{-# 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.Properties.BooleanAlgebra
import qualified MAlonzo.Code.Algebra.Structures
import qualified MAlonzo.Code.Data.Bool.Base
import qualified MAlonzo.Code.Data.Empty
import qualified MAlonzo.Code.Data.Sum.Base
import qualified MAlonzo.Code.Function.Equivalence
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

-- 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._.Absorptive
d_Absorptive_18 ::
  (Bool -> Bool -> Bool) -> (Bool -> Bool -> Bool) -> ()
d_Absorptive_18 :: (Bool -> Bool -> Bool) -> (Bool -> Bool -> Bool) -> ()
d_Absorptive_18 = (Bool -> Bool -> Bool) -> (Bool -> Bool -> Bool) -> ()
forall a. a
erased
-- Data.Bool.Properties._.Associative
d_Associative_26 :: (Bool -> Bool -> Bool) -> ()
d_Associative_26 :: (Bool -> Bool -> Bool) -> ()
d_Associative_26 = (Bool -> Bool -> Bool) -> ()
forall a. a
erased
-- Data.Bool.Properties._.Commutative
d_Commutative_30 :: (Bool -> Bool -> Bool) -> ()
d_Commutative_30 :: (Bool -> Bool -> Bool) -> ()
d_Commutative_30 = (Bool -> Bool -> Bool) -> ()
forall a. a
erased
-- Data.Bool.Properties._.Idempotent
d_Idempotent_38 :: (Bool -> Bool -> Bool) -> ()
d_Idempotent_38 :: (Bool -> Bool -> Bool) -> ()
d_Idempotent_38 = (Bool -> Bool -> Bool) -> ()
forall a. a
erased
-- Data.Bool.Properties._.Identity
d_Identity_42 :: Bool -> (Bool -> Bool -> Bool) -> ()
d_Identity_42 :: Bool -> (Bool -> Bool -> Bool) -> ()
d_Identity_42 = Bool -> (Bool -> Bool -> Bool) -> ()
forall a. a
erased
-- Data.Bool.Properties._.Inverse
d_Inverse_46 ::
  Bool -> (Bool -> Bool) -> (Bool -> Bool -> Bool) -> ()
d_Inverse_46 :: Bool -> (Bool -> Bool) -> (Bool -> Bool -> Bool) -> ()
d_Inverse_46 = Bool -> (Bool -> Bool) -> (Bool -> Bool -> Bool) -> ()
forall a. a
erased
-- Data.Bool.Properties._.Involutive
d_Involutive_48 :: (Bool -> Bool) -> ()
d_Involutive_48 :: (Bool -> Bool) -> ()
d_Involutive_48 = (Bool -> Bool) -> ()
forall a. a
erased
-- Data.Bool.Properties._.LeftIdentity
d_LeftIdentity_56 :: Bool -> (Bool -> Bool -> Bool) -> ()
d_LeftIdentity_56 :: Bool -> (Bool -> Bool -> Bool) -> ()
d_LeftIdentity_56 = Bool -> (Bool -> Bool -> Bool) -> ()
forall a. a
erased
-- Data.Bool.Properties._.LeftInverse
d_LeftInverse_58 ::
  Bool -> (Bool -> Bool) -> (Bool -> Bool -> Bool) -> ()
d_LeftInverse_58 :: Bool -> (Bool -> Bool) -> (Bool -> Bool -> Bool) -> ()
d_LeftInverse_58 = Bool -> (Bool -> Bool) -> (Bool -> Bool -> Bool) -> ()
forall a. a
erased
-- Data.Bool.Properties._.LeftZero
d_LeftZero_60 :: Bool -> (Bool -> Bool -> Bool) -> ()
d_LeftZero_60 :: Bool -> (Bool -> Bool -> Bool) -> ()
d_LeftZero_60 = Bool -> (Bool -> Bool -> Bool) -> ()
forall a. a
erased
-- Data.Bool.Properties._.RightIdentity
d_RightIdentity_68 :: Bool -> (Bool -> Bool -> Bool) -> ()
d_RightIdentity_68 :: Bool -> (Bool -> Bool -> Bool) -> ()
d_RightIdentity_68 = Bool -> (Bool -> Bool -> Bool) -> ()
forall a. a
erased
-- Data.Bool.Properties._.RightInverse
d_RightInverse_70 ::
  Bool -> (Bool -> Bool) -> (Bool -> Bool -> Bool) -> ()
d_RightInverse_70 :: Bool -> (Bool -> Bool) -> (Bool -> Bool -> Bool) -> ()
d_RightInverse_70 = Bool -> (Bool -> Bool) -> (Bool -> Bool -> Bool) -> ()
forall a. a
erased
-- Data.Bool.Properties._.RightZero
d_RightZero_72 :: Bool -> (Bool -> Bool -> Bool) -> ()
d_RightZero_72 :: Bool -> (Bool -> Bool -> Bool) -> ()
d_RightZero_72 = Bool -> (Bool -> Bool -> Bool) -> ()
forall a. a
erased
-- Data.Bool.Properties._.Selective
d_Selective_74 :: (Bool -> Bool -> Bool) -> ()
d_Selective_74 :: (Bool -> Bool -> Bool) -> ()
d_Selective_74 = (Bool -> Bool -> Bool) -> ()
forall a. a
erased
-- Data.Bool.Properties._.Zero
d_Zero_76 :: Bool -> (Bool -> Bool -> Bool) -> ()
d_Zero_76 :: Bool -> (Bool -> Bool -> Bool) -> ()
d_Zero_76 = Bool -> (Bool -> Bool -> Bool) -> ()
forall a. a
erased
-- Data.Bool.Properties._.IsAbelianGroup
d_IsAbelianGroup_80 :: p -> p -> p -> ()
d_IsAbelianGroup_80 p
a0 p
a1 p
a2 = ()
-- Data.Bool.Properties._.IsBand
d_IsBand_82 :: p -> ()
d_IsBand_82 p
a0 = ()
-- Data.Bool.Properties._.IsBooleanAlgebra
d_IsBooleanAlgebra_84 :: p -> p -> p -> p -> p -> ()
d_IsBooleanAlgebra_84 p
a0 p
a1 p
a2 p
a3 p
a4 = ()
-- Data.Bool.Properties._.IsCancellativeCommutativeSemiring
d_IsCancellativeCommutativeSemiring_88 :: p -> p -> p -> p -> ()
d_IsCancellativeCommutativeSemiring_88 p
a0 p
a1 p
a2 p
a3 = ()
-- Data.Bool.Properties._.IsCommutativeMagma
d_IsCommutativeMagma_90 :: p -> ()
d_IsCommutativeMagma_90 p
a0 = ()
-- Data.Bool.Properties._.IsCommutativeMonoid
d_IsCommutativeMonoid_92 :: p -> p -> ()
d_IsCommutativeMonoid_92 p
a0 p
a1 = ()
-- Data.Bool.Properties._.IsCommutativeRing
d_IsCommutativeRing_94 :: p -> p -> p -> p -> p -> ()
d_IsCommutativeRing_94 p
a0 p
a1 p
a2 p
a3 p
a4 = ()
-- Data.Bool.Properties._.IsCommutativeSemigroup
d_IsCommutativeSemigroup_96 :: p -> ()
d_IsCommutativeSemigroup_96 p
a0 = ()
-- Data.Bool.Properties._.IsCommutativeSemiring
d_IsCommutativeSemiring_98 :: p -> p -> p -> p -> ()
d_IsCommutativeSemiring_98 p
a0 p
a1 p
a2 p
a3 = ()
-- Data.Bool.Properties._.IsCommutativeSemiringWithoutOne
d_IsCommutativeSemiringWithoutOne_100 :: p -> p -> p -> ()
d_IsCommutativeSemiringWithoutOne_100 p
a0 p
a1 p
a2 = ()
-- Data.Bool.Properties._.IsDistributiveLattice
d_IsDistributiveLattice_102 :: p -> p -> ()
d_IsDistributiveLattice_102 p
a0 p
a1 = ()
-- Data.Bool.Properties._.IsGroup
d_IsGroup_104 :: p -> p -> p -> ()
d_IsGroup_104 p
a0 p
a1 p
a2 = ()
-- Data.Bool.Properties._.IsIdempotentCommutativeMonoid
d_IsIdempotentCommutativeMonoid_106 :: p -> p -> ()
d_IsIdempotentCommutativeMonoid_106 p
a0 p
a1 = ()
-- Data.Bool.Properties._.IsLattice
d_IsLattice_108 :: p -> p -> ()
d_IsLattice_108 p
a0 p
a1 = ()
-- Data.Bool.Properties._.IsMagma
d_IsMagma_110 :: p -> ()
d_IsMagma_110 p
a0 = ()
-- Data.Bool.Properties._.IsMonoid
d_IsMonoid_112 :: p -> p -> ()
d_IsMonoid_112 p
a0 p
a1 = ()
-- Data.Bool.Properties._.IsNearSemiring
d_IsNearSemiring_114 :: p -> p -> p -> ()
d_IsNearSemiring_114 p
a0 p
a1 p
a2 = ()
-- Data.Bool.Properties._.IsRing
d_IsRing_116 :: p -> p -> p -> p -> p -> ()
d_IsRing_116 p
a0 p
a1 p
a2 p
a3 p
a4 = ()
-- Data.Bool.Properties._.IsSelectiveMagma
d_IsSelectiveMagma_118 :: p -> ()
d_IsSelectiveMagma_118 p
a0 = ()
-- Data.Bool.Properties._.IsSemigroup
d_IsSemigroup_120 :: p -> ()
d_IsSemigroup_120 p
a0 = ()
-- Data.Bool.Properties._.IsSemilattice
d_IsSemilattice_122 :: p -> ()
d_IsSemilattice_122 p
a0 = ()
-- Data.Bool.Properties._.IsSemiring
d_IsSemiring_124 :: p -> p -> p -> p -> ()
d_IsSemiring_124 p
a0 p
a1 p
a2 p
a3 = ()
-- Data.Bool.Properties._.IsSemiringWithoutAnnihilatingZero
d_IsSemiringWithoutAnnihilatingZero_126 :: p -> p -> p -> p -> ()
d_IsSemiringWithoutAnnihilatingZero_126 p
a0 p
a1 p
a2 p
a3 = ()
-- Data.Bool.Properties._.IsSemiringWithoutOne
d_IsSemiringWithoutOne_128 :: p -> p -> p -> ()
d_IsSemiringWithoutOne_128 p
a0 p
a1 p
a2 = ()
-- Data.Bool.Properties._.IsAbelianGroup.assoc
d_assoc_134 ::
  MAlonzo.Code.Algebra.Structures.T_IsAbelianGroup_662 ->
  Bool ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_assoc_134 :: T_IsAbelianGroup_662 -> Bool -> Bool -> Bool -> T__'8801'__12
d_assoc_134 = T_IsAbelianGroup_662 -> Bool -> Bool -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsAbelianGroup.comm
d_comm_136 ::
  MAlonzo.Code.Algebra.Structures.T_IsAbelianGroup_662 ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_comm_136 :: T_IsAbelianGroup_662 -> Bool -> Bool -> T__'8801'__12
d_comm_136 = T_IsAbelianGroup_662 -> Bool -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsAbelianGroup.identity
d_identity_138 ::
  MAlonzo.Code.Algebra.Structures.T_IsAbelianGroup_662 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_identity_138 :: T_IsAbelianGroup_662 -> T_Σ_14
d_identity_138 T_IsAbelianGroup_662
v0
  = (T_IsMonoid_358 -> T_Σ_14) -> Any -> T_Σ_14
forall a b. a -> b
coe
      T_IsMonoid_358 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_identity_370
      ((T_IsGroup_580 -> T_IsMonoid_358) -> Any -> Any
forall a b. a -> b
coe
         T_IsGroup_580 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_594
         ((T_IsAbelianGroup_662 -> T_IsGroup_580) -> Any -> Any
forall a b. a -> b
coe T_IsAbelianGroup_662 -> T_IsGroup_580
MAlonzo.Code.Algebra.Structures.d_isGroup_674 (T_IsAbelianGroup_662 -> Any
forall a b. a -> b
coe T_IsAbelianGroup_662
v0)))
-- Data.Bool.Properties._.IsAbelianGroup.inverse
d_inverse_144 ::
  MAlonzo.Code.Algebra.Structures.T_IsAbelianGroup_662 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_inverse_144 :: T_IsAbelianGroup_662 -> T_Σ_14
d_inverse_144 T_IsAbelianGroup_662
v0
  = (T_IsGroup_580 -> T_Σ_14) -> Any -> T_Σ_14
forall a b. a -> b
coe
      T_IsGroup_580 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_inverse_596
      ((T_IsAbelianGroup_662 -> T_IsGroup_580) -> Any -> Any
forall a b. a -> b
coe T_IsAbelianGroup_662 -> T_IsGroup_580
MAlonzo.Code.Algebra.Structures.d_isGroup_674 (T_IsAbelianGroup_662 -> Any
forall a b. a -> b
coe T_IsAbelianGroup_662
v0))
-- Data.Bool.Properties._.IsAbelianGroup.isEquivalence
d_isEquivalence_156 ::
  MAlonzo.Code.Algebra.Structures.T_IsAbelianGroup_662 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_156 :: T_IsAbelianGroup_662 -> T_IsEquivalence_26
d_isEquivalence_156 T_IsAbelianGroup_662
v0
  = (T_IsMagma_86 -> T_IsEquivalence_26) -> Any -> T_IsEquivalence_26
forall a b. a -> b
coe
      T_IsMagma_86 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_94
      ((T_IsSemigroup_194 -> T_IsMagma_86) -> Any -> Any
forall a b. a -> b
coe
         T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202
         ((T_IsMonoid_358 -> T_IsSemigroup_194) -> Any -> Any
forall a b. a -> b
coe
            T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368
            ((T_IsGroup_580 -> T_IsMonoid_358) -> Any -> Any
forall a b. a -> b
coe
               T_IsGroup_580 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_594
               ((T_IsAbelianGroup_662 -> T_IsGroup_580) -> Any -> Any
forall a b. a -> b
coe T_IsAbelianGroup_662 -> T_IsGroup_580
MAlonzo.Code.Algebra.Structures.d_isGroup_674 (T_IsAbelianGroup_662 -> Any
forall a b. a -> b
coe T_IsAbelianGroup_662
v0)))))
-- Data.Bool.Properties._.IsAbelianGroup.isGroup
d_isGroup_158 ::
  MAlonzo.Code.Algebra.Structures.T_IsAbelianGroup_662 ->
  MAlonzo.Code.Algebra.Structures.T_IsGroup_580
d_isGroup_158 :: T_IsAbelianGroup_662 -> T_IsGroup_580
d_isGroup_158 T_IsAbelianGroup_662
v0
  = (T_IsAbelianGroup_662 -> T_IsGroup_580) -> Any -> T_IsGroup_580
forall a b. a -> b
coe T_IsAbelianGroup_662 -> T_IsGroup_580
MAlonzo.Code.Algebra.Structures.d_isGroup_674 (T_IsAbelianGroup_662 -> Any
forall a b. a -> b
coe T_IsAbelianGroup_662
v0)
-- Data.Bool.Properties._.IsAbelianGroup.isMagma
d_isMagma_160 ::
  MAlonzo.Code.Algebra.Structures.T_IsAbelianGroup_662 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_86
d_isMagma_160 :: T_IsAbelianGroup_662 -> T_IsMagma_86
d_isMagma_160 T_IsAbelianGroup_662
v0
  = (T_IsSemigroup_194 -> T_IsMagma_86) -> Any -> T_IsMagma_86
forall a b. a -> b
coe
      T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202
      ((T_IsMonoid_358 -> T_IsSemigroup_194) -> Any -> Any
forall a b. a -> b
coe
         T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368
         ((T_IsGroup_580 -> T_IsMonoid_358) -> Any -> Any
forall a b. a -> b
coe
            T_IsGroup_580 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_594
            ((T_IsAbelianGroup_662 -> T_IsGroup_580) -> Any -> Any
forall a b. a -> b
coe T_IsAbelianGroup_662 -> T_IsGroup_580
MAlonzo.Code.Algebra.Structures.d_isGroup_674 (T_IsAbelianGroup_662 -> Any
forall a b. a -> b
coe T_IsAbelianGroup_662
v0))))
-- Data.Bool.Properties._.IsAbelianGroup.isMonoid
d_isMonoid_162 ::
  MAlonzo.Code.Algebra.Structures.T_IsAbelianGroup_662 ->
  MAlonzo.Code.Algebra.Structures.T_IsMonoid_358
d_isMonoid_162 :: T_IsAbelianGroup_662 -> T_IsMonoid_358
d_isMonoid_162 T_IsAbelianGroup_662
v0
  = (T_IsGroup_580 -> T_IsMonoid_358) -> Any -> T_IsMonoid_358
forall a b. a -> b
coe
      T_IsGroup_580 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_594
      ((T_IsAbelianGroup_662 -> T_IsGroup_580) -> Any -> Any
forall a b. a -> b
coe T_IsAbelianGroup_662 -> T_IsGroup_580
MAlonzo.Code.Algebra.Structures.d_isGroup_674 (T_IsAbelianGroup_662 -> Any
forall a b. a -> b
coe T_IsAbelianGroup_662
v0))
-- Data.Bool.Properties._.IsAbelianGroup.isSemigroup
d_isSemigroup_166 ::
  MAlonzo.Code.Algebra.Structures.T_IsAbelianGroup_662 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_194
d_isSemigroup_166 :: T_IsAbelianGroup_662 -> T_IsSemigroup_194
d_isSemigroup_166 T_IsAbelianGroup_662
v0
  = (T_IsMonoid_358 -> T_IsSemigroup_194) -> Any -> T_IsSemigroup_194
forall a b. a -> b
coe
      T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368
      ((T_IsGroup_580 -> T_IsMonoid_358) -> Any -> Any
forall a b. a -> b
coe
         T_IsGroup_580 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_594
         ((T_IsAbelianGroup_662 -> T_IsGroup_580) -> Any -> Any
forall a b. a -> b
coe T_IsAbelianGroup_662 -> T_IsGroup_580
MAlonzo.Code.Algebra.Structures.d_isGroup_674 (T_IsAbelianGroup_662 -> Any
forall a b. a -> b
coe T_IsAbelianGroup_662
v0)))
-- Data.Bool.Properties._.IsAbelianGroup.⁻¹-cong
d_'8315''185''45'cong_182 ::
  MAlonzo.Code.Algebra.Structures.T_IsAbelianGroup_662 ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8315''185''45'cong_182 :: T_IsAbelianGroup_662
-> Bool -> Bool -> T__'8801'__12 -> T__'8801'__12
d_'8315''185''45'cong_182 = T_IsAbelianGroup_662
-> Bool -> Bool -> T__'8801'__12 -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsAbelianGroup.∙-cong
d_'8729''45'cong_184 ::
  MAlonzo.Code.Algebra.Structures.T_IsAbelianGroup_662 ->
  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_184 :: T_IsAbelianGroup_662
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong_184 = T_IsAbelianGroup_662
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsBand.assoc
d_assoc_192 ::
  MAlonzo.Code.Algebra.Structures.T_IsBand_230 ->
  Bool ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_assoc_192 :: T_IsBand_230 -> Bool -> Bool -> Bool -> T__'8801'__12
d_assoc_192 = T_IsBand_230 -> Bool -> Bool -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsBand.idem
d_idem_194 ::
  MAlonzo.Code.Algebra.Structures.T_IsBand_230 ->
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_idem_194 :: T_IsBand_230 -> Bool -> T__'8801'__12
d_idem_194 = T_IsBand_230 -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsBand.isEquivalence
d_isEquivalence_196 ::
  MAlonzo.Code.Algebra.Structures.T_IsBand_230 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_196 :: T_IsBand_230 -> T_IsEquivalence_26
d_isEquivalence_196 T_IsBand_230
v0
  = (T_IsMagma_86 -> T_IsEquivalence_26) -> Any -> T_IsEquivalence_26
forall a b. a -> b
coe
      T_IsMagma_86 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_94
      ((T_IsSemigroup_194 -> T_IsMagma_86) -> Any -> Any
forall a b. a -> b
coe
         T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202
         ((T_IsBand_230 -> T_IsSemigroup_194) -> Any -> Any
forall a b. a -> b
coe T_IsBand_230 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_238 (T_IsBand_230 -> Any
forall a b. a -> b
coe T_IsBand_230
v0)))
-- Data.Bool.Properties._.IsBand.isMagma
d_isMagma_198 ::
  MAlonzo.Code.Algebra.Structures.T_IsBand_230 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_86
d_isMagma_198 :: T_IsBand_230 -> T_IsMagma_86
d_isMagma_198 T_IsBand_230
v0
  = (T_IsSemigroup_194 -> T_IsMagma_86) -> Any -> T_IsMagma_86
forall a b. a -> b
coe
      T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202
      ((T_IsBand_230 -> T_IsSemigroup_194) -> Any -> Any
forall a b. a -> b
coe T_IsBand_230 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_238 (T_IsBand_230 -> Any
forall a b. a -> b
coe T_IsBand_230
v0))
-- Data.Bool.Properties._.IsBand.isSemigroup
d_isSemigroup_202 ::
  MAlonzo.Code.Algebra.Structures.T_IsBand_230 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_194
d_isSemigroup_202 :: T_IsBand_230 -> T_IsSemigroup_194
d_isSemigroup_202 T_IsBand_230
v0
  = (T_IsBand_230 -> T_IsSemigroup_194) -> Any -> T_IsSemigroup_194
forall a b. a -> b
coe T_IsBand_230 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_238 (T_IsBand_230 -> Any
forall a b. a -> b
coe T_IsBand_230
v0)
-- Data.Bool.Properties._.IsBand.∙-cong
d_'8729''45'cong_214 ::
  MAlonzo.Code.Algebra.Structures.T_IsBand_230 ->
  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_214 :: T_IsBand_230
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong_214 = T_IsBand_230
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsBooleanAlgebra.absorptive
d_absorptive_222 ::
  MAlonzo.Code.Algebra.Structures.T_IsBooleanAlgebra_1864 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_absorptive_222 :: T_IsBooleanAlgebra_1864 -> T_Σ_14
d_absorptive_222 T_IsBooleanAlgebra_1864
v0
  = (T_IsLattice_740 -> T_Σ_14) -> Any -> T_Σ_14
forall a b. a -> b
coe
      T_IsLattice_740 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_absorptive_776
      ((T_IsDistributiveLattice_814 -> T_IsLattice_740) -> Any -> Any
forall a b. a -> b
coe
         T_IsDistributiveLattice_814 -> T_IsLattice_740
MAlonzo.Code.Algebra.Structures.d_isLattice_824
         ((T_IsBooleanAlgebra_1864 -> T_IsDistributiveLattice_814)
-> Any -> Any
forall a b. a -> b
coe
            T_IsBooleanAlgebra_1864 -> T_IsDistributiveLattice_814
MAlonzo.Code.Algebra.Structures.d_isDistributiveLattice_1884
            (T_IsBooleanAlgebra_1864 -> Any
forall a b. a -> b
coe T_IsBooleanAlgebra_1864
v0)))
-- Data.Bool.Properties._.IsBooleanAlgebra.isDistributiveLattice
d_isDistributiveLattice_224 ::
  MAlonzo.Code.Algebra.Structures.T_IsBooleanAlgebra_1864 ->
  MAlonzo.Code.Algebra.Structures.T_IsDistributiveLattice_814
d_isDistributiveLattice_224 :: T_IsBooleanAlgebra_1864 -> T_IsDistributiveLattice_814
d_isDistributiveLattice_224 T_IsBooleanAlgebra_1864
v0
  = (T_IsBooleanAlgebra_1864 -> T_IsDistributiveLattice_814)
-> Any -> T_IsDistributiveLattice_814
forall a b. a -> b
coe
      T_IsBooleanAlgebra_1864 -> T_IsDistributiveLattice_814
MAlonzo.Code.Algebra.Structures.d_isDistributiveLattice_1884
      (T_IsBooleanAlgebra_1864 -> Any
forall a b. a -> b
coe T_IsBooleanAlgebra_1864
v0)
-- Data.Bool.Properties._.IsBooleanAlgebra.isEquivalence
d_isEquivalence_226 ::
  MAlonzo.Code.Algebra.Structures.T_IsBooleanAlgebra_1864 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_226 :: T_IsBooleanAlgebra_1864 -> T_IsEquivalence_26
d_isEquivalence_226 T_IsBooleanAlgebra_1864
v0
  = (T_IsLattice_740 -> T_IsEquivalence_26)
-> Any -> T_IsEquivalence_26
forall a b. a -> b
coe
      T_IsLattice_740 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_762
      ((T_IsDistributiveLattice_814 -> T_IsLattice_740) -> Any -> Any
forall a b. a -> b
coe
         T_IsDistributiveLattice_814 -> T_IsLattice_740
MAlonzo.Code.Algebra.Structures.d_isLattice_824
         ((T_IsBooleanAlgebra_1864 -> T_IsDistributiveLattice_814)
-> Any -> Any
forall a b. a -> b
coe
            T_IsBooleanAlgebra_1864 -> T_IsDistributiveLattice_814
MAlonzo.Code.Algebra.Structures.d_isDistributiveLattice_1884
            (T_IsBooleanAlgebra_1864 -> Any
forall a b. a -> b
coe T_IsBooleanAlgebra_1864
v0)))
-- Data.Bool.Properties._.IsBooleanAlgebra.isLattice
d_isLattice_228 ::
  MAlonzo.Code.Algebra.Structures.T_IsBooleanAlgebra_1864 ->
  MAlonzo.Code.Algebra.Structures.T_IsLattice_740
d_isLattice_228 :: T_IsBooleanAlgebra_1864 -> T_IsLattice_740
d_isLattice_228 T_IsBooleanAlgebra_1864
v0
  = (T_IsDistributiveLattice_814 -> T_IsLattice_740)
-> Any -> T_IsLattice_740
forall a b. a -> b
coe
      T_IsDistributiveLattice_814 -> T_IsLattice_740
MAlonzo.Code.Algebra.Structures.d_isLattice_824
      ((T_IsBooleanAlgebra_1864 -> T_IsDistributiveLattice_814)
-> Any -> Any
forall a b. a -> b
coe
         T_IsBooleanAlgebra_1864 -> T_IsDistributiveLattice_814
MAlonzo.Code.Algebra.Structures.d_isDistributiveLattice_1884
         (T_IsBooleanAlgebra_1864 -> Any
forall a b. a -> b
coe T_IsBooleanAlgebra_1864
v0))
-- Data.Bool.Properties._.IsBooleanAlgebra.¬-cong
d_'172''45'cong_240 ::
  MAlonzo.Code.Algebra.Structures.T_IsBooleanAlgebra_1864 ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'172''45'cong_240 :: T_IsBooleanAlgebra_1864
-> Bool -> Bool -> T__'8801'__12 -> T__'8801'__12
d_'172''45'cong_240 = T_IsBooleanAlgebra_1864
-> Bool -> Bool -> T__'8801'__12 -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsBooleanAlgebra.∧-assoc
d_'8743''45'assoc_244 ::
  MAlonzo.Code.Algebra.Structures.T_IsBooleanAlgebra_1864 ->
  Bool ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8743''45'assoc_244 :: T_IsBooleanAlgebra_1864 -> Bool -> Bool -> Bool -> T__'8801'__12
d_'8743''45'assoc_244 = T_IsBooleanAlgebra_1864 -> Bool -> Bool -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsBooleanAlgebra.∧-comm
d_'8743''45'comm_246 ::
  MAlonzo.Code.Algebra.Structures.T_IsBooleanAlgebra_1864 ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8743''45'comm_246 :: T_IsBooleanAlgebra_1864 -> Bool -> Bool -> T__'8801'__12
d_'8743''45'comm_246 = T_IsBooleanAlgebra_1864 -> Bool -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsBooleanAlgebra.∧-complementʳ
d_'8743''45'complement'691'_248 ::
  MAlonzo.Code.Algebra.Structures.T_IsBooleanAlgebra_1864 ->
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8743''45'complement'691'_248 :: T_IsBooleanAlgebra_1864 -> Bool -> T__'8801'__12
d_'8743''45'complement'691'_248 = T_IsBooleanAlgebra_1864 -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsBooleanAlgebra.∧-cong
d_'8743''45'cong_250 ::
  MAlonzo.Code.Algebra.Structures.T_IsBooleanAlgebra_1864 ->
  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_250 :: T_IsBooleanAlgebra_1864
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
d_'8743''45'cong_250 = T_IsBooleanAlgebra_1864
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsBooleanAlgebra.∨-assoc
d_'8744''45'assoc_258 ::
  MAlonzo.Code.Algebra.Structures.T_IsBooleanAlgebra_1864 ->
  Bool ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8744''45'assoc_258 :: T_IsBooleanAlgebra_1864 -> Bool -> Bool -> Bool -> T__'8801'__12
d_'8744''45'assoc_258 = T_IsBooleanAlgebra_1864 -> Bool -> Bool -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsBooleanAlgebra.∨-comm
d_'8744''45'comm_260 ::
  MAlonzo.Code.Algebra.Structures.T_IsBooleanAlgebra_1864 ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8744''45'comm_260 :: T_IsBooleanAlgebra_1864 -> Bool -> Bool -> T__'8801'__12
d_'8744''45'comm_260 = T_IsBooleanAlgebra_1864 -> Bool -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsBooleanAlgebra.∨-complementʳ
d_'8744''45'complement'691'_262 ::
  MAlonzo.Code.Algebra.Structures.T_IsBooleanAlgebra_1864 ->
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8744''45'complement'691'_262 :: T_IsBooleanAlgebra_1864 -> Bool -> T__'8801'__12
d_'8744''45'complement'691'_262 = T_IsBooleanAlgebra_1864 -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsBooleanAlgebra.∨-cong
d_'8744''45'cong_264 ::
  MAlonzo.Code.Algebra.Structures.T_IsBooleanAlgebra_1864 ->
  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_264 :: T_IsBooleanAlgebra_1864
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
d_'8744''45'cong_264 = T_IsBooleanAlgebra_1864
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsBooleanAlgebra.∨-distribʳ-∧
d_'8744''45'distrib'691''45''8743'_270 ::
  MAlonzo.Code.Algebra.Structures.T_IsBooleanAlgebra_1864 ->
  Bool ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8744''45'distrib'691''45''8743'_270 :: T_IsBooleanAlgebra_1864 -> Bool -> Bool -> Bool -> T__'8801'__12
d_'8744''45'distrib'691''45''8743'_270 = T_IsBooleanAlgebra_1864 -> Bool -> Bool -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsBoundedLattice.assoc
d_assoc_276 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_464 ->
  Bool ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_assoc_276 :: T_IsIdempotentCommutativeMonoid_464
-> Bool -> Bool -> Bool -> T__'8801'__12
d_assoc_276 = T_IsIdempotentCommutativeMonoid_464
-> Bool -> Bool -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsBoundedLattice.comm
d_comm_278 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_464 ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_comm_278 :: T_IsIdempotentCommutativeMonoid_464
-> Bool -> Bool -> T__'8801'__12
d_comm_278 = T_IsIdempotentCommutativeMonoid_464
-> Bool -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsBoundedLattice.idem
d_idem_280 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_464 ->
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_idem_280 :: T_IsIdempotentCommutativeMonoid_464 -> Bool -> T__'8801'__12
d_idem_280 = T_IsIdempotentCommutativeMonoid_464 -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsBoundedLattice.identity
d_identity_282 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_464 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_identity_282 :: T_IsIdempotentCommutativeMonoid_464 -> T_Σ_14
d_identity_282 T_IsIdempotentCommutativeMonoid_464
v0
  = (T_IsMonoid_358 -> T_Σ_14) -> Any -> T_Σ_14
forall a b. a -> b
coe
      T_IsMonoid_358 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_identity_370
      ((T_IsCommutativeMonoid_406 -> T_IsMonoid_358) -> Any -> Any
forall a b. a -> b
coe
         T_IsCommutativeMonoid_406 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_416
         ((T_IsIdempotentCommutativeMonoid_464 -> T_IsCommutativeMonoid_406)
-> Any -> Any
forall a b. a -> b
coe
            T_IsIdempotentCommutativeMonoid_464 -> T_IsCommutativeMonoid_406
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_474
            (T_IsIdempotentCommutativeMonoid_464 -> Any
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_464
v0)))
-- Data.Bool.Properties._.IsBoundedLattice.isCommutativeMonoid
d_isCommutativeMonoid_290 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_464 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMonoid_406
d_isCommutativeMonoid_290 :: T_IsIdempotentCommutativeMonoid_464 -> T_IsCommutativeMonoid_406
d_isCommutativeMonoid_290 T_IsIdempotentCommutativeMonoid_464
v0
  = (T_IsIdempotentCommutativeMonoid_464 -> T_IsCommutativeMonoid_406)
-> Any -> T_IsCommutativeMonoid_406
forall a b. a -> b
coe
      T_IsIdempotentCommutativeMonoid_464 -> T_IsCommutativeMonoid_406
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_474 (T_IsIdempotentCommutativeMonoid_464 -> Any
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_464
v0)
-- Data.Bool.Properties._.IsBoundedLattice.isEquivalence
d_isEquivalence_294 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_464 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_294 :: T_IsIdempotentCommutativeMonoid_464 -> T_IsEquivalence_26
d_isEquivalence_294 T_IsIdempotentCommutativeMonoid_464
v0
  = (T_IsMagma_86 -> T_IsEquivalence_26) -> Any -> T_IsEquivalence_26
forall a b. a -> b
coe
      T_IsMagma_86 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_94
      ((T_IsSemigroup_194 -> T_IsMagma_86) -> Any -> Any
forall a b. a -> b
coe
         T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202
         ((T_IsMonoid_358 -> T_IsSemigroup_194) -> Any -> Any
forall a b. a -> b
coe
            T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368
            ((T_IsCommutativeMonoid_406 -> T_IsMonoid_358) -> Any -> Any
forall a b. a -> b
coe
               T_IsCommutativeMonoid_406 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_416
               ((T_IsIdempotentCommutativeMonoid_464 -> T_IsCommutativeMonoid_406)
-> Any -> Any
forall a b. a -> b
coe
                  T_IsIdempotentCommutativeMonoid_464 -> T_IsCommutativeMonoid_406
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_474
                  (T_IsIdempotentCommutativeMonoid_464 -> Any
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_464
v0)))))
-- Data.Bool.Properties._.IsBoundedLattice.isMagma
d_isMagma_296 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_464 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_86
d_isMagma_296 :: T_IsIdempotentCommutativeMonoid_464 -> T_IsMagma_86
d_isMagma_296 T_IsIdempotentCommutativeMonoid_464
v0
  = (T_IsSemigroup_194 -> T_IsMagma_86) -> Any -> T_IsMagma_86
forall a b. a -> b
coe
      T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202
      ((T_IsMonoid_358 -> T_IsSemigroup_194) -> Any -> Any
forall a b. a -> b
coe
         T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368
         ((T_IsCommutativeMonoid_406 -> T_IsMonoid_358) -> Any -> Any
forall a b. a -> b
coe
            T_IsCommutativeMonoid_406 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_416
            ((T_IsIdempotentCommutativeMonoid_464 -> T_IsCommutativeMonoid_406)
-> Any -> Any
forall a b. a -> b
coe
               T_IsIdempotentCommutativeMonoid_464 -> T_IsCommutativeMonoid_406
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_474
               (T_IsIdempotentCommutativeMonoid_464 -> Any
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_464
v0))))
-- Data.Bool.Properties._.IsBoundedLattice.isMonoid
d_isMonoid_298 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_464 ->
  MAlonzo.Code.Algebra.Structures.T_IsMonoid_358
d_isMonoid_298 :: T_IsIdempotentCommutativeMonoid_464 -> T_IsMonoid_358
d_isMonoid_298 T_IsIdempotentCommutativeMonoid_464
v0
  = (T_IsCommutativeMonoid_406 -> T_IsMonoid_358)
-> Any -> T_IsMonoid_358
forall a b. a -> b
coe
      T_IsCommutativeMonoid_406 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_416
      ((T_IsIdempotentCommutativeMonoid_464 -> T_IsCommutativeMonoid_406)
-> Any -> Any
forall a b. a -> b
coe
         T_IsIdempotentCommutativeMonoid_464 -> T_IsCommutativeMonoid_406
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_474 (T_IsIdempotentCommutativeMonoid_464 -> Any
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_464
v0))
-- Data.Bool.Properties._.IsBoundedLattice.isSemigroup
d_isSemigroup_302 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_464 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_194
d_isSemigroup_302 :: T_IsIdempotentCommutativeMonoid_464 -> T_IsSemigroup_194
d_isSemigroup_302 T_IsIdempotentCommutativeMonoid_464
v0
  = (T_IsMonoid_358 -> T_IsSemigroup_194) -> Any -> T_IsSemigroup_194
forall a b. a -> b
coe
      T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368
      ((T_IsCommutativeMonoid_406 -> T_IsMonoid_358) -> Any -> Any
forall a b. a -> b
coe
         T_IsCommutativeMonoid_406 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_416
         ((T_IsIdempotentCommutativeMonoid_464 -> T_IsCommutativeMonoid_406)
-> Any -> Any
forall a b. a -> b
coe
            T_IsIdempotentCommutativeMonoid_464 -> T_IsCommutativeMonoid_406
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_474
            (T_IsIdempotentCommutativeMonoid_464 -> Any
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_464
v0)))
-- Data.Bool.Properties._.IsBoundedLattice.∙-cong
d_'8729''45'cong_314 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_464 ->
  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_314 :: T_IsIdempotentCommutativeMonoid_464
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong_314 = T_IsIdempotentCommutativeMonoid_464
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsCancellativeCommutativeSemiring.assoc
d_assoc_322 ::
  MAlonzo.Code.Algebra.Structures.T_IsCancellativeCommutativeSemiring_1462 ->
  Bool ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_assoc_322 :: T_IsCancellativeCommutativeSemiring_1462
-> Bool -> Bool -> Bool -> T__'8801'__12
d_assoc_322 = T_IsCancellativeCommutativeSemiring_1462
-> Bool -> Bool -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsCancellativeCommutativeSemiring.*-cancelˡ-nonZero
d_'42''45'cancel'737''45'nonZero_324 ::
  MAlonzo.Code.Algebra.Structures.T_IsCancellativeCommutativeSemiring_1462 ->
  Bool ->
  Bool ->
  Bool ->
  (MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
   MAlonzo.Code.Data.Empty.T_'8869'_4) ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'42''45'cancel'737''45'nonZero_324 :: T_IsCancellativeCommutativeSemiring_1462
-> Bool
-> Bool
-> Bool
-> (T__'8801'__12 -> T_'8869'_4)
-> T__'8801'__12
-> T__'8801'__12
d_'42''45'cancel'737''45'nonZero_324 = T_IsCancellativeCommutativeSemiring_1462
-> Bool
-> Bool
-> Bool
-> (T__'8801'__12 -> T_'8869'_4)
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsCancellativeCommutativeSemiring.*-comm
d_'42''45'comm_326 ::
  MAlonzo.Code.Algebra.Structures.T_IsCancellativeCommutativeSemiring_1462 ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'42''45'comm_326 :: T_IsCancellativeCommutativeSemiring_1462
-> Bool -> Bool -> T__'8801'__12
d_'42''45'comm_326 = T_IsCancellativeCommutativeSemiring_1462
-> Bool -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsCancellativeCommutativeSemiring.∙-cong
d_'8729''45'cong_328 ::
  MAlonzo.Code.Algebra.Structures.T_IsCancellativeCommutativeSemiring_1462 ->
  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_328 :: T_IsCancellativeCommutativeSemiring_1462
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong_328 = T_IsCancellativeCommutativeSemiring_1462
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsCancellativeCommutativeSemiring.identity
d_identity_334 ::
  MAlonzo.Code.Algebra.Structures.T_IsCancellativeCommutativeSemiring_1462 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_identity_334 :: T_IsCancellativeCommutativeSemiring_1462 -> T_Σ_14
d_identity_334 T_IsCancellativeCommutativeSemiring_1462
v0
  = (T_IsMonoid_358 -> T_Σ_14) -> Any -> T_Σ_14
forall a b. a -> b
coe
      T_IsMonoid_358 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_identity_370
      ((T_IsSemiringWithoutAnnihilatingZero_1142 -> T_IsMonoid_358)
-> Any -> Any
forall a b. a -> b
coe
         T_IsSemiringWithoutAnnihilatingZero_1142 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_'42''45'isMonoid_1160
         ((T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142)
-> Any -> Any
forall a b. a -> b
coe
            T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1252
            ((T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238) -> Any -> Any
forall a b. a -> b
coe
               T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238
MAlonzo.Code.Algebra.Structures.d_isSemiring_1358
               ((T_IsCancellativeCommutativeSemiring_1462
 -> T_IsCommutativeSemiring_1344)
-> Any -> Any
forall a b. a -> b
coe
                  T_IsCancellativeCommutativeSemiring_1462
-> T_IsCommutativeSemiring_1344
MAlonzo.Code.Algebra.Structures.d_isCommutativeSemiring_1476
                  (T_IsCancellativeCommutativeSemiring_1462 -> Any
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1462
v0)))))
-- Data.Bool.Properties._.IsCancellativeCommutativeSemiring.isMagma
d_isMagma_346 ::
  MAlonzo.Code.Algebra.Structures.T_IsCancellativeCommutativeSemiring_1462 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_86
d_isMagma_346 :: T_IsCancellativeCommutativeSemiring_1462 -> T_IsMagma_86
d_isMagma_346 T_IsCancellativeCommutativeSemiring_1462
v0
  = (T_IsSemigroup_194 -> T_IsMagma_86) -> Any -> T_IsMagma_86
forall a b. a -> b
coe
      T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202
      ((T_IsMonoid_358 -> T_IsSemigroup_194) -> Any -> Any
forall a b. a -> b
coe
         T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368
         ((T_IsSemiringWithoutAnnihilatingZero_1142 -> T_IsMonoid_358)
-> Any -> Any
forall a b. a -> b
coe
            T_IsSemiringWithoutAnnihilatingZero_1142 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_'42''45'isMonoid_1160
            ((T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142)
-> Any -> Any
forall a b. a -> b
coe
               T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1252
               ((T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238) -> Any -> Any
forall a b. a -> b
coe
                  T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238
MAlonzo.Code.Algebra.Structures.d_isSemiring_1358
                  ((T_IsCancellativeCommutativeSemiring_1462
 -> T_IsCommutativeSemiring_1344)
-> Any -> Any
forall a b. a -> b
coe
                     T_IsCancellativeCommutativeSemiring_1462
-> T_IsCommutativeSemiring_1344
MAlonzo.Code.Algebra.Structures.d_isCommutativeSemiring_1476
                     (T_IsCancellativeCommutativeSemiring_1462 -> Any
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1462
v0))))))
-- Data.Bool.Properties._.IsCancellativeCommutativeSemiring.*-isMonoid
d_'42''45'isMonoid_348 ::
  MAlonzo.Code.Algebra.Structures.T_IsCancellativeCommutativeSemiring_1462 ->
  MAlonzo.Code.Algebra.Structures.T_IsMonoid_358
d_'42''45'isMonoid_348 :: T_IsCancellativeCommutativeSemiring_1462 -> T_IsMonoid_358
d_'42''45'isMonoid_348 T_IsCancellativeCommutativeSemiring_1462
v0
  = (T_IsSemiringWithoutAnnihilatingZero_1142 -> T_IsMonoid_358)
-> Any -> T_IsMonoid_358
forall a b. a -> b
coe
      T_IsSemiringWithoutAnnihilatingZero_1142 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_'42''45'isMonoid_1160
      ((T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142)
-> Any -> Any
forall a b. a -> b
coe
         T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1252
         ((T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238) -> Any -> Any
forall a b. a -> b
coe
            T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238
MAlonzo.Code.Algebra.Structures.d_isSemiring_1358
            ((T_IsCancellativeCommutativeSemiring_1462
 -> T_IsCommutativeSemiring_1344)
-> Any -> Any
forall a b. a -> b
coe
               T_IsCancellativeCommutativeSemiring_1462
-> T_IsCommutativeSemiring_1344
MAlonzo.Code.Algebra.Structures.d_isCommutativeSemiring_1476
               (T_IsCancellativeCommutativeSemiring_1462 -> Any
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1462
v0))))
-- Data.Bool.Properties._.IsCancellativeCommutativeSemiring.isSemigroup
d_isSemigroup_350 ::
  MAlonzo.Code.Algebra.Structures.T_IsCancellativeCommutativeSemiring_1462 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_194
d_isSemigroup_350 :: T_IsCancellativeCommutativeSemiring_1462 -> T_IsSemigroup_194
