{-# 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.Integer.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.Construct.NaturalChoice.Base
import qualified MAlonzo.Code.Algebra.Construct.NaturalChoice.MinMaxOp
import qualified MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp
import qualified MAlonzo.Code.Algebra.Structures
import qualified MAlonzo.Code.Data.Bool.Properties
import qualified MAlonzo.Code.Data.Empty
import qualified MAlonzo.Code.Data.Integer.Base
import qualified MAlonzo.Code.Data.Nat.Base
import qualified MAlonzo.Code.Data.Nat.Properties
import qualified MAlonzo.Code.Data.Nat.Properties.Core
import qualified MAlonzo.Code.Data.Sign.Base
import qualified MAlonzo.Code.Data.Sum.Base
import qualified MAlonzo.Code.Function.Base
import qualified MAlonzo.Code.Relation.Binary.Bundles
import qualified MAlonzo.Code.Relation.Binary.Construct.Converse
import qualified MAlonzo.Code.Relation.Binary.Definitions
import qualified MAlonzo.Code.Relation.Binary.PropositionalEquality.Core
import qualified MAlonzo.Code.Relation.Binary.PropositionalEquality.Properties
import qualified MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple
import qualified MAlonzo.Code.Relation.Binary.Structures
import qualified MAlonzo.Code.Relation.Nullary
import qualified MAlonzo.Code.Relation.Nullary.Decidable.Core
import qualified MAlonzo.Code.Relation.Nullary.Negation.Core

-- Data.Integer.Properties._._DistributesOver_
d__DistributesOver__10 ::
  (Integer -> Integer -> Integer) ->
  (Integer -> Integer -> Integer) -> ()
d__DistributesOver__10 :: (Integer -> Integer -> Integer)
-> (Integer -> Integer -> Integer) -> ()
d__DistributesOver__10 = (Integer -> Integer -> Integer)
-> (Integer -> Integer -> Integer) -> ()
forall a. a
erased
-- Data.Integer.Properties._._DistributesOverʳ_
d__DistributesOver'691'__12 ::
  (Integer -> Integer -> Integer) ->
  (Integer -> Integer -> Integer) -> ()
d__DistributesOver'691'__12 :: (Integer -> Integer -> Integer)
-> (Integer -> Integer -> Integer) -> ()
d__DistributesOver'691'__12 = (Integer -> Integer -> Integer)
-> (Integer -> Integer -> Integer) -> ()
forall a. a
erased
-- Data.Integer.Properties._._DistributesOverˡ_
d__DistributesOver'737'__14 ::
  (Integer -> Integer -> Integer) ->
  (Integer -> Integer -> Integer) -> ()
d__DistributesOver'737'__14 :: (Integer -> Integer -> Integer)
-> (Integer -> Integer -> Integer) -> ()
d__DistributesOver'737'__14 = (Integer -> Integer -> Integer)
-> (Integer -> Integer -> Integer) -> ()
forall a. a
erased
-- Data.Integer.Properties._.Associative
d_Associative_26 :: (Integer -> Integer -> Integer) -> ()
d_Associative_26 :: (Integer -> Integer -> Integer) -> ()
d_Associative_26 = (Integer -> Integer -> Integer) -> ()
forall a. a
erased
-- Data.Integer.Properties._.Commutative
d_Commutative_30 :: (Integer -> Integer -> Integer) -> ()
d_Commutative_30 :: (Integer -> Integer -> Integer) -> ()
d_Commutative_30 = (Integer -> Integer -> Integer) -> ()
forall a. a
erased
-- Data.Integer.Properties._.Identity
d_Identity_42 :: Integer -> (Integer -> Integer -> Integer) -> ()
d_Identity_42 :: Integer -> (Integer -> Integer -> Integer) -> ()
d_Identity_42 = Integer -> (Integer -> Integer -> Integer) -> ()
forall a. a
erased
-- Data.Integer.Properties._.Inverse
d_Inverse_46 ::
  Integer ->
  (Integer -> Integer) -> (Integer -> Integer -> Integer) -> ()
d_Inverse_46 :: Integer
-> (Integer -> Integer) -> (Integer -> Integer -> Integer) -> ()
d_Inverse_46 = Integer
-> (Integer -> Integer) -> (Integer -> Integer -> Integer) -> ()
forall a. a
erased
-- Data.Integer.Properties._.LeftIdentity
d_LeftIdentity_56 ::
  Integer -> (Integer -> Integer -> Integer) -> ()
d_LeftIdentity_56 :: Integer -> (Integer -> Integer -> Integer) -> ()
d_LeftIdentity_56 = Integer -> (Integer -> Integer -> Integer) -> ()
forall a. a
erased
-- Data.Integer.Properties._.LeftInverse
d_LeftInverse_58 ::
  Integer ->
  (Integer -> Integer) -> (Integer -> Integer -> Integer) -> ()
d_LeftInverse_58 :: Integer
-> (Integer -> Integer) -> (Integer -> Integer -> Integer) -> ()
d_LeftInverse_58 = Integer
-> (Integer -> Integer) -> (Integer -> Integer -> Integer) -> ()
forall a. a
erased
-- Data.Integer.Properties._.LeftZero
d_LeftZero_60 :: Integer -> (Integer -> Integer -> Integer) -> ()
d_LeftZero_60 :: Integer -> (Integer -> Integer -> Integer) -> ()
d_LeftZero_60 = Integer -> (Integer -> Integer -> Integer) -> ()
forall a. a
erased
-- Data.Integer.Properties._.RightIdentity
d_RightIdentity_68 ::
  Integer -> (Integer -> Integer -> Integer) -> ()
d_RightIdentity_68 :: Integer -> (Integer -> Integer -> Integer) -> ()
d_RightIdentity_68 = Integer -> (Integer -> Integer -> Integer) -> ()
forall a. a
erased
-- Data.Integer.Properties._.RightInverse
d_RightInverse_70 ::
  Integer ->
  (Integer -> Integer) -> (Integer -> Integer -> Integer) -> ()
d_RightInverse_70 :: Integer
-> (Integer -> Integer) -> (Integer -> Integer -> Integer) -> ()
d_RightInverse_70 = Integer
-> (Integer -> Integer) -> (Integer -> Integer -> Integer) -> ()
forall a. a
erased
-- Data.Integer.Properties._.RightZero
d_RightZero_72 :: Integer -> (Integer -> Integer -> Integer) -> ()
d_RightZero_72 :: Integer -> (Integer -> Integer -> Integer) -> ()
d_RightZero_72 = Integer -> (Integer -> Integer -> Integer) -> ()
forall a. a
erased
-- Data.Integer.Properties._.Zero
d_Zero_76 :: Integer -> (Integer -> Integer -> Integer) -> ()
d_Zero_76 :: Integer -> (Integer -> Integer -> Integer) -> ()
d_Zero_76 = Integer -> (Integer -> Integer -> Integer) -> ()
forall a. a
erased
-- Data.Integer.Properties._.IsAbelianGroup
d_IsAbelianGroup_80 :: p -> p -> p -> ()
d_IsAbelianGroup_80 p
a0 p
a1 p
a2 = ()
-- Data.Integer.Properties._.IsBand
d_IsBand_82 :: p -> ()
d_IsBand_82 p
a0 = ()
-- Data.Integer.Properties._.IsCancellativeCommutativeSemiring
d_IsCancellativeCommutativeSemiring_88 :: p -> p -> p -> p -> ()
d_IsCancellativeCommutativeSemiring_88 p
a0 p
a1 p
a2 p
a3 = ()
-- Data.Integer.Properties._.IsCommutativeMagma
d_IsCommutativeMagma_90 :: p -> ()
d_IsCommutativeMagma_90 p
a0 = ()
-- Data.Integer.Properties._.IsCommutativeMonoid
d_IsCommutativeMonoid_92 :: p -> p -> ()
d_IsCommutativeMonoid_92 p
a0 p
a1 = ()
-- Data.Integer.Properties._.IsCommutativeRing
d_IsCommutativeRing_94 :: p -> p -> p -> p -> p -> ()
d_IsCommutativeRing_94 p
a0 p
a1 p
a2 p
a3 p
a4 = ()
-- Data.Integer.Properties._.IsCommutativeSemigroup
d_IsCommutativeSemigroup_96 :: p -> ()
d_IsCommutativeSemigroup_96 p
a0 = ()
-- Data.Integer.Properties._.IsCommutativeSemiring
d_IsCommutativeSemiring_98 :: p -> p -> p -> p -> ()
d_IsCommutativeSemiring_98 p
a0 p
a1 p
a2 p
a3 = ()
-- Data.Integer.Properties._.IsCommutativeSemiringWithoutOne
d_IsCommutativeSemiringWithoutOne_100 :: p -> p -> p -> ()
d_IsCommutativeSemiringWithoutOne_100 p
a0 p
a1 p
a2 = ()
-- Data.Integer.Properties._.IsGroup
d_IsGroup_104 :: p -> p -> p -> ()
d_IsGroup_104 p
a0 p
a1 p
a2 = ()
-- Data.Integer.Properties._.IsIdempotentCommutativeMonoid
d_IsIdempotentCommutativeMonoid_106 :: p -> p -> ()
d_IsIdempotentCommutativeMonoid_106 p
a0 p
a1 = ()
-- Data.Integer.Properties._.IsMagma
d_IsMagma_110 :: p -> ()
d_IsMagma_110 p
a0 = ()
-- Data.Integer.Properties._.IsMonoid
d_IsMonoid_112 :: p -> p -> ()
d_IsMonoid_112 p
a0 p
a1 = ()
-- Data.Integer.Properties._.IsNearSemiring
d_IsNearSemiring_114 :: p -> p -> p -> ()
d_IsNearSemiring_114 p
a0 p
a1 p
a2 = ()
-- Data.Integer.Properties._.IsRing
d_IsRing_116 :: p -> p -> p -> p -> p -> ()
d_IsRing_116 p
a0 p
a1 p
a2 p
a3 p
a4 = ()
-- Data.Integer.Properties._.IsSelectiveMagma
d_IsSelectiveMagma_118 :: p -> ()
d_IsSelectiveMagma_118 p
a0 = ()
-- Data.Integer.Properties._.IsSemigroup
d_IsSemigroup_120 :: p -> ()
d_IsSemigroup_120 p
a0 = ()
-- Data.Integer.Properties._.IsSemilattice
d_IsSemilattice_122 :: p -> ()
d_IsSemilattice_122 p
a0 = ()
-- Data.Integer.Properties._.IsSemiring
d_IsSemiring_124 :: p -> p -> p -> p -> ()
d_IsSemiring_124 p
a0 p
a1 p
a2 p
a3 = ()
-- Data.Integer.Properties._.IsSemiringWithoutAnnihilatingZero
d_IsSemiringWithoutAnnihilatingZero_126 :: p -> p -> p -> p -> ()
d_IsSemiringWithoutAnnihilatingZero_126 p
a0 p
a1 p
a2 p
a3 = ()
-- Data.Integer.Properties._.IsSemiringWithoutOne
d_IsSemiringWithoutOne_128 :: p -> p -> p -> ()
d_IsSemiringWithoutOne_128 p
a0 p
a1 p
a2 = ()
-- Data.Integer.Properties._.IsAbelianGroup.assoc
d_assoc_134 ::
  MAlonzo.Code.Algebra.Structures.T_IsAbelianGroup_662 ->
  Integer ->
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_assoc_134 :: T_IsAbelianGroup_662
-> Integer -> Integer -> Integer -> T__'8801'__12
d_assoc_134 = T_IsAbelianGroup_662
-> Integer -> Integer -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties._.IsAbelianGroup.comm
d_comm_136 ::
  MAlonzo.Code.Algebra.Structures.T_IsAbelianGroup_662 ->
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_comm_136 :: T_IsAbelianGroup_662 -> Integer -> Integer -> T__'8801'__12
d_comm_136 = T_IsAbelianGroup_662 -> Integer -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Integer.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.Integer.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.Integer.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.Integer.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.Integer.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.Integer.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.Integer.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.Integer.Properties._.IsAbelianGroup.⁻¹-cong
d_'8315''185''45'cong_182 ::
  MAlonzo.Code.Algebra.Structures.T_IsAbelianGroup_662 ->
  Integer ->
  Integer ->
  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
-> Integer -> Integer -> T__'8801'__12 -> T__'8801'__12
d_'8315''185''45'cong_182 = T_IsAbelianGroup_662
-> Integer -> Integer -> T__'8801'__12 -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties._.IsAbelianGroup.∙-cong
d_'8729''45'cong_184 ::
  MAlonzo.Code.Algebra.Structures.T_IsAbelianGroup_662 ->
  Integer ->
  Integer ->
  Integer ->
  Integer ->
  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
-> Integer
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong_184 = T_IsAbelianGroup_662
-> Integer
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties._.IsBand.assoc
d_assoc_192 ::
  MAlonzo.Code.Algebra.Structures.T_IsBand_230 ->
  Integer ->
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_assoc_192 :: T_IsBand_230 -> Integer -> Integer -> Integer -> T__'8801'__12
d_assoc_192 = T_IsBand_230 -> Integer -> Integer -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties._.IsBand.idem
d_idem_194 ::
  MAlonzo.Code.Algebra.Structures.T_IsBand_230 ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_idem_194 :: T_IsBand_230 -> Integer -> T__'8801'__12
d_idem_194 = T_IsBand_230 -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Integer.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.Integer.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.Integer.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.Integer.Properties._.IsBand.∙-cong
d_'8729''45'cong_214 ::
  MAlonzo.Code.Algebra.Structures.T_IsBand_230 ->
  Integer ->
  Integer ->
  Integer ->
  Integer ->
  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
-> Integer
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong_214 = T_IsBand_230
-> Integer
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties._.IsBoundedLattice.assoc
d_assoc_276 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_464 ->
  Integer ->
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_assoc_276 :: T_IsIdempotentCommutativeMonoid_464
-> Integer -> Integer -> Integer -> T__'8801'__12
d_assoc_276 = T_IsIdempotentCommutativeMonoid_464
-> Integer -> Integer -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties._.IsBoundedLattice.comm
d_comm_278 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_464 ->
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_comm_278 :: T_IsIdempotentCommutativeMonoid_464
-> Integer -> Integer -> T__'8801'__12
d_comm_278 = T_IsIdempotentCommutativeMonoid_464
-> Integer -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties._.IsBoundedLattice.idem
d_idem_280 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_464 ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_idem_280 :: T_IsIdempotentCommutativeMonoid_464 -> Integer -> T__'8801'__12
d_idem_280 = T_IsIdempotentCommutativeMonoid_464 -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Integer.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.Integer.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.Integer.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.Integer.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.Integer.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.Integer.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.Integer.Properties._.IsBoundedLattice.∙-cong
d_'8729''45'cong_314 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_464 ->
  Integer ->
  Integer ->
  Integer ->
  Integer ->
  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
-> Integer
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong_314 = T_IsIdempotentCommutativeMonoid_464
-> Integer
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties._.IsCancellativeCommutativeSemiring.assoc
d_assoc_322 ::
  MAlonzo.Code.Algebra.Structures.T_IsCancellativeCommutativeSemiring_1462 ->
  Integer ->
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_assoc_322 :: T_IsCancellativeCommutativeSemiring_1462
-> Integer -> Integer -> Integer -> T__'8801'__12
d_assoc_322 = T_IsCancellativeCommutativeSemiring_1462
-> Integer -> Integer -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties._.IsCancellativeCommutativeSemiring.*-cancelˡ-nonZero
d_'42''45'cancel'737''45'nonZero_324 ::
  MAlonzo.Code.Algebra.Structures.T_IsCancellativeCommutativeSemiring_1462 ->
  Integer ->
  Integer ->
  Integer ->
  (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
-> Integer
-> Integer
-> Integer
-> (T__'8801'__12 -> T_'8869'_4)
-> T__'8801'__12
-> T__'8801'__12
d_'42''45'cancel'737''45'nonZero_324 = T_IsCancellativeCommutativeSemiring_1462
-> Integer
-> Integer
-> Integer
-> (T__'8801'__12 -> T_'8869'_4)
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties._.IsCancellativeCommutativeSemiring.*-comm
d_'42''45'comm_326 ::
  MAlonzo.Code.Algebra.Structures.T_IsCancellativeCommutativeSemiring_1462 ->
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'42''45'comm_326 :: T_IsCancellativeCommutativeSemiring_1462
-> Integer -> Integer -> T__'8801'__12
d_'42''45'comm_326 = T_IsCancellativeCommutativeSemiring_1462
-> Integer -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties._.IsCancellativeCommutativeSemiring.∙-cong
d_'8729''45'cong_328 ::
  MAlonzo.Code.Algebra.Structures.T_IsCancellativeCommutativeSemiring_1462 ->
  Integer ->
  Integer ->
  Integer ->
  Integer ->
  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
-> Integer
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong_328 = T_IsCancellativeCommutativeSemiring_1462
-> Integer
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Integer.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.Integer.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.Integer.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.Integer.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.Integer.Properties._.IsCancellativeCommutativeSemiring.assoc
d_assoc_352 ::
  MAlonzo.Code.Algebra.Structures.T_IsCancellativeCommutativeSemiring_1462 ->
  Integer ->
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_assoc_352 :: T_IsCancellativeCommutativeSemiring_1462
-> Integer -> Integer -> Integer -> T__'8801'__12
d_assoc_352 = T_IsCancellativeCommutativeSemiring_1462
-> Integer -> Integer -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties._.IsCancellativeCommutativeSemiring.comm
d_comm_354 ::
  MAlonzo.Code.Algebra.Structures.T_IsCancellativeCommutativeSemiring_1462 ->
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_comm_354 :: T_IsCancellativeCommutativeSemiring_1462
-> Integer -> Integer -> T__'8801'__12
d_comm_354 = T_IsCancellativeCommutativeSemiring_1462
-> Integer -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties._.IsCancellativeCommutativeSemiring.∙-cong
d_'8729''45'cong_356 ::
  MAlonzo.Code.Algebra.Structures.T_IsCancellativeCommutativeSemiring_1462 ->
  Integer ->
  Integer ->
  Integer ->
  Integer ->
  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
-> Integer
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong_356 = T_IsCancellativeCommutativeSemiring_1462
-> Integer
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Integer.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.Integer.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.Integer.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.Integer.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.Integer.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.Integer.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.Integer.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.Integer.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.Integer.Properties._.IsCancellativeCommutativeSemiring.isNearSemiring
d_isNearSemiring_392 ::
  (Integer -> Integer -> Integer) ->
  (Integer -> Integer -> Integer) ->
  Integer ->
  Integer ->
  MAlonzo.Code.Algebra.Structures.T_IsCancellativeCommutativeSemiring_1462 ->
  MAlonzo.Code.Algebra.Structures.T_IsNearSemiring_876
d_isNearSemiring_392 :: (Integer -> Integer -> Integer)
-> (Integer -> Integer -> Integer)
-> Integer
-> Integer
-> T_IsCancellativeCommutativeSemiring_1462
-> T_IsNearSemiring_876
d_isNearSemiring_392 ~Integer -> Integer -> Integer
v0 ~Integer -> Integer -> Integer
v1 ~Integer
v2 ~Integer
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.Integer.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.Integer.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.Integer.Properties._.IsCancellativeCommutativeSemiring.isSemiringWithoutOne
d_isSemiringWithoutOne_400 ::
  (Integer -> Integer -> Integer) ->
  (Integer -> Integer -> Integer) ->
  Integer ->
  Integer ->
  MAlonzo.Code.Algebra.Structures.T_IsCancellativeCommutativeSemiring_1462 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutOne_952
d_isSemiringWithoutOne_400 :: (Integer -> Integer -> Integer)
-> (Integer -> Integer -> Integer)
-> Integer
-> Integer
-> T_IsCancellativeCommutativeSemiring_1462
-> T_IsSemiringWithoutOne_952
d_isSemiringWithoutOne_400 ~Integer -> Integer -> Integer
v0 ~Integer -> Integer -> Integer
v1 ~Integer
v2 ~Integer
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.Integer.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.Integer.Properties._.IsCommutativeMagma.comm
d_comm_420 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMagma_122 ->
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_comm_420 :: T_IsCommutativeMagma_122 -> Integer -> Integer -> T__'8801'__12
d_comm_420 = T_IsCommutativeMagma_122 -> Integer -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Integer.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.Integer.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.Integer.Properties._.IsCommutativeMagma.∙-cong
d_'8729''45'cong_438 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMagma_122 ->
  Integer ->
  Integer ->
  Integer ->
  Integer ->
  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
-> Integer
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong_438 = T_IsCommutativeMagma_122
-> Integer
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties._.IsCommutativeMonoid.assoc
d_assoc_446 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMonoid_406 ->
  Integer ->
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_assoc_446 :: T_IsCommutativeMonoid_406
-> Integer -> Integer -> Integer -> T__'8801'__12
d_assoc_446 = T_IsCommutativeMonoid_406
-> Integer -> Integer -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties._.IsCommutativeMonoid.comm
d_comm_448 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMonoid_406 ->
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_comm_448 :: T_IsCommutativeMonoid_406 -> Integer -> Integer -> T__'8801'__12
d_comm_448 = T_IsCommutativeMonoid_406 -> Integer -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Integer.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.Integer.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.Integer.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.Integer.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.Integer.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.Integer.Properties._.IsCommutativeMonoid.∙-cong
d_'8729''45'cong_480 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMonoid_406 ->
  Integer ->
  Integer ->
  Integer ->
  Integer ->
  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
-> Integer
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong_480 = T_IsCommutativeMonoid_406
-> Integer
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties._.IsCommutativeRing.assoc
d_assoc_490 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeRing_1720 ->
  Integer ->
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_assoc_490 :: T_IsCommutativeRing_1720
-> Integer -> Integer -> Integer -> T__'8801'__12
d_assoc_490 = T_IsCommutativeRing_1720
-> Integer -> Integer -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties._.IsCommutativeRing.*-comm
d_'42''45'comm_492 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeRing_1720 ->
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'42''45'comm_492 :: T_IsCommutativeRing_1720 -> Integer -> Integer -> T__'8801'__12
d_'42''45'comm_492 = T_IsCommutativeRing_1720 -> Integer -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties._.IsCommutativeRing.∙-cong
d_'8729''45'cong_494 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeRing_1720 ->
  Integer ->
  Integer ->
  Integer ->
  Integer ->
  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
-> Integer
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong_494 = T_IsCommutativeRing_1720
-> Integer
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Integer.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.Integer.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.Integer.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.Integer.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.Integer.Properties._.IsCommutativeRing.assoc
d_assoc_518 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeRing_1720 ->
  Integer ->
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_assoc_518 :: T_IsCommutativeRing_1720
-> Integer -> Integer -> Integer -> T__'8801'__12
d_assoc_518 = T_IsCommutativeRing_1720
-> Integer -> Integer -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties._.IsCommutativeRing.comm
d_comm_520 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeRing_1720 ->
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_comm_520 :: T_IsCommutativeRing_1720 -> Integer -> Integer -> T__'8801'__12
d_comm_520 = T_IsCommutativeRing_1720 -> Integer -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties._.IsCommutativeRing.∙-cong
d_'8729''45'cong_522 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeRing_1720 ->
  Integer ->
  Integer ->
  Integer ->
  Integer ->
  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
-> Integer
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong_522 = T_IsCommutativeRing_1720
-> Integer
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Integer.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.Integer.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.Integer.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.Integer.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.Integer.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.Integer.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.Integer.Properties._.IsCommutativeRing.⁻¹-cong
d_'8315''185''45'cong_550 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeRing_1720 ->
  Integer ->
  Integer ->
  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
-> Integer -> Integer -> T__'8801'__12 -> T__'8801'__12
d_'8315''185''45'cong_550 = T_IsCommutativeRing_1720
-> Integer -> Integer -> T__'8801'__12 -> T__'8801'__12
forall a. a
erased
-- Data.Integer.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.Integer.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.Integer.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.Integer.Properties._.IsCommutativeRing.isNearSemiring
d_isNearSemiring_570 ::
  (Integer -> Integer -> Integer) ->
  (Integer -> Integer -> Integer) ->
  (Integer -> Integer) ->
  Integer ->
  Integer ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeRing_1720 ->
  MAlonzo.Code.Algebra.Structures.T_IsNearSemiring_876
d_isNearSemiring_570 :: (Integer -> Integer -> Integer)
-> (Integer -> Integer -> Integer)
-> (Integer -> Integer)
-> Integer
-> Integer
-> T_IsCommutativeRing_1720
-> T_IsNearSemiring_876
d_isNearSemiring_570 ~Integer -> Integer -> Integer
v0 ~Integer -> Integer -> Integer
v1 ~Integer -> Integer
v2 ~Integer
v3 ~Integer
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.Integer.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.Integer.Properties._.IsCommutativeRing.isSemiring
d_isSemiring_576 ::
  (Integer -> Integer -> Integer) ->
  (Integer -> Integer -> Integer) ->
  (Integer -> Integer) ->
  Integer ->
  Integer ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeRing_1720 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemiring_1238
d_isSemiring_576 :: (Integer -> Integer -> Integer)
-> (Integer -> Integer -> Integer)
-> (Integer -> Integer)
-> Integer
-> Integer
-> T_IsCommutativeRing_1720
-> T_IsSemiring_1238
d_isSemiring_576 ~Integer -> Integer -> Integer
v0 ~Integer -> Integer -> Integer
v1 ~Integer -> Integer
v2 ~Integer
v3 ~Integer
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.Integer.Properties._.IsCommutativeRing.isSemiringWithoutOne
d_isSemiringWithoutOne_580 ::
  (Integer -> Integer -> Integer) ->
  (Integer -> Integer -> Integer) ->
  (Integer -> Integer) ->
  Integer ->
  Integer ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeRing_1720 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutOne_952
d_isSemiringWithoutOne_580 :: (Integer -> Integer -> Integer)
-> (Integer -> Integer -> Integer)
-> (Integer -> Integer)
-> Integer
-> Integer
-> T_IsCommutativeRing_1720
-> T_IsSemiringWithoutOne_952
d_isSemiringWithoutOne_580 ~Integer -> Integer -> Integer
v0 ~Integer -> Integer -> Integer
v1 ~Integer -> Integer
v2 ~Integer
v3 ~Integer
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.Integer.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.Integer.Properties._.IsCommutativeSemigroup.assoc
d_assoc_604 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_270 ->
  Integer ->
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_assoc_604 :: T_IsCommutativeSemigroup_270
-> Integer -> Integer -> Integer -> T__'8801'__12
d_assoc_604 = T_IsCommutativeSemigroup_270
-> Integer -> Integer -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties._.IsCommutativeSemigroup.comm
d_comm_606 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_270 ->
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_comm_606 :: T_IsCommutativeSemigroup_270 -> Integer -> Integer -> T__'8801'__12
d_comm_606 = T_IsCommutativeSemigroup_270 -> Integer -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Integer.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.Integer.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.Integer.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.Integer.Properties._.IsCommutativeSemigroup.∙-cong
d_'8729''45'cong_628 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_270 ->
  Integer ->
  Integer ->
  Integer ->
  Integer ->
  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
-> Integer
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong_628 = T_IsCommutativeSemigroup_270
-> Integer
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties._.IsCommutativeSemiring.assoc
d_assoc_636 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiring_1344 ->
  Integer ->
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_assoc_636 :: T_IsCommutativeSemiring_1344
-> Integer -> Integer -> Integer -> T__'8801'__12
d_assoc_636 = T_IsCommutativeSemiring_1344
-> Integer -> Integer -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties._.IsCommutativeSemiring.*-comm
d_'42''45'comm_638 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiring_1344 ->
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'42''45'comm_638 :: T_IsCommutativeSemiring_1344 -> Integer -> Integer -> T__'8801'__12
d_'42''45'comm_638 = T_IsCommutativeSemiring_1344 -> Integer -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties._.IsCommutativeSemiring.∙-cong
d_'8729''45'cong_640 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiring_1344 ->
  Integer ->
  Integer ->
  Integer ->
  Integer ->
  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
-> Integer
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong_640 = T_IsCommutativeSemiring_1344
-> Integer
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Integer.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.Integer.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.Integer.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.Integer.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.Integer.Properties._.IsCommutativeSemiring.assoc
d_assoc_664 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiring_1344 ->
  Integer ->
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_assoc_664 :: T_IsCommutativeSemiring_1344
-> Integer -> Integer -> Integer -> T__'8801'__12
d_assoc_664 = T_IsCommutativeSemiring_1344
-> Integer -> Integer -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties._.IsCommutativeSemiring.comm
d_comm_666 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiring_1344 ->
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_comm_666 :: T_IsCommutativeSemiring_1344 -> Integer -> Integer -> T__'8801'__12
d_comm_666 = T_IsCommutativeSemiring_1344 -> Integer -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties._.IsCommutativeSemiring.∙-cong
d_'8729''45'cong_668 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiring_1344 ->
  Integer ->
  Integer ->
  Integer ->
  Integer ->
  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
-> Integer
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong_668 = T_IsCommutativeSemiring_1344
-> Integer
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Integer.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.Integer.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.Integer.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.Integer.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.Integer.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.Integer.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.Integer.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.Integer.Properties._.IsCommutativeSemiring.isNearSemiring
d_isNearSemiring_702 ::
  (Integer -> Integer -> Integer) ->
  (Integer -> Integer -> Integer) ->
  Integer ->
  Integer ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiring_1344 ->
  MAlonzo.Code.Algebra.Structures.T_IsNearSemiring_876
d_isNearSemiring_702 :: (Integer -> Integer -> Integer)
-> (Integer -> Integer -> Integer)
-> Integer
-> Integer
