
forall a b. a -> b
coe
               T_IsSemiring_1640 -> T_IsSemiringWithoutAnnihilatingZero_1536
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1654
               ((T_IsIdempotentSemiring_1998 -> T_IsSemiring_1640) -> Any -> Any
forall a b. a -> b
coe T_IsIdempotentSemiring_1998 -> T_IsSemiring_1640
MAlonzo.Code.Algebra.Structures.d_isSemiring_2012 (T_IsIdempotentSemiring_1998 -> Any
forall a b. a -> b
coe T_IsIdempotentSemiring_1998
v0)))))
-- Data.Bool.Properties._.IsIdempotentSemiring.isUnitalMagma
d_isUnitalMagma_1240 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentSemiring_1998 ->
  MAlonzo.Code.Algebra.Structures.T_IsUnitalMagma_666
d_isUnitalMagma_1240 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> T_IsIdempotentSemiring_1998
-> T_IsUnitalMagma_666
d_isUnitalMagma_1240 ~Bool -> Bool -> Bool
v0 ~Bool -> Bool -> Bool
v1 ~Bool
v2 ~Bool
v3 T_IsIdempotentSemiring_1998
v4 = T_IsIdempotentSemiring_1998 -> T_IsUnitalMagma_666
du_isUnitalMagma_1240 T_IsIdempotentSemiring_1998
v4
du_isUnitalMagma_1240 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentSemiring_1998 ->
  MAlonzo.Code.Algebra.Structures.T_IsUnitalMagma_666
du_isUnitalMagma_1240 :: T_IsIdempotentSemiring_1998 -> T_IsUnitalMagma_666
du_isUnitalMagma_1240 T_IsIdempotentSemiring_1998
v0
  = let v1 :: T_IsSemiring_1640
v1
          = T_IsIdempotentSemiring_1998 -> T_IsSemiring_1640
MAlonzo.Code.Algebra.Structures.d_isSemiring_2012 (T_IsIdempotentSemiring_1998 -> T_IsIdempotentSemiring_1998
forall a b. a -> b
coe T_IsIdempotentSemiring_1998
v0) in
    Any -> T_IsUnitalMagma_666
forall a b. a -> b
coe
      (let v2 :: T_IsSemiringWithoutAnnihilatingZero_1536
v2
             = T_IsSemiring_1640 -> T_IsSemiringWithoutAnnihilatingZero_1536
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1654
                 (T_IsSemiring_1640 -> T_IsSemiring_1640
forall a b. a -> b
coe T_IsSemiring_1640
v1) in
       Any -> Any
forall a b. a -> b
coe
         (let v3 :: T_IsCommutativeMonoid_764
v3
                = T_IsSemiringWithoutAnnihilatingZero_1536
-> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1556
                    (T_IsSemiringWithoutAnnihilatingZero_1536
-> T_IsSemiringWithoutAnnihilatingZero_1536
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1536
v2) in
          Any -> Any
forall a b. a -> b
coe
            ((T_IsMonoid_712 -> T_IsUnitalMagma_666) -> Any -> Any
forall a b. a -> b
coe
               T_IsMonoid_712 -> T_IsUnitalMagma_666
MAlonzo.Code.Algebra.Structures.du_isUnitalMagma_756
               ((T_IsCommutativeMonoid_764 -> T_IsMonoid_712) -> Any -> Any
forall a b. a -> b
coe T_IsCommutativeMonoid_764 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_774 (T_IsCommutativeMonoid_764 -> Any
forall a b. a -> b
coe T_IsCommutativeMonoid_764
v3)))))
-- Data.Bool.Properties._.IsIdempotentSemiring.distrib
d_distrib_1242 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentSemiring_1998 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_distrib_1242 :: T_IsIdempotentSemiring_1998 -> T_Σ_14
d_distrib_1242 T_IsIdempotentSemiring_1998
v0
  = (T_IsSemiringWithoutAnnihilatingZero_1536 -> T_Σ_14)
-> Any -> T_Σ_14
forall a b. a -> b
coe
      T_IsSemiringWithoutAnnihilatingZero_1536 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_distrib_1564
      ((T_IsSemiring_1640 -> T_IsSemiringWithoutAnnihilatingZero_1536)
-> Any -> Any
forall a b. a -> b
coe
         T_IsSemiring_1640 -> T_IsSemiringWithoutAnnihilatingZero_1536
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1654
         ((T_IsIdempotentSemiring_1998 -> T_IsSemiring_1640) -> Any -> Any
forall a b. a -> b
coe T_IsIdempotentSemiring_1998 -> T_IsSemiring_1640
MAlonzo.Code.Algebra.Structures.d_isSemiring_2012 (T_IsIdempotentSemiring_1998 -> Any
forall a b. a -> b
coe T_IsIdempotentSemiring_1998
v0)))
-- Data.Bool.Properties._.IsIdempotentSemiring.distribʳ
d_distrib'691'_1244 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentSemiring_1998 ->
  Bool ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_distrib'691'_1244 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> T_IsIdempotentSemiring_1998
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
d_distrib'691'_1244 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> T_IsIdempotentSemiring_1998
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsIdempotentSemiring.distribˡ
d_distrib'737'_1246 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentSemiring_1998 ->
  Bool ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_distrib'737'_1246 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> T_IsIdempotentSemiring_1998
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
d_distrib'737'_1246 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> T_IsIdempotentSemiring_1998
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsIdempotentSemiring.isEquivalence
d_isEquivalence_1248 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentSemiring_1998 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
d_isEquivalence_1248 :: T_IsIdempotentSemiring_1998 -> T_IsEquivalence_28
d_isEquivalence_1248 T_IsIdempotentSemiring_1998
v0
  = (T_IsMagma_178 -> T_IsEquivalence_28) -> Any -> T_IsEquivalence_28
forall a b. a -> b
coe
      T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186
      ((T_IsSemigroup_488 -> T_IsMagma_178) -> Any -> Any
forall a b. a -> b
coe
         T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496
         ((T_IsMonoid_712 -> T_IsSemigroup_488) -> Any -> Any
forall a b. a -> b
coe
            T_IsMonoid_712 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_722
            ((T_IsCommutativeMonoid_764 -> T_IsMonoid_712) -> Any -> Any
forall a b. a -> b
coe
               T_IsCommutativeMonoid_764 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_774
               ((T_IsSemiringWithoutAnnihilatingZero_1536
 -> T_IsCommutativeMonoid_764)
-> Any -> Any
forall a b. a -> b
coe
                  T_IsSemiringWithoutAnnihilatingZero_1536
-> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1556
                  ((T_IsSemiring_1640 -> T_IsSemiringWithoutAnnihilatingZero_1536)
-> Any -> Any
forall a b. a -> b
coe
                     T_IsSemiring_1640 -> T_IsSemiringWithoutAnnihilatingZero_1536
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1654
                     ((T_IsIdempotentSemiring_1998 -> T_IsSemiring_1640) -> Any -> Any
forall a b. a -> b
coe
                        T_IsIdempotentSemiring_1998 -> T_IsSemiring_1640
MAlonzo.Code.Algebra.Structures.d_isSemiring_2012 (T_IsIdempotentSemiring_1998 -> Any
forall a b. a -> b
coe T_IsIdempotentSemiring_1998
v0)))))))
-- Data.Bool.Properties._.IsIdempotentSemiring.isNearSemiring
d_isNearSemiring_1250 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentSemiring_1998 ->
  MAlonzo.Code.Algebra.Structures.T_IsNearSemiring_1260
d_isNearSemiring_1250 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> T_IsIdempotentSemiring_1998
-> T_IsNearSemiring_1260
d_isNearSemiring_1250 ~Bool -> Bool -> Bool
v0 ~Bool -> Bool -> Bool
v1 ~Bool
v2 ~Bool
v3 T_IsIdempotentSemiring_1998
v4
  = T_IsIdempotentSemiring_1998 -> T_IsNearSemiring_1260
du_isNearSemiring_1250 T_IsIdempotentSemiring_1998
v4
du_isNearSemiring_1250 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentSemiring_1998 ->
  MAlonzo.Code.Algebra.Structures.T_IsNearSemiring_1260
du_isNearSemiring_1250 :: T_IsIdempotentSemiring_1998 -> T_IsNearSemiring_1260
du_isNearSemiring_1250 T_IsIdempotentSemiring_1998
v0
  = let v1 :: T_IsSemiring_1640
v1
          = T_IsIdempotentSemiring_1998 -> T_IsSemiring_1640
MAlonzo.Code.Algebra.Structures.d_isSemiring_2012 (T_IsIdempotentSemiring_1998 -> T_IsIdempotentSemiring_1998
forall a b. a -> b
coe T_IsIdempotentSemiring_1998
v0) in
    Any -> T_IsNearSemiring_1260
forall a b. a -> b
coe
      ((T_IsSemiringWithoutOne_1342 -> T_IsNearSemiring_1260)
-> Any -> Any
forall a b. a -> b
coe
         T_IsSemiringWithoutOne_1342 -> T_IsNearSemiring_1260
MAlonzo.Code.Algebra.Structures.du_isNearSemiring_1428
         ((T_IsSemiring_1640 -> T_IsSemiringWithoutOne_1342) -> Any -> Any
forall a b. a -> b
coe
            T_IsSemiring_1640 -> T_IsSemiringWithoutOne_1342
MAlonzo.Code.Algebra.Structures.du_isSemiringWithoutOne_1730
            (T_IsSemiring_1640 -> Any
forall a b. a -> b
coe T_IsSemiring_1640
v1)))
-- Data.Bool.Properties._.IsIdempotentSemiring.isPartialEquivalence
d_isPartialEquivalence_1252 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentSemiring_1998 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_1252 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> T_IsIdempotentSemiring_1998
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_1252 ~Bool -> Bool -> Bool
v0 ~Bool -> Bool -> Bool
v1 ~Bool
v2 ~Bool
v3 T_IsIdempotentSemiring_1998
v4
  = T_IsIdempotentSemiring_1998 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_1252 T_IsIdempotentSemiring_1998
v4
du_isPartialEquivalence_1252 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentSemiring_1998 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_1252 :: T_IsIdempotentSemiring_1998 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_1252 T_IsIdempotentSemiring_1998
v0
  = let v1 :: T_IsSemiring_1640
v1
          = T_IsIdempotentSemiring_1998 -> T_IsSemiring_1640
MAlonzo.Code.Algebra.Structures.d_isSemiring_2012 (T_IsIdempotentSemiring_1998 -> T_IsIdempotentSemiring_1998
forall a b. a -> b
coe T_IsIdempotentSemiring_1998
v0) in
    Any -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsSemiringWithoutAnnihilatingZero_1536
v2
             = T_IsSemiring_1640 -> T_IsSemiringWithoutAnnihilatingZero_1536
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1654
                 (T_IsSemiring_1640 -> T_IsSemiring_1640
forall a b. a -> b
coe T_IsSemiring_1640
v1) in
       Any -> Any
forall a b. a -> b
coe
         (let v3 :: T_IsCommutativeMonoid_764
v3
                = T_IsSemiringWithoutAnnihilatingZero_1536
-> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1556
                    (T_IsSemiringWithoutAnnihilatingZero_1536
-> T_IsSemiringWithoutAnnihilatingZero_1536
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1536
v2) in
          Any -> Any
forall a b. a -> b
coe
            (let v4 :: T_IsMonoid_712
v4
                   = T_IsCommutativeMonoid_764 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_774 (T_IsCommutativeMonoid_764 -> T_IsCommutativeMonoid_764
forall a b. a -> b
coe T_IsCommutativeMonoid_764
v3) in
             Any -> Any
forall a b. a -> b
coe
               (let v5 :: T_IsSemigroup_488
v5
                      = T_IsMonoid_712 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_722 (T_IsMonoid_712 -> T_IsMonoid_712
forall a b. a -> b
coe T_IsMonoid_712
v4) in
                Any -> Any
forall a b. a -> b
coe
                  (let v6 :: T_IsMagma_178
v6 = T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496 (T_IsSemigroup_488 -> T_IsSemigroup_488
forall a b. a -> b
coe T_IsSemigroup_488
v5) in
                   Any -> Any
forall a b. a -> b
coe
                     ((T_IsEquivalence_28 -> T_IsPartialEquivalence_16) -> Any -> Any
forall a b. a -> b
coe
                        T_IsEquivalence_28 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_44
                        ((T_IsMagma_178 -> T_IsEquivalence_28) -> Any -> Any
forall a b. a -> b
coe
                           T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186 (T_IsMagma_178 -> Any
forall a b. a -> b
coe T_IsMagma_178
v6))))))))
-- Data.Bool.Properties._.IsIdempotentSemiring.isSemiring
d_isSemiring_1254 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentSemiring_1998 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemiring_1640
d_isSemiring_1254 :: T_IsIdempotentSemiring_1998 -> T_IsSemiring_1640
d_isSemiring_1254 T_IsIdempotentSemiring_1998
v0
  = (T_IsIdempotentSemiring_1998 -> T_IsSemiring_1640)
-> Any -> T_IsSemiring_1640
forall a b. a -> b
coe T_IsIdempotentSemiring_1998 -> T_IsSemiring_1640
MAlonzo.Code.Algebra.Structures.d_isSemiring_2012 (T_IsIdempotentSemiring_1998 -> Any
forall a b. a -> b
coe T_IsIdempotentSemiring_1998
v0)
-- Data.Bool.Properties._.IsIdempotentSemiring.isSemiringWithoutAnnihilatingZero
d_isSemiringWithoutAnnihilatingZero_1256 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentSemiring_1998 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutAnnihilatingZero_1536
d_isSemiringWithoutAnnihilatingZero_1256 :: T_IsIdempotentSemiring_1998
-> T_IsSemiringWithoutAnnihilatingZero_1536
d_isSemiringWithoutAnnihilatingZero_1256 T_IsIdempotentSemiring_1998
v0
  = (T_IsSemiring_1640 -> T_IsSemiringWithoutAnnihilatingZero_1536)
-> Any -> T_IsSemiringWithoutAnnihilatingZero_1536
forall a b. a -> b
coe
      T_IsSemiring_1640 -> T_IsSemiringWithoutAnnihilatingZero_1536
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1654
      ((T_IsIdempotentSemiring_1998 -> T_IsSemiring_1640) -> Any -> Any
forall a b. a -> b
coe T_IsIdempotentSemiring_1998 -> T_IsSemiring_1640
MAlonzo.Code.Algebra.Structures.d_isSemiring_2012 (T_IsIdempotentSemiring_1998 -> Any
forall a b. a -> b
coe T_IsIdempotentSemiring_1998
v0))
-- Data.Bool.Properties._.IsIdempotentSemiring.isSemiringWithoutOne
d_isSemiringWithoutOne_1258 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentSemiring_1998 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutOne_1342
d_isSemiringWithoutOne_1258 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> T_IsIdempotentSemiring_1998
-> T_IsSemiringWithoutOne_1342
d_isSemiringWithoutOne_1258 ~Bool -> Bool -> Bool
v0 ~Bool -> Bool -> Bool
v1 ~Bool
v2 ~Bool
v3 T_IsIdempotentSemiring_1998
v4
  = T_IsIdempotentSemiring_1998 -> T_IsSemiringWithoutOne_1342
du_isSemiringWithoutOne_1258 T_IsIdempotentSemiring_1998
v4
du_isSemiringWithoutOne_1258 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentSemiring_1998 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutOne_1342
du_isSemiringWithoutOne_1258 :: T_IsIdempotentSemiring_1998 -> T_IsSemiringWithoutOne_1342
du_isSemiringWithoutOne_1258 T_IsIdempotentSemiring_1998
v0
  = (T_IsSemiring_1640 -> T_IsSemiringWithoutOne_1342)
-> Any -> T_IsSemiringWithoutOne_1342
forall a b. a -> b
coe
      T_IsSemiring_1640 -> T_IsSemiringWithoutOne_1342
MAlonzo.Code.Algebra.Structures.du_isSemiringWithoutOne_1730
      ((T_IsIdempotentSemiring_1998 -> T_IsSemiring_1640) -> Any -> Any
forall a b. a -> b
coe T_IsIdempotentSemiring_1998 -> T_IsSemiring_1640
MAlonzo.Code.Algebra.Structures.d_isSemiring_2012 (T_IsIdempotentSemiring_1998 -> Any
forall a b. a -> b
coe T_IsIdempotentSemiring_1998
v0))
-- Data.Bool.Properties._.IsIdempotentSemiring.refl
d_refl_1260 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentSemiring_1998 ->
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_refl_1260 :: T_IsIdempotentSemiring_1998 -> Bool -> T__'8801'__12
d_refl_1260 = T_IsIdempotentSemiring_1998 -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsIdempotentSemiring.reflexive
d_reflexive_1262 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentSemiring_1998 ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_reflexive_1262 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> T_IsIdempotentSemiring_1998
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_reflexive_1262 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> T_IsIdempotentSemiring_1998
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsIdempotentSemiring.setoid
d_setoid_1264 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentSemiring_1998 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
d_setoid_1264 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> T_IsIdempotentSemiring_1998
-> T_Setoid_46
d_setoid_1264 ~Bool -> Bool -> Bool
v0 ~Bool -> Bool -> Bool
v1 ~Bool
v2 ~Bool
v3 T_IsIdempotentSemiring_1998
v4 = T_IsIdempotentSemiring_1998 -> T_Setoid_46
du_setoid_1264 T_IsIdempotentSemiring_1998
v4
du_setoid_1264 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentSemiring_1998 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
du_setoid_1264 :: T_IsIdempotentSemiring_1998 -> T_Setoid_46
du_setoid_1264 T_IsIdempotentSemiring_1998
v0
  = let v1 :: T_IsSemiring_1640
v1
          = T_IsIdempotentSemiring_1998 -> T_IsSemiring_1640
MAlonzo.Code.Algebra.Structures.d_isSemiring_2012 (T_IsIdempotentSemiring_1998 -> T_IsIdempotentSemiring_1998
forall a b. a -> b
coe T_IsIdempotentSemiring_1998
v0) in
    Any -> T_Setoid_46
forall a b. a -> b
coe
      (let v2 :: T_IsSemiringWithoutAnnihilatingZero_1536
v2
             = T_IsSemiring_1640 -> T_IsSemiringWithoutAnnihilatingZero_1536
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1654
                 (T_IsSemiring_1640 -> T_IsSemiring_1640
forall a b. a -> b
coe T_IsSemiring_1640
v1) in
       Any -> Any
forall a b. a -> b
coe
         (let v3 :: T_IsCommutativeMonoid_764
v3
                = T_IsSemiringWithoutAnnihilatingZero_1536
-> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1556
                    (T_IsSemiringWithoutAnnihilatingZero_1536
-> T_IsSemiringWithoutAnnihilatingZero_1536
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1536
v2) in
          Any -> Any
forall a b. a -> b
coe
            (let v4 :: T_IsMonoid_712
v4
                   = T_IsCommutativeMonoid_764 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_774 (T_IsCommutativeMonoid_764 -> T_IsCommutativeMonoid_764
forall a b. a -> b
coe T_IsCommutativeMonoid_764
v3) in
             Any -> Any
forall a b. a -> b
coe
               (let v5 :: T_IsSemigroup_488
v5
                      = T_IsMonoid_712 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_722 (T_IsMonoid_712 -> T_IsMonoid_712
forall a b. a -> b
coe T_IsMonoid_712
v4) in
                Any -> Any
forall a b. a -> b
coe
                  ((T_IsMagma_178 -> T_Setoid_46) -> Any -> Any
forall a b. a -> b
coe
                     T_IsMagma_178 -> T_Setoid_46
MAlonzo.Code.Algebra.Structures.du_setoid_202
                     ((T_IsSemigroup_488 -> T_IsMagma_178) -> Any -> Any
forall a b. a -> b
coe T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496 (T_IsSemigroup_488 -> Any
forall a b. a -> b
coe T_IsSemigroup_488
v5)))))))
-- Data.Bool.Properties._.IsIdempotentSemiring.sym
d_sym_1266 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentSemiring_1998 ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_sym_1266 :: T_IsIdempotentSemiring_1998
-> Bool -> Bool -> T__'8801'__12 -> T__'8801'__12
d_sym_1266 = T_IsIdempotentSemiring_1998
-> Bool -> Bool -> T__'8801'__12 -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsIdempotentSemiring.trans
d_trans_1268 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentSemiring_1998 ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_trans_1268 :: T_IsIdempotentSemiring_1998
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
d_trans_1268 = T_IsIdempotentSemiring_1998
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsIdempotentSemiring.zero
d_zero_1270 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentSemiring_1998 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_zero_1270 :: T_IsIdempotentSemiring_1998 -> T_Σ_14
d_zero_1270 T_IsIdempotentSemiring_1998
v0
  = (T_IsSemiring_1640 -> T_Σ_14) -> Any -> T_Σ_14
forall a b. a -> b
coe
      T_IsSemiring_1640 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_zero_1656
      ((T_IsIdempotentSemiring_1998 -> T_IsSemiring_1640) -> Any -> Any
forall a b. a -> b
coe T_IsIdempotentSemiring_1998 -> T_IsSemiring_1640
MAlonzo.Code.Algebra.Structures.d_isSemiring_2012 (T_IsIdempotentSemiring_1998 -> Any
forall a b. a -> b
coe T_IsIdempotentSemiring_1998
v0))
-- Data.Bool.Properties._.IsIdempotentSemiring.zeroʳ
d_zero'691'_1272 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentSemiring_1998 ->
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_zero'691'_1272 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> T_IsIdempotentSemiring_1998
-> Bool
-> T__'8801'__12
d_zero'691'_1272 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> T_IsIdempotentSemiring_1998
-> Bool
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsIdempotentSemiring.zeroˡ
d_zero'737'_1274 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentSemiring_1998 ->
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_zero'737'_1274 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> T_IsIdempotentSemiring_1998
-> Bool
-> T__'8801'__12
d_zero'737'_1274 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> T_IsIdempotentSemiring_1998
-> Bool
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsInvertibleMagma.inverse
d_inverse_1278 ::
  MAlonzo.Code.Algebra.Structures.T_IsInvertibleMagma_958 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_inverse_1278 :: T_IsInvertibleMagma_958 -> T_Σ_14
d_inverse_1278 T_IsInvertibleMagma_958
v0
  = (T_IsInvertibleMagma_958 -> T_Σ_14) -> Any -> T_Σ_14
forall a b. a -> b
coe T_IsInvertibleMagma_958 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_inverse_974 (T_IsInvertibleMagma_958 -> Any
forall a b. a -> b
coe T_IsInvertibleMagma_958
v0)
-- Data.Bool.Properties._.IsInvertibleMagma.inverseʳ
d_inverse'691'_1280 ::
  (Bool -> Bool -> Bool) ->
  Bool ->
  (Bool -> Bool) ->
  MAlonzo.Code.Algebra.Structures.T_IsInvertibleMagma_958 ->
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_inverse'691'_1280 :: (Bool -> Bool -> Bool)
-> Bool
-> (Bool -> Bool)
-> T_IsInvertibleMagma_958
-> Bool
-> T__'8801'__12
d_inverse'691'_1280 = (Bool -> Bool -> Bool)
-> Bool
-> (Bool -> Bool)
-> T_IsInvertibleMagma_958
-> Bool
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsInvertibleMagma.inverseˡ
d_inverse'737'_1282 ::
  (Bool -> Bool -> Bool) ->
  Bool ->
  (Bool -> Bool) ->
  MAlonzo.Code.Algebra.Structures.T_IsInvertibleMagma_958 ->
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_inverse'737'_1282 :: (Bool -> Bool -> Bool)
-> Bool
-> (Bool -> Bool)
-> T_IsInvertibleMagma_958
-> Bool
-> T__'8801'__12
d_inverse'737'_1282 = (Bool -> Bool -> Bool)
-> Bool
-> (Bool -> Bool)
-> T_IsInvertibleMagma_958
-> Bool
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsInvertibleMagma.isEquivalence
d_isEquivalence_1284 ::
  MAlonzo.Code.Algebra.Structures.T_IsInvertibleMagma_958 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
d_isEquivalence_1284 :: T_IsInvertibleMagma_958 -> T_IsEquivalence_28
d_isEquivalence_1284 T_IsInvertibleMagma_958
v0
  = (T_IsMagma_178 -> T_IsEquivalence_28) -> Any -> T_IsEquivalence_28
forall a b. a -> b
coe
      T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186
      ((T_IsInvertibleMagma_958 -> T_IsMagma_178) -> Any -> Any
forall a b. a -> b
coe T_IsInvertibleMagma_958 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_972 (T_IsInvertibleMagma_958 -> Any
forall a b. a -> b
coe T_IsInvertibleMagma_958
v0))
-- Data.Bool.Properties._.IsInvertibleMagma.isMagma
d_isMagma_1286 ::
  MAlonzo.Code.Algebra.Structures.T_IsInvertibleMagma_958 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_178
d_isMagma_1286 :: T_IsInvertibleMagma_958 -> T_IsMagma_178
d_isMagma_1286 T_IsInvertibleMagma_958
v0
  = (T_IsInvertibleMagma_958 -> T_IsMagma_178) -> Any -> T_IsMagma_178
forall a b. a -> b
coe T_IsInvertibleMagma_958 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_972 (T_IsInvertibleMagma_958 -> Any
forall a b. a -> b
coe T_IsInvertibleMagma_958
v0)
-- Data.Bool.Properties._.IsInvertibleMagma.isPartialEquivalence
d_isPartialEquivalence_1288 ::
  (Bool -> Bool -> Bool) ->
  Bool ->
  (Bool -> Bool) ->
  MAlonzo.Code.Algebra.Structures.T_IsInvertibleMagma_958 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_1288 :: (Bool -> Bool -> Bool)
-> Bool
-> (Bool -> Bool)
-> T_IsInvertibleMagma_958
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_1288 ~Bool -> Bool -> Bool
v0 ~Bool
v1 ~Bool -> Bool
v2 T_IsInvertibleMagma_958
v3
  = T_IsInvertibleMagma_958 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_1288 T_IsInvertibleMagma_958
v3
du_isPartialEquivalence_1288 ::
  MAlonzo.Code.Algebra.Structures.T_IsInvertibleMagma_958 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_1288 :: T_IsInvertibleMagma_958 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_1288 T_IsInvertibleMagma_958
v0
  = let v1 :: T_IsMagma_178
v1
          = T_IsInvertibleMagma_958 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_972 (T_IsInvertibleMagma_958 -> T_IsInvertibleMagma_958
forall a b. a -> b
coe T_IsInvertibleMagma_958
v0) in
    Any -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      ((T_IsEquivalence_28 -> T_IsPartialEquivalence_16) -> Any -> Any
forall a b. a -> b
coe
         T_IsEquivalence_28 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_44
         ((T_IsMagma_178 -> T_IsEquivalence_28) -> Any -> Any
forall a b. a -> b
coe T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186 (T_IsMagma_178 -> Any
forall a b. a -> b
coe T_IsMagma_178
v1)))
-- Data.Bool.Properties._.IsInvertibleMagma.refl
d_refl_1290 ::
  MAlonzo.Code.Algebra.Structures.T_IsInvertibleMagma_958 ->
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_refl_1290 :: T_IsInvertibleMagma_958 -> Bool -> T__'8801'__12
d_refl_1290 = T_IsInvertibleMagma_958 -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsInvertibleMagma.reflexive
d_reflexive_1292 ::
  (Bool -> Bool -> Bool) ->
  Bool ->
  (Bool -> Bool) ->
  MAlonzo.Code.Algebra.Structures.T_IsInvertibleMagma_958 ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_reflexive_1292 :: (Bool -> Bool -> Bool)
-> Bool
-> (Bool -> Bool)
-> T_IsInvertibleMagma_958
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_reflexive_1292 = (Bool -> Bool -> Bool)
-> Bool
-> (Bool -> Bool)
-> T_IsInvertibleMagma_958
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsInvertibleMagma.setoid
d_setoid_1294 ::
  (Bool -> Bool -> Bool) ->
  Bool ->
  (Bool -> Bool) ->
  MAlonzo.Code.Algebra.Structures.T_IsInvertibleMagma_958 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
d_setoid_1294 :: (Bool -> Bool -> Bool)
-> Bool -> (Bool -> Bool) -> T_IsInvertibleMagma_958 -> T_Setoid_46
d_setoid_1294 ~Bool -> Bool -> Bool
v0 ~Bool
v1 ~Bool -> Bool
v2 T_IsInvertibleMagma_958
v3 = T_IsInvertibleMagma_958 -> T_Setoid_46
du_setoid_1294 T_IsInvertibleMagma_958
v3
du_setoid_1294 ::
  MAlonzo.Code.Algebra.Structures.T_IsInvertibleMagma_958 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
du_setoid_1294 :: T_IsInvertibleMagma_958 -> T_Setoid_46
du_setoid_1294 T_IsInvertibleMagma_958
v0
  = (T_IsMagma_178 -> T_Setoid_46) -> Any -> T_Setoid_46
forall a b. a -> b
coe
      T_IsMagma_178 -> T_Setoid_46
MAlonzo.Code.Algebra.Structures.du_setoid_202
      ((T_IsInvertibleMagma_958 -> T_IsMagma_178) -> Any -> Any
forall a b. a -> b
coe T_IsInvertibleMagma_958 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_972 (T_IsInvertibleMagma_958 -> Any
forall a b. a -> b
coe T_IsInvertibleMagma_958
v0))
-- Data.Bool.Properties._.IsInvertibleMagma.sym
d_sym_1296 ::
  MAlonzo.Code.Algebra.Structures.T_IsInvertibleMagma_958 ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_sym_1296 :: T_IsInvertibleMagma_958
-> Bool -> Bool -> T__'8801'__12 -> T__'8801'__12
d_sym_1296 = T_IsInvertibleMagma_958
-> Bool -> Bool -> T__'8801'__12 -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsInvertibleMagma.trans
d_trans_1298 ::
  MAlonzo.Code.Algebra.Structures.T_IsInvertibleMagma_958 ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_trans_1298 :: T_IsInvertibleMagma_958
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
d_trans_1298 = T_IsInvertibleMagma_958
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsInvertibleMagma.⁻¹-cong
d_'8315''185''45'cong_1300 ::
  MAlonzo.Code.Algebra.Structures.T_IsInvertibleMagma_958 ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8315''185''45'cong_1300 :: T_IsInvertibleMagma_958
-> Bool -> Bool -> T__'8801'__12 -> T__'8801'__12
d_'8315''185''45'cong_1300 = T_IsInvertibleMagma_958
-> Bool -> Bool -> T__'8801'__12 -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsInvertibleMagma.∙-cong
d_'8729''45'cong_1302 ::
  MAlonzo.Code.Algebra.Structures.T_IsInvertibleMagma_958 ->
  Bool ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8729''45'cong_1302 :: T_IsInvertibleMagma_958
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong_1302 = T_IsInvertibleMagma_958
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsInvertibleMagma.∙-congʳ
d_'8729''45'cong'691'_1304 ::
  (Bool -> Bool -> Bool) ->
  Bool ->
  (Bool -> Bool) ->
  MAlonzo.Code.Algebra.Structures.T_IsInvertibleMagma_958 ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8729''45'cong'691'_1304 :: (Bool -> Bool -> Bool)
-> Bool
-> (Bool -> Bool)
-> T_IsInvertibleMagma_958
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong'691'_1304 = (Bool -> Bool -> Bool)
-> Bool
-> (Bool -> Bool)
-> T_IsInvertibleMagma_958
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsInvertibleMagma.∙-congˡ
d_'8729''45'cong'737'_1306 ::
  (Bool -> Bool -> Bool) ->
  Bool ->
  (Bool -> Bool) ->
  MAlonzo.Code.Algebra.Structures.T_IsInvertibleMagma_958 ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8729''45'cong'737'_1306 :: (Bool -> Bool -> Bool)
-> Bool
-> (Bool -> Bool)
-> T_IsInvertibleMagma_958
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong'737'_1306 = (Bool -> Bool -> Bool)
-> Bool
-> (Bool -> Bool)
-> T_IsInvertibleMagma_958
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsInvertibleUnitalMagma.identity
d_identity_1310 ::
  MAlonzo.Code.Algebra.Structures.T_IsInvertibleUnitalMagma_1012 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_identity_1310 :: T_IsInvertibleUnitalMagma_1012 -> T_Σ_14
d_identity_1310 T_IsInvertibleUnitalMagma_1012
v0
  = (T_IsInvertibleUnitalMagma_1012 -> T_Σ_14) -> Any -> T_Σ_14
forall a b. a -> b
coe T_IsInvertibleUnitalMagma_1012 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_identity_1026 (T_IsInvertibleUnitalMagma_1012 -> Any
forall a b. a -> b
coe T_IsInvertibleUnitalMagma_1012
v0)
-- Data.Bool.Properties._.IsInvertibleUnitalMagma.identityʳ
d_identity'691'_1312 ::
  (Bool -> Bool -> Bool) ->
  Bool ->
  (Bool -> Bool) ->
  MAlonzo.Code.Algebra.Structures.T_IsInvertibleUnitalMagma_1012 ->
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_identity'691'_1312 :: (Bool -> Bool -> Bool)
-> Bool
-> (Bool -> Bool)
-> T_IsInvertibleUnitalMagma_1012
-> Bool
-> T__'8801'__12
d_identity'691'_1312 = (Bool -> Bool -> Bool)
-> Bool
-> (Bool -> Bool)
-> T_IsInvertibleUnitalMagma_1012
-> Bool
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsInvertibleUnitalMagma.identityˡ
d_identity'737'_1314 ::
  (Bool -> Bool -> Bool) ->
  Bool ->
  (Bool -> Bool) ->
  MAlonzo.Code.Algebra.Structures.T_IsInvertibleUnitalMagma_1012 ->
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_identity'737'_1314 :: (Bool -> Bool -> Bool)
-> Bool
-> (Bool -> Bool)
-> T_IsInvertibleUnitalMagma_1012
-> Bool
-> T__'8801'__12
d_identity'737'_1314 = (Bool -> Bool -> Bool)
-> Bool
-> (Bool -> Bool)
-> T_IsInvertibleUnitalMagma_1012
-> Bool
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsInvertibleUnitalMagma.inverse
d_inverse_1316 ::
  MAlonzo.Code.Algebra.Structures.T_IsInvertibleUnitalMagma_1012 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_inverse_1316 :: T_IsInvertibleUnitalMagma_1012 -> T_Σ_14
d_inverse_1316 T_IsInvertibleUnitalMagma_1012
v0
  = (T_IsInvertibleMagma_958 -> T_Σ_14) -> Any -> T_Σ_14
forall a b. a -> b
coe
      T_IsInvertibleMagma_958 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_inverse_974
      ((T_IsInvertibleUnitalMagma_1012 -> T_IsInvertibleMagma_958)
-> Any -> Any
forall a b. a -> b
coe
         T_IsInvertibleUnitalMagma_1012 -> T_IsInvertibleMagma_958
MAlonzo.Code.Algebra.Structures.d_isInvertibleMagma_1024 (T_IsInvertibleUnitalMagma_1012 -> Any
forall a b. a -> b
coe T_IsInvertibleUnitalMagma_1012
v0))
-- Data.Bool.Properties._.IsInvertibleUnitalMagma.inverseʳ
d_inverse'691'_1318 ::
  (Bool -> Bool -> Bool) ->
  Bool ->
  (Bool -> Bool) ->
  MAlonzo.Code.Algebra.Structures.T_IsInvertibleUnitalMagma_1012 ->
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_inverse'691'_1318 :: (Bool -> Bool -> Bool)
-> Bool
-> (Bool -> Bool)
-> T_IsInvertibleUnitalMagma_1012
-> Bool
-> T__'8801'__12
d_inverse'691'_1318 = (Bool -> Bool -> Bool)
-> Bool
-> (Bool -> Bool)
-> T_IsInvertibleUnitalMagma_1012
-> Bool
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsInvertibleUnitalMagma.inverseˡ
d_inverse'737'_1320 ::
  (Bool -> Bool -> Bool) ->
  Bool ->
  (Bool -> Bool) ->
  MAlonzo.Code.Algebra.Structures.T_IsInvertibleUnitalMagma_1012 ->
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_inverse'737'_1320 :: (Bool -> Bool -> Bool)
-> Bool
-> (Bool -> Bool)
-> T_IsInvertibleUnitalMagma_1012
-> Bool
-> T__'8801'__12
d_inverse'737'_1320 = (Bool -> Bool -> Bool)
-> Bool
-> (Bool -> Bool)
-> T_IsInvertibleUnitalMagma_1012
-> Bool
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsInvertibleUnitalMagma.isEquivalence
d_isEquivalence_1322 ::
  MAlonzo.Code.Algebra.Structures.T_IsInvertibleUnitalMagma_1012 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
d_isEquivalence_1322 :: T_IsInvertibleUnitalMagma_1012 -> T_IsEquivalence_28
d_isEquivalence_1322 T_IsInvertibleUnitalMagma_1012
v0
  = (T_IsMagma_178 -> T_IsEquivalence_28) -> Any -> T_IsEquivalence_28
forall a b. a -> b
coe
      T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186
      ((T_IsInvertibleMagma_958 -> T_IsMagma_178) -> Any -> Any
forall a b. a -> b
coe
         T_IsInvertibleMagma_958 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_972
         ((T_IsInvertibleUnitalMagma_1012 -> T_IsInvertibleMagma_958)
-> Any -> Any
forall a b. a -> b
coe
            T_IsInvertibleUnitalMagma_1012 -> T_IsInvertibleMagma_958
MAlonzo.Code.Algebra.Structures.d_isInvertibleMagma_1024 (T_IsInvertibleUnitalMagma_1012 -> Any
forall a b. a -> b
coe T_IsInvertibleUnitalMagma_1012
v0)))
-- Data.Bool.Properties._.IsInvertibleUnitalMagma.isInvertibleMagma
d_isInvertibleMagma_1324 ::
  MAlonzo.Code.Algebra.Structures.T_IsInvertibleUnitalMagma_1012 ->
  MAlonzo.Code.Algebra.Structures.T_IsInvertibleMagma_958
d_isInvertibleMagma_1324 :: T_IsInvertibleUnitalMagma_1012 -> T_IsInvertibleMagma_958
d_isInvertibleMagma_1324 T_IsInvertibleUnitalMagma_1012
v0
  = (T_IsInvertibleUnitalMagma_1012 -> T_IsInvertibleMagma_958)
-> Any -> T_IsInvertibleMagma_958
forall a b. a -> b
coe
      T_IsInvertibleUnitalMagma_1012 -> T_IsInvertibleMagma_958
MAlonzo.Code.Algebra.Structures.d_isInvertibleMagma_1024 (T_IsInvertibleUnitalMagma_1012 -> Any
forall a b. a -> b
coe T_IsInvertibleUnitalMagma_1012
v0)
-- Data.Bool.Properties._.IsInvertibleUnitalMagma.isMagma
d_isMagma_1326 ::
  MAlonzo.Code.Algebra.Structures.T_IsInvertibleUnitalMagma_1012 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_178
d_isMagma_1326 :: T_IsInvertibleUnitalMagma_1012 -> T_IsMagma_178
d_isMagma_1326 T_IsInvertibleUnitalMagma_1012
v0
  = (T_IsInvertibleMagma_958 -> T_IsMagma_178) -> Any -> T_IsMagma_178
forall a b. a -> b
coe
      T_IsInvertibleMagma_958 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_972
      ((T_IsInvertibleUnitalMagma_1012 -> T_IsInvertibleMagma_958)
-> Any -> Any
forall a b. a -> b
coe
         T_IsInvertibleUnitalMagma_1012 -> T_IsInvertibleMagma_958
MAlonzo.Code.Algebra.Structures.d_isInvertibleMagma_1024 (T_IsInvertibleUnitalMagma_1012 -> Any
forall a b. a -> b
coe T_IsInvertibleUnitalMagma_1012
v0))
-- Data.Bool.Properties._.IsInvertibleUnitalMagma.isPartialEquivalence
d_isPartialEquivalence_1328 ::
  (Bool -> Bool -> Bool) ->
  Bool ->
  (Bool -> Bool) ->
  MAlonzo.Code.Algebra.Structures.T_IsInvertibleUnitalMagma_1012 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_1328 :: (Bool -> Bool -> Bool)
-> Bool
-> (Bool -> Bool)
-> T_IsInvertibleUnitalMagma_1012
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_1328 ~Bool -> Bool -> Bool
v0 ~Bool
v1 ~Bool -> Bool
v2 T_IsInvertibleUnitalMagma_1012
v3
  = T_IsInvertibleUnitalMagma_1012 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_1328 T_IsInvertibleUnitalMagma_1012
v3
du_isPartialEquivalence_1328 ::
  MAlonzo.Code.Algebra.Structures.T_IsInvertibleUnitalMagma_1012 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_1328 :: T_IsInvertibleUnitalMagma_1012 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_1328 T_IsInvertibleUnitalMagma_1012
v0
  = let v1 :: T_IsInvertibleMagma_958
v1
          = T_IsInvertibleUnitalMagma_1012 -> T_IsInvertibleMagma_958
MAlonzo.Code.Algebra.Structures.d_isInvertibleMagma_1024
              (T_IsInvertibleUnitalMagma_1012 -> T_IsInvertibleUnitalMagma_1012
forall a b. a -> b
coe T_IsInvertibleUnitalMagma_1012
v0) in
    Any -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsMagma_178
v2 = T_IsInvertibleMagma_958 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_972 (T_IsInvertibleMagma_958 -> T_IsInvertibleMagma_958
forall a b. a -> b
coe T_IsInvertibleMagma_958
v1) in
       Any -> Any
forall a b. a -> b
coe
         ((T_IsEquivalence_28 -> T_IsPartialEquivalence_16) -> Any -> Any
forall a b. a -> b
coe
            T_IsEquivalence_28 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_44
            ((T_IsMagma_178 -> T_IsEquivalence_28) -> Any -> Any
forall a b. a -> b
coe
               T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186 (T_IsMagma_178 -> Any
forall a b. a -> b
coe T_IsMagma_178
v2))))
-- Data.Bool.Properties._.IsInvertibleUnitalMagma.isUnitalMagma
d_isUnitalMagma_1330 ::
  (Bool -> Bool -> Bool) ->
  Bool ->
  (Bool -> Bool) ->
  MAlonzo.Code.Algebra.Structures.T_IsInvertibleUnitalMagma_1012 ->
  MAlonzo.Code.Algebra.Structures.T_IsUnitalMagma_666
d_isUnitalMagma_1330 :: (Bool -> Bool -> Bool)
-> Bool
-> (Bool -> Bool)
-> T_IsInvertibleUnitalMagma_1012
-> T_IsUnitalMagma_666
d_isUnitalMagma_1330 Bool -> Bool -> Bool
v0 Bool
v1 Bool -> Bool
v2 T_IsInvertibleUnitalMagma_1012
v3
  = (T_IsInvertibleUnitalMagma_1012 -> T_IsUnitalMagma_666)
-> T_IsInvertibleUnitalMagma_1012 -> T_IsUnitalMagma_666
forall a b. a -> b
coe T_IsInvertibleUnitalMagma_1012 -> T_IsUnitalMagma_666
MAlonzo.Code.Algebra.Structures.du_isUnitalMagma_1064 T_IsInvertibleUnitalMagma_1012
v3
-- Data.Bool.Properties._.IsInvertibleUnitalMagma.refl
d_refl_1332 ::
  MAlonzo.Code.Algebra.Structures.T_IsInvertibleUnitalMagma_1012 ->
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_refl_1332 :: T_IsInvertibleUnitalMagma_1012 -> Bool -> T__'8801'__12
d_refl_1332 = T_IsInvertibleUnitalMagma_1012 -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsInvertibleUnitalMagma.reflexive
d_reflexive_1334 ::
  (Bool -> Bool -> Bool) ->
  Bool ->
  (Bool -> Bool) ->
  MAlonzo.Code.Algebra.Structures.T_IsInvertibleUnitalMagma_1012 ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_reflexive_1334 :: (Bool -> Bool -> Bool)
-> Bool
-> (Bool -> Bool)
-> T_IsInvertibleUnitalMagma_1012
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_reflexive_1334 = (Bool -> Bool -> Bool)
-> Bool
-> (Bool -> Bool)
-> T_IsInvertibleUnitalMagma_1012
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsInvertibleUnitalMagma.setoid
d_setoid_1336 ::
  (Bool -> Bool -> Bool) ->
  Bool ->
  (Bool -> Bool) ->
  MAlonzo.Code.Algebra.Structures.T_IsInvertibleUnitalMagma_1012 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
d_setoid_1336 :: (Bool -> Bool -> Bool)
-> Bool
-> (Bool -> Bool)
-> T_IsInvertibleUnitalMagma_1012
-> T_Setoid_46
d_setoid_1336 ~Bool -> Bool -> Bool
v0 ~Bool
v1 ~Bool -> Bool
v2 T_IsInvertibleUnitalMagma_1012
v3 = T_IsInvertibleUnitalMagma_1012 -> T_Setoid_46
du_setoid_1336 T_IsInvertibleUnitalMagma_1012
v3
du_setoid_1336 ::
  MAlonzo.Code.Algebra.Structures.T_IsInvertibleUnitalMagma_1012 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
du_setoid_1336 :: T_IsInvertibleUnitalMagma_1012 -> T_Setoid_46
du_setoid_1336 T_IsInvertibleUnitalMagma_1012
v0
  = let v1 :: T_IsInvertibleMagma_958
v1
          = T_IsInvertibleUnitalMagma_1012 -> T_IsInvertibleMagma_958
MAlonzo.Code.Algebra.Structures.d_isInvertibleMagma_1024
              (T_IsInvertibleUnitalMagma_1012 -> T_IsInvertibleUnitalMagma_1012
forall a b. a -> b
coe T_IsInvertibleUnitalMagma_1012
v0) in
    Any -> T_Setoid_46
forall a b. a -> b
coe
      ((T_IsMagma_178 -> T_Setoid_46) -> Any -> Any
forall a b. a -> b
coe
         T_IsMagma_178 -> T_Setoid_46
MAlonzo.Code.Algebra.Structures.du_setoid_202
         ((T_IsInvertibleMagma_958 -> T_IsMagma_178) -> Any -> Any
forall a b. a -> b
coe T_IsInvertibleMagma_958 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_972 (T_IsInvertibleMagma_958 -> Any
forall a b. a -> b
coe T_IsInvertibleMagma_958
v1)))
-- Data.Bool.Properties._.IsInvertibleUnitalMagma.sym
d_sym_1338 ::
  MAlonzo.Code.Algebra.Structures.T_IsInvertibleUnitalMagma_1012 ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_sym_1338 :: T_IsInvertibleUnitalMagma_1012
-> Bool -> Bool -> T__'8801'__12 -> T__'8801'__12
d_sym_1338 = T_IsInvertibleUnitalMagma_1012
-> Bool -> Bool -> T__'8801'__12 -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsInvertibleUnitalMagma.trans
d_trans_1340 ::
  MAlonzo.Code.Algebra.Structures.T_IsInvertibleUnitalMagma_1012 ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_trans_1340 :: T_IsInvertibleUnitalMagma_1012
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
d_trans_1340 = T_IsInvertibleUnitalMagma_1012
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsInvertibleUnitalMagma.⁻¹-cong
d_'8315''185''45'cong_1342 ::
  MAlonzo.Code.Algebra.Structures.T_IsInvertibleUnitalMagma_1012 ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8315''185''45'cong_1342 :: T_IsInvertibleUnitalMagma_1012
-> Bool -> Bool -> T__'8801'__12 -> T__'8801'__12
d_'8315''185''45'cong_1342 = T_IsInvertibleUnitalMagma_1012
-> Bool -> Bool -> T__'8801'__12 -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsInvertibleUnitalMagma.∙-cong
d_'8729''45'cong_1344 ::
  MAlonzo.Code.Algebra.Structures.T_IsInvertibleUnitalMagma_1012 ->
  Bool ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8729''45'cong_1344 :: T_IsInvertibleUnitalMagma_1012
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong_1344 = T_IsInvertibleUnitalMagma_1012
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsInvertibleUnitalMagma.∙-congʳ
d_'8729''45'cong'691'_1346 ::
  (Bool -> Bool -> Bool) ->
  Bool ->
  (Bool -> Bool) ->
  MAlonzo.Code.Algebra.Structures.T_IsInvertibleUnitalMagma_1012 ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8729''45'cong'691'_1346 :: (Bool -> Bool -> Bool)
-> Bool
-> (Bool -> Bool)
-> T_IsInvertibleUnitalMagma_1012
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong'691'_1346 = (Bool -> Bool -> Bool)
-> Bool
-> (Bool -> Bool)
-> T_IsInvertibleUnitalMagma_1012
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsInvertibleUnitalMagma.∙-congˡ
d_'8729''45'cong'737'_1348 ::
  (Bool -> Bool -> Bool) ->
  Bool ->
  (Bool -> Bool) ->
  MAlonzo.Code.Algebra.Structures.T_IsInvertibleUnitalMagma_1012 ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8729''45'cong'737'_1348 :: (Bool -> Bool -> Bool)
-> Bool
-> (Bool -> Bool)
-> T_IsInvertibleUnitalMagma_1012
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong'737'_1348 = (Bool -> Bool -> Bool)
-> Bool
-> (Bool -> Bool)
-> T_IsInvertibleUnitalMagma_1012
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsKleeneAlgebra.*-assoc
d_'42''45'assoc_1352 ::
  MAlonzo.Code.Algebra.Structures.T_IsKleeneAlgebra_2122 ->
  Bool ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'42''45'assoc_1352 :: T_IsKleeneAlgebra_2122 -> Bool -> Bool -> Bool -> T__'8801'__12
d_'42''45'assoc_1352 = T_IsKleeneAlgebra_2122 -> Bool -> Bool -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsKleeneAlgebra.*-cong
d_'42''45'cong_1354 ::
  MAlonzo.Code.Algebra.Structures.T_IsKleeneAlgebra_2122 ->
  Bool ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'42''45'cong_1354 :: T_IsKleeneAlgebra_2122
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
d_'42''45'cong_1354 = T_IsKleeneAlgebra_2122
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsKleeneAlgebra.∙-congʳ
d_'8729''45'cong'691'_1356 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsKleeneAlgebra_2122 ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8729''45'cong'691'_1356 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsKleeneAlgebra_2122
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong'691'_1356 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsKleeneAlgebra_2122
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsKleeneAlgebra.∙-congˡ
d_'8729''45'cong'737'_1358 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsKleeneAlgebra_2122 ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8729''45'cong'737'_1358 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsKleeneAlgebra_2122
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong'737'_1358 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsKleeneAlgebra_2122
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsKleeneAlgebra.*-identity
d_'42''45'identity_1360 ::
  MAlonzo.Code.Algebra.Structures.T_IsKleeneAlgebra_2122 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'42''45'identity_1360 :: T_IsKleeneAlgebra_2122 -> T_Σ_14
d_'42''45'identity_1360 T_IsKleeneAlgebra_2122
v0
  = (T_IsSemiringWithoutAnnihilatingZero_1536 -> T_Σ_14)
-> Any -> T_Σ_14
forall a b. a -> b
coe
      T_IsSemiringWithoutAnnihilatingZero_1536 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_'42''45'identity_1562
      ((T_IsSemiring_1640 -> T_IsSemiringWithoutAnnihilatingZero_1536)
-> Any -> Any
forall a b. a -> b
coe
         T_IsSemiring_1640 -> T_IsSemiringWithoutAnnihilatingZero_1536
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1654
         ((T_IsIdempotentSemiring_1998 -> T_IsSemiring_1640) -> Any -> Any
forall a b. a -> b
coe
            T_IsIdempotentSemiring_1998 -> T_IsSemiring_1640
MAlonzo.Code.Algebra.Structures.d_isSemiring_2012
            ((T_IsKleeneAlgebra_2122 -> T_IsIdempotentSemiring_1998)
-> Any -> Any
forall a b. a -> b
coe
               T_IsKleeneAlgebra_2122 -> T_IsIdempotentSemiring_1998
MAlonzo.Code.Algebra.Structures.d_isIdempotentSemiring_2140
               (T_IsKleeneAlgebra_2122 -> Any
forall a b. a -> b
coe T_IsKleeneAlgebra_2122
v0))))
-- Data.Bool.Properties._.IsKleeneAlgebra.identityʳ
d_identity'691'_1362 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsKleeneAlgebra_2122 ->
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_identity'691'_1362 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsKleeneAlgebra_2122
-> Bool
-> T__'8801'__12
d_identity'691'_1362 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsKleeneAlgebra_2122
-> Bool
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsKleeneAlgebra.identityˡ
d_identity'737'_1364 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsKleeneAlgebra_2122 ->
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_identity'737'_1364 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsKleeneAlgebra_2122
-> Bool
-> T__'8801'__12
d_identity'737'_1364 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsKleeneAlgebra_2122
-> Bool
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsKleeneAlgebra.*-isMagma
d_'42''45'isMagma_1366 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsKleeneAlgebra_2122 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_178
d_'42''45'isMagma_1366 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsKleeneAlgebra_2122
-> T_IsMagma_178
d_'42''45'isMagma_1366 ~Bool -> Bool -> Bool
v0 ~Bool -> Bool -> Bool
v1 ~Bool -> Bool
v2 ~Bool
v3 ~Bool
v4 T_IsKleeneAlgebra_2122
v5
  = T_IsKleeneAlgebra_2122 -> T_IsMagma_178
du_'42''45'isMagma_1366 T_IsKleeneAlgebra_2122
v5
du_'42''45'isMagma_1366 ::
  MAlonzo.Code.Algebra.Structures.T_IsKleeneAlgebra_2122 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_178
du_'42''45'isMagma_1366 :: T_IsKleeneAlgebra_2122 -> T_IsMagma_178
du_'42''45'isMagma_1366 T_IsKleeneAlgebra_2122
v0
  = let v1 :: T_IsIdempotentSemiring_1998
v1
          = T_IsKleeneAlgebra_2122 -> T_IsIdempotentSemiring_1998
MAlonzo.Code.Algebra.Structures.d_isIdempotentSemiring_2140
              (T_IsKleeneAlgebra_2122 -> T_IsKleeneAlgebra_2122
forall a b. a -> b
coe T_IsKleeneAlgebra_2122
v0) in
    Any -> T_IsMagma_178
forall a b. a -> b
coe
      (let v2 :: T_IsSemiring_1640
v2
             = T_IsIdempotentSemiring_1998 -> T_IsSemiring_1640
MAlonzo.Code.Algebra.Structures.d_isSemiring_2012 (T_IsIdempotentSemiring_1998 -> T_IsIdempotentSemiring_1998
forall a b. a -> b
coe T_IsIdempotentSemiring_1998
v1) in
       Any -> Any
forall a b. a -> b
coe
         ((T_IsSemiringWithoutAnnihilatingZero_1536 -> T_IsMagma_178)
-> Any -> Any
forall a b. a -> b
coe
            T_IsSemiringWithoutAnnihilatingZero_1536 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.du_'42''45'isMagma_1614
            ((T_IsSemiring_1640 -> T_IsSemiringWithoutAnnihilatingZero_1536)
-> Any -> Any
forall a b. a -> b
coe
               T_IsSemiring_1640 -> T_IsSemiringWithoutAnnihilatingZero_1536
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1654
               (T_IsSemiring_1640 -> Any
forall a b. a -> b
coe T_IsSemiring_1640
v2))))
-- Data.Bool.Properties._.IsKleeneAlgebra.*-isMonoid
d_'42''45'isMonoid_1368 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsKleeneAlgebra_2122 ->
  MAlonzo.Code.Algebra.Structures.T_IsMonoid_712
d_'42''45'isMonoid_1368 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsKleeneAlgebra_2122
-> T_IsMonoid_712
d_'42''45'isMonoid_1368 ~Bool -> Bool -> Bool
v0 ~Bool -> Bool -> Bool
v1 ~Bool -> Bool
v2 ~Bool
v3 ~Bool
v4 T_IsKleeneAlgebra_2122
v5
  = T_IsKleeneAlgebra_2122 -> T_IsMonoid_712
du_'42''45'isMonoid_1368 T_IsKleeneAlgebra_2122
v5
du_'42''45'isMonoid_1368 ::
  MAlonzo.Code.Algebra.Structures.T_IsKleeneAlgebra_2122 ->
  MAlonzo.Code.Algebra.Structures.T_IsMonoid_712
du_'42''45'isMonoid_1368 :: T_IsKleeneAlgebra_2122 -> T_IsMonoid_712
du_'42''45'isMonoid_1368 T_IsKleeneAlgebra_2122
v0
  = let v1 :: T_IsIdempotentSemiring_1998
v1
          = T_IsKleeneAlgebra_2122 -> T_IsIdempotentSemiring_1998
MAlonzo.Code.Algebra.Structures.d_isIdempotentSemiring_2140
              (T_IsKleeneAlgebra_2122 -> T_IsKleeneAlgebra_2122
forall a b. a -> b
coe T_IsKleeneAlgebra_2122
v0) in
    Any -> T_IsMonoid_712
forall a b. a -> b
coe
      (let v2 :: T_IsSemiring_1640
v2
             = T_IsIdempotentSemiring_1998 -> T_IsSemiring_1640
MAlonzo.Code.Algebra.Structures.d_isSemiring_2012 (T_IsIdempotentSemiring_1998 -> T_IsIdempotentSemiring_1998
forall a b. a -> b
coe T_IsIdempotentSemiring_1998
v1) in
       Any -> Any
forall a b. a -> b
coe
         ((T_IsSemiringWithoutAnnihilatingZero_1536 -> T_IsMonoid_712)
-> Any -> Any
forall a b. a -> b
coe
            T_IsSemiringWithoutAnnihilatingZero_1536 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.du_'42''45'isMonoid_1618
            ((T_IsSemiring_1640 -> T_IsSemiringWithoutAnnihilatingZero_1536)
-> Any -> Any
forall a b. a -> b
coe
               T_IsSemiring_1640 -> T_IsSemiringWithoutAnnihilatingZero_1536
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1654
               (T_IsSemiring_1640 -> Any
forall a b. a -> b
coe T_IsSemiring_1640
v2))))
-- Data.Bool.Properties._.IsKleeneAlgebra.*-isSemigroup
d_'42''45'isSemigroup_1370 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsKleeneAlgebra_2122 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_488
d_'42''45'isSemigroup_1370 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsKleeneAlgebra_2122
-> T_IsSemigroup_488
d_'42''45'isSemigroup_1370 ~Bool -> Bool -> Bool
v0 ~Bool -> Bool -> Bool
v1 ~Bool -> Bool
v2 ~Bool
v3 ~Bool
v4 T_IsKleeneAlgebra_2122
v5
  = T_IsKleeneAlgebra_2122 -> T_IsSemigroup_488
du_'42''45'isSemigroup_1370 T_IsKleeneAlgebra_2122
v5
du_'42''45'isSemigroup_1370 ::
  MAlonzo.Code.Algebra.Structures.T_IsKleeneAlgebra_2122 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_488
du_'42''45'isSemigroup_1370 :: T_IsKleeneAlgebra_2122 -> T_IsSemigroup_488
du_'42''45'isSemigroup_1370 T_IsKleeneAlgebra_2122
v0
  = let v1 :: T_IsIdempotentSemiring_1998
v1
          = T_IsKleeneAlgebra_2122 -> T_IsIdempotentSemiring_1998
MAlonzo.Code.Algebra.Structures.d_isIdempotentSemiring_2140
              (T_IsKleeneAlgebra_2122 -> T_IsKleeneAlgebra_2122
forall a b. a -> b
coe T_IsKleeneAlgebra_2122
v0) in
    Any -> T_IsSemigroup_488
forall a b. a -> b
coe
      (let v2 :: T_IsSemiring_1640
v2
             = T_IsIdempotentSemiring_1998 -> T_IsSemiring_1640
MAlonzo.Code.Algebra.Structures.d_isSemiring_2012 (T_IsIdempotentSemiring_1998 -> T_IsIdempotentSemiring_1998
forall a b. a -> b
coe T_IsIdempotentSemiring_1998
v1) in
       Any -> Any
forall a b. a -> b
coe
         ((T_IsSemiringWithoutAnnihilatingZero_1536 -> T_IsSemigroup_488)
-> Any -> Any
forall a b. a -> b
coe
            T_IsSemiringWithoutAnnihilatingZero_1536 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.du_'42''45'isSemigroup_1616
            ((T_IsSemiring_1640 -> T_IsSemiringWithoutAnnihilatingZero_1536)
-> Any -> Any
forall a b. a -> b
coe
               T_IsSemiring_1640 -> T_IsSemiringWithoutAnnihilatingZero_1536
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1654
               (T_IsSemiring_1640 -> Any
forall a b. a -> b
coe T_IsSemiring_1640
v2))))
-- Data.Bool.Properties._.IsKleeneAlgebra.assoc
d_assoc_1372 ::
  MAlonzo.Code.Algebra.Structures.T_IsKleeneAlgebra_2122 ->
  Bool ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_assoc_1372 :: T_IsKleeneAlgebra_2122 -> Bool -> Bool -> Bool -> T__'8801'__12
d_assoc_1372 = T_IsKleeneAlgebra_2122 -> Bool -> Bool -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsKleeneAlgebra.comm
d_comm_1374 ::
  MAlonzo.Code.Algebra.Structures.T_IsKleeneAlgebra_2122 ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_comm_1374 :: T_IsKleeneAlgebra_2122 -> Bool -> Bool -> T__'8801'__12
d_comm_1374 = T_IsKleeneAlgebra_2122 -> Bool -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsKleeneAlgebra.∙-cong
d_'8729''45'cong_1376 ::
  MAlonzo.Code.Algebra.Structures.T_IsKleeneAlgebra_2122 ->
  Bool ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8729''45'cong_1376 :: T_IsKleeneAlgebra_2122
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong_1376 = T_IsKleeneAlgebra_2122
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsKleeneAlgebra.∙-congʳ
d_'8729''45'cong'691'_1378 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsKleeneAlgebra_2122 ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8729''45'cong'691'_1378 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsKleeneAlgebra_2122
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong'691'_1378 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsKleeneAlgebra_2122
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsKleeneAlgebra.∙-congˡ
d_'8729''45'cong'737'_1380 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsKleeneAlgebra_2122 ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8729''45'cong'737'_1380 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsKleeneAlgebra_2122
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong'737'_1380 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsKleeneAlgebra_2122
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsKleeneAlgebra.+-idem
d_'43''45'idem_1382 ::
  MAlonzo.Code.Algebra.Structures.T_IsKleeneAlgebra_2122 ->
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'43''45'idem_1382 :: T_IsKleeneAlgebra_2122 -> Bool -> T__'8801'__12
d_'43''45'idem_1382 = T_IsKleeneAlgebra_2122 -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsKleeneAlgebra.identity
d_identity_1384 ::
  MAlonzo.Code.Algebra.Structures.T_IsKleeneAlgebra_2122 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_identity_1384 :: T_IsKleeneAlgebra_2122 -> T_Σ_14
d_identity_1384 T_IsKleeneAlgebra_2122
v0
  = (T_IsMonoid_712 -> T_Σ_14) -> Any -> T_Σ_14
forall a b. a -> b
coe
      T_IsMonoid_712 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_identity_724
      ((T_IsCommutativeMonoid_764 -> T_IsMonoid_712) -> Any -> Any
forall a b. a -> b
coe
         T_IsCommutativeMonoid_764 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_774
         ((T_IsSemiringWithoutAnnihilatingZero_1536
 -> T_IsCommutativeMonoid_764)
-> Any -> Any
forall a b. a -> b
coe
            T_IsSemiringWithoutAnnihilatingZero_1536
-> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1556
            ((T_IsSemiring_1640 -> T_IsSemiringWithoutAnnihilatingZero_1536)
-> Any -> Any
forall a b. a -> b
coe
               T_IsSemiring_1640 -> T_IsSemiringWithoutAnnihilatingZero_1536
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1654
               ((T_IsIdempotentSemiring_1998 -> T_IsSemiring_1640) -> Any -> Any
forall a b. a -> b
coe
                  T_IsIdempotentSemiring_1998 -> T_IsSemiring_1640
MAlonzo.Code.Algebra.Structures.d_isSemiring_2012
                  ((T_IsKleeneAlgebra_2122 -> T_IsIdempotentSemiring_1998)
-> Any -> Any
forall a b. a -> b
coe
                     T_IsKleeneAlgebra_2122 -> T_IsIdempotentSemiring_1998
MAlonzo.Code.Algebra.Structures.d_isIdempotentSemiring_2140
                     (T_IsKleeneAlgebra_2122 -> Any
forall a b. a -> b
coe T_IsKleeneAlgebra_2122
v0))))))
-- Data.Bool.Properties._.IsKleeneAlgebra.identityʳ
d_identity'691'_1386 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsKleeneAlgebra_2122 ->
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_identity'691'_1386 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsKleeneAlgebra_2122
-> Bool
-> T__'8801'__12
d_identity'691'_1386 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsKleeneAlgebra_2122
-> Bool
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsKleeneAlgebra.identityˡ
d_identity'737'_1388 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsKleeneAlgebra_2122 ->
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_identity'737'_1388 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsKleeneAlgebra_2122
-> Bool
-> T__'8801'__12
d_identity'737'_1388 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsKleeneAlgebra_2122
-> Bool
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsKleeneAlgebra.isBand
d_isBand_1390 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsKleeneAlgebra_2122 ->
  MAlonzo.Code.Algebra.Structures.T_IsBand_526
d_isBand_1390 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsKleeneAlgebra_2122
-> T_IsBand_526
d_isBand_1390 ~Bool -> Bool -> Bool
v0 ~Bool -> Bool -> Bool
v1 ~Bool -> Bool
v2 ~Bool
v3 ~Bool
v4 T_IsKleeneAlgebra_2122
v5 = T_IsKleeneAlgebra_2122 -> T_IsBand_526
du_isBand_1390 T_IsKleeneAlgebra_2122
v5
du_isBand_1390 ::
  MAlonzo.Code.Algebra.Structures.T_IsKleeneAlgebra_2122 ->
  MAlonzo.Code.Algebra.Structures.T_IsBand_526
du_isBand_1390 :: T_IsKleeneAlgebra_2122 -> T_IsBand_526
du_isBand_1390 T_IsKleeneAlgebra_2122
v0
  = let v1 :: T_IsIdempotentSemiring_1998
v1
          = T_IsKleeneAlgebra_2122 -> T_IsIdempotentSemiring_1998
MAlonzo.Code.Algebra.Structures.d_isIdempotentSemiring_2140
              (T_IsKleeneAlgebra_2122 -> T_IsKleeneAlgebra_2122
forall a b. a -> b
coe T_IsKleeneAlgebra_2122
v0) in
    Any -> T_IsBand_526
forall a b. a -> b
coe
      (let v2 :: Any
v2
             = (T_IsIdempotentSemiring_1998
 -> T_IsIdempotentCommutativeMonoid_884)
-> Any -> Any
forall a b. a -> b
coe
                 T_IsIdempotentSemiring_1998 -> T_IsIdempotentCommutativeMonoid_884
MAlonzo.Code.Algebra.Structures.du_'43''45'isIdempotentCommutativeMonoid_2100
                 (T_IsIdempotentSemiring_1998 -> Any
forall a b. a -> b
coe T_IsIdempotentSemiring_1998
v1) in
       Any -> Any
forall a b. a -> b
coe
         ((T_IsIdempotentMonoid_826 -> T_IsBand_526) -> Any -> Any
forall a b. a -> b
coe
            T_IsIdempotentMonoid_826 -> T_IsBand_526
MAlonzo.Code.Algebra.Structures.du_isBand_876
            ((T_IsIdempotentCommutativeMonoid_884 -> T_IsIdempotentMonoid_826)
-> Any -> Any
forall a b. a -> b
coe
               T_IsIdempotentCommutativeMonoid_884 -> T_IsIdempotentMonoid_826
MAlonzo.Code.Algebra.Structures.du_isIdempotentMonoid_942
               (Any -> Any
forall a b. a -> b
coe Any
v2))))
-- Data.Bool.Properties._.IsKleeneAlgebra.isCommutativeBand
d_isCommutativeBand_1392 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsKleeneAlgebra_2122 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_612
d_isCommutativeBand_1392 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsKleeneAlgebra_2122
-> T_IsCommutativeBand_612
d_isCommutativeBand_1392 ~Bool -> Bool -> Bool
v0 ~Bool -> Bool -> Bool
v1 ~Bool -> Bool
v2 ~Bool
v3 ~Bool
v4 T_IsKleeneAlgebra_2122
v5
  = T_IsKleeneAlgebra_2122 -> T_IsCommutativeBand_612
du_isCommutativeBand_1392 T_IsKleeneAlgebra_2122
v5
du_isCommutativeBand_1392 ::
  MAlonzo.Code.Algebra.Structures.T_IsKleeneAlgebra_2122 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_612
du_isCommutativeBand_1392 :: T_IsKleeneAlgebra_2122 -> T_IsCommutativeBand_612
du_isCommutativeBand_1392 T_IsKleeneAlgebra_2122
v0
  = let v1 :: T_IsIdempotentSemiring_1998
v1
          = T_IsKleeneAlgebra_2122 -> T_IsIdempotentSemiring_1998
MAlonzo.Code.Algebra.Structures.d_isIdempotentSemiring_2140
              (T_IsKleeneAlgebra_2122 -> T_IsKleeneAlgebra_2122
forall a b. a -> b
coe T_IsKleeneAlgebra_2122
v0) in
    Any -> T_IsCommutativeBand_612
forall a b. a -> b
coe
      ((T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeBand_612)
-> Any -> Any
forall a b. a -> b
coe
         T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeBand_612
MAlonzo.Code.Algebra.Structures.du_isCommutativeBand_948
         ((T_IsIdempotentSemiring_1998
 -> T_IsIdempotentCommutativeMonoid_884)
-> Any -> Any
forall a b. a -> b
coe
            T_IsIdempotentSemiring_1998 -> T_IsIdempotentCommutativeMonoid_884
MAlonzo.Code.Algebra.Structures.du_'43''45'isIdempotentCommutativeMonoid_2100
            (T_IsIdempotentSemiring_1998 -> Any
forall a b. a -> b
coe T_IsIdempotentSemiring_1998
v1)))
-- Data.Bool.Properties._.IsKleeneAlgebra.isCommutativeMagma
d_isCommutativeMagma_1394 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsKleeneAlgebra_2122 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMagma_214
d_isCommutativeMagma_1394 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsKleeneAlgebra_2122
-> T_IsCommutativeMagma_214
d_isCommutativeMagma_1394 ~Bool -> Bool -> Bool
v0 ~Bool -> Bool -> Bool
v1 ~Bool -> Bool
v2 ~Bool
v3 ~Bool
v4 T_IsKleeneAlgebra_2122
v5
  = T_IsKleeneAlgebra_2122 -> T_IsCommutativeMagma_214
du_isCommutativeMagma_1394 T_IsKleeneAlgebra_2122
v5
du_isCommutativeMagma_1394 ::
  MAlonzo.Code.Algebra.Structures.T_IsKleeneAlgebra_2122 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMagma_214
du_isCommutativeMagma_1394 :: T_IsKleeneAlgebra_2122 -> T_IsCommutativeMagma_214
du_isCommutativeMagma_1394 T_IsKleeneAlgebra_2122
v0
  = let v1 :: T_IsIdempotentSemiring_1998
v1
          = T_IsKleeneAlgebra_2122 -> T_IsIdempotentSemiring_1998
MAlonzo.Code.Algebra.Structures.d_isIdempotentSemiring_2140
              (T_IsKleeneAlgebra_2122 -> T_IsKleeneAlgebra_2122
forall a b. a -> b
coe T_IsKleeneAlgebra_2122
v0) in
    Any -> T_IsCommutativeMagma_214
forall a b. a -> b
coe
      (let v2 :: T_IsSemiring_1640
v2
             = T_IsIdempotentSemiring_1998 -> T_IsSemiring_1640
MAlonzo.Code.Algebra.Structures.d_isSemiring_2012 (T_IsIdempotentSemiring_1998 -> T_IsIdempotentSemiring_1998
forall a b. a -> b
coe T_IsIdempotentSemiring_1998
v1) in
       Any -> Any
forall a b. a -> b
coe
         (let v3 :: T_IsSemiringWithoutAnnihilatingZero_1536
v3
                = T_IsSemiring_1640 -> T_IsSemiringWithoutAnnihilatingZero_1536
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1654
                    (T_IsSemiring_1640 -> T_IsSemiring_1640
forall a b. a -> b
coe T_IsSemiring_1640
v2) in
          Any -> Any
forall a b. a -> b
coe
            (let v4 :: T_IsCommutativeMonoid_764
v4
                   = T_IsSemiringWithoutAnnihilatingZero_1536
-> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1556
                       (T_IsSemiringWithoutAnnihilatingZero_1536
-> T_IsSemiringWithoutAnnihilatingZero_1536
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1536
v3) in
             Any -> Any
forall a b. a -> b
coe
               ((T_IsCommutativeSemigroup_568 -> T_IsCommutativeMagma_214)
-> Any -> Any
forall a b. a -> b
coe
                  T_IsCommutativeSemigroup_568 -> T_IsCommutativeMagma_214
MAlonzo.Code.Algebra.Structures.du_isCommutativeMagma_606
                  ((T_IsCommutativeMonoid_764 -> T_IsCommutativeSemigroup_568)
-> Any -> Any
forall a b. a -> b
coe
                     T_IsCommutativeMonoid_764 -> T_IsCommutativeSemigroup_568
MAlonzo.Code.Algebra.Structures.du_isCommutativeSemigroup_814
                     (T_IsCommutativeMonoid_764 -> Any
forall a b. a -> b
coe T_IsCommutativeMonoid_764
v4))))))
-- Data.Bool.Properties._.IsKleeneAlgebra.+-isCommutativeMonoid
d_'43''45'isCommutativeMonoid_1396 ::
  MAlonzo.Code.Algebra.Structures.T_IsKleeneAlgebra_2122 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMonoid_764
d_'43''45'isCommutativeMonoid_1396 :: T_IsKleeneAlgebra_2122 -> T_IsCommutativeMonoid_764
d_'43''45'isCommutativeMonoid_1396 T_IsKleeneAlgebra_2122
v0
  = (T_IsSemiringWithoutAnnihilatingZero_1536
 -> T_IsCommutativeMonoid_764)
-> Any -> T_IsCommutativeMonoid_764
forall a b. a -> b
coe
      T_IsSemiringWithoutAnnihilatingZero_1536
-> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1556
      ((T_IsSemiring_1640 -> T_IsSemiringWithoutAnnihilatingZero_1536)
-> Any -> Any
forall a b. a -> b
coe
         T_IsSemiring_1640 -> T_IsSemiringWithoutAnnihilatingZero_1536
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1654
         ((T_IsIdempotentSemiring_1998 -> T_IsSemiring_1640) -> Any -> Any
forall a b. a -> b
coe
            T_IsIdempotentSemiring_1998 -> T_IsSemiring_1640
MAlonzo.Code.Algebra.Structures.d_isSemiring_2012
            ((T_IsKleeneAlgebra_2122 -> T_IsIdempotentSemiring_1998)
-> Any -> Any
forall a b. a -> b
coe
               T_IsKleeneAlgebra_2122 -> T_IsIdempotentSemiring_1998
MAlonzo.Code.Algebra.Structures.d_isIdempotentSemiring_2140
               (T_IsKleeneAlgebra_2122 -> Any
forall a b. a -> b
coe T_IsKleeneAlgebra_2122
v0))))
-- Data.Bool.Properties._.IsKleeneAlgebra.isCommutativeSemigroup
d_isCommutativeSemigroup_1398 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsKleeneAlgebra_2122 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_568
d_isCommutativeSemigroup_1398 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsKleeneAlgebra_2122
-> T_IsCommutativeSemigroup_568
d_isCommutativeSemigroup_1398 ~Bool -> Bool -> Bool
v0 ~Bool -> Bool -> Bool
v1 ~Bool -> Bool
v2 ~Bool
v3 ~Bool
v4 T_IsKleeneAlgebra_2122
v5
  = T_IsKleeneAlgebra_2122 -> T_IsCommutativeSemigroup_568
du_isCommutativeSemigroup_1398 T_IsKleeneAlgebra_2122
v5
du_isCommutativeSemigroup_1398 ::
  MAlonzo.Code.Algebra.Structures.T_IsKleeneAlgebra_2122 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_568
du_isCommutativeSemigroup_1398 :: T_IsKleeneAlgebra_2122 -> T_IsCommutativeSemigroup_568
du_isCommutativeSemigroup_1398 T_IsKleeneAlgebra_2122
v0
  = let v1 :: T_IsIdempotentSemiring_1998
v1
          = T_IsKleeneAlgebra_2122 -> T_IsIdempotentSemiring_1998
MAlonzo.Code.Algebra.Structures.d_isIdempotentSemiring_2140
              (T_IsKleeneAlgebra_2122 -> T_IsKleeneAlgebra_2122
forall a b. a -> b
coe T_IsKleeneAlgebra_2122
v0) in
    Any -> T_IsCommutativeSemigroup_568
forall a b. a -> b
coe
      (let v2 :: T_IsSemiring_1640
v2
             = T_IsIdempotentSemiring_1998 -> T_IsSemiring_1640
MAlonzo.Code.Algebra.Structures.d_isSemiring_2012 (T_IsIdempotentSemiring_1998 -> T_IsIdempotentSemiring_1998
forall a b. a -> b
coe T_IsIdempotentSemiring_1998
v1) in
       Any -> Any
forall a b. a -> b
coe
         (let v3 :: T_IsSemiringWithoutAnnihilatingZero_1536
v3
                = T_IsSemiring_1640 -> T_IsSemiringWithoutAnnihilatingZero_1536
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1654
                    (T_IsSemiring_1640 -> T_IsSemiring_1640
forall a b. a -> b
coe T_IsSemiring_1640
v2) in
          Any -> Any
forall a b. a -> b
coe
            ((T_IsCommutativeMonoid_764 -> T_IsCommutativeSemigroup_568)
-> Any -> Any
forall a b. a -> b
coe
               T_IsCommutativeMonoid_764 -> T_IsCommutativeSemigroup_568
MAlonzo.Code.Algebra.Structures.du_isCommutativeSemigroup_814
               ((T_IsSemiringWithoutAnnihilatingZero_1536
 -> T_IsCommutativeMonoid_764)
-> Any -> Any
forall a b. a -> b
coe
                  T_IsSemiringWithoutAnnihilatingZero_1536
-> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1556
                  (T_IsSemiringWithoutAnnihilatingZero_1536 -> Any
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1536
v3)))))
-- Data.Bool.Properties._.IsKleeneAlgebra.+-isIdempotentCommutativeMonoid
d_'43''45'isIdempotentCommutativeMonoid_1400 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsKleeneAlgebra_2122 ->
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884
d_'43''45'isIdempotentCommutativeMonoid_1400 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsKleeneAlgebra_2122
-> T_IsIdempotentCommutativeMonoid_884
d_'43''45'isIdempotentCommutativeMonoid_1400 ~Bool -> Bool -> Bool
v0 ~Bool -> Bool -> Bool
v1 ~Bool -> Bool
v2 ~Bool
v3 ~Bool
v4 T_IsKleeneAlgebra_2122
v5
  = T_IsKleeneAlgebra_2122 -> T_IsIdempotentCommutativeMonoid_884
du_'43''45'isIdempotentCommutativeMonoid_1400 T_IsKleeneAlgebra_2122
v5
du_'43''45'isIdempotentCommutativeMonoid_1400 ::
  MAlonzo.Code.Algebra.Structures.T_IsKleeneAlgebra_2122 ->
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884
du_'43''45'isIdempotentCommutativeMonoid_1400 :: T_IsKleeneAlgebra_2122 -> T_IsIdempotentCommutativeMonoid_884
du_'43''45'isIdempotentCommutativeMonoid_1400 T_IsKleeneAlgebra_2122
v0
  = (T_IsIdempotentSemiring_1998
 -> T_IsIdempotentCommutativeMonoid_884)
-> Any -> T_IsIdempotentCommutativeMonoid_884
forall a b. a -> b
coe
      T_IsIdempotentSemiring_1998 -> T_IsIdempotentCommutativeMonoid_884
MAlonzo.Code.Algebra.Structures.du_'43''45'isIdempotentCommutativeMonoid_2100
      ((T_IsKleeneAlgebra_2122 -> T_IsIdempotentSemiring_1998)
-> Any -> Any
forall a b. a -> b
coe
         T_IsKleeneAlgebra_2122 -> T_IsIdempotentSemiring_1998
MAlonzo.Code.Algebra.Structures.d_isIdempotentSemiring_2140
         (T_IsKleeneAlgebra_2122 -> Any
forall a b. a -> b
coe T_IsKleeneAlgebra_2122
v0))
-- Data.Bool.Properties._.IsKleeneAlgebra.isIdempotentMonoid
d_isIdempotentMonoid_1402 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsKleeneAlgebra_2122 ->
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentMonoid_826
d_isIdempotentMonoid_1402 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsKleeneAlgebra_2122
-> T_IsIdempotentMonoid_826
d_isIdempotentMonoid_1402 ~Bool -> Bool -> Bool
v0 ~Bool -> Bool -> Bool
v1 ~Bool -> Bool
v2 ~Bool
v3 ~Bool
v4 T_IsKleeneAlgebra_2122
v5
  = T_IsKleeneAlgebra_2122 -> T_IsIdempotentMonoid_826
du_isIdempotentMonoid_1402 T_IsKleeneAlgebra_2122
v5
du_isIdempotentMonoid_1402 ::
  MAlonzo.Code.Algebra.Structures.T_IsKleeneAlgebra_2122 ->
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentMonoid_826
du_isIdempotentMonoid_1402 :: T_IsKleeneAlgebra_2122 -> T_IsIdempotentMonoid_826
du_isIdempotentMonoid_1402 T_IsKleeneAlgebra_2122
v0
  = let v1 :: T_IsIdempotentSemiring_1998
v1
          = T_IsKleeneAlgebra_2122 -> T_IsIdempotentSemiring_1998
MAlonzo.Code.Algebra.Structures.d_isIdempotentSemiring_2140
              (T_IsKleeneAlgebra_2122 -> T_IsKleeneAlgebra_2122
forall a b. a -> b
coe T_IsKleeneAlgebra_2122
v0) in
    Any -> T_IsIdempotentMonoid_826
forall a b. a -> b
coe
      ((T_IsIdempotentCommutativeMonoid_884 -> T_IsIdempotentMonoid_826)
-> Any -> Any
forall a b. a -> b
coe
         T_IsIdempotentCommutativeMonoid_884 -> T_IsIdempotentMonoid_826
MAlonzo.Code.Algebra.Structures.du_isIdempotentMonoid_942
         ((T_IsIdempotentSemiring_1998
 -> T_IsIdempotentCommutativeMonoid_884)
-> Any -> Any
forall a b. a -> b
coe
            T_IsIdempotentSemiring_1998 -> T_IsIdempotentCommutativeMonoid_884
MAlonzo.Code.Algebra.Structures.du_'43''45'isIdempotentCommutativeMonoid_2100
            (T_IsIdempotentSemiring_1998 -> Any
forall a b. a -> b
coe T_IsIdempotentSemiring_1998
v1)))
-- Data.Bool.Properties._.IsKleeneAlgebra.isMagma
d_isMagma_1404 ::
  MAlonzo.Code.Algebra.Structures.T_IsKleeneAlgebra_2122 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_178
d_isMagma_1404 :: T_IsKleeneAlgebra_2122 -> T_IsMagma_178
d_isMagma_1404 T_IsKleeneAlgebra_2122
v0
  = (T_IsSemigroup_488 -> T_IsMagma_178) -> Any -> T_IsMagma_178
forall a b. a -> b
coe
      T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496
      ((T_IsMonoid_712 -> T_IsSemigroup_488) -> Any -> Any
forall a b. a -> b
coe
         T_IsMonoid_712 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_722
         ((T_IsCommutativeMonoid_764 -> T_IsMonoid_712) -> Any -> Any
forall a b. a -> b
coe
            T_IsCommutativeMonoid_764 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_774
            ((T_IsSemiringWithoutAnnihilatingZero_1536
 -> T_IsCommutativeMonoid_764)
-> Any -> Any
forall a b. a -> b
coe
               T_IsSemiringWithoutAnnihilatingZero_1536
-> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1556
               ((T_IsSemiring_1640 -> T_IsSemiringWithoutAnnihilatingZero_1536)
-> Any -> Any
forall a b. a -> b
coe
                  T_IsSemiring_1640 -> T_IsSemiringWithoutAnnihilatingZero_1536
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1654
                  ((T_IsIdempotentSemiring_1998 -> T_IsSemiring_1640) -> Any -> Any
forall a b. a -> b
coe
                     T_IsIdempotentSemiring_1998 -> T_IsSemiring_1640
MAlonzo.Code.Algebra.Structures.d_isSemiring_2012
                     ((T_IsKleeneAlgebra_2122 -> T_IsIdempotentSemiring_1998)
-> Any -> Any
forall a b. a -> b
coe
                        T_IsKleeneAlgebra_2122 -> T_IsIdempotentSemiring_1998
MAlonzo.Code.Algebra.Structures.d_isIdempotentSemiring_2140
                        (T_IsKleeneAlgebra_2122 -> Any
forall a b. a -> b
coe T_IsKleeneAlgebra_2122
v0)))))))
-- Data.Bool.Properties._.IsKleeneAlgebra.isMonoid
d_isMonoid_1406 ::
  MAlonzo.Code.Algebra.Structures.T_IsKleeneAlgebra_2122 ->
  MAlonzo.Code.Algebra.Structures.T_IsMonoid_712
d_isMonoid_1406 :: T_IsKleeneAlgebra_2122 -> T_IsMonoid_712
d_isMonoid_1406 T_IsKleeneAlgebra_2122
v0
  = (T_IsCommutativeMonoid_764 -> T_IsMonoid_712)
-> Any -> T_IsMonoid_712
forall a b. a -> b
coe
      T_IsCommutativeMonoid_764 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_774
      ((T_IsSemiringWithoutAnnihilatingZero_1536
 -> T_IsCommutativeMonoid_764)
-> Any -> Any
forall a b. a -> b
coe
         T_IsSemiringWithoutAnnihilatingZero_1536
-> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1556
         ((T_IsSemiring_1640 -> T_IsSemiringWithoutAnnihilatingZero_1536)
-> Any -> Any
forall a b. a -> b
coe
            T_IsSemiring_1640 -> T_IsSemiringWithoutAnnihilatingZero_1536
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1654
            ((T_IsIdempotentSemiring_1998 -> T_IsSemiring_1640) -> Any -> Any
forall a b. a -> b
coe
               T_IsIdempotentSemiring_1998 -> T_IsSemiring_1640
MAlonzo.Code.Algebra.Structures.d_isSemiring_2012
               ((T_IsKleeneAlgebra_2122 -> T_IsIdempotentSemiring_1998)
-> Any -> Any
forall a b. a -> b
coe
                  T_IsKleeneAlgebra_2122 -> T_IsIdempotentSemiring_1998
MAlonzo.Code.Algebra.Structures.d_isIdempotentSemiring_2140
                  (T_IsKleeneAlgebra_2122 -> Any
forall a b. a -> b
coe T_IsKleeneAlgebra_2122
v0)))))
-- Data.Bool.Properties._.IsKleeneAlgebra.isSemigroup
d_isSemigroup_1408 ::
  MAlonzo.Code.Algebra.Structures.T_IsKleeneAlgebra_2122 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_488
d_isSemigroup_1408 :: T_IsKleeneAlgebra_2122 -> T_IsSemigroup_488
d_isSemigroup_1408 T_IsKleeneAlgebra_2122
v0
  = (T_IsMonoid_712 -> T_IsSemigroup_488) -> Any -> T_IsSemigroup_488
forall a b. a -> b
coe
      T_IsMonoid_712 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_722
      ((T_IsCommutativeMonoid_764 -> T_IsMonoid_712) -> Any -> Any
forall a b. a -> b
coe
         T_IsCommutativeMonoid_764 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_774
         ((T_IsSemiringWithoutAnnihilatingZero_1536
 -> T_IsCommutativeMonoid_764)
-> Any -> Any
forall a b. a -> b
coe
            T_IsSemiringWithoutAnnihilatingZero_1536
-> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1556
            ((T_IsSemiring_1640 -> T_IsSemiringWithoutAnnihilatingZero_1536)
-> Any -> Any
forall a b. a -> b
coe
               T_IsSemiring_1640 -> T_IsSemiringWithoutAnnihilatingZero_1536
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1654
               ((T_IsIdempotentSemiring_1998 -> T_IsSemiring_1640) -> Any -> Any
forall a b. a -> b
coe
                  T_IsIdempotentSemiring_1998 -> T_IsSemiring_1640
MAlonzo.Code.Algebra.Structures.d_isSemiring_2012
                  ((T_IsKleeneAlgebra_2122 -> T_IsIdempotentSemiring_1998)
-> Any -> Any
forall a b. a -> b
coe
                     T_IsKleeneAlgebra_2122 -> T_IsIdempotentSemiring_1998
MAlonzo.Code.Algebra.Structures.d_isIdempotentSemiring_2140
                     (T_IsKleeneAlgebra_2122 -> Any
forall a b. a -> b
coe T_IsKleeneAlgebra_2122
v0))))))
-- Data.Bool.Properties._.IsKleeneAlgebra.isUnitalMagma
d_isUnitalMagma_1410 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsKleeneAlgebra_2122 ->
  MAlonzo.Code.Algebra.Structures.T_IsUnitalMagma_666
d_isUnitalMagma_1410 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsKleeneAlgebra_2122
-> T_IsUnitalMagma_666
d_isUnitalMagma_1410 ~Bool -> Bool -> Bool
v0 ~Bool -> Bool -> Bool
v1 ~Bool -> Bool
v2 ~Bool
v3 ~Bool
v4 T_IsKleeneAlgebra_2122
v5
  = T_IsKleeneAlgebra_2122 -> T_IsUnitalMagma_666
du_isUnitalMagma_1410 T_IsKleeneAlgebra_2122
v5
du_isUnitalMagma_1410 ::
  MAlonzo.Code.Algebra.Structures.T_IsKleeneAlgebra_2122 ->
  MAlonzo.Code.Algebra.Structures.T_IsUnitalMagma_666
du_isUnitalMagma_1410 :: T_IsKleeneAlgebra_2122 -> T_IsUnitalMagma_666
du_isUnitalMagma_1410 T_IsKleeneAlgebra_2122
v0
  = let v1 :: T_IsIdempotentSemiring_1998
v1
          = T_IsKleeneAlgebra_2122 -> T_IsIdempotentSemiring_1998
MAlonzo.Code.Algebra.Structures.d_isIdempotentSemiring_2140
              (T_IsKleeneAlgebra_2122 -> T_IsKleeneAlgebra_2122
forall a b. a -> b
coe T_IsKleeneAlgebra_2122
v0) in
    Any -> T_IsUnitalMagma_666
forall a b. a -> b
coe
      (let v2 :: T_IsSemiring_1640
v2
             = T_IsIdempotentSemiring_1998 -> T_IsSemiring_1640
MAlonzo.Code.Algebra.Structures.d_isSemiring_2012 (T_IsIdempotentSemiring_1998 -> T_IsIdempotentSemiring_1998
forall a b. a -> b
coe T_IsIdempotentSemiring_1998
v1) in
       Any -> Any
forall a b. a -> b
coe
         (let v3 :: T_IsSemiringWithoutAnnihilatingZero_1536
v3
                = T_IsSemiring_1640 -> T_IsSemiringWithoutAnnihilatingZero_1536
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1654
                    (T_IsSemiring_1640 -> T_IsSemiring_1640
forall a b. a -> b
coe T_IsSemiring_1640
v2) in
          Any -> Any
forall a b. a -> b
coe
            (let v4 :: T_IsCommutativeMonoid_764
v4
                   = T_IsSemiringWithoutAnnihilatingZero_1536
-> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1556
                       (T_IsSemiringWithoutAnnihilatingZero_1536
-> T_IsSemiringWithoutAnnihilatingZero_1536
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1536
v3) in
             Any -> Any
forall a b. a -> b
coe
               ((T_IsMonoid_712 -> T_IsUnitalMagma_666) -> Any -> Any
forall a b. a -> b
coe
                  T_IsMonoid_712 -> T_IsUnitalMagma_666
MAlonzo.Code.Algebra.Structures.du_isUnitalMagma_756
                  ((T_IsCommutativeMonoid_764 -> T_IsMonoid_712) -> Any -> Any
forall a b. a -> b
coe T_IsCommutativeMonoid_764 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_774 (T_IsCommutativeMonoid_764 -> Any
forall a b. a -> b
coe T_IsCommutativeMonoid_764
v4))))))
-- Data.Bool.Properties._.IsKleeneAlgebra.distrib
d_distrib_1412 ::
  MAlonzo.Code.Algebra.Structures.T_IsKleeneAlgebra_2122 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_distrib_1412 :: T_IsKleeneAlgebra_2122 -> T_Σ_14
d_distrib_1412 T_IsKleeneAlgebra_2122
v0
  = (T_IsSemiringWithoutAnnihilatingZero_1536 -> T_Σ_14)
-> Any -> T_Σ_14
forall a b. a -> b
coe
      T_IsSemiringWithoutAnnihilatingZero_1536 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_distrib_1564
      ((T_IsSemiring_1640 -> T_IsSemiringWithoutAnnihilatingZero_1536)
-> Any -> Any
forall a b. a -> b
coe
         T_IsSemiring_1640 -> T_IsSemiringWithoutAnnihilatingZero_1536
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1654
         ((T_IsIdempotentSemiring_1998 -> T_IsSemiring_1640) -> Any -> Any
forall a b. a -> b
coe
            T_IsIdempotentSemiring_1998 -> T_IsSemiring_1640
MAlonzo.Code.Algebra.Structures.d_isSemiring_2012
            ((T_IsKleeneAlgebra_2122 -> T_IsIdempotentSemiring_1998)
-> Any -> Any
forall a b. a -> b
coe
               T_IsKleeneAlgebra_2122 -> T_IsIdempotentSemiring_1998
MAlonzo.Code.Algebra.Structures.d_isIdempotentSemiring_2140
               (T_IsKleeneAlgebra_2122 -> Any
forall a b. a -> b
coe T_IsKleeneAlgebra_2122
v0))))
-- Data.Bool.Properties._.IsKleeneAlgebra.distribʳ
d_distrib'691'_1414 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsKleeneAlgebra_2122 ->
  Bool ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_distrib'691'_1414 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsKleeneAlgebra_2122
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
d_distrib'691'_1414 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsKleeneAlgebra_2122
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsKleeneAlgebra.distribˡ
d_distrib'737'_1416 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsKleeneAlgebra_2122 ->
  Bool ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_distrib'737'_1416 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsKleeneAlgebra_2122
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
d_distrib'737'_1416 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsKleeneAlgebra_2122
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsKleeneAlgebra.isEquivalence
d_isEquivalence_1418 ::
  MAlonzo.Code.Algebra.Structures.T_IsKleeneAlgebra_2122 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
d_isEquivalence_1418 :: T_IsKleeneAlgebra_2122 -> T_IsEquivalence_28
d_isEquivalence_1418 T_IsKleeneAlgebra_2122
v0
  = (T_IsMagma_178 -> T_IsEquivalence_28) -> Any -> T_IsEquivalence_28
forall a b. a -> b
coe
      T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186
      ((T_IsSemigroup_488 -> T_IsMagma_178) -> Any -> Any
forall a b. a -> b
coe
         T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496
         ((T_IsMonoid_712 -> T_IsSemigroup_488) -> Any -> Any
forall a b. a -> b
coe
            T_IsMonoid_712 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_722
            ((T_IsCommutativeMonoid_764 -> T_IsMonoid_712) -> Any -> Any
forall a b. a -> b
coe
               T_IsCommutativeMonoid_764 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_774
               ((T_IsSemiringWithoutAnnihilatingZero_1536
 -> T_IsCommutativeMonoid_764)
-> Any -> Any
forall a b. a -> b
coe
                  T_IsSemiringWithoutAnnihilatingZero_1536
-> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1556
                  ((T_IsSemiring_1640 -> T_IsSemiringWithoutAnnihilatingZero_1536)
-> Any -> Any
forall a b. a -> b
coe
                     T_IsSemiring_1640 -> T_IsSemiringWithoutAnnihilatingZero_1536
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1654
                     ((T_IsIdempotentSemiring_1998 -> T_IsSemiring_1640) -> Any -> Any
forall a b. a -> b
coe
                        T_IsIdempotentSemiring_1998 -> T_IsSemiring_1640
MAlonzo.Code.Algebra.Structures.d_isSemiring_2012
                        ((T_IsKleeneAlgebra_2122 -> T_IsIdempotentSemiring_1998)
-> Any -> Any
forall a b. a -> b
coe
                           T_IsKleeneAlgebra_2122 -> T_IsIdempotentSemiring_1998
MAlonzo.Code.Algebra.Structures.d_isIdempotentSemiring_2140
                           (T_IsKleeneAlgebra_2122 -> Any
forall a b. a -> b
coe T_IsKleeneAlgebra_2122
v0))))))))
-- Data.Bool.Properties._.IsKleeneAlgebra.isIdempotentSemiring
d_isIdempotentSemiring_1420 ::
  MAlonzo.Code.Algebra.Structures.T_IsKleeneAlgebra_2122 ->
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentSemiring_1998
d_isIdempotentSemiring_1420 :: T_IsKleeneAlgebra_2122 -> T_IsIdempotentSemiring_1998
d_isIdempotentSemiring_1420 T_IsKleeneAlgebra_2122
v0
  = (T_IsKleeneAlgebra_2122 -> T_IsIdempotentSemiring_1998)
-> Any -> T_IsIdempotentSemiring_1998
forall a b. a -> b
coe
      T_IsKleeneAlgebra_2122 -> T_IsIdempotentSemiring_1998
MAlonzo.Code.Algebra.Structures.d_isIdempotentSemiring_2140
      (T_IsKleeneAlgebra_2122 -> Any
forall a b. a -> b
coe T_IsKleeneAlgebra_2122
v0)
-- Data.Bool.Properties._.IsKleeneAlgebra.isNearSemiring
d_isNearSemiring_1422 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsKleeneAlgebra_2122 ->
  MAlonzo.Code.Algebra.Structures.T_IsNearSemiring_1260
d_isNearSemiring_1422 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsKleeneAlgebra_2122
-> T_IsNearSemiring_1260
d_isNearSemiring_1422 ~Bool -> Bool -> Bool
v0 ~Bool -> Bool -> Bool
v1 ~Bool -> Bool
v2 ~Bool
v3 ~Bool
v4 T_IsKleeneAlgebra_2122
v5
  = T_IsKleeneAlgebra_2122 -> T_IsNearSemiring_1260
du_isNearSemiring_1422 T_IsKleeneAlgebra_2122
v5
du_isNearSemiring_1422 ::
  MAlonzo.Code.Algebra.Structures.T_IsKleeneAlgebra_2122 ->
  MAlonzo.Code.Algebra.Structures.T_IsNearSemiring_1260
du_isNearSemiring_1422 :: T_IsKleeneAlgebra_2122 -> T_IsNearSemiring_1260
du_isNearSemiring_1422 T_IsKleeneAlgebra_2122
v0
  = let v1 :: T_IsIdempotentSemiring_1998
v1
          = T_IsKleeneAlgebra_2122 -> T_IsIdempotentSemiring_1998
MAlonzo.Code.Algebra.Structures.d_isIdempotentSemiring_2140
              (T_IsKleeneAlgebra_2122 -> T_IsKleeneAlgebra_2122
forall a b. a -> b
coe T_IsKleeneAlgebra_2122
v0) in
    Any -> T_IsNearSemiring_1260
forall a b. a -> b
coe
      (let v2 :: T_IsSemiring_1640
v2
             = T_IsIdempotentSemiring_1998 -> T_IsSemiring_1640
MAlonzo.Code.Algebra.Structures.d_isSemiring_2012 (T_IsIdempotentSemiring_1998 -> T_IsIdempotentSemiring_1998
forall a b. a -> b
coe T_IsIdempotentSemiring_1998
v1) in
       Any -> Any
forall a b. a -> b
coe
         ((T_IsSemiringWithoutOne_1342 -> T_IsNearSemiring_1260)
-> Any -> Any
forall a b. a -> b
coe
            T_IsSemiringWithoutOne_1342 -> T_IsNearSemiring_1260
MAlonzo.Code.Algebra.Structures.du_isNearSemiring_1428
            ((T_IsSemiring_1640 -> T_IsSemiringWithoutOne_1342) -> Any -> Any
forall a b. a -> b
coe
               T_IsSemiring_1640 -> T_IsSemiringWithoutOne_1342
MAlonzo.Code.Algebra.Structures.du_isSemiringWithoutOne_1730
               (T_IsSemiring_1640 -> Any
forall a b. a -> b
coe T_IsSemiring_1640
v2))))
-- Data.Bool.Properties._.IsKleeneAlgebra.isPartialEquivalence
d_isPartialEquivalence_1424 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsKleeneAlgebra_2122 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_1424 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsKleeneAlgebra_2122
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_1424 ~Bool -> Bool -> Bool
v0 ~Bool -> Bool -> Bool
v1 ~Bool -> Bool
v2 ~Bool
v3 ~Bool
v4 T_IsKleeneAlgebra_2122
v5
  = T_IsKleeneAlgebra_2122 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_1424 T_IsKleeneAlgebra_2122
v5
du_isPartialEquivalence_1424 ::
  MAlonzo.Code.Algebra.Structures.T_IsKleeneAlgebra_2122 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_1424 :: T_IsKleeneAlgebra_2122 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_1424 T_IsKleeneAlgebra_2122
v0
  = let v1 :: T_IsIdempotentSemiring_1998
v1
          = T_IsKleeneAlgebra_2122 -> T_IsIdempotentSemiring_1998
MAlonzo.Code.Algebra.Structures.d_isIdempotentSemiring_2140
              (T_IsKleeneAlgebra_2122 -> T_IsKleeneAlgebra_2122
forall a b. a -> b
coe T_IsKleeneAlgebra_2122
v0) in
    Any -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsSemiring_1640
v2
             = T_IsIdempotentSemiring_1998 -> T_IsSemiring_1640
MAlonzo.Code.Algebra.Structures.d_isSemiring_2012 (T_IsIdempotentSemiring_1998 -> T_IsIdempotentSemiring_1998
forall a b. a -> b
coe T_IsIdempotentSemiring_1998
v1) in
       Any -> Any
forall a b. a -> b
coe
         (let v3 :: T_IsSemiringWithoutAnnihilatingZero_1536
v3
                = T_IsSemiring_1640 -> T_IsSemiringWithoutAnnihilatingZero_1536
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1654
                    (T_IsSemiring_1640 -> T_IsSemiring_1640
forall a b. a -> b
coe T_IsSemiring_1640
v2) in
          Any -> Any
forall a b. a -> b
coe
            (let v4 :: T_IsCommutativeMonoid_764
v4
                   = T_IsSemiringWithoutAnnihilatingZero_1536
-> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1556
                       (T_IsSemiringWithoutAnnihilatingZero_1536
-> T_IsSemiringWithoutAnnihilatingZero_1536
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1536
v3) in
             Any -> Any
forall a b. a -> b
coe
               (let v5 :: T_IsMonoid_712
v5
                      = T_IsCommutativeMonoid_764 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_774 (T_IsCommutativeMonoid_764 -> T_IsCommutativeMonoid_764
forall a b. a -> b
coe T_IsCommutativeMonoid_764
v4) in
                Any -> Any
forall a b. a -> b
coe
                  (let v6 :: T_IsSemigroup_488
v6
                         = T_IsMonoid_712 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_722 (T_IsMonoid_712 -> T_IsMonoid_712
forall a b. a -> b
coe T_IsMonoid_712
v5) in
                   Any -> Any
forall a b. a -> b
coe
                     (let v7 :: T_IsMagma_178
v7 = T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496 (T_IsSemigroup_488 -> T_IsSemigroup_488
forall a b. a -> b
coe T_IsSemigroup_488
v6) in
                      Any -> Any
forall a b. a -> b
coe
                        ((T_IsEquivalence_28 -> T_IsPartialEquivalence_16) -> Any -> Any
forall a b. a -> b
coe
                           T_IsEquivalence_28 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_44
                           ((T_IsMagma_178 -> T_IsEquivalence_28) -> Any -> Any
forall a b. a -> b
coe
                              T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186
                              (T_IsMagma_178 -> Any
forall a b. a -> b
coe T_IsMagma_178
v7)))))))))
-- Data.Bool.Properties._.IsKleeneAlgebra.isSemiring
d_isSemiring_1426 ::
  MAlonzo.Code.Algebra.Structures.T_IsKleeneAlgebra_2122 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemiring_1640
d_isSemiring_1426 :: T_IsKleeneAlgebra_2122 -> T_IsSemiring_1640
d_isSemiring_1426 T_IsKleeneAlgebra_2122
v0
  = (T_IsIdempotentSemiring_1998 -> T_IsSemiring_1640)
-> Any -> T_IsSemiring_1640
forall a b. a -> b
coe
      T_IsIdempotentSemiring_1998 -> T_IsSemiring_1640
MAlonzo.Code.Algebra.Structures.d_isSemiring_2012
      ((T_IsKleeneAlgebra_2122 -> T_IsIdempotentSemiring_1998)
-> Any -> Any
forall a b. a -> b
coe
         T_IsKleeneAlgebra_2122 -> T_IsIdempotentSemiring_1998
MAlonzo.Code.Algebra.Structures.d_isIdempotentSemiring_2140
         (T_IsKleeneAlgebra_2122 -> Any
forall a b. a -> b
coe T_IsKleeneAlgebra_2122
v0))
-- Data.Bool.Properties._.IsKleeneAlgebra.isSemiringWithoutAnnihilatingZero
d_isSemiringWithoutAnnihilatingZero_1428 ::
  MAlonzo.Code.Algebra.Structures.T_IsKleeneAlgebra_2122 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutAnnihilatingZero_1536
d_isSemiringWithoutAnnihilatingZero_1428 :: T_IsKleeneAlgebra_2122 -> T_IsSemiringWithoutAnnihilatingZero_1536
d_isSemiringWithoutAnnihilatingZero_1428 T_IsKleeneAlgebra_2122
v0
  = (T_IsSemiring_1640 -> T_IsSemiringWithoutAnnihilatingZero_1536)
-> Any -> T_IsSemiringWithoutAnnihilatingZero_1536
forall a b. a -> b
coe
      T_IsSemiring_1640 -> T_IsSemiringWithoutAnnihilatingZero_1536
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1654
      ((T_IsIdempotentSemiring_1998 -> T_IsSemiring_1640) -> Any -> Any
forall a b. a -> b
coe
         T_IsIdempotentSemiring_1998 -> T_IsSemiring_1640
MAlonzo.Code.Algebra.Structures.d_isSemiring_2012
         ((T_IsKleeneAlgebra_2122 -> T_IsIdempotentSemiring_1998)
-> Any -> Any
forall a b. a -> b
coe
            T_IsKleeneAlgebra_2122 -> T_IsIdempotentSemiring_1998
MAlonzo.Code.Algebra.Structures.d_isIdempotentSemiring_2140
            (T_IsKleeneAlgebra_2122 -> Any
forall a b. a -> b
coe T_IsKleeneAlgebra_2122
v0)))
-- Data.Bool.Properties._.IsKleeneAlgebra.isSemiringWithoutOne
d_isSemiringWithoutOne_1430 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsKleeneAlgebra_2122 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutOne_1342
d_isSemiringWithoutOne_1430 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsKleeneAlgebra_2122
-> T_IsSemiringWithoutOne_1342
d_isSemiringWithoutOne_1430 ~Bool -> Bool -> Bool
v0 ~Bool -> Bool -> Bool
v1 ~Bool -> Bool
v2 ~Bool
v3 ~Bool
v4 T_IsKleeneAlgebra_2122
v5
  = T_IsKleeneAlgebra_2122 -> T_IsSemiringWithoutOne_1342
du_isSemiringWithoutOne_1430 T_IsKleeneAlgebra_2122
v5
du_isSemiringWithoutOne_1430 ::
  MAlonzo.Code.Algebra.Structures.T_IsKleeneAlgebra_2122 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutOne_1342
du_isSemiringWithoutOne_1430 :: T_IsKleeneAlgebra_2122 -> T_IsSemiringWithoutOne_1342
du_isSemiringWithoutOne_1430 T_IsKleeneAlgebra_2122
v0
  = let v1 :: T_IsIdempotentSemiring_1998
v1
          = T_IsKleeneAlgebra_2122 -> T_IsIdempotentSemiring_1998
MAlonzo.Code.Algebra.Structures.d_isIdempotentSemiring_2140
              (T_IsKleeneAlgebra_2122 -> T_IsKleeneAlgebra_2122
forall a b. a -> b
coe T_IsKleeneAlgebra_2122
v0) in
    Any -> T_IsSemiringWithoutOne_1342
forall a b. a -> b
coe
      ((T_IsSemiring_1640 -> T_IsSemiringWithoutOne_1342) -> Any -> Any
forall a b. a -> b
coe
         T_IsSemiring_1640 -> T_IsSemiringWithoutOne_1342
MAlonzo.Code.Algebra.Structures.du_isSemiringWithoutOne_1730
         ((T_IsIdempotentSemiring_1998 -> T_IsSemiring_1640) -> Any -> Any
forall a b. a -> b
coe T_IsIdempotentSemiring_1998 -> T_IsSemiring_1640
MAlonzo.Code.Algebra.Structures.d_isSemiring_2012 (T_IsIdempotentSemiring_1998 -> Any
forall a b. a -> b
coe T_IsIdempotentSemiring_1998
v1)))
-- Data.Bool.Properties._.IsKleeneAlgebra.refl
d_refl_1432 ::
  MAlonzo.Code.Algebra.Structures.T_IsKleeneAlgebra_2122 ->
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_refl_1432 :: T_IsKleeneAlgebra_2122 -> Bool -> T__'8801'__12
d_refl_1432 = T_IsKleeneAlgebra_2122 -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsKleeneAlgebra.reflexive
d_reflexive_1434 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsKleeneAlgebra_2122 ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_reflexive_1434 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsKleeneAlgebra_2122
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_reflexive_1434 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsKleeneAlgebra_2122
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsKleeneAlgebra.setoid
d_setoid_1436 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsKleeneAlgebra_2122 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
d_setoid_1436 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsKleeneAlgebra_2122
-> T_Setoid_46
d_setoid_1436 ~Bool -> Bool -> Bool
v0 ~Bool -> Bool -> Bool
v1 ~Bool -> Bool
v2 ~Bool
v3 ~Bool
v4 T_IsKleeneAlgebra_2122
v5 = T_IsKleeneAlgebra_2122 -> T_Setoid_46
du_setoid_1436 T_IsKleeneAlgebra_2122
v5
du_setoid_1436 ::
  MAlonzo.Code.Algebra.Structures.T_IsKleeneAlgebra_2122 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
du_setoid_1436 :: T_IsKleeneAlgebra_2122 -> T_Setoid_46
du_setoid_1436 T_IsKleeneAlgebra_2122
v0
  = let v1 :: T_IsIdempotentSemiring_1998
v1
          = T_IsKleeneAlgebra_2122 -> T_IsIdempotentSemiring_1998
MAlonzo.Code.Algebra.Structures.d_isIdempotentSemiring_2140
              (T_IsKleeneAlgebra_2122 -> T_IsKleeneAlgebra_2122
forall a b. a -> b
coe T_IsKleeneAlgebra_2122
v0) in
    Any -> T_Setoid_46
forall a b. a -> b
coe
      (let v2 :: T_IsSemiring_1640
v2
             = T_IsIdempotentSemiring_1998 -> T_IsSemiring_1640