d_isSemigroup_350 T_IsCancellativeCommutativeSemiring_1462
v0
  = (T_IsMonoid_358 -> T_IsSemigroup_194) -> Any -> T_IsSemigroup_194
forall a b. a -> b
coe
      T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368
      ((T_IsSemiringWithoutAnnihilatingZero_1142 -> T_IsMonoid_358)
-> Any -> Any
forall a b. a -> b
coe
         T_IsSemiringWithoutAnnihilatingZero_1142 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_'42''45'isMonoid_1160
         ((T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142)
-> Any -> Any
forall a b. a -> b
coe
            T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1252
            ((T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238) -> Any -> Any
forall a b. a -> b
coe
               T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238
MAlonzo.Code.Algebra.Structures.d_isSemiring_1358
               ((T_IsCancellativeCommutativeSemiring_1462
 -> T_IsCommutativeSemiring_1344)
-> Any -> Any
forall a b. a -> b
coe
                  T_IsCancellativeCommutativeSemiring_1462
-> T_IsCommutativeSemiring_1344
MAlonzo.Code.Algebra.Structures.d_isCommutativeSemiring_1476
                  (T_IsCancellativeCommutativeSemiring_1462 -> Any
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1462
v0)))))
-- Data.Bool.Properties._.IsCancellativeCommutativeSemiring.assoc
d_assoc_352 ::
  MAlonzo.Code.Algebra.Structures.T_IsCancellativeCommutativeSemiring_1462 ->
  Bool ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_assoc_352 :: T_IsCancellativeCommutativeSemiring_1462
-> Bool -> Bool -> Bool -> T__'8801'__12
d_assoc_352 = T_IsCancellativeCommutativeSemiring_1462
-> Bool -> Bool -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsCancellativeCommutativeSemiring.comm
d_comm_354 ::
  MAlonzo.Code.Algebra.Structures.T_IsCancellativeCommutativeSemiring_1462 ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_comm_354 :: T_IsCancellativeCommutativeSemiring_1462
-> Bool -> Bool -> T__'8801'__12
d_comm_354 = T_IsCancellativeCommutativeSemiring_1462
-> Bool -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsCancellativeCommutativeSemiring.∙-cong
d_'8729''45'cong_356 ::
  MAlonzo.Code.Algebra.Structures.T_IsCancellativeCommutativeSemiring_1462 ->
  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_356 :: T_IsCancellativeCommutativeSemiring_1462
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong_356 = T_IsCancellativeCommutativeSemiring_1462
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsCancellativeCommutativeSemiring.identity
d_identity_362 ::
  MAlonzo.Code.Algebra.Structures.T_IsCancellativeCommutativeSemiring_1462 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_identity_362 :: T_IsCancellativeCommutativeSemiring_1462 -> T_Σ_14
d_identity_362 T_IsCancellativeCommutativeSemiring_1462
v0
  = (T_IsMonoid_358 -> T_Σ_14) -> Any -> T_Σ_14
forall a b. a -> b
coe
      T_IsMonoid_358 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_identity_370
      ((T_IsCommutativeMonoid_406 -> T_IsMonoid_358) -> Any -> Any
forall a b. a -> b
coe
         T_IsCommutativeMonoid_406 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_416
         ((T_IsSemiringWithoutAnnihilatingZero_1142
 -> T_IsCommutativeMonoid_406)
-> Any -> Any
forall a b. a -> b
coe
            T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsCommutativeMonoid_406
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1158
            ((T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142)
-> Any -> Any
forall a b. a -> b
coe
               T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1252
               ((T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238) -> Any -> Any
forall a b. a -> b
coe
                  T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238
MAlonzo.Code.Algebra.Structures.d_isSemiring_1358
                  ((T_IsCancellativeCommutativeSemiring_1462
 -> T_IsCommutativeSemiring_1344)
-> Any -> Any
forall a b. a -> b
coe
                     T_IsCancellativeCommutativeSemiring_1462
-> T_IsCommutativeSemiring_1344
MAlonzo.Code.Algebra.Structures.d_isCommutativeSemiring_1476
                     (T_IsCancellativeCommutativeSemiring_1462 -> Any
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1462
v0))))))
-- Data.Bool.Properties._.IsCancellativeCommutativeSemiring.+-isCommutativeMonoid
d_'43''45'isCommutativeMonoid_370 ::
  MAlonzo.Code.Algebra.Structures.T_IsCancellativeCommutativeSemiring_1462 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMonoid_406
d_'43''45'isCommutativeMonoid_370 :: T_IsCancellativeCommutativeSemiring_1462
-> T_IsCommutativeMonoid_406
d_'43''45'isCommutativeMonoid_370 T_IsCancellativeCommutativeSemiring_1462
v0
  = (T_IsSemiringWithoutAnnihilatingZero_1142
 -> T_IsCommutativeMonoid_406)
-> Any -> T_IsCommutativeMonoid_406
forall a b. a -> b
coe
      T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsCommutativeMonoid_406
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1158
      ((T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142)
-> Any -> Any
forall a b. a -> b
coe
         T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1252
         ((T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238) -> Any -> Any
forall a b. a -> b
coe
            T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238
MAlonzo.Code.Algebra.Structures.d_isSemiring_1358
            ((T_IsCancellativeCommutativeSemiring_1462
 -> T_IsCommutativeSemiring_1344)
-> Any -> Any
forall a b. a -> b
coe
               T_IsCancellativeCommutativeSemiring_1462
-> T_IsCommutativeSemiring_1344
MAlonzo.Code.Algebra.Structures.d_isCommutativeSemiring_1476
               (T_IsCancellativeCommutativeSemiring_1462 -> Any
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1462
v0))))
-- Data.Bool.Properties._.IsCancellativeCommutativeSemiring.isMagma
d_isMagma_374 ::
  MAlonzo.Code.Algebra.Structures.T_IsCancellativeCommutativeSemiring_1462 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_86
d_isMagma_374 :: T_IsCancellativeCommutativeSemiring_1462 -> T_IsMagma_86
d_isMagma_374 T_IsCancellativeCommutativeSemiring_1462
v0
  = (T_IsSemigroup_194 -> T_IsMagma_86) -> Any -> T_IsMagma_86
forall a b. a -> b
coe
      T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202
      ((T_IsMonoid_358 -> T_IsSemigroup_194) -> Any -> Any
forall a b. a -> b
coe
         T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368
         ((T_IsCommutativeMonoid_406 -> T_IsMonoid_358) -> Any -> Any
forall a b. a -> b
coe
            T_IsCommutativeMonoid_406 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_416
            ((T_IsSemiringWithoutAnnihilatingZero_1142
 -> T_IsCommutativeMonoid_406)
-> Any -> Any
forall a b. a -> b
coe
               T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsCommutativeMonoid_406
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1158
               ((T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142)
-> Any -> Any
forall a b. a -> b
coe
                  T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1252
                  ((T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238) -> Any -> Any
forall a b. a -> b
coe
                     T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238
MAlonzo.Code.Algebra.Structures.d_isSemiring_1358
                     ((T_IsCancellativeCommutativeSemiring_1462
 -> T_IsCommutativeSemiring_1344)
-> Any -> Any
forall a b. a -> b
coe
                        T_IsCancellativeCommutativeSemiring_1462
-> T_IsCommutativeSemiring_1344
MAlonzo.Code.Algebra.Structures.d_isCommutativeSemiring_1476
                        (T_IsCancellativeCommutativeSemiring_1462 -> Any
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1462
v0)))))))
-- Data.Bool.Properties._.IsCancellativeCommutativeSemiring.isMonoid
d_isMonoid_376 ::
  MAlonzo.Code.Algebra.Structures.T_IsCancellativeCommutativeSemiring_1462 ->
  MAlonzo.Code.Algebra.Structures.T_IsMonoid_358
d_isMonoid_376 :: T_IsCancellativeCommutativeSemiring_1462 -> T_IsMonoid_358
d_isMonoid_376 T_IsCancellativeCommutativeSemiring_1462
v0
  = (T_IsCommutativeMonoid_406 -> T_IsMonoid_358)
-> Any -> T_IsMonoid_358
forall a b. a -> b
coe
      T_IsCommutativeMonoid_406 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_416
      ((T_IsSemiringWithoutAnnihilatingZero_1142
 -> T_IsCommutativeMonoid_406)
-> Any -> Any
forall a b. a -> b
coe
         T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsCommutativeMonoid_406
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1158
         ((T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142)
-> Any -> Any
forall a b. a -> b
coe
            T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1252
            ((T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238) -> Any -> Any
forall a b. a -> b
coe
               T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238
MAlonzo.Code.Algebra.Structures.d_isSemiring_1358
               ((T_IsCancellativeCommutativeSemiring_1462
 -> T_IsCommutativeSemiring_1344)
-> Any -> Any
forall a b. a -> b
coe
                  T_IsCancellativeCommutativeSemiring_1462
-> T_IsCommutativeSemiring_1344
MAlonzo.Code.Algebra.Structures.d_isCommutativeSemiring_1476
                  (T_IsCancellativeCommutativeSemiring_1462 -> Any
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1462
v0)))))
-- Data.Bool.Properties._.IsCancellativeCommutativeSemiring.isSemigroup
d_isSemigroup_378 ::
  MAlonzo.Code.Algebra.Structures.T_IsCancellativeCommutativeSemiring_1462 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_194
d_isSemigroup_378 :: T_IsCancellativeCommutativeSemiring_1462 -> T_IsSemigroup_194
d_isSemigroup_378 T_IsCancellativeCommutativeSemiring_1462
v0
  = (T_IsMonoid_358 -> T_IsSemigroup_194) -> Any -> T_IsSemigroup_194
forall a b. a -> b
coe
      T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368
      ((T_IsCommutativeMonoid_406 -> T_IsMonoid_358) -> Any -> Any
forall a b. a -> b
coe
         T_IsCommutativeMonoid_406 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_416
         ((T_IsSemiringWithoutAnnihilatingZero_1142
 -> T_IsCommutativeMonoid_406)
-> Any -> Any
forall a b. a -> b
coe
            T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsCommutativeMonoid_406
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1158
            ((T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142)
-> Any -> Any
forall a b. a -> b
coe
               T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1252
               ((T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238) -> Any -> Any
forall a b. a -> b
coe
                  T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238
MAlonzo.Code.Algebra.Structures.d_isSemiring_1358
                  ((T_IsCancellativeCommutativeSemiring_1462
 -> T_IsCommutativeSemiring_1344)
-> Any -> Any
forall a b. a -> b
coe
                     T_IsCancellativeCommutativeSemiring_1462
-> T_IsCommutativeSemiring_1344
MAlonzo.Code.Algebra.Structures.d_isCommutativeSemiring_1476
                     (T_IsCancellativeCommutativeSemiring_1462 -> Any
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1462
v0))))))
-- Data.Bool.Properties._.IsCancellativeCommutativeSemiring.distrib
d_distrib_380 ::
  MAlonzo.Code.Algebra.Structures.T_IsCancellativeCommutativeSemiring_1462 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_distrib_380 :: T_IsCancellativeCommutativeSemiring_1462 -> T_Σ_14
d_distrib_380 T_IsCancellativeCommutativeSemiring_1462
v0
  = (T_IsSemiringWithoutAnnihilatingZero_1142 -> T_Σ_14)
-> Any -> T_Σ_14
forall a b. a -> b
coe
      T_IsSemiringWithoutAnnihilatingZero_1142 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_distrib_1162
      ((T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142)
-> Any -> Any
forall a b. a -> b
coe
         T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1252
         ((T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238) -> Any -> Any
forall a b. a -> b
coe
            T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238
MAlonzo.Code.Algebra.Structures.d_isSemiring_1358
            ((T_IsCancellativeCommutativeSemiring_1462
 -> T_IsCommutativeSemiring_1344)
-> Any -> Any
forall a b. a -> b
coe
               T_IsCancellativeCommutativeSemiring_1462
-> T_IsCommutativeSemiring_1344
MAlonzo.Code.Algebra.Structures.d_isCommutativeSemiring_1476
               (T_IsCancellativeCommutativeSemiring_1462 -> Any
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1462
v0))))
-- Data.Bool.Properties._.IsCancellativeCommutativeSemiring.isCommutativeSemiring
d_isCommutativeSemiring_386 ::
  MAlonzo.Code.Algebra.Structures.T_IsCancellativeCommutativeSemiring_1462 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiring_1344
d_isCommutativeSemiring_386 :: T_IsCancellativeCommutativeSemiring_1462
-> T_IsCommutativeSemiring_1344
d_isCommutativeSemiring_386 T_IsCancellativeCommutativeSemiring_1462
v0
  = (T_IsCancellativeCommutativeSemiring_1462
 -> T_IsCommutativeSemiring_1344)
-> Any -> T_IsCommutativeSemiring_1344
forall a b. a -> b
coe
      T_IsCancellativeCommutativeSemiring_1462
-> T_IsCommutativeSemiring_1344
MAlonzo.Code.Algebra.Structures.d_isCommutativeSemiring_1476
      (T_IsCancellativeCommutativeSemiring_1462 -> Any
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1462
v0)
-- Data.Bool.Properties._.IsCancellativeCommutativeSemiring.isEquivalence
d_isEquivalence_390 ::
  MAlonzo.Code.Algebra.Structures.T_IsCancellativeCommutativeSemiring_1462 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_390 :: T_IsCancellativeCommutativeSemiring_1462 -> T_IsEquivalence_26
d_isEquivalence_390 T_IsCancellativeCommutativeSemiring_1462
v0
  = (T_IsMagma_86 -> T_IsEquivalence_26) -> Any -> T_IsEquivalence_26
forall a b. a -> b
coe
      T_IsMagma_86 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_94
      ((T_IsSemigroup_194 -> T_IsMagma_86) -> Any -> Any
forall a b. a -> b
coe
         T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202
         ((T_IsMonoid_358 -> T_IsSemigroup_194) -> Any -> Any
forall a b. a -> b
coe
            T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368
            ((T_IsCommutativeMonoid_406 -> T_IsMonoid_358) -> Any -> Any
forall a b. a -> b
coe
               T_IsCommutativeMonoid_406 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_416
               ((T_IsSemiringWithoutAnnihilatingZero_1142
 -> T_IsCommutativeMonoid_406)
-> Any -> Any
forall a b. a -> b
coe
                  T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsCommutativeMonoid_406
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1158
                  ((T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142)
-> Any -> Any
forall a b. a -> b
coe
                     T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1252
                     ((T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238) -> Any -> Any
forall a b. a -> b
coe
                        T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238
MAlonzo.Code.Algebra.Structures.d_isSemiring_1358
                        ((T_IsCancellativeCommutativeSemiring_1462
 -> T_IsCommutativeSemiring_1344)
-> Any -> Any
forall a b. a -> b
coe
                           T_IsCancellativeCommutativeSemiring_1462
-> T_IsCommutativeSemiring_1344
MAlonzo.Code.Algebra.Structures.d_isCommutativeSemiring_1476
                           (T_IsCancellativeCommutativeSemiring_1462 -> Any
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1462
v0))))))))
-- Data.Bool.Properties._.IsCancellativeCommutativeSemiring.isNearSemiring
d_isNearSemiring_392 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsCancellativeCommutativeSemiring_1462 ->
  MAlonzo.Code.Algebra.Structures.T_IsNearSemiring_876
d_isNearSemiring_392 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> T_IsCancellativeCommutativeSemiring_1462
-> T_IsNearSemiring_876
d_isNearSemiring_392 ~Bool -> Bool -> Bool
v0 ~Bool -> Bool -> Bool
v1 ~Bool
v2 ~Bool
v3 T_IsCancellativeCommutativeSemiring_1462
v4 = T_IsCancellativeCommutativeSemiring_1462 -> T_IsNearSemiring_876
du_isNearSemiring_392 T_IsCancellativeCommutativeSemiring_1462
v4
du_isNearSemiring_392 ::
  MAlonzo.Code.Algebra.Structures.T_IsCancellativeCommutativeSemiring_1462 ->
  MAlonzo.Code.Algebra.Structures.T_IsNearSemiring_876
du_isNearSemiring_392 :: T_IsCancellativeCommutativeSemiring_1462 -> T_IsNearSemiring_876
du_isNearSemiring_392 T_IsCancellativeCommutativeSemiring_1462
v0
  = let v1 :: T_IsCommutativeSemiring_1344
v1
          = T_IsCancellativeCommutativeSemiring_1462
-> T_IsCommutativeSemiring_1344
MAlonzo.Code.Algebra.Structures.d_isCommutativeSemiring_1476
              (T_IsCancellativeCommutativeSemiring_1462
-> T_IsCancellativeCommutativeSemiring_1462
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1462
v0) in
    Any -> T_IsNearSemiring_876
forall a b. a -> b
coe
      (let v2 :: T_IsSemiring_1238
v2
             = T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238
MAlonzo.Code.Algebra.Structures.d_isSemiring_1358 (T_IsCommutativeSemiring_1344 -> T_IsCommutativeSemiring_1344
forall a b. a -> b
coe T_IsCommutativeSemiring_1344
v1) in
       Any -> Any
forall a b. a -> b
coe
         ((T_IsSemiringWithoutOne_952 -> T_IsNearSemiring_876) -> Any -> Any
forall a b. a -> b
coe
            T_IsSemiringWithoutOne_952 -> T_IsNearSemiring_876
MAlonzo.Code.Algebra.Structures.du_isNearSemiring_990
            ((T_IsSemiring_1238 -> T_IsSemiringWithoutOne_952) -> Any -> Any
forall a b. a -> b
coe
               T_IsSemiring_1238 -> T_IsSemiringWithoutOne_952
MAlonzo.Code.Algebra.Structures.du_isSemiringWithoutOne_1326
               (T_IsSemiring_1238 -> Any
forall a b. a -> b
coe T_IsSemiring_1238
v2))))
-- Data.Bool.Properties._.IsCancellativeCommutativeSemiring.isSemiring
d_isSemiring_396 ::
  MAlonzo.Code.Algebra.Structures.T_IsCancellativeCommutativeSemiring_1462 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemiring_1238
d_isSemiring_396 :: T_IsCancellativeCommutativeSemiring_1462 -> T_IsSemiring_1238
d_isSemiring_396 T_IsCancellativeCommutativeSemiring_1462
v0
  = (T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238)
-> Any -> T_IsSemiring_1238
forall a b. a -> b
coe
      T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238
MAlonzo.Code.Algebra.Structures.d_isSemiring_1358
      ((T_IsCancellativeCommutativeSemiring_1462
 -> T_IsCommutativeSemiring_1344)
-> Any -> Any
forall a b. a -> b
coe
         T_IsCancellativeCommutativeSemiring_1462
-> T_IsCommutativeSemiring_1344
MAlonzo.Code.Algebra.Structures.d_isCommutativeSemiring_1476
         (T_IsCancellativeCommutativeSemiring_1462 -> Any
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1462
v0))
-- Data.Bool.Properties._.IsCancellativeCommutativeSemiring.isSemiringWithoutAnnihilatingZero
d_isSemiringWithoutAnnihilatingZero_398 ::
  MAlonzo.Code.Algebra.Structures.T_IsCancellativeCommutativeSemiring_1462 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutAnnihilatingZero_1142
d_isSemiringWithoutAnnihilatingZero_398 :: T_IsCancellativeCommutativeSemiring_1462
-> T_IsSemiringWithoutAnnihilatingZero_1142
d_isSemiringWithoutAnnihilatingZero_398 T_IsCancellativeCommutativeSemiring_1462
v0
  = (T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142)
-> Any -> T_IsSemiringWithoutAnnihilatingZero_1142
forall a b. a -> b
coe
      T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1252
      ((T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238) -> Any -> Any
forall a b. a -> b
coe
         T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238
MAlonzo.Code.Algebra.Structures.d_isSemiring_1358
         ((T_IsCancellativeCommutativeSemiring_1462
 -> T_IsCommutativeSemiring_1344)
-> Any -> Any
forall a b. a -> b
coe
            T_IsCancellativeCommutativeSemiring_1462
-> T_IsCommutativeSemiring_1344
MAlonzo.Code.Algebra.Structures.d_isCommutativeSemiring_1476
            (T_IsCancellativeCommutativeSemiring_1462 -> Any
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1462
v0)))
-- Data.Bool.Properties._.IsCancellativeCommutativeSemiring.isSemiringWithoutOne
d_isSemiringWithoutOne_400 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsCancellativeCommutativeSemiring_1462 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutOne_952
d_isSemiringWithoutOne_400 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> T_IsCancellativeCommutativeSemiring_1462
-> T_IsSemiringWithoutOne_952
d_isSemiringWithoutOne_400 ~Bool -> Bool -> Bool
v0 ~Bool -> Bool -> Bool
v1 ~Bool
v2 ~Bool
v3 T_IsCancellativeCommutativeSemiring_1462
v4
  = T_IsCancellativeCommutativeSemiring_1462
-> T_IsSemiringWithoutOne_952
du_isSemiringWithoutOne_400 T_IsCancellativeCommutativeSemiring_1462
v4
du_isSemiringWithoutOne_400 ::
  MAlonzo.Code.Algebra.Structures.T_IsCancellativeCommutativeSemiring_1462 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutOne_952
du_isSemiringWithoutOne_400 :: T_IsCancellativeCommutativeSemiring_1462
-> T_IsSemiringWithoutOne_952
du_isSemiringWithoutOne_400 T_IsCancellativeCommutativeSemiring_1462
v0
  = let v1 :: T_IsCommutativeSemiring_1344
v1
          = T_IsCancellativeCommutativeSemiring_1462
-> T_IsCommutativeSemiring_1344
MAlonzo.Code.Algebra.Structures.d_isCommutativeSemiring_1476
              (T_IsCancellativeCommutativeSemiring_1462
-> T_IsCancellativeCommutativeSemiring_1462
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1462
v0) in
    Any -> T_IsSemiringWithoutOne_952
forall a b. a -> b
coe
      ((T_IsSemiring_1238 -> T_IsSemiringWithoutOne_952) -> Any -> Any
forall a b. a -> b
coe
         T_IsSemiring_1238 -> T_IsSemiringWithoutOne_952
MAlonzo.Code.Algebra.Structures.du_isSemiringWithoutOne_1326
         ((T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238) -> Any -> Any
forall a b. a -> b
coe T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238
MAlonzo.Code.Algebra.Structures.d_isSemiring_1358 (T_IsCommutativeSemiring_1344 -> Any
forall a b. a -> b
coe T_IsCommutativeSemiring_1344
v1)))
-- Data.Bool.Properties._.IsCancellativeCommutativeSemiring.zero
d_zero_412 ::
  MAlonzo.Code.Algebra.Structures.T_IsCancellativeCommutativeSemiring_1462 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_zero_412 :: T_IsCancellativeCommutativeSemiring_1462 -> T_Σ_14
d_zero_412 T_IsCancellativeCommutativeSemiring_1462
v0
  = (T_IsSemiring_1238 -> T_Σ_14) -> Any -> T_Σ_14
forall a b. a -> b
coe
      T_IsSemiring_1238 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_zero_1254
      ((T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238) -> Any -> Any
forall a b. a -> b
coe
         T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238
MAlonzo.Code.Algebra.Structures.d_isSemiring_1358
         ((T_IsCancellativeCommutativeSemiring_1462
 -> T_IsCommutativeSemiring_1344)
-> Any -> Any
forall a b. a -> b
coe
            T_IsCancellativeCommutativeSemiring_1462
-> T_IsCommutativeSemiring_1344
MAlonzo.Code.Algebra.Structures.d_isCommutativeSemiring_1476
            (T_IsCancellativeCommutativeSemiring_1462 -> Any
forall a b. a -> b
coe T_IsCancellativeCommutativeSemiring_1462
v0)))
-- Data.Bool.Properties._.IsCommutativeMagma.comm
d_comm_420 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMagma_122 ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_comm_420 :: T_IsCommutativeMagma_122 -> Bool -> Bool -> T__'8801'__12
d_comm_420 = T_IsCommutativeMagma_122 -> Bool -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsCommutativeMagma.isEquivalence
d_isEquivalence_422 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMagma_122 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_422 :: T_IsCommutativeMagma_122 -> T_IsEquivalence_26
d_isEquivalence_422 T_IsCommutativeMagma_122
v0
  = (T_IsMagma_86 -> T_IsEquivalence_26) -> Any -> T_IsEquivalence_26
forall a b. a -> b
coe
      T_IsMagma_86 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_94
      ((T_IsCommutativeMagma_122 -> T_IsMagma_86) -> Any -> Any
forall a b. a -> b
coe T_IsCommutativeMagma_122 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_130 (T_IsCommutativeMagma_122 -> Any
forall a b. a -> b
coe T_IsCommutativeMagma_122
v0))
-- Data.Bool.Properties._.IsCommutativeMagma.isMagma
d_isMagma_424 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMagma_122 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_86
d_isMagma_424 :: T_IsCommutativeMagma_122 -> T_IsMagma_86
d_isMagma_424 T_IsCommutativeMagma_122
v0
  = (T_IsCommutativeMagma_122 -> T_IsMagma_86) -> Any -> T_IsMagma_86
forall a b. a -> b
coe T_IsCommutativeMagma_122 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_130 (T_IsCommutativeMagma_122 -> Any
forall a b. a -> b
coe T_IsCommutativeMagma_122
v0)
-- Data.Bool.Properties._.IsCommutativeMagma.∙-cong
d_'8729''45'cong_438 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMagma_122 ->
  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_438 :: T_IsCommutativeMagma_122
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong_438 = T_IsCommutativeMagma_122
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsCommutativeMonoid.assoc
d_assoc_446 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMonoid_406 ->
  Bool ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_assoc_446 :: T_IsCommutativeMonoid_406 -> Bool -> Bool -> Bool -> T__'8801'__12
d_assoc_446 = T_IsCommutativeMonoid_406 -> Bool -> Bool -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsCommutativeMonoid.comm
d_comm_448 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMonoid_406 ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_comm_448 :: T_IsCommutativeMonoid_406 -> Bool -> Bool -> T__'8801'__12
d_comm_448 = T_IsCommutativeMonoid_406 -> Bool -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsCommutativeMonoid.identity
d_identity_450 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMonoid_406 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_identity_450 :: T_IsCommutativeMonoid_406 -> T_Σ_14
d_identity_450 T_IsCommutativeMonoid_406
v0
  = (T_IsMonoid_358 -> T_Σ_14) -> Any -> T_Σ_14
forall a b. a -> b
coe
      T_IsMonoid_358 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_identity_370
      ((T_IsCommutativeMonoid_406 -> T_IsMonoid_358) -> Any -> Any
forall a b. a -> b
coe T_IsCommutativeMonoid_406 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_416 (T_IsCommutativeMonoid_406 -> Any
forall a b. a -> b
coe T_IsCommutativeMonoid_406
v0))
-- Data.Bool.Properties._.IsCommutativeMonoid.isEquivalence
d_isEquivalence_460 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMonoid_406 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_460 :: T_IsCommutativeMonoid_406 -> T_IsEquivalence_26
d_isEquivalence_460 T_IsCommutativeMonoid_406
v0
  = (T_IsMagma_86 -> T_IsEquivalence_26) -> Any -> T_IsEquivalence_26
forall a b. a -> b
coe
      T_IsMagma_86 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_94
      ((T_IsSemigroup_194 -> T_IsMagma_86) -> Any -> Any
forall a b. a -> b
coe
         T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202
         ((T_IsMonoid_358 -> T_IsSemigroup_194) -> Any -> Any
forall a b. a -> b
coe
            T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368
            ((T_IsCommutativeMonoid_406 -> T_IsMonoid_358) -> Any -> Any
forall a b. a -> b
coe T_IsCommutativeMonoid_406 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_416 (T_IsCommutativeMonoid_406 -> Any
forall a b. a -> b
coe T_IsCommutativeMonoid_406
v0))))
-- Data.Bool.Properties._.IsCommutativeMonoid.isMagma
d_isMagma_462 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMonoid_406 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_86
d_isMagma_462 :: T_IsCommutativeMonoid_406 -> T_IsMagma_86
d_isMagma_462 T_IsCommutativeMonoid_406
v0
  = (T_IsSemigroup_194 -> T_IsMagma_86) -> Any -> T_IsMagma_86
forall a b. a -> b
coe
      T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202
      ((T_IsMonoid_358 -> T_IsSemigroup_194) -> Any -> Any
forall a b. a -> b
coe
         T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368
         ((T_IsCommutativeMonoid_406 -> T_IsMonoid_358) -> Any -> Any
forall a b. a -> b
coe T_IsCommutativeMonoid_406 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_416 (T_IsCommutativeMonoid_406 -> Any
forall a b. a -> b
coe T_IsCommutativeMonoid_406
v0)))
-- Data.Bool.Properties._.IsCommutativeMonoid.isMonoid
d_isMonoid_464 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMonoid_406 ->
  MAlonzo.Code.Algebra.Structures.T_IsMonoid_358
d_isMonoid_464 :: T_IsCommutativeMonoid_406 -> T_IsMonoid_358
d_isMonoid_464 T_IsCommutativeMonoid_406
v0
  = (T_IsCommutativeMonoid_406 -> T_IsMonoid_358)
-> Any -> T_IsMonoid_358
forall a b. a -> b
coe T_IsCommutativeMonoid_406 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_416 (T_IsCommutativeMonoid_406 -> Any
forall a b. a -> b
coe T_IsCommutativeMonoid_406
v0)
-- Data.Bool.Properties._.IsCommutativeMonoid.isSemigroup
d_isSemigroup_468 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMonoid_406 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_194
d_isSemigroup_468 :: T_IsCommutativeMonoid_406 -> T_IsSemigroup_194
d_isSemigroup_468 T_IsCommutativeMonoid_406
v0
  = (T_IsMonoid_358 -> T_IsSemigroup_194) -> Any -> T_IsSemigroup_194
forall a b. a -> b
coe
      T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368
      ((T_IsCommutativeMonoid_406 -> T_IsMonoid_358) -> Any -> Any
forall a b. a -> b
coe T_IsCommutativeMonoid_406 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_416 (T_IsCommutativeMonoid_406 -> Any
forall a b. a -> b
coe T_IsCommutativeMonoid_406
v0))
-- Data.Bool.Properties._.IsCommutativeMonoid.∙-cong
d_'8729''45'cong_480 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMonoid_406 ->
  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_480 :: T_IsCommutativeMonoid_406
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong_480 = T_IsCommutativeMonoid_406
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsCommutativeRing.assoc
d_assoc_490 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeRing_1720 ->
  Bool ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_assoc_490 :: T_IsCommutativeRing_1720 -> Bool -> Bool -> Bool -> T__'8801'__12
d_assoc_490 = T_IsCommutativeRing_1720 -> Bool -> Bool -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsCommutativeRing.*-comm
d_'42''45'comm_492 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeRing_1720 ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'42''45'comm_492 :: T_IsCommutativeRing_1720 -> Bool -> Bool -> T__'8801'__12
d_'42''45'comm_492 = T_IsCommutativeRing_1720 -> Bool -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsCommutativeRing.∙-cong
d_'8729''45'cong_494 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeRing_1720 ->
  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_494 :: T_IsCommutativeRing_1720
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong_494 = T_IsCommutativeRing_1720
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsCommutativeRing.identity
d_identity_500 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeRing_1720 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_identity_500 :: T_IsCommutativeRing_1720 -> T_Σ_14
d_identity_500 T_IsCommutativeRing_1720
v0
  = (T_IsMonoid_358 -> T_Σ_14) -> Any -> T_Σ_14
forall a b. a -> b
coe
      T_IsMonoid_358 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_identity_370
      ((T_IsRing_1584 -> T_IsMonoid_358) -> Any -> Any
forall a b. a -> b
coe
         T_IsRing_1584 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_'42''45'isMonoid_1606
         ((T_IsCommutativeRing_1720 -> T_IsRing_1584) -> Any -> Any
forall a b. a -> b
coe T_IsCommutativeRing_1720 -> T_IsRing_1584
MAlonzo.Code.Algebra.Structures.d_isRing_1736 (T_IsCommutativeRing_1720 -> Any
forall a b. a -> b
coe T_IsCommutativeRing_1720
v0)))
-- Data.Bool.Properties._.IsCommutativeRing.isMagma
d_isMagma_512 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeRing_1720 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_86
d_isMagma_512 :: T_IsCommutativeRing_1720 -> T_IsMagma_86
d_isMagma_512 T_IsCommutativeRing_1720
v0
  = (T_IsSemigroup_194 -> T_IsMagma_86) -> Any -> T_IsMagma_86
forall a b. a -> b
coe
      T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202
      ((T_IsMonoid_358 -> T_IsSemigroup_194) -> Any -> Any
forall a b. a -> b
coe
         T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368
         ((T_IsRing_1584 -> T_IsMonoid_358) -> Any -> Any
forall a b. a -> b
coe
            T_IsRing_1584 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_'42''45'isMonoid_1606
            ((T_IsCommutativeRing_1720 -> T_IsRing_1584) -> Any -> Any
forall a b. a -> b
coe T_IsCommutativeRing_1720 -> T_IsRing_1584
MAlonzo.Code.Algebra.Structures.d_isRing_1736 (T_IsCommutativeRing_1720 -> Any
forall a b. a -> b
coe T_IsCommutativeRing_1720
v0))))
-- Data.Bool.Properties._.IsCommutativeRing.*-isMonoid
d_'42''45'isMonoid_514 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeRing_1720 ->
  MAlonzo.Code.Algebra.Structures.T_IsMonoid_358
d_'42''45'isMonoid_514 :: T_IsCommutativeRing_1720 -> T_IsMonoid_358
d_'42''45'isMonoid_514 T_IsCommutativeRing_1720
v0
  = (T_IsRing_1584 -> T_IsMonoid_358) -> Any -> T_IsMonoid_358
forall a b. a -> b
coe
      T_IsRing_1584 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_'42''45'isMonoid_1606
      ((T_IsCommutativeRing_1720 -> T_IsRing_1584) -> Any -> Any
forall a b. a -> b
coe T_IsCommutativeRing_1720 -> T_IsRing_1584
MAlonzo.Code.Algebra.Structures.d_isRing_1736 (T_IsCommutativeRing_1720 -> Any
forall a b. a -> b
coe T_IsCommutativeRing_1720
v0))
-- Data.Bool.Properties._.IsCommutativeRing.isSemigroup
d_isSemigroup_516 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeRing_1720 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_194
d_isSemigroup_516 :: T_IsCommutativeRing_1720 -> T_IsSemigroup_194
d_isSemigroup_516 T_IsCommutativeRing_1720
v0
  = (T_IsMonoid_358 -> T_IsSemigroup_194) -> Any -> T_IsSemigroup_194
forall a b. a -> b
coe
      T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368
      ((T_IsRing_1584 -> T_IsMonoid_358) -> Any -> Any
forall a b. a -> b
coe
         T_IsRing_1584 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_'42''45'isMonoid_1606
         ((T_IsCommutativeRing_1720 -> T_IsRing_1584) -> Any -> Any
forall a b. a -> b
coe T_IsCommutativeRing_1720 -> T_IsRing_1584
MAlonzo.Code.Algebra.Structures.d_isRing_1736 (T_IsCommutativeRing_1720 -> Any
forall a b. a -> b
coe T_IsCommutativeRing_1720
v0)))
-- Data.Bool.Properties._.IsCommutativeRing.assoc
d_assoc_518 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeRing_1720 ->
  Bool ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_assoc_518 :: T_IsCommutativeRing_1720 -> Bool -> Bool -> Bool -> T__'8801'__12
d_assoc_518 = T_IsCommutativeRing_1720 -> Bool -> Bool -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsCommutativeRing.comm
d_comm_520 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeRing_1720 ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_comm_520 :: T_IsCommutativeRing_1720 -> Bool -> Bool -> T__'8801'__12
d_comm_520 = T_IsCommutativeRing_1720 -> Bool -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsCommutativeRing.∙-cong
d_'8729''45'cong_522 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeRing_1720 ->
  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_522 :: T_IsCommutativeRing_1720
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong_522 = T_IsCommutativeRing_1720
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsCommutativeRing.identity
d_identity_528 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeRing_1720 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_identity_528 :: T_IsCommutativeRing_1720 -> T_Σ_14
d_identity_528 T_IsCommutativeRing_1720
v0
  = (T_IsMonoid_358 -> T_Σ_14) -> Any -> T_Σ_14
forall a b. a -> b
coe
      T_IsMonoid_358 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_identity_370
      ((T_IsGroup_580 -> T_IsMonoid_358) -> Any -> Any
forall a b. a -> b
coe
         T_IsGroup_580 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_594
         ((T_IsAbelianGroup_662 -> T_IsGroup_580) -> Any -> Any
forall a b. a -> b
coe
            T_IsAbelianGroup_662 -> T_IsGroup_580
MAlonzo.Code.Algebra.Structures.d_isGroup_674
            ((T_IsRing_1584 -> T_IsAbelianGroup_662) -> Any -> Any
forall a b. a -> b
coe
               T_IsRing_1584 -> T_IsAbelianGroup_662
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_1604
               ((T_IsCommutativeRing_1720 -> T_IsRing_1584) -> Any -> Any
forall a b. a -> b
coe T_IsCommutativeRing_1720 -> T_IsRing_1584
MAlonzo.Code.Algebra.Structures.d_isRing_1736 (T_IsCommutativeRing_1720 -> Any
forall a b. a -> b
coe T_IsCommutativeRing_1720
v0)))))
-- Data.Bool.Properties._.IsCommutativeRing.+-isAbelianGroup
d_'43''45'isAbelianGroup_534 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeRing_1720 ->
  MAlonzo.Code.Algebra.Structures.T_IsAbelianGroup_662
d_'43''45'isAbelianGroup_534 :: T_IsCommutativeRing_1720 -> T_IsAbelianGroup_662
d_'43''45'isAbelianGroup_534 T_IsCommutativeRing_1720
v0
  = (T_IsRing_1584 -> T_IsAbelianGroup_662)
-> Any -> T_IsAbelianGroup_662
forall a b. a -> b
coe
      T_IsRing_1584 -> T_IsAbelianGroup_662
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_1604
      ((T_IsCommutativeRing_1720 -> T_IsRing_1584) -> Any -> Any
forall a b. a -> b
coe T_IsCommutativeRing_1720 -> T_IsRing_1584
MAlonzo.Code.Algebra.Structures.d_isRing_1736 (T_IsCommutativeRing_1720 -> Any
forall a b. a -> b
coe T_IsCommutativeRing_1720
v0))
-- Data.Bool.Properties._.IsCommutativeRing.isGroup
d_isGroup_542 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeRing_1720 ->
  MAlonzo.Code.Algebra.Structures.T_IsGroup_580
d_isGroup_542 :: T_IsCommutativeRing_1720 -> T_IsGroup_580
d_isGroup_542 T_IsCommutativeRing_1720
v0
  = (T_IsAbelianGroup_662 -> T_IsGroup_580) -> Any -> T_IsGroup_580
forall a b. a -> b
coe
      T_IsAbelianGroup_662 -> T_IsGroup_580
MAlonzo.Code.Algebra.Structures.d_isGroup_674