-> T_IsCommutativeSemiring_1344
-> T_IsNearSemiring_876
d_isNearSemiring_702 ~Integer -> Integer -> Integer
v0 ~Integer -> Integer -> Integer
v1 ~Integer
v2 ~Integer
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.Integer.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.Integer.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.Integer.Properties._.IsCommutativeSemiring.isSemiringWithoutOne
d_isSemiringWithoutOne_710 ::
  (Integer -> Integer -> Integer) ->
  (Integer -> Integer -> Integer) ->
  Integer ->
  Integer ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiring_1344 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutOne_952
d_isSemiringWithoutOne_710 :: (Integer -> Integer -> Integer)
-> (Integer -> Integer -> Integer)
-> Integer
-> Integer
-> T_IsCommutativeSemiring_1344
-> T_IsSemiringWithoutOne_952
d_isSemiringWithoutOne_710 ~Integer -> Integer -> Integer
v0 ~Integer -> Integer -> Integer
v1 ~Integer
v2 ~Integer
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.Integer.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.Integer.Properties._.IsCommutativeSemiringWithoutOne.assoc
d_assoc_730 ::
  (Integer -> Integer -> Integer) ->
  (Integer -> Integer -> Integer) ->
  Integer ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiringWithoutOne_1044 ->
  Integer ->
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_assoc_730 :: (Integer -> Integer -> Integer)
-> (Integer -> Integer -> Integer)
-> Integer
-> T_IsCommutativeSemiringWithoutOne_1044
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
d_assoc_730 = (Integer -> Integer -> Integer)
-> (Integer -> Integer -> Integer)
-> Integer
-> T_IsCommutativeSemiringWithoutOne_1044
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties._.IsCommutativeSemiringWithoutOne.*-comm
d_'42''45'comm_732 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiringWithoutOne_1044 ->
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'42''45'comm_732 :: T_IsCommutativeSemiringWithoutOne_1044
-> Integer -> Integer -> T__'8801'__12
d_'42''45'comm_732 = T_IsCommutativeSemiringWithoutOne_1044
-> Integer -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties._.IsCommutativeSemiringWithoutOne.∙-cong
d_'8729''45'cong_734 ::
  (Integer -> Integer -> Integer) ->
  (Integer -> Integer -> Integer) ->
  Integer ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiringWithoutOne_1044 ->
  Integer ->
  Integer ->
  Integer ->
  Integer ->
  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 :: (Integer -> Integer -> Integer)
-> (Integer -> Integer -> Integer)
-> Integer
-> T_IsCommutativeSemiringWithoutOne_1044
-> Integer
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong_734 = (Integer -> Integer -> Integer)
-> (Integer -> Integer -> Integer)
-> Integer
-> T_IsCommutativeSemiringWithoutOne_1044
-> Integer
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties._.IsCommutativeSemiringWithoutOne.isMagma
d_isMagma_744 ::
  (Integer -> Integer -> Integer) ->
  (Integer -> Integer -> Integer) ->
  Integer ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiringWithoutOne_1044 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_86
d_isMagma_744 :: (Integer -> Integer -> Integer)
-> (Integer -> Integer -> Integer)
-> Integer
-> T_IsCommutativeSemiringWithoutOne_1044
-> T_IsMagma_86
d_isMagma_744 ~Integer -> Integer -> Integer
v0 ~Integer -> Integer -> Integer
v1 ~Integer
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.Integer.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.Integer.Properties._.IsCommutativeSemiringWithoutOne.assoc
d_assoc_748 ::
  (Integer -> Integer -> Integer) ->
  (Integer -> Integer -> Integer) ->
  Integer ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiringWithoutOne_1044 ->
  Integer ->
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_assoc_748 :: (Integer -> Integer -> Integer)
-> (Integer -> Integer -> Integer)
-> Integer
-> T_IsCommutativeSemiringWithoutOne_1044
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
d_assoc_748 = (Integer -> Integer -> Integer)
-> (Integer -> Integer -> Integer)
-> Integer
-> T_IsCommutativeSemiringWithoutOne_1044
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties._.IsCommutativeSemiringWithoutOne.comm
d_comm_750 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiringWithoutOne_1044 ->
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_comm_750 :: T_IsCommutativeSemiringWithoutOne_1044
-> Integer -> Integer -> T__'8801'__12
d_comm_750 = T_IsCommutativeSemiringWithoutOne_1044
-> Integer -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties._.IsCommutativeSemiringWithoutOne.∙-cong
d_'8729''45'cong_752 ::
  (Integer -> Integer -> Integer) ->
  (Integer -> Integer -> Integer) ->
  Integer ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiringWithoutOne_1044 ->
  Integer ->
  Integer ->
  Integer ->
  Integer ->
  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 :: (Integer -> Integer -> Integer)
-> (Integer -> Integer -> Integer)
-> Integer
-> T_IsCommutativeSemiringWithoutOne_1044
-> Integer
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong_752 = (Integer -> Integer -> Integer)
-> (Integer -> Integer -> Integer)
-> Integer
-> T_IsCommutativeSemiringWithoutOne_1044
-> Integer
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties._.IsCommutativeSemiringWithoutOne.identity
d_identity_758 ::
  (Integer -> Integer -> Integer) ->
  (Integer -> Integer -> Integer) ->
  Integer ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiringWithoutOne_1044 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_identity_758 :: (Integer -> Integer -> Integer)
-> (Integer -> Integer -> Integer)
-> Integer
-> T_IsCommutativeSemiringWithoutOne_1044
-> T_Σ_14
d_identity_758 ~Integer -> Integer -> Integer
v0 ~Integer -> Integer -> Integer
v1 ~Integer
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.Integer.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.Integer.Properties._.IsCommutativeSemiringWithoutOne.isMagma
d_isMagma_770 ::
  (Integer -> Integer -> Integer) ->
  (Integer -> Integer -> Integer) ->
  Integer ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiringWithoutOne_1044 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_86
d_isMagma_770 :: (Integer -> Integer -> Integer)
-> (Integer -> Integer -> Integer)
-> Integer
-> T_IsCommutativeSemiringWithoutOne_1044
-> T_IsMagma_86
d_isMagma_770 ~Integer -> Integer -> Integer
v0 ~Integer -> Integer -> Integer
v1 ~Integer
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.Integer.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.Integer.Properties._.IsCommutativeSemiringWithoutOne.isSemigroup
d_isSemigroup_774 ::
  (Integer -> Integer -> Integer) ->
  (Integer -> Integer -> Integer) ->
  Integer ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiringWithoutOne_1044 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_194
d_isSemigroup_774 :: (Integer -> Integer -> Integer)
-> (Integer -> Integer -> Integer)
-> Integer
-> T_IsCommutativeSemiringWithoutOne_1044
-> T_IsSemigroup_194
d_isSemigroup_774 ~Integer -> Integer -> Integer
v0 ~Integer -> Integer -> Integer
v1 ~Integer
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.Integer.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.Integer.Properties._.IsCommutativeSemiringWithoutOne.distribʳ
d_distrib'691'_778 ::
  (Integer -> Integer -> Integer) ->
  (Integer -> Integer -> Integer) ->
  Integer ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiringWithoutOne_1044 ->
  Integer ->
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_distrib'691'_778 :: (Integer -> Integer -> Integer)
-> (Integer -> Integer -> Integer)
-> Integer
-> T_IsCommutativeSemiringWithoutOne_1044
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
d_distrib'691'_778 = (Integer -> Integer -> Integer)
-> (Integer -> Integer -> Integer)
-> Integer
-> T_IsCommutativeSemiringWithoutOne_1044
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties._.IsCommutativeSemiringWithoutOne.isEquivalence
d_isEquivalence_780 ::
  (Integer -> Integer -> Integer) ->
  (Integer -> Integer -> Integer) ->
  Integer ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiringWithoutOne_1044 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_780 :: (Integer -> Integer -> Integer)
-> (Integer -> Integer -> Integer)
-> Integer
-> T_IsCommutativeSemiringWithoutOne_1044
-> T_IsEquivalence_26
d_isEquivalence_780 ~Integer -> Integer -> Integer
v0 ~Integer -> Integer -> Integer
v1 ~Integer
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.Integer.Properties._.IsCommutativeSemiringWithoutOne.isNearSemiring
d_isNearSemiring_782 ::
  (Integer -> Integer -> Integer) ->
  (Integer -> Integer -> Integer) ->
  Integer ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiringWithoutOne_1044 ->
  MAlonzo.Code.Algebra.Structures.T_IsNearSemiring_876
d_isNearSemiring_782 :: (Integer -> Integer -> Integer)
-> (Integer -> Integer -> Integer)
-> Integer
-> T_IsCommutativeSemiringWithoutOne_1044
-> T_IsNearSemiring_876
d_isNearSemiring_782 ~Integer -> Integer -> Integer
v0 ~Integer -> Integer -> Integer
v1 ~Integer
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.Integer.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.Integer.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.Integer.Properties._.IsGroup.assoc
d_assoc_854 ::
  MAlonzo.Code.Algebra.Structures.T_IsGroup_580 ->
  Integer ->
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_assoc_854 :: T_IsGroup_580 -> Integer -> Integer -> Integer -> T__'8801'__12
d_assoc_854 = T_IsGroup_580 -> Integer -> Integer -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Integer.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.Integer.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.Integer.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.Integer.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.Integer.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.Integer.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.Integer.Properties._.IsGroup.⁻¹-cong
d_'8315''185''45'cong_892 ::
  MAlonzo.Code.Algebra.Structures.T_IsGroup_580 ->
  Integer ->
  Integer ->
  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
-> Integer -> Integer -> T__'8801'__12 -> T__'8801'__12
d_'8315''185''45'cong_892 = T_IsGroup_580
-> Integer -> Integer -> T__'8801'__12 -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties._.IsGroup.∙-cong
d_'8729''45'cong_894 ::
  MAlonzo.Code.Algebra.Structures.T_IsGroup_580 ->
  Integer ->
  Integer ->
  Integer ->
  Integer ->
  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
-> Integer
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong_894 = T_IsGroup_580
-> Integer
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties._.IsIdempotentCommutativeMonoid.assoc
d_assoc_902 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_464 ->
  Integer ->
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_assoc_902 :: T_IsIdempotentCommutativeMonoid_464
-> Integer -> Integer -> Integer -> T__'8801'__12
d_assoc_902 = T_IsIdempotentCommutativeMonoid_464
-> Integer -> Integer -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties._.IsIdempotentCommutativeMonoid.comm
d_comm_904 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_464 ->
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_comm_904 :: T_IsIdempotentCommutativeMonoid_464
-> Integer -> Integer -> T__'8801'__12
d_comm_904 = T_IsIdempotentCommutativeMonoid_464
-> Integer -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties._.IsIdempotentCommutativeMonoid.idem
d_idem_906 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_464 ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_idem_906 :: T_IsIdempotentCommutativeMonoid_464 -> Integer -> T__'8801'__12
d_idem_906 = T_IsIdempotentCommutativeMonoid_464 -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Integer.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.Integer.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.Integer.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.Integer.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.Integer.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.Integer.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.Integer.Properties._.IsIdempotentCommutativeMonoid.∙-cong
d_'8729''45'cong_940 ::
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_464 ->
  Integer ->
  Integer ->
  Integer ->
  Integer ->
  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
-> Integer
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong_940 = T_IsIdempotentCommutativeMonoid_464
-> Integer
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Integer.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.Integer.Properties._.IsMagma.∙-cong
d_'8729''45'cong_1002 ::
  MAlonzo.Code.Algebra.Structures.T_IsMagma_86 ->
  Integer ->
  Integer ->
  Integer ->
  Integer ->
  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
-> Integer
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong_1002 = T_IsMagma_86
-> Integer
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties._.IsMonoid.assoc
d_assoc_1010 ::
  MAlonzo.Code.Algebra.Structures.T_IsMonoid_358 ->
  Integer ->
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_assoc_1010 :: T_IsMonoid_358 -> Integer -> Integer -> Integer -> T__'8801'__12
d_assoc_1010 = T_IsMonoid_358 -> Integer -> Integer -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Integer.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.Integer.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.Integer.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.Integer.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.Integer.Properties._.IsMonoid.∙-cong
d_'8729''45'cong_1036 ::
  MAlonzo.Code.Algebra.Structures.T_IsMonoid_358 ->
  Integer ->
  Integer ->
  Integer ->
  Integer ->
  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
-> Integer
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong_1036 = T_IsMonoid_358
-> Integer
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties._.IsNearSemiring.assoc
d_assoc_1044 ::
  MAlonzo.Code.Algebra.Structures.T_IsNearSemiring_876 ->
  Integer ->
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_assoc_1044 :: T_IsNearSemiring_876
-> Integer -> Integer -> Integer -> T__'8801'__12
d_assoc_1044 = T_IsNearSemiring_876
-> Integer -> Integer -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties._.IsNearSemiring.∙-cong
d_'8729''45'cong_1046 ::
  MAlonzo.Code.Algebra.Structures.T_IsNearSemiring_876 ->
  Integer ->
  Integer ->
  Integer ->
  Integer ->
  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
-> Integer
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong_1046 = T_IsNearSemiring_876
-> Integer
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Integer.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.Integer.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.Integer.Properties._.IsNearSemiring.assoc
d_assoc_1056 ::
  MAlonzo.Code.Algebra.Structures.T_IsNearSemiring_876 ->
  Integer ->
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_assoc_1056 :: T_IsNearSemiring_876
-> Integer -> Integer -> Integer -> T__'8801'__12
d_assoc_1056 = T_IsNearSemiring_876
-> Integer -> Integer -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties._.IsNearSemiring.∙-cong
d_'8729''45'cong_1058 ::
  MAlonzo.Code.Algebra.Structures.T_IsNearSemiring_876 ->
  Integer ->
  Integer ->
  Integer ->
  Integer ->
  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
-> Integer
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong_1058 = T_IsNearSemiring_876
-> Integer
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Integer.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.Integer.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.Integer.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.Integer.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.Integer.Properties._.IsNearSemiring.distribʳ
d_distrib'691'_1076 ::
  MAlonzo.Code.Algebra.Structures.T_IsNearSemiring_876 ->
  Integer ->
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_distrib'691'_1076 :: T_IsNearSemiring_876
-> Integer -> Integer -> Integer -> T__'8801'__12
d_distrib'691'_1076 = T_IsNearSemiring_876
-> Integer -> Integer -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Integer.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.Integer.Properties._.IsNearSemiring.zeroˡ
d_zero'737'_1092 ::
  MAlonzo.Code.Algebra.Structures.T_IsNearSemiring_876 ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_zero'737'_1092 :: T_IsNearSemiring_876 -> Integer -> T__'8801'__12
d_zero'737'_1092 = T_IsNearSemiring_876 -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties._.IsRing.assoc
d_assoc_1098 ::
  MAlonzo.Code.Algebra.Structures.T_IsRing_1584 ->
  Integer ->
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_assoc_1098 :: T_IsRing_1584 -> Integer -> Integer -> Integer -> T__'8801'__12
d_assoc_1098 = T_IsRing_1584 -> Integer -> Integer -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties._.IsRing.∙-cong
d_'8729''45'cong_1100 ::
  MAlonzo.Code.Algebra.Structures.T_IsRing_1584 ->
  Integer ->
  Integer ->
  Integer ->
  Integer ->
  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
-> Integer
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong_1100 = T_IsRing_1584
-> Integer
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Integer.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.Integer.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.Integer.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.Integer.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.Integer.Properties._.IsRing.assoc
d_assoc_1118 ::
  MAlonzo.Code.Algebra.Structures.T_IsRing_1584 ->
  Integer ->
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_assoc_1118 :: T_IsRing_1584 -> Integer -> Integer -> Integer -> T__'8801'__12
d_assoc_1118 = T_IsRing_1584 -> Integer -> Integer -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties._.IsRing.comm
d_comm_1120 ::
  MAlonzo.Code.Algebra.Structures.T_IsRing_1584 ->
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_comm_1120 :: T_IsRing_1584 -> Integer -> Integer -> T__'8801'__12
d_comm_1120 = T_IsRing_1584 -> Integer -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties._.IsRing.∙-cong
d_'8729''45'cong_1122 ::
  MAlonzo.Code.Algebra.Structures.T_IsRing_1584 ->
  Integer ->
  Integer ->
  Integer ->
  Integer ->
  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
-> Integer
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong_1122 = T_IsRing_1584
-> Integer
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Integer.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.Integer.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.Integer.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.Integer.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.Integer.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.Integer.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.Integer.Properties._.IsRing.⁻¹-cong
d_'8315''185''45'cong_1150 ::
  MAlonzo.Code.Algebra.Structures.T_IsRing_1584 ->
  Integer ->
  Integer ->
  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
-> Integer -> Integer -> T__'8801'__12 -> T__'8801'__12
d_'8315''185''45'cong_1150 = T_IsRing_1584
-> Integer -> Integer -> T__'8801'__12 -> T__'8801'__12
forall a. a
erased
-- Data.Integer.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.Integer.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.Integer.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.Integer.Properties._.IsRing.isNearSemiring
d_isNearSemiring_1166 ::
  (Integer -> Integer -> Integer) ->
  (Integer -> Integer -> Integer) ->
  (Integer -> Integer) ->
  Integer ->
  Integer ->
  MAlonzo.Code.Algebra.Structures.T_IsRing_1584 ->
  MAlonzo.Code.Algebra.Structures.T_IsNearSemiring_876
d_isNearSemiring_1166 :: (Integer -> Integer -> Integer)
-> (Integer -> Integer -> Integer)
-> (Integer -> Integer)
-> Integer
-> Integer
-> T_IsRing_1584
-> T_IsNearSemiring_876
d_isNearSemiring_1166 ~Integer -> Integer -> Integer
v0 ~Integer -> Integer -> Integer
v1 ~Integer -> Integer
v2 ~Integer
v3 ~Integer
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.Integer.Properties._.IsRing.isSemiring
d_isSemiring_1170 ::
  (Integer -> Integer -> Integer) ->
  (Integer -> Integer -> Integer) ->
  (Integer -> Integer) ->
  Integer ->
  Integer ->
  MAlonzo.Code.Algebra.Structures.T_IsRing_1584 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemiring_1238
d_isSemiring_1170 :: (Integer -> Integer -> Integer)
-> (Integer -> Integer -> Integer)
-> (Integer -> Integer)
-> Integer
-> Integer
-> T_IsRing_1584
-> T_IsSemiring_1238
d_isSemiring_1170 Integer -> Integer -> Integer
v0 Integer -> Integer -> Integer
v1 Integer -> Integer
v2 Integer
v3 Integer
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.Integer.Properties._.IsRing.isSemiringWithoutOne
d_isSemiringWithoutOne_1174 ::
  (Integer -> Integer -> Integer) ->
  (Integer -> Integer -> Integer) ->
  (Integer -> Integer) ->
  Integer ->
  Integer ->
  MAlonzo.Code.Algebra.Structures.T_IsRing_1584 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutOne_952
d_isSemiringWithoutOne_1174 :: (Integer -> Integer -> Integer)
-> (Integer -> Integer -> Integer)
-> (Integer -> Integer)
-> Integer
-> Integer
-> T_IsRing_1584
-> T_IsSemiringWithoutOne_952
d_isSemiringWithoutOne_1174 ~Integer -> Integer -> Integer
v0 ~Integer -> Integer -> Integer
v1 ~Integer -> Integer
v2 ~Integer
v3 ~Integer
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.Integer.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.Integer.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.Integer.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.Integer.Properties._.IsSelectiveMagma.sel
d_sel_1208 ::
  MAlonzo.Code.Algebra.Structures.T_IsSelectiveMagma_158 ->
  Integer -> Integer -> MAlonzo.Code.Data.Sum.Base.T__'8846'__30
d_sel_1208 :: T_IsSelectiveMagma_158 -> Integer -> Integer -> T__'8846'__30
d_sel_1208 T_IsSelectiveMagma_158
v0
  = (T_IsSelectiveMagma_158 -> Any -> Any -> T__'8846'__30)
-> Any -> Integer -> Integer -> 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.Integer.Properties._.IsSelectiveMagma.∙-cong
d_'8729''45'cong_1216 ::
  MAlonzo.Code.Algebra.Structures.T_IsSelectiveMagma_158 ->
  Integer ->
  Integer ->
  Integer ->
  Integer ->
  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
-> Integer
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong_1216 = T_IsSelectiveMagma_158
-> Integer
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties._.IsSemigroup.assoc
d_assoc_1224 ::
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_194 ->
  Integer ->
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_assoc_1224 :: T_IsSemigroup_194 -> Integer -> Integer -> Integer -> T__'8801'__12
d_assoc_1224 = T_IsSemigroup_194 -> Integer -> Integer -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Integer.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.Integer.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.Integer.Properties._.IsSemigroup.∙-cong
d_'8729''45'cong_1242 ::
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_194 ->
  Integer ->
  Integer ->
  Integer ->
  Integer ->
  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
-> Integer
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong_1242 = T_IsSemigroup_194
-> Integer
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties._.IsSemilattice.assoc
d_assoc_1250 ::
  MAlonzo.Code.Algebra.Structures.T_IsSemilattice_312 ->
  Integer ->
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_assoc_1250 :: T_IsSemilattice_312
-> Integer -> Integer -> Integer -> T__'8801'__12
d_assoc_1250 = T_IsSemilattice_312
-> Integer -> Integer -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties._.IsSemilattice.comm
d_comm_1252 ::
  MAlonzo.Code.Algebra.Structures.T_IsSemilattice_312 ->
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_comm_1252 :: T_IsSemilattice_312 -> Integer -> Integer -> T__'8801'__12
d_comm_1252 = T_IsSemilattice_312 -> Integer -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties._.IsSemilattice.idem
d_idem_1254 ::
  MAlonzo.Code.Algebra.Structures.T_IsSemilattice_312 ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_idem_1254 :: T_IsSemilattice_312 -> Integer -> T__'8801'__12
d_idem_1254 = T_IsSemilattice_312 -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Integer.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.Integer.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.Integer.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.Integer.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.Integer.Properties._.IsSemilattice.∙-cong
d_'8729''45'cong_1276 ::
  MAlonzo.Code.Algebra.Structures.T_IsSemilattice_312 ->
  Integer ->
  Integer ->
  Integer ->
  Integer ->
  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
-> Integer
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong_1276 = T_IsSemilattice_312
-> Integer
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties._.IsSemiring.assoc
d_assoc_1284 ::
  MAlonzo.Code.Algebra.Structures.T_IsSemiring_1238 ->
  Integer ->
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_assoc_1284 :: T_IsSemiring_1238 -> Integer -> Integer -> Integer -> T__'8801'__12
d_assoc_1284 = T_IsSemiring_1238 -> Integer -> Integer -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties._.IsSemiring.∙-cong
d_'8729''45'cong_1286 ::
  MAlonzo.Code.Algebra.Structures.T_IsSemiring_1238 ->
  Integer ->
  Integer ->
  Integer ->
  Integer ->
  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
-> Integer
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong_1286 = T_IsSemiring_1238
-> Integer
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Integer.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.Integer.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.Integer.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.Integer.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.Integer.Properties._.IsSemiring.assoc
d_assoc_1304 ::
  MAlonzo.Code.Algebra.Structures.T_IsSemiring_1238 ->
  Integer ->
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_assoc_1304 :: T_IsSemiring_1238 -> Integer -> Integer -> Integer -> T__'8801'__12
d_assoc_1304 = T_IsSemiring_1238 -> Integer -> Integer -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties._.IsSemiring.comm
d_comm_1306 ::
  MAlonzo.Code.Algebra.Structures.T_IsSemiring_1238 ->
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_comm_1306 :: T_IsSemiring_1238 -> Integer -> Integer -> T__'8801'__12
d_comm_1306 = T_IsSemiring_1238 -> Integer -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties._.IsSemiring.∙-cong
d_'8729''45'cong_1308 ::
  MAlonzo.Code.Algebra.Structures.T_IsSemiring_1238 ->
  Integer ->
  Integer ->
  Integer ->
  Integer ->
  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
-> Integer
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong_1308 = T_IsSemiring_1238
-> Integer
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Integer.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.Integer.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.Integer.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.Integer.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.Integer.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.Integer.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.Integer.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.Integer.Properties._.IsSemiring.isNearSemiring
d_isNearSemiring_1340 ::
  (Integer -> Integer -> Integer) ->
  (Integer -> Integer -> Integer) ->
  Integer ->
  Integer ->
  MAlonzo.Code.Algebra.Structures.T_IsSemiring_1238 ->
  MAlonzo.Code.Algebra.Structures.T_IsNearSemiring_876
d_isNearSemiring_1340 :: (Integer -> Integer -> Integer)
-> (Integer -> Integer -> Integer)
-> Integer
-> Integer
-> T_IsSemiring_1238
-> T_IsNearSemiring_876
d_isNearSemiring_1340 ~Integer -> Integer -> Integer
v0 ~Integer -> Integer -> Integer
v1 ~Integer
v2 ~Integer
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.Integer.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.Integer.Properties._.IsSemiring.isSemiringWithoutOne
d_isSemiringWithoutOne_1346 ::
  (Integer -> Integer -> Integer) ->
  (Integer -> Integer -> Integer) ->
  Integer ->
  Integer ->
  MAlonzo.Code.Algebra.Structures.T_IsSemiring_1238 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutOne_952
d_isSemiringWithoutOne_1346 :: (Integer -> Integer -> Integer)
-> (Integer -> Integer -> Integer)
-> Integer
-> Integer
-> T_IsSemiring_1238
-> T_IsSemiringWithoutOne_952
d_isSemiringWithoutOne_1346 Integer -> Integer -> Integer
v0 Integer -> Integer -> Integer
v1 Integer
v2 Integer
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.Integer.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.Integer.Properties._.IsSemiringWithoutAnnihilatingZero.assoc
d_assoc_1366 ::
  MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutAnnihilatingZero_1142 ->
  Integer ->
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_assoc_1366 :: T_IsSemiringWithoutAnnihilatingZero_1142
-> Integer -> Integer -> Integer -> T__'8801'__12
d_assoc_1366 = T_IsSemiringWithoutAnnihilatingZero_1142
-> Integer -> Integer -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties._.IsSemiringWithoutAnnihilatingZero.∙-cong
d_'8729''45'cong_1368 ::
  MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutAnnihilatingZero_1142 ->
  Integer ->
  Integer ->
  Integer ->
  Integer ->
  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
-> Integer
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong_1368 = T_IsSemiringWithoutAnnihilatingZero_1142
-> Integer
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Integer.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.Integer.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.Integer.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.Integer.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.Integer.Properties._.IsSemiringWithoutAnnihilatingZero.assoc
d_assoc_1386 ::
  MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutAnnihilatingZero_1142 ->
  Integer ->
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_assoc_1386 :: T_IsSemiringWithoutAnnihilatingZero_1142
-> Integer -> Integer -> Integer -> T__'8801'__12
d_assoc_1386 = T_IsSemiringWithoutAnnihilatingZero_1142
-> Integer -> Integer -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties._.IsSemiringWithoutAnnihilatingZero.comm
d_comm_1388 ::
  MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutAnnihilatingZero_1142 ->
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_comm_1388 :: T_IsSemiringWithoutAnnihilatingZero_1142
-> Integer -> Integer -> T__'8801'__12
d_comm_1388 = T_IsSemiringWithoutAnnihilatingZero_1142
-> Integer -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties._.IsSemiringWithoutAnnihilatingZero.∙-cong
d_'8729''45'cong_1390 ::
  MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutAnnihilatingZero_1142 ->
  Integer ->
  Integer ->
  Integer ->
  Integer ->
  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
-> Integer
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong_1390 = T_IsSemiringWithoutAnnihilatingZero_1142
-> Integer