MAlonzo.Code.Algebra.Structures.d_isSemiring_2012 (T_IsIdempotentSemiring_1998 -> T_IsIdempotentSemiring_1998
forall a b. a -> b
coe T_IsIdempotentSemiring_1998
v1) in
       Any -> Any
forall a b. a -> b
coe
         (let v3 :: T_IsSemiringWithoutAnnihilatingZero_1536
v3
                = T_IsSemiring_1640 -> T_IsSemiringWithoutAnnihilatingZero_1536
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1654
                    (T_IsSemiring_1640 -> T_IsSemiring_1640
forall a b. a -> b
coe T_IsSemiring_1640
v2) in
          Any -> Any
forall a b. a -> b
coe
            (let v4 :: T_IsCommutativeMonoid_764
v4
                   = T_IsSemiringWithoutAnnihilatingZero_1536
-> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1556
                       (T_IsSemiringWithoutAnnihilatingZero_1536
-> T_IsSemiringWithoutAnnihilatingZero_1536
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1536
v3) in
             Any -> Any
forall a b. a -> b
coe
               (let v5 :: T_IsMonoid_712
v5
                      = T_IsCommutativeMonoid_764 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_774 (T_IsCommutativeMonoid_764 -> T_IsCommutativeMonoid_764
forall a b. a -> b
coe T_IsCommutativeMonoid_764
v4) in
                Any -> Any
forall a b. a -> b
coe
                  (let v6 :: T_IsSemigroup_488
v6
                         = T_IsMonoid_712 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_722 (T_IsMonoid_712 -> T_IsMonoid_712
forall a b. a -> b
coe T_IsMonoid_712
v5) in
                   Any -> Any
forall a b. a -> b
coe
                     ((T_IsMagma_178 -> T_Setoid_46) -> Any -> Any
forall a b. a -> b
coe
                        T_IsMagma_178 -> T_Setoid_46
MAlonzo.Code.Algebra.Structures.du_setoid_202
                        ((T_IsSemigroup_488 -> T_IsMagma_178) -> Any -> Any
forall a b. a -> b
coe T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496 (T_IsSemigroup_488 -> Any
forall a b. a -> b
coe T_IsSemigroup_488
v6))))))))
-- Data.Bool.Properties._.IsKleeneAlgebra.starDestructive
d_starDestructive_1438 ::
  MAlonzo.Code.Algebra.Structures.T_IsKleeneAlgebra_2122 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_starDestructive_1438 :: T_IsKleeneAlgebra_2122 -> T_Σ_14
d_starDestructive_1438 T_IsKleeneAlgebra_2122
v0
  = (T_IsKleeneAlgebra_2122 -> T_Σ_14) -> Any -> T_Σ_14
forall a b. a -> b
coe
      T_IsKleeneAlgebra_2122 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_starDestructive_2144 (T_IsKleeneAlgebra_2122 -> Any
forall a b. a -> b
coe T_IsKleeneAlgebra_2122
v0)
-- Data.Bool.Properties._.IsKleeneAlgebra.starDestructiveʳ
d_starDestructive'691'_1440 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsKleeneAlgebra_2122 ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_starDestructive'691'_1440 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsKleeneAlgebra_2122
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_starDestructive'691'_1440 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsKleeneAlgebra_2122
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsKleeneAlgebra.starDestructiveˡ
d_starDestructive'737'_1442 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsKleeneAlgebra_2122 ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_starDestructive'737'_1442 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsKleeneAlgebra_2122
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_starDestructive'737'_1442 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsKleeneAlgebra_2122
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsKleeneAlgebra.starExpansive
d_starExpansive_1444 ::
  MAlonzo.Code.Algebra.Structures.T_IsKleeneAlgebra_2122 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_starExpansive_1444 :: T_IsKleeneAlgebra_2122 -> T_Σ_14
d_starExpansive_1444 T_IsKleeneAlgebra_2122
v0
  = (T_IsKleeneAlgebra_2122 -> T_Σ_14) -> Any -> T_Σ_14
forall a b. a -> b
coe T_IsKleeneAlgebra_2122 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_starExpansive_2142 (T_IsKleeneAlgebra_2122 -> Any
forall a b. a -> b
coe T_IsKleeneAlgebra_2122
v0)
-- Data.Bool.Properties._.IsKleeneAlgebra.starExpansiveʳ
d_starExpansive'691'_1446 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsKleeneAlgebra_2122 ->
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_starExpansive'691'_1446 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsKleeneAlgebra_2122
-> Bool
-> T__'8801'__12
d_starExpansive'691'_1446 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsKleeneAlgebra_2122
-> Bool
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsKleeneAlgebra.starExpansiveˡ
d_starExpansive'737'_1448 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsKleeneAlgebra_2122 ->
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_starExpansive'737'_1448 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsKleeneAlgebra_2122
-> Bool
-> T__'8801'__12
d_starExpansive'737'_1448 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsKleeneAlgebra_2122
-> Bool
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsKleeneAlgebra.sym
d_sym_1450 ::
  MAlonzo.Code.Algebra.Structures.T_IsKleeneAlgebra_2122 ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_sym_1450 :: T_IsKleeneAlgebra_2122
-> Bool -> Bool -> T__'8801'__12 -> T__'8801'__12
d_sym_1450 = T_IsKleeneAlgebra_2122
-> Bool -> Bool -> T__'8801'__12 -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsKleeneAlgebra.trans
d_trans_1452 ::
  MAlonzo.Code.Algebra.Structures.T_IsKleeneAlgebra_2122 ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_trans_1452 :: T_IsKleeneAlgebra_2122
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
d_trans_1452 = T_IsKleeneAlgebra_2122
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsKleeneAlgebra.zero
d_zero_1454 ::
  MAlonzo.Code.Algebra.Structures.T_IsKleeneAlgebra_2122 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_zero_1454 :: T_IsKleeneAlgebra_2122 -> T_Σ_14
d_zero_1454 T_IsKleeneAlgebra_2122
v0
  = (T_IsSemiring_1640 -> T_Σ_14) -> Any -> T_Σ_14
forall a b. a -> b
coe
      T_IsSemiring_1640 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_zero_1656
      ((T_IsIdempotentSemiring_1998 -> T_IsSemiring_1640) -> Any -> Any
forall a b. a -> b
coe
         T_IsIdempotentSemiring_1998 -> T_IsSemiring_1640
MAlonzo.Code.Algebra.Structures.d_isSemiring_2012
         ((T_IsKleeneAlgebra_2122 -> T_IsIdempotentSemiring_1998)
-> Any -> Any
forall a b. a -> b
coe
            T_IsKleeneAlgebra_2122 -> T_IsIdempotentSemiring_1998
MAlonzo.Code.Algebra.Structures.d_isIdempotentSemiring_2140
            (T_IsKleeneAlgebra_2122 -> Any
forall a b. a -> b
coe T_IsKleeneAlgebra_2122
v0)))
-- Data.Bool.Properties._.IsKleeneAlgebra.zeroʳ
d_zero'691'_1456 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsKleeneAlgebra_2122 ->
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_zero'691'_1456 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsKleeneAlgebra_2122
-> Bool
-> T__'8801'__12
d_zero'691'_1456 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsKleeneAlgebra_2122
-> Bool
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsKleeneAlgebra.zeroˡ
d_zero'737'_1458 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsKleeneAlgebra_2122 ->
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_zero'737'_1458 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsKleeneAlgebra_2122
-> Bool
-> T__'8801'__12
d_zero'737'_1458 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsKleeneAlgebra_2122
-> Bool
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsLeftBolLoop.//-cong
d_'47''47''45'cong_1462 ::
  MAlonzo.Code.Algebra.Structures.T_IsLeftBolLoop_3202 ->
  Bool ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'47''47''45'cong_1462 :: T_IsLeftBolLoop_3202
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
d_'47''47''45'cong_1462 = T_IsLeftBolLoop_3202
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsLeftBolLoop.//-congʳ
d_'47''47''45'cong'691'_1464 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsLeftBolLoop_3202 ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'47''47''45'cong'691'_1464 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsLeftBolLoop_3202
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_'47''47''45'cong'691'_1464 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsLeftBolLoop_3202
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsLeftBolLoop.//-congˡ
d_'47''47''45'cong'737'_1466 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsLeftBolLoop_3202 ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'47''47''45'cong'737'_1466 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsLeftBolLoop_3202
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_'47''47''45'cong'737'_1466 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsLeftBolLoop_3202
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsLeftBolLoop.\\-cong
d_'92''92''45'cong_1468 ::
  MAlonzo.Code.Algebra.Structures.T_IsLeftBolLoop_3202 ->
  Bool ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'92''92''45'cong_1468 :: T_IsLeftBolLoop_3202
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
d_'92''92''45'cong_1468 = T_IsLeftBolLoop_3202
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsLeftBolLoop.\\-congʳ
d_'92''92''45'cong'691'_1470 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsLeftBolLoop_3202 ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'92''92''45'cong'691'_1470 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsLeftBolLoop_3202
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_'92''92''45'cong'691'_1470 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsLeftBolLoop_3202
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsLeftBolLoop.\\-congˡ
d_'92''92''45'cong'737'_1472 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsLeftBolLoop_3202 ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'92''92''45'cong'737'_1472 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsLeftBolLoop_3202
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_'92''92''45'cong'737'_1472 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsLeftBolLoop_3202
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsLeftBolLoop.identity
d_identity_1474 ::
  MAlonzo.Code.Algebra.Structures.T_IsLeftBolLoop_3202 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_identity_1474 :: T_IsLeftBolLoop_3202 -> T_Σ_14
d_identity_1474 T_IsLeftBolLoop_3202
v0
  = (T_IsLoop_3122 -> T_Σ_14) -> Any -> T_Σ_14
forall a b. a -> b
coe
      T_IsLoop_3122 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_identity_3138
      ((T_IsLeftBolLoop_3202 -> T_IsLoop_3122) -> Any -> Any
forall a b. a -> b
coe T_IsLeftBolLoop_3202 -> T_IsLoop_3122
MAlonzo.Code.Algebra.Structures.d_isLoop_3216 (T_IsLeftBolLoop_3202 -> Any
forall a b. a -> b
coe T_IsLeftBolLoop_3202
v0))
-- Data.Bool.Properties._.IsLeftBolLoop.identityʳ
d_identity'691'_1476 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsLeftBolLoop_3202 ->
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_identity'691'_1476 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsLeftBolLoop_3202
-> Bool
-> T__'8801'__12
d_identity'691'_1476 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsLeftBolLoop_3202
-> Bool
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsLeftBolLoop.identityˡ
d_identity'737'_1478 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsLeftBolLoop_3202 ->
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_identity'737'_1478 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsLeftBolLoop_3202
-> Bool
-> T__'8801'__12
d_identity'737'_1478 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsLeftBolLoop_3202
-> Bool
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsLeftBolLoop.isEquivalence
d_isEquivalence_1480 ::
  MAlonzo.Code.Algebra.Structures.T_IsLeftBolLoop_3202 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
d_isEquivalence_1480 :: T_IsLeftBolLoop_3202 -> T_IsEquivalence_28
d_isEquivalence_1480 T_IsLeftBolLoop_3202
v0
  = (T_IsMagma_178 -> T_IsEquivalence_28) -> Any -> T_IsEquivalence_28
forall a b. a -> b
coe
      T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186
      ((T_IsQuasigroup_3038 -> T_IsMagma_178) -> Any -> Any
forall a b. a -> b
coe
         T_IsQuasigroup_3038 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_3056
         ((T_IsLoop_3122 -> T_IsQuasigroup_3038) -> Any -> Any
forall a b. a -> b
coe
            T_IsLoop_3122 -> T_IsQuasigroup_3038
MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3136
            ((T_IsLeftBolLoop_3202 -> T_IsLoop_3122) -> Any -> Any
forall a b. a -> b
coe T_IsLeftBolLoop_3202 -> T_IsLoop_3122
MAlonzo.Code.Algebra.Structures.d_isLoop_3216 (T_IsLeftBolLoop_3202 -> Any
forall a b. a -> b
coe T_IsLeftBolLoop_3202
v0))))
-- Data.Bool.Properties._.IsLeftBolLoop.isLoop
d_isLoop_1482 ::
  MAlonzo.Code.Algebra.Structures.T_IsLeftBolLoop_3202 ->
  MAlonzo.Code.Algebra.Structures.T_IsLoop_3122
d_isLoop_1482 :: T_IsLeftBolLoop_3202 -> T_IsLoop_3122
d_isLoop_1482 T_IsLeftBolLoop_3202
v0
  = (T_IsLeftBolLoop_3202 -> T_IsLoop_3122) -> Any -> T_IsLoop_3122
forall a b. a -> b
coe T_IsLeftBolLoop_3202 -> T_IsLoop_3122
MAlonzo.Code.Algebra.Structures.d_isLoop_3216 (T_IsLeftBolLoop_3202 -> Any
forall a b. a -> b
coe T_IsLeftBolLoop_3202
v0)
-- Data.Bool.Properties._.IsLeftBolLoop.isMagma
d_isMagma_1484 ::
  MAlonzo.Code.Algebra.Structures.T_IsLeftBolLoop_3202 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_178
d_isMagma_1484 :: T_IsLeftBolLoop_3202 -> T_IsMagma_178
d_isMagma_1484 T_IsLeftBolLoop_3202
v0
  = (T_IsQuasigroup_3038 -> T_IsMagma_178) -> Any -> T_IsMagma_178
forall a b. a -> b
coe
      T_IsQuasigroup_3038 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_3056
      ((T_IsLoop_3122 -> T_IsQuasigroup_3038) -> Any -> Any
forall a b. a -> b
coe
         T_IsLoop_3122 -> T_IsQuasigroup_3038
MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3136
         ((T_IsLeftBolLoop_3202 -> T_IsLoop_3122) -> Any -> Any
forall a b. a -> b
coe T_IsLeftBolLoop_3202 -> T_IsLoop_3122
MAlonzo.Code.Algebra.Structures.d_isLoop_3216 (T_IsLeftBolLoop_3202 -> Any
forall a b. a -> b
coe T_IsLeftBolLoop_3202
v0)))
-- Data.Bool.Properties._.IsLeftBolLoop.isPartialEquivalence
d_isPartialEquivalence_1486 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsLeftBolLoop_3202 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_1486 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsLeftBolLoop_3202
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_1486 ~Bool -> Bool -> Bool
v0 ~Bool -> Bool -> Bool
v1 ~Bool -> Bool -> Bool
v2 ~Bool
v3 T_IsLeftBolLoop_3202
v4
  = T_IsLeftBolLoop_3202 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_1486 T_IsLeftBolLoop_3202
v4
du_isPartialEquivalence_1486 ::
  MAlonzo.Code.Algebra.Structures.T_IsLeftBolLoop_3202 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_1486 :: T_IsLeftBolLoop_3202 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_1486 T_IsLeftBolLoop_3202
v0
  = let v1 :: T_IsLoop_3122
v1
          = T_IsLeftBolLoop_3202 -> T_IsLoop_3122
MAlonzo.Code.Algebra.Structures.d_isLoop_3216 (T_IsLeftBolLoop_3202 -> T_IsLeftBolLoop_3202
forall a b. a -> b
coe T_IsLeftBolLoop_3202
v0) in
    Any -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsQuasigroup_3038
v2
             = T_IsLoop_3122 -> T_IsQuasigroup_3038
MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3136 (T_IsLoop_3122 -> T_IsLoop_3122
forall a b. a -> b
coe T_IsLoop_3122
v1) in
       Any -> Any
forall a b. a -> b
coe
         (let v3 :: T_IsMagma_178
v3
                = T_IsQuasigroup_3038 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_3056 (T_IsQuasigroup_3038 -> T_IsQuasigroup_3038
forall a b. a -> b
coe T_IsQuasigroup_3038
v2) in
          Any -> Any
forall a b. a -> b
coe
            ((T_IsEquivalence_28 -> T_IsPartialEquivalence_16) -> Any -> Any
forall a b. a -> b
coe
               T_IsEquivalence_28 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_44
               ((T_IsMagma_178 -> T_IsEquivalence_28) -> Any -> Any
forall a b. a -> b
coe
                  T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186 (T_IsMagma_178 -> Any
forall a b. a -> b
coe T_IsMagma_178
v3)))))
-- Data.Bool.Properties._.IsLeftBolLoop.isQuasigroup
d_isQuasigroup_1488 ::
  MAlonzo.Code.Algebra.Structures.T_IsLeftBolLoop_3202 ->
  MAlonzo.Code.Algebra.Structures.T_IsQuasigroup_3038
d_isQuasigroup_1488 :: T_IsLeftBolLoop_3202 -> T_IsQuasigroup_3038
d_isQuasigroup_1488 T_IsLeftBolLoop_3202
v0
  = (T_IsLoop_3122 -> T_IsQuasigroup_3038)
-> Any -> T_IsQuasigroup_3038
forall a b. a -> b
coe
      T_IsLoop_3122 -> T_IsQuasigroup_3038
MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3136
      ((T_IsLeftBolLoop_3202 -> T_IsLoop_3122) -> Any -> Any
forall a b. a -> b
coe T_IsLeftBolLoop_3202 -> T_IsLoop_3122
MAlonzo.Code.Algebra.Structures.d_isLoop_3216 (T_IsLeftBolLoop_3202 -> Any
forall a b. a -> b
coe T_IsLeftBolLoop_3202
v0))
-- Data.Bool.Properties._.IsLeftBolLoop.leftBol
d_leftBol_1490 ::
  MAlonzo.Code.Algebra.Structures.T_IsLeftBolLoop_3202 ->
  Bool ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_leftBol_1490 :: T_IsLeftBolLoop_3202 -> Bool -> Bool -> Bool -> T__'8801'__12
d_leftBol_1490 = T_IsLeftBolLoop_3202 -> Bool -> Bool -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsLeftBolLoop.leftDivides
d_leftDivides_1492 ::
  MAlonzo.Code.Algebra.Structures.T_IsLeftBolLoop_3202 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_leftDivides_1492 :: T_IsLeftBolLoop_3202 -> T_Σ_14
d_leftDivides_1492 T_IsLeftBolLoop_3202
v0
  = (T_IsQuasigroup_3038 -> T_Σ_14) -> Any -> T_Σ_14
forall a b. a -> b
coe
      T_IsQuasigroup_3038 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_leftDivides_3062
      ((T_IsLoop_3122 -> T_IsQuasigroup_3038) -> Any -> Any
forall a b. a -> b
coe
         T_IsLoop_3122 -> T_IsQuasigroup_3038
MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3136
         ((T_IsLeftBolLoop_3202 -> T_IsLoop_3122) -> Any -> Any
forall a b. a -> b
coe T_IsLeftBolLoop_3202 -> T_IsLoop_3122
MAlonzo.Code.Algebra.Structures.d_isLoop_3216 (T_IsLeftBolLoop_3202 -> Any
forall a b. a -> b
coe T_IsLeftBolLoop_3202
v0)))
-- Data.Bool.Properties._.IsLeftBolLoop.leftDividesʳ
d_leftDivides'691'_1494 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsLeftBolLoop_3202 ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_leftDivides'691'_1494 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsLeftBolLoop_3202
-> Bool
-> Bool
-> T__'8801'__12
d_leftDivides'691'_1494 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsLeftBolLoop_3202
-> Bool
-> Bool
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsLeftBolLoop.leftDividesˡ
d_leftDivides'737'_1496 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsLeftBolLoop_3202 ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_leftDivides'737'_1496 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsLeftBolLoop_3202
-> Bool
-> Bool
-> T__'8801'__12
d_leftDivides'737'_1496 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsLeftBolLoop_3202
-> Bool
-> Bool
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsLeftBolLoop.refl
d_refl_1498 ::
  MAlonzo.Code.Algebra.Structures.T_IsLeftBolLoop_3202 ->
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_refl_1498 :: T_IsLeftBolLoop_3202 -> Bool -> T__'8801'__12
d_refl_1498 = T_IsLeftBolLoop_3202 -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsLeftBolLoop.reflexive
d_reflexive_1500 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsLeftBolLoop_3202 ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_reflexive_1500 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsLeftBolLoop_3202
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_reflexive_1500 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsLeftBolLoop_3202
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsLeftBolLoop.rightDivides
d_rightDivides_1502 ::
  MAlonzo.Code.Algebra.Structures.T_IsLeftBolLoop_3202 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_rightDivides_1502 :: T_IsLeftBolLoop_3202 -> T_Σ_14
d_rightDivides_1502 T_IsLeftBolLoop_3202
v0
  = (T_IsQuasigroup_3038 -> T_Σ_14) -> Any -> T_Σ_14
forall a b. a -> b
coe
      T_IsQuasigroup_3038 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_rightDivides_3064
      ((T_IsLoop_3122 -> T_IsQuasigroup_3038) -> Any -> Any
forall a b. a -> b
coe
         T_IsLoop_3122 -> T_IsQuasigroup_3038
MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3136
         ((T_IsLeftBolLoop_3202 -> T_IsLoop_3122) -> Any -> Any
forall a b. a -> b
coe T_IsLeftBolLoop_3202 -> T_IsLoop_3122
MAlonzo.Code.Algebra.Structures.d_isLoop_3216 (T_IsLeftBolLoop_3202 -> Any
forall a b. a -> b
coe T_IsLeftBolLoop_3202
v0)))
-- Data.Bool.Properties._.IsLeftBolLoop.rightDividesʳ
d_rightDivides'691'_1504 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsLeftBolLoop_3202 ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_rightDivides'691'_1504 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsLeftBolLoop_3202
-> Bool
-> Bool
-> T__'8801'__12
d_rightDivides'691'_1504 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsLeftBolLoop_3202
-> Bool
-> Bool
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsLeftBolLoop.rightDividesˡ
d_rightDivides'737'_1506 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsLeftBolLoop_3202 ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_rightDivides'737'_1506 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsLeftBolLoop_3202
-> Bool
-> Bool
-> T__'8801'__12
d_rightDivides'737'_1506 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsLeftBolLoop_3202
-> Bool
-> Bool
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsLeftBolLoop.setoid
d_setoid_1508 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsLeftBolLoop_3202 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
d_setoid_1508 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsLeftBolLoop_3202
-> T_Setoid_46
d_setoid_1508 ~Bool -> Bool -> Bool
v0 ~Bool -> Bool -> Bool
v1 ~Bool -> Bool -> Bool
v2 ~Bool
v3 T_IsLeftBolLoop_3202
v4 = T_IsLeftBolLoop_3202 -> T_Setoid_46
du_setoid_1508 T_IsLeftBolLoop_3202
v4
du_setoid_1508 ::
  MAlonzo.Code.Algebra.Structures.T_IsLeftBolLoop_3202 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
du_setoid_1508 :: T_IsLeftBolLoop_3202 -> T_Setoid_46
du_setoid_1508 T_IsLeftBolLoop_3202
v0
  = let v1 :: T_IsLoop_3122
v1
          = T_IsLeftBolLoop_3202 -> T_IsLoop_3122
MAlonzo.Code.Algebra.Structures.d_isLoop_3216 (T_IsLeftBolLoop_3202 -> T_IsLeftBolLoop_3202
forall a b. a -> b
coe T_IsLeftBolLoop_3202
v0) in
    Any -> T_Setoid_46
forall a b. a -> b
coe
      (let v2 :: T_IsQuasigroup_3038
v2
             = T_IsLoop_3122 -> T_IsQuasigroup_3038
MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3136 (T_IsLoop_3122 -> T_IsLoop_3122
forall a b. a -> b
coe T_IsLoop_3122
v1) in
       Any -> Any
forall a b. a -> b
coe
         ((T_IsMagma_178 -> T_Setoid_46) -> Any -> Any
forall a b. a -> b
coe
            T_IsMagma_178 -> T_Setoid_46
MAlonzo.Code.Algebra.Structures.du_setoid_202
            ((T_IsQuasigroup_3038 -> T_IsMagma_178) -> Any -> Any
forall a b. a -> b
coe T_IsQuasigroup_3038 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_3056 (T_IsQuasigroup_3038 -> Any
forall a b. a -> b
coe T_IsQuasigroup_3038
v2))))
-- Data.Bool.Properties._.IsLeftBolLoop.sym
d_sym_1510 ::
  MAlonzo.Code.Algebra.Structures.T_IsLeftBolLoop_3202 ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_sym_1510 :: T_IsLeftBolLoop_3202
-> Bool -> Bool -> T__'8801'__12 -> T__'8801'__12
d_sym_1510 = T_IsLeftBolLoop_3202
-> Bool -> Bool -> T__'8801'__12 -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsLeftBolLoop.trans
d_trans_1512 ::
  MAlonzo.Code.Algebra.Structures.T_IsLeftBolLoop_3202 ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_trans_1512 :: T_IsLeftBolLoop_3202
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
d_trans_1512 = T_IsLeftBolLoop_3202
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsLeftBolLoop.∙-cong
d_'8729''45'cong_1514 ::
  MAlonzo.Code.Algebra.Structures.T_IsLeftBolLoop_3202 ->
  Bool ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8729''45'cong_1514 :: T_IsLeftBolLoop_3202
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong_1514 = T_IsLeftBolLoop_3202
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsLeftBolLoop.∙-congʳ
d_'8729''45'cong'691'_1516 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsLeftBolLoop_3202 ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8729''45'cong'691'_1516 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsLeftBolLoop_3202
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong'691'_1516 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsLeftBolLoop_3202
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsLeftBolLoop.∙-congˡ
d_'8729''45'cong'737'_1518 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsLeftBolLoop_3202 ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8729''45'cong'737'_1518 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsLeftBolLoop_3202
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong'737'_1518 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsLeftBolLoop_3202
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsLoop.//-cong
d_'47''47''45'cong_1522 ::
  MAlonzo.Code.Algebra.Structures.T_IsLoop_3122 ->
  Bool ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'47''47''45'cong_1522 :: T_IsLoop_3122
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
d_'47''47''45'cong_1522 = T_IsLoop_3122
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsLoop.//-congʳ
d_'47''47''45'cong'691'_1524 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsLoop_3122 ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'47''47''45'cong'691'_1524 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsLoop_3122
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_'47''47''45'cong'691'_1524 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsLoop_3122
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsLoop.//-congˡ
d_'47''47''45'cong'737'_1526 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsLoop_3122 ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'47''47''45'cong'737'_1526 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsLoop_3122
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_'47''47''45'cong'737'_1526 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsLoop_3122
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsLoop.\\-cong
d_'92''92''45'cong_1528 ::
  MAlonzo.Code.Algebra.Structures.T_IsLoop_3122 ->
  Bool ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'92''92''45'cong_1528 :: T_IsLoop_3122
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
d_'92''92''45'cong_1528 = T_IsLoop_3122
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsLoop.\\-congʳ
d_'92''92''45'cong'691'_1530 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsLoop_3122 ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'92''92''45'cong'691'_1530 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsLoop_3122
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_'92''92''45'cong'691'_1530 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsLoop_3122
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsLoop.\\-congˡ
d_'92''92''45'cong'737'_1532 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsLoop_3122 ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'92''92''45'cong'737'_1532 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsLoop_3122
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_'92''92''45'cong'737'_1532 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsLoop_3122
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsLoop.identity
d_identity_1534 ::
  MAlonzo.Code.Algebra.Structures.T_IsLoop_3122 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_identity_1534 :: T_IsLoop_3122 -> T_Σ_14
d_identity_1534 T_IsLoop_3122
v0
  = (T_IsLoop_3122 -> T_Σ_14) -> Any -> T_Σ_14
forall a b. a -> b
coe T_IsLoop_3122 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_identity_3138 (T_IsLoop_3122 -> Any
forall a b. a -> b
coe T_IsLoop_3122
v0)
-- Data.Bool.Properties._.IsLoop.identityʳ
d_identity'691'_1536 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsLoop_3122 ->
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_identity'691'_1536 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsLoop_3122
-> Bool
-> T__'8801'__12
d_identity'691'_1536 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsLoop_3122
-> Bool
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsLoop.identityˡ
d_identity'737'_1538 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsLoop_3122 ->
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_identity'737'_1538 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsLoop_3122
-> Bool
-> T__'8801'__12
d_identity'737'_1538 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsLoop_3122
-> Bool
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsLoop.isEquivalence
d_isEquivalence_1540 ::
  MAlonzo.Code.Algebra.Structures.T_IsLoop_3122 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
d_isEquivalence_1540 :: T_IsLoop_3122 -> T_IsEquivalence_28
d_isEquivalence_1540 T_IsLoop_3122
v0
  = (T_IsMagma_178 -> T_IsEquivalence_28) -> Any -> T_IsEquivalence_28
forall a b. a -> b
coe
      T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186
      ((T_IsQuasigroup_3038 -> T_IsMagma_178) -> Any -> Any
forall a b. a -> b
coe
         T_IsQuasigroup_3038 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_3056
         ((T_IsLoop_3122 -> T_IsQuasigroup_3038) -> Any -> Any
forall a b. a -> b
coe T_IsLoop_3122 -> T_IsQuasigroup_3038
MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3136 (T_IsLoop_3122 -> Any
forall a b. a -> b
coe T_IsLoop_3122
v0)))
-- Data.Bool.Properties._.IsLoop.isMagma
d_isMagma_1542 ::
  MAlonzo.Code.Algebra.Structures.T_IsLoop_3122 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_178
d_isMagma_1542 :: T_IsLoop_3122 -> T_IsMagma_178
d_isMagma_1542 T_IsLoop_3122
v0
  = (T_IsQuasigroup_3038 -> T_IsMagma_178) -> Any -> T_IsMagma_178
forall a b. a -> b
coe
      T_IsQuasigroup_3038 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_3056
      ((T_IsLoop_3122 -> T_IsQuasigroup_3038) -> Any -> Any
forall a b. a -> b
coe T_IsLoop_3122 -> T_IsQuasigroup_3038
MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3136 (T_IsLoop_3122 -> Any
forall a b. a -> b
coe T_IsLoop_3122
v0))
-- Data.Bool.Properties._.IsLoop.isPartialEquivalence
d_isPartialEquivalence_1544 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsLoop_3122 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_1544 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsLoop_3122
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_1544 ~Bool -> Bool -> Bool
v0 ~Bool -> Bool -> Bool
v1 ~Bool -> Bool -> Bool
v2 ~Bool
v3 T_IsLoop_3122
v4
  = T_IsLoop_3122 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_1544 T_IsLoop_3122
v4
du_isPartialEquivalence_1544 ::
  MAlonzo.Code.Algebra.Structures.T_IsLoop_3122 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_1544 :: T_IsLoop_3122 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_1544 T_IsLoop_3122
v0
  = let v1 :: T_IsQuasigroup_3038
v1
          = T_IsLoop_3122 -> T_IsQuasigroup_3038
MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3136 (T_IsLoop_3122 -> T_IsLoop_3122
forall a b. a -> b
coe T_IsLoop_3122
v0) in
    Any -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsMagma_178
v2
             = T_IsQuasigroup_3038 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_3056 (T_IsQuasigroup_3038 -> T_IsQuasigroup_3038
forall a b. a -> b
coe T_IsQuasigroup_3038
v1) in
       Any -> Any
forall a b. a -> b
coe
         ((T_IsEquivalence_28 -> T_IsPartialEquivalence_16) -> Any -> Any
forall a b. a -> b
coe
            T_IsEquivalence_28 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_44
            ((T_IsMagma_178 -> T_IsEquivalence_28) -> Any -> Any
forall a b. a -> b
coe
               T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186 (T_IsMagma_178 -> Any
forall a b. a -> b
coe T_IsMagma_178
v2))))
-- Data.Bool.Properties._.IsLoop.isQuasigroup
d_isQuasigroup_1546 ::
  MAlonzo.Code.Algebra.Structures.T_IsLoop_3122 ->
  MAlonzo.Code.Algebra.Structures.T_IsQuasigroup_3038
d_isQuasigroup_1546 :: T_IsLoop_3122 -> T_IsQuasigroup_3038
d_isQuasigroup_1546 T_IsLoop_3122
v0
  = (T_IsLoop_3122 -> T_IsQuasigroup_3038)
-> Any -> T_IsQuasigroup_3038
forall a b. a -> b
coe T_IsLoop_3122 -> T_IsQuasigroup_3038
MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3136 (T_IsLoop_3122 -> Any
forall a b. a -> b
coe T_IsLoop_3122
v0)
-- Data.Bool.Properties._.IsLoop.leftDivides
d_leftDivides_1548 ::
  MAlonzo.Code.Algebra.Structures.T_IsLoop_3122 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_leftDivides_1548 :: T_IsLoop_3122 -> T_Σ_14
d_leftDivides_1548 T_IsLoop_3122
v0
  = (T_IsQuasigroup_3038 -> T_Σ_14) -> Any -> T_Σ_14
forall a b. a -> b
coe
      T_IsQuasigroup_3038 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_leftDivides_3062
      ((T_IsLoop_3122 -> T_IsQuasigroup_3038) -> Any -> Any
forall a b. a -> b
coe T_IsLoop_3122 -> T_IsQuasigroup_3038
MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3136 (T_IsLoop_3122 -> Any
forall a b. a -> b
coe T_IsLoop_3122
v0))
-- Data.Bool.Properties._.IsLoop.leftDividesʳ
d_leftDivides'691'_1550 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsLoop_3122 ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_leftDivides'691'_1550 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsLoop_3122
-> Bool
-> Bool
-> T__'8801'__12
d_leftDivides'691'_1550 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsLoop_3122
-> Bool
-> Bool
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsLoop.leftDividesˡ
d_leftDivides'737'_1552 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsLoop_3122 ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_leftDivides'737'_1552 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsLoop_3122
-> Bool
-> Bool
-> T__'8801'__12
d_leftDivides'737'_1552 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsLoop_3122
-> Bool
-> Bool
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsLoop.refl
d_refl_1554 ::
  MAlonzo.Code.Algebra.Structures.T_IsLoop_3122 ->
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_refl_1554 :: T_IsLoop_3122 -> Bool -> T__'8801'__12
d_refl_1554 = T_IsLoop_3122 -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsLoop.reflexive
d_reflexive_1556 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsLoop_3122 ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_reflexive_1556 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsLoop_3122
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_reflexive_1556 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsLoop_3122
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsLoop.rightDivides
d_rightDivides_1558 ::
  MAlonzo.Code.Algebra.Structures.T_IsLoop_3122 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_rightDivides_1558 :: T_IsLoop_3122 -> T_Σ_14
d_rightDivides_1558 T_IsLoop_3122
v0
  = (T_IsQuasigroup_3038 -> T_Σ_14) -> Any -> T_Σ_14
forall a b. a -> b
coe
      T_IsQuasigroup_3038 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_rightDivides_3064
      ((T_IsLoop_3122 -> T_IsQuasigroup_3038) -> Any -> Any
forall a b. a -> b
coe T_IsLoop_3122 -> T_IsQuasigroup_3038
MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3136 (T_IsLoop_3122 -> Any
forall a b. a -> b
coe T_IsLoop_3122
v0))
-- Data.Bool.Properties._.IsLoop.rightDividesʳ
d_rightDivides'691'_1560 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsLoop_3122 ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_rightDivides'691'_1560 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsLoop_3122
-> Bool
-> Bool
-> T__'8801'__12
d_rightDivides'691'_1560 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsLoop_3122
-> Bool
-> Bool
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsLoop.rightDividesˡ
d_rightDivides'737'_1562 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsLoop_3122 ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_rightDivides'737'_1562 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsLoop_3122
-> Bool
-> Bool
-> T__'8801'__12
d_rightDivides'737'_1562 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsLoop_3122
-> Bool
-> Bool
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsLoop.setoid
d_setoid_1564 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsLoop_3122 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
d_setoid_1564 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsLoop_3122
-> T_Setoid_46
d_setoid_1564 ~Bool -> Bool -> Bool
v0 ~Bool -> Bool -> Bool
v1 ~Bool -> Bool -> Bool
v2 ~Bool
v3 T_IsLoop_3122
v4 = T_IsLoop_3122 -> T_Setoid_46
du_setoid_1564 T_IsLoop_3122
v4
du_setoid_1564 ::
  MAlonzo.Code.Algebra.Structures.T_IsLoop_3122 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
du_setoid_1564 :: T_IsLoop_3122 -> T_Setoid_46
du_setoid_1564 T_IsLoop_3122
v0
  = let v1 :: T_IsQuasigroup_3038
v1
          = T_IsLoop_3122 -> T_IsQuasigroup_3038
MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3136 (T_IsLoop_3122 -> T_IsLoop_3122
forall a b. a -> b
coe T_IsLoop_3122
v0) in
    Any -> T_Setoid_46
forall a b. a -> b
coe
      ((T_IsMagma_178 -> T_Setoid_46) -> Any -> Any
forall a b. a -> b
coe
         T_IsMagma_178 -> T_Setoid_46
MAlonzo.Code.Algebra.Structures.du_setoid_202
         ((T_IsQuasigroup_3038 -> T_IsMagma_178) -> Any -> Any
forall a b. a -> b
coe T_IsQuasigroup_3038 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_3056 (T_IsQuasigroup_3038 -> Any
forall a b. a -> b
coe T_IsQuasigroup_3038
v1)))
-- Data.Bool.Properties._.IsLoop.sym
d_sym_1566 ::
  MAlonzo.Code.Algebra.Structures.T_IsLoop_3122 ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_sym_1566 :: T_IsLoop_3122 -> Bool -> Bool -> T__'8801'__12 -> T__'8801'__12
d_sym_1566 = T_IsLoop_3122 -> Bool -> Bool -> T__'8801'__12 -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsLoop.trans
d_trans_1568 ::
  MAlonzo.Code.Algebra.Structures.T_IsLoop_3122 ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_trans_1568 :: T_IsLoop_3122
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
d_trans_1568 = T_IsLoop_3122
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsLoop.∙-cong
d_'8729''45'cong_1570 ::
  MAlonzo.Code.Algebra.Structures.T_IsLoop_3122 ->
  Bool ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8729''45'cong_1570 :: T_IsLoop_3122
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong_1570 = T_IsLoop_3122
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsLoop.∙-congʳ
d_'8729''45'cong'691'_1572 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsLoop_3122 ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8729''45'cong'691'_1572 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsLoop_3122
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong'691'_1572 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsLoop_3122
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsLoop.∙-congˡ
d_'8729''45'cong'737'_1574 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsLoop_3122 ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8729''45'cong'737'_1574 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsLoop_3122
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong'737'_1574 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsLoop_3122
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsMagma.isEquivalence
d_isEquivalence_1578 ::
  MAlonzo.Code.Algebra.Structures.T_IsMagma_178 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
d_isEquivalence_1578 :: T_IsMagma_178 -> T_IsEquivalence_28
d_isEquivalence_1578 T_IsMagma_178
v0
  = (T_IsMagma_178 -> T_IsEquivalence_28) -> Any -> T_IsEquivalence_28
forall a b. a -> b
coe T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186 (T_IsMagma_178 -> Any
forall a b. a -> b
coe T_IsMagma_178
v0)
-- Data.Bool.Properties._.IsMagma.isPartialEquivalence
d_isPartialEquivalence_1580 ::
  (Bool -> Bool -> Bool) ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_178 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_1580 :: (Bool -> Bool -> Bool)
-> T_IsMagma_178 -> T_IsPartialEquivalence_16
d_isPartialEquivalence_1580 ~Bool -> Bool -> Bool
v0 T_IsMagma_178
v1
  = T_IsMagma_178 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_1580 T_IsMagma_178
v1
du_isPartialEquivalence_1580 ::
  MAlonzo.Code.Algebra.Structures.T_IsMagma_178 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_1580 :: T_IsMagma_178 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_1580 T_IsMagma_178
v0
  = (T_IsEquivalence_28 -> T_IsPartialEquivalence_16)
-> Any -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      T_IsEquivalence_28 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_44
      ((T_IsMagma_178 -> T_IsEquivalence_28) -> Any -> Any
forall a b. a -> b
coe T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186 (T_IsMagma_178 -> Any
forall a b. a -> b
coe T_IsMagma_178
v0))
-- Data.Bool.Properties._.IsMagma.refl
d_refl_1582 ::
  MAlonzo.Code.Algebra.Structures.T_IsMagma_178 ->
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_refl_1582 :: T_IsMagma_178 -> Bool -> T__'8801'__12
d_refl_1582 = T_IsMagma_178 -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsMagma.reflexive
d_reflexive_1584 ::
  (Bool -> Bool -> Bool) ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_178 ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_reflexive_1584 :: (Bool -> Bool -> Bool)
-> T_IsMagma_178 -> Bool -> Bool -> T__'8801'__12 -> T__'8801'__12
d_reflexive_1584 = (Bool -> Bool -> Bool)
-> T_IsMagma_178 -> Bool -> Bool -> T__'8801'__12 -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsMagma.setoid
d_setoid_1586 ::
  (Bool -> Bool -> Bool) ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_178 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
d_setoid_1586 :: (Bool -> Bool -> Bool) -> T_IsMagma_178 -> T_Setoid_46
d_setoid_1586 Bool -> Bool -> Bool
v0 T_IsMagma_178
v1
  = (T_IsMagma_178 -> T_Setoid_46) -> T_IsMagma_178 -> T_Setoid_46
forall a b. a -> b
coe T_IsMagma_178 -> T_Setoid_46
MAlonzo.Code.Algebra.Structures.du_setoid_202 T_IsMagma_178
v1
-- Data.Bool.Properties._.IsMagma.sym
d_sym_1588 ::
  MAlonzo.Code.Algebra.Structures.T_IsMagma_178 ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_sym_1588 :: T_IsMagma_178 -> Bool -> Bool -> T__'8801'__12 -> T__'8801'__12
d_sym_1588 = T_IsMagma_178 -> Bool -> Bool -> T__'8801'__12 -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsMagma.trans
d_trans_1590 ::
  MAlonzo.Code.Algebra.Structures.T_IsMagma_178 ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_trans_1590 :: T_IsMagma_178
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
d_trans_1590 = T_IsMagma_178
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsMagma.∙-cong
d_'8729''45'cong_1592 ::
  MAlonzo.Code.Algebra.Structures.T_IsMagma_178 ->
  Bool ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8729''45'cong_1592 :: T_IsMagma_178
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong_1592 = T_IsMagma_178
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsMagma.∙-congʳ
d_'8729''45'cong'691'_1594 ::
  (Bool -> Bool -> Bool) ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_178 ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8729''45'cong'691'_1594 :: (Bool -> Bool -> Bool)
-> T_IsMagma_178
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong'691'_1594 = (Bool -> Bool -> Bool)
-> T_IsMagma_178
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsMagma.∙-congˡ
d_'8729''45'cong'737'_1596 ::
  (Bool -> Bool -> Bool) ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_178 ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8729''45'cong'737'_1596 :: (Bool -> Bool -> Bool)
-> T_IsMagma_178
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong'737'_1596 = (Bool -> Bool -> Bool)
-> T_IsMagma_178
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsMedialMagma.isEquivalence
d_isEquivalence_1600 ::
  MAlonzo.Code.Algebra.Structures.T_IsMedialMagma_370 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
d_isEquivalence_1600 :: T_IsMedialMagma_370 -> T_IsEquivalence_28
d_isEquivalence_1600 T_IsMedialMagma_370
v0
  = (T_IsMagma_178 -> T_IsEquivalence_28) -> Any -> T_IsEquivalence_28
forall a b. a -> b
coe
      T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186
      ((T_IsMedialMagma_370 -> T_IsMagma_178) -> Any -> Any
forall a b. a -> b
coe T_IsMedialMagma_370 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_378 (T_IsMedialMagma_370 -> Any
forall a b. a -> b
coe T_IsMedialMagma_370
v0))
-- Data.Bool.Properties._.IsMedialMagma.isMagma
d_isMagma_1602 ::
  MAlonzo.Code.Algebra.Structures.T_IsMedialMagma_370 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_178
d_isMagma_1602 :: T_IsMedialMagma_370 -> T_IsMagma_178
d_isMagma_1602 T_IsMedialMagma_370
v0
  = (T_IsMedialMagma_370 -> T_IsMagma_178) -> Any -> T_IsMagma_178
forall a b. a -> b
coe T_IsMedialMagma_370 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_378 (T_IsMedialMagma_370 -> Any
forall a b. a -> b
coe T_IsMedialMagma_370
v0)
-- Data.Bool.Properties._.IsMedialMagma.isPartialEquivalence
d_isPartialEquivalence_1604 ::
  (Bool -> Bool -> Bool) ->
  MAlonzo.Code.Algebra.Structures.T_IsMedialMagma_370 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_1604 :: (Bool -> Bool -> Bool)
-> T_IsMedialMagma_370 -> T_IsPartialEquivalence_16
d_isPartialEquivalence_1604 ~Bool -> Bool -> Bool
v0 T_IsMedialMagma_370
v1
  = T_IsMedialMagma_370 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_1604 T_IsMedialMagma_370
v1
du_isPartialEquivalence_1604 ::
  MAlonzo.Code.Algebra.Structures.T_IsMedialMagma_370 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_1604 :: T_IsMedialMagma_370 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_1604 T_IsMedialMagma_370
v0
  = let v1 :: T_IsMagma_178
v1
          = T_IsMedialMagma_370 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_378 (T_IsMedialMagma_370 -> T_IsMedialMagma_370
forall a b. a -> b
coe T_IsMedialMagma_370
v0) in
    Any -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      ((T_IsEquivalence_28 -> T_IsPartialEquivalence_16) -> Any -> Any
forall a b. a -> b
coe
         T_IsEquivalence_28 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_44
         ((T_IsMagma_178 -> T_IsEquivalence_28) -> Any -> Any
forall a b. a -> b
coe T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186 (T_IsMagma_178 -> Any
forall a b. a -> b
coe T_IsMagma_178
v1)))
-- Data.Bool.Properties._.IsMedialMagma.medial
d_medial_1606 ::
  MAlonzo.Code.Algebra.Structures.T_IsMedialMagma_370 ->
  Bool ->
  Bool ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_medial_1606 :: T_IsMedialMagma_370
-> Bool -> Bool -> Bool -> Bool -> T__'8801'__12
d_medial_1606 = T_IsMedialMagma_370
-> Bool -> Bool -> Bool -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsMedialMagma.refl
d_refl_1608 ::
  MAlonzo.Code.Algebra.Structures.T_IsMedialMagma_370 ->
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_refl_1608 :: T_IsMedialMagma_370 -> Bool -> T__'8801'__12
d_refl_1608 = T_IsMedialMagma_370 -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsMedialMagma.reflexive
d_reflexive_1610 ::
  (Bool -> Bool -> Bool) ->
  MAlonzo.Code.Algebra.Structures.T_IsMedialMagma_370 ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_reflexive_1610 :: (Bool -> Bool -> Bool)
-> T_IsMedialMagma_370
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_reflexive_1610 = (Bool -> Bool -> Bool)
-> T_IsMedialMagma_370
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsMedialMagma.setoid
d_setoid_1612 ::
  (Bool -> Bool -> Bool) ->
  MAlonzo.Code.Algebra.Structures.T_IsMedialMagma_370 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
d_setoid_1612 :: (Bool -> Bool -> Bool) -> T_IsMedialMagma_370 -> T_Setoid_46
d_setoid_1612 ~Bool -> Bool -> Bool
v0 T_IsMedialMagma_370
v1 = T_IsMedialMagma_370 -> T_Setoid_46
du_setoid_1612 T_IsMedialMagma_370
v1
du_setoid_1612 ::
  MAlonzo.Code.Algebra.Structures.T_IsMedialMagma_370 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
du_setoid_1612 :: T_IsMedialMagma_370 -> T_Setoid_46
du_setoid_1612 T_IsMedialMagma_370
v0
  = (T_IsMagma_178 -> T_Setoid_46) -> Any -> T_Setoid_46
forall a b. a -> b
coe
      T_IsMagma_178 -> T_Setoid_46
MAlonzo.Code.Algebra.Structures.du_setoid_202
      ((T_IsMedialMagma_370 -> T_IsMagma_178) -> Any -> Any
forall a b. a -> b
coe T_IsMedialMagma_370 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_378 (T_IsMedialMagma_370 -> Any
forall a b. a -> b
coe T_IsMedialMagma_370
v0))
-- Data.Bool.Properties._.IsMedialMagma.sym
d_sym_1614 ::
  MAlonzo.Code.Algebra.Structures.T_IsMedialMagma_370 ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_sym_1614 :: T_IsMedialMagma_370
-> Bool -> Bool -> T__'8801'__12 -> T__'8801'__12
d_sym_1614 = T_IsMedialMagma_370
-> Bool -> Bool -> T__'8801'__12 -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsMedialMagma.trans
d_trans_1616 ::
  MAlonzo.Code.Algebra.Structures.T_IsMedialMagma_370 ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_trans_1616 :: T_IsMedialMagma_370
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
d_trans_1616 = T_IsMedialMagma_370
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsMedialMagma.∙-cong
d_'8729''45'cong_1618 ::
  MAlonzo.Code.Algebra.Structures.T_IsMedialMagma_370 ->
  Bool ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8729''45'cong_1618 :: T_IsMedialMagma_370
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong_1618 = T_IsMedialMagma_370
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsMedialMagma.∙-congʳ
d_'8729''45'cong'691'_1620 ::
  (Bool -> Bool -> Bool) ->
  MAlonzo.Code.Algebra.Structures.T_IsMedialMagma_370 ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8729''45'cong'691'_1620 :: (Bool -> Bool -> Bool)
-> T_IsMedialMagma_370
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong'691'_1620 = (Bool -> Bool -> Bool)
-> T_IsMedialMagma_370
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsMedialMagma.∙-congˡ
d_'8729''45'cong'737'_1622 ::
  (Bool -> Bool -> Bool) ->
  MAlonzo.Code.Algebra.Structures.T_IsMedialMagma_370 ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8729''45'cong'737'_1622 :: (Bool -> Bool -> Bool)
-> T_IsMedialMagma_370
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong'737'_1622 = (Bool -> Bool -> Bool)
-> T_IsMedialMagma_370
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsMiddleBolLoop.//-cong
d_'47''47''45'cong_1626 ::
  MAlonzo.Code.Algebra.Structures.T_IsMiddleBolLoop_3462 ->
  Bool ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'47''47''45'cong_1626 :: T_IsMiddleBolLoop_3462
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
d_'47''47''45'cong_1626 = T_IsMiddleBolLoop_3462
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsMiddleBolLoop.//-congʳ
d_'47''47''45'cong'691'_1628 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsMiddleBolLoop_3462 ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'47''47''45'cong'691'_1628 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsMiddleBolLoop_3462
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_'47''47''45'cong'691'_1628 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsMiddleBolLoop_3462
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsMiddleBolLoop.//-congˡ
d_'47''47''45'cong'737'_1630 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsMiddleBolLoop_3462 ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'47''47''45'cong'737'_1630 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsMiddleBolLoop_3462
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_'47''47''45'cong'737'_1630 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsMiddleBolLoop_3462
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsMiddleBolLoop.\\-cong
d_'92''92''45'cong_1632 ::
  MAlonzo.Code.Algebra.Structures.T_IsMiddleBolLoop_3462 ->
  Bool ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'92''92''45'cong_1632 :: T_IsMiddleBolLoop_3462
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
d_'92''92''45'cong_1632 = T_IsMiddleBolLoop_3462
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsMiddleBolLoop.\\-congʳ
d_'92''92''45'cong'691'_1634 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsMiddleBolLoop_3462 ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'92''92''45'cong'691'_1634 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsMiddleBolLoop_3462
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_'92''92''45'cong'691'_1634 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsMiddleBolLoop_3462
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsMiddleBolLoop.\\-congˡ
d_'92''92''45'cong'737'_1636 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsMiddleBolLoop_3462 ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'92''92''45'cong'737'_1636 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsMiddleBolLoop_3462
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_'92''92''45'cong'737'_1636 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsMiddleBolLoop_3462
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsMiddleBolLoop.identity
d_identity_1638 ::
  MAlonzo.Code.Algebra.Structures.T_IsMiddleBolLoop_3462 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_identity_1638 :: T_IsMiddleBolLoop_3462 -> T_Σ_14
d_identity_1638 T_IsMiddleBolLoop_3462
v0
  = (T_IsLoop_3122 -> T_Σ_14) -> Any -> T_Σ_14
forall a b. a -> b
coe
      T_IsLoop_3122 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_identity_3138
      ((T_IsMiddleBolLoop_3462 -> T_IsLoop_3122) -> Any -> Any
forall a b. a -> b
coe T_IsMiddleBolLoop_3462 -> T_IsLoop_3122
MAlonzo.Code.Algebra.Structures.d_isLoop_3476 (T_IsMiddleBolLoop_3462 -> Any
forall a b. a -> b
coe T_IsMiddleBolLoop_3462
v0))
-- Data.Bool.Properties._.IsMiddleBolLoop.identityʳ
d_identity'691'_1640 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsMiddleBolLoop_3462 ->
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_identity'691'_1640 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsMiddleBolLoop_3462
-> Bool
-> T__'8801'__12
d_identity'691'_1640 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsMiddleBolLoop_3462
-> Bool
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsMiddleBolLoop.identityˡ
d_identity'737'_1642 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsMiddleBolLoop_3462 ->
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_identity'737'_1642 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsMiddleBolLoop_3462
-> Bool
-> T__'8801'__12
d_identity'737'_1642 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsMiddleBolLoop_3462
-> Bool
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsMiddleBolLoop.isEquivalence
d_isEquivalence_1644 ::
  MAlonzo.Code.Algebra.Structures.T_IsMiddleBolLoop_3462 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
d_isEquivalence_1644 :: T_IsMiddleBolLoop_3462 -> T_IsEquivalence_28
d_isEquivalence_1644 T_IsMiddleBolLoop_3462
v0
  = (T_IsMagma_178 -> T_IsEquivalence_28) -> Any -> T_IsEquivalence_28
forall a b. a -> b
coe
      T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186
      ((T_IsQuasigroup_3038 -> T_IsMagma_178) -> Any -> Any
forall a b. a -> b
coe
         T_IsQuasigroup_3038 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_3056
         ((T_IsLoop_3122 -> T_IsQuasigroup_3038) -> Any -> Any
forall a b. a -> b
coe
            T_IsLoop_3122 -> T_IsQuasigroup_3038
MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3136
            ((T_IsMiddleBolLoop_3462 -> T_IsLoop_3122) -> Any -> Any
forall a b. a -> b
coe T_IsMiddleBolLoop_3462 -> T_IsLoop_3122
MAlonzo.Code.Algebra.Structures.d_isLoop_3476 (T_IsMiddleBolLoop_3462 -> Any
forall a b. a -> b
coe T_IsMiddleBolLoop_3462
v0))))
-- Data.Bool.Properties._.IsMiddleBolLoop.isLoop
d_isLoop_1646 ::
  MAlonzo.Code.Algebra.Structures.T_IsMiddleBolLoop_3462 ->
  MAlonzo.Code.Algebra.Structures.T_IsLoop_3122
d_isLoop_1646 :: T_IsMiddleBolLoop_3462 -> T_IsLoop_3122
d_isLoop_1646 T_IsMiddleBolLoop_3462
v0
  = (T_IsMiddleBolLoop_3462 -> T_IsLoop_3122) -> Any -> T_IsLoop_3122
forall a b. a -> b
coe T_IsMiddleBolLoop_3462 -> T_IsLoop_3122
MAlonzo.Code.Algebra.Structures.d_isLoop_3476 (T_IsMiddleBolLoop_3462 -> Any
forall a b. a -> b
coe T_IsMiddleBolLoop_3462
v0)
-- Data.Bool.Properties._.IsMiddleBolLoop.isMagma
d_isMagma_1648 ::
  MAlonzo.Code.Algebra.Structures.T_IsMiddleBolLoop_3462 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_178
d_isMagma_1648 :: T_IsMiddleBolLoop_3462 -> T_IsMagma_178
d_isMagma_1648 T_IsMiddleBolLoop_3462
v0
  = (T_IsQuasigroup_3038 -> T_IsMagma_178) -> Any -> T_IsMagma_178
forall a b. a -> b
coe
      T_IsQuasigroup_3038 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_3056
      ((T_IsLoop_3122 -> T_IsQuasigroup_3038) -> Any -> Any
forall a b. a -> b
coe
         T_IsLoop_3122 -> T_IsQuasigroup_3038
MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3136
         ((T_IsMiddleBolLoop_3462 -> T_IsLoop_3122) -> Any -> Any
forall a b. a -> b
coe T_IsMiddleBolLoop_3462 -> T_IsLoop_3122
MAlonzo.Code.Algebra.Structures.d_isLoop_3476 (T_IsMiddleBolLoop_3462 -> Any
forall a b. a -> b
coe T_IsMiddleBolLoop_3462
v0)))
-- Data.Bool.Properties._.IsMiddleBolLoop.isPartialEquivalence
d_isPartialEquivalence_1650 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsMiddleBolLoop_3462 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_1650 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsMiddleBolLoop_3462
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_1650 ~Bool -> Bool -> Bool
v0 ~Bool -> Bool -> Bool
v1 ~Bool -> Bool -> Bool
v2 ~Bool
v3 T_IsMiddleBolLoop_3462
v4
  = T_IsMiddleBolLoop_3462 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_1650 T_IsMiddleBolLoop_3462
v4
du_isPartialEquivalence_1650 ::
  MAlonzo.Code.Algebra.Structures.T_IsMiddleBolLoop_3462 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_1650 :: T_IsMiddleBolLoop_3462 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_1650 T_IsMiddleBolLoop_3462
v0
  = let v1 :: T_IsLoop_3122
v1
          = T_IsMiddleBolLoop_3462 -> T_IsLoop_3122
MAlonzo.Code.Algebra.Structures.d_isLoop_3476 (T_IsMiddleBolLoop_3462 -> T_IsMiddleBolLoop_3462
forall a b. a -> b
coe T_IsMiddleBolLoop_3462
v0) in
    Any -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsQuasigroup_3038
v2
             = T_IsLoop_3122 -> T_IsQuasigroup_3038
MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3136 (T_IsLoop_3122 -> T_IsLoop_3122
forall a b. a -> b
coe T_IsLoop_3122
v1) in
       Any -> Any
forall a b. a -> b
coe
         (let v3 :: T_IsMagma_178
v3
                = T_IsQuasigroup_3038 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_3056 (T_IsQuasigroup_3038 -> T_IsQuasigroup_3038
forall a b. a -> b
coe T_IsQuasigroup_3038
v2) in
          Any -> Any
forall a b. a -> b
coe
            ((T_IsEquivalence_28 -> T_IsPartialEquivalence_16) -> Any -> Any
forall a b. a -> b
coe
               T_IsEquivalence_28 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_44
               ((T_IsMagma_178 -> T_IsEquivalence_28) -> Any -> Any
forall a b. a -> b
coe
                  T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186 (T_IsMagma_178 -> Any
forall a b. a -> b
coe T_IsMagma_178
v3)))))
-- Data.Bool.Properties._.IsMiddleBolLoop.isQuasigroup
d_isQuasigroup_1652 ::
  MAlonzo.Code.Algebra.Structures.T_IsMiddleBolLoop_3462 ->
  MAlonzo.Code.Algebra.Structures.T_IsQuasigroup_3038
d_isQuasigroup_1652 :: T_IsMiddleBolLoop_3462 -> T_IsQuasigroup_3038
d_isQuasigroup_1652 T_IsMiddleBolLoop_3462
v0
  = (T_IsLoop_3122 -> T_IsQuasigroup_3038)
-> Any -> T_IsQuasigroup_3038
forall a b. a -> b
coe
      T_IsLoop_3122 -> T_IsQuasigroup_3038
MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3136
      ((T_IsMiddleBolLoop_3462 -> T_IsLoop_3122) -> Any -> Any
forall a b. a -> b
coe T_IsMiddleBolLoop_3462 -> T_IsLoop_3122
MAlonzo.Code.Algebra.Structures.d_isLoop_3476 (T_IsMiddleBolLoop_3462 -> Any
forall a b. a -> b
coe T_IsMiddleBolLoop_3462
v0))
-- Data.Bool.Properties._.IsMiddleBolLoop.leftDivides
d_leftDivides_1654 ::
  MAlonzo.Code.Algebra.Structures.T_IsMiddleBolLoop_3462 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_leftDivides_1654 :: T_IsMiddleBolLoop_3462 -> T_Σ_14
d_leftDivides_1654 T_IsMiddleBolLoop_3462
v0
  = (T_IsQuasigroup_3038 -> T_Σ_14) -> Any -> T_Σ_14
forall a b. a -> b
coe
      T_IsQuasigroup_3038 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_leftDivides_3062
      ((T_IsLoop_3122 -> T_IsQuasigroup_3038) -> Any -> Any
forall a b. a -> b
coe
         T_IsLoop_3122 -> T_IsQuasigroup_3038
MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3136
         ((T_IsMiddleBolLoop_3462 -> T_IsLoop_3122) -> Any -> Any
forall a b. a -> b
coe T_IsMiddleBolLoop_3462 -> T_IsLoop_3122
MAlonzo.Code.Algebra.Structures.d_isLoop_3476 (T_IsMiddleBolLoop_3462 -> Any
forall a b. a -> b
coe T_IsMiddleBolLoop_3462
v0)))
-- Data.Bool.Properties._.IsMiddleBolLoop.leftDividesʳ
d_leftDivides'691'_1656 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsMiddleBolLoop_3462 ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_leftDivides'691'_1656 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsMiddleBolLoop_3462
-> Bool
-> Bool
-> T__'8801'__12
d_leftDivides'691'_1656 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsMiddleBolLoop_3462
-> Bool
-> Bool
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsMiddleBolLoop.leftDividesˡ
d_leftDivides'737'_1658 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsMiddleBolLoop_3462 ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_leftDivides'737'_1658 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsMiddleBolLoop_3462
-> Bool
-> Bool
-> T__'8801'__12
d_leftDivides'737'_1658 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsMiddleBolLoop_3462
-> Bool
-> Bool
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsMiddleBolLoop.middleBol
d_middleBol_1660 ::
  MAlonzo.Code.Algebra.Structures.T_IsMiddleBolLoop_3462 ->
  Bool ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_middleBol_1660 :: T_IsMiddleBolLoop_3462 -> Bool -> Bool -> Bool -> T__'8801'__12
d_middleBol_1660 = T_IsMiddleBolLoop_3462 -> Bool -> Bool -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsMiddleBolLoop.refl
d_refl_1662 ::
  MAlonzo.Code.Algebra.Structures.T_IsMiddleBolLoop_3462 ->
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_refl_1662 :: T_IsMiddleBolLoop_3462 -> Bool -> T__'8801'__12
d_refl_1662 = T_IsMiddleBolLoop_3462 -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsMiddleBolLoop.reflexive
d_reflexive_1664 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsMiddleBolLoop_3462 ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_reflexive_1664 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsMiddleBolLoop_3462
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_reflexive_1664 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsMiddleBolLoop_3462
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsMiddleBolLoop.rightDivides
d_rightDivides_1666 ::
  MAlonzo.Code.Algebra.Structures.T_IsMiddleBolLoop_3462 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_rightDivides_1666 :: T_IsMiddleBolLoop_3462 -> T_Σ_14
d_rightDivides_1666 T_IsMiddleBolLoop_3462
v0
  = (T_IsQuasigroup_3038 -> T_Σ_14) -> Any -> T_Σ_14
forall a b. a -> b
coe
      T_IsQuasigroup_3038 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_rightDivides_3064
      ((T_IsLoop_3122 -> T_IsQuasigroup_3038) -> Any -> Any
forall a b. a -> b
coe
         T_IsLoop_3122 -> T_IsQuasigroup_3038
MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3136
         ((T_IsMiddleBolLoop_3462 -> T_IsLoop_3122) -> Any -> Any
forall a b. a -> b
coe T_IsMiddleBolLoop_3462 -> T_IsLoop_3122
MAlonzo.Code.Algebra.Structures.d_isLoop_3476 (T_IsMiddleBolLoop_3462 -> Any
forall a b. a -> b
coe T_IsMiddleBolLoop_3462
v0)))
-- Data.Bool.Properties._.IsMiddleBolLoop.rightDividesʳ
d_rightDivides'691'_1668 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsMiddleBolLoop_3462 ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_rightDivides'691'_1668 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsMiddleBolLoop_3462
-> Bool
-> Bool
-> T__'8801'__12
d_rightDivides'691'_1668 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsMiddleBolLoop_3462
-> Bool
-> Bool
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsMiddleBolLoop.rightDividesˡ
d_rightDivides'737'_1670 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsMiddleBolLoop_3462 ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_rightDivides'737'_1670 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsMiddleBolLoop_3462
-> Bool
-> Bool
-> T__'8801'__12
d_rightDivides'737'_1670 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsMiddleBolLoop_3462
-> Bool
-> Bool
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsMiddleBolLoop.setoid
d_setoid_1672 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsMiddleBolLoop_3462 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
d_setoid_1672 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsMiddleBolLoop_3462
-> T_Setoid_46
d_setoid_1672 ~Bool -> Bool -> Bool
v0 ~Bool -> Bool -> Bool
v1 ~Bool -> Bool -> Bool
v2 ~Bool
v3 T_IsMiddleBolLoop_3462
v4 = T_IsMiddleBolLoop_3462 -> T_Setoid_46
du_setoid_1672 T_IsMiddleBolLoop_3462
v4
du_setoid_1672 ::
  MAlonzo.Code.Algebra.Structures.T_IsMiddleBolLoop_3462 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
du_setoid_1672 :: T_IsMiddleBolLoop_3462 -> T_Setoid_46
du_setoid_1672 T_IsMiddleBolLoop_3462
v0
  = let v1 :: T_IsLoop_3122
v1
          = T_IsMiddleBolLoop_3462 -> T_IsLoop_3122
MAlonzo.Code.Algebra.Structures.d_isLoop_3476 (T_IsMiddleBolLoop_3462 -> T_IsMiddleBolLoop_3462
forall a b. a -> b
coe T_IsMiddleBolLoop_3462
v0) in
    Any -> T_Setoid_46
forall a b. a -> b
coe
      (let v2 :: T_IsQuasigroup_3038
v2
             = T_IsLoop_3122 -> T_IsQuasigroup_3038
MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3136 (T_IsLoop_3122 -> T_IsLoop_3122
forall a b. a -> b
coe T_IsLoop_3122
v1) in
       Any -> Any
forall a b. a -> b
coe
         ((T_IsMagma_178 -> T_Setoid_46) -> Any -> Any
forall a b. a -> b
coe
            T_IsMagma_178 -> T_Setoid_46
MAlonzo.Code.Algebra.Structures.du_setoid_202
            ((T_IsQuasigroup_3038 -> T_IsMagma_178) -> Any -> Any
forall a b. a -> b
coe T_IsQuasigroup_3038 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_3056 (T_IsQuasigroup_3038 -> Any
forall a b. a -> b
coe T_IsQuasigroup_3038
v2))))
-- Data.Bool.Properties._.IsMiddleBolLoop.sym
d_sym_1674 ::
  MAlonzo.Code.Algebra.Structures.T_IsMiddleBolLoop_3462 ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_sym_1674 :: T_IsMiddleBolLoop_3462
-> Bool -> Bool -> T__'8801'__12 -> T__'8801'__12
d_sym_1674 = T_IsMiddleBolLoop_3462
-> Bool -> Bool -> T__'8801'__12 -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsMiddleBolLoop.trans
d_trans_1676 ::
  MAlonzo.Code.Algebra.Structures.T_IsMiddleBolLoop_3462 ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_trans_1676 :: T_IsMiddleBolLoop_3462
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
d_trans_1676 = T_IsMiddleBolLoop_3462
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsMiddleBolLoop.∙-cong
d_'8729''45'cong_1678 ::
  MAlonzo.Code.Algebra.Structures.T_IsMiddleBolLoop_3462 ->
  Bool ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8729''45'cong_1678 :: T_IsMiddleBolLoop_3462
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong_1678 = T_IsMiddleBolLoop_3462
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsMiddleBolLoop.∙-congʳ
d_'8729''45'cong'691'_1680 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsMiddleBolLoop_3462 ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8729''45'cong'691'_1680 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsMiddleBolLoop_3462
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong'691'_1680 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsMiddleBolLoop_3462
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsMiddleBolLoop.∙-congˡ
d_'8729''45'cong'737'_1682 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsMiddleBolLoop_3462 ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8729''45'cong'737'_1682 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsMiddleBolLoop_3462
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong'737'_1682 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsMiddleBolLoop_3462
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsMonoid.assoc
d_assoc_1686 ::
  MAlonzo.Code.Algebra.Structures.T_IsMonoid_712 ->
  Bool ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_assoc_1686 :: T_IsMonoid_712 -> Bool -> Bool -> Bool -> T__'8801'__12
d_assoc_1686 = T_IsMonoid_712 -> Bool -> Bool -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsMonoid.identity
d_identity_1688 ::
  MAlonzo.Code.Algebra.Structures.T_IsMonoid_712 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_identity_1688 :: T_IsMonoid_712 -> T_Σ_14
d_identity_1688 T_IsMonoid_712
v0
  = (T_IsMonoid_712 -> T_Σ_14) -> Any -> T_Σ_14
forall a b. a -> b
coe T_IsMonoid_712 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_identity_724 (T_IsMonoid_712 -> Any
forall a b. a -> b
coe T_IsMonoid_712
v0)
-- Data.Bool.Properties._.IsMonoid.identityʳ
d_identity'691'_1690 ::
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsMonoid_712 ->
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_identity'691'_1690 :: (Bool -> Bool -> Bool)
-> Bool -> T_IsMonoid_712 -> Bool -> T__'8801'__12
d_identity'691'_1690 = (Bool -> Bool -> Bool)
-> Bool -> T_IsMonoid_712 -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsMonoid.identityˡ
d_identity'737'_1692 ::
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsMonoid_712 ->
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_identity'737'_1692 :: (Bool -> Bool -> Bool)
-> Bool -> T_IsMonoid_712 -> Bool -> T__'8801'__12
d_identity'737'_1692 = (Bool -> Bool -> Bool)
-> Bool -> T_IsMonoid_712 -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsMonoid.isEquivalence
d_isEquivalence_1694 ::
  MAlonzo.Code.Algebra.Structures.T_IsMonoid_712 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
d_isEquivalence_1694 :: T_IsMonoid_712 -> T_IsEquivalence_28
d_isEquivalence_1694 T_IsMonoid_712
v0
  = (T_IsMagma_178 -> T_IsEquivalence_28) -> Any -> T_IsEquivalence_28
forall a b. a -> b
coe
      T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186
      ((T_IsSemigroup_488 -> T_IsMagma_178) -> Any -> Any
forall a b. a -> b
coe
         T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496
         ((T_IsMonoid_712 -> T_IsSemigroup_488) -> Any -> Any
forall a b. a -> b
coe T_IsMonoid_712 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_722 (T_IsMonoid_712 -> Any
forall a b. a -> b
coe T_IsMonoid_712
v0)))
-- Data.Bool.Properties._.IsMonoid.isMagma
d_isMagma_1696 ::
  MAlonzo.Code.Algebra.Structures.T_IsMonoid_712 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_178
d_isMagma_1696 :: T_IsMonoid_712 -> T_IsMagma_178
d_isMagma_1696 T_IsMonoid_712
v0
  = (T_IsSemigroup_488 -> T_IsMagma_178) -> Any -> T_IsMagma_178
forall a b. a -> b
coe
      T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496
      ((T_IsMonoid_712 -> T_IsSemigroup_488) -> Any -> Any
forall a b. a -> b
coe T_IsMonoid_712 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_722 (T_IsMonoid_712 -> Any
forall a b. a -> b
coe T_IsMonoid_712
v0))
-- Data.Bool.Properties._.IsMonoid.isPartialEquivalence
d_isPartialEquivalence_1698 ::
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsMonoid_712 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_1698 :: (Bool -> Bool -> Bool)
-> Bool -> T_IsMonoid_712 -> T_IsPartialEquivalence_16
d_isPartialEquivalence_1698 ~Bool -> Bool -> Bool
v0 ~Bool
v1 T_IsMonoid_712
v2
  = T_IsMonoid_712 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_1698 T_IsMonoid_712
v2
du_isPartialEquivalence_1698 ::
  MAlonzo.Code.Algebra.Structures.T_IsMonoid_712 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_1698 :: T_IsMonoid_712 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_1698 T_IsMonoid_712
v0
  = let v1 :: T_IsSemigroup_488
v1
          = T_IsMonoid_712 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_722 (T_IsMonoid_712 -> T_IsMonoid_712
forall a b. a -> b
coe T_IsMonoid_712
v0) in
    Any -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsMagma_178
v2 = T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496 (T_IsSemigroup_488 -> T_IsSemigroup_488
forall a b. a -> b
coe T_IsSemigroup_488
v1) in
       Any -> Any
forall a b. a -> b
coe
         ((T_IsEquivalence_28 -> T_IsPartialEquivalence_16) -> Any -> Any
forall a b. a -> b
coe
            T_IsEquivalence_28 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_44
            ((T_IsMagma_178 -> T_IsEquivalence_28) -> Any -> Any
forall a b. a -> b
coe
               T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186 (T_IsMagma_178 -> Any
forall a b. a -> b
coe T_IsMagma_178
v2))))
-- Data.Bool.Properties._.IsMonoid.isSemigroup
d_isSemigroup_1700 ::
  MAlonzo.Code.Algebra.Structures.T_IsMonoid_712 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_488
d_isSemigroup_1700 :: T_IsMonoid_712 -> T_IsSemigroup_488
d_isSemigroup_1700 T_IsMonoid_712
v0
  = (T_IsMonoid_712 -> T_IsSemigroup_488) -> Any -> T_IsSemigroup_488
forall a b. a -> b
coe T_IsMonoid_712 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_722 (T_IsMonoid_712 -> Any
forall a b. a -> b
coe T_IsMonoid_712
v0)
-- Data.Bool.Properties._.IsMonoid.isUnitalMagma
d_isUnitalMagma_1702 ::
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsMonoid_712 ->
  MAlonzo.Code.Algebra.Structures.T_IsUnitalMagma_666
d_isUnitalMagma_1702 :: (Bool -> Bool -> Bool)
-> Bool -> T_IsMonoid_712 -> T_IsUnitalMagma_666
d_isUnitalMagma_1702 Bool -> Bool -> Bool
v0 Bool
v1 T_IsMonoid_712
v2
  = (T_IsMonoid_712 -> T_IsUnitalMagma_666)
-> T_IsMonoid_712 -> T_IsUnitalMagma_666
forall a b. a -> b
coe T_IsMonoid_712 -> T_IsUnitalMagma_666
MAlonzo.Code.Algebra.Structures.du_isUnitalMagma_756 T_IsMonoid_712
v2
-- Data.Bool.Properties._.IsMonoid.refl
d_refl_1704 ::
  MAlonzo.Code.Algebra.Structures.T_IsMonoid_712 ->
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_refl_1704 :: T_IsMonoid_712 -> Bool -> T__'8801'__12
d_refl_1704 = T_IsMonoid_712 -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsMonoid.reflexive
d_reflexive_1706 ::
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsMonoid_712 ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_reflexive_1706 :: (Bool -> Bool -> Bool)
-> Bool
-> T_IsMonoid_712
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_reflexive_1706 = (Bool -> Bool -> Bool)
-> Bool
-> T_IsMonoid_712
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsMonoid.setoid
d_setoid_1708 ::
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsMonoid_712 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
d_setoid_1708 :: (Bool -> Bool -> Bool) -> Bool -> T_IsMonoid_712 -> T_Setoid_46
d_setoid_1708 ~Bool -> Bool -> Bool
v0 ~Bool
v1 T_IsMonoid_712
v2 = T_IsMonoid_712 -> T_Setoid_46
du_setoid_1708 T_IsMonoid_712
v2
du_setoid_1708 ::
  MAlonzo.Code.Algebra.Structures.T_IsMonoid_712 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
du_setoid_1708 :: T_IsMonoid_712 -> T_Setoid_46
du_setoid_1708 T_IsMonoid_712
v0
  = let v1 :: T_IsSemigroup_488
v1
          = T_IsMonoid_712 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_722 (T_IsMonoid_712 -> T_IsMonoid_712
forall a b. a -> b
coe T_IsMonoid_712
v0) in
    Any -> T_Setoid_46
forall a b. a -> b
coe
      ((T_IsMagma_178 -> T_Setoid_46) -> Any -> Any
forall a b. a -> b
coe
         T_IsMagma_178 -> T_Setoid_46
MAlonzo.Code.Algebra.Structures.du_setoid_202
         ((T_IsSemigroup_488 -> T_IsMagma_178) -> Any -> Any
forall a b. a -> b
coe T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496 (T_IsSemigroup_488 -> Any
forall a b. a -> b
coe T_IsSemigroup_488
v1)))
-- Data.Bool.Properties._.IsMonoid.sym
d_sym_1710 ::
  MAlonzo.Code.Algebra.Structures.T_IsMonoid_712 ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_sym_1710 :: T_IsMonoid_712 -> Bool -> Bool -> T__'8801'__12 -> T__'8801'__12
d_sym_1710 = T_IsMonoid_712 -> Bool -> Bool -> T__'8801'__12 -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsMonoid.trans
d_trans_1712 ::
  MAlonzo.Code.Algebra.Structures.T_IsMonoid_712 ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_trans_1712 :: T_IsMonoid_712
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
d_trans_1712 = T_IsMonoid_712
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsMonoid.∙-cong
d_'8729''45'cong_1714 ::
  MAlonzo.Code.Algebra.Structures.T_IsMonoid_712 ->
  Bool ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8729''45'cong_1714 :: T_IsMonoid_712
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong_1714 = T_IsMonoid_712
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsMonoid.∙-congʳ
d_'8729''45'cong'691'_1716 ::
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsMonoid_712 ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8729''45'cong'691'_1716 :: (Bool -> Bool -> Bool)
-> Bool
-> T_IsMonoid_712
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong'691'_1716 = (Bool -> Bool -> Bool)
-> Bool
-> T_IsMonoid_712
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsMonoid.∙-congˡ
d_'8729''45'cong'737'_1718 ::
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsMonoid_712 ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8729''45'cong'737'_1718 :: (Bool -> Bool -> Bool)
-> Bool
-> T_IsMonoid_712
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong'737'_1718 = (Bool -> Bool -> Bool)
-> Bool
-> T_IsMonoid_712
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsMoufangLoop.//-cong
d_'47''47''45'cong_1722 ::
  MAlonzo.Code.Algebra.Structures.T_IsMoufangLoop_3370 ->
  Bool ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'47''47''45'cong_1722 :: T_IsMoufangLoop_3370
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
d_'47''47''45'cong_1722 = T_IsMoufangLoop_3370
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsMoufangLoop.//-congʳ
d_'47''47''45'cong'691'_1724 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsMoufangLoop_3370 ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'47''47''45'cong'691'_1724 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsMoufangLoop_3370
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_'47''47''45'cong'691'_1724 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsMoufangLoop_3370
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsMoufangLoop.//-congˡ
d_'47''47''45'cong'737'_1726 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsMoufangLoop_3370 ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'47''47''45'cong'737'_1726 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsMoufangLoop_3370
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_'47''47''45'cong'737'_1726 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsMoufangLoop_3370
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsMoufangLoop.\\-cong
d_'92''92''45'cong_1728 ::
  MAlonzo.Code.Algebra.Structures.T_IsMoufangLoop_3370 ->
  Bool ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'92''92''45'cong_1728 :: T_IsMoufangLoop_3370
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
d_'92''92''45'cong_1728 = T_IsMoufangLoop_3370
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsMoufangLoop.\\-congʳ
d_'92''92''45'cong'691'_1730 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsMoufangLoop_3370 ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'92''92''45'cong'691'_1730 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsMoufangLoop_3370
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_'92''92''45'cong'691'_1730 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsMoufangLoop_3370
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsMoufangLoop.\\-congˡ
d_'92''92''45'cong'737'_1732 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsMoufangLoop_3370 ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'92''92''45'cong'737'_1732 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsMoufangLoop_3370
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_'92''92''45'cong'737'_1732 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsMoufangLoop_3370
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsMoufangLoop.identical
d_identical_1734 ::
  MAlonzo.Code.Algebra.Structures.T_IsMoufangLoop_3370 ->
  Bool ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_identical_1734 :: T_IsMoufangLoop_3370 -> Bool -> Bool -> Bool -> T__'8801'__12
d_identical_1734 = T_IsMoufangLoop_3370 -> Bool -> Bool -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsMoufangLoop.identity
d_identity_1736 ::
  MAlonzo.Code.Algebra.Structures.T_IsMoufangLoop_3370 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_identity_1736 :: T_IsMoufangLoop_3370 -> T_Σ_14
d_identity_1736 T_IsMoufangLoop_3370
v0
  = (T_IsLoop_3122 -> T_Σ_14) -> Any -> T_Σ_14
forall a b. a -> b
coe
      T_IsLoop_3122 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_identity_3138
      ((T_IsLeftBolLoop_3202 -> T_IsLoop_3122) -> Any -> Any
forall a b. a -> b
coe
         T_IsLeftBolLoop_3202 -> T_IsLoop_3122
MAlonzo.Code.Algebra.Structures.d_isLoop_3216
         ((T_IsMoufangLoop_3370 -> T_IsLeftBolLoop_3202) -> Any -> Any
forall a b. a -> b
coe
            T_IsMoufangLoop_3370 -> T_IsLeftBolLoop_3202
MAlonzo.Code.Algebra.Structures.d_isLeftBolLoop_3386 (T_IsMoufangLoop_3370 -> Any
forall a b. a -> b
coe T_IsMoufangLoop_3370
v0)))
-- Data.Bool.Properties._.IsMoufangLoop.identityʳ
d_identity'691'_1738 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsMoufangLoop_3370 ->
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_identity'691'_1738 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsMoufangLoop_3370
-> Bool
-> T__'8801'__12
d_identity'691'_1738 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsMoufangLoop_3370
-> Bool
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsMoufangLoop.identityˡ
d_identity'737'_1740 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsMoufangLoop_3370 ->
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_identity'737'_1740 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsMoufangLoop_3370
-> Bool
-> T__'8801'__12
d_identity'737'_1740 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsMoufangLoop_3370
-> Bool
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsMoufangLoop.isEquivalence
d_isEquivalence_1742 ::
  MAlonzo.Code.Algebra.Structures.T_IsMoufangLoop_3370 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
d_isEquivalence_1742 :: T_IsMoufangLoop_3370 -> T_IsEquivalence_28
d_isEquivalence_1742 T_IsMoufangLoop_3370
v0
  = (T_IsMagma_178 -> T_IsEquivalence_28) -> Any -> T_IsEquivalence_28
forall a b. a -> b
coe
      T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186
      ((T_IsQuasigroup_3038 -> T_IsMagma_178) -> Any -> Any
forall a b. a -> b
coe
         T_IsQuasigroup_3038 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_3056
         ((T_IsLoop_3122 -> T_IsQuasigroup_3038) -> Any -> Any
forall a b. a -> b
coe
            T_IsLoop_3122 -> T_IsQuasigroup_3038
MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3136
            ((T_IsLeftBolLoop_3202 -> T_IsLoop_3122) -> Any -> Any
forall a b. a -> b
coe
               T_IsLeftBolLoop_3202 -> T_IsLoop_3122
MAlonzo.Code.Algebra.Structures.d_isLoop_3216
               ((T_IsMoufangLoop_3370 -> T_IsLeftBolLoop_3202) -> Any -> Any
forall a b. a -> b
coe
                  T_IsMoufangLoop_3370 -> T_IsLeftBolLoop_3202
MAlonzo.Code.Algebra.Structures.d_isLeftBolLoop_3386 (T_IsMoufangLoop_3370 -> Any
forall a b. a -> b
coe T_IsMoufangLoop_3370
v0)))))
-- Data.Bool.Properties._.IsMoufangLoop.isLeftBolLoop
d_isLeftBolLoop_1744 ::
  MAlonzo.Code.Algebra.Structures.T_IsMoufangLoop_3370 ->
  MAlonzo.Code.Algebra.Structures.T_IsLeftBolLoop_3202
d_isLeftBolLoop_1744 :: T_IsMoufangLoop_3370 -> T_IsLeftBolLoop_3202
d_isLeftBolLoop_1744 T_IsMoufangLoop_3370
v0
  = (T_IsMoufangLoop_3370 -> T_IsLeftBolLoop_3202)
-> Any -> T_IsLeftBolLoop_3202
forall a b. a -> b
coe T_IsMoufangLoop_3370 -> T_IsLeftBolLoop_3202
MAlonzo.Code.Algebra.Structures.d_isLeftBolLoop_3386 (T_IsMoufangLoop_3370 -> Any
forall a b. a -> b
coe T_IsMoufangLoop_3370
v0)
-- Data.Bool.Properties._.IsMoufangLoop.isLoop
d_isLoop_1746 ::
  MAlonzo.Code.Algebra.Structures.T_IsMoufangLoop_3370 ->
  MAlonzo.Code.Algebra.Structures.T_IsLoop_3122
d_isLoop_1746 :: T_IsMoufangLoop_3370 -> T_IsLoop_3122
d_isLoop_1746 T_IsMoufangLoop_3370
v0
  = (T_IsLeftBolLoop_3202 -> T_IsLoop_3122) -> Any -> T_IsLoop_3122
forall a b. a -> b
coe
      T_IsLeftBolLoop_3202 -> T_IsLoop_3122
MAlonzo.Code.Algebra.Structures.d_isLoop_3216
      ((T_IsMoufangLoop_3370 -> T_IsLeftBolLoop_3202) -> Any -> Any
forall a b. a -> b
coe T_IsMoufangLoop_3370 -> T_IsLeftBolLoop_3202
MAlonzo.Code.Algebra.Structures.d_isLeftBolLoop_3386 (T_IsMoufangLoop_3370 -> Any
forall a b. a -> b
coe T_IsMoufangLoop_3370
v0))
-- Data.Bool.Properties._.IsMoufangLoop.isMagma
d_isMagma_1748 ::
  MAlonzo.Code.Algebra.Structures.T_IsMoufangLoop_3370 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_178
d_isMagma_1748 :: T_IsMoufangLoop_3370 -> T_IsMagma_178
d_isMagma_1748 T_IsMoufangLoop_3370
v0
  = (T_IsQuasigroup_3038 -> T_IsMagma_178) -> Any -> T_IsMagma_178
forall a b. a -> b
coe
      T_IsQuasigroup_3038 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_3056
      ((T_IsLoop_3122 -> T_IsQuasigroup_3038) -> Any -> Any
forall a b. a -> b
coe
         T_IsLoop_3122 -> T_IsQuasigroup_3038
MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3136
         ((T_IsLeftBolLoop_3202 -> T_IsLoop_3122) -> Any -> Any
forall a b. a -> b
coe
            T_IsLeftBolLoop_3202 -> T_IsLoop_3122
MAlonzo.Code.Algebra.Structures.d_isLoop_3216
            ((T_IsMoufangLoop_3370 -> T_IsLeftBolLoop_3202) -> Any -> Any
forall a b. a -> b
coe
               T_IsMoufangLoop_3370 -> T_IsLeftBolLoop_3202
MAlonzo.Code.Algebra.Structures.d_isLeftBolLoop_3386 (T_IsMoufangLoop_3370 -> Any
forall a b. a -> b
coe T_IsMoufangLoop_3370
v0))))
-- Data.Bool.Properties._.IsMoufangLoop.isPartialEquivalence
d_isPartialEquivalence_1750 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsMoufangLoop_3370 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_1750 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsMoufangLoop_3370
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_1750 ~Bool -> Bool -> Bool
v0 ~Bool -> Bool -> Bool
v1 ~Bool -> Bool -> Bool
v2 ~Bool
v3 T_IsMoufangLoop_3370
v4
  = T_IsMoufangLoop_3370 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_1750 T_IsMoufangLoop_3370
v4
du_isPartialEquivalence_1750 ::
  MAlonzo.Code.Algebra.Structures.T_IsMoufangLoop_3370 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_1750 :: T_IsMoufangLoop_3370 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_1750 T_IsMoufangLoop_3370
v0
  = let v1 :: T_IsLeftBolLoop_3202
v1
          = T_IsMoufangLoop_3370 -> T_IsLeftBolLoop_3202
MAlonzo.Code.Algebra.Structures.d_isLeftBolLoop_3386 (T_IsMoufangLoop_3370 -> T_IsMoufangLoop_3370
forall a b. a -> b
coe T_IsMoufangLoop_3370
v0) in
    Any -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsLoop_3122
v2 = T_IsLeftBolLoop_3202 -> T_IsLoop_3122
MAlonzo.Code.Algebra.Structures.d_isLoop_3216 (T_IsLeftBolLoop_3202 -> T_IsLeftBolLoop_3202
forall a b. a -> b
coe T_IsLeftBolLoop_3202
v1) in
       Any -> Any
forall a b. a -> b
coe
         (let v3 :: T_IsQuasigroup_3038
v3
                = T_IsLoop_3122 -> T_IsQuasigroup_3038
MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3136 (T_IsLoop_3122 -> T_IsLoop_3122
forall a b. a -> b
coe T_IsLoop_3122
v2) in
          Any -> Any
forall a b. a -> b
coe
            (let v4 :: T_IsMagma_178
v4
                   = T_IsQuasigroup_3038 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_3056 (T_IsQuasigroup_3038 -> T_IsQuasigroup_3038
forall a b. a -> b
coe T_IsQuasigroup_3038
v3) in
             Any -> Any
forall a b. a -> b
coe
               ((T_IsEquivalence_28 -> T_IsPartialEquivalence_16) -> Any -> Any
forall a b. a -> b
coe
                  T_IsEquivalence_28 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_44
                  ((T_IsMagma_178 -> T_IsEquivalence_28) -> Any -> Any
forall a b. a -> b
coe
                     T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186 (T_IsMagma_178 -> Any
forall a b. a -> b
coe T_IsMagma_178
v4))))))
-- Data.Bool.Properties._.IsMoufangLoop.isQuasigroup
d_isQuasigroup_1752 ::
  MAlonzo.Code.Algebra.Structures.T_IsMoufangLoop_3370 ->
  MAlonzo.Code.Algebra.Structures.T_IsQuasigroup_3038
d_isQuasigroup_1752 :: T_IsMoufangLoop_3370 -> T_IsQuasigroup_3038
d_isQuasigroup_1752 T_IsMoufangLoop_3370
v0
  = (T_IsLoop_3122 -> T_IsQuasigroup_3038)
-> Any -> T_IsQuasigroup_3038
forall a b. a -> b
coe
      T_IsLoop_3122 -> T_IsQuasigroup_3038
MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3136
      ((T_IsLeftBolLoop_3202 -> T_IsLoop_3122) -> Any -> Any
forall a b. a -> b
coe
         T_IsLeftBolLoop_3202 -> T_IsLoop_3122
MAlonzo.Code.Algebra.Structures.d_isLoop_3216
         ((T_IsMoufangLoop_3370 -> T_IsLeftBolLoop_3202) -> Any -> Any
forall a b. a -> b
coe
            T_IsMoufangLoop_3370 -> T_IsLeftBolLoop_3202
MAlonzo.Code.Algebra.Structures.d_isLeftBolLoop_3386 (T_IsMoufangLoop_3370 -> Any
forall a b. a -> b
coe T_IsMoufangLoop_3370
v0)))
-- Data.Bool.Properties._.IsMoufangLoop.leftBol
d_leftBol_1754 ::
  MAlonzo.Code.Algebra.Structures.T_IsMoufangLoop_3370 ->
  Bool ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_leftBol_1754 :: T_IsMoufangLoop_3370 -> Bool -> Bool -> Bool -> T__'8801'__12
d_leftBol_1754 = T_IsMoufangLoop_3370 -> Bool -> Bool -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsMoufangLoop.leftDivides
d_leftDivides_1756 ::
  MAlonzo.Code.Algebra.Structures.T_IsMoufangLoop_3370 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_leftDivides_1756 :: T_IsMoufangLoop_3370 -> T_Σ_14
d_leftDivides_1756 T_IsMoufangLoop_3370
v0
  = (T_IsQuasigroup_3038 -> T_Σ_14) -> Any -> T_Σ_14
forall a b. a -> b
coe
      T_IsQuasigroup_3038 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_leftDivides_3062
      ((T_IsLoop_3122 -> T_IsQuasigroup_3038) -> Any -> Any
forall a b. a -> b
coe
         T_IsLoop_3122 -> T_IsQuasigroup_3038
MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3136
         ((T_IsLeftBolLoop_3202 -> T_IsLoop_3122) -> Any -> Any
forall a b. a -> b
coe
            T_IsLeftBolLoop_3202 -> T_IsLoop_3122
MAlonzo.Code.Algebra.Structures.d_isLoop_3216
            ((T_IsMoufangLoop_3370 -> T_IsLeftBolLoop_3202) -> Any -> Any
forall a b. a -> b
coe
               T_IsMoufangLoop_3370 -> T_IsLeftBolLoop_3202
MAlonzo.Code.Algebra.Structures.d_isLeftBolLoop_3386 (T_IsMoufangLoop_3370 -> Any
forall a b. a -> b
coe T_IsMoufangLoop_3370
v0))))
-- Data.Bool.Properties._.IsMoufangLoop.leftDividesʳ
d_leftDivides'691'_1758 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsMoufangLoop_3370 ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_leftDivides'691'_1758 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsMoufangLoop_3370
-> Bool
-> Bool
-> T__'8801'__12
d_leftDivides'691'_1758 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsMoufangLoop_3370
-> Bool
-> Bool
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsMoufangLoop.leftDividesˡ
d_leftDivides'737'_1760 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsMoufangLoop_3370 ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_leftDivides'737'_1760 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsMoufangLoop_3370
-> Bool
-> Bool
-> T__'8801'__12
d_leftDivides'737'_1760 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsMoufangLoop_3370
-> Bool
-> Bool
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsMoufangLoop.refl
d_refl_1762 ::
  MAlonzo.Code.Algebra.Structures.T_IsMoufangLoop_3370 ->
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_refl_1762 :: T_IsMoufangLoop_3370 -> Bool -> T__'8801'__12
d_refl_1762 = T_IsMoufangLoop_3370 -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsMoufangLoop.reflexive
d_reflexive_1764 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsMoufangLoop_3370 ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_reflexive_1764 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsMoufangLoop_3370
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_reflexive_1764 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsMoufangLoop_3370
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsMoufangLoop.rightBol
d_rightBol_1766 ::
  MAlonzo.Code.Algebra.Structures.T_IsMoufangLoop_3370 ->
  Bool ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_rightBol_1766 :: T_IsMoufangLoop_3370 -> Bool -> Bool -> Bool -> T__'8801'__12
d_rightBol_1766 = T_IsMoufangLoop_3370 -> Bool -> Bool -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsMoufangLoop.rightDivides
d_rightDivides_1768 ::
  MAlonzo.Code.Algebra.Structures.T_IsMoufangLoop_3370 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_rightDivides_1768 :: T_IsMoufangLoop_3370 -> T_Σ_14
d_rightDivides_1768 T_IsMoufangLoop_3370
v0
  = (T_IsQuasigroup_3038 -> T_Σ_14) -> Any -> T_Σ_14
forall a b. a -> b
coe
      T_IsQuasigroup_3038 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_rightDivides_3064
      ((T_IsLoop_3122 -> T_IsQuasigroup_3038) -> Any -> Any
forall a b. a -> b
coe
         T_IsLoop_3122 -> T_IsQuasigroup_3038
MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3136
         ((T_IsLeftBolLoop_3202 -> T_IsLoop_3122) -> Any -> Any
forall a b. a -> b
coe
            T_IsLeftBolLoop_3202 -> T_IsLoop_3122
MAlonzo.Code.Algebra.Structures.d_isLoop_3216
            ((T_IsMoufangLoop_3370 -> T_IsLeftBolLoop_3202) -> Any -> Any
forall a b. a -> b
coe
               T_IsMoufangLoop_3370 -> T_IsLeftBolLoop_3202
MAlonzo.Code.Algebra.Structures.d_isLeftBolLoop_3386 (T_IsMoufangLoop_3370 -> Any
forall a b. a -> b
coe T_IsMoufangLoop_3370
v0))))
-- Data.Bool.Properties._.IsMoufangLoop.rightDividesʳ
d_rightDivides'691'_1770 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsMoufangLoop_3370 ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_rightDivides'691'_1770 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsMoufangLoop_3370
-> Bool
-> Bool
-> T__'8801'__12
d_rightDivides'691'_1770 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsMoufangLoop_3370
-> Bool
-> Bool
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsMoufangLoop.rightDividesˡ
d_rightDivides'737'_1772 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsMoufangLoop_3370 ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_rightDivides'737'_1772 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsMoufangLoop_3370
-> Bool
-> Bool
-> T__'8801'__12
d_rightDivides'737'_1772 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsMoufangLoop_3370
-> Bool
-> Bool
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsMoufangLoop.setoid
d_setoid_1774 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsMoufangLoop_3370 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
d_setoid_1774 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsMoufangLoop_3370
-> T_Setoid_46
d_setoid_1774 ~Bool -> Bool -> Bool
v0 ~Bool -> Bool -> Bool
v1 ~Bool -> Bool -> Bool
v2 ~Bool
v3 T_IsMoufangLoop_3370
v4 = T_IsMoufangLoop_3370 -> T_Setoid_46
du_setoid_1774 T_IsMoufangLoop_3370
v4
du_setoid_1774 ::
  MAlonzo.Code.Algebra.Structures.T_IsMoufangLoop_3370 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
du_setoid_1774 :: T_IsMoufangLoop_3370 -> T_Setoid_46
du_setoid_1774 T_IsMoufangLoop_3370
v0
  = let v1 :: T_IsLeftBolLoop_3202
v1
          = T_IsMoufangLoop_3370 -> T_IsLeftBolLoop_3202
MAlonzo.Code.Algebra.Structures.d_isLeftBolLoop_3386 (T_IsMoufangLoop_3370 -> T_IsMoufangLoop_3370
forall a b. a -> b
coe T_IsMoufangLoop_3370
v0) in
    Any -> T_Setoid_46
forall a b. a -> b
coe
      (let v2 :: T_IsLoop_3122
v2 = T_IsLeftBolLoop_3202 -> T_IsLoop_3122
MAlonzo.Code.Algebra.Structures.d_isLoop_3216 (T_IsLeftBolLoop_3202 -> T_IsLeftBolLoop_3202