      ((T_IsRing_1584 -> T_IsAbelianGroup_662) -> Any -> Any
forall a b. a -> b
coe
         T_IsRing_1584 -> T_IsAbelianGroup_662
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_1604
         ((T_IsCommutativeRing_1720 -> T_IsRing_1584) -> Any -> Any
forall a b. a -> b
coe T_IsCommutativeRing_1720 -> T_IsRing_1584
MAlonzo.Code.Algebra.Structures.d_isRing_1736 (T_IsCommutativeRing_1720 -> Any
forall a b. a -> b
coe T_IsCommutativeRing_1720
v0)))
-- Data.Bool.Properties._.IsCommutativeRing.isMagma
d_isMagma_544 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeRing_1720 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_86
d_isMagma_544 :: T_IsCommutativeRing_1720 -> T_IsMagma_86
d_isMagma_544 T_IsCommutativeRing_1720
v0
  = (T_IsSemigroup_194 -> T_IsMagma_86) -> Any -> T_IsMagma_86
forall a b. a -> b
coe
      T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202
      ((T_IsMonoid_358 -> T_IsSemigroup_194) -> Any -> Any
forall a b. a -> b
coe
         T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368
         ((T_IsGroup_580 -> T_IsMonoid_358) -> Any -> Any
forall a b. a -> b
coe
            T_IsGroup_580 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_594
            ((T_IsAbelianGroup_662 -> T_IsGroup_580) -> Any -> Any
forall a b. a -> b
coe
               T_IsAbelianGroup_662 -> T_IsGroup_580
MAlonzo.Code.Algebra.Structures.d_isGroup_674
               ((T_IsRing_1584 -> T_IsAbelianGroup_662) -> Any -> Any
forall a b. a -> b
coe
                  T_IsRing_1584 -> T_IsAbelianGroup_662
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_1604
                  ((T_IsCommutativeRing_1720 -> T_IsRing_1584) -> Any -> Any
forall a b. a -> b
coe T_IsCommutativeRing_1720 -> T_IsRing_1584
MAlonzo.Code.Algebra.Structures.d_isRing_1736 (T_IsCommutativeRing_1720 -> Any
forall a b. a -> b
coe T_IsCommutativeRing_1720
v0))))))
-- Data.Bool.Properties._.IsCommutativeRing.isMonoid
d_isMonoid_546 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeRing_1720 ->
  MAlonzo.Code.Algebra.Structures.T_IsMonoid_358
d_isMonoid_546 :: T_IsCommutativeRing_1720 -> T_IsMonoid_358
d_isMonoid_546 T_IsCommutativeRing_1720
v0
  = (T_IsGroup_580 -> T_IsMonoid_358) -> Any -> T_IsMonoid_358
forall a b. a -> b
coe
      T_IsGroup_580 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_594
      ((T_IsAbelianGroup_662 -> T_IsGroup_580) -> Any -> Any
forall a b. a -> b
coe
         T_IsAbelianGroup_662 -> T_IsGroup_580
MAlonzo.Code.Algebra.Structures.d_isGroup_674
         ((T_IsRing_1584 -> T_IsAbelianGroup_662) -> Any -> Any
forall a b. a -> b
coe
            T_IsRing_1584 -> T_IsAbelianGroup_662
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_1604
            ((T_IsCommutativeRing_1720 -> T_IsRing_1584) -> Any -> Any
forall a b. a -> b
coe T_IsCommutativeRing_1720 -> T_IsRing_1584
MAlonzo.Code.Algebra.Structures.d_isRing_1736 (T_IsCommutativeRing_1720 -> Any
forall a b. a -> b
coe T_IsCommutativeRing_1720
v0))))
-- Data.Bool.Properties._.IsCommutativeRing.isSemigroup
d_isSemigroup_548 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeRing_1720 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_194
d_isSemigroup_548 :: T_IsCommutativeRing_1720 -> T_IsSemigroup_194
d_isSemigroup_548 T_IsCommutativeRing_1720
v0
  = (T_IsMonoid_358 -> T_IsSemigroup_194) -> Any -> T_IsSemigroup_194
forall a b. a -> b
coe
      T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368
      ((T_IsGroup_580 -> T_IsMonoid_358) -> Any -> Any
forall a b. a -> b
coe
         T_IsGroup_580 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_594
         ((T_IsAbelianGroup_662 -> T_IsGroup_580) -> Any -> Any
forall a b. a -> b
coe
            T_IsAbelianGroup_662 -> T_IsGroup_580
MAlonzo.Code.Algebra.Structures.d_isGroup_674
            ((T_IsRing_1584 -> T_IsAbelianGroup_662) -> Any -> Any
forall a b. a -> b
coe
               T_IsRing_1584 -> T_IsAbelianGroup_662
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_1604
               ((T_IsCommutativeRing_1720 -> T_IsRing_1584) -> Any -> Any
forall a b. a -> b
coe T_IsCommutativeRing_1720 -> T_IsRing_1584
MAlonzo.Code.Algebra.Structures.d_isRing_1736 (T_IsCommutativeRing_1720 -> Any
forall a b. a -> b
coe T_IsCommutativeRing_1720
v0)))))
-- Data.Bool.Properties._.IsCommutativeRing.⁻¹-cong
d_'8315''185''45'cong_550 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeRing_1720 ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8315''185''45'cong_550 :: T_IsCommutativeRing_1720
-> Bool -> Bool -> T__'8801'__12 -> T__'8801'__12
d_'8315''185''45'cong_550 = T_IsCommutativeRing_1720
-> Bool -> Bool -> T__'8801'__12 -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsCommutativeRing.inverse
d_inverse_552 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeRing_1720 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_inverse_552 :: T_IsCommutativeRing_1720 -> T_Σ_14
d_inverse_552 T_IsCommutativeRing_1720
v0
  = (T_IsGroup_580 -> T_Σ_14) -> Any -> T_Σ_14
forall a b. a -> b
coe
      T_IsGroup_580 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_inverse_596
      ((T_IsAbelianGroup_662 -> T_IsGroup_580) -> Any -> Any
forall a b. a -> b
coe
         T_IsAbelianGroup_662 -> T_IsGroup_580
MAlonzo.Code.Algebra.Structures.d_isGroup_674
         ((T_IsRing_1584 -> T_IsAbelianGroup_662) -> Any -> Any
forall a b. a -> b
coe
            T_IsRing_1584 -> T_IsAbelianGroup_662
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_1604
            ((T_IsCommutativeRing_1720 -> T_IsRing_1584) -> Any -> Any
forall a b. a -> b
coe T_IsCommutativeRing_1720 -> T_IsRing_1584
MAlonzo.Code.Algebra.Structures.d_isRing_1736 (T_IsCommutativeRing_1720 -> Any
forall a b. a -> b
coe T_IsCommutativeRing_1720
v0))))
-- Data.Bool.Properties._.IsCommutativeRing.distrib
d_distrib_558 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeRing_1720 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_distrib_558 :: T_IsCommutativeRing_1720 -> T_Σ_14
d_distrib_558 T_IsCommutativeRing_1720
v0
  = (T_IsRing_1584 -> T_Σ_14) -> Any -> T_Σ_14
forall a b. a -> b
coe
      T_IsRing_1584 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_distrib_1608
      ((T_IsCommutativeRing_1720 -> T_IsRing_1584) -> Any -> Any
forall a b. a -> b
coe T_IsCommutativeRing_1720 -> T_IsRing_1584
MAlonzo.Code.Algebra.Structures.d_isRing_1736 (T_IsCommutativeRing_1720 -> Any
forall a b. a -> b
coe T_IsCommutativeRing_1720
v0))
-- Data.Bool.Properties._.IsCommutativeRing.isEquivalence
d_isEquivalence_568 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeRing_1720 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_568 :: T_IsCommutativeRing_1720 -> T_IsEquivalence_26
d_isEquivalence_568 T_IsCommutativeRing_1720
v0
  = (T_IsMagma_86 -> T_IsEquivalence_26) -> Any -> T_IsEquivalence_26
forall a b. a -> b
coe
      T_IsMagma_86 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_94
      ((T_IsSemigroup_194 -> T_IsMagma_86) -> Any -> Any
forall a b. a -> b
coe
         T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202
         ((T_IsMonoid_358 -> T_IsSemigroup_194) -> Any -> Any
forall a b. a -> b
coe
            T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368
            ((T_IsGroup_580 -> T_IsMonoid_358) -> Any -> Any
forall a b. a -> b
coe
               T_IsGroup_580 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_594
               ((T_IsAbelianGroup_662 -> T_IsGroup_580) -> Any -> Any
forall a b. a -> b
coe
                  T_IsAbelianGroup_662 -> T_IsGroup_580
MAlonzo.Code.Algebra.Structures.d_isGroup_674
                  ((T_IsRing_1584 -> T_IsAbelianGroup_662) -> Any -> Any
forall a b. a -> b
coe
                     T_IsRing_1584 -> T_IsAbelianGroup_662
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_1604
                     ((T_IsCommutativeRing_1720 -> T_IsRing_1584) -> Any -> Any
forall a b. a -> b
coe T_IsCommutativeRing_1720 -> T_IsRing_1584
MAlonzo.Code.Algebra.Structures.d_isRing_1736 (T_IsCommutativeRing_1720 -> Any
forall a b. a -> b
coe T_IsCommutativeRing_1720
v0)))))))
-- Data.Bool.Properties._.IsCommutativeRing.isNearSemiring
d_isNearSemiring_570 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeRing_1720 ->
  MAlonzo.Code.Algebra.Structures.T_IsNearSemiring_876
d_isNearSemiring_570 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsCommutativeRing_1720
-> T_IsNearSemiring_876
d_isNearSemiring_570 ~Bool -> Bool -> Bool
v0 ~Bool -> Bool -> Bool
v1 ~Bool -> Bool
v2 ~Bool
v3 ~Bool
v4 T_IsCommutativeRing_1720
v5
  = T_IsCommutativeRing_1720 -> T_IsNearSemiring_876
du_isNearSemiring_570 T_IsCommutativeRing_1720
v5
du_isNearSemiring_570 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeRing_1720 ->
  MAlonzo.Code.Algebra.Structures.T_IsNearSemiring_876
du_isNearSemiring_570 :: T_IsCommutativeRing_1720 -> T_IsNearSemiring_876
du_isNearSemiring_570 T_IsCommutativeRing_1720
v0
  = let v1 :: T_IsRing_1584
v1
          = T_IsCommutativeRing_1720 -> T_IsRing_1584
MAlonzo.Code.Algebra.Structures.d_isRing_1736 (T_IsCommutativeRing_1720 -> T_IsCommutativeRing_1720
forall a b. a -> b
coe T_IsCommutativeRing_1720
v0) in
    Any -> T_IsNearSemiring_876
forall a b. a -> b
coe
      (let v2 :: t
v2
             = (T_IsRing_1584 -> T_IsSemiring_1238) -> Any -> t
forall a b. a -> b
coe
                 T_IsRing_1584 -> T_IsSemiring_1238
MAlonzo.Code.Algebra.Structures.du_isSemiring_1698 (T_IsRing_1584 -> Any
forall a b. a -> b
coe T_IsRing_1584
v1) in
       Any -> Any
forall a b. a -> b
coe
         ((T_IsSemiringWithoutOne_952 -> T_IsNearSemiring_876) -> Any -> Any
forall a b. a -> b
coe
            T_IsSemiringWithoutOne_952 -> T_IsNearSemiring_876
MAlonzo.Code.Algebra.Structures.du_isNearSemiring_990
            ((T_IsSemiring_1238 -> T_IsSemiringWithoutOne_952) -> Any -> Any
forall a b. a -> b
coe
               T_IsSemiring_1238 -> T_IsSemiringWithoutOne_952
MAlonzo.Code.Algebra.Structures.du_isSemiringWithoutOne_1326
               (Any -> Any
forall a b. a -> b
coe Any
forall a. a
v2))))
-- Data.Bool.Properties._.IsCommutativeRing.isRing
d_isRing_574 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeRing_1720 ->
  MAlonzo.Code.Algebra.Structures.T_IsRing_1584
d_isRing_574 :: T_IsCommutativeRing_1720 -> T_IsRing_1584
d_isRing_574 T_IsCommutativeRing_1720
v0
  = (T_IsCommutativeRing_1720 -> T_IsRing_1584) -> Any -> T_IsRing_1584
forall a b. a -> b
coe T_IsCommutativeRing_1720 -> T_IsRing_1584
MAlonzo.Code.Algebra.Structures.d_isRing_1736 (T_IsCommutativeRing_1720 -> Any
forall a b. a -> b
coe T_IsCommutativeRing_1720
v0)
-- Data.Bool.Properties._.IsCommutativeRing.isSemiring
d_isSemiring_576 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeRing_1720 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemiring_1238
d_isSemiring_576 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsCommutativeRing_1720
-> T_IsSemiring_1238
d_isSemiring_576 ~Bool -> Bool -> Bool
v0 ~Bool -> Bool -> Bool
v1 ~Bool -> Bool
v2 ~Bool
v3 ~Bool
v4 T_IsCommutativeRing_1720
v5 = T_IsCommutativeRing_1720 -> T_IsSemiring_1238
du_isSemiring_576 T_IsCommutativeRing_1720
v5
du_isSemiring_576 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeRing_1720 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemiring_1238
du_isSemiring_576 :: T_IsCommutativeRing_1720 -> T_IsSemiring_1238
du_isSemiring_576 T_IsCommutativeRing_1720
v0
  = (T_IsRing_1584 -> T_IsSemiring_1238) -> Any -> T_IsSemiring_1238
forall a b. a -> b
coe
      T_IsRing_1584 -> T_IsSemiring_1238
MAlonzo.Code.Algebra.Structures.du_isSemiring_1698
      ((T_IsCommutativeRing_1720 -> T_IsRing_1584) -> Any -> Any
forall a b. a -> b
coe T_IsCommutativeRing_1720 -> T_IsRing_1584
MAlonzo.Code.Algebra.Structures.d_isRing_1736 (T_IsCommutativeRing_1720 -> Any
forall a b. a -> b
coe T_IsCommutativeRing_1720
v0))
-- Data.Bool.Properties._.IsCommutativeRing.isSemiringWithoutOne
d_isSemiringWithoutOne_580 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeRing_1720 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutOne_952
d_isSemiringWithoutOne_580 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsCommutativeRing_1720
-> T_IsSemiringWithoutOne_952
d_isSemiringWithoutOne_580 ~Bool -> Bool -> Bool
v0 ~Bool -> Bool -> Bool
v1 ~Bool -> Bool
v2 ~Bool
v3 ~Bool
v4 T_IsCommutativeRing_1720
v5
  = T_IsCommutativeRing_1720 -> T_IsSemiringWithoutOne_952
du_isSemiringWithoutOne_580 T_IsCommutativeRing_1720
v5
du_isSemiringWithoutOne_580 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeRing_1720 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutOne_952
du_isSemiringWithoutOne_580 :: T_IsCommutativeRing_1720 -> T_IsSemiringWithoutOne_952
du_isSemiringWithoutOne_580 T_IsCommutativeRing_1720
v0
  = let v1 :: T_IsRing_1584
v1
          = T_IsCommutativeRing_1720 -> T_IsRing_1584
MAlonzo.Code.Algebra.Structures.d_isRing_1736 (T_IsCommutativeRing_1720 -> T_IsCommutativeRing_1720
forall a b. a -> b
coe T_IsCommutativeRing_1720
v0) in
    Any -> T_IsSemiringWithoutOne_952
forall a b. a -> b
coe
      ((T_IsSemiring_1238 -> T_IsSemiringWithoutOne_952) -> Any -> Any
forall a b. a -> b
coe
         T_IsSemiring_1238 -> T_IsSemiringWithoutOne_952
MAlonzo.Code.Algebra.Structures.du_isSemiringWithoutOne_1326
         ((T_IsRing_1584 -> T_IsSemiring_1238) -> Any -> Any
forall a b. a -> b
coe T_IsRing_1584 -> T_IsSemiring_1238
MAlonzo.Code.Algebra.Structures.du_isSemiring_1698 (T_IsRing_1584 -> Any
forall a b. a -> b
coe T_IsRing_1584
v1)))
-- Data.Bool.Properties._.IsCommutativeRing.zero
d_zero_596 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeRing_1720 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_zero_596 :: T_IsCommutativeRing_1720 -> T_Σ_14
d_zero_596 T_IsCommutativeRing_1720
v0
  = (T_IsRing_1584 -> T_Σ_14) -> Any -> T_Σ_14
forall a b. a -> b
coe
      T_IsRing_1584 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_zero_1610
      ((T_IsCommutativeRing_1720 -> T_IsRing_1584) -> Any -> Any
forall a b. a -> b
coe T_IsCommutativeRing_1720 -> T_IsRing_1584
MAlonzo.Code.Algebra.Structures.d_isRing_1736 (T_IsCommutativeRing_1720 -> Any
forall a b. a -> b
coe T_IsCommutativeRing_1720
v0))
-- Data.Bool.Properties._.IsCommutativeSemigroup.assoc
d_assoc_604 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_270 ->
  Bool ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_assoc_604 :: T_IsCommutativeSemigroup_270
-> Bool -> Bool -> Bool -> T__'8801'__12
d_assoc_604 = T_IsCommutativeSemigroup_270
-> Bool -> Bool -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsCommutativeSemigroup.comm
d_comm_606 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_270 ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_comm_606 :: T_IsCommutativeSemigroup_270 -> Bool -> Bool -> T__'8801'__12
d_comm_606 = T_IsCommutativeSemigroup_270 -> Bool -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsCommutativeSemigroup.isEquivalence
d_isEquivalence_610 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_270 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_610 :: T_IsCommutativeSemigroup_270 -> T_IsEquivalence_26
d_isEquivalence_610 T_IsCommutativeSemigroup_270
v0
  = (T_IsMagma_86 -> T_IsEquivalence_26) -> Any -> T_IsEquivalence_26
forall a b. a -> b
coe
      T_IsMagma_86 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_94
      ((T_IsSemigroup_194 -> T_IsMagma_86) -> Any -> Any
forall a b. a -> b
coe
         T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202
         ((T_IsCommutativeSemigroup_270 -> T_IsSemigroup_194) -> Any -> Any
forall a b. a -> b
coe T_IsCommutativeSemigroup_270 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_278 (T_IsCommutativeSemigroup_270 -> Any
forall a b. a -> b
coe T_IsCommutativeSemigroup_270
v0)))
-- Data.Bool.Properties._.IsCommutativeSemigroup.isMagma
d_isMagma_612 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_270 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_86
d_isMagma_612 :: T_IsCommutativeSemigroup_270 -> T_IsMagma_86
d_isMagma_612 T_IsCommutativeSemigroup_270
v0
  = (T_IsSemigroup_194 -> T_IsMagma_86) -> Any -> T_IsMagma_86
forall a b. a -> b
coe
      T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202
      ((T_IsCommutativeSemigroup_270 -> T_IsSemigroup_194) -> Any -> Any
forall a b. a -> b
coe T_IsCommutativeSemigroup_270 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_278 (T_IsCommutativeSemigroup_270 -> Any
forall a b. a -> b
coe T_IsCommutativeSemigroup_270
v0))
-- Data.Bool.Properties._.IsCommutativeSemigroup.isSemigroup
d_isSemigroup_616 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_270 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_194
d_isSemigroup_616 :: T_IsCommutativeSemigroup_270 -> T_IsSemigroup_194
d_isSemigroup_616 T_IsCommutativeSemigroup_270
v0
  = (T_IsCommutativeSemigroup_270 -> T_IsSemigroup_194)
-> Any -> T_IsSemigroup_194
forall a b. a -> b
coe T_IsCommutativeSemigroup_270 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_278 (T_IsCommutativeSemigroup_270 -> Any
forall a b. a -> b
coe T_IsCommutativeSemigroup_270
v0)
-- Data.Bool.Properties._.IsCommutativeSemigroup.∙-cong
d_'8729''45'cong_628 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_270 ->
  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_628 :: T_IsCommutativeSemigroup_270
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong_628 = T_IsCommutativeSemigroup_270
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsCommutativeSemiring.assoc
d_assoc_636 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiring_1344 ->
  Bool ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_assoc_636 :: T_IsCommutativeSemiring_1344
-> Bool -> Bool -> Bool -> T__'8801'__12
d_assoc_636 = T_IsCommutativeSemiring_1344
-> Bool -> Bool -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsCommutativeSemiring.*-comm
d_'42''45'comm_638 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiring_1344 ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'42''45'comm_638 :: T_IsCommutativeSemiring_1344 -> Bool -> Bool -> T__'8801'__12
d_'42''45'comm_638 = T_IsCommutativeSemiring_1344 -> Bool -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsCommutativeSemiring.∙-cong
d_'8729''45'cong_640 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiring_1344 ->
  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_IsCommutativeSemiring_1344
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong_640 = T_IsCommutativeSemiring_1344
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsCommutativeSemiring.identity
d_identity_646 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiring_1344 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_identity_646 :: T_IsCommutativeSemiring_1344 -> T_Σ_14
d_identity_646 T_IsCommutativeSemiring_1344
v0
  = (T_IsMonoid_358 -> T_Σ_14) -> Any -> T_Σ_14
forall a b. a -> b
coe
      T_IsMonoid_358 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_identity_370
      ((T_IsSemiringWithoutAnnihilatingZero_1142 -> T_IsMonoid_358)
-> Any -> Any
forall a b. a -> b
coe
         T_IsSemiringWithoutAnnihilatingZero_1142 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_'42''45'isMonoid_1160
         ((T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142)
-> Any -> Any
forall a b. a -> b
coe
            T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1252
            ((T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238) -> Any -> Any
forall a b. a -> b
coe T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238
MAlonzo.Code.Algebra.Structures.d_isSemiring_1358 (T_IsCommutativeSemiring_1344 -> Any
forall a b. a -> b
coe T_IsCommutativeSemiring_1344
v0))))
-- Data.Bool.Properties._.IsCommutativeSemiring.isMagma
d_isMagma_658 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiring_1344 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_86
d_isMagma_658 :: T_IsCommutativeSemiring_1344 -> T_IsMagma_86
d_isMagma_658 T_IsCommutativeSemiring_1344
v0
  = (T_IsSemigroup_194 -> T_IsMagma_86) -> Any -> T_IsMagma_86
forall a b. a -> b
coe
      T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202
      ((T_IsMonoid_358 -> T_IsSemigroup_194) -> Any -> Any
forall a b. a -> b
coe
         T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368
         ((T_IsSemiringWithoutAnnihilatingZero_1142 -> T_IsMonoid_358)
-> Any -> Any
forall a b. a -> b
coe
            T_IsSemiringWithoutAnnihilatingZero_1142 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_'42''45'isMonoid_1160
            ((T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142)
-> Any -> Any
forall a b. a -> b
coe
               T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1252
               ((T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238) -> Any -> Any
forall a b. a -> b
coe T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238
MAlonzo.Code.Algebra.Structures.d_isSemiring_1358 (T_IsCommutativeSemiring_1344 -> Any
forall a b. a -> b
coe T_IsCommutativeSemiring_1344
v0)))))
-- Data.Bool.Properties._.IsCommutativeSemiring.*-isMonoid
d_'42''45'isMonoid_660 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiring_1344 ->
  MAlonzo.Code.Algebra.Structures.T_IsMonoid_358
d_'42''45'isMonoid_660 :: T_IsCommutativeSemiring_1344 -> T_IsMonoid_358
d_'42''45'isMonoid_660 T_IsCommutativeSemiring_1344
v0
  = (T_IsSemiringWithoutAnnihilatingZero_1142 -> T_IsMonoid_358)
-> Any -> T_IsMonoid_358
forall a b. a -> b
coe
      T_IsSemiringWithoutAnnihilatingZero_1142 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_'42''45'isMonoid_1160
      ((T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142)
-> Any -> Any
forall a b. a -> b
coe
         T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1252
         ((T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238) -> Any -> Any
forall a b. a -> b
coe T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238
MAlonzo.Code.Algebra.Structures.d_isSemiring_1358 (T_IsCommutativeSemiring_1344 -> Any
forall a b. a -> b
coe T_IsCommutativeSemiring_1344
v0)))
-- Data.Bool.Properties._.IsCommutativeSemiring.isSemigroup
d_isSemigroup_662 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiring_1344 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_194
d_isSemigroup_662 :: T_IsCommutativeSemiring_1344 -> T_IsSemigroup_194
d_isSemigroup_662 T_IsCommutativeSemiring_1344
v0
  = (T_IsMonoid_358 -> T_IsSemigroup_194) -> Any -> T_IsSemigroup_194
forall a b. a -> b
coe
      T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368
      ((T_IsSemiringWithoutAnnihilatingZero_1142 -> T_IsMonoid_358)
-> Any -> Any
forall a b. a -> b
coe
         T_IsSemiringWithoutAnnihilatingZero_1142 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_'42''45'isMonoid_1160
         ((T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142)
-> Any -> Any
forall a b. a -> b
coe
            T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1252
            ((T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238) -> Any -> Any
forall a b. a -> b
coe T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238
MAlonzo.Code.Algebra.Structures.d_isSemiring_1358 (T_IsCommutativeSemiring_1344 -> Any
forall a b. a -> b
coe T_IsCommutativeSemiring_1344
v0))))
-- Data.Bool.Properties._.IsCommutativeSemiring.assoc
d_assoc_664 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiring_1344 ->
  Bool ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_assoc_664 :: T_IsCommutativeSemiring_1344
-> Bool -> Bool -> Bool -> T__'8801'__12
d_assoc_664 = T_IsCommutativeSemiring_1344
-> Bool -> Bool -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsCommutativeSemiring.comm
d_comm_666 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiring_1344 ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_comm_666 :: T_IsCommutativeSemiring_1344 -> Bool -> Bool -> T__'8801'__12
d_comm_666 = T_IsCommutativeSemiring_1344 -> Bool -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsCommutativeSemiring.∙-cong
d_'8729''45'cong_668 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiring_1344 ->
  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_668 :: T_IsCommutativeSemiring_1344
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong_668 = T_IsCommutativeSemiring_1344
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsCommutativeSemiring.identity
d_identity_674 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiring_1344 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_identity_674 :: T_IsCommutativeSemiring_1344 -> T_Σ_14
d_identity_674 T_IsCommutativeSemiring_1344
v0
  = (T_IsMonoid_358 -> T_Σ_14) -> Any -> T_Σ_14
forall a b. a -> b
coe
      T_IsMonoid_358 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_identity_370
      ((T_IsCommutativeMonoid_406 -> T_IsMonoid_358) -> Any -> Any
forall a b. a -> b
coe
         T_IsCommutativeMonoid_406 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_416
         ((T_IsSemiringWithoutAnnihilatingZero_1142
 -> T_IsCommutativeMonoid_406)
-> Any -> Any
forall a b. a -> b
coe
            T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsCommutativeMonoid_406
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1158
            ((T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142)
-> Any -> Any
forall a b. a -> b
coe
               T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1252
               ((T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238) -> Any -> Any
forall a b. a -> b
coe T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238
MAlonzo.Code.Algebra.Structures.d_isSemiring_1358 (T_IsCommutativeSemiring_1344 -> Any
forall a b. a -> b
coe T_IsCommutativeSemiring_1344
v0)))))
-- Data.Bool.Properties._.IsCommutativeSemiring.+-isCommutativeMonoid
d_'43''45'isCommutativeMonoid_682 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiring_1344 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMonoid_406
d_'43''45'isCommutativeMonoid_682 :: T_IsCommutativeSemiring_1344 -> T_IsCommutativeMonoid_406
d_'43''45'isCommutativeMonoid_682 T_IsCommutativeSemiring_1344
v0
  = (T_IsSemiringWithoutAnnihilatingZero_1142
 -> T_IsCommutativeMonoid_406)
-> Any -> T_IsCommutativeMonoid_406
forall a b. a -> b
coe
      T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsCommutativeMonoid_406
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1158
      ((T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142)
-> Any -> Any
forall a b. a -> b
coe
         T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1252
         ((T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238) -> Any -> Any
forall a b. a -> b
coe T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238
MAlonzo.Code.Algebra.Structures.d_isSemiring_1358 (T_IsCommutativeSemiring_1344 -> Any
forall a b. a -> b
coe T_IsCommutativeSemiring_1344
v0)))
-- Data.Bool.Properties._.IsCommutativeSemiring.isMagma
d_isMagma_686 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiring_1344 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_86
d_isMagma_686 :: T_IsCommutativeSemiring_1344 -> T_IsMagma_86
d_isMagma_686 T_IsCommutativeSemiring_1344
v0
  = (T_IsSemigroup_194 -> T_IsMagma_86) -> Any -> T_IsMagma_86
forall a b. a -> b
coe
      T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202
      ((T_IsMonoid_358 -> T_IsSemigroup_194) -> Any -> Any
forall a b. a -> b
coe
         T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368
         ((T_IsCommutativeMonoid_406 -> T_IsMonoid_358) -> Any -> Any
forall a b. a -> b
coe
            T_IsCommutativeMonoid_406 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_416
            ((T_IsSemiringWithoutAnnihilatingZero_1142
 -> T_IsCommutativeMonoid_406)
-> Any -> Any
forall a b. a -> b
coe
               T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsCommutativeMonoid_406
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1158
               ((T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142)
-> Any -> Any
forall a b. a -> b
coe
                  T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1252
                  ((T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238) -> Any -> Any
forall a b. a -> b
coe
                     T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238
MAlonzo.Code.Algebra.Structures.d_isSemiring_1358 (T_IsCommutativeSemiring_1344 -> Any
forall a b. a -> b
coe T_IsCommutativeSemiring_1344
v0))))))
-- Data.Bool.Properties._.IsCommutativeSemiring.isMonoid
d_isMonoid_688 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiring_1344 ->
  MAlonzo.Code.Algebra.Structures.T_IsMonoid_358
d_isMonoid_688 :: T_IsCommutativeSemiring_1344 -> T_IsMonoid_358
d_isMonoid_688 T_IsCommutativeSemiring_1344
v0
  = (T_IsCommutativeMonoid_406 -> T_IsMonoid_358)
-> Any -> T_IsMonoid_358
forall a b. a -> b
coe
      T_IsCommutativeMonoid_406 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_416
      ((T_IsSemiringWithoutAnnihilatingZero_1142
 -> T_IsCommutativeMonoid_406)
-> Any -> Any
forall a b. a -> b
coe
         T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsCommutativeMonoid_406
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1158
         ((T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142)
-> Any -> Any
forall a b. a -> b
coe
            T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1252
            ((T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238) -> Any -> Any
forall a b. a -> b
coe T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238
MAlonzo.Code.Algebra.Structures.d_isSemiring_1358 (T_IsCommutativeSemiring_1344 -> Any
forall a b. a -> b
coe T_IsCommutativeSemiring_1344
v0))))
-- Data.Bool.Properties._.IsCommutativeSemiring.isSemigroup
d_isSemigroup_690 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiring_1344 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_194
d_isSemigroup_690 :: T_IsCommutativeSemiring_1344 -> T_IsSemigroup_194
d_isSemigroup_690 T_IsCommutativeSemiring_1344
v0
  = (T_IsMonoid_358 -> T_IsSemigroup_194) -> Any -> T_IsSemigroup_194
forall a b. a -> b
coe
      T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368
      ((T_IsCommutativeMonoid_406 -> T_IsMonoid_358) -> Any -> Any
forall a b. a -> b
coe
         T_IsCommutativeMonoid_406 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_416
         ((T_IsSemiringWithoutAnnihilatingZero_1142
 -> T_IsCommutativeMonoid_406)
-> Any -> Any
forall a b. a -> b
coe
            T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsCommutativeMonoid_406
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1158
            ((T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142)
-> Any -> Any
forall a b. a -> b
coe
               T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1252
               ((T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238) -> Any -> Any
forall a b. a -> b
coe T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238
MAlonzo.Code.Algebra.Structures.d_isSemiring_1358 (T_IsCommutativeSemiring_1344 -> Any
forall a b. a -> b
coe T_IsCommutativeSemiring_1344
v0)))))
-- Data.Bool.Properties._.IsCommutativeSemiring.distrib
d_distrib_692 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiring_1344 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_distrib_692 :: T_IsCommutativeSemiring_1344 -> T_Σ_14
d_distrib_692 T_IsCommutativeSemiring_1344
v0
  = (T_IsSemiringWithoutAnnihilatingZero_1142 -> T_Σ_14)
-> Any -> T_Σ_14
forall a b. a -> b
coe
      T_IsSemiringWithoutAnnihilatingZero_1142 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_distrib_1162
      ((T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142)
-> Any -> Any
forall a b. a -> b
coe
         T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1252
         ((T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238) -> Any -> Any
forall a b. a -> b
coe T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238
MAlonzo.Code.Algebra.Structures.d_isSemiring_1358 (T_IsCommutativeSemiring_1344 -> Any
forall a b. a -> b
coe T_IsCommutativeSemiring_1344
v0)))
-- Data.Bool.Properties._.IsCommutativeSemiring.isEquivalence
d_isEquivalence_700 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiring_1344 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_700 :: T_IsCommutativeSemiring_1344 -> T_IsEquivalence_26
d_isEquivalence_700 T_IsCommutativeSemiring_1344
v0
  = (T_IsMagma_86 -> T_IsEquivalence_26) -> Any -> T_IsEquivalence_26
forall a b. a -> b
coe
      T_IsMagma_86 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_94
      ((T_IsSemigroup_194 -> T_IsMagma_86) -> Any -> Any
forall a b. a -> b
coe
         T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202
         ((T_IsMonoid_358 -> T_IsSemigroup_194) -> Any -> Any
forall a b. a -> b
coe
            T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368
            ((T_IsCommutativeMonoid_406 -> T_IsMonoid_358) -> Any -> Any
forall a b. a -> b
coe
               T_IsCommutativeMonoid_406 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_416
               ((T_IsSemiringWithoutAnnihilatingZero_1142
 -> T_IsCommutativeMonoid_406)
-> Any -> Any
forall a b. a -> b
coe
                  T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsCommutativeMonoid_406
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1158
                  ((T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142)
-> Any -> Any
forall a b. a -> b
coe
                     T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1252
                     ((T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238) -> Any -> Any
forall a b. a -> b
coe
                        T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238
MAlonzo.Code.Algebra.Structures.d_isSemiring_1358 (T_IsCommutativeSemiring_1344 -> Any
forall a b. a -> b
coe T_IsCommutativeSemiring_1344
v0)))))))
-- Data.Bool.Properties._.IsCommutativeSemiring.isNearSemiring
d_isNearSemiring_702 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiring_1344 ->
  MAlonzo.Code.Algebra.Structures.T_IsNearSemiring_876
d_isNearSemiring_702 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> T_IsCommutativeSemiring_1344
-> T_IsNearSemiring_876
d_isNearSemiring_702 ~Bool -> Bool -> Bool
v0 ~Bool -> Bool -> Bool
v1 ~Bool
v2 ~Bool
v3 T_IsCommutativeSemiring_1344
v4 = T_IsCommutativeSemiring_1344 -> T_IsNearSemiring_876
du_isNearSemiring_702 T_IsCommutativeSemiring_1344
v4
du_isNearSemiring_702 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiring_1344 ->
  MAlonzo.Code.Algebra.Structures.T_IsNearSemiring_876
du_isNearSemiring_702 :: T_IsCommutativeSemiring_1344 -> T_IsNearSemiring_876
du_isNearSemiring_702 T_IsCommutativeSemiring_1344
v0
  = let v1 :: T_IsSemiring_1238
v1
          = T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238
MAlonzo.Code.Algebra.Structures.d_isSemiring_1358 (T_IsCommutativeSemiring_1344 -> T_IsCommutativeSemiring_1344
forall a b. a -> b
coe T_IsCommutativeSemiring_1344
v0) in
    Any -> T_IsNearSemiring_876
forall a b. a -> b
coe
      ((T_IsSemiringWithoutOne_952 -> T_IsNearSemiring_876) -> Any -> Any
forall a b. a -> b
coe
         T_IsSemiringWithoutOne_952 -> T_IsNearSemiring_876
MAlonzo.Code.Algebra.Structures.du_isNearSemiring_990
         ((T_IsSemiring_1238 -> T_IsSemiringWithoutOne_952) -> Any -> Any
forall a b. a -> b
coe
            T_IsSemiring_1238 -> T_IsSemiringWithoutOne_952
MAlonzo.Code.Algebra.Structures.du_isSemiringWithoutOne_1326
            (T_IsSemiring_1238 -> Any
forall a b. a -> b
coe T_IsSemiring_1238
v1)))
-- Data.Bool.Properties._.IsCommutativeSemiring.isSemiring
d_isSemiring_706 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiring_1344 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemiring_1238
d_isSemiring_706 :: T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238
d_isSemiring_706 T_IsCommutativeSemiring_1344
v0
  = (T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238)
-> Any -> T_IsSemiring_1238
forall a b. a -> b
coe T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238
MAlonzo.Code.Algebra.Structures.d_isSemiring_1358 (T_IsCommutativeSemiring_1344 -> Any
forall a b. a -> b
coe T_IsCommutativeSemiring_1344
v0)
-- Data.Bool.Properties._.IsCommutativeSemiring.isSemiringWithoutAnnihilatingZero
d_isSemiringWithoutAnnihilatingZero_708 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiring_1344 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutAnnihilatingZero_1142
d_isSemiringWithoutAnnihilatingZero_708 :: T_IsCommutativeSemiring_1344
-> T_IsSemiringWithoutAnnihilatingZero_1142
d_isSemiringWithoutAnnihilatingZero_708 T_IsCommutativeSemiring_1344
v0
  = (T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142)
-> Any -> T_IsSemiringWithoutAnnihilatingZero_1142
forall a b. a -> b
coe
      T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1252
      ((T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238) -> Any -> Any
forall a b. a -> b
coe T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238
MAlonzo.Code.Algebra.Structures.d_isSemiring_1358 (T_IsCommutativeSemiring_1344 -> Any
forall a b. a -> b
coe T_IsCommutativeSemiring_1344
v0))
-- Data.Bool.Properties._.IsCommutativeSemiring.isSemiringWithoutOne
d_isSemiringWithoutOne_710 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiring_1344 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutOne_952
d_isSemiringWithoutOne_710 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> T_IsCommutativeSemiring_1344
-> T_IsSemiringWithoutOne_952
d_isSemiringWithoutOne_710 ~Bool -> Bool -> Bool
v0 ~Bool -> Bool -> Bool
v1 ~Bool
v2 ~Bool
v3 T_IsCommutativeSemiring_1344
v4
  = T_IsCommutativeSemiring_1344 -> T_IsSemiringWithoutOne_952
du_isSemiringWithoutOne_710 T_IsCommutativeSemiring_1344
v4
du_isSemiringWithoutOne_710 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiring_1344 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutOne_952
du_isSemiringWithoutOne_710 :: T_IsCommutativeSemiring_1344 -> T_IsSemiringWithoutOne_952
du_isSemiringWithoutOne_710 T_IsCommutativeSemiring_1344
v0
  = (T_IsSemiring_1238 -> T_IsSemiringWithoutOne_952)
-> Any -> T_IsSemiringWithoutOne_952
forall a b. a -> b
coe
      T_IsSemiring_1238 -> T_IsSemiringWithoutOne_952