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Integer.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.Integer.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.Integer.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.Integer.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.Integer.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.Integer.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.Integer.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.Integer.Properties._.IsSemiringWithoutOne.assoc
d_assoc_1436 ::
  (Integer -> Integer -> Integer) ->
  (Integer -> Integer -> Integer) ->
  Integer ->
  MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutOne_952 ->
  Integer ->
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_assoc_1436 :: (Integer -> Integer -> Integer)
-> (Integer -> Integer -> Integer)
-> Integer
-> T_IsSemiringWithoutOne_952
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
d_assoc_1436 = (Integer -> Integer -> Integer)
-> (Integer -> Integer -> Integer)
-> Integer
-> T_IsSemiringWithoutOne_952
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties._.IsSemiringWithoutOne.∙-cong
d_'8729''45'cong_1438 ::
  (Integer -> Integer -> Integer) ->
  (Integer -> Integer -> Integer) ->
  Integer ->
  MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutOne_952 ->
  Integer ->
  Integer ->
  Integer ->
  Integer ->
  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 :: (Integer -> Integer -> Integer)
-> (Integer -> Integer -> Integer)
-> Integer
-> T_IsSemiringWithoutOne_952
-> Integer
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong_1438 = (Integer -> Integer -> Integer)
-> (Integer -> Integer -> Integer)
-> Integer
-> T_IsSemiringWithoutOne_952
-> Integer
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties._.IsSemiringWithoutOne.isMagma
d_isMagma_1444 ::
  (Integer -> Integer -> Integer) ->
  (Integer -> Integer -> Integer) ->
  Integer ->
  MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutOne_952 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_86
d_isMagma_1444 :: (Integer -> Integer -> Integer)
-> (Integer -> Integer -> Integer)
-> Integer
-> T_IsSemiringWithoutOne_952
-> T_IsMagma_86
d_isMagma_1444 ~Integer -> Integer -> Integer
v0 ~Integer -> Integer -> Integer
v1 ~Integer
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.Integer.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.Integer.Properties._.IsSemiringWithoutOne.assoc
d_assoc_1448 ::
  (Integer -> Integer -> Integer) ->
  (Integer -> Integer -> Integer) ->
  Integer ->
  MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutOne_952 ->
  Integer ->
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_assoc_1448 :: (Integer -> Integer -> Integer)
-> (Integer -> Integer -> Integer)
-> Integer
-> T_IsSemiringWithoutOne_952
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
d_assoc_1448 = (Integer -> Integer -> Integer)
-> (Integer -> Integer -> Integer)
-> Integer
-> T_IsSemiringWithoutOne_952
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties._.IsSemiringWithoutOne.comm
d_comm_1450 ::
  MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutOne_952 ->
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_comm_1450 :: T_IsSemiringWithoutOne_952 -> Integer -> Integer -> T__'8801'__12
d_comm_1450 = T_IsSemiringWithoutOne_952 -> Integer -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties._.IsSemiringWithoutOne.∙-cong
d_'8729''45'cong_1452 ::
  (Integer -> Integer -> Integer) ->
  (Integer -> Integer -> Integer) ->
  Integer ->
  MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutOne_952 ->
  Integer ->
  Integer ->
  Integer ->
  Integer ->
  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 :: (Integer -> Integer -> Integer)
-> (Integer -> Integer -> Integer)
-> Integer
-> T_IsSemiringWithoutOne_952
-> Integer
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong_1452 = (Integer -> Integer -> Integer)
-> (Integer -> Integer -> Integer)
-> Integer
-> T_IsSemiringWithoutOne_952
-> Integer
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties._.IsSemiringWithoutOne.identity
d_identity_1458 ::
  (Integer -> Integer -> Integer) ->
  (Integer -> Integer -> Integer) ->
  Integer ->
  MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutOne_952 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_identity_1458 :: (Integer -> Integer -> Integer)
-> (Integer -> Integer -> Integer)
-> Integer
-> T_IsSemiringWithoutOne_952
-> T_Σ_14
d_identity_1458 ~Integer -> Integer -> Integer
v0 ~Integer -> Integer -> Integer
v1 ~Integer
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.Integer.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.Integer.Properties._.IsSemiringWithoutOne.isMagma
d_isMagma_1470 ::
  (Integer -> Integer -> Integer) ->
  (Integer -> Integer -> Integer) ->
  Integer ->
  MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutOne_952 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_86
d_isMagma_1470 :: (Integer -> Integer -> Integer)
-> (Integer -> Integer -> Integer)
-> Integer
-> T_IsSemiringWithoutOne_952
-> T_IsMagma_86
d_isMagma_1470 ~Integer -> Integer -> Integer
v0 ~Integer -> Integer -> Integer
v1 ~Integer
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.Integer.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.Integer.Properties._.IsSemiringWithoutOne.isSemigroup
d_isSemigroup_1474 ::
  (Integer -> Integer -> Integer) ->
  (Integer -> Integer -> Integer) ->
  Integer ->
  MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutOne_952 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_194
d_isSemigroup_1474 :: (Integer -> Integer -> Integer)
-> (Integer -> Integer -> Integer)
-> Integer
-> T_IsSemiringWithoutOne_952
-> T_IsSemigroup_194
d_isSemigroup_1474 ~Integer -> Integer -> Integer
v0 ~Integer -> Integer -> Integer
v1 ~Integer
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.Integer.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.Integer.Properties._.IsSemiringWithoutOne.distribʳ
d_distrib'691'_1478 ::
  (Integer -> Integer -> Integer) ->
  (Integer -> Integer -> Integer) ->
  Integer ->
  MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutOne_952 ->
  Integer ->
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_distrib'691'_1478 :: (Integer -> Integer -> Integer)
-> (Integer -> Integer -> Integer)
-> Integer
-> T_IsSemiringWithoutOne_952
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
d_distrib'691'_1478 = (Integer -> Integer -> Integer)
-> (Integer -> Integer -> Integer)
-> Integer
-> T_IsSemiringWithoutOne_952
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties._.IsSemiringWithoutOne.isEquivalence
d_isEquivalence_1480 ::
  (Integer -> Integer -> Integer) ->
  (Integer -> Integer -> Integer) ->
  Integer ->
  MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutOne_952 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_1480 :: (Integer -> Integer -> Integer)
-> (Integer -> Integer -> Integer)
-> Integer
-> T_IsSemiringWithoutOne_952
-> T_IsEquivalence_26
d_isEquivalence_1480 ~Integer -> Integer -> Integer
v0 ~Integer -> Integer -> Integer
v1 ~Integer
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.Integer.Properties._.IsSemiringWithoutOne.isNearSemiring
d_isNearSemiring_1482 ::
  (Integer -> Integer -> Integer) ->
  (Integer -> Integer -> Integer) ->
  Integer ->
  MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutOne_952 ->
  MAlonzo.Code.Algebra.Structures.T_IsNearSemiring_876
d_isNearSemiring_1482 :: (Integer -> Integer -> Integer)
-> (Integer -> Integer -> Integer)
-> Integer
-> T_IsSemiringWithoutOne_952
-> T_IsNearSemiring_876
d_isNearSemiring_1482 Integer -> Integer -> Integer
v0 Integer -> Integer -> Integer
v1 Integer
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.Integer.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.Integer.Properties.ℤtoℕ.Homomorphic₀
d_Homomorphic'8320'_1504 ::
  (Integer -> Integer) -> Integer -> Integer -> ()
d_Homomorphic'8320'_1504 :: (Integer -> Integer) -> Integer -> Integer -> ()
d_Homomorphic'8320'_1504 = (Integer -> Integer) -> Integer -> Integer -> ()
forall a. a
erased
-- Data.Integer.Properties.ℤtoℕ.Homomorphic₁
d_Homomorphic'8321'_1506 ::
  (Integer -> Integer) ->
  (Integer -> Integer) -> (Integer -> Integer) -> ()
d_Homomorphic'8321'_1506 :: (Integer -> Integer)
-> (Integer -> Integer) -> (Integer -> Integer) -> ()
d_Homomorphic'8321'_1506 = (Integer -> Integer)
-> (Integer -> Integer) -> (Integer -> Integer) -> ()
forall a. a
erased
-- Data.Integer.Properties.ℤtoℕ.Homomorphic₂
d_Homomorphic'8322'_1508 ::
  (Integer -> Integer) ->
  (Integer -> Integer -> Integer) ->
  (Integer -> Integer -> Integer) -> ()
d_Homomorphic'8322'_1508 :: (Integer -> Integer)
-> (Integer -> Integer -> Integer)
-> (Integer -> Integer -> Integer)
-> ()
d_Homomorphic'8322'_1508 = (Integer -> Integer)
-> (Integer -> Integer -> Integer)
-> (Integer -> Integer -> Integer)
-> ()
forall a. a
erased
-- Data.Integer.Properties.ℤtoℕ.Morphism
d_Morphism_1510 :: ()
d_Morphism_1510 :: ()
d_Morphism_1510 = ()
forall a. a
erased
-- Data.Integer.Properties.ℕtoℤ.Homomorphic₀
d_Homomorphic'8320'_1514 ::
  (Integer -> Integer) -> Integer -> Integer -> ()
d_Homomorphic'8320'_1514 :: (Integer -> Integer) -> Integer -> Integer -> ()
d_Homomorphic'8320'_1514 = (Integer -> Integer) -> Integer -> Integer -> ()
forall a. a
erased
-- Data.Integer.Properties.ℕtoℤ.Homomorphic₁
d_Homomorphic'8321'_1516 ::
  (Integer -> Integer) ->
  (Integer -> Integer) -> (Integer -> Integer) -> ()
d_Homomorphic'8321'_1516 :: (Integer -> Integer)
-> (Integer -> Integer) -> (Integer -> Integer) -> ()
d_Homomorphic'8321'_1516 = (Integer -> Integer)
-> (Integer -> Integer) -> (Integer -> Integer) -> ()
forall a. a
erased
-- Data.Integer.Properties.ℕtoℤ.Homomorphic₂
d_Homomorphic'8322'_1518 ::
  (Integer -> Integer) ->
  (Integer -> Integer -> Integer) ->
  (Integer -> Integer -> Integer) -> ()
d_Homomorphic'8322'_1518 :: (Integer -> Integer)
-> (Integer -> Integer -> Integer)
-> (Integer -> Integer -> Integer)
-> ()
d_Homomorphic'8322'_1518 = (Integer -> Integer)
-> (Integer -> Integer -> Integer)
-> (Integer -> Integer -> Integer)
-> ()
forall a. a
erased
-- Data.Integer.Properties.ℕtoℤ.Morphism
d_Morphism_1520 :: ()
d_Morphism_1520 :: ()
d_Morphism_1520 = ()
forall a. a
erased
-- Data.Integer.Properties.+-injective
d_'43''45'injective_1526 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'43''45'injective_1526 :: Integer -> Integer -> T__'8801'__12 -> T__'8801'__12
d_'43''45'injective_1526 = Integer -> Integer -> T__'8801'__12 -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.-[1+-injective
d_'45''91'1'43''45'injective_1532 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'45''91'1'43''45'injective_1532 :: Integer -> Integer -> T__'8801'__12 -> T__'8801'__12
d_'45''91'1'43''45'injective_1532 = Integer -> Integer -> T__'8801'__12 -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.+[1+-injective
d_'43''91'1'43''45'injective_1538 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'43''91'1'43''45'injective_1538 :: Integer -> Integer -> T__'8801'__12 -> T__'8801'__12
d_'43''91'1'43''45'injective_1538 = Integer -> Integer -> T__'8801'__12 -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties._≟_
d__'8799'__1540 ::
  Integer -> Integer -> MAlonzo.Code.Relation.Nullary.T_Dec_32
d__'8799'__1540 :: Integer -> Integer -> T_Dec_32
d__'8799'__1540 Integer
v0 Integer
v1
  = case Integer -> Any
forall a b. a -> b
coe Integer
v0 of
      Any
_ | (Integer -> Integer -> Bool) -> Any -> Any -> Bool
forall a b. a -> b
coe Integer -> Integer -> Bool
geqInt (Integer -> Any
forall a b. a -> b
coe Integer
v0) (Integer -> Any
forall a b. a -> b
coe (Integer
0 :: Integer)) ->
          case Integer -> Any
forall a b. a -> b
coe Integer
v1 of
            Any
_ | (Integer -> Integer -> Bool) -> Any -> Any -> Bool
forall a b. a -> b
coe Integer -> Integer -> Bool
geqInt (Integer -> Any
forall a b. a -> b
coe Integer
v1) (Integer -> Any
forall a b. a -> b
coe (Integer
0 :: Integer)) ->
                ((Any -> Any) -> T_Dec_32 -> T_Dec_32) -> Any -> Any -> T_Dec_32
forall a b. a -> b
coe
                  (Any -> Any) -> T_Dec_32 -> T_Dec_32
MAlonzo.Code.Relation.Nullary.Decidable.Core.du_map'8242'_168
                  Any
forall a. a
erased
                  ((Integer -> Integer -> T_Dec_32) -> Any -> Any -> Any
forall a b. a -> b
coe
                     Integer -> Integer -> T_Dec_32
MAlonzo.Code.Data.Nat.Properties.d__'8799'__1528 (Integer -> Any
forall a b. a -> b
coe Integer
v0) (Integer -> Any
forall a b. a -> b
coe Integer
v1))
            Any
_ -> (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)
      Any
_ -> let v2 :: Integer
v2 = Integer -> Integer -> Integer
subInt (Integer -> Integer
forall a b. a -> b
coe (-Integer
1 :: Integer)) (Integer -> Integer
forall a b. a -> b
coe Integer
v0) in
           Any -> T_Dec_32
forall a b. a -> b
coe
             (case Integer -> Any
forall a b. a -> b
coe Integer
v1 of
                Any
_ | (Integer -> Integer -> Bool) -> Any -> Any -> Bool
forall a b. a -> b
coe Integer -> Integer -> Bool
geqInt (Integer -> Any
forall a b. a -> b
coe Integer
v1) (Integer -> Any
forall a b. a -> b
coe (Integer
0 :: Integer)) ->
                    (Bool -> T_Reflects_14 -> T_Dec_32) -> Any -> Any -> Any
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)
                Any
_ -> let v3 :: Integer
v3 = Integer -> Integer -> Integer
subInt (Integer -> Integer
forall a b. a -> b
coe (-Integer
1 :: Integer)) (Integer -> Integer
forall a b. a -> b
coe Integer
v1) in
                     Any -> Any
forall a b. a -> b
coe
                       (((Any -> Any) -> T_Dec_32 -> T_Dec_32) -> Any -> Any -> Any
forall a b. a -> b
coe
                          (Any -> Any) -> T_Dec_32 -> T_Dec_32
MAlonzo.Code.Relation.Nullary.Decidable.Core.du_map'8242'_168
                          Any
forall a. a
erased
                          ((Integer -> Integer -> T_Dec_32) -> Any -> Any -> Any
forall a b. a -> b
coe
                             Integer -> Integer -> T_Dec_32
MAlonzo.Code.Data.Nat.Properties.d__'8799'__1528 (Integer -> Any
forall a b. a -> b
coe Integer
v2)
                             (Integer -> Any
forall a b. a -> b
coe Integer
v3))))
-- Data.Integer.Properties.≡-setoid
d_'8801''45'setoid_1558 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_'8801''45'setoid_1558 :: T_Setoid_44
d_'8801''45'setoid_1558
  = 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.Integer.Properties.≡-decSetoid
d_'8801''45'decSetoid_1560 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_DecSetoid_84
d_'8801''45'decSetoid_1560 :: T_DecSetoid_84
d_'8801''45'decSetoid_1560
  = ((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
      ((Integer -> Integer -> T_Dec_32) -> Any
forall a b. a -> b
coe Integer -> Integer -> T_Dec_32
d__'8799'__1540)
-- Data.Integer.Properties.drop‿+≤+
d_drop'8255''43''8804''43'_1566 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__18
d_drop'8255''43''8804''43'_1566 :: Integer -> Integer -> T__'8804'__26 -> T__'8804'__18
d_drop'8255''43''8804''43'_1566 ~Integer
v0 ~Integer
v1 T__'8804'__26
v2
  = T__'8804'__26 -> T__'8804'__18
du_drop'8255''43''8804''43'_1566 T__'8804'__26
v2
du_drop'8255''43''8804''43'_1566 ::
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__18
du_drop'8255''43''8804''43'_1566 :: T__'8804'__26 -> T__'8804'__18
du_drop'8255''43''8804''43'_1566 T__'8804'__26
v0
  = case T__'8804'__26 -> T__'8804'__26
forall a b. a -> b
coe T__'8804'__26
v0 of
      MAlonzo.Code.Data.Integer.Base.C_'43''8804''43'_48 T__'8804'__18
v3 -> T__'8804'__18 -> T__'8804'__18
forall a b. a -> b
coe T__'8804'__18
v3
      T__'8804'__26
_ -> T__'8804'__18
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Data.Integer.Properties.drop‿-≤-
d_drop'8255''45''8804''45'_1574 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__18
d_drop'8255''45''8804''45'_1574 :: Integer -> Integer -> T__'8804'__26 -> T__'8804'__18
d_drop'8255''45''8804''45'_1574 ~Integer
v0 ~Integer
v1 T__'8804'__26
v2
  = T__'8804'__26 -> T__'8804'__18
du_drop'8255''45''8804''45'_1574 T__'8804'__26
v2
du_drop'8255''45''8804''45'_1574 ::
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__18
du_drop'8255''45''8804''45'_1574 :: T__'8804'__26 -> T__'8804'__18
du_drop'8255''45''8804''45'_1574 T__'8804'__26
v0
  = case T__'8804'__26 -> T__'8804'__26
forall a b. a -> b
coe T__'8804'__26
v0 of
      MAlonzo.Code.Data.Integer.Base.C_'45''8804''45'_34 T__'8804'__18
v3 -> T__'8804'__18 -> T__'8804'__18
forall a b. a -> b
coe T__'8804'__18
v3
      T__'8804'__26
_ -> T__'8804'__18
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Data.Integer.Properties.≤-reflexive
d_'8804''45'reflexive_1578 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26
d_'8804''45'reflexive_1578 :: Integer -> Integer -> T__'8801'__12 -> T__'8804'__26
d_'8804''45'reflexive_1578 Integer
v0 ~Integer
v1 ~T__'8801'__12
v2
  = Integer -> T__'8804'__26
du_'8804''45'reflexive_1578 Integer
v0
du_'8804''45'reflexive_1578 ::
  Integer -> MAlonzo.Code.Data.Integer.Base.T__'8804'__26
du_'8804''45'reflexive_1578 :: Integer -> T__'8804'__26
du_'8804''45'reflexive_1578 Integer
v0
  = case Integer -> Any
forall a b. a -> b
coe Integer
v0 of
      Any
_ | (Integer -> Integer -> Bool) -> Any -> Any -> Bool
forall a b. a -> b
coe Integer -> Integer -> Bool
geqInt (Integer -> Any
forall a b. a -> b
coe Integer
v0) (Integer -> Any
forall a b. a -> b
coe (Integer
0 :: Integer)) ->
          (T__'8804'__18 -> T__'8804'__26) -> T__'8804'__18 -> T__'8804'__26
forall a b. a -> b
coe
            T__'8804'__18 -> T__'8804'__26
MAlonzo.Code.Data.Integer.Base.C_'43''8804''43'_48
            (Integer -> T__'8804'__18
MAlonzo.Code.Data.Nat.Properties.d_'8804''45'refl_1634 (Integer -> Integer
forall a b. a -> b
coe Integer
v0))
      Any
_ -> let v1 :: Integer
v1 = Integer -> Integer -> Integer
subInt (Integer -> Integer
forall a b. a -> b
coe (-Integer
1 :: Integer)) (Integer -> Integer
forall a b. a -> b
coe Integer
v0) in
           Any -> T__'8804'__26
forall a b. a -> b
coe
             ((T__'8804'__18 -> T__'8804'__26) -> T__'8804'__18 -> Any
forall a b. a -> b
coe
                T__'8804'__18 -> T__'8804'__26
MAlonzo.Code.Data.Integer.Base.C_'45''8804''45'_34
                (Integer -> T__'8804'__18
MAlonzo.Code.Data.Nat.Properties.d_'8804''45'refl_1634 (Integer -> Integer
forall a b. a -> b
coe Integer
v1)))
-- Data.Integer.Properties.≤-refl
d_'8804''45'refl_1584 ::
  Integer -> MAlonzo.Code.Data.Integer.Base.T__'8804'__26
d_'8804''45'refl_1584 :: Integer -> T__'8804'__26
d_'8804''45'refl_1584 Integer
v0 = (Integer -> T__'8804'__26) -> Any -> T__'8804'__26
forall a b. a -> b
coe Integer -> T__'8804'__26
du_'8804''45'reflexive_1578 (Integer -> Any
forall a b. a -> b
coe Integer
v0)
-- Data.Integer.Properties.≤-trans
d_'8804''45'trans_1586 ::
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26 ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26 ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26
d_'8804''45'trans_1586 :: Integer
-> Integer
-> Integer
-> T__'8804'__26
-> T__'8804'__26
-> T__'8804'__26
d_'8804''45'trans_1586 ~Integer
v0 ~Integer
v1 ~Integer
v2 T__'8804'__26
v3 T__'8804'__26
v4
  = T__'8804'__26 -> T__'8804'__26 -> T__'8804'__26
du_'8804''45'trans_1586 T__'8804'__26
v3 T__'8804'__26
v4
du_'8804''45'trans_1586 ::
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26 ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26 ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26
du_'8804''45'trans_1586 :: T__'8804'__26 -> T__'8804'__26 -> T__'8804'__26
du_'8804''45'trans_1586 T__'8804'__26
v0 T__'8804'__26
v1
  = case T__'8804'__26 -> T__'8804'__26
forall a b. a -> b
coe T__'8804'__26
v0 of
      MAlonzo.Code.Data.Integer.Base.C_'45''8804''45'_34 T__'8804'__18
v4
        -> case T__'8804'__26 -> T__'8804'__26
forall a b. a -> b
coe T__'8804'__26
v1 of
             MAlonzo.Code.Data.Integer.Base.C_'45''8804''45'_34 T__'8804'__18
v7
               -> (T__'8804'__18 -> T__'8804'__26) -> Any -> T__'8804'__26
forall a b. a -> b
coe
                    T__'8804'__18 -> T__'8804'__26
MAlonzo.Code.Data.Integer.Base.C_'45''8804''45'_34
                    ((T__'8804'__18 -> T__'8804'__18 -> T__'8804'__18)
-> Any -> Any -> Any
forall a b. a -> b
coe
                       T__'8804'__18 -> T__'8804'__18 -> T__'8804'__18
MAlonzo.Code.Data.Nat.Properties.du_'8804''45'trans_1642 (T__'8804'__18 -> Any
forall a b. a -> b
coe T__'8804'__18
v7)
                       (T__'8804'__18 -> Any
forall a b. a -> b
coe T__'8804'__18
v4))
             T__'8804'__26
MAlonzo.Code.Data.Integer.Base.C_'45''8804''43'_40
               -> T__'8804'__26 -> T__'8804'__26
forall a b. a -> b
coe T__'8804'__26
MAlonzo.Code.Data.Integer.Base.C_'45''8804''43'_40
             T__'8804'__26
_ -> T__'8804'__26
forall a. a
MAlonzo.RTE.mazUnreachableError
      T__'8804'__26
MAlonzo.Code.Data.Integer.Base.C_'45''8804''43'_40
        -> (Any -> Any -> Any) -> Any -> Any -> T__'8804'__26
forall a b. a -> b
coe
             Any -> Any -> Any
forall a b. a -> b -> b
seq (T__'8804'__26 -> Any
forall a b. a -> b
coe T__'8804'__26
v1)
             (T__'8804'__26 -> Any
forall a b. a -> b
coe T__'8804'__26
MAlonzo.Code.Data.Integer.Base.C_'45''8804''43'_40)
      MAlonzo.Code.Data.Integer.Base.C_'43''8804''43'_48 T__'8804'__18
v4
        -> case T__'8804'__26 -> T__'8804'__26
forall a b. a -> b
coe T__'8804'__26
v1 of
             MAlonzo.Code.Data.Integer.Base.C_'43''8804''43'_48 T__'8804'__18
v7
               -> (T__'8804'__18 -> T__'8804'__26) -> Any -> T__'8804'__26
forall a b. a -> b
coe
                    T__'8804'__18 -> T__'8804'__26
MAlonzo.Code.Data.Integer.Base.C_'43''8804''43'_48
                    ((T__'8804'__18 -> T__'8804'__18 -> T__'8804'__18)
-> Any -> Any -> Any
forall a b. a -> b
coe
                       T__'8804'__18 -> T__'8804'__18 -> T__'8804'__18
MAlonzo.Code.Data.Nat.Properties.du_'8804''45'trans_1642 (T__'8804'__18 -> Any
forall a b. a -> b
coe T__'8804'__18
v4)
                       (T__'8804'__18 -> Any
forall a b. a -> b
coe T__'8804'__18
v7))
             T__'8804'__26
_ -> T__'8804'__26
forall a. a
MAlonzo.RTE.mazUnreachableError
      T__'8804'__26
_ -> T__'8804'__26
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Data.Integer.Properties.≤-antisym
d_'8804''45'antisym_1600 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26 ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8804''45'antisym_1600 :: Integer
-> Integer -> T__'8804'__26 -> T__'8804'__26 -> T__'8801'__12
d_'8804''45'antisym_1600 = Integer
-> Integer -> T__'8804'__26 -> T__'8804'__26 -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.≤-total
d_'8804''45'total_1610 ::
  Integer -> Integer -> MAlonzo.Code.Data.Sum.Base.T__'8846'__30
d_'8804''45'total_1610 :: Integer -> Integer -> T__'8846'__30
d_'8804''45'total_1610 Integer
v0 Integer
v1
  = case Integer -> Any
forall a b. a -> b
coe Integer
v0 of
      Any
_ | (Integer -> Integer -> Bool) -> Any -> Any -> Bool
forall a b. a -> b
coe Integer -> Integer -> Bool
geqInt (Integer -> Any
forall a b. a -> b
coe Integer
v0) (Integer -> Any
forall a b. a -> b
coe (Integer
0 :: Integer)) ->
          case Integer -> Any
forall a b. a -> b
coe Integer
v1 of
            Any
_ | (Integer -> Integer -> Bool) -> Any -> Any -> Bool
forall a b. a -> b
coe Integer -> Integer -> Bool
geqInt (Integer -> Any
forall a b. a -> b
coe Integer
v1) (Integer -> Any
forall a b. a -> b
coe (Integer
0 :: Integer)) ->
                ((Any -> Any) -> (Any -> Any) -> T__'8846'__30 -> T__'8846'__30)
-> Any -> Any -> T__'8846'__30 -> T__'8846'__30
forall a b. a -> b
coe
                  (Any -> Any) -> (Any -> Any) -> T__'8846'__30 -> T__'8846'__30
MAlonzo.Code.Data.Sum.Base.du_map_84
                  ((T__'8804'__18 -> T__'8804'__26) -> Any
forall a b. a -> b
coe T__'8804'__18 -> T__'8804'__26
MAlonzo.Code.Data.Integer.Base.C_'43''8804''43'_48)
                  ((T__'8804'__18 -> T__'8804'__26) -> Any
forall a b. a -> b
coe T__'8804'__18 -> T__'8804'__26
MAlonzo.Code.Data.Integer.Base.C_'43''8804''43'_48)
                  (Integer -> Integer -> T__'8846'__30
MAlonzo.Code.Data.Nat.Properties.d_'8804''45'total_1648
                     (Integer -> Integer
forall a b. a -> b
coe Integer
v0) (Integer -> Integer
forall a b. a -> b
coe Integer
v1))
            Any
_ -> (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
                   (T__'8804'__26 -> Any
forall a b. a -> b
coe T__'8804'__26
MAlonzo.Code.Data.Integer.Base.C_'45''8804''43'_40)
      Any
_ -> let v2 :: Integer
v2 = Integer -> Integer -> Integer
subInt (Integer -> Integer
forall a b. a -> b
coe (-Integer
1 :: Integer)) (Integer -> Integer
forall a b. a -> b
coe Integer
v0) in
           Any -> T__'8846'__30
forall a b. a -> b
coe
             (case Integer -> Any
forall a b. a -> b
coe Integer
v1 of
                Any
_ | (Integer -> Integer -> Bool) -> Any -> Any -> Bool
forall a b. a -> b
coe Integer -> Integer -> Bool
geqInt (Integer -> Any
forall a b. a -> b
coe Integer
v1) (Integer -> Any
forall a b. a -> b
coe (Integer
0 :: Integer)) ->
                    (Any -> T__'8846'__30) -> Any -> Any
forall a b. a -> b
coe
                      Any -> T__'8846'__30
MAlonzo.Code.Data.Sum.Base.C_inj'8321'_38
                      (T__'8804'__26 -> Any
forall a b. a -> b
coe T__'8804'__26
MAlonzo.Code.Data.Integer.Base.C_'45''8804''43'_40)
                Any
_ -> let v3 :: Integer
v3 = Integer -> Integer -> Integer
subInt (Integer -> Integer
forall a b. a -> b
coe (-Integer
1 :: Integer)) (Integer -> Integer
forall a b. a -> b
coe Integer
v1) in
                     Any -> Any
forall a b. a -> b
coe
                       (((Any -> Any) -> (Any -> Any) -> T__'8846'__30 -> T__'8846'__30)
-> Any -> Any -> T__'8846'__30 -> Any
forall a b. a -> b
coe
                          (Any -> Any) -> (Any -> Any) -> T__'8846'__30 -> T__'8846'__30
MAlonzo.Code.Data.Sum.Base.du_map_84
                          ((T__'8804'__18 -> T__'8804'__26) -> Any
forall a b. a -> b
coe T__'8804'__18 -> T__'8804'__26
MAlonzo.Code.Data.Integer.Base.C_'45''8804''45'_34)
                          ((T__'8804'__18 -> T__'8804'__26) -> Any
forall a b. a -> b
coe T__'8804'__18 -> T__'8804'__26
MAlonzo.Code.Data.Integer.Base.C_'45''8804''45'_34)
                          (Integer -> Integer -> T__'8846'__30
MAlonzo.Code.Data.Nat.Properties.d_'8804''45'total_1648
                             (Integer -> Integer
forall a b. a -> b
coe Integer
v3) (Integer -> Integer
forall a b. a -> b
coe Integer
v2))))
-- Data.Integer.Properties._≤?_
d__'8804''63'__1628 ::
  Integer -> Integer -> MAlonzo.Code.Relation.Nullary.T_Dec_32
d__'8804''63'__1628 :: Integer -> Integer -> T_Dec_32
d__'8804''63'__1628 Integer
v0 Integer
v1
  = case Integer -> Any
forall a b. a -> b
coe Integer
v0 of
      Any
_ | (Integer -> Integer -> Bool) -> Any -> Any -> Bool
forall a b. a -> b
coe Integer -> Integer -> Bool
geqInt (Integer -> Any
forall a b. a -> b
coe Integer
v0) (Integer -> Any
forall a b. a -> b
coe (Integer
0 :: Integer)) ->
          case Integer -> Any
forall a b. a -> b
coe Integer
v1 of
            Any
_ | (Integer -> Integer -> Bool) -> Any -> Any -> Bool
forall a b. a -> b
coe Integer -> Integer -> Bool
geqInt (Integer -> Any
forall a b. a -> b
coe Integer
v1) (Integer -> Any
forall a b. a -> b
coe (Integer
0 :: Integer)) ->
                ((Any -> Any) -> T_Dec_32 -> T_Dec_32) -> Any -> Any -> T_Dec_32
forall a b. a -> b
coe
                  (Any -> Any) -> T_Dec_32 -> T_Dec_32
MAlonzo.Code.Relation.Nullary.Decidable.Core.du_map'8242'_168
                  ((T__'8804'__18 -> T__'8804'__26) -> Any
forall a b. a -> b
coe T__'8804'__18 -> T__'8804'__26
MAlonzo.Code.Data.Integer.Base.C_'43''8804''43'_48)
                  ((Integer -> Integer -> T_Dec_32) -> Any -> Any -> Any
forall a b. a -> b
coe
                     Integer -> Integer -> T_Dec_32
MAlonzo.Code.Data.Nat.Properties.d__'8804''63'__1676 (Integer -> Any
forall a b. a -> b
coe Integer
v0)
                     (Integer -> Any
forall a b. a -> b
coe Integer
v1))
            Any
_ -> (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)
      Any
_ -> let v2 :: Integer
v2 = Integer -> Integer -> Integer
subInt (Integer -> Integer
forall a b. a -> b
coe (-Integer
1 :: Integer)) (Integer -> Integer
forall a b. a -> b
coe Integer
v0) in
           Any -> T_Dec_32
forall a b. a -> b
coe
             (case Integer -> Any
forall a b. a -> b
coe Integer
v1 of
                Any
_ | (Integer -> Integer -> Bool) -> Any -> Any -> Bool
forall a b. a -> b
coe Integer -> Integer -> Bool
geqInt (Integer -> Any
forall a b. a -> b
coe Integer
v1) (Integer -> Any
forall a b. a -> b
coe (Integer
0 :: Integer)) ->
                    (Bool -> T_Reflects_14 -> T_Dec_32) -> Any -> Any -> Any
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
                         (T__'8804'__26 -> Any
forall a b. a -> b
coe T__'8804'__26
MAlonzo.Code.Data.Integer.Base.C_'45''8804''43'_40))
                Any
_ -> let v3 :: Integer
v3 = Integer -> Integer -> Integer
subInt (Integer -> Integer
forall a b. a -> b
coe (-Integer
1 :: Integer)) (Integer -> Integer
forall a b. a -> b
coe Integer
v1) in
                     Any -> Any
forall a b. a -> b
coe
                       (((Any -> Any) -> T_Dec_32 -> T_Dec_32) -> Any -> Any -> Any
forall a b. a -> b
coe
                          (Any -> Any) -> T_Dec_32 -> T_Dec_32
MAlonzo.Code.Relation.Nullary.Decidable.Core.du_map'8242'_168
                          ((T__'8804'__18 -> T__'8804'__26) -> Any
forall a b. a -> b
coe T__'8804'__18 -> T__'8804'__26
MAlonzo.Code.Data.Integer.Base.C_'45''8804''45'_34)
                          ((Integer -> Integer -> T_Dec_32) -> Any -> Any -> Any
forall a b. a -> b
coe
                             Integer -> Integer -> T_Dec_32
MAlonzo.Code.Data.Nat.Properties.d__'8804''63'__1676 (Integer -> Any
forall a b. a -> b
coe Integer
v3)
                             (Integer -> Any
forall a b. a -> b
coe Integer
v2))))
-- Data.Integer.Properties.≤-irrelevant
d_'8804''45'irrelevant_1646 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26 ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8804''45'irrelevant_1646 :: Integer
-> Integer -> T__'8804'__26 -> T__'8804'__26 -> T__'8801'__12
d_'8804''45'irrelevant_1646 = Integer
-> Integer -> T__'8804'__26 -> T__'8804'__26 -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.≤-isPreorder
d_'8804''45'isPreorder_1656 ::
  MAlonzo.Code.Relation.Binary.Structures.T_IsPreorder_70
d_'8804''45'isPreorder_1656 :: T_IsPreorder_70
d_'8804''45'isPreorder_1656
  = (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 -> (Integer -> T__'8804'__26) -> Any -> Any
forall a b. a -> b
coe Integer -> T__'8804'__26
du_'8804''45'reflexive_1578 Any
v0)
      (\ Any
v0 Any
v1 Any
v2 Any
v3 Any
v4 -> (T__'8804'__26 -> T__'8804'__26 -> T__'8804'__26)
-> Any -> Any -> Any
forall a b. a -> b
coe T__'8804'__26 -> T__'8804'__26 -> T__'8804'__26
du_'8804''45'trans_1586 Any
v3 Any
v4)
-- Data.Integer.Properties.≤-isTotalPreorder
d_'8804''45'isTotalPreorder_1658 ::
  MAlonzo.Code.Relation.Binary.Structures.T_IsTotalPreorder_118
d_'8804''45'isTotalPreorder_1658 :: T_IsTotalPreorder_118
d_'8804''45'isTotalPreorder_1658
  = (T_IsPreorder_70
 -> (Any -> Any -> T__'8846'__30) -> T_IsTotalPreorder_118)
-> Any -> Any -> T_IsTotalPreorder_118
forall a b. a -> b
coe
      T_IsPreorder_70
-> (Any -> Any -> T__'8846'__30) -> T_IsTotalPreorder_118
MAlonzo.Code.Relation.Binary.Structures.C_IsTotalPreorder'46'constructor_7939