forall a b. a -> b
coe T_IsLeftBolLoop_3202
v1) in
       Any -> Any
forall a b. a -> b
coe
         (let v3 :: T_IsQuasigroup_3038
v3
                = T_IsLoop_3122 -> T_IsQuasigroup_3038
MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3136 (T_IsLoop_3122 -> T_IsLoop_3122
forall a b. a -> b
coe T_IsLoop_3122
v2) in
          Any -> Any
forall a b. a -> b
coe
            ((T_IsMagma_178 -> T_Setoid_46) -> Any -> Any
forall a b. a -> b
coe
               T_IsMagma_178 -> T_Setoid_46
MAlonzo.Code.Algebra.Structures.du_setoid_202
               ((T_IsQuasigroup_3038 -> T_IsMagma_178) -> Any -> Any
forall a b. a -> b
coe T_IsQuasigroup_3038 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_3056 (T_IsQuasigroup_3038 -> Any
forall a b. a -> b
coe T_IsQuasigroup_3038
v3)))))
-- Data.Bool.Properties._.IsMoufangLoop.sym
d_sym_1776 ::
  MAlonzo.Code.Algebra.Structures.T_IsMoufangLoop_3370 ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_sym_1776 :: T_IsMoufangLoop_3370
-> Bool -> Bool -> T__'8801'__12 -> T__'8801'__12
d_sym_1776 = T_IsMoufangLoop_3370
-> Bool -> Bool -> T__'8801'__12 -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsMoufangLoop.trans
d_trans_1778 ::
  MAlonzo.Code.Algebra.Structures.T_IsMoufangLoop_3370 ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_trans_1778 :: T_IsMoufangLoop_3370
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
d_trans_1778 = T_IsMoufangLoop_3370
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsMoufangLoop.∙-cong
d_'8729''45'cong_1780 ::
  MAlonzo.Code.Algebra.Structures.T_IsMoufangLoop_3370 ->
  Bool ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8729''45'cong_1780 :: T_IsMoufangLoop_3370
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong_1780 = T_IsMoufangLoop_3370
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsMoufangLoop.∙-congʳ
d_'8729''45'cong'691'_1782 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsMoufangLoop_3370 ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8729''45'cong'691'_1782 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsMoufangLoop_3370
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong'691'_1782 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsMoufangLoop_3370
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsMoufangLoop.∙-congˡ
d_'8729''45'cong'737'_1784 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsMoufangLoop_3370 ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8729''45'cong'737'_1784 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsMoufangLoop_3370
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong'737'_1784 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsMoufangLoop_3370
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsNearSemiring.*-assoc
d_'42''45'assoc_1788 ::
  MAlonzo.Code.Algebra.Structures.T_IsNearSemiring_1260 ->
  Bool ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'42''45'assoc_1788 :: T_IsNearSemiring_1260 -> Bool -> Bool -> Bool -> T__'8801'__12
d_'42''45'assoc_1788 = T_IsNearSemiring_1260 -> Bool -> Bool -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsNearSemiring.*-cong
d_'42''45'cong_1790 ::
  MAlonzo.Code.Algebra.Structures.T_IsNearSemiring_1260 ->
  Bool ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'42''45'cong_1790 :: T_IsNearSemiring_1260
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
d_'42''45'cong_1790 = T_IsNearSemiring_1260
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsNearSemiring.∙-congʳ
d_'8729''45'cong'691'_1792 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsNearSemiring_1260 ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8729''45'cong'691'_1792 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsNearSemiring_1260
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong'691'_1792 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsNearSemiring_1260
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsNearSemiring.∙-congˡ
d_'8729''45'cong'737'_1794 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsNearSemiring_1260 ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8729''45'cong'737'_1794 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsNearSemiring_1260
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong'737'_1794 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsNearSemiring_1260
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsNearSemiring.*-isMagma
d_'42''45'isMagma_1796 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsNearSemiring_1260 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_178
d_'42''45'isMagma_1796 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsNearSemiring_1260
-> T_IsMagma_178
d_'42''45'isMagma_1796 Bool -> Bool -> Bool
v0 Bool -> Bool -> Bool
v1 Bool
v2 T_IsNearSemiring_1260
v3
  = (T_IsNearSemiring_1260 -> T_IsMagma_178)
-> T_IsNearSemiring_1260 -> T_IsMagma_178
forall a b. a -> b
coe T_IsNearSemiring_1260 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.du_'42''45'isMagma_1324 T_IsNearSemiring_1260
v3
-- Data.Bool.Properties._.IsNearSemiring.*-isSemigroup
d_'42''45'isSemigroup_1798 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsNearSemiring_1260 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_488
d_'42''45'isSemigroup_1798 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsNearSemiring_1260
-> T_IsSemigroup_488
d_'42''45'isSemigroup_1798 Bool -> Bool -> Bool
v0 Bool -> Bool -> Bool
v1 Bool
v2 T_IsNearSemiring_1260
v3
  = (T_IsNearSemiring_1260 -> T_IsSemigroup_488)
-> T_IsNearSemiring_1260 -> T_IsSemigroup_488
forall a b. a -> b
coe
      T_IsNearSemiring_1260 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.du_'42''45'isSemigroup_1326 T_IsNearSemiring_1260
v3
-- Data.Bool.Properties._.IsNearSemiring.assoc
d_assoc_1800 ::
  MAlonzo.Code.Algebra.Structures.T_IsNearSemiring_1260 ->
  Bool ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_assoc_1800 :: T_IsNearSemiring_1260 -> Bool -> Bool -> Bool -> T__'8801'__12
d_assoc_1800 = T_IsNearSemiring_1260 -> Bool -> Bool -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsNearSemiring.∙-cong
d_'8729''45'cong_1802 ::
  MAlonzo.Code.Algebra.Structures.T_IsNearSemiring_1260 ->
  Bool ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8729''45'cong_1802 :: T_IsNearSemiring_1260
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong_1802 = T_IsNearSemiring_1260
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsNearSemiring.∙-congʳ
d_'8729''45'cong'691'_1804 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsNearSemiring_1260 ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8729''45'cong'691'_1804 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsNearSemiring_1260
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong'691'_1804 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsNearSemiring_1260
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsNearSemiring.∙-congˡ
d_'8729''45'cong'737'_1806 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsNearSemiring_1260 ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8729''45'cong'737'_1806 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsNearSemiring_1260
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong'737'_1806 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsNearSemiring_1260
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsNearSemiring.identity
d_identity_1808 ::
  MAlonzo.Code.Algebra.Structures.T_IsNearSemiring_1260 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_identity_1808 :: T_IsNearSemiring_1260 -> T_Σ_14
d_identity_1808 T_IsNearSemiring_1260
v0
  = (T_IsMonoid_712 -> T_Σ_14) -> Any -> T_Σ_14
forall a b. a -> b
coe
      T_IsMonoid_712 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_identity_724
      ((T_IsNearSemiring_1260 -> T_IsMonoid_712) -> Any -> Any
forall a b. a -> b
coe
         T_IsNearSemiring_1260 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_'43''45'isMonoid_1278 (T_IsNearSemiring_1260 -> Any
forall a b. a -> b
coe T_IsNearSemiring_1260
v0))
-- Data.Bool.Properties._.IsNearSemiring.identityʳ
d_identity'691'_1810 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsNearSemiring_1260 ->
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_identity'691'_1810 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsNearSemiring_1260
-> Bool
-> T__'8801'__12
d_identity'691'_1810 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsNearSemiring_1260
-> Bool
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsNearSemiring.identityˡ
d_identity'737'_1812 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsNearSemiring_1260 ->
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_identity'737'_1812 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsNearSemiring_1260
-> Bool
-> T__'8801'__12
d_identity'737'_1812 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsNearSemiring_1260
-> Bool
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsNearSemiring.isMagma
d_isMagma_1814 ::
  MAlonzo.Code.Algebra.Structures.T_IsNearSemiring_1260 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_178
d_isMagma_1814 :: T_IsNearSemiring_1260 -> T_IsMagma_178
d_isMagma_1814 T_IsNearSemiring_1260
v0
  = (T_IsSemigroup_488 -> T_IsMagma_178) -> Any -> T_IsMagma_178
forall a b. a -> b
coe
      T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496
      ((T_IsMonoid_712 -> T_IsSemigroup_488) -> Any -> Any
forall a b. a -> b
coe
         T_IsMonoid_712 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_722
         ((T_IsNearSemiring_1260 -> T_IsMonoid_712) -> Any -> Any
forall a b. a -> b
coe
            T_IsNearSemiring_1260 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_'43''45'isMonoid_1278 (T_IsNearSemiring_1260 -> Any
forall a b. a -> b
coe T_IsNearSemiring_1260
v0)))
-- Data.Bool.Properties._.IsNearSemiring.+-isMonoid
d_'43''45'isMonoid_1816 ::
  MAlonzo.Code.Algebra.Structures.T_IsNearSemiring_1260 ->
  MAlonzo.Code.Algebra.Structures.T_IsMonoid_712
d_'43''45'isMonoid_1816 :: T_IsNearSemiring_1260 -> T_IsMonoid_712
d_'43''45'isMonoid_1816 T_IsNearSemiring_1260
v0
  = (T_IsNearSemiring_1260 -> T_IsMonoid_712) -> Any -> T_IsMonoid_712
forall a b. a -> b
coe
      T_IsNearSemiring_1260 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_'43''45'isMonoid_1278 (T_IsNearSemiring_1260 -> Any
forall a b. a -> b
coe T_IsNearSemiring_1260
v0)
-- Data.Bool.Properties._.IsNearSemiring.isSemigroup
d_isSemigroup_1818 ::
  MAlonzo.Code.Algebra.Structures.T_IsNearSemiring_1260 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_488
d_isSemigroup_1818 :: T_IsNearSemiring_1260 -> T_IsSemigroup_488
d_isSemigroup_1818 T_IsNearSemiring_1260
v0
  = (T_IsMonoid_712 -> T_IsSemigroup_488) -> Any -> T_IsSemigroup_488
forall a b. a -> b
coe
      T_IsMonoid_712 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_722
      ((T_IsNearSemiring_1260 -> T_IsMonoid_712) -> Any -> Any
forall a b. a -> b
coe
         T_IsNearSemiring_1260 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_'43''45'isMonoid_1278 (T_IsNearSemiring_1260 -> Any
forall a b. a -> b
coe T_IsNearSemiring_1260
v0))
-- Data.Bool.Properties._.IsNearSemiring.isUnitalMagma
d_isUnitalMagma_1820 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsNearSemiring_1260 ->
  MAlonzo.Code.Algebra.Structures.T_IsUnitalMagma_666
d_isUnitalMagma_1820 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsNearSemiring_1260
-> T_IsUnitalMagma_666
d_isUnitalMagma_1820 ~Bool -> Bool -> Bool
v0 ~Bool -> Bool -> Bool
v1 ~Bool
v2 T_IsNearSemiring_1260
v3 = T_IsNearSemiring_1260 -> T_IsUnitalMagma_666
du_isUnitalMagma_1820 T_IsNearSemiring_1260
v3
du_isUnitalMagma_1820 ::
  MAlonzo.Code.Algebra.Structures.T_IsNearSemiring_1260 ->
  MAlonzo.Code.Algebra.Structures.T_IsUnitalMagma_666
du_isUnitalMagma_1820 :: T_IsNearSemiring_1260 -> T_IsUnitalMagma_666
du_isUnitalMagma_1820 T_IsNearSemiring_1260
v0
  = (T_IsMonoid_712 -> T_IsUnitalMagma_666)
-> Any -> T_IsUnitalMagma_666
forall a b. a -> b
coe
      T_IsMonoid_712 -> T_IsUnitalMagma_666
MAlonzo.Code.Algebra.Structures.du_isUnitalMagma_756
      ((T_IsNearSemiring_1260 -> T_IsMonoid_712) -> Any -> Any
forall a b. a -> b
coe
         T_IsNearSemiring_1260 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_'43''45'isMonoid_1278 (T_IsNearSemiring_1260 -> Any
forall a b. a -> b
coe T_IsNearSemiring_1260
v0))
-- Data.Bool.Properties._.IsNearSemiring.distribʳ
d_distrib'691'_1822 ::
  MAlonzo.Code.Algebra.Structures.T_IsNearSemiring_1260 ->
  Bool ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_distrib'691'_1822 :: T_IsNearSemiring_1260 -> Bool -> Bool -> Bool -> T__'8801'__12
d_distrib'691'_1822 = T_IsNearSemiring_1260 -> Bool -> Bool -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsNearSemiring.isEquivalence
d_isEquivalence_1824 ::
  MAlonzo.Code.Algebra.Structures.T_IsNearSemiring_1260 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
d_isEquivalence_1824 :: T_IsNearSemiring_1260 -> T_IsEquivalence_28
d_isEquivalence_1824 T_IsNearSemiring_1260
v0
  = (T_IsMagma_178 -> T_IsEquivalence_28) -> Any -> T_IsEquivalence_28
forall a b. a -> b
coe
      T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186
      ((T_IsSemigroup_488 -> T_IsMagma_178) -> Any -> Any
forall a b. a -> b
coe
         T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496
         ((T_IsMonoid_712 -> T_IsSemigroup_488) -> Any -> Any
forall a b. a -> b
coe
            T_IsMonoid_712 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_722
            ((T_IsNearSemiring_1260 -> T_IsMonoid_712) -> Any -> Any
forall a b. a -> b
coe
               T_IsNearSemiring_1260 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_'43''45'isMonoid_1278 (T_IsNearSemiring_1260 -> Any
forall a b. a -> b
coe T_IsNearSemiring_1260
v0))))
-- Data.Bool.Properties._.IsNearSemiring.isPartialEquivalence
d_isPartialEquivalence_1826 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsNearSemiring_1260 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_1826 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsNearSemiring_1260
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_1826 ~Bool -> Bool -> Bool
v0 ~Bool -> Bool -> Bool
v1 ~Bool
v2 T_IsNearSemiring_1260
v3
  = T_IsNearSemiring_1260 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_1826 T_IsNearSemiring_1260
v3
du_isPartialEquivalence_1826 ::
  MAlonzo.Code.Algebra.Structures.T_IsNearSemiring_1260 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_1826 :: T_IsNearSemiring_1260 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_1826 T_IsNearSemiring_1260
v0
  = let v1 :: T_IsMonoid_712
v1
          = T_IsNearSemiring_1260 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_'43''45'isMonoid_1278
              (T_IsNearSemiring_1260 -> T_IsNearSemiring_1260
forall a b. a -> b
coe T_IsNearSemiring_1260
v0) in
    Any -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsSemigroup_488
v2
             = T_IsMonoid_712 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_722 (T_IsMonoid_712 -> T_IsMonoid_712
forall a b. a -> b
coe T_IsMonoid_712
v1) in
       Any -> Any
forall a b. a -> b
coe
         (let v3 :: T_IsMagma_178
v3 = T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496 (T_IsSemigroup_488 -> T_IsSemigroup_488
forall a b. a -> b
coe T_IsSemigroup_488
v2) in
          Any -> Any
forall a b. a -> b
coe
            ((T_IsEquivalence_28 -> T_IsPartialEquivalence_16) -> Any -> Any
forall a b. a -> b
coe
               T_IsEquivalence_28 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_44
               ((T_IsMagma_178 -> T_IsEquivalence_28) -> Any -> Any
forall a b. a -> b
coe
                  T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186 (T_IsMagma_178 -> Any
forall a b. a -> b
coe T_IsMagma_178
v3)))))
-- Data.Bool.Properties._.IsNearSemiring.refl
d_refl_1828 ::
  MAlonzo.Code.Algebra.Structures.T_IsNearSemiring_1260 ->
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_refl_1828 :: T_IsNearSemiring_1260 -> Bool -> T__'8801'__12
d_refl_1828 = T_IsNearSemiring_1260 -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsNearSemiring.reflexive
d_reflexive_1830 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsNearSemiring_1260 ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_reflexive_1830 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsNearSemiring_1260
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_reflexive_1830 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsNearSemiring_1260
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsNearSemiring.setoid
d_setoid_1832 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsNearSemiring_1260 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
d_setoid_1832 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsNearSemiring_1260
-> T_Setoid_46
d_setoid_1832 ~Bool -> Bool -> Bool
v0 ~Bool -> Bool -> Bool
v1 ~Bool
v2 T_IsNearSemiring_1260
v3 = T_IsNearSemiring_1260 -> T_Setoid_46
du_setoid_1832 T_IsNearSemiring_1260
v3
du_setoid_1832 ::
  MAlonzo.Code.Algebra.Structures.T_IsNearSemiring_1260 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
du_setoid_1832 :: T_IsNearSemiring_1260 -> T_Setoid_46
du_setoid_1832 T_IsNearSemiring_1260
v0
  = let v1 :: T_IsMonoid_712
v1
          = T_IsNearSemiring_1260 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_'43''45'isMonoid_1278
              (T_IsNearSemiring_1260 -> T_IsNearSemiring_1260
forall a b. a -> b
coe T_IsNearSemiring_1260
v0) in
    Any -> T_Setoid_46
forall a b. a -> b
coe
      (let v2 :: T_IsSemigroup_488
v2
             = T_IsMonoid_712 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_722 (T_IsMonoid_712 -> T_IsMonoid_712
forall a b. a -> b
coe T_IsMonoid_712
v1) in
       Any -> Any
forall a b. a -> b
coe
         ((T_IsMagma_178 -> T_Setoid_46) -> Any -> Any
forall a b. a -> b
coe
            T_IsMagma_178 -> T_Setoid_46
MAlonzo.Code.Algebra.Structures.du_setoid_202
            ((T_IsSemigroup_488 -> T_IsMagma_178) -> Any -> Any
forall a b. a -> b
coe T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496 (T_IsSemigroup_488 -> Any
forall a b. a -> b
coe T_IsSemigroup_488
v2))))
-- Data.Bool.Properties._.IsNearSemiring.sym
d_sym_1834 ::
  MAlonzo.Code.Algebra.Structures.T_IsNearSemiring_1260 ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_sym_1834 :: T_IsNearSemiring_1260
-> Bool -> Bool -> T__'8801'__12 -> T__'8801'__12
d_sym_1834 = T_IsNearSemiring_1260
-> Bool -> Bool -> T__'8801'__12 -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsNearSemiring.trans
d_trans_1836 ::
  MAlonzo.Code.Algebra.Structures.T_IsNearSemiring_1260 ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_trans_1836 :: T_IsNearSemiring_1260
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
d_trans_1836 = T_IsNearSemiring_1260
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsNearSemiring.zeroˡ
d_zero'737'_1838 ::
  MAlonzo.Code.Algebra.Structures.T_IsNearSemiring_1260 ->
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_zero'737'_1838 :: T_IsNearSemiring_1260 -> Bool -> T__'8801'__12
d_zero'737'_1838 = T_IsNearSemiring_1260 -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsNearring.*-assoc
d_'42''45'assoc_1842 ::
  MAlonzo.Code.Algebra.Structures.T_IsNearring_2626 ->
  Bool ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'42''45'assoc_1842 :: T_IsNearring_2626 -> Bool -> Bool -> Bool -> T__'8801'__12
d_'42''45'assoc_1842 = T_IsNearring_2626 -> Bool -> Bool -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsNearring.*-cong
d_'42''45'cong_1844 ::
  MAlonzo.Code.Algebra.Structures.T_IsNearring_2626 ->
  Bool ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'42''45'cong_1844 :: T_IsNearring_2626
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
d_'42''45'cong_1844 = T_IsNearring_2626
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsNearring.∙-congʳ
d_'8729''45'cong'691'_1846 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  Bool ->
  (Bool -> Bool) ->
  MAlonzo.Code.Algebra.Structures.T_IsNearring_2626 ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8729''45'cong'691'_1846 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> (Bool -> Bool)
-> T_IsNearring_2626
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong'691'_1846 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> (Bool -> Bool)
-> T_IsNearring_2626
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsNearring.∙-congˡ
d_'8729''45'cong'737'_1848 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  Bool ->
  (Bool -> Bool) ->
  MAlonzo.Code.Algebra.Structures.T_IsNearring_2626 ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8729''45'cong'737'_1848 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> (Bool -> Bool)
-> T_IsNearring_2626
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong'737'_1848 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> (Bool -> Bool)
-> T_IsNearring_2626
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsNearring.*-identity
d_'42''45'identity_1850 ::
  MAlonzo.Code.Algebra.Structures.T_IsNearring_2626 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'42''45'identity_1850 :: T_IsNearring_2626 -> T_Σ_14
d_'42''45'identity_1850 T_IsNearring_2626
v0
  = (T_IsQuasiring_2260 -> T_Σ_14) -> Any -> T_Σ_14
forall a b. a -> b
coe
      T_IsQuasiring_2260 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_'42''45'identity_2288
      ((T_IsNearring_2626 -> T_IsQuasiring_2260) -> Any -> Any
forall a b. a -> b
coe T_IsNearring_2626 -> T_IsQuasiring_2260
MAlonzo.Code.Algebra.Structures.d_isQuasiring_2644 (T_IsNearring_2626 -> Any
forall a b. a -> b
coe T_IsNearring_2626
v0))
-- Data.Bool.Properties._.IsNearring.identityʳ
d_identity'691'_1852 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  Bool ->
  (Bool -> Bool) ->
  MAlonzo.Code.Algebra.Structures.T_IsNearring_2626 ->
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_identity'691'_1852 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> (Bool -> Bool)
-> T_IsNearring_2626
-> Bool
-> T__'8801'__12
d_identity'691'_1852 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> (Bool -> Bool)
-> T_IsNearring_2626
-> Bool
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsNearring.identityˡ
d_identity'737'_1854 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  Bool ->
  (Bool -> Bool) ->
  MAlonzo.Code.Algebra.Structures.T_IsNearring_2626 ->
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_identity'737'_1854 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> (Bool -> Bool)
-> T_IsNearring_2626
-> Bool
-> T__'8801'__12
d_identity'737'_1854 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> (Bool -> Bool)
-> T_IsNearring_2626
-> Bool
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsNearring.*-isMagma
d_'42''45'isMagma_1856 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  Bool ->
  (Bool -> Bool) ->
  MAlonzo.Code.Algebra.Structures.T_IsNearring_2626 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_178
d_'42''45'isMagma_1856 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> (Bool -> Bool)
-> T_IsNearring_2626
-> T_IsMagma_178
d_'42''45'isMagma_1856 ~Bool -> Bool -> Bool
v0 ~Bool -> Bool -> Bool
v1 ~Bool
v2 ~Bool
v3 ~Bool -> Bool
v4 T_IsNearring_2626
v5
  = T_IsNearring_2626 -> T_IsMagma_178
du_'42''45'isMagma_1856 T_IsNearring_2626
v5
du_'42''45'isMagma_1856 ::
  MAlonzo.Code.Algebra.Structures.T_IsNearring_2626 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_178
du_'42''45'isMagma_1856 :: T_IsNearring_2626 -> T_IsMagma_178
du_'42''45'isMagma_1856 T_IsNearring_2626
v0
  = (T_IsQuasiring_2260 -> T_IsMagma_178) -> Any -> T_IsMagma_178
forall a b. a -> b
coe
      T_IsQuasiring_2260 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.du_'42''45'isMagma_2342
      ((T_IsNearring_2626 -> T_IsQuasiring_2260) -> Any -> Any
forall a b. a -> b
coe T_IsNearring_2626 -> T_IsQuasiring_2260
MAlonzo.Code.Algebra.Structures.d_isQuasiring_2644 (T_IsNearring_2626 -> Any
forall a b. a -> b
coe T_IsNearring_2626
v0))
-- Data.Bool.Properties._.IsNearring.*-isMonoid
d_'42''45'isMonoid_1858 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  Bool ->
  (Bool -> Bool) ->
  MAlonzo.Code.Algebra.Structures.T_IsNearring_2626 ->
  MAlonzo.Code.Algebra.Structures.T_IsMonoid_712
d_'42''45'isMonoid_1858 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> (Bool -> Bool)
-> T_IsNearring_2626
-> T_IsMonoid_712
d_'42''45'isMonoid_1858 ~Bool -> Bool -> Bool
v0 ~Bool -> Bool -> Bool
v1 ~Bool
v2 ~Bool
v3 ~Bool -> Bool
v4 T_IsNearring_2626
v5
  = T_IsNearring_2626 -> T_IsMonoid_712
du_'42''45'isMonoid_1858 T_IsNearring_2626
v5
du_'42''45'isMonoid_1858 ::
  MAlonzo.Code.Algebra.Structures.T_IsNearring_2626 ->
  MAlonzo.Code.Algebra.Structures.T_IsMonoid_712
du_'42''45'isMonoid_1858 :: T_IsNearring_2626 -> T_IsMonoid_712
du_'42''45'isMonoid_1858 T_IsNearring_2626
v0
  = (T_IsQuasiring_2260 -> T_IsMonoid_712) -> Any -> T_IsMonoid_712
forall a b. a -> b
coe
      T_IsQuasiring_2260 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.du_'42''45'isMonoid_2346
      ((T_IsNearring_2626 -> T_IsQuasiring_2260) -> Any -> Any
forall a b. a -> b
coe T_IsNearring_2626 -> T_IsQuasiring_2260
MAlonzo.Code.Algebra.Structures.d_isQuasiring_2644 (T_IsNearring_2626 -> Any
forall a b. a -> b
coe T_IsNearring_2626
v0))
-- Data.Bool.Properties._.IsNearring.*-isSemigroup
d_'42''45'isSemigroup_1860 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  Bool ->
  (Bool -> Bool) ->
  MAlonzo.Code.Algebra.Structures.T_IsNearring_2626 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_488
d_'42''45'isSemigroup_1860 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> (Bool -> Bool)
-> T_IsNearring_2626
-> T_IsSemigroup_488
d_'42''45'isSemigroup_1860 ~Bool -> Bool -> Bool
v0 ~Bool -> Bool -> Bool
v1 ~Bool
v2 ~Bool
v3 ~Bool -> Bool
v4 T_IsNearring_2626
v5
  = T_IsNearring_2626 -> T_IsSemigroup_488
du_'42''45'isSemigroup_1860 T_IsNearring_2626
v5
du_'42''45'isSemigroup_1860 ::
  MAlonzo.Code.Algebra.Structures.T_IsNearring_2626 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_488
du_'42''45'isSemigroup_1860 :: T_IsNearring_2626 -> T_IsSemigroup_488
du_'42''45'isSemigroup_1860 T_IsNearring_2626
v0
  = (T_IsQuasiring_2260 -> T_IsSemigroup_488)
-> Any -> T_IsSemigroup_488
forall a b. a -> b
coe
      T_IsQuasiring_2260 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.du_'42''45'isSemigroup_2344
      ((T_IsNearring_2626 -> T_IsQuasiring_2260) -> Any -> Any
forall a b. a -> b
coe T_IsNearring_2626 -> T_IsQuasiring_2260
MAlonzo.Code.Algebra.Structures.d_isQuasiring_2644 (T_IsNearring_2626 -> Any
forall a b. a -> b
coe T_IsNearring_2626
v0))
-- Data.Bool.Properties._.IsNearring.assoc
d_assoc_1862 ::
  MAlonzo.Code.Algebra.Structures.T_IsNearring_2626 ->
  Bool ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_assoc_1862 :: T_IsNearring_2626 -> Bool -> Bool -> Bool -> T__'8801'__12
d_assoc_1862 = T_IsNearring_2626 -> Bool -> Bool -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsNearring.∙-cong
d_'8729''45'cong_1864 ::
  MAlonzo.Code.Algebra.Structures.T_IsNearring_2626 ->
  Bool ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8729''45'cong_1864 :: T_IsNearring_2626
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong_1864 = T_IsNearring_2626
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsNearring.∙-congʳ
d_'8729''45'cong'691'_1866 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  Bool ->
  (Bool -> Bool) ->
  MAlonzo.Code.Algebra.Structures.T_IsNearring_2626 ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8729''45'cong'691'_1866 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> (Bool -> Bool)
-> T_IsNearring_2626
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong'691'_1866 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> (Bool -> Bool)
-> T_IsNearring_2626
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsNearring.∙-congˡ
d_'8729''45'cong'737'_1868 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  Bool ->
  (Bool -> Bool) ->
  MAlonzo.Code.Algebra.Structures.T_IsNearring_2626 ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8729''45'cong'737'_1868 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> (Bool -> Bool)
-> T_IsNearring_2626
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong'737'_1868 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> (Bool -> Bool)
-> T_IsNearring_2626
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsNearring.identity
d_identity_1870 ::
  MAlonzo.Code.Algebra.Structures.T_IsNearring_2626 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_identity_1870 :: T_IsNearring_2626 -> T_Σ_14
d_identity_1870 T_IsNearring_2626
v0
  = (T_IsMonoid_712 -> T_Σ_14) -> Any -> T_Σ_14
forall a b. a -> b
coe
      T_IsMonoid_712 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_identity_724
      ((T_IsQuasiring_2260 -> T_IsMonoid_712) -> Any -> Any
forall a b. a -> b
coe
         T_IsQuasiring_2260 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_'43''45'isMonoid_2282
         ((T_IsNearring_2626 -> T_IsQuasiring_2260) -> Any -> Any
forall a b. a -> b
coe T_IsNearring_2626 -> T_IsQuasiring_2260
MAlonzo.Code.Algebra.Structures.d_isQuasiring_2644 (T_IsNearring_2626 -> Any
forall a b. a -> b
coe T_IsNearring_2626
v0)))
-- Data.Bool.Properties._.IsNearring.identityʳ
d_identity'691'_1872 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  Bool ->
  (Bool -> Bool) ->
  MAlonzo.Code.Algebra.Structures.T_IsNearring_2626 ->
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_identity'691'_1872 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> (Bool -> Bool)
-> T_IsNearring_2626
-> Bool
-> T__'8801'__12
d_identity'691'_1872 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> (Bool -> Bool)
-> T_IsNearring_2626
-> Bool
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsNearring.identityˡ
d_identity'737'_1874 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  Bool ->
  (Bool -> Bool) ->
  MAlonzo.Code.Algebra.Structures.T_IsNearring_2626 ->
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_identity'737'_1874 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> (Bool -> Bool)
-> T_IsNearring_2626
-> Bool
-> T__'8801'__12
d_identity'737'_1874 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> (Bool -> Bool)
-> T_IsNearring_2626
-> Bool
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsNearring.+-inverse
d_'43''45'inverse_1876 ::
  MAlonzo.Code.Algebra.Structures.T_IsNearring_2626 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'43''45'inverse_1876 :: T_IsNearring_2626 -> T_Σ_14
d_'43''45'inverse_1876 T_IsNearring_2626
v0
  = (T_IsNearring_2626 -> T_Σ_14) -> Any -> T_Σ_14
forall a b. a -> b
coe
      T_IsNearring_2626 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_'43''45'inverse_2646 (T_IsNearring_2626 -> Any
forall a b. a -> b
coe T_IsNearring_2626
v0)
-- Data.Bool.Properties._.IsNearring.+-inverseʳ
d_'43''45'inverse'691'_1878 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  Bool ->
  (Bool -> Bool) ->
  MAlonzo.Code.Algebra.Structures.T_IsNearring_2626 ->
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'43''45'inverse'691'_1878 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> (Bool -> Bool)
-> T_IsNearring_2626
-> Bool
-> T__'8801'__12
d_'43''45'inverse'691'_1878 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> (Bool -> Bool)
-> T_IsNearring_2626
-> Bool
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsNearring.+-inverseˡ
d_'43''45'inverse'737'_1880 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  Bool ->
  (Bool -> Bool) ->
  MAlonzo.Code.Algebra.Structures.T_IsNearring_2626 ->
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'43''45'inverse'737'_1880 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> (Bool -> Bool)
-> T_IsNearring_2626
-> Bool
-> T__'8801'__12
d_'43''45'inverse'737'_1880 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> (Bool -> Bool)
-> T_IsNearring_2626
-> Bool
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsNearring.isMagma
d_isMagma_1882 ::
  MAlonzo.Code.Algebra.Structures.T_IsNearring_2626 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_178
d_isMagma_1882 :: T_IsNearring_2626 -> T_IsMagma_178
d_isMagma_1882 T_IsNearring_2626
v0
  = (T_IsSemigroup_488 -> T_IsMagma_178) -> Any -> T_IsMagma_178
forall a b. a -> b
coe
      T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496
      ((T_IsMonoid_712 -> T_IsSemigroup_488) -> Any -> Any
forall a b. a -> b
coe
         T_IsMonoid_712 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_722
         ((T_IsQuasiring_2260 -> T_IsMonoid_712) -> Any -> Any
forall a b. a -> b
coe
            T_IsQuasiring_2260 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_'43''45'isMonoid_2282
            ((T_IsNearring_2626 -> T_IsQuasiring_2260) -> Any -> Any
forall a b. a -> b
coe T_IsNearring_2626 -> T_IsQuasiring_2260
MAlonzo.Code.Algebra.Structures.d_isQuasiring_2644 (T_IsNearring_2626 -> Any
forall a b. a -> b
coe T_IsNearring_2626
v0))))
-- Data.Bool.Properties._.IsNearring.+-isMonoid
d_'43''45'isMonoid_1884 ::
  MAlonzo.Code.Algebra.Structures.T_IsNearring_2626 ->
  MAlonzo.Code.Algebra.Structures.T_IsMonoid_712
d_'43''45'isMonoid_1884 :: T_IsNearring_2626 -> T_IsMonoid_712
d_'43''45'isMonoid_1884 T_IsNearring_2626
v0
  = (T_IsQuasiring_2260 -> T_IsMonoid_712) -> Any -> T_IsMonoid_712
forall a b. a -> b
coe
      T_IsQuasiring_2260 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_'43''45'isMonoid_2282
      ((T_IsNearring_2626 -> T_IsQuasiring_2260) -> Any -> Any
forall a b. a -> b
coe T_IsNearring_2626 -> T_IsQuasiring_2260
MAlonzo.Code.Algebra.Structures.d_isQuasiring_2644 (T_IsNearring_2626 -> Any
forall a b. a -> b
coe T_IsNearring_2626
v0))
-- Data.Bool.Properties._.IsNearring.isSemigroup
d_isSemigroup_1886 ::
  MAlonzo.Code.Algebra.Structures.T_IsNearring_2626 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_488
d_isSemigroup_1886 :: T_IsNearring_2626 -> T_IsSemigroup_488
d_isSemigroup_1886 T_IsNearring_2626
v0
  = (T_IsMonoid_712 -> T_IsSemigroup_488) -> Any -> T_IsSemigroup_488
forall a b. a -> b
coe
      T_IsMonoid_712 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_722
      ((T_IsQuasiring_2260 -> T_IsMonoid_712) -> Any -> Any
forall a b. a -> b
coe
         T_IsQuasiring_2260 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_'43''45'isMonoid_2282
         ((T_IsNearring_2626 -> T_IsQuasiring_2260) -> Any -> Any
forall a b. a -> b
coe T_IsNearring_2626 -> T_IsQuasiring_2260
MAlonzo.Code.Algebra.Structures.d_isQuasiring_2644 (T_IsNearring_2626 -> Any
forall a b. a -> b
coe T_IsNearring_2626
v0)))
-- Data.Bool.Properties._.IsNearring.isUnitalMagma
d_isUnitalMagma_1888 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  Bool ->
  (Bool -> Bool) ->
  MAlonzo.Code.Algebra.Structures.T_IsNearring_2626 ->
  MAlonzo.Code.Algebra.Structures.T_IsUnitalMagma_666
d_isUnitalMagma_1888 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> (Bool -> Bool)
-> T_IsNearring_2626
-> T_IsUnitalMagma_666
d_isUnitalMagma_1888 ~Bool -> Bool -> Bool
v0 ~Bool -> Bool -> Bool
v1 ~Bool
v2 ~Bool
v3 ~Bool -> Bool
v4 T_IsNearring_2626
v5
  = T_IsNearring_2626 -> T_IsUnitalMagma_666
du_isUnitalMagma_1888 T_IsNearring_2626
v5
du_isUnitalMagma_1888 ::
  MAlonzo.Code.Algebra.Structures.T_IsNearring_2626 ->
  MAlonzo.Code.Algebra.Structures.T_IsUnitalMagma_666
du_isUnitalMagma_1888 :: T_IsNearring_2626 -> T_IsUnitalMagma_666
du_isUnitalMagma_1888 T_IsNearring_2626
v0
  = let v1 :: T_IsQuasiring_2260
v1
          = T_IsNearring_2626 -> T_IsQuasiring_2260
MAlonzo.Code.Algebra.Structures.d_isQuasiring_2644 (T_IsNearring_2626 -> T_IsNearring_2626
forall a b. a -> b
coe T_IsNearring_2626
v0) in
    Any -> T_IsUnitalMagma_666
forall a b. a -> b
coe
      ((T_IsMonoid_712 -> T_IsUnitalMagma_666) -> Any -> Any
forall a b. a -> b
coe
         T_IsMonoid_712 -> T_IsUnitalMagma_666
MAlonzo.Code.Algebra.Structures.du_isUnitalMagma_756
         ((T_IsQuasiring_2260 -> T_IsMonoid_712) -> Any -> Any
forall a b. a -> b
coe
            T_IsQuasiring_2260 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_'43''45'isMonoid_2282 (T_IsQuasiring_2260 -> Any
forall a b. a -> b
coe T_IsQuasiring_2260
v1)))
-- Data.Bool.Properties._.IsNearring.distrib
d_distrib_1890 ::
  MAlonzo.Code.Algebra.Structures.T_IsNearring_2626 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_distrib_1890 :: T_IsNearring_2626 -> T_Σ_14
d_distrib_1890 T_IsNearring_2626
v0
  = (T_IsQuasiring_2260 -> T_Σ_14) -> Any -> T_Σ_14
forall a b. a -> b
coe
      T_IsQuasiring_2260 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_distrib_2290
      ((T_IsNearring_2626 -> T_IsQuasiring_2260) -> Any -> Any
forall a b. a -> b
coe T_IsNearring_2626 -> T_IsQuasiring_2260
MAlonzo.Code.Algebra.Structures.d_isQuasiring_2644 (T_IsNearring_2626 -> Any
forall a b. a -> b
coe T_IsNearring_2626
v0))
-- Data.Bool.Properties._.IsNearring.distribʳ
d_distrib'691'_1892 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  Bool ->
  (Bool -> Bool) ->
  MAlonzo.Code.Algebra.Structures.T_IsNearring_2626 ->
  Bool ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_distrib'691'_1892 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> (Bool -> Bool)
-> T_IsNearring_2626
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
d_distrib'691'_1892 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> (Bool -> Bool)
-> T_IsNearring_2626
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsNearring.distribˡ
d_distrib'737'_1894 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  Bool ->
  (Bool -> Bool) ->
  MAlonzo.Code.Algebra.Structures.T_IsNearring_2626 ->
  Bool ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_distrib'737'_1894 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> (Bool -> Bool)
-> T_IsNearring_2626
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
d_distrib'737'_1894 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> (Bool -> Bool)
-> T_IsNearring_2626
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsNearring.identityʳ
d_identity'691'_1896 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  Bool ->
  (Bool -> Bool) ->
  MAlonzo.Code.Algebra.Structures.T_IsNearring_2626 ->
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_identity'691'_1896 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> (Bool -> Bool)
-> T_IsNearring_2626
-> Bool
-> T__'8801'__12
d_identity'691'_1896 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> (Bool -> Bool)
-> T_IsNearring_2626
-> Bool
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsNearring.identityˡ
d_identity'737'_1898 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  Bool ->
  (Bool -> Bool) ->
  MAlonzo.Code.Algebra.Structures.T_IsNearring_2626 ->
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_identity'737'_1898 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> (Bool -> Bool)
-> T_IsNearring_2626
-> Bool
-> T__'8801'__12
d_identity'737'_1898 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> (Bool -> Bool)
-> T_IsNearring_2626
-> Bool
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsNearring.isEquivalence
d_isEquivalence_1900 ::
  MAlonzo.Code.Algebra.Structures.T_IsNearring_2626 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
d_isEquivalence_1900 :: T_IsNearring_2626 -> T_IsEquivalence_28
d_isEquivalence_1900 T_IsNearring_2626
v0
  = (T_IsMagma_178 -> T_IsEquivalence_28) -> Any -> T_IsEquivalence_28
forall a b. a -> b
coe
      T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186
      ((T_IsSemigroup_488 -> T_IsMagma_178) -> Any -> Any
forall a b. a -> b
coe
         T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496
         ((T_IsMonoid_712 -> T_IsSemigroup_488) -> Any -> Any
forall a b. a -> b
coe
            T_IsMonoid_712 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_722
            ((T_IsQuasiring_2260 -> T_IsMonoid_712) -> Any -> Any
forall a b. a -> b
coe
               T_IsQuasiring_2260 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_'43''45'isMonoid_2282
               ((T_IsNearring_2626 -> T_IsQuasiring_2260) -> Any -> Any
forall a b. a -> b
coe
                  T_IsNearring_2626 -> T_IsQuasiring_2260
MAlonzo.Code.Algebra.Structures.d_isQuasiring_2644 (T_IsNearring_2626 -> Any
forall a b. a -> b
coe T_IsNearring_2626
v0)))))
-- Data.Bool.Properties._.IsNearring.isPartialEquivalence
d_isPartialEquivalence_1902 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  Bool ->
  (Bool -> Bool) ->
  MAlonzo.Code.Algebra.Structures.T_IsNearring_2626 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_1902 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> (Bool -> Bool)
-> T_IsNearring_2626
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_1902 ~Bool -> Bool -> Bool
v0 ~Bool -> Bool -> Bool
v1 ~Bool
v2 ~Bool
v3 ~Bool -> Bool
v4 T_IsNearring_2626
v5
  = T_IsNearring_2626 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_1902 T_IsNearring_2626
v5
du_isPartialEquivalence_1902 ::
  MAlonzo.Code.Algebra.Structures.T_IsNearring_2626 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_1902 :: T_IsNearring_2626 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_1902 T_IsNearring_2626
v0
  = let v1 :: T_IsQuasiring_2260
v1
          = T_IsNearring_2626 -> T_IsQuasiring_2260
MAlonzo.Code.Algebra.Structures.d_isQuasiring_2644 (T_IsNearring_2626 -> T_IsNearring_2626
forall a b. a -> b
coe T_IsNearring_2626
v0) in
    Any -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsMonoid_712
v2
             = T_IsQuasiring_2260 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_'43''45'isMonoid_2282
                 (T_IsQuasiring_2260 -> T_IsQuasiring_2260
forall a b. a -> b
coe T_IsQuasiring_2260
v1) in
       Any -> Any
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_488
v3
                = T_IsMonoid_712 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_722 (T_IsMonoid_712 -> T_IsMonoid_712
forall a b. a -> b
coe T_IsMonoid_712
v2) in
          Any -> Any
forall a b. a -> b
coe
            (let v4 :: T_IsMagma_178
v4 = T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496 (T_IsSemigroup_488 -> T_IsSemigroup_488
forall a b. a -> b
coe T_IsSemigroup_488
v3) in
             Any -> Any
forall a b. a -> b
coe
               ((T_IsEquivalence_28 -> T_IsPartialEquivalence_16) -> Any -> Any
forall a b. a -> b
coe
                  T_IsEquivalence_28 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_44
                  ((T_IsMagma_178 -> T_IsEquivalence_28) -> Any -> Any
forall a b. a -> b
coe
                     T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186 (T_IsMagma_178 -> Any
forall a b. a -> b
coe T_IsMagma_178
v4))))))
-- Data.Bool.Properties._.IsNearring.isQuasiring
d_isQuasiring_1904 ::
  MAlonzo.Code.Algebra.Structures.T_IsNearring_2626 ->
  MAlonzo.Code.Algebra.Structures.T_IsQuasiring_2260
d_isQuasiring_1904 :: T_IsNearring_2626 -> T_IsQuasiring_2260
d_isQuasiring_1904 T_IsNearring_2626
v0
  = (T_IsNearring_2626 -> T_IsQuasiring_2260)
-> Any -> T_IsQuasiring_2260
forall a b. a -> b
coe T_IsNearring_2626 -> T_IsQuasiring_2260
MAlonzo.Code.Algebra.Structures.d_isQuasiring_2644 (T_IsNearring_2626 -> Any
forall a b. a -> b
coe T_IsNearring_2626
v0)
-- Data.Bool.Properties._.IsNearring.refl
d_refl_1906 ::
  MAlonzo.Code.Algebra.Structures.T_IsNearring_2626 ->
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_refl_1906 :: T_IsNearring_2626 -> Bool -> T__'8801'__12
d_refl_1906 = T_IsNearring_2626 -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsNearring.reflexive
d_reflexive_1908 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  Bool ->
  (Bool -> Bool) ->
  MAlonzo.Code.Algebra.Structures.T_IsNearring_2626 ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_reflexive_1908 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> (Bool -> Bool)
-> T_IsNearring_2626
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_reflexive_1908 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> (Bool -> Bool)
-> T_IsNearring_2626
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsNearring.setoid
d_setoid_1910 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  Bool ->
  (Bool -> Bool) ->
  MAlonzo.Code.Algebra.Structures.T_IsNearring_2626 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
d_setoid_1910 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> (Bool -> Bool)
-> T_IsNearring_2626
-> T_Setoid_46
d_setoid_1910 ~Bool -> Bool -> Bool
v0 ~Bool -> Bool -> Bool
v1 ~Bool
v2 ~Bool
v3 ~Bool -> Bool
v4 T_IsNearring_2626
v5 = T_IsNearring_2626 -> T_Setoid_46
du_setoid_1910 T_IsNearring_2626
v5
du_setoid_1910 ::
  MAlonzo.Code.Algebra.Structures.T_IsNearring_2626 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
du_setoid_1910 :: T_IsNearring_2626 -> T_Setoid_46
du_setoid_1910 T_IsNearring_2626
v0
  = let v1 :: T_IsQuasiring_2260
v1
          = T_IsNearring_2626 -> T_IsQuasiring_2260
MAlonzo.Code.Algebra.Structures.d_isQuasiring_2644 (T_IsNearring_2626 -> T_IsNearring_2626
forall a b. a -> b
coe T_IsNearring_2626
v0) in
    Any -> T_Setoid_46
forall a b. a -> b
coe
      (let v2 :: T_IsMonoid_712
v2
             = T_IsQuasiring_2260 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_'43''45'isMonoid_2282
                 (T_IsQuasiring_2260 -> T_IsQuasiring_2260
forall a b. a -> b
coe T_IsQuasiring_2260
v1) in
       Any -> Any
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_488
v3
                = T_IsMonoid_712 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_722 (T_IsMonoid_712 -> T_IsMonoid_712
forall a b. a -> b
coe T_IsMonoid_712
v2) in
          Any -> Any
forall a b. a -> b
coe
            ((T_IsMagma_178 -> T_Setoid_46) -> Any -> Any
forall a b. a -> b
coe
               T_IsMagma_178 -> T_Setoid_46
MAlonzo.Code.Algebra.Structures.du_setoid_202
               ((T_IsSemigroup_488 -> T_IsMagma_178) -> Any -> Any
forall a b. a -> b
coe T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496 (T_IsSemigroup_488 -> Any
forall a b. a -> b
coe T_IsSemigroup_488
v3)))))
-- Data.Bool.Properties._.IsNearring.sym
d_sym_1912 ::
  MAlonzo.Code.Algebra.Structures.T_IsNearring_2626 ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_sym_1912 :: T_IsNearring_2626 -> Bool -> Bool -> T__'8801'__12 -> T__'8801'__12
d_sym_1912 = T_IsNearring_2626 -> Bool -> Bool -> T__'8801'__12 -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsNearring.trans
d_trans_1914 ::
  MAlonzo.Code.Algebra.Structures.T_IsNearring_2626 ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_trans_1914 :: T_IsNearring_2626
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
d_trans_1914 = T_IsNearring_2626
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsNearring.zero
d_zero_1916 ::
  MAlonzo.Code.Algebra.Structures.T_IsNearring_2626 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_zero_1916 :: T_IsNearring_2626 -> T_Σ_14
d_zero_1916 T_IsNearring_2626
v0
  = (T_IsQuasiring_2260 -> T_Σ_14) -> Any -> T_Σ_14
forall a b. a -> b
coe
      T_IsQuasiring_2260 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_zero_2292
      ((T_IsNearring_2626 -> T_IsQuasiring_2260) -> Any -> Any
forall a b. a -> b
coe T_IsNearring_2626 -> T_IsQuasiring_2260
MAlonzo.Code.Algebra.Structures.d_isQuasiring_2644 (T_IsNearring_2626 -> Any
forall a b. a -> b
coe T_IsNearring_2626
v0))
-- Data.Bool.Properties._.IsNearring.zeroʳ
d_zero'691'_1918 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  Bool ->
  (Bool -> Bool) ->
  MAlonzo.Code.Algebra.Structures.T_IsNearring_2626 ->
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_zero'691'_1918 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> (Bool -> Bool)
-> T_IsNearring_2626
-> Bool
-> T__'8801'__12
d_zero'691'_1918 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> (Bool -> Bool)
-> T_IsNearring_2626
-> Bool
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsNearring.zeroˡ
d_zero'737'_1920 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  Bool ->
  (Bool -> Bool) ->
  MAlonzo.Code.Algebra.Structures.T_IsNearring_2626 ->
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_zero'737'_1920 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> (Bool -> Bool)
-> T_IsNearring_2626
-> Bool
-> T__'8801'__12
d_zero'737'_1920 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> (Bool -> Bool)
-> T_IsNearring_2626
-> Bool
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsNearring.⁻¹-cong
d_'8315''185''45'cong_1922 ::
  MAlonzo.Code.Algebra.Structures.T_IsNearring_2626 ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8315''185''45'cong_1922 :: T_IsNearring_2626 -> Bool -> Bool -> T__'8801'__12 -> T__'8801'__12
d_'8315''185''45'cong_1922 = T_IsNearring_2626 -> Bool -> Bool -> T__'8801'__12 -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsNonAssociativeRing._//_
d__'47''47'__1926 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsNonAssociativeRing_2494 ->
  Bool -> Bool -> Bool
d__'47''47'__1926 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsNonAssociativeRing_2494
-> Bool
-> Bool
-> Bool
d__'47''47'__1926 Bool -> Bool -> Bool
v0 ~Bool -> Bool -> Bool
v1 Bool -> Bool
v2 ~Bool
v3 ~Bool
v4 ~T_IsNonAssociativeRing_2494
v5 = (Bool -> Bool -> Bool) -> (Bool -> Bool) -> Bool -> Bool -> Bool
du__'47''47'__1926 Bool -> Bool -> Bool
v0 Bool -> Bool
v2
du__'47''47'__1926 ::
  (Bool -> Bool -> Bool) -> (Bool -> Bool) -> Bool -> Bool -> Bool
du__'47''47'__1926 :: (Bool -> Bool -> Bool) -> (Bool -> Bool) -> Bool -> Bool -> Bool
du__'47''47'__1926 Bool -> Bool -> Bool
v0 Bool -> Bool
v1
  = ((Any -> Any -> Any) -> (Any -> Any) -> Any -> Any -> Any)
-> Any -> Any -> Bool -> Bool -> Bool
forall a b. a -> b
coe
      (Any -> Any -> Any) -> (Any -> Any) -> Any -> Any -> Any
MAlonzo.Code.Algebra.Structures.du__'47''47'__1136 ((Bool -> Bool -> Bool) -> Any
forall a b. a -> b
coe Bool -> Bool -> Bool
v0)
      ((Bool -> Bool) -> Any
forall a b. a -> b
coe Bool -> Bool
v1)
-- Data.Bool.Properties._.IsNonAssociativeRing.*-cong
d_'42''45'cong_1928 ::
  MAlonzo.Code.Algebra.Structures.T_IsNonAssociativeRing_2494 ->
  Bool ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'42''45'cong_1928 :: T_IsNonAssociativeRing_2494
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
d_'42''45'cong_1928 = T_IsNonAssociativeRing_2494
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsNonAssociativeRing.∙-congʳ
d_'8729''45'cong'691'_1930 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsNonAssociativeRing_2494 ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8729''45'cong'691'_1930 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsNonAssociativeRing_2494
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong'691'_1930 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsNonAssociativeRing_2494
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsNonAssociativeRing.∙-congˡ
d_'8729''45'cong'737'_1932 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsNonAssociativeRing_2494 ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8729''45'cong'737'_1932 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsNonAssociativeRing_2494
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong'737'_1932 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsNonAssociativeRing_2494
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsNonAssociativeRing.*-identity
d_'42''45'identity_1934 ::
  MAlonzo.Code.Algebra.Structures.T_IsNonAssociativeRing_2494 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'42''45'identity_1934 :: T_IsNonAssociativeRing_2494 -> T_Σ_14
d_'42''45'identity_1934 T_IsNonAssociativeRing_2494
v0
  = (T_IsNonAssociativeRing_2494 -> T_Σ_14) -> Any -> T_Σ_14
forall a b. a -> b
coe
      T_IsNonAssociativeRing_2494 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_'42''45'identity_2520 (T_IsNonAssociativeRing_2494 -> Any
forall a b. a -> b
coe T_IsNonAssociativeRing_2494
v0)
-- Data.Bool.Properties._.IsNonAssociativeRing.*-identityʳ
d_'42''45'identity'691'_1936 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsNonAssociativeRing_2494 ->
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'42''45'identity'691'_1936 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsNonAssociativeRing_2494
-> Bool
-> T__'8801'__12
d_'42''45'identity'691'_1936 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsNonAssociativeRing_2494
-> Bool
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsNonAssociativeRing.*-identityˡ
d_'42''45'identity'737'_1938 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsNonAssociativeRing_2494 ->
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'42''45'identity'737'_1938 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsNonAssociativeRing_2494
-> Bool
-> T__'8801'__12
d_'42''45'identity'737'_1938 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsNonAssociativeRing_2494
-> Bool
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsNonAssociativeRing.*-isMagma
d_'42''45'isMagma_1940 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsNonAssociativeRing_2494 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_178
d_'42''45'isMagma_1940 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsNonAssociativeRing_2494
-> T_IsMagma_178
d_'42''45'isMagma_1940 Bool -> Bool -> Bool
v0 Bool -> Bool -> Bool
v1 Bool -> Bool
v2 Bool
v3 Bool
v4 T_IsNonAssociativeRing_2494
v5
  = (T_IsNonAssociativeRing_2494 -> T_IsMagma_178)
-> T_IsNonAssociativeRing_2494 -> T_IsMagma_178
forall a b. a -> b
coe T_IsNonAssociativeRing_2494 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.du_'42''45'isMagma_2600 T_IsNonAssociativeRing_2494
v5
-- Data.Bool.Properties._.IsNonAssociativeRing.*-isUnitalMagma
d_'42''45'isUnitalMagma_1942 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsNonAssociativeRing_2494 ->
  MAlonzo.Code.Algebra.Structures.T_IsUnitalMagma_666
d_'42''45'isUnitalMagma_1942 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsNonAssociativeRing_2494
-> T_IsUnitalMagma_666
d_'42''45'isUnitalMagma_1942 Bool -> Bool -> Bool
v0 Bool -> Bool -> Bool
v1 Bool -> Bool
v2 Bool
v3 Bool
v4 T_IsNonAssociativeRing_2494
v5
  = (T_IsNonAssociativeRing_2494 -> T_IsUnitalMagma_666)
-> T_IsNonAssociativeRing_2494 -> T_IsUnitalMagma_666
forall a b. a -> b
coe
      T_IsNonAssociativeRing_2494 -> T_IsUnitalMagma_666
MAlonzo.Code.Algebra.Structures.du_'42''45'isUnitalMagma_2606 T_IsNonAssociativeRing_2494
v5
-- Data.Bool.Properties._.IsNonAssociativeRing.assoc
d_assoc_1944 ::
  MAlonzo.Code.Algebra.Structures.T_IsNonAssociativeRing_2494 ->
  Bool ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_assoc_1944 :: T_IsNonAssociativeRing_2494
-> Bool -> Bool -> Bool -> T__'8801'__12
d_assoc_1944 = T_IsNonAssociativeRing_2494
-> Bool -> Bool -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsNonAssociativeRing.comm
d_comm_1946 ::
  MAlonzo.Code.Algebra.Structures.T_IsNonAssociativeRing_2494 ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_comm_1946 :: T_IsNonAssociativeRing_2494 -> Bool -> Bool -> T__'8801'__12
d_comm_1946 = T_IsNonAssociativeRing_2494 -> Bool -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsNonAssociativeRing.∙-cong
d_'8729''45'cong_1948 ::
  MAlonzo.Code.Algebra.Structures.T_IsNonAssociativeRing_2494 ->
  Bool ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8729''45'cong_1948 :: T_IsNonAssociativeRing_2494
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong_1948 = T_IsNonAssociativeRing_2494
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsNonAssociativeRing.∙-congʳ
d_'8729''45'cong'691'_1950 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsNonAssociativeRing_2494 ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8729''45'cong'691'_1950 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsNonAssociativeRing_2494
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong'691'_1950 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsNonAssociativeRing_2494
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsNonAssociativeRing.∙-congˡ
d_'8729''45'cong'737'_1952 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsNonAssociativeRing_2494 ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8729''45'cong'737'_1952 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsNonAssociativeRing_2494
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong'737'_1952 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsNonAssociativeRing_2494
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsNonAssociativeRing.identity
d_identity_1954 ::
  MAlonzo.Code.Algebra.Structures.T_IsNonAssociativeRing_2494 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_identity_1954 :: T_IsNonAssociativeRing_2494 -> T_Σ_14
d_identity_1954 T_IsNonAssociativeRing_2494
v0
  = (T_IsMonoid_712 -> T_Σ_14) -> Any -> T_Σ_14
forall a b. a -> b
coe
      T_IsMonoid_712 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_identity_724
      ((T_IsGroup_1074 -> T_IsMonoid_712) -> Any -> Any
forall a b. a -> b
coe
         T_IsGroup_1074 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_1088
         ((T_IsAbelianGroup_1172 -> T_IsGroup_1074) -> Any -> Any
forall a b. a -> b
coe
            T_IsAbelianGroup_1172 -> T_IsGroup_1074
MAlonzo.Code.Algebra.Structures.d_isGroup_1184
            ((T_IsNonAssociativeRing_2494 -> T_IsAbelianGroup_1172)
-> Any -> Any
forall a b. a -> b
coe
               T_IsNonAssociativeRing_2494 -> T_IsAbelianGroup_1172
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2516
               (T_IsNonAssociativeRing_2494 -> Any
forall a b. a -> b
coe T_IsNonAssociativeRing_2494
v0))))
-- Data.Bool.Properties._.IsNonAssociativeRing.identityʳ
d_identity'691'_1956 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsNonAssociativeRing_2494 ->
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_identity'691'_1956 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsNonAssociativeRing_2494
-> Bool
-> T__'8801'__12
d_identity'691'_1956 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsNonAssociativeRing_2494
-> Bool
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsNonAssociativeRing.identityˡ
d_identity'737'_1958 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsNonAssociativeRing_2494 ->
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_identity'737'_1958 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsNonAssociativeRing_2494
-> Bool
-> T__'8801'__12
d_identity'737'_1958 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsNonAssociativeRing_2494
-> Bool
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsNonAssociativeRing.+-isAbelianGroup
d_'43''45'isAbelianGroup_1960 ::
  MAlonzo.Code.Algebra.Structures.T_IsNonAssociativeRing_2494 ->
  MAlonzo.Code.Algebra.Structures.T_IsAbelianGroup_1172
d_'43''45'isAbelianGroup_1960 :: T_IsNonAssociativeRing_2494 -> T_IsAbelianGroup_1172
d_'43''45'isAbelianGroup_1960 T_IsNonAssociativeRing_2494
v0
  = (T_IsNonAssociativeRing_2494 -> T_IsAbelianGroup_1172)
-> Any -> T_IsAbelianGroup_1172
forall a b. a -> b
coe
      T_IsNonAssociativeRing_2494 -> T_IsAbelianGroup_1172
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2516
      (T_IsNonAssociativeRing_2494 -> Any
forall a b. a -> b
coe T_IsNonAssociativeRing_2494
v0)
-- Data.Bool.Properties._.IsNonAssociativeRing.isCommutativeMagma
d_isCommutativeMagma_1962 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsNonAssociativeRing_2494 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMagma_214
d_isCommutativeMagma_1962 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsNonAssociativeRing_2494
-> T_IsCommutativeMagma_214
d_isCommutativeMagma_1962 ~Bool -> Bool -> Bool
v0 ~Bool -> Bool -> Bool
v1 ~Bool -> Bool
v2 ~Bool
v3 ~Bool
v4 T_IsNonAssociativeRing_2494
v5
  = T_IsNonAssociativeRing_2494 -> T_IsCommutativeMagma_214
du_isCommutativeMagma_1962 T_IsNonAssociativeRing_2494
v5
du_isCommutativeMagma_1962 ::
  MAlonzo.Code.Algebra.Structures.T_IsNonAssociativeRing_2494 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMagma_214
du_isCommutativeMagma_1962 :: T_IsNonAssociativeRing_2494 -> T_IsCommutativeMagma_214
du_isCommutativeMagma_1962 T_IsNonAssociativeRing_2494
v0
  = let v1 :: T_IsAbelianGroup_1172
v1
          = T_IsNonAssociativeRing_2494 -> T_IsAbelianGroup_1172
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2516
              (T_IsNonAssociativeRing_2494 -> T_IsNonAssociativeRing_2494
forall a b. a -> b
coe T_IsNonAssociativeRing_2494
v0) in
    Any -> T_IsCommutativeMagma_214
forall a b. a -> b
coe
      (let v2 :: Any
v2
             = (T_IsAbelianGroup_1172 -> T_IsCommutativeMonoid_764) -> Any -> Any
forall a b. a -> b
coe
                 T_IsAbelianGroup_1172 -> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.du_isCommutativeMonoid_1244
                 (T_IsAbelianGroup_1172 -> Any
forall a b. a -> b
coe T_IsAbelianGroup_1172
v1) in
       Any -> Any
forall a b. a -> b
coe
         ((T_IsCommutativeSemigroup_568 -> T_IsCommutativeMagma_214)
-> Any -> Any
forall a b. a -> b
coe
            T_IsCommutativeSemigroup_568 -> T_IsCommutativeMagma_214
MAlonzo.Code.Algebra.Structures.du_isCommutativeMagma_606
            ((T_IsCommutativeMonoid_764 -> T_IsCommutativeSemigroup_568)
-> Any -> Any
forall a b. a -> b
coe
               T_IsCommutativeMonoid_764 -> T_IsCommutativeSemigroup_568
MAlonzo.Code.Algebra.Structures.du_isCommutativeSemigroup_814
               (Any -> Any
forall a b. a -> b
coe Any
v2))))
-- Data.Bool.Properties._.IsNonAssociativeRing.isCommutativeMonoid
d_isCommutativeMonoid_1964 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsNonAssociativeRing_2494 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMonoid_764
d_isCommutativeMonoid_1964 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsNonAssociativeRing_2494
-> T_IsCommutativeMonoid_764
d_isCommutativeMonoid_1964 ~Bool -> Bool -> Bool
v0 ~Bool -> Bool -> Bool
v1 ~Bool -> Bool
v2 ~Bool
v3 ~Bool
v4 T_IsNonAssociativeRing_2494
v5
  = T_IsNonAssociativeRing_2494 -> T_IsCommutativeMonoid_764
du_isCommutativeMonoid_1964 T_IsNonAssociativeRing_2494
v5
du_isCommutativeMonoid_1964 ::
  MAlonzo.Code.Algebra.Structures.T_IsNonAssociativeRing_2494 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMonoid_764
du_isCommutativeMonoid_1964 :: T_IsNonAssociativeRing_2494 -> T_IsCommutativeMonoid_764
du_isCommutativeMonoid_1964 T_IsNonAssociativeRing_2494
v0
  = (T_IsAbelianGroup_1172 -> T_IsCommutativeMonoid_764)
-> Any -> T_IsCommutativeMonoid_764
forall a b. a -> b
coe
      T_IsAbelianGroup_1172 -> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.du_isCommutativeMonoid_1244
      ((T_IsNonAssociativeRing_2494 -> T_IsAbelianGroup_1172)
-> Any -> Any
forall a b. a -> b
coe
         T_IsNonAssociativeRing_2494 -> T_IsAbelianGroup_1172
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2516
         (T_IsNonAssociativeRing_2494 -> Any
forall a b. a -> b
coe T_IsNonAssociativeRing_2494
v0))
-- Data.Bool.Properties._.IsNonAssociativeRing.isCommutativeSemigroup
d_isCommutativeSemigroup_1966 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsNonAssociativeRing_2494 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_568
d_isCommutativeSemigroup_1966 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsNonAssociativeRing_2494
-> T_IsCommutativeSemigroup_568
d_isCommutativeSemigroup_1966 ~Bool -> Bool -> Bool
v0 ~Bool -> Bool -> Bool
v1 ~Bool -> Bool
v2 ~Bool
v3 ~Bool
v4 T_IsNonAssociativeRing_2494
v5
  = T_IsNonAssociativeRing_2494 -> T_IsCommutativeSemigroup_568
du_isCommutativeSemigroup_1966 T_IsNonAssociativeRing_2494
v5
du_isCommutativeSemigroup_1966 ::
  MAlonzo.Code.Algebra.Structures.T_IsNonAssociativeRing_2494 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_568
du_isCommutativeSemigroup_1966 :: T_IsNonAssociativeRing_2494 -> T_IsCommutativeSemigroup_568
du_isCommutativeSemigroup_1966 T_IsNonAssociativeRing_2494
v0
  = let v1 :: T_IsAbelianGroup_1172
v1
          = T_IsNonAssociativeRing_2494 -> T_IsAbelianGroup_1172
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2516
              (T_IsNonAssociativeRing_2494 -> T_IsNonAssociativeRing_2494
forall a b. a -> b
coe T_IsNonAssociativeRing_2494
v0) in
    Any -> T_IsCommutativeSemigroup_568
forall a b. a -> b
coe
      ((T_IsCommutativeMonoid_764 -> T_IsCommutativeSemigroup_568)
-> Any -> Any
forall a b. a -> b
coe
         T_IsCommutativeMonoid_764 -> T_IsCommutativeSemigroup_568
MAlonzo.Code.Algebra.Structures.du_isCommutativeSemigroup_814
         ((T_IsAbelianGroup_1172 -> T_IsCommutativeMonoid_764) -> Any -> Any
forall a b. a -> b
coe
            T_IsAbelianGroup_1172 -> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.du_isCommutativeMonoid_1244
            (T_IsAbelianGroup_1172 -> Any
forall a b. a -> b
coe T_IsAbelianGroup_1172
v1)))
-- Data.Bool.Properties._.IsNonAssociativeRing.isGroup
d_isGroup_1968 ::
  MAlonzo.Code.Algebra.Structures.T_IsNonAssociativeRing_2494 ->
  MAlonzo.Code.Algebra.Structures.T_IsGroup_1074
d_isGroup_1968 :: T_IsNonAssociativeRing_2494 -> T_IsGroup_1074
d_isGroup_1968 T_IsNonAssociativeRing_2494
v0
  = (T_IsAbelianGroup_1172 -> T_IsGroup_1074) -> Any -> T_IsGroup_1074
forall a b. a -> b
coe
      T_IsAbelianGroup_1172 -> T_IsGroup_1074
MAlonzo.Code.Algebra.Structures.d_isGroup_1184
      ((T_IsNonAssociativeRing_2494 -> T_IsAbelianGroup_1172)
-> Any -> Any
forall a b. a -> b
coe
         T_IsNonAssociativeRing_2494 -> T_IsAbelianGroup_1172
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2516
         (T_IsNonAssociativeRing_2494 -> Any
forall a b. a -> b
coe T_IsNonAssociativeRing_2494
v0))
-- Data.Bool.Properties._.IsNonAssociativeRing.isInvertibleMagma
d_isInvertibleMagma_1970 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsNonAssociativeRing_2494 ->
  MAlonzo.Code.Algebra.Structures.T_IsInvertibleMagma_958
d_isInvertibleMagma_1970 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsNonAssociativeRing_2494
-> T_IsInvertibleMagma_958
d_isInvertibleMagma_1970 ~Bool -> Bool -> Bool
v0 ~Bool -> Bool -> Bool
v1 ~Bool -> Bool
v2 ~Bool
v3 ~Bool
v4 T_IsNonAssociativeRing_2494
v5
  = T_IsNonAssociativeRing_2494 -> T_IsInvertibleMagma_958
du_isInvertibleMagma_1970 T_IsNonAssociativeRing_2494
v5
du_isInvertibleMagma_1970 ::
  MAlonzo.Code.Algebra.Structures.T_IsNonAssociativeRing_2494 ->
  MAlonzo.Code.Algebra.Structures.T_IsInvertibleMagma_958
du_isInvertibleMagma_1970 :: T_IsNonAssociativeRing_2494 -> T_IsInvertibleMagma_958
du_isInvertibleMagma_1970 T_IsNonAssociativeRing_2494
v0
  = let v1 :: T_IsAbelianGroup_1172
v1
          = T_IsNonAssociativeRing_2494 -> T_IsAbelianGroup_1172
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2516
              (T_IsNonAssociativeRing_2494 -> T_IsNonAssociativeRing_2494
forall a b. a -> b
coe T_IsNonAssociativeRing_2494
v0) in
    Any -> T_IsInvertibleMagma_958
forall a b. a -> b
coe
      ((T_IsGroup_1074 -> T_IsInvertibleMagma_958) -> Any -> Any
forall a b. a -> b
coe
         T_IsGroup_1074 -> T_IsInvertibleMagma_958
MAlonzo.Code.Algebra.Structures.du_isInvertibleMagma_1160
         ((T_IsAbelianGroup_1172 -> T_IsGroup_1074) -> Any -> Any
forall a b. a -> b
coe T_IsAbelianGroup_1172 -> T_IsGroup_1074
MAlonzo.Code.Algebra.Structures.d_isGroup_1184 (T_IsAbelianGroup_1172 -> Any
forall a b. a -> b
coe T_IsAbelianGroup_1172
v1)))
-- Data.Bool.Properties._.IsNonAssociativeRing.isInvertibleUnitalMagma
d_isInvertibleUnitalMagma_1972 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsNonAssociativeRing_2494 ->
  MAlonzo.Code.Algebra.Structures.T_IsInvertibleUnitalMagma_1012
d_isInvertibleUnitalMagma_1972 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsNonAssociativeRing_2494
-> T_IsInvertibleUnitalMagma_1012
d_isInvertibleUnitalMagma_1972 ~Bool -> Bool -> Bool
v0 ~Bool -> Bool -> Bool
v1 ~Bool -> Bool
v2 ~Bool
v3 ~Bool
v4 T_IsNonAssociativeRing_2494
v5
  = T_IsNonAssociativeRing_2494 -> T_IsInvertibleUnitalMagma_1012
du_isInvertibleUnitalMagma_1972 T_IsNonAssociativeRing_2494
v5
du_isInvertibleUnitalMagma_1972 ::
  MAlonzo.Code.Algebra.Structures.T_IsNonAssociativeRing_2494 ->
  MAlonzo.Code.Algebra.Structures.T_IsInvertibleUnitalMagma_1012
du_isInvertibleUnitalMagma_1972 :: T_IsNonAssociativeRing_2494 -> T_IsInvertibleUnitalMagma_1012
du_isInvertibleUnitalMagma_1972 T_IsNonAssociativeRing_2494
v0
  = let v1 :: T_IsAbelianGroup_1172
v1
          = T_IsNonAssociativeRing_2494 -> T_IsAbelianGroup_1172
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2516
              (T_IsNonAssociativeRing_2494 -> T_IsNonAssociativeRing_2494
forall a b. a -> b
coe T_IsNonAssociativeRing_2494
v0) in
    Any -> T_IsInvertibleUnitalMagma_1012
forall a b. a -> b
coe
      ((T_IsGroup_1074 -> T_IsInvertibleUnitalMagma_1012) -> Any -> Any
forall a b. a -> b
coe
         T_IsGroup_1074 -> T_IsInvertibleUnitalMagma_1012
MAlonzo.Code.Algebra.Structures.du_isInvertibleUnitalMagma_1162
         ((T_IsAbelianGroup_1172 -> T_IsGroup_1074) -> Any -> Any
forall a b. a -> b
coe T_IsAbelianGroup_1172 -> T_IsGroup_1074
MAlonzo.Code.Algebra.Structures.d_isGroup_1184 (T_IsAbelianGroup_1172 -> Any
forall a b. a -> b
coe T_IsAbelianGroup_1172
v1)))
-- Data.Bool.Properties._.IsNonAssociativeRing.isMagma
d_isMagma_1974 ::
  MAlonzo.Code.Algebra.Structures.T_IsNonAssociativeRing_2494 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_178
d_isMagma_1974 :: T_IsNonAssociativeRing_2494 -> T_IsMagma_178
d_isMagma_1974 T_IsNonAssociativeRing_2494
v0
  = (T_IsSemigroup_488 -> T_IsMagma_178) -> Any -> T_IsMagma_178
forall a b. a -> b
coe
      T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496
      ((T_IsMonoid_712 -> T_IsSemigroup_488) -> Any -> Any
forall a b. a -> b
coe
         T_IsMonoid_712 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_722
         ((T_IsGroup_1074 -> T_IsMonoid_712) -> Any -> Any
forall a b. a -> b
coe
            T_IsGroup_1074 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_1088
            ((T_IsAbelianGroup_1172 -> T_IsGroup_1074) -> Any -> Any
forall a b. a -> b
coe
               T_IsAbelianGroup_1172 -> T_IsGroup_1074
MAlonzo.Code.Algebra.Structures.d_isGroup_1184
               ((T_IsNonAssociativeRing_2494 -> T_IsAbelianGroup_1172)
-> Any -> Any
forall a b. a -> b
coe
                  T_IsNonAssociativeRing_2494 -> T_IsAbelianGroup_1172
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2516
                  (T_IsNonAssociativeRing_2494 -> Any
forall a b. a -> b
coe T_IsNonAssociativeRing_2494
v0)))))
-- Data.Bool.Properties._.IsNonAssociativeRing.isMonoid
d_isMonoid_1976 ::
  MAlonzo.Code.Algebra.Structures.T_IsNonAssociativeRing_2494 ->
  MAlonzo.Code.Algebra.Structures.T_IsMonoid_712
d_isMonoid_1976 :: T_IsNonAssociativeRing_2494 -> T_IsMonoid_712
d_isMonoid_1976 T_IsNonAssociativeRing_2494
v0
  = (T_IsGroup_1074 -> T_IsMonoid_712) -> Any -> T_IsMonoid_712
forall a b. a -> b
coe
      T_IsGroup_1074 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_1088
      ((T_IsAbelianGroup_1172 -> T_IsGroup_1074) -> Any -> Any
forall a b. a -> b
coe
         T_IsAbelianGroup_1172 -> T_IsGroup_1074
MAlonzo.Code.Algebra.Structures.d_isGroup_1184
         ((T_IsNonAssociativeRing_2494 -> T_IsAbelianGroup_1172)
-> Any -> Any
forall a b. a -> b
coe
            T_IsNonAssociativeRing_2494 -> T_IsAbelianGroup_1172
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2516
            (T_IsNonAssociativeRing_2494 -> Any
forall a b. a -> b
coe T_IsNonAssociativeRing_2494
v0)))
-- Data.Bool.Properties._.IsNonAssociativeRing.isSemigroup
d_isSemigroup_1978 ::
  MAlonzo.Code.Algebra.Structures.T_IsNonAssociativeRing_2494 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_488
d_isSemigroup_1978 :: T_IsNonAssociativeRing_2494 -> T_IsSemigroup_488
d_isSemigroup_1978 T_IsNonAssociativeRing_2494
v0
  = (T_IsMonoid_712 -> T_IsSemigroup_488) -> Any -> T_IsSemigroup_488
forall a b. a -> b
coe
      T_IsMonoid_712 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_722
      ((T_IsGroup_1074 -> T_IsMonoid_712) -> Any -> Any
forall a b. a -> b
coe
         T_IsGroup_1074 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_1088
         ((T_IsAbelianGroup_1172 -> T_IsGroup_1074) -> Any -> Any
forall a b. a -> b
coe
            T_IsAbelianGroup_1172 -> T_IsGroup_1074
MAlonzo.Code.Algebra.Structures.d_isGroup_1184
            ((T_IsNonAssociativeRing_2494 -> T_IsAbelianGroup_1172)
-> Any -> Any
forall a b. a -> b
coe
               T_IsNonAssociativeRing_2494 -> T_IsAbelianGroup_1172
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2516
               (T_IsNonAssociativeRing_2494 -> Any
forall a b. a -> b
coe T_IsNonAssociativeRing_2494
v0))))
-- Data.Bool.Properties._.IsNonAssociativeRing.isUnitalMagma
d_isUnitalMagma_1980 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsNonAssociativeRing_2494 ->
  MAlonzo.Code.Algebra.Structures.T_IsUnitalMagma_666
d_isUnitalMagma_1980 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsNonAssociativeRing_2494
-> T_IsUnitalMagma_666
d_isUnitalMagma_1980 ~Bool -> Bool -> Bool
v0 ~Bool -> Bool -> Bool
v1 ~Bool -> Bool
v2 ~Bool
v3 ~Bool
v4 T_IsNonAssociativeRing_2494
v5
  = T_IsNonAssociativeRing_2494 -> T_IsUnitalMagma_666
du_isUnitalMagma_1980 T_IsNonAssociativeRing_2494
v5
du_isUnitalMagma_1980 ::
  MAlonzo.Code.Algebra.Structures.T_IsNonAssociativeRing_2494 ->
  MAlonzo.Code.Algebra.Structures.T_IsUnitalMagma_666
du_isUnitalMagma_1980 :: T_IsNonAssociativeRing_2494 -> T_IsUnitalMagma_666
du_isUnitalMagma_1980 T_IsNonAssociativeRing_2494
v0
  = let v1 :: T_IsAbelianGroup_1172
v1
          = T_IsNonAssociativeRing_2494 -> T_IsAbelianGroup_1172
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2516
              (T_IsNonAssociativeRing_2494 -> T_IsNonAssociativeRing_2494
forall a b. a -> b
coe T_IsNonAssociativeRing_2494
v0) in
    Any -> T_IsUnitalMagma_666
forall a b. a -> b
coe
      (let v2 :: T_IsGroup_1074
v2
             = T_IsAbelianGroup_1172 -> T_IsGroup_1074
MAlonzo.Code.Algebra.Structures.d_isGroup_1184 (T_IsAbelianGroup_1172 -> T_IsAbelianGroup_1172
forall a b. a -> b
coe T_IsAbelianGroup_1172
v1) in
       Any -> Any
forall a b. a -> b
coe
         ((T_IsMonoid_712 -> T_IsUnitalMagma_666) -> Any -> Any
forall a b. a -> b
coe
            T_IsMonoid_712 -> T_IsUnitalMagma_666
MAlonzo.Code.Algebra.Structures.du_isUnitalMagma_756
            ((T_IsGroup_1074 -> T_IsMonoid_712) -> Any -> Any
forall a b. a -> b
coe T_IsGroup_1074 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_1088 (T_IsGroup_1074 -> Any
forall a b. a -> b
coe T_IsGroup_1074
v2))))
-- Data.Bool.Properties._.IsNonAssociativeRing.⁻¹-cong
d_'8315''185''45'cong_1982 ::
  MAlonzo.Code.Algebra.Structures.T_IsNonAssociativeRing_2494 ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8315''185''45'cong_1982 :: T_IsNonAssociativeRing_2494
-> Bool -> Bool -> T__'8801'__12 -> T__'8801'__12
d_'8315''185''45'cong_1982 = T_IsNonAssociativeRing_2494
-> Bool -> Bool -> T__'8801'__12 -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsNonAssociativeRing.inverse
d_inverse_1984 ::
  MAlonzo.Code.Algebra.Structures.T_IsNonAssociativeRing_2494 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_inverse_1984 :: T_IsNonAssociativeRing_2494 -> T_Σ_14
d_inverse_1984 T_IsNonAssociativeRing_2494
v0
  = (T_IsGroup_1074 -> T_Σ_14) -> Any -> T_Σ_14
forall a b. a -> b
coe
      T_IsGroup_1074 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_inverse_1090
      ((T_IsAbelianGroup_1172 -> T_IsGroup_1074) -> Any -> Any
forall a b. a -> b
coe
         T_IsAbelianGroup_1172 -> T_IsGroup_1074
MAlonzo.Code.Algebra.Structures.d_isGroup_1184
         ((T_IsNonAssociativeRing_2494 -> T_IsAbelianGroup_1172)
-> Any -> Any
forall a b. a -> b
coe
            T_IsNonAssociativeRing_2494 -> T_IsAbelianGroup_1172
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2516
            (T_IsNonAssociativeRing_2494 -> Any
forall a b. a -> b
coe T_IsNonAssociativeRing_2494
v0)))
-- Data.Bool.Properties._.IsNonAssociativeRing.inverseʳ
d_inverse'691'_1986 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsNonAssociativeRing_2494 ->
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_inverse'691'_1986 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsNonAssociativeRing_2494
-> Bool
-> T__'8801'__12
d_inverse'691'_1986 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsNonAssociativeRing_2494
-> Bool
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsNonAssociativeRing.inverseˡ
d_inverse'737'_1988 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsNonAssociativeRing_2494 ->
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_inverse'737'_1988 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsNonAssociativeRing_2494
-> Bool
-> T__'8801'__12
d_inverse'737'_1988 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsNonAssociativeRing_2494
-> Bool
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsNonAssociativeRing.distrib
d_distrib_1990 ::
  MAlonzo.Code.Algebra.Structures.T_IsNonAssociativeRing_2494 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_distrib_1990 :: T_IsNonAssociativeRing_2494 -> T_Σ_14
d_distrib_1990 T_IsNonAssociativeRing_2494
v0
  = (T_IsNonAssociativeRing_2494 -> T_Σ_14) -> Any -> T_Σ_14
forall a b. a -> b
coe T_IsNonAssociativeRing_2494 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_distrib_2522 (T_IsNonAssociativeRing_2494 -> Any
forall a b. a -> b
coe T_IsNonAssociativeRing_2494
v0)
-- Data.Bool.Properties._.IsNonAssociativeRing.distribʳ
d_distrib'691'_1992 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsNonAssociativeRing_2494 ->
  Bool ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_distrib'691'_1992 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsNonAssociativeRing_2494
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
d_distrib'691'_1992 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsNonAssociativeRing_2494
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsNonAssociativeRing.distribˡ
d_distrib'737'_1994 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsNonAssociativeRing_2494 ->
  Bool ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_distrib'737'_1994 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsNonAssociativeRing_2494
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
d_distrib'737'_1994 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsNonAssociativeRing_2494
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsNonAssociativeRing.isEquivalence
d_isEquivalence_1996 ::
  MAlonzo.Code.Algebra.Structures.T_IsNonAssociativeRing_2494 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
d_isEquivalence_1996 :: T_IsNonAssociativeRing_2494 -> T_IsEquivalence_28
d_isEquivalence_1996 T_IsNonAssociativeRing_2494
v0
  = (T_IsMagma_178 -> T_IsEquivalence_28) -> Any -> T_IsEquivalence_28
forall a b. a -> b
coe
      T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186
      ((T_IsSemigroup_488 -> T_IsMagma_178) -> Any -> Any
forall a b. a -> b
coe
         T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496
         ((T_IsMonoid_712 -> T_IsSemigroup_488) -> Any -> Any
forall a b. a -> b
coe
            T_IsMonoid_712 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_722
            ((T_IsGroup_1074 -> T_IsMonoid_712) -> Any -> Any
forall a b. a -> b
coe
               T_IsGroup_1074 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_1088
               ((T_IsAbelianGroup_1172 -> T_IsGroup_1074) -> Any -> Any
forall a b. a -> b
coe
                  T_IsAbelianGroup_1172 -> T_IsGroup_1074
MAlonzo.Code.Algebra.Structures.d_isGroup_1184
                  ((T_IsNonAssociativeRing_2494 -> T_IsAbelianGroup_1172)
-> Any -> Any
forall a b. a -> b
coe
                     T_IsNonAssociativeRing_2494 -> T_IsAbelianGroup_1172
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2516
                     (T_IsNonAssociativeRing_2494 -> Any
forall a b. a -> b
coe T_IsNonAssociativeRing_2494
v0))))))
-- Data.Bool.Properties._.IsNonAssociativeRing.isPartialEquivalence
d_isPartialEquivalence_1998 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsNonAssociativeRing_2494 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_1998 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsNonAssociativeRing_2494
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_1998 ~Bool -> Bool -> Bool
v0 ~Bool -> Bool -> Bool
v1 ~Bool -> Bool
v2 ~Bool
v3 ~Bool
v4 T_IsNonAssociativeRing_2494
v5
  = T_IsNonAssociativeRing_2494 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_1998 T_IsNonAssociativeRing_2494
v5
du_isPartialEquivalence_1998 ::
  MAlonzo.Code.Algebra.Structures.T_IsNonAssociativeRing_2494 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_1998 :: T_IsNonAssociativeRing_2494 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_1998 T_IsNonAssociativeRing_2494
v0
  = let v1 :: T_IsAbelianGroup_1172
v1
          = T_IsNonAssociativeRing_2494 -> T_IsAbelianGroup_1172
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2516
              (T_IsNonAssociativeRing_2494 -> T_IsNonAssociativeRing_2494
forall a b. a -> b
coe T_IsNonAssociativeRing_2494
v0) in
    Any -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsGroup_1074
v2
             = T_IsAbelianGroup_1172 -> T_IsGroup_1074
MAlonzo.Code.Algebra.Structures.d_isGroup_1184 (T_IsAbelianGroup_1172 -> T_IsAbelianGroup_1172
forall a b. a -> b
coe T_IsAbelianGroup_1172
v1) in
       Any -> Any
forall a b. a -> b
coe
         (let v3 :: T_IsMonoid_712
v3
                = T_IsGroup_1074 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_1088 (T_IsGroup_1074 -> T_IsGroup_1074
forall a b. a -> b
coe T_IsGroup_1074
v2) in
          Any -> Any
forall a b. a -> b
coe
            (let v4 :: T_IsSemigroup_488
v4
                   = T_IsMonoid_712 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_722 (T_IsMonoid_712 -> T_IsMonoid_712
forall a b. a -> b
coe T_IsMonoid_712
v3) in
             Any -> Any
forall a b. a -> b
coe
               (let v5 :: T_IsMagma_178
v5 = T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496 (T_IsSemigroup_488 -> T_IsSemigroup_488
forall a b. a -> b
coe T_IsSemigroup_488
v4) in
                Any -> Any
forall a b. a -> b
coe
                  ((T_IsEquivalence_28 -> T_IsPartialEquivalence_16) -> Any -> Any
forall a b. a -> b
coe
                     T_IsEquivalence_28 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_44
                     ((T_IsMagma_178 -> T_IsEquivalence_28) -> Any -> Any
forall a b. a -> b
coe
                        T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186 (T_IsMagma_178 -> Any
forall a b. a -> b
coe T_IsMagma_178
v5)))))))
-- Data.Bool.Properties._.IsNonAssociativeRing.refl
d_refl_2000 ::
  MAlonzo.Code.Algebra.Structures.T_IsNonAssociativeRing_2494 ->
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_refl_2000 :: T_IsNonAssociativeRing_2494 -> Bool -> T__'8801'__12
d_refl_2000 = T_IsNonAssociativeRing_2494 -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsNonAssociativeRing.reflexive
d_reflexive_2002 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsNonAssociativeRing_2494 ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_reflexive_2002 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsNonAssociativeRing_2494
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_reflexive_2002 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsNonAssociativeRing_2494
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsNonAssociativeRing.setoid
d_setoid_2004 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsNonAssociativeRing_2494 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
d_setoid_2004 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsNonAssociativeRing_2494
-> T_Setoid_46
d_setoid_2004 ~Bool -> Bool -> Bool
v0 ~Bool -> Bool -> Bool
v1 ~Bool -> Bool
v2 ~Bool
v3 ~Bool
v4 T_IsNonAssociativeRing_2494
v5 = T_IsNonAssociativeRing_2494 -> T_Setoid_46
du_setoid_2004 T_IsNonAssociativeRing_2494
v5
du_setoid_2004 ::
  MAlonzo.Code.Algebra.Structures.T_IsNonAssociativeRing_2494 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
du_setoid_2004 :: T_IsNonAssociativeRing_2494 -> T_Setoid_46
du_setoid_2004 T_IsNonAssociativeRing_2494
v0
  = let v1 :: T_IsAbelianGroup_1172
v1
          = T_IsNonAssociativeRing_2494 -> T_IsAbelianGroup_1172
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2516
              (T_IsNonAssociativeRing_2494 -> T_IsNonAssociativeRing_2494
forall a b. a -> b
coe T_IsNonAssociativeRing_2494
v0) in
    Any -> T_Setoid_46
forall a b. a -> b
coe
      (let v2 :: T_IsGroup_1074
v2
             = T_IsAbelianGroup_1172 -> T_IsGroup_1074
MAlonzo.Code.Algebra.Structures.d_isGroup_1184 (T_IsAbelianGroup_1172 -> T_IsAbelianGroup_1172
forall a b. a -> b
coe T_IsAbelianGroup_1172
v1) in
       Any -> Any
forall a b. a -> b
coe
         (let v3 :: T_IsMonoid_712
v3
                = T_IsGroup_1074 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_1088 (T_IsGroup_1074 -> T_IsGroup_1074
forall a b. a -> b
coe T_IsGroup_1074
v2) in
          Any -> Any
forall a b. a -> b
coe
            (let v4 :: T_IsSemigroup_488
v4
                   = T_IsMonoid_712 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_722 (T_IsMonoid_712 -> T_IsMonoid_712
forall a b. a -> b
coe T_IsMonoid_712
v3) in
             Any -> Any
forall a b. a -> b
coe
               ((T_IsMagma_178 -> T_Setoid_46) -> Any -> Any
forall a b. a -> b
coe
                  T_IsMagma_178 -> T_Setoid_46
MAlonzo.Code.Algebra.Structures.du_setoid_202
                  ((T_IsSemigroup_488 -> T_IsMagma_178) -> Any -> Any
forall a b. a -> b
coe T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496 (T_IsSemigroup_488 -> Any
forall a b. a -> b
coe T_IsSemigroup_488
v4))))))
-- Data.Bool.Properties._.IsNonAssociativeRing.sym
d_sym_2006 ::
  MAlonzo.Code.Algebra.Structures.T_IsNonAssociativeRing_2494 ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_sym_2006 :: T_IsNonAssociativeRing_2494
-> Bool -> Bool -> T__'8801'__12 -> T__'8801'__12
d_sym_2006 = T_IsNonAssociativeRing_2494
-> Bool -> Bool -> T__'8801'__12 -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsNonAssociativeRing.trans
d_trans_2008 ::
  MAlonzo.Code.Algebra.Structures.T_IsNonAssociativeRing_2494 ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_trans_2008 :: T_IsNonAssociativeRing_2494
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
d_trans_2008 = T_IsNonAssociativeRing_2494
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsNonAssociativeRing.uniqueʳ-⁻¹
d_unique'691''45''8315''185'_2010 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsNonAssociativeRing_2494 ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_unique'691''45''8315''185'_2010 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsNonAssociativeRing_2494
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_unique'691''45''8315''185'_2010 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsNonAssociativeRing_2494
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsNonAssociativeRing.uniqueˡ-⁻¹
d_unique'737''45''8315''185'_2012 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsNonAssociativeRing_2494 ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_unique'737''45''8315''185'_2012 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsNonAssociativeRing_2494
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_unique'737''45''8315''185'_2012 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsNonAssociativeRing_2494
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsNonAssociativeRing.zero
d_zero_2014 ::
  MAlonzo.Code.Algebra.Structures.T_IsNonAssociativeRing_2494 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_zero_2014 :: T_IsNonAssociativeRing_2494 -> T_Σ_14
d_zero_2014 T_IsNonAssociativeRing_2494
v0
  = (T_IsNonAssociativeRing_2494 -> T_Σ_14) -> Any -> T_Σ_14
forall a b. a -> b
coe T_IsNonAssociativeRing_2494 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_zero_2524 (T_IsNonAssociativeRing_2494 -> Any
forall a b. a -> b
coe T_IsNonAssociativeRing_2494
v0)
-- Data.Bool.Properties._.IsNonAssociativeRing.zeroʳ
d_zero'691'_2016 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsNonAssociativeRing_2494 ->
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_zero'691'_2016 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsNonAssociativeRing_2494
-> Bool
-> T__'8801'__12
d_zero'691'_2016 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsNonAssociativeRing_2494
-> Bool
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsNonAssociativeRing.zeroˡ
d_zero'737'_2018 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsNonAssociativeRing_2494 ->
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_zero'737'_2018 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsNonAssociativeRing_2494
-> Bool
-> T__'8801'__12
d_zero'737'_2018 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsNonAssociativeRing_2494
-> Bool
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsQuasigroup.//-cong
d_'47''47''45'cong_2022 ::
  MAlonzo.Code.Algebra.Structures.T_IsQuasigroup_3038 ->
  Bool ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'47''47''45'cong_2022 :: T_IsQuasigroup_3038
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
d_'47''47''45'cong_2022 = T_IsQuasigroup_3038
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsQuasigroup.//-congʳ
d_'47''47''45'cong'691'_2024 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  MAlonzo.Code.Algebra.Structures.T_IsQuasigroup_3038 ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'47''47''45'cong'691'_2024 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> T_IsQuasigroup_3038
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_'47''47''45'cong'691'_2024 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> T_IsQuasigroup_3038
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsQuasigroup.//-congˡ
d_'47''47''45'cong'737'_2026 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  MAlonzo.Code.Algebra.Structures.T_IsQuasigroup_3038 ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'47''47''45'cong'737'_2026 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> T_IsQuasigroup_3038
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_'47''47''45'cong'737'_2026 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> T_IsQuasigroup_3038
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsQuasigroup.\\-cong
d_'92''92''45'cong_2028 ::
  MAlonzo.Code.Algebra.Structures.T_IsQuasigroup_3038 ->
  Bool ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'92''92''45'cong_2028 :: T_IsQuasigroup_3038
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
d_'92''92''45'cong_2028 = T_IsQuasigroup_3038
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsQuasigroup.\\-congʳ
d_'92''92''45'cong'691'_2030 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  MAlonzo.Code.Algebra.Structures.T_IsQuasigroup_3038 ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'92''92''45'cong'691'_2030 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> T_IsQuasigroup_3038
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_'92''92''45'cong'691'_2030 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> T_IsQuasigroup_3038
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsQuasigroup.\\-congˡ
d_'92''92''45'cong'737'_2032 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  MAlonzo.Code.Algebra.Structures.T_IsQuasigroup_3038 ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'92''92''45'cong'737'_2032 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> T_IsQuasigroup_3038
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_'92''92''45'cong'737'_2032 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> T_IsQuasigroup_3038
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsQuasigroup.isEquivalence
d_isEquivalence_2034 ::
  MAlonzo.Code.Algebra.Structures.T_IsQuasigroup_3038 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
d_isEquivalence_2034 :: T_IsQuasigroup_3038 -> T_IsEquivalence_28
d_isEquivalence_2034 T_IsQuasigroup_3038
v0
  = (T_IsMagma_178 -> T_IsEquivalence_28) -> Any -> T_IsEquivalence_28
forall a b. a -> b
coe
      T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186
      ((T_IsQuasigroup_3038 -> T_IsMagma_178) -> Any -> Any
forall a b. a -> b
coe T_IsQuasigroup_3038 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_3056 (T_IsQuasigroup_3038 -> Any
forall a b. a -> b
coe T_IsQuasigroup_3038
v0))
-- Data.Bool.Properties._.IsQuasigroup.isMagma
d_isMagma_2036 ::
  MAlonzo.Code.Algebra.Structures.T_IsQuasigroup_3038 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_178
d_isMagma_2036 :: T_IsQuasigroup_3038 -> T_IsMagma_178
d_isMagma_2036 T_IsQuasigroup_3038
v0
  = (T_IsQuasigroup_3038 -> T_IsMagma_178) -> Any -> T_IsMagma_178
forall a b. a -> b
coe T_IsQuasigroup_3038 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_3056 (T_IsQuasigroup_3038 -> Any
forall a b. a -> b
coe T_IsQuasigroup_3038
v0)
-- Data.Bool.Properties._.IsQuasigroup.isPartialEquivalence
d_isPartialEquivalence_2038 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  MAlonzo.Code.Algebra.Structures.T_IsQuasigroup_3038 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_2038 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> T_IsQuasigroup_3038
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_2038 ~Bool -> Bool -> Bool
v0 ~Bool -> Bool -> Bool
v1 ~Bool -> Bool -> Bool
v2 T_IsQuasigroup_3038
v3
  = T_IsQuasigroup_3038 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_2038 T_IsQuasigroup_3038
v3
du_isPartialEquivalence_2038 ::
  MAlonzo.Code.Algebra.Structures.T_IsQuasigroup_3038 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_2038 :: T_IsQuasigroup_3038 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_2038 T_IsQuasigroup_3038
v0
  = let v1 :: T_IsMagma_178
v1
          = T_IsQuasigroup_3038 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_3056 (T_IsQuasigroup_3038 -> T_IsQuasigroup_3038
forall a b. a -> b
coe T_IsQuasigroup_3038
v0) in
    Any -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      ((T_IsEquivalence_28 -> T_IsPartialEquivalence_16) -> Any -> Any
forall a b. a -> b
coe
         T_IsEquivalence_28 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_44
         ((T_IsMagma_178 -> T_IsEquivalence_28) -> Any -> Any
forall a b. a -> b
coe T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186 (T_IsMagma_178 -> Any
forall a b. a -> b
coe T_IsMagma_178
v1)))
-- Data.Bool.Properties._.IsQuasigroup.leftDivides
d_leftDivides_2040 ::
  MAlonzo.Code.Algebra.Structures.T_IsQuasigroup_3038 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_leftDivides_2040 :: T_IsQuasigroup_3038 -> T_Σ_14
d_leftDivides_2040 T_IsQuasigroup_3038
v0
  = (T_IsQuasigroup_3038 -> T_Σ_14) -> Any -> T_Σ_14
forall a b. a -> b
coe T_IsQuasigroup_3038 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_leftDivides_3062 (T_IsQuasigroup_3038 -> Any
forall a b. a -> b
coe T_IsQuasigroup_3038
v0)
-- Data.Bool.Properties._.IsQuasigroup.leftDividesʳ
d_leftDivides'691'_2042 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  MAlonzo.Code.Algebra.Structures.T_IsQuasigroup_3038 ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_leftDivides'691'_2042 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> T_IsQuasigroup_3038
-> Bool
-> Bool
-> T__'8801'__12
d_leftDivides'691'_2042 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> T_IsQuasigroup_3038
-> Bool
-> Bool
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsQuasigroup.leftDividesˡ
d_leftDivides'737'_2044 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  MAlonzo.Code.Algebra.Structures.T_IsQuasigroup_3038 ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_leftDivides'737'_2044 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> T_IsQuasigroup_3038
-> Bool
-> Bool
-> T__'8801'__12
d_leftDivides'737'_2044 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> T_IsQuasigroup_3038
-> Bool
-> Bool
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsQuasigroup.refl
d_refl_2046 ::
  MAlonzo.Code.Algebra.Structures.T_IsQuasigroup_3038 ->
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_refl_2046 :: T_IsQuasigroup_3038 -> Bool -> T__'8801'__12
d_refl_2046 = T_IsQuasigroup_3038 -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsQuasigroup.reflexive
d_reflexive_2048 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  MAlonzo.Code.Algebra.Structures.T_IsQuasigroup_3038 ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_reflexive_2048 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> T_IsQuasigroup_3038