MAlonzo.Code.Algebra.Structures.du_isSemiringWithoutOne_1326
      ((T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238) -> Any -> Any
forall a b. a -> b
coe T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238
MAlonzo.Code.Algebra.Structures.d_isSemiring_1358 (T_IsCommutativeSemiring_1344 -> Any
forall a b. a -> b
coe T_IsCommutativeSemiring_1344
v0))
-- Data.Bool.Properties._.IsCommutativeSemiring.zero
d_zero_722 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiring_1344 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_zero_722 :: T_IsCommutativeSemiring_1344 -> T_Σ_14
d_zero_722 T_IsCommutativeSemiring_1344
v0
  = (T_IsSemiring_1238 -> T_Σ_14) -> Any -> T_Σ_14
forall a b. a -> b
coe
      T_IsSemiring_1238 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_zero_1254
      ((T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238) -> Any -> Any
forall a b. a -> b
coe T_IsCommutativeSemiring_1344 -> T_IsSemiring_1238
MAlonzo.Code.Algebra.Structures.d_isSemiring_1358 (T_IsCommutativeSemiring_1344 -> Any
forall a b. a -> b
coe T_IsCommutativeSemiring_1344
v0))
-- Data.Bool.Properties._.IsCommutativeSemiringWithoutOne.assoc
d_assoc_730 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiringWithoutOne_1044 ->
  Bool ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_assoc_730 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsCommutativeSemiringWithoutOne_1044
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
d_assoc_730 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsCommutativeSemiringWithoutOne_1044
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsCommutativeSemiringWithoutOne.*-comm
d_'42''45'comm_732 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiringWithoutOne_1044 ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'42''45'comm_732 :: T_IsCommutativeSemiringWithoutOne_1044
-> Bool -> Bool -> T__'8801'__12
d_'42''45'comm_732 = T_IsCommutativeSemiringWithoutOne_1044
-> Bool -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsCommutativeSemiringWithoutOne.∙-cong
d_'8729''45'cong_734 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiringWithoutOne_1044 ->
  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_734 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsCommutativeSemiringWithoutOne_1044
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong_734 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsCommutativeSemiringWithoutOne_1044
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsCommutativeSemiringWithoutOne.isMagma
d_isMagma_744 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiringWithoutOne_1044 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_86
d_isMagma_744 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsCommutativeSemiringWithoutOne_1044
-> T_IsMagma_86
d_isMagma_744 ~Bool -> Bool -> Bool
v0 ~Bool -> Bool -> Bool
v1 ~Bool
v2 T_IsCommutativeSemiringWithoutOne_1044
v3 = T_IsCommutativeSemiringWithoutOne_1044 -> T_IsMagma_86
du_isMagma_744 T_IsCommutativeSemiringWithoutOne_1044
v3
du_isMagma_744 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiringWithoutOne_1044 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_86
du_isMagma_744 :: T_IsCommutativeSemiringWithoutOne_1044 -> T_IsMagma_86
du_isMagma_744 T_IsCommutativeSemiringWithoutOne_1044
v0
  = let v1 :: T_IsSemiringWithoutOne_952
v1
          = T_IsCommutativeSemiringWithoutOne_1044
-> T_IsSemiringWithoutOne_952
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutOne_1056
              (T_IsCommutativeSemiringWithoutOne_1044
-> T_IsCommutativeSemiringWithoutOne_1044
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1044
v0) in
    Any -> T_IsMagma_86
forall a b. a -> b
coe
      ((T_IsSemigroup_194 -> T_IsMagma_86) -> Any -> Any
forall a b. a -> b
coe
         T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202
         ((T_IsSemiringWithoutOne_952 -> T_IsSemigroup_194) -> Any -> Any
forall a b. a -> b
coe
            T_IsSemiringWithoutOne_952 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_'42''45'isSemigroup_970
            (T_IsSemiringWithoutOne_952 -> Any
forall a b. a -> b
coe T_IsSemiringWithoutOne_952
v1)))
-- Data.Bool.Properties._.IsCommutativeSemiringWithoutOne.*-isSemigroup
d_'42''45'isSemigroup_746 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiringWithoutOne_1044 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_194
d_'42''45'isSemigroup_746 :: T_IsCommutativeSemiringWithoutOne_1044 -> T_IsSemigroup_194
d_'42''45'isSemigroup_746 T_IsCommutativeSemiringWithoutOne_1044
v0
  = (T_IsSemiringWithoutOne_952 -> T_IsSemigroup_194)
-> Any -> T_IsSemigroup_194
forall a b. a -> b
coe
      T_IsSemiringWithoutOne_952 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_'42''45'isSemigroup_970
      ((T_IsCommutativeSemiringWithoutOne_1044
 -> T_IsSemiringWithoutOne_952)
-> Any -> Any
forall a b. a -> b
coe
         T_IsCommutativeSemiringWithoutOne_1044
-> T_IsSemiringWithoutOne_952
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutOne_1056
         (T_IsCommutativeSemiringWithoutOne_1044 -> Any
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1044
v0))
-- Data.Bool.Properties._.IsCommutativeSemiringWithoutOne.assoc
d_assoc_748 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiringWithoutOne_1044 ->
  Bool ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_assoc_748 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsCommutativeSemiringWithoutOne_1044
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
d_assoc_748 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsCommutativeSemiringWithoutOne_1044
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsCommutativeSemiringWithoutOne.comm
d_comm_750 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiringWithoutOne_1044 ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_comm_750 :: T_IsCommutativeSemiringWithoutOne_1044
-> Bool -> Bool -> T__'8801'__12
d_comm_750 = T_IsCommutativeSemiringWithoutOne_1044
-> Bool -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsCommutativeSemiringWithoutOne.∙-cong
d_'8729''45'cong_752 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiringWithoutOne_1044 ->
  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_752 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsCommutativeSemiringWithoutOne_1044
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong_752 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsCommutativeSemiringWithoutOne_1044
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsCommutativeSemiringWithoutOne.identity
d_identity_758 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiringWithoutOne_1044 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_identity_758 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsCommutativeSemiringWithoutOne_1044
-> T_Σ_14
d_identity_758 ~Bool -> Bool -> Bool
v0 ~Bool -> Bool -> Bool
v1 ~Bool
v2 T_IsCommutativeSemiringWithoutOne_1044
v3 = T_IsCommutativeSemiringWithoutOne_1044 -> T_Σ_14
du_identity_758 T_IsCommutativeSemiringWithoutOne_1044
v3
du_identity_758 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiringWithoutOne_1044 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
du_identity_758 :: T_IsCommutativeSemiringWithoutOne_1044 -> T_Σ_14
du_identity_758 T_IsCommutativeSemiringWithoutOne_1044
v0
  = let v1 :: T_IsSemiringWithoutOne_952
v1
          = T_IsCommutativeSemiringWithoutOne_1044
-> T_IsSemiringWithoutOne_952
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutOne_1056
              (T_IsCommutativeSemiringWithoutOne_1044
-> T_IsCommutativeSemiringWithoutOne_1044
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1044
v0) in
    Any -> T_Σ_14
forall a b. a -> b
coe
      ((T_IsMonoid_358 -> T_Σ_14) -> Any -> Any
forall a b. a -> b
coe
         T_IsMonoid_358 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_identity_370
         ((T_IsCommutativeMonoid_406 -> T_IsMonoid_358) -> Any -> Any
forall a b. a -> b
coe
            T_IsCommutativeMonoid_406 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_416
            ((T_IsSemiringWithoutOne_952 -> T_IsCommutativeMonoid_406)
-> Any -> Any
forall a b. a -> b
coe
               T_IsSemiringWithoutOne_952 -> T_IsCommutativeMonoid_406
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_968
               (T_IsSemiringWithoutOne_952 -> Any
forall a b. a -> b
coe T_IsSemiringWithoutOne_952
v1))))
-- Data.Bool.Properties._.IsCommutativeSemiringWithoutOne.+-isCommutativeMonoid
d_'43''45'isCommutativeMonoid_766 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiringWithoutOne_1044 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMonoid_406
d_'43''45'isCommutativeMonoid_766 :: T_IsCommutativeSemiringWithoutOne_1044 -> T_IsCommutativeMonoid_406
d_'43''45'isCommutativeMonoid_766 T_IsCommutativeSemiringWithoutOne_1044
v0
  = (T_IsSemiringWithoutOne_952 -> T_IsCommutativeMonoid_406)
-> Any -> T_IsCommutativeMonoid_406
forall a b. a -> b
coe
      T_IsSemiringWithoutOne_952 -> T_IsCommutativeMonoid_406
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_968
      ((T_IsCommutativeSemiringWithoutOne_1044
 -> T_IsSemiringWithoutOne_952)
-> Any -> Any
forall a b. a -> b
coe
         T_IsCommutativeSemiringWithoutOne_1044
-> T_IsSemiringWithoutOne_952
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutOne_1056
         (T_IsCommutativeSemiringWithoutOne_1044 -> Any
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1044
v0))
-- Data.Bool.Properties._.IsCommutativeSemiringWithoutOne.isMagma
d_isMagma_770 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiringWithoutOne_1044 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_86
d_isMagma_770 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsCommutativeSemiringWithoutOne_1044
-> T_IsMagma_86
d_isMagma_770 ~Bool -> Bool -> Bool
v0 ~Bool -> Bool -> Bool
v1 ~Bool
v2 T_IsCommutativeSemiringWithoutOne_1044
v3 = T_IsCommutativeSemiringWithoutOne_1044 -> T_IsMagma_86
du_isMagma_770 T_IsCommutativeSemiringWithoutOne_1044
v3
du_isMagma_770 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiringWithoutOne_1044 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_86
du_isMagma_770 :: T_IsCommutativeSemiringWithoutOne_1044 -> T_IsMagma_86
du_isMagma_770 T_IsCommutativeSemiringWithoutOne_1044
v0
  = let v1 :: T_IsSemiringWithoutOne_952
v1
          = T_IsCommutativeSemiringWithoutOne_1044
-> T_IsSemiringWithoutOne_952
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutOne_1056
              (T_IsCommutativeSemiringWithoutOne_1044
-> T_IsCommutativeSemiringWithoutOne_1044
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1044
v0) in
    Any -> T_IsMagma_86
forall a b. a -> b
coe
      ((T_IsSemigroup_194 -> T_IsMagma_86) -> Any -> Any
forall a b. a -> b
coe
         T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202
         ((T_IsMonoid_358 -> T_IsSemigroup_194) -> Any -> Any
forall a b. a -> b
coe
            T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368
            ((T_IsCommutativeMonoid_406 -> T_IsMonoid_358) -> Any -> Any
forall a b. a -> b
coe
               T_IsCommutativeMonoid_406 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_416
               ((T_IsSemiringWithoutOne_952 -> T_IsCommutativeMonoid_406)
-> Any -> Any
forall a b. a -> b
coe
                  T_IsSemiringWithoutOne_952 -> T_IsCommutativeMonoid_406
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_968
                  (T_IsSemiringWithoutOne_952 -> Any
forall a b. a -> b
coe T_IsSemiringWithoutOne_952
v1)))))
-- Data.Bool.Properties._.IsCommutativeSemiringWithoutOne.isMonoid
d_isMonoid_772 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiringWithoutOne_1044 ->
  MAlonzo.Code.Algebra.Structures.T_IsMonoid_358
d_isMonoid_772 :: T_IsCommutativeSemiringWithoutOne_1044 -> T_IsMonoid_358
d_isMonoid_772 T_IsCommutativeSemiringWithoutOne_1044
v0
  = (T_IsCommutativeMonoid_406 -> T_IsMonoid_358)
-> Any -> T_IsMonoid_358
forall a b. a -> b
coe
      T_IsCommutativeMonoid_406 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_416
      ((T_IsSemiringWithoutOne_952 -> T_IsCommutativeMonoid_406)
-> Any -> Any
forall a b. a -> b
coe
         T_IsSemiringWithoutOne_952 -> T_IsCommutativeMonoid_406
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_968
         ((T_IsCommutativeSemiringWithoutOne_1044
 -> T_IsSemiringWithoutOne_952)
-> Any -> Any
forall a b. a -> b
coe
            T_IsCommutativeSemiringWithoutOne_1044
-> T_IsSemiringWithoutOne_952
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutOne_1056
            (T_IsCommutativeSemiringWithoutOne_1044 -> Any
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1044
v0)))
-- Data.Bool.Properties._.IsCommutativeSemiringWithoutOne.isSemigroup
d_isSemigroup_774 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiringWithoutOne_1044 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_194
d_isSemigroup_774 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsCommutativeSemiringWithoutOne_1044
-> T_IsSemigroup_194
d_isSemigroup_774 ~Bool -> Bool -> Bool
v0 ~Bool -> Bool -> Bool
v1 ~Bool
v2 T_IsCommutativeSemiringWithoutOne_1044
v3 = T_IsCommutativeSemiringWithoutOne_1044 -> T_IsSemigroup_194
du_isSemigroup_774 T_IsCommutativeSemiringWithoutOne_1044
v3
du_isSemigroup_774 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiringWithoutOne_1044 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_194
du_isSemigroup_774 :: T_IsCommutativeSemiringWithoutOne_1044 -> T_IsSemigroup_194
du_isSemigroup_774 T_IsCommutativeSemiringWithoutOne_1044
v0
  = let v1 :: T_IsSemiringWithoutOne_952
v1
          = T_IsCommutativeSemiringWithoutOne_1044
-> T_IsSemiringWithoutOne_952
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutOne_1056
              (T_IsCommutativeSemiringWithoutOne_1044
-> T_IsCommutativeSemiringWithoutOne_1044
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1044
v0) in
    Any -> T_IsSemigroup_194
forall a b. a -> b
coe
      ((T_IsMonoid_358 -> T_IsSemigroup_194) -> Any -> Any
forall a b. a -> b
coe
         T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368
         ((T_IsCommutativeMonoid_406 -> T_IsMonoid_358) -> Any -> Any
forall a b. a -> b
coe
            T_IsCommutativeMonoid_406 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_416
            ((T_IsSemiringWithoutOne_952 -> T_IsCommutativeMonoid_406)
-> Any -> Any
forall a b. a -> b
coe
               T_IsSemiringWithoutOne_952 -> T_IsCommutativeMonoid_406
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_968
               (T_IsSemiringWithoutOne_952 -> Any
forall a b. a -> b
coe T_IsSemiringWithoutOne_952
v1))))
-- Data.Bool.Properties._.IsCommutativeSemiringWithoutOne.distrib
d_distrib_776 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiringWithoutOne_1044 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_distrib_776 :: T_IsCommutativeSemiringWithoutOne_1044 -> T_Σ_14
d_distrib_776 T_IsCommutativeSemiringWithoutOne_1044
v0
  = (T_IsSemiringWithoutOne_952 -> T_Σ_14) -> Any -> T_Σ_14
forall a b. a -> b
coe
      T_IsSemiringWithoutOne_952 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_distrib_972
      ((T_IsCommutativeSemiringWithoutOne_1044
 -> T_IsSemiringWithoutOne_952)
-> Any -> Any
forall a b. a -> b
coe
         T_IsCommutativeSemiringWithoutOne_1044
-> T_IsSemiringWithoutOne_952
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutOne_1056
         (T_IsCommutativeSemiringWithoutOne_1044 -> Any
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1044
v0))
-- Data.Bool.Properties._.IsCommutativeSemiringWithoutOne.distribʳ
d_distrib'691'_778 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiringWithoutOne_1044 ->
  Bool ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_distrib'691'_778 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsCommutativeSemiringWithoutOne_1044
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
d_distrib'691'_778 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsCommutativeSemiringWithoutOne_1044
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsCommutativeSemiringWithoutOne.isEquivalence
d_isEquivalence_780 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiringWithoutOne_1044 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_780 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsCommutativeSemiringWithoutOne_1044
-> T_IsEquivalence_26
d_isEquivalence_780 ~Bool -> Bool -> Bool
v0 ~Bool -> Bool -> Bool
v1 ~Bool
v2 T_IsCommutativeSemiringWithoutOne_1044
v3 = T_IsCommutativeSemiringWithoutOne_1044 -> T_IsEquivalence_26
du_isEquivalence_780 T_IsCommutativeSemiringWithoutOne_1044
v3
du_isEquivalence_780 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiringWithoutOne_1044 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
du_isEquivalence_780 :: T_IsCommutativeSemiringWithoutOne_1044 -> T_IsEquivalence_26
du_isEquivalence_780 T_IsCommutativeSemiringWithoutOne_1044
v0
  = let v1 :: T_IsSemiringWithoutOne_952
v1
          = T_IsCommutativeSemiringWithoutOne_1044
-> T_IsSemiringWithoutOne_952
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutOne_1056
              (T_IsCommutativeSemiringWithoutOne_1044
-> T_IsCommutativeSemiringWithoutOne_1044
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1044
v0) in
    Any -> T_IsEquivalence_26
forall a b. a -> b
coe
      ((T_IsMagma_86 -> T_IsEquivalence_26) -> Any -> Any
forall a b. a -> b
coe
         T_IsMagma_86 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_94
         ((T_IsSemigroup_194 -> T_IsMagma_86) -> Any -> Any
forall a b. a -> b
coe
            T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202
            ((T_IsMonoid_358 -> T_IsSemigroup_194) -> Any -> Any
forall a b. a -> b
coe
               T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368
               ((T_IsCommutativeMonoid_406 -> T_IsMonoid_358) -> Any -> Any
forall a b. a -> b
coe
                  T_IsCommutativeMonoid_406 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_416
                  ((T_IsSemiringWithoutOne_952 -> T_IsCommutativeMonoid_406)
-> Any -> Any
forall a b. a -> b
coe
                     T_IsSemiringWithoutOne_952 -> T_IsCommutativeMonoid_406
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_968
                     (T_IsSemiringWithoutOne_952 -> Any
forall a b. a -> b
coe T_IsSemiringWithoutOne_952
v1))))))
-- Data.Bool.Properties._.IsCommutativeSemiringWithoutOne.isNearSemiring
d_isNearSemiring_782 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiringWithoutOne_1044 ->
  MAlonzo.Code.Algebra.Structures.T_IsNearSemiring_876
d_isNearSemiring_782 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsCommutativeSemiringWithoutOne_1044
-> T_IsNearSemiring_876
d_isNearSemiring_782 ~Bool -> Bool -> Bool
v0 ~Bool -> Bool -> Bool
v1 ~Bool
v2 T_IsCommutativeSemiringWithoutOne_1044
v3 = T_IsCommutativeSemiringWithoutOne_1044 -> T_IsNearSemiring_876
du_isNearSemiring_782 T_IsCommutativeSemiringWithoutOne_1044
v3
du_isNearSemiring_782 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiringWithoutOne_1044 ->
  MAlonzo.Code.Algebra.Structures.T_IsNearSemiring_876
du_isNearSemiring_782 :: T_IsCommutativeSemiringWithoutOne_1044 -> T_IsNearSemiring_876
du_isNearSemiring_782 T_IsCommutativeSemiringWithoutOne_1044
v0
  = (T_IsSemiringWithoutOne_952 -> T_IsNearSemiring_876)
-> Any -> T_IsNearSemiring_876
forall a b. a -> b
coe
      T_IsSemiringWithoutOne_952 -> T_IsNearSemiring_876
MAlonzo.Code.Algebra.Structures.du_isNearSemiring_990
      ((T_IsCommutativeSemiringWithoutOne_1044
 -> T_IsSemiringWithoutOne_952)
-> Any -> Any
forall a b. a -> b
coe
         T_IsCommutativeSemiringWithoutOne_1044
-> T_IsSemiringWithoutOne_952
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutOne_1056
         (T_IsCommutativeSemiringWithoutOne_1044 -> Any
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1044
v0))
-- Data.Bool.Properties._.IsCommutativeSemiringWithoutOne.isSemiringWithoutOne
d_isSemiringWithoutOne_786 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiringWithoutOne_1044 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutOne_952
d_isSemiringWithoutOne_786 :: T_IsCommutativeSemiringWithoutOne_1044
-> T_IsSemiringWithoutOne_952
d_isSemiringWithoutOne_786 T_IsCommutativeSemiringWithoutOne_1044
v0
  = (T_IsCommutativeSemiringWithoutOne_1044
 -> T_IsSemiringWithoutOne_952)
-> Any -> T_IsSemiringWithoutOne_952
forall a b. a -> b
coe
      T_IsCommutativeSemiringWithoutOne_1044
-> T_IsSemiringWithoutOne_952
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutOne_1056
      (T_IsCommutativeSemiringWithoutOne_1044 -> Any
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1044
v0)
-- Data.Bool.Properties._.IsCommutativeSemiringWithoutOne.zero
d_zero_798 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiringWithoutOne_1044 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_zero_798 :: T_IsCommutativeSemiringWithoutOne_1044 -> T_Σ_14
d_zero_798 T_IsCommutativeSemiringWithoutOne_1044
v0
  = (T_IsSemiringWithoutOne_952 -> T_Σ_14) -> Any -> T_Σ_14
forall a b. a -> b
coe
      T_IsSemiringWithoutOne_952 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_zero_974
      ((T_IsCommutativeSemiringWithoutOne_1044
 -> T_IsSemiringWithoutOne_952)
-> Any -> Any
forall a b. a -> b
coe
         T_IsCommutativeSemiringWithoutOne_1044
-> T_IsSemiringWithoutOne_952
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutOne_1056
         (T_IsCommutativeSemiringWithoutOne_1044 -> Any
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1044
v0))
-- Data.Bool.Properties._.IsDistributiveLattice.absorptive
d_absorptive_806 ::
  MAlonzo.Code.Algebra.Structures.T_IsDistributiveLattice_814 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_absorptive_806 :: T_IsDistributiveLattice_814 -> T_Σ_14
d_absorptive_806 T_IsDistributiveLattice_814
v0
  = (T_IsLattice_740 -> T_Σ_14) -> Any -> T_Σ_14
forall a b. a -> b
coe
      T_IsLattice_740 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_absorptive_776
      ((T_IsDistributiveLattice_814 -> T_IsLattice_740) -> Any -> Any
forall a b. a -> b
coe T_IsDistributiveLattice_814 -> T_IsLattice_740
MAlonzo.Code.Algebra.Structures.d_isLattice_824 (T_IsDistributiveLattice_814 -> Any
forall a b. a -> b
coe T_IsDistributiveLattice_814
v0))
-- Data.Bool.Properties._.IsDistributiveLattice.isEquivalence
d_isEquivalence_808 ::
  MAlonzo.Code.Algebra.Structures.T_IsDistributiveLattice_814 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_808 :: T_IsDistributiveLattice_814 -> T_IsEquivalence_26
d_isEquivalence_808 T_IsDistributiveLattice_814
v0
  = (T_IsLattice_740 -> T_IsEquivalence_26)
-> Any -> T_IsEquivalence_26
forall a b. a -> b
coe
      T_IsLattice_740 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_762
      ((T_IsDistributiveLattice_814 -> T_IsLattice_740) -> Any -> Any
forall a b. a -> b
coe T_IsDistributiveLattice_814 -> T_IsLattice_740
MAlonzo.Code.Algebra.Structures.d_isLattice_824 (T_IsDistributiveLattice_814 -> Any
forall a b. a -> b
coe T_IsDistributiveLattice_814
v0))
-- Data.Bool.Properties._.IsDistributiveLattice.isLattice
d_isLattice_810 ::
  MAlonzo.Code.Algebra.Structures.T_IsDistributiveLattice_814 ->
  MAlonzo.Code.Algebra.Structures.T_IsLattice_740
d_isLattice_810 :: T_IsDistributiveLattice_814 -> T_IsLattice_740
d_isLattice_810 T_IsDistributiveLattice_814
v0
  = (T_IsDistributiveLattice_814 -> T_IsLattice_740)
-> Any -> T_IsLattice_740
forall a b. a -> b
coe T_IsDistributiveLattice_814 -> T_IsLattice_740
MAlonzo.Code.Algebra.Structures.d_isLattice_824 (T_IsDistributiveLattice_814 -> Any
forall a b. a -> b
coe T_IsDistributiveLattice_814
v0)
-- Data.Bool.Properties._.IsDistributiveLattice.∧-assoc
d_'8743''45'assoc_824 ::
  MAlonzo.Code.Algebra.Structures.T_IsDistributiveLattice_814 ->
  Bool ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8743''45'assoc_824 :: T_IsDistributiveLattice_814
-> Bool -> Bool -> Bool -> T__'8801'__12
d_'8743''45'assoc_824 = T_IsDistributiveLattice_814
-> Bool -> Bool -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsDistributiveLattice.∧-comm
d_'8743''45'comm_826 ::
  MAlonzo.Code.Algebra.Structures.T_IsDistributiveLattice_814 ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8743''45'comm_826 :: T_IsDistributiveLattice_814 -> Bool -> Bool -> T__'8801'__12
d_'8743''45'comm_826 = T_IsDistributiveLattice_814 -> Bool -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsDistributiveLattice.∧-cong
d_'8743''45'cong_828 ::
  MAlonzo.Code.Algebra.Structures.T_IsDistributiveLattice_814 ->
  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_828 :: T_IsDistributiveLattice_814
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
d_'8743''45'cong_828 = T_IsDistributiveLattice_814
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsDistributiveLattice.∨-assoc
d_'8744''45'assoc_836 ::
  MAlonzo.Code.Algebra.Structures.T_IsDistributiveLattice_814 ->
  Bool ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8744''45'assoc_836 :: T_IsDistributiveLattice_814
-> Bool -> Bool -> Bool -> T__'8801'__12
d_'8744''45'assoc_836 = T_IsDistributiveLattice_814
-> Bool -> Bool -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsDistributiveLattice.∨-comm
d_'8744''45'comm_838 ::
  MAlonzo.Code.Algebra.Structures.T_IsDistributiveLattice_814 ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8744''45'comm_838 :: T_IsDistributiveLattice_814 -> Bool -> Bool -> T__'8801'__12
d_'8744''45'comm_838 = T_IsDistributiveLattice_814 -> Bool -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsDistributiveLattice.∨-cong
d_'8744''45'cong_840 ::
  MAlonzo.Code.Algebra.Structures.T_IsDistributiveLattice_814 ->
  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_840 :: T_IsDistributiveLattice_814
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
d_'8744''45'cong_840 = T_IsDistributiveLattice_814
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsDistributiveLattice.∨-distribʳ-∧
d_'8744''45'distrib'691''45''8743'_846 ::
  MAlonzo.Code.Algebra.Structures.T_IsDistributiveLattice_814 ->
  Bool ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8744''45'distrib'691''45''8743'_846 :: T_IsDistributiveLattice_814
-> Bool -> Bool -> Bool -> T__'8801'__12
d_'8744''45'distrib'691''45''8743'_846 = T_IsDistributiveLattice_814
-> Bool -> Bool -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsGroup.assoc
d_assoc_854 ::
  MAlonzo.Code.Algebra.Structures.T_IsGroup_580 ->
  Bool ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_assoc_854 :: T_IsGroup_580 -> Bool -> Bool -> Bool -> T__'8801'__12
d_assoc_854 = T_IsGroup_580 -> Bool -> Bool -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsGroup.identity
d_identity_856 ::
  MAlonzo.Code.Algebra.Structures.T_IsGroup_580 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_identity_856 :: T_IsGroup_580 -> T_Σ_14
d_identity_856 T_IsGroup_580
v0
  = (T_IsMonoid_358 -> T_Σ_14) -> Any -> T_Σ_14
forall a b. a -> b
coe
      T_IsMonoid_358 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_identity_370
      ((T_IsGroup_580 -> T_IsMonoid_358) -> Any -> Any
forall a b. a -> b
coe T_IsGroup_580 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_594 (T_IsGroup_580 -> Any
forall a b. a -> b
coe T_IsGroup_580
v0))
-- Data.Bool.Properties._.IsGroup.inverse
d_inverse_862 ::
  MAlonzo.Code.Algebra.Structures.T_IsGroup_580 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_inverse_862 :: T_IsGroup_580 -> T_Σ_14
d_inverse_862 T_IsGroup_580
v0
  = (T_IsGroup_580 -> T_Σ_14) -> Any -> T_Σ_14
forall a b. a -> b
coe T_IsGroup_580 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_inverse_596 (T_IsGroup_580 -> Any
forall a b. a -> b
coe T_IsGroup_580
v0)
-- Data.Bool.Properties._.IsGroup.isEquivalence
d_isEquivalence_868 ::
  MAlonzo.Code.Algebra.Structures.T_IsGroup_580 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_868 :: T_IsGroup_580 -> T_IsEquivalence_26
d_isEquivalence_868 T_IsGroup_580
v0
  = (T_IsMagma_86 -> T_IsEquivalence_26) -> Any -> T_IsEquivalence_26
forall a b. a -> b
coe
      T_IsMagma_86 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_94
      ((T_IsSemigroup_194 -> T_IsMagma_86) -> Any -> Any
forall a b. a -> b
coe
         T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202
         ((T_IsMonoid_358 -> T_IsSemigroup_194) -> Any -> Any
forall a b. a -> b
coe
            T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368
            ((T_IsGroup_580 -> T_IsMonoid_358) -> Any -> Any
forall a b. a -> b
coe T_IsGroup_580 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_594 (T_IsGroup_580 -> Any
forall a b. a -> b
coe T_IsGroup_580
v0))))
-- Data.Bool.Properties._.IsGroup.isMagma
d_isMagma_870 ::
  MAlonzo.Code.Algebra.Structures.T_IsGroup_580 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_86
d_isMagma_870 :: T_IsGroup_580 -> T_IsMagma_86
d_isMagma_870 T_IsGroup_580
v0
  = (T_IsSemigroup_194 -> T_IsMagma_86) -> Any -> T_IsMagma_86
forall a b. a -> b
coe
      T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202
      ((T_IsMonoid_358 -> T_IsSemigroup_194) -> Any -> Any
forall a b. a -> b
coe
         T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368
         ((T_IsGroup_580 -> T_IsMonoid_358) -> Any -> Any
forall a b. a -> b
coe T_IsGroup_580 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_594 (T_IsGroup_580 -> Any
forall a b. a -> b
coe T_IsGroup_580
v0)))
-- Data.Bool.Properties._.IsGroup.isMonoid
d_isMonoid_872 ::
  MAlonzo.Code.Algebra.Structures.T_IsGroup_580 ->
  MAlonzo.Code.Algebra.Structures.T_IsMonoid_358
d_isMonoid_872 :: T_IsGroup_580 -> T_IsMonoid_358
d_isMonoid_872 T_IsGroup_580
v0
  = (T_IsGroup_580 -> T_IsMonoid_358) -> Any -> T_IsMonoid_358
forall a b. a -> b
coe T_IsGroup_580 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_594 (T_IsGroup_580 -> Any
forall a b. a -> b
coe T_IsGroup_580
v0)
-- Data.Bool.Properties._.IsGroup.isSemigroup
d_isSemigroup_876 ::
  MAlonzo.Code.Algebra.Structures.T_IsGroup_580 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_194
d_isSemigroup_876 :: T_IsGroup_580 -> T_IsSemigroup_194
d_isSemigroup_876 T_IsGroup_580
v0
  = (T_IsMonoid_358 -> T_IsSemigroup_194) -> Any -> T_IsSemigroup_194
forall a b. a -> b
coe
      T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368
      ((T_IsGroup_580 -> T_IsMonoid_358) -> Any -> Any
forall a b. a -> b
coe T_IsGroup_580 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_594 (T_IsGroup_580 -> Any
forall a b. a -> b
coe T_IsGroup_580
v0))
-- Data.Bool.Properties._.IsGroup.⁻¹-cong
d_'8315''185''45'cong_892 ::
  MAlonzo.Code.Algebra.Structures.T_IsGroup_580 ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8315''185''45'cong_892 :: T_IsGroup_580 -> Bool -> Bool -> T__'8801'__12 -> T__'8801'__12
d_'8315''185''45'cong_892 = T_IsGroup_580 -> Bool -> Bool -> T__'8801'__12 -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsGroup.∙-cong
d_'8729''45'cong_894 ::
  MAlonzo.Code.Algebra.Structures.T_IsGroup_580 ->
  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_894 :: T_IsGroup_580
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong_894 = T_IsGroup_580
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsIdempotentCommutativeMonoid.assoc
d_assoc_902 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_464 ->
  Bool ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_assoc_902 :: T_IsIdempotentCommutativeMonoid_464
-> Bool -> Bool -> Bool -> T__'8801'__12
d_assoc_902 = T_IsIdempotentCommutativeMonoid_464
-> Bool -> Bool -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsIdempotentCommutativeMonoid.comm
d_comm_904 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_464 ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_comm_904 :: T_IsIdempotentCommutativeMonoid_464
-> Bool -> Bool -> T__'8801'__12
d_comm_904 = T_IsIdempotentCommutativeMonoid_464
-> Bool -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsIdempotentCommutativeMonoid.idem
d_idem_906 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_464 ->
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_idem_906 :: T_IsIdempotentCommutativeMonoid_464 -> Bool -> T__'8801'__12
d_idem_906 = T_IsIdempotentCommutativeMonoid_464 -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsIdempotentCommutativeMonoid.identity
d_identity_908 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_464 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_identity_908 :: T_IsIdempotentCommutativeMonoid_464 -> T_Σ_14
d_identity_908 T_IsIdempotentCommutativeMonoid_464
v0
  = (T_IsMonoid_358 -> T_Σ_14) -> Any -> T_Σ_14
forall a b. a -> b
coe
      T_IsMonoid_358 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_identity_370
      ((T_IsCommutativeMonoid_406 -> T_IsMonoid_358) -> Any -> Any
forall a b. a -> b
coe
         T_IsCommutativeMonoid_406 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_416
         ((T_IsIdempotentCommutativeMonoid_464 -> T_IsCommutativeMonoid_406)
-> Any -> Any
forall a b. a -> b
coe
            T_IsIdempotentCommutativeMonoid_464 -> T_IsCommutativeMonoid_406
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_474
            (T_IsIdempotentCommutativeMonoid_464 -> Any
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_464
v0)))
-- Data.Bool.Properties._.IsIdempotentCommutativeMonoid.isCommutativeMonoid
d_isCommutativeMonoid_916 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_464 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMonoid_406
d_isCommutativeMonoid_916 :: T_IsIdempotentCommutativeMonoid_464 -> T_IsCommutativeMonoid_406
d_isCommutativeMonoid_916 T_IsIdempotentCommutativeMonoid_464
v0
  = (T_IsIdempotentCommutativeMonoid_464 -> T_IsCommutativeMonoid_406)
-> Any -> T_IsCommutativeMonoid_406
forall a b. a -> b
coe
      T_IsIdempotentCommutativeMonoid_464 -> T_IsCommutativeMonoid_406
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_474 (T_IsIdempotentCommutativeMonoid_464 -> Any
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_464
v0)
-- Data.Bool.Properties._.IsIdempotentCommutativeMonoid.isEquivalence
d_isEquivalence_920 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_464 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_920 :: T_IsIdempotentCommutativeMonoid_464 -> T_IsEquivalence_26
d_isEquivalence_920 T_IsIdempotentCommutativeMonoid_464
v0
  = (T_IsMagma_86 -> T_IsEquivalence_26) -> Any -> T_IsEquivalence_26
forall a b. a -> b
coe
      T_IsMagma_86 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_94
      ((T_IsSemigroup_194 -> T_IsMagma_86) -> Any -> Any
forall a b. a -> b
coe
         T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202
         ((T_IsMonoid_358 -> T_IsSemigroup_194) -> Any -> Any
forall a b. a -> b
coe
            T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368
            ((T_IsCommutativeMonoid_406 -> T_IsMonoid_358) -> Any -> Any
forall a b. a -> b
coe
               T_IsCommutativeMonoid_406 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_416
               ((T_IsIdempotentCommutativeMonoid_464 -> T_IsCommutativeMonoid_406)
-> Any -> Any
forall a b. a -> b
coe
                  T_IsIdempotentCommutativeMonoid_464 -> T_IsCommutativeMonoid_406
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_474
                  (T_IsIdempotentCommutativeMonoid_464 -> Any
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_464
v0)))))
-- Data.Bool.Properties._.IsIdempotentCommutativeMonoid.isMagma
d_isMagma_922 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_464 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_86
d_isMagma_922 :: T_IsIdempotentCommutativeMonoid_464 -> T_IsMagma_86
d_isMagma_922 T_IsIdempotentCommutativeMonoid_464
v0
  = (T_IsSemigroup_194 -> T_IsMagma_86) -> Any -> T_IsMagma_86
forall a b. a -> b
coe
      T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202
      ((T_IsMonoid_358 -> T_IsSemigroup_194) -> Any -> Any
forall a b. a -> b
coe
         T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368
         ((T_IsCommutativeMonoid_406 -> T_IsMonoid_358) -> Any -> Any
forall a b. a -> b
coe
            T_IsCommutativeMonoid_406 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_416
            ((T_IsIdempotentCommutativeMonoid_464 -> T_IsCommutativeMonoid_406)
-> Any -> Any
forall a b. a -> b
coe
               T_IsIdempotentCommutativeMonoid_464 -> T_IsCommutativeMonoid_406
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_474
               (T_IsIdempotentCommutativeMonoid_464 -> Any
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_464
v0))))
-- Data.Bool.Properties._.IsIdempotentCommutativeMonoid.isMonoid
d_isMonoid_924 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_464 ->
  MAlonzo.Code.Algebra.Structures.T_IsMonoid_358
d_isMonoid_924 :: T_IsIdempotentCommutativeMonoid_464 -> T_IsMonoid_358
d_isMonoid_924 T_IsIdempotentCommutativeMonoid_464
v0
  = (T_IsCommutativeMonoid_406 -> T_IsMonoid_358)
-> Any -> T_IsMonoid_358
forall a b. a -> b
coe
      T_IsCommutativeMonoid_406 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_416
      ((T_IsIdempotentCommutativeMonoid_464 -> T_IsCommutativeMonoid_406)
-> Any -> Any
forall a b. a -> b
coe
         T_IsIdempotentCommutativeMonoid_464 -> T_IsCommutativeMonoid_406
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_474 (T_IsIdempotentCommutativeMonoid_464 -> Any
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_464
v0))
-- Data.Bool.Properties._.IsIdempotentCommutativeMonoid.isSemigroup
d_isSemigroup_928 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_464 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_194
d_isSemigroup_928 :: T_IsIdempotentCommutativeMonoid_464 -> T_IsSemigroup_194
d_isSemigroup_928 T_IsIdempotentCommutativeMonoid_464
v0
  = (T_IsMonoid_358 -> T_IsSemigroup_194) -> Any -> T_IsSemigroup_194
forall a b. a -> b
coe
      T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368
      ((T_IsCommutativeMonoid_406 -> T_IsMonoid_358) -> Any -> Any
forall a b. a -> b
coe
         T_IsCommutativeMonoid_406 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_416
         ((T_IsIdempotentCommutativeMonoid_464 -> T_IsCommutativeMonoid_406)
-> Any -> Any
forall a b. a -> b
coe
            T_IsIdempotentCommutativeMonoid_464 -> T_IsCommutativeMonoid_406