      (T_IsPreorder_70 -> Any
forall a b. a -> b
coe T_IsPreorder_70
d_'8804''45'isPreorder_1656) ((Integer -> Integer -> T__'8846'__30) -> Any
forall a b. a -> b
coe Integer -> Integer -> T__'8846'__30
d_'8804''45'total_1610)
-- Data.Integer.Properties.≤-isPartialOrder
d_'8804''45'isPartialOrder_1660 ::
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialOrder_162
d_'8804''45'isPartialOrder_1660 :: T_IsPartialOrder_162
d_'8804''45'isPartialOrder_1660
  = (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_1656) Any
forall a. a
erased
-- Data.Integer.Properties.≤-isTotalOrder
d_'8804''45'isTotalOrder_1662 ::
  MAlonzo.Code.Relation.Binary.Structures.T_IsTotalOrder_384
d_'8804''45'isTotalOrder_1662 :: T_IsTotalOrder_384
d_'8804''45'isTotalOrder_1662
  = (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_1660) ((Integer -> Integer -> T__'8846'__30) -> Any
forall a b. a -> b
coe Integer -> Integer -> T__'8846'__30
d_'8804''45'total_1610)
-- Data.Integer.Properties.≤-isDecTotalOrder
d_'8804''45'isDecTotalOrder_1664 ::
  MAlonzo.Code.Relation.Binary.Structures.T_IsDecTotalOrder_434
d_'8804''45'isDecTotalOrder_1664 :: T_IsDecTotalOrder_434
d_'8804''45'isDecTotalOrder_1664
  = (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_1662) ((Integer -> Integer -> T_Dec_32) -> Any
forall a b. a -> b
coe Integer -> Integer -> T_Dec_32
d__'8799'__1540)
      ((Integer -> Integer -> T_Dec_32) -> Any
forall a b. a -> b
coe Integer -> Integer -> T_Dec_32
d__'8804''63'__1628)
-- Data.Integer.Properties.≤-preorder
d_'8804''45'preorder_1666 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Preorder_132
d_'8804''45'preorder_1666 :: T_Preorder_132
d_'8804''45'preorder_1666
  = (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_1656
-- Data.Integer.Properties.≤-totalPreorder
d_'8804''45'totalPreorder_1668 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_204
d_'8804''45'totalPreorder_1668 :: T_TotalPreorder_204
d_'8804''45'totalPreorder_1668
  = (T_IsTotalPreorder_118 -> T_TotalPreorder_204)
-> T_IsTotalPreorder_118 -> T_TotalPreorder_204
forall a b. a -> b
coe
      T_IsTotalPreorder_118 -> T_TotalPreorder_204
MAlonzo.Code.Relation.Binary.Bundles.C_TotalPreorder'46'constructor_3669
      T_IsTotalPreorder_118
d_'8804''45'isTotalPreorder_1658
-- Data.Integer.Properties.≤-poset
d_'8804''45'poset_1670 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Poset_282
d_'8804''45'poset_1670 :: T_Poset_282
d_'8804''45'poset_1670
  = (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_1660
-- Data.Integer.Properties.≤-totalOrder
d_'8804''45'totalOrder_1672 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_TotalOrder_652
d_'8804''45'totalOrder_1672 :: T_TotalOrder_652
d_'8804''45'totalOrder_1672
  = (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_1662
-- Data.Integer.Properties.≤-decTotalOrder
d_'8804''45'decTotalOrder_1674 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_DecTotalOrder_740
d_'8804''45'decTotalOrder_1674 :: T_DecTotalOrder_740
d_'8804''45'decTotalOrder_1674
  = (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_1664
-- Data.Integer.Properties.≤ᵇ⇒≤
d_'8804''7495''8658''8804'_1680 ::
  Integer ->
  Integer -> AgdaAny -> MAlonzo.Code.Data.Integer.Base.T__'8804'__26
d_'8804''7495''8658''8804'_1680 :: Integer -> Integer -> Any -> T__'8804'__26
d_'8804''7495''8658''8804'_1680 Integer
v0 Integer
v1 ~Any
v2
  = Integer -> Integer -> T__'8804'__26
du_'8804''7495''8658''8804'_1680 Integer
v0 Integer
v1
du_'8804''7495''8658''8804'_1680 ::
  Integer -> Integer -> MAlonzo.Code.Data.Integer.Base.T__'8804'__26
du_'8804''7495''8658''8804'_1680 :: Integer -> Integer -> T__'8804'__26
du_'8804''7495''8658''8804'_1680 Integer
v0 Integer
v1
  = case Integer -> Any
forall a b. a -> b
coe Integer
v0 of
      Any
_ | (Integer -> Integer -> Bool) -> Any -> Any -> Bool
forall a b. a -> b
coe Integer -> Integer -> Bool
geqInt (Integer -> Any
forall a b. a -> b
coe Integer
v0) (Integer -> Any
forall a b. a -> b
coe (Integer
0 :: Integer)) ->
          (T__'8804'__18 -> T__'8804'__26) -> Any -> T__'8804'__26
forall a b. a -> b
coe
            T__'8804'__18 -> T__'8804'__26
MAlonzo.Code.Data.Integer.Base.C_'43''8804''43'_48
            ((Integer -> T__'8804'__18) -> Any -> Any
forall a b. a -> b
coe
               Integer -> T__'8804'__18
MAlonzo.Code.Data.Nat.Properties.du_'8804''7495''8658''8804'_1600
               (Integer -> Any
forall a b. a -> b
coe Integer
v0))
      Any
_ -> case Integer -> Any
forall a b. a -> b
coe Integer
v1 of
             Any
_ | (Integer -> Integer -> Bool) -> Any -> Any -> Bool
forall a b. a -> b
coe Integer -> Integer -> Bool
geqInt (Integer -> Any
forall a b. a -> b
coe Integer
v1) (Integer -> Any
forall a b. a -> b
coe (Integer
0 :: Integer)) ->
                 T__'8804'__26 -> T__'8804'__26
forall a b. a -> b
coe T__'8804'__26
MAlonzo.Code.Data.Integer.Base.C_'45''8804''43'_40
             Any
_ -> let v2 :: Integer
v2 = Integer -> Integer -> Integer
subInt (Integer -> Integer
forall a b. a -> b
coe (-Integer
1 :: Integer)) (Integer -> Integer
forall a b. a -> b
coe Integer
v1) in
                  Any -> T__'8804'__26
forall a b. a -> b
coe
                    ((T__'8804'__18 -> T__'8804'__26) -> Any -> Any
forall a b. a -> b
coe
                       T__'8804'__18 -> T__'8804'__26
MAlonzo.Code.Data.Integer.Base.C_'45''8804''45'_34
                       ((Integer -> T__'8804'__18) -> Any -> Any
forall a b. a -> b
coe
                          Integer -> T__'8804'__18
MAlonzo.Code.Data.Nat.Properties.du_'8804''7495''8658''8804'_1600
                          (Integer -> Any
forall a b. a -> b
coe Integer
v2)))
-- Data.Integer.Properties.≤⇒≤ᵇ
d_'8804''8658''8804''7495'_1692 ::
  Integer ->
  Integer -> MAlonzo.Code.Data.Integer.Base.T__'8804'__26 -> AgdaAny
d_'8804''8658''8804''7495'_1692 :: Integer -> Integer -> T__'8804'__26 -> Any
d_'8804''8658''8804''7495'_1692 ~Integer
v0 ~Integer
v1 T__'8804'__26
v2
  = T__'8804'__26 -> Any
du_'8804''8658''8804''7495'_1692 T__'8804'__26
v2
du_'8804''8658''8804''7495'_1692 ::
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26 -> AgdaAny
du_'8804''8658''8804''7495'_1692 :: T__'8804'__26 -> Any
du_'8804''8658''8804''7495'_1692 T__'8804'__26
v0
  = case T__'8804'__26 -> T__'8804'__26
forall a b. a -> b
coe T__'8804'__26
v0 of
      MAlonzo.Code.Data.Integer.Base.C_'45''8804''45'_34 T__'8804'__18
v3
        -> (T__'8804'__18 -> Any) -> Any -> Any
forall a b. a -> b
coe
             T__'8804'__18 -> Any
MAlonzo.Code.Data.Nat.Properties.du_'8804''8658''8804''7495'_1616
             (T__'8804'__18 -> Any
forall a b. a -> b
coe T__'8804'__18
v3)
      T__'8804'__26
MAlonzo.Code.Data.Integer.Base.C_'45''8804''43'_40
        -> () -> Any
forall a b. a -> b
coe ()
MAlonzo.Code.Agda.Builtin.Unit.C_tt_8
      MAlonzo.Code.Data.Integer.Base.C_'43''8804''43'_48 T__'8804'__18
v3
        -> (T__'8804'__18 -> Any) -> Any -> Any
forall a b. a -> b
coe
             T__'8804'__18 -> Any
MAlonzo.Code.Data.Nat.Properties.du_'8804''8658''8804''7495'_1616
             (T__'8804'__18 -> Any
forall a b. a -> b
coe T__'8804'__18
v3)
      T__'8804'__26
_ -> Any
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Data.Integer.Properties.drop‿+<+
d_drop'8255''43''60''43'_1702 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Integer.Base.T__'60'__50 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__18
d_drop'8255''43''60''43'_1702 :: Integer -> Integer -> T__'60'__50 -> T__'8804'__18
d_drop'8255''43''60''43'_1702 ~Integer
v0 ~Integer
v1 T__'60'__50
v2
  = T__'60'__50 -> T__'8804'__18
du_drop'8255''43''60''43'_1702 T__'60'__50
v2
du_drop'8255''43''60''43'_1702 ::
  MAlonzo.Code.Data.Integer.Base.T__'60'__50 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__18
du_drop'8255''43''60''43'_1702 :: T__'60'__50 -> T__'8804'__18
du_drop'8255''43''60''43'_1702 T__'60'__50
v0
  = case T__'60'__50 -> T__'60'__50
forall a b. a -> b
coe T__'60'__50
v0 of
      MAlonzo.Code.Data.Integer.Base.C_'43''60''43'_72 T__'8804'__18
v3 -> T__'8804'__18 -> T__'8804'__18
forall a b. a -> b
coe T__'8804'__18
v3
      T__'60'__50
_ -> T__'8804'__18
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Data.Integer.Properties.drop‿-<-
d_drop'8255''45''60''45'_1710 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Integer.Base.T__'60'__50 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__18
d_drop'8255''45''60''45'_1710 :: Integer -> Integer -> T__'60'__50 -> T__'8804'__18
d_drop'8255''45''60''45'_1710 ~Integer
v0 ~Integer
v1 T__'60'__50
v2
  = T__'60'__50 -> T__'8804'__18
du_drop'8255''45''60''45'_1710 T__'60'__50
v2
du_drop'8255''45''60''45'_1710 ::
  MAlonzo.Code.Data.Integer.Base.T__'60'__50 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__18
du_drop'8255''45''60''45'_1710 :: T__'60'__50 -> T__'8804'__18
du_drop'8255''45''60''45'_1710 T__'60'__50
v0
  = case T__'60'__50 -> T__'60'__50
forall a b. a -> b
coe T__'60'__50
v0 of
      MAlonzo.Code.Data.Integer.Base.C_'45''60''45'_58 T__'8804'__18
v3 -> T__'8804'__18 -> T__'8804'__18
forall a b. a -> b
coe T__'8804'__18
v3
      T__'60'__50
_ -> T__'8804'__18
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Data.Integer.Properties.+≮0
d_'43''8814'0_1716 ::
  Integer ->
  MAlonzo.Code.Data.Integer.Base.T__'60'__50 ->
  MAlonzo.Code.Data.Empty.T_'8869'_4
d_'43''8814'0_1716 :: Integer -> T__'60'__50 -> T_'8869'_4
d_'43''8814'0_1716 = Integer -> T__'60'__50 -> T_'8869'_4
forall a. a
erased
-- Data.Integer.Properties.+≮-
d_'43''8814''45'_1722 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Integer.Base.T__'60'__50 ->
  MAlonzo.Code.Data.Empty.T_'8869'_4
d_'43''8814''45'_1722 :: Integer -> Integer -> T__'60'__50 -> T_'8869'_4
d_'43''8814''45'_1722 = Integer -> Integer -> T__'60'__50 -> T_'8869'_4
forall a. a
erased
-- Data.Integer.Properties.<⇒≤
d_'60''8658''8804'_1724 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Integer.Base.T__'60'__50 ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26
d_'60''8658''8804'_1724 :: Integer -> Integer -> T__'60'__50 -> T__'8804'__26
d_'60''8658''8804'_1724 Integer
v0 Integer
v1 T__'60'__50
v2
  = case T__'60'__50 -> T__'60'__50
forall a b. a -> b
coe T__'60'__50
v2 of
      MAlonzo.Code.Data.Integer.Base.C_'45''60''45'_58 T__'8804'__18
v5
        -> let v6 :: Integer
v6 = Integer -> Integer -> Integer
subInt (Integer -> Integer
forall a b. a -> b
coe (-Integer
1 :: Integer)) (Integer -> Integer
forall a b. a -> b
coe Integer
v0) in
           Any -> T__'8804'__26
forall a b. a -> b
coe
             ((T__'8804'__18 -> T__'8804'__26) -> Any -> Any
forall a b. a -> b
coe
                T__'8804'__18 -> T__'8804'__26
MAlonzo.Code.Data.Integer.Base.C_'45''8804''45'_34
                ((Integer -> T__'8804'__18 -> T__'8804'__18) -> Any -> Any -> Any
forall a b. a -> b
coe
                   Integer -> T__'8804'__18 -> T__'8804'__18
MAlonzo.Code.Data.Nat.Properties.du_'60''8658''8804'_1736 (Integer -> Any
forall a b. a -> b
coe Integer
v6)
                   (T__'8804'__18 -> Any
forall a b. a -> b
coe T__'8804'__18
v5)))
      T__'60'__50
MAlonzo.Code.Data.Integer.Base.C_'45''60''43'_64
        -> T__'8804'__26 -> T__'8804'__26
forall a b. a -> b
coe T__'8804'__26
MAlonzo.Code.Data.Integer.Base.C_'45''8804''43'_40
      MAlonzo.Code.Data.Integer.Base.C_'43''60''43'_72 T__'8804'__18
v5
        -> (T__'8804'__18 -> T__'8804'__26) -> Any -> T__'8804'__26
forall a b. a -> b
coe
             T__'8804'__18 -> T__'8804'__26
MAlonzo.Code.Data.Integer.Base.C_'43''8804''43'_48
             ((Integer -> T__'8804'__18 -> T__'8804'__18) -> Any -> Any -> Any
forall a b. a -> b
coe
                Integer -> T__'8804'__18 -> T__'8804'__18
MAlonzo.Code.Data.Nat.Properties.du_'60''8658''8804'_1736 (Integer -> Any
forall a b. a -> b
coe Integer
v1)
                (T__'8804'__18 -> Any
forall a b. a -> b
coe T__'8804'__18
v5))
      T__'60'__50
_ -> T__'8804'__26
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Data.Integer.Properties.<⇒≢
d_'60''8658''8802'_1730 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Integer.Base.T__'60'__50 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Data.Empty.T_'8869'_4
d_'60''8658''8802'_1730 :: Integer -> Integer -> T__'60'__50 -> T__'8801'__12 -> T_'8869'_4
d_'60''8658''8802'_1730 = Integer -> Integer -> T__'60'__50 -> T__'8801'__12 -> T_'8869'_4
forall a. a
erased
-- Data.Integer.Properties.<⇒≱
d_'60''8658''8817'_1736 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Integer.Base.T__'60'__50 ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26 ->
  MAlonzo.Code.Data.Empty.T_'8869'_4
d_'60''8658''8817'_1736 :: Integer -> Integer -> T__'60'__50 -> T__'8804'__26 -> T_'8869'_4
d_'60''8658''8817'_1736 = Integer -> Integer -> T__'60'__50 -> T__'8804'__26 -> T_'8869'_4
forall a. a
erased
-- Data.Integer.Properties.≤⇒≯
d_'8804''8658''8815'_1742 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26 ->
  MAlonzo.Code.Data.Integer.Base.T__'60'__50 ->
  MAlonzo.Code.Data.Empty.T_'8869'_4
d_'8804''8658''8815'_1742 :: Integer -> Integer -> T__'8804'__26 -> T__'60'__50 -> T_'8869'_4
d_'8804''8658''8815'_1742 = Integer -> Integer -> T__'8804'__26 -> T__'60'__50 -> T_'8869'_4
forall a. a
erased
-- Data.Integer.Properties.≰⇒>
d_'8816''8658''62'_1752 ::
  Integer ->
  Integer ->
  (MAlonzo.Code.Data.Integer.Base.T__'8804'__26 ->
   MAlonzo.Code.Data.Empty.T_'8869'_4) ->
  MAlonzo.Code.Data.Integer.Base.T__'60'__50
d_'8816''8658''62'_1752 :: Integer -> Integer -> (T__'8804'__26 -> T_'8869'_4) -> T__'60'__50
d_'8816''8658''62'_1752 Integer
v0 Integer
v1 ~T__'8804'__26 -> T_'8869'_4
v2 = Integer -> Integer -> T__'60'__50
du_'8816''8658''62'_1752 Integer
v0 Integer
v1
du_'8816''8658''62'_1752 ::
  Integer -> Integer -> MAlonzo.Code.Data.Integer.Base.T__'60'__50
du_'8816''8658''62'_1752 :: Integer -> Integer -> T__'60'__50
du_'8816''8658''62'_1752 Integer
v0 Integer
v1
  = case Integer -> Any
forall a b. a -> b
coe Integer
v0 of
      Any
_ | (Integer -> Integer -> Bool) -> Any -> Any -> Bool
forall a b. a -> b
coe Integer -> Integer -> Bool
geqInt (Integer -> Any
forall a b. a -> b
coe Integer
v0) (Integer -> Any
forall a b. a -> b
coe (Integer
0 :: Integer)) ->
          case Integer -> Any
forall a b. a -> b
coe Integer
v1 of
            Any
_ | (Integer -> Integer -> Bool) -> Any -> Any -> Bool
forall a b. a -> b
coe Integer -> Integer -> Bool
geqInt (Integer -> Any
forall a b. a -> b
coe Integer
v1) (Integer -> Any
forall a b. a -> b
coe (Integer
0 :: Integer)) ->
                (T__'8804'__18 -> T__'60'__50) -> Any -> T__'60'__50
forall a b. a -> b
coe
                  T__'8804'__18 -> T__'60'__50
MAlonzo.Code.Data.Integer.Base.C_'43''60''43'_72
                  ((Integer -> Integer -> T__'8804'__18) -> Any -> Any -> Any
forall a b. a -> b
coe
                     Integer -> Integer -> T__'8804'__18
MAlonzo.Code.Data.Nat.Properties.du_'8816''8658''62'_1770 (Integer -> Any
forall a b. a -> b
coe Integer
v0)
                     (Integer -> Any
forall a b. a -> b
coe Integer
v1))
            Any
_ -> T__'60'__50 -> T__'60'__50
forall a b. a -> b
coe T__'60'__50
MAlonzo.Code.Data.Integer.Base.C_'45''60''43'_64
      Any
_ -> let v2 :: Integer
v2 = Integer -> Integer -> Integer
subInt (Integer -> Integer
forall a b. a -> b
coe (-Integer
1 :: Integer)) (Integer -> Integer
forall a b. a -> b
coe Integer
v0) in
           Any -> T__'60'__50
forall a b. a -> b
coe
             (case Integer -> Any
forall a b. a -> b
coe Integer
v1 of
                Any
_ | (Integer -> Integer -> Bool) -> Any -> Any -> Bool
forall a b. a -> b
coe Integer -> Integer -> Bool
geqInt (Integer -> Any
forall a b. a -> b
coe Integer
v1) (Integer -> Any
forall a b. a -> b
coe (Integer
0 :: Integer)) ->
                    Any -> Any
forall a b. a -> b
coe Any
MAlonzo.Code.Relation.Nullary.Negation.Core.du_contradiction_24
                Any
_ -> let v3 :: Integer
v3 = Integer -> Integer -> Integer
subInt (Integer -> Integer
forall a b. a -> b
coe (-Integer
1 :: Integer)) (Integer -> Integer
forall a b. a -> b
coe Integer
v1) in
                     Any -> Any
forall a b. a -> b
coe
                       ((T__'8804'__18 -> T__'60'__50) -> Any -> Any
forall a b. a -> b
coe
                          T__'8804'__18 -> T__'60'__50
MAlonzo.Code.Data.Integer.Base.C_'45''60''45'_58
                          ((Integer -> Integer -> T__'8804'__18) -> Any -> Any -> Any
forall a b. a -> b
coe
                             Integer -> Integer -> T__'8804'__18
MAlonzo.Code.Data.Nat.Properties.du_'8816''8658''62'_1770 (Integer -> Any
forall a b. a -> b
coe Integer
v3)
                             (Integer -> Any
forall a b. a -> b
coe Integer
v2))))
-- Data.Integer.Properties.≮⇒≥
d_'8814''8658''8805'_1778 ::
  Integer ->
  Integer ->
  (MAlonzo.Code.Data.Integer.Base.T__'60'__50 ->
   MAlonzo.Code.Data.Empty.T_'8869'_4) ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26
d_'8814''8658''8805'_1778 :: Integer -> Integer -> (T__'60'__50 -> T_'8869'_4) -> T__'8804'__26
d_'8814''8658''8805'_1778 Integer
v0 Integer
v1 ~T__'60'__50 -> T_'8869'_4
v2
  = Integer -> Integer -> T__'8804'__26
du_'8814''8658''8805'_1778 Integer
v0 Integer
v1
du_'8814''8658''8805'_1778 ::
  Integer -> Integer -> MAlonzo.Code.Data.Integer.Base.T__'8804'__26
du_'8814''8658''8805'_1778 :: Integer -> Integer -> T__'8804'__26
du_'8814''8658''8805'_1778 Integer
v0 Integer
v1
  = case Integer -> Any
forall a b. a -> b
coe Integer
v0 of
      Any
_ | (Integer -> Integer -> Bool) -> Any -> Any -> Bool
forall a b. a -> b
coe Integer -> Integer -> Bool
geqInt (Integer -> Any
forall a b. a -> b
coe Integer
v0) (Integer -> Any
forall a b. a -> b
coe (Integer
0 :: Integer)) ->
          case Integer -> Any
forall a b. a -> b
coe Integer
v1 of
            Any
_ | (Integer -> Integer -> Bool) -> Any -> Any -> Bool
forall a b. a -> b
coe Integer -> Integer -> Bool
geqInt (Integer -> Any
forall a b. a -> b
coe Integer
v1) (Integer -> Any
forall a b. a -> b
coe (Integer
0 :: Integer)) ->
                (T__'8804'__18 -> T__'8804'__26) -> Any -> T__'8804'__26
forall a b. a -> b
coe
                  T__'8804'__18 -> T__'8804'__26
MAlonzo.Code.Data.Integer.Base.C_'43''8804''43'_48
                  ((Integer -> Integer -> T__'8804'__18) -> Any -> Any -> Any
forall a b. a -> b
coe
                     Integer -> Integer -> T__'8804'__18
MAlonzo.Code.Data.Nat.Properties.du_'8814''8658''8805'_1784
                     (Integer -> Any
forall a b. a -> b
coe Integer
v0) (Integer -> Any
forall a b. a -> b
coe Integer
v1))
            Any
_ -> T__'8804'__26 -> T__'8804'__26
forall a b. a -> b
coe T__'8804'__26
MAlonzo.Code.Data.Integer.Base.C_'45''8804''43'_40
      Any
_ -> let v2 :: Integer
v2 = Integer -> Integer -> Integer
subInt (Integer -> Integer
forall a b. a -> b
coe (-Integer
1 :: Integer)) (Integer -> Integer
forall a b. a -> b
coe Integer
v0) in
           Any -> T__'8804'__26
forall a b. a -> b
coe
             (case Integer -> Any
forall a b. a -> b
coe Integer
v1 of
                Any
_ | (Integer -> Integer -> Bool) -> Any -> Any -> Bool
forall a b. a -> b
coe Integer -> Integer -> Bool
geqInt (Integer -> Any
forall a b. a -> b
coe Integer
v1) (Integer -> Any
forall a b. a -> b
coe (Integer
0 :: Integer)) ->
                    Any -> Any
forall a b. a -> b
coe Any
MAlonzo.Code.Relation.Nullary.Negation.Core.du_contradiction_24
                Any
_ -> let v3 :: Integer
v3 = Integer -> Integer -> Integer
subInt (Integer -> Integer
forall a b. a -> b
coe (-Integer
1 :: Integer)) (Integer -> Integer
forall a b. a -> b
coe Integer
v1) in
                     Any -> Any
forall a b. a -> b
coe
                       ((T__'8804'__18 -> T__'8804'__26) -> Any -> Any
forall a b. a -> b
coe
                          T__'8804'__18 -> T__'8804'__26
MAlonzo.Code.Data.Integer.Base.C_'45''8804''45'_34
                          ((Integer -> Integer -> T__'8804'__18) -> Any -> Any -> Any
forall a b. a -> b
coe
                             Integer -> Integer -> T__'8804'__18
MAlonzo.Code.Data.Nat.Properties.du_'8814''8658''8805'_1784
                             (Integer -> Any
forall a b. a -> b
coe Integer
v3) (Integer -> Any
forall a b. a -> b
coe Integer
v2))))
-- Data.Integer.Properties.>⇒≰
d_'62''8658''8816'_1804 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Integer.Base.T__'60'__50 ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26 ->
  MAlonzo.Code.Data.Empty.T_'8869'_4
d_'62''8658''8816'_1804 :: Integer -> Integer -> T__'60'__50 -> T__'8804'__26 -> T_'8869'_4
d_'62''8658''8816'_1804 = Integer -> Integer -> T__'60'__50 -> T__'8804'__26 -> T_'8869'_4
forall a. a
erased
-- Data.Integer.Properties.≤∧≢⇒<
d_'8804''8743''8802''8658''60'_1810 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26 ->
  (MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
   MAlonzo.Code.Data.Empty.T_'8869'_4) ->
  MAlonzo.Code.Data.Integer.Base.T__'60'__50
d_'8804''8743''8802''8658''60'_1810 :: Integer
-> Integer
-> T__'8804'__26
-> (T__'8801'__12 -> T_'8869'_4)
-> T__'60'__50
d_'8804''8743''8802''8658''60'_1810 Integer
v0 Integer
v1 T__'8804'__26
v2 ~T__'8801'__12 -> T_'8869'_4
v3
  = Integer -> Integer -> T__'8804'__26 -> T__'60'__50
du_'8804''8743''8802''8658''60'_1810 Integer
v0 Integer
v1 T__'8804'__26
v2
du_'8804''8743''8802''8658''60'_1810 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26 ->
  MAlonzo.Code.Data.Integer.Base.T__'60'__50
du_'8804''8743''8802''8658''60'_1810 :: Integer -> Integer -> T__'8804'__26 -> T__'60'__50
du_'8804''8743''8802''8658''60'_1810 Integer
v0 Integer
v1 T__'8804'__26
v2
  = case T__'8804'__26 -> T__'8804'__26
forall a b. a -> b
coe T__'8804'__26
v2 of
      MAlonzo.Code.Data.Integer.Base.C_'45''8804''45'_34 T__'8804'__18
v5
        -> let v6 :: Integer
v6 = Integer -> Integer -> Integer
subInt (Integer -> Integer
forall a b. a -> b
coe (-Integer
1 :: Integer)) (Integer -> Integer
forall a b. a -> b
coe Integer
v0) in
           Any -> T__'60'__50
forall a b. a -> b
coe
             ((T__'8804'__18 -> T__'60'__50) -> Any -> Any
forall a b. a -> b
coe
                T__'8804'__18 -> T__'60'__50
MAlonzo.Code.Data.Integer.Base.C_'45''60''45'_58
                ((Integer -> T__'8804'__18 -> T__'8804'__18) -> Any -> Any -> Any
forall a b. a -> b
coe
                   Integer -> T__'8804'__18 -> T__'8804'__18
MAlonzo.Code.Data.Nat.Properties.du_'8804''8743''8802''8658''60'_1800
                   (Integer -> Any
forall a b. a -> b
coe Integer
v6) (T__'8804'__18 -> Any
forall a b. a -> b
coe T__'8804'__18
v5)))
      T__'8804'__26
MAlonzo.Code.Data.Integer.Base.C_'45''8804''43'_40
        -> T__'60'__50 -> T__'60'__50
forall a b. a -> b
coe T__'60'__50
MAlonzo.Code.Data.Integer.Base.C_'45''60''43'_64
      MAlonzo.Code.Data.Integer.Base.C_'43''8804''43'_48 T__'8804'__18
v5
        -> (T__'8804'__18 -> T__'60'__50) -> Any -> T__'60'__50
forall a b. a -> b
coe
             T__'8804'__18 -> T__'60'__50
MAlonzo.Code.Data.Integer.Base.C_'43''60''43'_72
             ((Integer -> T__'8804'__18 -> T__'8804'__18) -> Any -> Any -> Any
forall a b. a -> b
coe
                Integer -> T__'8804'__18 -> T__'8804'__18
MAlonzo.Code.Data.Nat.Properties.du_'8804''8743''8802''8658''60'_1800
                (Integer -> Any
forall a b. a -> b
coe Integer
v1) (T__'8804'__18 -> Any
forall a b. a -> b
coe T__'8804'__18
v5))
      T__'8804'__26
_ -> T__'60'__50
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Data.Integer.Properties.≤∧≮⇒≡
d_'8804''8743''8814''8658''8801'_1826 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26 ->
  (MAlonzo.Code.Data.Integer.Base.T__'60'__50 ->
   MAlonzo.Code.Data.Empty.T_'8869'_4) ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8804''8743''8814''8658''8801'_1826 :: Integer
-> Integer
-> T__'8804'__26
-> (T__'60'__50 -> T_'8869'_4)
-> T__'8801'__12
d_'8804''8743''8814''8658''8801'_1826 = Integer
-> Integer
-> T__'8804'__26
-> (T__'60'__50 -> T_'8869'_4)
-> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.<-irrefl
d_'60''45'irrefl_1832 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Data.Integer.Base.T__'60'__50 ->
  MAlonzo.Code.Data.Empty.T_'8869'_4
d_'60''45'irrefl_1832 :: Integer -> Integer -> T__'8801'__12 -> T__'60'__50 -> T_'8869'_4
d_'60''45'irrefl_1832 = Integer -> Integer -> T__'8801'__12 -> T__'60'__50 -> T_'8869'_4
forall a. a
erased
-- Data.Integer.Properties.<-asym
d_'60''45'asym_1838 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Integer.Base.T__'60'__50 ->
  MAlonzo.Code.Data.Integer.Base.T__'60'__50 ->
  MAlonzo.Code.Data.Empty.T_'8869'_4
d_'60''45'asym_1838 :: Integer -> Integer -> T__'60'__50 -> T__'60'__50 -> T_'8869'_4
d_'60''45'asym_1838 = Integer -> Integer -> T__'60'__50 -> T__'60'__50 -> T_'8869'_4
forall a. a
erased
-- Data.Integer.Properties.≤-<-trans
d_'8804''45''60''45'trans_1844 ::
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26 ->
  MAlonzo.Code.Data.Integer.Base.T__'60'__50 ->
  MAlonzo.Code.Data.Integer.Base.T__'60'__50
d_'8804''45''60''45'trans_1844 :: Integer
-> Integer
-> Integer
-> T__'8804'__26
-> T__'60'__50
-> T__'60'__50
d_'8804''45''60''45'trans_1844 ~Integer
v0 ~Integer
v1 ~Integer
v2 T__'8804'__26
v3 T__'60'__50
v4
  = T__'8804'__26 -> T__'60'__50 -> T__'60'__50
du_'8804''45''60''45'trans_1844 T__'8804'__26
v3 T__'60'__50
v4
du_'8804''45''60''45'trans_1844 ::
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26 ->
  MAlonzo.Code.Data.Integer.Base.T__'60'__50 ->
  MAlonzo.Code.Data.Integer.Base.T__'60'__50
du_'8804''45''60''45'trans_1844 :: T__'8804'__26 -> T__'60'__50 -> T__'60'__50
du_'8804''45''60''45'trans_1844 T__'8804'__26
v0 T__'60'__50
v1
  = case T__'8804'__26 -> T__'8804'__26
forall a b. a -> b
coe T__'8804'__26
v0 of
      MAlonzo.Code.Data.Integer.Base.C_'45''8804''45'_34 T__'8804'__18
v4
        -> case T__'60'__50 -> T__'60'__50
forall a b. a -> b
coe T__'60'__50
v1 of
             MAlonzo.Code.Data.Integer.Base.C_'45''60''45'_58 T__'8804'__18
v7
               -> (T__'8804'__18 -> T__'60'__50) -> Any -> T__'60'__50
forall a b. a -> b
coe
                    T__'8804'__18 -> T__'60'__50
MAlonzo.Code.Data.Integer.Base.C_'45''60''45'_58
                    ((T__'8804'__18 -> T__'8804'__18 -> T__'8804'__18)
-> Any -> Any -> Any
forall a b. a -> b
coe
                       T__'8804'__18 -> T__'8804'__18 -> T__'8804'__18
MAlonzo.Code.Data.Nat.Properties.du_'60''45'trans'737'_1874
                       (T__'8804'__18 -> Any
forall a b. a -> b
coe T__'8804'__18
v7) (T__'8804'__18 -> Any
forall a b. a -> b
coe T__'8804'__18
v4))
             T__'60'__50
MAlonzo.Code.Data.Integer.Base.C_'45''60''43'_64
               -> T__'60'__50 -> T__'60'__50
forall a b. a -> b
coe T__'60'__50
MAlonzo.Code.Data.Integer.Base.C_'45''60''43'_64
             T__'60'__50
_ -> T__'60'__50
forall a. a
MAlonzo.RTE.mazUnreachableError
      T__'8804'__26
MAlonzo.Code.Data.Integer.Base.C_'45''8804''43'_40
        -> (Any -> Any -> Any) -> Any -> Any -> T__'60'__50
forall a b. a -> b
coe
             Any -> Any -> Any
forall a b. a -> b -> b
seq (T__'60'__50 -> Any
forall a b. a -> b
coe T__'60'__50
v1) (T__'60'__50 -> Any
forall a b. a -> b
coe T__'60'__50
MAlonzo.Code.Data.Integer.Base.C_'45''60''43'_64)
      MAlonzo.Code.Data.Integer.Base.C_'43''8804''43'_48 T__'8804'__18
v4
        -> case T__'60'__50 -> T__'60'__50
forall a b. a -> b
coe T__'60'__50
v1 of
             MAlonzo.Code.Data.Integer.Base.C_'43''60''43'_72 T__'8804'__18
v7
               -> (T__'8804'__18 -> T__'60'__50) -> Any -> T__'60'__50
forall a b. a -> b
coe
                    T__'8804'__18 -> T__'60'__50
MAlonzo.Code.Data.Integer.Base.C_'43''60''43'_72
                    ((T__'8804'__18 -> T__'8804'__18 -> T__'8804'__18)
-> Any -> Any -> Any
forall a b. a -> b
coe
                       T__'8804'__18 -> T__'8804'__18 -> T__'8804'__18
MAlonzo.Code.Data.Nat.Properties.du_'60''45'trans'691'_1868
                       (T__'8804'__18 -> Any
forall a b. a -> b
coe T__'8804'__18
v4) (T__'8804'__18 -> Any
forall a b. a -> b
coe T__'8804'__18
v7))
             T__'60'__50
_ -> T__'60'__50
forall a. a
MAlonzo.RTE.mazUnreachableError
      T__'8804'__26
_ -> T__'60'__50
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Data.Integer.Properties.<-≤-trans
d_'60''45''8804''45'trans_1858 ::
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Integer.Base.T__'60'__50 ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26 ->
  MAlonzo.Code.Data.Integer.Base.T__'60'__50
d_'60''45''8804''45'trans_1858 :: Integer
-> Integer
-> Integer
-> T__'60'__50
-> T__'8804'__26
-> T__'60'__50
d_'60''45''8804''45'trans_1858 ~Integer
v0 ~Integer
v1 ~Integer
v2 T__'60'__50
v3 T__'8804'__26
v4
  = T__'60'__50 -> T__'8804'__26 -> T__'60'__50
du_'60''45''8804''45'trans_1858 T__'60'__50
v3 T__'8804'__26
v4
du_'60''45''8804''45'trans_1858 ::
  MAlonzo.Code.Data.Integer.Base.T__'60'__50 ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26 ->
  MAlonzo.Code.Data.Integer.Base.T__'60'__50
du_'60''45''8804''45'trans_1858 :: T__'60'__50 -> T__'8804'__26 -> T__'60'__50
du_'60''45''8804''45'trans_1858 T__'60'__50
v0 T__'8804'__26
v1
  = case T__'60'__50 -> T__'60'__50
forall a b. a -> b
coe T__'60'__50
v0 of
      MAlonzo.Code.Data.Integer.Base.C_'45''60''45'_58 T__'8804'__18
v4
        -> case T__'8804'__26 -> T__'8804'__26
forall a b. a -> b
coe T__'8804'__26
v1 of
             MAlonzo.Code.Data.Integer.Base.C_'45''8804''45'_34 T__'8804'__18
v7
               -> (T__'8804'__18 -> T__'60'__50) -> Any -> T__'60'__50
forall a b. a -> b
coe
                    T__'8804'__18 -> T__'60'__50
MAlonzo.Code.Data.Integer.Base.C_'45''60''45'_58
                    ((T__'8804'__18 -> T__'8804'__18 -> T__'8804'__18)
-> Any -> Any -> Any
forall a b. a -> b
coe
                       T__'8804'__18 -> T__'8804'__18 -> T__'8804'__18
MAlonzo.Code.Data.Nat.Properties.du_'60''45'trans'691'_1868
                       (T__'8804'__18 -> Any
forall a b. a -> b
coe T__'8804'__18
v7) (T__'8804'__18 -> Any
forall a b. a -> b
coe T__'8804'__18
v4))
             T__'8804'__26
MAlonzo.Code.Data.Integer.Base.C_'45''8804''43'_40
               -> T__'60'__50 -> T__'60'__50
forall a b. a -> b
coe T__'60'__50
MAlonzo.Code.Data.Integer.Base.C_'45''60''43'_64
             T__'8804'__26
_ -> T__'60'__50
forall a. a
MAlonzo.RTE.mazUnreachableError
      T__'60'__50
MAlonzo.Code.Data.Integer.Base.C_'45''60''43'_64
        -> (Any -> Any -> Any) -> Any -> Any -> T__'60'__50
forall a b. a -> b
coe
             Any -> Any -> Any
forall a b. a -> b -> b
seq (T__'8804'__26 -> Any
forall a b. a -> b
coe T__'8804'__26
v1) (T__'60'__50 -> Any
forall a b. a -> b
coe T__'60'__50
MAlonzo.Code.Data.Integer.Base.C_'45''60''43'_64)
      MAlonzo.Code.Data.Integer.Base.C_'43''60''43'_72 T__'8804'__18
v4
        -> case T__'8804'__26 -> T__'8804'__26
forall a b. a -> b
coe T__'8804'__26
v1 of
             MAlonzo.Code.Data.Integer.Base.C_'43''8804''43'_48 T__'8804'__18
v7
               -> (T__'8804'__18 -> T__'60'__50) -> Any -> T__'60'__50
forall a b. a -> b
coe
                    T__'8804'__18 -> T__'60'__50
MAlonzo.Code.Data.Integer.Base.C_'43''60''43'_72
                    ((T__'8804'__18 -> T__'8804'__18 -> T__'8804'__18)
-> Any -> Any -> Any
forall a b. a -> b
coe
                       T__'8804'__18 -> T__'8804'__18 -> T__'8804'__18
MAlonzo.Code.Data.Nat.Properties.du_'60''45'trans'737'_1874
                       (T__'8804'__18 -> Any
forall a b. a -> b
coe T__'8804'__18
v4) (T__'8804'__18 -> Any
forall a b. a -> b
coe T__'8804'__18
v7))
             T__'8804'__26