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_reflexive_2048 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> T_IsQuasigroup_3038
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsQuasigroup.rightDivides
d_rightDivides_2050 ::
  MAlonzo.Code.Algebra.Structures.T_IsQuasigroup_3038 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_rightDivides_2050 :: T_IsQuasigroup_3038 -> T_Σ_14
d_rightDivides_2050 T_IsQuasigroup_3038
v0
  = (T_IsQuasigroup_3038 -> T_Σ_14) -> Any -> T_Σ_14
forall a b. a -> b
coe T_IsQuasigroup_3038 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_rightDivides_3064 (T_IsQuasigroup_3038 -> Any
forall a b. a -> b
coe T_IsQuasigroup_3038
v0)
-- Data.Bool.Properties._.IsQuasigroup.rightDividesʳ
d_rightDivides'691'_2052 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  MAlonzo.Code.Algebra.Structures.T_IsQuasigroup_3038 ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_rightDivides'691'_2052 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> T_IsQuasigroup_3038
-> Bool
-> Bool
-> T__'8801'__12
d_rightDivides'691'_2052 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> T_IsQuasigroup_3038
-> Bool
-> Bool
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsQuasigroup.rightDividesˡ
d_rightDivides'737'_2054 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  MAlonzo.Code.Algebra.Structures.T_IsQuasigroup_3038 ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_rightDivides'737'_2054 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> T_IsQuasigroup_3038
-> Bool
-> Bool
-> T__'8801'__12
d_rightDivides'737'_2054 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> T_IsQuasigroup_3038
-> Bool
-> Bool
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsQuasigroup.setoid
d_setoid_2056 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  MAlonzo.Code.Algebra.Structures.T_IsQuasigroup_3038 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
d_setoid_2056 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> T_IsQuasigroup_3038
-> T_Setoid_46
d_setoid_2056 ~Bool -> Bool -> Bool
v0 ~Bool -> Bool -> Bool
v1 ~Bool -> Bool -> Bool
v2 T_IsQuasigroup_3038
v3 = T_IsQuasigroup_3038 -> T_Setoid_46
du_setoid_2056 T_IsQuasigroup_3038
v3
du_setoid_2056 ::
  MAlonzo.Code.Algebra.Structures.T_IsQuasigroup_3038 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
du_setoid_2056 :: T_IsQuasigroup_3038 -> T_Setoid_46
du_setoid_2056 T_IsQuasigroup_3038
v0
  = (T_IsMagma_178 -> T_Setoid_46) -> Any -> T_Setoid_46
forall a b. a -> b
coe
      T_IsMagma_178 -> T_Setoid_46
MAlonzo.Code.Algebra.Structures.du_setoid_202
      ((T_IsQuasigroup_3038 -> T_IsMagma_178) -> Any -> Any
forall a b. a -> b
coe T_IsQuasigroup_3038 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_3056 (T_IsQuasigroup_3038 -> Any
forall a b. a -> b
coe T_IsQuasigroup_3038
v0))
-- Data.Bool.Properties._.IsQuasigroup.sym
d_sym_2058 ::
  MAlonzo.Code.Algebra.Structures.T_IsQuasigroup_3038 ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_sym_2058 :: T_IsQuasigroup_3038
-> Bool -> Bool -> T__'8801'__12 -> T__'8801'__12
d_sym_2058 = T_IsQuasigroup_3038
-> Bool -> Bool -> T__'8801'__12 -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsQuasigroup.trans
d_trans_2060 ::
  MAlonzo.Code.Algebra.Structures.T_IsQuasigroup_3038 ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_trans_2060 :: T_IsQuasigroup_3038
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
d_trans_2060 = T_IsQuasigroup_3038
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsQuasigroup.∙-cong
d_'8729''45'cong_2062 ::
  MAlonzo.Code.Algebra.Structures.T_IsQuasigroup_3038 ->
  Bool ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8729''45'cong_2062 :: T_IsQuasigroup_3038
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong_2062 = T_IsQuasigroup_3038
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsQuasigroup.∙-congʳ
d_'8729''45'cong'691'_2064 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  MAlonzo.Code.Algebra.Structures.T_IsQuasigroup_3038 ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8729''45'cong'691'_2064 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> T_IsQuasigroup_3038
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong'691'_2064 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> T_IsQuasigroup_3038
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsQuasigroup.∙-congˡ
d_'8729''45'cong'737'_2066 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  MAlonzo.Code.Algebra.Structures.T_IsQuasigroup_3038 ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8729''45'cong'737'_2066 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> T_IsQuasigroup_3038
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong'737'_2066 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> T_IsQuasigroup_3038
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsQuasiring.*-assoc
d_'42''45'assoc_2070 ::
  MAlonzo.Code.Algebra.Structures.T_IsQuasiring_2260 ->
  Bool ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'42''45'assoc_2070 :: T_IsQuasiring_2260 -> Bool -> Bool -> Bool -> T__'8801'__12
d_'42''45'assoc_2070 = T_IsQuasiring_2260 -> Bool -> Bool -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsQuasiring.*-cong
d_'42''45'cong_2072 ::
  MAlonzo.Code.Algebra.Structures.T_IsQuasiring_2260 ->
  Bool ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'42''45'cong_2072 :: T_IsQuasiring_2260
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
d_'42''45'cong_2072 = T_IsQuasiring_2260
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsQuasiring.∙-congʳ
d_'8729''45'cong'691'_2074 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsQuasiring_2260 ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8729''45'cong'691'_2074 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> T_IsQuasiring_2260
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong'691'_2074 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> T_IsQuasiring_2260
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsQuasiring.∙-congˡ
d_'8729''45'cong'737'_2076 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsQuasiring_2260 ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8729''45'cong'737'_2076 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> T_IsQuasiring_2260
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong'737'_2076 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> T_IsQuasiring_2260
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsQuasiring.*-identity
d_'42''45'identity_2078 ::
  MAlonzo.Code.Algebra.Structures.T_IsQuasiring_2260 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'42''45'identity_2078 :: T_IsQuasiring_2260 -> T_Σ_14
d_'42''45'identity_2078 T_IsQuasiring_2260
v0
  = (T_IsQuasiring_2260 -> T_Σ_14) -> Any -> T_Σ_14
forall a b. a -> b
coe
      T_IsQuasiring_2260 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_'42''45'identity_2288 (T_IsQuasiring_2260 -> Any
forall a b. a -> b
coe T_IsQuasiring_2260
v0)
-- Data.Bool.Properties._.IsQuasiring.identityʳ
d_identity'691'_2080 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsQuasiring_2260 ->
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_identity'691'_2080 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> T_IsQuasiring_2260
-> Bool
-> T__'8801'__12
d_identity'691'_2080 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> T_IsQuasiring_2260
-> Bool
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsQuasiring.identityˡ
d_identity'737'_2082 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsQuasiring_2260 ->
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_identity'737'_2082 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> T_IsQuasiring_2260
-> Bool
-> T__'8801'__12
d_identity'737'_2082 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> T_IsQuasiring_2260
-> Bool
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsQuasiring.*-isMagma
d_'42''45'isMagma_2084 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsQuasiring_2260 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_178
d_'42''45'isMagma_2084 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> T_IsQuasiring_2260
-> T_IsMagma_178
d_'42''45'isMagma_2084 Bool -> Bool -> Bool
v0 Bool -> Bool -> Bool
v1 Bool
v2 Bool
v3 T_IsQuasiring_2260
v4
  = (T_IsQuasiring_2260 -> T_IsMagma_178)
-> T_IsQuasiring_2260 -> T_IsMagma_178
forall a b. a -> b
coe T_IsQuasiring_2260 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.du_'42''45'isMagma_2342 T_IsQuasiring_2260
v4
-- Data.Bool.Properties._.IsQuasiring.*-isMonoid
d_'42''45'isMonoid_2086 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsQuasiring_2260 ->
  MAlonzo.Code.Algebra.Structures.T_IsMonoid_712
d_'42''45'isMonoid_2086 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> T_IsQuasiring_2260
-> T_IsMonoid_712
d_'42''45'isMonoid_2086 Bool -> Bool -> Bool
v0 Bool -> Bool -> Bool
v1 Bool
v2 Bool
v3 T_IsQuasiring_2260
v4
  = (T_IsQuasiring_2260 -> T_IsMonoid_712)
-> T_IsQuasiring_2260 -> T_IsMonoid_712
forall a b. a -> b
coe T_IsQuasiring_2260 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.du_'42''45'isMonoid_2346 T_IsQuasiring_2260
v4
-- Data.Bool.Properties._.IsQuasiring.*-isSemigroup
d_'42''45'isSemigroup_2088 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsQuasiring_2260 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_488
d_'42''45'isSemigroup_2088 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> T_IsQuasiring_2260
-> T_IsSemigroup_488
d_'42''45'isSemigroup_2088 Bool -> Bool -> Bool
v0 Bool -> Bool -> Bool
v1 Bool
v2 Bool
v3 T_IsQuasiring_2260
v4
  = (T_IsQuasiring_2260 -> T_IsSemigroup_488)
-> T_IsQuasiring_2260 -> T_IsSemigroup_488
forall a b. a -> b
coe
      T_IsQuasiring_2260 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.du_'42''45'isSemigroup_2344 T_IsQuasiring_2260
v4
-- Data.Bool.Properties._.IsQuasiring.assoc
d_assoc_2090 ::
  MAlonzo.Code.Algebra.Structures.T_IsQuasiring_2260 ->
  Bool ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_assoc_2090 :: T_IsQuasiring_2260 -> Bool -> Bool -> Bool -> T__'8801'__12
d_assoc_2090 = T_IsQuasiring_2260 -> Bool -> Bool -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsQuasiring.∙-cong
d_'8729''45'cong_2092 ::
  MAlonzo.Code.Algebra.Structures.T_IsQuasiring_2260 ->
  Bool ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8729''45'cong_2092 :: T_IsQuasiring_2260
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong_2092 = T_IsQuasiring_2260
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsQuasiring.∙-congʳ
d_'8729''45'cong'691'_2094 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsQuasiring_2260 ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8729''45'cong'691'_2094 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> T_IsQuasiring_2260
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong'691'_2094 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> T_IsQuasiring_2260
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsQuasiring.∙-congˡ
d_'8729''45'cong'737'_2096 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsQuasiring_2260 ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8729''45'cong'737'_2096 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> T_IsQuasiring_2260
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong'737'_2096 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> T_IsQuasiring_2260
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsQuasiring.identity
d_identity_2098 ::
  MAlonzo.Code.Algebra.Structures.T_IsQuasiring_2260 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_identity_2098 :: T_IsQuasiring_2260 -> T_Σ_14
d_identity_2098 T_IsQuasiring_2260
v0
  = (T_IsMonoid_712 -> T_Σ_14) -> Any -> T_Σ_14
forall a b. a -> b
coe
      T_IsMonoid_712 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_identity_724
      ((T_IsQuasiring_2260 -> T_IsMonoid_712) -> Any -> Any
forall a b. a -> b
coe
         T_IsQuasiring_2260 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_'43''45'isMonoid_2282 (T_IsQuasiring_2260 -> Any
forall a b. a -> b
coe T_IsQuasiring_2260
v0))
-- Data.Bool.Properties._.IsQuasiring.identityʳ
d_identity'691'_2100 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsQuasiring_2260 ->
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_identity'691'_2100 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> T_IsQuasiring_2260
-> Bool
-> T__'8801'__12
d_identity'691'_2100 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> T_IsQuasiring_2260
-> Bool
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsQuasiring.identityˡ
d_identity'737'_2102 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsQuasiring_2260 ->
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_identity'737'_2102 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> T_IsQuasiring_2260
-> Bool
-> T__'8801'__12
d_identity'737'_2102 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> T_IsQuasiring_2260
-> Bool
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsQuasiring.isMagma
d_isMagma_2104 ::
  MAlonzo.Code.Algebra.Structures.T_IsQuasiring_2260 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_178
d_isMagma_2104 :: T_IsQuasiring_2260 -> T_IsMagma_178
d_isMagma_2104 T_IsQuasiring_2260
v0
  = (T_IsSemigroup_488 -> T_IsMagma_178) -> Any -> T_IsMagma_178
forall a b. a -> b
coe
      T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496
      ((T_IsMonoid_712 -> T_IsSemigroup_488) -> Any -> Any
forall a b. a -> b
coe
         T_IsMonoid_712 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_722
         ((T_IsQuasiring_2260 -> T_IsMonoid_712) -> Any -> Any
forall a b. a -> b
coe
            T_IsQuasiring_2260 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_'43''45'isMonoid_2282 (T_IsQuasiring_2260 -> Any
forall a b. a -> b
coe T_IsQuasiring_2260
v0)))
-- Data.Bool.Properties._.IsQuasiring.+-isMonoid
d_'43''45'isMonoid_2106 ::
  MAlonzo.Code.Algebra.Structures.T_IsQuasiring_2260 ->
  MAlonzo.Code.Algebra.Structures.T_IsMonoid_712
d_'43''45'isMonoid_2106 :: T_IsQuasiring_2260 -> T_IsMonoid_712
d_'43''45'isMonoid_2106 T_IsQuasiring_2260
v0
  = (T_IsQuasiring_2260 -> T_IsMonoid_712) -> Any -> T_IsMonoid_712
forall a b. a -> b
coe
      T_IsQuasiring_2260 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_'43''45'isMonoid_2282 (T_IsQuasiring_2260 -> Any
forall a b. a -> b
coe T_IsQuasiring_2260
v0)
-- Data.Bool.Properties._.IsQuasiring.isSemigroup
d_isSemigroup_2108 ::
  MAlonzo.Code.Algebra.Structures.T_IsQuasiring_2260 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_488
d_isSemigroup_2108 :: T_IsQuasiring_2260 -> T_IsSemigroup_488
d_isSemigroup_2108 T_IsQuasiring_2260
v0
  = (T_IsMonoid_712 -> T_IsSemigroup_488) -> Any -> T_IsSemigroup_488
forall a b. a -> b
coe
      T_IsMonoid_712 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_722
      ((T_IsQuasiring_2260 -> T_IsMonoid_712) -> Any -> Any
forall a b. a -> b
coe
         T_IsQuasiring_2260 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_'43''45'isMonoid_2282 (T_IsQuasiring_2260 -> Any
forall a b. a -> b
coe T_IsQuasiring_2260
v0))
-- Data.Bool.Properties._.IsQuasiring.isUnitalMagma
d_isUnitalMagma_2110 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsQuasiring_2260 ->
  MAlonzo.Code.Algebra.Structures.T_IsUnitalMagma_666
d_isUnitalMagma_2110 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> T_IsQuasiring_2260
-> T_IsUnitalMagma_666
d_isUnitalMagma_2110 ~Bool -> Bool -> Bool
v0 ~Bool -> Bool -> Bool
v1 ~Bool
v2 ~Bool
v3 T_IsQuasiring_2260
v4 = T_IsQuasiring_2260 -> T_IsUnitalMagma_666
du_isUnitalMagma_2110 T_IsQuasiring_2260
v4
du_isUnitalMagma_2110 ::
  MAlonzo.Code.Algebra.Structures.T_IsQuasiring_2260 ->
  MAlonzo.Code.Algebra.Structures.T_IsUnitalMagma_666
du_isUnitalMagma_2110 :: T_IsQuasiring_2260 -> T_IsUnitalMagma_666
du_isUnitalMagma_2110 T_IsQuasiring_2260
v0
  = (T_IsMonoid_712 -> T_IsUnitalMagma_666)
-> Any -> T_IsUnitalMagma_666
forall a b. a -> b
coe
      T_IsMonoid_712 -> T_IsUnitalMagma_666
MAlonzo.Code.Algebra.Structures.du_isUnitalMagma_756
      ((T_IsQuasiring_2260 -> T_IsMonoid_712) -> Any -> Any
forall a b. a -> b
coe
         T_IsQuasiring_2260 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_'43''45'isMonoid_2282 (T_IsQuasiring_2260 -> Any
forall a b. a -> b
coe T_IsQuasiring_2260
v0))
-- Data.Bool.Properties._.IsQuasiring.distrib
d_distrib_2112 ::
  MAlonzo.Code.Algebra.Structures.T_IsQuasiring_2260 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_distrib_2112 :: T_IsQuasiring_2260 -> T_Σ_14
d_distrib_2112 T_IsQuasiring_2260
v0
  = (T_IsQuasiring_2260 -> T_Σ_14) -> Any -> T_Σ_14
forall a b. a -> b
coe T_IsQuasiring_2260 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_distrib_2290 (T_IsQuasiring_2260 -> Any
forall a b. a -> b
coe T_IsQuasiring_2260
v0)
-- Data.Bool.Properties._.IsQuasiring.distribʳ
d_distrib'691'_2114 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsQuasiring_2260 ->
  Bool ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_distrib'691'_2114 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> T_IsQuasiring_2260
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
d_distrib'691'_2114 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> T_IsQuasiring_2260
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsQuasiring.distribˡ
d_distrib'737'_2116 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsQuasiring_2260 ->
  Bool ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_distrib'737'_2116 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> T_IsQuasiring_2260
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
d_distrib'737'_2116 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> T_IsQuasiring_2260
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsQuasiring.identityʳ
d_identity'691'_2118 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsQuasiring_2260 ->
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_identity'691'_2118 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> T_IsQuasiring_2260
-> Bool
-> T__'8801'__12
d_identity'691'_2118 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> T_IsQuasiring_2260
-> Bool
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsQuasiring.identityˡ
d_identity'737'_2120 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsQuasiring_2260 ->
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_identity'737'_2120 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> T_IsQuasiring_2260
-> Bool
-> T__'8801'__12
d_identity'737'_2120 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> T_IsQuasiring_2260
-> Bool
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsQuasiring.isEquivalence
d_isEquivalence_2122 ::
  MAlonzo.Code.Algebra.Structures.T_IsQuasiring_2260 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
d_isEquivalence_2122 :: T_IsQuasiring_2260 -> T_IsEquivalence_28
d_isEquivalence_2122 T_IsQuasiring_2260
v0
  = (T_IsMagma_178 -> T_IsEquivalence_28) -> Any -> T_IsEquivalence_28
forall a b. a -> b
coe
      T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186
      ((T_IsSemigroup_488 -> T_IsMagma_178) -> Any -> Any
forall a b. a -> b
coe
         T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496
         ((T_IsMonoid_712 -> T_IsSemigroup_488) -> Any -> Any
forall a b. a -> b
coe
            T_IsMonoid_712 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_722
            ((T_IsQuasiring_2260 -> T_IsMonoid_712) -> Any -> Any
forall a b. a -> b
coe
               T_IsQuasiring_2260 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_'43''45'isMonoid_2282 (T_IsQuasiring_2260 -> Any
forall a b. a -> b
coe T_IsQuasiring_2260
v0))))
-- Data.Bool.Properties._.IsQuasiring.isPartialEquivalence
d_isPartialEquivalence_2124 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsQuasiring_2260 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_2124 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> T_IsQuasiring_2260
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_2124 ~Bool -> Bool -> Bool
v0 ~Bool -> Bool -> Bool
v1 ~Bool
v2 ~Bool
v3 T_IsQuasiring_2260
v4
  = T_IsQuasiring_2260 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_2124 T_IsQuasiring_2260
v4
du_isPartialEquivalence_2124 ::
  MAlonzo.Code.Algebra.Structures.T_IsQuasiring_2260 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_2124 :: T_IsQuasiring_2260 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_2124 T_IsQuasiring_2260
v0
  = let v1 :: T_IsMonoid_712
v1
          = T_IsQuasiring_2260 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_'43''45'isMonoid_2282
              (T_IsQuasiring_2260 -> T_IsQuasiring_2260
forall a b. a -> b
coe T_IsQuasiring_2260
v0) in
    Any -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsSemigroup_488
v2
             = T_IsMonoid_712 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_722 (T_IsMonoid_712 -> T_IsMonoid_712
forall a b. a -> b
coe T_IsMonoid_712
v1) in
       Any -> Any
forall a b. a -> b
coe
         (let v3 :: T_IsMagma_178
v3 = T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496 (T_IsSemigroup_488 -> T_IsSemigroup_488
forall a b. a -> b
coe T_IsSemigroup_488
v2) in
          Any -> Any
forall a b. a -> b
coe
            ((T_IsEquivalence_28 -> T_IsPartialEquivalence_16) -> Any -> Any
forall a b. a -> b
coe
               T_IsEquivalence_28 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_44
               ((T_IsMagma_178 -> T_IsEquivalence_28) -> Any -> Any
forall a b. a -> b
coe
                  T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186 (T_IsMagma_178 -> Any
forall a b. a -> b
coe T_IsMagma_178
v3)))))
-- Data.Bool.Properties._.IsQuasiring.refl
d_refl_2126 ::
  MAlonzo.Code.Algebra.Structures.T_IsQuasiring_2260 ->
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_refl_2126 :: T_IsQuasiring_2260 -> Bool -> T__'8801'__12
d_refl_2126 = T_IsQuasiring_2260 -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsQuasiring.reflexive
d_reflexive_2128 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsQuasiring_2260 ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_reflexive_2128 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> T_IsQuasiring_2260
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_reflexive_2128 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> T_IsQuasiring_2260
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsQuasiring.setoid
d_setoid_2130 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsQuasiring_2260 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
d_setoid_2130 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> T_IsQuasiring_2260
-> T_Setoid_46
d_setoid_2130 ~Bool -> Bool -> Bool
v0 ~Bool -> Bool -> Bool
v1 ~Bool
v2 ~Bool
v3 T_IsQuasiring_2260
v4 = T_IsQuasiring_2260 -> T_Setoid_46
du_setoid_2130 T_IsQuasiring_2260
v4
du_setoid_2130 ::
  MAlonzo.Code.Algebra.Structures.T_IsQuasiring_2260 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
du_setoid_2130 :: T_IsQuasiring_2260 -> T_Setoid_46
du_setoid_2130 T_IsQuasiring_2260
v0
  = let v1 :: T_IsMonoid_712
v1
          = T_IsQuasiring_2260 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_'43''45'isMonoid_2282
              (T_IsQuasiring_2260 -> T_IsQuasiring_2260
forall a b. a -> b
coe T_IsQuasiring_2260
v0) in
    Any -> T_Setoid_46
forall a b. a -> b
coe
      (let v2 :: T_IsSemigroup_488
v2
             = T_IsMonoid_712 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_722 (T_IsMonoid_712 -> T_IsMonoid_712
forall a b. a -> b
coe T_IsMonoid_712
v1) in
       Any -> Any
forall a b. a -> b
coe
         ((T_IsMagma_178 -> T_Setoid_46) -> Any -> Any
forall a b. a -> b
coe
            T_IsMagma_178 -> T_Setoid_46
MAlonzo.Code.Algebra.Structures.du_setoid_202
            ((T_IsSemigroup_488 -> T_IsMagma_178) -> Any -> Any
forall a b. a -> b
coe T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496 (T_IsSemigroup_488 -> Any
forall a b. a -> b
coe T_IsSemigroup_488
v2))))
-- Data.Bool.Properties._.IsQuasiring.sym
d_sym_2132 ::
  MAlonzo.Code.Algebra.Structures.T_IsQuasiring_2260 ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_sym_2132 :: T_IsQuasiring_2260
-> Bool -> Bool -> T__'8801'__12 -> T__'8801'__12
d_sym_2132 = T_IsQuasiring_2260
-> Bool -> Bool -> T__'8801'__12 -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsQuasiring.trans
d_trans_2134 ::
  MAlonzo.Code.Algebra.Structures.T_IsQuasiring_2260 ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_trans_2134 :: T_IsQuasiring_2260
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
d_trans_2134 = T_IsQuasiring_2260
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsQuasiring.zero
d_zero_2136 ::
  MAlonzo.Code.Algebra.Structures.T_IsQuasiring_2260 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_zero_2136 :: T_IsQuasiring_2260 -> T_Σ_14
d_zero_2136 T_IsQuasiring_2260
v0
  = (T_IsQuasiring_2260 -> T_Σ_14) -> Any -> T_Σ_14
forall a b. a -> b
coe T_IsQuasiring_2260 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_zero_2292 (T_IsQuasiring_2260 -> Any
forall a b. a -> b
coe T_IsQuasiring_2260
v0)
-- Data.Bool.Properties._.IsQuasiring.zeroʳ
d_zero'691'_2138 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsQuasiring_2260 ->
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_zero'691'_2138 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> T_IsQuasiring_2260
-> Bool
-> T__'8801'__12
d_zero'691'_2138 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> T_IsQuasiring_2260
-> Bool
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsQuasiring.zeroˡ
d_zero'737'_2140 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsQuasiring_2260 ->
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_zero'737'_2140 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> T_IsQuasiring_2260
-> Bool
-> T__'8801'__12
d_zero'737'_2140 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> T_IsQuasiring_2260
-> Bool
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsRightBolLoop.//-cong
d_'47''47''45'cong_2144 ::
  MAlonzo.Code.Algebra.Structures.T_IsRightBolLoop_3286 ->
  Bool ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'47''47''45'cong_2144 :: T_IsRightBolLoop_3286
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
d_'47''47''45'cong_2144 = T_IsRightBolLoop_3286
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsRightBolLoop.//-congʳ
d_'47''47''45'cong'691'_2146 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsRightBolLoop_3286 ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'47''47''45'cong'691'_2146 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsRightBolLoop_3286
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_'47''47''45'cong'691'_2146 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsRightBolLoop_3286
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsRightBolLoop.//-congˡ
d_'47''47''45'cong'737'_2148 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsRightBolLoop_3286 ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'47''47''45'cong'737'_2148 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsRightBolLoop_3286
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_'47''47''45'cong'737'_2148 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsRightBolLoop_3286
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsRightBolLoop.\\-cong
d_'92''92''45'cong_2150 ::
  MAlonzo.Code.Algebra.Structures.T_IsRightBolLoop_3286 ->
  Bool ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'92''92''45'cong_2150 :: T_IsRightBolLoop_3286
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
d_'92''92''45'cong_2150 = T_IsRightBolLoop_3286
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsRightBolLoop.\\-congʳ
d_'92''92''45'cong'691'_2152 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsRightBolLoop_3286 ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'92''92''45'cong'691'_2152 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsRightBolLoop_3286
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_'92''92''45'cong'691'_2152 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsRightBolLoop_3286
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsRightBolLoop.\\-congˡ
d_'92''92''45'cong'737'_2154 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsRightBolLoop_3286 ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'92''92''45'cong'737'_2154 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsRightBolLoop_3286
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_'92''92''45'cong'737'_2154 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsRightBolLoop_3286
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsRightBolLoop.identity
d_identity_2156 ::
  MAlonzo.Code.Algebra.Structures.T_IsRightBolLoop_3286 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_identity_2156 :: T_IsRightBolLoop_3286 -> T_Σ_14
d_identity_2156 T_IsRightBolLoop_3286
v0
  = (T_IsLoop_3122 -> T_Σ_14) -> Any -> T_Σ_14
forall a b. a -> b
coe
      T_IsLoop_3122 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_identity_3138
      ((T_IsRightBolLoop_3286 -> T_IsLoop_3122) -> Any -> Any
forall a b. a -> b
coe T_IsRightBolLoop_3286 -> T_IsLoop_3122
MAlonzo.Code.Algebra.Structures.d_isLoop_3300 (T_IsRightBolLoop_3286 -> Any
forall a b. a -> b
coe T_IsRightBolLoop_3286
v0))
-- Data.Bool.Properties._.IsRightBolLoop.identityʳ
d_identity'691'_2158 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsRightBolLoop_3286 ->
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_identity'691'_2158 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsRightBolLoop_3286
-> Bool
-> T__'8801'__12
d_identity'691'_2158 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsRightBolLoop_3286
-> Bool
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsRightBolLoop.identityˡ
d_identity'737'_2160 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsRightBolLoop_3286 ->
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_identity'737'_2160 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsRightBolLoop_3286
-> Bool
-> T__'8801'__12
d_identity'737'_2160 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsRightBolLoop_3286
-> Bool
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsRightBolLoop.isEquivalence
d_isEquivalence_2162 ::
  MAlonzo.Code.Algebra.Structures.T_IsRightBolLoop_3286 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
d_isEquivalence_2162 :: T_IsRightBolLoop_3286 -> T_IsEquivalence_28
d_isEquivalence_2162 T_IsRightBolLoop_3286
v0
  = (T_IsMagma_178 -> T_IsEquivalence_28) -> Any -> T_IsEquivalence_28
forall a b. a -> b
coe
      T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186
      ((T_IsQuasigroup_3038 -> T_IsMagma_178) -> Any -> Any
forall a b. a -> b
coe
         T_IsQuasigroup_3038 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_3056
         ((T_IsLoop_3122 -> T_IsQuasigroup_3038) -> Any -> Any
forall a b. a -> b
coe
            T_IsLoop_3122 -> T_IsQuasigroup_3038
MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3136
            ((T_IsRightBolLoop_3286 -> T_IsLoop_3122) -> Any -> Any
forall a b. a -> b
coe T_IsRightBolLoop_3286 -> T_IsLoop_3122
MAlonzo.Code.Algebra.Structures.d_isLoop_3300 (T_IsRightBolLoop_3286 -> Any
forall a b. a -> b
coe T_IsRightBolLoop_3286
v0))))
-- Data.Bool.Properties._.IsRightBolLoop.isLoop
d_isLoop_2164 ::
  MAlonzo.Code.Algebra.Structures.T_IsRightBolLoop_3286 ->
  MAlonzo.Code.Algebra.Structures.T_IsLoop_3122
d_isLoop_2164 :: T_IsRightBolLoop_3286 -> T_IsLoop_3122
d_isLoop_2164 T_IsRightBolLoop_3286
v0
  = (T_IsRightBolLoop_3286 -> T_IsLoop_3122) -> Any -> T_IsLoop_3122
forall a b. a -> b
coe T_IsRightBolLoop_3286 -> T_IsLoop_3122
MAlonzo.Code.Algebra.Structures.d_isLoop_3300 (T_IsRightBolLoop_3286 -> Any
forall a b. a -> b
coe T_IsRightBolLoop_3286
v0)
-- Data.Bool.Properties._.IsRightBolLoop.isMagma
d_isMagma_2166 ::
  MAlonzo.Code.Algebra.Structures.T_IsRightBolLoop_3286 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_178
d_isMagma_2166 :: T_IsRightBolLoop_3286 -> T_IsMagma_178
d_isMagma_2166 T_IsRightBolLoop_3286
v0
  = (T_IsQuasigroup_3038 -> T_IsMagma_178) -> Any -> T_IsMagma_178
forall a b. a -> b
coe
      T_IsQuasigroup_3038 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_3056
      ((T_IsLoop_3122 -> T_IsQuasigroup_3038) -> Any -> Any
forall a b. a -> b
coe
         T_IsLoop_3122 -> T_IsQuasigroup_3038
MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3136
         ((T_IsRightBolLoop_3286 -> T_IsLoop_3122) -> Any -> Any
forall a b. a -> b
coe T_IsRightBolLoop_3286 -> T_IsLoop_3122
MAlonzo.Code.Algebra.Structures.d_isLoop_3300 (T_IsRightBolLoop_3286 -> Any
forall a b. a -> b
coe T_IsRightBolLoop_3286
v0)))
-- Data.Bool.Properties._.IsRightBolLoop.isPartialEquivalence
d_isPartialEquivalence_2168 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsRightBolLoop_3286 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_2168 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsRightBolLoop_3286
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_2168 ~Bool -> Bool -> Bool
v0 ~Bool -> Bool -> Bool
v1 ~Bool -> Bool -> Bool
v2 ~Bool
v3 T_IsRightBolLoop_3286
v4
  = T_IsRightBolLoop_3286 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_2168 T_IsRightBolLoop_3286
v4
du_isPartialEquivalence_2168 ::
  MAlonzo.Code.Algebra.Structures.T_IsRightBolLoop_3286 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_2168 :: T_IsRightBolLoop_3286 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_2168 T_IsRightBolLoop_3286
v0
  = let v1 :: T_IsLoop_3122
v1
          = T_IsRightBolLoop_3286 -> T_IsLoop_3122
MAlonzo.Code.Algebra.Structures.d_isLoop_3300 (T_IsRightBolLoop_3286 -> T_IsRightBolLoop_3286
forall a b. a -> b
coe T_IsRightBolLoop_3286
v0) in
    Any -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsQuasigroup_3038
v2
             = T_IsLoop_3122 -> T_IsQuasigroup_3038
MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3136 (T_IsLoop_3122 -> T_IsLoop_3122
forall a b. a -> b
coe T_IsLoop_3122
v1) in
       Any -> Any
forall a b. a -> b
coe
         (let v3 :: T_IsMagma_178
v3
                = T_IsQuasigroup_3038 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_3056 (T_IsQuasigroup_3038 -> T_IsQuasigroup_3038
forall a b. a -> b
coe T_IsQuasigroup_3038
v2) in
          Any -> Any
forall a b. a -> b
coe
            ((T_IsEquivalence_28 -> T_IsPartialEquivalence_16) -> Any -> Any
forall a b. a -> b
coe
               T_IsEquivalence_28 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_44
               ((T_IsMagma_178 -> T_IsEquivalence_28) -> Any -> Any
forall a b. a -> b
coe
                  T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186 (T_IsMagma_178 -> Any
forall a b. a -> b
coe T_IsMagma_178
v3)))))
-- Data.Bool.Properties._.IsRightBolLoop.isQuasigroup
d_isQuasigroup_2170 ::
  MAlonzo.Code.Algebra.Structures.T_IsRightBolLoop_3286 ->
  MAlonzo.Code.Algebra.Structures.T_IsQuasigroup_3038
d_isQuasigroup_2170 :: T_IsRightBolLoop_3286 -> T_IsQuasigroup_3038
d_isQuasigroup_2170 T_IsRightBolLoop_3286
v0
  = (T_IsLoop_3122 -> T_IsQuasigroup_3038)
-> Any -> T_IsQuasigroup_3038
forall a b. a -> b
coe
      T_IsLoop_3122 -> T_IsQuasigroup_3038
MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3136
      ((T_IsRightBolLoop_3286 -> T_IsLoop_3122) -> Any -> Any
forall a b. a -> b
coe T_IsRightBolLoop_3286 -> T_IsLoop_3122
MAlonzo.Code.Algebra.Structures.d_isLoop_3300 (T_IsRightBolLoop_3286 -> Any
forall a b. a -> b
coe T_IsRightBolLoop_3286
v0))
-- Data.Bool.Properties._.IsRightBolLoop.leftDivides
d_leftDivides_2172 ::
  MAlonzo.Code.Algebra.Structures.T_IsRightBolLoop_3286 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_leftDivides_2172 :: T_IsRightBolLoop_3286 -> T_Σ_14
d_leftDivides_2172 T_IsRightBolLoop_3286
v0
  = (T_IsQuasigroup_3038 -> T_Σ_14) -> Any -> T_Σ_14
forall a b. a -> b
coe
      T_IsQuasigroup_3038 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_leftDivides_3062
      ((T_IsLoop_3122 -> T_IsQuasigroup_3038) -> Any -> Any
forall a b. a -> b
coe
         T_IsLoop_3122 -> T_IsQuasigroup_3038
MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3136
         ((T_IsRightBolLoop_3286 -> T_IsLoop_3122) -> Any -> Any
forall a b. a -> b
coe T_IsRightBolLoop_3286 -> T_IsLoop_3122
MAlonzo.Code.Algebra.Structures.d_isLoop_3300 (T_IsRightBolLoop_3286 -> Any
forall a b. a -> b
coe T_IsRightBolLoop_3286
v0)))
-- Data.Bool.Properties._.IsRightBolLoop.leftDividesʳ
d_leftDivides'691'_2174 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsRightBolLoop_3286 ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_leftDivides'691'_2174 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsRightBolLoop_3286
-> Bool
-> Bool
-> T__'8801'__12
d_leftDivides'691'_2174 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsRightBolLoop_3286
-> Bool
-> Bool
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsRightBolLoop.leftDividesˡ
d_leftDivides'737'_2176 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsRightBolLoop_3286 ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_leftDivides'737'_2176 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsRightBolLoop_3286
-> Bool
-> Bool
-> T__'8801'__12
d_leftDivides'737'_2176 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsRightBolLoop_3286
-> Bool
-> Bool
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsRightBolLoop.refl
d_refl_2178 ::
  MAlonzo.Code.Algebra.Structures.T_IsRightBolLoop_3286 ->
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_refl_2178 :: T_IsRightBolLoop_3286 -> Bool -> T__'8801'__12
d_refl_2178 = T_IsRightBolLoop_3286 -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsRightBolLoop.reflexive
d_reflexive_2180 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsRightBolLoop_3286 ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_reflexive_2180 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsRightBolLoop_3286
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_reflexive_2180 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsRightBolLoop_3286
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsRightBolLoop.rightBol
d_rightBol_2182 ::
  MAlonzo.Code.Algebra.Structures.T_IsRightBolLoop_3286 ->
  Bool ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_rightBol_2182 :: T_IsRightBolLoop_3286 -> Bool -> Bool -> Bool -> T__'8801'__12
d_rightBol_2182 = T_IsRightBolLoop_3286 -> Bool -> Bool -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsRightBolLoop.rightDivides
d_rightDivides_2184 ::
  MAlonzo.Code.Algebra.Structures.T_IsRightBolLoop_3286 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_rightDivides_2184 :: T_IsRightBolLoop_3286 -> T_Σ_14
d_rightDivides_2184 T_IsRightBolLoop_3286
v0
  = (T_IsQuasigroup_3038 -> T_Σ_14) -> Any -> T_Σ_14
forall a b. a -> b
coe
      T_IsQuasigroup_3038 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_rightDivides_3064
      ((T_IsLoop_3122 -> T_IsQuasigroup_3038) -> Any -> Any
forall a b. a -> b
coe
         T_IsLoop_3122 -> T_IsQuasigroup_3038
MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3136
         ((T_IsRightBolLoop_3286 -> T_IsLoop_3122) -> Any -> Any
forall a b. a -> b
coe T_IsRightBolLoop_3286 -> T_IsLoop_3122
MAlonzo.Code.Algebra.Structures.d_isLoop_3300 (T_IsRightBolLoop_3286 -> Any
forall a b. a -> b
coe T_IsRightBolLoop_3286
v0)))
-- Data.Bool.Properties._.IsRightBolLoop.rightDividesʳ
d_rightDivides'691'_2186 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsRightBolLoop_3286 ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_rightDivides'691'_2186 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsRightBolLoop_3286
-> Bool
-> Bool
-> T__'8801'__12
d_rightDivides'691'_2186 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsRightBolLoop_3286
-> Bool
-> Bool
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsRightBolLoop.rightDividesˡ
d_rightDivides'737'_2188 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsRightBolLoop_3286 ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_rightDivides'737'_2188 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsRightBolLoop_3286
-> Bool
-> Bool
-> T__'8801'__12
d_rightDivides'737'_2188 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsRightBolLoop_3286
-> Bool
-> Bool
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsRightBolLoop.setoid
d_setoid_2190 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsRightBolLoop_3286 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
d_setoid_2190 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsRightBolLoop_3286
-> T_Setoid_46
d_setoid_2190 ~Bool -> Bool -> Bool
v0 ~Bool -> Bool -> Bool
v1 ~Bool -> Bool -> Bool
v2 ~Bool
v3 T_IsRightBolLoop_3286
v4 = T_IsRightBolLoop_3286 -> T_Setoid_46
du_setoid_2190 T_IsRightBolLoop_3286
v4
du_setoid_2190 ::
  MAlonzo.Code.Algebra.Structures.T_IsRightBolLoop_3286 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
du_setoid_2190 :: T_IsRightBolLoop_3286 -> T_Setoid_46
du_setoid_2190 T_IsRightBolLoop_3286
v0
  = let v1 :: T_IsLoop_3122
v1
          = T_IsRightBolLoop_3286 -> T_IsLoop_3122
MAlonzo.Code.Algebra.Structures.d_isLoop_3300 (T_IsRightBolLoop_3286 -> T_IsRightBolLoop_3286
forall a b. a -> b
coe T_IsRightBolLoop_3286
v0) in
    Any -> T_Setoid_46
forall a b. a -> b
coe
      (let v2 :: T_IsQuasigroup_3038
v2
             = T_IsLoop_3122 -> T_IsQuasigroup_3038
MAlonzo.Code.Algebra.Structures.d_isQuasigroup_3136 (T_IsLoop_3122 -> T_IsLoop_3122
forall a b. a -> b
coe T_IsLoop_3122
v1) in
       Any -> Any
forall a b. a -> b
coe
         ((T_IsMagma_178 -> T_Setoid_46) -> Any -> Any
forall a b. a -> b
coe
            T_IsMagma_178 -> T_Setoid_46
MAlonzo.Code.Algebra.Structures.du_setoid_202
            ((T_IsQuasigroup_3038 -> T_IsMagma_178) -> Any -> Any
forall a b. a -> b
coe T_IsQuasigroup_3038 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_3056 (T_IsQuasigroup_3038 -> Any
forall a b. a -> b
coe T_IsQuasigroup_3038
v2))))
-- Data.Bool.Properties._.IsRightBolLoop.sym
d_sym_2192 ::
  MAlonzo.Code.Algebra.Structures.T_IsRightBolLoop_3286 ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_sym_2192 :: T_IsRightBolLoop_3286
-> Bool -> Bool -> T__'8801'__12 -> T__'8801'__12
d_sym_2192 = T_IsRightBolLoop_3286
-> Bool -> Bool -> T__'8801'__12 -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsRightBolLoop.trans
d_trans_2194 ::
  MAlonzo.Code.Algebra.Structures.T_IsRightBolLoop_3286 ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_trans_2194 :: T_IsRightBolLoop_3286
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
d_trans_2194 = T_IsRightBolLoop_3286
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsRightBolLoop.∙-cong
d_'8729''45'cong_2196 ::
  MAlonzo.Code.Algebra.Structures.T_IsRightBolLoop_3286 ->
  Bool ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8729''45'cong_2196 :: T_IsRightBolLoop_3286
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong_2196 = T_IsRightBolLoop_3286
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsRightBolLoop.∙-congʳ
d_'8729''45'cong'691'_2198 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsRightBolLoop_3286 ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8729''45'cong'691'_2198 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsRightBolLoop_3286
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong'691'_2198 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsRightBolLoop_3286
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsRightBolLoop.∙-congˡ
d_'8729''45'cong'737'_2200 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsRightBolLoop_3286 ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8729''45'cong'737'_2200 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsRightBolLoop_3286
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong'737'_2200 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsRightBolLoop_3286
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsRing._//_
d__'47''47'__2204 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsRing_2740 ->
  Bool -> Bool -> Bool
d__'47''47'__2204 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsRing_2740
-> Bool
-> Bool
-> Bool
d__'47''47'__2204 Bool -> Bool -> Bool
v0 ~Bool -> Bool -> Bool
v1 Bool -> Bool
v2 ~Bool
v3 ~Bool
v4 ~T_IsRing_2740
v5 = (Bool -> Bool -> Bool) -> (Bool -> Bool) -> Bool -> Bool -> Bool
du__'47''47'__2204 Bool -> Bool -> Bool
v0 Bool -> Bool
v2
du__'47''47'__2204 ::
  (Bool -> Bool -> Bool) -> (Bool -> Bool) -> Bool -> Bool -> Bool
du__'47''47'__2204 :: (Bool -> Bool -> Bool) -> (Bool -> Bool) -> Bool -> Bool -> Bool
du__'47''47'__2204 Bool -> Bool -> Bool
v0 Bool -> Bool
v1
  = ((Any -> Any -> Any) -> (Any -> Any) -> Any -> Any -> Any)
-> Any -> Any -> Bool -> Bool -> Bool
forall a b. a -> b
coe
      (Any -> Any -> Any) -> (Any -> Any) -> Any -> Any -> Any
MAlonzo.Code.Algebra.Structures.du__'47''47'__1136 ((Bool -> Bool -> Bool) -> Any
forall a b. a -> b
coe Bool -> Bool -> Bool
v0)
      ((Bool -> Bool) -> Any
forall a b. a -> b
coe Bool -> Bool
v1)
-- Data.Bool.Properties._.IsRing.*-assoc
d_'42''45'assoc_2206 ::
  MAlonzo.Code.Algebra.Structures.T_IsRing_2740 ->
  Bool ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'42''45'assoc_2206 :: T_IsRing_2740 -> Bool -> Bool -> Bool -> T__'8801'__12
d_'42''45'assoc_2206 = T_IsRing_2740 -> Bool -> Bool -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsRing.*-cong
d_'42''45'cong_2208 ::
  MAlonzo.Code.Algebra.Structures.T_IsRing_2740 ->
  Bool ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'42''45'cong_2208 :: T_IsRing_2740
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
d_'42''45'cong_2208 = T_IsRing_2740
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsRing.∙-congʳ
d_'8729''45'cong'691'_2210 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsRing_2740 ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8729''45'cong'691'_2210 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsRing_2740
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong'691'_2210 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsRing_2740
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsRing.∙-congˡ
d_'8729''45'cong'737'_2212 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsRing_2740 ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8729''45'cong'737'_2212 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsRing_2740
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong'737'_2212 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsRing_2740
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsRing.*-identity
d_'42''45'identity_2214 ::
  MAlonzo.Code.Algebra.Structures.T_IsRing_2740 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'42''45'identity_2214 :: T_IsRing_2740 -> T_Σ_14
d_'42''45'identity_2214 T_IsRing_2740
v0
  = (T_IsRing_2740 -> T_Σ_14) -> Any -> T_Σ_14
forall a b. a -> b
coe
      T_IsRing_2740 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_'42''45'identity_2768 (T_IsRing_2740 -> Any
forall a b. a -> b
coe T_IsRing_2740
v0)
-- Data.Bool.Properties._.IsRing.identityʳ
d_identity'691'_2216 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsRing_2740 ->
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_identity'691'_2216 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsRing_2740
-> Bool
-> T__'8801'__12
d_identity'691'_2216 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsRing_2740
-> Bool
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsRing.identityˡ
d_identity'737'_2218 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsRing_2740 ->
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_identity'737'_2218 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsRing_2740
-> Bool
-> T__'8801'__12
d_identity'737'_2218 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsRing_2740
-> Bool
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsRing.*-isMagma
d_'42''45'isMagma_2220 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsRing_2740 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_178
d_'42''45'isMagma_2220 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsRing_2740
-> T_IsMagma_178
d_'42''45'isMagma_2220 Bool -> Bool -> Bool
v0 Bool -> Bool -> Bool
v1 Bool -> Bool
v2 Bool
v3 ~Bool
v4 T_IsRing_2740
v5
  = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> T_IsRing_2740
-> T_IsMagma_178
du_'42''45'isMagma_2220 Bool -> Bool -> Bool
v0 Bool -> Bool -> Bool
v1 Bool -> Bool
v2 Bool
v3 T_IsRing_2740
v5
du_'42''45'isMagma_2220 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsRing_2740 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_178
du_'42''45'isMagma_2220 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> T_IsRing_2740
-> T_IsMagma_178
du_'42''45'isMagma_2220 Bool -> Bool -> Bool
v0 Bool -> Bool -> Bool
v1 Bool -> Bool
v2 Bool
v3 T_IsRing_2740
v4
  = let v5 :: Any
v5
          = (T_IsRing_2740 -> T_IsRingWithoutOne_2368) -> Any -> Any
forall a b. a -> b
coe
              T_IsRing_2740 -> T_IsRingWithoutOne_2368
MAlonzo.Code.Algebra.Structures.du_isRingWithoutOne_2772
              (T_IsRing_2740 -> Any
forall a b. a -> b
coe T_IsRing_2740
v4) in
    Any -> T_IsMagma_178
forall a b. a -> b
coe
      ((T_IsNearSemiring_1260 -> T_IsMagma_178) -> Any -> Any
forall a b. a -> b
coe
         T_IsNearSemiring_1260 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.du_'42''45'isMagma_1324
         (((Any -> Any -> Any)
 -> (Any -> Any -> Any)
 -> (Any -> Any)
 -> Any
 -> T_IsRingWithoutOne_2368
 -> T_IsNearSemiring_1260)
-> Any -> Any -> Any -> Any -> Any -> Any
forall a b. a -> b
coe
            (Any -> Any -> Any)
-> (Any -> Any -> Any)
-> (Any -> Any)
-> Any
-> T_IsRingWithoutOne_2368
-> T_IsNearSemiring_1260
MAlonzo.Code.Algebra.Structures.du_isNearSemiring_2470 ((Bool -> Bool -> Bool) -> Any
forall a b. a -> b
coe Bool -> Bool -> Bool
v0)
            ((Bool -> Bool -> Bool) -> Any
forall a b. a -> b
coe Bool -> Bool -> Bool
v1) ((Bool -> Bool) -> Any
forall a b. a -> b
coe Bool -> Bool
v2) (Bool -> Any
forall a b. a -> b
coe Bool
v3) (Any -> Any
forall a b. a -> b
coe Any
v5)))
-- Data.Bool.Properties._.IsRing.*-isMonoid
d_'42''45'isMonoid_2222 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsRing_2740 ->
  MAlonzo.Code.Algebra.Structures.T_IsMonoid_712
d_'42''45'isMonoid_2222 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsRing_2740
-> T_IsMonoid_712
d_'42''45'isMonoid_2222 Bool -> Bool -> Bool
v0 Bool -> Bool -> Bool
v1 Bool -> Bool
v2 Bool
v3 Bool
v4 T_IsRing_2740
v5
  = ((Any -> Any -> Any)
 -> (Any -> Any -> Any)
 -> (Any -> Any)
 -> Any
 -> T_IsRing_2740
 -> T_IsMonoid_712)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> T_IsRing_2740
-> T_IsMonoid_712
forall a b. a -> b
coe
      (Any -> Any -> Any)
-> (Any -> Any -> Any)
-> (Any -> Any)
-> Any
-> T_IsRing_2740
-> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.du_'42''45'isMonoid_2860 Bool -> Bool -> Bool
v0 Bool -> Bool -> Bool
v1 Bool -> Bool
v2
      Bool
v3 T_IsRing_2740
v5
-- Data.Bool.Properties._.IsRing.*-isSemigroup
d_'42''45'isSemigroup_2224 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsRing_2740 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_488
d_'42''45'isSemigroup_2224 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsRing_2740
-> T_IsSemigroup_488
d_'42''45'isSemigroup_2224 Bool -> Bool -> Bool
v0 Bool -> Bool -> Bool
v1 Bool -> Bool
v2 Bool
v3 ~Bool
v4 T_IsRing_2740
v5
  = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> T_IsRing_2740
-> T_IsSemigroup_488
du_'42''45'isSemigroup_2224 Bool -> Bool -> Bool
v0 Bool -> Bool -> Bool
v1 Bool -> Bool
v2 Bool
v3 T_IsRing_2740
v5
du_'42''45'isSemigroup_2224 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsRing_2740 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_488
du_'42''45'isSemigroup_2224 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> T_IsRing_2740
-> T_IsSemigroup_488
du_'42''45'isSemigroup_2224 Bool -> Bool -> Bool
v0 Bool -> Bool -> Bool
v1 Bool -> Bool
v2 Bool
v3 T_IsRing_2740
v4
  = let v5 :: Any
v5
          = (T_IsRing_2740 -> T_IsRingWithoutOne_2368) -> Any -> Any
forall a b. a -> b
coe
              T_IsRing_2740 -> T_IsRingWithoutOne_2368
MAlonzo.Code.Algebra.Structures.du_isRingWithoutOne_2772
              (T_IsRing_2740 -> Any
forall a b. a -> b
coe T_IsRing_2740
v4) in
    Any -> T_IsSemigroup_488
forall a b. a -> b
coe
      ((T_IsNearSemiring_1260 -> T_IsSemigroup_488) -> Any -> Any
forall a b. a -> b
coe
         T_IsNearSemiring_1260 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.du_'42''45'isSemigroup_1326
         (((Any -> Any -> Any)
 -> (Any -> Any -> Any)
 -> (Any -> Any)
 -> Any
 -> T_IsRingWithoutOne_2368
 -> T_IsNearSemiring_1260)
-> Any -> Any -> Any -> Any -> Any -> Any
forall a b. a -> b
coe
            (Any -> Any -> Any)
-> (Any -> Any -> Any)
-> (Any -> Any)
-> Any
-> T_IsRingWithoutOne_2368
-> T_IsNearSemiring_1260
MAlonzo.Code.Algebra.Structures.du_isNearSemiring_2470 ((Bool -> Bool -> Bool) -> Any
forall a b. a -> b
coe Bool -> Bool -> Bool
v0)
            ((Bool -> Bool -> Bool) -> Any
forall a b. a -> b
coe Bool -> Bool -> Bool
v1) ((Bool -> Bool) -> Any
forall a b. a -> b
coe Bool -> Bool
v2) (Bool -> Any
forall a b. a -> b
coe Bool
v3) (Any -> Any
forall a b. a -> b
coe Any
v5)))
-- Data.Bool.Properties._.IsRing.assoc
d_assoc_2226 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsRing_2740 ->
  Bool ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_assoc_2226 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsRing_2740
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
d_assoc_2226 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsRing_2740
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsRing.comm
d_comm_2228 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsRing_2740 ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_comm_2228 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsRing_2740
-> Bool
-> Bool
-> T__'8801'__12
d_comm_2228 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsRing_2740
-> Bool
-> Bool
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsRing.∙-cong
d_'8729''45'cong_2230 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsRing_2740 ->
  Bool ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8729''45'cong_2230 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsRing_2740
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong_2230 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsRing_2740
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsRing.∙-congʳ
d_'8729''45'cong'691'_2232 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsRing_2740 ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8729''45'cong'691'_2232 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsRing_2740
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong'691'_2232 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsRing_2740
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsRing.∙-congˡ
d_'8729''45'cong'737'_2234 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsRing_2740 ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8729''45'cong'737'_2234 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsRing_2740
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong'737'_2234 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsRing_2740
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsRing.identity
d_identity_2236 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsRing_2740 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_identity_2236 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsRing_2740
-> T_Σ_14
d_identity_2236 ~Bool -> Bool -> Bool
v0 ~Bool -> Bool -> Bool
v1 ~Bool -> Bool
v2 ~Bool
v3 ~Bool
v4 T_IsRing_2740
v5 = T_IsRing_2740 -> T_Σ_14
du_identity_2236 T_IsRing_2740
v5
du_identity_2236 ::
  MAlonzo.Code.Algebra.Structures.T_IsRing_2740 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
du_identity_2236 :: T_IsRing_2740 -> T_Σ_14
du_identity_2236 T_IsRing_2740
v0
  = (T_IsMonoid_712 -> T_Σ_14) -> Any -> T_Σ_14
forall a b. a -> b
coe
      T_IsMonoid_712 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_identity_724
      ((T_IsGroup_1074 -> T_IsMonoid_712) -> Any -> Any
forall a b. a -> b
coe
         T_IsGroup_1074 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_1088
         ((T_IsAbelianGroup_1172 -> T_IsGroup_1074) -> Any -> Any
forall a b. a -> b
coe
            T_IsAbelianGroup_1172 -> T_IsGroup_1074
MAlonzo.Code.Algebra.Structures.d_isGroup_1184
            ((T_IsRing_2740 -> T_IsAbelianGroup_1172) -> Any -> Any
forall a b. a -> b
coe
               T_IsRing_2740 -> T_IsAbelianGroup_1172
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2762
               (T_IsRing_2740 -> Any
forall a b. a -> b
coe T_IsRing_2740
v0))))
-- Data.Bool.Properties._.IsRing.identityʳ
d_identity'691'_2238 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsRing_2740 ->
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_identity'691'_2238 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsRing_2740
-> Bool
-> T__'8801'__12
d_identity'691'_2238 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsRing_2740
-> Bool
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsRing.identityˡ
d_identity'737'_2240 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsRing_2740 ->
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_identity'737'_2240 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsRing_2740
-> Bool
-> T__'8801'__12
d_identity'737'_2240 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsRing_2740
-> Bool
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsRing.+-isAbelianGroup
d_'43''45'isAbelianGroup_2242 ::
  MAlonzo.Code.Algebra.Structures.T_IsRing_2740 ->
  MAlonzo.Code.Algebra.Structures.T_IsAbelianGroup_1172
d_'43''45'isAbelianGroup_2242 :: T_IsRing_2740 -> T_IsAbelianGroup_1172
d_'43''45'isAbelianGroup_2242 T_IsRing_2740
v0
  = (T_IsRing_2740 -> T_IsAbelianGroup_1172)
-> Any -> T_IsAbelianGroup_1172
forall a b. a -> b
coe
      T_IsRing_2740 -> T_IsAbelianGroup_1172
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2762
      (T_IsRing_2740 -> Any
forall a b. a -> b
coe T_IsRing_2740
v0)
-- Data.Bool.Properties._.IsRing.isCommutativeMagma
d_isCommutativeMagma_2244 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsRing_2740 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMagma_214
d_isCommutativeMagma_2244 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsRing_2740
-> T_IsCommutativeMagma_214
d_isCommutativeMagma_2244 ~Bool -> Bool -> Bool
v0 ~Bool -> Bool -> Bool
v1 ~Bool -> Bool
v2 ~Bool
v3 ~Bool
v4 T_IsRing_2740
v5
  = T_IsRing_2740 -> T_IsCommutativeMagma_214
du_isCommutativeMagma_2244 T_IsRing_2740
v5
du_isCommutativeMagma_2244 ::
  MAlonzo.Code.Algebra.Structures.T_IsRing_2740 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMagma_214
du_isCommutativeMagma_2244 :: T_IsRing_2740 -> T_IsCommutativeMagma_214
du_isCommutativeMagma_2244 T_IsRing_2740
v0
  = let v1 :: Any
v1
          = (T_IsRing_2740 -> T_IsRingWithoutOne_2368) -> Any -> Any
forall a b. a -> b
coe
              T_IsRing_2740 -> T_IsRingWithoutOne_2368
MAlonzo.Code.Algebra.Structures.du_isRingWithoutOne_2772
              (T_IsRing_2740 -> Any
forall a b. a -> b
coe T_IsRing_2740
v0) in
    Any -> T_IsCommutativeMagma_214
forall a b. a -> b
coe
      (let v2 :: T_IsAbelianGroup_1172
v2
             = T_IsRingWithoutOne_2368 -> T_IsAbelianGroup_1172
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2386
                 (Any -> T_IsRingWithoutOne_2368
forall a b. a -> b
coe Any
v1) in
       Any -> Any
forall a b. a -> b
coe
         (let v3 :: Any
v3
                = (T_IsAbelianGroup_1172 -> T_IsCommutativeMonoid_764) -> Any -> Any
forall a b. a -> b
coe
                    T_IsAbelianGroup_1172 -> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.du_isCommutativeMonoid_1244
                    (T_IsAbelianGroup_1172 -> Any
forall a b. a -> b
coe T_IsAbelianGroup_1172
v2) in
          Any -> Any
forall a b. a -> b
coe
            ((T_IsCommutativeSemigroup_568 -> T_IsCommutativeMagma_214)
-> Any -> Any
forall a b. a -> b
coe
               T_IsCommutativeSemigroup_568 -> T_IsCommutativeMagma_214
MAlonzo.Code.Algebra.Structures.du_isCommutativeMagma_606
               ((T_IsCommutativeMonoid_764 -> T_IsCommutativeSemigroup_568)
-> Any -> Any
forall a b. a -> b
coe
                  T_IsCommutativeMonoid_764 -> T_IsCommutativeSemigroup_568
MAlonzo.Code.Algebra.Structures.du_isCommutativeSemigroup_814
                  (Any -> Any
forall a b. a -> b
coe Any
v3)))))
-- Data.Bool.Properties._.IsRing.isCommutativeMonoid
d_isCommutativeMonoid_2246 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsRing_2740 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMonoid_764
d_isCommutativeMonoid_2246 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsRing_2740
-> T_IsCommutativeMonoid_764
d_isCommutativeMonoid_2246 ~Bool -> Bool -> Bool
v0 ~Bool -> Bool -> Bool
v1 ~Bool -> Bool
v2 ~Bool
v3 ~Bool
v4 T_IsRing_2740
v5
  = T_IsRing_2740 -> T_IsCommutativeMonoid_764
du_isCommutativeMonoid_2246 T_IsRing_2740
v5
du_isCommutativeMonoid_2246 ::
  MAlonzo.Code.Algebra.Structures.T_IsRing_2740 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMonoid_764
du_isCommutativeMonoid_2246 :: T_IsRing_2740 -> T_IsCommutativeMonoid_764
du_isCommutativeMonoid_2246 T_IsRing_2740
v0
  = let v1 :: Any
v1
          = (T_IsRing_2740 -> T_IsRingWithoutOne_2368) -> Any -> Any
forall a b. a -> b
coe
              T_IsRing_2740 -> T_IsRingWithoutOne_2368
MAlonzo.Code.Algebra.Structures.du_isRingWithoutOne_2772
              (T_IsRing_2740 -> Any
forall a b. a -> b
coe T_IsRing_2740
v0) in
    Any -> T_IsCommutativeMonoid_764
forall a b. a -> b
coe
      ((T_IsAbelianGroup_1172 -> T_IsCommutativeMonoid_764) -> Any -> Any
forall a b. a -> b
coe
         T_IsAbelianGroup_1172 -> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.du_isCommutativeMonoid_1244
         ((T_IsRingWithoutOne_2368 -> T_IsAbelianGroup_1172) -> Any -> Any
forall a b. a -> b
coe
            T_IsRingWithoutOne_2368 -> T_IsAbelianGroup_1172
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2386
            (Any -> Any
forall a b. a -> b
coe Any
v1)))
-- Data.Bool.Properties._.IsRing.isCommutativeSemigroup
d_isCommutativeSemigroup_2248 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsRing_2740 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_568
d_isCommutativeSemigroup_2248 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsRing_2740
-> T_IsCommutativeSemigroup_568
d_isCommutativeSemigroup_2248 ~Bool -> Bool -> Bool
v0 ~Bool -> Bool -> Bool
v1 ~Bool -> Bool
v2 ~Bool
v3 ~Bool
v4 T_IsRing_2740
v5
  = T_IsRing_2740 -> T_IsCommutativeSemigroup_568
du_isCommutativeSemigroup_2248 T_IsRing_2740
v5
du_isCommutativeSemigroup_2248 ::
  MAlonzo.Code.Algebra.Structures.T_IsRing_2740 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_568
du_isCommutativeSemigroup_2248 :: T_IsRing_2740 -> T_IsCommutativeSemigroup_568
du_isCommutativeSemigroup_2248 T_IsRing_2740
v0
  = let v1 :: Any
v1
          = (T_IsRing_2740 -> T_IsRingWithoutOne_2368) -> Any -> Any
forall a b. a -> b
coe
              T_IsRing_2740 -> T_IsRingWithoutOne_2368
MAlonzo.Code.Algebra.Structures.du_isRingWithoutOne_2772
              (T_IsRing_2740 -> Any
forall a b. a -> b
coe T_IsRing_2740
v0) in
    Any -> T_IsCommutativeSemigroup_568
forall a b. a -> b
coe
      (let v2 :: T_IsAbelianGroup_1172
v2
             = T_IsRingWithoutOne_2368 -> T_IsAbelianGroup_1172
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2386
                 (Any -> T_IsRingWithoutOne_2368
forall a b. a -> b
coe Any
v1) in
       Any -> Any
forall a b. a -> b
coe
         ((T_IsCommutativeMonoid_764 -> T_IsCommutativeSemigroup_568)
-> Any -> Any
forall a b. a -> b
coe
            T_IsCommutativeMonoid_764 -> T_IsCommutativeSemigroup_568
MAlonzo.Code.Algebra.Structures.du_isCommutativeSemigroup_814
            ((T_IsAbelianGroup_1172 -> T_IsCommutativeMonoid_764) -> Any -> Any
forall a b. a -> b
coe
               T_IsAbelianGroup_1172 -> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.du_isCommutativeMonoid_1244
               (T_IsAbelianGroup_1172 -> Any
forall a b. a -> b
coe T_IsAbelianGroup_1172
v2))))
-- Data.Bool.Properties._.IsRing.isGroup
d_isGroup_2250 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsRing_2740 ->
  MAlonzo.Code.Algebra.Structures.T_IsGroup_1074
d_isGroup_2250 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsRing_2740
-> T_IsGroup_1074
d_isGroup_2250 ~Bool -> Bool -> Bool
v0 ~Bool -> Bool -> Bool
v1 ~Bool -> Bool
v2 ~Bool
v3 ~Bool
v4 T_IsRing_2740
v5 = T_IsRing_2740 -> T_IsGroup_1074
du_isGroup_2250 T_IsRing_2740
v5
du_isGroup_2250 ::
  MAlonzo.Code.Algebra.Structures.T_IsRing_2740 ->
  MAlonzo.Code.Algebra.Structures.T_IsGroup_1074
du_isGroup_2250 :: T_IsRing_2740 -> T_IsGroup_1074
du_isGroup_2250 T_IsRing_2740
v0
  = (T_IsAbelianGroup_1172 -> T_IsGroup_1074) -> Any -> T_IsGroup_1074
forall a b. a -> b
coe
      T_IsAbelianGroup_1172 -> T_IsGroup_1074
MAlonzo.Code.Algebra.Structures.d_isGroup_1184
      ((T_IsRing_2740 -> T_IsAbelianGroup_1172) -> Any -> Any
forall a b. a -> b
coe
         T_IsRing_2740 -> T_IsAbelianGroup_1172
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2762
         (T_IsRing_2740 -> Any
forall a b. a -> b
coe T_IsRing_2740
v0))
-- Data.Bool.Properties._.IsRing.isInvertibleMagma
d_isInvertibleMagma_2252 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsRing_2740 ->
  MAlonzo.Code.Algebra.Structures.T_IsInvertibleMagma_958
d_isInvertibleMagma_2252 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsRing_2740
-> T_IsInvertibleMagma_958
d_isInvertibleMagma_2252 ~Bool -> Bool -> Bool
v0 ~Bool -> Bool -> Bool
v1 ~Bool -> Bool
v2 ~Bool
v3 ~Bool
v4 T_IsRing_2740
v5
  = T_IsRing_2740 -> T_IsInvertibleMagma_958
du_isInvertibleMagma_2252 T_IsRing_2740
v5
du_isInvertibleMagma_2252 ::
  MAlonzo.Code.Algebra.Structures.T_IsRing_2740 ->
  MAlonzo.Code.Algebra.Structures.T_IsInvertibleMagma_958
du_isInvertibleMagma_2252 :: T_IsRing_2740 -> T_IsInvertibleMagma_958
du_isInvertibleMagma_2252 T_IsRing_2740
v0
  = let v1 :: Any
v1
          = (T_IsRing_2740 -> T_IsRingWithoutOne_2368) -> Any -> Any
forall a b. a -> b
coe
              T_IsRing_2740 -> T_IsRingWithoutOne_2368
MAlonzo.Code.Algebra.Structures.du_isRingWithoutOne_2772
              (T_IsRing_2740 -> Any
forall a b. a -> b
coe T_IsRing_2740
v0) in
    Any -> T_IsInvertibleMagma_958
forall a b. a -> b
coe
      (let v2 :: T_IsAbelianGroup_1172
v2
             = T_IsRingWithoutOne_2368 -> T_IsAbelianGroup_1172
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2386
                 (Any -> T_IsRingWithoutOne_2368
forall a b. a -> b
coe Any
v1) in
       Any -> Any
forall a b. a -> b
coe
         ((T_IsGroup_1074 -> T_IsInvertibleMagma_958) -> Any -> Any
forall a b. a -> b
coe
            T_IsGroup_1074 -> T_IsInvertibleMagma_958
MAlonzo.Code.Algebra.Structures.du_isInvertibleMagma_1160
            ((T_IsAbelianGroup_1172 -> T_IsGroup_1074) -> Any -> Any
forall a b. a -> b
coe T_IsAbelianGroup_1172 -> T_IsGroup_1074
MAlonzo.Code.Algebra.Structures.d_isGroup_1184 (T_IsAbelianGroup_1172 -> Any
forall a b. a -> b
coe T_IsAbelianGroup_1172
v2))))
-- Data.Bool.Properties._.IsRing.isInvertibleUnitalMagma
d_isInvertibleUnitalMagma_2254 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsRing_2740 ->
  MAlonzo.Code.Algebra.Structures.T_IsInvertibleUnitalMagma_1012
d_isInvertibleUnitalMagma_2254 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsRing_2740
-> T_IsInvertibleUnitalMagma_1012
d_isInvertibleUnitalMagma_2254 ~Bool -> Bool -> Bool
v0 ~Bool -> Bool -> Bool
v1 ~Bool -> Bool
v2 ~Bool
v3 ~Bool
v4 T_IsRing_2740
v5
  = T_IsRing_2740 -> T_IsInvertibleUnitalMagma_1012
du_isInvertibleUnitalMagma_2254 T_IsRing_2740
v5
du_isInvertibleUnitalMagma_2254 ::
  MAlonzo.Code.Algebra.Structures.T_IsRing_2740 ->
  MAlonzo.Code.Algebra.Structures.T_IsInvertibleUnitalMagma_1012
du_isInvertibleUnitalMagma_2254 :: T_IsRing_2740 -> T_IsInvertibleUnitalMagma_1012
du_isInvertibleUnitalMagma_2254 T_IsRing_2740
v0
  = let v1 :: Any
v1
          = (T_IsRing_2740 -> T_IsRingWithoutOne_2368) -> Any -> Any
forall a b. a -> b
coe
              T_IsRing_2740 -> T_IsRingWithoutOne_2368
MAlonzo.Code.Algebra.Structures.du_isRingWithoutOne_2772
              (T_IsRing_2740 -> Any
forall a b. a -> b
coe T_IsRing_2740
v0) in
    Any -> T_IsInvertibleUnitalMagma_1012
forall a b. a -> b
coe
      (let v2 :: T_IsAbelianGroup_1172
v2
             = T_IsRingWithoutOne_2368 -> T_IsAbelianGroup_1172
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2386
                 (Any -> T_IsRingWithoutOne_2368
forall a b. a -> b
coe Any
v1) in
       Any -> Any
forall a b. a -> b
coe
         ((T_IsGroup_1074 -> T_IsInvertibleUnitalMagma_1012) -> Any -> Any
forall a b. a -> b
coe
            T_IsGroup_1074 -> T_IsInvertibleUnitalMagma_1012
MAlonzo.Code.Algebra.Structures.du_isInvertibleUnitalMagma_1162
            ((T_IsAbelianGroup_1172 -> T_IsGroup_1074) -> Any -> Any
forall a b. a -> b
coe T_IsAbelianGroup_1172 -> T_IsGroup_1074
MAlonzo.Code.Algebra.Structures.d_isGroup_1184 (T_IsAbelianGroup_1172 -> Any
forall a b. a -> b
coe T_IsAbelianGroup_1172
v2))))
-- Data.Bool.Properties._.IsRing.isMagma
d_isMagma_2256 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsRing_2740 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_178
d_isMagma_2256 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsRing_2740
-> T_IsMagma_178
d_isMagma_2256 ~Bool -> Bool -> Bool
v0 ~Bool -> Bool -> Bool
v1 ~Bool -> Bool
v2 ~Bool
v3 ~Bool
v4 T_IsRing_2740
v5 = T_IsRing_2740 -> T_IsMagma_178
du_isMagma_2256 T_IsRing_2740
v5
du_isMagma_2256 ::
  MAlonzo.Code.Algebra.Structures.T_IsRing_2740 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_178
du_isMagma_2256 :: T_IsRing_2740 -> T_IsMagma_178
du_isMagma_2256 T_IsRing_2740
v0
  = (T_IsSemigroup_488 -> T_IsMagma_178) -> Any -> T_IsMagma_178
forall a b. a -> b
coe
      T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496
      ((T_IsMonoid_712 -> T_IsSemigroup_488) -> Any -> Any
forall a b. a -> b
coe
         T_IsMonoid_712 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_722
         ((T_IsGroup_1074 -> T_IsMonoid_712) -> Any -> Any
forall a b. a -> b
coe
            T_IsGroup_1074 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_1088
            ((T_IsAbelianGroup_1172 -> T_IsGroup_1074) -> Any -> Any
forall a b. a -> b
coe
               T_IsAbelianGroup_1172 -> T_IsGroup_1074
MAlonzo.Code.Algebra.Structures.d_isGroup_1184
               ((T_IsRing_2740 -> T_IsAbelianGroup_1172) -> Any -> Any
forall a b. a -> b
coe
                  T_IsRing_2740 -> T_IsAbelianGroup_1172
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2762
                  (T_IsRing_2740 -> Any
forall a b. a -> b
coe T_IsRing_2740
v0)))))
-- Data.Bool.Properties._.IsRing.isMonoid
d_isMonoid_2258 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsRing_2740 ->
  MAlonzo.Code.Algebra.Structures.T_IsMonoid_712
d_isMonoid_2258 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsRing_2740
-> T_IsMonoid_712
d_isMonoid_2258 ~Bool -> Bool -> Bool
v0 ~Bool -> Bool -> Bool
v1 ~Bool -> Bool
v2 ~Bool
v3 ~Bool
v4 T_IsRing_2740
v5 = T_IsRing_2740 -> T_IsMonoid_712
du_isMonoid_2258 T_IsRing_2740
v5
du_isMonoid_2258 ::
  MAlonzo.Code.Algebra.Structures.T_IsRing_2740 ->
  MAlonzo.Code.Algebra.Structures.T_IsMonoid_712
du_isMonoid_2258 :: T_IsRing_2740 -> T_IsMonoid_712
du_isMonoid_2258 T_IsRing_2740
v0
  = (T_IsGroup_1074 -> T_IsMonoid_712) -> Any -> T_IsMonoid_712
forall a b. a -> b
coe
      T_IsGroup_1074 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_1088
      ((T_IsAbelianGroup_1172 -> T_IsGroup_1074) -> Any -> Any
forall a b. a -> b
coe
         T_IsAbelianGroup_1172 -> T_IsGroup_1074
MAlonzo.Code.Algebra.Structures.d_isGroup_1184
         ((T_IsRing_2740 -> T_IsAbelianGroup_1172) -> Any -> Any
forall a b. a -> b
coe
            T_IsRing_2740 -> T_IsAbelianGroup_1172
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2762
            (T_IsRing_2740 -> Any
forall a b. a -> b
coe T_IsRing_2740
v0)))
-- Data.Bool.Properties._.IsRing.isSemigroup
d_isSemigroup_2260 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsRing_2740 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_488
d_isSemigroup_2260 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsRing_2740
-> T_IsSemigroup_488
d_isSemigroup_2260 ~Bool -> Bool -> Bool
v0 ~Bool -> Bool -> Bool
v1 ~Bool -> Bool
v2 ~Bool
v3 ~Bool
v4 T_IsRing_2740
v5 = T_IsRing_2740 -> T_IsSemigroup_488
du_isSemigroup_2260 T_IsRing_2740
v5
du_isSemigroup_2260 ::
  MAlonzo.Code.Algebra.Structures.T_IsRing_2740 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_488
du_isSemigroup_2260 :: T_IsRing_2740 -> T_IsSemigroup_488
du_isSemigroup_2260 T_IsRing_2740
v0
  = (T_IsMonoid_712 -> T_IsSemigroup_488) -> Any -> T_IsSemigroup_488
forall a b. a -> b
coe
      T_IsMonoid_712 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_722
      ((T_IsGroup_1074 -> T_IsMonoid_712) -> Any -> Any
forall a b. a -> b
coe
         T_IsGroup_1074 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_1088
         ((T_IsAbelianGroup_1172 -> T_IsGroup_1074) -> Any -> Any
forall a b. a -> b
coe
            T_IsAbelianGroup_1172 -> T_IsGroup_1074
MAlonzo.Code.Algebra.Structures.d_isGroup_1184
            ((T_IsRing_2740 -> T_IsAbelianGroup_1172) -> Any -> Any
forall a b. a -> b
coe
               T_IsRing_2740 -> T_IsAbelianGroup_1172
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2762
               (T_IsRing_2740 -> Any
forall a b. a -> b
coe T_IsRing_2740
v0))))
-- Data.Bool.Properties._.IsRing.isUnitalMagma
d_isUnitalMagma_2262 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsRing_2740 ->
  MAlonzo.Code.Algebra.Structures.T_IsUnitalMagma_666
d_isUnitalMagma_2262 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsRing_2740
-> T_IsUnitalMagma_666
d_isUnitalMagma_2262 ~Bool -> Bool -> Bool
v0 ~Bool -> Bool -> Bool
v1 ~Bool -> Bool
v2 ~Bool
v3 ~Bool
v4 T_IsRing_2740
v5
  = T_IsRing_2740 -> T_IsUnitalMagma_666
du_isUnitalMagma_2262 T_IsRing_2740
v5
du_isUnitalMagma_2262 ::
  MAlonzo.Code.Algebra.Structures.T_IsRing_2740 ->
  MAlonzo.Code.Algebra.Structures.T_IsUnitalMagma_666
du_isUnitalMagma_2262 :: T_IsRing_2740 -> T_IsUnitalMagma_666
du_isUnitalMagma_2262 T_IsRing_2740
v0
  = let v1 :: Any
v1
          = (T_IsRing_2740 -> T_IsRingWithoutOne_2368) -> Any -> Any
forall a b. a -> b
coe
              T_IsRing_2740 -> T_IsRingWithoutOne_2368
MAlonzo.Code.Algebra.Structures.du_isRingWithoutOne_2772
              (T_IsRing_2740 -> Any
forall a b. a -> b
coe T_IsRing_2740
v0) in
    Any -> T_IsUnitalMagma_666
forall a b. a -> b
coe
      (let v2 :: T_IsAbelianGroup_1172
v2
             = T_IsRingWithoutOne_2368 -> T_IsAbelianGroup_1172
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2386
                 (Any -> T_IsRingWithoutOne_2368
forall a b. a -> b
coe Any
v1) in
       Any -> Any
forall a b. a -> b
coe
         (let v3 :: T_IsGroup_1074
v3
                = T_IsAbelianGroup_1172 -> T_IsGroup_1074
MAlonzo.Code.Algebra.Structures.d_isGroup_1184 (T_IsAbelianGroup_1172 -> T_IsAbelianGroup_1172
forall a b. a -> b
coe T_IsAbelianGroup_1172
v2) in
          Any -> Any
forall a b. a -> b
coe
            ((T_IsMonoid_712 -> T_IsUnitalMagma_666) -> Any -> Any
forall a b. a -> b
coe
               T_IsMonoid_712 -> T_IsUnitalMagma_666
MAlonzo.Code.Algebra.Structures.du_isUnitalMagma_756
               ((T_IsGroup_1074 -> T_IsMonoid_712) -> Any -> Any
forall a b. a -> b
coe T_IsGroup_1074 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_1088 (T_IsGroup_1074 -> Any
forall a b. a -> b
coe T_IsGroup_1074
v3)))))
-- Data.Bool.Properties._.IsRing.⁻¹-cong
d_'8315''185''45'cong_2264 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsRing_2740 ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8315''185''45'cong_2264 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsRing_2740
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_'8315''185''45'cong_2264 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsRing_2740
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsRing.inverse
d_inverse_2266 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsRing_2740 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_inverse_2266 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsRing_2740
-> T_Σ_14
d_inverse_2266 ~Bool -> Bool -> Bool
v0 ~Bool -> Bool -> Bool
v1 ~Bool -> Bool
v2 ~Bool
v3 ~Bool
v4 T_IsRing_2740
v5 = T_IsRing_2740 -> T_Σ_14
du_inverse_2266 T_IsRing_2740
v5
du_inverse_2266 ::
  MAlonzo.Code.Algebra.Structures.T_IsRing_2740 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
du_inverse_2266 :: T_IsRing_2740 -> T_Σ_14
du_inverse_2266 T_IsRing_2740
v0
  = (T_IsGroup_1074 -> T_Σ_14) -> Any -> T_Σ_14
forall a b. a -> b
coe
      T_IsGroup_1074 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_inverse_1090
      ((T_IsAbelianGroup_1172 -> T_IsGroup_1074) -> Any -> Any
forall a b. a -> b
coe
         T_IsAbelianGroup_1172 -> T_IsGroup_1074
MAlonzo.Code.Algebra.Structures.d_isGroup_1184
         ((T_IsRing_2740 -> T_IsAbelianGroup_1172) -> Any -> Any
forall a b. a -> b
coe
            T_IsRing_2740 -> T_IsAbelianGroup_1172
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2762
            (T_IsRing_2740 -> Any
forall a b. a -> b
coe T_IsRing_2740
v0)))
-- Data.Bool.Properties._.IsRing.inverseʳ
d_inverse'691'_2268 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsRing_2740 ->
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_inverse'691'_2268 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsRing_2740
-> Bool
-> T__'8801'__12
d_inverse'691'_2268 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsRing_2740
-> Bool
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsRing.inverseˡ
d_inverse'737'_2270 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsRing_2740 ->
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_inverse'737'_2270 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsRing_2740
-> Bool
-> T__'8801'__12
d_inverse'737'_2270 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsRing_2740
-> Bool
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsRing.distrib
d_distrib_2272 ::
  MAlonzo.Code.Algebra.Structures.T_IsRing_2740 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_distrib_2272 :: T_IsRing_2740 -> T_Σ_14
d_distrib_2272 T_IsRing_2740
v0
  = (T_IsRing_2740 -> T_Σ_14) -> Any -> T_Σ_14
forall a b. a -> b
coe T_IsRing_2740 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_distrib_2770 (T_IsRing_2740 -> Any
forall a b. a -> b
coe T_IsRing_2740
v0)
-- Data.Bool.Properties._.IsRing.distribʳ
d_distrib'691'_2274 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsRing_2740 ->
  Bool ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_distrib'691'_2274 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsRing_2740
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
d_distrib'691'_2274 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsRing_2740
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsRing.distribˡ
d_distrib'737'_2276 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsRing_2740 ->
  Bool ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_distrib'737'_2276 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsRing_2740
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
d_distrib'737'_2276 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsRing_2740
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsRing.isEquivalence
d_isEquivalence_2278 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsRing_2740 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
d_isEquivalence_2278 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsRing_2740
-> T_IsEquivalence_28
d_isEquivalence_2278 ~Bool -> Bool -> Bool
v0 ~Bool -> Bool -> Bool
v1 ~Bool -> Bool
v2 ~Bool
v3 ~Bool
v4 T_IsRing_2740
v5
  = T_IsRing_2740 -> T_IsEquivalence_28
du_isEquivalence_2278 T_IsRing_2740
v5
du_isEquivalence_2278 ::
  MAlonzo.Code.Algebra.Structures.T_IsRing_2740 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
du_isEquivalence_2278 :: T_IsRing_2740 -> T_IsEquivalence_28
du_isEquivalence_2278 T_IsRing_2740
v0
  = (T_IsMagma_178 -> T_IsEquivalence_28) -> Any -> T_IsEquivalence_28
forall a b. a -> b
coe
      T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186
      ((T_IsSemigroup_488 -> T_IsMagma_178) -> Any -> Any
forall a b. a -> b
coe
         T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496
         ((T_IsMonoid_712 -> T_IsSemigroup_488) -> Any -> Any
forall a b. a -> b
coe
            T_IsMonoid_712 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_722
            ((T_IsGroup_1074 -> T_IsMonoid_712) -> Any -> Any
forall a b. a -> b
coe
               T_IsGroup_1074 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_1088
               ((T_IsAbelianGroup_1172 -> T_IsGroup_1074) -> Any -> Any
forall a b. a -> b
coe
                  T_IsAbelianGroup_1172 -> T_IsGroup_1074
MAlonzo.Code.Algebra.Structures.d_isGroup_1184
                  ((T_IsRing_2740 -> T_IsAbelianGroup_1172) -> Any -> Any
forall a b. a -> b
coe
                     T_IsRing_2740 -> T_IsAbelianGroup_1172
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2762
                     (T_IsRing_2740 -> Any
forall a b. a -> b
coe T_IsRing_2740
v0))))))
-- Data.Bool.Properties._.IsRing.isNearSemiring
d_isNearSemiring_2280 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsRing_2740 ->
  MAlonzo.Code.Algebra.Structures.T_IsNearSemiring_1260
d_isNearSemiring_2280 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsRing_2740
-> T_IsNearSemiring_1260
d_isNearSemiring_2280 Bool -> Bool -> Bool
v0 Bool -> Bool -> Bool
v1 Bool -> Bool
v2 Bool
v3 ~Bool
v4 T_IsRing_2740
v5
  = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> T_IsRing_2740
-> T_IsNearSemiring_1260
du_isNearSemiring_2280 Bool -> Bool -> Bool
v0 Bool -> Bool -> Bool
v1 Bool -> Bool
v2 Bool
v3 T_IsRing_2740
v5
du_isNearSemiring_2280 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsRing_2740 ->
  MAlonzo.Code.Algebra.Structures.T_IsNearSemiring_1260
du_isNearSemiring_2280 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> T_IsRing_2740
-> T_IsNearSemiring_1260
du_isNearSemiring_2280 Bool -> Bool -> Bool
v0 Bool -> Bool -> Bool
v1 Bool -> Bool
v2 Bool
v3 T_IsRing_2740
v4
  = ((Any -> Any -> Any)
 -> (Any -> Any -> Any)
 -> (Any -> Any)
 -> Any
 -> T_IsRingWithoutOne_2368
 -> T_IsNearSemiring_1260)
-> Any -> Any -> Any -> Any -> Any -> T_IsNearSemiring_1260
forall a b. a -> b
coe
      (Any -> Any -> Any)
-> (Any -> Any -> Any)
-> (Any -> Any)
-> Any
-> T_IsRingWithoutOne_2368
-> T_IsNearSemiring_1260
MAlonzo.Code.Algebra.Structures.du_isNearSemiring_2470 ((Bool -> Bool -> Bool) -> Any
forall a b. a -> b
coe Bool -> Bool -> Bool
v0)
      ((Bool -> Bool -> Bool) -> Any
forall a b. a -> b
coe Bool -> Bool -> Bool
v1) ((Bool -> Bool) -> Any
forall a b. a -> b
coe Bool -> Bool
v2) (Bool -> Any
forall a b. a -> b
coe Bool
v3)
      ((T_IsRing_2740 -> T_IsRingWithoutOne_2368) -> Any -> Any
forall a b. a -> b
coe
         T_IsRing_2740 -> T_IsRingWithoutOne_2368
MAlonzo.Code.Algebra.Structures.du_isRingWithoutOne_2772 (T_IsRing_2740 -> Any
forall a b. a -> b
coe T_IsRing_2740
v4))
-- Data.Bool.Properties._.IsRing.isPartialEquivalence
d_isPartialEquivalence_2282 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsRing_2740 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_2282 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsRing_2740
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_2282 ~Bool -> Bool -> Bool
v0 ~Bool -> Bool -> Bool
v1 ~Bool -> Bool
v2 ~Bool
v3 ~Bool
v4 T_IsRing_2740
v5
  = T_IsRing_2740 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_2282 T_IsRing_2740
v5
du_isPartialEquivalence_2282 ::
  MAlonzo.Code.Algebra.Structures.T_IsRing_2740 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_2282 :: T_IsRing_2740 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_2282 T_IsRing_2740
v0
  = let v1 :: Any
v1
          = (T_IsRing_2740 -> T_IsRingWithoutOne_2368) -> Any -> Any
forall a b. a -> b
coe
              T_IsRing_2740 -> T_IsRingWithoutOne_2368
MAlonzo.Code.Algebra.Structures.du_isRingWithoutOne_2772
              (T_IsRing_2740 -> Any
forall a b. a -> b
coe T_IsRing_2740
v0) in
    Any -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsAbelianGroup_1172
v2
             = T_IsRingWithoutOne_2368 -> T_IsAbelianGroup_1172
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2386
                 (Any -> T_IsRingWithoutOne_2368
forall a b. a -> b
coe Any
v1) in
       Any -> Any
forall a b. a -> b
coe
         (let v3 :: T_IsGroup_1074
v3
                = T_IsAbelianGroup_1172 -> T_IsGroup_1074
MAlonzo.Code.Algebra.Structures.d_isGroup_1184 (T_IsAbelianGroup_1172 -> T_IsAbelianGroup_1172
forall a b. a -> b
coe T_IsAbelianGroup_1172
v2) in
          Any -> Any
forall a b. a -> b
coe
            (let v4 :: T_IsMonoid_712
v4
                   = T_IsGroup_1074 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_1088 (T_IsGroup_1074 -> T_IsGroup_1074
forall a b. a -> b
coe T_IsGroup_1074
v3) in
             Any -> Any
forall a b. a -> b
coe
               (let v5 :: T_IsSemigroup_488
v5
                      = T_IsMonoid_712 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_722 (T_IsMonoid_712 -> T_IsMonoid_712
forall a b. a -> b
coe T_IsMonoid_712
v4) in
                Any -> Any
forall a b. a -> b
coe
                  (let v6 :: T_IsMagma_178
v6 = T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496 (T_IsSemigroup_488 -> T_IsSemigroup_488
forall a b. a -> b
coe T_IsSemigroup_488
v5) in
                   Any -> Any
forall a b. a -> b
coe
                     ((T_IsEquivalence_28 -> T_IsPartialEquivalence_16) -> Any -> Any
forall a b. a -> b
coe
                        T_IsEquivalence_28 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_44
                        ((T_IsMagma_178 -> T_IsEquivalence_28) -> Any -> Any
forall a b. a -> b
coe
                           T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186 (T_IsMagma_178 -> Any
forall a b. a -> b
coe T_IsMagma_178
v6))))))))
-- Data.Bool.Properties._.IsRing.isRingWithoutOne
d_isRingWithoutOne_2284 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsRing_2740 ->
  MAlonzo.Code.Algebra.Structures.T_IsRingWithoutOne_2368
d_isRingWithoutOne_2284 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsRing_2740
-> T_IsRingWithoutOne_2368
d_isRingWithoutOne_2284 Bool -> Bool -> Bool
v0 Bool -> Bool -> Bool
v1 Bool -> Bool
v2 Bool
v3 Bool
v4 T_IsRing_2740
v5
  = (T_IsRing_2740 -> T_IsRingWithoutOne_2368)
-> T_IsRing_2740 -> T_IsRingWithoutOne_2368
forall a b. a -> b
coe T_IsRing_2740 -> T_IsRingWithoutOne_2368
MAlonzo.Code.Algebra.Structures.du_isRingWithoutOne_2772 T_IsRing_2740
v5
-- Data.Bool.Properties._.IsRing.isSemiring
d_isSemiring_2286 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsRing_2740 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemiring_1640
d_isSemiring_2286 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsRing_2740
-> T_IsSemiring_1640
d_isSemiring_2286 Bool -> Bool -> Bool
v0 Bool -> Bool -> Bool
v1 Bool -> Bool
v2 Bool
v3 Bool
v4 T_IsRing_2740
v5
  = ((Any -> Any -> Any)
 -> (Any -> Any -> Any)
 -> (Any -> Any)
 -> Any
 -> T_IsRing_2740
 -> T_IsSemiring_1640)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> T_IsRing_2740
-> T_IsSemiring_1640
forall a b. a -> b
coe
      (Any -> Any -> Any)
-> (Any -> Any -> Any)
-> (Any -> Any)
-> Any
-> T_IsRing_2740
-> T_IsSemiring_1640
MAlonzo.Code.Algebra.Structures.du_isSemiring_2870 Bool -> Bool -> Bool
v0 Bool -> Bool -> Bool
v1 Bool -> Bool
v2 Bool
v3 T_IsRing_2740
v5
-- Data.Bool.Properties._.IsRing.isSemiringWithoutAnnihilatingZero
d_isSemiringWithoutAnnihilatingZero_2288 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsRing_2740 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutAnnihilatingZero_1536
d_isSemiringWithoutAnnihilatingZero_2288 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsRing_2740
-> T_IsSemiringWithoutAnnihilatingZero_1536
d_isSemiringWithoutAnnihilatingZero_2288 Bool -> Bool -> Bool
v0 Bool -> Bool -> Bool
v1 Bool -> Bool
v2 Bool
v3 Bool
v4 T_IsRing_2740
v5
  = (T_IsRing_2740 -> T_IsSemiringWithoutAnnihilatingZero_1536)
-> T_IsRing_2740 -> T_IsSemiringWithoutAnnihilatingZero_1536
forall a b. a -> b
coe
      T_IsRing_2740 -> T_IsSemiringWithoutAnnihilatingZero_1536
MAlonzo.Code.Algebra.Structures.du_isSemiringWithoutAnnihilatingZero_2868
      T_IsRing_2740
v5
-- Data.Bool.Properties._.IsRing.isSemiringWithoutOne
d_isSemiringWithoutOne_2290 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsRing_2740 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutOne_1342
d_isSemiringWithoutOne_2290 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsRing_2740
-> T_IsSemiringWithoutOne_1342
d_isSemiringWithoutOne_2290 Bool -> Bool -> Bool
v0 Bool -> Bool -> Bool
v1 Bool -> Bool
v2 Bool
v3 ~Bool
v4 T_IsRing_2740
v5
  = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> T_IsRing_2740
-> T_IsSemiringWithoutOne_1342
du_isSemiringWithoutOne_2290 Bool -> Bool -> Bool
v0 Bool -> Bool -> Bool
v1 Bool -> Bool
v2 Bool
v3 T_IsRing_2740
v5
du_isSemiringWithoutOne_2290 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsRing_2740 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutOne_1342
du_isSemiringWithoutOne_2290 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> T_IsRing_2740
-> T_IsSemiringWithoutOne_1342
du_isSemiringWithoutOne_2290 Bool -> Bool -> Bool
v0 Bool -> Bool -> Bool
v1 Bool -> Bool
v2 Bool
v3 T_IsRing_2740
v4
  = (T_IsSemiring_1640 -> T_IsSemiringWithoutOne_1342)
-> Any -> T_IsSemiringWithoutOne_1342
forall a b. a -> b
coe
      T_IsSemiring_1640 -> T_IsSemiringWithoutOne_1342
MAlonzo.Code.Algebra.Structures.du_isSemiringWithoutOne_1730
      (((Any -> Any -> Any)
 -> (Any -> Any -> Any)
 -> (Any -> Any)
 -> Any
 -> T_IsRing_2740
 -> T_IsSemiring_1640)
-> Any -> Any -> Any -> Any -> Any -> Any
forall a b. a -> b
coe
         (Any -> Any -> Any)
-> (Any -> Any -> Any)
-> (Any -> Any)
-> Any
-> T_IsRing_2740
-> T_IsSemiring_1640
MAlonzo.Code.Algebra.Structures.du_isSemiring_2870 ((Bool -> Bool -> Bool) -> Any
forall a b. a -> b
coe Bool -> Bool -> Bool
v0)
         ((Bool -> Bool -> Bool) -> Any
forall a b. a -> b
coe Bool -> Bool -> Bool
v1) ((Bool -> Bool) -> Any
forall a b. a -> b
coe Bool -> Bool
v2) (Bool -> Any
forall a b. a -> b
coe Bool
v3) (T_IsRing_2740 -> Any
forall a b. a -> b
coe T_IsRing_2740
v4))
-- Data.Bool.Properties._.IsRing.refl
d_refl_2292 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsRing_2740 ->
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_refl_2292 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsRing_2740
-> Bool
-> T__'8801'__12
d_refl_2292 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsRing_2740
-> Bool
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsRing.reflexive
d_reflexive_2294 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsRing_2740 ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_reflexive_2294 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsRing_2740
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_reflexive_2294 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsRing_2740
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsRing.setoid
d_setoid_2296 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsRing_2740 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
d_setoid_2296 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsRing_2740
-> T_Setoid_46
d_setoid_2296 ~Bool -> Bool -> Bool
v0 ~Bool -> Bool -> Bool
v1 ~Bool -> Bool
v2 ~Bool
v3 ~Bool
v4 T_IsRing_2740
v5 = T_IsRing_2740 -> T_Setoid_46
du_setoid_2296 T_IsRing_2740
v5
du_setoid_2296 ::
  MAlonzo.Code.Algebra.Structures.T_IsRing_2740 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
du_setoid_2296 :: T_IsRing_2740 -> T_Setoid_46
du_setoid_2296 T_IsRing_2740
v0
  = let v1 :: Any
v1
          = (T_IsRing_2740 -> T_IsRingWithoutOne_2368) -> Any -> Any
forall a b. a -> b
coe
              T_IsRing_2740 -> T_IsRingWithoutOne_2368
MAlonzo.Code.Algebra.Structures.du_isRingWithoutOne_2772
              (T_IsRing_2740 -> Any
forall a b. a -> b
coe T_IsRing_2740
v0) in
    Any -> T_Setoid_46
forall a b. a -> b
coe
      (let v2 :: T_IsAbelianGroup_1172
v2
             = T_IsRingWithoutOne_2368 -> T_IsAbelianGroup_1172
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2386
                 (Any -> T_IsRingWithoutOne_2368
forall a b. a -> b
coe Any
v1) in
       Any -> Any
forall a b. a -> b
coe
         (let v3 :: T_IsGroup_1074
v3
                = T_IsAbelianGroup_1172 -> T_IsGroup_1074
MAlonzo.Code.Algebra.Structures.d_isGroup_1184 (T_IsAbelianGroup_1172 -> T_IsAbelianGroup_1172
forall a b. a -> b
coe T_IsAbelianGroup_1172
v2) in
          Any -> Any
forall a b. a -> b
coe
            (let v4 :: T_IsMonoid_712
v4
                   = T_IsGroup_1074 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_1088 (T_IsGroup_1074 -> T_IsGroup_1074
forall a b. a -> b
coe T_IsGroup_1074
v3) in
             Any -> Any
forall a b. a -> b
coe
               (let v5 :: T_IsSemigroup_488
v5
                      = T_IsMonoid_712 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_722 (T_IsMonoid_712 -> T_IsMonoid_712
forall a b. a -> b
coe T_IsMonoid_712
v4) in
                Any -> Any
forall a b. a -> b
coe
                  ((T_IsMagma_178 -> T_Setoid_46) -> Any -> Any
forall a b. a -> b
coe
                     T_IsMagma_178 -> T_Setoid_46
MAlonzo.Code.Algebra.Structures.du_setoid_202
                     ((T_IsSemigroup_488 -> T_IsMagma_178) -> Any -> Any
forall a b. a -> b
coe T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496 (T_IsSemigroup_488 -> Any
forall a b. a -> b
coe T_IsSemigroup_488
v5)))))))
-- Data.Bool.Properties._.IsRing.sym
d_sym_2298 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsRing_2740 ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_sym_2298 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsRing_2740
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_sym_2298 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsRing_2740
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsRing.trans
d_trans_2300 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsRing_2740 ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_trans_2300 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsRing_2740
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
d_trans_2300 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsRing_2740
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsRing.uniqueʳ-⁻¹
d_unique'691''45''8315''185'_2302 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsRing_2740 ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_unique'691''45''8315''185'_2302 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsRing_2740
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_unique'691''45''8315''185'_2302 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsRing_2740
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsRing.uniqueˡ-⁻¹
d_unique'737''45''8315''185'_2304 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsRing_2740 ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_unique'737''45''8315''185'_2304 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsRing_2740
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_unique'737''45''8315''185'_2304 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsRing_2740
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsRing.zero
d_zero_2306 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsRing_2740 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_zero_2306 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsRing_2740
-> T_Σ_14
d_zero_2306 Bool -> Bool -> Bool
v0 Bool -> Bool -> Bool
v1 Bool -> Bool
v2 Bool
v3 ~Bool
v4 T_IsRing_2740
v5 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> T_IsRing_2740
-> T_Σ_14
du_zero_2306 Bool -> Bool -> Bool
v0 Bool -> Bool -> Bool
v1 Bool -> Bool
v2 Bool
v3 T_IsRing_2740
v5
du_zero_2306 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsRing_2740 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