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_474
            (T_IsIdempotentCommutativeMonoid_464 -> Any
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_464
v0)))
-- Data.Bool.Properties._.IsIdempotentCommutativeMonoid.∙-cong
d_'8729''45'cong_940 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_464 ->
  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_940 :: T_IsIdempotentCommutativeMonoid_464
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong_940 = T_IsIdempotentCommutativeMonoid_464
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsLattice.absorptive
d_absorptive_948 ::
  MAlonzo.Code.Algebra.Structures.T_IsLattice_740 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_absorptive_948 :: T_IsLattice_740 -> T_Σ_14
d_absorptive_948 T_IsLattice_740
v0
  = (T_IsLattice_740 -> T_Σ_14) -> Any -> T_Σ_14
forall a b. a -> b
coe T_IsLattice_740 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_absorptive_776 (T_IsLattice_740 -> Any
forall a b. a -> b
coe T_IsLattice_740
v0)
-- Data.Bool.Properties._.IsLattice.isEquivalence
d_isEquivalence_950 ::
  MAlonzo.Code.Algebra.Structures.T_IsLattice_740 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_950 :: T_IsLattice_740 -> T_IsEquivalence_26
d_isEquivalence_950 T_IsLattice_740
v0
  = (T_IsLattice_740 -> T_IsEquivalence_26)
-> Any -> T_IsEquivalence_26
forall a b. a -> b
coe T_IsLattice_740 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_762 (T_IsLattice_740 -> Any
forall a b. a -> b
coe T_IsLattice_740
v0)
-- Data.Bool.Properties._.IsLattice.∧-assoc
d_'8743''45'assoc_964 ::
  MAlonzo.Code.Algebra.Structures.T_IsLattice_740 ->
  Bool ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8743''45'assoc_964 :: T_IsLattice_740 -> Bool -> Bool -> Bool -> T__'8801'__12
d_'8743''45'assoc_964 = T_IsLattice_740 -> Bool -> Bool -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsLattice.∧-comm
d_'8743''45'comm_966 ::
  MAlonzo.Code.Algebra.Structures.T_IsLattice_740 ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8743''45'comm_966 :: T_IsLattice_740 -> Bool -> Bool -> T__'8801'__12
d_'8743''45'comm_966 = T_IsLattice_740 -> Bool -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsLattice.∧-cong
d_'8743''45'cong_968 ::
  MAlonzo.Code.Algebra.Structures.T_IsLattice_740 ->
  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_968 :: T_IsLattice_740
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
d_'8743''45'cong_968 = T_IsLattice_740
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsLattice.∨-assoc
d_'8744''45'assoc_976 ::
  MAlonzo.Code.Algebra.Structures.T_IsLattice_740 ->
  Bool ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8744''45'assoc_976 :: T_IsLattice_740 -> Bool -> Bool -> Bool -> T__'8801'__12
d_'8744''45'assoc_976 = T_IsLattice_740 -> Bool -> Bool -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsLattice.∨-comm
d_'8744''45'comm_978 ::
  MAlonzo.Code.Algebra.Structures.T_IsLattice_740 ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8744''45'comm_978 :: T_IsLattice_740 -> Bool -> Bool -> T__'8801'__12
d_'8744''45'comm_978 = T_IsLattice_740 -> Bool -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsLattice.∨-cong
d_'8744''45'cong_980 ::
  MAlonzo.Code.Algebra.Structures.T_IsLattice_740 ->
  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_980 :: T_IsLattice_740
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
d_'8744''45'cong_980 = T_IsLattice_740
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsMagma.isEquivalence
d_isEquivalence_988 ::
  MAlonzo.Code.Algebra.Structures.T_IsMagma_86 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_988 :: T_IsMagma_86 -> T_IsEquivalence_26
d_isEquivalence_988 T_IsMagma_86
v0
  = (T_IsMagma_86 -> T_IsEquivalence_26) -> Any -> T_IsEquivalence_26
forall a b. a -> b
coe T_IsMagma_86 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_94 (T_IsMagma_86 -> Any
forall a b. a -> b
coe T_IsMagma_86
v0)
-- Data.Bool.Properties._.IsMagma.∙-cong
d_'8729''45'cong_1002 ::
  MAlonzo.Code.Algebra.Structures.T_IsMagma_86 ->
  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_1002 :: T_IsMagma_86
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong_1002 = T_IsMagma_86
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsMonoid.assoc
d_assoc_1010 ::
  MAlonzo.Code.Algebra.Structures.T_IsMonoid_358 ->
  Bool ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_assoc_1010 :: T_IsMonoid_358 -> Bool -> Bool -> Bool -> T__'8801'__12
d_assoc_1010 = T_IsMonoid_358 -> Bool -> Bool -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsMonoid.identity
d_identity_1012 ::
  MAlonzo.Code.Algebra.Structures.T_IsMonoid_358 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_identity_1012 :: T_IsMonoid_358 -> T_Σ_14
d_identity_1012 T_IsMonoid_358
v0
  = (T_IsMonoid_358 -> T_Σ_14) -> Any -> T_Σ_14
forall a b. a -> b
coe T_IsMonoid_358 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_identity_370 (T_IsMonoid_358 -> Any
forall a b. a -> b
coe T_IsMonoid_358
v0)
-- Data.Bool.Properties._.IsMonoid.isEquivalence
d_isEquivalence_1018 ::
  MAlonzo.Code.Algebra.Structures.T_IsMonoid_358 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_1018 :: T_IsMonoid_358 -> T_IsEquivalence_26
d_isEquivalence_1018 T_IsMonoid_358
v0
  = (T_IsMagma_86 -> T_IsEquivalence_26) -> Any -> T_IsEquivalence_26
forall a b. a -> b
coe
      T_IsMagma_86 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_94
      ((T_IsSemigroup_194 -> T_IsMagma_86) -> Any -> Any
forall a b. a -> b
coe
         T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202
         ((T_IsMonoid_358 -> T_IsSemigroup_194) -> Any -> Any
forall a b. a -> b
coe T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368 (T_IsMonoid_358 -> Any
forall a b. a -> b
coe T_IsMonoid_358
v0)))
-- Data.Bool.Properties._.IsMonoid.isMagma
d_isMagma_1020 ::
  MAlonzo.Code.Algebra.Structures.T_IsMonoid_358 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_86
d_isMagma_1020 :: T_IsMonoid_358 -> T_IsMagma_86
d_isMagma_1020 T_IsMonoid_358
v0
  = (T_IsSemigroup_194 -> T_IsMagma_86) -> Any -> T_IsMagma_86
forall a b. a -> b
coe
      T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202
      ((T_IsMonoid_358 -> T_IsSemigroup_194) -> Any -> Any
forall a b. a -> b
coe T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368 (T_IsMonoid_358 -> Any
forall a b. a -> b
coe T_IsMonoid_358
v0))
-- Data.Bool.Properties._.IsMonoid.isSemigroup
d_isSemigroup_1024 ::
  MAlonzo.Code.Algebra.Structures.T_IsMonoid_358 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_194
d_isSemigroup_1024 :: T_IsMonoid_358 -> T_IsSemigroup_194
d_isSemigroup_1024 T_IsMonoid_358
v0
  = (T_IsMonoid_358 -> T_IsSemigroup_194) -> Any -> T_IsSemigroup_194
forall a b. a -> b
coe T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368 (T_IsMonoid_358 -> Any
forall a b. a -> b
coe T_IsMonoid_358
v0)
-- Data.Bool.Properties._.IsMonoid.∙-cong
d_'8729''45'cong_1036 ::
  MAlonzo.Code.Algebra.Structures.T_IsMonoid_358 ->
  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_1036 :: T_IsMonoid_358
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong_1036 = T_IsMonoid_358
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsNearSemiring.assoc
d_assoc_1044 ::
  MAlonzo.Code.Algebra.Structures.T_IsNearSemiring_876 ->
  Bool ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_assoc_1044 :: T_IsNearSemiring_876 -> Bool -> Bool -> Bool -> T__'8801'__12
d_assoc_1044 = T_IsNearSemiring_876 -> Bool -> Bool -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsNearSemiring.∙-cong
d_'8729''45'cong_1046 ::
  MAlonzo.Code.Algebra.Structures.T_IsNearSemiring_876 ->
  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_1046 :: T_IsNearSemiring_876
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong_1046 = T_IsNearSemiring_876
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsNearSemiring.isMagma
d_isMagma_1052 ::
  MAlonzo.Code.Algebra.Structures.T_IsNearSemiring_876 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_86
d_isMagma_1052 :: T_IsNearSemiring_876 -> T_IsMagma_86
d_isMagma_1052 T_IsNearSemiring_876
v0
  = (T_IsSemigroup_194 -> T_IsMagma_86) -> Any -> T_IsMagma_86
forall a b. a -> b
coe
      T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202
      ((T_IsNearSemiring_876 -> T_IsSemigroup_194) -> Any -> Any
forall a b. a -> b
coe
         T_IsNearSemiring_876 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_'42''45'isSemigroup_894 (T_IsNearSemiring_876 -> Any
forall a b. a -> b
coe T_IsNearSemiring_876
v0))
-- Data.Bool.Properties._.IsNearSemiring.*-isSemigroup
d_'42''45'isSemigroup_1054 ::
  MAlonzo.Code.Algebra.Structures.T_IsNearSemiring_876 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_194
d_'42''45'isSemigroup_1054 :: T_IsNearSemiring_876 -> T_IsSemigroup_194
d_'42''45'isSemigroup_1054 T_IsNearSemiring_876
v0
  = (T_IsNearSemiring_876 -> T_IsSemigroup_194)
-> Any -> T_IsSemigroup_194
forall a b. a -> b
coe
      T_IsNearSemiring_876 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_'42''45'isSemigroup_894 (T_IsNearSemiring_876 -> Any
forall a b. a -> b
coe T_IsNearSemiring_876
v0)
-- Data.Bool.Properties._.IsNearSemiring.assoc
d_assoc_1056 ::
  MAlonzo.Code.Algebra.Structures.T_IsNearSemiring_876 ->
  Bool ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_assoc_1056 :: T_IsNearSemiring_876 -> Bool -> Bool -> Bool -> T__'8801'__12
d_assoc_1056 = T_IsNearSemiring_876 -> Bool -> Bool -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsNearSemiring.∙-cong
d_'8729''45'cong_1058 ::
  MAlonzo.Code.Algebra.Structures.T_IsNearSemiring_876 ->
  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_1058 :: T_IsNearSemiring_876
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong_1058 = T_IsNearSemiring_876
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsNearSemiring.identity
d_identity_1064 ::
  MAlonzo.Code.Algebra.Structures.T_IsNearSemiring_876 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_identity_1064 :: T_IsNearSemiring_876 -> T_Σ_14
d_identity_1064 T_IsNearSemiring_876
v0
  = (T_IsMonoid_358 -> T_Σ_14) -> Any -> T_Σ_14
forall a b. a -> b
coe
      T_IsMonoid_358 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_identity_370
      ((T_IsNearSemiring_876 -> T_IsMonoid_358) -> Any -> Any
forall a b. a -> b
coe
         T_IsNearSemiring_876 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_'43''45'isMonoid_892 (T_IsNearSemiring_876 -> Any
forall a b. a -> b
coe T_IsNearSemiring_876
v0))
-- Data.Bool.Properties._.IsNearSemiring.isMagma
d_isMagma_1070 ::
  MAlonzo.Code.Algebra.Structures.T_IsNearSemiring_876 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_86
d_isMagma_1070 :: T_IsNearSemiring_876 -> T_IsMagma_86
d_isMagma_1070 T_IsNearSemiring_876
v0
  = (T_IsSemigroup_194 -> T_IsMagma_86) -> Any -> T_IsMagma_86
forall a b. a -> b
coe
      T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202
      ((T_IsMonoid_358 -> T_IsSemigroup_194) -> Any -> Any
forall a b. a -> b
coe
         T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368
         ((T_IsNearSemiring_876 -> T_IsMonoid_358) -> Any -> Any
forall a b. a -> b
coe
            T_IsNearSemiring_876 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_'43''45'isMonoid_892 (T_IsNearSemiring_876 -> Any
forall a b. a -> b
coe T_IsNearSemiring_876
v0)))
-- Data.Bool.Properties._.IsNearSemiring.+-isMonoid
d_'43''45'isMonoid_1072 ::
  MAlonzo.Code.Algebra.Structures.T_IsNearSemiring_876 ->
  MAlonzo.Code.Algebra.Structures.T_IsMonoid_358
d_'43''45'isMonoid_1072 :: T_IsNearSemiring_876 -> T_IsMonoid_358
d_'43''45'isMonoid_1072 T_IsNearSemiring_876
v0
  = (T_IsNearSemiring_876 -> T_IsMonoid_358) -> Any -> T_IsMonoid_358
forall a b. a -> b
coe
      T_IsNearSemiring_876 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_'43''45'isMonoid_892 (T_IsNearSemiring_876 -> Any
forall a b. a -> b
coe T_IsNearSemiring_876
v0)
-- Data.Bool.Properties._.IsNearSemiring.isSemigroup
d_isSemigroup_1074 ::
  MAlonzo.Code.Algebra.Structures.T_IsNearSemiring_876 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_194
d_isSemigroup_1074 :: T_IsNearSemiring_876 -> T_IsSemigroup_194
d_isSemigroup_1074 T_IsNearSemiring_876
v0
  = (T_IsMonoid_358 -> T_IsSemigroup_194) -> Any -> T_IsSemigroup_194
forall a b. a -> b
coe
      T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368
      ((T_IsNearSemiring_876 -> T_IsMonoid_358) -> Any -> Any
forall a b. a -> b
coe
         T_IsNearSemiring_876 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_'43''45'isMonoid_892 (T_IsNearSemiring_876 -> Any
forall a b. a -> b
coe T_IsNearSemiring_876
v0))
-- Data.Bool.Properties._.IsNearSemiring.distribʳ
d_distrib'691'_1076 ::
  MAlonzo.Code.Algebra.Structures.T_IsNearSemiring_876 ->
  Bool ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_distrib'691'_1076 :: T_IsNearSemiring_876 -> Bool -> Bool -> Bool -> T__'8801'__12
d_distrib'691'_1076 = T_IsNearSemiring_876 -> Bool -> Bool -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsNearSemiring.isEquivalence
d_isEquivalence_1078 ::
  MAlonzo.Code.Algebra.Structures.T_IsNearSemiring_876 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_1078 :: T_IsNearSemiring_876 -> T_IsEquivalence_26
d_isEquivalence_1078 T_IsNearSemiring_876
v0
  = (T_IsMagma_86 -> T_IsEquivalence_26) -> Any -> T_IsEquivalence_26
forall a b. a -> b
coe
      T_IsMagma_86 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_94
      ((T_IsSemigroup_194 -> T_IsMagma_86) -> Any -> Any
forall a b. a -> b
coe
         T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202
         ((T_IsMonoid_358 -> T_IsSemigroup_194) -> Any -> Any
forall a b. a -> b
coe
            T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368
            ((T_IsNearSemiring_876 -> T_IsMonoid_358) -> Any -> Any
forall a b. a -> b
coe
               T_IsNearSemiring_876 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_'43''45'isMonoid_892 (T_IsNearSemiring_876 -> Any
forall a b. a -> b
coe T_IsNearSemiring_876
v0))))
-- Data.Bool.Properties._.IsNearSemiring.zeroˡ
d_zero'737'_1092 ::
  MAlonzo.Code.Algebra.Structures.T_IsNearSemiring_876 ->
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_zero'737'_1092 :: T_IsNearSemiring_876 -> Bool -> T__'8801'__12
d_zero'737'_1092 = T_IsNearSemiring_876 -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsRing.assoc
d_assoc_1098 ::
  MAlonzo.Code.Algebra.Structures.T_IsRing_1584 ->
  Bool ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_assoc_1098 :: T_IsRing_1584 -> Bool -> Bool -> Bool -> T__'8801'__12
d_assoc_1098 = T_IsRing_1584 -> Bool -> Bool -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsRing.∙-cong
d_'8729''45'cong_1100 ::
  MAlonzo.Code.Algebra.Structures.T_IsRing_1584 ->
  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_1100 :: T_IsRing_1584
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong_1100 = T_IsRing_1584
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsRing.identity
d_identity_1106 ::
  MAlonzo.Code.Algebra.Structures.T_IsRing_1584 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_identity_1106 :: T_IsRing_1584 -> T_Σ_14
d_identity_1106 T_IsRing_1584
v0
  = (T_IsMonoid_358 -> T_Σ_14) -> Any -> T_Σ_14
forall a b. a -> b
coe
      T_IsMonoid_358 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_identity_370
      ((T_IsRing_1584 -> T_IsMonoid_358) -> Any -> Any
forall a b. a -> b
coe
         T_IsRing_1584 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_'42''45'isMonoid_1606 (T_IsRing_1584 -> Any
forall a b. a -> b
coe T_IsRing_1584
v0))
-- Data.Bool.Properties._.IsRing.isMagma
d_isMagma_1112 ::
  MAlonzo.Code.Algebra.Structures.T_IsRing_1584 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_86
d_isMagma_1112 :: T_IsRing_1584 -> T_IsMagma_86
d_isMagma_1112 T_IsRing_1584
v0
  = (T_IsSemigroup_194 -> T_IsMagma_86) -> Any -> T_IsMagma_86
forall a b. a -> b
coe
      T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202
      ((T_IsMonoid_358 -> T_IsSemigroup_194) -> Any -> Any
forall a b. a -> b
coe
         T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368
         ((T_IsRing_1584 -> T_IsMonoid_358) -> Any -> Any
forall a b. a -> b
coe
            T_IsRing_1584 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_'42''45'isMonoid_1606 (T_IsRing_1584 -> Any
forall a b. a -> b
coe T_IsRing_1584
v0)))
-- Data.Bool.Properties._.IsRing.*-isMonoid
d_'42''45'isMonoid_1114 ::
  MAlonzo.Code.Algebra.Structures.T_IsRing_1584 ->
  MAlonzo.Code.Algebra.Structures.T_IsMonoid_358
d_'42''45'isMonoid_1114 :: T_IsRing_1584 -> T_IsMonoid_358
d_'42''45'isMonoid_1114 T_IsRing_1584
v0
  = (T_IsRing_1584 -> T_IsMonoid_358) -> Any -> T_IsMonoid_358
forall a b. a -> b
coe
      T_IsRing_1584 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_'42''45'isMonoid_1606 (T_IsRing_1584 -> Any
forall a b. a -> b
coe T_IsRing_1584
v0)
-- Data.Bool.Properties._.IsRing.isSemigroup
d_isSemigroup_1116 ::
  MAlonzo.Code.Algebra.Structures.T_IsRing_1584 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_194
d_isSemigroup_1116 :: T_IsRing_1584 -> T_IsSemigroup_194
d_isSemigroup_1116 T_IsRing_1584
v0
  = (T_IsMonoid_358 -> T_IsSemigroup_194) -> Any -> T_IsSemigroup_194
forall a b. a -> b
coe
      T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368
      ((T_IsRing_1584 -> T_IsMonoid_358) -> Any -> Any
forall a b. a -> b
coe
         T_IsRing_1584 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_'42''45'isMonoid_1606 (T_IsRing_1584 -> Any
forall a b. a -> b
coe T_IsRing_1584
v0))
-- Data.Bool.Properties._.IsRing.assoc
d_assoc_1118 ::
  MAlonzo.Code.Algebra.Structures.T_IsRing_1584 ->
  Bool ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_assoc_1118 :: T_IsRing_1584 -> Bool -> Bool -> Bool -> T__'8801'__12
d_assoc_1118 = T_IsRing_1584 -> Bool -> Bool -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsRing.comm
d_comm_1120 ::
  MAlonzo.Code.Algebra.Structures.T_IsRing_1584 ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_comm_1120 :: T_IsRing_1584 -> Bool -> Bool -> T__'8801'__12
d_comm_1120 = T_IsRing_1584 -> Bool -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsRing.∙-cong
d_'8729''45'cong_1122 ::
  MAlonzo.Code.Algebra.Structures.T_IsRing_1584 ->
  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_1122 :: T_IsRing_1584
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong_1122 = T_IsRing_1584
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsRing.identity
d_identity_1128 ::
  MAlonzo.Code.Algebra.Structures.T_IsRing_1584 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_identity_1128 :: T_IsRing_1584 -> T_Σ_14
d_identity_1128 T_IsRing_1584
v0
  = (T_IsMonoid_358 -> T_Σ_14) -> Any -> T_Σ_14
forall a b. a -> b
coe
      T_IsMonoid_358 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_identity_370
      ((T_IsGroup_580 -> T_IsMonoid_358) -> Any -> Any
forall a b. a -> b
coe
         T_IsGroup_580 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_594
         ((T_IsAbelianGroup_662 -> T_IsGroup_580) -> Any -> Any
forall a b. a -> b
coe
            T_IsAbelianGroup_662 -> T_IsGroup_580
MAlonzo.Code.Algebra.Structures.d_isGroup_674
            ((T_IsRing_1584 -> T_IsAbelianGroup_662) -> Any -> Any
forall a b. a -> b
coe
               T_IsRing_1584 -> T_IsAbelianGroup_662
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_1604
               (T_IsRing_1584 -> Any
forall a b. a -> b
coe T_IsRing_1584
v0))))
-- Data.Bool.Properties._.IsRing.+-isAbelianGroup
d_'43''45'isAbelianGroup_1134 ::
  MAlonzo.Code.Algebra.Structures.T_IsRing_1584 ->
  MAlonzo.Code.Algebra.Structures.T_IsAbelianGroup_662
d_'43''45'isAbelianGroup_1134 :: T_IsRing_1584 -> T_IsAbelianGroup_662
d_'43''45'isAbelianGroup_1134 T_IsRing_1584
v0
  = (T_IsRing_1584 -> T_IsAbelianGroup_662)
-> Any -> T_IsAbelianGroup_662
forall a b. a -> b
coe
      T_IsRing_1584 -> T_IsAbelianGroup_662
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_1604
      (T_IsRing_1584 -> Any
forall a b. a -> b
coe T_IsRing_1584
v0)
-- Data.Bool.Properties._.IsRing.isGroup
d_isGroup_1142 ::
  MAlonzo.Code.Algebra.Structures.T_IsRing_1584 ->
  MAlonzo.Code.Algebra.Structures.T_IsGroup_580
d_isGroup_1142 :: T_IsRing_1584 -> T_IsGroup_580
d_isGroup_1142 T_IsRing_1584
v0
  = (T_IsAbelianGroup_662 -> T_IsGroup_580) -> Any -> T_IsGroup_580
forall a b. a -> b
coe
      T_IsAbelianGroup_662 -> T_IsGroup_580
MAlonzo.Code.Algebra.Structures.d_isGroup_674
      ((T_IsRing_1584 -> T_IsAbelianGroup_662) -> Any -> Any
forall a b. a -> b
coe
         T_IsRing_1584 -> T_IsAbelianGroup_662
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_1604
         (T_IsRing_1584 -> Any
forall a b. a -> b
coe T_IsRing_1584
v0))
-- Data.Bool.Properties._.IsRing.isMagma
d_isMagma_1144 ::
  MAlonzo.Code.Algebra.Structures.T_IsRing_1584 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_86
d_isMagma_1144 :: T_IsRing_1584 -> T_IsMagma_86
d_isMagma_1144 T_IsRing_1584
v0
  = (T_IsSemigroup_194 -> T_IsMagma_86) -> Any -> T_IsMagma_86
forall a b. a -> b
coe
      T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202
      ((T_IsMonoid_358 -> T_IsSemigroup_194) -> Any -> Any
forall a b. a -> b
coe
         T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368
         ((T_IsGroup_580 -> T_IsMonoid_358) -> Any -> Any
forall a b. a -> b
coe
            T_IsGroup_580 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_594
            ((T_IsAbelianGroup_662 -> T_IsGroup_580) -> Any -> Any
forall a b. a -> b
coe
               T_IsAbelianGroup_662 -> T_IsGroup_580
MAlonzo.Code.Algebra.Structures.d_isGroup_674
               ((T_IsRing_1584 -> T_IsAbelianGroup_662) -> Any -> Any
forall a b. a -> b
coe
                  T_IsRing_1584 -> T_IsAbelianGroup_662
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_1604
                  (T_IsRing_1584 -> Any
forall a b. a -> b
coe T_IsRing_1584
v0)))))
-- Data.Bool.Properties._.IsRing.isMonoid
d_isMonoid_1146 ::
  MAlonzo.Code.Algebra.Structures.T_IsRing_1584 ->
  MAlonzo.Code.Algebra.Structures.T_IsMonoid_358
d_isMonoid_1146 :: T_IsRing_1584 -> T_IsMonoid_358
d_isMonoid_1146 T_IsRing_1584
v0
  = (T_IsGroup_580 -> T_IsMonoid_358) -> Any -> T_IsMonoid_358
forall a b. a -> b
coe
      T_IsGroup_580 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_594
      ((T_IsAbelianGroup_662 -> T_IsGroup_580) -> Any -> Any
forall a b. a -> b
coe
         T_IsAbelianGroup_662 -> T_IsGroup_580
MAlonzo.Code.Algebra.Structures.d_isGroup_674
         ((T_IsRing_1584 -> T_IsAbelianGroup_662) -> Any -> Any
forall a b. a -> b
coe
            T_IsRing_1584 -> T_IsAbelianGroup_662
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_1604
            (T_IsRing_1584 -> Any
forall a b. a -> b
coe T_IsRing_1584
v0)))
-- Data.Bool.Properties._.IsRing.isSemigroup
d_isSemigroup_1148 ::
  MAlonzo.Code.Algebra.Structures.T_IsRing_1584 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_194
d_isSemigroup_1148 :: T_IsRing_1584 -> T_IsSemigroup_194
d_isSemigroup_1148 T_IsRing_1584
v0
  = (T_IsMonoid_358 -> T_IsSemigroup_194) -> Any -> T_IsSemigroup_194
forall a b. a -> b
coe
      T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368
      ((T_IsGroup_580 -> T_IsMonoid_358) -> Any -> Any
forall a b. a -> b
coe
         T_IsGroup_580 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_594
         ((T_IsAbelianGroup_662 -> T_IsGroup_580) -> Any -> Any
forall a b. a -> b
coe
            T_IsAbelianGroup_662 -> T_IsGroup_580
MAlonzo.Code.Algebra.Structures.d_isGroup_674
            ((T_IsRing_1584 -> T_IsAbelianGroup_662) -> Any -> Any
forall a b. a -> b
coe
               T_IsRing_1584 -> T_IsAbelianGroup_662
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_1604
               (T_IsRing_1584 -> Any
forall a b. a -> b
coe T_IsRing_1584
v0))))
-- Data.Bool.Properties._.IsRing.⁻¹-cong
d_'8315''185''45'cong_1150 ::
  MAlonzo.Code.Algebra.Structures.T_IsRing_1584 ->
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8315''185''45'cong_1150 :: T_IsRing_1584 -> Bool -> Bool -> T__'8801'__12 -> T__'8801'__12
d_'8315''185''45'cong_1150 = T_IsRing_1584 -> Bool -> Bool -> T__'8801'__12 -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsRing.inverse
d_inverse_1152 ::
  MAlonzo.Code.Algebra.Structures.T_IsRing_1584 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_inverse_1152 :: T_IsRing_1584 -> T_Σ_14
d_inverse_1152 T_IsRing_1584
v0
  = (T_IsGroup_580 -> T_Σ_14) -> Any -> T_Σ_14
forall a b. a -> b
coe
      T_IsGroup_580 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_inverse_596
      ((T_IsAbelianGroup_662 -> T_IsGroup_580) -> Any -> Any
forall a b. a -> b
coe
         T_IsAbelianGroup_662 -> T_IsGroup_580
MAlonzo.Code.Algebra.Structures.d_isGroup_674
         ((T_IsRing_1584 -> T_IsAbelianGroup_662) -> Any -> Any
forall a b. a -> b
coe
            T_IsRing_1584 -> T_IsAbelianGroup_662
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_1604
            (T_IsRing_1584 -> Any
forall a b. a -> b
coe T_IsRing_1584
v0)))
-- Data.Bool.Properties._.IsRing.distrib
d_distrib_1158 ::
  MAlonzo.Code.Algebra.Structures.T_IsRing_1584 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_distrib_1158 :: T_IsRing_1584 -> T_Σ_14
d_distrib_1158 T_IsRing_1584
v0
  = (T_IsRing_1584 -> T_Σ_14) -> Any -> T_Σ_14
forall a b. a -> b
coe T_IsRing_1584 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_distrib_1608 (T_IsRing_1584 -> Any
forall a b. a -> b
coe T_IsRing_1584
v0)
-- Data.Bool.Properties._.IsRing.isEquivalence
d_isEquivalence_1164 ::
  MAlonzo.Code.Algebra.Structures.T_IsRing_1584 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_1164 :: T_IsRing_1584 -> T_IsEquivalence_26
d_isEquivalence_1164 T_IsRing_1584
v0
  = (T_IsMagma_86 -> T_IsEquivalence_26) -> Any -> T_IsEquivalence_26
forall a b. a -> b
coe
      T_IsMagma_86 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_94
      ((T_IsSemigroup_194 -> T_IsMagma_86) -> Any -> Any
forall a b. a -> b
coe
         T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202
         ((T_IsMonoid_358 -> T_IsSemigroup_194) -> Any -> Any
forall a b. a -> b
coe
            T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368
            ((T_IsGroup_580 -> T_IsMonoid_358) -> Any -> Any
forall a b. a -> b
coe
               T_IsGroup_580 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_594
               ((T_IsAbelianGroup_662 -> T_IsGroup_580) -> Any -> Any
forall a b. a -> b
coe
                  T_IsAbelianGroup_662 -> T_IsGroup_580
MAlonzo.Code.Algebra.Structures.d_isGroup_674
                  ((T_IsRing_1584 -> T_IsAbelianGroup_662) -> Any -> Any
forall a b. a -> b
coe
                     T_IsRing_1584 -> T_IsAbelianGroup_662
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_1604
                     (T_IsRing_1584 -> Any
forall a b. a -> b
coe T_IsRing_1584
v0))))))
-- Data.Bool.Properties._.IsRing.isNearSemiring
d_isNearSemiring_1166 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsRing_1584 ->
  MAlonzo.Code.Algebra.Structures.T_IsNearSemiring_876
d_isNearSemiring_1166 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsRing_1584
-> T_IsNearSemiring_876
d_isNearSemiring_1166 ~Bool -> Bool -> Bool
v0 ~Bool -> Bool -> Bool
v1 ~Bool -> Bool
v2 ~Bool
v3 ~Bool
v4 T_IsRing_1584
v5
  = T_IsRing_1584 -> T_IsNearSemiring_876
du_isNearSemiring_1166 T_IsRing_1584
v5
du_isNearSemiring_1166 ::
  MAlonzo.Code.Algebra.Structures.T_IsRing_1584 ->
  MAlonzo.Code.Algebra.Structures.T_IsNearSemiring_876
du_isNearSemiring_1166 :: T_IsRing_1584 -> T_IsNearSemiring_876
du_isNearSemiring_1166 T_IsRing_1584
v0
  = let v1 :: t
v1
          = (T_IsRing_1584 -> T_IsSemiring_1238) -> Any -> t
forall a b. a -> b
coe
              T_IsRing_1584 -> T_IsSemiring_1238
MAlonzo.Code.Algebra.Structures.du_isSemiring_1698 (T_IsRing_1584 -> Any
forall a b. a -> b
coe T_IsRing_1584
v0) in
    Any -> T_IsNearSemiring_876
forall a b. a -> b
coe
      ((T_IsSemiringWithoutOne_952 -> T_IsNearSemiring_876) -> Any -> Any
forall a b. a -> b
coe
         T_IsSemiringWithoutOne_952 -> T_IsNearSemiring_876
MAlonzo.Code.Algebra.Structures.du_isNearSemiring_990
         ((T_IsSemiring_1238 -> T_IsSemiringWithoutOne_952) -> Any -> Any
forall a b. a -> b
coe
            T_IsSemiring_1238 -> T_IsSemiringWithoutOne_952
MAlonzo.Code.Algebra.Structures.du_isSemiringWithoutOne_1326
            (Any -> Any
forall a b. a -> b
coe Any
forall a. a
v1)))
-- Data.Bool.Properties._.IsRing.isSemiring
d_isSemiring_1170 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsRing_1584 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemiring_1238
d_isSemiring_1170 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsRing_1584
-> T_IsSemiring_1238
d_isSemiring_1170 Bool -> Bool -> Bool
v0 Bool -> Bool -> Bool
v1 Bool -> Bool
v2 Bool
v3 Bool
v4 T_IsRing_1584
v5
  = (T_IsRing_1584 -> T_IsSemiring_1238)
-> T_IsRing_1584 -> T_IsSemiring_1238
forall a b. a -> b
coe T_IsRing_1584 -> T_IsSemiring_1238
MAlonzo.Code.Algebra.Structures.du_isSemiring_1698 T_IsRing_1584
v5
-- Data.Bool.Properties._.IsRing.isSemiringWithoutOne
d_isSemiringWithoutOne_1174 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsRing_1584 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutOne_952
d_isSemiringWithoutOne_1174 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Bool
-> Bool
-> T_IsRing_1584
-> T_IsSemiringWithoutOne_952
d_isSemiringWithoutOne_1174 ~Bool -> Bool -> Bool
v0 ~Bool -> Bool -> Bool
v1 ~Bool -> Bool
v2 ~Bool
v3 ~Bool
v4 T_IsRing_1584
v5
  = T_IsRing_1584 -> T_IsSemiringWithoutOne_952
du_isSemiringWithoutOne_1174 T_IsRing_1584
v5
du_isSemiringWithoutOne_1174 ::
  MAlonzo.Code.Algebra.Structures.T_IsRing_1584 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutOne_952
du_isSemiringWithoutOne_1174 :: T_IsRing_1584 -> T_IsSemiringWithoutOne_952
du_isSemiringWithoutOne_1174 T_IsRing_1584
v0
  = (T_IsSemiring_1238 -> T_IsSemiringWithoutOne_952)
-> Any -> T_IsSemiringWithoutOne_952
forall a b. a -> b
coe
      T_IsSemiring_1238 -> T_IsSemiringWithoutOne_952
MAlonzo.Code.Algebra.Structures.du_isSemiringWithoutOne_1326
      ((T_IsRing_1584 -> T_IsSemiring_1238) -> Any -> Any
forall a b. a -> b
coe T_IsRing_1584 -> T_IsSemiring_1238
MAlonzo.Code.Algebra.Structures.du_isSemiring_1698 (T_IsRing_1584 -> Any
forall a b. a -> b
coe T_IsRing_1584
v0))
-- Data.Bool.Properties._.IsRing.zero
d_zero_1190 ::
  MAlonzo.Code.Algebra.Structures.T_IsRing_1584 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_zero_1190 :: T_IsRing_1584 -> T_Σ_14
d_zero_1190 T_IsRing_1584
v0
  = (T_IsRing_1584 -> T_Σ_14) -> Any -> T_Σ_14
forall a b. a -> b
coe T_IsRing_1584 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_zero_1610 (T_IsRing_1584 -> Any
forall a b. a -> b
coe T_IsRing_1584
v0)
-- Data.Bool.Properties._.IsSelectiveMagma.isEquivalence
d_isEquivalence_1198 ::
  MAlonzo.Code.Algebra.Structures.T_IsSelectiveMagma_158 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_1198 :: T_IsSelectiveMagma_158 -> T_IsEquivalence_26
d_isEquivalence_1198 T_IsSelectiveMagma_158
v0
  = (T_IsMagma_86 -> T_IsEquivalence_26) -> Any -> T_IsEquivalence_26
forall a b. a -> b
coe
      T_IsMagma_86 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_94
      ((T_IsSelectiveMagma_158 -> T_IsMagma_86) -> Any -> Any
forall a b. a -> b
coe T_IsSelectiveMagma_158 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_166 (T_IsSelectiveMagma_158 -> Any
forall a b. a -> b
coe T_IsSelectiveMagma_158
v0))
-- Data.Bool.Properties._.IsSelectiveMagma.isMagma
d_isMagma_1200 ::
  MAlonzo.Code.Algebra.Structures.T_IsSelectiveMagma_158 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_86
d_isMagma_1200 :: T_IsSelectiveMagma_158 -> T_IsMagma_86
d_isMagma_1200 T_IsSelectiveMagma_158
v0
  = (T_IsSelectiveMagma_158 -> T_IsMagma_86) -> Any -> T_IsMagma_86
forall a b. a -> b
coe T_IsSelectiveMagma_158 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_166 (T_IsSelectiveMagma_158 -> Any
forall a b. a -> b
coe T_IsSelectiveMagma_158
v0)
-- Data.Bool.Properties._.IsSelectiveMagma.sel
d_sel_1208 ::
  MAlonzo.Code.Algebra.Structures.T_IsSelectiveMagma_158 ->
  Bool -> Bool -> MAlonzo.Code.Data.Sum.Base.T__'8846'__30
d_sel_1208 :: T_IsSelectiveMagma_158 -> Bool -> Bool -> T__'8846'__30
d_sel_1208 T_IsSelectiveMagma_158
v0
  = (T_IsSelectiveMagma_158 -> Any -> Any -> T__'8846'__30)
-> Any -> Bool -> Bool -> T__'8846'__30
forall a b. a -> b
coe T_IsSelectiveMagma_158 -> Any -> Any -> T__'8846'__30
MAlonzo.Code.Algebra.Structures.d_sel_168 (T_IsSelectiveMagma_158 -> Any
forall a b. a -> b
coe T_IsSelectiveMagma_158
v0)
-- Data.Bool.Properties._.IsSelectiveMagma.∙-cong
d_'8729''45'cong_1216 ::
  MAlonzo.Code.Algebra.Structures.T_IsSelectiveMagma_158 ->
  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_1216 :: T_IsSelectiveMagma_158
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong_1216 = T_IsSelectiveMagma_158
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsSemigroup.assoc
d_assoc_1224 ::
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_194 ->
  Bool ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_assoc_1224 :: T_IsSemigroup_194 -> Bool -> Bool -> Bool -> T__'8801'__12
d_assoc_1224 = T_IsSemigroup_194 -> Bool -> Bool -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsSemigroup.isEquivalence
d_isEquivalence_1226 ::
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_194 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_1226 :: T_IsSemigroup_194 -> T_IsEquivalence_26
d_isEquivalence_1226 T_IsSemigroup_194
v0
  = (T_IsMagma_86 -> T_IsEquivalence_26) -> Any -> T_IsEquivalence_26
forall a b. a -> b
coe
      T_IsMagma_86 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_94
      ((T_IsSemigroup_194 -> T_IsMagma_86) -> Any -> Any
forall a b. a -> b
coe T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202 (T_IsSemigroup_194 -> Any
forall a b. a -> b
coe T_IsSemigroup_194
v0))
-- Data.Bool.Properties._.IsSemigroup.isMagma
d_isMagma_1228 ::
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_194 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_86
d_isMagma_1228 :: T_IsSemigroup_194 -> T_IsMagma_86
d_isMagma_1228 T_IsSemigroup_194
v0
  = (T_IsSemigroup_194 -> T_IsMagma_86) -> Any -> T_IsMagma_86
forall a b. a -> b
coe T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202 (T_IsSemigroup_194 -> Any
forall a b. a -> b
coe T_IsSemigroup_194
v0)
-- Data.Bool.Properties._.IsSemigroup.∙-cong
d_'8729''45'cong_1242 ::
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_194 ->
  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_1242 :: T_IsSemigroup_194
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong_1242 = T_IsSemigroup_194
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsSemilattice.assoc
d_assoc_1250 ::
  MAlonzo.Code.Algebra.Structures.T_IsSemilattice_312 ->
  Bool ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_assoc_1250 :: T_IsSemilattice_312 -> Bool -> Bool -> Bool -> T__'8801'__12
d_assoc_1250 = T_IsSemilattice_312 -> Bool -> Bool -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsSemilattice.comm
d_comm_1252 ::
  MAlonzo.Code.Algebra.Structures.T_IsSemilattice_312 ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_comm_1252 :: T_IsSemilattice_312 -> Bool -> Bool -> T__'8801'__12
d_comm_1252 = T_IsSemilattice_312 -> Bool -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsSemilattice.idem
d_idem_1254 ::
  MAlonzo.Code.Algebra.Structures.T_IsSemilattice_312 ->
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_idem_1254 :: T_IsSemilattice_312 -> Bool -> T__'8801'__12
d_idem_1254 = T_IsSemilattice_312 -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsSemilattice.isBand
d_isBand_1256 ::
  MAlonzo.Code.Algebra.Structures.T_IsSemilattice_312 ->
  MAlonzo.Code.Algebra.Structures.T_IsBand_230
d_isBand_1256 :: T_IsSemilattice_312 -> T_IsBand_230
d_isBand_1256 T_IsSemilattice_312
v0
  = (T_IsSemilattice_312 -> T_IsBand_230) -> Any -> T_IsBand_230
forall a b. a -> b
coe T_IsSemilattice_312 -> T_IsBand_230
MAlonzo.Code.Algebra.Structures.d_isBand_320 (T_IsSemilattice_312 -> Any
forall a b. a -> b
coe T_IsSemilattice_312
v0)
-- Data.Bool.Properties._.IsSemilattice.isEquivalence
d_isEquivalence_1258 ::
  MAlonzo.Code.Algebra.Structures.T_IsSemilattice_312 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_1258 :: T_IsSemilattice_312 -> T_IsEquivalence_26
d_isEquivalence_1258 T_IsSemilattice_312
v0
  = (T_IsMagma_86 -> T_IsEquivalence_26) -> Any -> T_IsEquivalence_26
forall a b. a -> b
coe
      T_IsMagma_86 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_94
      ((T_IsSemigroup_194 -> T_IsMagma_86) -> Any -> Any
forall a b. a -> b
coe
         T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202
         ((T_IsBand_230 -> T_IsSemigroup_194) -> Any -> Any
forall a b. a -> b
coe
            T_IsBand_230 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_238
            ((T_IsSemilattice_312 -> T_IsBand_230) -> Any -> Any
forall a b. a -> b
coe T_IsSemilattice_312 -> T_IsBand_230
MAlonzo.Code.Algebra.Structures.d_isBand_320 (T_IsSemilattice_312 -> Any
forall a b. a -> b
coe T_IsSemilattice_312
v0))))
-- Data.Bool.Properties._.IsSemilattice.isMagma
d_isMagma_1260 ::
  MAlonzo.Code.Algebra.Structures.T_IsSemilattice_312 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_86
d_isMagma_1260 :: T_IsSemilattice_312 -> T_IsMagma_86
d_isMagma_1260 T_IsSemilattice_312
v0
  = (T_IsSemigroup_194 -> T_IsMagma_86) -> Any -> T_IsMagma_86
forall a b. a -> b
coe
      T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202
      ((T_IsBand_230 -> T_IsSemigroup_194) -> Any -> Any
forall a b. a -> b
coe
         T_IsBand_230 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_238
         ((T_IsSemilattice_312 -> T_IsBand_230) -> Any -> Any
forall a b. a -> b
coe T_IsSemilattice_312 -> T_IsBand_230
MAlonzo.Code.Algebra.Structures.d_isBand_320 (T_IsSemilattice_312 -> Any
forall a b. a -> b
coe T_IsSemilattice_312
v0)))
-- Data.Bool.Properties._.IsSemilattice.isSemigroup
d_isSemigroup_1264 ::
  MAlonzo.Code.Algebra.Structures.T_IsSemilattice_312 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_194
d_isSemigroup_1264 :: T_IsSemilattice_312 -> T_IsSemigroup_194
d_isSemigroup_1264 T_IsSemilattice_312