_ -> T__'60'__50
forall a. a
MAlonzo.RTE.mazUnreachableError
      T__'60'__50
_ -> T__'60'__50
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Data.Integer.Properties.<-trans
d_'60''45'trans_1872 ::
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Integer.Base.T__'60'__50 ->
  MAlonzo.Code.Data.Integer.Base.T__'60'__50 ->
  MAlonzo.Code.Data.Integer.Base.T__'60'__50
d_'60''45'trans_1872 :: Integer
-> Integer -> Integer -> T__'60'__50 -> T__'60'__50 -> T__'60'__50
d_'60''45'trans_1872 Integer
v0 Integer
v1 ~Integer
v2 T__'60'__50
v3 T__'60'__50
v4
  = Integer -> Integer -> T__'60'__50 -> T__'60'__50 -> T__'60'__50
du_'60''45'trans_1872 Integer
v0 Integer
v1 T__'60'__50
v3 T__'60'__50
v4
du_'60''45'trans_1872 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Integer.Base.T__'60'__50 ->
  MAlonzo.Code.Data.Integer.Base.T__'60'__50 ->
  MAlonzo.Code.Data.Integer.Base.T__'60'__50
du_'60''45'trans_1872 :: Integer -> Integer -> T__'60'__50 -> T__'60'__50 -> T__'60'__50
du_'60''45'trans_1872 Integer
v0 Integer
v1 T__'60'__50
v2 T__'60'__50
v3
  = (T__'8804'__26 -> T__'60'__50 -> T__'60'__50)
-> Any -> Any -> T__'60'__50
forall a b. a -> b
coe
      T__'8804'__26 -> T__'60'__50 -> T__'60'__50
du_'8804''45''60''45'trans_1844
      ((Integer -> Integer -> T__'60'__50 -> T__'8804'__26)
-> Any -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> T__'60'__50 -> T__'8804'__26
d_'60''8658''8804'_1724 (Integer -> Any
forall a b. a -> b
coe Integer
v0) (Integer -> Any
forall a b. a -> b
coe Integer
v1) (T__'60'__50 -> Any
forall a b. a -> b
coe T__'60'__50
v2)) (T__'60'__50 -> Any
forall a b. a -> b
coe T__'60'__50
v3)
-- Data.Integer.Properties.<-cmp
d_'60''45'cmp_1878 ::
  Integer ->
  Integer -> MAlonzo.Code.Relation.Binary.Definitions.T_Tri_136
d_'60''45'cmp_1878 :: Integer -> Integer -> T_Tri_136
d_'60''45'cmp_1878 Integer
v0 Integer
v1
  = case Integer -> Any
forall a b. a -> b
coe Integer
v0 of
      Any
_ | (Integer -> Integer -> Bool) -> Any -> Any -> Bool
forall a b. a -> b
coe Integer -> Integer -> Bool
geqInt (Integer -> Any
forall a b. a -> b
coe Integer
v0) (Integer -> Any
forall a b. a -> b
coe (Integer
0 :: Integer)) ->
          let v2 :: t
v2
                = (Any -> T_Tri_136) -> Any -> t
forall a b. a -> b
coe
                    Any -> T_Tri_136
MAlonzo.Code.Relation.Binary.Definitions.C_tri'62'_166
                    (T__'60'__50 -> Any
forall a b. a -> b
coe T__'60'__50
MAlonzo.Code.Data.Integer.Base.C_'45''60''43'_64) in
          Any -> T_Tri_136
forall a b. a -> b
coe
            (case Integer -> Integer
forall a b. a -> b
coe Integer
v0 of
               Integer
0 -> case Integer -> Integer
forall a b. a -> b
coe Integer
v1 of
                      Integer
0 -> (Any -> T_Tri_136) -> Any -> Any
forall a b. a -> b
coe
                             Any -> T_Tri_136
MAlonzo.Code.Relation.Binary.Definitions.C_tri'8776'_158 Any
forall a. a
erased
                      Integer
_ | (Integer -> Integer -> Bool) -> Any -> Any -> Bool
forall a b. a -> b
coe Integer -> Integer -> Bool
geqInt (Integer -> Any
forall a b. a -> b
coe Integer
v1) (Integer -> Any
forall a b. a -> b
coe (Integer
1 :: Integer)) ->
                          (Any -> T_Tri_136) -> Any -> Any
forall a b. a -> b
coe
                            Any -> T_Tri_136
MAlonzo.Code.Relation.Binary.Definitions.C_tri'60'_150
                            ((T__'8804'__18 -> T__'60'__50) -> Any -> Any
forall a b. a -> b
coe
                               T__'8804'__18 -> T__'60'__50
MAlonzo.Code.Data.Integer.Base.C_'43''60''43'_72
                               ((T__'8804'__18 -> T__'8804'__18) -> Any -> Any
forall a b. a -> b
coe
                                  T__'8804'__18 -> T__'8804'__18
MAlonzo.Code.Data.Nat.Base.C_s'8804's_30
                                  (T__'8804'__18 -> Any
forall a b. a -> b
coe T__'8804'__18
MAlonzo.Code.Data.Nat.Base.C_z'8804'n_22)))
                      Integer
_ -> Any -> Any
forall a b. a -> b
coe Any
forall a. a
v2
               Integer
_ -> let v3 :: Integer
v3 = Integer -> Integer -> Integer
subInt (Integer -> Integer
forall a b. a -> b
coe Integer
v0) (Integer -> Integer
forall a b. a -> b
coe (Integer
1 :: Integer)) in
                    Any -> Any
forall a b. a -> b
coe
                      (case Integer -> Integer
forall a b. a -> b
coe Integer
v1 of
                         Integer
0 -> (Any -> T_Tri_136) -> Any -> Any
forall a b. a -> b
coe
                                Any -> T_Tri_136
MAlonzo.Code.Relation.Binary.Definitions.C_tri'62'_166
                                ((T__'8804'__18 -> T__'60'__50) -> Any -> Any
forall a b. a -> b
coe
                                   T__'8804'__18 -> T__'60'__50
MAlonzo.Code.Data.Integer.Base.C_'43''60''43'_72
                                   ((T__'8804'__18 -> T__'8804'__18) -> Any -> Any
forall a b. a -> b
coe
                                      T__'8804'__18 -> T__'8804'__18
MAlonzo.Code.Data.Nat.Base.C_s'8804's_30
                                      (T__'8804'__18 -> Any
forall a b. a -> b
coe T__'8804'__18
MAlonzo.Code.Data.Nat.Base.C_z'8804'n_22)))
                         Integer
_ | (Integer -> Integer -> Bool) -> Any -> Any -> Bool
forall a b. a -> b
coe Integer -> Integer -> Bool
geqInt (Integer -> Any
forall a b. a -> b
coe Integer
v1) (Integer -> Any
forall a b. a -> b
coe (Integer
1 :: Integer)) ->
                             let v4 :: Integer
v4 = Integer -> Integer -> Integer
subInt (Integer -> Integer
forall a b. a -> b
coe Integer
v1) (Integer -> Integer
forall a b. a -> b
coe (Integer
1 :: Integer)) in
                             Any -> Any
forall a b. a -> b
coe
                               (let v5 :: t
v5
                                      = ((Any -> Any) -> T_Dec_32 -> T_Dec_32) -> Any -> Any -> t
forall a b. a -> b
coe
                                          (Any -> Any) -> T_Dec_32 -> T_Dec_32
MAlonzo.Code.Relation.Nullary.Decidable.Core.du_map'8242'_168
                                          Any
forall a. a
erased
                                          ((Bool -> T_Dec_32) -> Any -> Any
forall a b. a -> b
coe
                                             Bool -> T_Dec_32
MAlonzo.Code.Data.Bool.Properties.d_T'63'_2210
                                             ((Integer -> Integer -> Bool) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> Bool
eqInt (Integer -> Any
forall a b. a -> b
coe Integer
v0) (Integer -> Any
forall a b. a -> b
coe Integer
v1))) in
                                Any -> Any
forall a b. a -> b
coe
                                  (let v6 :: T_Dec_32
v6
                                         = Bool -> T_Dec_32
MAlonzo.Code.Data.Bool.Properties.d_T'63'_2210
                                             ((Integer -> Integer -> Bool) -> Any -> Any -> Bool
forall a b. a -> b
coe Integer -> Integer -> Bool
ltInt (Integer -> Any
forall a b. a -> b
coe Integer
v0) (Integer -> Any
forall a b. a -> b
coe Integer
v1)) in
                                   Any -> Any
forall a b. a -> b
coe
                                     (case Any -> T_Dec_32
forall a b. a -> b
coe Any
forall a. a
v5 of
                                        MAlonzo.Code.Relation.Nullary.C__because__46 Bool
v7 T_Reflects_14
v8
                                          -> if Bool -> Bool
forall a b. a -> b
coe Bool
v7
                                               then (Any -> Any -> Any) -> Any -> Any -> Any
forall a b. a -> b
coe
                                                      Any -> Any -> Any
forall a b. a -> b -> b
seq (T_Reflects_14 -> Any
forall a b. a -> b
coe T_Reflects_14
v8)
                                                      ((Any -> T_Tri_136) -> Any -> Any
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 (let v9 :: b
v9
                                                           = Any -> b -> b
forall a b. a -> b -> b
seq
                                                               (T_Reflects_14 -> Any
forall a b. a -> b
coe T_Reflects_14
v8)
                                                               (case T_Dec_32 -> T_Dec_32
forall a b. a -> b
coe T_Dec_32
v6 of
                                                                  MAlonzo.Code.Relation.Nullary.C__because__46 Bool
v9 T_Reflects_14
v10
                                                                    -> if Bool -> Bool
forall a b. a -> b
coe Bool
v9
                                                                         then (Any -> Any -> Any) -> Any -> Any -> b
forall a b. a -> b
coe
                                                                                Any -> Any -> Any
forall a b. a -> b -> b
seq (T_Reflects_14 -> Any
forall a b. a -> b
coe T_Reflects_14
v10)
                                                                                ((Any -> T_Tri_136) -> Any -> Any
forall a b. a -> b
coe
                                                                                   Any -> T_Tri_136
MAlonzo.Code.Relation.Binary.Definitions.C_tri'60'_150
                                                                                   ((Integer -> T__'8804'__18) -> Any -> Any
forall a b. a -> b
coe
                                                                                      Integer -> T__'8804'__18
MAlonzo.Code.Data.Nat.Properties.du_'60''7495''8658''60'_1566
                                                                                      (Integer -> Any
forall a b. a -> b
coe Integer
v3)))
                                                                         else (Any -> Any -> Any) -> Any -> Any -> b
forall a b. a -> b
coe
                                                                                Any -> Any -> Any
forall a b. a -> b -> b
seq (T_Reflects_14 -> Any
forall a b. a -> b
coe T_Reflects_14
v10)
                                                                                ((Any -> T_Tri_136) -> Any -> Any
forall a b. a -> b
coe
                                                                                   Any -> T_Tri_136
MAlonzo.Code.Relation.Binary.Definitions.C_tri'62'_166
                                                                                   ((Integer -> T__'8804'__18 -> T__'8804'__18) -> Any -> Any -> Any
forall a b. a -> b
coe
                                                                                      Integer -> T__'8804'__18 -> T__'8804'__18
MAlonzo.Code.Data.Nat.Properties.du_'8804''8743''8802''8658''60'_1800
                                                                                      (Integer -> Any
forall a b. a -> b
coe Integer
v3)
                                                                                      ((Integer -> Integer -> T__'8804'__18) -> Any -> Any -> Any
forall a b. a -> b
coe
                                                                                         Integer -> Integer -> T__'8804'__18
MAlonzo.Code.Data.Nat.Properties.du_'8814''8658''8805'_1784
                                                                                         (Integer -> Any
forall a b. a -> b
coe Integer
v3)
                                                                                         (Integer -> Any
forall a b. a -> b
coe Integer
v4))))
                                                                  T_Dec_32
_ -> b
forall a. a
MAlonzo.RTE.mazUnreachableError) in
                                                     Any -> Any
forall a b. a -> b
coe
                                                       (case Any -> T_Tri_136
forall a b. a -> b
coe Any
forall a. a
v9 of
                                                          MAlonzo.Code.Relation.Binary.Definitions.C_tri'60'_150 Any
v10
                                                            -> (Any -> T_Tri_136) -> Any -> Any
forall a b. a -> b
coe
                                                                 Any -> T_Tri_136
MAlonzo.Code.Relation.Binary.Definitions.C_tri'60'_150
                                                                 ((T__'8804'__18 -> T__'60'__50) -> Any -> Any
forall a b. a -> b
coe
                                                                    T__'8804'__18 -> T__'60'__50
MAlonzo.Code.Data.Integer.Base.C_'43''60''43'_72
                                                                    ((T__'8804'__18 -> T__'8804'__18) -> Any -> Any
forall a b. a -> b
coe
                                                                       T__'8804'__18 -> T__'8804'__18
MAlonzo.Code.Data.Nat.Base.C_s'8804's_30
                                                                       Any
v10))
                                                          MAlonzo.Code.Relation.Binary.Definitions.C_tri'8776'_158 Any
v11
                                                            -> (Any -> T_Tri_136) -> Any -> Any
forall a b. a -> b
coe
                                                                 Any -> T_Tri_136
MAlonzo.Code.Relation.Binary.Definitions.C_tri'8776'_158
                                                                 Any
forall a. a
erased
                                                          MAlonzo.Code.Relation.Binary.Definitions.C_tri'62'_166 Any
v12
                                                            -> (Any -> T_Tri_136) -> Any -> Any
forall a b. a -> b
coe
                                                                 Any -> T_Tri_136
MAlonzo.Code.Relation.Binary.Definitions.C_tri'62'_166
                                                                 ((T__'8804'__18 -> T__'60'__50) -> Any -> Any
forall a b. a -> b
coe
                                                                    T__'8804'__18 -> T__'60'__50
MAlonzo.Code.Data.Integer.Base.C_'43''60''43'_72
                                                                    ((T__'8804'__18 -> T__'8804'__18) -> Any -> Any
forall a b. a -> b
coe
                                                                       T__'8804'__18 -> T__'8804'__18
MAlonzo.Code.Data.Nat.Base.C_s'8804's_30
                                                                       Any
v12))
                                                          T_Tri_136
_ -> Any
forall a. a
MAlonzo.RTE.mazUnreachableError))
                                        T_Dec_32
_ -> Any
forall a. a
MAlonzo.RTE.mazUnreachableError)))
                         Integer
_ -> (Any -> T_Tri_136) -> Any -> Any
forall a b. a -> b
coe
                                Any -> T_Tri_136
MAlonzo.Code.Relation.Binary.Definitions.C_tri'62'_166
                                (T__'60'__50 -> Any
forall a b. a -> b
coe T__'60'__50
MAlonzo.Code.Data.Integer.Base.C_'45''60''43'_64)))
      Any
_ -> let v2 :: Integer
v2 = Integer -> Integer -> Integer
subInt (Integer -> Integer
forall a b. a -> b
coe (-Integer
1 :: Integer)) (Integer -> Integer
forall a b. a -> b
coe Integer
v0) in
           Any -> T_Tri_136
forall a b. a -> b
coe
             (case Integer -> Any
forall a b. a -> b
coe Integer
v1 of
                Any
_ | (Integer -> Integer -> Bool) -> Any -> Any -> Bool
forall a b. a -> b
coe Integer -> Integer -> Bool
geqInt (Integer -> Any
forall a b. a -> b
coe Integer
v1) (Integer -> Any
forall a b. a -> b
coe (Integer
0 :: Integer)) ->
                    (Any -> T_Tri_136) -> Any -> Any
forall a b. a -> b
coe
                      Any -> T_Tri_136
MAlonzo.Code.Relation.Binary.Definitions.C_tri'60'_150
                      (T__'60'__50 -> Any
forall a b. a -> b
coe T__'60'__50
MAlonzo.Code.Data.Integer.Base.C_'45''60''43'_64)
                Any
_ -> let v3 :: Integer
v3 = Integer -> Integer -> Integer
subInt (Integer -> Integer
forall a b. a -> b
coe (-Integer
1 :: Integer)) (Integer -> Integer
forall a b. a -> b
coe Integer
v1) in
                     Any -> Any
forall a b. a -> b
coe
                       (let v4 :: t
v4
                              = ((Any -> Any) -> T_Dec_32 -> T_Dec_32) -> Any -> Any -> t
forall a b. a -> b
coe
                                  (Any -> Any) -> T_Dec_32 -> T_Dec_32
MAlonzo.Code.Relation.Nullary.Decidable.Core.du_map'8242'_168
                                  Any
forall a. a
erased
                                  ((Bool -> T_Dec_32) -> Any -> Any
forall a b. a -> b
coe
                                     Bool -> T_Dec_32
MAlonzo.Code.Data.Bool.Properties.d_T'63'_2210
                                     ((Integer -> Integer -> Bool) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> Bool
eqInt (Integer -> Any
forall a b. a -> b
coe Integer
v0) (Integer -> Any
forall a b. a -> b
coe Integer
v1))) in
                        Any -> Any
forall a b. a -> b
coe
                          (let v5 :: T_Dec_32
v5
                                 = Bool -> T_Dec_32
MAlonzo.Code.Data.Bool.Properties.d_T'63'_2210
                                     ((Integer -> Integer -> Bool) -> Any -> Any -> Bool
forall a b. a -> b
coe Integer -> Integer -> Bool
ltInt (Integer -> Any
forall a b. a -> b
coe Integer
v1) (Integer -> Any
forall a b. a -> b
coe Integer
v0)) in
                           Any -> Any
forall a b. a -> b
coe
                             (case Any -> T_Dec_32
forall a b. a -> b
coe Any
forall a. a
v4 of
                                MAlonzo.Code.Relation.Nullary.C__because__46 Bool
v6 T_Reflects_14
v7
                                  -> if Bool -> Bool
forall a b. a -> b
coe Bool
v6
                                       then (Any -> Any -> Any) -> Any -> Any -> Any
forall a b. a -> b
coe
                                              Any -> Any -> Any
forall a b. a -> b -> b
seq (T_Reflects_14 -> Any
forall a b. a -> b
coe T_Reflects_14
v7)
                                              ((Any -> T_Tri_136) -> Any -> Any
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 (let v8 :: b
v8
                                                   = Any -> b -> b
forall a b. a -> b -> b
seq
                                                       (T_Reflects_14 -> Any
forall a b. a -> b
coe T_Reflects_14
v7)
                                                       (case T_Dec_32 -> T_Dec_32
forall a b. a -> b
coe T_Dec_32
v5 of
                                                          MAlonzo.Code.Relation.Nullary.C__because__46 Bool
v8 T_Reflects_14
v9
                                                            -> if Bool -> Bool
forall a b. a -> b
coe Bool
v8
                                                                 then (Any -> Any -> Any) -> Any -> Any -> b
forall a b. a -> b
coe
                                                                        Any -> Any -> Any
forall a b. a -> b -> b
seq (T_Reflects_14 -> Any
forall a b. a -> b
coe T_Reflects_14
v9)
                                                                        ((Any -> T_Tri_136) -> Any -> Any
forall a b. a -> b
coe
                                                                           Any -> T_Tri_136
MAlonzo.Code.Relation.Binary.Definitions.C_tri'60'_150
                                                                           ((Integer -> T__'8804'__18) -> Any -> Any
forall a b. a -> b
coe
                                                                              Integer -> T__'8804'__18
MAlonzo.Code.Data.Nat.Properties.du_'60''7495''8658''60'_1566
                                                                              (Integer -> Any
forall a b. a -> b
coe Integer
v2)))
                                                                 else (Any -> Any -> Any) -> Any -> Any -> b
forall a b. a -> b
coe
                                                                        Any -> Any -> Any
forall a b. a -> b -> b
seq (T_Reflects_14 -> Any
forall a b. a -> b
coe T_Reflects_14
v9)
                                                                        ((Any -> T_Tri_136) -> Any -> Any
forall a b. a -> b
coe
                                                                           Any -> T_Tri_136
MAlonzo.Code.Relation.Binary.Definitions.C_tri'62'_166
                                                                           ((Integer -> T__'8804'__18 -> T__'8804'__18) -> Any -> Any -> Any
forall a b. a -> b
coe
                                                                              Integer -> T__'8804'__18 -> T__'8804'__18
MAlonzo.Code.Data.Nat.Properties.du_'8804''8743''8802''8658''60'_1800
                                                                              (Integer -> Any
forall a b. a -> b
coe Integer
v2)
                                                                              ((Integer -> Integer -> T__'8804'__18) -> Any -> Any -> Any
forall a b. a -> b
coe
                                                                                 Integer -> Integer -> T__'8804'__18
MAlonzo.Code.Data.Nat.Properties.du_'8814''8658''8805'_1784
                                                                                 (Integer -> Any
forall a b. a -> b
coe Integer
v2)
                                                                                 (Integer -> Any
forall a b. a -> b
coe Integer
v3))))
                                                          T_Dec_32
_ -> b
forall a. a
MAlonzo.RTE.mazUnreachableError) in
                                             Any -> Any
forall a b. a -> b
coe
                                               (case Any -> T_Tri_136
forall a b. a -> b
coe Any
forall a. a
v8 of
                                                  MAlonzo.Code.Relation.Binary.Definitions.C_tri'60'_150 Any
v9
                                                    -> (Any -> T_Tri_136) -> Any -> Any
forall a b. a -> b
coe
                                                         Any -> T_Tri_136
MAlonzo.Code.Relation.Binary.Definitions.C_tri'62'_166
                                                         ((T__'8804'__18 -> T__'60'__50) -> Any -> Any
forall a b. a -> b
coe
                                                            T__'8804'__18 -> T__'60'__50
MAlonzo.Code.Data.Integer.Base.C_'45''60''45'_58
                                                            Any
v9)
                                                  MAlonzo.Code.Relation.Binary.Definitions.C_tri'8776'_158 Any
v10
                                                    -> (Any -> T_Tri_136) -> Any -> Any
forall a b. a -> b
coe
                                                         Any -> T_Tri_136
MAlonzo.Code.Relation.Binary.Definitions.C_tri'8776'_158
                                                         Any
forall a. a
erased
                                                  MAlonzo.Code.Relation.Binary.Definitions.C_tri'62'_166 Any
v11
                                                    -> (Any -> T_Tri_136) -> Any -> Any
forall a b. a -> b
coe
                                                         Any -> T_Tri_136
MAlonzo.Code.Relation.Binary.Definitions.C_tri'60'_150
                                                         ((T__'8804'__18 -> T__'60'__50) -> Any -> Any
forall a b. a -> b
coe
                                                            T__'8804'__18 -> T__'60'__50
MAlonzo.Code.Data.Integer.Base.C_'45''60''45'_58
                                                            Any
v11)
                                                  T_Tri_136
_ -> Any
forall a. a
MAlonzo.RTE.mazUnreachableError))
                                T_Dec_32
_ -> Any
forall a. a
MAlonzo.RTE.mazUnreachableError))))
-- Data.Integer.Properties._<?_
d__'60''63'__1968 ::
  Integer -> Integer -> MAlonzo.Code.Relation.Nullary.T_Dec_32
d__'60''63'__1968 :: Integer -> Integer -> T_Dec_32
d__'60''63'__1968 Integer
v0 Integer
v1
  = case Integer -> Any
forall a b. a -> b
coe Integer
v0 of
      Any
_ | (Integer -> Integer -> Bool) -> Any -> Any -> Bool
forall a b. a -> b
coe Integer -> Integer -> Bool
geqInt (Integer -> Any
forall a b. a -> b
coe Integer
v0) (Integer -> Any
forall a b. a -> b
coe (Integer
0 :: Integer)) ->
          case Integer -> Any
forall a b. a -> b
coe Integer
v1 of
            Any
_ | (Integer -> Integer -> Bool) -> Any -> Any -> Bool
forall a b. a -> b
coe Integer -> Integer -> Bool
geqInt (Integer -> Any
forall a b. a -> b
coe Integer
v1) (Integer -> Any
forall a b. a -> b
coe (Integer
0 :: Integer)) ->
                ((Any -> Any) -> T_Dec_32 -> T_Dec_32) -> Any -> Any -> T_Dec_32
forall a b. a -> b
coe
                  (Any -> Any) -> T_Dec_32 -> T_Dec_32
MAlonzo.Code.Relation.Nullary.Decidable.Core.du_map'8242'_168
                  ((T__'8804'__18 -> T__'60'__50) -> Any
forall a b. a -> b
coe T__'8804'__18 -> T__'60'__50
MAlonzo.Code.Data.Integer.Base.C_'43''60''43'_72)
                  ((Integer -> Integer -> T_Dec_32) -> Any -> Any -> Any
forall a b. a -> b
coe
                     Integer -> Integer -> T_Dec_32
MAlonzo.Code.Data.Nat.Properties.d__'60''63'__1912 (Integer -> Any
forall a b. a -> b
coe Integer
v0)
                     (Integer -> Any
forall a b. a -> b
coe Integer
v1))
            Any
_ -> (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)
      Any
_ -> let v2 :: Integer
v2 = Integer -> Integer -> Integer
subInt (Integer -> Integer
forall a b. a -> b
coe (-Integer
1 :: Integer)) (Integer -> Integer
forall a b. a -> b
coe Integer
v0) in
           Any -> T_Dec_32
forall a b. a -> b
coe
             (case Integer -> Any
forall a b. a -> b
coe Integer
v1 of
                Any
_ | (Integer -> Integer -> Bool) -> Any -> Any -> Bool
forall a b. a -> b
coe Integer -> Integer -> Bool
geqInt (Integer -> Any
forall a b. a -> b
coe Integer
v1) (Integer -> Any
forall a b. a -> b
coe (Integer
0 :: Integer)) ->
                    (Bool -> T_Reflects_14 -> T_Dec_32) -> Any -> Any -> Any
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
                         (T__'60'__50 -> Any
forall a b. a -> b
coe T__'60'__50
MAlonzo.Code.Data.Integer.Base.C_'45''60''43'_64))
                Any
_ -> let v3 :: Integer
v3 = Integer -> Integer -> Integer
subInt (Integer -> Integer
forall a b. a -> b
coe (-Integer
1 :: Integer)) (Integer -> Integer
forall a b. a -> b
coe Integer
v1) in
                     Any -> Any
forall a b. a -> b
coe
                       (((Any -> Any) -> T_Dec_32 -> T_Dec_32) -> Any -> Any -> Any
forall a b. a -> b
coe
                          (Any -> Any) -> T_Dec_32 -> T_Dec_32
MAlonzo.Code.Relation.Nullary.Decidable.Core.du_map'8242'_168
                          ((T__'8804'__18 -> T__'60'__50) -> Any
forall a b. a -> b
coe T__'8804'__18 -> T__'60'__50
MAlonzo.Code.Data.Integer.Base.C_'45''60''45'_58)
                          ((Integer -> Integer -> T_Dec_32) -> Any -> Any -> Any
forall a b. a -> b
coe
                             Integer -> Integer -> T_Dec_32
MAlonzo.Code.Data.Nat.Properties.d__'60''63'__1912 (Integer -> Any
forall a b. a -> b
coe Integer
v3)
                             (Integer -> Any
forall a b. a -> b
coe Integer
v2))))
-- Data.Integer.Properties.<-irrelevant
d_'60''45'irrelevant_1986 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Integer.Base.T__'60'__50 ->
  MAlonzo.Code.Data.Integer.Base.T__'60'__50 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'60''45'irrelevant_1986 :: Integer -> Integer -> T__'60'__50 -> T__'60'__50 -> T__'8801'__12
d_'60''45'irrelevant_1986 = Integer -> Integer -> T__'60'__50 -> T__'60'__50 -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.<-isStrictPartialOrder
d_'60''45'isStrictPartialOrder_1996 ::
  MAlonzo.Code.Relation.Binary.Structures.T_IsStrictPartialOrder_266
d_'60''45'isStrictPartialOrder_1996 :: T_IsStrictPartialOrder_266
d_'60''45'isStrictPartialOrder_1996
  = (T_IsEquivalence_26
 -> (Any -> Any -> Any -> Any -> Any -> Any)
 -> T_Σ_14
 -> T_IsStrictPartialOrder_266)
-> Any
-> (Any -> Any -> Any -> Any -> Any -> Any)
-> Any
-> 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
v0 Any
v1 Any
v2 Any
v3 Any
v4 -> (Integer -> Integer -> T__'60'__50 -> T__'60'__50 -> T__'60'__50)
-> Any -> Any -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> T__'60'__50 -> T__'60'__50 -> T__'60'__50
du_'60''45'trans_1872 Any
v0 Any
v1 Any
v3 Any
v4)
      ((Any -> Any -> T_Σ_14) -> Any -> Any -> Any
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.Integer.Properties.<-isStrictTotalOrder
d_'60''45'isStrictTotalOrder_2002 ::
  MAlonzo.Code.Relation.Binary.Structures.T_IsStrictTotalOrder_502
d_'60''45'isStrictTotalOrder_2002 :: T_IsStrictTotalOrder_502
d_'60''45'isStrictTotalOrder_2002
  = (T_IsEquivalence_26
 -> (Any -> Any -> Any -> Any -> Any -> Any)
 -> (Any -> Any -> T_Tri_136)
 -> T_IsStrictTotalOrder_502)
-> Any
-> (Any -> Any -> Any -> Any -> 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
v0 Any
v1 Any
v2 Any
v3 Any
v4 -> (Integer -> Integer -> T__'60'__50 -> T__'60'__50 -> T__'60'__50)
-> Any -> Any -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> T__'60'__50 -> T__'60'__50 -> T__'60'__50
du_'60''45'trans_1872 Any
v0 Any
v1 Any
v3 Any
v4)
      ((Integer -> Integer -> T_Tri_136) -> Any
forall a b. a -> b
coe Integer -> Integer -> T_Tri_136
d_'60''45'cmp_1878)
-- Data.Integer.Properties.<-strictPartialOrder
d_'60''45'strictPartialOrder_2004 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_StrictPartialOrder_472
d_'60''45'strictPartialOrder_2004 :: T_StrictPartialOrder_472
d_'60''45'strictPartialOrder_2004
  = (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_1996
-- Data.Integer.Properties.<-strictTotalOrder
d_'60''45'strictTotalOrder_2006 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_StrictTotalOrder_864
d_'60''45'strictTotalOrder_2006 :: T_StrictTotalOrder_864
d_'60''45'strictTotalOrder_2006
  = (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_2002
-- Data.Integer.Properties.n≮n
d_n'8814'n_2010 ::
  Integer ->
  MAlonzo.Code.Data.Integer.Base.T__'60'__50 ->
  MAlonzo.Code.Data.Empty.T_'8869'_4
d_n'8814'n_2010 :: Integer -> T__'60'__50 -> T_'8869'_4
d_n'8814'n_2010 = Integer -> T__'60'__50 -> T_'8869'_4
forall a. a
erased
-- Data.Integer.Properties.>-irrefl
d_'62''45'irrefl_2014 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Data.Integer.Base.T__'60'__50 ->
  MAlonzo.Code.Data.Empty.T_'8869'_4
d_'62''45'irrefl_2014 :: Integer -> Integer -> T__'8801'__12 -> T__'60'__50 -> T_'8869'_4
d_'62''45'irrefl_2014 = Integer -> Integer -> T__'8801'__12 -> T__'60'__50 -> T_'8869'_4
forall a. a
erased
-- Data.Integer.Properties.≤-Reasoning._._IsRelatedTo_
d__IsRelatedTo__2020 :: p -> p -> ()
d__IsRelatedTo__2020 p
a0 p
a1 = ()
-- Data.Integer.Properties.≤-Reasoning._._∎
d__'8718'_2022 ::
  Integer ->
  MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.T__IsRelatedTo__70
d__'8718'_2022 :: Integer -> T__IsRelatedTo__70
d__'8718'_2022
  = (T_IsPreorder_70 -> Any -> T__IsRelatedTo__70)
-> Any -> Integer -> T__IsRelatedTo__70
forall a b. a -> b
coe
      T_IsPreorder_70 -> Any -> T__IsRelatedTo__70
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du__'8718'_346
      (T_IsPreorder_70 -> Any
forall a b. a -> b
coe T_IsPreorder_70
d_'8804''45'isPreorder_1656)
-- Data.Integer.Properties.≤-Reasoning._._≡⟨⟩_
d__'8801''10216''10217'__2024 ::
  MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.T__IsRelatedTo__70 ->
  MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.T__IsRelatedTo__70
d__'8801''10216''10217'__2024 :: T__IsRelatedTo__70 -> T__IsRelatedTo__70
d__'8801''10216''10217'__2024 T__IsRelatedTo__70
v0 = T__IsRelatedTo__70 -> T__IsRelatedTo__70
forall a b. a -> b
coe T__IsRelatedTo__70
v0
-- Data.Integer.Properties.≤-Reasoning._.IsEquality
d_IsEquality_2026 :: p -> p -> p -> ()
d_IsEquality_2026 p
a0 p
a1 p
a2 = ()
-- Data.Integer.Properties.≤-Reasoning._.IsEquality?