du_zero_2306 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> T_IsRing_2740
-> T_Σ_14
du_zero_2306 Bool -> Bool -> Bool
v0 Bool -> Bool -> Bool
v1 Bool -> Bool
v2 Bool
v3 T_IsRing_2740
v4
  = ((Any -> Any -> Any)
 -> (Any -> Any -> Any)
 -> (Any -> Any)
 -> Any
 -> T_IsRingWithoutOne_2368
 -> T_Σ_14)
-> Any -> Any -> Any -> Any -> Any -> T_Σ_14
forall a b. a -> b
coe
      (Any -> Any -> Any)
-> (Any -> Any -> Any)
-> (Any -> Any)
-> Any
-> T_IsRingWithoutOne_2368
-> T_Σ_14
MAlonzo.Code.Algebra.Structures.du_zero_2468 ((Bool -> Bool -> Bool) -> Any
forall a b. a -> b
coe Bool -> Bool -> Bool
v0) ((Bool -> Bool -> Bool) -> Any
forall a b. a -> b
coe Bool -> Bool -> Bool
v1)
      ((Bool -> Bool) -> Any
forall a b. a -> b
coe Bool -> Bool
v2) (Bool -> Any
forall a b. a -> b
coe Bool
v3)
      ((T_IsRing_2740 -> T_IsRingWithoutOne_2368) -> Any -> Any
forall a b. a -> b
coe
         T_IsRing_2740 -> T_IsRingWithoutOne_2368
MAlonzo.Code.Algebra.Structures.du_isRingWithoutOne_2772 (T_IsRing_2740 -> Any
forall a b. a -> b
coe T_IsRing_2740
v4))
-- Data.Bool.Properties._.IsRing.zeroʳ
d_zero'691'_2308 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsRing_2740 ->
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_zero'691'_2308 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsRing_2740
-> Bool
-> T__'8801'__12
d_zero'691'_2308 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsRing_2740
-> Bool
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsRing.zeroˡ
d_zero'737'_2310 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsRing_2740 ->
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_zero'737'_2310 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsRing_2740
-> Bool
-> T__'8801'__12
d_zero'737'_2310 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsRing_2740
-> Bool
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsRingWithoutOne._//_
d__'47''47'__2314 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsRingWithoutOne_2368 ->
  Bool -> Bool -> Bool
d__'47''47'__2314 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> T_IsRingWithoutOne_2368
-> Bool
-> Bool
-> Bool
d__'47''47'__2314 Bool -> Bool -> Bool
v0 ~Bool -> Bool -> Bool
v1 Bool -> Bool
v2 ~Bool
v3 ~T_IsRingWithoutOne_2368
v4 = (Bool -> Bool -> Bool) -> (Bool -> Bool) -> Bool -> Bool -> Bool
du__'47''47'__2314 Bool -> Bool -> Bool
v0 Bool -> Bool
v2
du__'47''47'__2314 ::
  (Bool -> Bool -> Bool) -> (Bool -> Bool) -> Bool -> Bool -> Bool
du__'47''47'__2314 :: (Bool -> Bool -> Bool) -> (Bool -> Bool) -> Bool -> Bool -> Bool
du__'47''47'__2314 Bool -> Bool -> Bool
v0 Bool -> Bool
v1
  = ((Any -> Any -> Any) -> (Any -> Any) -> Any -> Any -> Any)
-> Any -> Any -> Bool -> Bool -> Bool
forall a b. a -> b
coe
      (Any -> Any -> Any) -> (Any -> Any) -> Any -> Any -> Any
MAlonzo.Code.Algebra.Structures.du__'47''47'__1136 ((Bool -> Bool -> Bool) -> Any
forall a b. a -> b
coe Bool -> Bool -> Bool
v0)
      ((Bool -> Bool) -> Any
forall a b. a -> b
coe Bool -> Bool
v1)
-- Data.Bool.Properties._.IsRingWithoutOne.*-assoc
d_'42''45'assoc_2316 ::
  MAlonzo.Code.Algebra.Structures.T_IsRingWithoutOne_2368 ->
  Bool ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'42''45'assoc_2316 :: T_IsRingWithoutOne_2368 -> Bool -> Bool -> Bool -> T__'8801'__12
d_'42''45'assoc_2316 = T_IsRingWithoutOne_2368 -> Bool -> Bool -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsRingWithoutOne.*-cong
d_'42''45'cong_2318 ::
  MAlonzo.Code.Algebra.Structures.T_IsRingWithoutOne_2368 ->
  Bool ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'42''45'cong_2318 :: T_IsRingWithoutOne_2368
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
d_'42''45'cong_2318 = T_IsRingWithoutOne_2368
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsRingWithoutOne.∙-congʳ
d_'8729''45'cong'691'_2320 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsRingWithoutOne_2368 ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8729''45'cong'691'_2320 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> T_IsRingWithoutOne_2368
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong'691'_2320 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> T_IsRingWithoutOne_2368
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsRingWithoutOne.∙-congˡ
d_'8729''45'cong'737'_2322 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsRingWithoutOne_2368 ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8729''45'cong'737'_2322 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> T_IsRingWithoutOne_2368
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong'737'_2322 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> T_IsRingWithoutOne_2368
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsRingWithoutOne.*-isMagma
d_'42''45'isMagma_2324 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsRingWithoutOne_2368 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_178
d_'42''45'isMagma_2324 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> T_IsRingWithoutOne_2368
-> T_IsMagma_178
d_'42''45'isMagma_2324 Bool -> Bool -> Bool
v0 Bool -> Bool -> Bool
v1 Bool -> Bool
v2 Bool
v3 T_IsRingWithoutOne_2368
v4
  = (T_IsNearSemiring_1260 -> T_IsMagma_178) -> Any -> T_IsMagma_178
forall a b. a -> b
coe
      T_IsNearSemiring_1260 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.du_'42''45'isMagma_1324
      (((Any -> Any -> Any)
 -> (Any -> Any -> Any)
 -> (Any -> Any)
 -> Any
 -> T_IsRingWithoutOne_2368
 -> T_IsNearSemiring_1260)
-> Any -> Any -> Any -> Any -> Any -> Any
forall a b. a -> b
coe
         (Any -> Any -> Any)
-> (Any -> Any -> Any)
-> (Any -> Any)
-> Any
-> T_IsRingWithoutOne_2368
-> T_IsNearSemiring_1260
MAlonzo.Code.Algebra.Structures.du_isNearSemiring_2470 ((Bool -> Bool -> Bool) -> Any
forall a b. a -> b
coe Bool -> Bool -> Bool
v0)
         ((Bool -> Bool -> Bool) -> Any
forall a b. a -> b
coe Bool -> Bool -> Bool
v1) ((Bool -> Bool) -> Any
forall a b. a -> b
coe Bool -> Bool
v2) (Bool -> Any
forall a b. a -> b
coe Bool
v3) (T_IsRingWithoutOne_2368 -> Any
forall a b. a -> b
coe T_IsRingWithoutOne_2368
v4))
-- Data.Bool.Properties._.IsRingWithoutOne.*-isSemigroup
d_'42''45'isSemigroup_2326 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsRingWithoutOne_2368 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_488
d_'42''45'isSemigroup_2326 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> T_IsRingWithoutOne_2368
-> T_IsSemigroup_488
d_'42''45'isSemigroup_2326 Bool -> Bool -> Bool
v0 Bool -> Bool -> Bool
v1 Bool -> Bool
v2 Bool
v3 T_IsRingWithoutOne_2368
v4
  = (T_IsNearSemiring_1260 -> T_IsSemigroup_488)
-> Any -> T_IsSemigroup_488
forall a b. a -> b
coe
      T_IsNearSemiring_1260 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.du_'42''45'isSemigroup_1326
      (((Any -> Any -> Any)
 -> (Any -> Any -> Any)
 -> (Any -> Any)
 -> Any
 -> T_IsRingWithoutOne_2368
 -> T_IsNearSemiring_1260)
-> Any -> Any -> Any -> Any -> Any -> Any
forall a b. a -> b
coe
         (Any -> Any -> Any)
-> (Any -> Any -> Any)
-> (Any -> Any)
-> Any
-> T_IsRingWithoutOne_2368
-> T_IsNearSemiring_1260
MAlonzo.Code.Algebra.Structures.du_isNearSemiring_2470 ((Bool -> Bool -> Bool) -> Any
forall a b. a -> b
coe Bool -> Bool -> Bool
v0)
         ((Bool -> Bool -> Bool) -> Any
forall a b. a -> b
coe Bool -> Bool -> Bool
v1) ((Bool -> Bool) -> Any
forall a b. a -> b
coe Bool -> Bool
v2) (Bool -> Any
forall a b. a -> b
coe Bool
v3) (T_IsRingWithoutOne_2368 -> Any
forall a b. a -> b
coe T_IsRingWithoutOne_2368
v4))
-- Data.Bool.Properties._.IsRingWithoutOne.assoc
d_assoc_2328 ::
  MAlonzo.Code.Algebra.Structures.T_IsRingWithoutOne_2368 ->
  Bool ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_assoc_2328 :: T_IsRingWithoutOne_2368 -> Bool -> Bool -> Bool -> T__'8801'__12
d_assoc_2328 = T_IsRingWithoutOne_2368 -> Bool -> Bool -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsRingWithoutOne.comm
d_comm_2330 ::
  MAlonzo.Code.Algebra.Structures.T_IsRingWithoutOne_2368 ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_comm_2330 :: T_IsRingWithoutOne_2368 -> Bool -> Bool -> T__'8801'__12
d_comm_2330 = T_IsRingWithoutOne_2368 -> Bool -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsRingWithoutOne.∙-cong
d_'8729''45'cong_2332 ::
  MAlonzo.Code.Algebra.Structures.T_IsRingWithoutOne_2368 ->
  Bool ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8729''45'cong_2332 :: T_IsRingWithoutOne_2368
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong_2332 = T_IsRingWithoutOne_2368
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsRingWithoutOne.∙-congʳ
d_'8729''45'cong'691'_2334 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsRingWithoutOne_2368 ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8729''45'cong'691'_2334 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> T_IsRingWithoutOne_2368
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong'691'_2334 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> T_IsRingWithoutOne_2368
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsRingWithoutOne.∙-congˡ
d_'8729''45'cong'737'_2336 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsRingWithoutOne_2368 ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8729''45'cong'737'_2336 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> T_IsRingWithoutOne_2368
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong'737'_2336 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> T_IsRingWithoutOne_2368
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsRingWithoutOne.identity
d_identity_2338 ::
  MAlonzo.Code.Algebra.Structures.T_IsRingWithoutOne_2368 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_identity_2338 :: T_IsRingWithoutOne_2368 -> T_Σ_14
d_identity_2338 T_IsRingWithoutOne_2368
v0
  = (T_IsMonoid_712 -> T_Σ_14) -> Any -> T_Σ_14
forall a b. a -> b
coe
      T_IsMonoid_712 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_identity_724
      ((T_IsGroup_1074 -> T_IsMonoid_712) -> Any -> Any
forall a b. a -> b
coe
         T_IsGroup_1074 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_1088
         ((T_IsAbelianGroup_1172 -> T_IsGroup_1074) -> Any -> Any
forall a b. a -> b
coe
            T_IsAbelianGroup_1172 -> T_IsGroup_1074
MAlonzo.Code.Algebra.Structures.d_isGroup_1184
            ((T_IsRingWithoutOne_2368 -> T_IsAbelianGroup_1172) -> Any -> Any
forall a b. a -> b
coe
               T_IsRingWithoutOne_2368 -> T_IsAbelianGroup_1172
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2386
               (T_IsRingWithoutOne_2368 -> Any
forall a b. a -> b
coe T_IsRingWithoutOne_2368
v0))))
-- Data.Bool.Properties._.IsRingWithoutOne.identityʳ
d_identity'691'_2340 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsRingWithoutOne_2368 ->
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_identity'691'_2340 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> T_IsRingWithoutOne_2368
-> Bool
-> T__'8801'__12
d_identity'691'_2340 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> T_IsRingWithoutOne_2368
-> Bool
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsRingWithoutOne.identityˡ
d_identity'737'_2342 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsRingWithoutOne_2368 ->
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_identity'737'_2342 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> T_IsRingWithoutOne_2368
-> Bool
-> T__'8801'__12
d_identity'737'_2342 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> T_IsRingWithoutOne_2368
-> Bool
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsRingWithoutOne.+-isAbelianGroup
d_'43''45'isAbelianGroup_2344 ::
  MAlonzo.Code.Algebra.Structures.T_IsRingWithoutOne_2368 ->
  MAlonzo.Code.Algebra.Structures.T_IsAbelianGroup_1172
d_'43''45'isAbelianGroup_2344 :: T_IsRingWithoutOne_2368 -> T_IsAbelianGroup_1172
d_'43''45'isAbelianGroup_2344 T_IsRingWithoutOne_2368
v0
  = (T_IsRingWithoutOne_2368 -> T_IsAbelianGroup_1172)
-> Any -> T_IsAbelianGroup_1172
forall a b. a -> b
coe
      T_IsRingWithoutOne_2368 -> T_IsAbelianGroup_1172
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2386
      (T_IsRingWithoutOne_2368 -> Any
forall a b. a -> b
coe T_IsRingWithoutOne_2368
v0)
-- Data.Bool.Properties._.IsRingWithoutOne.isCommutativeMagma
d_isCommutativeMagma_2346 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsRingWithoutOne_2368 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMagma_214
d_isCommutativeMagma_2346 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> T_IsRingWithoutOne_2368
-> T_IsCommutativeMagma_214
d_isCommutativeMagma_2346 ~Bool -> Bool -> Bool
v0 ~Bool -> Bool -> Bool
v1 ~Bool -> Bool
v2 ~Bool
v3 T_IsRingWithoutOne_2368
v4
  = T_IsRingWithoutOne_2368 -> T_IsCommutativeMagma_214
du_isCommutativeMagma_2346 T_IsRingWithoutOne_2368
v4
du_isCommutativeMagma_2346 ::
  MAlonzo.Code.Algebra.Structures.T_IsRingWithoutOne_2368 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMagma_214
du_isCommutativeMagma_2346 :: T_IsRingWithoutOne_2368 -> T_IsCommutativeMagma_214
du_isCommutativeMagma_2346 T_IsRingWithoutOne_2368
v0
  = let v1 :: T_IsAbelianGroup_1172
v1
          = T_IsRingWithoutOne_2368 -> T_IsAbelianGroup_1172
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2386
              (T_IsRingWithoutOne_2368 -> T_IsRingWithoutOne_2368
forall a b. a -> b
coe T_IsRingWithoutOne_2368
v0) in
    Any -> T_IsCommutativeMagma_214
forall a b. a -> b
coe
      (let v2 :: Any
v2
             = (T_IsAbelianGroup_1172 -> T_IsCommutativeMonoid_764) -> Any -> Any
forall a b. a -> b
coe
                 T_IsAbelianGroup_1172 -> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.du_isCommutativeMonoid_1244
                 (T_IsAbelianGroup_1172 -> Any
forall a b. a -> b
coe T_IsAbelianGroup_1172
v1) in
       Any -> Any
forall a b. a -> b
coe
         ((T_IsCommutativeSemigroup_568 -> T_IsCommutativeMagma_214)
-> Any -> Any
forall a b. a -> b
coe
            T_IsCommutativeSemigroup_568 -> T_IsCommutativeMagma_214
MAlonzo.Code.Algebra.Structures.du_isCommutativeMagma_606
            ((T_IsCommutativeMonoid_764 -> T_IsCommutativeSemigroup_568)
-> Any -> Any
forall a b. a -> b
coe
               T_IsCommutativeMonoid_764 -> T_IsCommutativeSemigroup_568
MAlonzo.Code.Algebra.Structures.du_isCommutativeSemigroup_814
               (Any -> Any
forall a b. a -> b
coe Any
v2))))
-- Data.Bool.Properties._.IsRingWithoutOne.isCommutativeMonoid
d_isCommutativeMonoid_2348 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsRingWithoutOne_2368 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMonoid_764
d_isCommutativeMonoid_2348 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> T_IsRingWithoutOne_2368
-> T_IsCommutativeMonoid_764
d_isCommutativeMonoid_2348 ~Bool -> Bool -> Bool
v0 ~Bool -> Bool -> Bool
v1 ~Bool -> Bool
v2 ~Bool
v3 T_IsRingWithoutOne_2368
v4
  = T_IsRingWithoutOne_2368 -> T_IsCommutativeMonoid_764
du_isCommutativeMonoid_2348 T_IsRingWithoutOne_2368
v4
du_isCommutativeMonoid_2348 ::
  MAlonzo.Code.Algebra.Structures.T_IsRingWithoutOne_2368 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMonoid_764
du_isCommutativeMonoid_2348 :: T_IsRingWithoutOne_2368 -> T_IsCommutativeMonoid_764
du_isCommutativeMonoid_2348 T_IsRingWithoutOne_2368
v0
  = (T_IsAbelianGroup_1172 -> T_IsCommutativeMonoid_764)
-> Any -> T_IsCommutativeMonoid_764
forall a b. a -> b
coe
      T_IsAbelianGroup_1172 -> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.du_isCommutativeMonoid_1244
      ((T_IsRingWithoutOne_2368 -> T_IsAbelianGroup_1172) -> Any -> Any
forall a b. a -> b
coe
         T_IsRingWithoutOne_2368 -> T_IsAbelianGroup_1172
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2386
         (T_IsRingWithoutOne_2368 -> Any
forall a b. a -> b
coe T_IsRingWithoutOne_2368
v0))
-- Data.Bool.Properties._.IsRingWithoutOne.isCommutativeSemigroup
d_isCommutativeSemigroup_2350 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsRingWithoutOne_2368 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_568
d_isCommutativeSemigroup_2350 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> T_IsRingWithoutOne_2368
-> T_IsCommutativeSemigroup_568
d_isCommutativeSemigroup_2350 ~Bool -> Bool -> Bool
v0 ~Bool -> Bool -> Bool
v1 ~Bool -> Bool
v2 ~Bool
v3 T_IsRingWithoutOne_2368
v4
  = T_IsRingWithoutOne_2368 -> T_IsCommutativeSemigroup_568
du_isCommutativeSemigroup_2350 T_IsRingWithoutOne_2368
v4
du_isCommutativeSemigroup_2350 ::
  MAlonzo.Code.Algebra.Structures.T_IsRingWithoutOne_2368 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_568
du_isCommutativeSemigroup_2350 :: T_IsRingWithoutOne_2368 -> T_IsCommutativeSemigroup_568
du_isCommutativeSemigroup_2350 T_IsRingWithoutOne_2368
v0
  = let v1 :: T_IsAbelianGroup_1172
v1
          = T_IsRingWithoutOne_2368 -> T_IsAbelianGroup_1172
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2386
              (T_IsRingWithoutOne_2368 -> T_IsRingWithoutOne_2368
forall a b. a -> b
coe T_IsRingWithoutOne_2368
v0) in
    Any -> T_IsCommutativeSemigroup_568
forall a b. a -> b
coe
      ((T_IsCommutativeMonoid_764 -> T_IsCommutativeSemigroup_568)
-> Any -> Any
forall a b. a -> b
coe
         T_IsCommutativeMonoid_764 -> T_IsCommutativeSemigroup_568
MAlonzo.Code.Algebra.Structures.du_isCommutativeSemigroup_814
         ((T_IsAbelianGroup_1172 -> T_IsCommutativeMonoid_764) -> Any -> Any
forall a b. a -> b
coe
            T_IsAbelianGroup_1172 -> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.du_isCommutativeMonoid_1244
            (T_IsAbelianGroup_1172 -> Any
forall a b. a -> b
coe T_IsAbelianGroup_1172
v1)))
-- Data.Bool.Properties._.IsRingWithoutOne.isGroup
d_isGroup_2352 ::
  MAlonzo.Code.Algebra.Structures.T_IsRingWithoutOne_2368 ->
  MAlonzo.Code.Algebra.Structures.T_IsGroup_1074
d_isGroup_2352 :: T_IsRingWithoutOne_2368 -> T_IsGroup_1074
d_isGroup_2352 T_IsRingWithoutOne_2368
v0
  = (T_IsAbelianGroup_1172 -> T_IsGroup_1074) -> Any -> T_IsGroup_1074
forall a b. a -> b
coe
      T_IsAbelianGroup_1172 -> T_IsGroup_1074
MAlonzo.Code.Algebra.Structures.d_isGroup_1184
      ((T_IsRingWithoutOne_2368 -> T_IsAbelianGroup_1172) -> Any -> Any
forall a b. a -> b
coe
         T_IsRingWithoutOne_2368 -> T_IsAbelianGroup_1172
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2386
         (T_IsRingWithoutOne_2368 -> Any
forall a b. a -> b
coe T_IsRingWithoutOne_2368
v0))
-- Data.Bool.Properties._.IsRingWithoutOne.isInvertibleMagma
d_isInvertibleMagma_2354 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsRingWithoutOne_2368 ->
  MAlonzo.Code.Algebra.Structures.T_IsInvertibleMagma_958
d_isInvertibleMagma_2354 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> T_IsRingWithoutOne_2368
-> T_IsInvertibleMagma_958
d_isInvertibleMagma_2354 ~Bool -> Bool -> Bool
v0 ~Bool -> Bool -> Bool
v1 ~Bool -> Bool
v2 ~Bool
v3 T_IsRingWithoutOne_2368
v4
  = T_IsRingWithoutOne_2368 -> T_IsInvertibleMagma_958
du_isInvertibleMagma_2354 T_IsRingWithoutOne_2368
v4
du_isInvertibleMagma_2354 ::
  MAlonzo.Code.Algebra.Structures.T_IsRingWithoutOne_2368 ->
  MAlonzo.Code.Algebra.Structures.T_IsInvertibleMagma_958
du_isInvertibleMagma_2354 :: T_IsRingWithoutOne_2368 -> T_IsInvertibleMagma_958
du_isInvertibleMagma_2354 T_IsRingWithoutOne_2368
v0
  = let v1 :: T_IsAbelianGroup_1172
v1
          = T_IsRingWithoutOne_2368 -> T_IsAbelianGroup_1172
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2386
              (T_IsRingWithoutOne_2368 -> T_IsRingWithoutOne_2368
forall a b. a -> b
coe T_IsRingWithoutOne_2368
v0) in
    Any -> T_IsInvertibleMagma_958
forall a b. a -> b
coe
      ((T_IsGroup_1074 -> T_IsInvertibleMagma_958) -> Any -> Any
forall a b. a -> b
coe
         T_IsGroup_1074 -> T_IsInvertibleMagma_958
MAlonzo.Code.Algebra.Structures.du_isInvertibleMagma_1160
         ((T_IsAbelianGroup_1172 -> T_IsGroup_1074) -> Any -> Any
forall a b. a -> b
coe T_IsAbelianGroup_1172 -> T_IsGroup_1074
MAlonzo.Code.Algebra.Structures.d_isGroup_1184 (T_IsAbelianGroup_1172 -> Any
forall a b. a -> b
coe T_IsAbelianGroup_1172
v1)))
-- Data.Bool.Properties._.IsRingWithoutOne.isInvertibleUnitalMagma
d_isInvertibleUnitalMagma_2356 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsRingWithoutOne_2368 ->
  MAlonzo.Code.Algebra.Structures.T_IsInvertibleUnitalMagma_1012
d_isInvertibleUnitalMagma_2356 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> T_IsRingWithoutOne_2368
-> T_IsInvertibleUnitalMagma_1012
d_isInvertibleUnitalMagma_2356 ~Bool -> Bool -> Bool
v0 ~Bool -> Bool -> Bool
v1 ~Bool -> Bool
v2 ~Bool
v3 T_IsRingWithoutOne_2368
v4
  = T_IsRingWithoutOne_2368 -> T_IsInvertibleUnitalMagma_1012
du_isInvertibleUnitalMagma_2356 T_IsRingWithoutOne_2368
v4
du_isInvertibleUnitalMagma_2356 ::
  MAlonzo.Code.Algebra.Structures.T_IsRingWithoutOne_2368 ->
  MAlonzo.Code.Algebra.Structures.T_IsInvertibleUnitalMagma_1012
du_isInvertibleUnitalMagma_2356 :: T_IsRingWithoutOne_2368 -> T_IsInvertibleUnitalMagma_1012
du_isInvertibleUnitalMagma_2356 T_IsRingWithoutOne_2368
v0
  = let v1 :: T_IsAbelianGroup_1172
v1
          = T_IsRingWithoutOne_2368 -> T_IsAbelianGroup_1172
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2386
              (T_IsRingWithoutOne_2368 -> T_IsRingWithoutOne_2368
forall a b. a -> b
coe T_IsRingWithoutOne_2368
v0) in
    Any -> T_IsInvertibleUnitalMagma_1012
forall a b. a -> b
coe
      ((T_IsGroup_1074 -> T_IsInvertibleUnitalMagma_1012) -> Any -> Any
forall a b. a -> b
coe
         T_IsGroup_1074 -> T_IsInvertibleUnitalMagma_1012
MAlonzo.Code.Algebra.Structures.du_isInvertibleUnitalMagma_1162
         ((T_IsAbelianGroup_1172 -> T_IsGroup_1074) -> Any -> Any
forall a b. a -> b
coe T_IsAbelianGroup_1172 -> T_IsGroup_1074
MAlonzo.Code.Algebra.Structures.d_isGroup_1184 (T_IsAbelianGroup_1172 -> Any
forall a b. a -> b
coe T_IsAbelianGroup_1172
v1)))
-- Data.Bool.Properties._.IsRingWithoutOne.isMagma
d_isMagma_2358 ::
  MAlonzo.Code.Algebra.Structures.T_IsRingWithoutOne_2368 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_178
d_isMagma_2358 :: T_IsRingWithoutOne_2368 -> T_IsMagma_178
d_isMagma_2358 T_IsRingWithoutOne_2368
v0
  = (T_IsSemigroup_488 -> T_IsMagma_178) -> Any -> T_IsMagma_178
forall a b. a -> b
coe
      T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496
      ((T_IsMonoid_712 -> T_IsSemigroup_488) -> Any -> Any
forall a b. a -> b
coe
         T_IsMonoid_712 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_722
         ((T_IsGroup_1074 -> T_IsMonoid_712) -> Any -> Any
forall a b. a -> b
coe
            T_IsGroup_1074 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_1088
            ((T_IsAbelianGroup_1172 -> T_IsGroup_1074) -> Any -> Any
forall a b. a -> b
coe
               T_IsAbelianGroup_1172 -> T_IsGroup_1074
MAlonzo.Code.Algebra.Structures.d_isGroup_1184
               ((T_IsRingWithoutOne_2368 -> T_IsAbelianGroup_1172) -> Any -> Any
forall a b. a -> b
coe
                  T_IsRingWithoutOne_2368 -> T_IsAbelianGroup_1172
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2386
                  (T_IsRingWithoutOne_2368 -> Any
forall a b. a -> b
coe T_IsRingWithoutOne_2368
v0)))))
-- Data.Bool.Properties._.IsRingWithoutOne.isMonoid
d_isMonoid_2360 ::
  MAlonzo.Code.Algebra.Structures.T_IsRingWithoutOne_2368 ->
  MAlonzo.Code.Algebra.Structures.T_IsMonoid_712
d_isMonoid_2360 :: T_IsRingWithoutOne_2368 -> T_IsMonoid_712
d_isMonoid_2360 T_IsRingWithoutOne_2368
v0
  = (T_IsGroup_1074 -> T_IsMonoid_712) -> Any -> T_IsMonoid_712
forall a b. a -> b
coe
      T_IsGroup_1074 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_1088
      ((T_IsAbelianGroup_1172 -> T_IsGroup_1074) -> Any -> Any
forall a b. a -> b
coe
         T_IsAbelianGroup_1172 -> T_IsGroup_1074
MAlonzo.Code.Algebra.Structures.d_isGroup_1184
         ((T_IsRingWithoutOne_2368 -> T_IsAbelianGroup_1172) -> Any -> Any
forall a b. a -> b
coe
            T_IsRingWithoutOne_2368 -> T_IsAbelianGroup_1172
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2386
            (T_IsRingWithoutOne_2368 -> Any
forall a b. a -> b
coe T_IsRingWithoutOne_2368
v0)))
-- Data.Bool.Properties._.IsRingWithoutOne.isSemigroup
d_isSemigroup_2362 ::
  MAlonzo.Code.Algebra.Structures.T_IsRingWithoutOne_2368 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_488
d_isSemigroup_2362 :: T_IsRingWithoutOne_2368 -> T_IsSemigroup_488
d_isSemigroup_2362 T_IsRingWithoutOne_2368
v0
  = (T_IsMonoid_712 -> T_IsSemigroup_488) -> Any -> T_IsSemigroup_488
forall a b. a -> b
coe
      T_IsMonoid_712 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_722
      ((T_IsGroup_1074 -> T_IsMonoid_712) -> Any -> Any
forall a b. a -> b
coe
         T_IsGroup_1074 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_1088
         ((T_IsAbelianGroup_1172 -> T_IsGroup_1074) -> Any -> Any
forall a b. a -> b
coe
            T_IsAbelianGroup_1172 -> T_IsGroup_1074
MAlonzo.Code.Algebra.Structures.d_isGroup_1184
            ((T_IsRingWithoutOne_2368 -> T_IsAbelianGroup_1172) -> Any -> Any
forall a b. a -> b
coe
               T_IsRingWithoutOne_2368 -> T_IsAbelianGroup_1172
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2386
               (T_IsRingWithoutOne_2368 -> Any
forall a b. a -> b
coe T_IsRingWithoutOne_2368
v0))))
-- Data.Bool.Properties._.IsRingWithoutOne.isUnitalMagma
d_isUnitalMagma_2364 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsRingWithoutOne_2368 ->
  MAlonzo.Code.Algebra.Structures.T_IsUnitalMagma_666
d_isUnitalMagma_2364 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> T_IsRingWithoutOne_2368
-> T_IsUnitalMagma_666
d_isUnitalMagma_2364 ~Bool -> Bool -> Bool
v0 ~Bool -> Bool -> Bool
v1 ~Bool -> Bool
v2 ~Bool
v3 T_IsRingWithoutOne_2368
v4 = T_IsRingWithoutOne_2368 -> T_IsUnitalMagma_666
du_isUnitalMagma_2364 T_IsRingWithoutOne_2368
v4
du_isUnitalMagma_2364 ::
  MAlonzo.Code.Algebra.Structures.T_IsRingWithoutOne_2368 ->
  MAlonzo.Code.Algebra.Structures.T_IsUnitalMagma_666
du_isUnitalMagma_2364 :: T_IsRingWithoutOne_2368 -> T_IsUnitalMagma_666
du_isUnitalMagma_2364 T_IsRingWithoutOne_2368
v0
  = let v1 :: T_IsAbelianGroup_1172
v1
          = T_IsRingWithoutOne_2368 -> T_IsAbelianGroup_1172
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2386
              (T_IsRingWithoutOne_2368 -> T_IsRingWithoutOne_2368
forall a b. a -> b
coe T_IsRingWithoutOne_2368
v0) in
    Any -> T_IsUnitalMagma_666
forall a b. a -> b
coe
      (let v2 :: T_IsGroup_1074
v2
             = T_IsAbelianGroup_1172 -> T_IsGroup_1074
MAlonzo.Code.Algebra.Structures.d_isGroup_1184 (T_IsAbelianGroup_1172 -> T_IsAbelianGroup_1172
forall a b. a -> b
coe T_IsAbelianGroup_1172
v1) in
       Any -> Any
forall a b. a -> b
coe
         ((T_IsMonoid_712 -> T_IsUnitalMagma_666) -> Any -> Any
forall a b. a -> b
coe
            T_IsMonoid_712 -> T_IsUnitalMagma_666
MAlonzo.Code.Algebra.Structures.du_isUnitalMagma_756
            ((T_IsGroup_1074 -> T_IsMonoid_712) -> Any -> Any
forall a b. a -> b
coe T_IsGroup_1074 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_1088 (T_IsGroup_1074 -> Any
forall a b. a -> b
coe T_IsGroup_1074
v2))))
-- Data.Bool.Properties._.IsRingWithoutOne.⁻¹-cong
d_'8315''185''45'cong_2366 ::
  MAlonzo.Code.Algebra.Structures.T_IsRingWithoutOne_2368 ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8315''185''45'cong_2366 :: T_IsRingWithoutOne_2368
-> Bool -> Bool -> T__'8801'__12 -> T__'8801'__12
d_'8315''185''45'cong_2366 = T_IsRingWithoutOne_2368
-> Bool -> Bool -> T__'8801'__12 -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsRingWithoutOne.inverse
d_inverse_2368 ::
  MAlonzo.Code.Algebra.Structures.T_IsRingWithoutOne_2368 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_inverse_2368 :: T_IsRingWithoutOne_2368 -> T_Σ_14
d_inverse_2368 T_IsRingWithoutOne_2368
v0
  = (T_IsGroup_1074 -> T_Σ_14) -> Any -> T_Σ_14
forall a b. a -> b
coe
      T_IsGroup_1074 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_inverse_1090
      ((T_IsAbelianGroup_1172 -> T_IsGroup_1074) -> Any -> Any
forall a b. a -> b
coe
         T_IsAbelianGroup_1172 -> T_IsGroup_1074
MAlonzo.Code.Algebra.Structures.d_isGroup_1184
         ((T_IsRingWithoutOne_2368 -> T_IsAbelianGroup_1172) -> Any -> Any
forall a b. a -> b
coe
            T_IsRingWithoutOne_2368 -> T_IsAbelianGroup_1172
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2386
            (T_IsRingWithoutOne_2368 -> Any
forall a b. a -> b
coe T_IsRingWithoutOne_2368
v0)))
-- Data.Bool.Properties._.IsRingWithoutOne.inverseʳ
d_inverse'691'_2370 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsRingWithoutOne_2368 ->
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_inverse'691'_2370 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> T_IsRingWithoutOne_2368
-> Bool
-> T__'8801'__12
d_inverse'691'_2370 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> T_IsRingWithoutOne_2368
-> Bool
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsRingWithoutOne.inverseˡ
d_inverse'737'_2372 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsRingWithoutOne_2368 ->
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_inverse'737'_2372 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> T_IsRingWithoutOne_2368
-> Bool
-> T__'8801'__12
d_inverse'737'_2372 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> T_IsRingWithoutOne_2368
-> Bool
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsRingWithoutOne.distrib
d_distrib_2374 ::
  MAlonzo.Code.Algebra.Structures.T_IsRingWithoutOne_2368 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_distrib_2374 :: T_IsRingWithoutOne_2368 -> T_Σ_14
d_distrib_2374 T_IsRingWithoutOne_2368
v0
  = (T_IsRingWithoutOne_2368 -> T_Σ_14) -> Any -> T_Σ_14
forall a b. a -> b
coe T_IsRingWithoutOne_2368 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_distrib_2392 (T_IsRingWithoutOne_2368 -> Any
forall a b. a -> b
coe T_IsRingWithoutOne_2368
v0)
-- Data.Bool.Properties._.IsRingWithoutOne.distribʳ
d_distrib'691'_2376 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsRingWithoutOne_2368 ->
  Bool ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_distrib'691'_2376 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> T_IsRingWithoutOne_2368
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
d_distrib'691'_2376 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> T_IsRingWithoutOne_2368
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsRingWithoutOne.distribˡ
d_distrib'737'_2378 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsRingWithoutOne_2368 ->
  Bool ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_distrib'737'_2378 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> T_IsRingWithoutOne_2368
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
d_distrib'737'_2378 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> T_IsRingWithoutOne_2368
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsRingWithoutOne.isEquivalence
d_isEquivalence_2380 ::
  MAlonzo.Code.Algebra.Structures.T_IsRingWithoutOne_2368 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
d_isEquivalence_2380 :: T_IsRingWithoutOne_2368 -> T_IsEquivalence_28
d_isEquivalence_2380 T_IsRingWithoutOne_2368
v0
  = (T_IsMagma_178 -> T_IsEquivalence_28) -> Any -> T_IsEquivalence_28
forall a b. a -> b
coe
      T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186
      ((T_IsSemigroup_488 -> T_IsMagma_178) -> Any -> Any
forall a b. a -> b
coe
         T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496
         ((T_IsMonoid_712 -> T_IsSemigroup_488) -> Any -> Any
forall a b. a -> b
coe
            T_IsMonoid_712 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_722
            ((T_IsGroup_1074 -> T_IsMonoid_712) -> Any -> Any
forall a b. a -> b
coe
               T_IsGroup_1074 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_1088
               ((T_IsAbelianGroup_1172 -> T_IsGroup_1074) -> Any -> Any
forall a b. a -> b
coe
                  T_IsAbelianGroup_1172 -> T_IsGroup_1074
MAlonzo.Code.Algebra.Structures.d_isGroup_1184
                  ((T_IsRingWithoutOne_2368 -> T_IsAbelianGroup_1172) -> Any -> Any
forall a b. a -> b
coe
                     T_IsRingWithoutOne_2368 -> T_IsAbelianGroup_1172
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2386
                     (T_IsRingWithoutOne_2368 -> Any
forall a b. a -> b
coe T_IsRingWithoutOne_2368
v0))))))
-- Data.Bool.Properties._.IsRingWithoutOne.isNearSemiring
d_isNearSemiring_2382 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsRingWithoutOne_2368 ->
  MAlonzo.Code.Algebra.Structures.T_IsNearSemiring_1260
d_isNearSemiring_2382 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> T_IsRingWithoutOne_2368
-> T_IsNearSemiring_1260
d_isNearSemiring_2382
  = ((Any -> Any -> Any)
 -> (Any -> Any -> Any)
 -> (Any -> Any)
 -> Any
 -> T_IsRingWithoutOne_2368
 -> T_IsNearSemiring_1260)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> T_IsRingWithoutOne_2368
-> T_IsNearSemiring_1260
forall a b. a -> b
coe (Any -> Any -> Any)
-> (Any -> Any -> Any)
-> (Any -> Any)
-> Any
-> T_IsRingWithoutOne_2368
-> T_IsNearSemiring_1260
MAlonzo.Code.Algebra.Structures.du_isNearSemiring_2470
-- Data.Bool.Properties._.IsRingWithoutOne.isPartialEquivalence
d_isPartialEquivalence_2384 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsRingWithoutOne_2368 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_2384 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> T_IsRingWithoutOne_2368
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_2384 ~Bool -> Bool -> Bool
v0 ~Bool -> Bool -> Bool
v1 ~Bool -> Bool
v2 ~Bool
v3 T_IsRingWithoutOne_2368
v4
  = T_IsRingWithoutOne_2368 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_2384 T_IsRingWithoutOne_2368
v4
du_isPartialEquivalence_2384 ::
  MAlonzo.Code.Algebra.Structures.T_IsRingWithoutOne_2368 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_2384 :: T_IsRingWithoutOne_2368 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_2384 T_IsRingWithoutOne_2368
v0
  = let v1 :: T_IsAbelianGroup_1172
v1
          = T_IsRingWithoutOne_2368 -> T_IsAbelianGroup_1172
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2386
              (T_IsRingWithoutOne_2368 -> T_IsRingWithoutOne_2368
forall a b. a -> b
coe T_IsRingWithoutOne_2368
v0) in
    Any -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsGroup_1074
v2
             = T_IsAbelianGroup_1172 -> T_IsGroup_1074
MAlonzo.Code.Algebra.Structures.d_isGroup_1184 (T_IsAbelianGroup_1172 -> T_IsAbelianGroup_1172
forall a b. a -> b
coe T_IsAbelianGroup_1172
v1) in
       Any -> Any
forall a b. a -> b
coe
         (let v3 :: T_IsMonoid_712
v3
                = T_IsGroup_1074 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_1088 (T_IsGroup_1074 -> T_IsGroup_1074
forall a b. a -> b
coe T_IsGroup_1074
v2) in
          Any -> Any
forall a b. a -> b
coe
            (let v4 :: T_IsSemigroup_488
v4
                   = T_IsMonoid_712 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_722 (T_IsMonoid_712 -> T_IsMonoid_712
forall a b. a -> b
coe T_IsMonoid_712
v3) in
             Any -> Any
forall a b. a -> b
coe
               (let v5 :: T_IsMagma_178
v5 = T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496 (T_IsSemigroup_488 -> T_IsSemigroup_488
forall a b. a -> b
coe T_IsSemigroup_488
v4) in
                Any -> Any
forall a b. a -> b
coe
                  ((T_IsEquivalence_28 -> T_IsPartialEquivalence_16) -> Any -> Any
forall a b. a -> b
coe
                     T_IsEquivalence_28 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_44
                     ((T_IsMagma_178 -> T_IsEquivalence_28) -> Any -> Any
forall a b. a -> b
coe
                        T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186 (T_IsMagma_178 -> Any
forall a b. a -> b
coe T_IsMagma_178
v5)))))))
-- Data.Bool.Properties._.IsRingWithoutOne.refl
d_refl_2386 ::
  MAlonzo.Code.Algebra.Structures.T_IsRingWithoutOne_2368 ->
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_refl_2386 :: T_IsRingWithoutOne_2368 -> Bool -> T__'8801'__12
d_refl_2386 = T_IsRingWithoutOne_2368 -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsRingWithoutOne.reflexive
d_reflexive_2388 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsRingWithoutOne_2368 ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_reflexive_2388 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> T_IsRingWithoutOne_2368
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_reflexive_2388 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> T_IsRingWithoutOne_2368
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsRingWithoutOne.setoid
d_setoid_2390 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsRingWithoutOne_2368 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
d_setoid_2390 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> T_IsRingWithoutOne_2368
-> T_Setoid_46
d_setoid_2390 ~Bool -> Bool -> Bool
v0 ~Bool -> Bool -> Bool
v1 ~Bool -> Bool
v2 ~Bool
v3 T_IsRingWithoutOne_2368
v4 = T_IsRingWithoutOne_2368 -> T_Setoid_46
du_setoid_2390 T_IsRingWithoutOne_2368
v4
du_setoid_2390 ::
  MAlonzo.Code.Algebra.Structures.T_IsRingWithoutOne_2368 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
du_setoid_2390 :: T_IsRingWithoutOne_2368 -> T_Setoid_46
du_setoid_2390 T_IsRingWithoutOne_2368
v0
  = let v1 :: T_IsAbelianGroup_1172
v1
          = T_IsRingWithoutOne_2368 -> T_IsAbelianGroup_1172
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2386
              (T_IsRingWithoutOne_2368 -> T_IsRingWithoutOne_2368
forall a b. a -> b
coe T_IsRingWithoutOne_2368
v0) in
    Any -> T_Setoid_46
forall a b. a -> b
coe
      (let v2 :: T_IsGroup_1074
v2
             = T_IsAbelianGroup_1172 -> T_IsGroup_1074
MAlonzo.Code.Algebra.Structures.d_isGroup_1184 (T_IsAbelianGroup_1172 -> T_IsAbelianGroup_1172
forall a b. a -> b
coe T_IsAbelianGroup_1172
v1) in
       Any -> Any
forall a b. a -> b
coe
         (let v3 :: T_IsMonoid_712
v3
                = T_IsGroup_1074 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_1088 (T_IsGroup_1074 -> T_IsGroup_1074
forall a b. a -> b
coe T_IsGroup_1074
v2) in
          Any -> Any
forall a b. a -> b
coe
            (let v4 :: T_IsSemigroup_488
v4
                   = T_IsMonoid_712 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_722 (T_IsMonoid_712 -> T_IsMonoid_712
forall a b. a -> b
coe T_IsMonoid_712
v3) in
             Any -> Any
forall a b. a -> b
coe
               ((T_IsMagma_178 -> T_Setoid_46) -> Any -> Any
forall a b. a -> b
coe
                  T_IsMagma_178 -> T_Setoid_46
MAlonzo.Code.Algebra.Structures.du_setoid_202
                  ((T_IsSemigroup_488 -> T_IsMagma_178) -> Any -> Any
forall a b. a -> b
coe T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496 (T_IsSemigroup_488 -> Any
forall a b. a -> b
coe T_IsSemigroup_488
v4))))))
-- Data.Bool.Properties._.IsRingWithoutOne.sym
d_sym_2392 ::
  MAlonzo.Code.Algebra.Structures.T_IsRingWithoutOne_2368 ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_sym_2392 :: T_IsRingWithoutOne_2368
-> Bool -> Bool -> T__'8801'__12 -> T__'8801'__12
d_sym_2392 = T_IsRingWithoutOne_2368
-> Bool -> Bool -> T__'8801'__12 -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsRingWithoutOne.trans
d_trans_2394 ::
  MAlonzo.Code.Algebra.Structures.T_IsRingWithoutOne_2368 ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_trans_2394 :: T_IsRingWithoutOne_2368
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
d_trans_2394 = T_IsRingWithoutOne_2368
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsRingWithoutOne.uniqueʳ-⁻¹
d_unique'691''45''8315''185'_2396 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsRingWithoutOne_2368 ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_unique'691''45''8315''185'_2396 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> T_IsRingWithoutOne_2368
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_unique'691''45''8315''185'_2396 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> T_IsRingWithoutOne_2368
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsRingWithoutOne.uniqueˡ-⁻¹
d_unique'737''45''8315''185'_2398 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsRingWithoutOne_2368 ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_unique'737''45''8315''185'_2398 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> T_IsRingWithoutOne_2368
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_unique'737''45''8315''185'_2398 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> T_IsRingWithoutOne_2368
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsRingWithoutOne.zero
d_zero_2400 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsRingWithoutOne_2368 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_zero_2400 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> T_IsRingWithoutOne_2368
-> T_Σ_14
d_zero_2400 = ((Any -> Any -> Any)
 -> (Any -> Any -> Any)
 -> (Any -> Any)
 -> Any
 -> T_IsRingWithoutOne_2368
 -> T_Σ_14)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> T_IsRingWithoutOne_2368
-> T_Σ_14
forall a b. a -> b
coe (Any -> Any -> Any)
-> (Any -> Any -> Any)
-> (Any -> Any)
-> Any
-> T_IsRingWithoutOne_2368
-> T_Σ_14
MAlonzo.Code.Algebra.Structures.du_zero_2468
-- Data.Bool.Properties._.IsRingWithoutOne.zeroʳ
d_zero'691'_2402 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsRingWithoutOne_2368 ->
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_zero'691'_2402 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> T_IsRingWithoutOne_2368
-> Bool
-> T__'8801'__12
d_zero'691'_2402 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> T_IsRingWithoutOne_2368
-> Bool
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsRingWithoutOne.zeroˡ
d_zero'737'_2404 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsRingWithoutOne_2368 ->
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_zero'737'_2404 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> T_IsRingWithoutOne_2368
-> Bool
-> T__'8801'__12
d_zero'737'_2404 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> T_IsRingWithoutOne_2368
-> Bool
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsSelectiveMagma.isEquivalence
d_isEquivalence_2408 ::
  MAlonzo.Code.Algebra.Structures.T_IsSelectiveMagma_450 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
d_isEquivalence_2408 :: T_IsSelectiveMagma_450 -> T_IsEquivalence_28
d_isEquivalence_2408 T_IsSelectiveMagma_450
v0
  = (T_IsMagma_178 -> T_IsEquivalence_28) -> Any -> T_IsEquivalence_28
forall a b. a -> b
coe
      T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186
      ((T_IsSelectiveMagma_450 -> T_IsMagma_178) -> Any -> Any
forall a b. a -> b
coe T_IsSelectiveMagma_450 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_458 (T_IsSelectiveMagma_450 -> Any
forall a b. a -> b
coe T_IsSelectiveMagma_450
v0))
-- Data.Bool.Properties._.IsSelectiveMagma.isMagma
d_isMagma_2410 ::
  MAlonzo.Code.Algebra.Structures.T_IsSelectiveMagma_450 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_178
d_isMagma_2410 :: T_IsSelectiveMagma_450 -> T_IsMagma_178
d_isMagma_2410 T_IsSelectiveMagma_450
v0
  = (T_IsSelectiveMagma_450 -> T_IsMagma_178) -> Any -> T_IsMagma_178
forall a b. a -> b
coe T_IsSelectiveMagma_450 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_458 (T_IsSelectiveMagma_450 -> Any
forall a b. a -> b
coe T_IsSelectiveMagma_450
v0)
-- Data.Bool.Properties._.IsSelectiveMagma.isPartialEquivalence
d_isPartialEquivalence_2412 ::
  (Bool -> Bool -> Bool) ->
  MAlonzo.Code.Algebra.Structures.T_IsSelectiveMagma_450 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_2412 :: (Bool -> Bool -> Bool)
-> T_IsSelectiveMagma_450 -> T_IsPartialEquivalence_16
d_isPartialEquivalence_2412 ~Bool -> Bool -> Bool
v0 T_IsSelectiveMagma_450
v1
  = T_IsSelectiveMagma_450 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_2412 T_IsSelectiveMagma_450
v1
du_isPartialEquivalence_2412 ::
  MAlonzo.Code.Algebra.Structures.T_IsSelectiveMagma_450 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_2412 :: T_IsSelectiveMagma_450 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_2412 T_IsSelectiveMagma_450
v0
  = let v1 :: T_IsMagma_178
v1
          = T_IsSelectiveMagma_450 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_458 (T_IsSelectiveMagma_450 -> T_IsSelectiveMagma_450
forall a b. a -> b
coe T_IsSelectiveMagma_450
v0) in
    Any -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      ((T_IsEquivalence_28 -> T_IsPartialEquivalence_16) -> Any -> Any
forall a b. a -> b
coe
         T_IsEquivalence_28 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_44
         ((T_IsMagma_178 -> T_IsEquivalence_28) -> Any -> Any
forall a b. a -> b
coe T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186 (T_IsMagma_178 -> Any
forall a b. a -> b
coe T_IsMagma_178
v1)))
-- Data.Bool.Properties._.IsSelectiveMagma.refl
d_refl_2414 ::
  MAlonzo.Code.Algebra.Structures.T_IsSelectiveMagma_450 ->
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_refl_2414 :: T_IsSelectiveMagma_450 -> Bool -> T__'8801'__12
d_refl_2414 = T_IsSelectiveMagma_450 -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsSelectiveMagma.reflexive
d_reflexive_2416 ::
  (Bool -> Bool -> Bool) ->
  MAlonzo.Code.Algebra.Structures.T_IsSelectiveMagma_450 ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_reflexive_2416 :: (Bool -> Bool -> Bool)
-> T_IsSelectiveMagma_450
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_reflexive_2416 = (Bool -> Bool -> Bool)
-> T_IsSelectiveMagma_450
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsSelectiveMagma.sel
d_sel_2418 ::
  MAlonzo.Code.Algebra.Structures.T_IsSelectiveMagma_450 ->
  Bool -> Bool -> MAlonzo.Code.Data.Sum.Base.T__'8846'__30
d_sel_2418 :: T_IsSelectiveMagma_450 -> Bool -> Bool -> T__'8846'__30
d_sel_2418 T_IsSelectiveMagma_450
v0
  = (T_IsSelectiveMagma_450 -> Any -> Any -> T__'8846'__30)
-> Any -> Bool -> Bool -> T__'8846'__30
forall a b. a -> b
coe T_IsSelectiveMagma_450 -> Any -> Any -> T__'8846'__30
MAlonzo.Code.Algebra.Structures.d_sel_460 (T_IsSelectiveMagma_450 -> Any
forall a b. a -> b
coe T_IsSelectiveMagma_450
v0)
-- Data.Bool.Properties._.IsSelectiveMagma.setoid
d_setoid_2420 ::
  (Bool -> Bool -> Bool) ->
  MAlonzo.Code.Algebra.Structures.T_IsSelectiveMagma_450 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
d_setoid_2420 :: (Bool -> Bool -> Bool) -> T_IsSelectiveMagma_450 -> T_Setoid_46
d_setoid_2420 ~Bool -> Bool -> Bool
v0 T_IsSelectiveMagma_450
v1 = T_IsSelectiveMagma_450 -> T_Setoid_46
du_setoid_2420 T_IsSelectiveMagma_450
v1
du_setoid_2420 ::
  MAlonzo.Code.Algebra.Structures.T_IsSelectiveMagma_450 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
du_setoid_2420 :: T_IsSelectiveMagma_450 -> T_Setoid_46
du_setoid_2420 T_IsSelectiveMagma_450
v0
  = (T_IsMagma_178 -> T_Setoid_46) -> Any -> T_Setoid_46
forall a b. a -> b
coe
      T_IsMagma_178 -> T_Setoid_46
MAlonzo.Code.Algebra.Structures.du_setoid_202
      ((T_IsSelectiveMagma_450 -> T_IsMagma_178) -> Any -> Any
forall a b. a -> b
coe T_IsSelectiveMagma_450 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_458 (T_IsSelectiveMagma_450 -> Any
forall a b. a -> b
coe T_IsSelectiveMagma_450
v0))
-- Data.Bool.Properties._.IsSelectiveMagma.sym
d_sym_2422 ::
  MAlonzo.Code.Algebra.Structures.T_IsSelectiveMagma_450 ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_sym_2422 :: T_IsSelectiveMagma_450
-> Bool -> Bool -> T__'8801'__12 -> T__'8801'__12
d_sym_2422 = T_IsSelectiveMagma_450
-> Bool -> Bool -> T__'8801'__12 -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsSelectiveMagma.trans
d_trans_2424 ::
  MAlonzo.Code.Algebra.Structures.T_IsSelectiveMagma_450 ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_trans_2424 :: T_IsSelectiveMagma_450
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
d_trans_2424 = T_IsSelectiveMagma_450
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsSelectiveMagma.∙-cong
d_'8729''45'cong_2426 ::
  MAlonzo.Code.Algebra.Structures.T_IsSelectiveMagma_450 ->
  Bool ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8729''45'cong_2426 :: T_IsSelectiveMagma_450
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong_2426 = T_IsSelectiveMagma_450
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsSelectiveMagma.∙-congʳ
d_'8729''45'cong'691'_2428 ::
  (Bool -> Bool -> Bool) ->
  MAlonzo.Code.Algebra.Structures.T_IsSelectiveMagma_450 ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8729''45'cong'691'_2428 :: (Bool -> Bool -> Bool)
-> T_IsSelectiveMagma_450
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong'691'_2428 = (Bool -> Bool -> Bool)
-> T_IsSelectiveMagma_450
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsSelectiveMagma.∙-congˡ
d_'8729''45'cong'737'_2430 ::
  (Bool -> Bool -> Bool) ->
  MAlonzo.Code.Algebra.Structures.T_IsSelectiveMagma_450 ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8729''45'cong'737'_2430 :: (Bool -> Bool -> Bool)
-> T_IsSelectiveMagma_450
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong'737'_2430 = (Bool -> Bool -> Bool)
-> T_IsSelectiveMagma_450
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsSemigroup.assoc
d_assoc_2434 ::
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_488 ->
  Bool ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_assoc_2434 :: T_IsSemigroup_488 -> Bool -> Bool -> Bool -> T__'8801'__12
d_assoc_2434 = T_IsSemigroup_488 -> Bool -> Bool -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsSemigroup.isEquivalence
d_isEquivalence_2436 ::
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_488 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
d_isEquivalence_2436 :: T_IsSemigroup_488 -> T_IsEquivalence_28
d_isEquivalence_2436 T_IsSemigroup_488
v0
  = (T_IsMagma_178 -> T_IsEquivalence_28) -> Any -> T_IsEquivalence_28
forall a b. a -> b
coe
      T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186
      ((T_IsSemigroup_488 -> T_IsMagma_178) -> Any -> Any
forall a b. a -> b
coe T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496 (T_IsSemigroup_488 -> Any
forall a b. a -> b
coe T_IsSemigroup_488
v0))
-- Data.Bool.Properties._.IsSemigroup.isMagma
d_isMagma_2438 ::
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_488 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_178
d_isMagma_2438 :: T_IsSemigroup_488 -> T_IsMagma_178
d_isMagma_2438 T_IsSemigroup_488
v0
  = (T_IsSemigroup_488 -> T_IsMagma_178) -> Any -> T_IsMagma_178
forall a b. a -> b
coe T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496 (T_IsSemigroup_488 -> Any
forall a b. a -> b
coe T_IsSemigroup_488
v0)
-- Data.Bool.Properties._.IsSemigroup.isPartialEquivalence
d_isPartialEquivalence_2440 ::
  (Bool -> Bool -> Bool) ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_488 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_2440 :: (Bool -> Bool -> Bool)
-> T_IsSemigroup_488 -> T_IsPartialEquivalence_16
d_isPartialEquivalence_2440 ~Bool -> Bool -> Bool
v0 T_IsSemigroup_488
v1
  = T_IsSemigroup_488 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_2440 T_IsSemigroup_488
v1
du_isPartialEquivalence_2440 ::
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_488 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_2440 :: T_IsSemigroup_488 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_2440 T_IsSemigroup_488
v0
  = let v1 :: T_IsMagma_178
v1
          = T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496 (T_IsSemigroup_488 -> T_IsSemigroup_488
forall a b. a -> b
coe T_IsSemigroup_488
v0) in
    Any -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      ((T_IsEquivalence_28 -> T_IsPartialEquivalence_16) -> Any -> Any
forall a b. a -> b
coe
         T_IsEquivalence_28 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_44
         ((T_IsMagma_178 -> T_IsEquivalence_28) -> Any -> Any
forall a b. a -> b
coe T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186 (T_IsMagma_178 -> Any
forall a b. a -> b
coe T_IsMagma_178
v1)))
-- Data.Bool.Properties._.IsSemigroup.refl
d_refl_2442 ::
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_488 ->
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_refl_2442 :: T_IsSemigroup_488 -> Bool -> T__'8801'__12
d_refl_2442 = T_IsSemigroup_488 -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsSemigroup.reflexive
d_reflexive_2444 ::
  (Bool -> Bool -> Bool) ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_488 ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_reflexive_2444 :: (Bool -> Bool -> Bool)
-> T_IsSemigroup_488
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_reflexive_2444 = (Bool -> Bool -> Bool)
-> T_IsSemigroup_488
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsSemigroup.setoid
d_setoid_2446 ::
  (Bool -> Bool -> Bool) ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_488 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
d_setoid_2446 :: (Bool -> Bool -> Bool) -> T_IsSemigroup_488 -> T_Setoid_46
d_setoid_2446 ~Bool -> Bool -> Bool
v0 T_IsSemigroup_488
v1 = T_IsSemigroup_488 -> T_Setoid_46
du_setoid_2446 T_IsSemigroup_488
v1
du_setoid_2446 ::
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_488 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
du_setoid_2446 :: T_IsSemigroup_488 -> T_Setoid_46
du_setoid_2446 T_IsSemigroup_488
v0
  = (T_IsMagma_178 -> T_Setoid_46) -> Any -> T_Setoid_46
forall a b. a -> b
coe
      T_IsMagma_178 -> T_Setoid_46
MAlonzo.Code.Algebra.Structures.du_setoid_202
      ((T_IsSemigroup_488 -> T_IsMagma_178) -> Any -> Any
forall a b. a -> b
coe T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496 (T_IsSemigroup_488 -> Any
forall a b. a -> b
coe T_IsSemigroup_488
v0))
-- Data.Bool.Properties._.IsSemigroup.sym
d_sym_2448 ::
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_488 ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_sym_2448 :: T_IsSemigroup_488 -> Bool -> Bool -> T__'8801'__12 -> T__'8801'__12
d_sym_2448 = T_IsSemigroup_488 -> Bool -> Bool -> T__'8801'__12 -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsSemigroup.trans
d_trans_2450 ::
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_488 ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_trans_2450 :: T_IsSemigroup_488
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
d_trans_2450 = T_IsSemigroup_488
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsSemigroup.∙-cong
d_'8729''45'cong_2452 ::
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_488 ->
  Bool ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8729''45'cong_2452 :: T_IsSemigroup_488
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong_2452 = T_IsSemigroup_488
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsSemigroup.∙-congʳ
d_'8729''45'cong'691'_2454 ::
  (Bool -> Bool -> Bool) ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_488 ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8729''45'cong'691'_2454 :: (Bool -> Bool -> Bool)
-> T_IsSemigroup_488
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong'691'_2454 = (Bool -> Bool -> Bool)
-> T_IsSemigroup_488
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsSemigroup.∙-congˡ
d_'8729''45'cong'737'_2456 ::
  (Bool -> Bool -> Bool) ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_488 ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8729''45'cong'737'_2456 :: (Bool -> Bool -> Bool)
-> T_IsSemigroup_488
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong'737'_2456 = (Bool -> Bool -> Bool)
-> T_IsSemigroup_488
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsSemimedialMagma.isEquivalence
d_isEquivalence_2460 ::
  MAlonzo.Code.Algebra.Structures.T_IsSemimedialMagma_408 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
d_isEquivalence_2460 :: T_IsSemimedialMagma_408 -> T_IsEquivalence_28
d_isEquivalence_2460 T_IsSemimedialMagma_408
v0
  = (T_IsMagma_178 -> T_IsEquivalence_28) -> Any -> T_IsEquivalence_28
forall a b. a -> b
coe
      T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186
      ((T_IsSemimedialMagma_408 -> T_IsMagma_178) -> Any -> Any
forall a b. a -> b
coe T_IsSemimedialMagma_408 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_416 (T_IsSemimedialMagma_408 -> Any
forall a b. a -> b
coe T_IsSemimedialMagma_408
v0))
-- Data.Bool.Properties._.IsSemimedialMagma.isMagma
d_isMagma_2462 ::
  MAlonzo.Code.Algebra.Structures.T_IsSemimedialMagma_408 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_178
d_isMagma_2462 :: T_IsSemimedialMagma_408 -> T_IsMagma_178
d_isMagma_2462 T_IsSemimedialMagma_408
v0
  = (T_IsSemimedialMagma_408 -> T_IsMagma_178) -> Any -> T_IsMagma_178
forall a b. a -> b
coe T_IsSemimedialMagma_408 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_416 (T_IsSemimedialMagma_408 -> Any
forall a b. a -> b
coe T_IsSemimedialMagma_408
v0)
-- Data.Bool.Properties._.IsSemimedialMagma.isPartialEquivalence
d_isPartialEquivalence_2464 ::
  (Bool -> Bool -> Bool) ->
  MAlonzo.Code.Algebra.Structures.T_IsSemimedialMagma_408 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_2464 :: (Bool -> Bool -> Bool)
-> T_IsSemimedialMagma_408 -> T_IsPartialEquivalence_16
d_isPartialEquivalence_2464 ~Bool -> Bool -> Bool
v0 T_IsSemimedialMagma_408
v1
  = T_IsSemimedialMagma_408 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_2464 T_IsSemimedialMagma_408
v1
du_isPartialEquivalence_2464 ::
  MAlonzo.Code.Algebra.Structures.T_IsSemimedialMagma_408 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_2464 :: T_IsSemimedialMagma_408 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_2464 T_IsSemimedialMagma_408
v0
  = let v1 :: T_IsMagma_178
v1
          = T_IsSemimedialMagma_408 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_416 (T_IsSemimedialMagma_408 -> T_IsSemimedialMagma_408
forall a b. a -> b
coe T_IsSemimedialMagma_408
v0) in
    Any -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      ((T_IsEquivalence_28 -> T_IsPartialEquivalence_16) -> Any -> Any
forall a b. a -> b
coe
         T_IsEquivalence_28 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_44
         ((T_IsMagma_178 -> T_IsEquivalence_28) -> Any -> Any
forall a b. a -> b
coe T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186 (T_IsMagma_178 -> Any
forall a b. a -> b
coe T_IsMagma_178
v1)))
-- Data.Bool.Properties._.IsSemimedialMagma.refl
d_refl_2466 ::
  MAlonzo.Code.Algebra.Structures.T_IsSemimedialMagma_408 ->
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_refl_2466 :: T_IsSemimedialMagma_408 -> Bool -> T__'8801'__12
d_refl_2466 = T_IsSemimedialMagma_408 -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsSemimedialMagma.reflexive
d_reflexive_2468 ::
  (Bool -> Bool -> Bool) ->
  MAlonzo.Code.Algebra.Structures.T_IsSemimedialMagma_408 ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_reflexive_2468 :: (Bool -> Bool -> Bool)
-> T_IsSemimedialMagma_408
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_reflexive_2468 = (Bool -> Bool -> Bool)
-> T_IsSemimedialMagma_408
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsSemimedialMagma.semiMedial
d_semiMedial_2470 ::
  MAlonzo.Code.Algebra.Structures.T_IsSemimedialMagma_408 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_semiMedial_2470 :: T_IsSemimedialMagma_408 -> T_Σ_14
d_semiMedial_2470 T_IsSemimedialMagma_408
v0
  = (T_IsSemimedialMagma_408 -> T_Σ_14) -> Any -> T_Σ_14
forall a b. a -> b
coe T_IsSemimedialMagma_408 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_semiMedial_418 (T_IsSemimedialMagma_408 -> Any
forall a b. a -> b
coe T_IsSemimedialMagma_408
v0)
-- Data.Bool.Properties._.IsSemimedialMagma.semimedialʳ
d_semimedial'691'_2472 ::
  (Bool -> Bool -> Bool) ->
  MAlonzo.Code.Algebra.Structures.T_IsSemimedialMagma_408 ->
  Bool ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_semimedial'691'_2472 :: (Bool -> Bool -> Bool)
-> T_IsSemimedialMagma_408 -> Bool -> Bool -> Bool -> T__'8801'__12
d_semimedial'691'_2472 = (Bool -> Bool -> Bool)
-> T_IsSemimedialMagma_408 -> Bool -> Bool -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsSemimedialMagma.semimedialˡ
d_semimedial'737'_2474 ::
  (Bool -> Bool -> Bool) ->
  MAlonzo.Code.Algebra.Structures.T_IsSemimedialMagma_408 ->
  Bool ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_semimedial'737'_2474 :: (Bool -> Bool -> Bool)
-> T_IsSemimedialMagma_408 -> Bool -> Bool -> Bool -> T__'8801'__12
d_semimedial'737'_2474 = (Bool -> Bool -> Bool)
-> T_IsSemimedialMagma_408 -> Bool -> Bool -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsSemimedialMagma.setoid
d_setoid_2476 ::
  (Bool -> Bool -> Bool) ->
  MAlonzo.Code.Algebra.Structures.T_IsSemimedialMagma_408 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
d_setoid_2476 :: (Bool -> Bool -> Bool) -> T_IsSemimedialMagma_408 -> T_Setoid_46
d_setoid_2476 ~Bool -> Bool -> Bool
v0 T_IsSemimedialMagma_408
v1 = T_IsSemimedialMagma_408 -> T_Setoid_46
du_setoid_2476 T_IsSemimedialMagma_408
v1
du_setoid_2476 ::
  MAlonzo.Code.Algebra.Structures.T_IsSemimedialMagma_408 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
du_setoid_2476 :: T_IsSemimedialMagma_408 -> T_Setoid_46
du_setoid_2476 T_IsSemimedialMagma_408
v0
  = (T_IsMagma_178 -> T_Setoid_46) -> Any -> T_Setoid_46
forall a b. a -> b
coe
      T_IsMagma_178 -> T_Setoid_46
MAlonzo.Code.Algebra.Structures.du_setoid_202
      ((T_IsSemimedialMagma_408 -> T_IsMagma_178) -> Any -> Any
forall a b. a -> b
coe T_IsSemimedialMagma_408 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_416 (T_IsSemimedialMagma_408 -> Any
forall a b. a -> b
coe T_IsSemimedialMagma_408
v0))
-- Data.Bool.Properties._.IsSemimedialMagma.sym
d_sym_2478 ::
  MAlonzo.Code.Algebra.Structures.T_IsSemimedialMagma_408 ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_sym_2478 :: T_IsSemimedialMagma_408
-> Bool -> Bool -> T__'8801'__12 -> T__'8801'__12
d_sym_2478 = T_IsSemimedialMagma_408
-> Bool -> Bool -> T__'8801'__12 -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsSemimedialMagma.trans
d_trans_2480 ::
  MAlonzo.Code.Algebra.Structures.T_IsSemimedialMagma_408 ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_trans_2480 :: T_IsSemimedialMagma_408
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
d_trans_2480 = T_IsSemimedialMagma_408
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsSemimedialMagma.∙-cong
d_'8729''45'cong_2482 ::
  MAlonzo.Code.Algebra.Structures.T_IsSemimedialMagma_408 ->
  Bool ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8729''45'cong_2482 :: T_IsSemimedialMagma_408
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong_2482 = T_IsSemimedialMagma_408
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsSemimedialMagma.∙-congʳ
d_'8729''45'cong'691'_2484 ::
  (Bool -> Bool -> Bool) ->
  MAlonzo.Code.Algebra.Structures.T_IsSemimedialMagma_408 ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8729''45'cong'691'_2484 :: (Bool -> Bool -> Bool)
-> T_IsSemimedialMagma_408
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong'691'_2484 = (Bool -> Bool -> Bool)
-> T_IsSemimedialMagma_408
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsSemimedialMagma.∙-congˡ
d_'8729''45'cong'737'_2486 ::
  (Bool -> Bool -> Bool) ->
  MAlonzo.Code.Algebra.Structures.T_IsSemimedialMagma_408 ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8729''45'cong'737'_2486 :: (Bool -> Bool -> Bool)
-> T_IsSemimedialMagma_408
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong'737'_2486 = (Bool -> Bool -> Bool)
-> T_IsSemimedialMagma_408
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsSemiring.*-assoc
d_'42''45'assoc_2490 ::
  MAlonzo.Code.Algebra.Structures.T_IsSemiring_1640 ->
  Bool ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'42''45'assoc_2490 :: T_IsSemiring_1640 -> Bool -> Bool -> Bool -> T__'8801'__12
d_'42''45'assoc_2490 = T_IsSemiring_1640 -> Bool -> Bool -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsSemiring.*-cong
d_'42''45'cong_2492 ::
  MAlonzo.Code.Algebra.Structures.T_IsSemiring_1640 ->
  Bool ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'42''45'cong_2492 :: T_IsSemiring_1640
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
d_'42''45'cong_2492 = T_IsSemiring_1640
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsSemiring.∙-congʳ
d_'8729''45'cong'691'_2494 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsSemiring_1640 ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8729''45'cong'691'_2494 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> T_IsSemiring_1640
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong'691'_2494 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> T_IsSemiring_1640
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsSemiring.∙-congˡ
d_'8729''45'cong'737'_2496 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsSemiring_1640 ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8729''45'cong'737'_2496 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> T_IsSemiring_1640
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong'737'_2496 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> T_IsSemiring_1640
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsSemiring.*-identity
d_'42''45'identity_2498 ::
  MAlonzo.Code.Algebra.Structures.T_IsSemiring_1640 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'42''45'identity_2498 :: T_IsSemiring_1640 -> T_Σ_14
d_'42''45'identity_2498 T_IsSemiring_1640
v0
  = (T_IsSemiringWithoutAnnihilatingZero_1536 -> T_Σ_14)
-> Any -> T_Σ_14
forall a b. a -> b
coe
      T_IsSemiringWithoutAnnihilatingZero_1536 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_'42''45'identity_1562
      ((T_IsSemiring_1640 -> T_IsSemiringWithoutAnnihilatingZero_1536)
-> Any -> Any
forall a b. a -> b
coe
         T_IsSemiring_1640 -> T_IsSemiringWithoutAnnihilatingZero_1536
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1654
         (T_IsSemiring_1640 -> Any
forall a b. a -> b
coe T_IsSemiring_1640
v0))
-- Data.Bool.Properties._.IsSemiring.identityʳ
d_identity'691'_2500 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsSemiring_1640 ->
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_identity'691'_2500 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> T_IsSemiring_1640
-> Bool
-> T__'8801'__12
d_identity'691'_2500 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> T_IsSemiring_1640
-> Bool
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsSemiring.identityˡ
d_identity'737'_2502 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsSemiring_1640 ->
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_identity'737'_2502 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> T_IsSemiring_1640
-> Bool
-> T__'8801'__12
d_identity'737'_2502 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> T_IsSemiring_1640
-> Bool
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsSemiring.*-isMagma
d_'42''45'isMagma_2504 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsSemiring_1640 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_178
d_'42''45'isMagma_2504 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> T_IsSemiring_1640
-> T_IsMagma_178
d_'42''45'isMagma_2504 ~Bool -> Bool -> Bool
v0 ~Bool -> Bool -> Bool
v1 ~Bool
v2 ~Bool
v3 T_IsSemiring_1640
v4
  = T_IsSemiring_1640 -> T_IsMagma_178
du_'42''45'isMagma_2504 T_IsSemiring_1640
v4
du_'42''45'isMagma_2504 ::
  MAlonzo.Code.Algebra.Structures.T_IsSemiring_1640 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_178
du_'42''45'isMagma_2504 :: T_IsSemiring_1640 -> T_IsMagma_178
du_'42''45'isMagma_2504 T_IsSemiring_1640
v0
  = (T_IsSemiringWithoutAnnihilatingZero_1536 -> T_IsMagma_178)
-> Any -> T_IsMagma_178
forall a b. a -> b
coe
      T_IsSemiringWithoutAnnihilatingZero_1536 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.du_'42''45'isMagma_1614
      ((T_IsSemiring_1640 -> T_IsSemiringWithoutAnnihilatingZero_1536)
-> Any -> Any
forall a b. a -> b
coe
         T_IsSemiring_1640 -> T_IsSemiringWithoutAnnihilatingZero_1536
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1654
         (T_IsSemiring_1640 -> Any
forall a b. a -> b
coe T_IsSemiring_1640
v0))
-- Data.Bool.Properties._.IsSemiring.*-isMonoid
d_'42''45'isMonoid_2506 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsSemiring_1640 ->
  MAlonzo.Code.Algebra.Structures.T_IsMonoid_712
d_'42''45'isMonoid_2506 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> T_IsSemiring_1640
-> T_IsMonoid_712
d_'42''45'isMonoid_2506 ~Bool -> Bool -> Bool
v0 ~Bool -> Bool -> Bool
v1 ~Bool
v2 ~Bool
v3 T_IsSemiring_1640
v4
  = T_IsSemiring_1640 -> T_IsMonoid_712
du_'42''45'isMonoid_2506 T_IsSemiring_1640
v4
du_'42''45'isMonoid_2506 ::
  MAlonzo.Code.Algebra.Structures.T_IsSemiring_1640 ->
  MAlonzo.Code.Algebra.Structures.T_IsMonoid_712
du_'42''45'isMonoid_2506 :: T_IsSemiring_1640 -> T_IsMonoid_712
du_'42''45'isMonoid_2506 T_IsSemiring_1640
v0
  = (T_IsSemiringWithoutAnnihilatingZero_1536 -> T_IsMonoid_712)
-> Any -> T_IsMonoid_712
forall a b. a -> b
coe
      T_IsSemiringWithoutAnnihilatingZero_1536 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.du_'42''45'isMonoid_1618
      ((T_IsSemiring_1640 -> T_IsSemiringWithoutAnnihilatingZero_1536)
-> Any -> Any
forall a b. a -> b
coe
         T_IsSemiring_1640 -> T_IsSemiringWithoutAnnihilatingZero_1536
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1654
         (T_IsSemiring_1640 -> Any
forall a b. a -> b
coe T_IsSemiring_1640
v0))
-- Data.Bool.Properties._.IsSemiring.*-isSemigroup
d_'42''45'isSemigroup_2508 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsSemiring_1640 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_488
d_'42''45'isSemigroup_2508 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> T_IsSemiring_1640
-> T_IsSemigroup_488
d_'42''45'isSemigroup_2508 ~Bool -> Bool -> Bool
v0 ~Bool -> Bool -> Bool
v1 ~Bool
v2 ~Bool
v3 T_IsSemiring_1640
v4
  = T_IsSemiring_1640 -> T_IsSemigroup_488
du_'42''45'isSemigroup_2508 T_IsSemiring_1640
v4
du_'42''45'isSemigroup_2508 ::
  MAlonzo.Code.Algebra.Structures.T_IsSemiring_1640 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_488
du_'42''45'isSemigroup_2508 :: T_IsSemiring_1640 -> T_IsSemigroup_488
du_'42''45'isSemigroup_2508 T_IsSemiring_1640
v0
  = (T_IsSemiringWithoutAnnihilatingZero_1536 -> T_IsSemigroup_488)
-> Any -> T_IsSemigroup_488
forall a b. a -> b
coe
      T_IsSemiringWithoutAnnihilatingZero_1536 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.du_'42''45'isSemigroup_1616
      ((T_IsSemiring_1640 -> T_IsSemiringWithoutAnnihilatingZero_1536)
-> Any -> Any
forall a b. a -> b
coe
         T_IsSemiring_1640 -> T_IsSemiringWithoutAnnihilatingZero_1536
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1654
         (T_IsSemiring_1640 -> Any
forall a b. a -> b
coe T_IsSemiring_1640
v0))
-- Data.Bool.Properties._.IsSemiring.assoc
d_assoc_2510 ::
  MAlonzo.Code.Algebra.Structures.T_IsSemiring_1640 ->
  Bool ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_assoc_2510 :: T_IsSemiring_1640 -> Bool -> Bool -> Bool -> T__'8801'__12
d_assoc_2510 = T_IsSemiring_1640 -> Bool -> Bool -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsSemiring.comm
d_comm_2512 ::
  MAlonzo.Code.Algebra.Structures.T_IsSemiring_1640 ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_comm_2512 :: T_IsSemiring_1640 -> Bool -> Bool -> T__'8801'__12
d_comm_2512 = T_IsSemiring_1640 -> Bool -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsSemiring.∙-cong
d_'8729''45'cong_2514 ::
  MAlonzo.Code.Algebra.Structures.T_IsSemiring_1640 ->
  Bool ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8729''45'cong_2514 :: T_IsSemiring_1640
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong_2514 = T_IsSemiring_1640
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsSemiring.∙-congʳ
d_'8729''45'cong'691'_2516 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsSemiring_1640 ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8729''45'cong'691'_2516 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> T_IsSemiring_1640
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong'691'_2516 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> T_IsSemiring_1640
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsSemiring.∙-congˡ
d_'8729''45'cong'737'_2518 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsSemiring_1640 ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8729''45'cong'737'_2518 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> T_IsSemiring_1640
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong'737'_2518 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> T_IsSemiring_1640
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsSemiring.identity
d_identity_2520 ::
  MAlonzo.Code.Algebra.Structures.T_IsSemiring_1640 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_identity_2520 :: T_IsSemiring_1640 -> T_Σ_14
d_identity_2520 T_IsSemiring_1640
v0
  = (T_IsMonoid_712 -> T_Σ_14) -> Any -> T_Σ_14
forall a b. a -> b
coe
      T_IsMonoid_712 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_identity_724
      ((T_IsCommutativeMonoid_764 -> T_IsMonoid_712) -> Any -> Any
forall a b. a -> b
coe
         T_IsCommutativeMonoid_764 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_774
         ((T_IsSemiringWithoutAnnihilatingZero_1536
 -> T_IsCommutativeMonoid_764)
-> Any -> Any
forall a b. a -> b
coe
            T_IsSemiringWithoutAnnihilatingZero_1536
-> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1556
            ((T_IsSemiring_1640 -> T_IsSemiringWithoutAnnihilatingZero_1536)
-> Any -> Any
forall a b. a -> b
coe
               T_IsSemiring_1640 -> T_IsSemiringWithoutAnnihilatingZero_1536
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1654
               (T_IsSemiring_1640 -> Any
forall a b. a -> b
coe T_IsSemiring_1640
v0))))
-- Data.Bool.Properties._.IsSemiring.identityʳ
d_identity'691'_2522 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsSemiring_1640 ->
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_identity'691'_2522 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> T_IsSemiring_1640
-> Bool
-> T__'8801'__12
d_identity'691'_2522 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> T_IsSemiring_1640
-> Bool
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsSemiring.identityˡ
d_identity'737'_2524 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsSemiring_1640 ->
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_identity'737'_2524 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> T_IsSemiring_1640
-> Bool
-> T__'8801'__12
d_identity'737'_2524 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> T_IsSemiring_1640
-> Bool
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsSemiring.isCommutativeMagma
d_isCommutativeMagma_2526 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsSemiring_1640 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMagma_214
d_isCommutativeMagma_2526 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> T_IsSemiring_1640
-> T_IsCommutativeMagma_214
d_isCommutativeMagma_2526 ~Bool -> Bool -> Bool
v0 ~Bool -> Bool -> Bool
v1 ~Bool
v2 ~Bool
v3 T_IsSemiring_1640
v4
  = T_IsSemiring_1640 -> T_IsCommutativeMagma_214
du_isCommutativeMagma_2526 T_IsSemiring_1640
v4
du_isCommutativeMagma_2526 ::
  MAlonzo.Code.Algebra.Structures.T_IsSemiring_1640 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMagma_214
du_isCommutativeMagma_2526 :: T_IsSemiring_1640 -> T_IsCommutativeMagma_214
du_isCommutativeMagma_2526 T_IsSemiring_1640
v0
  = let v1 :: T_IsSemiringWithoutAnnihilatingZero_1536
v1
          = T_IsSemiring_1640 -> T_IsSemiringWithoutAnnihilatingZero_1536
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1654
              (T_IsSemiring_1640 -> T_IsSemiring_1640
forall a b. a -> b
coe T_IsSemiring_1640
v0) in
    Any -> T_IsCommutativeMagma_214
forall a b. a -> b
coe
      (let v2 :: T_IsCommutativeMonoid_764
v2
             = T_IsSemiringWithoutAnnihilatingZero_1536
-> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1556
                 (T_IsSemiringWithoutAnnihilatingZero_1536
-> T_IsSemiringWithoutAnnihilatingZero_1536
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1536
v1) in
       Any -> Any
forall a b. a -> b
coe
         ((T_IsCommutativeSemigroup_568 -> T_IsCommutativeMagma_214)
-> Any -> Any
forall a b. a -> b
coe
            T_IsCommutativeSemigroup_568 -> T_IsCommutativeMagma_214
MAlonzo.Code.Algebra.Structures.du_isCommutativeMagma_606
            ((T_IsCommutativeMonoid_764 -> T_IsCommutativeSemigroup_568)
-> Any -> Any
forall a b. a -> b
coe
               T_IsCommutativeMonoid_764 -> T_IsCommutativeSemigroup_568
MAlonzo.Code.Algebra.Structures.du_isCommutativeSemigroup_814
               (T_IsCommutativeMonoid_764 -> Any
forall a b. a -> b
coe T_IsCommutativeMonoid_764
v2))))
-- Data.Bool.Properties._.IsSemiring.+-isCommutativeMonoid
d_'43''45'isCommutativeMonoid_2528 ::
  MAlonzo.Code.Algebra.Structures.T_IsSemiring_1640 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMonoid_764
d_'43''45'isCommutativeMonoid_2528 :: T_IsSemiring_1640 -> T_IsCommutativeMonoid_764
d_'43''45'isCommutativeMonoid_2528 T_IsSemiring_1640
v0
  = (T_IsSemiringWithoutAnnihilatingZero_1536
 -> T_IsCommutativeMonoid_764)
-> Any -> T_IsCommutativeMonoid_764
forall a b. a -> b
coe
      T_IsSemiringWithoutAnnihilatingZero_1536
-> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1556
      ((T_IsSemiring_1640 -> T_IsSemiringWithoutAnnihilatingZero_1536)
-> Any -> Any
forall a b. a -> b
coe
         T_IsSemiring_1640 -> T_IsSemiringWithoutAnnihilatingZero_1536
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1654
         (T_IsSemiring_1640 -> Any
forall a b. a -> b
coe T_IsSemiring_1640
v0))
-- Data.Bool.Properties._.IsSemiring.isCommutativeSemigroup
d_isCommutativeSemigroup_2530 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsSemiring_1640 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_568
d_isCommutativeSemigroup_2530 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> T_IsSemiring_1640
-> T_IsCommutativeSemigroup_568
d_isCommutativeSemigroup_2530 ~Bool -> Bool -> Bool
v0 ~Bool -> Bool -> Bool
v1 ~Bool
v2 ~Bool
v3 T_IsSemiring_1640
v4
  = T_IsSemiring_1640 -> T_IsCommutativeSemigroup_568
du_isCommutativeSemigroup_2530 T_IsSemiring_1640
v4
du_isCommutativeSemigroup_2530 ::
  MAlonzo.Code.Algebra.Structures.T_IsSemiring_1640 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_568
du_isCommutativeSemigroup_2530 :: T_IsSemiring_1640 -> T_IsCommutativeSemigroup_568
du_isCommutativeSemigroup_2530 T_IsSemiring_1640
v0
  = let v1 :: T_IsSemiringWithoutAnnihilatingZero_1536
v1
          = T_IsSemiring_1640 -> T_IsSemiringWithoutAnnihilatingZero_1536
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1654
              (T_IsSemiring_1640 -> T_IsSemiring_1640
forall a b. a -> b
coe T_IsSemiring_1640
v0) in
    Any -> T_IsCommutativeSemigroup_568
forall a b. a -> b
coe
      ((T_IsCommutativeMonoid_764 -> T_IsCommutativeSemigroup_568)
-> Any -> Any
forall a b. a -> b
coe
         T_IsCommutativeMonoid_764 -> T_IsCommutativeSemigroup_568
MAlonzo.Code.Algebra.Structures.du_isCommutativeSemigroup_814
         ((T_IsSemiringWithoutAnnihilatingZero_1536
 -> T_IsCommutativeMonoid_764)
-> Any -> Any
forall a b. a -> b
coe
            T_IsSemiringWithoutAnnihilatingZero_1536
-> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1556
            (T_IsSemiringWithoutAnnihilatingZero_1536 -> Any
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1536
v1)))
-- Data.Bool.Properties._.IsSemiring.isMagma
d_isMagma_2532 ::
  MAlonzo.Code.Algebra.Structures.T_IsSemiring_1640 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_178
d_isMagma_2532 :: T_IsSemiring_1640 -> T_IsMagma_178
d_isMagma_2532 T_IsSemiring_1640
v0
  = (T_IsSemigroup_488 -> T_IsMagma_178) -> Any -> T_IsMagma_178
forall a b. a -> b
coe
      T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496
      ((T_IsMonoid_712 -> T_IsSemigroup_488) -> Any -> Any
forall a b. a -> b
coe
         T_IsMonoid_712 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_722
         ((T_IsCommutativeMonoid_764 -> T_IsMonoid_712) -> Any -> Any
forall a b. a -> b
coe
            T_IsCommutativeMonoid_764 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_774
            ((T_IsSemiringWithoutAnnihilatingZero_1536
 -> T_IsCommutativeMonoid_764)
-> Any -> Any
forall a b. a -> b
coe
               T_IsSemiringWithoutAnnihilatingZero_1536
-> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1556
               ((T_IsSemiring_1640 -> T_IsSemiringWithoutAnnihilatingZero_1536)
-> Any -> Any
forall a b. a -> b
coe
                  T_IsSemiring_1640 -> T_IsSemiringWithoutAnnihilatingZero_1536
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1654
                  (T_IsSemiring_1640 -> Any
forall a b. a -> b
coe T_IsSemiring_1640
v0)))))
-- Data.Bool.Properties._.IsSemiring.isMonoid
d_isMonoid_2534 ::
  MAlonzo.Code.Algebra.Structures.T_IsSemiring_1640 ->
  MAlonzo.Code.Algebra.Structures.T_IsMonoid_712
d_isMonoid_2534 :: T_IsSemiring_1640 -> T_IsMonoid_712
d_isMonoid_2534 T_IsSemiring_1640
v0
  = (T_IsCommutativeMonoid_764 -> T_IsMonoid_712)
-> Any -> T_IsMonoid_712
forall a b. a -> b
coe
      T_IsCommutativeMonoid_764 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_774
      ((T_IsSemiringWithoutAnnihilatingZero_1536
 -> T_IsCommutativeMonoid_764)
-> Any -> Any
forall a b. a -> b
coe
         T_IsSemiringWithoutAnnihilatingZero_1536
-> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1556
         ((T_IsSemiring_1640 -> T_IsSemiringWithoutAnnihilatingZero_1536)
-> Any -> Any
forall a b. a -> b
coe
            T_IsSemiring_1640 -> T_IsSemiringWithoutAnnihilatingZero_1536
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1654
            (T_IsSemiring_1640 -> Any
forall a b. a -> b
coe T_IsSemiring_1640
v0)))
-- Data.Bool.Properties._.IsSemiring.isSemigroup
d_isSemigroup_2536 ::
  MAlonzo.Code.Algebra.Structures.T_IsSemiring_1640 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_488
d_isSemigroup_2536 :: T_IsSemiring_1640 -> T_IsSemigroup_488
d_isSemigroup_2536 T_IsSemiring_1640
v0
  = (T_IsMonoid_712 -> T_IsSemigroup_488) -> Any -> T_IsSemigroup_488
forall a b. a -> b
coe
      T_IsMonoid_712 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_722
      ((T_IsCommutativeMonoid_764 -> T_IsMonoid_712) -> Any -> Any
forall a b. a -> b
coe
         T_IsCommutativeMonoid_764 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_774
         ((T_IsSemiringWithoutAnnihilatingZero_1536
 -> T_IsCommutativeMonoid_764)
-> Any -> Any
forall a b. a -> b
coe
            T_IsSemiringWithoutAnnihilatingZero_1536
-> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1556
            ((T_IsSemiring_1640 -> T_IsSemiringWithoutAnnihilatingZero_1536)
-> Any -> Any
forall a b. a -> b
coe
               T_IsSemiring_1640 -> T_IsSemiringWithoutAnnihilatingZero_1536
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1654
               (T_IsSemiring_1640 -> Any
forall a b. a -> b
coe T_IsSemiring_1640
v0))))
-- Data.Bool.Properties._.IsSemiring.isUnitalMagma
d_isUnitalMagma_2538 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsSemiring_1640 ->
  MAlonzo.Code.Algebra.Structures.T_IsUnitalMagma_666
d_isUnitalMagma_2538 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> T_IsSemiring_1640
-> T_IsUnitalMagma_666
d_isUnitalMagma_2538 ~Bool -> Bool -> Bool
v0 ~Bool -> Bool -> Bool
v1 ~Bool
v2 ~Bool
v3 T_IsSemiring_1640
v4 = T_IsSemiring_1640 -> T_IsUnitalMagma_666
du_isUnitalMagma_2538 T_IsSemiring_1640
v4
du_isUnitalMagma_2538 ::
  MAlonzo.Code.Algebra.Structures.T_IsSemiring_1640 ->
  MAlonzo.Code.Algebra.Structures.T_IsUnitalMagma_666
du_isUnitalMagma_2538 :: T_IsSemiring_1640 -> T_IsUnitalMagma_666
du_isUnitalMagma_2538 T_IsSemiring_1640
v0
  = let v1 :: T_IsSemiringWithoutAnnihilatingZero_1536
v1
          = T_IsSemiring_1640 -> T_IsSemiringWithoutAnnihilatingZero_1536
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1654
              (T_IsSemiring_1640 -> T_IsSemiring_1640
forall a b. a -> b
coe T_IsSemiring_1640
v0) in
    Any -> T_IsUnitalMagma_666
forall a b. a -> b
coe
      (let v2 :: T_IsCommutativeMonoid_764
v2
             = T_IsSemiringWithoutAnnihilatingZero_1536
-> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1556
                 (T_IsSemiringWithoutAnnihilatingZero_1536
-> T_IsSemiringWithoutAnnihilatingZero_1536
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1536
v1) in
       Any -> Any
forall a b. a -> b
coe
         ((T_IsMonoid_712 -> T_IsUnitalMagma_666) -> Any -> Any
forall a b. a -> b
coe
            T_IsMonoid_712 -> T_IsUnitalMagma_666
MAlonzo.Code.Algebra.Structures.du_isUnitalMagma_756
            ((T_IsCommutativeMonoid_764 -> T_IsMonoid_712) -> Any -> Any
forall a b. a -> b
coe T_IsCommutativeMonoid_764 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_774 (T_IsCommutativeMonoid_764 -> Any
forall a b. a -> b
coe T_IsCommutativeMonoid_764
v2))))
-- Data.Bool.Properties._.IsSemiring.distrib
d_distrib_2540 ::
  MAlonzo.Code.Algebra.Structures.T_IsSemiring_1640 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_distrib_2540 :: T_IsSemiring_1640 -> T_Σ_14
d_distrib_2540 T_IsSemiring_1640
v0
  = (T_IsSemiringWithoutAnnihilatingZero_1536 -> T_Σ_14)
-> Any -> T_Σ_14
forall a b. a -> b
coe
      T_IsSemiringWithoutAnnihilatingZero_1536 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_distrib_1564
      ((T_IsSemiring_1640 -> T_IsSemiringWithoutAnnihilatingZero_1536)
-> Any -> Any
forall a b. a -> b
coe
         T_IsSemiring_1640 -> T_IsSemiringWithoutAnnihilatingZero_1536
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1654
         (T_IsSemiring_1640 -> Any
forall a b. a -> b
coe T_IsSemiring_1640
v0))
-- Data.Bool.Properties._.IsSemiring.distribʳ
d_distrib'691'_2542 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsSemiring_1640 ->
  Bool ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_distrib'691'_2542 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> T_IsSemiring_1640
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
d_distrib'691'_2542 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> T_IsSemiring_1640
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsSemiring.distribˡ
d_distrib'737'_2544 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsSemiring_1640 ->
  Bool ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_distrib'737'_2544 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> T_IsSemiring_1640
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
d_distrib'737'_2544 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> T_IsSemiring_1640
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsSemiring.isEquivalence
d_isEquivalence_2546 ::
  MAlonzo.Code.Algebra.Structures.T_IsSemiring_1640 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
d_isEquivalence_2546 :: T_IsSemiring_1640 -> T_IsEquivalence_28
d_isEquivalence_2546 T_IsSemiring_1640
v0
  = (T_IsMagma_178 -> T_IsEquivalence_28) -> Any -> T_IsEquivalence_28
forall a b. a -> b
coe
      T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186
      ((T_IsSemigroup_488 -> T_IsMagma_178) -> Any -> Any
forall a b. a -> b
coe
         T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496
         ((T_IsMonoid_712 -> T_IsSemigroup_488) -> Any -> Any
forall a b. a -> b
coe
            T_IsMonoid_712 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_722
            ((T_IsCommutativeMonoid_764 -> T_IsMonoid_712) -> Any -> Any
forall a b. a -> b
coe
               T_IsCommutativeMonoid_764 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_774
               ((T_IsSemiringWithoutAnnihilatingZero_1536
 -> T_IsCommutativeMonoid_764)
-> Any -> Any
forall a b. a -> b
coe
                  T_IsSemiringWithoutAnnihilatingZero_1536
-> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1556
                  ((T_IsSemiring_1640 -> T_IsSemiringWithoutAnnihilatingZero_1536)
-> Any -> Any
forall a b. a -> b
coe
                     T_IsSemiring_1640 -> T_IsSemiringWithoutAnnihilatingZero_1536
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1654
                     (T_IsSemiring_1640 -> Any
forall a b. a -> b
coe T_IsSemiring_1640
v0))))))
-- Data.Bool.Properties._.IsSemiring.isNearSemiring
d_isNearSemiring_2548 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsSemiring_1640 ->
  MAlonzo.Code.Algebra.Structures.T_IsNearSemiring_1260
d_isNearSemiring_2548 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> T_IsSemiring_1640
-> T_IsNearSemiring_1260
d_isNearSemiring_2548 ~Bool -> Bool -> Bool
v0 ~Bool -> Bool -> Bool
v1 ~Bool
v2 ~Bool
v3 T_IsSemiring_1640
v4
  = T_IsSemiring_1640 -> T_IsNearSemiring_1260
du_isNearSemiring_2548 T_IsSemiring_1640
v4
du_isNearSemiring_2548 ::
  MAlonzo.Code.Algebra.Structures.T_IsSemiring_1640 ->
  MAlonzo.Code.Algebra.Structures.T_IsNearSemiring_1260
du_isNearSemiring_2548 :: T_IsSemiring_1640 -> T_IsNearSemiring_1260
du_isNearSemiring_2548 T_IsSemiring_1640
v0
  = (T_IsSemiringWithoutOne_1342 -> T_IsNearSemiring_1260)
-> Any -> T_IsNearSemiring_1260
forall a b. a -> b
coe
      T_IsSemiringWithoutOne_1342 -> T_IsNearSemiring_1260
MAlonzo.Code.Algebra.Structures.du_isNearSemiring_1428
      ((T_IsSemiring_1640 -> T_IsSemiringWithoutOne_1342) -> Any -> Any
forall a b. a -> b
coe
         T_IsSemiring_1640 -> T_IsSemiringWithoutOne_1342
MAlonzo.Code.Algebra.Structures.du_isSemiringWithoutOne_1730
         (T_IsSemiring_1640 -> Any
forall a b. a -> b
coe T_IsSemiring_1640
v0))
-- Data.Bool.Properties._.IsSemiring.isPartialEquivalence
d_isPartialEquivalence_2550 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsSemiring_1640 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_2550 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> T_IsSemiring_1640
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_2550 ~Bool -> Bool -> Bool
v0 ~Bool -> Bool -> Bool
v1 ~Bool
v2 ~Bool
v3 T_IsSemiring_1640
v4
  = T_IsSemiring_1640 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_2550 T_IsSemiring_1640
v4
du_isPartialEquivalence_2550 ::
  MAlonzo.Code.Algebra.Structures.T_IsSemiring_1640 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_2550 :: T_IsSemiring_1640 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_2550 T_IsSemiring_1640
v0
  = let v1 :: T_IsSemiringWithoutAnnihilatingZero_1536
v1
          = T_IsSemiring_1640 -> T_IsSemiringWithoutAnnihilatingZero_1536
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1654
              (T_IsSemiring_1640 -> T_IsSemiring_1640
forall a b. a -> b
coe T_IsSemiring_1640
v0) in
    Any -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsCommutativeMonoid_764
v2
             = T_IsSemiringWithoutAnnihilatingZero_1536
-> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1556
                 (T_IsSemiringWithoutAnnihilatingZero_1536
-> T_IsSemiringWithoutAnnihilatingZero_1536
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1536
v1) in
       Any -> Any
forall a b. a -> b
coe
         (let v3 :: T_IsMonoid_712
v3
                = T_IsCommutativeMonoid_764 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_774 (T_IsCommutativeMonoid_764 -> T_IsCommutativeMonoid_764
forall a b. a -> b
coe T_IsCommutativeMonoid_764
v2) in
          Any -> Any
forall a b. a -> b
coe
            (let v4 :: T_IsSemigroup_488
v4
                   = T_IsMonoid_712 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_722 (T_IsMonoid_712 -> T_IsMonoid_712
forall a b. a -> b
coe T_IsMonoid_712
v3) in
             Any -> Any
forall a b. a -> b
coe
               (let v5 :: T_IsMagma_178
v5 = T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496 (T_IsSemigroup_488 -> T_IsSemigroup_488
forall a b. a -> b
coe T_IsSemigroup_488
v4) in
                Any -> Any
forall a b. a -> b
coe
                  ((T_IsEquivalence_28 -> T_IsPartialEquivalence_16) -> Any -> Any
forall a b. a -> b
coe
                     T_IsEquivalence_28 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_44
                     ((T_IsMagma_178 -> T_IsEquivalence_28) -> Any -> Any
forall a b. a -> b
coe
                        T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186 (T_IsMagma_178 -> Any
forall a b. a -> b
coe T_IsMagma_178
v5)))))))
-- Data.Bool.Properties._.IsSemiring.isSemiringWithoutAnnihilatingZero
d_isSemiringWithoutAnnihilatingZero_2552 ::
  MAlonzo.Code.Algebra.Structures.T_IsSemiring_1640 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutAnnihilatingZero_1536
d_isSemiringWithoutAnnihilatingZero_2552 :: T_IsSemiring_1640 -> T_IsSemiringWithoutAnnihilatingZero_1536
d_isSemiringWithoutAnnihilatingZero_2552 T_IsSemiring_1640
v0
  = (T_IsSemiring_1640 -> T_IsSemiringWithoutAnnihilatingZero_1536)
-> Any -> T_IsSemiringWithoutAnnihilatingZero_1536
forall a b. a -> b
coe
      T_IsSemiring_1640 -> T_IsSemiringWithoutAnnihilatingZero_1536
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1654
      (T_IsSemiring_1640 -> Any
forall a b. a -> b
coe T_IsSemiring_1640
v0)
-- Data.Bool.Properties._.IsSemiring.isSemiringWithoutOne
d_isSemiringWithoutOne_2554 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsSemiring_1640 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutOne_1342
d_isSemiringWithoutOne_2554 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> T_IsSemiring_1640
-> T_IsSemiringWithoutOne_1342
d_isSemiringWithoutOne_2554 Bool -> Bool -> Bool
v0 Bool -> Bool -> Bool
v1 Bool
v2 Bool
v3 T_IsSemiring_1640
v4
  = (T_IsSemiring_1640 -> T_IsSemiringWithoutOne_1342)
-> T_IsSemiring_1640 -> T_IsSemiringWithoutOne_1342
forall a b. a -> b
coe
      T_IsSemiring_1640 -> T_IsSemiringWithoutOne_1342
MAlonzo.Code.Algebra.Structures.du_isSemiringWithoutOne_1730 T_IsSemiring_1640
v4
-- Data.Bool.Properties._.IsSemiring.refl
d_refl_2556 ::
  MAlonzo.Code.Algebra.Structures.T_IsSemiring_1640 ->
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_refl_2556 :: T_IsSemiring_1640 -> Bool -> T__'8801'__12
d_refl_2556 = T_IsSemiring_1640 -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsSemiring.reflexive
d_reflexive_2558 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsSemiring_1640 ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_reflexive_2558 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> T_IsSemiring_1640
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_reflexive_2558 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> T_IsSemiring_1640
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsSemiring.setoid
d_setoid_2560 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsSemiring_1640 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
d_setoid_2560 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> T_IsSemiring_1640
-> T_Setoid_46
d_setoid_2560 ~Bool -> Bool -> Bool
v0 ~Bool -> Bool -> Bool
v1 ~Bool
v2 ~Bool
v3 T_IsSemiring_1640
v4 = T_IsSemiring_1640 -> T_Setoid_46
du_setoid_2560 T_IsSemiring_1640
v4
du_setoid_2560 ::
  MAlonzo.Code.Algebra.Structures.T_IsSemiring_1640 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
du_setoid_2560 :: T_IsSemiring_1640 -> T_Setoid_46
du_setoid_2560 T_IsSemiring_1640
v0
  = let v1 :: T_IsSemiringWithoutAnnihilatingZero_1536
v1
          = T_IsSemiring_1640 -> T_IsSemiringWithoutAnnihilatingZero_1536
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1654
              (T_IsSemiring_1640 -> T_IsSemiring_1640
forall a b. a -> b
coe T_IsSemiring_1640
v0) in
    Any -> T_Setoid_46
forall a b. a -> b
coe
      (let v2 :: T_IsCommutativeMonoid_764
v2
             = T_IsSemiringWithoutAnnihilatingZero_1536
-> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1556
                 (T_IsSemiringWithoutAnnihilatingZero_1536
-> T_IsSemiringWithoutAnnihilatingZero_1536
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1536
v1) in
       Any -> Any
forall a b. a -> b
coe
         (let v3 :: T_IsMonoid_712
v3
                = T_IsCommutativeMonoid_764 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_774 (T_IsCommutativeMonoid_764 -> T_IsCommutativeMonoid_764
forall a b. a -> b
coe T_IsCommutativeMonoid_764
v2) in
          Any -> Any
forall a b. a -> b
coe
            (let v4 :: T_IsSemigroup_488
v4
                   = T_IsMonoid_712 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_722 (T_IsMonoid_712 -> T_IsMonoid_712
forall a b. a -> b
coe T_IsMonoid_712
v3) in
             Any -> Any
forall a b. a -> b
coe
               ((T_IsMagma_178 -> T_Setoid_46) -> Any -> Any
forall a b. a -> b
coe
                  T_IsMagma_178 -> T_Setoid_46
MAlonzo.Code.Algebra.Structures.du_setoid_202