v0
  = (T_IsBand_230 -> T_IsSemigroup_194) -> Any -> T_IsSemigroup_194
forall a b. a -> b
coe
      T_IsBand_230 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_238
      ((T_IsSemilattice_312 -> T_IsBand_230) -> Any -> Any
forall a b. a -> b
coe T_IsSemilattice_312 -> T_IsBand_230
MAlonzo.Code.Algebra.Structures.d_isBand_320 (T_IsSemilattice_312 -> Any
forall a b. a -> b
coe T_IsSemilattice_312
v0))
-- Data.Bool.Properties._.IsSemilattice.∙-cong
d_'8729''45'cong_1276 ::
  MAlonzo.Code.Algebra.Structures.T_IsSemilattice_312 ->
  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_1276 :: T_IsSemilattice_312
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong_1276 = T_IsSemilattice_312
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsSemiring.assoc
d_assoc_1284 ::
  MAlonzo.Code.Algebra.Structures.T_IsSemiring_1238 ->
  Bool ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_assoc_1284 :: T_IsSemiring_1238 -> Bool -> Bool -> Bool -> T__'8801'__12
d_assoc_1284 = T_IsSemiring_1238 -> Bool -> Bool -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsSemiring.∙-cong
d_'8729''45'cong_1286 ::
  MAlonzo.Code.Algebra.Structures.T_IsSemiring_1238 ->
  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_1286 :: T_IsSemiring_1238
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong_1286 = T_IsSemiring_1238
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsSemiring.identity
d_identity_1292 ::
  MAlonzo.Code.Algebra.Structures.T_IsSemiring_1238 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_identity_1292 :: T_IsSemiring_1238 -> T_Σ_14
d_identity_1292 T_IsSemiring_1238
v0
  = (T_IsMonoid_358 -> T_Σ_14) -> Any -> T_Σ_14
forall a b. a -> b
coe
      T_IsMonoid_358 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_identity_370
      ((T_IsSemiringWithoutAnnihilatingZero_1142 -> T_IsMonoid_358)
-> Any -> Any
forall a b. a -> b
coe
         T_IsSemiringWithoutAnnihilatingZero_1142 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_'42''45'isMonoid_1160
         ((T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142)
-> Any -> Any
forall a b. a -> b
coe
            T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1252
            (T_IsSemiring_1238 -> Any
forall a b. a -> b
coe T_IsSemiring_1238
v0)))
-- Data.Bool.Properties._.IsSemiring.isMagma
d_isMagma_1298 ::
  MAlonzo.Code.Algebra.Structures.T_IsSemiring_1238 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_86
d_isMagma_1298 :: T_IsSemiring_1238 -> T_IsMagma_86
d_isMagma_1298 T_IsSemiring_1238
v0
  = (T_IsSemigroup_194 -> T_IsMagma_86) -> Any -> T_IsMagma_86
forall a b. a -> b
coe
      T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202
      ((T_IsMonoid_358 -> T_IsSemigroup_194) -> Any -> Any
forall a b. a -> b
coe
         T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368
         ((T_IsSemiringWithoutAnnihilatingZero_1142 -> T_IsMonoid_358)
-> Any -> Any
forall a b. a -> b
coe
            T_IsSemiringWithoutAnnihilatingZero_1142 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_'42''45'isMonoid_1160
            ((T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142)
-> Any -> Any
forall a b. a -> b
coe
               T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1252
               (T_IsSemiring_1238 -> Any
forall a b. a -> b
coe T_IsSemiring_1238
v0))))
-- Data.Bool.Properties._.IsSemiring.*-isMonoid
d_'42''45'isMonoid_1300 ::
  MAlonzo.Code.Algebra.Structures.T_IsSemiring_1238 ->
  MAlonzo.Code.Algebra.Structures.T_IsMonoid_358
d_'42''45'isMonoid_1300 :: T_IsSemiring_1238 -> T_IsMonoid_358
d_'42''45'isMonoid_1300 T_IsSemiring_1238
v0
  = (T_IsSemiringWithoutAnnihilatingZero_1142 -> T_IsMonoid_358)
-> Any -> T_IsMonoid_358
forall a b. a -> b
coe
      T_IsSemiringWithoutAnnihilatingZero_1142 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_'42''45'isMonoid_1160
      ((T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142)
-> Any -> Any
forall a b. a -> b
coe
         T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1252
         (T_IsSemiring_1238 -> Any
forall a b. a -> b
coe T_IsSemiring_1238
v0))
-- Data.Bool.Properties._.IsSemiring.isSemigroup
d_isSemigroup_1302 ::
  MAlonzo.Code.Algebra.Structures.T_IsSemiring_1238 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_194
d_isSemigroup_1302 :: T_IsSemiring_1238 -> T_IsSemigroup_194
d_isSemigroup_1302 T_IsSemiring_1238
v0
  = (T_IsMonoid_358 -> T_IsSemigroup_194) -> Any -> T_IsSemigroup_194
forall a b. a -> b
coe
      T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368
      ((T_IsSemiringWithoutAnnihilatingZero_1142 -> T_IsMonoid_358)
-> Any -> Any
forall a b. a -> b
coe
         T_IsSemiringWithoutAnnihilatingZero_1142 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_'42''45'isMonoid_1160
         ((T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142)
-> Any -> Any
forall a b. a -> b
coe
            T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1252
            (T_IsSemiring_1238 -> Any
forall a b. a -> b
coe T_IsSemiring_1238
v0)))
-- Data.Bool.Properties._.IsSemiring.assoc
d_assoc_1304 ::
  MAlonzo.Code.Algebra.Structures.T_IsSemiring_1238 ->
  Bool ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_assoc_1304 :: T_IsSemiring_1238 -> Bool -> Bool -> Bool -> T__'8801'__12
d_assoc_1304 = T_IsSemiring_1238 -> Bool -> Bool -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsSemiring.comm
d_comm_1306 ::
  MAlonzo.Code.Algebra.Structures.T_IsSemiring_1238 ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_comm_1306 :: T_IsSemiring_1238 -> Bool -> Bool -> T__'8801'__12
d_comm_1306 = T_IsSemiring_1238 -> Bool -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsSemiring.∙-cong
d_'8729''45'cong_1308 ::
  MAlonzo.Code.Algebra.Structures.T_IsSemiring_1238 ->
  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_1308 :: T_IsSemiring_1238
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong_1308 = T_IsSemiring_1238
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsSemiring.identity
d_identity_1314 ::
  MAlonzo.Code.Algebra.Structures.T_IsSemiring_1238 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_identity_1314 :: T_IsSemiring_1238 -> T_Σ_14
d_identity_1314 T_IsSemiring_1238
v0
  = (T_IsMonoid_358 -> T_Σ_14) -> Any -> T_Σ_14
forall a b. a -> b
coe
      T_IsMonoid_358 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_identity_370
      ((T_IsCommutativeMonoid_406 -> T_IsMonoid_358) -> Any -> Any
forall a b. a -> b
coe
         T_IsCommutativeMonoid_406 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_416
         ((T_IsSemiringWithoutAnnihilatingZero_1142
 -> T_IsCommutativeMonoid_406)
-> Any -> Any
forall a b. a -> b
coe
            T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsCommutativeMonoid_406
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1158
            ((T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142)
-> Any -> Any
forall a b. a -> b
coe
               T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1252
               (T_IsSemiring_1238 -> Any
forall a b. a -> b
coe T_IsSemiring_1238
v0))))
-- Data.Bool.Properties._.IsSemiring.+-isCommutativeMonoid
d_'43''45'isCommutativeMonoid_1322 ::
  MAlonzo.Code.Algebra.Structures.T_IsSemiring_1238 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMonoid_406
d_'43''45'isCommutativeMonoid_1322 :: T_IsSemiring_1238 -> T_IsCommutativeMonoid_406
d_'43''45'isCommutativeMonoid_1322 T_IsSemiring_1238
v0
  = (T_IsSemiringWithoutAnnihilatingZero_1142
 -> T_IsCommutativeMonoid_406)
-> Any -> T_IsCommutativeMonoid_406
forall a b. a -> b
coe
      T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsCommutativeMonoid_406
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1158
      ((T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142)
-> Any -> Any
forall a b. a -> b
coe
         T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1252
         (T_IsSemiring_1238 -> Any
forall a b. a -> b
coe T_IsSemiring_1238
v0))
-- Data.Bool.Properties._.IsSemiring.isMagma
d_isMagma_1326 ::
  MAlonzo.Code.Algebra.Structures.T_IsSemiring_1238 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_86
d_isMagma_1326 :: T_IsSemiring_1238 -> T_IsMagma_86
d_isMagma_1326 T_IsSemiring_1238
v0
  = (T_IsSemigroup_194 -> T_IsMagma_86) -> Any -> T_IsMagma_86
forall a b. a -> b
coe
      T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202
      ((T_IsMonoid_358 -> T_IsSemigroup_194) -> Any -> Any
forall a b. a -> b
coe
         T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368
         ((T_IsCommutativeMonoid_406 -> T_IsMonoid_358) -> Any -> Any
forall a b. a -> b
coe
            T_IsCommutativeMonoid_406 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_416
            ((T_IsSemiringWithoutAnnihilatingZero_1142
 -> T_IsCommutativeMonoid_406)
-> Any -> Any
forall a b. a -> b
coe
               T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsCommutativeMonoid_406
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1158
               ((T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142)
-> Any -> Any
forall a b. a -> b
coe
                  T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1252
                  (T_IsSemiring_1238 -> Any
forall a b. a -> b
coe T_IsSemiring_1238
v0)))))
-- Data.Bool.Properties._.IsSemiring.isMonoid
d_isMonoid_1328 ::
  MAlonzo.Code.Algebra.Structures.T_IsSemiring_1238 ->
  MAlonzo.Code.Algebra.Structures.T_IsMonoid_358
d_isMonoid_1328 :: T_IsSemiring_1238 -> T_IsMonoid_358
d_isMonoid_1328 T_IsSemiring_1238
v0
  = (T_IsCommutativeMonoid_406 -> T_IsMonoid_358)
-> Any -> T_IsMonoid_358
forall a b. a -> b
coe
      T_IsCommutativeMonoid_406 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_416
      ((T_IsSemiringWithoutAnnihilatingZero_1142
 -> T_IsCommutativeMonoid_406)
-> Any -> Any
forall a b. a -> b
coe
         T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsCommutativeMonoid_406
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1158
         ((T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142)
-> Any -> Any
forall a b. a -> b
coe
            T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1252
            (T_IsSemiring_1238 -> Any
forall a b. a -> b
coe T_IsSemiring_1238
v0)))
-- Data.Bool.Properties._.IsSemiring.isSemigroup
d_isSemigroup_1330 ::
  MAlonzo.Code.Algebra.Structures.T_IsSemiring_1238 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_194
d_isSemigroup_1330 :: T_IsSemiring_1238 -> T_IsSemigroup_194
d_isSemigroup_1330 T_IsSemiring_1238
v0
  = (T_IsMonoid_358 -> T_IsSemigroup_194) -> Any -> T_IsSemigroup_194
forall a b. a -> b
coe
      T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368
      ((T_IsCommutativeMonoid_406 -> T_IsMonoid_358) -> Any -> Any
forall a b. a -> b
coe
         T_IsCommutativeMonoid_406 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_416
         ((T_IsSemiringWithoutAnnihilatingZero_1142
 -> T_IsCommutativeMonoid_406)
-> Any -> Any
forall a b. a -> b
coe
            T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsCommutativeMonoid_406
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1158
            ((T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142)
-> Any -> Any
forall a b. a -> b
coe
               T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1252
               (T_IsSemiring_1238 -> Any
forall a b. a -> b
coe T_IsSemiring_1238
v0))))
-- Data.Bool.Properties._.IsSemiring.distrib
d_distrib_1332 ::
  MAlonzo.Code.Algebra.Structures.T_IsSemiring_1238 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_distrib_1332 :: T_IsSemiring_1238 -> T_Σ_14
d_distrib_1332 T_IsSemiring_1238
v0
  = (T_IsSemiringWithoutAnnihilatingZero_1142 -> T_Σ_14)
-> Any -> T_Σ_14
forall a b. a -> b
coe
      T_IsSemiringWithoutAnnihilatingZero_1142 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_distrib_1162
      ((T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142)
-> Any -> Any
forall a b. a -> b
coe
         T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1252
         (T_IsSemiring_1238 -> Any
forall a b. a -> b
coe T_IsSemiring_1238
v0))
-- Data.Bool.Properties._.IsSemiring.isEquivalence
d_isEquivalence_1338 ::
  MAlonzo.Code.Algebra.Structures.T_IsSemiring_1238 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_1338 :: T_IsSemiring_1238 -> T_IsEquivalence_26
d_isEquivalence_1338 T_IsSemiring_1238
v0
  = (T_IsMagma_86 -> T_IsEquivalence_26) -> Any -> T_IsEquivalence_26
forall a b. a -> b
coe
      T_IsMagma_86 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_94
      ((T_IsSemigroup_194 -> T_IsMagma_86) -> Any -> Any
forall a b. a -> b
coe
         T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202
         ((T_IsMonoid_358 -> T_IsSemigroup_194) -> Any -> Any
forall a b. a -> b
coe
            T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368
            ((T_IsCommutativeMonoid_406 -> T_IsMonoid_358) -> Any -> Any
forall a b. a -> b
coe
               T_IsCommutativeMonoid_406 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_416
               ((T_IsSemiringWithoutAnnihilatingZero_1142
 -> T_IsCommutativeMonoid_406)
-> Any -> Any
forall a b. a -> b
coe
                  T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsCommutativeMonoid_406
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1158
                  ((T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142)
-> Any -> Any
forall a b. a -> b
coe
                     T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1252
                     (T_IsSemiring_1238 -> Any
forall a b. a -> b
coe T_IsSemiring_1238
v0))))))
-- Data.Bool.Properties._.IsSemiring.isNearSemiring
d_isNearSemiring_1340 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsSemiring_1238 ->
  MAlonzo.Code.Algebra.Structures.T_IsNearSemiring_876
d_isNearSemiring_1340 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> T_IsSemiring_1238
-> T_IsNearSemiring_876
d_isNearSemiring_1340 ~Bool -> Bool -> Bool
v0 ~Bool -> Bool -> Bool
v1 ~Bool
v2 ~Bool
v3 T_IsSemiring_1238
v4
  = T_IsSemiring_1238 -> T_IsNearSemiring_876
du_isNearSemiring_1340 T_IsSemiring_1238
v4
du_isNearSemiring_1340 ::
  MAlonzo.Code.Algebra.Structures.T_IsSemiring_1238 ->
  MAlonzo.Code.Algebra.Structures.T_IsNearSemiring_876
du_isNearSemiring_1340 :: T_IsSemiring_1238 -> T_IsNearSemiring_876
du_isNearSemiring_1340 T_IsSemiring_1238
v0
  = (T_IsSemiringWithoutOne_952 -> T_IsNearSemiring_876)
-> Any -> T_IsNearSemiring_876
forall a b. a -> b
coe
      T_IsSemiringWithoutOne_952 -> T_IsNearSemiring_876
MAlonzo.Code.Algebra.Structures.du_isNearSemiring_990
      ((T_IsSemiring_1238 -> T_IsSemiringWithoutOne_952) -> Any -> Any
forall a b. a -> b
coe
         T_IsSemiring_1238 -> T_IsSemiringWithoutOne_952
MAlonzo.Code.Algebra.Structures.du_isSemiringWithoutOne_1326
         (T_IsSemiring_1238 -> Any
forall a b. a -> b
coe T_IsSemiring_1238
v0))
-- Data.Bool.Properties._.IsSemiring.isSemiringWithoutAnnihilatingZero
d_isSemiringWithoutAnnihilatingZero_1344 ::
  MAlonzo.Code.Algebra.Structures.T_IsSemiring_1238 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutAnnihilatingZero_1142
d_isSemiringWithoutAnnihilatingZero_1344 :: T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
d_isSemiringWithoutAnnihilatingZero_1344 T_IsSemiring_1238
v0
  = (T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142)
-> Any -> T_IsSemiringWithoutAnnihilatingZero_1142
forall a b. a -> b
coe
      T_IsSemiring_1238 -> T_IsSemiringWithoutAnnihilatingZero_1142
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1252
      (T_IsSemiring_1238 -> Any
forall a b. a -> b
coe T_IsSemiring_1238
v0)
-- Data.Bool.Properties._.IsSemiring.isSemiringWithoutOne
d_isSemiringWithoutOne_1346 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsSemiring_1238 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutOne_952
d_isSemiringWithoutOne_1346 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> Bool
-> T_IsSemiring_1238
-> T_IsSemiringWithoutOne_952
d_isSemiringWithoutOne_1346 Bool -> Bool -> Bool
v0 Bool -> Bool -> Bool
v1 Bool
v2 Bool
v3 T_IsSemiring_1238
v4
  = (T_IsSemiring_1238 -> T_IsSemiringWithoutOne_952)
-> T_IsSemiring_1238 -> T_IsSemiringWithoutOne_952
forall a b. a -> b
coe
      T_IsSemiring_1238 -> T_IsSemiringWithoutOne_952
MAlonzo.Code.Algebra.Structures.du_isSemiringWithoutOne_1326 T_IsSemiring_1238
v4
-- Data.Bool.Properties._.IsSemiring.zero
d_zero_1358 ::
  MAlonzo.Code.Algebra.Structures.T_IsSemiring_1238 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_zero_1358 :: T_IsSemiring_1238 -> T_Σ_14
d_zero_1358 T_IsSemiring_1238
v0
  = (T_IsSemiring_1238 -> T_Σ_14) -> Any -> T_Σ_14
forall a b. a -> b
coe T_IsSemiring_1238 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_zero_1254 (T_IsSemiring_1238 -> Any
forall a b. a -> b
coe T_IsSemiring_1238
v0)
-- Data.Bool.Properties._.IsSemiringWithoutAnnihilatingZero.assoc
d_assoc_1366 ::
  MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutAnnihilatingZero_1142 ->
  Bool ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_assoc_1366 :: T_IsSemiringWithoutAnnihilatingZero_1142
-> Bool -> Bool -> Bool -> T__'8801'__12
d_assoc_1366 = T_IsSemiringWithoutAnnihilatingZero_1142
-> Bool -> Bool -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsSemiringWithoutAnnihilatingZero.∙-cong
d_'8729''45'cong_1368 ::
  MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutAnnihilatingZero_1142 ->
  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_1368 :: T_IsSemiringWithoutAnnihilatingZero_1142
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong_1368 = T_IsSemiringWithoutAnnihilatingZero_1142
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsSemiringWithoutAnnihilatingZero.identity
d_identity_1374 ::
  MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutAnnihilatingZero_1142 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_identity_1374 :: T_IsSemiringWithoutAnnihilatingZero_1142 -> T_Σ_14
d_identity_1374 T_IsSemiringWithoutAnnihilatingZero_1142
v0
  = (T_IsMonoid_358 -> T_Σ_14) -> Any -> T_Σ_14
forall a b. a -> b
coe
      T_IsMonoid_358 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_identity_370
      ((T_IsSemiringWithoutAnnihilatingZero_1142 -> T_IsMonoid_358)
-> Any -> Any
forall a b. a -> b
coe
         T_IsSemiringWithoutAnnihilatingZero_1142 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_'42''45'isMonoid_1160 (T_IsSemiringWithoutAnnihilatingZero_1142 -> Any
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1142
v0))
-- Data.Bool.Properties._.IsSemiringWithoutAnnihilatingZero.isMagma
d_isMagma_1380 ::
  MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutAnnihilatingZero_1142 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_86
d_isMagma_1380 :: T_IsSemiringWithoutAnnihilatingZero_1142 -> T_IsMagma_86
d_isMagma_1380 T_IsSemiringWithoutAnnihilatingZero_1142
v0
  = (T_IsSemigroup_194 -> T_IsMagma_86) -> Any -> T_IsMagma_86
forall a b. a -> b
coe
      T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202
      ((T_IsMonoid_358 -> T_IsSemigroup_194) -> Any -> Any
forall a b. a -> b
coe
         T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368
         ((T_IsSemiringWithoutAnnihilatingZero_1142 -> T_IsMonoid_358)
-> Any -> Any
forall a b. a -> b
coe
            T_IsSemiringWithoutAnnihilatingZero_1142 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_'42''45'isMonoid_1160 (T_IsSemiringWithoutAnnihilatingZero_1142 -> Any
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1142
v0)))
-- Data.Bool.Properties._.IsSemiringWithoutAnnihilatingZero.*-isMonoid
d_'42''45'isMonoid_1382 ::
  MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutAnnihilatingZero_1142 ->
  MAlonzo.Code.Algebra.Structures.T_IsMonoid_358
d_'42''45'isMonoid_1382 :: T_IsSemiringWithoutAnnihilatingZero_1142 -> T_IsMonoid_358
d_'42''45'isMonoid_1382 T_IsSemiringWithoutAnnihilatingZero_1142
v0
  = (T_IsSemiringWithoutAnnihilatingZero_1142 -> T_IsMonoid_358)
-> Any -> T_IsMonoid_358
forall a b. a -> b
coe
      T_IsSemiringWithoutAnnihilatingZero_1142 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_'42''45'isMonoid_1160 (T_IsSemiringWithoutAnnihilatingZero_1142 -> Any
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1142
v0)
-- Data.Bool.Properties._.IsSemiringWithoutAnnihilatingZero.isSemigroup
d_isSemigroup_1384 ::
  MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutAnnihilatingZero_1142 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_194
d_isSemigroup_1384 :: T_IsSemiringWithoutAnnihilatingZero_1142 -> T_IsSemigroup_194
d_isSemigroup_1384 T_IsSemiringWithoutAnnihilatingZero_1142
v0
  = (T_IsMonoid_358 -> T_IsSemigroup_194) -> Any -> T_IsSemigroup_194
forall a b. a -> b
coe
      T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368
      ((T_IsSemiringWithoutAnnihilatingZero_1142 -> T_IsMonoid_358)
-> Any -> Any
forall a b. a -> b
coe
         T_IsSemiringWithoutAnnihilatingZero_1142 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_'42''45'isMonoid_1160 (T_IsSemiringWithoutAnnihilatingZero_1142 -> Any
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1142
v0))
-- Data.Bool.Properties._.IsSemiringWithoutAnnihilatingZero.assoc
d_assoc_1386 ::
  MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutAnnihilatingZero_1142 ->
  Bool ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_assoc_1386 :: T_IsSemiringWithoutAnnihilatingZero_1142
-> Bool -> Bool -> Bool -> T__'8801'__12
d_assoc_1386 = T_IsSemiringWithoutAnnihilatingZero_1142
-> Bool -> Bool -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsSemiringWithoutAnnihilatingZero.comm
d_comm_1388 ::
  MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutAnnihilatingZero_1142 ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_comm_1388 :: T_IsSemiringWithoutAnnihilatingZero_1142
-> Bool -> Bool -> T__'8801'__12
d_comm_1388 = T_IsSemiringWithoutAnnihilatingZero_1142
-> Bool -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsSemiringWithoutAnnihilatingZero.∙-cong
d_'8729''45'cong_1390 ::
  MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutAnnihilatingZero_1142 ->
  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_1390 :: T_IsSemiringWithoutAnnihilatingZero_1142
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong_1390 = T_IsSemiringWithoutAnnihilatingZero_1142
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsSemiringWithoutAnnihilatingZero.identity
d_identity_1396 ::
  MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutAnnihilatingZero_1142 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_identity_1396 :: T_IsSemiringWithoutAnnihilatingZero_1142 -> T_Σ_14
d_identity_1396 T_IsSemiringWithoutAnnihilatingZero_1142
v0
  = (T_IsMonoid_358 -> T_Σ_14) -> Any -> T_Σ_14
forall a b. a -> b
coe
      T_IsMonoid_358 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_identity_370
      ((T_IsCommutativeMonoid_406 -> T_IsMonoid_358) -> Any -> Any
forall a b. a -> b
coe
         T_IsCommutativeMonoid_406 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_416
         ((T_IsSemiringWithoutAnnihilatingZero_1142
 -> T_IsCommutativeMonoid_406)
-> Any -> Any
forall a b. a -> b
coe
            T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsCommutativeMonoid_406
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1158
            (T_IsSemiringWithoutAnnihilatingZero_1142 -> Any
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1142
v0)))
-- Data.Bool.Properties._.IsSemiringWithoutAnnihilatingZero.+-isCommutativeMonoid
d_'43''45'isCommutativeMonoid_1404 ::
  MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutAnnihilatingZero_1142 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMonoid_406
d_'43''45'isCommutativeMonoid_1404 :: T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsCommutativeMonoid_406
d_'43''45'isCommutativeMonoid_1404 T_IsSemiringWithoutAnnihilatingZero_1142
v0
  = (T_IsSemiringWithoutAnnihilatingZero_1142
 -> T_IsCommutativeMonoid_406)
-> Any -> T_IsCommutativeMonoid_406
forall a b. a -> b
coe
      T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsCommutativeMonoid_406
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1158
      (T_IsSemiringWithoutAnnihilatingZero_1142 -> Any
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1142
v0)
-- Data.Bool.Properties._.IsSemiringWithoutAnnihilatingZero.isMagma
d_isMagma_1408 ::
  MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutAnnihilatingZero_1142 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_86
d_isMagma_1408 :: T_IsSemiringWithoutAnnihilatingZero_1142 -> T_IsMagma_86
d_isMagma_1408 T_IsSemiringWithoutAnnihilatingZero_1142
v0
  = (T_IsSemigroup_194 -> T_IsMagma_86) -> Any -> T_IsMagma_86
forall a b. a -> b
coe
      T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202
      ((T_IsMonoid_358 -> T_IsSemigroup_194) -> Any -> Any
forall a b. a -> b
coe
         T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368
         ((T_IsCommutativeMonoid_406 -> T_IsMonoid_358) -> Any -> Any
forall a b. a -> b
coe
            T_IsCommutativeMonoid_406 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_416
            ((T_IsSemiringWithoutAnnihilatingZero_1142
 -> T_IsCommutativeMonoid_406)
-> Any -> Any
forall a b. a -> b
coe
               T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsCommutativeMonoid_406
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1158
               (T_IsSemiringWithoutAnnihilatingZero_1142 -> Any
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1142
v0))))
-- Data.Bool.Properties._.IsSemiringWithoutAnnihilatingZero.isMonoid
d_isMonoid_1410 ::
  MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutAnnihilatingZero_1142 ->
  MAlonzo.Code.Algebra.Structures.T_IsMonoid_358
d_isMonoid_1410 :: T_IsSemiringWithoutAnnihilatingZero_1142 -> T_IsMonoid_358
d_isMonoid_1410 T_IsSemiringWithoutAnnihilatingZero_1142
v0
  = (T_IsCommutativeMonoid_406 -> T_IsMonoid_358)
-> Any -> T_IsMonoid_358
forall a b. a -> b
coe
      T_IsCommutativeMonoid_406 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_416
      ((T_IsSemiringWithoutAnnihilatingZero_1142
 -> T_IsCommutativeMonoid_406)
-> Any -> Any
forall a b. a -> b
coe
         T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsCommutativeMonoid_406
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1158
         (T_IsSemiringWithoutAnnihilatingZero_1142 -> Any
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1142
v0))
-- Data.Bool.Properties._.IsSemiringWithoutAnnihilatingZero.isSemigroup
d_isSemigroup_1412 ::
  MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutAnnihilatingZero_1142 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_194
d_isSemigroup_1412 :: T_IsSemiringWithoutAnnihilatingZero_1142 -> T_IsSemigroup_194
d_isSemigroup_1412 T_IsSemiringWithoutAnnihilatingZero_1142
v0
  = (T_IsMonoid_358 -> T_IsSemigroup_194) -> Any -> T_IsSemigroup_194
forall a b. a -> b
coe
      T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368
      ((T_IsCommutativeMonoid_406 -> T_IsMonoid_358) -> Any -> Any
forall a b. a -> b
coe
         T_IsCommutativeMonoid_406 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_416
         ((T_IsSemiringWithoutAnnihilatingZero_1142
 -> T_IsCommutativeMonoid_406)
-> Any -> Any
forall a b. a -> b
coe
            T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsCommutativeMonoid_406
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1158
            (T_IsSemiringWithoutAnnihilatingZero_1142 -> Any
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1142
v0)))
-- Data.Bool.Properties._.IsSemiringWithoutAnnihilatingZero.distrib
d_distrib_1414 ::
  MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutAnnihilatingZero_1142 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_distrib_1414 :: T_IsSemiringWithoutAnnihilatingZero_1142 -> T_Σ_14
d_distrib_1414 T_IsSemiringWithoutAnnihilatingZero_1142
v0
  = (T_IsSemiringWithoutAnnihilatingZero_1142 -> T_Σ_14)
-> Any -> T_Σ_14
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1142 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_distrib_1162 (T_IsSemiringWithoutAnnihilatingZero_1142 -> Any
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1142
v0)
-- Data.Bool.Properties._.IsSemiringWithoutAnnihilatingZero.isEquivalence
d_isEquivalence_1420 ::
  MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutAnnihilatingZero_1142 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_1420 :: T_IsSemiringWithoutAnnihilatingZero_1142 -> T_IsEquivalence_26
d_isEquivalence_1420 T_IsSemiringWithoutAnnihilatingZero_1142
v0
  = (T_IsMagma_86 -> T_IsEquivalence_26) -> Any -> T_IsEquivalence_26
forall a b. a -> b
coe
      T_IsMagma_86 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_94
      ((T_IsSemigroup_194 -> T_IsMagma_86) -> Any -> Any
forall a b. a -> b
coe
         T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202
         ((T_IsMonoid_358 -> T_IsSemigroup_194) -> Any -> Any
forall a b. a -> b
coe
            T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368
            ((T_IsCommutativeMonoid_406 -> T_IsMonoid_358) -> Any -> Any
forall a b. a -> b
coe
               T_IsCommutativeMonoid_406 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_416
               ((T_IsSemiringWithoutAnnihilatingZero_1142
 -> T_IsCommutativeMonoid_406)
-> Any -> Any
forall a b. a -> b
coe
                  T_IsSemiringWithoutAnnihilatingZero_1142
-> T_IsCommutativeMonoid_406
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1158
                  (T_IsSemiringWithoutAnnihilatingZero_1142 -> Any
forall a b. a -> b
coe T_IsSemiringWithoutAnnihilatingZero_1142
v0)))))
-- Data.Bool.Properties._.IsSemiringWithoutOne.assoc
d_assoc_1436 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutOne_952 ->
  Bool ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_assoc_1436 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsSemiringWithoutOne_952
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
d_assoc_1436 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsSemiringWithoutOne_952
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsSemiringWithoutOne.∙-cong
d_'8729''45'cong_1438 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutOne_952 ->
  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_1438 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsSemiringWithoutOne_952
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong_1438 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsSemiringWithoutOne_952
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsSemiringWithoutOne.isMagma
d_isMagma_1444 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutOne_952 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_86
d_isMagma_1444 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsSemiringWithoutOne_952
-> T_IsMagma_86
d_isMagma_1444 ~Bool -> Bool -> Bool
v0 ~Bool -> Bool -> Bool
v1 ~Bool
v2 T_IsSemiringWithoutOne_952
v3 = T_IsSemiringWithoutOne_952 -> T_IsMagma_86
du_isMagma_1444 T_IsSemiringWithoutOne_952
v3
du_isMagma_1444 ::
  MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutOne_952 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_86
du_isMagma_1444 :: T_IsSemiringWithoutOne_952 -> T_IsMagma_86
du_isMagma_1444 T_IsSemiringWithoutOne_952
v0
  = (T_IsSemigroup_194 -> T_IsMagma_86) -> Any -> T_IsMagma_86
forall a b. a -> b
coe
      T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202
      ((T_IsSemiringWithoutOne_952 -> T_IsSemigroup_194) -> Any -> Any
forall a b. a -> b
coe
         T_IsSemiringWithoutOne_952 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_'42''45'isSemigroup_970 (T_IsSemiringWithoutOne_952 -> Any
forall a b. a -> b
coe T_IsSemiringWithoutOne_952
v0))
-- Data.Bool.Properties._.IsSemiringWithoutOne.*-isSemigroup
d_'42''45'isSemigroup_1446 ::
  MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutOne_952 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_194
d_'42''45'isSemigroup_1446 :: T_IsSemiringWithoutOne_952 -> T_IsSemigroup_194
d_'42''45'isSemigroup_1446 T_IsSemiringWithoutOne_952
v0
  = (T_IsSemiringWithoutOne_952 -> T_IsSemigroup_194)
-> Any -> T_IsSemigroup_194
forall a b. a -> b
coe
      T_IsSemiringWithoutOne_952 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_'42''45'isSemigroup_970 (T_IsSemiringWithoutOne_952 -> Any
forall a b. a -> b
coe T_IsSemiringWithoutOne_952
v0)
-- Data.Bool.Properties._.IsSemiringWithoutOne.assoc
d_assoc_1448 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutOne_952 ->
  Bool ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_assoc_1448 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsSemiringWithoutOne_952
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
d_assoc_1448 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsSemiringWithoutOne_952
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsSemiringWithoutOne.comm
d_comm_1450 ::
  MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutOne_952 ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_comm_1450 :: T_IsSemiringWithoutOne_952 -> Bool -> Bool -> T__'8801'__12
d_comm_1450 = T_IsSemiringWithoutOne_952 -> Bool -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsSemiringWithoutOne.∙-cong
d_'8729''45'cong_1452 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutOne_952 ->
  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_1452 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsSemiringWithoutOne_952
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong_1452 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsSemiringWithoutOne_952
-> Bool
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsSemiringWithoutOne.identity
d_identity_1458 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutOne_952 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_identity_1458 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsSemiringWithoutOne_952
-> T_Σ_14
d_identity_1458 ~Bool -> Bool -> Bool
v0 ~Bool -> Bool -> Bool
v1 ~Bool
v2 T_IsSemiringWithoutOne_952
v3 = T_IsSemiringWithoutOne_952 -> T_Σ_14
du_identity_1458 T_IsSemiringWithoutOne_952
v3
du_identity_1458 ::
  MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutOne_952 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
du_identity_1458 :: T_IsSemiringWithoutOne_952 -> T_Σ_14
du_identity_1458 T_IsSemiringWithoutOne_952
v0
  = (T_IsMonoid_358 -> T_Σ_14) -> Any -> T_Σ_14
forall a b. a -> b
coe
      T_IsMonoid_358 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_identity_370
      ((T_IsCommutativeMonoid_406 -> T_IsMonoid_358) -> Any -> Any
forall a b. a -> b
coe
         T_IsCommutativeMonoid_406 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_416
         ((T_IsSemiringWithoutOne_952 -> T_IsCommutativeMonoid_406)
-> Any -> Any
forall a b. a -> b
coe
            T_IsSemiringWithoutOne_952 -> T_IsCommutativeMonoid_406
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_968
            (T_IsSemiringWithoutOne_952 -> Any
forall a b. a -> b
coe T_IsSemiringWithoutOne_952
v0)))
-- Data.Bool.Properties._.IsSemiringWithoutOne.+-isCommutativeMonoid
d_'43''45'isCommutativeMonoid_1466 ::
  MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutOne_952 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMonoid_406
d_'43''45'isCommutativeMonoid_1466 :: T_IsSemiringWithoutOne_952 -> T_IsCommutativeMonoid_406
d_'43''45'isCommutativeMonoid_1466 T_IsSemiringWithoutOne_952
v0
  = (T_IsSemiringWithoutOne_952 -> T_IsCommutativeMonoid_406)
-> Any -> T_IsCommutativeMonoid_406
forall a b. a -> b
coe
      T_IsSemiringWithoutOne_952 -> T_IsCommutativeMonoid_406
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_968
      (T_IsSemiringWithoutOne_952 -> Any
forall a b. a -> b
coe T_IsSemiringWithoutOne_952
v0)
-- Data.Bool.Properties._.IsSemiringWithoutOne.isMagma
d_isMagma_1470 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutOne_952 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_86
d_isMagma_1470 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsSemiringWithoutOne_952
-> T_IsMagma_86
d_isMagma_1470 ~Bool -> Bool -> Bool
v0 ~Bool -> Bool -> Bool
v1 ~Bool
v2 T_IsSemiringWithoutOne_952
v3 = T_IsSemiringWithoutOne_952 -> T_IsMagma_86
du_isMagma_1470 T_IsSemiringWithoutOne_952
v3
du_isMagma_1470 ::
  MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutOne_952 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_86
du_isMagma_1470 :: T_IsSemiringWithoutOne_952 -> T_IsMagma_86
du_isMagma_1470 T_IsSemiringWithoutOne_952
v0
  = (T_IsSemigroup_194 -> T_IsMagma_86) -> Any -> T_IsMagma_86
forall a b. a -> b
coe
      T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202
      ((T_IsMonoid_358 -> T_IsSemigroup_194) -> Any -> Any
forall a b. a -> b
coe
         T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368
         ((T_IsCommutativeMonoid_406 -> T_IsMonoid_358) -> Any -> Any
forall a b. a -> b
coe
            T_IsCommutativeMonoid_406 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_416
            ((T_IsSemiringWithoutOne_952 -> T_IsCommutativeMonoid_406)
-> Any -> Any
forall a b. a -> b
coe
               T_IsSemiringWithoutOne_952 -> T_IsCommutativeMonoid_406
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_968
               (T_IsSemiringWithoutOne_952 -> Any
forall a b. a -> b
coe T_IsSemiringWithoutOne_952
v0))))
-- Data.Bool.Properties._.IsSemiringWithoutOne.isMonoid
d_isMonoid_1472 ::
  MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutOne_952 ->
  MAlonzo.Code.Algebra.Structures.T_IsMonoid_358
d_isMonoid_1472 :: T_IsSemiringWithoutOne_952 -> T_IsMonoid_358
d_isMonoid_1472 T_IsSemiringWithoutOne_952
v0
  = (T_IsCommutativeMonoid_406 -> T_IsMonoid_358)
-> Any -> T_IsMonoid_358
forall a b. a -> b
coe
      T_IsCommutativeMonoid_406 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_416
      ((T_IsSemiringWithoutOne_952 -> T_IsCommutativeMonoid_406)
-> Any -> Any
forall a b. a -> b
coe
         T_IsSemiringWithoutOne_952 -> T_IsCommutativeMonoid_406
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_968
         (T_IsSemiringWithoutOne_952 -> Any
forall a b. a -> b
coe T_IsSemiringWithoutOne_952
v0))