d_IsEquality'63'_2028 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.T__IsRelatedTo__70 ->
  MAlonzo.Code.Relation.Nullary.T_Dec_32
d_IsEquality'63'_2028 :: Integer -> Integer -> T__IsRelatedTo__70 -> T_Dec_32
d_IsEquality'63'_2028 Integer
v0 Integer
v1 T__IsRelatedTo__70
v2
  = (T__IsRelatedTo__70 -> T_Dec_32) -> T__IsRelatedTo__70 -> T_Dec_32
forall a b. a -> b
coe
      T__IsRelatedTo__70 -> T_Dec_32
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_IsEquality'63'_142
      T__IsRelatedTo__70
v2
-- Data.Integer.Properties.≤-Reasoning._.IsStrict
d_IsStrict_2030 :: p -> p -> p -> ()
d_IsStrict_2030 p
a0 p
a1 p
a2 = ()
-- Data.Integer.Properties.≤-Reasoning._.IsStrict?
d_IsStrict'63'_2032 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.T__IsRelatedTo__70 ->
  MAlonzo.Code.Relation.Nullary.T_Dec_32
d_IsStrict'63'_2032 :: Integer -> Integer -> T__IsRelatedTo__70 -> T_Dec_32
d_IsStrict'63'_2032 Integer
v0 Integer
v1 T__IsRelatedTo__70
v2
  = (T__IsRelatedTo__70 -> T_Dec_32) -> T__IsRelatedTo__70 -> T_Dec_32
forall a b. a -> b
coe
      T__IsRelatedTo__70 -> T_Dec_32
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_IsStrict'63'_108
      T__IsRelatedTo__70
v2
-- Data.Integer.Properties.≤-Reasoning._.begin_
d_begin__2034 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.T__IsRelatedTo__70 ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26
d_begin__2034 :: Integer -> Integer -> T__IsRelatedTo__70 -> T__'8804'__26
d_begin__2034
  = (T_IsPreorder_70
 -> (Any -> Any -> Any -> Any)
 -> Any
 -> Any
 -> T__IsRelatedTo__70
 -> Any)
-> Any
-> Any
-> Integer
-> Integer
-> T__IsRelatedTo__70
-> T__'8804'__26
forall a b. a -> b
coe
      T_IsPreorder_70
-> (Any -> Any -> Any -> Any)
-> Any
-> Any
-> T__IsRelatedTo__70
-> Any
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_begin__160
      (T_IsPreorder_70 -> Any
forall a b. a -> b
coe T_IsPreorder_70
d_'8804''45'isPreorder_1656) ((Integer -> Integer -> T__'60'__50 -> T__'8804'__26) -> Any
forall a b. a -> b
coe Integer -> Integer -> T__'60'__50 -> T__'8804'__26
d_'60''8658''8804'_1724)
-- Data.Integer.Properties.≤-Reasoning._.begin-equality_
d_begin'45'equality__2036 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.T__IsRelatedTo__70 ->
  AgdaAny -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_begin'45'equality__2036 :: Integer -> Integer -> T__IsRelatedTo__70 -> Any -> T__'8801'__12
d_begin'45'equality__2036 = Integer -> Integer -> T__IsRelatedTo__70 -> Any -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.≤-Reasoning._.begin-strict_
d_begin'45'strict__2038 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.T__IsRelatedTo__70 ->
  AgdaAny -> MAlonzo.Code.Data.Integer.Base.T__'60'__50
d_begin'45'strict__2038 :: Integer -> Integer -> T__IsRelatedTo__70 -> Any -> T__'60'__50
d_begin'45'strict__2038 Integer
v0 Integer
v1 T__IsRelatedTo__70
v2 Any
v3
  = (T__IsRelatedTo__70 -> Any) -> T__IsRelatedTo__70 -> T__'60'__50
forall a b. a -> b
coe
      T__IsRelatedTo__70 -> Any
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_begin'45'strict__176
      T__IsRelatedTo__70
v2
-- Data.Integer.Properties.≤-Reasoning._.extractEquality
d_extractEquality_2042 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.T__IsRelatedTo__70 ->
  MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.T_IsEquality_126 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_extractEquality_2042 :: Integer
-> Integer
-> T__IsRelatedTo__70
-> T_IsEquality_126
-> T__'8801'__12
d_extractEquality_2042 = Integer
-> Integer
-> T__IsRelatedTo__70
-> T_IsEquality_126
-> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.≤-Reasoning._.extractStrict
d_extractStrict_2044 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.T__IsRelatedTo__70 ->
  MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.T_IsStrict_92 ->
  MAlonzo.Code.Data.Integer.Base.T__'60'__50
d_extractStrict_2044 :: Integer
-> Integer -> T__IsRelatedTo__70 -> T_IsStrict_92 -> T__'60'__50
d_extractStrict_2044 Integer
v0 Integer
v1 T__IsRelatedTo__70
v2 T_IsStrict_92
v3
  = (T__IsRelatedTo__70 -> T_IsStrict_92 -> Any)
-> T__IsRelatedTo__70 -> T_IsStrict_92 -> T__'60'__50
forall a b. a -> b
coe
      T__IsRelatedTo__70 -> T_IsStrict_92 -> Any
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_extractStrict_118
      T__IsRelatedTo__70
v2 T_IsStrict_92
v3
-- Data.Integer.Properties.≤-Reasoning._.step-<
d_step'45''60'_2052 ::
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.T__IsRelatedTo__70 ->
  MAlonzo.Code.Data.Integer.Base.T__'60'__50 ->
  MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.T__IsRelatedTo__70
d_step'45''60'_2052 :: Integer
-> Integer
-> Integer
-> T__IsRelatedTo__70
-> T__'60'__50
-> T__IsRelatedTo__70
d_step'45''60'_2052
  = ((Any -> Any -> Any -> Any -> Any -> Any)
 -> T_Σ_14
 -> (Any -> Any -> Any -> Any -> Any -> Any)
 -> Any
 -> Any
 -> Any
 -> T__IsRelatedTo__70
 -> Any
 -> T__IsRelatedTo__70)
-> (Any -> Any -> Any -> Any -> Any -> Any)
-> Any
-> (Any -> Any -> Any -> Any -> Any -> Any)
-> Integer
-> Integer
-> Integer
-> T__IsRelatedTo__70
-> T__'60'__50
-> T__IsRelatedTo__70
forall a b. a -> b
coe
      (Any -> Any -> Any -> Any -> Any -> Any)
-> T_Σ_14
-> (Any -> Any -> Any -> Any -> Any -> Any)
-> Any
-> Any
-> Any
-> T__IsRelatedTo__70
-> Any
-> T__IsRelatedTo__70
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_step'45''60'_202
      (\ Any
v0 Any
v1 Any
v2 Any
v3 Any
v4 -> (Integer -> Integer -> T__'60'__50 -> T__'60'__50 -> T__'60'__50)
-> Any -> Any -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> T__'60'__50 -> T__'60'__50 -> T__'60'__50
du_'60''45'trans_1872 Any
v0 Any
v1 Any
v3 Any
v4)
      (T_Σ_14 -> Any
forall a b. a -> b
coe
         T_Σ_14
MAlonzo.Code.Relation.Binary.PropositionalEquality.Core.du_resp'8322'_144)
      (\ Any
v0 Any
v1 Any
v2 Any
v3 Any
v4 -> (T__'60'__50 -> T__'8804'__26 -> T__'60'__50) -> Any -> Any -> Any
forall a b. a -> b
coe T__'60'__50 -> T__'8804'__26 -> T__'60'__50
du_'60''45''8804''45'trans_1858 Any
v3 Any
v4)
-- Data.Integer.Properties.≤-Reasoning._.step-≡
d_step'45''8801'_2054 ::
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.T__IsRelatedTo__70 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.T__IsRelatedTo__70
d_step'45''8801'_2054 :: Integer
-> Integer
-> Integer
-> T__IsRelatedTo__70
-> T__'8801'__12
-> T__IsRelatedTo__70
d_step'45''8801'_2054 ~Integer
v0 ~Integer
v1 ~Integer
v2 T__IsRelatedTo__70
v3 ~T__'8801'__12
v4
  = T__IsRelatedTo__70 -> T__IsRelatedTo__70
du_step'45''8801'_2054 T__IsRelatedTo__70
v3
du_step'45''8801'_2054 ::
  MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.T__IsRelatedTo__70 ->
  MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.T__IsRelatedTo__70
du_step'45''8801'_2054 :: T__IsRelatedTo__70 -> T__IsRelatedTo__70
du_step'45''8801'_2054 T__IsRelatedTo__70
v0 = T__IsRelatedTo__70 -> T__IsRelatedTo__70
forall a b. a -> b
coe T__IsRelatedTo__70
v0
-- Data.Integer.Properties.≤-Reasoning._.step-≡˘
d_step'45''8801''728'_2056 ::
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.T__IsRelatedTo__70 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.T__IsRelatedTo__70
d_step'45''8801''728'_2056 :: Integer
-> Integer
-> Integer
-> T__IsRelatedTo__70
-> T__'8801'__12
-> T__IsRelatedTo__70
d_step'45''8801''728'_2056 ~Integer
v0 ~Integer
v1 ~Integer
v2 T__IsRelatedTo__70
v3 ~T__'8801'__12
v4
  = T__IsRelatedTo__70 -> T__IsRelatedTo__70
du_step'45''8801''728'_2056 T__IsRelatedTo__70
v3
du_step'45''8801''728'_2056 ::
  MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.T__IsRelatedTo__70 ->
  MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.T__IsRelatedTo__70
du_step'45''8801''728'_2056 :: T__IsRelatedTo__70 -> T__IsRelatedTo__70
du_step'45''8801''728'_2056 T__IsRelatedTo__70
v0 = T__IsRelatedTo__70 -> T__IsRelatedTo__70
forall a b. a -> b
coe T__IsRelatedTo__70
v0
-- Data.Integer.Properties.≤-Reasoning._.step-≤
d_step'45''8804'_2058 ::
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.T__IsRelatedTo__70 ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26 ->
  MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.T__IsRelatedTo__70
d_step'45''8804'_2058 :: Integer
-> Integer
-> Integer
-> T__IsRelatedTo__70
-> T__'8804'__26
-> T__IsRelatedTo__70
d_step'45''8804'_2058
  = (T_IsPreorder_70
 -> (Any -> Any -> Any -> Any -> Any -> Any)
 -> Any
 -> Any
 -> Any
 -> T__IsRelatedTo__70
 -> Any
 -> T__IsRelatedTo__70)
-> Any
-> (Any -> Any -> Any -> Any -> Any -> Any)
-> Integer
-> Integer
-> Integer
-> T__IsRelatedTo__70
-> T__'8804'__26
-> T__IsRelatedTo__70
forall a b. a -> b
coe
      T_IsPreorder_70
-> (Any -> Any -> Any -> Any -> Any -> Any)
-> Any
-> Any
-> Any
-> T__IsRelatedTo__70
-> Any
-> T__IsRelatedTo__70
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_step'45''8804'_228
      (T_IsPreorder_70 -> Any
forall a b. a -> b
coe T_IsPreorder_70
d_'8804''45'isPreorder_1656)
      (\ Any
v0 Any
v1 Any
v2 Any
v3 Any
v4 -> (T__'8804'__26 -> T__'60'__50 -> T__'60'__50) -> Any -> Any -> Any
forall a b. a -> b
coe T__'8804'__26 -> T__'60'__50 -> T__'60'__50
du_'8804''45''60''45'trans_1844 Any
v3 Any
v4)
-- Data.Integer.Properties.positive⁻¹
d_positive'8315''185'_2080 ::
  Integer -> AgdaAny -> MAlonzo.Code.Data.Integer.Base.T__'60'__50
d_positive'8315''185'_2080 :: Integer -> Any -> T__'60'__50
d_positive'8315''185'_2080 ~Integer
v0 ~Any
v1 = T__'60'__50
du_positive'8315''185'_2080
du_positive'8315''185'_2080 ::
  MAlonzo.Code.Data.Integer.Base.T__'60'__50
du_positive'8315''185'_2080 :: T__'60'__50
du_positive'8315''185'_2080
  = (T__'8804'__18 -> T__'60'__50) -> Any -> T__'60'__50
forall a b. a -> b
coe
      T__'8804'__18 -> T__'60'__50
MAlonzo.Code.Data.Integer.Base.C_'43''60''43'_72
      ((T__'8804'__18 -> T__'8804'__18) -> Any -> Any
forall a b. a -> b
coe
         T__'8804'__18 -> T__'8804'__18
MAlonzo.Code.Data.Nat.Base.C_s'8804's_30
         (T__'8804'__18 -> Any
forall a b. a -> b
coe T__'8804'__18
MAlonzo.Code.Data.Nat.Base.C_z'8804'n_22))
-- Data.Integer.Properties.nonNegative⁻¹
d_nonNegative'8315''185'_2086 ::
  Integer -> AgdaAny -> MAlonzo.Code.Data.Integer.Base.T__'8804'__26
d_nonNegative'8315''185'_2086 :: Integer -> Any -> T__'8804'__26
d_nonNegative'8315''185'_2086 ~Integer
v0 ~Any
v1
  = T__'8804'__26
du_nonNegative'8315''185'_2086
du_nonNegative'8315''185'_2086 ::
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26
du_nonNegative'8315''185'_2086 :: T__'8804'__26
du_nonNegative'8315''185'_2086
  = (T__'8804'__18 -> T__'8804'__26) -> Any -> T__'8804'__26
forall a b. a -> b
coe
      T__'8804'__18 -> T__'8804'__26
MAlonzo.Code.Data.Integer.Base.C_'43''8804''43'_48
      (T__'8804'__18 -> Any
forall a b. a -> b
coe T__'8804'__18
MAlonzo.Code.Data.Nat.Base.C_z'8804'n_22)
-- Data.Integer.Properties.negative⁻¹
d_negative'8315''185'_2092 ::
  Integer -> AgdaAny -> MAlonzo.Code.Data.Integer.Base.T__'60'__50
d_negative'8315''185'_2092 :: Integer -> Any -> T__'60'__50
d_negative'8315''185'_2092 ~Integer
v0 ~Any
v1 = T__'60'__50
du_negative'8315''185'_2092
du_negative'8315''185'_2092 ::
  MAlonzo.Code.Data.Integer.Base.T__'60'__50
du_negative'8315''185'_2092 :: T__'60'__50
du_negative'8315''185'_2092
  = T__'60'__50 -> T__'60'__50
forall a b. a -> b
coe T__'60'__50
MAlonzo.Code.Data.Integer.Base.C_'45''60''43'_64
-- Data.Integer.Properties.nonPositive⁻¹
d_nonPositive'8315''185'_2098 ::
  Integer -> AgdaAny -> MAlonzo.Code.Data.Integer.Base.T__'8804'__26
d_nonPositive'8315''185'_2098 :: Integer -> Any -> T__'8804'__26
d_nonPositive'8315''185'_2098 Integer
v0 ~Any
v1
  = Integer -> T__'8804'__26
du_nonPositive'8315''185'_2098 Integer
v0
du_nonPositive'8315''185'_2098 ::
  Integer -> MAlonzo.Code.Data.Integer.Base.T__'8804'__26
du_nonPositive'8315''185'_2098 :: Integer -> T__'8804'__26
du_nonPositive'8315''185'_2098 Integer
v0
  = case Integer -> Integer
forall a b. a -> b
coe Integer
v0 of
      Integer
0 -> (T__'8804'__18 -> T__'8804'__26) -> Any -> T__'8804'__26
forall a b. a -> b
coe
             T__'8804'__18 -> T__'8804'__26
MAlonzo.Code.Data.Integer.Base.C_'43''8804''43'_48
             (T__'8804'__18 -> Any
forall a b. a -> b
coe T__'8804'__18
MAlonzo.Code.Data.Nat.Base.C_z'8804'n_22)
      Integer
_ -> T__'8804'__26 -> T__'8804'__26
forall a b. a -> b
coe T__'8804'__26
MAlonzo.Code.Data.Integer.Base.C_'45''8804''43'_40
-- Data.Integer.Properties.negative<positive
d_negative'60'positive_2106 ::
  Integer ->
  Integer ->
  AgdaAny -> AgdaAny -> MAlonzo.Code.Data.Integer.Base.T__'60'__50
d_negative'60'positive_2106 :: Integer -> Integer -> Any -> Any -> T__'60'__50
d_negative'60'positive_2106 Integer
v0 ~Integer
v1 ~Any
v2 ~Any
v3
  = Integer -> T__'60'__50
du_negative'60'positive_2106 Integer
v0
du_negative'60'positive_2106 ::
  Integer -> MAlonzo.Code.Data.Integer.Base.T__'60'__50
du_negative'60'positive_2106 :: Integer -> T__'60'__50
du_negative'60'positive_2106 Integer
v0
  = (Integer -> Integer -> T__'60'__50 -> T__'60'__50 -> T__'60'__50)
-> Any -> Any -> Any -> Any -> T__'60'__50
forall a b. a -> b
coe
      Integer -> Integer -> T__'60'__50 -> T__'60'__50 -> T__'60'__50
du_'60''45'trans_1872 (Integer -> Any
forall a b. a -> b
coe Integer
v0)
      (Integer -> Any
forall a b. a -> b
coe Integer
MAlonzo.Code.Data.Integer.Base.d_0ℤ_12)
      (T__'60'__50 -> Any
forall a b. a -> b
coe T__'60'__50
du_negative'8315''185'_2092) (T__'60'__50 -> Any
forall a b. a -> b
coe T__'60'__50
du_positive'8315''185'_2080)
-- Data.Integer.Properties.neg-involutive
d_neg'45'involutive_2114 ::
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_neg'45'involutive_2114 :: Integer -> T__'8801'__12
d_neg'45'involutive_2114 = Integer -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.neg-injective
d_neg'45'injective_2124 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_neg'45'injective_2124 :: Integer -> Integer -> T__'8801'__12 -> T__'8801'__12
d_neg'45'injective_2124 = Integer -> Integer -> T__'8801'__12 -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.neg-≤-pos
d_neg'45''8804''45'pos_2140 ::
  Integer -> Integer -> MAlonzo.Code.Data.Integer.Base.T__'8804'__26
d_neg'45''8804''45'pos_2140 :: Integer -> Integer -> T__'8804'__26
d_neg'45''8804''45'pos_2140 Integer
v0 ~Integer
v1
  = Integer -> T__'8804'__26
du_neg'45''8804''45'pos_2140 Integer
v0
du_neg'45''8804''45'pos_2140 ::
  Integer -> MAlonzo.Code.Data.Integer.Base.T__'8804'__26
du_neg'45''8804''45'pos_2140 :: Integer -> T__'8804'__26
du_neg'45''8804''45'pos_2140 Integer
v0
  = case Integer -> Integer
forall a b. a -> b
coe Integer
v0 of
      Integer
0 -> (T__'8804'__18 -> T__'8804'__26) -> Any -> T__'8804'__26
forall a b. a -> b
coe
             T__'8804'__18 -> T__'8804'__26
MAlonzo.Code.Data.Integer.Base.C_'43''8804''43'_48
             (T__'8804'__18 -> Any
forall a b. a -> b
coe T__'8804'__18
MAlonzo.Code.Data.Nat.Base.C_z'8804'n_22)
      Integer
_ -> T__'8804'__26 -> T__'8804'__26
forall a b. a -> b
coe T__'8804'__26
MAlonzo.Code.Data.Integer.Base.C_'45''8804''43'_40
-- Data.Integer.Properties.neg-mono-<
d_neg'45'mono'45''60'_2144 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Integer.Base.T__'60'__50 ->
  MAlonzo.Code.Data.Integer.Base.T__'60'__50
d_neg'45'mono'45''60'_2144 :: Integer -> Integer -> T__'60'__50 -> T__'60'__50
d_neg'45'mono'45''60'_2144 Integer
v0 Integer
v1 T__'60'__50
v2
  = case Integer -> Integer
forall a b. a -> b
coe Integer
v0 of
      Integer
0 -> (Any -> Any -> Any) -> Any -> Any -> T__'60'__50
forall a b. a -> b
coe
             Any -> Any -> Any
forall a b. a -> b -> b
seq (T__'60'__50 -> Any
forall a b. a -> b
coe T__'60'__50
v2) (T__'60'__50 -> Any
forall a b. a -> b
coe T__'60'__50
MAlonzo.Code.Data.Integer.Base.C_'45''60''43'_64)
      Integer
_ | (Integer -> Integer -> Bool) -> Any -> Any -> Bool
forall a b. a -> b
coe Integer -> Integer -> Bool
geqInt (Integer -> Any
forall a b. a -> b
coe Integer
v0) (Integer -> Any
forall a b. a -> b
coe (Integer
1 :: Integer)) ->
          case T__'60'__50 -> T__'60'__50
forall a b. a -> b
coe T__'60'__50
v2 of
            MAlonzo.Code.Data.Integer.Base.C_'43''60''43'_72 T__'8804'__18
v5
              -> (T__'8804'__18 -> T__'60'__50) -> Any -> T__'60'__50
forall a b. a -> b
coe
                   T__'8804'__18 -> T__'60'__50
MAlonzo.Code.Data.Integer.Base.C_'45''60''45'_58
                   ((T__'8804'__18 -> T__'8804'__18) -> Any -> Any
forall a b. a -> b
coe
                      T__'8804'__18 -> T__'8804'__18
MAlonzo.Code.Data.Nat.Properties.Core.du_'8804''45'pred_12
                      (T__'8804'__18 -> Any
forall a b. a -> b
coe T__'8804'__18
v5))
            T__'60'__50
_ -> T__'60'__50
forall a. a
MAlonzo.RTE.mazUnreachableError
      Integer
_ -> case Integer -> Integer
forall a b. a -> b
coe Integer
v1 of
             Integer
0 -> (Any -> Any -> Any) -> Any -> Any -> T__'60'__50
forall a b. a -> b
coe
                    Any -> Any -> Any
forall a b. a -> b -> b
seq (T__'60'__50 -> Any
forall a b. a -> b
coe T__'60'__50
v2)
                    ((T__'8804'__18 -> T__'60'__50) -> Any -> Any
forall a b. a -> b
coe
                       T__'8804'__18 -> T__'60'__50
MAlonzo.Code.Data.Integer.Base.C_'43''60''43'_72
                       ((T__'8804'__18 -> T__'8804'__18) -> Any -> Any
forall a b. a -> b
coe
                          T__'8804'__18 -> T__'8804'__18
MAlonzo.Code.Data.Nat.Base.C_s'8804's_30
                          (T__'8804'__18 -> Any
forall a b. a -> b
coe T__'8804'__18
MAlonzo.Code.Data.Nat.Base.C_z'8804'n_22)))
             Integer
_ | (Integer -> Integer -> Bool) -> Any -> Any -> Bool
forall a b. a -> b
coe Integer -> Integer -> Bool
geqInt (Integer -> Any
forall a b. a -> b
coe Integer
v1) (Integer -> Any
forall a b. a -> b
coe (Integer
1 :: Integer)) ->
                 (Any -> Any -> Any) -> Any -> Any -> T__'60'__50
forall a b. a -> b
coe
                   Any -> Any -> Any
forall a b. a -> b -> b
seq (T__'60'__50 -> Any
forall a b. a -> b
coe T__'60'__50
v2) (T__'60'__50 -> Any
forall a b. a -> b
coe T__'60'__50
MAlonzo.Code.Data.Integer.Base.C_'45''60''43'_64)
             Integer
_ -> case T__'60'__50 -> T__'60'__50
forall a b. a -> b
coe T__'60'__50
v2 of
                    MAlonzo.Code.Data.Integer.Base.C_'45''60''45'_58 T__'8804'__18
v5
                      -> (T__'8804'__18 -> T__'60'__50) -> Any -> T__'60'__50
forall a b. a -> b
coe
                           T__'8804'__18 -> T__'60'__50
MAlonzo.Code.Data.Integer.Base.C_'43''60''43'_72
                           ((T__'8804'__18 -> T__'8804'__18) -> T__'8804'__18 -> Any
forall a b. a -> b
coe T__'8804'__18 -> T__'8804'__18
MAlonzo.Code.Data.Nat.Base.C_s'8804's_30 T__'8804'__18
v5)
                    T__'60'__50
_ -> T__'60'__50
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Data.Integer.Properties.neg-cancel-<
d_neg'45'cancel'45''60'_2162 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Integer.Base.T__'60'__50 ->
  MAlonzo.Code.Data.Integer.Base.T__'60'__50
d_neg'45'cancel'45''60'_2162 :: Integer -> Integer -> T__'60'__50 -> T__'60'__50
d_neg'45'cancel'45''60'_2162 Integer
v0 Integer
v1 T__'60'__50
v2
  = case Integer -> Integer
forall a b. a -> b
coe Integer
v0 of
      Integer
0 -> T__'60'__50 -> T__'60'__50
forall a b. a -> b
coe T__'60'__50
MAlonzo.Code.Data.Integer.Base.C_'45''60''43'_64
      Integer
_ | (Integer -> Integer -> Bool) -> Any -> Any -> Bool
forall a b. a -> b
coe Integer -> Integer -> Bool
geqInt (Integer -> Any
forall a b. a -> b
coe Integer
v0) (Integer -> Any
forall a b. a -> b
coe (Integer
1 :: Integer)) ->
          case Integer -> Integer
forall a b. a -> b
coe Integer
v1 of
            Integer
0 -> (Any -> Any -> Any) -> Any -> Any -> T__'60'__50
forall a b. a -> b
coe
                   Any -> Any -> Any
forall a b. a -> b -> b
seq (T__'60'__50 -> Any
forall a b. a -> b
coe T__'60'__50
v2)
                   ((T__'8804'__18 -> T__'60'__50) -> Any -> Any
forall a b. a -> b
coe
                      T__'8804'__18 -> T__'60'__50
MAlonzo.Code.Data.Integer.Base.C_'43''60''43'_72
                      ((T__'8804'__18 -> T__'8804'__18) -> Any -> Any
forall a b. a -> b
coe
                         T__'8804'__18 -> T__'8804'__18
MAlonzo.Code.Data.Nat.Base.C_s'8804's_30
                         (T__'8804'__18 -> Any
forall a b. a -> b
coe T__'8804'__18
MAlonzo.Code.Data.Nat.Base.C_z'8804'n_22)))
            Integer
_ | (Integer -> Integer -> Bool) -> Any -> Any -> Bool
forall a b. a -> b
coe Integer -> Integer -> Bool
geqInt (Integer -> Any
forall a b. a -> b
coe Integer
v1) (Integer -> Any
forall a b. a -> b
coe (Integer
1 :: Integer)) ->
                case T__'60'__50 -> T__'60'__50
forall a b. a -> b
coe T__'60'__50
v2 of
                  MAlonzo.Code.Data.Integer.Base.C_'45''60''45'_58 T__'8804'__18
v5
                    -> (T__'8804'__18 -> T__'60'__50) -> Any -> T__'60'__50
forall a b. a -> b
coe
                         T__'8804'__18 -> T__'60'__50
MAlonzo.Code.Data.Integer.Base.C_'43''60''43'_72
                         ((T__'8804'__18 -> T__'8804'__18) -> T__'8804'__18 -> Any
forall a b. a -> b
coe T__'8804'__18 -> T__'8804'__18
MAlonzo.Code.Data.Nat.Base.C_s'8804's_30 T__'8804'__18
v5)
                  T__'60'__50
_ -> T__'60'__50
forall a. a
MAlonzo.RTE.mazUnreachableError
            Integer
_ -> (Any -> Any -> Any) -> Any -> Any -> T__'60'__50
forall a b. a -> b
coe
                   Any -> Any -> Any
forall a b. a -> b -> b
seq (T__'60'__50 -> Any
forall a b. a -> b
coe T__'60'__50
v2) (T__'60'__50 -> Any
forall a b. a -> b
coe T__'60'__50
MAlonzo.Code.Data.Integer.Base.C_'45''60''43'_64)
      Integer
_ -> case T__'60'__50 -> T__'60'__50
forall a b. a -> b
coe T__'60'__50
v2 of
             MAlonzo.Code.Data.Integer.Base.C_'43''60''43'_72 T__'8804'__18
v5
               -> case T__'8804'__18 -> T__'8804'__18
forall a b. a -> b
coe T__'8804'__18
v5 of
                    MAlonzo.Code.Data.Nat.Base.C_s'8804's_30 T__'8804'__18
v8
                      -> (T__'8804'__18 -> T__'60'__50) -> T__'8804'__18 -> T__'60'__50
forall a b. a -> b
coe T__'8804'__18 -> T__'60'__50
MAlonzo.Code.Data.Integer.Base.C_'45''60''45'_58 T__'8804'__18
v8
                    T__'8804'__18
_ -> T__'60'__50
forall a. a
MAlonzo.RTE.mazUnreachableError
             T__'60'__50
_ -> T__'60'__50
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Data.Integer.Properties.∣n∣≡0⇒n≡0
d_'8739'n'8739''8801'0'8658'n'8801'0_2188 ::
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8739'n'8739''8801'0'8658'n'8801'0_2188 :: Integer -> T__'8801'__12 -> T__'8801'__12
d_'8739'n'8739''8801'0'8658'n'8801'0_2188 = Integer -> T__'8801'__12 -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.∣-n∣≡∣n∣
d_'8739''45'n'8739''8801''8739'n'8739'_2192 ::
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8739''45'n'8739''8801''8739'n'8739'_2192 :: Integer -> T__'8801'__12
d_'8739''45'n'8739''8801''8739'n'8739'_2192 = Integer -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.0≤n⇒+∣n∣≡n
d_0'8804'n'8658''43''8739'n'8739''8801'n_2200 ::
  Integer ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_0'8804'n'8658''43''8739'n'8739''8801'n_2200 :: Integer -> T__'8804'__26 -> T__'8801'__12
d_0'8804'n'8658''43''8739'n'8739''8801'n_2200 = Integer -> T__'8804'__26 -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.+∣n∣≡n⇒0≤n
d_'43''8739'n'8739''8801'n'8658'0'8804'n_2206 ::
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26
d_'43''8739'n'8739''8801'n'8658'0'8804'n_2206 :: Integer -> T__'8801'__12 -> T__'8804'__26
d_'43''8739'n'8739''8801'n'8658'0'8804'n_2206 ~Integer
v0 ~T__'8801'__12
v1
  = T__'8804'__26
du_'43''8739'n'8739''8801'n'8658'0'8804'n_2206
du_'43''8739'n'8739''8801'n'8658'0'8804'n_2206 ::
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26
du_'43''8739'n'8739''8801'n'8658'0'8804'n_2206 :: T__'8804'__26
du_'43''8739'n'8739''8801'n'8658'0'8804'n_2206
  = (T__'8804'__18 -> T__'8804'__26) -> Any -> T__'8804'__26
forall a b. a -> b
coe
      T__'8804'__18 -> T__'8804'__26
MAlonzo.Code.Data.Integer.Base.C_'43''8804''43'_48
      (T__'8804'__18 -> Any
forall a b. a -> b
coe T__'8804'__18
MAlonzo.Code.Data.Nat.Base.C_z'8804'n_22)
-- Data.Integer.Properties.+∣n∣≡n⊎+∣n∣≡-n
d_'43''8739'n'8739''8801'n'8846''43''8739'n'8739''8801''45'n_2212 ::
  Integer -> MAlonzo.Code.Data.Sum.Base.T__'8846'__30
d_'43''8739'n'8739''8801'n'8846''43''8739'n'8739''8801''45'n_2212 :: Integer -> T__'8846'__30
d_'43''8739'n'8739''8801'n'8846''43''8739'n'8739''8801''45'n_2212 Integer
v0
  = case Integer -> Any
forall a b. a -> b
coe Integer
v0 of
      Any
_ | (Integer -> Integer -> Bool) -> Any -> Any -> Bool
forall a b. a -> b
coe Integer -> Integer -> Bool
geqInt (Integer -> Any
forall a b. a -> b
coe Integer
v0) (Integer -> Any
forall a b. a -> b
coe (Integer
0 :: Integer)) ->
          (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
      Any
_ -> (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.Integer.Properties.∣m⊝n∣≤m⊔n
d_'8739'm'8861'n'8739''8804'm'8852'n_2222 ::
  Integer -> Integer -> MAlonzo.Code.Data.Nat.Base.T__'8804'__18
d_'8739'm'8861'n'8739''8804'm'8852'n_2222 :: Integer -> Integer -> T__'8804'__18
d_'8739'm'8861'n'8739''8804'm'8852'n_2222 Integer
v0 Integer
v1
  = let v2 :: Bool
v2 = Integer -> Integer -> Bool
ltInt (Integer -> Integer
forall a b. a -> b
coe Integer
v0) (Integer -> Integer
forall a b. a -> b
coe Integer
v1) in
    Any -> T__'8804'__18
forall a b. a -> b
coe
      (if Bool -> Bool
forall a b. a -> b
coe Bool
v2
         then (T_IsPreorder_70
 -> (Any -> Any -> Any -> Any)
 -> Any
 -> Any
 -> T__IsRelatedTo__70
 -> Any)
-> Any -> (Any -> Any -> Any -> Any) -> Any -> Any -> Any -> Any
forall a b. a -> b
coe
                T_IsPreorder_70
-> (Any -> Any -> Any -> Any)
-> Any
-> Any
-> T__IsRelatedTo__70
-> Any
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_begin__160
                (T_IsPreorder_70 -> Any
forall a b. a -> b
coe T_IsPreorder_70
MAlonzo.Code.Data.Nat.Properties.d_'8804''45'isPreorder_1684)
                (\ Any
v3 Any
v4 Any
v5 ->
                   (Integer -> T__'8804'__18 -> T__'8804'__18) -> Any -> Any -> Any
forall a b. a -> b
coe
                     Integer -> T__'8804'__18 -> T__'8804'__18
MAlonzo.Code.Data.Nat.Properties.du_'60''8658''8804'_1736 Any
v4 Any
v5)
                ((Integer -> Integer) -> Any -> Any
forall a b. a -> b
coe
                   Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d_'8739'_'8739'_18
                   ((Integer -> Integer) -> Any -> Any
forall a b. a -> b
coe
                      Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d_'45'__218
                      ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> Integer
subInt (Integer -> Any
forall a b. a -> b
coe Integer
v1) (Integer -> Any
forall a b. a -> b
coe Integer
v0))))
                ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> Integer
MAlonzo.Code.Data.Nat.Base.d__'8852'__106 (Integer -> Any
forall a b. a -> b
coe Integer
v0) (Integer -> Any
forall a b. a -> b
coe Integer
v1))
                ((T_IsPreorder_70
 -> (Any -> Any -> Any -> Any -> Any -> Any)
 -> Any
 -> Any
 -> Any
 -> T__IsRelatedTo__70
 -> Any
 -> T__IsRelatedTo__70)
-> Any
-> (Any -> Any -> Any -> Any -> Any -> Any)