                  ((T_IsSemigroup_488 -> T_IsMagma_178) -> Any -> Any
forall a b. a -> b
coe T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496 (T_IsSemigroup_488 -> Any
forall a b. a -> b
coe T_IsSemigroup_488
v4))))))
-- Data.Bool.Properties._.IsSemiring.sym
d_sym_2562 ::
  MAlonzo.Code.Algebra.Structures.T_IsSemiring_1640 ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_sym_2562 :: T_IsSemiring_1640 -> Bool -> Bool -> T__'8801'__12 -> T__'8801'__12
d_sym_2562 = T_IsSemiring_1640 -> Bool -> Bool -> T__'8801'__12 -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsSemiring.trans
d_trans_2564 ::
  MAlonzo.Code.Algebra.Structures.T_IsSemiring_1640 ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_trans_2564 :: T_IsSemiring_1640
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
d_trans_2564 = T_IsSemiring_1640
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsSemiring.zero
d_zero_2566 ::
  MAlonzo.Code.Algebra.Structures.T_IsSemiring_1640 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_zero_2566 :: T_IsSemiring_1640 -> T_Σ_14
d_zero_2566 T_IsSemiring_1640
v0
  = (T_IsSemiring_1640 -> T_Σ_14) -> Any -> T_Σ_14
forall a b. a -> b
coe T_IsSemiring_1640 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_zero_1656 (T_IsSemiring_1640 -> Any
forall a b. a -> b
coe T_IsSemiring_1640
v0)
-- Data.Bool.Properties._.IsSemiring.zeroʳ
d_zero'691'_2568 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsSemiring_1640 ->
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_zero'691'_2568 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> T_IsSemiring_1640
-> Bool
-> T__'8801'__12
d_zero'691'_2568 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> T_IsSemiring_1640
-> Bool
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsSemiring.zeroˡ
d_zero'737'_2570 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsSemiring_1640 ->
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_zero'737'_2570 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> T_IsSemiring_1640
-> Bool
-> T__'8801'__12
d_zero'737'_2570 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> T_IsSemiring_1640
-> Bool
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsSemiringWithoutAnnihilatingZero.*-assoc
d_'42''45'assoc_2574 ::
  MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutAnnihilatingZero_1536 ->
  Bool ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'42''45'assoc_2574 :: T_IsSemiringWithoutAnnihilatingZero_1536
-> Bool -> Bool -> Bool -> T__'8801'__12
d_'42''45'assoc_2574 = T_IsSemiringWithoutAnnihilatingZero_1536
-> Bool -> Bool -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsSemiringWithoutAnnihilatingZero.*-cong
d_'42''45'cong_2576 ::
  MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutAnnihilatingZero_1536 ->
  Bool ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'42''45'cong_2576 :: T_IsSemiringWithoutAnnihilatingZero_1536
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
d_'42''45'cong_2576 = T_IsSemiringWithoutAnnihilatingZero_1536
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsSemiringWithoutAnnihilatingZero.∙-congʳ
d_'8729''45'cong'691'_2578 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutAnnihilatingZero_1536 ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8729''45'cong'691'_2578 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> T_IsSemiringWithoutAnnihilatingZero_1536
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong'691'_2578 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> T_IsSemiringWithoutAnnihilatingZero_1536
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsSemiringWithoutAnnihilatingZero.∙-congˡ
d_'8729''45'cong'737'_2580 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutAnnihilatingZero_1536 ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8729''45'cong'737'_2580 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> T_IsSemiringWithoutAnnihilatingZero_1536
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong'737'_2580 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> T_IsSemiringWithoutAnnihilatingZero_1536
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsSemiringWithoutAnnihilatingZero.*-identity
d_'42''45'identity_2582 ::
  MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutAnnihilatingZero_1536 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'42''45'identity_2582 :: T_IsSemiringWithoutAnnihilatingZero_1536 -> T_Σ_14
d_'42''45'identity_2582 T_IsSemiringWithoutAnnihilatingZero_1536
v0
  = (T_IsSemiringWithoutAnnihilatingZero_1536 -> T_Σ_14)
-> Any -> T_Σ_14
forall a b. a -> b
coe
      T_IsSemiringWithoutAnnihilatingZero_1536 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_'42''45'identity_1562 (T_IsSemiringWithoutAnnihilatingZero_1536 -> Any
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1536
v0)
-- Data.Bool.Properties._.IsSemiringWithoutAnnihilatingZero.identityʳ
d_identity'691'_2584 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutAnnihilatingZero_1536 ->
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_identity'691'_2584 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> T_IsSemiringWithoutAnnihilatingZero_1536
-> Bool
-> T__'8801'__12
d_identity'691'_2584 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> T_IsSemiringWithoutAnnihilatingZero_1536
-> Bool
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsSemiringWithoutAnnihilatingZero.identityˡ
d_identity'737'_2586 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutAnnihilatingZero_1536 ->
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_identity'737'_2586 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> T_IsSemiringWithoutAnnihilatingZero_1536
-> Bool
-> T__'8801'__12
d_identity'737'_2586 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> T_IsSemiringWithoutAnnihilatingZero_1536
-> Bool
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsSemiringWithoutAnnihilatingZero.*-isMagma
d_'42''45'isMagma_2588 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutAnnihilatingZero_1536 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_178
d_'42''45'isMagma_2588 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> T_IsSemiringWithoutAnnihilatingZero_1536
-> T_IsMagma_178
d_'42''45'isMagma_2588 Bool -> Bool -> Bool
v0 Bool -> Bool -> Bool
v1 Bool
v2 Bool
v3 T_IsSemiringWithoutAnnihilatingZero_1536
v4
  = (T_IsSemiringWithoutAnnihilatingZero_1536 -> T_IsMagma_178)
-> T_IsSemiringWithoutAnnihilatingZero_1536 -> T_IsMagma_178
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1536 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.du_'42''45'isMagma_1614 T_IsSemiringWithoutAnnihilatingZero_1536
v4
-- Data.Bool.Properties._.IsSemiringWithoutAnnihilatingZero.*-isMonoid
d_'42''45'isMonoid_2590 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutAnnihilatingZero_1536 ->
  MAlonzo.Code.Algebra.Structures.T_IsMonoid_712
d_'42''45'isMonoid_2590 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> T_IsSemiringWithoutAnnihilatingZero_1536
-> T_IsMonoid_712
d_'42''45'isMonoid_2590 Bool -> Bool -> Bool
v0 Bool -> Bool -> Bool
v1 Bool
v2 Bool
v3 T_IsSemiringWithoutAnnihilatingZero_1536
v4
  = (T_IsSemiringWithoutAnnihilatingZero_1536 -> T_IsMonoid_712)
-> T_IsSemiringWithoutAnnihilatingZero_1536 -> T_IsMonoid_712
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1536 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.du_'42''45'isMonoid_1618 T_IsSemiringWithoutAnnihilatingZero_1536
v4
-- Data.Bool.Properties._.IsSemiringWithoutAnnihilatingZero.*-isSemigroup
d_'42''45'isSemigroup_2592 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutAnnihilatingZero_1536 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_488
d_'42''45'isSemigroup_2592 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> T_IsSemiringWithoutAnnihilatingZero_1536
-> T_IsSemigroup_488
d_'42''45'isSemigroup_2592 Bool -> Bool -> Bool
v0 Bool -> Bool -> Bool
v1 Bool
v2 Bool
v3 T_IsSemiringWithoutAnnihilatingZero_1536
v4
  = (T_IsSemiringWithoutAnnihilatingZero_1536 -> T_IsSemigroup_488)
-> T_IsSemiringWithoutAnnihilatingZero_1536 -> T_IsSemigroup_488
forall a b. a -> b
coe
      T_IsSemiringWithoutAnnihilatingZero_1536 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.du_'42''45'isSemigroup_1616 T_IsSemiringWithoutAnnihilatingZero_1536
v4
-- Data.Bool.Properties._.IsSemiringWithoutAnnihilatingZero.assoc
d_assoc_2594 ::
  MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutAnnihilatingZero_1536 ->
  Bool ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_assoc_2594 :: T_IsSemiringWithoutAnnihilatingZero_1536
-> Bool -> Bool -> Bool -> T__'8801'__12
d_assoc_2594 = T_IsSemiringWithoutAnnihilatingZero_1536
-> Bool -> Bool -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsSemiringWithoutAnnihilatingZero.comm
d_comm_2596 ::
  MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutAnnihilatingZero_1536 ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_comm_2596 :: T_IsSemiringWithoutAnnihilatingZero_1536
-> Bool -> Bool -> T__'8801'__12
d_comm_2596 = T_IsSemiringWithoutAnnihilatingZero_1536
-> Bool -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsSemiringWithoutAnnihilatingZero.∙-cong
d_'8729''45'cong_2598 ::
  MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutAnnihilatingZero_1536 ->
  Bool ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8729''45'cong_2598 :: T_IsSemiringWithoutAnnihilatingZero_1536
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong_2598 = T_IsSemiringWithoutAnnihilatingZero_1536
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsSemiringWithoutAnnihilatingZero.∙-congʳ
d_'8729''45'cong'691'_2600 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutAnnihilatingZero_1536 ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8729''45'cong'691'_2600 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> T_IsSemiringWithoutAnnihilatingZero_1536
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong'691'_2600 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> T_IsSemiringWithoutAnnihilatingZero_1536
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsSemiringWithoutAnnihilatingZero.∙-congˡ
d_'8729''45'cong'737'_2602 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutAnnihilatingZero_1536 ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8729''45'cong'737'_2602 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> T_IsSemiringWithoutAnnihilatingZero_1536
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong'737'_2602 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> T_IsSemiringWithoutAnnihilatingZero_1536
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsSemiringWithoutAnnihilatingZero.identity
d_identity_2604 ::
  MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutAnnihilatingZero_1536 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_identity_2604 :: T_IsSemiringWithoutAnnihilatingZero_1536 -> T_Σ_14
d_identity_2604 T_IsSemiringWithoutAnnihilatingZero_1536
v0
  = (T_IsMonoid_712 -> T_Σ_14) -> Any -> T_Σ_14
forall a b. a -> b
coe
      T_IsMonoid_712 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_identity_724
      ((T_IsCommutativeMonoid_764 -> T_IsMonoid_712) -> Any -> Any
forall a b. a -> b
coe
         T_IsCommutativeMonoid_764 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_774
         ((T_IsSemiringWithoutAnnihilatingZero_1536
 -> T_IsCommutativeMonoid_764)
-> Any -> Any
forall a b. a -> b
coe
            T_IsSemiringWithoutAnnihilatingZero_1536
-> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1556
            (T_IsSemiringWithoutAnnihilatingZero_1536 -> Any
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1536
v0)))
-- Data.Bool.Properties._.IsSemiringWithoutAnnihilatingZero.identityʳ
d_identity'691'_2606 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutAnnihilatingZero_1536 ->
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_identity'691'_2606 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> T_IsSemiringWithoutAnnihilatingZero_1536
-> Bool
-> T__'8801'__12
d_identity'691'_2606 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> T_IsSemiringWithoutAnnihilatingZero_1536
-> Bool
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsSemiringWithoutAnnihilatingZero.identityˡ
d_identity'737'_2608 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutAnnihilatingZero_1536 ->
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_identity'737'_2608 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> T_IsSemiringWithoutAnnihilatingZero_1536
-> Bool
-> T__'8801'__12
d_identity'737'_2608 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> T_IsSemiringWithoutAnnihilatingZero_1536
-> Bool
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsSemiringWithoutAnnihilatingZero.isCommutativeMagma
d_isCommutativeMagma_2610 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutAnnihilatingZero_1536 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMagma_214
d_isCommutativeMagma_2610 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> T_IsSemiringWithoutAnnihilatingZero_1536
-> T_IsCommutativeMagma_214
d_isCommutativeMagma_2610 ~Bool -> Bool -> Bool
v0 ~Bool -> Bool -> Bool
v1 ~Bool
v2 ~Bool
v3 T_IsSemiringWithoutAnnihilatingZero_1536
v4
  = T_IsSemiringWithoutAnnihilatingZero_1536
-> T_IsCommutativeMagma_214
du_isCommutativeMagma_2610 T_IsSemiringWithoutAnnihilatingZero_1536
v4
du_isCommutativeMagma_2610 ::
  MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutAnnihilatingZero_1536 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMagma_214
du_isCommutativeMagma_2610 :: T_IsSemiringWithoutAnnihilatingZero_1536
-> T_IsCommutativeMagma_214
du_isCommutativeMagma_2610 T_IsSemiringWithoutAnnihilatingZero_1536
v0
  = let v1 :: T_IsCommutativeMonoid_764
v1
          = T_IsSemiringWithoutAnnihilatingZero_1536
-> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1556
              (T_IsSemiringWithoutAnnihilatingZero_1536
-> T_IsSemiringWithoutAnnihilatingZero_1536
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1536
v0) in
    Any -> T_IsCommutativeMagma_214
forall a b. a -> b
coe
      ((T_IsCommutativeSemigroup_568 -> T_IsCommutativeMagma_214)
-> Any -> Any
forall a b. a -> b
coe
         T_IsCommutativeSemigroup_568 -> T_IsCommutativeMagma_214
MAlonzo.Code.Algebra.Structures.du_isCommutativeMagma_606
         ((T_IsCommutativeMonoid_764 -> T_IsCommutativeSemigroup_568)
-> Any -> Any
forall a b. a -> b
coe
            T_IsCommutativeMonoid_764 -> T_IsCommutativeSemigroup_568
MAlonzo.Code.Algebra.Structures.du_isCommutativeSemigroup_814
            (T_IsCommutativeMonoid_764 -> Any
forall a b. a -> b
coe T_IsCommutativeMonoid_764
v1)))
-- Data.Bool.Properties._.IsSemiringWithoutAnnihilatingZero.+-isCommutativeMonoid
d_'43''45'isCommutativeMonoid_2612 ::
  MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutAnnihilatingZero_1536 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMonoid_764
d_'43''45'isCommutativeMonoid_2612 :: T_IsSemiringWithoutAnnihilatingZero_1536
-> T_IsCommutativeMonoid_764
d_'43''45'isCommutativeMonoid_2612 T_IsSemiringWithoutAnnihilatingZero_1536
v0
  = (T_IsSemiringWithoutAnnihilatingZero_1536
 -> T_IsCommutativeMonoid_764)
-> Any -> T_IsCommutativeMonoid_764
forall a b. a -> b
coe
      T_IsSemiringWithoutAnnihilatingZero_1536
-> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1556
      (T_IsSemiringWithoutAnnihilatingZero_1536 -> Any
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1536
v0)
-- Data.Bool.Properties._.IsSemiringWithoutAnnihilatingZero.isCommutativeSemigroup
d_isCommutativeSemigroup_2614 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutAnnihilatingZero_1536 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_568
d_isCommutativeSemigroup_2614 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> T_IsSemiringWithoutAnnihilatingZero_1536
-> T_IsCommutativeSemigroup_568
d_isCommutativeSemigroup_2614 ~Bool -> Bool -> Bool
v0 ~Bool -> Bool -> Bool
v1 ~Bool
v2 ~Bool
v3 T_IsSemiringWithoutAnnihilatingZero_1536
v4
  = T_IsSemiringWithoutAnnihilatingZero_1536
-> T_IsCommutativeSemigroup_568
du_isCommutativeSemigroup_2614 T_IsSemiringWithoutAnnihilatingZero_1536
v4
du_isCommutativeSemigroup_2614 ::
  MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutAnnihilatingZero_1536 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_568
du_isCommutativeSemigroup_2614 :: T_IsSemiringWithoutAnnihilatingZero_1536
-> T_IsCommutativeSemigroup_568
du_isCommutativeSemigroup_2614 T_IsSemiringWithoutAnnihilatingZero_1536
v0
  = (T_IsCommutativeMonoid_764 -> T_IsCommutativeSemigroup_568)
-> Any -> T_IsCommutativeSemigroup_568
forall a b. a -> b
coe
      T_IsCommutativeMonoid_764 -> T_IsCommutativeSemigroup_568
MAlonzo.Code.Algebra.Structures.du_isCommutativeSemigroup_814
      ((T_IsSemiringWithoutAnnihilatingZero_1536
 -> T_IsCommutativeMonoid_764)
-> Any -> Any
forall a b. a -> b
coe
         T_IsSemiringWithoutAnnihilatingZero_1536
-> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1556
         (T_IsSemiringWithoutAnnihilatingZero_1536 -> Any
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1536
v0))
-- Data.Bool.Properties._.IsSemiringWithoutAnnihilatingZero.isMagma
d_isMagma_2616 ::
  MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutAnnihilatingZero_1536 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_178
d_isMagma_2616 :: T_IsSemiringWithoutAnnihilatingZero_1536 -> T_IsMagma_178
d_isMagma_2616 T_IsSemiringWithoutAnnihilatingZero_1536
v0
  = (T_IsSemigroup_488 -> T_IsMagma_178) -> Any -> T_IsMagma_178
forall a b. a -> b
coe
      T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496
      ((T_IsMonoid_712 -> T_IsSemigroup_488) -> Any -> Any
forall a b. a -> b
coe
         T_IsMonoid_712 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_722
         ((T_IsCommutativeMonoid_764 -> T_IsMonoid_712) -> Any -> Any
forall a b. a -> b
coe
            T_IsCommutativeMonoid_764 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_774
            ((T_IsSemiringWithoutAnnihilatingZero_1536
 -> T_IsCommutativeMonoid_764)
-> Any -> Any
forall a b. a -> b
coe
               T_IsSemiringWithoutAnnihilatingZero_1536
-> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1556
               (T_IsSemiringWithoutAnnihilatingZero_1536 -> Any
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1536
v0))))
-- Data.Bool.Properties._.IsSemiringWithoutAnnihilatingZero.isMonoid
d_isMonoid_2618 ::
  MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutAnnihilatingZero_1536 ->
  MAlonzo.Code.Algebra.Structures.T_IsMonoid_712
d_isMonoid_2618 :: T_IsSemiringWithoutAnnihilatingZero_1536 -> T_IsMonoid_712
d_isMonoid_2618 T_IsSemiringWithoutAnnihilatingZero_1536
v0
  = (T_IsCommutativeMonoid_764 -> T_IsMonoid_712)
-> Any -> T_IsMonoid_712
forall a b. a -> b
coe
      T_IsCommutativeMonoid_764 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_774
      ((T_IsSemiringWithoutAnnihilatingZero_1536
 -> T_IsCommutativeMonoid_764)
-> Any -> Any
forall a b. a -> b
coe
         T_IsSemiringWithoutAnnihilatingZero_1536
-> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1556
         (T_IsSemiringWithoutAnnihilatingZero_1536 -> Any
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1536
v0))
-- Data.Bool.Properties._.IsSemiringWithoutAnnihilatingZero.isSemigroup
d_isSemigroup_2620 ::
  MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutAnnihilatingZero_1536 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_488
d_isSemigroup_2620 :: T_IsSemiringWithoutAnnihilatingZero_1536 -> T_IsSemigroup_488
d_isSemigroup_2620 T_IsSemiringWithoutAnnihilatingZero_1536
v0
  = (T_IsMonoid_712 -> T_IsSemigroup_488) -> Any -> T_IsSemigroup_488
forall a b. a -> b
coe
      T_IsMonoid_712 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_722
      ((T_IsCommutativeMonoid_764 -> T_IsMonoid_712) -> Any -> Any
forall a b. a -> b
coe
         T_IsCommutativeMonoid_764 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_774
         ((T_IsSemiringWithoutAnnihilatingZero_1536
 -> T_IsCommutativeMonoid_764)
-> Any -> Any
forall a b. a -> b
coe
            T_IsSemiringWithoutAnnihilatingZero_1536
-> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1556
            (T_IsSemiringWithoutAnnihilatingZero_1536 -> Any
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1536
v0)))
-- Data.Bool.Properties._.IsSemiringWithoutAnnihilatingZero.isUnitalMagma
d_isUnitalMagma_2622 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutAnnihilatingZero_1536 ->
  MAlonzo.Code.Algebra.Structures.T_IsUnitalMagma_666
d_isUnitalMagma_2622 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> T_IsSemiringWithoutAnnihilatingZero_1536
-> T_IsUnitalMagma_666
d_isUnitalMagma_2622 ~Bool -> Bool -> Bool
v0 ~Bool -> Bool -> Bool
v1 ~Bool
v2 ~Bool
v3 T_IsSemiringWithoutAnnihilatingZero_1536
v4 = T_IsSemiringWithoutAnnihilatingZero_1536 -> T_IsUnitalMagma_666
du_isUnitalMagma_2622 T_IsSemiringWithoutAnnihilatingZero_1536
v4
du_isUnitalMagma_2622 ::
  MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutAnnihilatingZero_1536 ->
  MAlonzo.Code.Algebra.Structures.T_IsUnitalMagma_666
du_isUnitalMagma_2622 :: T_IsSemiringWithoutAnnihilatingZero_1536 -> T_IsUnitalMagma_666
du_isUnitalMagma_2622 T_IsSemiringWithoutAnnihilatingZero_1536
v0
  = let v1 :: T_IsCommutativeMonoid_764
v1
          = T_IsSemiringWithoutAnnihilatingZero_1536
-> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1556
              (T_IsSemiringWithoutAnnihilatingZero_1536
-> T_IsSemiringWithoutAnnihilatingZero_1536
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1536
v0) in
    Any -> T_IsUnitalMagma_666
forall a b. a -> b
coe
      ((T_IsMonoid_712 -> T_IsUnitalMagma_666) -> Any -> Any
forall a b. a -> b
coe
         T_IsMonoid_712 -> T_IsUnitalMagma_666
MAlonzo.Code.Algebra.Structures.du_isUnitalMagma_756
         ((T_IsCommutativeMonoid_764 -> T_IsMonoid_712) -> Any -> Any
forall a b. a -> b
coe T_IsCommutativeMonoid_764 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_774 (T_IsCommutativeMonoid_764 -> Any
forall a b. a -> b
coe T_IsCommutativeMonoid_764
v1)))
-- Data.Bool.Properties._.IsSemiringWithoutAnnihilatingZero.distrib
d_distrib_2624 ::
  MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutAnnihilatingZero_1536 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_distrib_2624 :: T_IsSemiringWithoutAnnihilatingZero_1536 -> T_Σ_14
d_distrib_2624 T_IsSemiringWithoutAnnihilatingZero_1536
v0
  = (T_IsSemiringWithoutAnnihilatingZero_1536 -> T_Σ_14)
-> Any -> T_Σ_14
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1536 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_distrib_1564 (T_IsSemiringWithoutAnnihilatingZero_1536 -> Any
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1536
v0)
-- Data.Bool.Properties._.IsSemiringWithoutAnnihilatingZero.distribʳ
d_distrib'691'_2626 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutAnnihilatingZero_1536 ->
  Bool ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_distrib'691'_2626 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> T_IsSemiringWithoutAnnihilatingZero_1536
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
d_distrib'691'_2626 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> T_IsSemiringWithoutAnnihilatingZero_1536
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsSemiringWithoutAnnihilatingZero.distribˡ
d_distrib'737'_2628 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutAnnihilatingZero_1536 ->
  Bool ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_distrib'737'_2628 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> T_IsSemiringWithoutAnnihilatingZero_1536
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
d_distrib'737'_2628 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> T_IsSemiringWithoutAnnihilatingZero_1536
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsSemiringWithoutAnnihilatingZero.isEquivalence
d_isEquivalence_2630 ::
  MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutAnnihilatingZero_1536 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
d_isEquivalence_2630 :: T_IsSemiringWithoutAnnihilatingZero_1536 -> T_IsEquivalence_28
d_isEquivalence_2630 T_IsSemiringWithoutAnnihilatingZero_1536
v0
  = (T_IsMagma_178 -> T_IsEquivalence_28) -> Any -> T_IsEquivalence_28
forall a b. a -> b
coe
      T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186
      ((T_IsSemigroup_488 -> T_IsMagma_178) -> Any -> Any
forall a b. a -> b
coe
         T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496
         ((T_IsMonoid_712 -> T_IsSemigroup_488) -> Any -> Any
forall a b. a -> b
coe
            T_IsMonoid_712 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_722
            ((T_IsCommutativeMonoid_764 -> T_IsMonoid_712) -> Any -> Any
forall a b. a -> b
coe
               T_IsCommutativeMonoid_764 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_774
               ((T_IsSemiringWithoutAnnihilatingZero_1536
 -> T_IsCommutativeMonoid_764)
-> Any -> Any
forall a b. a -> b
coe
                  T_IsSemiringWithoutAnnihilatingZero_1536
-> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1556
                  (T_IsSemiringWithoutAnnihilatingZero_1536 -> Any
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1536
v0)))))
-- Data.Bool.Properties._.IsSemiringWithoutAnnihilatingZero.isPartialEquivalence
d_isPartialEquivalence_2632 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutAnnihilatingZero_1536 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_2632 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> T_IsSemiringWithoutAnnihilatingZero_1536
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_2632 ~Bool -> Bool -> Bool
v0 ~Bool -> Bool -> Bool
v1 ~Bool
v2 ~Bool
v3 T_IsSemiringWithoutAnnihilatingZero_1536
v4
  = T_IsSemiringWithoutAnnihilatingZero_1536
-> T_IsPartialEquivalence_16
du_isPartialEquivalence_2632 T_IsSemiringWithoutAnnihilatingZero_1536
v4
du_isPartialEquivalence_2632 ::
  MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutAnnihilatingZero_1536 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_2632 :: T_IsSemiringWithoutAnnihilatingZero_1536
-> T_IsPartialEquivalence_16
du_isPartialEquivalence_2632 T_IsSemiringWithoutAnnihilatingZero_1536
v0
  = let v1 :: T_IsCommutativeMonoid_764
v1
          = T_IsSemiringWithoutAnnihilatingZero_1536
-> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1556
              (T_IsSemiringWithoutAnnihilatingZero_1536
-> T_IsSemiringWithoutAnnihilatingZero_1536
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1536
v0) in
    Any -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsMonoid_712
v2
             = T_IsCommutativeMonoid_764 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_774 (T_IsCommutativeMonoid_764 -> T_IsCommutativeMonoid_764
forall a b. a -> b
coe T_IsCommutativeMonoid_764
v1) in
       Any -> Any
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_488
v3
                = T_IsMonoid_712 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_722 (T_IsMonoid_712 -> T_IsMonoid_712
forall a b. a -> b
coe T_IsMonoid_712
v2) in
          Any -> Any
forall a b. a -> b
coe
            (let v4 :: T_IsMagma_178
v4 = T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496 (T_IsSemigroup_488 -> T_IsSemigroup_488
forall a b. a -> b
coe T_IsSemigroup_488
v3) in
             Any -> Any
forall a b. a -> b
coe
               ((T_IsEquivalence_28 -> T_IsPartialEquivalence_16) -> Any -> Any
forall a b. a -> b
coe
                  T_IsEquivalence_28 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_44
                  ((T_IsMagma_178 -> T_IsEquivalence_28) -> Any -> Any
forall a b. a -> b
coe
                     T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186 (T_IsMagma_178 -> Any
forall a b. a -> b
coe T_IsMagma_178
v4))))))
-- Data.Bool.Properties._.IsSemiringWithoutAnnihilatingZero.refl
d_refl_2634 ::
  MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutAnnihilatingZero_1536 ->
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_refl_2634 :: T_IsSemiringWithoutAnnihilatingZero_1536 -> Bool -> T__'8801'__12
d_refl_2634 = T_IsSemiringWithoutAnnihilatingZero_1536 -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsSemiringWithoutAnnihilatingZero.reflexive
d_reflexive_2636 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutAnnihilatingZero_1536 ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_reflexive_2636 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> T_IsSemiringWithoutAnnihilatingZero_1536
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_reflexive_2636 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> T_IsSemiringWithoutAnnihilatingZero_1536
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsSemiringWithoutAnnihilatingZero.setoid
d_setoid_2638 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutAnnihilatingZero_1536 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
d_setoid_2638 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> T_IsSemiringWithoutAnnihilatingZero_1536
-> T_Setoid_46
d_setoid_2638 ~Bool -> Bool -> Bool
v0 ~Bool -> Bool -> Bool
v1 ~Bool
v2 ~Bool
v3 T_IsSemiringWithoutAnnihilatingZero_1536
v4 = T_IsSemiringWithoutAnnihilatingZero_1536 -> T_Setoid_46
du_setoid_2638 T_IsSemiringWithoutAnnihilatingZero_1536
v4
du_setoid_2638 ::
  MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutAnnihilatingZero_1536 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
du_setoid_2638 :: T_IsSemiringWithoutAnnihilatingZero_1536 -> T_Setoid_46
du_setoid_2638 T_IsSemiringWithoutAnnihilatingZero_1536
v0
  = let v1 :: T_IsCommutativeMonoid_764
v1
          = T_IsSemiringWithoutAnnihilatingZero_1536
-> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1556
              (T_IsSemiringWithoutAnnihilatingZero_1536
-> T_IsSemiringWithoutAnnihilatingZero_1536
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1536
v0) in
    Any -> T_Setoid_46
forall a b. a -> b
coe
      (let v2 :: T_IsMonoid_712
v2
             = T_IsCommutativeMonoid_764 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_774 (T_IsCommutativeMonoid_764 -> T_IsCommutativeMonoid_764
forall a b. a -> b
coe T_IsCommutativeMonoid_764
v1) in
       Any -> Any
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_488
v3
                = T_IsMonoid_712 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_722 (T_IsMonoid_712 -> T_IsMonoid_712
forall a b. a -> b
coe T_IsMonoid_712
v2) in
          Any -> Any
forall a b. a -> b
coe
            ((T_IsMagma_178 -> T_Setoid_46) -> Any -> Any
forall a b. a -> b
coe
               T_IsMagma_178 -> T_Setoid_46
MAlonzo.Code.Algebra.Structures.du_setoid_202
               ((T_IsSemigroup_488 -> T_IsMagma_178) -> Any -> Any
forall a b. a -> b
coe T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496 (T_IsSemigroup_488 -> Any
forall a b. a -> b
coe T_IsSemigroup_488
v3)))))
-- Data.Bool.Properties._.IsSemiringWithoutAnnihilatingZero.sym
d_sym_2640 ::
  MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutAnnihilatingZero_1536 ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_sym_2640 :: T_IsSemiringWithoutAnnihilatingZero_1536
-> Bool -> Bool -> T__'8801'__12 -> T__'8801'__12
d_sym_2640 = T_IsSemiringWithoutAnnihilatingZero_1536
-> Bool -> Bool -> T__'8801'__12 -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsSemiringWithoutAnnihilatingZero.trans
d_trans_2642 ::
  MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutAnnihilatingZero_1536 ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_trans_2642 :: T_IsSemiringWithoutAnnihilatingZero_1536
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
d_trans_2642 = T_IsSemiringWithoutAnnihilatingZero_1536
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsSemiringWithoutOne.*-assoc
d_'42''45'assoc_2646 ::
  MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutOne_1342 ->
  Bool ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'42''45'assoc_2646 :: T_IsSemiringWithoutOne_1342
-> Bool -> Bool -> Bool -> T__'8801'__12
d_'42''45'assoc_2646 = T_IsSemiringWithoutOne_1342
-> Bool -> Bool -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsSemiringWithoutOne.*-cong
d_'42''45'cong_2648 ::
  MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutOne_1342 ->
  Bool ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'42''45'cong_2648 :: T_IsSemiringWithoutOne_1342
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
d_'42''45'cong_2648 = T_IsSemiringWithoutOne_1342
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsSemiringWithoutOne.∙-congʳ
d_'8729''45'cong'691'_2650 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutOne_1342 ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8729''45'cong'691'_2650 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsSemiringWithoutOne_1342
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong'691'_2650 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsSemiringWithoutOne_1342
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsSemiringWithoutOne.∙-congˡ
d_'8729''45'cong'737'_2652 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutOne_1342 ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8729''45'cong'737'_2652 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsSemiringWithoutOne_1342
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong'737'_2652 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsSemiringWithoutOne_1342
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsSemiringWithoutOne.*-isMagma
d_'42''45'isMagma_2654 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutOne_1342 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_178
d_'42''45'isMagma_2654 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsSemiringWithoutOne_1342
-> T_IsMagma_178
d_'42''45'isMagma_2654 Bool -> Bool -> Bool
v0 Bool -> Bool -> Bool
v1 Bool
v2 T_IsSemiringWithoutOne_1342
v3
  = (T_IsSemiringWithoutOne_1342 -> T_IsMagma_178)
-> T_IsSemiringWithoutOne_1342 -> T_IsMagma_178
forall a b. a -> b
coe T_IsSemiringWithoutOne_1342 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.du_'42''45'isMagma_1410 T_IsSemiringWithoutOne_1342
v3
-- Data.Bool.Properties._.IsSemiringWithoutOne.*-isSemigroup
d_'42''45'isSemigroup_2656 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutOne_1342 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_488
d_'42''45'isSemigroup_2656 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsSemiringWithoutOne_1342
-> T_IsSemigroup_488
d_'42''45'isSemigroup_2656 Bool -> Bool -> Bool
v0 Bool -> Bool -> Bool
v1 Bool
v2 T_IsSemiringWithoutOne_1342
v3
  = (T_IsSemiringWithoutOne_1342 -> T_IsSemigroup_488)
-> T_IsSemiringWithoutOne_1342 -> T_IsSemigroup_488
forall a b. a -> b
coe
      T_IsSemiringWithoutOne_1342 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.du_'42''45'isSemigroup_1412 T_IsSemiringWithoutOne_1342
v3
-- Data.Bool.Properties._.IsSemiringWithoutOne.assoc
d_assoc_2658 ::
  MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutOne_1342 ->
  Bool ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_assoc_2658 :: T_IsSemiringWithoutOne_1342
-> Bool -> Bool -> Bool -> T__'8801'__12
d_assoc_2658 = T_IsSemiringWithoutOne_1342
-> Bool -> Bool -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsSemiringWithoutOne.comm
d_comm_2660 ::
  MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutOne_1342 ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_comm_2660 :: T_IsSemiringWithoutOne_1342 -> Bool -> Bool -> T__'8801'__12
d_comm_2660 = T_IsSemiringWithoutOne_1342 -> Bool -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsSemiringWithoutOne.∙-cong
d_'8729''45'cong_2662 ::
  MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutOne_1342 ->
  Bool ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8729''45'cong_2662 :: T_IsSemiringWithoutOne_1342
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong_2662 = T_IsSemiringWithoutOne_1342
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsSemiringWithoutOne.∙-congʳ
d_'8729''45'cong'691'_2664 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutOne_1342 ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8729''45'cong'691'_2664 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsSemiringWithoutOne_1342
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong'691'_2664 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsSemiringWithoutOne_1342
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsSemiringWithoutOne.∙-congˡ
d_'8729''45'cong'737'_2666 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutOne_1342 ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8729''45'cong'737'_2666 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsSemiringWithoutOne_1342
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong'737'_2666 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsSemiringWithoutOne_1342
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsSemiringWithoutOne.identity
d_identity_2668 ::
  MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutOne_1342 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_identity_2668 :: T_IsSemiringWithoutOne_1342 -> T_Σ_14
d_identity_2668 T_IsSemiringWithoutOne_1342
v0
  = (T_IsMonoid_712 -> T_Σ_14) -> Any -> T_Σ_14
forall a b. a -> b
coe
      T_IsMonoid_712 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_identity_724
      ((T_IsCommutativeMonoid_764 -> T_IsMonoid_712) -> Any -> Any
forall a b. a -> b
coe
         T_IsCommutativeMonoid_764 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_774
         ((T_IsSemiringWithoutOne_1342 -> T_IsCommutativeMonoid_764)
-> Any -> Any
forall a b. a -> b
coe
            T_IsSemiringWithoutOne_1342 -> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1360
            (T_IsSemiringWithoutOne_1342 -> Any
forall a b. a -> b
coe T_IsSemiringWithoutOne_1342
v0)))
-- Data.Bool.Properties._.IsSemiringWithoutOne.identityʳ
d_identity'691'_2670 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutOne_1342 ->
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_identity'691'_2670 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsSemiringWithoutOne_1342
-> Bool
-> T__'8801'__12
d_identity'691'_2670 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsSemiringWithoutOne_1342
-> Bool
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsSemiringWithoutOne.identityˡ
d_identity'737'_2672 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutOne_1342 ->
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_identity'737'_2672 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsSemiringWithoutOne_1342
-> Bool
-> T__'8801'__12
d_identity'737'_2672 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsSemiringWithoutOne_1342
-> Bool
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsSemiringWithoutOne.isCommutativeMagma
d_isCommutativeMagma_2674 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutOne_1342 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMagma_214
d_isCommutativeMagma_2674 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsSemiringWithoutOne_1342
-> T_IsCommutativeMagma_214
d_isCommutativeMagma_2674 ~Bool -> Bool -> Bool
v0 ~Bool -> Bool -> Bool
v1 ~Bool
v2 T_IsSemiringWithoutOne_1342
v3
  = T_IsSemiringWithoutOne_1342 -> T_IsCommutativeMagma_214
du_isCommutativeMagma_2674 T_IsSemiringWithoutOne_1342
v3
du_isCommutativeMagma_2674 ::
  MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutOne_1342 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMagma_214
du_isCommutativeMagma_2674 :: T_IsSemiringWithoutOne_1342 -> T_IsCommutativeMagma_214
du_isCommutativeMagma_2674 T_IsSemiringWithoutOne_1342
v0
  = let v1 :: T_IsCommutativeMonoid_764
v1
          = T_IsSemiringWithoutOne_1342 -> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1360
              (T_IsSemiringWithoutOne_1342 -> T_IsSemiringWithoutOne_1342
forall a b. a -> b
coe T_IsSemiringWithoutOne_1342
v0) in
    Any -> T_IsCommutativeMagma_214
forall a b. a -> b
coe
      ((T_IsCommutativeSemigroup_568 -> T_IsCommutativeMagma_214)
-> Any -> Any
forall a b. a -> b
coe
         T_IsCommutativeSemigroup_568 -> T_IsCommutativeMagma_214
MAlonzo.Code.Algebra.Structures.du_isCommutativeMagma_606
         ((T_IsCommutativeMonoid_764 -> T_IsCommutativeSemigroup_568)
-> Any -> Any
forall a b. a -> b
coe
            T_IsCommutativeMonoid_764 -> T_IsCommutativeSemigroup_568
MAlonzo.Code.Algebra.Structures.du_isCommutativeSemigroup_814
            (T_IsCommutativeMonoid_764 -> Any
forall a b. a -> b
coe T_IsCommutativeMonoid_764
v1)))
-- Data.Bool.Properties._.IsSemiringWithoutOne.+-isCommutativeMonoid
d_'43''45'isCommutativeMonoid_2676 ::
  MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutOne_1342 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMonoid_764
d_'43''45'isCommutativeMonoid_2676 :: T_IsSemiringWithoutOne_1342 -> T_IsCommutativeMonoid_764
d_'43''45'isCommutativeMonoid_2676 T_IsSemiringWithoutOne_1342
v0
  = (T_IsSemiringWithoutOne_1342 -> T_IsCommutativeMonoid_764)
-> Any -> T_IsCommutativeMonoid_764
forall a b. a -> b
coe
      T_IsSemiringWithoutOne_1342 -> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1360
      (T_IsSemiringWithoutOne_1342 -> Any
forall a b. a -> b
coe T_IsSemiringWithoutOne_1342
v0)
-- Data.Bool.Properties._.IsSemiringWithoutOne.isCommutativeSemigroup
d_isCommutativeSemigroup_2678 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutOne_1342 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_568
d_isCommutativeSemigroup_2678 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsSemiringWithoutOne_1342
-> T_IsCommutativeSemigroup_568
d_isCommutativeSemigroup_2678 ~Bool -> Bool -> Bool
v0 ~Bool -> Bool -> Bool
v1 ~Bool
v2 T_IsSemiringWithoutOne_1342
v3
  = T_IsSemiringWithoutOne_1342 -> T_IsCommutativeSemigroup_568
du_isCommutativeSemigroup_2678 T_IsSemiringWithoutOne_1342
v3
du_isCommutativeSemigroup_2678 ::
  MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutOne_1342 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_568
du_isCommutativeSemigroup_2678 :: T_IsSemiringWithoutOne_1342 -> T_IsCommutativeSemigroup_568
du_isCommutativeSemigroup_2678 T_IsSemiringWithoutOne_1342
v0
  = (T_IsCommutativeMonoid_764 -> T_IsCommutativeSemigroup_568)
-> Any -> T_IsCommutativeSemigroup_568
forall a b. a -> b
coe
      T_IsCommutativeMonoid_764 -> T_IsCommutativeSemigroup_568
MAlonzo.Code.Algebra.Structures.du_isCommutativeSemigroup_814
      ((T_IsSemiringWithoutOne_1342 -> T_IsCommutativeMonoid_764)
-> Any -> Any
forall a b. a -> b
coe
         T_IsSemiringWithoutOne_1342 -> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1360
         (T_IsSemiringWithoutOne_1342 -> Any
forall a b. a -> b
coe T_IsSemiringWithoutOne_1342
v0))
-- Data.Bool.Properties._.IsSemiringWithoutOne.isMonoid
d_isMonoid_2680 ::
  MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutOne_1342 ->
  MAlonzo.Code.Algebra.Structures.T_IsMonoid_712
d_isMonoid_2680 :: T_IsSemiringWithoutOne_1342 -> T_IsMonoid_712
d_isMonoid_2680 T_IsSemiringWithoutOne_1342
v0
  = (T_IsCommutativeMonoid_764 -> T_IsMonoid_712)
-> Any -> T_IsMonoid_712
forall a b. a -> b
coe
      T_IsCommutativeMonoid_764 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_774
      ((T_IsSemiringWithoutOne_1342 -> T_IsCommutativeMonoid_764)
-> Any -> Any
forall a b. a -> b
coe
         T_IsSemiringWithoutOne_1342 -> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1360
         (T_IsSemiringWithoutOne_1342 -> Any
forall a b. a -> b
coe T_IsSemiringWithoutOne_1342
v0))
-- Data.Bool.Properties._.IsSemiringWithoutOne.distrib
d_distrib_2682 ::
  MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutOne_1342 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_distrib_2682 :: T_IsSemiringWithoutOne_1342 -> T_Σ_14
d_distrib_2682 T_IsSemiringWithoutOne_1342
v0
  = (T_IsSemiringWithoutOne_1342 -> T_Σ_14) -> Any -> T_Σ_14
forall a b. a -> b
coe T_IsSemiringWithoutOne_1342 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_distrib_1366 (T_IsSemiringWithoutOne_1342 -> Any
forall a b. a -> b
coe T_IsSemiringWithoutOne_1342
v0)
-- Data.Bool.Properties._.IsSemiringWithoutOne.distribʳ
d_distrib'691'_2684 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutOne_1342 ->
  Bool ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_distrib'691'_2684 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsSemiringWithoutOne_1342
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
d_distrib'691'_2684 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsSemiringWithoutOne_1342
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsSemiringWithoutOne.distribˡ
d_distrib'737'_2686 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutOne_1342 ->
  Bool ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_distrib'737'_2686 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsSemiringWithoutOne_1342
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
d_distrib'737'_2686 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsSemiringWithoutOne_1342
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsSemiringWithoutOne.isEquivalence
d_isEquivalence_2688 ::
  MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutOne_1342 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
d_isEquivalence_2688 :: T_IsSemiringWithoutOne_1342 -> T_IsEquivalence_28
d_isEquivalence_2688 T_IsSemiringWithoutOne_1342
v0
  = (T_IsMagma_178 -> T_IsEquivalence_28) -> Any -> T_IsEquivalence_28
forall a b. a -> b
coe
      T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186
      ((T_IsSemigroup_488 -> T_IsMagma_178) -> Any -> Any
forall a b. a -> b
coe
         T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496
         ((T_IsMonoid_712 -> T_IsSemigroup_488) -> Any -> Any
forall a b. a -> b
coe
            T_IsMonoid_712 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_722
            ((T_IsCommutativeMonoid_764 -> T_IsMonoid_712) -> Any -> Any
forall a b. a -> b
coe
               T_IsCommutativeMonoid_764 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_774
               ((T_IsSemiringWithoutOne_1342 -> T_IsCommutativeMonoid_764)
-> Any -> Any
forall a b. a -> b
coe
                  T_IsSemiringWithoutOne_1342 -> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1360
                  (T_IsSemiringWithoutOne_1342 -> Any
forall a b. a -> b
coe T_IsSemiringWithoutOne_1342
v0)))))
-- Data.Bool.Properties._.IsSemiringWithoutOne.isNearSemiring
d_isNearSemiring_2690 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutOne_1342 ->
  MAlonzo.Code.Algebra.Structures.T_IsNearSemiring_1260
d_isNearSemiring_2690 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsSemiringWithoutOne_1342
-> T_IsNearSemiring_1260
d_isNearSemiring_2690 Bool -> Bool -> Bool
v0 Bool -> Bool -> Bool
v1 Bool
v2 T_IsSemiringWithoutOne_1342
v3
  = (T_IsSemiringWithoutOne_1342 -> T_IsNearSemiring_1260)
-> T_IsSemiringWithoutOne_1342 -> T_IsNearSemiring_1260
forall a b. a -> b
coe T_IsSemiringWithoutOne_1342 -> T_IsNearSemiring_1260
MAlonzo.Code.Algebra.Structures.du_isNearSemiring_1428 T_IsSemiringWithoutOne_1342
v3
-- Data.Bool.Properties._.IsSemiringWithoutOne.isPartialEquivalence
d_isPartialEquivalence_2692 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutOne_1342 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_2692 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsSemiringWithoutOne_1342
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_2692 ~Bool -> Bool -> Bool
v0 ~Bool -> Bool -> Bool
v1 ~Bool
v2 T_IsSemiringWithoutOne_1342
v3
  = T_IsSemiringWithoutOne_1342 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_2692 T_IsSemiringWithoutOne_1342
v3
du_isPartialEquivalence_2692 ::
  MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutOne_1342 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_2692 :: T_IsSemiringWithoutOne_1342 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_2692 T_IsSemiringWithoutOne_1342
v0
  = (T_IsEquivalence_28 -> T_IsPartialEquivalence_16)
-> Any -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      T_IsEquivalence_28 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_44
      ((T_IsMagma_178 -> T_IsEquivalence_28) -> Any -> Any
forall a b. a -> b
coe
         T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186
         ((T_IsSemigroup_488 -> T_IsMagma_178) -> Any -> Any
forall a b. a -> b
coe
            T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496
            ((T_IsMonoid_712 -> T_IsSemigroup_488) -> Any -> Any
forall a b. a -> b
coe
               T_IsMonoid_712 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_722
               ((T_IsCommutativeMonoid_764 -> T_IsMonoid_712) -> Any -> Any
forall a b. a -> b
coe
                  T_IsCommutativeMonoid_764 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_774
                  ((T_IsSemiringWithoutOne_1342 -> T_IsCommutativeMonoid_764)
-> Any -> Any
forall a b. a -> b
coe
                     T_IsSemiringWithoutOne_1342 -> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1360
                     (T_IsSemiringWithoutOne_1342 -> Any
forall a b. a -> b
coe T_IsSemiringWithoutOne_1342
v0))))))
-- Data.Bool.Properties._.IsSemiringWithoutOne.refl
d_refl_2694 ::
  MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutOne_1342 ->
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_refl_2694 :: T_IsSemiringWithoutOne_1342 -> Bool -> T__'8801'__12
d_refl_2694 = T_IsSemiringWithoutOne_1342 -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsSemiringWithoutOne.reflexive
d_reflexive_2696 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutOne_1342 ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_reflexive_2696 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsSemiringWithoutOne_1342
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_reflexive_2696 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsSemiringWithoutOne_1342
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsSemiringWithoutOne.setoid
d_setoid_2698 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutOne_1342 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
d_setoid_2698 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsSemiringWithoutOne_1342
-> T_Setoid_46
d_setoid_2698 ~Bool -> Bool -> Bool
v0 ~Bool -> Bool -> Bool
v1 ~Bool
v2 T_IsSemiringWithoutOne_1342
v3 = T_IsSemiringWithoutOne_1342 -> T_Setoid_46
du_setoid_2698 T_IsSemiringWithoutOne_1342
v3
du_setoid_2698 ::
  MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutOne_1342 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
du_setoid_2698 :: T_IsSemiringWithoutOne_1342 -> T_Setoid_46
du_setoid_2698 T_IsSemiringWithoutOne_1342
v0
  = let v1 :: T_IsCommutativeMonoid_764
v1
          = T_IsSemiringWithoutOne_1342 -> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1360
              (T_IsSemiringWithoutOne_1342 -> T_IsSemiringWithoutOne_1342
forall a b. a -> b
coe T_IsSemiringWithoutOne_1342
v0) in
    Any -> T_Setoid_46
forall a b. a -> b
coe
      (let v2 :: T_IsMonoid_712
v2
             = T_IsCommutativeMonoid_764 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_774 (T_IsCommutativeMonoid_764 -> T_IsCommutativeMonoid_764
forall a b. a -> b
coe T_IsCommutativeMonoid_764
v1) in
       Any -> Any
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_488
v3
                = T_IsMonoid_712 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_722 (T_IsMonoid_712 -> T_IsMonoid_712
forall a b. a -> b
coe T_IsMonoid_712
v2) in
          Any -> Any
forall a b. a -> b
coe
            ((T_IsMagma_178 -> T_Setoid_46) -> Any -> Any
forall a b. a -> b
coe
               T_IsMagma_178 -> T_Setoid_46
MAlonzo.Code.Algebra.Structures.du_setoid_202
               ((T_IsSemigroup_488 -> T_IsMagma_178) -> Any -> Any
forall a b. a -> b
coe T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496 (T_IsSemigroup_488 -> Any
forall a b. a -> b
coe T_IsSemigroup_488
v3)))))
-- Data.Bool.Properties._.IsSemiringWithoutOne.sym
d_sym_2700 ::
  MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutOne_1342 ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_sym_2700 :: T_IsSemiringWithoutOne_1342
-> Bool -> Bool -> T__'8801'__12 -> T__'8801'__12
d_sym_2700 = T_IsSemiringWithoutOne_1342
-> Bool -> Bool -> T__'8801'__12 -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsSemiringWithoutOne.trans
d_trans_2702 ::
  MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutOne_1342 ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_trans_2702 :: T_IsSemiringWithoutOne_1342
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
d_trans_2702 = T_IsSemiringWithoutOne_1342
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsSemiringWithoutOne.zero
d_zero_2704 ::
  MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutOne_1342 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_zero_2704 :: T_IsSemiringWithoutOne_1342 -> T_Σ_14
d_zero_2704 T_IsSemiringWithoutOne_1342
v0
  = (T_IsSemiringWithoutOne_1342 -> T_Σ_14) -> Any -> T_Σ_14
forall a b. a -> b
coe T_IsSemiringWithoutOne_1342 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_zero_1368 (T_IsSemiringWithoutOne_1342 -> Any
forall a b. a -> b
coe T_IsSemiringWithoutOne_1342
v0)
-- Data.Bool.Properties._.IsSemiringWithoutOne.zeroʳ
d_zero'691'_2706 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutOne_1342 ->
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_zero'691'_2706 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsSemiringWithoutOne_1342
-> Bool
-> T__'8801'__12
d_zero'691'_2706 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsSemiringWithoutOne_1342
-> Bool
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsSemiringWithoutOne.zeroˡ
d_zero'737'_2708 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutOne_1342 ->
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_zero'737'_2708 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsSemiringWithoutOne_1342
-> Bool
-> T__'8801'__12
d_zero'737'_2708 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsSemiringWithoutOne_1342
-> Bool
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsSuccessorSet.isEquivalence
d_isEquivalence_2712 ::
  MAlonzo.Code.Algebra.Structures.T_IsSuccessorSet_146 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
d_isEquivalence_2712 :: T_IsSuccessorSet_146 -> T_IsEquivalence_28
d_isEquivalence_2712 T_IsSuccessorSet_146
v0
  = (T_IsSuccessorSet_146 -> T_IsEquivalence_28)
-> Any -> T_IsEquivalence_28
forall a b. a -> b
coe T_IsSuccessorSet_146 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_156 (T_IsSuccessorSet_146 -> Any
forall a b. a -> b
coe T_IsSuccessorSet_146
v0)
-- Data.Bool.Properties._.IsSuccessorSet.isPartialEquivalence
d_isPartialEquivalence_2714 ::
  (Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsSuccessorSet_146 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_2714 :: (Bool -> Bool)
-> Bool -> T_IsSuccessorSet_146 -> T_IsPartialEquivalence_16
d_isPartialEquivalence_2714 ~Bool -> Bool
v0 ~Bool
v1 T_IsSuccessorSet_146
v2
  = T_IsSuccessorSet_146 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_2714 T_IsSuccessorSet_146
v2
du_isPartialEquivalence_2714 ::
  MAlonzo.Code.Algebra.Structures.T_IsSuccessorSet_146 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_2714 :: T_IsSuccessorSet_146 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_2714 T_IsSuccessorSet_146
v0
  = (T_IsEquivalence_28 -> T_IsPartialEquivalence_16)
-> Any -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      T_IsEquivalence_28 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_44
      ((T_IsSuccessorSet_146 -> T_IsEquivalence_28) -> Any -> Any
forall a b. a -> b
coe T_IsSuccessorSet_146 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_156 (T_IsSuccessorSet_146 -> Any
forall a b. a -> b
coe T_IsSuccessorSet_146
v0))
-- Data.Bool.Properties._.IsSuccessorSet.refl
d_refl_2716 ::
  MAlonzo.Code.Algebra.Structures.T_IsSuccessorSet_146 ->
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_refl_2716 :: T_IsSuccessorSet_146 -> Bool -> T__'8801'__12
d_refl_2716 = T_IsSuccessorSet_146 -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsSuccessorSet.reflexive
d_reflexive_2718 ::
  (Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsSuccessorSet_146 ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_reflexive_2718 :: (Bool -> Bool)
-> Bool
-> T_IsSuccessorSet_146
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_reflexive_2718 = (Bool -> Bool)
-> Bool
-> T_IsSuccessorSet_146
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsSuccessorSet.setoid
d_setoid_2720 ::
  (Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsSuccessorSet_146 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
d_setoid_2720 :: (Bool -> Bool) -> Bool -> T_IsSuccessorSet_146 -> T_Setoid_46
d_setoid_2720 Bool -> Bool
v0 Bool
v1 T_IsSuccessorSet_146
v2
  = (T_IsSuccessorSet_146 -> T_Setoid_46)
-> T_IsSuccessorSet_146 -> T_Setoid_46
forall a b. a -> b
coe T_IsSuccessorSet_146 -> T_Setoid_46
MAlonzo.Code.Algebra.Structures.du_setoid_172 T_IsSuccessorSet_146
v2
-- Data.Bool.Properties._.IsSuccessorSet.suc#-cong
d_suc'35''45'cong_2722 ::
  MAlonzo.Code.Algebra.Structures.T_IsSuccessorSet_146 ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_suc'35''45'cong_2722 :: T_IsSuccessorSet_146
-> Bool -> Bool -> T__'8801'__12 -> T__'8801'__12
d_suc'35''45'cong_2722 = T_IsSuccessorSet_146
-> Bool -> Bool -> T__'8801'__12 -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsSuccessorSet.sym
d_sym_2724 ::
  MAlonzo.Code.Algebra.Structures.T_IsSuccessorSet_146 ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_sym_2724 :: T_IsSuccessorSet_146
-> Bool -> Bool -> T__'8801'__12 -> T__'8801'__12
d_sym_2724 = T_IsSuccessorSet_146
-> Bool -> Bool -> T__'8801'__12 -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsSuccessorSet.trans
d_trans_2726 ::
  MAlonzo.Code.Algebra.Structures.T_IsSuccessorSet_146 ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_trans_2726 :: T_IsSuccessorSet_146
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
d_trans_2726 = T_IsSuccessorSet_146
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsUnitalMagma.identity
d_identity_2730 ::
  MAlonzo.Code.Algebra.Structures.T_IsUnitalMagma_666 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_identity_2730 :: T_IsUnitalMagma_666 -> T_Σ_14
d_identity_2730 T_IsUnitalMagma_666
v0
  = (T_IsUnitalMagma_666 -> T_Σ_14) -> Any -> T_Σ_14
forall a b. a -> b
coe T_IsUnitalMagma_666 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_identity_678 (T_IsUnitalMagma_666 -> Any
forall a b. a -> b
coe T_IsUnitalMagma_666
v0)
-- Data.Bool.Properties._.IsUnitalMagma.identityʳ
d_identity'691'_2732 ::
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsUnitalMagma_666 ->
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_identity'691'_2732 :: (Bool -> Bool -> Bool)
-> Bool -> T_IsUnitalMagma_666 -> Bool -> T__'8801'__12
d_identity'691'_2732 = (Bool -> Bool -> Bool)
-> Bool -> T_IsUnitalMagma_666 -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsUnitalMagma.identityˡ
d_identity'737'_2734 ::
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsUnitalMagma_666 ->
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_identity'737'_2734 :: (Bool -> Bool -> Bool)
-> Bool -> T_IsUnitalMagma_666 -> Bool -> T__'8801'__12
d_identity'737'_2734 = (Bool -> Bool -> Bool)
-> Bool -> T_IsUnitalMagma_666 -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsUnitalMagma.isEquivalence
d_isEquivalence_2736 ::
  MAlonzo.Code.Algebra.Structures.T_IsUnitalMagma_666 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
d_isEquivalence_2736 :: T_IsUnitalMagma_666 -> T_IsEquivalence_28
d_isEquivalence_2736 T_IsUnitalMagma_666
v0
  = (T_IsMagma_178 -> T_IsEquivalence_28) -> Any -> T_IsEquivalence_28
forall a b. a -> b
coe
      T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186
      ((T_IsUnitalMagma_666 -> T_IsMagma_178) -> Any -> Any
forall a b. a -> b
coe T_IsUnitalMagma_666 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_676 (T_IsUnitalMagma_666 -> Any
forall a b. a -> b
coe T_IsUnitalMagma_666
v0))
-- Data.Bool.Properties._.IsUnitalMagma.isMagma
d_isMagma_2738 ::
  MAlonzo.Code.Algebra.Structures.T_IsUnitalMagma_666 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_178
d_isMagma_2738 :: T_IsUnitalMagma_666 -> T_IsMagma_178
d_isMagma_2738 T_IsUnitalMagma_666
v0
  = (T_IsUnitalMagma_666 -> T_IsMagma_178) -> Any -> T_IsMagma_178
forall a b. a -> b
coe T_IsUnitalMagma_666 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_676 (T_IsUnitalMagma_666 -> Any
forall a b. a -> b
coe T_IsUnitalMagma_666
v0)
-- Data.Bool.Properties._.IsUnitalMagma.isPartialEquivalence
d_isPartialEquivalence_2740 ::
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsUnitalMagma_666 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_2740 :: (Bool -> Bool -> Bool)
-> Bool -> T_IsUnitalMagma_666 -> T_IsPartialEquivalence_16
d_isPartialEquivalence_2740 ~Bool -> Bool -> Bool
v0 ~Bool
v1 T_IsUnitalMagma_666
v2
  = T_IsUnitalMagma_666 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_2740 T_IsUnitalMagma_666
v2
du_isPartialEquivalence_2740 ::
  MAlonzo.Code.Algebra.Structures.T_IsUnitalMagma_666 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_2740 :: T_IsUnitalMagma_666 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_2740 T_IsUnitalMagma_666
v0
  = let v1 :: T_IsMagma_178
v1
          = T_IsUnitalMagma_666 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_676 (T_IsUnitalMagma_666 -> T_IsUnitalMagma_666
forall a b. a -> b
coe T_IsUnitalMagma_666
v0) in
    Any -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      ((T_IsEquivalence_28 -> T_IsPartialEquivalence_16) -> Any -> Any
forall a b. a -> b
coe
         T_IsEquivalence_28 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_44
         ((T_IsMagma_178 -> T_IsEquivalence_28) -> Any -> Any
forall a b. a -> b
coe T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186 (T_IsMagma_178 -> Any
forall a b. a -> b
coe T_IsMagma_178
v1)))
-- Data.Bool.Properties._.IsUnitalMagma.refl
d_refl_2742 ::
  MAlonzo.Code.Algebra.Structures.T_IsUnitalMagma_666 ->
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_refl_2742 :: T_IsUnitalMagma_666 -> Bool -> T__'8801'__12
d_refl_2742 = T_IsUnitalMagma_666 -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsUnitalMagma.reflexive
d_reflexive_2744 ::
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsUnitalMagma_666 ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_reflexive_2744 :: (Bool -> Bool -> Bool)
-> Bool
-> T_IsUnitalMagma_666
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_reflexive_2744 = (Bool -> Bool -> Bool)
-> Bool
-> T_IsUnitalMagma_666
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsUnitalMagma.setoid
d_setoid_2746 ::
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsUnitalMagma_666 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
d_setoid_2746 :: (Bool -> Bool -> Bool)
-> Bool -> T_IsUnitalMagma_666 -> T_Setoid_46
d_setoid_2746 ~Bool -> Bool -> Bool
v0 ~Bool
v1 T_IsUnitalMagma_666
v2 = T_IsUnitalMagma_666 -> T_Setoid_46
du_setoid_2746 T_IsUnitalMagma_666
v2
du_setoid_2746 ::
  MAlonzo.Code.Algebra.Structures.T_IsUnitalMagma_666 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
du_setoid_2746 :: T_IsUnitalMagma_666 -> T_Setoid_46
du_setoid_2746 T_IsUnitalMagma_666
v0
  = (T_IsMagma_178 -> T_Setoid_46) -> Any -> T_Setoid_46
forall a b. a -> b
coe
      T_IsMagma_178 -> T_Setoid_46
MAlonzo.Code.Algebra.Structures.du_setoid_202
      ((T_IsUnitalMagma_666 -> T_IsMagma_178) -> Any -> Any
forall a b. a -> b
coe T_IsUnitalMagma_666 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_676 (T_IsUnitalMagma_666 -> Any
forall a b. a -> b
coe T_IsUnitalMagma_666
v0))
-- Data.Bool.Properties._.IsUnitalMagma.sym
d_sym_2748 ::
  MAlonzo.Code.Algebra.Structures.T_IsUnitalMagma_666 ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_sym_2748 :: T_IsUnitalMagma_666
-> Bool -> Bool -> T__'8801'__12 -> T__'8801'__12
d_sym_2748 = T_IsUnitalMagma_666
-> Bool -> Bool -> T__'8801'__12 -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsUnitalMagma.trans
d_trans_2750 ::
  MAlonzo.Code.Algebra.Structures.T_IsUnitalMagma_666 ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_trans_2750 :: T_IsUnitalMagma_666
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
d_trans_2750 = T_IsUnitalMagma_666
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsUnitalMagma.∙-cong
d_'8729''45'cong_2752 ::
  MAlonzo.Code.Algebra.Structures.T_IsUnitalMagma_666 ->
  Bool ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8729''45'cong_2752 :: T_IsUnitalMagma_666
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong_2752 = T_IsUnitalMagma_666
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsUnitalMagma.∙-congʳ
d_'8729''45'cong'691'_2754 ::
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsUnitalMagma_666 ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8729''45'cong'691'_2754 :: (Bool -> Bool -> Bool)
-> Bool
-> T_IsUnitalMagma_666
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong'691'_2754 = (Bool -> Bool -> Bool)
-> Bool
-> T_IsUnitalMagma_666
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsUnitalMagma.∙-congˡ
d_'8729''45'cong'737'_2756 ::
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsUnitalMagma_666 ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8729''45'cong'737'_2756 :: (Bool -> Bool -> Bool)
-> Bool
-> T_IsUnitalMagma_666
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong'737'_2756 = (Bool -> Bool -> Bool)
-> Bool
-> T_IsUnitalMagma_666
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsBooleanAlgebra
d_IsBooleanAlgebra_2760 :: p -> p -> p -> p -> p -> ()
d_IsBooleanAlgebra_2760 p
a0 p
a1 p
a2 p
a3 p
a4 = ()
-- Data.Bool.Properties._.IsBoundedJoinSemilattice
d_IsBoundedJoinSemilattice_2764 ::
  (Bool -> Bool -> Bool) -> Bool -> ()
d_IsBoundedJoinSemilattice_2764 :: (Bool -> Bool -> Bool) -> Bool -> ()
d_IsBoundedJoinSemilattice_2764 = (Bool -> Bool -> Bool) -> Bool -> ()
forall a. a
erased
-- Data.Bool.Properties._.IsBoundedMeetSemilattice
d_IsBoundedMeetSemilattice_2766 ::
  (Bool -> Bool -> Bool) -> Bool -> ()
d_IsBoundedMeetSemilattice_2766 :: (Bool -> Bool -> Bool) -> Bool -> ()
d_IsBoundedMeetSemilattice_2766 = (Bool -> Bool -> Bool) -> Bool -> ()
forall a. a
erased
-- Data.Bool.Properties._.IsBoundedSemilattice
d_IsBoundedSemilattice_2768 :: (Bool -> Bool -> Bool) -> Bool -> ()
d_IsBoundedSemilattice_2768 :: (Bool -> Bool -> Bool) -> Bool -> ()
d_IsBoundedSemilattice_2768 = (Bool -> Bool -> Bool) -> Bool -> ()
forall a. a
erased
-- Data.Bool.Properties._.IsDistributiveLattice
d_IsDistributiveLattice_2770 :: p -> p -> ()
d_IsDistributiveLattice_2770 p
a0 p
a1 = ()
-- Data.Bool.Properties._.IsJoinSemilattice
d_IsJoinSemilattice_2774 :: (Bool -> Bool -> Bool) -> ()
d_IsJoinSemilattice_2774 :: (Bool -> Bool -> Bool) -> ()
d_IsJoinSemilattice_2774 = (Bool -> Bool -> Bool) -> ()
forall a. a
erased
-- Data.Bool.Properties._.IsLattice
d_IsLattice_2776 :: p -> p -> ()
d_IsLattice_2776 p
a0 p
a1 = ()
-- Data.Bool.Properties._.IsMeetSemilattice
d_IsMeetSemilattice_2780 :: (Bool -> Bool -> Bool) -> ()
d_IsMeetSemilattice_2780 :: (Bool -> Bool -> Bool) -> ()
d_IsMeetSemilattice_2780 = (Bool -> Bool -> Bool) -> ()
forall a. a
erased
-- Data.Bool.Properties._.IsSemilattice
d_IsSemilattice_2782 :: (Bool -> Bool -> Bool) -> ()
d_IsSemilattice_2782 :: (Bool -> Bool -> Bool) -> ()
d_IsSemilattice_2782 = (Bool -> Bool -> Bool) -> ()
forall a. a
erased
-- Data.Bool.Properties._.IsBooleanAlgebra.absorptive
d_absorptive_2786 ::
  MAlonzo.Code.Algebra.Lattice.Structures.T_IsBooleanAlgebra_3224 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_absorptive_2786 :: T_IsBooleanAlgebra_3224 -> T_Σ_14
d_absorptive_2786 T_IsBooleanAlgebra_3224
v0
  = (T_IsLattice_3070 -> T_Σ_14) -> Any -> T_Σ_14
forall a b. a -> b
coe
      T_IsLattice_3070 -> T_Σ_14
MAlonzo.Code.Algebra.Lattice.Structures.d_absorptive_3106
      ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070) -> Any -> Any
forall a b. a -> b
coe
         T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
         ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> Any -> Any
forall a b. a -> b
coe
            T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
            (T_IsBooleanAlgebra_3224 -> Any
forall a b. a -> b
coe T_IsBooleanAlgebra_3224
v0)))
-- Data.Bool.Properties._.IsBooleanAlgebra.isDistributiveLattice
d_isDistributiveLattice_2788 ::
  MAlonzo.Code.Algebra.Lattice.Structures.T_IsBooleanAlgebra_3224 ->
  MAlonzo.Code.Algebra.Lattice.Structures.T_IsDistributiveLattice_3146
d_isDistributiveLattice_2788 :: T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
d_isDistributiveLattice_2788 T_IsBooleanAlgebra_3224
v0
  = (T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> Any -> T_IsDistributiveLattice_3146
forall a b. a -> b
coe
      T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
      (T_IsBooleanAlgebra_3224 -> Any
forall a b. a -> b
coe T_IsBooleanAlgebra_3224
v0)
-- Data.Bool.Properties._.IsBooleanAlgebra.isEquivalence
d_isEquivalence_2790 ::
  MAlonzo.Code.Algebra.Lattice.Structures.T_IsBooleanAlgebra_3224 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
d_isEquivalence_2790 :: T_IsBooleanAlgebra_3224 -> T_IsEquivalence_28
d_isEquivalence_2790 T_IsBooleanAlgebra_3224
v0
  = (T_IsLattice_3070 -> T_IsEquivalence_28)
-> Any -> T_IsEquivalence_28
forall a b. a -> b
coe
      T_IsLattice_3070 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_3092
      ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070) -> Any -> Any
forall a b. a -> b
coe
         T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
         ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> Any -> Any
forall a b. a -> b
coe
            T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
            (T_IsBooleanAlgebra_3224 -> Any
forall a b. a -> b
coe T_IsBooleanAlgebra_3224
v0)))
-- Data.Bool.Properties._.IsBooleanAlgebra.isLattice
d_isLattice_2792 ::
  MAlonzo.Code.Algebra.Lattice.Structures.T_IsBooleanAlgebra_3224 ->
  MAlonzo.Code.Algebra.Lattice.Structures.T_IsLattice_3070
d_isLattice_2792 :: T_IsBooleanAlgebra_3224 -> T_IsLattice_3070
d_isLattice_2792 T_IsBooleanAlgebra_3224
v0
  = (T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> Any -> T_IsLattice_3070
forall a b. a -> b
coe
      T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
      ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> Any -> Any
forall a b. a -> b
coe
         T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
         (T_IsBooleanAlgebra_3224 -> Any
forall a b. a -> b
coe T_IsBooleanAlgebra_3224
v0))
-- Data.Bool.Properties._.IsBooleanAlgebra.isPartialEquivalence
d_isPartialEquivalence_2794 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Lattice.Structures.T_IsBooleanAlgebra_3224 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_2794 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsBooleanAlgebra_3224
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_2794 ~Bool -> Bool -> Bool
v0 ~Bool -> Bool -> Bool
v1 ~Bool -> Bool
v2 ~Bool
v3 ~Bool
v4 T_IsBooleanAlgebra_3224
v5
  = T_IsBooleanAlgebra_3224 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_2794 T_IsBooleanAlgebra_3224
v5
du_isPartialEquivalence_2794 ::
  MAlonzo.Code.Algebra.Lattice.Structures.T_IsBooleanAlgebra_3224 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_2794 :: T_IsBooleanAlgebra_3224 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_2794 T_IsBooleanAlgebra_3224
v0
  = let v1 :: T_IsDistributiveLattice_3146
v1
          = T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
              (T_IsBooleanAlgebra_3224 -> T_IsBooleanAlgebra_3224
forall a b. a -> b
coe T_IsBooleanAlgebra_3224
v0) in
    Any -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsLattice_3070
v2
             = T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
                 (T_IsDistributiveLattice_3146 -> T_IsDistributiveLattice_3146
forall a b. a -> b
coe T_IsDistributiveLattice_3146
v1) in
       Any -> Any
forall a b. a -> b
coe
         ((T_IsEquivalence_28 -> T_IsPartialEquivalence_16) -> Any -> Any
forall a b. a -> b
coe
            T_IsEquivalence_28 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_44
            ((T_IsLattice_3070 -> T_IsEquivalence_28) -> Any -> Any
forall a b. a -> b
coe
               T_IsLattice_3070 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_3092
               (T_IsLattice_3070 -> Any
forall a b. a -> b
coe T_IsLattice_3070
v2))))
-- Data.Bool.Properties._.IsBooleanAlgebra.refl
d_refl_2796 ::
  MAlonzo.Code.Algebra.Lattice.Structures.T_IsBooleanAlgebra_3224 ->
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_refl_2796 :: T_IsBooleanAlgebra_3224 -> Bool -> T__'8801'__12
d_refl_2796 = T_IsBooleanAlgebra_3224 -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsBooleanAlgebra.reflexive
d_reflexive_2798 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Lattice.Structures.T_IsBooleanAlgebra_3224 ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_reflexive_2798 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsBooleanAlgebra_3224
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_reflexive_2798 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsBooleanAlgebra_3224
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsBooleanAlgebra.sym
d_sym_2800 ::
  MAlonzo.Code.Algebra.Lattice.Structures.T_IsBooleanAlgebra_3224 ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_sym_2800 :: T_IsBooleanAlgebra_3224
-> Bool -> Bool -> T__'8801'__12 -> T__'8801'__12
d_sym_2800 = T_IsBooleanAlgebra_3224
-> Bool -> Bool -> T__'8801'__12 -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsBooleanAlgebra.trans
d_trans_2802 ::
  MAlonzo.Code.Algebra.Lattice.Structures.T_IsBooleanAlgebra_3224 ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_trans_2802 :: T_IsBooleanAlgebra_3224
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
d_trans_2802 = T_IsBooleanAlgebra_3224
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsBooleanAlgebra.¬-cong
d_'172''45'cong_2804 ::
  MAlonzo.Code.Algebra.Lattice.Structures.T_IsBooleanAlgebra_3224 ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'172''45'cong_2804 :: T_IsBooleanAlgebra_3224
-> Bool -> Bool -> T__'8801'__12 -> T__'8801'__12
d_'172''45'cong_2804 = T_IsBooleanAlgebra_3224
-> Bool -> Bool -> T__'8801'__12 -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsBooleanAlgebra.∧-absorbs-∨
d_'8743''45'absorbs'45''8744'_2806 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Lattice.Structures.T_IsBooleanAlgebra_3224 ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8743''45'absorbs'45''8744'_2806 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsBooleanAlgebra_3224
-> Bool
-> Bool
-> T__'8801'__12
d_'8743''45'absorbs'45''8744'_2806 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsBooleanAlgebra_3224
-> Bool
-> Bool
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsBooleanAlgebra.∧-assoc
d_'8743''45'assoc_2808 ::
  MAlonzo.Code.Algebra.Lattice.Structures.T_IsBooleanAlgebra_3224 ->
  Bool ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8743''45'assoc_2808 :: T_IsBooleanAlgebra_3224 -> Bool -> Bool -> Bool -> T__'8801'__12
d_'8743''45'assoc_2808 = T_IsBooleanAlgebra_3224 -> Bool -> Bool -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsBooleanAlgebra.∧-comm
d_'8743''45'comm_2810 ::
  MAlonzo.Code.Algebra.Lattice.Structures.T_IsBooleanAlgebra_3224 ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8743''45'comm_2810 :: T_IsBooleanAlgebra_3224 -> Bool -> Bool -> T__'8801'__12
d_'8743''45'comm_2810 = T_IsBooleanAlgebra_3224 -> Bool -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsBooleanAlgebra.∧-complement
d_'8743''45'complement_2812 ::
  MAlonzo.Code.Algebra.Lattice.Structures.T_IsBooleanAlgebra_3224 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'8743''45'complement_2812 :: T_IsBooleanAlgebra_3224 -> T_Σ_14
d_'8743''45'complement_2812 T_IsBooleanAlgebra_3224
v0
  = (T_IsBooleanAlgebra_3224 -> T_Σ_14) -> Any -> T_Σ_14
forall a b. a -> b
coe
      T_IsBooleanAlgebra_3224 -> T_Σ_14
MAlonzo.Code.Algebra.Lattice.Structures.d_'8743''45'complement_3248
      (T_IsBooleanAlgebra_3224 -> Any
forall a b. a -> b
coe T_IsBooleanAlgebra_3224
v0)
-- Data.Bool.Properties._.IsBooleanAlgebra.∧-complementʳ
d_'8743''45'complement'691'_2814 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Lattice.Structures.T_IsBooleanAlgebra_3224 ->
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8743''45'complement'691'_2814 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsBooleanAlgebra_3224
-> Bool
-> T__'8801'__12
d_'8743''45'complement'691'_2814 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsBooleanAlgebra_3224
-> Bool
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsBooleanAlgebra.∧-complementˡ
d_'8743''45'complement'737'_2816 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Lattice.Structures.T_IsBooleanAlgebra_3224 ->
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8743''45'complement'737'_2816 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsBooleanAlgebra_3224
-> Bool
-> T__'8801'__12
d_'8743''45'complement'737'_2816 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsBooleanAlgebra_3224
-> Bool
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsBooleanAlgebra.∧-cong
d_'8743''45'cong_2818 ::
  MAlonzo.Code.Algebra.Lattice.Structures.T_IsBooleanAlgebra_3224 ->
  Bool ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8743''45'cong_2818 :: T_IsBooleanAlgebra_3224
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
d_'8743''45'cong_2818 = T_IsBooleanAlgebra_3224
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsBooleanAlgebra.∧-congʳ
d_'8743''45'cong'691'_2820 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Lattice.Structures.T_IsBooleanAlgebra_3224 ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8743''45'cong'691'_2820 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsBooleanAlgebra_3224
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_'8743''45'cong'691'_2820 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsBooleanAlgebra_3224
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsBooleanAlgebra.∧-congˡ
d_'8743''45'cong'737'_2822 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Lattice.Structures.T_IsBooleanAlgebra_3224 ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8743''45'cong'737'_2822 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsBooleanAlgebra_3224
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_'8743''45'cong'737'_2822 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsBooleanAlgebra_3224
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsBooleanAlgebra.∧-distrib-∨
d_'8743''45'distrib'45''8744'_2824 ::
  MAlonzo.Code.Algebra.Lattice.Structures.T_IsBooleanAlgebra_3224 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'8743''45'distrib'45''8744'_2824 :: T_IsBooleanAlgebra_3224 -> T_Σ_14
d_'8743''45'distrib'45''8744'_2824 T_IsBooleanAlgebra_3224
v0
  = (T_IsDistributiveLattice_3146 -> T_Σ_14) -> Any -> T_Σ_14
forall a b. a -> b
coe
      T_IsDistributiveLattice_3146 -> T_Σ_14
MAlonzo.Code.Algebra.Lattice.Structures.d_'8743''45'distrib'45''8744'_3162
      ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> Any -> Any
forall a b. a -> b
coe
         T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
         (T_IsBooleanAlgebra_3224 -> Any
forall a b. a -> b
coe T_IsBooleanAlgebra_3224
v0))
-- Data.Bool.Properties._.IsBooleanAlgebra.∧-distribʳ-∨
d_'8743''45'distrib'691''45''8744'_2826 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Lattice.Structures.T_IsBooleanAlgebra_3224 ->
  Bool ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8743''45'distrib'691''45''8744'_2826 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsBooleanAlgebra_3224
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
d_'8743''45'distrib'691''45''8744'_2826 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsBooleanAlgebra_3224
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsBooleanAlgebra.∧-distribˡ-∨
d_'8743''45'distrib'737''45''8744'_2828 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Lattice.Structures.T_IsBooleanAlgebra_3224 ->
  Bool ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8743''45'distrib'737''45''8744'_2828 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsBooleanAlgebra_3224
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
d_'8743''45'distrib'737''45''8744'_2828 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsBooleanAlgebra_3224
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsBooleanAlgebra.∨-absorbs-∧
d_'8744''45'absorbs'45''8743'_2830 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Lattice.Structures.T_IsBooleanAlgebra_3224 ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8744''45'absorbs'45''8743'_2830 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsBooleanAlgebra_3224
-> Bool
-> Bool
-> T__'8801'__12
d_'8744''45'absorbs'45''8743'_2830 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsBooleanAlgebra_3224
-> Bool
-> Bool
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsBooleanAlgebra.∨-assoc
d_'8744''45'assoc_2832 ::
  MAlonzo.Code.Algebra.Lattice.Structures.T_IsBooleanAlgebra_3224 ->
  Bool ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8744''45'assoc_2832 :: T_IsBooleanAlgebra_3224 -> Bool -> Bool -> Bool -> T__'8801'__12
d_'8744''45'assoc_2832 = T_IsBooleanAlgebra_3224 -> Bool -> Bool -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsBooleanAlgebra.∨-comm
d_'8744''45'comm_2834 ::
  MAlonzo.Code.Algebra.Lattice.Structures.T_IsBooleanAlgebra_3224 ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8744''45'comm_2834 :: T_IsBooleanAlgebra_3224 -> Bool -> Bool -> T__'8801'__12
d_'8744''45'comm_2834 = T_IsBooleanAlgebra_3224 -> Bool -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsBooleanAlgebra.∨-complement
d_'8744''45'complement_2836 ::
  MAlonzo.Code.Algebra.Lattice.Structures.T_IsBooleanAlgebra_3224 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'8744''45'complement_2836 :: T_IsBooleanAlgebra_3224 -> T_Σ_14
d_'8744''45'complement_2836 T_IsBooleanAlgebra_3224
v0
  = (T_IsBooleanAlgebra_3224 -> T_Σ_14) -> Any -> T_Σ_14
forall a b. a -> b
coe
      T_IsBooleanAlgebra_3224 -> T_Σ_14
MAlonzo.Code.Algebra.Lattice.Structures.d_'8744''45'complement_3246
      (T_IsBooleanAlgebra_3224 -> Any
forall a b. a -> b
coe T_IsBooleanAlgebra_3224
v0)
-- Data.Bool.Properties._.IsBooleanAlgebra.∨-complementʳ
d_'8744''45'complement'691'_2838 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Lattice.Structures.T_IsBooleanAlgebra_3224 ->
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8744''45'complement'691'_2838 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsBooleanAlgebra_3224
-> Bool
-> T__'8801'__12
d_'8744''45'complement'691'_2838 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsBooleanAlgebra_3224
-> Bool
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsBooleanAlgebra.∨-complementˡ
d_'8744''45'complement'737'_2840 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Lattice.Structures.T_IsBooleanAlgebra_3224 ->
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8744''45'complement'737'_2840 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsBooleanAlgebra_3224
-> Bool
-> T__'8801'__12
d_'8744''45'complement'737'_2840 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsBooleanAlgebra_3224
-> Bool
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsBooleanAlgebra.∨-cong
d_'8744''45'cong_2842 ::
  MAlonzo.Code.Algebra.Lattice.Structures.T_IsBooleanAlgebra_3224 ->
  Bool ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8744''45'cong_2842 :: T_IsBooleanAlgebra_3224
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
d_'8744''45'cong_2842 = T_IsBooleanAlgebra_3224
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsBooleanAlgebra.∨-congʳ
d_'8744''45'cong'691'_2844 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Lattice.Structures.T_IsBooleanAlgebra_3224 ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8744''45'cong'691'_2844 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsBooleanAlgebra_3224
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_'8744''45'cong'691'_2844 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsBooleanAlgebra_3224
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsBooleanAlgebra.∨-congˡ
d_'8744''45'cong'737'_2846 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Lattice.Structures.T_IsBooleanAlgebra_3224 ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8744''45'cong'737'_2846 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsBooleanAlgebra_3224
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_'8744''45'cong'737'_2846 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsBooleanAlgebra_3224
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsBooleanAlgebra.∨-distrib-∧
d_'8744''45'distrib'45''8743'_2848 ::
  MAlonzo.Code.Algebra.Lattice.Structures.T_IsBooleanAlgebra_3224 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'8744''45'distrib'45''8743'_2848 :: T_IsBooleanAlgebra_3224 -> T_Σ_14
d_'8744''45'distrib'45''8743'_2848 T_IsBooleanAlgebra_3224
v0
  = (T_IsDistributiveLattice_3146 -> T_Σ_14) -> Any -> T_Σ_14
forall a b. a -> b
coe
      T_IsDistributiveLattice_3146 -> T_Σ_14
MAlonzo.Code.Algebra.Lattice.Structures.d_'8744''45'distrib'45''8743'_3160
      ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> Any -> Any
forall a b. a -> b
coe
         T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
         (T_IsBooleanAlgebra_3224 -> Any
forall a b. a -> b
coe T_IsBooleanAlgebra_3224
v0))
-- Data.Bool.Properties._.IsBooleanAlgebra.∨-distribʳ-∧
d_'8744''45'distrib'691''45''8743'_2850 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Lattice.Structures.T_IsBooleanAlgebra_3224 ->
  Bool ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8744''45'distrib'691''45''8743'_2850 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsBooleanAlgebra_3224
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
d_'8744''45'distrib'691''45''8743'_2850 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsBooleanAlgebra_3224
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsBooleanAlgebra.∨-distribˡ-∧
d_'8744''45'distrib'737''45''8743'_2852 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Lattice.Structures.T_IsBooleanAlgebra_3224 ->
  Bool ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8744''45'distrib'737''45''8743'_2852 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsBooleanAlgebra_3224
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
d_'8744''45'distrib'737''45''8743'_2852 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsBooleanAlgebra_3224
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsBoundedJoinSemilattice.assoc
d_assoc_2856 ::
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  Bool ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_assoc_2856 :: (Bool -> Bool -> Bool)
-> Bool
-> T_IsIdempotentCommutativeMonoid_884
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
d_assoc_2856 = (Bool -> Bool -> Bool)
-> Bool
-> T_IsIdempotentCommutativeMonoid_884
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsBoundedJoinSemilattice.comm
d_comm_2858 ::
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_comm_2858 :: (Bool -> Bool -> Bool)
-> Bool
-> T_IsIdempotentCommutativeMonoid_884
-> Bool
-> Bool
-> T__'8801'__12
d_comm_2858 = (Bool -> Bool -> Bool)
-> Bool
-> T_IsIdempotentCommutativeMonoid_884
-> Bool
-> Bool
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsBoundedJoinSemilattice.idem
d_idem_2860 ::
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_idem_2860 :: (Bool -> Bool -> Bool)
-> Bool
-> T_IsIdempotentCommutativeMonoid_884
-> Bool
-> T__'8801'__12
d_idem_2860 = (Bool -> Bool -> Bool)
-> Bool
-> T_IsIdempotentCommutativeMonoid_884
-> Bool
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsBoundedJoinSemilattice.identity
d_identity_2862 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_identity_2862 :: T_IsIdempotentCommutativeMonoid_884 -> T_Σ_14
d_identity_2862 T_IsIdempotentCommutativeMonoid_884
v0
  = (T_IsMonoid_712 -> T_Σ_14) -> Any -> T_Σ_14
forall a b. a -> b
coe
      T_IsMonoid_712 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_identity_724
      ((T_IsCommutativeMonoid_764 -> T_IsMonoid_712) -> Any -> Any
forall a b. a -> b
coe
         T_IsCommutativeMonoid_764 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_774
         ((T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764)
-> Any -> Any
forall a b. a -> b
coe
            T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_894
            (T_IsIdempotentCommutativeMonoid_884 -> Any
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884
v0)))
-- Data.Bool.Properties._.IsBoundedJoinSemilattice.identityʳ
d_identity'691'_2864 ::
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_identity'691'_2864 :: (Bool -> Bool -> Bool)
-> Bool
-> T_IsIdempotentCommutativeMonoid_884
-> Bool
-> T__'8801'__12
d_identity'691'_2864 = (Bool -> Bool -> Bool)
-> Bool
-> T_IsIdempotentCommutativeMonoid_884
-> Bool
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsBoundedJoinSemilattice.identityˡ
d_identity'737'_2866 ::
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_identity'737'_2866 :: (Bool -> Bool -> Bool)
-> Bool
-> T_IsIdempotentCommutativeMonoid_884
-> Bool
-> T__'8801'__12
d_identity'737'_2866 = (Bool -> Bool -> Bool)
-> Bool
-> T_IsIdempotentCommutativeMonoid_884
-> Bool
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsBoundedJoinSemilattice.isBand
d_isBand_2868 ::
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  MAlonzo.Code.Algebra.Structures.T_IsBand_526
d_isBand_2868 :: (Bool -> Bool -> Bool)
-> Bool -> T_IsIdempotentCommutativeMonoid_884 -> T_IsBand_526
d_isBand_2868 ~Bool -> Bool -> Bool
v0 ~Bool
v1 T_IsIdempotentCommutativeMonoid_884
v2 = T_IsIdempotentCommutativeMonoid_884 -> T_IsBand_526
du_isBand_2868 T_IsIdempotentCommutativeMonoid_884
v2
du_isBand_2868 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  MAlonzo.Code.Algebra.Structures.T_IsBand_526
du_isBand_2868 :: T_IsIdempotentCommutativeMonoid_884 -> T_IsBand_526
du_isBand_2868 T_IsIdempotentCommutativeMonoid_884
v0
  = (T_IsIdempotentMonoid_826 -> T_IsBand_526) -> Any -> T_IsBand_526
forall a b. a -> b
coe
      T_IsIdempotentMonoid_826 -> T_IsBand_526
MAlonzo.Code.Algebra.Structures.du_isBand_876
      ((T_IsIdempotentCommutativeMonoid_884 -> T_IsIdempotentMonoid_826)
-> Any -> Any
forall a b. a -> b
coe
         T_IsIdempotentCommutativeMonoid_884 -> T_IsIdempotentMonoid_826
MAlonzo.Code.Algebra.Structures.du_isIdempotentMonoid_942 (T_IsIdempotentCommutativeMonoid_884 -> Any
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884
v0))
-- Data.Bool.Properties._.IsBoundedJoinSemilattice.isEquivalence
d_isEquivalence_2870 ::
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
d_isEquivalence_2870 :: (Bool -> Bool -> Bool)
-> Bool
-> T_IsIdempotentCommutativeMonoid_884
-> T_IsEquivalence_28
d_isEquivalence_2870 ~Bool -> Bool -> Bool
v0 ~Bool
v1 T_IsIdempotentCommutativeMonoid_884
v2 = T_IsIdempotentCommutativeMonoid_884 -> T_IsEquivalence_28
du_isEquivalence_2870 T_IsIdempotentCommutativeMonoid_884
v2
du_isEquivalence_2870 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
du_isEquivalence_2870 :: T_IsIdempotentCommutativeMonoid_884 -> T_IsEquivalence_28
du_isEquivalence_2870 T_IsIdempotentCommutativeMonoid_884
v0
  = let v1 :: Any
v1
          = (T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeBand_612)
-> Any -> Any
forall a b. a -> b
coe
              T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeBand_612
MAlonzo.Code.Algebra.Structures.du_isCommutativeBand_948
              (T_IsIdempotentCommutativeMonoid_884 -> Any
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884
v0) in
    Any -> T_IsEquivalence_28
forall a b. a -> b
coe
      ((T_IsMagma_178 -> T_IsEquivalence_28) -> Any -> Any
forall a b. a -> b
coe
         T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186
         ((T_IsSemigroup_488 -> T_IsMagma_178) -> Any -> Any
forall a b. a -> b
coe
            T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496
            ((T_IsBand_526 -> T_IsSemigroup_488) -> Any -> Any
forall a b. a -> b
coe
               T_IsBand_526 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_534
               ((T_IsCommutativeBand_612 -> T_IsBand_526) -> Any -> Any
forall a b. a -> b
coe T_IsCommutativeBand_612 -> T_IsBand_526
MAlonzo.Code.Algebra.Structures.d_isBand_620 (Any -> Any
forall a b. a -> b
coe Any
v1)))))
-- Data.Bool.Properties._.IsBoundedJoinSemilattice.isCommutativeBand
d_isCommutativeBand_2872 ::
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_612
d_isCommutativeBand_2872 :: (Bool -> Bool -> Bool)
-> Bool
-> T_IsIdempotentCommutativeMonoid_884
-> T_IsCommutativeBand_612
d_isCommutativeBand_2872 ~Bool -> Bool -> Bool
v0 ~Bool
v1 T_IsIdempotentCommutativeMonoid_884
v2 = T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeBand_612
du_isCommutativeBand_2872 T_IsIdempotentCommutativeMonoid_884
v2
du_isCommutativeBand_2872 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_612
du_isCommutativeBand_2872 :: T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeBand_612
du_isCommutativeBand_2872 T_IsIdempotentCommutativeMonoid_884
v0
  = (T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeBand_612)
-> Any -> T_IsCommutativeBand_612
forall a b. a -> b
coe
      T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeBand_612
MAlonzo.Code.Algebra.Structures.du_isCommutativeBand_948 (T_IsIdempotentCommutativeMonoid_884 -> Any
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884
v0)
-- Data.Bool.Properties._.IsBoundedJoinSemilattice.isMagma
d_isMagma_2874 ::
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_178
d_isMagma_2874 :: (Bool -> Bool -> Bool)
-> Bool -> T_IsIdempotentCommutativeMonoid_884 -> T_IsMagma_178
d_isMagma_2874 ~Bool -> Bool -> Bool
v0 ~Bool
v1 T_IsIdempotentCommutativeMonoid_884
v2 = T_IsIdempotentCommutativeMonoid_884 -> T_IsMagma_178
du_isMagma_2874 T_IsIdempotentCommutativeMonoid_884
v2
du_isMagma_2874 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_178
du_isMagma_2874 :: T_IsIdempotentCommutativeMonoid_884 -> T_IsMagma_178
du_isMagma_2874 T_IsIdempotentCommutativeMonoid_884
v0
  = let v1 :: Any
v1
          = (T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeBand_612)
-> Any -> Any
forall a b. a -> b
coe
              T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeBand_612
MAlonzo.Code.Algebra.Structures.du_isCommutativeBand_948
              (T_IsIdempotentCommutativeMonoid_884 -> Any
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884
v0) in
    Any -> T_IsMagma_178
forall a b. a -> b
coe
      ((T_IsSemigroup_488 -> T_IsMagma_178) -> Any -> Any
forall a b. a -> b
coe
         T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496
         ((T_IsBand_526 -> T_IsSemigroup_488) -> Any -> Any
forall a b. a -> b
coe
            T_IsBand_526 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_534
            ((T_IsCommutativeBand_612 -> T_IsBand_526) -> Any -> Any
forall a b. a -> b
coe T_IsCommutativeBand_612 -> T_IsBand_526
MAlonzo.Code.Algebra.Structures.d_isBand_620 (Any -> Any
forall a b. a -> b
coe Any
v1))))
-- Data.Bool.Properties._.IsBoundedJoinSemilattice.isPartialEquivalence
d_isPartialEquivalence_2876 ::
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_2876 :: (Bool -> Bool -> Bool)
-> Bool
-> T_IsIdempotentCommutativeMonoid_884
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_2876 ~Bool -> Bool -> Bool
v0 ~Bool
v1 T_IsIdempotentCommutativeMonoid_884
v2
  = T_IsIdempotentCommutativeMonoid_884 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_2876 T_IsIdempotentCommutativeMonoid_884
v2
du_isPartialEquivalence_2876 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_2876 :: T_IsIdempotentCommutativeMonoid_884 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_2876 T_IsIdempotentCommutativeMonoid_884
v0
  = let v1 :: Any
v1
          = (T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeBand_612)
-> Any -> Any
forall a b. a -> b
coe
              T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeBand_612