-- Data.Bool.Properties._.IsSemiringWithoutOne.isSemigroup
d_isSemigroup_1474 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutOne_952 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_194
d_isSemigroup_1474 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsSemiringWithoutOne_952
-> T_IsSemigroup_194
d_isSemigroup_1474 ~Bool -> Bool -> Bool
v0 ~Bool -> Bool -> Bool
v1 ~Bool
v2 T_IsSemiringWithoutOne_952
v3 = T_IsSemiringWithoutOne_952 -> T_IsSemigroup_194
du_isSemigroup_1474 T_IsSemiringWithoutOne_952
v3
du_isSemigroup_1474 ::
  MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutOne_952 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_194
du_isSemigroup_1474 :: T_IsSemiringWithoutOne_952 -> T_IsSemigroup_194
du_isSemigroup_1474 T_IsSemiringWithoutOne_952
v0
  = (T_IsMonoid_358 -> T_IsSemigroup_194) -> Any -> T_IsSemigroup_194
forall a b. a -> b
coe
      T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368
      ((T_IsCommutativeMonoid_406 -> T_IsMonoid_358) -> Any -> Any
forall a b. a -> b
coe
         T_IsCommutativeMonoid_406 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_416
         ((T_IsSemiringWithoutOne_952 -> T_IsCommutativeMonoid_406)
-> Any -> Any
forall a b. a -> b
coe
            T_IsSemiringWithoutOne_952 -> T_IsCommutativeMonoid_406
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_968
            (T_IsSemiringWithoutOne_952 -> Any
forall a b. a -> b
coe T_IsSemiringWithoutOne_952
v0)))
-- Data.Bool.Properties._.IsSemiringWithoutOne.distrib
d_distrib_1476 ::
  MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutOne_952 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_distrib_1476 :: T_IsSemiringWithoutOne_952 -> T_Σ_14
d_distrib_1476 T_IsSemiringWithoutOne_952
v0
  = (T_IsSemiringWithoutOne_952 -> T_Σ_14) -> Any -> T_Σ_14
forall a b. a -> b
coe T_IsSemiringWithoutOne_952 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_distrib_972 (T_IsSemiringWithoutOne_952 -> Any
forall a b. a -> b
coe T_IsSemiringWithoutOne_952
v0)
-- Data.Bool.Properties._.IsSemiringWithoutOne.distribʳ
d_distrib'691'_1478 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutOne_952 ->
  Bool ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_distrib'691'_1478 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsSemiringWithoutOne_952
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
d_distrib'691'_1478 = (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsSemiringWithoutOne_952
-> Bool
-> Bool
-> Bool
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties._.IsSemiringWithoutOne.isEquivalence
d_isEquivalence_1480 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutOne_952 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_1480 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsSemiringWithoutOne_952
-> T_IsEquivalence_26
d_isEquivalence_1480 ~Bool -> Bool -> Bool
v0 ~Bool -> Bool -> Bool
v1 ~Bool
v2 T_IsSemiringWithoutOne_952
v3 = T_IsSemiringWithoutOne_952 -> T_IsEquivalence_26
du_isEquivalence_1480 T_IsSemiringWithoutOne_952
v3
du_isEquivalence_1480 ::
  MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutOne_952 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
du_isEquivalence_1480 :: T_IsSemiringWithoutOne_952 -> T_IsEquivalence_26
du_isEquivalence_1480 T_IsSemiringWithoutOne_952
v0
  = (T_IsMagma_86 -> T_IsEquivalence_26) -> Any -> T_IsEquivalence_26
forall a b. a -> b
coe
      T_IsMagma_86 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_94
      ((T_IsSemigroup_194 -> T_IsMagma_86) -> Any -> Any
forall a b. a -> b
coe
         T_IsSemigroup_194 -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.d_isMagma_202
         ((T_IsMonoid_358 -> T_IsSemigroup_194) -> Any -> Any
forall a b. a -> b
coe
            T_IsMonoid_358 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.d_isSemigroup_368
            ((T_IsCommutativeMonoid_406 -> T_IsMonoid_358) -> Any -> Any
forall a b. a -> b
coe
               T_IsCommutativeMonoid_406 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.d_isMonoid_416
               ((T_IsSemiringWithoutOne_952 -> T_IsCommutativeMonoid_406)
-> Any -> Any
forall a b. a -> b
coe
                  T_IsSemiringWithoutOne_952 -> T_IsCommutativeMonoid_406
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_968
                  (T_IsSemiringWithoutOne_952 -> Any
forall a b. a -> b
coe T_IsSemiringWithoutOne_952
v0)))))
-- Data.Bool.Properties._.IsSemiringWithoutOne.isNearSemiring
d_isNearSemiring_1482 ::
  (Bool -> Bool -> Bool) ->
  (Bool -> Bool -> Bool) ->
  Bool ->
  MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutOne_952 ->
  MAlonzo.Code.Algebra.Structures.T_IsNearSemiring_876
d_isNearSemiring_1482 :: (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Bool
-> T_IsSemiringWithoutOne_952
-> T_IsNearSemiring_876
d_isNearSemiring_1482 Bool -> Bool -> Bool
v0 Bool -> Bool -> Bool
v1 Bool
v2 T_IsSemiringWithoutOne_952
v3
  = (T_IsSemiringWithoutOne_952 -> T_IsNearSemiring_876)
-> T_IsSemiringWithoutOne_952 -> T_IsNearSemiring_876
forall a b. a -> b
coe T_IsSemiringWithoutOne_952 -> T_IsNearSemiring_876
MAlonzo.Code.Algebra.Structures.du_isNearSemiring_990 T_IsSemiringWithoutOne_952
v3
-- Data.Bool.Properties._.IsSemiringWithoutOne.zero
d_zero_1496 ::
  MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutOne_952 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_zero_1496 :: T_IsSemiringWithoutOne_952 -> T_Σ_14
d_zero_1496 T_IsSemiringWithoutOne_952
v0
  = (T_IsSemiringWithoutOne_952 -> T_Σ_14) -> Any -> T_Σ_14
forall a b. a -> b
coe T_IsSemiringWithoutOne_952 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_zero_974 (T_IsSemiringWithoutOne_952 -> Any
forall a b. a -> b
coe T_IsSemiringWithoutOne_952
v0)
-- Data.Bool.Properties._≟_
d__'8799'__1510 ::
  Bool -> Bool -> MAlonzo.Code.Relation.Nullary.T_Dec_32
d__'8799'__1510 :: Bool -> Bool -> T_Dec_32
d__'8799'__1510 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_14 -> T_Dec_32) -> Any -> Any -> T_Dec_32
forall a b. a -> b
coe
                    Bool -> T_Reflects_14 -> T_Dec_32
MAlonzo.Code.Relation.Nullary.C__because__46 (Bool -> Any
forall a b. a -> b
coe Bool
v1)
                    ((Any -> T_Reflects_14) -> Any -> Any
forall a b. a -> b
coe Any -> T_Reflects_14
MAlonzo.Code.Relation.Nullary.C_of'696'_22 Any
forall a. a
erased)
             else (Bool -> T_Reflects_14 -> T_Dec_32) -> Any -> Any -> T_Dec_32
forall a b. a -> b
coe
                    Bool -> T_Reflects_14 -> T_Dec_32
MAlonzo.Code.Relation.Nullary.C__because__46 (Bool -> Any
forall a b. a -> b
coe Bool
v1)
                    (T_Reflects_14 -> Any
forall a b. a -> b
coe T_Reflects_14
MAlonzo.Code.Relation.Nullary.C_of'8319'_26)
      else (if Bool -> Bool
forall a b. a -> b
coe Bool
v1
              then (Bool -> T_Reflects_14 -> T_Dec_32) -> Any -> Any -> T_Dec_32
forall a b. a -> b
coe
                     Bool -> T_Reflects_14 -> T_Dec_32
MAlonzo.Code.Relation.Nullary.C__because__46 (Bool -> Any
forall a b. a -> b
coe Bool
v0)
                     (T_Reflects_14 -> Any
forall a b. a -> b
coe T_Reflects_14
MAlonzo.Code.Relation.Nullary.C_of'8319'_26)
              else (Bool -> T_Reflects_14 -> T_Dec_32) -> Any -> Any -> T_Dec_32
forall a b. a -> b
coe
                     Bool -> T_Reflects_14 -> T_Dec_32
MAlonzo.Code.Relation.Nullary.C__because__46
                     (Bool -> Any
forall a b. a -> b
coe Bool
MAlonzo.Code.Agda.Builtin.Bool.C_true_10)
                     ((Any -> T_Reflects_14) -> Any -> Any
forall a b. a -> b
coe Any -> T_Reflects_14
MAlonzo.Code.Relation.Nullary.C_of'696'_22 Any
forall a. a
erased))
-- Data.Bool.Properties.≡-setoid
d_'8801''45'setoid_1512 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_'8801''45'setoid_1512 :: T_Setoid_44
d_'8801''45'setoid_1512
  = T_Setoid_44 -> T_Setoid_44
forall a b. a -> b
coe
      T_Setoid_44
MAlonzo.Code.Relation.Binary.PropositionalEquality.Properties.du_setoid_250
-- Data.Bool.Properties.≡-decSetoid
d_'8801''45'decSetoid_1514 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_DecSetoid_84
d_'8801''45'decSetoid_1514 :: T_DecSetoid_84
d_'8801''45'decSetoid_1514
  = ((Any -> Any -> T_Dec_32) -> T_DecSetoid_84)
-> Any -> T_DecSetoid_84
forall a b. a -> b
coe
      (Any -> Any -> T_Dec_32) -> T_DecSetoid_84
MAlonzo.Code.Relation.Binary.PropositionalEquality.Properties.du_decSetoid_254
      ((Bool -> Bool -> T_Dec_32) -> Any
forall a b. a -> b
coe Bool -> Bool -> T_Dec_32
d__'8799'__1510)
-- Data.Bool.Properties.≤-reflexive
d_'8804''45'reflexive_1516 ::
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Data.Bool.Base.T__'8804'__10
d_'8804''45'reflexive_1516 :: Bool -> Bool -> T__'8801'__12 -> T__'8804'__10
d_'8804''45'reflexive_1516 ~Bool
v0 ~Bool
v1 ~T__'8801'__12
v2
  = T__'8804'__10
du_'8804''45'reflexive_1516
du_'8804''45'reflexive_1516 ::
  MAlonzo.Code.Data.Bool.Base.T__'8804'__10
du_'8804''45'reflexive_1516 :: T__'8804'__10
du_'8804''45'reflexive_1516
  = 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_1518 ::
  Bool -> MAlonzo.Code.Data.Bool.Base.T__'8804'__10
d_'8804''45'refl_1518 :: Bool -> T__'8804'__10
d_'8804''45'refl_1518 ~Bool
v0 = T__'8804'__10
du_'8804''45'refl_1518
du_'8804''45'refl_1518 :: MAlonzo.Code.Data.Bool.Base.T__'8804'__10
du_'8804''45'refl_1518 :: T__'8804'__10
du_'8804''45'refl_1518 = T__'8804'__10 -> T__'8804'__10
forall a b. a -> b
coe T__'8804'__10
du_'8804''45'reflexive_1516
-- Data.Bool.Properties.≤-trans
d_'8804''45'trans_1520 ::
  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_1520 :: Bool
-> Bool -> Bool -> T__'8804'__10 -> T__'8804'__10 -> T__'8804'__10
d_'8804''45'trans_1520 ~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_1520 T__'8804'__10
v3 T__'8804'__10
v4
du_'8804''45'trans_1520 ::
  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_1520 :: T__'8804'__10 -> T__'8804'__10 -> T__'8804'__10
du_'8804''45'trans_1520 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_1524 ::
  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_1524 :: Bool -> Bool -> T__'8804'__10 -> T__'8804'__10 -> T__'8801'__12
d_'8804''45'antisym_1524 = Bool -> Bool -> T__'8804'__10 -> T__'8804'__10 -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties.≤-minimum
d_'8804''45'minimum_1526 ::
  Bool -> MAlonzo.Code.Data.Bool.Base.T__'8804'__10
d_'8804''45'minimum_1526 :: Bool -> T__'8804'__10
d_'8804''45'minimum_1526 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_1528 ::
  Bool -> MAlonzo.Code.Data.Bool.Base.T__'8804'__10
d_'8804''45'maximum_1528 :: Bool -> T__'8804'__10
d_'8804''45'maximum_1528 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_1530 ::
  Bool -> Bool -> MAlonzo.Code.Data.Sum.Base.T__'8846'__30
d_'8804''45'total_1530 :: Bool -> Bool -> T__'8846'__30
d_'8804''45'total_1530 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_1528 (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_1526 (Bool -> Any
forall a b. a -> b
coe Bool
v1))
-- Data.Bool.Properties._≤?_
d__'8804''63'__1536 ::
  Bool -> Bool -> MAlonzo.Code.Relation.Nullary.T_Dec_32
d__'8804''63'__1536 :: Bool -> Bool -> T_Dec_32
d__'8804''63'__1536 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_14 -> T_Dec_32) -> Any -> Any -> T_Dec_32
forall a b. a -> b
coe
                    Bool -> T_Reflects_14 -> T_Dec_32
MAlonzo.Code.Relation.Nullary.C__because__46 (Bool -> Any
forall a b. a -> b
coe Bool
v1)
                    ((Any -> T_Reflects_14) -> Any -> Any
forall a b. a -> b
coe
                       Any -> T_Reflects_14
MAlonzo.Code.Relation.Nullary.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_14 -> T_Dec_32) -> Any -> Any -> T_Dec_32
forall a b. a -> b
coe
                    Bool -> T_Reflects_14 -> T_Dec_32
MAlonzo.Code.Relation.Nullary.C__because__46 (Bool -> Any
forall a b. a -> b
coe Bool
v1)
                    (T_Reflects_14 -> Any
forall a b. a -> b
coe T_Reflects_14
MAlonzo.Code.Relation.Nullary.C_of'8319'_26)
      else (Bool -> T_Reflects_14 -> T_Dec_32) -> Any -> Any -> T_Dec_32
forall a b. a -> b
coe
             Bool -> T_Reflects_14 -> T_Dec_32
MAlonzo.Code.Relation.Nullary.C__because__46
             (Bool -> Any
forall a b. a -> b
coe Bool
MAlonzo.Code.Agda.Builtin.Bool.C_true_10)
             ((Any -> T_Reflects_14) -> Any -> Any
forall a b. a -> b
coe
                Any -> T_Reflects_14
MAlonzo.Code.Relation.Nullary.C_of'696'_22
                ((Bool -> T__'8804'__10) -> Any -> Any
forall a b. a -> b
coe Bool -> T__'8804'__10
d_'8804''45'minimum_1526 (Bool -> Any
forall a b. a -> b
coe Bool
v1)))
-- Data.Bool.Properties.≤-irrelevant
d_'8804''45'irrelevant_1540 ::
  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_1540 :: Bool -> Bool -> T__'8804'__10 -> T__'8804'__10 -> T__'8801'__12
d_'8804''45'irrelevant_1540 = Bool -> Bool -> T__'8804'__10 -> T__'8804'__10 -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties.≤-isPreorder
d_'8804''45'isPreorder_1542 ::
  MAlonzo.Code.Relation.Binary.Structures.T_IsPreorder_70
d_'8804''45'isPreorder_1542 :: T_IsPreorder_70
d_'8804''45'isPreorder_1542
  = (T_IsEquivalence_26
 -> (Any -> Any -> Any -> Any)
 -> (Any -> Any -> Any -> Any -> Any -> Any)
 -> T_IsPreorder_70)
-> Any
-> (Any -> Any -> Any -> Any)
-> (Any -> Any -> Any -> Any -> Any -> Any)
-> T_IsPreorder_70
forall a b. a -> b
coe
      T_IsEquivalence_26
-> (Any -> Any -> Any -> Any)
-> (Any -> Any -> Any -> Any -> Any -> Any)
-> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.C_IsPreorder'46'constructor_3993
      (T_IsEquivalence_26 -> Any
forall a b. a -> b
coe
         T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.PropositionalEquality.Properties.du_isEquivalence_242)
      (\ Any
v0 Any
v1 Any
v2 -> T__'8804'__10 -> Any
forall a b. a -> b
coe T__'8804'__10
du_'8804''45'reflexive_1516)
      (\ 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_1520 Any
v3 Any
v4)
-- Data.Bool.Properties.≤-isPartialOrder
d_'8804''45'isPartialOrder_1544 ::
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialOrder_162
d_'8804''45'isPartialOrder_1544 :: T_IsPartialOrder_162
d_'8804''45'isPartialOrder_1544
  = (T_IsPreorder_70
 -> (Any -> Any -> Any -> Any -> Any) -> T_IsPartialOrder_162)
-> Any -> Any -> T_IsPartialOrder_162
forall a b. a -> b
coe
      T_IsPreorder_70
-> (Any -> Any -> Any -> Any -> Any) -> T_IsPartialOrder_162
MAlonzo.Code.Relation.Binary.Structures.C_IsPartialOrder'46'constructor_9297
      (T_IsPreorder_70 -> Any
forall a b. a -> b
coe T_IsPreorder_70
d_'8804''45'isPreorder_1542) Any
forall a. a
erased
-- Data.Bool.Properties.≤-isTotalOrder
d_'8804''45'isTotalOrder_1546 ::
  MAlonzo.Code.Relation.Binary.Structures.T_IsTotalOrder_384
d_'8804''45'isTotalOrder_1546 :: T_IsTotalOrder_384
d_'8804''45'isTotalOrder_1546
  = (T_IsPartialOrder_162
 -> (Any -> Any -> T__'8846'__30) -> T_IsTotalOrder_384)
-> Any -> Any -> T_IsTotalOrder_384
forall a b. a -> b
coe
      T_IsPartialOrder_162
-> (Any -> Any -> T__'8846'__30) -> T_IsTotalOrder_384
MAlonzo.Code.Relation.Binary.Structures.C_IsTotalOrder'46'constructor_19815
      (T_IsPartialOrder_162 -> Any
forall a b. a -> b
coe T_IsPartialOrder_162
d_'8804''45'isPartialOrder_1544) ((Bool -> Bool -> T__'8846'__30) -> Any
forall a b. a -> b
coe Bool -> Bool -> T__'8846'__30
d_'8804''45'total_1530)
-- Data.Bool.Properties.≤-isDecTotalOrder
d_'8804''45'isDecTotalOrder_1548 ::
  MAlonzo.Code.Relation.Binary.Structures.T_IsDecTotalOrder_434
d_'8804''45'isDecTotalOrder_1548 :: T_IsDecTotalOrder_434
d_'8804''45'isDecTotalOrder_1548
  = (T_IsTotalOrder_384
 -> (Any -> Any -> T_Dec_32)
 -> (Any -> Any -> T_Dec_32)
 -> T_IsDecTotalOrder_434)
-> Any -> Any -> Any -> T_IsDecTotalOrder_434
forall a b. a -> b
coe
      T_IsTotalOrder_384
-> (Any -> Any -> T_Dec_32)
-> (Any -> Any -> T_Dec_32)
-> T_IsDecTotalOrder_434
MAlonzo.Code.Relation.Binary.Structures.C_IsDecTotalOrder'46'constructor_21785
      (T_IsTotalOrder_384 -> Any
forall a b. a -> b
coe T_IsTotalOrder_384
d_'8804''45'isTotalOrder_1546) ((Bool -> Bool -> T_Dec_32) -> Any
forall a b. a -> b
coe Bool -> Bool -> T_Dec_32
d__'8799'__1510)
      ((Bool -> Bool -> T_Dec_32) -> Any
forall a b. a -> b
coe Bool -> Bool -> T_Dec_32
d__'8804''63'__1536)
-- Data.Bool.Properties.≤-poset
d_'8804''45'poset_1550 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Poset_282
d_'8804''45'poset_1550 :: T_Poset_282
d_'8804''45'poset_1550
  = (T_IsPartialOrder_162 -> T_Poset_282)
-> T_IsPartialOrder_162 -> T_Poset_282
forall a b. a -> b
coe
      T_IsPartialOrder_162 -> T_Poset_282
MAlonzo.Code.Relation.Binary.Bundles.C_Poset'46'constructor_5219
      T_IsPartialOrder_162
d_'8804''45'isPartialOrder_1544
-- Data.Bool.Properties.≤-preorder
d_'8804''45'preorder_1552 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Preorder_132
d_'8804''45'preorder_1552 :: T_Preorder_132
d_'8804''45'preorder_1552
  = (T_IsPreorder_70 -> T_Preorder_132)
-> T_IsPreorder_70 -> T_Preorder_132
forall a b. a -> b
coe
      T_IsPreorder_70 -> T_Preorder_132
MAlonzo.Code.Relation.Binary.Bundles.C_Preorder'46'constructor_2269
      T_IsPreorder_70
d_'8804''45'isPreorder_1542
-- Data.Bool.Properties.≤-totalOrder
d_'8804''45'totalOrder_1554 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_TotalOrder_652
d_'8804''45'totalOrder_1554 :: T_TotalOrder_652
d_'8804''45'totalOrder_1554
  = (T_IsTotalOrder_384 -> T_TotalOrder_652)
-> T_IsTotalOrder_384 -> T_TotalOrder_652
forall a b. a -> b
coe
      T_IsTotalOrder_384 -> T_TotalOrder_652
MAlonzo.Code.Relation.Binary.Bundles.C_TotalOrder'46'constructor_12489
      T_IsTotalOrder_384
d_'8804''45'isTotalOrder_1546
-- Data.Bool.Properties.≤-decTotalOrder
d_'8804''45'decTotalOrder_1556 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_DecTotalOrder_740
d_'8804''45'decTotalOrder_1556 :: T_DecTotalOrder_740
d_'8804''45'decTotalOrder_1556
  = (T_IsDecTotalOrder_434 -> T_DecTotalOrder_740)
-> T_IsDecTotalOrder_434 -> T_DecTotalOrder_740
forall a b. a -> b
coe
      T_IsDecTotalOrder_434 -> T_DecTotalOrder_740
MAlonzo.Code.Relation.Binary.Bundles.C_DecTotalOrder'46'constructor_14337
      T_IsDecTotalOrder_434
d_'8804''45'isDecTotalOrder_1548
-- Data.Bool.Properties.<-irrefl
d_'60''45'irrefl_1558 ::
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Data.Bool.Base.T__'60'__18 ->
  MAlonzo.Code.Data.Empty.T_'8869'_4
d_'60''45'irrefl_1558 :: Bool -> Bool -> T__'8801'__12 -> T__'60'__18 -> T_'8869'_4
d_'60''45'irrefl_1558 = Bool -> Bool -> T__'8801'__12 -> T__'60'__18 -> T_'8869'_4
forall a. a
erased
-- Data.Bool.Properties.<-asym
d_'60''45'asym_1560 ::
  Bool ->
  Bool ->
  MAlonzo.Code.Data.Bool.Base.T__'60'__18 ->
  MAlonzo.Code.Data.Bool.Base.T__'60'__18 ->
  MAlonzo.Code.Data.Empty.T_'8869'_4
d_'60''45'asym_1560 :: Bool -> Bool -> T__'60'__18 -> T__'60'__18 -> T_'8869'_4
d_'60''45'asym_1560 = Bool -> Bool -> T__'60'__18 -> T__'60'__18 -> T_'8869'_4
forall a. a
erased
-- Data.Bool.Properties.<-trans
d_'60''45'trans_1562 ::
  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_1562 :: Bool -> Bool -> Bool -> T__'60'__18 -> T__'60'__18 -> T__'60'__18
d_'60''45'trans_1562 = 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'_1564 ::
  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'_1564 :: Bool -> Bool -> Bool -> T__'8804'__10 -> T__'60'__18 -> T__'60'__18
d_'60''45'trans'691'_1564 = 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'_1566 ::
  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'_1566 :: Bool -> Bool -> Bool -> T__'60'__18 -> T__'8804'__10 -> T__'60'__18
d_'60''45'trans'737'_1566 = Bool -> Bool -> Bool -> T__'60'__18 -> T__'8804'__10 -> T__'60'__18
forall a. a
erased
-- Data.Bool.Properties.<-cmp
d_'60''45'cmp_1568 ::
  Bool -> Bool -> MAlonzo.Code.Relation.Binary.Definitions.T_Tri_136
d_'60''45'cmp_1568 :: Bool -> Bool -> T_Tri_136
d_'60''45'cmp_1568 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_136) -> Any -> T_Tri_136
forall a b. a -> b
coe
                    Any -> T_Tri_136
MAlonzo.Code.Relation.Binary.Definitions.C_tri'8776'_158 Any
forall a. a
erased
             else (Any -> T_Tri_136) -> Any -> T_Tri_136
forall a b. a -> b
coe
                    Any -> T_Tri_136
MAlonzo.Code.Relation.Binary.Definitions.C_tri'62'_166 Any
forall a. a
erased
      else (if Bool -> Bool
forall a b. a -> b
coe Bool
v1
              then (Any -> T_Tri_136) -> Any -> T_Tri_136
forall a b. a -> b
coe
                     Any -> T_Tri_136
MAlonzo.Code.Relation.Binary.Definitions.C_tri'60'_150 Any
forall a. a
erased
              else (Any -> T_Tri_136) -> Any -> T_Tri_136
forall a b. a -> b
coe
                     Any -> T_Tri_136
MAlonzo.Code.Relation.Binary.Definitions.C_tri'8776'_158 Any
forall a. a
erased)
-- Data.Bool.Properties._<?_
d__'60''63'__1570 ::
  Bool -> Bool -> MAlonzo.Code.Relation.Nullary.T_Dec_32
d__'60''63'__1570 :: Bool -> Bool -> T_Dec_32
d__'60''63'__1570 Bool
v0 Bool
v1
  = if Bool -> Bool
forall a b. a -> b
coe Bool
v0
      then (Bool -> T_Reflects_14 -> T_Dec_32) -> Any -> Any -> T_Dec_32
forall a b. a -> b
coe
             Bool -> T_Reflects_14 -> T_Dec_32
MAlonzo.Code.Relation.Nullary.C__because__46
             (Bool -> Any
forall a b. a -> b
coe Bool
MAlonzo.Code.Agda.Builtin.Bool.C_false_8)
             (T_Reflects_14 -> Any
forall a b. a -> b
coe T_Reflects_14
MAlonzo.Code.Relation.Nullary.C_of'8319'_26)
      else (if Bool -> Bool
forall a b. a -> b
coe Bool
v1
              then (Bool -> T_Reflects_14 -> T_Dec_32) -> Any -> Any -> T_Dec_32
forall a b. a -> b
coe
                     Bool -> T_Reflects_14 -> T_Dec_32
MAlonzo.Code.Relation.Nullary.C__because__46 (Bool -> Any
forall a b. a -> b
coe Bool
v1)
                     ((Any -> T_Reflects_14) -> Any -> Any
forall a b. a -> b
coe Any -> T_Reflects_14
MAlonzo.Code.Relation.Nullary.C_of'696'_22 Any
forall a. a
erased)
              else (Bool -> T_Reflects_14 -> T_Dec_32) -> Any -> Any -> T_Dec_32
forall a b. a -> b
coe
                     Bool -> T_Reflects_14 -> T_Dec_32
MAlonzo.Code.Relation.Nullary.C__because__46 (Bool -> Any
forall a b. a -> b
coe Bool
v1)
                     (T_Reflects_14 -> Any
forall a b. a -> b
coe T_Reflects_14
MAlonzo.Code.Relation.Nullary.C_of'8319'_26))
-- Data.Bool.Properties.<-resp₂-≡
d_'60''45'resp'8322''45''8801'_1572 ::
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'60''45'resp'8322''45''8801'_1572 :: T_Σ_14
d_'60''45'resp'8322''45''8801'_1572
  = (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_1578 ::
  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_1578 :: Bool -> Bool -> T__'60'__18 -> T__'60'__18 -> T__'8801'__12
d_'60''45'irrelevant_1578 = Bool -> Bool -> T__'60'__18 -> T__'60'__18 -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties.<-isStrictPartialOrder
d_'60''45'isStrictPartialOrder_1580 ::
  MAlonzo.Code.Relation.Binary.Structures.T_IsStrictPartialOrder_266
d_'60''45'isStrictPartialOrder_1580 :: T_IsStrictPartialOrder_266
d_'60''45'isStrictPartialOrder_1580
  = (T_IsEquivalence_26
 -> (Any -> Any -> Any -> Any -> Any -> Any)
 -> T_Σ_14
 -> T_IsStrictPartialOrder_266)
-> Any -> Any -> T_Σ_14 -> T_IsStrictPartialOrder_266
forall a b. a -> b
coe
      T_IsEquivalence_26
-> (Any -> Any -> Any -> Any -> Any -> Any)
-> T_Σ_14
-> T_IsStrictPartialOrder_266
MAlonzo.Code.Relation.Binary.Structures.C_IsStrictPartialOrder'46'constructor_13145
      (T_IsEquivalence_26 -> Any
forall a b. a -> b
coe
         T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.PropositionalEquality.Properties.du_isEquivalence_242)
      Any
forall a. a
erased T_Σ_14
d_'60''45'resp'8322''45''8801'_1572
-- Data.Bool.Properties.<-isStrictTotalOrder
d_'60''45'isStrictTotalOrder_1582 ::
  MAlonzo.Code.Relation.Binary.Structures.T_IsStrictTotalOrder_502
d_'60''45'isStrictTotalOrder_1582 :: T_IsStrictTotalOrder_502
d_'60''45'isStrictTotalOrder_1582
  = (T_IsEquivalence_26
 -> (Any -> Any -> Any -> Any -> Any -> Any)
 -> (Any -> Any -> T_Tri_136)
 -> T_IsStrictTotalOrder_502)
-> Any -> Any -> Any -> T_IsStrictTotalOrder_502
forall a b. a -> b
coe
      T_IsEquivalence_26
-> (Any -> Any -> Any -> Any -> Any -> Any)
-> (Any -> Any -> T_Tri_136)
-> T_IsStrictTotalOrder_502
MAlonzo.Code.Relation.Binary.Structures.C_IsStrictTotalOrder'46'constructor_23999
      (T_IsEquivalence_26 -> Any
forall a b. a -> b
coe
         T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.PropositionalEquality.Properties.du_isEquivalence_242)
      Any
forall a. a
erased ((Bool -> Bool -> T_Tri_136) -> Any
forall a b. a -> b
coe Bool -> Bool -> T_Tri_136
d_'60''45'cmp_1568)
-- Data.Bool.Properties.<-strictPartialOrder
d_'60''45'strictPartialOrder_1584 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_StrictPartialOrder_472
d_'60''45'strictPartialOrder_1584 :: T_StrictPartialOrder_472
d_'60''45'strictPartialOrder_1584
  = (T_IsStrictPartialOrder_266 -> T_StrictPartialOrder_472)
-> T_IsStrictPartialOrder_266 -> T_StrictPartialOrder_472
forall a b. a -> b
coe
      T_IsStrictPartialOrder_266 -> T_StrictPartialOrder_472
MAlonzo.Code.Relation.Binary.Bundles.C_StrictPartialOrder'46'constructor_8957
      T_IsStrictPartialOrder_266
d_'60''45'isStrictPartialOrder_1580
-- Data.Bool.Properties.<-strictTotalOrder
d_'60''45'strictTotalOrder_1586 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_StrictTotalOrder_864
d_'60''45'strictTotalOrder_1586 :: T_StrictTotalOrder_864
d_'60''45'strictTotalOrder_1586
  = (T_IsStrictTotalOrder_502 -> T_StrictTotalOrder_864)
-> T_IsStrictTotalOrder_502 -> T_StrictTotalOrder_864
forall a b. a -> b
coe
      T_IsStrictTotalOrder_502 -> T_StrictTotalOrder_864
MAlonzo.Code.Relation.Binary.Bundles.C_StrictTotalOrder'46'constructor_16739
      T_IsStrictTotalOrder_502
d_'60''45'isStrictTotalOrder_1582
-- Data.Bool.Properties.∨-assoc
d_'8744''45'assoc_1588 ::
  Bool ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8744''45'assoc_1588 :: Bool -> Bool -> Bool -> T__'8801'__12
d_'8744''45'assoc_1588 = Bool -> Bool -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties.∨-comm
d_'8744''45'comm_1598 ::
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8744''45'comm_1598 :: Bool -> Bool -> T__'8801'__12
d_'8744''45'comm_1598 = Bool -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties.∨-identityˡ
d_'8744''45'identity'737'_1600 ::
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8744''45'identity'737'_1600 :: Bool -> T__'8801'__12
d_'8744''45'identity'737'_1600 = Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties.∨-identityʳ
d_'8744''45'identity'691'_1602 ::
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8744''45'identity'691'_1602 :: Bool -> T__'8801'__12
d_'8744''45'identity'691'_1602 = Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties.∨-identity
d_'8744''45'identity_1604 :: MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'8744''45'identity_1604 :: T_Σ_14
d_'8744''45'identity_1604
  = (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'_1606 ::
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8744''45'zero'737'_1606 :: Bool -> T__'8801'__12
d_'8744''45'zero'737'_1606 = Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties.∨-zeroʳ
d_'8744''45'zero'691'_1608 ::
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8744''45'zero'691'_1608 :: Bool -> T__'8801'__12
d_'8744''45'zero'691'_1608 = Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties.∨-zero
d_'8744''45'zero_1610 :: MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'8744''45'zero_1610 :: T_Σ_14
d_'8744''45'zero_1610
  = (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'_1612 ::
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8744''45'inverse'737'_1612 :: Bool -> T__'8801'__12
d_'8744''45'inverse'737'_1612 = Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties.∨-inverseʳ
d_'8744''45'inverse'691'_1614 ::
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8744''45'inverse'691'_1614 :: Bool -> T__'8801'__12
d_'8744''45'inverse'691'_1614 = Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties.∨-inverse
d_'8744''45'inverse_1618 :: MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'8744''45'inverse_1618 :: T_Σ_14
d_'8744''45'inverse_1618
  = (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_1620 ::
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8744''45'idem_1620 :: Bool -> T__'8801'__12
d_'8744''45'idem_1620 = Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties.∨-sel
d_'8744''45'sel_1622 ::
  Bool -> Bool -> MAlonzo.Code.Data.Sum.Base.T__'8846'__30
d_'8744''45'sel_1622 :: Bool -> Bool -> T__'8846'__30
d_'8744''45'sel_1622 Bool
v0 ~Bool
v1 = Bool -> T__'8846'__30
du_'8744''45'sel_1622 Bool
v0
du_'8744''45'sel_1622 ::
  Bool -> MAlonzo.Code.Data.Sum.Base.T__'8846'__30
du_'8744''45'sel_1622 :: Bool -> T__'8846'__30
du_'8744''45'sel_1622 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.∨-isMagma
d_'8744''45'isMagma_1628 ::
  MAlonzo.Code.Algebra.Structures.T_IsMagma_86
d_'8744''45'isMagma_1628 :: T_IsMagma_86
d_'8744''45'isMagma_1628
  = (T_IsEquivalence_26
 -> (Any -> Any -> Any -> Any -> Any -> Any -> Any) -> T_IsMagma_86)
-> Any -> Any -> T_IsMagma_86
forall a b. a -> b
coe
      T_IsEquivalence_26
-> (Any -> Any -> Any -> Any -> Any -> Any -> Any) -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.C_IsMagma'46'constructor_553
      (T_IsEquivalence_26 -> Any
forall a b. a -> b
coe
         T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.PropositionalEquality.Properties.du_isEquivalence_242)
      Any
forall a. a
erased
-- Data.Bool.Properties.∨-magma
d_'8744''45'magma_1630 :: MAlonzo.Code.Algebra.Bundles.T_Magma_36
d_'8744''45'magma_1630 :: T_Magma_36
d_'8744''45'magma_1630
  = ((Any -> Any -> Any) -> T_IsMagma_86 -> T_Magma_36)
-> (Bool -> Bool -> Bool) -> T_IsMagma_86 -> T_Magma_36
forall a b. a -> b
coe
      (Any -> Any -> Any) -> T_IsMagma_86 -> T_Magma_36
MAlonzo.Code.Algebra.Bundles.C_Magma'46'constructor_581
      Bool -> Bool -> Bool
MAlonzo.Code.Data.Bool.Base.d__'8744'__30 T_IsMagma_86
d_'8744''45'isMagma_1628
-- Data.Bool.Properties.∨-isSemigroup
d_'8744''45'isSemigroup_1632 ::
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_194
d_'8744''45'isSemigroup_1632 :: T_IsSemigroup_194
d_'8744''45'isSemigroup_1632
  = (T_IsMagma_86 -> (Any -> Any -> Any -> Any) -> T_IsSemigroup_194)
-> Any -> Any -> T_IsSemigroup_194
forall a b. a -> b
coe
      T_IsMagma_86 -> (Any -> Any -> Any -> Any) -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.C_IsSemigroup'46'constructor_4001
      (T_IsMagma_86 -> Any
forall a b. a -> b
coe T_IsMagma_86
d_'8744''45'isMagma_1628) Any
forall a. a
erased
-- Data.Bool.Properties.∨-semigroup
d_'8744''45'semigroup_1634 ::
  MAlonzo.Code.Algebra.Bundles.T_Semigroup_206
d_'8744''45'semigroup_1634 :: T_Semigroup_206
d_'8744''45'semigroup_1634
  = ((Any -> Any -> Any) -> T_IsSemigroup_194 -> T_Semigroup_206)
-> (Bool -> Bool -> Bool) -> T_IsSemigroup_194 -> T_Semigroup_206
forall a b. a -> b
coe
      (Any -> Any -> Any) -> T_IsSemigroup_194 -> T_Semigroup_206
MAlonzo.Code.Algebra.Bundles.C_Semigroup'46'constructor_3669
      Bool -> Bool -> Bool
MAlonzo.Code.Data.Bool.Base.d__'8744'__30
      T_IsSemigroup_194
d_'8744''45'isSemigroup_1632
-- Data.Bool.Properties.∨-isBand
d_'8744''45'isBand_1636 ::
  MAlonzo.Code.Algebra.Structures.T_IsBand_230
d_'8744''45'isBand_1636 :: T_IsBand_230
d_'8744''45'isBand_1636
  = (T_IsSemigroup_194 -> (Any -> Any) -> T_IsBand_230)
-> Any -> Any -> T_IsBand_230
forall a b. a -> b
coe
      T_IsSemigroup_194 -> (Any -> Any) -> T_IsBand_230
MAlonzo.Code.Algebra.Structures.C_IsBand'46'constructor_4787
      (T_IsSemigroup_194 -> Any
forall a b. a -> b
coe T_IsSemigroup_194
d_'8744''45'isSemigroup_1632) Any
forall a. a
erased
-- Data.Bool.Properties.∨-band
d_'8744''45'band_1638 :: MAlonzo.Code.Algebra.Bundles.T_Band_266
d_'8744''45'band_1638 :: T_Band_266
d_'8744''45'band_1638
  = ((Any -> Any -> Any) -> T_IsBand_230 -> T_Band_266)
-> (Bool -> Bool -> Bool) -> T_IsBand_230 -> T_Band_266
forall a b. a -> b
coe
      (Any -> Any -> Any) -> T_IsBand_230 -> T_Band_266
MAlonzo.Code.Algebra.Bundles.C_Band'46'constructor_4745
      Bool -> Bool -> Bool
MAlonzo.Code.Data.Bool.Base.d__'8744'__30 T_IsBand_230
d_'8744''45'isBand_1636
-- Data.Bool.Properties.∨-isSemilattice
d_'8744''45'isSemilattice_1640 ::
  MAlonzo.Code.Algebra.Structures.T_IsSemilattice_312
d_'8744''45'isSemilattice_1640 :: T_IsSemilattice_312
d_'8744''45'isSemilattice_1640
  = (T_IsBand_230 -> (Any -> Any -> Any) -> T_IsSemilattice_312)
-> Any -> Any -> T_IsSemilattice_312
forall a b. a -> b
coe
      T_IsBand_230 -> (Any -> Any -> Any) -> T_IsSemilattice_312
MAlonzo.Code.Algebra.Structures.C_IsSemilattice'46'constructor_6687
      (T_IsBand_230 -> Any
forall a b. a -> b
coe T_IsBand_230
d_'8744''45'isBand_1636) Any
forall a. a
erased
-- Data.Bool.Properties.∨-semilattice
d_'8744''45'semilattice_1642 ::
  MAlonzo.Code.Algebra.Bundles.T_Semilattice_402
d_'8744''45'semilattice_1642 :: T_Semilattice_402
d_'8744''45'semilattice_1642
  = ((Any -> Any -> Any) -> T_IsSemilattice_312 -> T_Semilattice_402)
-> (Bool -> Bool -> Bool)
-> T_IsSemilattice_312
-> T_Semilattice_402
forall a b. a -> b
coe
      (Any -> Any -> Any) -> T_IsSemilattice_312 -> T_Semilattice_402
MAlonzo.Code.Algebra.Bundles.C_Semilattice'46'constructor_7205
      Bool -> Bool -> Bool
MAlonzo.Code.Data.Bool.Base.d__'8744'__30
      T_IsSemilattice_312
d_'8744''45'isSemilattice_1640
-- Data.Bool.Properties.∨-isMonoid
d_'8744''45'isMonoid_1644 ::
  MAlonzo.Code.Algebra.Structures.T_IsMonoid_358
d_'8744''45'isMonoid_1644 :: T_IsMonoid_358
d_'8744''45'isMonoid_1644
  = (T_IsSemigroup_194 -> T_Σ_14 -> T_IsMonoid_358)
-> Any -> Any -> T_IsMonoid_358
forall a b. a -> b
coe
      T_IsSemigroup_194 -> T_Σ_14 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.C_IsMonoid'46'constructor_7687
      (T_IsSemigroup_194 -> Any
forall a b. a -> b
coe T_IsSemigroup_194
d_'8744''45'isSemigroup_1632) (T_Σ_14 -> Any
forall a b. a -> b
coe T_Σ_14
d_'8744''45'identity_1604)
-- Data.Bool.Properties.∨-isCommutativeMonoid
d_'8744''45'isCommutativeMonoid_1646 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMonoid_406
d_'8744''45'isCommutativeMonoid_1646 :: T_IsCommutativeMonoid_406
d_'8744''45'isCommutativeMonoid_1646
  = (T_IsMonoid_358
 -> (Any -> Any -> Any) -> T_IsCommutativeMonoid_406)
-> Any -> Any -> T_IsCommutativeMonoid_406
forall a b. a -> b
coe
      T_IsMonoid_358 -> (Any -> Any -> Any) -> T_IsCommutativeMonoid_406
MAlonzo.Code.Algebra.Structures.C_IsCommutativeMonoid'46'constructor_9361
      (T_IsMonoid_358 -> Any
forall a b. a -> b
coe T_IsMonoid_358
d_'8744''45'isMonoid_1644) Any
forall a. a
erased
-- Data.Bool.Properties.∨-commutativeMonoid
d_'8744''45'commutativeMonoid_1648 ::
  MAlonzo.Code.Algebra.Bundles.T_CommutativeMonoid_582
d_'8744''45'commutativeMonoid_1648 :: T_CommutativeMonoid_582
d_'8744''45'commutativeMonoid_1648
  = ((Any -> Any -> Any)
 -> Any -> T_IsCommutativeMonoid_406 -> T_CommutativeMonoid_582)
-> (Bool -> Bool -> Bool)
-> Any
-> T_IsCommutativeMonoid_406
-> T_CommutativeMonoid_582
forall a b. a -> b
coe
      (Any -> Any -> Any)
-> Any -> T_IsCommutativeMonoid_406 -> T_CommutativeMonoid_582
MAlonzo.Code.Algebra.Bundles.C_CommutativeMonoid'46'constructor_10343
      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_406
d_'8744''45'isCommutativeMonoid_1646
-- Data.Bool.Properties.∨-isIdempotentCommutativeMonoid
d_'8744''45'isIdempotentCommutativeMonoid_1650 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_464
d_'8744''45'isIdempotentCommutativeMonoid_1650 :: T_IsIdempotentCommutativeMonoid_464
d_'8744''45'isIdempotentCommutativeMonoid_1650
  = (T_IsCommutativeMonoid_406
 -> (Any -> Any) -> T_IsIdempotentCommutativeMonoid_464)
-> Any -> Any -> T_IsIdempotentCommutativeMonoid_464
forall a b. a -> b
coe
      T_IsCommutativeMonoid_406
-> (Any -> Any) -> T_IsIdempotentCommutativeMonoid_464
MAlonzo.Code.Algebra.Structures.C_IsIdempotentCommutativeMonoid'46'constructor_10859
      (T_IsCommutativeMonoid_406 -> Any
forall a b. a -> b
coe T_IsCommutativeMonoid_406
d_'8744''45'isCommutativeMonoid_1646) Any
forall a. a
erased
-- Data.Bool.Properties.∨-idempotentCommutativeMonoid
d_'8744''45'idempotentCommutativeMonoid_1652 ::
  MAlonzo.Code.Algebra.Bundles.T_IdempotentCommutativeMonoid_674
d_'8744''45'idempotentCommutativeMonoid_1652 :: T_IdempotentCommutativeMonoid_674
d_'8744''45'idempotentCommutativeMonoid_1652
  = ((Any -> Any -> Any)
 -> Any
 -> T_IsIdempotentCommutativeMonoid_464
 -> T_IdempotentCommutativeMonoid_674)
-> (Bool -> Bool -> Bool)
-> Any
-> T_IsIdempotentCommutativeMonoid_464
-> T_IdempotentCommutativeMonoid_674
forall a b. a -> b
coe
      (Any -> Any -> Any)
-> Any
-> T_IsIdempotentCommutativeMonoid_464
-> T_IdempotentCommutativeMonoid_674
MAlonzo.Code.Algebra.Bundles.C_IdempotentCommutativeMonoid'46'constructor_12109
      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_464
d_'8744''45'isIdempotentCommutativeMonoid_1650
-- Data.Bool.Properties.∧-assoc
d_'8743''45'assoc_1654 ::
  Bool ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8743''45'assoc_1654 :: Bool -> Bool -> Bool -> T__'8801'__12
d_'8743''45'assoc_1654 = Bool -> Bool -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties.∧-comm
d_'8743''45'comm_1664 ::
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8743''45'comm_1664 :: Bool -> Bool -> T__'8801'__12
d_'8743''45'comm_1664 = Bool -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties.∧-identityˡ
d_'8743''45'identity'737'_1666 ::
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8743''45'identity'737'_1666 :: Bool -> T__'8801'__12
d_'8743''45'identity'737'_1666 = Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties.∧-identityʳ
d_'8743''45'identity'691'_1668 ::
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8743''45'identity'691'_1668 :: Bool -> T__'8801'__12
d_'8743''45'identity'691'_1668 = Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties.∧-identity
d_'8743''45'identity_1670 :: MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'8743''45'identity_1670 :: T_Σ_14
d_'8743''45'identity_1670
  = (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'_1672 ::
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8743''45'zero'737'_1672 :: Bool -> T__'8801'__12
d_'8743''45'zero'737'_1672 = Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties.∧-zeroʳ
d_'8743''45'zero'691'_1674 ::