-> Any
-> Any
-> Any
-> Any
-> Any
-> Any
forall a b. a -> b
coe
                   T_IsPreorder_70
-> (Any -> Any -> Any -> Any -> Any -> Any)
-> Any
-> Any
-> Any
-> T__IsRelatedTo__70
-> Any
-> T__IsRelatedTo__70
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_step'45''8804'_228
                   (T_IsPreorder_70 -> Any
forall a b. a -> b
coe T_IsPreorder_70
MAlonzo.Code.Data.Nat.Properties.d_'8804''45'isPreorder_1684)
                   (\ Any
v3 Any
v4 Any
v5 Any
v6 Any
v7 ->
                      (T__'8804'__18 -> T__'8804'__18 -> T__'8804'__18)
-> Any -> Any -> Any
forall a b. a -> b
coe
                        T__'8804'__18 -> T__'8804'__18 -> T__'8804'__18
MAlonzo.Code.Data.Nat.Properties.du_'60''45'trans'691'_1868 Any
v6 Any
v7)
                   ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> Integer
subInt (Integer -> Any
forall a b. a -> b
coe Integer
v1) (Integer -> Any
forall a b. a -> b
coe Integer
v0)) (Integer -> Any
forall a b. a -> b
coe Integer
v1)
                   ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> Integer
MAlonzo.Code.Data.Nat.Base.d__'8852'__106 (Integer -> Any
forall a b. a -> b
coe Integer
v0) (Integer -> Any
forall a b. a -> b
coe Integer
v1))
                   ((T_IsPreorder_70
 -> (Any -> Any -> Any -> Any -> Any -> Any)
 -> Any
 -> Any
 -> Any
 -> T__IsRelatedTo__70
 -> Any
 -> T__IsRelatedTo__70)
-> Any
-> (Any -> Any -> Any -> Any -> Any -> Any)
-> Any
-> Any
-> Any
-> Any
-> Any
-> Any
forall a b. a -> b
coe
                      T_IsPreorder_70
-> (Any -> Any -> Any -> Any -> Any -> Any)
-> Any
-> Any
-> Any
-> T__IsRelatedTo__70
-> Any
-> T__IsRelatedTo__70
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_step'45''8804'_228
                      (T_IsPreorder_70 -> Any
forall a b. a -> b
coe T_IsPreorder_70
MAlonzo.Code.Data.Nat.Properties.d_'8804''45'isPreorder_1684)
                      (\ Any
v3 Any
v4 Any
v5 Any
v6 Any
v7 ->
                         (T__'8804'__18 -> T__'8804'__18 -> T__'8804'__18)
-> Any -> Any -> Any
forall a b. a -> b
coe
                           T__'8804'__18 -> T__'8804'__18 -> T__'8804'__18
MAlonzo.Code.Data.Nat.Properties.du_'60''45'trans'691'_1868 Any
v6 Any
v7)
                      (Integer -> Any
forall a b. a -> b
coe Integer
v1)
                      ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> Integer
MAlonzo.Code.Data.Nat.Base.d__'8852'__106 (Integer -> Any
forall a b. a -> b
coe Integer
v0) (Integer -> Any
forall a b. a -> b
coe Integer
v1))
                      ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> Integer
MAlonzo.Code.Data.Nat.Base.d__'8852'__106 (Integer -> Any
forall a b. a -> b
coe Integer
v0) (Integer -> Any
forall a b. a -> b
coe Integer
v1))
                      ((T_IsPreorder_70 -> Any -> T__IsRelatedTo__70) -> Any -> Any -> Any
forall a b. a -> b
coe
                         T_IsPreorder_70 -> Any -> T__IsRelatedTo__70
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du__'8718'_346
                         (T_IsPreorder_70 -> Any
forall a b. a -> b
coe T_IsPreorder_70
MAlonzo.Code.Data.Nat.Properties.d_'8804''45'isPreorder_1684)
                         ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> Integer
MAlonzo.Code.Data.Nat.Base.d__'8852'__106 (Integer -> Any
forall a b. a -> b
coe Integer
v0) (Integer -> Any
forall a b. a -> b
coe Integer
v1)))
                      ((Integer -> Integer -> T__'8804'__18) -> Integer -> Integer -> Any
forall a b. a -> b
coe
                         Integer -> Integer -> T__'8804'__18
MAlonzo.Code.Data.Nat.Properties.d_n'8804'm'8852'n_5132 Integer
v0 Integer
v1))
                   ((Integer -> Integer -> T__'8804'__18) -> Any -> Any -> Any
forall a b. a -> b
coe
                      Integer -> Integer -> T__'8804'__18
MAlonzo.Code.Data.Nat.Properties.d_n'8760'm'8804'n_5094 (Integer -> Any
forall a b. a -> b
coe Integer
v0)
                      (Integer -> Any
forall a b. a -> b
coe Integer
v1)))
         else (T_IsPreorder_70
 -> (Any -> Any -> Any -> Any)
 -> Any
 -> Any
 -> T__IsRelatedTo__70
 -> Any)
-> Any -> (Any -> Any -> Any -> Any) -> Any -> Any -> Any -> Any
forall a b. a -> b
coe
                T_IsPreorder_70
-> (Any -> Any -> Any -> Any)
-> Any
-> Any
-> T__IsRelatedTo__70
-> Any
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_begin__160
                (T_IsPreorder_70 -> Any
forall a b. a -> b
coe T_IsPreorder_70
MAlonzo.Code.Data.Nat.Properties.d_'8804''45'isPreorder_1684)
                (\ Any
v3 Any
v4 Any
v5 ->
                   (Integer -> T__'8804'__18 -> T__'8804'__18) -> Any -> Any -> Any
forall a b. a -> b
coe
                     Integer -> T__'8804'__18 -> T__'8804'__18
MAlonzo.Code.Data.Nat.Properties.du_'60''8658''8804'_1736 Any
v4 Any
v5)
                ((Integer -> Integer) -> Any -> Any
forall a b. a -> b
coe
                   Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d_'8739'_'8739'_18
                   ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> Integer
subInt (Integer -> Any
forall a b. a -> b
coe Integer
v0) (Integer -> Any
forall a b. a -> b
coe Integer
v1)))
                ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> Integer
MAlonzo.Code.Data.Nat.Base.d__'8852'__106 (Integer -> Any
forall a b. a -> b
coe Integer
v0) (Integer -> Any
forall a b. a -> b
coe Integer
v1))
                ((T_IsPreorder_70
 -> (Any -> Any -> Any -> Any -> Any -> Any)
 -> Any
 -> Any
 -> Any
 -> T__IsRelatedTo__70
 -> Any
 -> T__IsRelatedTo__70)
-> Any
-> (Any -> Any -> Any -> Any -> Any -> Any)
-> Any
-> Any
-> Any
-> Any
-> Any
-> Any
forall a b. a -> b
coe
                   T_IsPreorder_70
-> (Any -> Any -> Any -> Any -> Any -> Any)
-> Any
-> Any
-> Any
-> T__IsRelatedTo__70
-> Any
-> T__IsRelatedTo__70
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_step'45''8804'_228
                   (T_IsPreorder_70 -> Any
forall a b. a -> b
coe T_IsPreorder_70
MAlonzo.Code.Data.Nat.Properties.d_'8804''45'isPreorder_1684)
                   (\ Any
v3 Any
v4 Any
v5 Any
v6 Any
v7 ->
                      (T__'8804'__18 -> T__'8804'__18 -> T__'8804'__18)
-> Any -> Any -> Any
forall a b. a -> b
coe
                        T__'8804'__18 -> T__'8804'__18 -> T__'8804'__18
MAlonzo.Code.Data.Nat.Properties.du_'60''45'trans'691'_1868 Any
v6 Any
v7)
                   ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> Integer
subInt (Integer -> Any
forall a b. a -> b
coe Integer
v0) (Integer -> Any
forall a b. a -> b
coe Integer
v1)) (Integer -> Any
forall a b. a -> b
coe Integer
v0)
                   ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> Integer
MAlonzo.Code.Data.Nat.Base.d__'8852'__106 (Integer -> Any
forall a b. a -> b
coe Integer
v0) (Integer -> Any
forall a b. a -> b
coe Integer
v1))
                   ((T_IsPreorder_70
 -> (Any -> Any -> Any -> Any -> Any -> Any)
 -> Any
 -> Any
 -> Any
 -> T__IsRelatedTo__70
 -> Any
 -> T__IsRelatedTo__70)
-> Any
-> (Any -> Any -> Any -> Any -> Any -> Any)
-> Any
-> Any
-> Any
-> Any
-> Any
-> Any
forall a b. a -> b
coe
                      T_IsPreorder_70
-> (Any -> Any -> Any -> Any -> Any -> Any)
-> Any
-> Any
-> Any
-> T__IsRelatedTo__70
-> Any
-> T__IsRelatedTo__70
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_step'45''8804'_228
                      (T_IsPreorder_70 -> Any
forall a b. a -> b
coe T_IsPreorder_70
MAlonzo.Code.Data.Nat.Properties.d_'8804''45'isPreorder_1684)
                      (\ Any
v3 Any
v4 Any
v5 Any
v6 Any
v7 ->
                         (T__'8804'__18 -> T__'8804'__18 -> T__'8804'__18)
-> Any -> Any -> Any
forall a b. a -> b
coe
                           T__'8804'__18 -> T__'8804'__18 -> T__'8804'__18
MAlonzo.Code.Data.Nat.Properties.du_'60''45'trans'691'_1868 Any
v6 Any
v7)
                      (Integer -> Any
forall a b. a -> b
coe Integer
v0)
                      ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> Integer
MAlonzo.Code.Data.Nat.Base.d__'8852'__106 (Integer -> Any
forall a b. a -> b
coe Integer
v0) (Integer -> Any
forall a b. a -> b
coe Integer
v1))
                      ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> Integer
MAlonzo.Code.Data.Nat.Base.d__'8852'__106 (Integer -> Any
forall a b. a -> b
coe Integer
v0) (Integer -> Any
forall a b. a -> b
coe Integer
v1))
                      ((T_IsPreorder_70 -> Any -> T__IsRelatedTo__70) -> Any -> Any -> Any
forall a b. a -> b
coe
                         T_IsPreorder_70 -> Any -> T__IsRelatedTo__70
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du__'8718'_346
                         (T_IsPreorder_70 -> Any
forall a b. a -> b
coe T_IsPreorder_70
MAlonzo.Code.Data.Nat.Properties.d_'8804''45'isPreorder_1684)
                         ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> Integer
MAlonzo.Code.Data.Nat.Base.d__'8852'__106 (Integer -> Any
forall a b. a -> b
coe Integer
v0) (Integer -> Any
forall a b. a -> b
coe Integer
v1)))
                      (let v3 :: T_TotalPreorder_204
v3
                             = T_TotalPreorder_204
MAlonzo.Code.Data.Nat.Properties.d_'8804''45'totalPreorder_1696 in
                       Any -> Any
forall a b. a -> b
coe
                         (let v4 :: T_MaxOperator_114
v4
                                = T_MaxOperator_114
MAlonzo.Code.Data.Nat.Properties.d_'8852''45'operator_3096 in
                          Any -> Any
forall a b. a -> b
coe
                            ((T_TotalPreorder_204 -> T_MinOperator_84 -> Any -> Any -> Any)
-> Any -> Any -> Any -> Any -> Any
forall a b. a -> b
coe
                               T_TotalPreorder_204 -> T_MinOperator_84 -> Any -> Any -> Any
MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_x'8851'y'8804'x_1626
                               ((T_TotalPreorder_204 -> T_TotalPreorder_204) -> Any -> Any
forall a b. a -> b
coe
                                  T_TotalPreorder_204 -> T_TotalPreorder_204
MAlonzo.Code.Relation.Binary.Construct.Converse.du_totalPreorder_718
                                  (T_TotalPreorder_204 -> Any
forall a b. a -> b
coe T_TotalPreorder_204
v3))
                               ((T_MaxOperator_114 -> T_MinOperator_84) -> Any -> Any
forall a b. a -> b
coe
                                  T_MaxOperator_114 -> T_MinOperator_84
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.du_MaxOp'8658'MinOp_160
                                  (T_MaxOperator_114 -> Any
forall a b. a -> b
coe T_MaxOperator_114
v4))
                               (Integer -> Any
forall a b. a -> b
coe Integer
v0) (Integer -> Any
forall a b. a -> b
coe Integer
v1)))))
                   ((Integer -> Integer -> T__'8804'__18) -> Any -> Any -> Any
forall a b. a -> b
coe
                      Integer -> Integer -> T__'8804'__18
MAlonzo.Code.Data.Nat.Properties.d_n'8760'm'8804'n_5094 (Integer -> Any
forall a b. a -> b
coe Integer
v1)
                      (Integer -> Any
forall a b. a -> b
coe Integer
v0))))
-- Data.Integer.Properties.∣m+n∣≤∣m∣+∣n∣
d_'8739'm'43'n'8739''8804''8739'm'8739''43''8739'n'8739'_2252 ::
  Integer -> Integer -> MAlonzo.Code.Data.Nat.Base.T__'8804'__18
d_'8739'm'43'n'8739''8804''8739'm'8739''43''8739'n'8739'_2252 :: Integer -> Integer -> T__'8804'__18
d_'8739'm'43'n'8739''8804''8739'm'8739''43''8739'n'8739'_2252 Integer
v0 Integer
v1
  = case Integer -> Integer
forall a b. a -> b
coe Integer
v0 of
      Integer
0 -> (Any -> Any -> Any) -> Any -> Any -> T__'8804'__18
forall a b. a -> b
coe
             Any -> Any -> Any
forall a b. a -> b -> b
seq (Integer -> Any
forall a b. a -> b
coe Integer
v1)
             ((Integer -> T__'8804'__18) -> Any -> Any
forall a b. a -> b
coe
                Integer -> T__'8804'__18
MAlonzo.Code.Data.Nat.Properties.d_'8804''45'refl_1634
                ((Integer -> Integer) -> Any -> Any
forall a b. a -> b
coe
                   Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d_'8739'_'8739'_18
                   ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe
                      Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'43'__242 (Integer -> Any
forall a b. a -> b
coe (Integer
0 :: Integer))
                      (Integer -> Any
forall a b. a -> b
coe Integer
v1))))
      Integer
_ | (Integer -> Integer -> Bool) -> Any -> Any -> Bool
forall a b. a -> b
coe Integer -> Integer -> Bool
geqInt (Integer -> Any
forall a b. a -> b
coe Integer
v0) (Integer -> Any
forall a b. a -> b
coe (Integer
1 :: Integer)) ->
          case Integer -> Any
forall a b. a -> b
coe Integer
v1 of
            Any
_ | (Integer -> Integer -> Bool) -> Any -> Any -> Bool
forall a b. a -> b
coe Integer -> Integer -> Bool
geqInt (Integer -> Any
forall a b. a -> b
coe Integer
v1) (Integer -> Any
forall a b. a -> b
coe (Integer
0 :: Integer)) ->
                (Integer -> T__'8804'__18) -> Any -> T__'8804'__18
forall a b. a -> b
coe
                  Integer -> T__'8804'__18
MAlonzo.Code.Data.Nat.Properties.d_'8804''45'refl_1634
                  ((Integer -> Integer) -> Any -> Any
forall a b. a -> b
coe
                     Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d_'8739'_'8739'_18
                     ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe
                        Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'43'__242 (Integer -> Any
forall a b. a -> b
coe Integer
v0) (Integer -> Any
forall a b. a -> b
coe Integer
v1)))
            Any
_ -> (T_IsPreorder_70
 -> (Any -> Any -> Any -> Any)
 -> Any
 -> Any
 -> T__IsRelatedTo__70
 -> Any)
-> Any
-> (Any -> Any -> Any -> Any)
-> Any
-> Any
-> Any
-> T__'8804'__18
forall a b. a -> b
coe
                   T_IsPreorder_70
-> (Any -> Any -> Any -> Any)
-> Any
-> Any
-> T__IsRelatedTo__70
-> Any
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_begin__160
                   (T_IsPreorder_70 -> Any
forall a b. a -> b
coe T_IsPreorder_70
MAlonzo.Code.Data.Nat.Properties.d_'8804''45'isPreorder_1684)
                   (\ Any
v2 Any
v3 Any
v4 ->
                      (Integer -> T__'8804'__18 -> T__'8804'__18) -> Any -> Any -> Any
forall a b. a -> b
coe
                        Integer -> T__'8804'__18 -> T__'8804'__18
MAlonzo.Code.Data.Nat.Properties.du_'60''8658''8804'_1736 Any
v3 Any
v4)
                   ((Integer -> Integer) -> Any -> Any
forall a b. a -> b
coe
                      Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d_'8739'_'8739'_18
                      ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe
                         Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'43'__242 (Integer -> Any
forall a b. a -> b
coe Integer
v0) (Integer -> Any
forall a b. a -> b
coe Integer
v1)))
                   ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe
                      Integer -> Integer -> Integer
addInt
                      ((Integer -> Integer) -> Any -> Any
forall a b. a -> b
coe Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d_'8739'_'8739'_18 (Integer -> Any
forall a b. a -> b
coe Integer
v0))
                      ((Integer -> Integer) -> Any -> Any
forall a b. a -> b
coe Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d_'8739'_'8739'_18 (Integer -> Any
forall a b. a -> b
coe Integer
v1)))
                   ((T_IsPreorder_70
 -> (Any -> Any -> Any -> Any -> Any -> Any)
 -> Any
 -> Any
 -> Any
 -> T__IsRelatedTo__70
 -> Any
 -> T__IsRelatedTo__70)
-> Any
-> (Any -> Any -> Any -> Any -> Any -> Any)
-> Any
-> Any
-> Any
-> Any
-> Any
-> Any
forall a b. a -> b
coe
                      T_IsPreorder_70
-> (Any -> Any -> Any -> Any -> Any -> Any)
-> Any
-> Any
-> Any
-> T__IsRelatedTo__70
-> Any
-> T__IsRelatedTo__70
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_step'45''8804'_228
                      (T_IsPreorder_70 -> Any
forall a b. a -> b
coe T_IsPreorder_70
MAlonzo.Code.Data.Nat.Properties.d_'8804''45'isPreorder_1684)
                      (\ Any
v2 Any
v3 Any
v4 Any
v5 Any
v6 ->
                         (T__'8804'__18 -> T__'8804'__18 -> T__'8804'__18)
-> Any -> Any -> Any
forall a b. a -> b
coe
                           T__'8804'__18 -> T__'8804'__18 -> T__'8804'__18
MAlonzo.Code.Data.Nat.Properties.du_'60''45'trans'691'_1868 Any
v5 Any
v6)
                      ((Integer -> Integer) -> Any -> Any
forall a b. a -> b
coe
                         Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d_'8739'_'8739'_18
                         ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe
                            Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'8854'__224 (Integer -> Any
forall a b. a -> b
coe Integer
v0)
                            ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> Integer
subInt (Integer -> Any
forall a b. a -> b
coe (Integer
0 :: Integer)) (Integer -> Any
forall a b. a -> b
coe Integer
v1))))
                      ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe
                         Integer -> Integer -> Integer
MAlonzo.Code.Data.Nat.Base.d__'8852'__106 (Integer -> Any
forall a b. a -> b
coe Integer
v0)
                         ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> Integer
subInt (Integer -> Any
forall a b. a -> b
coe (Integer
0 :: Integer)) (Integer -> Any
forall a b. a -> b
coe Integer
v1)))
                      ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe
                         Integer -> Integer -> Integer
addInt
                         ((Integer -> Integer) -> Any -> Any
forall a b. a -> b
coe Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d_'8739'_'8739'_18 (Integer -> Any
forall a b. a -> b
coe Integer
v0))
                         ((Integer -> Integer) -> Any -> Any
forall a b. a -> b
coe Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d_'8739'_'8739'_18 (Integer -> Any
forall a b. a -> b
coe Integer
v1)))
                      ((T_IsPreorder_70
 -> (Any -> Any -> Any -> Any -> Any -> Any)
 -> Any
 -> Any
 -> Any
 -> T__IsRelatedTo__70
 -> Any
 -> T__IsRelatedTo__70)
-> Any
-> (Any -> Any -> Any -> Any -> Any -> Any)
-> Any
-> Any
-> Any
-> Any
-> Any
-> Any
forall a b. a -> b
coe
                         T_IsPreorder_70
-> (Any -> Any -> Any -> Any -> Any -> Any)
-> Any
-> Any
-> Any
-> T__IsRelatedTo__70
-> Any
-> T__IsRelatedTo__70
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_step'45''8804'_228
                         (T_IsPreorder_70 -> Any
forall a b. a -> b
coe T_IsPreorder_70
MAlonzo.Code.Data.Nat.Properties.d_'8804''45'isPreorder_1684)
                         (\ Any
v2 Any
v3 Any
v4 Any
v5 Any
v6 ->
                            (T__'8804'__18 -> T__'8804'__18 -> T__'8804'__18)
-> Any -> Any -> Any
forall a b. a -> b
coe
                              T__'8804'__18 -> T__'8804'__18 -> T__'8804'__18
MAlonzo.Code.Data.Nat.Properties.du_'60''45'trans'691'_1868 Any
v5 Any
v6)
                         ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe
                            Integer -> Integer -> Integer
MAlonzo.Code.Data.Nat.Base.d__'8852'__106 (Integer -> Any
forall a b. a -> b
coe Integer
v0)
                            ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> Integer
subInt (Integer -> Any
forall a b. a -> b
coe (Integer
0 :: Integer)) (Integer -> Any
forall a b. a -> b
coe Integer
v1)))
                         ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> Integer
subInt (Integer -> Any
forall a b. a -> b
coe Integer
v0) (Integer -> Any
forall a b. a -> b
coe Integer
v1))
                         ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe
                            Integer -> Integer -> Integer
addInt
                            ((Integer -> Integer) -> Any -> Any
forall a b. a -> b
coe Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d_'8739'_'8739'_18 (Integer -> Any
forall a b. a -> b
coe Integer
v0))
                            ((Integer -> Integer) -> Any -> Any
forall a b. a -> b
coe Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d_'8739'_'8739'_18 (Integer -> Any
forall a b. a -> b
coe Integer
v1)))
                         ((T_IsPreorder_70 -> Any -> T__IsRelatedTo__70) -> Any -> Any -> Any
forall a b. a -> b
coe
                            T_IsPreorder_70 -> Any -> T__IsRelatedTo__70
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du__'8718'_346
                            (T_IsPreorder_70 -> Any
forall a b. a -> b
coe T_IsPreorder_70
MAlonzo.Code.Data.Nat.Properties.d_'8804''45'isPreorder_1684)
                            ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> Integer
subInt (Integer -> Any
forall a b. a -> b
coe Integer
v0) (Integer -> Any
forall a b. a -> b
coe Integer
v1)))
                         ((Integer -> Integer -> T__'8804'__18) -> Any -> Any -> Any
forall a b. a -> b
coe
                            Integer -> Integer -> T__'8804'__18
MAlonzo.Code.Data.Nat.Properties.d_m'8852'n'8804'm'43'n_3446
                            (Integer -> Any
forall a b. a -> b
coe Integer
v0) ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> Integer
subInt (Integer -> Any
forall a b. a -> b
coe (Integer
0 :: Integer)) (Integer -> Any
forall a b. a -> b
coe Integer
v1))))
                      ((Integer -> Integer -> T__'8804'__18) -> Any -> Any -> Any
forall a b. a -> b
coe
                         Integer -> Integer -> T__'8804'__18
d_'8739'm'8861'n'8739''8804'm'8852'n_2222 (Integer -> Any
forall a b. a -> b
coe Integer
v0)
                         ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> Integer
subInt (Integer -> Any
forall a b. a -> b
coe (Integer
0 :: Integer)) (Integer -> Any
forall a b. a -> b
coe Integer
v1))))
      Integer
_ -> case Integer -> Any
forall a b. a -> b
coe Integer
v1 of
             Any
_ | (Integer -> Integer -> Bool) -> Any -> Any -> Bool
forall a b. a -> b
coe Integer -> Integer -> Bool
geqInt (Integer -> Any
forall a b. a -> b
coe Integer
v1) (Integer -> Any
forall a b. a -> b
coe (Integer
0 :: Integer)) ->
                 (T_IsPreorder_70
 -> (Any -> Any -> Any -> Any)
 -> Any
 -> Any
 -> T__IsRelatedTo__70
 -> Any)
-> Any
-> (Any -> Any -> Any -> Any)
-> Any
-> Any
-> Any
-> T__'8804'__18
forall a b. a -> b
coe
                   T_IsPreorder_70
-> (Any -> Any -> Any -> Any)
-> Any
-> Any
-> T__IsRelatedTo__70
-> Any
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_begin__160
                   (T_IsPreorder_70 -> Any
forall a b. a -> b
coe T_IsPreorder_70
MAlonzo.Code.Data.Nat.Properties.d_'8804''45'isPreorder_1684)
                   (\ Any
v2 Any
v3 Any
v4 ->
                      (Integer -> T__'8804'__18 -> T__'8804'__18) -> Any -> Any -> Any
forall a b. a -> b
coe
                        Integer -> T__'8804'__18 -> T__'8804'__18
MAlonzo.Code.Data.Nat.Properties.du_'60''8658''8804'_1736 Any
v3 Any
v4)
                   ((Integer -> Integer) -> Any -> Any
forall a b. a -> b
coe
                      Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d_'8739'_'8739'_18
                      ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe
                         Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'43'__242 (Integer -> Any
forall a b. a -> b
coe Integer
v0) (Integer -> Any
forall a b. a -> b
coe Integer
v1)))
                   ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe
                      Integer -> Integer -> Integer
addInt
                      ((Integer -> Integer) -> Any -> Any
forall a b. a -> b
coe Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d_'8739'_'8739'_18 (Integer -> Any
forall a b. a -> b
coe Integer
v0))
                      ((Integer -> Integer) -> Any -> Any
forall a b. a -> b
coe Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d_'8739'_'8739'_18 (Integer -> Any
forall a b. a -> b
coe Integer
v1)))
                   ((T_IsPreorder_70
 -> (Any -> Any -> Any -> Any -> Any -> Any)
 -> Any
 -> Any
 -> Any
 -> T__IsRelatedTo__70
 -> Any
 -> T__IsRelatedTo__70)
-> Any
-> (Any -> Any -> Any -> Any -> Any -> Any)
-> Any
-> Any
-> Any
-> Any
-> Any
-> Any
forall a b. a -> b
coe
                      T_IsPreorder_70
-> (Any -> Any -> Any -> Any -> Any -> Any)
-> Any
-> Any
-> Any
-> T__IsRelatedTo__70
-> Any
-> T__IsRelatedTo__70
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_step'45''8804'_228
                      (T_IsPreorder_70 -> Any
forall a b. a -> b
coe T_IsPreorder_70
MAlonzo.Code.Data.Nat.Properties.d_'8804''45'isPreorder_1684)
                      (\ Any
v2 Any
v3 Any
v4 Any
v5 Any
v6 ->
                         (T__'8804'__18 -> T__'8804'__18 -> T__'8804'__18)
-> Any -> Any -> Any
forall a b. a -> b
coe
                           T__'8804'__18 -> T__'8804'__18 -> T__'8804'__18
MAlonzo.Code.Data.Nat.Properties.du_'60''45'trans'691'_1868 Any
v5 Any
v6)
                      ((Integer -> Integer) -> Any -> Any
forall a b. a -> b
coe
                         Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d_'8739'_'8739'_18
                         ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe
                            Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'8854'__224 (Integer -> Any
forall a b. a -> b
coe Integer
v1)
                            ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> Integer
subInt (Integer -> Any
forall a b. a -> b
coe (Integer
0 :: Integer)) (Integer -> Any
forall a b. a -> b
coe Integer
v0))))
                      ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe
                         Integer -> Integer -> Integer
MAlonzo.Code.Data.Nat.Base.d__'8852'__106 (Integer -> Any
forall a b. a -> b
coe Integer
v1)
                         ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> Integer
subInt (Integer -> Any
forall a b. a -> b
coe (Integer
0 :: Integer)) (Integer -> Any
forall a b. a -> b
coe Integer
v0)))
                      ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe
                         Integer -> Integer -> Integer
addInt
                         ((Integer -> Integer) -> Any -> Any
forall a b. a -> b
coe Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d_'8739'_'8739'_18 (Integer -> Any
forall a b. a -> b
coe Integer
v0))
                         ((Integer -> Integer) -> Any -> Any
forall a b. a -> b
coe Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d_'8739'_'8739'_18 (Integer -> Any
forall a b. a -> b
coe Integer
v1)))
                      ((T_IsPreorder_70
 -> (Any -> Any -> Any -> Any -> Any -> Any)
 -> Any
 -> Any
 -> Any
 -> T__IsRelatedTo__70
 -> Any
 -> T__IsRelatedTo__70)
-> Any
-> (Any -> Any -> Any -> Any -> Any -> Any)
-> Any
-> Any
-> Any
-> Any
-> Any
-> Any
forall a b. a -> b
coe
                         T_IsPreorder_70
-> (Any -> Any -> Any -> Any -> Any -> Any)
-> Any
-> Any
-> Any
-> T__IsRelatedTo__70
-> Any
-> T__IsRelatedTo__70
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_step'45''8804'_228
                         (T_IsPreorder_70 -> Any
forall a b. a -> b
coe T_IsPreorder_70
MAlonzo.Code.Data.Nat.Properties.d_'8804''45'isPreorder_1684)
                         (\ Any
v2 Any
v3 Any
v4 Any
v5 Any
v6 ->
                            (T__'8804'__18 -> T__'8804'__18 -> T__'8804'__18)
-> Any -> Any -> Any
forall a b. a -> b
coe