MAlonzo.Code.Algebra.Structures.du_isCommutativeBand_948
              (T_IsIdempotentCommutativeMonoid_884 -> Any
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884
v0) in
    Any -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsBand_526
v2 = T_IsCommutativeBand_612 -> T_IsBand_526
MAlonzo.Code.Algebra.Structures.d_isBand_620 (Any -> T_IsCommutativeBand_612
forall a b. a -> b
coe Any
v1) in
       Any -> Any
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_488
v3
                = T_IsBand_526 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_534 (T_IsBand_526 -> T_IsBand_526
forall a b. a -> b
coe T_IsBand_526
v2) in
          Any -> Any
forall a b. a -> b
coe
            (let v4 :: T_IsMagma_178
v4 = T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496 (T_IsSemigroup_488 -> T_IsSemigroup_488
forall a b. a -> b
coe T_IsSemigroup_488
v3) in
             Any -> Any
forall a b. a -> b
coe
               ((T_IsEquivalence_28 -> T_IsPartialEquivalence_16) -> Any -> Any
forall a b. a -> b
coe
                  T_IsEquivalence_28 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_44
                  ((T_IsMagma_178 -> T_IsEquivalence_28) -> Any -> Any
forall a b. a -> b
coe
                     T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186 (T_IsMagma_178 -> Any
forall a b. a -> b
coe T_IsMagma_178
v4))))))
-- Data.Bool.Properties._.IsBoundedJoinSemilattice.isSemigroup
d_isSemigroup_2878 ::
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_488
d_isSemigroup_2878 :: (Bool -> Bool -> Bool)
-> Bool -> T_IsIdempotentCommutativeMonoid_884 -> T_IsSemigroup_488
d_isSemigroup_2878 ~Bool -> Bool -> Bool
v0 ~Bool
v1 T_IsIdempotentCommutativeMonoid_884
v2 = T_IsIdempotentCommutativeMonoid_884 -> T_IsSemigroup_488
du_isSemigroup_2878 T_IsIdempotentCommutativeMonoid_884
v2
du_isSemigroup_2878 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_488
du_isSemigroup_2878 :: T_IsIdempotentCommutativeMonoid_884 -> T_IsSemigroup_488
du_isSemigroup_2878 T_IsIdempotentCommutativeMonoid_884
v0
  = let v1 :: Any
v1
          = (T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeBand_612)
-> Any -> Any
forall a b. a -> b
coe
              T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeBand_612
MAlonzo.Code.Algebra.Structures.du_isCommutativeBand_948
              (T_IsIdempotentCommutativeMonoid_884 -> Any
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884
v0) in
    Any -> T_IsSemigroup_488
forall a b. a -> b
coe
      ((T_IsBand_526 -> T_IsSemigroup_488) -> Any -> Any
forall a b. a -> b
coe
         T_IsBand_526 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_534
         ((T_IsCommutativeBand_612 -> T_IsBand_526) -> Any -> Any
forall a b. a -> b
coe T_IsCommutativeBand_612 -> T_IsBand_526
MAlonzo.Code.Algebra.Structures.d_isBand_620 (Any -> Any
forall a b. a -> b
coe Any
v1)))
-- Data.Bool.Properties._.IsBoundedJoinSemilattice.refl
d_refl_2880 ::
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_refl_2880 :: (Bool -> Bool -> Bool)
-> Bool
-> T_IsIdempotentCommutativeMonoid_884
-> Bool
-> T__'8801'__12
d_refl_2880 = (Bool -> Bool -> Bool)
-> Bool
-> T_IsIdempotentCommutativeMonoid_884
-> Bool
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsBoundedJoinSemilattice.reflexive
d_reflexive_2882 ::
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_reflexive_2882 :: (Bool -> Bool -> Bool)
-> Bool
-> T_IsIdempotentCommutativeMonoid_884
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_reflexive_2882 = (Bool -> Bool -> Bool)
-> Bool
-> T_IsIdempotentCommutativeMonoid_884
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsBoundedJoinSemilattice.setoid
d_setoid_2884 ::
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
d_setoid_2884 :: (Bool -> Bool -> Bool)
-> Bool -> T_IsIdempotentCommutativeMonoid_884 -> T_Setoid_46
d_setoid_2884 ~Bool -> Bool -> Bool
v0 ~Bool
v1 T_IsIdempotentCommutativeMonoid_884
v2 = T_IsIdempotentCommutativeMonoid_884 -> T_Setoid_46
du_setoid_2884 T_IsIdempotentCommutativeMonoid_884
v2
du_setoid_2884 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
du_setoid_2884 :: T_IsIdempotentCommutativeMonoid_884 -> T_Setoid_46
du_setoid_2884 T_IsIdempotentCommutativeMonoid_884
v0
  = let v1 :: Any
v1
          = (T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeBand_612)
-> Any -> Any
forall a b. a -> b
coe
              T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeBand_612
MAlonzo.Code.Algebra.Structures.du_isCommutativeBand_948
              (T_IsIdempotentCommutativeMonoid_884 -> Any
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884
v0) in
    Any -> T_Setoid_46
forall a b. a -> b
coe
      (let v2 :: T_IsBand_526
v2 = T_IsCommutativeBand_612 -> T_IsBand_526
MAlonzo.Code.Algebra.Structures.d_isBand_620 (Any -> T_IsCommutativeBand_612
forall a b. a -> b
coe Any
v1) in
       Any -> Any
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_488
v3
                = T_IsBand_526 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_534 (T_IsBand_526 -> T_IsBand_526
forall a b. a -> b
coe T_IsBand_526
v2) in
          Any -> Any
forall a b. a -> b
coe
            ((T_IsMagma_178 -> T_Setoid_46) -> Any -> Any
forall a b. a -> b
coe
               T_IsMagma_178 -> T_Setoid_46
MAlonzo.Code.Algebra.Structures.du_setoid_202
               ((T_IsSemigroup_488 -> T_IsMagma_178) -> Any -> Any
forall a b. a -> b
coe T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496 (T_IsSemigroup_488 -> Any
forall a b. a -> b
coe T_IsSemigroup_488
v3)))))
-- Data.Bool.Properties._.IsBoundedJoinSemilattice.sym
d_sym_2886 ::
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_sym_2886 :: (Bool -> Bool -> Bool)
-> Bool
-> T_IsIdempotentCommutativeMonoid_884
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_sym_2886 = (Bool -> Bool -> Bool)
-> Bool
-> T_IsIdempotentCommutativeMonoid_884
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsBoundedJoinSemilattice.trans
d_trans_2888 ::
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_trans_2888 :: (Bool -> Bool -> Bool)
-> Bool
-> T_IsIdempotentCommutativeMonoid_884
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
d_trans_2888 = (Bool -> Bool -> Bool)
-> Bool
-> T_IsIdempotentCommutativeMonoid_884
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsBoundedJoinSemilattice.∙-cong
d_'8729''45'cong_2890 ::
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  Bool ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8729''45'cong_2890 :: (Bool -> Bool -> Bool)
-> Bool
-> T_IsIdempotentCommutativeMonoid_884
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong_2890 = (Bool -> Bool -> Bool)
-> Bool
-> T_IsIdempotentCommutativeMonoid_884
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsBoundedJoinSemilattice.∙-congʳ
d_'8729''45'cong'691'_2892 ::
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8729''45'cong'691'_2892 :: (Bool -> Bool -> Bool)
-> Bool
-> T_IsIdempotentCommutativeMonoid_884
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong'691'_2892 = (Bool -> Bool -> Bool)
-> Bool
-> T_IsIdempotentCommutativeMonoid_884
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsBoundedJoinSemilattice.∙-congˡ
d_'8729''45'cong'737'_2894 ::
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8729''45'cong'737'_2894 :: (Bool -> Bool -> Bool)
-> Bool
-> T_IsIdempotentCommutativeMonoid_884
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong'737'_2894 = (Bool -> Bool -> Bool)
-> Bool
-> T_IsIdempotentCommutativeMonoid_884
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsBoundedMeetSemilattice.assoc
d_assoc_2898 ::
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  Bool ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_assoc_2898 :: (Bool -> Bool -> Bool)
-> Bool
-> T_IsIdempotentCommutativeMonoid_884
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
d_assoc_2898 = (Bool -> Bool -> Bool)
-> Bool
-> T_IsIdempotentCommutativeMonoid_884
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsBoundedMeetSemilattice.comm
d_comm_2900 ::
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_comm_2900 :: (Bool -> Bool -> Bool)
-> Bool
-> T_IsIdempotentCommutativeMonoid_884
-> Bool
-> Bool
-> T__'8801'__12
d_comm_2900 = (Bool -> Bool -> Bool)
-> Bool
-> T_IsIdempotentCommutativeMonoid_884
-> Bool
-> Bool
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsBoundedMeetSemilattice.idem
d_idem_2902 ::
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_idem_2902 :: (Bool -> Bool -> Bool)
-> Bool
-> T_IsIdempotentCommutativeMonoid_884
-> Bool
-> T__'8801'__12
d_idem_2902 = (Bool -> Bool -> Bool)
-> Bool
-> T_IsIdempotentCommutativeMonoid_884
-> Bool
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsBoundedMeetSemilattice.identity
d_identity_2904 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_identity_2904 :: T_IsIdempotentCommutativeMonoid_884 -> T_Σ_14
d_identity_2904 T_IsIdempotentCommutativeMonoid_884
v0
  = (T_IsMonoid_712 -> T_Σ_14) -> Any -> T_Σ_14
forall a b. a -> b
coe
      T_IsMonoid_712 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_identity_724
      ((T_IsCommutativeMonoid_764 -> T_IsMonoid_712) -> Any -> Any
forall a b. a -> b
coe
         T_IsCommutativeMonoid_764 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_774
         ((T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764)
-> Any -> Any
forall a b. a -> b
coe
            T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_894
            (T_IsIdempotentCommutativeMonoid_884 -> Any
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884
v0)))
-- Data.Bool.Properties._.IsBoundedMeetSemilattice.identityʳ
d_identity'691'_2906 ::
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_identity'691'_2906 :: (Bool -> Bool -> Bool)
-> Bool
-> T_IsIdempotentCommutativeMonoid_884
-> Bool
-> T__'8801'__12
d_identity'691'_2906 = (Bool -> Bool -> Bool)
-> Bool
-> T_IsIdempotentCommutativeMonoid_884
-> Bool
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsBoundedMeetSemilattice.identityˡ
d_identity'737'_2908 ::
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_identity'737'_2908 :: (Bool -> Bool -> Bool)
-> Bool
-> T_IsIdempotentCommutativeMonoid_884
-> Bool
-> T__'8801'__12
d_identity'737'_2908 = (Bool -> Bool -> Bool)
-> Bool
-> T_IsIdempotentCommutativeMonoid_884
-> Bool
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsBoundedMeetSemilattice.isBand
d_isBand_2910 ::
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  MAlonzo.Code.Algebra.Structures.T_IsBand_526
d_isBand_2910 :: (Bool -> Bool -> Bool)
-> Bool -> T_IsIdempotentCommutativeMonoid_884 -> T_IsBand_526
d_isBand_2910 ~Bool -> Bool -> Bool
v0 ~Bool
v1 T_IsIdempotentCommutativeMonoid_884
v2 = T_IsIdempotentCommutativeMonoid_884 -> T_IsBand_526
du_isBand_2910 T_IsIdempotentCommutativeMonoid_884
v2
du_isBand_2910 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  MAlonzo.Code.Algebra.Structures.T_IsBand_526
du_isBand_2910 :: T_IsIdempotentCommutativeMonoid_884 -> T_IsBand_526
du_isBand_2910 T_IsIdempotentCommutativeMonoid_884
v0
  = (T_IsIdempotentMonoid_826 -> T_IsBand_526) -> Any -> T_IsBand_526
forall a b. a -> b
coe
      T_IsIdempotentMonoid_826 -> T_IsBand_526
MAlonzo.Code.Algebra.Structures.du_isBand_876
      ((T_IsIdempotentCommutativeMonoid_884 -> T_IsIdempotentMonoid_826)
-> Any -> Any
forall a b. a -> b
coe
         T_IsIdempotentCommutativeMonoid_884 -> T_IsIdempotentMonoid_826
MAlonzo.Code.Algebra.Structures.du_isIdempotentMonoid_942 (T_IsIdempotentCommutativeMonoid_884 -> Any
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884
v0))
-- Data.Bool.Properties._.IsBoundedMeetSemilattice.isEquivalence
d_isEquivalence_2912 ::
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
d_isEquivalence_2912 :: (Bool -> Bool -> Bool)
-> Bool
-> T_IsIdempotentCommutativeMonoid_884
-> T_IsEquivalence_28
d_isEquivalence_2912 ~Bool -> Bool -> Bool
v0 ~Bool
v1 T_IsIdempotentCommutativeMonoid_884
v2 = T_IsIdempotentCommutativeMonoid_884 -> T_IsEquivalence_28
du_isEquivalence_2912 T_IsIdempotentCommutativeMonoid_884
v2
du_isEquivalence_2912 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
du_isEquivalence_2912 :: T_IsIdempotentCommutativeMonoid_884 -> T_IsEquivalence_28
du_isEquivalence_2912 T_IsIdempotentCommutativeMonoid_884
v0
  = let v1 :: Any
v1
          = (T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeBand_612)
-> Any -> Any
forall a b. a -> b
coe
              T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeBand_612
MAlonzo.Code.Algebra.Structures.du_isCommutativeBand_948
              (T_IsIdempotentCommutativeMonoid_884 -> Any
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884
v0) in
    Any -> T_IsEquivalence_28
forall a b. a -> b
coe
      ((T_IsMagma_178 -> T_IsEquivalence_28) -> Any -> Any
forall a b. a -> b
coe
         T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186
         ((T_IsSemigroup_488 -> T_IsMagma_178) -> Any -> Any
forall a b. a -> b
coe
            T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496
            ((T_IsBand_526 -> T_IsSemigroup_488) -> Any -> Any
forall a b. a -> b
coe
               T_IsBand_526 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_534
               ((T_IsCommutativeBand_612 -> T_IsBand_526) -> Any -> Any
forall a b. a -> b
coe T_IsCommutativeBand_612 -> T_IsBand_526
MAlonzo.Code.Algebra.Structures.d_isBand_620 (Any -> Any
forall a b. a -> b
coe Any
v1)))))
-- Data.Bool.Properties._.IsBoundedMeetSemilattice.isMagma
d_isMagma_2914 ::
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_178
d_isMagma_2914 :: (Bool -> Bool -> Bool)
-> Bool -> T_IsIdempotentCommutativeMonoid_884 -> T_IsMagma_178
d_isMagma_2914 ~Bool -> Bool -> Bool
v0 ~Bool
v1 T_IsIdempotentCommutativeMonoid_884
v2 = T_IsIdempotentCommutativeMonoid_884 -> T_IsMagma_178
du_isMagma_2914 T_IsIdempotentCommutativeMonoid_884
v2
du_isMagma_2914 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_178
du_isMagma_2914 :: T_IsIdempotentCommutativeMonoid_884 -> T_IsMagma_178
du_isMagma_2914 T_IsIdempotentCommutativeMonoid_884
v0
  = let v1 :: Any
v1
          = (T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeBand_612)
-> Any -> Any
forall a b. a -> b
coe
              T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeBand_612
MAlonzo.Code.Algebra.Structures.du_isCommutativeBand_948
              (T_IsIdempotentCommutativeMonoid_884 -> Any
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884
v0) in
    Any -> T_IsMagma_178
forall a b. a -> b
coe
      ((T_IsSemigroup_488 -> T_IsMagma_178) -> Any -> Any
forall a b. a -> b
coe
         T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496
         ((T_IsBand_526 -> T_IsSemigroup_488) -> Any -> Any
forall a b. a -> b
coe
            T_IsBand_526 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_534
            ((T_IsCommutativeBand_612 -> T_IsBand_526) -> Any -> Any
forall a b. a -> b
coe T_IsCommutativeBand_612 -> T_IsBand_526
MAlonzo.Code.Algebra.Structures.d_isBand_620 (Any -> Any
forall a b. a -> b
coe Any
v1))))
-- Data.Bool.Properties._.IsBoundedMeetSemilattice.isCommutativeBand
d_isCommutativeBand_2916 ::
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_612
d_isCommutativeBand_2916 :: (Bool -> Bool -> Bool)
-> Bool
-> T_IsIdempotentCommutativeMonoid_884
-> T_IsCommutativeBand_612
d_isCommutativeBand_2916 ~Bool -> Bool -> Bool
v0 ~Bool
v1 T_IsIdempotentCommutativeMonoid_884
v2 = T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeBand_612
du_isCommutativeBand_2916 T_IsIdempotentCommutativeMonoid_884
v2
du_isCommutativeBand_2916 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_612
du_isCommutativeBand_2916 :: T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeBand_612
du_isCommutativeBand_2916 T_IsIdempotentCommutativeMonoid_884
v0
  = (T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeBand_612)
-> Any -> T_IsCommutativeBand_612
forall a b. a -> b
coe
      T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeBand_612
MAlonzo.Code.Algebra.Structures.du_isCommutativeBand_948 (T_IsIdempotentCommutativeMonoid_884 -> Any
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884
v0)
-- Data.Bool.Properties._.IsBoundedMeetSemilattice.isPartialEquivalence
d_isPartialEquivalence_2918 ::
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_2918 :: (Bool -> Bool -> Bool)
-> Bool
-> T_IsIdempotentCommutativeMonoid_884
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_2918 ~Bool -> Bool -> Bool
v0 ~Bool
v1 T_IsIdempotentCommutativeMonoid_884
v2
  = T_IsIdempotentCommutativeMonoid_884 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_2918 T_IsIdempotentCommutativeMonoid_884
v2
du_isPartialEquivalence_2918 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_2918 :: T_IsIdempotentCommutativeMonoid_884 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_2918 T_IsIdempotentCommutativeMonoid_884
v0
  = let v1 :: Any
v1
          = (T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeBand_612)
-> Any -> Any
forall a b. a -> b
coe
              T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeBand_612
MAlonzo.Code.Algebra.Structures.du_isCommutativeBand_948
              (T_IsIdempotentCommutativeMonoid_884 -> Any
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884
v0) in
    Any -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsBand_526
v2 = T_IsCommutativeBand_612 -> T_IsBand_526
MAlonzo.Code.Algebra.Structures.d_isBand_620 (Any -> T_IsCommutativeBand_612
forall a b. a -> b
coe Any
v1) in
       Any -> Any
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_488
v3
                = T_IsBand_526 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_534 (T_IsBand_526 -> T_IsBand_526
forall a b. a -> b
coe T_IsBand_526
v2) in
          Any -> Any
forall a b. a -> b
coe
            (let v4 :: T_IsMagma_178
v4 = T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496 (T_IsSemigroup_488 -> T_IsSemigroup_488
forall a b. a -> b
coe T_IsSemigroup_488
v3) in
             Any -> Any
forall a b. a -> b
coe
               ((T_IsEquivalence_28 -> T_IsPartialEquivalence_16) -> Any -> Any
forall a b. a -> b
coe
                  T_IsEquivalence_28 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_44
                  ((T_IsMagma_178 -> T_IsEquivalence_28) -> Any -> Any
forall a b. a -> b
coe
                     T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186 (T_IsMagma_178 -> Any
forall a b. a -> b
coe T_IsMagma_178
v4))))))
-- Data.Bool.Properties._.IsBoundedMeetSemilattice.isSemigroup
d_isSemigroup_2920 ::
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_488
d_isSemigroup_2920 :: (Bool -> Bool -> Bool)
-> Bool -> T_IsIdempotentCommutativeMonoid_884 -> T_IsSemigroup_488
d_isSemigroup_2920 ~Bool -> Bool -> Bool
v0 ~Bool
v1 T_IsIdempotentCommutativeMonoid_884
v2 = T_IsIdempotentCommutativeMonoid_884 -> T_IsSemigroup_488
du_isSemigroup_2920 T_IsIdempotentCommutativeMonoid_884
v2
du_isSemigroup_2920 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_488
du_isSemigroup_2920 :: T_IsIdempotentCommutativeMonoid_884 -> T_IsSemigroup_488
du_isSemigroup_2920 T_IsIdempotentCommutativeMonoid_884
v0
  = let v1 :: Any
v1
          = (T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeBand_612)
-> Any -> Any
forall a b. a -> b
coe
              T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeBand_612
MAlonzo.Code.Algebra.Structures.du_isCommutativeBand_948
              (T_IsIdempotentCommutativeMonoid_884 -> Any
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884
v0) in
    Any -> T_IsSemigroup_488
forall a b. a -> b
coe
      ((T_IsBand_526 -> T_IsSemigroup_488) -> Any -> Any
forall a b. a -> b
coe
         T_IsBand_526 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_534
         ((T_IsCommutativeBand_612 -> T_IsBand_526) -> Any -> Any
forall a b. a -> b
coe T_IsCommutativeBand_612 -> T_IsBand_526
MAlonzo.Code.Algebra.Structures.d_isBand_620 (Any -> Any
forall a b. a -> b
coe Any
v1)))
-- Data.Bool.Properties._.IsBoundedMeetSemilattice.refl
d_refl_2922 ::
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_refl_2922 :: (Bool -> Bool -> Bool)
-> Bool
-> T_IsIdempotentCommutativeMonoid_884
-> Bool
-> T__'8801'__12
d_refl_2922 = (Bool -> Bool -> Bool)
-> Bool
-> T_IsIdempotentCommutativeMonoid_884
-> Bool
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsBoundedMeetSemilattice.reflexive
d_reflexive_2924 ::
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_reflexive_2924 :: (Bool -> Bool -> Bool)
-> Bool
-> T_IsIdempotentCommutativeMonoid_884
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_reflexive_2924 = (Bool -> Bool -> Bool)
-> Bool
-> T_IsIdempotentCommutativeMonoid_884
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsBoundedMeetSemilattice.setoid
d_setoid_2926 ::
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
d_setoid_2926 :: (Bool -> Bool -> Bool)
-> Bool -> T_IsIdempotentCommutativeMonoid_884 -> T_Setoid_46
d_setoid_2926 ~Bool -> Bool -> Bool
v0 ~Bool
v1 T_IsIdempotentCommutativeMonoid_884
v2 = T_IsIdempotentCommutativeMonoid_884 -> T_Setoid_46
du_setoid_2926 T_IsIdempotentCommutativeMonoid_884
v2
du_setoid_2926 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
du_setoid_2926 :: T_IsIdempotentCommutativeMonoid_884 -> T_Setoid_46
du_setoid_2926 T_IsIdempotentCommutativeMonoid_884
v0
  = let v1 :: Any
v1
          = (T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeBand_612)
-> Any -> Any
forall a b. a -> b
coe
              T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeBand_612
MAlonzo.Code.Algebra.Structures.du_isCommutativeBand_948
              (T_IsIdempotentCommutativeMonoid_884 -> Any
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884
v0) in
    Any -> T_Setoid_46
forall a b. a -> b
coe
      (let v2 :: T_IsBand_526
v2 = T_IsCommutativeBand_612 -> T_IsBand_526
MAlonzo.Code.Algebra.Structures.d_isBand_620 (Any -> T_IsCommutativeBand_612
forall a b. a -> b
coe Any
v1) in
       Any -> Any
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_488
v3
                = T_IsBand_526 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_534 (T_IsBand_526 -> T_IsBand_526
forall a b. a -> b
coe T_IsBand_526
v2) in
          Any -> Any
forall a b. a -> b
coe
            ((T_IsMagma_178 -> T_Setoid_46) -> Any -> Any
forall a b. a -> b
coe
               T_IsMagma_178 -> T_Setoid_46
MAlonzo.Code.Algebra.Structures.du_setoid_202
               ((T_IsSemigroup_488 -> T_IsMagma_178) -> Any -> Any
forall a b. a -> b
coe T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496 (T_IsSemigroup_488 -> Any
forall a b. a -> b
coe T_IsSemigroup_488
v3)))))
-- Data.Bool.Properties._.IsBoundedMeetSemilattice.sym
d_sym_2928 ::
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_sym_2928 :: (Bool -> Bool -> Bool)
-> Bool
-> T_IsIdempotentCommutativeMonoid_884
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_sym_2928 = (Bool -> Bool -> Bool)
-> Bool
-> T_IsIdempotentCommutativeMonoid_884
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsBoundedMeetSemilattice.trans
d_trans_2930 ::
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_trans_2930 :: (Bool -> Bool -> Bool)
-> Bool
-> T_IsIdempotentCommutativeMonoid_884
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
d_trans_2930 = (Bool -> Bool -> Bool)
-> Bool
-> T_IsIdempotentCommutativeMonoid_884
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsBoundedMeetSemilattice.∙-cong
d_'8729''45'cong_2932 ::
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  Bool ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8729''45'cong_2932 :: (Bool -> Bool -> Bool)
-> Bool
-> T_IsIdempotentCommutativeMonoid_884
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong_2932 = (Bool -> Bool -> Bool)
-> Bool
-> T_IsIdempotentCommutativeMonoid_884
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsBoundedMeetSemilattice.∙-congʳ
d_'8729''45'cong'691'_2934 ::
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8729''45'cong'691'_2934 :: (Bool -> Bool -> Bool)
-> Bool
-> T_IsIdempotentCommutativeMonoid_884
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong'691'_2934 = (Bool -> Bool -> Bool)
-> Bool
-> T_IsIdempotentCommutativeMonoid_884
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsBoundedMeetSemilattice.∙-congˡ
d_'8729''45'cong'737'_2936 ::
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8729''45'cong'737'_2936 :: (Bool -> Bool -> Bool)
-> Bool
-> T_IsIdempotentCommutativeMonoid_884
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong'737'_2936 = (Bool -> Bool -> Bool)
-> Bool
-> T_IsIdempotentCommutativeMonoid_884
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsBoundedSemilattice.assoc
d_assoc_2940 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  Bool ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_assoc_2940 :: T_IsIdempotentCommutativeMonoid_884
-> Bool -> Bool -> Bool -> T__'8801'__12
d_assoc_2940 = T_IsIdempotentCommutativeMonoid_884
-> Bool -> Bool -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsBoundedSemilattice.comm
d_comm_2942 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_comm_2942 :: T_IsIdempotentCommutativeMonoid_884
-> Bool -> Bool -> T__'8801'__12
d_comm_2942 = T_IsIdempotentCommutativeMonoid_884
-> Bool -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsBoundedSemilattice.idem
d_idem_2944 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_idem_2944 :: T_IsIdempotentCommutativeMonoid_884 -> Bool -> T__'8801'__12
d_idem_2944 = T_IsIdempotentCommutativeMonoid_884 -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsBoundedSemilattice.identity
d_identity_2946 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_identity_2946 :: T_IsIdempotentCommutativeMonoid_884 -> T_Σ_14
d_identity_2946 T_IsIdempotentCommutativeMonoid_884
v0
  = (T_IsMonoid_712 -> T_Σ_14) -> Any -> T_Σ_14
forall a b. a -> b
coe
      T_IsMonoid_712 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_identity_724
      ((T_IsCommutativeMonoid_764 -> T_IsMonoid_712) -> Any -> Any
forall a b. a -> b
coe
         T_IsCommutativeMonoid_764 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_774
         ((T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764)
-> Any -> Any
forall a b. a -> b
coe
            T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_894
            (T_IsIdempotentCommutativeMonoid_884 -> Any
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884
v0)))
-- Data.Bool.Properties._.IsBoundedSemilattice.identityʳ
d_identity'691'_2948 ::
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_identity'691'_2948 :: (Bool -> Bool -> Bool)
-> Bool
-> T_IsIdempotentCommutativeMonoid_884
-> Bool
-> T__'8801'__12
d_identity'691'_2948 = (Bool -> Bool -> Bool)
-> Bool
-> T_IsIdempotentCommutativeMonoid_884
-> Bool
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsBoundedSemilattice.identityˡ
d_identity'737'_2950 ::
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_identity'737'_2950 :: (Bool -> Bool -> Bool)
-> Bool
-> T_IsIdempotentCommutativeMonoid_884
-> Bool
-> T__'8801'__12
d_identity'737'_2950 = (Bool -> Bool -> Bool)
-> Bool
-> T_IsIdempotentCommutativeMonoid_884
-> Bool
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsBoundedSemilattice.isBand
d_isBand_2952 ::
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  MAlonzo.Code.Algebra.Structures.T_IsBand_526
d_isBand_2952 :: (Bool -> Bool -> Bool)
-> Bool -> T_IsIdempotentCommutativeMonoid_884 -> T_IsBand_526
d_isBand_2952 ~Bool -> Bool -> Bool
v0 ~Bool
v1 T_IsIdempotentCommutativeMonoid_884
v2 = T_IsIdempotentCommutativeMonoid_884 -> T_IsBand_526
du_isBand_2952 T_IsIdempotentCommutativeMonoid_884
v2
du_isBand_2952 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  MAlonzo.Code.Algebra.Structures.T_IsBand_526
du_isBand_2952 :: T_IsIdempotentCommutativeMonoid_884 -> T_IsBand_526
du_isBand_2952 T_IsIdempotentCommutativeMonoid_884
v0
  = (T_IsIdempotentMonoid_826 -> T_IsBand_526) -> Any -> T_IsBand_526
forall a b. a -> b
coe
      T_IsIdempotentMonoid_826 -> T_IsBand_526
MAlonzo.Code.Algebra.Structures.du_isBand_876
      ((T_IsIdempotentCommutativeMonoid_884 -> T_IsIdempotentMonoid_826)
-> Any -> Any
forall a b. a -> b
coe
         T_IsIdempotentCommutativeMonoid_884 -> T_IsIdempotentMonoid_826
MAlonzo.Code.Algebra.Structures.du_isIdempotentMonoid_942 (T_IsIdempotentCommutativeMonoid_884 -> Any
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884
v0))
-- Data.Bool.Properties._.IsBoundedSemilattice.isCommutativeMagma
d_isCommutativeMagma_2954 ::
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMagma_214
d_isCommutativeMagma_2954 :: (Bool -> Bool -> Bool)
-> Bool
-> T_IsIdempotentCommutativeMonoid_884
-> T_IsCommutativeMagma_214
d_isCommutativeMagma_2954 ~Bool -> Bool -> Bool
v0 ~Bool
v1 T_IsIdempotentCommutativeMonoid_884
v2
  = T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMagma_214
du_isCommutativeMagma_2954 T_IsIdempotentCommutativeMonoid_884
v2
du_isCommutativeMagma_2954 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMagma_214
du_isCommutativeMagma_2954 :: T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMagma_214
du_isCommutativeMagma_2954 T_IsIdempotentCommutativeMonoid_884
v0
  = let v1 :: T_IsCommutativeMonoid_764
v1
          = T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_894
              (T_IsIdempotentCommutativeMonoid_884
-> T_IsIdempotentCommutativeMonoid_884
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884
v0) in
    Any -> T_IsCommutativeMagma_214
forall a b. a -> b
coe
      ((T_IsCommutativeSemigroup_568 -> T_IsCommutativeMagma_214)
-> Any -> Any
forall a b. a -> b
coe
         T_IsCommutativeSemigroup_568 -> T_IsCommutativeMagma_214
MAlonzo.Code.Algebra.Structures.du_isCommutativeMagma_606
         ((T_IsCommutativeMonoid_764 -> T_IsCommutativeSemigroup_568)
-> Any -> Any
forall a b. a -> b
coe
            T_IsCommutativeMonoid_764 -> T_IsCommutativeSemigroup_568
MAlonzo.Code.Algebra.Structures.du_isCommutativeSemigroup_814
            (T_IsCommutativeMonoid_764 -> Any
forall a b. a -> b
coe T_IsCommutativeMonoid_764
v1)))
-- Data.Bool.Properties._.IsBoundedSemilattice.isCommutativeMonoid
d_isCommutativeMonoid_2956 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMonoid_764
d_isCommutativeMonoid_2956 :: T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764
d_isCommutativeMonoid_2956 T_IsIdempotentCommutativeMonoid_884
v0
  = (T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764)
-> Any -> T_IsCommutativeMonoid_764
forall a b. a -> b
coe
      T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_894 (T_IsIdempotentCommutativeMonoid_884 -> Any
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884
v0)
-- Data.Bool.Properties._.IsBoundedSemilattice.isCommutativeSemigroup
d_isCommutativeSemigroup_2958 ::
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_568
d_isCommutativeSemigroup_2958 :: (Bool -> Bool -> Bool)
-> Bool
-> T_IsIdempotentCommutativeMonoid_884
-> T_IsCommutativeSemigroup_568
d_isCommutativeSemigroup_2958 ~Bool -> Bool -> Bool
v0 ~Bool
v1 T_IsIdempotentCommutativeMonoid_884
v2
  = T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeSemigroup_568
du_isCommutativeSemigroup_2958 T_IsIdempotentCommutativeMonoid_884
v2
du_isCommutativeSemigroup_2958 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_568
du_isCommutativeSemigroup_2958 :: T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeSemigroup_568
du_isCommutativeSemigroup_2958 T_IsIdempotentCommutativeMonoid_884
v0
  = (T_IsCommutativeMonoid_764 -> T_IsCommutativeSemigroup_568)
-> Any -> T_IsCommutativeSemigroup_568
forall a b. a -> b
coe
      T_IsCommutativeMonoid_764 -> T_IsCommutativeSemigroup_568
MAlonzo.Code.Algebra.Structures.du_isCommutativeSemigroup_814
      ((T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764)
-> Any -> Any
forall a b. a -> b
coe
         T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_894 (T_IsIdempotentCommutativeMonoid_884 -> Any
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884
v0))
-- Data.Bool.Properties._.IsBoundedSemilattice.isEquivalence
d_isEquivalence_2960 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
d_isEquivalence_2960 :: T_IsIdempotentCommutativeMonoid_884 -> T_IsEquivalence_28
d_isEquivalence_2960 T_IsIdempotentCommutativeMonoid_884
v0
  = (T_IsMagma_178 -> T_IsEquivalence_28) -> Any -> T_IsEquivalence_28
forall a b. a -> b
coe
      T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186
      ((T_IsSemigroup_488 -> T_IsMagma_178) -> Any -> Any
forall a b. a -> b
coe
         T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496
         ((T_IsMonoid_712 -> T_IsSemigroup_488) -> Any -> Any
forall a b. a -> b
coe
            T_IsMonoid_712 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_722
            ((T_IsCommutativeMonoid_764 -> T_IsMonoid_712) -> Any -> Any
forall a b. a -> b
coe
               T_IsCommutativeMonoid_764 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_774
               ((T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764)
-> Any -> Any
forall a b. a -> b
coe
                  T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_894
                  (T_IsIdempotentCommutativeMonoid_884 -> Any
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884
v0)))))
-- Data.Bool.Properties._.IsBoundedSemilattice.isIdempotentMonoid
d_isIdempotentMonoid_2962 ::
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentMonoid_826
d_isIdempotentMonoid_2962 :: (Bool -> Bool -> Bool)
-> Bool
-> T_IsIdempotentCommutativeMonoid_884
-> T_IsIdempotentMonoid_826
d_isIdempotentMonoid_2962 ~Bool -> Bool -> Bool
v0 ~Bool
v1 T_IsIdempotentCommutativeMonoid_884
v2
  = T_IsIdempotentCommutativeMonoid_884 -> T_IsIdempotentMonoid_826
du_isIdempotentMonoid_2962 T_IsIdempotentCommutativeMonoid_884
v2
du_isIdempotentMonoid_2962 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentMonoid_826
du_isIdempotentMonoid_2962 :: T_IsIdempotentCommutativeMonoid_884 -> T_IsIdempotentMonoid_826
du_isIdempotentMonoid_2962 T_IsIdempotentCommutativeMonoid_884
v0
  = (T_IsIdempotentCommutativeMonoid_884 -> T_IsIdempotentMonoid_826)
-> Any -> T_IsIdempotentMonoid_826
forall a b. a -> b
coe
      T_IsIdempotentCommutativeMonoid_884 -> T_IsIdempotentMonoid_826
MAlonzo.Code.Algebra.Structures.du_isIdempotentMonoid_942 (T_IsIdempotentCommutativeMonoid_884 -> Any
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884
v0)
-- Data.Bool.Properties._.IsBoundedSemilattice.isMagma
d_isMagma_2964 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_178
d_isMagma_2964 :: T_IsIdempotentCommutativeMonoid_884 -> T_IsMagma_178
d_isMagma_2964 T_IsIdempotentCommutativeMonoid_884
v0
  = (T_IsSemigroup_488 -> T_IsMagma_178) -> Any -> T_IsMagma_178
forall a b. a -> b
coe
      T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496
      ((T_IsMonoid_712 -> T_IsSemigroup_488) -> Any -> Any
forall a b. a -> b
coe
         T_IsMonoid_712 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_722
         ((T_IsCommutativeMonoid_764 -> T_IsMonoid_712) -> Any -> Any
forall a b. a -> b
coe
            T_IsCommutativeMonoid_764 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_774
            ((T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764)
-> Any -> Any
forall a b. a -> b
coe
               T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_894
               (T_IsIdempotentCommutativeMonoid_884 -> Any
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884
v0))))
-- Data.Bool.Properties._.IsBoundedSemilattice.isMonoid
d_isMonoid_2966 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  MAlonzo.Code.Algebra.Structures.T_IsMonoid_712
d_isMonoid_2966 :: T_IsIdempotentCommutativeMonoid_884 -> T_IsMonoid_712
d_isMonoid_2966 T_IsIdempotentCommutativeMonoid_884
v0
  = (T_IsCommutativeMonoid_764 -> T_IsMonoid_712)
-> Any -> T_IsMonoid_712
forall a b. a -> b
coe
      T_IsCommutativeMonoid_764 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_774
      ((T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764)
-> Any -> Any
forall a b. a -> b
coe
         T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_894 (T_IsIdempotentCommutativeMonoid_884 -> Any
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884
v0))
-- Data.Bool.Properties._.IsBoundedSemilattice.isPartialEquivalence
d_isPartialEquivalence_2968 ::
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_2968 :: (Bool -> Bool -> Bool)
-> Bool
-> T_IsIdempotentCommutativeMonoid_884
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_2968 ~Bool -> Bool -> Bool
v0 ~Bool
v1 T_IsIdempotentCommutativeMonoid_884
v2
  = T_IsIdempotentCommutativeMonoid_884 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_2968 T_IsIdempotentCommutativeMonoid_884
v2
du_isPartialEquivalence_2968 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_2968 :: T_IsIdempotentCommutativeMonoid_884 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_2968 T_IsIdempotentCommutativeMonoid_884
v0
  = let v1 :: T_IsCommutativeMonoid_764
v1
          = T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_894
              (T_IsIdempotentCommutativeMonoid_884
-> T_IsIdempotentCommutativeMonoid_884
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884
v0) in
    Any -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsMonoid_712
v2
             = T_IsCommutativeMonoid_764 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_774 (T_IsCommutativeMonoid_764 -> T_IsCommutativeMonoid_764
forall a b. a -> b
coe T_IsCommutativeMonoid_764
v1) in
       Any -> Any
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_488
v3
                = T_IsMonoid_712 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_722 (T_IsMonoid_712 -> T_IsMonoid_712
forall a b. a -> b
coe T_IsMonoid_712
v2) in
          Any -> Any
forall a b. a -> b
coe
            (let v4 :: T_IsMagma_178
v4 = T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496 (T_IsSemigroup_488 -> T_IsSemigroup_488
forall a b. a -> b
coe T_IsSemigroup_488
v3) in
             Any -> Any
forall a b. a -> b
coe
               ((T_IsEquivalence_28 -> T_IsPartialEquivalence_16) -> Any -> Any
forall a b. a -> b
coe
                  T_IsEquivalence_28 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_44
                  ((T_IsMagma_178 -> T_IsEquivalence_28) -> Any -> Any
forall a b. a -> b
coe
                     T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186 (T_IsMagma_178 -> Any
forall a b. a -> b
coe T_IsMagma_178
v4))))))
-- Data.Bool.Properties._.IsBoundedSemilattice.isSemigroup
d_isSemigroup_2970 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_488
d_isSemigroup_2970 :: T_IsIdempotentCommutativeMonoid_884 -> T_IsSemigroup_488
d_isSemigroup_2970 T_IsIdempotentCommutativeMonoid_884
v0
  = (T_IsMonoid_712 -> T_IsSemigroup_488) -> Any -> T_IsSemigroup_488
forall a b. a -> b
coe
      T_IsMonoid_712 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_722
      ((T_IsCommutativeMonoid_764 -> T_IsMonoid_712) -> Any -> Any
forall a b. a -> b
coe
         T_IsCommutativeMonoid_764 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_774
         ((T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764)
-> Any -> Any
forall a b. a -> b
coe
            T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_894
            (T_IsIdempotentCommutativeMonoid_884 -> Any
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884
v0)))
-- Data.Bool.Properties._.IsBoundedSemilattice.isCommutativeBand
d_isCommutativeBand_2972 ::
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_612
d_isCommutativeBand_2972 :: (Bool -> Bool -> Bool)
-> Bool
-> T_IsIdempotentCommutativeMonoid_884
-> T_IsCommutativeBand_612
d_isCommutativeBand_2972 ~Bool -> Bool -> Bool
v0 ~Bool
v1 T_IsIdempotentCommutativeMonoid_884
v2 = T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeBand_612
du_isCommutativeBand_2972 T_IsIdempotentCommutativeMonoid_884
v2
du_isCommutativeBand_2972 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_612
du_isCommutativeBand_2972 :: T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeBand_612
du_isCommutativeBand_2972 T_IsIdempotentCommutativeMonoid_884
v0
  = (T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeBand_612)
-> Any -> T_IsCommutativeBand_612
forall a b. a -> b
coe
      T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeBand_612
MAlonzo.Code.Algebra.Structures.du_isCommutativeBand_948 (T_IsIdempotentCommutativeMonoid_884 -> Any
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884
v0)
-- Data.Bool.Properties._.IsBoundedSemilattice.isUnitalMagma
d_isUnitalMagma_2974 ::
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  MAlonzo.Code.Algebra.Structures.T_IsUnitalMagma_666
d_isUnitalMagma_2974 :: (Bool -> Bool -> Bool)
-> Bool
-> T_IsIdempotentCommutativeMonoid_884
-> T_IsUnitalMagma_666
d_isUnitalMagma_2974 ~Bool -> Bool -> Bool
v0 ~Bool
v1 T_IsIdempotentCommutativeMonoid_884
v2 = T_IsIdempotentCommutativeMonoid_884 -> T_IsUnitalMagma_666
du_isUnitalMagma_2974 T_IsIdempotentCommutativeMonoid_884
v2
du_isUnitalMagma_2974 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  MAlonzo.Code.Algebra.Structures.T_IsUnitalMagma_666
du_isUnitalMagma_2974 :: T_IsIdempotentCommutativeMonoid_884 -> T_IsUnitalMagma_666
du_isUnitalMagma_2974 T_IsIdempotentCommutativeMonoid_884
v0
  = let v1 :: T_IsCommutativeMonoid_764
v1
          = T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_894
              (T_IsIdempotentCommutativeMonoid_884
-> T_IsIdempotentCommutativeMonoid_884
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884
v0) in
    Any -> T_IsUnitalMagma_666
forall a b. a -> b
coe
      ((T_IsMonoid_712 -> T_IsUnitalMagma_666) -> Any -> Any
forall a b. a -> b
coe
         T_IsMonoid_712 -> T_IsUnitalMagma_666
MAlonzo.Code.Algebra.Structures.du_isUnitalMagma_756
         ((T_IsCommutativeMonoid_764 -> T_IsMonoid_712) -> Any -> Any
forall a b. a -> b
coe T_IsCommutativeMonoid_764 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_774 (T_IsCommutativeMonoid_764 -> Any
forall a b. a -> b
coe T_IsCommutativeMonoid_764
v1)))
-- Data.Bool.Properties._.IsBoundedSemilattice.refl
d_refl_2976 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_refl_2976 :: T_IsIdempotentCommutativeMonoid_884 -> Bool -> T__'8801'__12
d_refl_2976 = T_IsIdempotentCommutativeMonoid_884 -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsBoundedSemilattice.reflexive
d_reflexive_2978 ::
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_reflexive_2978 :: (Bool -> Bool -> Bool)
-> Bool
-> T_IsIdempotentCommutativeMonoid_884
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_reflexive_2978 = (Bool -> Bool -> Bool)
-> Bool
-> T_IsIdempotentCommutativeMonoid_884
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsBoundedSemilattice.setoid
d_setoid_2980 ::
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
d_setoid_2980 :: (Bool -> Bool -> Bool)
-> Bool -> T_IsIdempotentCommutativeMonoid_884 -> T_Setoid_46
d_setoid_2980 ~Bool -> Bool -> Bool
v0 ~Bool
v1 T_IsIdempotentCommutativeMonoid_884
v2 = T_IsIdempotentCommutativeMonoid_884 -> T_Setoid_46
du_setoid_2980 T_IsIdempotentCommutativeMonoid_884
v2
du_setoid_2980 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
du_setoid_2980 :: T_IsIdempotentCommutativeMonoid_884 -> T_Setoid_46
du_setoid_2980 T_IsIdempotentCommutativeMonoid_884
v0
  = let v1 :: T_IsCommutativeMonoid_764
v1
          = T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_894
              (T_IsIdempotentCommutativeMonoid_884
-> T_IsIdempotentCommutativeMonoid_884
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884
v0) in
    Any -> T_Setoid_46
forall a b. a -> b
coe
      (let v2 :: T_IsMonoid_712
v2
             = T_IsCommutativeMonoid_764 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_774 (T_IsCommutativeMonoid_764 -> T_IsCommutativeMonoid_764
forall a b. a -> b
coe T_IsCommutativeMonoid_764
v1) in
       Any -> Any
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_488
v3
                = T_IsMonoid_712 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_722 (T_IsMonoid_712 -> T_IsMonoid_712
forall a b. a -> b
coe T_IsMonoid_712
v2) in
          Any -> Any
forall a b. a -> b
coe
            ((T_IsMagma_178 -> T_Setoid_46) -> Any -> Any
forall a b. a -> b
coe
               T_IsMagma_178 -> T_Setoid_46
MAlonzo.Code.Algebra.Structures.du_setoid_202
               ((T_IsSemigroup_488 -> T_IsMagma_178) -> Any -> Any
forall a b. a -> b
coe T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496 (T_IsSemigroup_488 -> Any
forall a b. a -> b
coe T_IsSemigroup_488
v3)))))
-- Data.Bool.Properties._.IsBoundedSemilattice.sym
d_sym_2982 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_sym_2982 :: T_IsIdempotentCommutativeMonoid_884
-> Bool -> Bool -> T__'8801'__12 -> T__'8801'__12
d_sym_2982 = T_IsIdempotentCommutativeMonoid_884
-> Bool -> Bool -> T__'8801'__12 -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsBoundedSemilattice.trans
d_trans_2984 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_trans_2984 :: T_IsIdempotentCommutativeMonoid_884
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
d_trans_2984 = T_IsIdempotentCommutativeMonoid_884
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsBoundedSemilattice.∙-cong
d_'8729''45'cong_2986 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  Bool ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8729''45'cong_2986 :: T_IsIdempotentCommutativeMonoid_884
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong_2986 = T_IsIdempotentCommutativeMonoid_884
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsBoundedSemilattice.∙-congʳ
d_'8729''45'cong'691'_2988 ::
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8729''45'cong'691'_2988 :: (Bool -> Bool -> Bool)
-> Bool
-> T_IsIdempotentCommutativeMonoid_884
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong'691'_2988 = (Bool -> Bool -> Bool)
-> Bool
-> T_IsIdempotentCommutativeMonoid_884
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsBoundedSemilattice.∙-congˡ
d_'8729''45'cong'737'_2990 ::
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884 ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8729''45'cong'737'_2990 :: (Bool -> Bool -> Bool)
-> Bool
-> T_IsIdempotentCommutativeMonoid_884
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong'737'_2990 = (Bool -> Bool -> Bool)
-> Bool
-> T_IsIdempotentCommutativeMonoid_884
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsDistributiveLattice.absorptive
d_absorptive_2994 ::
  MAlonzo.Code.Algebra.Lattice.Structures.T_IsDistributiveLattice_3146 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_absorptive_2994 :: T_IsDistributiveLattice_3146 -> T_Σ_14
d_absorptive_2994 T_IsDistributiveLattice_3146
v0
  = (T_IsLattice_3070 -> T_Σ_14) -> Any -> T_Σ_14
forall a b. a -> b
coe
      T_IsLattice_3070 -> T_Σ_14
MAlonzo.Code.Algebra.Lattice.Structures.d_absorptive_3106
      ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070) -> Any -> Any
forall a b. a -> b
coe
         T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158 (T_IsDistributiveLattice_3146 -> Any
forall a b. a -> b
coe T_IsDistributiveLattice_3146
v0))
-- Data.Bool.Properties._.IsDistributiveLattice.isEquivalence
d_isEquivalence_2996 ::
  MAlonzo.Code.Algebra.Lattice.Structures.T_IsDistributiveLattice_3146 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
d_isEquivalence_2996 :: T_IsDistributiveLattice_3146 -> T_IsEquivalence_28
d_isEquivalence_2996 T_IsDistributiveLattice_3146
v0
  = (T_IsLattice_3070 -> T_IsEquivalence_28)
-> Any -> T_IsEquivalence_28
forall a b. a -> b
coe
      T_IsLattice_3070 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_3092
      ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070) -> Any -> Any
forall a b. a -> b
coe
         T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158 (T_IsDistributiveLattice_3146 -> Any
forall a b. a -> b
coe T_IsDistributiveLattice_3146
v0))
-- Data.Bool.Properties._.IsDistributiveLattice.isLattice
d_isLattice_2998 ::
  MAlonzo.Code.Algebra.Lattice.Structures.T_IsDistributiveLattice_3146 ->
  MAlonzo.Code.Algebra.Lattice.Structures.T_IsLattice_3070
d_isLattice_2998 :: T_IsDistributiveLattice_3146 -> T_IsLattice_3070
d_isLattice_2998 T_IsDistributiveLattice_3146
v0
  = (T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> Any -> T_IsLattice_3070
forall a b. a -> b
coe
      T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158 (T_IsDistributiveLattice_3146 -> Any
forall a b. a -> b
coe T_IsDistributiveLattice_3146
v0)
-- Data.Bool.Properties._.IsDistributiveLattice.isPartialEquivalence
d_isPartialEquivalence_3000 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  MAlonzo.Code.Algebra.Lattice.Structures.T_IsDistributiveLattice_3146 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_3000 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> T_IsDistributiveLattice_3146
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_3000 ~Bool -> Bool -> Bool
v0 ~Bool -> Bool -> Bool
v1 T_IsDistributiveLattice_3146
v2
  = T_IsDistributiveLattice_3146 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_3000 T_IsDistributiveLattice_3146
v2
du_isPartialEquivalence_3000 ::
  MAlonzo.Code.Algebra.Lattice.Structures.T_IsDistributiveLattice_3146 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_3000 :: T_IsDistributiveLattice_3146 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_3000 T_IsDistributiveLattice_3146
v0
  = let v1 :: T_IsLattice_3070
v1
          = T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
              (T_IsDistributiveLattice_3146 -> T_IsDistributiveLattice_3146
forall a b. a -> b
coe T_IsDistributiveLattice_3146
v0) in
    Any -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      ((T_IsEquivalence_28 -> T_IsPartialEquivalence_16) -> Any -> Any
forall a b. a -> b
coe
         T_IsEquivalence_28 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_44
         ((T_IsLattice_3070 -> T_IsEquivalence_28) -> Any -> Any
forall a b. a -> b
coe
            T_IsLattice_3070 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_3092
            (T_IsLattice_3070 -> Any
forall a b. a -> b
coe T_IsLattice_3070
v1)))
-- Data.Bool.Properties._.IsDistributiveLattice.refl
d_refl_3002 ::
  MAlonzo.Code.Algebra.Lattice.Structures.T_IsDistributiveLattice_3146 ->
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_refl_3002 :: T_IsDistributiveLattice_3146 -> Bool -> T__'8801'__12
d_refl_3002 = T_IsDistributiveLattice_3146 -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsDistributiveLattice.reflexive
d_reflexive_3004 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  MAlonzo.Code.Algebra.Lattice.Structures.T_IsDistributiveLattice_3146 ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_reflexive_3004 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> T_IsDistributiveLattice_3146
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_reflexive_3004 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> T_IsDistributiveLattice_3146
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsDistributiveLattice.sym
d_sym_3006 ::
  MAlonzo.Code.Algebra.Lattice.Structures.T_IsDistributiveLattice_3146 ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_sym_3006 :: T_IsDistributiveLattice_3146
-> Bool -> Bool -> T__'8801'__12 -> T__'8801'__12
d_sym_3006 = T_IsDistributiveLattice_3146
-> Bool -> Bool -> T__'8801'__12 -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsDistributiveLattice.trans
d_trans_3008 ::
  MAlonzo.Code.Algebra.Lattice.Structures.T_IsDistributiveLattice_3146 ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_trans_3008 :: T_IsDistributiveLattice_3146
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
d_trans_3008 = T_IsDistributiveLattice_3146
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsDistributiveLattice.∧-absorbs-∨
d_'8743''45'absorbs'45''8744'_3010 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  MAlonzo.Code.Algebra.Lattice.Structures.T_IsDistributiveLattice_3146 ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8743''45'absorbs'45''8744'_3010 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> T_IsDistributiveLattice_3146
-> Bool
-> Bool
-> T__'8801'__12
d_'8743''45'absorbs'45''8744'_3010 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> T_IsDistributiveLattice_3146
-> Bool
-> Bool
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsDistributiveLattice.∧-assoc
d_'8743''45'assoc_3012 ::
  MAlonzo.Code.Algebra.Lattice.Structures.T_IsDistributiveLattice_3146 ->
  Bool ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8743''45'assoc_3012 :: T_IsDistributiveLattice_3146
-> Bool -> Bool -> Bool -> T__'8801'__12
d_'8743''45'assoc_3012 = T_IsDistributiveLattice_3146
-> Bool -> Bool -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsDistributiveLattice.∧-comm
d_'8743''45'comm_3014 ::
  MAlonzo.Code.Algebra.Lattice.Structures.T_IsDistributiveLattice_3146 ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8743''45'comm_3014 :: T_IsDistributiveLattice_3146 -> Bool -> Bool -> T__'8801'__12
d_'8743''45'comm_3014 = T_IsDistributiveLattice_3146 -> Bool -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsDistributiveLattice.∧-cong
d_'8743''45'cong_3016 ::
  MAlonzo.Code.Algebra.Lattice.Structures.T_IsDistributiveLattice_3146 ->
  Bool ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8743''45'cong_3016 :: T_IsDistributiveLattice_3146
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
d_'8743''45'cong_3016 = T_IsDistributiveLattice_3146
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsDistributiveLattice.∧-congʳ
d_'8743''45'cong'691'_3018 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  MAlonzo.Code.Algebra.Lattice.Structures.T_IsDistributiveLattice_3146 ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8743''45'cong'691'_3018 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> T_IsDistributiveLattice_3146
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_'8743''45'cong'691'_3018 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> T_IsDistributiveLattice_3146
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsDistributiveLattice.∧-congˡ
d_'8743''45'cong'737'_3020 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  MAlonzo.Code.Algebra.Lattice.Structures.T_IsDistributiveLattice_3146 ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8743''45'cong'737'_3020 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> T_IsDistributiveLattice_3146
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_'8743''45'cong'737'_3020 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> T_IsDistributiveLattice_3146
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsDistributiveLattice.∧-distrib-∨
d_'8743''45'distrib'45''8744'_3022 ::
  MAlonzo.Code.Algebra.Lattice.Structures.T_IsDistributiveLattice_3146 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'8743''45'distrib'45''8744'_3022 :: T_IsDistributiveLattice_3146 -> T_Σ_14
d_'8743''45'distrib'45''8744'_3022 T_IsDistributiveLattice_3146
v0
  = (T_IsDistributiveLattice_3146 -> T_Σ_14) -> Any -> T_Σ_14
forall a b. a -> b
coe
      T_IsDistributiveLattice_3146 -> T_Σ_14
MAlonzo.Code.Algebra.Lattice.Structures.d_'8743''45'distrib'45''8744'_3162
      (T_IsDistributiveLattice_3146 -> Any
forall a b. a -> b
coe T_IsDistributiveLattice_3146
v0)
-- Data.Bool.Properties._.IsDistributiveLattice.∧-distribʳ-∨
d_'8743''45'distrib'691''45''8744'_3024 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  MAlonzo.Code.Algebra.Lattice.Structures.T_IsDistributiveLattice_3146 ->
  Bool ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8743''45'distrib'691''45''8744'_3024 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> T_IsDistributiveLattice_3146
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
d_'8743''45'distrib'691''45''8744'_3024 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> T_IsDistributiveLattice_3146
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsDistributiveLattice.∧-distribˡ-∨
d_'8743''45'distrib'737''45''8744'_3026 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  MAlonzo.Code.Algebra.Lattice.Structures.T_IsDistributiveLattice_3146 ->
  Bool ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8743''45'distrib'737''45''8744'_3026 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> T_IsDistributiveLattice_3146
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
d_'8743''45'distrib'737''45''8744'_3026 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> T_IsDistributiveLattice_3146
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsDistributiveLattice.∨-absorbs-∧
d_'8744''45'absorbs'45''8743'_3028 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  MAlonzo.Code.Algebra.Lattice.Structures.T_IsDistributiveLattice_3146 ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8744''45'absorbs'45''8743'_3028 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> T_IsDistributiveLattice_3146
-> Bool
-> Bool
-> T__'8801'__12
d_'8744''45'absorbs'45''8743'_3028 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> T_IsDistributiveLattice_3146
-> Bool
-> Bool
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsDistributiveLattice.∨-assoc
d_'8744''45'assoc_3030 ::
  MAlonzo.Code.Algebra.Lattice.Structures.T_IsDistributiveLattice_3146 ->
  Bool ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8744''45'assoc_3030 :: T_IsDistributiveLattice_3146
-> Bool -> Bool -> Bool -> T__'8801'__12
d_'8744''45'assoc_3030 = T_IsDistributiveLattice_3146
-> Bool -> Bool -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsDistributiveLattice.∨-comm
d_'8744''45'comm_3032 ::
  MAlonzo.Code.Algebra.Lattice.Structures.T_IsDistributiveLattice_3146 ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8744''45'comm_3032 :: T_IsDistributiveLattice_3146 -> Bool -> Bool -> T__'8801'__12
d_'8744''45'comm_3032 = T_IsDistributiveLattice_3146 -> Bool -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsDistributiveLattice.∨-cong
d_'8744''45'cong_3034 ::
  MAlonzo.Code.Algebra.Lattice.Structures.T_IsDistributiveLattice_3146 ->
  Bool ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8744''45'cong_3034 :: T_IsDistributiveLattice_3146
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
d_'8744''45'cong_3034 = T_IsDistributiveLattice_3146
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsDistributiveLattice.∨-congʳ
d_'8744''45'cong'691'_3036 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  MAlonzo.Code.Algebra.Lattice.Structures.T_IsDistributiveLattice_3146 ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8744''45'cong'691'_3036 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> T_IsDistributiveLattice_3146
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_'8744''45'cong'691'_3036 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> T_IsDistributiveLattice_3146
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsDistributiveLattice.∨-congˡ
d_'8744''45'cong'737'_3038 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  MAlonzo.Code.Algebra.Lattice.Structures.T_IsDistributiveLattice_3146 ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8744''45'cong'737'_3038 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> T_IsDistributiveLattice_3146
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_'8744''45'cong'737'_3038 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> T_IsDistributiveLattice_3146
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsDistributiveLattice.∨-distrib-∧
d_'8744''45'distrib'45''8743'_3040 ::
  MAlonzo.Code.Algebra.Lattice.Structures.T_IsDistributiveLattice_3146 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'8744''45'distrib'45''8743'_3040 :: T_IsDistributiveLattice_3146 -> T_Σ_14
d_'8744''45'distrib'45''8743'_3040 T_IsDistributiveLattice_3146
v0
  = (T_IsDistributiveLattice_3146 -> T_Σ_14) -> Any -> T_Σ_14
forall a b. a -> b
coe
      T_IsDistributiveLattice_3146 -> T_Σ_14
MAlonzo.Code.Algebra.Lattice.Structures.d_'8744''45'distrib'45''8743'_3160
      (T_IsDistributiveLattice_3146 -> Any
forall a b. a -> b
coe T_IsDistributiveLattice_3146
v0)
-- Data.Bool.Properties._.IsDistributiveLattice.∨-distribʳ-∧
d_'8744''45'distrib'691''45''8743'_3042 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  MAlonzo.Code.Algebra.Lattice.Structures.T_IsDistributiveLattice_3146 ->
  Bool ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8744''45'distrib'691''45''8743'_3042 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> T_IsDistributiveLattice_3146
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
d_'8744''45'distrib'691''45''8743'_3042 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> T_IsDistributiveLattice_3146
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsDistributiveLattice.∨-distribˡ-∧
d_'8744''45'distrib'737''45''8743'_3044 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  MAlonzo.Code.Algebra.Lattice.Structures.T_IsDistributiveLattice_3146 ->
  Bool ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8744''45'distrib'737''45''8743'_3044 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> T_IsDistributiveLattice_3146
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
d_'8744''45'distrib'737''45''8743'_3044 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> T_IsDistributiveLattice_3146
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsJoinSemilattice.assoc
d_assoc_3048 ::
  (Bool -> Bool -> Bool) ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_612 ->
  Bool ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_assoc_3048 :: (Bool -> Bool -> Bool)
-> T_IsCommutativeBand_612 -> Bool -> Bool -> Bool -> T__'8801'__12
d_assoc_3048 = (Bool -> Bool -> Bool)
-> T_IsCommutativeBand_612 -> Bool -> Bool -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsJoinSemilattice.comm
d_comm_3050 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_612 ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_comm_3050 :: T_IsCommutativeBand_612 -> Bool -> Bool -> T__'8801'__12
d_comm_3050 = T_IsCommutativeBand_612 -> Bool -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsJoinSemilattice.idem
d_idem_3052 ::
  (Bool -> Bool -> Bool) ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_612 ->
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_idem_3052 :: (Bool -> Bool -> Bool)
-> T_IsCommutativeBand_612 -> Bool -> T__'8801'__12
d_idem_3052 = (Bool -> Bool -> Bool)
-> T_IsCommutativeBand_612 -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsJoinSemilattice.isBand
d_isBand_3054 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_612 ->
  MAlonzo.Code.Algebra.Structures.T_IsBand_526
d_isBand_3054 :: T_IsCommutativeBand_612 -> T_IsBand_526
d_isBand_3054 T_IsCommutativeBand_612
v0
  = (T_IsCommutativeBand_612 -> T_IsBand_526) -> Any -> T_IsBand_526
forall a b. a -> b
coe T_IsCommutativeBand_612 -> T_IsBand_526
MAlonzo.Code.Algebra.Structures.d_isBand_620 (T_IsCommutativeBand_612 -> Any
forall a b. a -> b
coe T_IsCommutativeBand_612
v0)
-- Data.Bool.Properties._.IsJoinSemilattice.isEquivalence
d_isEquivalence_3056 ::
  (Bool -> Bool -> Bool) ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_612 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
d_isEquivalence_3056 :: (Bool -> Bool -> Bool)
-> T_IsCommutativeBand_612 -> T_IsEquivalence_28
d_isEquivalence_3056 ~Bool -> Bool -> Bool
v0 T_IsCommutativeBand_612
v1 = T_IsCommutativeBand_612 -> T_IsEquivalence_28
du_isEquivalence_3056 T_IsCommutativeBand_612
v1
du_isEquivalence_3056 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_612 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
du_isEquivalence_3056 :: T_IsCommutativeBand_612 -> T_IsEquivalence_28
du_isEquivalence_3056 T_IsCommutativeBand_612
v0
  = (T_IsMagma_178 -> T_IsEquivalence_28) -> Any -> T_IsEquivalence_28
forall a b. a -> b
coe
      T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186
      ((T_IsSemigroup_488 -> T_IsMagma_178) -> Any -> Any
forall a b. a -> b
coe
         T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496
         ((T_IsBand_526 -> T_IsSemigroup_488) -> Any -> Any
forall a b. a -> b
coe
            T_IsBand_526 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_534
            ((T_IsCommutativeBand_612 -> T_IsBand_526) -> Any -> Any
forall a b. a -> b
coe T_IsCommutativeBand_612 -> T_IsBand_526
MAlonzo.Code.Algebra.Structures.d_isBand_620 (T_IsCommutativeBand_612 -> Any
forall a b. a -> b
coe T_IsCommutativeBand_612
v0))))
-- Data.Bool.Properties._.IsJoinSemilattice.isMagma
d_isMagma_3058 ::
  (Bool -> Bool -> Bool) ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_612 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_178
d_isMagma_3058 :: (Bool -> Bool -> Bool) -> T_IsCommutativeBand_612 -> T_IsMagma_178
d_isMagma_3058 ~Bool -> Bool -> Bool
v0 T_IsCommutativeBand_612
v1 = T_IsCommutativeBand_612 -> T_IsMagma_178
du_isMagma_3058 T_IsCommutativeBand_612
v1
du_isMagma_3058 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_612 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_178
du_isMagma_3058 :: T_IsCommutativeBand_612 -> T_IsMagma_178
du_isMagma_3058 T_IsCommutativeBand_612
v0
  = (T_IsSemigroup_488 -> T_IsMagma_178) -> Any -> T_IsMagma_178
forall a b. a -> b
coe
      T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496
      ((T_IsBand_526 -> T_IsSemigroup_488) -> Any -> Any
forall a b. a -> b
coe
         T_IsBand_526 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_534
         ((T_IsCommutativeBand_612 -> T_IsBand_526) -> Any -> Any
forall a b. a -> b
coe T_IsCommutativeBand_612 -> T_IsBand_526
MAlonzo.Code.Algebra.Structures.d_isBand_620 (T_IsCommutativeBand_612 -> Any
forall a b. a -> b
coe T_IsCommutativeBand_612
v0)))
-- Data.Bool.Properties._.IsJoinSemilattice.isPartialEquivalence
d_isPartialEquivalence_3060 ::
  (Bool -> Bool -> Bool) ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_612 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_3060 :: (Bool -> Bool -> Bool)
-> T_IsCommutativeBand_612 -> T_IsPartialEquivalence_16
d_isPartialEquivalence_3060 ~Bool -> Bool -> Bool
v0 T_IsCommutativeBand_612
v1
  = T_IsCommutativeBand_612 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_3060 T_IsCommutativeBand_612
v1
du_isPartialEquivalence_3060 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_612 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_3060 :: T_IsCommutativeBand_612 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_3060 T_IsCommutativeBand_612
v0
  = let v1 :: T_IsBand_526
v1 = T_IsCommutativeBand_612 -> T_IsBand_526
MAlonzo.Code.Algebra.Structures.d_isBand_620 (T_IsCommutativeBand_612 -> T_IsCommutativeBand_612
forall a b. a -> b
coe T_IsCommutativeBand_612
v0) in
    Any -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsSemigroup_488
v2
             = T_IsBand_526 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_534 (T_IsBand_526 -> T_IsBand_526
forall a b. a -> b
coe T_IsBand_526
v1) in
       Any -> Any
forall a b. a -> b
coe
         (let v3 :: T_IsMagma_178
v3 = T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496 (T_IsSemigroup_488 -> T_IsSemigroup_488
forall a b. a -> b
coe T_IsSemigroup_488
v2) in
          Any -> Any
forall a b. a -> b
coe
            ((T_IsEquivalence_28 -> T_IsPartialEquivalence_16) -> Any -> Any
forall a b. a -> b
coe
               T_IsEquivalence_28 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_44
               ((T_IsMagma_178 -> T_IsEquivalence_28) -> Any -> Any
forall a b. a -> b
coe
                  T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186 (T_IsMagma_178 -> Any
forall a b. a -> b
coe T_IsMagma_178
v3)))))
-- Data.Bool.Properties._.IsJoinSemilattice.isSemigroup
d_isSemigroup_3062 ::
  (Bool -> Bool -> Bool) ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_612 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_488
d_isSemigroup_3062 :: (Bool -> Bool -> Bool)
-> T_IsCommutativeBand_612 -> T_IsSemigroup_488
d_isSemigroup_3062 ~Bool -> Bool -> Bool
v0 T_IsCommutativeBand_612
v1 = T_IsCommutativeBand_612 -> T_IsSemigroup_488
du_isSemigroup_3062 T_IsCommutativeBand_612
v1
du_isSemigroup_3062 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_612 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_488
du_isSemigroup_3062 :: T_IsCommutativeBand_612 -> T_IsSemigroup_488
du_isSemigroup_3062 T_IsCommutativeBand_612
v0
  = (T_IsBand_526 -> T_IsSemigroup_488) -> Any -> T_IsSemigroup_488
forall a b. a -> b
coe
      T_IsBand_526 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_534
      ((T_IsCommutativeBand_612 -> T_IsBand_526) -> Any -> Any
forall a b. a -> b
coe T_IsCommutativeBand_612 -> T_IsBand_526
MAlonzo.Code.Algebra.Structures.d_isBand_620 (T_IsCommutativeBand_612 -> Any
forall a b. a -> b
coe T_IsCommutativeBand_612
v0))
-- Data.Bool.Properties._.IsJoinSemilattice.refl
d_refl_3064 ::
  (Bool -> Bool -> Bool) ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_612 ->
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_refl_3064 :: (Bool -> Bool -> Bool)
-> T_IsCommutativeBand_612 -> Bool -> T__'8801'__12
d_refl_3064 = (Bool -> Bool -> Bool)
-> T_IsCommutativeBand_612 -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsJoinSemilattice.reflexive
d_reflexive_3066 ::
  (Bool -> Bool -> Bool) ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_612 ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_reflexive_3066 :: (Bool -> Bool -> Bool)
-> T_IsCommutativeBand_612
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_reflexive_3066 = (Bool -> Bool -> Bool)
-> T_IsCommutativeBand_612
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsJoinSemilattice.setoid
d_setoid_3068 ::
  (Bool -> Bool -> Bool) ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_612 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
d_setoid_3068 :: (Bool -> Bool -> Bool) -> T_IsCommutativeBand_612 -> T_Setoid_46
d_setoid_3068 ~Bool -> Bool -> Bool
v0 T_IsCommutativeBand_612
v1 = T_IsCommutativeBand_612 -> T_Setoid_46
du_setoid_3068 T_IsCommutativeBand_612
v1
du_setoid_3068 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_612 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
du_setoid_3068 :: T_IsCommutativeBand_612 -> T_Setoid_46
du_setoid_3068 T_IsCommutativeBand_612
v0
  = let v1 :: T_IsBand_526
v1 = T_IsCommutativeBand_612 -> T_IsBand_526
MAlonzo.Code.Algebra.Structures.d_isBand_620 (T_IsCommutativeBand_612 -> T_IsCommutativeBand_612
forall a b. a -> b
coe T_IsCommutativeBand_612
v0) in
    Any -> T_Setoid_46
forall a b. a -> b
coe
      (let v2 :: T_IsSemigroup_488
v2
             = T_IsBand_526 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_534 (T_IsBand_526 -> T_IsBand_526
forall a b. a -> b
coe T_IsBand_526
v1) in
       Any -> Any
forall a b. a -> b
coe
         ((T_IsMagma_178 -> T_Setoid_46) -> Any -> Any
forall a b. a -> b
coe
            T_IsMagma_178 -> T_Setoid_46
MAlonzo.Code.Algebra.Structures.du_setoid_202
            ((T_IsSemigroup_488 -> T_IsMagma_178) -> Any -> Any
forall a b. a -> b
coe T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496 (T_IsSemigroup_488 -> Any
forall a b. a -> b
coe T_IsSemigroup_488
v2))))
-- Data.Bool.Properties._.IsJoinSemilattice.sym
d_sym_3070 ::
  (Bool -> Bool -> Bool) ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_612 ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_sym_3070 :: (Bool -> Bool -> Bool)
-> T_IsCommutativeBand_612
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_sym_3070 = (Bool -> Bool -> Bool)
-> T_IsCommutativeBand_612
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsJoinSemilattice.trans
d_trans_3072 ::
  (Bool -> Bool -> Bool) ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_612 ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_trans_3072 :: (Bool -> Bool -> Bool)
-> T_IsCommutativeBand_612
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
d_trans_3072 = (Bool -> Bool -> Bool)
-> T_IsCommutativeBand_612
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsJoinSemilattice.∙-cong
d_'8729''45'cong_3074 ::
  (Bool -> Bool -> Bool) ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_612 ->
  Bool ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8729''45'cong_3074 :: (Bool -> Bool -> Bool)
-> T_IsCommutativeBand_612
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong_3074 = (Bool -> Bool -> Bool)
-> T_IsCommutativeBand_612
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsJoinSemilattice.∙-congʳ
d_'8729''45'cong'691'_3076 ::
  (Bool -> Bool -> Bool) ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_612 ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8729''45'cong'691'_3076 :: (Bool -> Bool -> Bool)
-> T_IsCommutativeBand_612
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong'691'_3076 = (Bool -> Bool -> Bool)
-> T_IsCommutativeBand_612
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsJoinSemilattice.∙-congˡ
d_'8729''45'cong'737'_3078 ::
  (Bool -> Bool -> Bool) ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_612 ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8729''45'cong'737'_3078 :: (Bool -> Bool -> Bool)
-> T_IsCommutativeBand_612
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong'737'_3078 = (Bool -> Bool -> Bool)
-> T_IsCommutativeBand_612
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsLattice.absorptive
d_absorptive_3082 ::
  MAlonzo.Code.Algebra.Lattice.Structures.T_IsLattice_3070 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_absorptive_3082 :: T_IsLattice_3070 -> T_Σ_14
d_absorptive_3082 T_IsLattice_3070
v0
  = (T_IsLattice_3070 -> T_Σ_14) -> Any -> T_Σ_14
forall a b. a -> b
coe
      T_IsLattice_3070 -> T_Σ_14
MAlonzo.Code.Algebra.Lattice.Structures.d_absorptive_3106 (T_IsLattice_3070 -> Any
forall a b. a -> b
coe T_IsLattice_3070
v0)
-- Data.Bool.Properties._.IsLattice.isEquivalence
d_isEquivalence_3084 ::
  MAlonzo.Code.Algebra.Lattice.Structures.T_IsLattice_3070 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
d_isEquivalence_3084 :: T_IsLattice_3070 -> T_IsEquivalence_28
d_isEquivalence_3084 T_IsLattice_3070
v0
  = (T_IsLattice_3070 -> T_IsEquivalence_28)
-> Any -> T_IsEquivalence_28
forall a b. a -> b
coe
      T_IsLattice_3070 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_3092
      (T_IsLattice_3070 -> Any
forall a b. a -> b
coe T_IsLattice_3070
v0)
-- Data.Bool.Properties._.IsLattice.isPartialEquivalence
d_isPartialEquivalence_3086 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  MAlonzo.Code.Algebra.Lattice.Structures.T_IsLattice_3070 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_3086 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> T_IsLattice_3070
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_3086 ~Bool -> Bool -> Bool
v0 ~Bool -> Bool -> Bool
v1 T_IsLattice_3070
v2
  = T_IsLattice_3070 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_3086 T_IsLattice_3070
v2
du_isPartialEquivalence_3086 ::
  MAlonzo.Code.Algebra.Lattice.Structures.T_IsLattice_3070 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_3086 :: T_IsLattice_3070 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_3086 T_IsLattice_3070
v0
  = (T_IsEquivalence_28 -> T_IsPartialEquivalence_16)
-> Any -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      T_IsEquivalence_28 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_44
      ((T_IsLattice_3070 -> T_IsEquivalence_28) -> Any -> Any
forall a b. a -> b
coe
         T_IsLattice_3070 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_3092
         (T_IsLattice_3070 -> Any
forall a b. a -> b
coe T_IsLattice_3070
v0))
-- Data.Bool.Properties._.IsLattice.refl
d_refl_3088 ::
  MAlonzo.Code.Algebra.Lattice.Structures.T_IsLattice_3070 ->
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_refl_3088 :: T_IsLattice_3070 -> Bool -> T__'8801'__12
d_refl_3088 = T_IsLattice_3070 -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsLattice.reflexive
d_reflexive_3090 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  MAlonzo.Code.Algebra.Lattice.Structures.T_IsLattice_3070 ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_reflexive_3090 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> T_IsLattice_3070
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_reflexive_3090 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> T_IsLattice_3070
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsLattice.sym
d_sym_3092 ::
  MAlonzo.Code.Algebra.Lattice.Structures.T_IsLattice_3070 ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_sym_3092 :: T_IsLattice_3070 -> Bool -> Bool -> T__'8801'__12 -> T__'8801'__12
d_sym_3092 = T_IsLattice_3070 -> Bool -> Bool -> T__'8801'__12 -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsLattice.trans
d_trans_3094 ::
  MAlonzo.Code.Algebra.Lattice.Structures.T_IsLattice_3070 ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_trans_3094 :: T_IsLattice_3070
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
d_trans_3094 = T_IsLattice_3070
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsLattice.∧-absorbs-∨
d_'8743''45'absorbs'45''8744'_3096 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  MAlonzo.Code.Algebra.Lattice.Structures.T_IsLattice_3070 ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8743''45'absorbs'45''8744'_3096 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> T_IsLattice_3070
-> Bool
-> Bool
-> T__'8801'__12
d_'8743''45'absorbs'45''8744'_3096 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> T_IsLattice_3070
-> Bool
-> Bool
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsLattice.∧-assoc
d_'8743''45'assoc_3098 ::
  MAlonzo.Code.Algebra.Lattice.Structures.T_IsLattice_3070 ->
  Bool ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8743''45'assoc_3098 :: T_IsLattice_3070 -> Bool -> Bool -> Bool -> T__'8801'__12
d_'8743''45'assoc_3098 = T_IsLattice_3070 -> Bool -> Bool -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsLattice.∧-comm
d_'8743''45'comm_3100 ::
  MAlonzo.Code.Algebra.Lattice.Structures.T_IsLattice_3070 ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8743''45'comm_3100 :: T_IsLattice_3070 -> Bool -> Bool -> T__'8801'__12
d_'8743''45'comm_3100 = T_IsLattice_3070 -> Bool -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsLattice.∧-cong
d_'8743''45'cong_3102 ::
  MAlonzo.Code.Algebra.Lattice.Structures.T_IsLattice_3070 ->
  Bool ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8743''45'cong_3102 :: T_IsLattice_3070
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
d_'8743''45'cong_3102 = T_IsLattice_3070
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsLattice.∧-congʳ
d_'8743''45'cong'691'_3104 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  MAlonzo.Code.Algebra.Lattice.Structures.T_IsLattice_3070 ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8743''45'cong'691'_3104 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> T_IsLattice_3070
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_'8743''45'cong'691'_3104 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> T_IsLattice_3070
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsLattice.∧-congˡ
d_'8743''45'cong'737'_3106 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  MAlonzo.Code.Algebra.Lattice.Structures.T_IsLattice_3070 ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8743''45'cong'737'_3106 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> T_IsLattice_3070
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_'8743''45'cong'737'_3106 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> T_IsLattice_3070
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsLattice.∨-absorbs-∧
d_'8744''45'absorbs'45''8743'_3108 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  MAlonzo.Code.Algebra.Lattice.Structures.T_IsLattice_3070 ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8744''45'absorbs'45''8743'_3108 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> T_IsLattice_3070
-> Bool
-> Bool
-> T__'8801'__12
d_'8744''45'absorbs'45''8743'_3108 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> T_IsLattice_3070
-> Bool
-> Bool
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsLattice.∨-assoc
d_'8744''45'assoc_3110 ::
  MAlonzo.Code.Algebra.Lattice.Structures.T_IsLattice_3070 ->
  Bool ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8744''45'assoc_3110 :: T_IsLattice_3070 -> Bool -> Bool -> Bool -> T__'8801'__12
d_'8744''45'assoc_3110 = T_IsLattice_3070 -> Bool -> Bool -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsLattice.∨-comm
d_'8744''45'comm_3112 ::
  MAlonzo.Code.Algebra.Lattice.Structures.T_IsLattice_3070 ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8744''45'comm_3112 :: T_IsLattice_3070 -> Bool -> Bool -> T__'8801'__12
d_'8744''45'comm_3112 = T_IsLattice_3070 -> Bool -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsLattice.∨-cong
d_'8744''45'cong_3114 ::
  MAlonzo.Code.Algebra.Lattice.Structures.T_IsLattice_3070 ->
  Bool ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8744''45'cong_3114 :: T_IsLattice_3070
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
d_'8744''45'cong_3114 = T_IsLattice_3070
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsLattice.∨-congʳ
d_'8744''45'cong'691'_3116 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  MAlonzo.Code.Algebra.Lattice.Structures.T_IsLattice_3070 ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8744''45'cong'691'_3116 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> T_IsLattice_3070
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_'8744''45'cong'691'_3116 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> T_IsLattice_3070
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsLattice.∨-congˡ
d_'8744''45'cong'737'_3118 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  MAlonzo.Code.Algebra.Lattice.Structures.T_IsLattice_3070 ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8744''45'cong'737'_3118 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> T_IsLattice_3070
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_'8744''45'cong'737'_3118 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> T_IsLattice_3070
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsMeetSemilattice.assoc
d_assoc_3122 ::
  (Bool -> Bool -> Bool) ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_612 ->
  Bool ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_assoc_3122 :: (Bool -> Bool -> Bool)
-> T_IsCommutativeBand_612 -> Bool -> Bool -> Bool -> T__'8801'__12
d_assoc_3122 = (Bool -> Bool -> Bool)
-> T_IsCommutativeBand_612 -> Bool -> Bool -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsMeetSemilattice.comm
d_comm_3124 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_612 ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_comm_3124 :: T_IsCommutativeBand_612 -> Bool -> Bool -> T__'8801'__12
d_comm_3124 = T_IsCommutativeBand_612 -> Bool -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsMeetSemilattice.idem
d_idem_3126 ::
  (Bool -> Bool -> Bool) ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_612 ->
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_idem_3126 :: (Bool -> Bool -> Bool)
-> T_IsCommutativeBand_612 -> Bool -> T__'8801'__12
d_idem_3126 = (Bool -> Bool -> Bool)
-> T_IsCommutativeBand_612 -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsMeetSemilattice.isBand
d_isBand_3128 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_612 ->
  MAlonzo.Code.Algebra.Structures.T_IsBand_526
d_isBand_3128 :: T_IsCommutativeBand_612 -> T_IsBand_526
d_isBand_3128 T_IsCommutativeBand_612
v0
  = (T_IsCommutativeBand_612 -> T_IsBand_526) -> Any -> T_IsBand_526
forall a b. a -> b
coe T_IsCommutativeBand_612 -> T_IsBand_526
MAlonzo.Code.Algebra.Structures.d_isBand_620 (T_IsCommutativeBand_612 -> Any
forall a b. a -> b
coe T_IsCommutativeBand_612
v0)
-- Data.Bool.Properties._.IsMeetSemilattice.isEquivalence
d_isEquivalence_3130 ::
  (Bool -> Bool -> Bool) ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_612 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
d_isEquivalence_3130 :: (Bool -> Bool -> Bool)
-> T_IsCommutativeBand_612 -> T_IsEquivalence_28
d_isEquivalence_3130 ~Bool -> Bool -> Bool
v0 T_IsCommutativeBand_612
v1 = T_IsCommutativeBand_612 -> T_IsEquivalence_28
du_isEquivalence_3130 T_IsCommutativeBand_612
v1
du_isEquivalence_3130 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_612 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
du_isEquivalence_3130 :: T_IsCommutativeBand_612 -> T_IsEquivalence_28
du_isEquivalence_3130 T_IsCommutativeBand_612
v0
  = (T_IsMagma_178 -> T_IsEquivalence_28) -> Any -> T_IsEquivalence_28
forall a b. a -> b
coe
      T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186
      ((T_IsSemigroup_488 -> T_IsMagma_178) -> Any -> Any
forall a b. a -> b
coe
         T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496
         ((T_IsBand_526 -> T_IsSemigroup_488) -> Any -> Any
forall a b. a -> b
coe
            T_IsBand_526 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_534
            ((T_IsCommutativeBand_612 -> T_IsBand_526) -> Any -> Any
forall a b. a -> b
coe T_IsCommutativeBand_612 -> T_IsBand_526
MAlonzo.Code.Algebra.Structures.d_isBand_620 (T_IsCommutativeBand_612 -> Any
forall a b. a -> b
coe T_IsCommutativeBand_612
v0))))
-- Data.Bool.Properties._.IsMeetSemilattice.isMagma
d_isMagma_3132 ::
  (Bool -> Bool -> Bool) ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_612 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_178
d_isMagma_3132 :: (Bool -> Bool -> Bool) -> T_IsCommutativeBand_612 -> T_IsMagma_178
d_isMagma_3132 ~Bool -> Bool -> Bool
v0 T_IsCommutativeBand_612
v1 = T_IsCommutativeBand_612 -> T_IsMagma_178
du_isMagma_3132 T_IsCommutativeBand_612
v1
du_isMagma_3132 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_612 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_178
du_isMagma_3132 :: T_IsCommutativeBand_612 -> T_IsMagma_178
du_isMagma_3132 T_IsCommutativeBand_612
v0
  = (T_IsSemigroup_488 -> T_IsMagma_178) -> Any -> T_IsMagma_178
forall a b. a -> b
coe
      T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496
      ((T_IsBand_526 -> T_IsSemigroup_488) -> Any -> Any
forall a b. a -> b
coe
         T_IsBand_526 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_534
         ((T_IsCommutativeBand_612 -> T_IsBand_526) -> Any -> Any
forall a b. a -> b
coe T_IsCommutativeBand_612 -> T_IsBand_526
MAlonzo.Code.Algebra.Structures.d_isBand_620 (T_IsCommutativeBand_612 -> Any
forall a b. a -> b
coe T_IsCommutativeBand_612
v0)))
-- Data.Bool.Properties._.IsMeetSemilattice.isPartialEquivalence
d_isPartialEquivalence_3134 ::
  (Bool -> Bool -> Bool) ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_612 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_3134 :: (Bool -> Bool -> Bool)
-> T_IsCommutativeBand_612 -> T_IsPartialEquivalence_16
d_isPartialEquivalence_3134 ~Bool -> Bool -> Bool
v0 T_IsCommutativeBand_612
v1
  = T_IsCommutativeBand_612 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_3134 T_IsCommutativeBand_612
v1
du_isPartialEquivalence_3134 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_612 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_3134 :: T_IsCommutativeBand_612 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_3134 T_IsCommutativeBand_612
v0
  = let v1 :: T_IsBand_526
v1 = T_IsCommutativeBand_612 -> T_IsBand_526
MAlonzo.Code.Algebra.Structures.d_isBand_620 (T_IsCommutativeBand_612 -> T_IsCommutativeBand_612
forall a b. a -> b
coe T_IsCommutativeBand_612
v0) in
    Any -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsSemigroup_488
v2
             = T_IsBand_526 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_534 (T_IsBand_526 -> T_IsBand_526
forall a b. a -> b
coe T_IsBand_526
v1) in
       Any -> Any
forall a b. a -> b
coe
         (let v3 :: T_IsMagma_178
v3 = T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496 (T_IsSemigroup_488 -> T_IsSemigroup_488
forall a b. a -> b
coe T_IsSemigroup_488
v2) in
          Any -> Any
forall a b. a -> b
coe
            ((T_IsEquivalence_28 -> T_IsPartialEquivalence_16) -> Any -> Any
forall a b. a -> b
coe
               T_IsEquivalence_28 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_44
               ((T_IsMagma_178 -> T_IsEquivalence_28) -> Any -> Any
forall a b. a -> b
coe
                  T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186 (T_IsMagma_178 -> Any
forall a b. a -> b
coe T_IsMagma_178
v3)))))
-- Data.Bool.Properties._.IsMeetSemilattice.isSemigroup
d_isSemigroup_3136 ::
  (Bool -> Bool -> Bool) ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_612 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_488
d_isSemigroup_3136 :: (Bool -> Bool -> Bool)
-> T_IsCommutativeBand_612 -> T_IsSemigroup_488
d_isSemigroup_3136 ~Bool -> Bool -> Bool
v0 T_IsCommutativeBand_612
v1 = T_IsCommutativeBand_612 -> T_IsSemigroup_488
du_isSemigroup_3136 T_IsCommutativeBand_612
v1
du_isSemigroup_3136 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_612 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_488
du_isSemigroup_3136 :: T_IsCommutativeBand_612 -> T_IsSemigroup_488
du_isSemigroup_3136 T_IsCommutativeBand_612
v0
  = (T_IsBand_526 -> T_IsSemigroup_488) -> Any -> T_IsSemigroup_488
forall a b. a -> b
coe
      T_IsBand_526 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_534
      ((T_IsCommutativeBand_612 -> T_IsBand_526) -> Any -> Any
forall a b. a -> b
coe T_IsCommutativeBand_612 -> T_IsBand_526
MAlonzo.Code.Algebra.Structures.d_isBand_620 (T_IsCommutativeBand_612 -> Any
forall a b. a -> b
coe T_IsCommutativeBand_612
v0))
-- Data.Bool.Properties._.IsMeetSemilattice.refl
d_refl_3138 ::
  (Bool -> Bool -> Bool) ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_612 ->
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_refl_3138 :: (Bool -> Bool -> Bool)
-> T_IsCommutativeBand_612 -> Bool -> T__'8801'__12
d_refl_3138 = (Bool -> Bool -> Bool)
-> T_IsCommutativeBand_612 -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsMeetSemilattice.reflexive
d_reflexive_3140 ::
  (Bool -> Bool -> Bool) ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_612 ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_reflexive_3140 :: (Bool -> Bool -> Bool)
-> T_IsCommutativeBand_612
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_reflexive_3140 = (Bool -> Bool -> Bool)
-> T_IsCommutativeBand_612
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsMeetSemilattice.setoid
d_setoid_3142 ::
  (Bool -> Bool -> Bool) ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_612 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
d_setoid_3142 :: (Bool -> Bool -> Bool) -> T_IsCommutativeBand_612 -> T_Setoid_46
d_setoid_3142 ~Bool -> Bool -> Bool
v0 T_IsCommutativeBand_612
v1 = T_IsCommutativeBand_612 -> T_Setoid_46
du_setoid_3142 T_IsCommutativeBand_612
v1
du_setoid_3142 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_612 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
du_setoid_3142 :: T_IsCommutativeBand_612 -> T_Setoid_46
du_setoid_3142 T_IsCommutativeBand_612
v0
  = let v1 :: T_IsBand_526
v1 = T_IsCommutativeBand_612 -> T_IsBand_526
MAlonzo.Code.Algebra.Structures.d_isBand_620 (T_IsCommutativeBand_612 -> T_IsCommutativeBand_612
forall a b. a -> b
coe T_IsCommutativeBand_612
v0) in
    Any -> T_Setoid_46
forall a b. a -> b
coe
      (let v2 :: T_IsSemigroup_488
v2
             = T_IsBand_526 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_534 (T_IsBand_526 -> T_IsBand_526
forall a b. a -> b
coe T_IsBand_526
v1) in
       Any -> Any
forall a b. a -> b
coe
         ((T_IsMagma_178 -> T_Setoid_46) -> Any -> Any
forall a b. a -> b
coe
            T_IsMagma_178 -> T_Setoid_46
MAlonzo.Code.Algebra.Structures.du_setoid_202
            ((T_IsSemigroup_488 -> T_IsMagma_178) -> Any -> Any
forall a b. a -> b
coe T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496 (T_IsSemigroup_488 -> Any
forall a b. a -> b
coe T_IsSemigroup_488
v2))))
-- Data.Bool.Properties._.IsMeetSemilattice.sym
d_sym_3144 ::
  (Bool -> Bool -> Bool) ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_612 ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_sym_3144 :: (Bool -> Bool -> Bool)
-> T_IsCommutativeBand_612
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_sym_3144 = (Bool -> Bool -> Bool)
-> T_IsCommutativeBand_612
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsMeetSemilattice.trans
d_trans_3146 ::
  (Bool -> Bool -> Bool) ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_612 ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_trans_3146 :: (Bool -> Bool -> Bool)
-> T_IsCommutativeBand_612
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
d_trans_3146 = (Bool -> Bool -> Bool)
-> T_IsCommutativeBand_612
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsMeetSemilattice.∙-cong
d_'8729''45'cong_3148 ::
  (Bool -> Bool -> Bool) ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_612 ->
  Bool ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8729''45'cong_3148 :: (Bool -> Bool -> Bool)
-> T_IsCommutativeBand_612
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong_3148 = (Bool -> Bool -> Bool)
-> T_IsCommutativeBand_612
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsMeetSemilattice.∙-congʳ
d_'8729''45'cong'691'_3150 ::
  (Bool -> Bool -> Bool) ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_612 ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8729''45'cong'691'_3150 :: (Bool -> Bool -> Bool)
-> T_IsCommutativeBand_612
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong'691'_3150 = (Bool -> Bool -> Bool)
-> T_IsCommutativeBand_612
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsMeetSemilattice.∙-congˡ
d_'8729''45'cong'737'_3152 ::
  (Bool -> Bool -> Bool) ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_612 ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8729''45'cong'737'_3152 :: (Bool -> Bool -> Bool)
-> T_IsCommutativeBand_612
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong'737'_3152 = (Bool -> Bool -> Bool)
-> T_IsCommutativeBand_612
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsSemilattice.assoc
d_assoc_3156 ::
  (Bool -> Bool -> Bool) ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_612 ->
  Bool ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_assoc_3156 :: (Bool -> Bool -> Bool)
-> T_IsCommutativeBand_612 -> Bool -> Bool -> Bool -> T__'8801'__12
d_assoc_3156 = (Bool -> Bool -> Bool)
-> T_IsCommutativeBand_612 -> Bool -> Bool -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsSemilattice.comm
d_comm_3158 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_612 ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_comm_3158 :: T_IsCommutativeBand_612 -> Bool -> Bool -> T__'8801'__12
d_comm_3158 = T_IsCommutativeBand_612 -> Bool -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsSemilattice.idem
d_idem_3160 ::
  (Bool -> Bool -> Bool) ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_612 ->
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_idem_3160 :: (Bool -> Bool -> Bool)
-> T_IsCommutativeBand_612 -> Bool -> T__'8801'__12
d_idem_3160 = (Bool -> Bool -> Bool)
-> T_IsCommutativeBand_612 -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsSemilattice.isBand
d_isBand_3162 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_612 ->
  MAlonzo.Code.Algebra.Structures.T_IsBand_526
d_isBand_3162 :: T_IsCommutativeBand_612 -> T_IsBand_526
d_isBand_3162 T_IsCommutativeBand_612
v0
  = (T_IsCommutativeBand_612 -> T_IsBand_526) -> Any -> T_IsBand_526
forall a b. a -> b
coe T_IsCommutativeBand_612 -> T_IsBand_526
MAlonzo.Code.Algebra.Structures.d_isBand_620 (T_IsCommutativeBand_612 -> Any
forall a b. a -> b
coe T_IsCommutativeBand_612
v0)
-- Data.Bool.Properties._.IsSemilattice.isEquivalence
d_isEquivalence_3164 ::
  (Bool -> Bool -> Bool) ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_612 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
d_isEquivalence_3164 :: (Bool -> Bool -> Bool)
-> T_IsCommutativeBand_612 -> T_IsEquivalence_28
d_isEquivalence_3164 ~Bool -> Bool -> Bool
v0 T_IsCommutativeBand_612
v1 = T_IsCommutativeBand_612 -> T_IsEquivalence_28
du_isEquivalence_3164 T_IsCommutativeBand_612
v1
du_isEquivalence_3164 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_612 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
du_isEquivalence_3164 :: T_IsCommutativeBand_612 -> T_IsEquivalence_28