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8743''45'zero'691'_1674 :: Bool -> T__'8801'__12
d_'8743''45'zero'691'_1674 = Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties.∧-zero
d_'8743''45'zero_1676 :: MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'8743''45'zero_1676 :: T_Σ_14
d_'8743''45'zero_1676
  = (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'_1678 ::
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8743''45'inverse'737'_1678 :: Bool -> T__'8801'__12
d_'8743''45'inverse'737'_1678 = Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties.∧-inverseʳ
d_'8743''45'inverse'691'_1680 ::
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8743''45'inverse'691'_1680 :: Bool -> T__'8801'__12
d_'8743''45'inverse'691'_1680 = Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties.∧-inverse
d_'8743''45'inverse_1684 :: MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'8743''45'inverse_1684 :: T_Σ_14
d_'8743''45'inverse_1684
  = (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_1686 ::
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8743''45'idem_1686 :: Bool -> T__'8801'__12
d_'8743''45'idem_1686 = Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties.∧-sel
d_'8743''45'sel_1688 ::
  Bool -> Bool -> MAlonzo.Code.Data.Sum.Base.T__'8846'__30
d_'8743''45'sel_1688 :: Bool -> Bool -> T__'8846'__30
d_'8743''45'sel_1688 Bool
v0 ~Bool
v1 = Bool -> T__'8846'__30
du_'8743''45'sel_1688 Bool
v0
du_'8743''45'sel_1688 ::
  Bool -> MAlonzo.Code.Data.Sum.Base.T__'8846'__30
du_'8743''45'sel_1688 :: Bool -> T__'8846'__30
du_'8743''45'sel_1688 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.∧-distribˡ-∨
d_'8743''45'distrib'737''45''8744'_1694 ::
  Bool ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8743''45'distrib'737''45''8744'_1694 :: Bool -> Bool -> Bool -> T__'8801'__12
d_'8743''45'distrib'737''45''8744'_1694 = Bool -> Bool -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties.∧-distribʳ-∨
d_'8743''45'distrib'691''45''8744'_1704 ::
  Bool ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8743''45'distrib'691''45''8744'_1704 :: Bool -> Bool -> Bool -> T__'8801'__12
d_'8743''45'distrib'691''45''8744'_1704 = Bool -> Bool -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties.∧-distrib-∨
d_'8743''45'distrib'45''8744'_1712 ::
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'8743''45'distrib'45''8744'_1712 :: T_Σ_14
d_'8743''45'distrib'45''8744'_1712
  = (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'_1714 ::
  Bool ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8744''45'distrib'737''45''8743'_1714 :: Bool -> Bool -> Bool -> T__'8801'__12
d_'8744''45'distrib'737''45''8743'_1714 = Bool -> Bool -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties.∨-distribʳ-∧
d_'8744''45'distrib'691''45''8743'_1724 ::
  Bool ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8744''45'distrib'691''45''8743'_1724 :: Bool -> Bool -> Bool -> T__'8801'__12
d_'8744''45'distrib'691''45''8743'_1724 = Bool -> Bool -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties.∨-distrib-∧
d_'8744''45'distrib'45''8743'_1732 ::
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'8744''45'distrib'45''8743'_1732 :: T_Σ_14
d_'8744''45'distrib'45''8743'_1732
  = (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'_1734 ::
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8743''45'abs'45''8744'_1734 :: Bool -> Bool -> T__'8801'__12
d_'8743''45'abs'45''8744'_1734 = Bool -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties.∨-abs-∧
d_'8744''45'abs'45''8743'_1740 ::
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8744''45'abs'45''8743'_1740 :: Bool -> Bool -> T__'8801'__12
d_'8744''45'abs'45''8743'_1740 = Bool -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties.∨-∧-absorptive
d_'8744''45''8743''45'absorptive_1746 ::
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'8744''45''8743''45'absorptive_1746 :: T_Σ_14
d_'8744''45''8743''45'absorptive_1746
  = (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_1748 ::
  MAlonzo.Code.Algebra.Structures.T_IsMagma_86
d_'8743''45'isMagma_1748 :: T_IsMagma_86
d_'8743''45'isMagma_1748
  = (T_IsEquivalence_26
 -> (Any -> Any -> Any -> Any -> Any -> Any -> Any) -> T_IsMagma_86)
-> Any -> Any -> T_IsMagma_86
forall a b. a -> b
coe
      T_IsEquivalence_26
-> (Any -> Any -> Any -> Any -> Any -> Any -> Any) -> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.C_IsMagma'46'constructor_553
      (T_IsEquivalence_26 -> Any
forall a b. a -> b
coe
         T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.PropositionalEquality.Properties.du_isEquivalence_242)
      Any
forall a. a
erased
-- Data.Bool.Properties.∧-magma
d_'8743''45'magma_1750 :: MAlonzo.Code.Algebra.Bundles.T_Magma_36
d_'8743''45'magma_1750 :: T_Magma_36
d_'8743''45'magma_1750
  = ((Any -> Any -> Any) -> T_IsMagma_86 -> T_Magma_36)
-> (Bool -> Bool -> Bool) -> T_IsMagma_86 -> T_Magma_36
forall a b. a -> b
coe
      (Any -> Any -> Any) -> T_IsMagma_86 -> T_Magma_36
MAlonzo.Code.Algebra.Bundles.C_Magma'46'constructor_581
      Bool -> Bool -> Bool
MAlonzo.Code.Data.Bool.Base.d__'8743'__24 T_IsMagma_86
d_'8743''45'isMagma_1748
-- Data.Bool.Properties.∧-isSemigroup
d_'8743''45'isSemigroup_1752 ::
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_194
d_'8743''45'isSemigroup_1752 :: T_IsSemigroup_194
d_'8743''45'isSemigroup_1752
  = (T_IsMagma_86 -> (Any -> Any -> Any -> Any) -> T_IsSemigroup_194)
-> Any -> Any -> T_IsSemigroup_194
forall a b. a -> b
coe
      T_IsMagma_86 -> (Any -> Any -> Any -> Any) -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.C_IsSemigroup'46'constructor_4001
      (T_IsMagma_86 -> Any
forall a b. a -> b
coe T_IsMagma_86
d_'8743''45'isMagma_1748) Any
forall a. a
erased
-- Data.Bool.Properties.∧-semigroup
d_'8743''45'semigroup_1754 ::
  MAlonzo.Code.Algebra.Bundles.T_Semigroup_206
d_'8743''45'semigroup_1754 :: T_Semigroup_206
d_'8743''45'semigroup_1754
  = ((Any -> Any -> Any) -> T_IsSemigroup_194 -> T_Semigroup_206)
-> (Bool -> Bool -> Bool) -> T_IsSemigroup_194 -> T_Semigroup_206
forall a b. a -> b
coe
      (Any -> Any -> Any) -> T_IsSemigroup_194 -> T_Semigroup_206
MAlonzo.Code.Algebra.Bundles.C_Semigroup'46'constructor_3669
      Bool -> Bool -> Bool
MAlonzo.Code.Data.Bool.Base.d__'8743'__24
      T_IsSemigroup_194
d_'8743''45'isSemigroup_1752
-- Data.Bool.Properties.∧-isBand
d_'8743''45'isBand_1756 ::
  MAlonzo.Code.Algebra.Structures.T_IsBand_230
d_'8743''45'isBand_1756 :: T_IsBand_230
d_'8743''45'isBand_1756
  = (T_IsSemigroup_194 -> (Any -> Any) -> T_IsBand_230)
-> Any -> Any -> T_IsBand_230
forall a b. a -> b
coe
      T_IsSemigroup_194 -> (Any -> Any) -> T_IsBand_230
MAlonzo.Code.Algebra.Structures.C_IsBand'46'constructor_4787
      (T_IsSemigroup_194 -> Any
forall a b. a -> b
coe T_IsSemigroup_194
d_'8743''45'isSemigroup_1752) Any
forall a. a
erased
-- Data.Bool.Properties.∧-band
d_'8743''45'band_1758 :: MAlonzo.Code.Algebra.Bundles.T_Band_266
d_'8743''45'band_1758 :: T_Band_266
d_'8743''45'band_1758
  = ((Any -> Any -> Any) -> T_IsBand_230 -> T_Band_266)
-> (Bool -> Bool -> Bool) -> T_IsBand_230 -> T_Band_266
forall a b. a -> b
coe
      (Any -> Any -> Any) -> T_IsBand_230 -> T_Band_266
MAlonzo.Code.Algebra.Bundles.C_Band'46'constructor_4745
      Bool -> Bool -> Bool
MAlonzo.Code.Data.Bool.Base.d__'8743'__24 T_IsBand_230
d_'8743''45'isBand_1756
-- Data.Bool.Properties.∧-isSemilattice
d_'8743''45'isSemilattice_1760 ::
  MAlonzo.Code.Algebra.Structures.T_IsSemilattice_312
d_'8743''45'isSemilattice_1760 :: T_IsSemilattice_312
d_'8743''45'isSemilattice_1760
  = (T_IsBand_230 -> (Any -> Any -> Any) -> T_IsSemilattice_312)
-> Any -> Any -> T_IsSemilattice_312
forall a b. a -> b
coe
      T_IsBand_230 -> (Any -> Any -> Any) -> T_IsSemilattice_312
MAlonzo.Code.Algebra.Structures.C_IsSemilattice'46'constructor_6687
      (T_IsBand_230 -> Any
forall a b. a -> b
coe T_IsBand_230
d_'8743''45'isBand_1756) Any
forall a. a
erased
-- Data.Bool.Properties.∧-semilattice
d_'8743''45'semilattice_1762 ::
  MAlonzo.Code.Algebra.Bundles.T_Semilattice_402
d_'8743''45'semilattice_1762 :: T_Semilattice_402
d_'8743''45'semilattice_1762
  = ((Any -> Any -> Any) -> T_IsSemilattice_312 -> T_Semilattice_402)
-> (Bool -> Bool -> Bool)
-> T_IsSemilattice_312
-> T_Semilattice_402
forall a b. a -> b
coe
      (Any -> Any -> Any) -> T_IsSemilattice_312 -> T_Semilattice_402
MAlonzo.Code.Algebra.Bundles.C_Semilattice'46'constructor_7205
      Bool -> Bool -> Bool
MAlonzo.Code.Data.Bool.Base.d__'8743'__24
      T_IsSemilattice_312
d_'8743''45'isSemilattice_1760
-- Data.Bool.Properties.∧-isMonoid
d_'8743''45'isMonoid_1764 ::
  MAlonzo.Code.Algebra.Structures.T_IsMonoid_358
d_'8743''45'isMonoid_1764 :: T_IsMonoid_358
d_'8743''45'isMonoid_1764
  = (T_IsSemigroup_194 -> T_Σ_14 -> T_IsMonoid_358)
-> Any -> Any -> T_IsMonoid_358
forall a b. a -> b
coe
      T_IsSemigroup_194 -> T_Σ_14 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.C_IsMonoid'46'constructor_7687
      (T_IsSemigroup_194 -> Any
forall a b. a -> b
coe T_IsSemigroup_194
d_'8743''45'isSemigroup_1752) (T_Σ_14 -> Any
forall a b. a -> b
coe T_Σ_14
d_'8743''45'identity_1670)
-- Data.Bool.Properties.∧-isCommutativeMonoid
d_'8743''45'isCommutativeMonoid_1766 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMonoid_406
d_'8743''45'isCommutativeMonoid_1766 :: T_IsCommutativeMonoid_406
d_'8743''45'isCommutativeMonoid_1766
  = (T_IsMonoid_358
 -> (Any -> Any -> Any) -> T_IsCommutativeMonoid_406)
-> Any -> Any -> T_IsCommutativeMonoid_406
forall a b. a -> b
coe
      T_IsMonoid_358 -> (Any -> Any -> Any) -> T_IsCommutativeMonoid_406
MAlonzo.Code.Algebra.Structures.C_IsCommutativeMonoid'46'constructor_9361
      (T_IsMonoid_358 -> Any
forall a b. a -> b
coe T_IsMonoid_358
d_'8743''45'isMonoid_1764) Any
forall a. a
erased
-- Data.Bool.Properties.∧-commutativeMonoid
d_'8743''45'commutativeMonoid_1768 ::
  MAlonzo.Code.Algebra.Bundles.T_CommutativeMonoid_582
d_'8743''45'commutativeMonoid_1768 :: T_CommutativeMonoid_582
d_'8743''45'commutativeMonoid_1768
  = ((Any -> Any -> Any)
 -> Any -> T_IsCommutativeMonoid_406 -> T_CommutativeMonoid_582)
-> (Bool -> Bool -> Bool)
-> Any
-> T_IsCommutativeMonoid_406
-> T_CommutativeMonoid_582
forall a b. a -> b
coe
      (Any -> Any -> Any)
-> Any -> T_IsCommutativeMonoid_406 -> T_CommutativeMonoid_582
MAlonzo.Code.Algebra.Bundles.C_CommutativeMonoid'46'constructor_10343
      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_406
d_'8743''45'isCommutativeMonoid_1766
-- Data.Bool.Properties.∧-isIdempotentCommutativeMonoid
d_'8743''45'isIdempotentCommutativeMonoid_1770 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_464
d_'8743''45'isIdempotentCommutativeMonoid_1770 :: T_IsIdempotentCommutativeMonoid_464
d_'8743''45'isIdempotentCommutativeMonoid_1770
  = (T_IsCommutativeMonoid_406
 -> (Any -> Any) -> T_IsIdempotentCommutativeMonoid_464)
-> Any -> Any -> T_IsIdempotentCommutativeMonoid_464
forall a b. a -> b
coe
      T_IsCommutativeMonoid_406
-> (Any -> Any) -> T_IsIdempotentCommutativeMonoid_464
MAlonzo.Code.Algebra.Structures.C_IsIdempotentCommutativeMonoid'46'constructor_10859
      (T_IsCommutativeMonoid_406 -> Any
forall a b. a -> b
coe T_IsCommutativeMonoid_406
d_'8743''45'isCommutativeMonoid_1766) Any
forall a. a
erased
-- Data.Bool.Properties.∧-idempotentCommutativeMonoid
d_'8743''45'idempotentCommutativeMonoid_1772 ::
  MAlonzo.Code.Algebra.Bundles.T_IdempotentCommutativeMonoid_674
d_'8743''45'idempotentCommutativeMonoid_1772 :: T_IdempotentCommutativeMonoid_674
d_'8743''45'idempotentCommutativeMonoid_1772
  = ((Any -> Any -> Any)
 -> Any
 -> T_IsIdempotentCommutativeMonoid_464
 -> T_IdempotentCommutativeMonoid_674)
-> (Bool -> Bool -> Bool)
-> Any
-> T_IsIdempotentCommutativeMonoid_464
-> T_IdempotentCommutativeMonoid_674
forall a b. a -> b
coe
      (Any -> Any -> Any)
-> Any
-> T_IsIdempotentCommutativeMonoid_464
-> T_IdempotentCommutativeMonoid_674
MAlonzo.Code.Algebra.Bundles.C_IdempotentCommutativeMonoid'46'constructor_12109
      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_464
d_'8743''45'isIdempotentCommutativeMonoid_1770
-- Data.Bool.Properties.∨-∧-isSemiring
d_'8744''45''8743''45'isSemiring_1774 ::
  MAlonzo.Code.Algebra.Structures.T_IsSemiring_1238
d_'8744''45''8743''45'isSemiring_1774 :: T_IsSemiring_1238
d_'8744''45''8743''45'isSemiring_1774
  = (T_IsSemiringWithoutAnnihilatingZero_1142
 -> T_Σ_14 -> T_IsSemiring_1238)
-> Any -> Any -> T_IsSemiring_1238
forall a b. a -> b
coe
      T_IsSemiringWithoutAnnihilatingZero_1142
-> T_Σ_14 -> T_IsSemiring_1238
MAlonzo.Code.Algebra.Structures.C_IsSemiring'46'constructor_37213
      ((T_IsCommutativeMonoid_406
 -> T_IsMonoid_358
 -> T_Σ_14
 -> T_IsSemiringWithoutAnnihilatingZero_1142)
-> Any -> Any -> Any -> Any
forall a b. a -> b
coe
         T_IsCommutativeMonoid_406
-> T_IsMonoid_358
-> T_Σ_14
-> T_IsSemiringWithoutAnnihilatingZero_1142
MAlonzo.Code.Algebra.Structures.C_IsSemiringWithoutAnnihilatingZero'46'constructor_33703
         (T_IsCommutativeMonoid_406 -> Any
forall a b. a -> b
coe T_IsCommutativeMonoid_406
d_'8744''45'isCommutativeMonoid_1646)
         (T_IsMonoid_358 -> Any
forall a b. a -> b
coe T_IsMonoid_358
d_'8743''45'isMonoid_1764)
         (T_Σ_14 -> Any
forall a b. a -> b
coe T_Σ_14
d_'8743''45'distrib'45''8744'_1712))
      (T_Σ_14 -> Any
forall a b. a -> b
coe T_Σ_14
d_'8743''45'zero_1676)
-- Data.Bool.Properties.∨-∧-isCommutativeSemiring
d_'8744''45''8743''45'isCommutativeSemiring_1776 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiring_1344
d_'8744''45''8743''45'isCommutativeSemiring_1776 :: T_IsCommutativeSemiring_1344
d_'8744''45''8743''45'isCommutativeSemiring_1776
  = (T_IsSemiring_1238
 -> (Any -> Any -> Any) -> T_IsCommutativeSemiring_1344)
-> Any -> Any -> T_IsCommutativeSemiring_1344
forall a b. a -> b
coe
      T_IsSemiring_1238
-> (Any -> Any -> Any) -> T_IsCommutativeSemiring_1344
MAlonzo.Code.Algebra.Structures.C_IsCommutativeSemiring'46'constructor_40675
      (T_IsSemiring_1238 -> Any
forall a b. a -> b
coe T_IsSemiring_1238
d_'8744''45''8743''45'isSemiring_1774) Any
forall a. a
erased
-- Data.Bool.Properties.∨-∧-commutativeSemiring
d_'8744''45''8743''45'commutativeSemiring_1778 ::
  MAlonzo.Code.Algebra.Bundles.T_CommutativeSemiring_2094
d_'8744''45''8743''45'commutativeSemiring_1778 :: T_CommutativeSemiring_2094
d_'8744''45''8743''45'commutativeSemiring_1778
  = ((Any -> Any -> Any)
 -> (Any -> Any -> Any)
 -> Any
 -> Any
 -> T_IsCommutativeSemiring_1344
 -> T_CommutativeSemiring_2094)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Any
-> Any
-> T_IsCommutativeSemiring_1344
-> T_CommutativeSemiring_2094
forall a b. a -> b
coe
      (Any -> Any -> Any)
-> (Any -> Any -> Any)
-> Any
-> Any
-> T_IsCommutativeSemiring_1344
-> T_CommutativeSemiring_2094
MAlonzo.Code.Algebra.Bundles.C_CommutativeSemiring'46'constructor_36513
      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_1344
d_'8744''45''8743''45'isCommutativeSemiring_1776
-- Data.Bool.Properties.∧-∨-isSemiring
d_'8743''45''8744''45'isSemiring_1780 ::
  MAlonzo.Code.Algebra.Structures.T_IsSemiring_1238
d_'8743''45''8744''45'isSemiring_1780 :: T_IsSemiring_1238
d_'8743''45''8744''45'isSemiring_1780
  = (T_IsSemiringWithoutAnnihilatingZero_1142
 -> T_Σ_14 -> T_IsSemiring_1238)
-> Any -> Any -> T_IsSemiring_1238
forall a b. a -> b
coe
      T_IsSemiringWithoutAnnihilatingZero_1142
-> T_Σ_14 -> T_IsSemiring_1238
MAlonzo.Code.Algebra.Structures.C_IsSemiring'46'constructor_37213
      ((T_IsCommutativeMonoid_406
 -> T_IsMonoid_358
 -> T_Σ_14
 -> T_IsSemiringWithoutAnnihilatingZero_1142)
-> Any -> Any -> Any -> Any
forall a b. a -> b
coe
         T_IsCommutativeMonoid_406
-> T_IsMonoid_358
-> T_Σ_14
-> T_IsSemiringWithoutAnnihilatingZero_1142
MAlonzo.Code.Algebra.Structures.C_IsSemiringWithoutAnnihilatingZero'46'constructor_33703
         (T_IsCommutativeMonoid_406 -> Any
forall a b. a -> b
coe T_IsCommutativeMonoid_406
d_'8743''45'isCommutativeMonoid_1766)
         (T_IsMonoid_358 -> Any
forall a b. a -> b
coe T_IsMonoid_358
d_'8744''45'isMonoid_1644)
         (T_Σ_14 -> Any
forall a b. a -> b
coe T_Σ_14
d_'8744''45'distrib'45''8743'_1732))
      (T_Σ_14 -> Any
forall a b. a -> b
coe T_Σ_14
d_'8744''45'zero_1610)
-- Data.Bool.Properties.∧-∨-isCommutativeSemiring
d_'8743''45''8744''45'isCommutativeSemiring_1782 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiring_1344
d_'8743''45''8744''45'isCommutativeSemiring_1782 :: T_IsCommutativeSemiring_1344
d_'8743''45''8744''45'isCommutativeSemiring_1782
  = (T_IsSemiring_1238
 -> (Any -> Any -> Any) -> T_IsCommutativeSemiring_1344)
-> Any -> Any -> T_IsCommutativeSemiring_1344
forall a b. a -> b
coe
      T_IsSemiring_1238
-> (Any -> Any -> Any) -> T_IsCommutativeSemiring_1344
MAlonzo.Code.Algebra.Structures.C_IsCommutativeSemiring'46'constructor_40675
      (T_IsSemiring_1238 -> Any
forall a b. a -> b
coe T_IsSemiring_1238
d_'8743''45''8744''45'isSemiring_1780) Any
forall a. a
erased
-- Data.Bool.Properties.∧-∨-commutativeSemiring
d_'8743''45''8744''45'commutativeSemiring_1784 ::
  MAlonzo.Code.Algebra.Bundles.T_CommutativeSemiring_2094
d_'8743''45''8744''45'commutativeSemiring_1784 :: T_CommutativeSemiring_2094
d_'8743''45''8744''45'commutativeSemiring_1784
  = ((Any -> Any -> Any)
 -> (Any -> Any -> Any)
 -> Any
 -> Any
 -> T_IsCommutativeSemiring_1344
 -> T_CommutativeSemiring_2094)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> Any
-> Any
-> T_IsCommutativeSemiring_1344
-> T_CommutativeSemiring_2094
forall a b. a -> b
coe
      (Any -> Any -> Any)
-> (Any -> Any -> Any)
-> Any
-> Any
-> T_IsCommutativeSemiring_1344
-> T_CommutativeSemiring_2094
MAlonzo.Code.Algebra.Bundles.C_CommutativeSemiring'46'constructor_36513
      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_1344
d_'8743''45''8744''45'isCommutativeSemiring_1782
-- Data.Bool.Properties.∨-∧-isLattice
d_'8744''45''8743''45'isLattice_1786 ::
  MAlonzo.Code.Algebra.Structures.T_IsLattice_740
d_'8744''45''8743''45'isLattice_1786 :: T_IsLattice_740
d_'8744''45''8743''45'isLattice_1786
  = (T_IsEquivalence_26
 -> (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_740)
-> Any
-> Any
-> Any
-> Any
-> Any
-> Any
-> Any
-> Any
-> T_IsLattice_740
forall a b. a -> b
coe
      T_IsEquivalence_26
-> (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_740
MAlonzo.Code.Algebra.Structures.C_IsLattice'46'constructor_20027
      (T_IsEquivalence_26 -> Any
forall a b. a -> b
coe
         T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.PropositionalEquality.Properties.du_isEquivalence_242)
      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_1746)
-- Data.Bool.Properties.∨-∧-lattice
d_'8744''45''8743''45'lattice_1788 ::
  MAlonzo.Code.Algebra.Bundles.T_Lattice_1144
d_'8744''45''8743''45'lattice_1788 :: T_Lattice_1144
d_'8744''45''8743''45'lattice_1788
  = ((Any -> Any -> Any)
 -> (Any -> Any -> Any) -> T_IsLattice_740 -> T_Lattice_1144)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> T_IsLattice_740
-> T_Lattice_1144
forall a b. a -> b
coe
      (Any -> Any -> Any)
-> (Any -> Any -> Any) -> T_IsLattice_740 -> T_Lattice_1144
MAlonzo.Code.Algebra.Bundles.C_Lattice'46'constructor_19309
      Bool -> Bool -> Bool
MAlonzo.Code.Data.Bool.Base.d__'8744'__30
      Bool -> Bool -> Bool
MAlonzo.Code.Data.Bool.Base.d__'8743'__24
      T_IsLattice_740
d_'8744''45''8743''45'isLattice_1786
-- Data.Bool.Properties.∨-∧-isDistributiveLattice
d_'8744''45''8743''45'isDistributiveLattice_1790 ::
  MAlonzo.Code.Algebra.Structures.T_IsDistributiveLattice_814
d_'8744''45''8743''45'isDistributiveLattice_1790 :: T_IsDistributiveLattice_814
d_'8744''45''8743''45'isDistributiveLattice_1790
  = (T_IsLattice_740
 -> (Any -> Any -> Any -> Any) -> T_IsDistributiveLattice_814)
-> Any -> Any -> T_IsDistributiveLattice_814
forall a b. a -> b
coe
      T_IsLattice_740
-> (Any -> Any -> Any -> Any) -> T_IsDistributiveLattice_814
MAlonzo.Code.Algebra.Structures.C_IsDistributiveLattice'46'constructor_24097
      (T_IsLattice_740 -> Any
forall a b. a -> b
coe T_IsLattice_740
d_'8744''45''8743''45'isLattice_1786) Any
forall a. a
erased
-- Data.Bool.Properties.∨-∧-distributiveLattice
d_'8744''45''8743''45'distributiveLattice_1792 ::
  MAlonzo.Code.Algebra.Bundles.T_DistributiveLattice_1228
d_'8744''45''8743''45'distributiveLattice_1792 :: T_DistributiveLattice_1228
d_'8744''45''8743''45'distributiveLattice_1792
  = ((Any -> Any -> Any)
 -> (Any -> Any -> Any)
 -> T_IsDistributiveLattice_814
 -> T_DistributiveLattice_1228)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> T_IsDistributiveLattice_814
-> T_DistributiveLattice_1228
forall a b. a -> b
coe
      (Any -> Any -> Any)
-> (Any -> Any -> Any)
-> T_IsDistributiveLattice_814
-> T_DistributiveLattice_1228
MAlonzo.Code.Algebra.Bundles.C_DistributiveLattice'46'constructor_20939
      Bool -> Bool -> Bool
MAlonzo.Code.Data.Bool.Base.d__'8744'__30
      Bool -> Bool -> Bool
MAlonzo.Code.Data.Bool.Base.d__'8743'__24
      T_IsDistributiveLattice_814
d_'8744''45''8743''45'isDistributiveLattice_1790
-- Data.Bool.Properties.∨-∧-isBooleanAlgebra
d_'8744''45''8743''45'isBooleanAlgebra_1794 ::
  MAlonzo.Code.Algebra.Structures.T_IsBooleanAlgebra_1864
d_'8744''45''8743''45'isBooleanAlgebra_1794 :: T_IsBooleanAlgebra_1864
d_'8744''45''8743''45'isBooleanAlgebra_1794
  = (T_IsDistributiveLattice_814
 -> (Any -> Any)
 -> (Any -> Any)
 -> (Any -> Any -> Any -> Any)
 -> T_IsBooleanAlgebra_1864)
-> Any -> Any -> Any -> Any -> T_IsBooleanAlgebra_1864
forall a b. a -> b
coe
      T_IsDistributiveLattice_814
-> (Any -> Any)
-> (Any -> Any)
-> (Any -> Any -> Any -> Any)
-> T_IsBooleanAlgebra_1864
MAlonzo.Code.Algebra.Structures.C_IsBooleanAlgebra'46'constructor_59337
      (T_IsDistributiveLattice_814 -> Any
forall a b. a -> b
coe T_IsDistributiveLattice_814
d_'8744''45''8743''45'isDistributiveLattice_1790) Any
forall a. a
erased
      Any
forall a. a
erased Any
forall a. a
erased
-- Data.Bool.Properties.∨-∧-booleanAlgebra
d_'8744''45''8743''45'booleanAlgebra_1796 ::
  MAlonzo.Code.Algebra.Bundles.T_BooleanAlgebra_2920
d_'8744''45''8743''45'booleanAlgebra_1796 :: T_BooleanAlgebra_2920
d_'8744''45''8743''45'booleanAlgebra_1796
  = ((Any -> Any -> Any)
 -> (Any -> Any -> Any)
 -> (Any -> Any)
 -> Any
 -> Any
 -> T_IsBooleanAlgebra_1864
 -> T_BooleanAlgebra_2920)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool -> Bool)
-> (Bool -> Bool)
-> Any
-> Any
-> T_IsBooleanAlgebra_1864
-> T_BooleanAlgebra_2920
forall a b. a -> b
coe
      (Any -> Any -> Any)
-> (Any -> Any -> Any)
-> (Any -> Any)
-> Any
-> Any
-> T_IsBooleanAlgebra_1864
-> T_BooleanAlgebra_2920
MAlonzo.Code.Algebra.Bundles.C_BooleanAlgebra'46'constructor_50705
      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_1864
d_'8744''45''8743''45'isBooleanAlgebra_1794
-- Data.Bool.Properties.xor-is-ok
d_xor'45'is'45'ok_1802 ::
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_xor'45'is'45'ok_1802 :: Bool -> Bool -> T__'8801'__12
d_xor'45'is'45'ok_1802 = Bool -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties.xor-∧-commutativeRing
d_xor'45''8743''45'commutativeRing_1808 ::
  MAlonzo.Code.Algebra.Bundles.T_CommutativeRing_2704
d_xor'45''8743''45'commutativeRing_1808 :: T_CommutativeRing_2704
d_xor'45''8743''45'commutativeRing_1808
  = (T_BooleanAlgebra_2920
 -> (Any -> Any -> Any)
 -> (Any -> Any -> Any)
 -> T_CommutativeRing_2704)
-> Any -> Any -> Any -> T_CommutativeRing_2704
forall a b. a -> b
coe
      T_BooleanAlgebra_2920
-> (Any -> Any -> Any)
-> (Any -> Any -> Any)
-> T_CommutativeRing_2704
MAlonzo.Code.Algebra.Properties.BooleanAlgebra.du_commutativeRing_2050
      (T_BooleanAlgebra_2920 -> Any
forall a b. a -> b
coe T_BooleanAlgebra_2920
d_'8744''45''8743''45'booleanAlgebra_1796)
      ((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.not-involutive
d_not'45'involutive_2140 ::
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_not'45'involutive_2140 :: Bool -> T__'8801'__12
d_not'45'involutive_2140 = Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties.not-injective
d_not'45'injective_2146 ::
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_not'45'injective_2146 :: Bool -> Bool -> T__'8801'__12 -> T__'8801'__12
d_not'45'injective_2146 = Bool -> Bool -> T__'8801'__12 -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties.not-¬
d_not'45''172'_2156 ::
  Bool ->
  Bool ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Data.Empty.T_'8869'_4
d_not'45''172'_2156 :: Bool -> Bool -> T__'8801'__12 -> T__'8801'__12 -> T_'8869'_4
d_not'45''172'_2156 = Bool -> Bool -> T__'8801'__12 -> T__'8801'__12 -> T_'8869'_4
forall a. a
erased
-- Data.Bool.Properties.¬-not
d_'172''45'not_2162 ::
  Bool ->
  Bool ->
  (MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
   MAlonzo.Code.Data.Empty.T_'8869'_4) ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'172''45'not_2162 :: Bool -> Bool -> (T__'8801'__12 -> T_'8869'_4) -> T__'8801'__12
d_'172''45'not_2162 = Bool -> Bool -> (T__'8801'__12 -> T_'8869'_4) -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties.⇔→≡
d_'8660''8594''8801'_2174 ::
  Bool ->
  Bool ->
  Bool ->
  MAlonzo.Code.Function.Equivalence.T_Equivalence_16 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8660''8594''8801'_2174 :: Bool -> Bool -> Bool -> T_Equivalence_16 -> T__'8801'__12
d_'8660''8594''8801'_2174 = Bool -> Bool -> Bool -> T_Equivalence_16 -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties.T-≡
d_T'45''8801'_2190 ::
  Bool -> MAlonzo.Code.Function.Equivalence.T_Equivalence_16
d_T'45''8801'_2190 :: Bool -> T_Equivalence_16
d_T'45''8801'_2190 Bool
v0
  = if Bool -> Bool
forall a b. a -> b
coe Bool
v0
      then ((Any -> Any) -> (Any -> Any) -> T_Equivalence_16)
-> Any -> Any -> T_Equivalence_16
forall a b. a -> b
coe
             (Any -> Any) -> (Any -> Any) -> T_Equivalence_16
MAlonzo.Code.Function.Equivalence.du_equivalence_56 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_16)
-> Any -> Any -> T_Equivalence_16
forall a b. a -> b
coe
             (Any -> Any) -> (Any -> Any) -> T_Equivalence_16
MAlonzo.Code.Function.Equivalence.du_equivalence_56 Any
forall a. a
erased Any
forall a. a
erased
-- Data.Bool.Properties.T-not-≡
d_T'45'not'45''8801'_2194 ::
  Bool -> MAlonzo.Code.Function.Equivalence.T_Equivalence_16
d_T'45'not'45''8801'_2194 :: Bool -> T_Equivalence_16
d_T'45'not'45''8801'_2194 Bool
v0
  = if Bool -> Bool
forall a b. a -> b
coe Bool
v0
      then ((Any -> Any) -> (Any -> Any) -> T_Equivalence_16)
-> Any -> Any -> T_Equivalence_16
forall a b. a -> b
coe
             (Any -> Any) -> (Any -> Any) -> T_Equivalence_16
MAlonzo.Code.Function.Equivalence.du_equivalence_56 Any
forall a. a
erased Any
forall a. a
erased
      else ((Any -> Any) -> (Any -> Any) -> T_Equivalence_16)
-> Any -> Any -> T_Equivalence_16
forall a b. a -> b
coe
             (Any -> Any) -> (Any -> Any) -> T_Equivalence_16
MAlonzo.Code.Function.Equivalence.du_equivalence_56 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'_2200 ::
  Bool -> Bool -> MAlonzo.Code.Function.Equivalence.T_Equivalence_16
d_T'45''8743'_2200 :: Bool -> Bool -> T_Equivalence_16
d_T'45''8743'_2200 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_16)
-> Any -> Any -> T_Equivalence_16
forall a b. a -> b
coe
                    (Any -> Any) -> (Any -> Any) -> T_Equivalence_16
MAlonzo.Code.Function.Equivalence.du_equivalence_56
                    (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_16)
-> Any -> Any -> T_Equivalence_16
forall a b. a -> b
coe
                    (Any -> Any) -> (Any -> Any) -> T_Equivalence_16
MAlonzo.Code.Function.Equivalence.du_equivalence_56 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_16)
-> Any -> Any -> T_Equivalence_16
forall a b. a -> b
coe
             (Any -> Any) -> (Any -> Any) -> T_Equivalence_16
MAlonzo.Code.Function.Equivalence.du_equivalence_56 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'_2206 ::
  Bool -> Bool -> MAlonzo.Code.Function.Equivalence.T_Equivalence_16
d_T'45''8744'_2206 :: Bool -> Bool -> T_Equivalence_16
d_T'45''8744'_2206 Bool
v0 Bool
v1
  = if Bool -> Bool
forall a b. a -> b
coe Bool
v0
      then ((Any -> Any) -> (Any -> Any) -> T_Equivalence_16)
-> Any -> Any -> T_Equivalence_16
forall a b. a -> b
coe
             (Any -> Any) -> (Any -> Any) -> T_Equivalence_16
MAlonzo.Code.Function.Equivalence.du_equivalence_56
             ((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_16)
-> Any -> Any -> T_Equivalence_16
forall a b. a -> b
coe
                     (Any -> Any) -> (Any -> Any) -> T_Equivalence_16
MAlonzo.Code.Function.Equivalence.du_equivalence_56
                     ((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_16)
-> Any -> Any -> T_Equivalence_16
forall a b. a -> b
coe
                     (Any -> Any) -> (Any -> Any) -> T_Equivalence_16
MAlonzo.Code.Function.Equivalence.du_equivalence_56
                     ((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_2208 ::
  Bool ->
  AgdaAny ->
  AgdaAny -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_T'45'irrelevant_2208 :: Bool -> Any -> Any -> T__'8801'__12
d_T'45'irrelevant_2208 = Bool -> Any -> Any -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties.T?
d_T'63'_2210 :: Bool -> MAlonzo.Code.Relation.Nullary.T_Dec_32
d_T'63'_2210 :: Bool -> T_Dec_32
d_T'63'_2210 Bool
v0
  = (Bool -> T_Reflects_14 -> T_Dec_32) -> Any -> Any -> T_Dec_32
forall a b. a -> b
coe
      Bool -> T_Reflects_14 -> T_Dec_32
MAlonzo.Code.Relation.Nullary.C__because__46 (Bool -> Any
forall a b. a -> b
coe Bool
v0)
      (if Bool -> Bool
forall a b. a -> b
coe Bool
v0
         then (Any -> T_Reflects_14) -> Any -> Any
forall a b. a -> b
coe
                Any -> T_Reflects_14
MAlonzo.Code.Relation.Nullary.C_of'696'_22
                (() -> Any
forall a b. a -> b
coe ()
MAlonzo.Code.Agda.Builtin.Unit.C_tt_8)
         else T_Reflects_14 -> Any
forall a b. a -> b
coe T_Reflects_14
MAlonzo.Code.Relation.Nullary.C_of'8319'_26)
-- Data.Bool.Properties.T?-diag
d_T'63''45'diag_2216 :: Bool -> AgdaAny -> AgdaAny
d_T'63''45'diag_2216 :: Bool -> Any -> Any
d_T'63''45'diag_2216 Bool
v0 ~Any
v1 = Bool -> Any
du_T'63''45'diag_2216 Bool
v0
du_T'63''45'diag_2216 :: Bool -> AgdaAny
du_T'63''45'diag_2216 :: Bool -> Any
du_T'63''45'diag_2216 Bool
v0
  = (Any -> Any -> Any) -> Any -> Any -> Any
forall a b. a -> b
coe Any -> Any -> Any
forall a b. a -> b -> b
seq (Bool -> Any
forall a b. a -> b
coe Bool
v0) (() -> Any
forall a b. a -> b
coe ()
MAlonzo.Code.Agda.Builtin.Unit.C_tt_8)
-- Data.Bool.Properties.push-function-into-if
d_push'45'function'45'into'45'if_2226 ::
  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_2226 :: ()
-> ()
-> ()
-> ()
-> (Any -> Any)
-> Bool
-> Any
-> Any
-> T__'8801'__12
d_push'45'function'45'into'45'if_2226 = ()
-> ()
-> ()
-> ()
-> (Any -> Any)
-> Bool
-> Any
-> Any
-> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties.∧-∨-distˡ
d_'8743''45''8744''45'dist'737'_2228 ::
  Bool ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8743''45''8744''45'dist'737'_2228 :: Bool -> Bool -> Bool -> T__'8801'__12
d_'8743''45''8744''45'dist'737'_2228 = Bool -> Bool -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties.∧-∨-distʳ
d_'8743''45''8744''45'dist'691'_2230 ::
  Bool ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8743''45''8744''45'dist'691'_2230 :: Bool -> Bool -> Bool -> T__'8801'__12
d_'8743''45''8744''45'dist'691'_2230 = Bool -> Bool -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties.distrib-∧-∨
d_distrib'45''8743''45''8744'_2232 ::
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_distrib'45''8743''45''8744'_2232 :: T_Σ_14
d_distrib'45''8743''45''8744'_2232
  = T_Σ_14 -> T_Σ_14
forall a b. a -> b
coe T_Σ_14
d_'8743''45'distrib'45''8744'_1712
-- Data.Bool.Properties.∨-∧-distˡ
d_'8744''45''8743''45'dist'737'_2234 ::
  Bool ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8744''45''8743''45'dist'737'_2234 :: Bool -> Bool -> Bool -> T__'8801'__12
d_'8744''45''8743''45'dist'737'_2234 = Bool -> Bool -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties.∨-∧-distʳ
d_'8744''45''8743''45'dist'691'_2236 ::
  Bool ->
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8744''45''8743''45'dist'691'_2236 :: Bool -> Bool -> Bool -> T__'8801'__12
d_'8744''45''8743''45'dist'691'_2236 = Bool -> Bool -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties.∨-∧-distrib
d_'8744''45''8743''45'distrib_2238 ::
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'8744''45''8743''45'distrib_2238 :: T_Σ_14
d_'8744''45''8743''45'distrib_2238
  = T_Σ_14 -> T_Σ_14
forall a b. a -> b
coe T_Σ_14
d_'8744''45'distrib'45''8743'_1732
-- Data.Bool.Properties.∨-∧-abs
d_'8744''45''8743''45'abs_2240 ::
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8744''45''8743''45'abs_2240 :: Bool -> Bool -> T__'8801'__12
d_'8744''45''8743''45'abs_2240 = Bool -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties.∧-∨-abs
d_'8743''45''8744''45'abs_2242 ::
  Bool -> Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8743''45''8744''45'abs_2242 :: Bool -> Bool -> T__'8801'__12
d_'8743''45''8744''45'abs_2242 = Bool -> Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties.not-∧-inverseˡ
d_not'45''8743''45'inverse'737'_2244 ::
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_not'45''8743''45'inverse'737'_2244 :: Bool -> T__'8801'__12
d_not'45''8743''45'inverse'737'_2244 = Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties.not-∧-inverseʳ
d_not'45''8743''45'inverse'691'_2246 ::
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_not'45''8743''45'inverse'691'_2246 :: Bool -> T__'8801'__12
d_not'45''8743''45'inverse'691'_2246 = Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties.not-∧-inverse
d_not'45''8743''45'inverse_2248 ::
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_not'45''8743''45'inverse_2248 :: T_Σ_14
d_not'45''8743''45'inverse_2248 = T_Σ_14 -> T_Σ_14
forall a b. a -> b
coe T_Σ_14
d_'8743''45'inverse_1684
-- Data.Bool.Properties.not-∨-inverseˡ
d_not'45''8744''45'inverse'737'_2250 ::
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_not'45''8744''45'inverse'737'_2250 :: Bool -> T__'8801'__12
d_not'45''8744''45'inverse'737'_2250 = Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties.not-∨-inverseʳ
d_not'45''8744''45'inverse'691'_2252 ::
  Bool -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_not'45''8744''45'inverse'691'_2252 :: Bool -> T__'8801'__12
d_not'45''8744''45'inverse'691'_2252 = Bool -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties.not-∨-inverse
d_not'45''8744''45'inverse_2254 ::
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_not'45''8744''45'inverse_2254 :: T_Σ_14
d_not'45''8744''45'inverse_2254 = T_Σ_14 -> T_Σ_14
forall a b. a -> b
coe T_Σ_14
d_'8744''45'inverse_1618
-- Data.Bool.Properties.isCommutativeSemiring-∨-∧
d_isCommutativeSemiring'45''8744''45''8743'_2256 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiring_1344
d_isCommutativeSemiring'45''8744''45''8743'_2256 :: T_IsCommutativeSemiring_1344
d_isCommutativeSemiring'45''8744''45''8743'_2256
  = T_IsCommutativeSemiring_1344 -> T_IsCommutativeSemiring_1344
forall a b. a -> b
coe T_IsCommutativeSemiring_1344
d_'8744''45''8743''45'isCommutativeSemiring_1776
-- Data.Bool.Properties.commutativeSemiring-∨-∧
d_commutativeSemiring'45''8744''45''8743'_2258 ::
  MAlonzo.Code.Algebra.Bundles.T_CommutativeSemiring_2094
d_commutativeSemiring'45''8744''45''8743'_2258 :: T_CommutativeSemiring_2094
d_commutativeSemiring'45''8744''45''8743'_2258
  = T_CommutativeSemiring_2094 -> T_CommutativeSemiring_2094
forall a b. a -> b
coe T_CommutativeSemiring_2094
d_'8744''45''8743''45'commutativeSemiring_1778
-- Data.Bool.Properties.isCommutativeSemiring-∧-∨
d_isCommutativeSemiring'45''8743''45''8744'_2260 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiring_1344
d_isCommutativeSemiring'45''8743''45''8744'_2260 :: T_IsCommutativeSemiring_1344
d_isCommutativeSemiring'45''8743''45''8744'_2260
  = T_IsCommutativeSemiring_1344 -> T_IsCommutativeSemiring_1344
forall a b. a -> b
coe T_IsCommutativeSemiring_1344
d_'8743''45''8744''45'isCommutativeSemiring_1782
-- Data.Bool.Properties.commutativeSemiring-∧-∨
d_commutativeSemiring'45''8743''45''8744'_2262 ::
  MAlonzo.Code.Algebra.Bundles.T_CommutativeSemiring_2094
d_commutativeSemiring'45''8743''45''8744'_2262 :: T_CommutativeSemiring_2094
d_commutativeSemiring'45''8743''45''8744'_2262
  = T_CommutativeSemiring_2094 -> T_CommutativeSemiring_2094
forall a b. a -> b
coe T_CommutativeSemiring_2094
d_'8743''45''8744''45'commutativeSemiring_1784
-- Data.Bool.Properties.isBooleanAlgebra
d_isBooleanAlgebra_2264 ::
  MAlonzo.Code.Algebra.Structures.T_IsBooleanAlgebra_1864
d_isBooleanAlgebra_2264 :: T_IsBooleanAlgebra_1864
d_isBooleanAlgebra_2264
  = T_IsBooleanAlgebra_1864 -> T_IsBooleanAlgebra_1864
forall a b. a -> b
coe T_IsBooleanAlgebra_1864
d_'8744''45''8743''45'isBooleanAlgebra_1794
-- Data.Bool.Properties.booleanAlgebra
d_booleanAlgebra_2266 ::
  MAlonzo.Code.Algebra.Bundles.T_BooleanAlgebra_2920
d_booleanAlgebra_2266 :: T_BooleanAlgebra_2920
d_booleanAlgebra_2266
  = T_BooleanAlgebra_2920 -> T_BooleanAlgebra_2920
forall a b. a -> b
coe T_BooleanAlgebra_2920
d_'8744''45''8743''45'booleanAlgebra_1796
-- Data.Bool.Properties.commutativeRing-xor-∧
d_commutativeRing'45'xor'45''8743'_2268 ::
  MAlonzo.Code.Algebra.Bundles.T_CommutativeRing_2704
d_commutativeRing'45'xor'45''8743'_2268 :: T_CommutativeRing_2704
d_commutativeRing'45'xor'45''8743'_2268
  = T_CommutativeRing_2704 -> T_CommutativeRing_2704
forall a b. a -> b
coe T_CommutativeRing_2704
d_xor'45''8743''45'commutativeRing_1808
-- Data.Bool.Properties.proof-irrelevance
d_proof'45'irrelevance_2270 ::
  Bool ->
  AgdaAny ->
  AgdaAny -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_proof'45'irrelevance_2270 :: Bool -> Any -> Any -> T__'8801'__12
d_proof'45'irrelevance_2270 = Bool -> Any -> Any -> T__'8801'__12
forall a. a
erased
-- Data.Bool.Properties.T-irrelevance
d_T'45'irrelevance_2272 ::
  Bool ->
  AgdaAny ->
  AgdaAny -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_T'45'irrelevance_2272 :: Bool -> Any -> Any -> T__'8801'__12
d_T'45'irrelevance_2272 = Bool -> Any -> Any -> T__'8801'__12
forall a. a
erased