du_isEquivalence_3164 T_IsCommutativeBand_612
v0
  = (T_IsMagma_178 -> T_IsEquivalence_28) -> Any -> T_IsEquivalence_28
forall a b. a -> b
coe
      T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186
      ((T_IsSemigroup_488 -> T_IsMagma_178) -> Any -> Any
forall a b. a -> b
coe
         T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496
         ((T_IsBand_526 -> T_IsSemigroup_488) -> Any -> Any
forall a b. a -> b
coe
            T_IsBand_526 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_534
            ((T_IsCommutativeBand_612 -> T_IsBand_526) -> Any -> Any
forall a b. a -> b
coe T_IsCommutativeBand_612 -> T_IsBand_526
MAlonzo.Code.Algebra.Structures.d_isBand_620 (T_IsCommutativeBand_612 -> Any
forall a b. a -> b
coe T_IsCommutativeBand_612
v0))))
-- Data.Bool.Properties._.IsSemilattice.isMagma
d_isMagma_3166 ::
  (Bool -> Bool -> Bool) ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_612 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_178
d_isMagma_3166 :: (Bool -> Bool -> Bool) -> T_IsCommutativeBand_612 -> T_IsMagma_178
d_isMagma_3166 ~Bool -> Bool -> Bool
v0 T_IsCommutativeBand_612
v1 = T_IsCommutativeBand_612 -> T_IsMagma_178
du_isMagma_3166 T_IsCommutativeBand_612
v1
du_isMagma_3166 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_612 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_178
du_isMagma_3166 :: T_IsCommutativeBand_612 -> T_IsMagma_178
du_isMagma_3166 T_IsCommutativeBand_612
v0
  = (T_IsSemigroup_488 -> T_IsMagma_178) -> Any -> T_IsMagma_178
forall a b. a -> b
coe
      T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496
      ((T_IsBand_526 -> T_IsSemigroup_488) -> Any -> Any
forall a b. a -> b
coe
         T_IsBand_526 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_534
         ((T_IsCommutativeBand_612 -> T_IsBand_526) -> Any -> Any
forall a b. a -> b
coe T_IsCommutativeBand_612 -> T_IsBand_526
MAlonzo.Code.Algebra.Structures.d_isBand_620 (T_IsCommutativeBand_612 -> Any
forall a b. a -> b
coe T_IsCommutativeBand_612
v0)))
-- Data.Bool.Properties._.IsSemilattice.isPartialEquivalence
d_isPartialEquivalence_3168 ::
  (Bool -> Bool -> Bool) ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_612 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_3168 :: (Bool -> Bool -> Bool)
-> T_IsCommutativeBand_612 -> T_IsPartialEquivalence_16
d_isPartialEquivalence_3168 ~Bool -> Bool -> Bool
v0 T_IsCommutativeBand_612
v1
  = T_IsCommutativeBand_612 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_3168 T_IsCommutativeBand_612
v1
du_isPartialEquivalence_3168 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_612 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_3168 :: T_IsCommutativeBand_612 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_3168 T_IsCommutativeBand_612
v0
  = let v1 :: T_IsBand_526
v1 = T_IsCommutativeBand_612 -> T_IsBand_526
MAlonzo.Code.Algebra.Structures.d_isBand_620 (T_IsCommutativeBand_612 -> T_IsCommutativeBand_612
forall a b. a -> b
coe T_IsCommutativeBand_612
v0) in
    Any -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsSemigroup_488
v2
             = T_IsBand_526 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_534 (T_IsBand_526 -> T_IsBand_526
forall a b. a -> b
coe T_IsBand_526
v1) in
       Any -> Any
forall a b. a -> b
coe
         (let v3 :: T_IsMagma_178
v3 = T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496 (T_IsSemigroup_488 -> T_IsSemigroup_488
forall a b. a -> b
coe T_IsSemigroup_488
v2) in
          Any -> Any
forall a b. a -> b
coe
            ((T_IsEquivalence_28 -> T_IsPartialEquivalence_16) -> Any -> Any
forall a b. a -> b
coe
               T_IsEquivalence_28 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_44
               ((T_IsMagma_178 -> T_IsEquivalence_28) -> Any -> Any
forall a b. a -> b
coe
                  T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186 (T_IsMagma_178 -> Any
forall a b. a -> b
coe T_IsMagma_178
v3)))))
-- Data.Bool.Properties._.IsSemilattice.isSemigroup
d_isSemigroup_3170 ::
  (Bool -> Bool -> Bool) ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_612 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_488
d_isSemigroup_3170 :: (Bool -> Bool -> Bool)
-> T_IsCommutativeBand_612 -> T_IsSemigroup_488
d_isSemigroup_3170 ~Bool -> Bool -> Bool
v0 T_IsCommutativeBand_612
v1 = T_IsCommutativeBand_612 -> T_IsSemigroup_488
du_isSemigroup_3170 T_IsCommutativeBand_612
v1
du_isSemigroup_3170 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_612 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_488
du_isSemigroup_3170 :: T_IsCommutativeBand_612 -> T_IsSemigroup_488
du_isSemigroup_3170 T_IsCommutativeBand_612
v0
  = (T_IsBand_526 -> T_IsSemigroup_488) -> Any -> T_IsSemigroup_488
forall a b. a -> b
coe
      T_IsBand_526 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_534
      ((T_IsCommutativeBand_612 -> T_IsBand_526) -> Any -> Any
forall a b. a -> b
coe T_IsCommutativeBand_612 -> T_IsBand_526
MAlonzo.Code.Algebra.Structures.d_isBand_620 (T_IsCommutativeBand_612 -> Any
forall a b. a -> b
coe T_IsCommutativeBand_612
v0))
-- Data.Bool.Properties._.IsSemilattice.refl
d_refl_3172 ::
  (Bool -> Bool -> Bool) ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_612 ->
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_refl_3172 :: (Bool -> Bool -> Bool)
-> T_IsCommutativeBand_612 -> Bool -> T__'8801'__12
d_refl_3172 = (Bool -> Bool -> Bool)
-> T_IsCommutativeBand_612 -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsSemilattice.reflexive
d_reflexive_3174 ::
  (Bool -> Bool -> Bool) ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_612 ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_reflexive_3174 :: (Bool -> Bool -> Bool)
-> T_IsCommutativeBand_612
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_reflexive_3174 = (Bool -> Bool -> Bool)
-> T_IsCommutativeBand_612
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsSemilattice.setoid
d_setoid_3176 ::
  (Bool -> Bool -> Bool) ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_612 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
d_setoid_3176 :: (Bool -> Bool -> Bool) -> T_IsCommutativeBand_612 -> T_Setoid_46
d_setoid_3176 ~Bool -> Bool -> Bool
v0 T_IsCommutativeBand_612
v1 = T_IsCommutativeBand_612 -> T_Setoid_46
du_setoid_3176 T_IsCommutativeBand_612
v1
du_setoid_3176 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_612 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
du_setoid_3176 :: T_IsCommutativeBand_612 -> T_Setoid_46
du_setoid_3176 T_IsCommutativeBand_612
v0
  = let v1 :: T_IsBand_526
v1 = T_IsCommutativeBand_612 -> T_IsBand_526
MAlonzo.Code.Algebra.Structures.d_isBand_620 (T_IsCommutativeBand_612 -> T_IsCommutativeBand_612
forall a b. a -> b
coe T_IsCommutativeBand_612
v0) in
    Any -> T_Setoid_46
forall a b. a -> b
coe
      (let v2 :: T_IsSemigroup_488
v2
             = T_IsBand_526 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_534 (T_IsBand_526 -> T_IsBand_526
forall a b. a -> b
coe T_IsBand_526
v1) in
       Any -> Any
forall a b. a -> b
coe
         ((T_IsMagma_178 -> T_Setoid_46) -> Any -> Any
forall a b. a -> b
coe
            T_IsMagma_178 -> T_Setoid_46
MAlonzo.Code.Algebra.Structures.du_setoid_202
            ((T_IsSemigroup_488 -> T_IsMagma_178) -> Any -> Any
forall a b. a -> b
coe T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496 (T_IsSemigroup_488 -> Any
forall a b. a -> b
coe T_IsSemigroup_488
v2))))
-- Data.Bool.Properties._.IsSemilattice.sym
d_sym_3178 ::
  (Bool -> Bool -> Bool) ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_612 ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_sym_3178 :: (Bool -> Bool -> Bool)
-> T_IsCommutativeBand_612
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_sym_3178 = (Bool -> Bool -> Bool)
-> T_IsCommutativeBand_612
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsSemilattice.trans
d_trans_3180 ::
  (Bool -> Bool -> Bool) ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_612 ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_trans_3180 :: (Bool -> Bool -> Bool)
-> T_IsCommutativeBand_612
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
d_trans_3180 = (Bool -> Bool -> Bool)
-> T_IsCommutativeBand_612
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsSemilattice.∙-cong
d_'8729''45'cong_3182 ::
  (Bool -> Bool -> Bool) ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_612 ->
  Bool ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8729''45'cong_3182 :: (Bool -> Bool -> Bool)
-> T_IsCommutativeBand_612
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong_3182 = (Bool -> Bool -> Bool)
-> T_IsCommutativeBand_612
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsSemilattice.∙-congʳ
d_'8729''45'cong'691'_3184 ::
  (Bool -> Bool -> Bool) ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_612 ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8729''45'cong'691'_3184 :: (Bool -> Bool -> Bool)
-> T_IsCommutativeBand_612
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong'691'_3184 = (Bool -> Bool -> Bool)
-> T_IsCommutativeBand_612
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsSemilattice.∙-congˡ
d_'8729''45'cong'737'_3186 ::
  (Bool -> Bool -> Bool) ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_612 ->
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8729''45'cong'737'_3186 :: (Bool -> Bool -> Bool)
-> T_IsCommutativeBand_612
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong'737'_3186 = (Bool -> Bool -> Bool)
-> T_IsCommutativeBand_612
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._≟_
d__'8799'__3196 ::
  Bool ->
  Bool -> MAlonzo.Code.Relation.Nullary.Decidable.Core.T_Dec_20
d__'8799'__3196 :: Bool -> Bool -> T_Dec_20
d__'8799'__3196 Bool
v0 Bool
v1
  = if Bool -> Bool
forall a b. a -> b
coe Bool
v0
      then if Bool -> Bool
forall a b. a -> b
coe Bool
v1
             then (Bool -> T_Reflects_16 -> T_Dec_20) -> Any -> Any -> T_Dec_20
forall a b. a -> b
coe
                    Bool -> T_Reflects_16 -> T_Dec_20
MAlonzo.Code.Relation.Nullary.Decidable.Core.C__because__32
                    (Bool -> Any
forall a b. a -> b
coe Bool
v1)
                    ((Any -> T_Reflects_16) -> Any -> Any
forall a b. a -> b
coe Any -> T_Reflects_16
MAlonzo.Code.Relation.Nullary.Reflects.C_of'696'_22 Any
forall a. a
erased)
             else (Bool -> T_Reflects_16 -> T_Dec_20) -> Any -> Any -> T_Dec_20
forall a b. a -> b
coe
                    Bool -> T_Reflects_16 -> T_Dec_20
MAlonzo.Code.Relation.Nullary.Decidable.Core.C__because__32
                    (Bool -> Any
forall a b. a -> b
coe Bool
v1) (T_Reflects_16 -> Any
forall a b. a -> b
coe T_Reflects_16
MAlonzo.Code.Relation.Nullary.Reflects.C_of'8319'_26)
      else (if Bool -> Bool
forall a b. a -> b
coe Bool
v1
              then (Bool -> T_Reflects_16 -> T_Dec_20) -> Any -> Any -> T_Dec_20
forall a b. a -> b
coe
                     Bool -> T_Reflects_16 -> T_Dec_20
MAlonzo.Code.Relation.Nullary.Decidable.Core.C__because__32
                     (Bool -> Any
forall a b. a -> b
coe Bool
v0) (T_Reflects_16 -> Any
forall a b. a -> b
coe T_Reflects_16
MAlonzo.Code.Relation.Nullary.Reflects.C_of'8319'_26)
              else (Bool -> T_Reflects_16 -> T_Dec_20) -> Any -> Any -> T_Dec_20
forall a b. a -> b
coe
                     Bool -> T_Reflects_16 -> T_Dec_20
MAlonzo.Code.Relation.Nullary.Decidable.Core.C__because__32
                     (Bool -> Any
forall a b. a -> b
coe Bool
MAlonzo.Code.Agda.Builtin.Bool.C_true_10)
                     ((Any -> T_Reflects_16) -> Any -> Any
forall a b. a -> b
coe Any -> T_Reflects_16
MAlonzo.Code.Relation.Nullary.Reflects.C_of'696'_22 Any
forall a. a
erased))
-- Data.Bool.Properties.≡-setoid
d_'8801''45'setoid_3198 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
d_'8801''45'setoid_3198 :: T_Setoid_46
d_'8801''45'setoid_3198
  = T_Setoid_46 -> T_Setoid_46
forall a b. a -> b
coe
      T_Setoid_46
MAlonzo.Code.Relation.Binary.PropositionalEquality.Properties.du_setoid_402
-- Data.Bool.Properties.≡-decSetoid
d_'8801''45'decSetoid_3200 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_DecSetoid_90
d_'8801''45'decSetoid_3200 :: T_DecSetoid_90
d_'8801''45'decSetoid_3200
  = ((Any -> Any -> T_Dec_20) -> T_DecSetoid_90)
-> Any -> T_DecSetoid_90
forall a b. a -> b
coe
      (Any -> Any -> T_Dec_20) -> T_DecSetoid_90
MAlonzo.Code.Relation.Binary.PropositionalEquality.Properties.du_decSetoid_406
      ((Bool -> Bool -> T_Dec_20) -> Any
forall a b. a -> b
coe Bool -> Bool -> T_Dec_20
d__'8799'__3196)
-- Data.Bool.Properties.≤-reflexive
d_'8804''45'reflexive_3202 ::
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Data.Bool.Base.T__'8804'__10
d_'8804''45'reflexive_3202 :: Bool -> Bool -> T__'8801'__12 -> T__'8804'__10
d_'8804''45'reflexive_3202 ~Bool
v0 ~Bool
v1 ~T__'8801'__12
v2
  = T__'8804'__10
du_'8804''45'reflexive_3202
du_'8804''45'reflexive_3202 ::
  MAlonzo.Code.Data.Bool.Base.T__'8804'__10
du_'8804''45'reflexive_3202 :: T__'8804'__10
du_'8804''45'reflexive_3202
  = T__'8804'__10 -> T__'8804'__10
forall a b. a -> b
coe T__'8804'__10
MAlonzo.Code.Data.Bool.Base.C_b'8804'b_16
-- Data.Bool.Properties.≤-refl
d_'8804''45'refl_3204 ::
  Bool -> MAlonzo.Code.Data.Bool.Base.T__'8804'__10
d_'8804''45'refl_3204 :: Bool -> T__'8804'__10
d_'8804''45'refl_3204 ~Bool
v0 = T__'8804'__10
du_'8804''45'refl_3204
du_'8804''45'refl_3204 :: MAlonzo.Code.Data.Bool.Base.T__'8804'__10
du_'8804''45'refl_3204 :: T__'8804'__10
du_'8804''45'refl_3204 = T__'8804'__10 -> T__'8804'__10
forall a b. a -> b
coe T__'8804'__10
du_'8804''45'reflexive_3202
-- Data.Bool.Properties.≤-trans
d_'8804''45'trans_3206 ::
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Data.Bool.Base.T__'8804'__10 ->
  MAlonzo.Code.Data.Bool.Base.T__'8804'__10 ->
  MAlonzo.Code.Data.Bool.Base.T__'8804'__10
d_'8804''45'trans_3206 :: Bool
-> Bool -> Bool -> T__'8804'__10 -> T__'8804'__10 -> T__'8804'__10
d_'8804''45'trans_3206 ~Bool
v0 ~Bool
v1 ~Bool
v2 T__'8804'__10
v3 T__'8804'__10
v4
  = T__'8804'__10 -> T__'8804'__10 -> T__'8804'__10
du_'8804''45'trans_3206 T__'8804'__10
v3 T__'8804'__10
v4
du_'8804''45'trans_3206 ::
  MAlonzo.Code.Data.Bool.Base.T__'8804'__10 ->
  MAlonzo.Code.Data.Bool.Base.T__'8804'__10 ->
  MAlonzo.Code.Data.Bool.Base.T__'8804'__10
du_'8804''45'trans_3206 :: T__'8804'__10 -> T__'8804'__10 -> T__'8804'__10
du_'8804''45'trans_3206 T__'8804'__10
v0 T__'8804'__10
v1
  = case T__'8804'__10 -> T__'8804'__10
forall a b. a -> b
coe T__'8804'__10
v0 of
      T__'8804'__10
MAlonzo.Code.Data.Bool.Base.C_f'8804't_12
        -> (Any -> Any -> Any) -> Any -> Any -> T__'8804'__10
forall a b. a -> b
coe Any -> Any -> Any
forall a b. a -> b -> b
seq (T__'8804'__10 -> Any
forall a b. a -> b
coe T__'8804'__10
v1) (T__'8804'__10 -> Any
forall a b. a -> b
coe T__'8804'__10
v0)
      T__'8804'__10
MAlonzo.Code.Data.Bool.Base.C_b'8804'b_16 -> T__'8804'__10 -> T__'8804'__10
forall a b. a -> b
coe T__'8804'__10
v1
      T__'8804'__10
_ -> T__'8804'__10
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Data.Bool.Properties.≤-antisym
d_'8804''45'antisym_3210 ::
  Bool ->
  Bool ->
  MAlonzo.Code.Data.Bool.Base.T__'8804'__10 ->
  MAlonzo.Code.Data.Bool.Base.T__'8804'__10 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8804''45'antisym_3210 :: Bool -> Bool -> T__'8804'__10 -> T__'8804'__10 -> T__'8801'__12
d_'8804''45'antisym_3210 = Bool -> Bool -> T__'8804'__10 -> T__'8804'__10 -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties.≤-minimum
d_'8804''45'minimum_3212 ::
  Bool -> MAlonzo.Code.Data.Bool.Base.T__'8804'__10
d_'8804''45'minimum_3212 :: Bool -> T__'8804'__10
d_'8804''45'minimum_3212 Bool
v0
  = if Bool -> Bool
forall a b. a -> b
coe Bool
v0
      then T__'8804'__10 -> T__'8804'__10
forall a b. a -> b
coe T__'8804'__10
MAlonzo.Code.Data.Bool.Base.C_f'8804't_12
      else T__'8804'__10 -> T__'8804'__10
forall a b. a -> b
coe T__'8804'__10
MAlonzo.Code.Data.Bool.Base.C_b'8804'b_16
-- Data.Bool.Properties.≤-maximum
d_'8804''45'maximum_3214 ::
  Bool -> MAlonzo.Code.Data.Bool.Base.T__'8804'__10
d_'8804''45'maximum_3214 :: Bool -> T__'8804'__10
d_'8804''45'maximum_3214 Bool
v0
  = if Bool -> Bool
forall a b. a -> b
coe Bool
v0
      then T__'8804'__10 -> T__'8804'__10
forall a b. a -> b
coe T__'8804'__10
MAlonzo.Code.Data.Bool.Base.C_b'8804'b_16
      else T__'8804'__10 -> T__'8804'__10
forall a b. a -> b
coe T__'8804'__10
MAlonzo.Code.Data.Bool.Base.C_f'8804't_12
-- Data.Bool.Properties.≤-total
d_'8804''45'total_3216 ::
  Bool -> Bool -> MAlonzo.Code.Data.Sum.Base.T__'8846'__30
d_'8804''45'total_3216 :: Bool -> Bool -> T__'8846'__30
d_'8804''45'total_3216 Bool
v0 Bool
v1
  = if Bool -> Bool
forall a b. a -> b
coe Bool
v0
      then (Any -> T__'8846'__30) -> Any -> T__'8846'__30
forall a b. a -> b
coe
             Any -> T__'8846'__30
MAlonzo.Code.Data.Sum.Base.C_inj'8322'_42
             ((Bool -> T__'8804'__10) -> Any -> Any
forall a b. a -> b
coe Bool -> T__'8804'__10
d_'8804''45'maximum_3214 (Bool -> Any
forall a b. a -> b
coe Bool
v1))
      else (Any -> T__'8846'__30) -> Any -> T__'8846'__30
forall a b. a -> b
coe
             Any -> T__'8846'__30
MAlonzo.Code.Data.Sum.Base.C_inj'8321'_38
             ((Bool -> T__'8804'__10) -> Any -> Any
forall a b. a -> b
coe Bool -> T__'8804'__10
d_'8804''45'minimum_3212 (Bool -> Any
forall a b. a -> b
coe Bool
v1))
-- Data.Bool.Properties._≤?_
d__'8804''63'__3222 ::
  Bool ->
  Bool -> MAlonzo.Code.Relation.Nullary.Decidable.Core.T_Dec_20
d__'8804''63'__3222 :: Bool -> Bool -> T_Dec_20
d__'8804''63'__3222 Bool
v0 Bool
v1
  = if Bool -> Bool
forall a b. a -> b
coe Bool
v0
      then if Bool -> Bool
forall a b. a -> b
coe Bool
v1
             then (Bool -> T_Reflects_16 -> T_Dec_20) -> Any -> Any -> T_Dec_20
forall a b. a -> b
coe
                    Bool -> T_Reflects_16 -> T_Dec_20
MAlonzo.Code.Relation.Nullary.Decidable.Core.C__because__32
                    (Bool -> Any
forall a b. a -> b
coe Bool
v1)
                    ((Any -> T_Reflects_16) -> Any -> Any
forall a b. a -> b
coe
                       Any -> T_Reflects_16
MAlonzo.Code.Relation.Nullary.Reflects.C_of'696'_22
                       (T__'8804'__10 -> Any
forall a b. a -> b
coe T__'8804'__10
MAlonzo.Code.Data.Bool.Base.C_b'8804'b_16))
             else (Bool -> T_Reflects_16 -> T_Dec_20) -> Any -> Any -> T_Dec_20
forall a b. a -> b
coe
                    Bool -> T_Reflects_16 -> T_Dec_20
MAlonzo.Code.Relation.Nullary.Decidable.Core.C__because__32
                    (Bool -> Any
forall a b. a -> b
coe Bool
v1) (T_Reflects_16 -> Any
forall a b. a -> b
coe T_Reflects_16
MAlonzo.Code.Relation.Nullary.Reflects.C_of'8319'_26)
      else (Bool -> T_Reflects_16 -> T_Dec_20) -> Any -> Any -> T_Dec_20
forall a b. a -> b
coe
             Bool -> T_Reflects_16 -> T_Dec_20
MAlonzo.Code.Relation.Nullary.Decidable.Core.C__because__32
             (Bool -> Any
forall a b. a -> b
coe Bool
MAlonzo.Code.Agda.Builtin.Bool.C_true_10)
             ((Any -> T_Reflects_16) -> Any -> Any
forall a b. a -> b
coe
                Any -> T_Reflects_16
MAlonzo.Code.Relation.Nullary.Reflects.C_of'696'_22
                ((Bool -> T__'8804'__10) -> Any -> Any
forall a b. a -> b
coe Bool -> T__'8804'__10
d_'8804''45'minimum_3212 (Bool -> Any
forall a b. a -> b
coe Bool
v1)))
-- Data.Bool.Properties.≤-irrelevant
d_'8804''45'irrelevant_3226 ::
  Bool ->
  Bool ->
  MAlonzo.Code.Data.Bool.Base.T__'8804'__10 ->
  MAlonzo.Code.Data.Bool.Base.T__'8804'__10 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8804''45'irrelevant_3226 :: Bool -> Bool -> T__'8804'__10 -> T__'8804'__10 -> T__'8801'__12
d_'8804''45'irrelevant_3226 = Bool -> Bool -> T__'8804'__10 -> T__'8804'__10 -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties.≤-isPreorder
d_'8804''45'isPreorder_3228 ::
  MAlonzo.Code.Relation.Binary.Structures.T_IsPreorder_76
d_'8804''45'isPreorder_3228 :: T_IsPreorder_76
d_'8804''45'isPreorder_3228
  = (T_IsEquivalence_28
 -> (Any -> Any -> Any -> Any)
 -> (Any -> Any -> Any -> Any -> Any -> Any)
 -> T_IsPreorder_76)
-> Any
-> (Any -> Any -> Any -> Any)
-> (Any -> Any -> Any -> Any -> Any -> Any)
-> T_IsPreorder_76
forall a b. a -> b
coe
      T_IsEquivalence_28
-> (Any -> Any -> Any -> Any)
-> (Any -> Any -> Any -> Any -> Any -> Any)
-> T_IsPreorder_76
MAlonzo.Code.Relation.Binary.Structures.C_constructor_126
      (T_IsEquivalence_28 -> Any
forall a b. a -> b
coe
         T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.PropositionalEquality.Properties.du_isEquivalence_396)
      (\ Any
v0 Any
v1 Any
v2 -> T__'8804'__10 -> Any
forall a b. a -> b
coe T__'8804'__10
du_'8804''45'reflexive_3202)
      (\ Any
v0 Any
v1 Any
v2 Any
v3 Any
v4 -> (T__'8804'__10 -> T__'8804'__10 -> T__'8804'__10)
-> Any -> Any -> Any
forall a b. a -> b
coe T__'8804'__10 -> T__'8804'__10 -> T__'8804'__10
du_'8804''45'trans_3206 Any
v3 Any
v4)
-- Data.Bool.Properties.≤-isPartialOrder
d_'8804''45'isPartialOrder_3230 ::
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialOrder_248
d_'8804''45'isPartialOrder_3230 :: T_IsPartialOrder_248
d_'8804''45'isPartialOrder_3230
  = (T_IsPreorder_76
 -> (Any -> Any -> Any -> Any -> Any) -> T_IsPartialOrder_248)
-> Any -> Any -> T_IsPartialOrder_248
forall a b. a -> b
coe
      T_IsPreorder_76
-> (Any -> Any -> Any -> Any -> Any) -> T_IsPartialOrder_248
MAlonzo.Code.Relation.Binary.Structures.C_constructor_294
      (T_IsPreorder_76 -> Any
forall a b. a -> b
coe T_IsPreorder_76
d_'8804''45'isPreorder_3228) Any
forall a. a
erased
-- Data.Bool.Properties.≤-isTotalOrder
d_'8804''45'isTotalOrder_3232 ::
  MAlonzo.Code.Relation.Binary.Structures.T_IsTotalOrder_488
d_'8804''45'isTotalOrder_3232 :: T_IsTotalOrder_488
d_'8804''45'isTotalOrder_3232
  = (T_IsPartialOrder_248
 -> (Any -> Any -> T__'8846'__30) -> T_IsTotalOrder_488)
-> Any -> Any -> T_IsTotalOrder_488
forall a b. a -> b
coe
      T_IsPartialOrder_248
-> (Any -> Any -> T__'8846'__30) -> T_IsTotalOrder_488
MAlonzo.Code.Relation.Binary.Structures.C_constructor_540
      (T_IsPartialOrder_248 -> Any
forall a b. a -> b
coe T_IsPartialOrder_248
d_'8804''45'isPartialOrder_3230) ((Bool -> Bool -> T__'8846'__30) -> Any
forall a b. a -> b
coe Bool -> Bool -> T__'8846'__30
d_'8804''45'total_3216)
-- Data.Bool.Properties.≤-isDecTotalOrder
d_'8804''45'isDecTotalOrder_3234 ::
  MAlonzo.Code.Relation.Binary.Structures.T_IsDecTotalOrder_546
d_'8804''45'isDecTotalOrder_3234 :: T_IsDecTotalOrder_546
d_'8804''45'isDecTotalOrder_3234
  = (T_IsTotalOrder_488
 -> (Any -> Any -> T_Dec_20)
 -> (Any -> Any -> T_Dec_20)
 -> T_IsDecTotalOrder_546)
-> Any -> Any -> Any -> T_IsDecTotalOrder_546
forall a b. a -> b
coe
      T_IsTotalOrder_488
-> (Any -> Any -> T_Dec_20)
-> (Any -> Any -> T_Dec_20)
-> T_IsDecTotalOrder_546
MAlonzo.Code.Relation.Binary.Structures.C_constructor_618
      (T_IsTotalOrder_488 -> Any
forall a b. a -> b
coe T_IsTotalOrder_488
d_'8804''45'isTotalOrder_3232) ((Bool -> Bool -> T_Dec_20) -> Any
forall a b. a -> b
coe Bool -> Bool -> T_Dec_20
d__'8799'__3196)
      ((Bool -> Bool -> T_Dec_20) -> Any
forall a b. a -> b
coe Bool -> Bool -> T_Dec_20
d__'8804''63'__3222)
-- Data.Bool.Properties.≤-poset
d_'8804''45'poset_3236 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Poset_492
d_'8804''45'poset_3236 :: T_Poset_492
d_'8804''45'poset_3236
  = (T_IsPartialOrder_248 -> T_Poset_492)
-> T_IsPartialOrder_248 -> T_Poset_492
forall a b. a -> b
coe
      T_IsPartialOrder_248 -> T_Poset_492
MAlonzo.Code.Relation.Binary.Bundles.C_constructor_588
      T_IsPartialOrder_248
d_'8804''45'isPartialOrder_3230
-- Data.Bool.Properties.≤-preorder
d_'8804''45'preorder_3238 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Preorder_142
d_'8804''45'preorder_3238 :: T_Preorder_142
d_'8804''45'preorder_3238
  = (T_IsPreorder_76 -> T_Preorder_142)
-> T_IsPreorder_76 -> T_Preorder_142
forall a b. a -> b
coe
      T_IsPreorder_76 -> T_Preorder_142
MAlonzo.Code.Relation.Binary.Bundles.C_constructor_232
      T_IsPreorder_76
d_'8804''45'isPreorder_3228
-- Data.Bool.Properties.≤-totalOrder
d_'8804''45'totalOrder_3240 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_TotalOrder_986
d_'8804''45'totalOrder_3240 :: T_TotalOrder_986
d_'8804''45'totalOrder_3240
  = (T_IsTotalOrder_488 -> T_TotalOrder_986)
-> T_IsTotalOrder_488 -> T_TotalOrder_986
forall a b. a -> b
coe
      T_IsTotalOrder_488 -> T_TotalOrder_986
MAlonzo.Code.Relation.Binary.Bundles.C_constructor_1090
      T_IsTotalOrder_488
d_'8804''45'isTotalOrder_3232
-- Data.Bool.Properties.≤-decTotalOrder
d_'8804''45'decTotalOrder_3242 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_DecTotalOrder_1098
d_'8804''45'decTotalOrder_3242 :: T_DecTotalOrder_1098
d_'8804''45'decTotalOrder_3242
  = (T_IsDecTotalOrder_546 -> T_DecTotalOrder_1098)
-> T_IsDecTotalOrder_546 -> T_DecTotalOrder_1098
forall a b. a -> b
coe
      T_IsDecTotalOrder_546 -> T_DecTotalOrder_1098
MAlonzo.Code.Relation.Binary.Bundles.C_constructor_1272
      T_IsDecTotalOrder_546
d_'8804''45'isDecTotalOrder_3234
-- Data.Bool.Properties.<-irrefl
d_'60''45'irrefl_3244 ::
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Data.Bool.Base.T__'60'__18 ->
  MAlonzo.Code.Data.Irrelevant.T_Irrelevant_20
d_'60''45'irrefl_3244 :: Bool -> Bool -> T__'8801'__12 -> T__'60'__18 -> T_Irrelevant_20
d_'60''45'irrefl_3244 = Bool -> Bool -> T__'8801'__12 -> T__'60'__18 -> T_Irrelevant_20
forall a. a
erased
-- Data.Bool.Properties.<-asym
d_'60''45'asym_3246 ::
  Bool ->
  Bool ->
  MAlonzo.Code.Data.Bool.Base.T__'60'__18 ->
  MAlonzo.Code.Data.Bool.Base.T__'60'__18 ->
  MAlonzo.Code.Data.Irrelevant.T_Irrelevant_20
d_'60''45'asym_3246 :: Bool -> Bool -> T__'60'__18 -> T__'60'__18 -> T_Irrelevant_20
d_'60''45'asym_3246 = Bool -> Bool -> T__'60'__18 -> T__'60'__18 -> T_Irrelevant_20
forall a. a
erased
-- Data.Bool.Properties.<-trans
d_'60''45'trans_3248 ::
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Data.Bool.Base.T__'60'__18 ->
  MAlonzo.Code.Data.Bool.Base.T__'60'__18 ->
  MAlonzo.Code.Data.Bool.Base.T__'60'__18
d_'60''45'trans_3248 :: Bool -> Bool -> Bool -> T__'60'__18 -> T__'60'__18 -> T__'60'__18
d_'60''45'trans_3248 = Bool -> Bool -> Bool -> T__'60'__18 -> T__'60'__18 -> T__'60'__18
forall a. a
erased
-- Data.Bool.Properties.<-transʳ
d_'60''45'trans'691'_3250 ::
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Data.Bool.Base.T__'8804'__10 ->
  MAlonzo.Code.Data.Bool.Base.T__'60'__18 ->
  MAlonzo.Code.Data.Bool.Base.T__'60'__18
d_'60''45'trans'691'_3250 :: Bool -> Bool -> Bool -> T__'8804'__10 -> T__'60'__18 -> T__'60'__18
d_'60''45'trans'691'_3250 = Bool -> Bool -> Bool -> T__'8804'__10 -> T__'60'__18 -> T__'60'__18
forall a. a
erased
-- Data.Bool.Properties.<-transˡ
d_'60''45'trans'737'_3252 ::
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Data.Bool.Base.T__'60'__18 ->
  MAlonzo.Code.Data.Bool.Base.T__'8804'__10 ->
  MAlonzo.Code.Data.Bool.Base.T__'60'__18
d_'60''45'trans'737'_3252 :: Bool -> Bool -> Bool -> T__'60'__18 -> T__'8804'__10 -> T__'60'__18
d_'60''45'trans'737'_3252 = Bool -> Bool -> Bool -> T__'60'__18 -> T__'8804'__10 -> T__'60'__18
forall a. a
erased
-- Data.Bool.Properties.<-cmp
d_'60''45'cmp_3254 ::
  Bool -> Bool -> MAlonzo.Code.Relation.Binary.Definitions.T_Tri_158
d_'60''45'cmp_3254 :: Bool -> Bool -> T_Tri_158
d_'60''45'cmp_3254 Bool
v0 Bool
v1
  = if Bool -> Bool
forall a b. a -> b
coe Bool
v0
      then if Bool -> Bool
forall a b. a -> b
coe Bool
v1
             then (Any -> T_Tri_158) -> Any -> T_Tri_158
forall a b. a -> b
coe
                    Any -> T_Tri_158
MAlonzo.Code.Relation.Binary.Definitions.C_tri'8776'_180 Any
forall a. a
erased
             else (Any -> T_Tri_158) -> Any -> T_Tri_158
forall a b. a -> b
coe
                    Any -> T_Tri_158
MAlonzo.Code.Relation.Binary.Definitions.C_tri'62'_188 Any
forall a. a
erased
      else (if Bool -> Bool
forall a b. a -> b
coe Bool
v1
              then (Any -> T_Tri_158) -> Any -> T_Tri_158
forall a b. a -> b
coe
                     Any -> T_Tri_158
MAlonzo.Code.Relation.Binary.Definitions.C_tri'60'_172 Any
forall a. a
erased
              else (Any -> T_Tri_158) -> Any -> T_Tri_158
forall a b. a -> b
coe
                     Any -> T_Tri_158
MAlonzo.Code.Relation.Binary.Definitions.C_tri'8776'_180 Any
forall a. a
erased)
-- Data.Bool.Properties._<?_
d__'60''63'__3256 ::
  Bool ->
  Bool -> MAlonzo.Code.Relation.Nullary.Decidable.Core.T_Dec_20
d__'60''63'__3256 :: Bool -> Bool -> T_Dec_20
d__'60''63'__3256 Bool
v0 Bool
v1
  = if Bool -> Bool
forall a b. a -> b
coe Bool
v0
      then (Bool -> T_Reflects_16 -> T_Dec_20) -> Any -> Any -> T_Dec_20
forall a b. a -> b
coe
             Bool -> T_Reflects_16 -> T_Dec_20
MAlonzo.Code.Relation.Nullary.Decidable.Core.C__because__32
             (Bool -> Any
forall a b. a -> b
coe Bool
MAlonzo.Code.Agda.Builtin.Bool.C_false_8)
             (T_Reflects_16 -> Any
forall a b. a -> b
coe T_Reflects_16
MAlonzo.Code.Relation.Nullary.Reflects.C_of'8319'_26)
      else (if Bool -> Bool
forall a b. a -> b
coe Bool
v1
              then (Bool -> T_Reflects_16 -> T_Dec_20) -> Any -> Any -> T_Dec_20
forall a b. a -> b
coe
                     Bool -> T_Reflects_16 -> T_Dec_20
MAlonzo.Code.Relation.Nullary.Decidable.Core.C__because__32
                     (Bool -> Any
forall a b. a -> b
coe Bool
v1)
                     ((Any -> T_Reflects_16) -> Any -> Any
forall a b. a -> b
coe Any -> T_Reflects_16
MAlonzo.Code.Relation.Nullary.Reflects.C_of'696'_22 Any
forall a. a
erased)
              else (Bool -> T_Reflects_16 -> T_Dec_20) -> Any -> Any -> T_Dec_20
forall a b. a -> b
coe
                     Bool -> T_Reflects_16 -> T_Dec_20
MAlonzo.Code.Relation.Nullary.Decidable.Core.C__because__32
                     (Bool -> Any
forall a b. a -> b
coe Bool
v1)
                     (T_Reflects_16 -> Any
forall a b. a -> b
coe T_Reflects_16
MAlonzo.Code.Relation.Nullary.Reflects.C_of'8319'_26))
-- Data.Bool.Properties.<-resp₂-≡
d_'60''45'resp'8322''45''8801'_3258 ::
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'60''45'resp'8322''45''8801'_3258 :: T_Σ_14
d_'60''45'resp'8322''45''8801'_3258
  = (Any -> Any -> T_Σ_14) -> Any -> Any -> T_Σ_14
forall a b. a -> b
coe
      Any -> Any -> T_Σ_14
MAlonzo.Code.Agda.Builtin.Sigma.C__'44'__32
      ((Any -> Any -> Any -> Any -> Any -> Any) -> Any
forall a b. a -> b
coe (\ Any
v0 Any
v1 Any
v2 Any
v3 Any
v4 -> Any
v4)) ((Any -> Any -> Any -> Any -> Any -> Any) -> Any
forall a b. a -> b
coe (\ Any
v0 Any
v1 Any
v2 Any
v3 Any
v4 -> Any
v4))
-- Data.Bool.Properties.<-irrelevant
d_'60''45'irrelevant_3264 ::
  Bool ->
  Bool ->
  MAlonzo.Code.Data.Bool.Base.T__'60'__18 ->
  MAlonzo.Code.Data.Bool.Base.T__'60'__18 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'60''45'irrelevant_3264 :: Bool -> Bool -> T__'60'__18 -> T__'60'__18 -> T__'8801'__12
d_'60''45'irrelevant_3264 = Bool -> Bool -> T__'60'__18 -> T__'60'__18 -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties.<-wellFounded
d_'60''45'wellFounded_3266 ::
  Bool -> MAlonzo.Code.Induction.WellFounded.T_Acc_42
d_'60''45'wellFounded_3266 :: Bool -> T_Acc_42
d_'60''45'wellFounded_3266 = Bool -> T_Acc_42
forall a. a
erased
-- Data.Bool.Properties._.<-acc
d_'60''45'acc_3276 ::
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Data.Bool.Base.T__'60'__18 ->
  MAlonzo.Code.Induction.WellFounded.T_Acc_42
d_'60''45'acc_3276 :: Bool -> Bool -> Bool -> T__'60'__18 -> T_Acc_42
d_'60''45'acc_3276 = Bool -> Bool -> Bool -> T__'60'__18 -> T_Acc_42
forall a. a
erased
-- Data.Bool.Properties.<-isStrictPartialOrder
d_'60''45'isStrictPartialOrder_3278 ::
  MAlonzo.Code.Relation.Binary.Structures.T_IsStrictPartialOrder_370
d_'60''45'isStrictPartialOrder_3278 :: T_IsStrictPartialOrder_370
d_'60''45'isStrictPartialOrder_3278
  = (T_IsEquivalence_28
 -> (Any -> Any -> Any -> Any -> Any -> Any)
 -> T_Σ_14
 -> T_IsStrictPartialOrder_370)
-> Any -> Any -> T_Σ_14 -> T_IsStrictPartialOrder_370
forall a b. a -> b
coe
      T_IsEquivalence_28
-> (Any -> Any -> Any -> Any -> Any -> Any)
-> T_Σ_14
-> T_IsStrictPartialOrder_370
MAlonzo.Code.Relation.Binary.Structures.C_constructor_412
      (T_IsEquivalence_28 -> Any
forall a b. a -> b
coe
         T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.PropositionalEquality.Properties.du_isEquivalence_396)
      Any
forall a. a
erased T_Σ_14
d_'60''45'resp'8322''45''8801'_3258
-- Data.Bool.Properties.<-isStrictTotalOrder
d_'60''45'isStrictTotalOrder_3280 ::
  MAlonzo.Code.Relation.Binary.Structures.T_IsStrictTotalOrder_624
d_'60''45'isStrictTotalOrder_3280 :: T_IsStrictTotalOrder_624
d_'60''45'isStrictTotalOrder_3280
  = (T_IsStrictPartialOrder_370
 -> (Any -> Any -> T_Tri_158) -> T_IsStrictTotalOrder_624)
-> Any -> Any -> T_IsStrictTotalOrder_624
forall a b. a -> b
coe
      T_IsStrictPartialOrder_370
-> (Any -> Any -> T_Tri_158) -> T_IsStrictTotalOrder_624
MAlonzo.Code.Relation.Binary.Structures.C_constructor_680
      (T_IsStrictPartialOrder_370 -> Any
forall a b. a -> b
coe T_IsStrictPartialOrder_370
d_'60''45'isStrictPartialOrder_3278) ((Bool -> Bool -> T_Tri_158) -> Any
forall a b. a -> b
coe Bool -> Bool -> T_Tri_158
d_'60''45'cmp_3254)
-- Data.Bool.Properties.<-strictPartialOrder
d_'60''45'strictPartialOrder_3282 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_StrictPartialOrder_760
d_'60''45'strictPartialOrder_3282 :: T_StrictPartialOrder_760
d_'60''45'strictPartialOrder_3282
  = (T_IsStrictPartialOrder_370 -> T_StrictPartialOrder_760)
-> T_IsStrictPartialOrder_370 -> T_StrictPartialOrder_760
forall a b. a -> b
coe
      T_IsStrictPartialOrder_370 -> T_StrictPartialOrder_760
MAlonzo.Code.Relation.Binary.Bundles.C_constructor_842
      T_IsStrictPartialOrder_370
d_'60''45'isStrictPartialOrder_3278
-- Data.Bool.Properties.<-strictTotalOrder
d_'60''45'strictTotalOrder_3284 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_StrictTotalOrder_1280
d_'60''45'strictTotalOrder_3284 :: T_StrictTotalOrder_1280
d_'60''45'strictTotalOrder_3284
  = (T_IsStrictTotalOrder_624 -> T_StrictTotalOrder_1280)
-> T_IsStrictTotalOrder_624 -> T_StrictTotalOrder_1280
forall a b. a -> b
coe
      T_IsStrictTotalOrder_624 -> T_StrictTotalOrder_1280
MAlonzo.Code.Relation.Binary.Bundles.C_constructor_1386
      T_IsStrictTotalOrder_624
d_'60''45'isStrictTotalOrder_3280
-- Data.Bool.Properties.∨-assoc
d_'8744''45'assoc_3286 ::
  Bool ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8744''45'assoc_3286 :: Bool -> Bool -> Bool -> T__'8801'__12
d_'8744''45'assoc_3286 = Bool -> Bool -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties.∨-comm
d_'8744''45'comm_3296 ::
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8744''45'comm_3296 :: Bool -> Bool -> T__'8801'__12
d_'8744''45'comm_3296 = Bool -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties.∨-identityˡ
d_'8744''45'identity'737'_3298 ::
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8744''45'identity'737'_3298 :: Bool -> T__'8801'__12
d_'8744''45'identity'737'_3298 = Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties.∨-identityʳ
d_'8744''45'identity'691'_3300 ::
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8744''45'identity'691'_3300 :: Bool -> T__'8801'__12
d_'8744''45'identity'691'_3300 = Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties.∨-identity
d_'8744''45'identity_3302 :: MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'8744''45'identity_3302 :: T_Σ_14
d_'8744''45'identity_3302
  = (Any -> Any -> T_Σ_14) -> Any -> Any -> T_Σ_14
forall a b. a -> b
coe Any -> Any -> T_Σ_14
MAlonzo.Code.Agda.Builtin.Sigma.C__'44'__32 Any
forall a. a
erased Any
forall a. a
erased
-- Data.Bool.Properties.∨-zeroˡ
d_'8744''45'zero'737'_3304 ::
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8744''45'zero'737'_3304 :: Bool -> T__'8801'__12
d_'8744''45'zero'737'_3304 = Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties.∨-zeroʳ
d_'8744''45'zero'691'_3306 ::
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8744''45'zero'691'_3306 :: Bool -> T__'8801'__12
d_'8744''45'zero'691'_3306 = Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties.∨-zero
d_'8744''45'zero_3308 :: MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'8744''45'zero_3308 :: T_Σ_14
d_'8744''45'zero_3308
  = (Any -> Any -> T_Σ_14) -> Any -> Any -> T_Σ_14
forall a b. a -> b
coe Any -> Any -> T_Σ_14
MAlonzo.Code.Agda.Builtin.Sigma.C__'44'__32 Any
forall a. a
erased Any
forall a. a
erased
-- Data.Bool.Properties.∨-inverseˡ
d_'8744''45'inverse'737'_3310 ::
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8744''45'inverse'737'_3310 :: Bool -> T__'8801'__12
d_'8744''45'inverse'737'_3310 = Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties.∨-inverseʳ
d_'8744''45'inverse'691'_3312 ::
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8744''45'inverse'691'_3312 :: Bool -> T__'8801'__12
d_'8744''45'inverse'691'_3312 = Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties.∨-inverse
d_'8744''45'inverse_3316 :: MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'8744''45'inverse_3316 :: T_Σ_14
d_'8744''45'inverse_3316
  = (Any -> Any -> T_Σ_14) -> Any -> Any -> T_Σ_14
forall a b. a -> b
coe Any -> Any -> T_Σ_14
MAlonzo.Code.Agda.Builtin.Sigma.C__'44'__32 Any
forall a. a
erased Any
forall a. a
erased
-- Data.Bool.Properties.∨-idem
d_'8744''45'idem_3318 ::
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8744''45'idem_3318 :: Bool -> T__'8801'__12
d_'8744''45'idem_3318 = Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties.∨-sel
d_'8744''45'sel_3320 ::
  Bool -> Bool -> MAlonzo.Code.Data.Sum.Base.T__'8846'__30
d_'8744''45'sel_3320 :: Bool -> Bool -> T__'8846'__30
d_'8744''45'sel_3320 Bool
v0 ~Bool
v1 = Bool -> T__'8846'__30
du_'8744''45'sel_3320 Bool
v0
du_'8744''45'sel_3320 ::
  Bool -> MAlonzo.Code.Data.Sum.Base.T__'8846'__30
du_'8744''45'sel_3320 :: Bool -> T__'8846'__30
du_'8744''45'sel_3320 Bool
v0
  = if Bool -> Bool
forall a b. a -> b
coe Bool
v0
      then (Any -> T__'8846'__30) -> Any -> T__'8846'__30
forall a b. a -> b
coe Any -> T__'8846'__30
MAlonzo.Code.Data.Sum.Base.C_inj'8321'_38 Any
forall a. a
erased
      else (Any -> T__'8846'__30) -> Any -> T__'8846'__30
forall a b. a -> b
coe Any -> T__'8846'__30
MAlonzo.Code.Data.Sum.Base.C_inj'8322'_42 Any
forall a. a
erased
-- Data.Bool.Properties.∨-conicalˡ
d_'8744''45'conical'737'_3326 ::
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8744''45'conical'737'_3326 :: Bool -> Bool -> T__'8801'__12 -> T__'8801'__12
d_'8744''45'conical'737'_3326 = Bool -> Bool -> T__'8801'__12 -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties.∨-conicalʳ
d_'8744''45'conical'691'_3328 ::
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8744''45'conical'691'_3328 :: Bool -> Bool -> T__'8801'__12 -> T__'8801'__12
d_'8744''45'conical'691'_3328 = Bool -> Bool -> T__'8801'__12 -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties.∨-conical
d_'8744''45'conical_3330 :: MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'8744''45'conical_3330 :: T_Σ_14
d_'8744''45'conical_3330
  = (Any -> Any -> T_Σ_14) -> Any -> Any -> T_Σ_14
forall a b. a -> b
coe Any -> Any -> T_Σ_14
MAlonzo.Code.Agda.Builtin.Sigma.C__'44'__32 Any
forall a. a
erased Any
forall a. a
erased
-- Data.Bool.Properties.∨-isMagma
d_'8744''45'isMagma_3332 ::
  MAlonzo.Code.Algebra.Structures.T_IsMagma_178
d_'8744''45'isMagma_3332 :: T_IsMagma_178
d_'8744''45'isMagma_3332
  = (T_IsEquivalence_28
 -> (Any -> Any -> Any -> Any -> Any -> Any -> Any)
 -> T_IsMagma_178)
-> Any -> Any -> T_IsMagma_178
forall a b. a -> b
coe
      T_IsEquivalence_28
-> (Any -> Any -> Any -> Any -> Any -> Any -> Any) -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.C_constructor_210
      (T_IsEquivalence_28 -> Any
forall a b. a -> b
coe
         T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.PropositionalEquality.Properties.du_isEquivalence_396)
      Any
forall a. a
erased
-- Data.Bool.Properties.∨-magma
d_'8744''45'magma_3334 :: MAlonzo.Code.Algebra.Bundles.T_Magma_74
d_'8744''45'magma_3334 :: T_Magma_74
d_'8744''45'magma_3334
  = ((Any -> Any -> Any) -> T_IsMagma_178 -> T_Magma_74)
-> (Bool -> Bool -> Bool) -> T_IsMagma_178 -> T_Magma_74
forall a b. a -> b
coe
      (Any -> Any -> Any) -> T_IsMagma_178 -> T_Magma_74
MAlonzo.Code.Algebra.Bundles.C_constructor_124
      Bool -> Bool -> Bool
MAlonzo.Code.Data.Bool.Base.d__'8744'__30 T_IsMagma_178
d_'8744''45'isMagma_3332
-- Data.Bool.Properties.∨-isSemigroup
d_'8744''45'isSemigroup_3336 ::
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_488
d_'8744''45'isSemigroup_3336 :: T_IsSemigroup_488
d_'8744''45'isSemigroup_3336
  = (T_IsMagma_178 -> (Any -> Any -> Any -> Any) -> T_IsSemigroup_488)
-> Any -> Any -> T_IsSemigroup_488
forall a b. a -> b
coe
      T_IsMagma_178 -> (Any -> Any -> Any -> Any) -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.C_constructor_522
      (T_IsMagma_178 -> Any
forall a b. a -> b
coe T_IsMagma_178
d_'8744''45'isMagma_3332) Any
forall a. a
erased
-- Data.Bool.Properties.∨-semigroup
d_'8744''45'semigroup_3338 ::
  MAlonzo.Code.Algebra.Bundles.T_Semigroup_558
d_'8744''45'semigroup_3338 :: T_Semigroup_558
d_'8744''45'semigroup_3338
  = ((Any -> Any -> Any) -> T_IsSemigroup_488 -> T_Semigroup_558)
-> (Bool -> Bool -> Bool) -> T_IsSemigroup_488 -> T_Semigroup_558
forall a b. a -> b
coe
      (Any -> Any -> Any) -> T_IsSemigroup_488 -> T_Semigroup_558
MAlonzo.Code.Algebra.Bundles.C_constructor_614
      Bool -> Bool -> Bool
MAlonzo.Code.Data.Bool.Base.d__'8744'__30
      T_IsSemigroup_488
d_'8744''45'isSemigroup_3336
-- Data.Bool.Properties.∨-isBand
d_'8744''45'isBand_3340 ::
  MAlonzo.Code.Algebra.Structures.T_IsBand_526
d_'8744''45'isBand_3340 :: T_IsBand_526
d_'8744''45'isBand_3340
  = (T_IsSemigroup_488 -> (Any -> Any) -> T_IsBand_526)
-> Any -> Any -> T_IsBand_526
forall a b. a -> b
coe
      T_IsSemigroup_488 -> (Any -> Any) -> T_IsBand_526
MAlonzo.Code.Algebra.Structures.C_constructor_564
      (T_IsSemigroup_488 -> Any
forall a b. a -> b
coe T_IsSemigroup_488
d_'8744''45'isSemigroup_3336) Any
forall a. a
erased
-- Data.Bool.Properties.∨-band
d_'8744''45'band_3342 :: MAlonzo.Code.Algebra.Bundles.T_Band_620
d_'8744''45'band_3342 :: T_Band_620
d_'8744''45'band_3342
  = ((Any -> Any -> Any) -> T_IsBand_526 -> T_Band_620)
-> (Bool -> Bool -> Bool) -> T_IsBand_526 -> T_Band_620
forall a b. a -> b
coe
      (Any -> Any -> Any) -> T_IsBand_526 -> T_Band_620
MAlonzo.Code.Algebra.Bundles.C_constructor_682
      Bool -> Bool -> Bool
MAlonzo.Code.Data.Bool.Base.d__'8744'__30 T_IsBand_526
d_'8744''45'isBand_3340
-- Data.Bool.Properties.∨-isSemilattice
d_'8744''45'isSemilattice_3344 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_612
d_'8744''45'isSemilattice_3344 :: T_IsCommutativeBand_612
d_'8744''45'isSemilattice_3344
  = (T_IsBand_526 -> (Any -> Any -> Any) -> T_IsCommutativeBand_612)
-> Any -> Any -> T_IsCommutativeBand_612
forall a b. a -> b
coe
      T_IsBand_526 -> (Any -> Any -> Any) -> T_IsCommutativeBand_612
MAlonzo.Code.Algebra.Structures.C_constructor_660
      (T_IsBand_526 -> Any
forall a b. a -> b
coe T_IsBand_526
d_'8744''45'isBand_3340) Any
forall a. a
erased
-- Data.Bool.Properties.∨-semilattice
d_'8744''45'semilattice_3346 ::
  MAlonzo.Code.Algebra.Lattice.Bundles.T_Semilattice_10
d_'8744''45'semilattice_3346 :: T_Semilattice_10
d_'8744''45'semilattice_3346
  = ((Any -> Any -> Any)
 -> T_IsCommutativeBand_612 -> T_Semilattice_10)
-> (Bool -> Bool -> Bool)
-> T_IsCommutativeBand_612
-> T_Semilattice_10
forall a b. a -> b
coe
      (Any -> Any -> Any) -> T_IsCommutativeBand_612 -> T_Semilattice_10
MAlonzo.Code.Algebra.Lattice.Bundles.C_constructor_84
      Bool -> Bool -> Bool
MAlonzo.Code.Data.Bool.Base.d__'8744'__30
      T_IsCommutativeBand_612
d_'8744''45'isSemilattice_3344
-- Data.Bool.Properties.∨-isMonoid
d_'8744''45'isMonoid_3348 ::
  MAlonzo.Code.Algebra.Structures.T_IsMonoid_712
d_'8744''45'isMonoid_3348 :: T_IsMonoid_712
d_'8744''45'isMonoid_3348
  = (T_IsSemigroup_488 -> T_Σ_14 -> T_IsMonoid_712)
-> Any -> Any -> T_IsMonoid_712
forall a b. a -> b
coe
      T_IsSemigroup_488 -> T_Σ_14 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.C_constructor_758
      (T_IsSemigroup_488 -> Any
forall a b. a -> b
coe T_IsSemigroup_488
d_'8744''45'isSemigroup_3336) (T_Σ_14 -> Any
forall a b. a -> b
coe T_Σ_14
d_'8744''45'identity_3302)
-- Data.Bool.Properties.∨-isCommutativeMonoid
d_'8744''45'isCommutativeMonoid_3350 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMonoid_764
d_'8744''45'isCommutativeMonoid_3350 :: T_IsCommutativeMonoid_764
d_'8744''45'isCommutativeMonoid_3350
  = (T_IsMonoid_712
 -> (Any -> Any -> Any) -> T_IsCommutativeMonoid_764)
-> Any -> Any -> T_IsCommutativeMonoid_764
forall a b. a -> b
coe
      T_IsMonoid_712 -> (Any -> Any -> Any) -> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.C_constructor_820
      (T_IsMonoid_712 -> Any
forall a b. a -> b
coe T_IsMonoid_712
d_'8744''45'isMonoid_3348) Any
forall a. a
erased
-- Data.Bool.Properties.∨-commutativeMonoid
d_'8744''45'commutativeMonoid_3352 ::
  MAlonzo.Code.Algebra.Bundles.T_CommutativeMonoid_996
d_'8744''45'commutativeMonoid_3352 :: T_CommutativeMonoid_996
d_'8744''45'commutativeMonoid_3352
  = ((Any -> Any -> Any)
 -> Any -> T_IsCommutativeMonoid_764 -> T_CommutativeMonoid_996)
-> (Bool -> Bool -> Bool)
-> Any
-> T_IsCommutativeMonoid_764
-> T_CommutativeMonoid_996
forall a b. a -> b
coe
      (Any -> Any -> Any)
-> Any -> T_IsCommutativeMonoid_764 -> T_CommutativeMonoid_996
MAlonzo.Code.Algebra.Bundles.C_constructor_1088
      Bool -> Bool -> Bool
MAlonzo.Code.Data.Bool.Base.d__'8744'__30
      (Bool -> Any
forall a b. a -> b
coe Bool
MAlonzo.Code.Agda.Builtin.Bool.C_false_8)
      T_IsCommutativeMonoid_764
d_'8744''45'isCommutativeMonoid_3350
-- Data.Bool.Properties.∨-isIdempotentCommutativeMonoid
d_'8744''45'isIdempotentCommutativeMonoid_3354 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884
d_'8744''45'isIdempotentCommutativeMonoid_3354 :: T_IsIdempotentCommutativeMonoid_884
d_'8744''45'isIdempotentCommutativeMonoid_3354
  = (T_IsCommutativeMonoid_764
 -> (Any -> Any) -> T_IsIdempotentCommutativeMonoid_884)
-> Any -> Any -> T_IsIdempotentCommutativeMonoid_884
forall a b. a -> b
coe
      T_IsCommutativeMonoid_764
-> (Any -> Any) -> T_IsIdempotentCommutativeMonoid_884
MAlonzo.Code.Algebra.Structures.C_constructor_950
      (T_IsCommutativeMonoid_764 -> Any
forall a b. a -> b
coe T_IsCommutativeMonoid_764
d_'8744''45'isCommutativeMonoid_3350) Any
forall a. a
erased
-- Data.Bool.Properties.∨-idempotentCommutativeMonoid
d_'8744''45'idempotentCommutativeMonoid_3356 ::
  MAlonzo.Code.Algebra.Bundles.T_IdempotentCommutativeMonoid_1186
d_'8744''45'idempotentCommutativeMonoid_3356 :: T_IdempotentCommutativeMonoid_1186
d_'8744''45'idempotentCommutativeMonoid_3356
  = ((Any -> Any -> Any)
 -> Any
 -> T_IsIdempotentCommutativeMonoid_884
 -> T_IdempotentCommutativeMonoid_1186)
-> (Bool -> Bool -> Bool)
-> Any
-> T_IsIdempotentCommutativeMonoid_884
-> T_IdempotentCommutativeMonoid_1186
forall a b. a -> b
coe
      (Any -> Any -> Any)
-> Any
-> T_IsIdempotentCommutativeMonoid_884
-> T_IdempotentCommutativeMonoid_1186
MAlonzo.Code.Algebra.Bundles.C_constructor_1296
      Bool -> Bool -> Bool
MAlonzo.Code.Data.Bool.Base.d__'8744'__30
      (Bool -> Any
forall a b. a -> b
coe Bool
MAlonzo.Code.Agda.Builtin.Bool.C_false_8)
      T_IsIdempotentCommutativeMonoid_884
d_'8744''45'isIdempotentCommutativeMonoid_3354
-- Data.Bool.Properties.∧-assoc
d_'8743''45'assoc_3358 ::
  Bool ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8743''45'assoc_3358 :: Bool -> Bool -> Bool -> T__'8801'__12
d_'8743''45'assoc_3358 = Bool -> Bool -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties.∧-comm
d_'8743''45'comm_3368 ::
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8743''45'comm_3368 :: Bool -> Bool -> T__'8801'__12
d_'8743''45'comm_3368 = Bool -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties.∧-identityˡ
d_'8743''45'identity'737'_3370 ::
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8743''45'identity'737'_3370 :: Bool -> T__'8801'__12
d_'8743''45'identity'737'_3370 = Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties.∧-identityʳ
d_'8743''45'identity'691'_3372 ::
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8743''45'identity'691'_3372 :: Bool -> T__'8801'__12
d_'8743''45'identity'691'_3372 = Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties.∧-identity
d_'8743''45'identity_3374 :: MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'8743''45'identity_3374 :: T_Σ_14
d_'8743''45'identity_3374
  = (Any -> Any -> T_Σ_14) -> Any -> Any -> T_Σ_14
forall a b. a -> b
coe Any -> Any -> T_Σ_14
MAlonzo.Code.Agda.Builtin.Sigma.C__'44'__32 Any
forall a. a
erased Any
forall a. a
erased
-- Data.Bool.Properties.∧-zeroˡ
d_'8743''45'zero'737'_3376 ::
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8743''45'zero'737'_3376 :: Bool -> T__'8801'__12
d_'8743''45'zero'737'_3376 = Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties.∧-zeroʳ
d_'8743''45'zero'691'_3378 ::
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8743''45'zero'691'_3378 :: Bool -> T__'8801'__12
d_'8743''45'zero'691'_3378 = Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties.∧-zero
d_'8743''45'zero_3380 :: MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'8743''45'zero_3380 :: T_Σ_14
d_'8743''45'zero_3380
  = (Any -> Any -> T_Σ_14) -> Any -> Any -> T_Σ_14
forall a b. a -> b
coe Any -> Any -> T_Σ_14
MAlonzo.Code.Agda.Builtin.Sigma.C__'44'__32 Any
forall a. a
erased Any
forall a. a
erased
-- Data.Bool.Properties.∧-inverseˡ
d_'8743''45'inverse'737'_3382 ::
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8743''45'inverse'737'_3382 :: Bool -> T__'8801'__12
d_'8743''45'inverse'737'_3382 = Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties.∧-inverseʳ
d_'8743''45'inverse'691'_3384 ::
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8743''45'inverse'691'_3384 :: Bool -> T__'8801'__12
d_'8743''45'inverse'691'_3384 = Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties.∧-inverse
d_'8743''45'inverse_3388 :: MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'8743''45'inverse_3388 :: T_Σ_14
d_'8743''45'inverse_3388
  = (Any -> Any -> T_Σ_14) -> Any -> Any -> T_Σ_14
forall a b. a -> b
coe Any -> Any -> T_Σ_14
MAlonzo.Code.Agda.Builtin.Sigma.C__'44'__32 Any
forall a. a
erased Any
forall a. a
erased
-- Data.Bool.Properties.∧-idem
d_'8743''45'idem_3390 ::
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8743''45'idem_3390 :: Bool -> T__'8801'__12
d_'8743''45'idem_3390 = Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties.∧-sel
d_'8743''45'sel_3392 ::
  Bool -> Bool -> MAlonzo.Code.Data.Sum.Base.T__'8846'__30
d_'8743''45'sel_3392 :: Bool -> Bool -> T__'8846'__30
d_'8743''45'sel_3392 Bool
v0 ~Bool
v1 = Bool -> T__'8846'__30
du_'8743''45'sel_3392 Bool
v0
du_'8743''45'sel_3392 ::
  Bool -> MAlonzo.Code.Data.Sum.Base.T__'8846'__30
du_'8743''45'sel_3392 :: Bool -> T__'8846'__30
du_'8743''45'sel_3392 Bool
v0
  = if Bool -> Bool
forall a b. a -> b
coe Bool
v0
      then (Any -> T__'8846'__30) -> Any -> T__'8846'__30
forall a b. a -> b
coe Any -> T__'8846'__30
MAlonzo.Code.Data.Sum.Base.C_inj'8322'_42 Any
forall a. a
erased
      else (Any -> T__'8846'__30) -> Any -> T__'8846'__30
forall a b. a -> b
coe Any -> T__'8846'__30
MAlonzo.Code.Data.Sum.Base.C_inj'8321'_38 Any
forall a. a
erased
-- Data.Bool.Properties.∧-conicalˡ
d_'8743''45'conical'737'_3398 ::
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8743''45'conical'737'_3398 :: Bool -> Bool -> T__'8801'__12 -> T__'8801'__12
d_'8743''45'conical'737'_3398 = Bool -> Bool -> T__'8801'__12 -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties.∧-conicalʳ
d_'8743''45'conical'691'_3400 ::
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8743''45'conical'691'_3400 :: Bool -> Bool -> T__'8801'__12 -> T__'8801'__12
d_'8743''45'conical'691'_3400 = Bool -> Bool -> T__'8801'__12 -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties.∧-conical
d_'8743''45'conical_3402 :: MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'8743''45'conical_3402 :: T_Σ_14
d_'8743''45'conical_3402
  = (Any -> Any -> T_Σ_14) -> Any -> Any -> T_Σ_14
forall a b. a -> b
coe Any -> Any -> T_Σ_14
MAlonzo.Code.Agda.Builtin.Sigma.C__'44'__32 Any
forall a. a
erased Any
forall a. a
erased
-- Data.Bool.Properties.∧-distribˡ-∨
d_'8743''45'distrib'737''45''8744'_3404 ::
  Bool ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8743''45'distrib'737''45''8744'_3404 :: Bool -> Bool -> Bool -> T__'8801'__12
d_'8743''45'distrib'737''45''8744'_3404 = Bool -> Bool -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties.∧-distribʳ-∨
d_'8743''45'distrib'691''45''8744'_3414 ::
  Bool ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8743''45'distrib'691''45''8744'_3414 :: Bool -> Bool -> Bool -> T__'8801'__12
d_'8743''45'distrib'691''45''8744'_3414 = Bool -> Bool -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties.∧-distrib-∨
d_'8743''45'distrib'45''8744'_3422 ::
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'8743''45'distrib'45''8744'_3422 :: T_Σ_14
d_'8743''45'distrib'45''8744'_3422
  = (Any -> Any -> T_Σ_14) -> Any -> Any -> T_Σ_14
forall a b. a -> b
coe Any -> Any -> T_Σ_14
MAlonzo.Code.Agda.Builtin.Sigma.C__'44'__32 Any
forall a. a
erased Any
forall a. a
erased
-- Data.Bool.Properties.∨-distribˡ-∧
d_'8744''45'distrib'737''45''8743'_3424 ::
  Bool ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8744''45'distrib'737''45''8743'_3424 :: Bool -> Bool -> Bool -> T__'8801'__12
d_'8744''45'distrib'737''45''8743'_3424 = Bool -> Bool -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties.∨-distribʳ-∧
d_'8744''45'distrib'691''45''8743'_3434 ::
  Bool ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8744''45'distrib'691''45''8743'_3434 :: Bool -> Bool -> Bool -> T__'8801'__12
d_'8744''45'distrib'691''45''8743'_3434 = Bool -> Bool -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties.∨-distrib-∧
d_'8744''45'distrib'45''8743'_3442 ::
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'8744''45'distrib'45''8743'_3442 :: T_Σ_14
d_'8744''45'distrib'45''8743'_3442
  = (Any -> Any -> T_Σ_14) -> Any -> Any -> T_Σ_14
forall a b. a -> b
coe Any -> Any -> T_Σ_14
MAlonzo.Code.Agda.Builtin.Sigma.C__'44'__32 Any
forall a. a
erased Any
forall a. a
erased
-- Data.Bool.Properties.∧-abs-∨
d_'8743''45'abs'45''8744'_3444 ::
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8743''45'abs'45''8744'_3444 :: Bool -> Bool -> T__'8801'__12
d_'8743''45'abs'45''8744'_3444 = Bool -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties.∨-abs-∧
d_'8744''45'abs'45''8743'_3450 ::
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8744''45'abs'45''8743'_3450 :: Bool -> Bool -> T__'8801'__12
d_'8744''45'abs'45''8743'_3450 = Bool -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties.∨-∧-absorptive
d_'8744''45''8743''45'absorptive_3456 ::
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'8744''45''8743''45'absorptive_3456 :: T_Σ_14
d_'8744''45''8743''45'absorptive_3456
  = (Any -> Any -> T_Σ_14) -> Any -> Any -> T_Σ_14
forall a b. a -> b
coe Any -> Any -> T_Σ_14
MAlonzo.Code.Agda.Builtin.Sigma.C__'44'__32 Any
forall a. a
erased Any
forall a. a
erased
-- Data.Bool.Properties.∧-isMagma
d_'8743''45'isMagma_3458 ::
  MAlonzo.Code.Algebra.Structures.T_IsMagma_178
d_'8743''45'isMagma_3458 :: T_IsMagma_178
d_'8743''45'isMagma_3458
  = (T_IsEquivalence_28
 -> (Any -> Any -> Any -> Any -> Any -> Any -> Any)
 -> T_IsMagma_178)
-> Any -> Any -> T_IsMagma_178
forall a b. a -> b
coe
      T_IsEquivalence_28
-> (Any -> Any -> Any -> Any -> Any -> Any -> Any) -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.C_constructor_210
      (T_IsEquivalence_28 -> Any
forall a b. a -> b
coe
         T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.PropositionalEquality.Properties.du_isEquivalence_396)
      Any
forall a. a
erased
-- Data.Bool.Properties.∧-magma
d_'8743''45'magma_3460 :: MAlonzo.Code.Algebra.Bundles.T_Magma_74
d_'8743''45'magma_3460 :: T_Magma_74
d_'8743''45'magma_3460
  = ((Any -> Any -> Any) -> T_IsMagma_178 -> T_Magma_74)
-> (Bool -> Bool -> Bool) -> T_IsMagma_178 -> T_Magma_74
forall a b. a -> b
coe
      (Any -> Any -> Any) -> T_IsMagma_178 -> T_Magma_74
MAlonzo.Code.Algebra.Bundles.C_constructor_124
      Bool -> Bool -> Bool
MAlonzo.Code.Data.Bool.Base.d__'8743'__24 T_IsMagma_178
d_'8743''45'isMagma_3458
-- Data.Bool.Properties.∧-isSemigroup
d_'8743''45'isSemigroup_3462 ::
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_488
d_'8743''45'isSemigroup_3462 :: T_IsSemigroup_488
d_'8743''45'isSemigroup_3462
  = (T_IsMagma_178 -> (Any -> Any -> Any -> Any) -> T_IsSemigroup_488)
-> Any -> Any -> T_IsSemigroup_488
forall a b. a -> b
coe
      T_IsMagma_178 -> (Any -> Any -> Any -> Any) -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.C_constructor_522
      (T_IsMagma_178 -> Any
forall a b. a -> b
coe T_IsMagma_178
d_'8743''45'isMagma_3458) Any
forall a. a
erased
-- Data.Bool.Properties.∧-semigroup
d_'8743''45'semigroup_3464 ::
  MAlonzo.Code.Algebra.Bundles.T_Semigroup_558
d_'8743''45'semigroup_3464 :: T_Semigroup_558
d_'8743''45'semigroup_3464
  = ((Any -> Any -> Any) -> T_IsSemigroup_488 -> T_Semigroup_558)
-> (Bool -> Bool -> Bool) -> T_IsSemigroup_488 -> T_Semigroup_558
forall a b. a -> b
coe
      (Any -> Any -> Any) -> T_IsSemigroup_488 -> T_Semigroup_558
MAlonzo.Code.Algebra.Bundles.C_constructor_614
      Bool -> Bool -> Bool
MAlonzo.Code.Data.Bool.Base.d__'8743'__24
      T_IsSemigroup_488
d_'8743''45'isSemigroup_3462
-- Data.Bool.Properties.∧-isBand
d_'8743''45'isBand_3466 ::
  MAlonzo.Code.Algebra.Structures.T_IsBand_526
d_'8743''45'isBand_3466 :: T_IsBand_526
d_'8743''45'isBand_3466
  = (T_IsSemigroup_488 -> (Any -> Any) -> T_IsBand_526)
-> Any -> Any -> T_IsBand_526
forall a b. a -> b
coe
      T_IsSemigroup_488 -> (Any -> Any) -> T_IsBand_526
MAlonzo.Code.Algebra.Structures.C_constructor_564
      (T_IsSemigroup_488 -> Any
forall a b. a -> b
coe T_IsSemigroup_488
d_'8743''45'isSemigroup_3462) Any
forall a. a
erased
-- Data.Bool.Properties.∧-band
d_'8743''45'band_3468 :: MAlonzo.Code.Algebra.Bundles.T_Band_620
d_'8743''45'band_3468 :: T_Band_620
d_'8743''45'band_3468
  = ((Any -> Any -> Any) -> T_IsBand_526 -> T_Band_620)
-> (Bool -> Bool -> Bool) -> T_IsBand_526 -> T_Band_620
forall a b. a -> b
coe
      (Any -> Any -> Any) -> T_IsBand_526 -> T_Band_620
MAlonzo.Code.Algebra.Bundles.C_constructor_682
      Bool -> Bool -> Bool
MAlonzo.Code.Data.Bool.Base.d__'8743'__24 T_IsBand_526
d_'8743''45'isBand_3466
-- Data.Bool.Properties.∧-isSemilattice
d_'8743''45'isSemilattice_3470 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_612
d_'8743''45'isSemilattice_3470 :: T_IsCommutativeBand_612
d_'8743''45'isSemilattice_3470
  = (T_IsBand_526 -> (Any -> Any -> Any) -> T_IsCommutativeBand_612)
-> Any -> Any -> T_IsCommutativeBand_612
forall a b. a -> b
coe
      T_IsBand_526 -> (Any -> Any -> Any) -> T_IsCommutativeBand_612
MAlonzo.Code.Algebra.Structures.C_constructor_660
      (T_IsBand_526 -> Any
forall a b. a -> b
coe T_IsBand_526
d_'8743''45'isBand_3466) Any
forall a. a
erased
-- Data.Bool.Properties.∧-semilattice
d_'8743''45'semilattice_3472 ::
  MAlonzo.Code.Algebra.Lattice.Bundles.T_Semilattice_10
d_'8743''45'semilattice_3472 :: T_Semilattice_10
d_'8743''45'semilattice_3472
  = ((Any -> Any -> Any)
 -> T_IsCommutativeBand_612 -> T_Semilattice_10)
-> (Bool -> Bool -> Bool)
-> T_IsCommutativeBand_612
-> T_Semilattice_10
forall a b. a -> b
coe
      (Any -> Any -> Any) -> T_IsCommutativeBand_612 -> T_Semilattice_10
MAlonzo.Code.Algebra.Lattice.Bundles.C_constructor_84
      Bool -> Bool -> Bool
MAlonzo.Code.Data.Bool.Base.d__'8743'__24
      T_IsCommutativeBand_612
d_'8743''45'isSemilattice_3470
-- Data.Bool.Properties.∧-isMonoid
d_'8743''45'isMonoid_3474 ::
  MAlonzo.Code.Algebra.Structures.T_IsMonoid_712
d_'8743''45'isMonoid_3474 :: T_IsMonoid_712
d_'8743''45'isMonoid_3474
  = (T_IsSemigroup_488 -> T_Σ_14 -> T_IsMonoid_712)
-> Any -> Any -> T_IsMonoid_712
forall a b. a -> b
coe
      T_IsSemigroup_488 -> T_Σ_14 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.C_constructor_758
      (T_IsSemigroup_488 -> Any
forall a b. a -> b
coe T_IsSemigroup_488
d_'8743''45'isSemigroup_3462) (T_Σ_14 -> Any
forall a b. a -> b
coe T_Σ_14
d_'8743''45'identity_3374)
-- Data.Bool.Properties.∧-isCommutativeMonoid
d_'8743''45'isCommutativeMonoid_3476 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMonoid_764
d_'8743''45'isCommutativeMonoid_3476 :: T_IsCommutativeMonoid_764
d_'8743''45'isCommutativeMonoid_3476
  = (T_IsMonoid_712
 -> (Any -> Any -> Any) -> T_IsCommutativeMonoid_764)
-> Any -> Any -> T_IsCommutativeMonoid_764
forall a b. a -> b
coe
      T_IsMonoid_712 -> (Any -> Any -> Any) -> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.C_constructor_820
      (T_IsMonoid_712 -> Any
forall a b. a -> b
coe T_IsMonoid_712
d_'8743''45'isMonoid_3474) Any
forall a. a
erased
-- Data.Bool.Properties.∧-commutativeMonoid
d_'8743''45'commutativeMonoid_3478 ::
  MAlonzo.Code.Algebra.Bundles.T_CommutativeMonoid_996
d_'8743''45'commutativeMonoid_3478 :: T_CommutativeMonoid_996
d_'8743''45'commutativeMonoid_3478
  = ((Any -> Any -> Any)
 -> Any -> T_IsCommutativeMonoid_764 -> T_CommutativeMonoid_996)
-> (Bool -> Bool -> Bool)
-> Any
-> T_IsCommutativeMonoid_764
-> T_CommutativeMonoid_996
forall a b. a -> b
coe
      (Any -> Any -> Any)
-> Any -> T_IsCommutativeMonoid_764 -> T_CommutativeMonoid_996
MAlonzo.Code.Algebra.Bundles.C_constructor_1088
      Bool -> Bool -> Bool
MAlonzo.Code.Data.Bool.Base.d__'8743'__24
      (Bool -> Any
forall a b. a -> b
coe Bool
MAlonzo.Code.Agda.Builtin.Bool.C_true_10)
      T_IsCommutativeMonoid_764
d_'8743''45'isCommutativeMonoid_3476
-- Data.Bool.Properties.∧-isIdempotentCommutativeMonoid
d_'8743''45'isIdempotentCommutativeMonoid_3480 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884
d_'8743''45'isIdempotentCommutativeMonoid_3480 :: T_IsIdempotentCommutativeMonoid_884
d_'8743''45'isIdempotentCommutativeMonoid_3480
  = (T_IsCommutativeMonoid_764
 -> (Any -> Any) -> T_IsIdempotentCommutativeMonoid_884)
-> Any -> Any -> T_IsIdempotentCommutativeMonoid_884
forall a b. a -> b
coe
      T_IsCommutativeMonoid_764
-> (Any -> Any) -> T_IsIdempotentCommutativeMonoid_884
MAlonzo.Code.Algebra.Structures.C_constructor_950
      (T_IsCommutativeMonoid_764 -> Any
forall a b. a -> b
coe T_IsCommutativeMonoid_764
d_'8743''45'isCommutativeMonoid_3476) Any
forall a. a
erased
-- Data.Bool.Properties.∧-idempotentCommutativeMonoid
d_'8743''45'idempotentCommutativeMonoid_3482 ::
  MAlonzo.Code.Algebra.Bundles.T_IdempotentCommutativeMonoid_1186
d_'8743''45'idempotentCommutativeMonoid_3482 :: T_IdempotentCommutativeMonoid_1186
d_'8743''45'idempotentCommutativeMonoid_3482
  = ((Any -> Any -> Any)
 -> Any
 -> T_IsIdempotentCommutativeMonoid_884
 -> T_IdempotentCommutativeMonoid_1186)
-> (Bool -> Bool -> Bool)
-> Any
-> T_IsIdempotentCommutativeMonoid_884
-> T_IdempotentCommutativeMonoid_1186
forall a b. a -> b
coe
      (Any -> Any -> Any)
-> Any
-> T_IsIdempotentCommutativeMonoid_884
-> T_IdempotentCommutativeMonoid_1186
MAlonzo.Code.Algebra.Bundles.C_constructor_1296
      Bool -> Bool -> Bool
MAlonzo.Code.Data.Bool.Base.d__'8743'__24
      (Bool -> Any
forall a b. a -> b
coe Bool
MAlonzo.Code.Agda.Builtin.Bool.C_true_10)
      T_IsIdempotentCommutativeMonoid_884
d_'8743''45'isIdempotentCommutativeMonoid_3480
-- Data.Bool.Properties.∨-∧-isSemiring
d_'8744''45''8743''45'isSemiring_3484 ::
  MAlonzo.Code.Algebra.Structures.T_IsSemiring_1640
d_'8744''45''8743''45'isSemiring_3484 :: T_IsSemiring_1640
d_'8744''45''8743''45'isSemiring_3484
  = (T_IsSemiringWithoutAnnihilatingZero_1536
 -> T_Σ_14 -> T_IsSemiring_1640)
-> Any -> Any -> T_IsSemiring_1640
forall a b. a -> b
coe
      T_IsSemiringWithoutAnnihilatingZero_1536
-> T_Σ_14 -> T_IsSemiring_1640
MAlonzo.Code.Algebra.Structures.C_constructor_1740
      ((T_IsCommutativeMonoid_764
 -> (Any -> Any -> Any -> Any -> Any -> Any -> Any)
 -> (Any -> Any -> Any -> Any)
 -> T_Σ_14
 -> T_Σ_14
 -> T_IsSemiringWithoutAnnihilatingZero_1536)
-> Any -> Any -> Any -> Any -> Any -> Any
forall a b. a -> b
coe
         T_IsCommutativeMonoid_764
-> (Any -> Any -> Any -> Any -> Any -> Any -> Any)
-> (Any -> Any -> Any -> Any)
-> T_Σ_14
-> T_Σ_14
-> T_IsSemiringWithoutAnnihilatingZero_1536
MAlonzo.Code.Algebra.Structures.C_constructor_1630
         (T_IsCommutativeMonoid_764 -> Any
forall a b. a -> b
coe T_IsCommutativeMonoid_764
d_'8744''45'isCommutativeMonoid_3350) Any
forall a. a
erased Any
forall a. a
erased
         (T_Σ_14 -> Any
forall a b. a -> b
coe T_Σ_14
d_'8743''45'identity_3374)
         (T_Σ_14 -> Any
forall a b. a -> b
coe T_Σ_14
d_'8743''45'distrib'45''8744'_3422))
      (T_Σ_14 -> Any
forall a b. a -> b
coe T_Σ_14
d_'8743''45'zero_3380)
-- Data.Bool.Properties.∨-∧-isCommutativeSemiring
d_'8744''45''8743''45'isCommutativeSemiring_3486 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiring_1750
d_'8744''45''8743''45'isCommutativeSemiring_3486 :: T_IsCommutativeSemiring_1750
d_'8744''45''8743''45'isCommutativeSemiring_3486
  = (T_IsSemiring_1640
 -> (Any -> Any -> Any) -> T_IsCommutativeSemiring_1750)
-> Any -> Any -> T_IsCommutativeSemiring_1750
forall a b. a -> b
coe
      T_IsSemiring_1640
-> (Any -> Any -> Any) -> T_IsCommutativeSemiring_1750
MAlonzo.Code.Algebra.Structures.C_constructor_1862
      (T_IsSemiring_1640 -> Any
forall a b. a -> b
coe T_IsSemiring_1640
d_'8744''45''8743''45'isSemiring_3484) Any
forall a. a
erased
-- Data.Bool.Properties.∨-∧-commutativeSemiring
d_'8744''45''8743''45'commutativeSemiring_3488 ::
  MAlonzo.Code.Algebra.Bundles.T_CommutativeSemiring_2524
d_'8744''45''8743''45'commutativeSemiring_3488 :: T_CommutativeSemiring_2524
d_'8744''45''8743''45'commutativeSemiring_3488
  = ((Any -> Any -> Any)
 -> (Any -> Any -> Any)
 -> Any
 -> Any
 -> T_IsCommutativeSemiring_1750
 -> T_CommutativeSemiring_2524)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Any
-> Any
-> T_IsCommutativeSemiring_1750
-> T_CommutativeSemiring_2524
forall a b. a -> b
coe
      (Any -> Any -> Any)
-> (Any -> Any -> Any)
-> Any
-> Any
-> T_IsCommutativeSemiring_1750
-> T_CommutativeSemiring_2524
MAlonzo.Code.Algebra.Bundles.C_constructor_2706
      Bool -> Bool -> Bool
MAlonzo.Code.Data.Bool.Base.d__'8744'__30
      Bool -> Bool -> Bool
MAlonzo.Code.Data.Bool.Base.d__'8743'__24
      (Bool -> Any
forall a b. a -> b
coe Bool
MAlonzo.Code.Agda.Builtin.Bool.C_false_8)
      (Bool -> Any
forall a b. a -> b
coe Bool
MAlonzo.Code.Agda.Builtin.Bool.C_true_10)
      T_IsCommutativeSemiring_1750
d_'8744''45''8743''45'isCommutativeSemiring_3486
-- Data.Bool.Properties.∧-∨-isSemiring
d_'8743''45''8744''45'isSemiring_3490 ::
  MAlonzo.Code.Algebra.Structures.T_IsSemiring_1640
d_'8743''45''8744''45'isSemiring_3490 :: T_IsSemiring_1640
d_'8743''45''8744''45'isSemiring_3490
  = (T_IsSemiringWithoutAnnihilatingZero_1536
 -> T_Σ_14 -> T_IsSemiring_1640)
-> Any -> Any -> T_IsSemiring_1640
forall a b. a -> b
coe
      T_IsSemiringWithoutAnnihilatingZero_1536
-> T_Σ_14 -> T_IsSemiring_1640
MAlonzo.Code.Algebra.Structures.C_constructor_1740
      ((T_IsCommutativeMonoid_764
 -> (Any -> Any -> Any -> Any -> Any -> Any -> Any)
 -> (Any -> Any -> Any -> Any)
 -> T_Σ_14
 -> T_Σ_14
 -> T_IsSemiringWithoutAnnihilatingZero_1536)
-> Any -> Any -> Any -> Any -> Any -> Any
forall a b. a -> b
coe
         T_IsCommutativeMonoid_764
-> (Any -> Any -> Any -> Any -> Any -> Any -> Any)
-> (Any -> Any -> Any -> Any)
-> T_Σ_14
-> T_Σ_14
-> T_IsSemiringWithoutAnnihilatingZero_1536
MAlonzo.Code.Algebra.Structures.C_constructor_1630
         (T_IsCommutativeMonoid_764 -> Any
forall a b. a -> b
coe T_IsCommutativeMonoid_764
d_'8743''45'isCommutativeMonoid_3476) Any
forall a. a
erased Any
forall a. a
erased
         (T_Σ_14 -> Any
forall a b. a -> b
coe T_Σ_14
d_'8744''45'identity_3302)
         (T_Σ_14 -> Any
forall a b. a -> b
coe T_Σ_14
d_'8744''45'distrib'45''8743'_3442))
      (T_Σ_14 -> Any
forall a b. a -> b
coe T_Σ_14
d_'8744''45'zero_3308)
-- Data.Bool.Properties.∧-∨-isCommutativeSemiring
d_'8743''45''8744''45'isCommutativeSemiring_3492 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiring_1750
d_'8743''45''8744''45'isCommutativeSemiring_3492 :: T_IsCommutativeSemiring_1750
d_'8743''45''8744''45'isCommutativeSemiring_3492
  = (T_IsSemiring_1640
 -> (Any -> Any -> Any) -> T_IsCommutativeSemiring_1750)
-> Any -> Any -> T_IsCommutativeSemiring_1750
forall a b. a -> b
coe
      T_IsSemiring_1640
-> (Any -> Any -> Any) -> T_IsCommutativeSemiring_1750
MAlonzo.Code.Algebra.Structures.C_constructor_1862
      (T_IsSemiring_1640 -> Any
forall a b. a -> b
coe T_IsSemiring_1640
d_'8743''45''8744''45'isSemiring_3490) Any
forall a. a
erased
-- Data.Bool.Properties.∧-∨-commutativeSemiring
d_'8743''45''8744''45'commutativeSemiring_3494 ::
  MAlonzo.Code.Algebra.Bundles.T_CommutativeSemiring_2524
d_'8743''45''8744''45'commutativeSemiring_3494 :: T_CommutativeSemiring_2524
d_'8743''45''8744''45'commutativeSemiring_3494
  = ((Any -> Any -> Any)
 -> (Any -> Any -> Any)
 -> Any
 -> Any
 -> T_IsCommutativeSemiring_1750
 -> T_CommutativeSemiring_2524)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Any
-> Any
-> T_IsCommutativeSemiring_1750
-> T_CommutativeSemiring_2524
forall a b. a -> b
coe
      (Any -> Any -> Any)
-> (Any -> Any -> Any)
-> Any
-> Any
-> T_IsCommutativeSemiring_1750
-> T_CommutativeSemiring_2524
MAlonzo.Code.Algebra.Bundles.C_constructor_2706
      Bool -> Bool -> Bool
MAlonzo.Code.Data.Bool.Base.d__'8743'__24
      Bool -> Bool -> Bool
MAlonzo.Code.Data.Bool.Base.d__'8744'__30
      (Bool -> Any
forall a b. a -> b
coe Bool
MAlonzo.Code.Agda.Builtin.Bool.C_true_10)
      (Bool -> Any
forall a b. a -> b
coe Bool
MAlonzo.Code.Agda.Builtin.Bool.C_false_8)
      T_IsCommutativeSemiring_1750
d_'8743''45''8744''45'isCommutativeSemiring_3492
-- Data.Bool.Properties.∨-∧-isLattice
d_'8744''45''8743''45'isLattice_3496 ::
  MAlonzo.Code.Algebra.Lattice.Structures.T_IsLattice_3070
d_'8744''45''8743''45'isLattice_3496 :: T_IsLattice_3070
d_'8744''45''8743''45'isLattice_3496
  = (T_IsEquivalence_28
 -> (Any -> Any -> Any)
 -> (Any -> Any -> Any -> Any)
 -> (Any -> Any -> Any -> Any -> Any -> Any -> Any)
 -> (Any -> Any -> Any)
 -> (Any -> Any -> Any -> Any)
 -> (Any -> Any -> Any -> Any -> Any -> Any -> Any)
 -> T_Σ_14
 -> T_IsLattice_3070)
-> Any
-> Any
-> Any
-> Any
-> Any
-> Any
-> Any
-> Any
-> T_IsLattice_3070
forall a b. a -> b
coe
      T_IsEquivalence_28
-> (Any -> Any -> Any)
-> (Any -> Any -> Any -> Any)
-> (Any -> Any -> Any -> Any -> Any -> Any -> Any)
-> (Any -> Any -> Any)
-> (Any -> Any -> Any -> Any)
-> (Any -> Any -> Any -> Any -> Any -> Any -> Any)
-> T_Σ_14
-> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.C_constructor_3140
      (T_IsEquivalence_28 -> Any
forall a b. a -> b
coe
         T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.PropositionalEquality.Properties.du_isEquivalence_396)
      Any
forall a. a
erased Any
forall a. a
erased Any
forall a. a
erased Any
forall a. a
erased Any
forall a. a
erased Any
forall a. a
erased
      (T_Σ_14 -> Any
forall a b. a -> b
coe T_Σ_14
d_'8744''45''8743''45'absorptive_3456)
-- Data.Bool.Properties.∨-∧-lattice
d_'8744''45''8743''45'lattice_3498 ::
  MAlonzo.Code.Algebra.Lattice.Bundles.T_Lattice_512
d_'8744''45''8743''45'lattice_3498 :: T_Lattice_512
d_'8744''45''8743''45'lattice_3498
  = ((Any -> Any -> Any)
 -> (Any -> Any -> Any) -> T_IsLattice_3070 -> T_Lattice_512)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> T_IsLattice_3070
-> T_Lattice_512
forall a b. a -> b
coe
      (Any -> Any -> Any)
-> (Any -> Any -> Any) -> T_IsLattice_3070 -> T_Lattice_512
MAlonzo.Code.Algebra.Lattice.Bundles.C_constructor_592
      Bool -> Bool -> Bool
MAlonzo.Code.Data.Bool.Base.d__'8744'__30
      Bool -> Bool -> Bool
MAlonzo.Code.Data.Bool.Base.d__'8743'__24
      T_IsLattice_3070
d_'8744''45''8743''45'isLattice_3496
-- Data.Bool.Properties.∨-∧-isDistributiveLattice
d_'8744''45''8743''45'isDistributiveLattice_3500 ::
  MAlonzo.Code.Algebra.Lattice.Structures.T_IsDistributiveLattice_3146
d_'8744''45''8743''45'isDistributiveLattice_3500 :: T_IsDistributiveLattice_3146
d_'8744''45''8743''45'isDistributiveLattice_3500
  = (T_IsLattice_3070
 -> T_Σ_14 -> T_Σ_14 -> T_IsDistributiveLattice_3146)
-> Any -> Any -> Any -> T_IsDistributiveLattice_3146
forall a b. a -> b
coe
      T_IsLattice_3070
-> T_Σ_14 -> T_Σ_14 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.C_constructor_3212
      (T_IsLattice_3070 -> Any
forall a b. a -> b
coe T_IsLattice_3070
d_'8744''45''8743''45'isLattice_3496)
      (T_Σ_14 -> Any
forall a b. a -> b
coe T_Σ_14
d_'8744''45'distrib'45''8743'_3442)
      (T_Σ_14 -> Any
forall a b. a -> b
coe T_Σ_14
d_'8743''45'distrib'45''8744'_3422)
-- Data.Bool.Properties.∨-∧-distributiveLattice
d_'8744''45''8743''45'distributiveLattice_3502 ::
  MAlonzo.Code.Algebra.Lattice.Bundles.T_DistributiveLattice_598
d_'8744''45''8743''45'distributiveLattice_3502 :: T_DistributiveLattice_598
d_'8744''45''8743''45'distributiveLattice_3502
  = ((Any -> Any -> Any)
 -> (Any -> Any -> Any)
 -> T_IsDistributiveLattice_3146
 -> T_DistributiveLattice_598)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> T_IsDistributiveLattice_3146
-> T_DistributiveLattice_598
forall a b. a -> b
coe
      (Any -> Any -> Any)
-> (Any -> Any -> Any)
-> T_IsDistributiveLattice_3146
-> T_DistributiveLattice_598
MAlonzo.Code.Algebra.Lattice.Bundles.C_constructor_692
      Bool -> Bool -> Bool
MAlonzo.Code.Data.Bool.Base.d__'8744'__30
      Bool -> Bool -> Bool
MAlonzo.Code.Data.Bool.Base.d__'8743'__24
      T_IsDistributiveLattice_3146
d_'8744''45''8743''45'isDistributiveLattice_3500
-- Data.Bool.Properties.∨-∧-isBooleanAlgebra
d_'8744''45''8743''45'isBooleanAlgebra_3504 ::
  MAlonzo.Code.Algebra.Lattice.Structures.T_IsBooleanAlgebra_3224
d_'8744''45''8743''45'isBooleanAlgebra_3504 :: T_IsBooleanAlgebra_3224
d_'8744''45''8743''45'isBooleanAlgebra_3504
  = (T_IsDistributiveLattice_3146
 -> T_Σ_14
 -> T_Σ_14
 -> (Any -> Any -> Any -> Any)
 -> T_IsBooleanAlgebra_3224)
-> Any -> Any -> Any -> Any -> T_IsBooleanAlgebra_3224
forall a b. a -> b
coe
      T_IsDistributiveLattice_3146
-> T_Σ_14
-> T_Σ_14
-> (Any -> Any -> Any -> Any)
-> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Structures.C_constructor_3314
      (T_IsDistributiveLattice_3146 -> Any
forall a b. a -> b
coe T_IsDistributiveLattice_3146
d_'8744''45''8743''45'isDistributiveLattice_3500)
      (T_Σ_14 -> Any
forall a b. a -> b
coe T_Σ_14
d_'8744''45'inverse_3316) (T_Σ_14 -> Any
forall a b. a -> b
coe T_Σ_14
d_'8743''45'inverse_3388)
      Any
forall a. a
erased
-- Data.Bool.Properties.∨-∧-booleanAlgebra
d_'8744''45''8743''45'booleanAlgebra_3506 ::
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698
d_'8744''45''8743''45'booleanAlgebra_3506 :: T_BooleanAlgebra_698
d_'8744''45''8743''45'booleanAlgebra_3506
  = ((Any -> Any -> Any)
 -> (Any -> Any -> Any)
 -> (Any -> Any)
 -> Any
 -> Any
 -> T_IsBooleanAlgebra_3224
 -> T_BooleanAlgebra_698)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Any
-> Any
-> T_IsBooleanAlgebra_3224
-> T_BooleanAlgebra_698
forall a b. a -> b
coe
      (Any -> Any -> Any)
-> (Any -> Any -> Any)
-> (Any -> Any)
-> Any
-> Any
-> T_IsBooleanAlgebra_3224
-> T_BooleanAlgebra_698
MAlonzo.Code.Algebra.Lattice.Bundles.C_constructor_822
      Bool -> Bool -> Bool
MAlonzo.Code.Data.Bool.Base.d__'8744'__30
      Bool -> Bool -> Bool
MAlonzo.Code.Data.Bool.Base.d__'8743'__24
      Bool -> Bool
MAlonzo.Code.Data.Bool.Base.d_not_22
      (Bool -> Any
forall a b. a -> b
coe Bool
MAlonzo.Code.Agda.Builtin.Bool.C_true_10)
      (Bool -> Any
forall a b. a -> b
coe Bool
MAlonzo.Code.Agda.Builtin.Bool.C_false_8)
      T_IsBooleanAlgebra_3224
d_'8744''45''8743''45'isBooleanAlgebra_3504
-- Data.Bool.Properties.not-involutive
d_not'45'involutive_3508 ::
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_not'45'involutive_3508 :: Bool -> T__'8801'__12
d_not'45'involutive_3508 = Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties.not-injective
d_not'45'injective_3514 ::
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_not'45'injective_3514 :: Bool -> Bool -> T__'8801'__12 -> T__'8801'__12
d_not'45'injective_3514 = Bool -> Bool -> T__'8801'__12 -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties.not-¬
d_not'45''172'_3524 ::
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Data.Irrelevant.T_Irrelevant_20
d_not'45''172'_3524 :: Bool -> Bool -> T__'8801'__12 -> T__'8801'__12 -> T_Irrelevant_20
d_not'45''172'_3524 = Bool -> Bool -> T__'8801'__12 -> T__'8801'__12 -> T_Irrelevant_20
forall a. a
erased
-- Data.Bool.Properties.¬-not
d_'172''45'not_3530 ::
  Bool ->
  Bool ->
  (MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
   MAlonzo.Code.Data.Irrelevant.T_Irrelevant_20) ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'172''45'not_3530 :: Bool -> Bool -> (T__'8801'__12 -> T_Irrelevant_20) -> T__'8801'__12
d_'172''45'not_3530 = Bool -> Bool -> (T__'8801'__12 -> T_Irrelevant_20) -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties.xor-is-ok
d_xor'45'is'45'ok_3540 ::
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_xor'45'is'45'ok_3540 :: Bool -> Bool -> T__'8801'__12
d_xor'45'is'45'ok_3540 = Bool -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties.true-xor
d_true'45'xor_3548 ::
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_true'45'xor_3548 :: Bool -> T__'8801'__12
d_true'45'xor_3548 = Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties.xor-same
d_xor'45'same_3552 ::
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_xor'45'same_3552 :: Bool -> T__'8801'__12
d_xor'45'same_3552 = Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties.not-distribˡ-xor
d_not'45'distrib'737''45'xor_3558 ::
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_not'45'distrib'737''45'xor_3558 :: Bool -> Bool -> T__'8801'__12
d_not'45'distrib'737''45'xor_3558 = Bool -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties.not-distribʳ-xor
d_not'45'distrib'691''45'xor_3568 ::
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_not'45'distrib'691''45'xor_3568 :: Bool -> Bool -> T__'8801'__12
d_not'45'distrib'691''45'xor_3568 = Bool -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties.xor-assoc
d_xor'45'assoc_3574 ::
  Bool ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_xor'45'assoc_3574 :: Bool -> Bool -> Bool -> T__'8801'__12
d_xor'45'assoc_3574 = Bool -> Bool -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties.xor-comm
d_xor'45'comm_3584 ::
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_xor'45'comm_3584 :: Bool -> Bool -> T__'8801'__12
d_xor'45'comm_3584 = Bool -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties.xor-identityˡ
d_xor'45'identity'737'_3586 ::
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_xor'45'identity'737'_3586 :: Bool -> T__'8801'__12
d_xor'45'identity'737'_3586 = Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties.xor-identityʳ
d_xor'45'identity'691'_3588 ::
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_xor'45'identity'691'_3588 :: Bool -> T__'8801'__12
d_xor'45'identity'691'_3588 = Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties.xor-identity
d_xor'45'identity_3590 :: MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_xor'45'identity_3590 :: T_Σ_14
d_xor'45'identity_3590
  = (Any -> Any -> T_Σ_14) -> Any -> Any -> T_Σ_14
forall a b. a -> b
coe Any -> Any -> T_Σ_14
MAlonzo.Code.Agda.Builtin.Sigma.C__'44'__32 Any
forall a. a
erased Any
forall a. a
erased
-- Data.Bool.Properties.xor-inverseˡ
d_xor'45'inverse'737'_3592 ::
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_xor'45'inverse'737'_3592 :: Bool -> T__'8801'__12
d_xor'45'inverse'737'_3592 = Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties.xor-inverseʳ
d_xor'45'inverse'691'_3594 ::
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_xor'45'inverse'691'_3594 :: Bool -> T__'8801'__12
d_xor'45'inverse'691'_3594 = Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties.xor-inverse
d_xor'45'inverse_3598 :: MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_xor'45'inverse_3598 :: T_Σ_14
d_xor'45'inverse_3598
  = (Any -> Any -> T_Σ_14) -> Any -> Any -> T_Σ_14
forall a b. a -> b
coe Any -> Any -> T_Σ_14
MAlonzo.Code.Agda.Builtin.Sigma.C__'44'__32 Any
forall a. a
erased Any
forall a. a
erased
-- Data.Bool.Properties.∧-distribˡ-xor
d_'8743''45'distrib'737''45'xor_3600 ::
  Bool ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8743''45'distrib'737''45'xor_3600 :: Bool -> Bool -> Bool -> T__'8801'__12
d_'8743''45'distrib'737''45'xor_3600 = Bool -> Bool -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties.∧-distribʳ-xor
d_'8743''45'distrib'691''45'xor_3610 ::
  Bool ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8743''45'distrib'691''45'xor_3610 :: Bool -> Bool -> Bool -> T__'8801'__12
d_'8743''45'distrib'691''45'xor_3610 = Bool -> Bool -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties.∧-distrib-xor
d_'8743''45'distrib'45'xor_3620 ::
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'8743''45'distrib'45'xor_3620 :: T_Σ_14
d_'8743''45'distrib'45'xor_3620
  = (Any -> Any -> T_Σ_14) -> Any -> Any -> T_Σ_14
forall a b. a -> b
coe Any -> Any -> T_Σ_14
MAlonzo.Code.Agda.Builtin.Sigma.C__'44'__32 Any
forall a. a
erased Any
forall a. a
erased
-- Data.Bool.Properties.xor-annihilates-not
d_xor'45'annihilates'45'not_3626 ::
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_xor'45'annihilates'45'not_3626 :: Bool -> Bool -> T__'8801'__12
d_xor'45'annihilates'45'not_3626 = Bool -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties.xor-∧-commutativeRing
d_xor'45''8743''45'commutativeRing_3632 ::
  MAlonzo.Code.Algebra.Bundles.T_CommutativeRing_4126
d_xor'45''8743''45'commutativeRing_3632 :: T_CommutativeRing_4126
d_xor'45''8743''45'commutativeRing_3632
  = (T_BooleanAlgebra_698
 -> (Any -> Any -> Any)
 -> (Any -> Any -> Any)
 -> T_CommutativeRing_4126)
-> Any -> Any -> Any -> T_CommutativeRing_4126
forall a b. a -> b
coe
      T_BooleanAlgebra_698
-> (Any -> Any -> Any)
-> (Any -> Any -> Any)
-> T_CommutativeRing_4126
MAlonzo.Code.Algebra.Lattice.Properties.BooleanAlgebra.du_'8853''45''8743''45'commutativeRing_3826
      (T_BooleanAlgebra_698 -> Any
forall a b. a -> b
coe T_BooleanAlgebra_698
d_'8744''45''8743''45'booleanAlgebra_3506)
      ((Bool -> Bool -> Bool) -> Any
forall a b. a -> b
coe Bool -> Bool -> Bool
MAlonzo.Code.Data.Bool.Base.d__xor__36) Any
forall a. a
erased
-- Data.Bool.Properties.if-float
d_if'45'float_3910 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny) ->
  Bool ->
  AgdaAny ->
  AgdaAny -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_if'45'float_3910 :: ()
-> ()
-> ()
-> ()
-> (Any -> Any)
-> Bool
-> Any
-> Any
-> T__'8801'__12
d_if'45'float_3910 = ()
-> ()
-> ()
-> ()
-> (Any -> Any)
-> Bool
-> Any
-> Any
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties.if-eta
d_if'45'eta_3916 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  Bool -> AgdaAny -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_if'45'eta_3916 :: () -> () -> Bool -> Any -> T__'8801'__12
d_if'45'eta_3916 = () -> () -> Bool -> Any -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties.if-idem-then
d_if'45'idem'45'then_3924 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  Bool ->
  AgdaAny ->
  AgdaAny -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_if'45'idem'45'then_3924 :: () -> () -> Bool -> Any -> Any -> T__'8801'__12
d_if'45'idem'45'then_3924 = () -> () -> Bool -> Any -> Any -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties.if-idem-else
d_if'45'idem'45'else_3932 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  Bool ->
  AgdaAny ->
  AgdaAny -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_if'45'idem'45'else_3932 :: () -> () -> Bool -> Any -> Any -> T__'8801'__12
d_if'45'idem'45'else_3932 = () -> () -> Bool -> Any -> Any -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties.if-swap-then
d_if'45'swap'45'then_3942 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  Bool ->
  Bool ->
  AgdaAny ->
  AgdaAny -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_if'45'swap'45'then_3942 :: () -> () -> Bool -> Bool -> Any -> Any -> T__'8801'__12
d_if'45'swap'45'then_3942 = () -> () -> Bool -> Bool -> Any -> Any -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties.if-swap-else
d_if'45'swap'45'else_3952 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  Bool ->
  Bool ->
  AgdaAny ->
  AgdaAny -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_if'45'swap'45'else_3952 :: () -> () -> Bool -> Bool -> Any -> Any -> T__'8801'__12
d_if'45'swap'45'else_3952 = () -> () -> Bool -> Bool -> Any -> Any -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties.if-not
d_if'45'not_3960 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  Bool ->
  AgdaAny ->
  AgdaAny -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_if'45'not_3960 :: () -> () -> Bool -> Any -> Any -> T__'8801'__12
d_if'45'not_3960 = () -> () -> Bool -> Any -> Any -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties.if-∧
d_if'45''8743'_3970 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  Bool ->
  Bool ->
  AgdaAny ->
  AgdaAny -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_if'45''8743'_3970 :: () -> () -> Bool -> Bool -> Any -> Any -> T__'8801'__12
d_if'45''8743'_3970 = () -> () -> Bool -> Bool -> Any -> Any -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties.if-∨
d_if'45''8744'_3980 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  Bool ->
  Bool ->
  AgdaAny ->
  AgdaAny -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_if'45''8744'_3980 :: () -> () -> Bool -> Bool -> Any -> Any -> T__'8801'__12
d_if'45''8744'_3980 = () -> () -> Bool -> Bool -> Any -> Any -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties.if-xor
d_if'45'xor_3990 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  Bool ->
  Bool ->
  AgdaAny ->
  AgdaAny -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_if'45'xor_3990 :: () -> () -> Bool -> Bool -> Any -> Any -> T__'8801'__12
d_if'45'xor_3990 = () -> () -> Bool -> Bool -> Any -> Any -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties.if-cong
d_if'45'cong_4000 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  Bool ->
  Bool ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_if'45'cong_4000 :: ()
-> ()
-> Bool
-> Bool
-> Any
-> Any
-> T__'8801'__12
-> T__'8801'__12
d_if'45'cong_4000 = ()
-> ()
-> Bool
-> Bool
-> Any
-> Any
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties.if-cong-then
d_if'45'cong'45'then_4010 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  Bool ->
  AgdaAny ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_if'45'cong'45'then_4010 :: ()
-> ()
-> Bool
-> Any
-> Any
-> Any
-> T__'8801'__12
-> T__'8801'__12
d_if'45'cong'45'then_4010 = ()
-> ()
-> Bool
-> Any
-> Any
-> Any
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties.if-cong-else
d_if'45'cong'45'else_4020 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  Bool ->
  AgdaAny ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_if'45'cong'45'else_4020 :: ()
-> ()
-> Bool
-> Any
-> Any
-> Any
-> T__'8801'__12
-> T__'8801'__12
d_if'45'cong'45'else_4020 = ()
-> ()
-> Bool
-> Any
-> Any
-> Any
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties.if-cong₂
d_if'45'cong'8322'_4032 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  Bool ->
  AgdaAny ->
  AgdaAny ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_if'45'cong'8322'_4032 :: ()
-> ()
-> Bool
-> Any
-> Any
-> Any
-> Any
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
d_if'45'cong'8322'_4032 = ()
-> ()
-> Bool
-> Any
-> Any
-> Any
-> Any
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties.T-≡
d_T'45''8801'_4036 ::
  Bool -> MAlonzo.Code.Function.Bundles.T_Equivalence_1858
d_T'45''8801'_4036 :: Bool -> T_Equivalence_1858
d_T'45''8801'_4036 Bool
v0
  = if Bool -> Bool
forall a b. a -> b
coe Bool
v0
      then ((Any -> Any) -> (Any -> Any) -> T_Equivalence_1858)
-> Any -> Any -> T_Equivalence_1858
forall a b. a -> b
coe
             (Any -> Any) -> (Any -> Any) -> T_Equivalence_1858
MAlonzo.Code.Function.Bundles.du_mk'8660'_2474 Any
forall a. a
erased
             (let v1 :: b
v1 = () -> b
forall a b. a -> b
coe ()
MAlonzo.Code.Agda.Builtin.Unit.C_tt_8 in
              Any -> Any
forall a b. a -> b
coe ((Any -> Any) -> Any
forall a b. a -> b
coe (\ Any
v2 -> Any
forall a. a
v1)))
      else ((Any -> Any) -> (Any -> Any) -> T_Equivalence_1858)
-> Any -> Any -> T_Equivalence_1858
forall a b. a -> b
coe
             (Any -> Any) -> (Any -> Any) -> T_Equivalence_1858
MAlonzo.Code.Function.Bundles.du_mk'8660'_2474 Any
forall a. a
erased Any
forall a. a
erased
-- Data.Bool.Properties.T-not-≡
d_T'45'not'45''8801'_4040 ::
  Bool -> MAlonzo.Code.Function.Bundles.T_Equivalence_1858
d_T'45'not'45''8801'_4040 :: Bool -> T_Equivalence_1858
d_T'45'not'45''8801'_4040 Bool
v0
  = if Bool -> Bool
forall a b. a -> b
coe Bool
v0
      then ((Any -> Any) -> (Any -> Any) -> T_Equivalence_1858)
-> Any -> Any -> T_Equivalence_1858
forall a b. a -> b
coe
             (Any -> Any) -> (Any -> Any) -> T_Equivalence_1858
MAlonzo.Code.Function.Bundles.du_mk'8660'_2474 Any
forall a. a
erased Any
forall a. a
erased
      else ((Any -> Any) -> (Any -> Any) -> T_Equivalence_1858)
-> Any -> Any -> T_Equivalence_1858
forall a b. a -> b
coe
             (Any -> Any) -> (Any -> Any) -> T_Equivalence_1858
MAlonzo.Code.Function.Bundles.du_mk'8660'_2474 Any
forall a. a
erased
             (let v1 :: b
v1 = () -> b
forall a b. a -> b
coe ()
MAlonzo.Code.Agda.Builtin.Unit.C_tt_8 in
              Any -> Any
forall a b. a -> b
coe ((Any -> Any) -> Any
forall a b. a -> b
coe (\ Any
v2 -> Any
forall a. a
v1)))
-- Data.Bool.Properties.T-∧
d_T'45''8743'_4046 ::
  Bool -> Bool -> MAlonzo.Code.Function.Bundles.T_Equivalence_1858
d_T'45''8743'_4046 :: Bool -> Bool -> T_Equivalence_1858
d_T'45''8743'_4046 Bool
v0 Bool
v1
  = if Bool -> Bool
forall a b. a -> b
coe Bool
v0
      then if Bool -> Bool
forall a b. a -> b
coe Bool
v1
             then ((Any -> Any) -> (Any -> Any) -> T_Equivalence_1858)
-> Any -> Any -> T_Equivalence_1858
forall a b. a -> b
coe
                    (Any -> Any) -> (Any -> Any) -> T_Equivalence_1858
MAlonzo.Code.Function.Bundles.du_mk'8660'_2474
                    (let v2 :: t
v2
                           = (Any -> Any -> T_Σ_14) -> Any -> Any -> t
forall a b. a -> b
coe
                               Any -> Any -> T_Σ_14
MAlonzo.Code.Agda.Builtin.Sigma.C__'44'__32
                               (() -> Any
forall a b. a -> b
coe ()
MAlonzo.Code.Agda.Builtin.Unit.C_tt_8)
                               (() -> Any
forall a b. a -> b
coe ()
MAlonzo.Code.Agda.Builtin.Unit.C_tt_8) in
                     Any -> Any
forall a b. a -> b
coe ((Any -> Any) -> Any
forall a b. a -> b
coe (\ Any
v3 -> Any
forall a. a
v2)))
                    (let v2 :: b
v2 = () -> b
forall a b. a -> b
coe ()
MAlonzo.Code.Agda.Builtin.Unit.C_tt_8 in
                     Any -> Any
forall a b. a -> b
coe ((Any -> Any) -> Any
forall a b. a -> b
coe (\ Any
v3 -> Any
forall a. a
v2)))
             else ((Any -> Any) -> (Any -> Any) -> T_Equivalence_1858)
-> Any -> Any -> T_Equivalence_1858
forall a b. a -> b
coe
                    (Any -> Any) -> (Any -> Any) -> T_Equivalence_1858
MAlonzo.Code.Function.Bundles.du_mk'8660'_2474 Any
forall a. a
erased
                    ((Any -> Any) -> Any
forall a b. a -> b
coe (\ Any
v2 -> T_Σ_14 -> Any
MAlonzo.Code.Agda.Builtin.Sigma.d_snd_30 (Any -> T_Σ_14
forall a b. a -> b
coe Any
v2)))
      else ((Any -> Any) -> (Any -> Any) -> T_Equivalence_1858)
-> Any -> Any -> T_Equivalence_1858
forall a b. a -> b
coe
             (Any -> Any) -> (Any -> Any) -> T_Equivalence_1858
MAlonzo.Code.Function.Bundles.du_mk'8660'_2474 Any
forall a. a
erased
             ((Any -> Any) -> Any
forall a b. a -> b
coe (\ Any
v2 -> T_Σ_14 -> Any
MAlonzo.Code.Agda.Builtin.Sigma.d_fst_28 (Any -> T_Σ_14
forall a b. a -> b
coe Any
v2)))
-- Data.Bool.Properties.T-∨
d_T'45''8744'_4052 ::
  Bool -> Bool -> MAlonzo.Code.Function.Bundles.T_Equivalence_1858
d_T'45''8744'_4052 :: Bool -> Bool -> T_Equivalence_1858
d_T'45''8744'_4052 Bool
v0 Bool
v1
  = if Bool -> Bool
forall a b. a -> b
coe Bool
v0
      then ((Any -> Any) -> (Any -> Any) -> T_Equivalence_1858)
-> Any -> Any -> T_Equivalence_1858
forall a b. a -> b
coe
             (Any -> Any) -> (Any -> Any) -> T_Equivalence_1858
MAlonzo.Code.Function.Bundles.du_mk'8660'_2474
             ((Any -> T__'8846'__30) -> Any
forall a b. a -> b
coe Any -> T__'8846'__30
MAlonzo.Code.Data.Sum.Base.C_inj'8321'_38)
             (let v2 :: b
v2 = () -> b
forall a b. a -> b
coe ()
MAlonzo.Code.Agda.Builtin.Unit.C_tt_8 in
              Any -> Any
forall a b. a -> b
coe ((Any -> Any) -> Any
forall a b. a -> b
coe (\ Any
v3 -> Any
forall a. a
v2)))
      else (if Bool -> Bool
forall a b. a -> b
coe Bool
v1
              then ((Any -> Any) -> (Any -> Any) -> T_Equivalence_1858)
-> Any -> Any -> T_Equivalence_1858
forall a b. a -> b
coe
                     (Any -> Any) -> (Any -> Any) -> T_Equivalence_1858
MAlonzo.Code.Function.Bundles.du_mk'8660'_2474
                     ((Any -> T__'8846'__30) -> Any
forall a b. a -> b
coe Any -> T__'8846'__30
MAlonzo.Code.Data.Sum.Base.C_inj'8322'_42)
                     (let v2 :: b
v2 = () -> b
forall a b. a -> b
coe ()
MAlonzo.Code.Agda.Builtin.Unit.C_tt_8 in
                      Any -> Any
forall a b. a -> b
coe ((Any -> Any) -> Any
forall a b. a -> b
coe (\ Any
v3 -> Any
forall a. a
v2)))
              else ((Any -> Any) -> (Any -> Any) -> T_Equivalence_1858)
-> Any -> Any -> T_Equivalence_1858
forall a b. a -> b
coe
                     (Any -> Any) -> (Any -> Any) -> T_Equivalence_1858
MAlonzo.Code.Function.Bundles.du_mk'8660'_2474
                     ((Any -> T__'8846'__30) -> Any
forall a b. a -> b
coe Any -> T__'8846'__30
MAlonzo.Code.Data.Sum.Base.C_inj'8321'_38)
                     (((Any -> Any) -> (Any -> Any) -> T__'8846'__30 -> Any)
-> Any -> Any -> Any
forall a b. a -> b
coe
                        (Any -> Any) -> (Any -> Any) -> T__'8846'__30 -> Any
MAlonzo.Code.Data.Sum.Base.du_'91'_'44'_'93'_52 ((Any -> Any) -> Any
forall a b. a -> b
coe (\ Any
v2 -> Any
v2))
                        ((Any -> Any) -> Any
forall a b. a -> b
coe (\ Any
v2 -> Any
v2))))
-- Data.Bool.Properties.T-irrelevant
d_T'45'irrelevant_4054 ::
  Bool ->
  AgdaAny ->
  AgdaAny -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_T'45'irrelevant_4054 :: Bool -> Any -> Any -> T__'8801'__12
d_T'45'irrelevant_4054 = Bool -> Any -> Any -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties.T?-diag
d_T'63''45'diag_4058 :: Bool -> AgdaAny -> AgdaAny
d_T'63''45'diag_4058 :: Bool -> Any -> Any
d_T'63''45'diag_4058 Bool
v0
  = (T_Dec_20 -> Any -> Any) -> Any -> Any -> Any
forall a b. a -> b
coe
      T_Dec_20 -> Any -> Any
MAlonzo.Code.Relation.Nullary.Decidable.Core.du_fromWitness_150
      ((Bool -> T_Reflects_16 -> T_Dec_20) -> Any -> Any -> Any
forall a b. a -> b
coe
         Bool -> T_Reflects_16 -> T_Dec_20
MAlonzo.Code.Relation.Nullary.Decidable.Core.C__because__32
         (Bool -> Any
forall a b. a -> b
coe Bool
v0)
         ((Bool -> T_Reflects_16) -> Any -> Any
forall a b. a -> b
coe
            Bool -> T_Reflects_16
MAlonzo.Code.Relation.Nullary.Reflects.d_T'45'reflects_70
            (Bool -> Any
forall a b. a -> b
coe Bool
v0)))
-- Data.Bool.Properties.⇔→≡
d_'8660''8594''8801'_4068 ::
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Function.Bundles.T_Equivalence_1858 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8660''8594''8801'_4068 :: Bool -> Bool -> Bool -> T_Equivalence_1858 -> T__'8801'__12
d_'8660''8594''8801'_4068 = Bool -> Bool -> Bool -> T_Equivalence_1858 -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties.push-function-into-if
d_push'45'function'45'into'45'if_4082 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny) ->
  Bool ->
  AgdaAny ->
  AgdaAny -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_push'45'function'45'into'45'if_4082 :: ()
-> ()
-> ()
-> ()
-> (Any -> Any)
-> Bool
-> Any
-> Any
-> T__'8801'__12
d_push'45'function'45'into'45'if_4082 = ()
-> ()
-> ()
-> ()
-> (Any -> Any)
-> Bool
-> Any
-> Any
-> T__'8801'__12
forall a. a
erased