                              T__'8804'__18 -> T__'8804'__18 -> T__'8804'__18
MAlonzo.Code.Data.Nat.Properties.du_'60''45'trans'691'_1868 Any
v5 Any
v6)
                         ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe
                            Integer -> Integer -> Integer
MAlonzo.Code.Data.Nat.Base.d__'8852'__106 (Integer -> Any
forall a b. a -> b
coe Integer
v1)
                            ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> Integer
subInt (Integer -> Any
forall a b. a -> b
coe (Integer
0 :: Integer)) (Integer -> Any
forall a b. a -> b
coe Integer
v0)))
                         ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> Integer
subInt (Integer -> Any
forall a b. a -> b
coe Integer
v1) (Integer -> Any
forall a b. a -> b
coe Integer
v0))
                         ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe
                            Integer -> Integer -> Integer
addInt
                            ((Integer -> Integer) -> Any -> Any
forall a b. a -> b
coe Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d_'8739'_'8739'_18 (Integer -> Any
forall a b. a -> b
coe Integer
v0))
                            ((Integer -> Integer) -> Any -> Any
forall a b. a -> b
coe Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d_'8739'_'8739'_18 (Integer -> Any
forall a b. a -> b
coe Integer
v1)))
                         ((T_IsPreorder_70 -> Any -> T__IsRelatedTo__70) -> Any -> Any -> Any
forall a b. a -> b
coe
                            T_IsPreorder_70 -> Any -> T__IsRelatedTo__70
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du__'8718'_346
                            (T_IsPreorder_70 -> Any
forall a b. a -> b
coe T_IsPreorder_70
MAlonzo.Code.Data.Nat.Properties.d_'8804''45'isPreorder_1684)
                            ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> Integer
subInt (Integer -> Any
forall a b. a -> b
coe Integer
v1) (Integer -> Any
forall a b. a -> b
coe Integer
v0)))
                         ((Integer -> Integer -> T__'8804'__18) -> Any -> Any -> Any
forall a b. a -> b
coe
                            Integer -> Integer -> T__'8804'__18
MAlonzo.Code.Data.Nat.Properties.d_m'8852'n'8804'm'43'n_3446
                            (Integer -> Any
forall a b. a -> b
coe Integer
v1) ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> Integer
subInt (Integer -> Any
forall a b. a -> b
coe (Integer
0 :: Integer)) (Integer -> Any
forall a b. a -> b
coe Integer
v0))))
                      ((Integer -> Integer -> T__'8804'__18) -> Any -> Any -> Any
forall a b. a -> b
coe
                         Integer -> Integer -> T__'8804'__18
d_'8739'm'8861'n'8739''8804'm'8852'n_2222 (Integer -> Any
forall a b. a -> b
coe Integer
v1)
                         ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> Integer
subInt (Integer -> Any
forall a b. a -> b
coe (Integer
0 :: Integer)) (Integer -> Any
forall a b. a -> b
coe Integer
v0))))
             Any
_ -> (Integer -> T__'8804'__18) -> Any -> T__'8804'__18
forall a b. a -> b
coe
                    Integer -> T__'8804'__18
MAlonzo.Code.Data.Nat.Properties.d_'8804''45'refl_1634
                    ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> Integer
subInt ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> Integer
subInt (Integer -> Any
forall a b. a -> b
coe (Integer
0 :: Integer)) (Integer -> Any
forall a b. a -> b
coe Integer
v0)) (Integer -> Any
forall a b. a -> b
coe Integer
v1))
-- Data.Integer.Properties.∣m-n∣≤∣m∣+∣n∣
d_'8739'm'45'n'8739''8804''8739'm'8739''43''8739'n'8739'_2290 ::
  Integer -> Integer -> MAlonzo.Code.Data.Nat.Base.T__'8804'__18
d_'8739'm'45'n'8739''8804''8739'm'8739''43''8739'n'8739'_2290 :: Integer -> Integer -> T__'8804'__18
d_'8739'm'45'n'8739''8804''8739'm'8739''43''8739'n'8739'_2290 Integer
v0 Integer
v1
  = (T_IsPreorder_70
 -> (Any -> Any -> Any -> Any)
 -> Any
 -> Any
 -> T__IsRelatedTo__70
 -> Any)
-> Any
-> (Any -> Any -> Any -> Any)
-> Any
-> Any
-> Any
-> T__'8804'__18
forall a b. a -> b
coe
      T_IsPreorder_70
-> (Any -> Any -> Any -> Any)
-> Any
-> Any
-> T__IsRelatedTo__70
-> Any
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_begin__160
      (T_IsPreorder_70 -> Any
forall a b. a -> b
coe T_IsPreorder_70
MAlonzo.Code.Data.Nat.Properties.d_'8804''45'isPreorder_1684)
      (\ Any
v2 Any
v3 Any
v4 ->
         (Integer -> T__'8804'__18 -> T__'8804'__18) -> Any -> Any -> Any
forall a b. a -> b
coe
           Integer -> T__'8804'__18 -> T__'8804'__18
MAlonzo.Code.Data.Nat.Properties.du_'60''8658''8804'_1736 Any
v3 Any
v4)
      ((Integer -> Integer) -> Any -> Any
forall a b. a -> b
coe
         Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d_'8739'_'8739'_18
         ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe
            Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'45'__260 (Integer -> Any
forall a b. a -> b
coe Integer
v0) (Integer -> Any
forall a b. a -> b
coe Integer
v1)))
      ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe
         Integer -> Integer -> Integer
addInt
         ((Integer -> Integer) -> Any -> Any
forall a b. a -> b
coe Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d_'8739'_'8739'_18 (Integer -> Any
forall a b. a -> b
coe Integer
v0))
         ((Integer -> Integer) -> Any -> Any
forall a b. a -> b
coe Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d_'8739'_'8739'_18 (Integer -> Any
forall a b. a -> b
coe Integer
v1)))
      ((T_IsPreorder_70
 -> (Any -> Any -> Any -> Any -> Any -> Any)
 -> Any
 -> Any
 -> Any
 -> T__IsRelatedTo__70
 -> Any
 -> T__IsRelatedTo__70)
-> Any
-> (Any -> Any -> Any -> Any -> Any -> Any)
-> Any
-> Any
-> Any
-> Any
-> Any
-> Any
forall a b. a -> b
coe
         T_IsPreorder_70
-> (Any -> Any -> Any -> Any -> Any -> Any)
-> Any
-> Any
-> Any
-> T__IsRelatedTo__70
-> Any
-> T__IsRelatedTo__70
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_step'45''8804'_228
         (T_IsPreorder_70 -> Any
forall a b. a -> b
coe T_IsPreorder_70
MAlonzo.Code.Data.Nat.Properties.d_'8804''45'isPreorder_1684)
         (\ Any
v2 Any
v3 Any
v4 Any
v5 Any
v6 ->
            (T__'8804'__18 -> T__'8804'__18 -> T__'8804'__18)
-> Any -> Any -> Any
forall a b. a -> b
coe
              T__'8804'__18 -> T__'8804'__18 -> T__'8804'__18
MAlonzo.Code.Data.Nat.Properties.du_'60''45'trans'691'_1868 Any
v5 Any
v6)
         ((Integer -> Integer) -> Any -> Any
forall a b. a -> b
coe
            Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d_'8739'_'8739'_18
            ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe
               Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'45'__260 (Integer -> Any
forall a b. a -> b
coe Integer
v0) (Integer -> Any
forall a b. a -> b
coe Integer
v1)))
         ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe
            Integer -> Integer -> Integer
addInt
            ((Integer -> Integer) -> Any -> Any
forall a b. a -> b
coe
               Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d_'8739'_'8739'_18
               ((Integer -> Integer) -> Any -> Any
forall a b. a -> b
coe Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d_'45'__218 (Integer -> Any
forall a b. a -> b
coe Integer
v1)))
            ((Integer -> Integer) -> Any -> Any
forall a b. a -> b
coe Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d_'8739'_'8739'_18 (Integer -> Any
forall a b. a -> b
coe Integer
v0)))
         ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe
            Integer -> Integer -> Integer
addInt
            ((Integer -> Integer) -> Any -> Any
forall a b. a -> b
coe Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d_'8739'_'8739'_18 (Integer -> Any
forall a b. a -> b
coe Integer
v0))
            ((Integer -> Integer) -> Any -> Any
forall a b. a -> b
coe Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d_'8739'_'8739'_18 (Integer -> Any
forall a b. a -> b
coe Integer
v1)))
         ((T_IsPreorder_70 -> Any -> T__IsRelatedTo__70) -> Any -> Any -> Any
forall a b. a -> b
coe
            T_IsPreorder_70 -> Any -> T__IsRelatedTo__70
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du__'8718'_346
            (T_IsPreorder_70 -> Any
forall a b. a -> b
coe T_IsPreorder_70
MAlonzo.Code.Data.Nat.Properties.d_'8804''45'isPreorder_1684)
            ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe
               Integer -> Integer -> Integer
addInt
               ((Integer -> Integer) -> Any -> Any
forall a b. a -> b
coe Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d_'8739'_'8739'_18 (Integer -> Any
forall a b. a -> b
coe Integer
v0))
               ((Integer -> Integer) -> Any -> Any
forall a b. a -> b
coe Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d_'8739'_'8739'_18 (Integer -> Any
forall a b. a -> b
coe Integer
v1))))
         ((Integer -> Integer -> T__'8804'__18) -> Any -> Any -> Any
forall a b. a -> b
coe
            Integer -> Integer -> T__'8804'__18
d_'8739'm'43'n'8739''8804''8739'm'8739''43''8739'n'8739'_2252
            (Integer -> Any
forall a b. a -> b
coe Integer
v0)
            ((Integer -> Integer) -> Any -> Any
forall a b. a -> b
coe Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d_'45'__218 (Integer -> Any
forall a b. a -> b
coe Integer
v1))))
-- Data.Integer.Properties.◃-inverse
d_'9667''45'inverse_2304 ::
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'9667''45'inverse_2304 :: Integer -> T__'8801'__12
d_'9667''45'inverse_2304 = Integer -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.◃-cong
d_'9667''45'cong_2314 ::
  Integer ->
  Integer ->
  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_'9667''45'cong_2314 :: Integer
-> Integer -> T__'8801'__12 -> T__'8801'__12 -> T__'8801'__12
d_'9667''45'cong_2314 = Integer
-> Integer -> T__'8801'__12 -> T__'8801'__12 -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.+◃n≡+n
d_'43''9667'n'8801''43'n_2330 ::
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'43''9667'n'8801''43'n_2330 :: Integer -> T__'8801'__12
d_'43''9667'n'8801''43'n_2330 = Integer -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.-◃n≡-n
d_'45''9667'n'8801''45'n_2334 ::
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'45''9667'n'8801''45'n_2334 :: Integer -> T__'8801'__12
d_'45''9667'n'8801''45'n_2334 = Integer -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.sign-◃
d_sign'45''9667'_2340 ::
  MAlonzo.Code.Data.Sign.Base.T_Sign_6 ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_sign'45''9667'_2340 :: T_Sign_6 -> Integer -> T__'8801'__12
d_sign'45''9667'_2340 = T_Sign_6 -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.abs-◃
d_abs'45''9667'_2346 ::
  MAlonzo.Code.Data.Sign.Base.T_Sign_6 ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_abs'45''9667'_2346 :: T_Sign_6 -> Integer -> T__'8801'__12
d_abs'45''9667'_2346 = T_Sign_6 -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.signₙ◃∣n∣≡n
d_sign'8345''9667''8739'n'8739''8801'n_2354 ::
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_sign'8345''9667''8739'n'8739''8801'n_2354 :: Integer -> T__'8801'__12
d_sign'8345''9667''8739'n'8739''8801'n_2354 = Integer -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.sign-cong
d_sign'45'cong_2368 ::
  MAlonzo.Code.Data.Sign.Base.T_Sign_6 ->
  MAlonzo.Code.Data.Sign.Base.T_Sign_6 ->
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_sign'45'cong_2368 :: T_Sign_6
-> T_Sign_6 -> Integer -> Integer -> T__'8801'__12 -> T__'8801'__12
d_sign'45'cong_2368 = T_Sign_6
-> T_Sign_6 -> Integer -> Integer -> T__'8801'__12 -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.abs-cong
d_abs'45'cong_2392 ::
  MAlonzo.Code.Data.Sign.Base.T_Sign_6 ->
  MAlonzo.Code.Data.Sign.Base.T_Sign_6 ->
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_abs'45'cong_2392 :: T_Sign_6
-> T_Sign_6 -> Integer -> Integer -> T__'8801'__12 -> T__'8801'__12
d_abs'45'cong_2392 = T_Sign_6
-> T_Sign_6 -> Integer -> Integer -> T__'8801'__12 -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.∣s◃m∣*∣t◃n∣≡m*n
d_'8739's'9667'm'8739''42''8739't'9667'n'8739''8801'm'42'n_2416 ::
  MAlonzo.Code.Data.Sign.Base.T_Sign_6 ->
  MAlonzo.Code.Data.Sign.Base.T_Sign_6 ->
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8739's'9667'm'8739''42''8739't'9667'n'8739''8801'm'42'n_2416 :: T_Sign_6 -> T_Sign_6 -> Integer -> Integer -> T__'8801'__12
d_'8739's'9667'm'8739''42''8739't'9667'n'8739''8801'm'42'n_2416
  = T_Sign_6 -> T_Sign_6 -> Integer -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.◃-≡
d_'9667''45''8801'_2430 ::
  Integer ->
  Integer ->
  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_'9667''45''8801'_2430 :: Integer
-> Integer -> T__'8801'__12 -> T__'8801'__12 -> T__'8801'__12
d_'9667''45''8801'_2430 = Integer
-> Integer -> T__'8801'__12 -> T__'8801'__12 -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.+◃-mono-<
d_'43''9667''45'mono'45''60'_2448 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__18 ->
  MAlonzo.Code.Data.Integer.Base.T__'60'__50
d_'43''9667''45'mono'45''60'_2448 :: Integer -> Integer -> T__'8804'__18 -> T__'60'__50
d_'43''9667''45'mono'45''60'_2448 Integer
v0 ~Integer
v1 T__'8804'__18
v2
  = Integer -> T__'8804'__18 -> T__'60'__50
du_'43''9667''45'mono'45''60'_2448 Integer
v0 T__'8804'__18
v2
du_'43''9667''45'mono'45''60'_2448 ::
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__18 ->
  MAlonzo.Code.Data.Integer.Base.T__'60'__50
du_'43''9667''45'mono'45''60'_2448 :: Integer -> T__'8804'__18 -> T__'60'__50
du_'43''9667''45'mono'45''60'_2448 Integer
v0 T__'8804'__18
v1
  = (Any -> Any -> Any) -> Any -> Any -> T__'60'__50
forall a b. a -> b
coe
      Any -> Any -> Any
forall a b. a -> b -> b
seq (Integer -> Any
forall a b. a -> b
coe Integer
v0)
      ((T__'8804'__18 -> T__'60'__50) -> T__'8804'__18 -> Any
forall a b. a -> b
coe T__'8804'__18 -> T__'60'__50
MAlonzo.Code.Data.Integer.Base.C_'43''60''43'_72 T__'8804'__18
v1)
-- Data.Integer.Properties.+◃-cancel-<
d_'43''9667''45'cancel'45''60'_2464 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Integer.Base.T__'60'__50 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__18
d_'43''9667''45'cancel'45''60'_2464 :: Integer -> Integer -> T__'60'__50 -> T__'8804'__18
d_'43''9667''45'cancel'45''60'_2464 Integer
v0 ~Integer
v1 T__'60'__50
v2
  = Integer -> T__'60'__50 -> T__'8804'__18
du_'43''9667''45'cancel'45''60'_2464 Integer
v0 T__'60'__50
v2
du_'43''9667''45'cancel'45''60'_2464 ::
  Integer ->
  MAlonzo.Code.Data.Integer.Base.T__'60'__50 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__18
du_'43''9667''45'cancel'45''60'_2464 :: Integer -> T__'60'__50 -> T__'8804'__18
du_'43''9667''45'cancel'45''60'_2464 Integer
v0 T__'60'__50
v1
  = (Any -> Any -> Any) -> Any -> Any -> T__'8804'__18
forall a b. a -> b
coe
      Any -> Any -> Any
forall a b. a -> b -> b
seq (Integer -> Any
forall a b. a -> b
coe Integer
v0)
      (case T__'60'__50 -> T__'60'__50
forall a b. a -> b
coe T__'60'__50
v1 of
         MAlonzo.Code.Data.Integer.Base.C_'43''60''43'_72 T__'8804'__18
v4 -> T__'8804'__18 -> Any
forall a b. a -> b
coe T__'8804'__18
v4
         T__'60'__50
_ -> Any
forall a. a
MAlonzo.RTE.mazUnreachableError)
-- Data.Integer.Properties.neg◃-cancel-<
d_neg'9667''45'cancel'45''60'_2482 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Integer.Base.T__'60'__50 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__18
d_neg'9667''45'cancel'45''60'_2482 :: Integer -> Integer -> T__'60'__50 -> T__'8804'__18
d_neg'9667''45'cancel'45''60'_2482 ~Integer
v0 Integer
v1 T__'60'__50
v2
  = Integer -> T__'60'__50 -> T__'8804'__18
du_neg'9667''45'cancel'45''60'_2482 Integer
v1 T__'60'__50
v2
du_neg'9667''45'cancel'45''60'_2482 ::
  Integer ->
  MAlonzo.Code.Data.Integer.Base.T__'60'__50 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__18
du_neg'9667''45'cancel'45''60'_2482 :: Integer -> T__'60'__50 -> T__'8804'__18
du_neg'9667''45'cancel'45''60'_2482 Integer
v0 T__'60'__50
v1
  = case Integer -> Integer
forall a b. a -> b
coe Integer
v0 of
      Integer
0 -> (Any -> Any -> Any) -> Any -> Any -> T__'8804'__18
forall a b. a -> b
coe
             Any -> Any -> Any
forall a b. a -> b -> b
seq (T__'60'__50 -> Any
forall a b. a -> b
coe T__'60'__50
v1)
             ((T__'8804'__18 -> T__'8804'__18) -> Any -> Any
forall a b. a -> b
coe
                T__'8804'__18 -> T__'8804'__18
MAlonzo.Code.Data.Nat.Base.C_s'8804's_30
                (T__'8804'__18 -> Any
forall a b. a -> b
coe T__'8804'__18
MAlonzo.Code.Data.Nat.Base.C_z'8804'n_22))
      Integer
_ -> case T__'60'__50 -> T__'60'__50
forall a b. a -> b
coe T__'60'__50
v1 of
             MAlonzo.Code.Data.Integer.Base.C_'45''60''45'_58 T__'8804'__18
v4
               -> (T__'8804'__18 -> T__'8804'__18) -> T__'8804'__18 -> T__'8804'__18
forall a b. a -> b
coe T__'8804'__18 -> T__'8804'__18
MAlonzo.Code.Data.Nat.Base.C_s'8804's_30 T__'8804'__18
v4
             T__'60'__50
_ -> T__'8804'__18
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Data.Integer.Properties.-◃<+◃
d_'45''9667''60''43''9667'_2498 ::
  Integer -> Integer -> MAlonzo.Code.Data.Integer.Base.T__'60'__50
d_'45''9667''60''43''9667'_2498 :: Integer -> Integer -> T__'60'__50
d_'45''9667''60''43''9667'_2498 ~Integer
v0 Integer
v1
  = Integer -> T__'60'__50
du_'45''9667''60''43''9667'_2498 Integer
v1
du_'45''9667''60''43''9667'_2498 ::
  Integer -> MAlonzo.Code.Data.Integer.Base.T__'60'__50
du_'45''9667''60''43''9667'_2498 :: Integer -> T__'60'__50
du_'45''9667''60''43''9667'_2498 Integer
v0
  = (Any -> Any -> Any) -> Any -> Any -> T__'60'__50
forall a b. a -> b
coe
      Any -> Any -> Any
forall a b. a -> b -> b
seq (Integer -> Any
forall a b. a -> b
coe Integer
v0) (T__'60'__50 -> Any
forall a b. a -> b
coe T__'60'__50
MAlonzo.Code.Data.Integer.Base.C_'45''60''43'_64)
-- Data.Integer.Properties.+◃≮-◃
d_'43''9667''8814''45''9667'_2510 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Integer.Base.T__'60'__50 ->
  MAlonzo.Code.Data.Empty.T_'8869'_4
d_'43''9667''8814''45''9667'_2510 :: Integer -> Integer -> T__'60'__50 -> T_'8869'_4
d_'43''9667''8814''45''9667'_2510 = Integer -> Integer -> T__'60'__50 -> T_'8869'_4
forall a. a
erased
-- Data.Integer.Properties.n⊖n≡0
d_n'8854'n'8801'0_2516 ::
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_n'8854'n'8801'0_2516 :: Integer -> T__'8801'__12
d_n'8854'n'8801'0_2516 = Integer -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.[1+m]⊖[1+n]≡m⊖n
d_'91'1'43'm'93''8854''91'1'43'n'93''8801'm'8854'n_2532 ::
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'91'1'43'm'93''8854''91'1'43'n'93''8801'm'8854'n_2532 :: Integer -> Integer -> T__'8801'__12
d_'91'1'43'm'93''8854''91'1'43'n'93''8801'm'8854'n_2532 = Integer -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.⊖-swap
d_'8854''45'swap_2554 ::
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8854''45'swap_2554 :: Integer -> Integer -> T__'8801'__12
d_'8854''45'swap_2554 = Integer -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.⊖-≥
d_'8854''45''8805'_2572 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__18 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8854''45''8805'_2572 :: Integer -> Integer -> T__'8804'__18 -> T__'8801'__12
d_'8854''45''8805'_2572 = Integer -> Integer -> T__'8804'__18 -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.⊖-≤
d_'8854''45''8804'_2604 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__18 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8854''45''8804'_2604 :: Integer -> Integer -> T__'8804'__18 -> T__'8801'__12
d_'8854''45''8804'_2604 = Integer -> Integer -> T__'8804'__18 -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.⊖-<
d_'8854''45''60'_2644 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__18 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8854''45''60'_2644 :: Integer -> Integer -> T__'8804'__18 -> T__'8801'__12
d_'8854''45''60'_2644 = Integer -> Integer -> T__'8804'__18 -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.⊖-≰
d_'8854''45''8816'_2650 ::
  Integer ->
  Integer ->
  (MAlonzo.Code.Data.Nat.Base.T__'8804'__18 ->
   MAlonzo.Code.Data.Empty.T_'8869'_4) ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8854''45''8816'_2650 :: Integer
-> Integer -> (T__'8804'__18 -> T_'8869'_4) -> T__'8801'__12
d_'8854''45''8816'_2650 = Integer
-> Integer -> (T__'8804'__18 -> T_'8869'_4) -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.∣⊖∣-<
d_'8739''8854''8739''45''60'_2656 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__18 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8739''8854''8739''45''60'_2656 :: Integer -> Integer -> T__'8804'__18 -> T__'8801'__12
d_'8739''8854''8739''45''60'_2656 = Integer -> Integer -> T__'8804'__18 -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.∣⊖∣-≰
d_'8739''8854''8739''45''8816'_2672 ::
  Integer ->
  Integer ->
  (MAlonzo.Code.Data.Nat.Base.T__'8804'__18 ->
   MAlonzo.Code.Data.Empty.T_'8869'_4) ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8739''8854''8739''45''8816'_2672 :: Integer
-> Integer -> (T__'8804'__18 -> T_'8869'_4) -> T__'8801'__12
d_'8739''8854''8739''45''8816'_2672 = Integer
-> Integer -> (T__'8804'__18 -> T_'8869'_4) -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.-m+n≡n⊖m
d_'45'm'43'n'8801'n'8854'm_2678 ::
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'45'm'43'n'8801'n'8854'm_2678 :: Integer -> Integer -> T__'8801'__12
d_'45'm'43'n'8801'n'8854'm_2678 = Integer -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.m-n≡m⊖n
d_m'45'n'8801'm'8854'n_2690 ::
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_m'45'n'8801'm'8854'n_2690 :: Integer -> Integer -> T__'8801'__12
d_m'45'n'8801'm'8854'n_2690 = Integer -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.-[n⊖m]≡-m+n
d_'45''91'n'8854'm'93''8801''45'm'43'n_2704 ::
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'45''91'n'8854'm'93''8801''45'm'43'n_2704 :: Integer -> Integer -> T__'8801'__12
d_'45''91'n'8854'm'93''8801''45'm'43'n_2704 = Integer -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.∣m⊖n∣≡∣n⊖m∣
d_'8739'm'8854'n'8739''8801''8739'n'8854'm'8739'_2738 ::
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8739'm'8854'n'8739''8801''8739'n'8854'm'8739'_2738 :: Integer -> Integer -> T__'8801'__12
d_'8739'm'8854'n'8739''8801''8739'n'8854'm'8739'_2738 = Integer -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.+-cancelˡ-⊖
d_'43''45'cancel'737''45''8854'_2754 ::
  Integer ->
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'43''45'cancel'737''45''8854'_2754 :: Integer -> Integer -> Integer -> T__'8801'__12
d_'43''45'cancel'737''45''8854'_2754 = Integer -> Integer -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.m⊖n≤m
d_m'8854'n'8804'm_2774 ::
  Integer -> Integer -> MAlonzo.Code.Data.Integer.Base.T__'8804'__26
d_m'8854'n'8804'm_2774 :: Integer -> Integer -> T__'8804'__26
d_m'8854'n'8804'm_2774 Integer
v0 Integer
v1
  = case Integer -> Integer
forall a b. a -> b
coe Integer
v1 of
      Integer
0 -> (Integer -> T__'8804'__26) -> Any -> T__'8804'__26
forall a b. a -> b
coe
             Integer -> T__'8804'__26
d_'8804''45'refl_1584
             ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe
                Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'8854'__224 (Integer -> Any
forall a b. a -> b
coe Integer
v0)
                (Integer -> Any
forall a b. a -> b
coe (Integer
0 :: Integer)))
      Integer
_ -> let v2 :: Integer
v2 = Integer -> Integer -> Integer
subInt (Integer -> Integer
forall a b. a -> b
coe Integer
v1) (Integer -> Integer
forall a b. a -> b
coe (Integer
1 :: Integer)) in
           Any -> T__'8804'__26
forall a b. a -> b
coe
             (case Integer -> Integer
forall a b. a -> b
coe Integer
v0 of
                Integer
0 -> T__'8804'__26 -> Any
forall a b. a -> b
coe T__'8804'__26
MAlonzo.Code.Data.Integer.Base.C_'45''8804''43'_40
                Integer
_ -> let v3 :: Integer
v3 = Integer -> Integer -> Integer
subInt (Integer -> Integer
forall a b. a -> b
coe Integer
v0) (Integer -> Integer
forall a b. a -> b
coe (Integer
1 :: Integer)) in
                     Any -> Any
forall a b. a -> b
coe
                       ((T_IsPreorder_70
 -> (Any -> Any -> Any -> Any)
 -> Any
 -> Any
 -> T__IsRelatedTo__70
 -> Any)
-> Any -> Any -> Any -> Any -> Any -> Any
forall a b. a -> b
coe
                          T_IsPreorder_70
-> (Any -> Any -> Any -> Any)
-> Any
-> Any
-> T__IsRelatedTo__70
-> Any
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_begin__160
                          (T_IsPreorder_70 -> Any
forall a b. a -> b
coe T_IsPreorder_70
d_'8804''45'isPreorder_1656) ((Integer -> Integer -> T__'60'__50 -> T__'8804'__26) -> Any
forall a b. a -> b
coe Integer -> Integer -> T__'60'__50 -> T__'8804'__26
d_'60''8658''8804'_1724)
                          ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe
                             Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'8854'__224 (Integer -> Any
forall a b. a -> b
coe Integer
v0) (Integer -> Any
forall a b. a -> b
coe Integer
v1))
                          (Integer -> Any
forall a b. a -> b
coe Integer
v0)
                          ((T_IsPreorder_70
 -> (Any -> Any -> Any -> Any -> Any -> Any)
 -> Any
 -> Any
 -> Any
 -> T__IsRelatedTo__70
 -> Any
 -> T__IsRelatedTo__70)
-> Any
-> (Any -> Any -> Any -> Any -> Any -> Any)
-> Any
-> Any
-> Any
-> Any
-> Any
-> Any
forall a b. a -> b
coe
                             T_IsPreorder_70
-> (Any -> Any -> Any -> Any -> Any -> Any)
-> Any
-> Any
-> Any
-> T__IsRelatedTo__70
-> Any
-> T__IsRelatedTo__70
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_step'45''8804'_228
                             (T_IsPreorder_70 -> Any
forall a b. a -> b
coe T_IsPreorder_70
d_'8804''45'isPreorder_1656)
                             (\ Any
v4 Any
v5 Any
v6 Any
v7 Any
v8 -> (T__'8804'__26 -> T__'60'__50 -> T__'60'__50) -> Any -> Any -> Any
forall a b. a -> b
coe T__'8804'__26 -> T__'60'__50 -> T__'60'__50
du_'8804''45''60''45'trans_1844 Any
v7 Any
v8)
                             ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe
                                Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'8854'__224 (Integer -> Any
forall a b. a -> b
coe Integer
v3) (Integer -> Any
forall a b. a -> b
coe Integer
v2))
                             (Integer -> Any
forall a b. a -> b
coe Integer
v3) (Integer -> Any
forall a b. a -> b
coe Integer
v0)
                             ((T_IsPreorder_70
 -> (Any -> Any -> Any -> Any -> Any -> Any)
 -> Any
 -> Any
 -> Any
 -> T__IsRelatedTo__70
 -> Any
 -> T__IsRelatedTo__70)
-> Any
-> (Any -> Any -> Any -> Any -> Any -> Any)
-> Any
-> Any
-> Any
-> Any
-> Any
-> Any
forall a b. a -> b
coe
                                T_IsPreorder_70
-> (Any -> Any -> Any -> Any -> Any -> Any)
-> Any
-> Any
-> Any
-> T__IsRelatedTo__70
-> Any
-> T__IsRelatedTo__70
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_step'45''8804'_228
                                (T_IsPreorder_70 -> Any
forall a b. a -> b
coe T_IsPreorder_70
d_'8804''45'isPreorder_1656)
                                (\ Any
v4 Any
v5 Any
v6 Any
v7 Any
v8 -> (T__'8804'__26 -> T__'60'__50 -> T__'60'__50) -> Any -> Any -> Any
forall a b. a -> b
coe T__'8804'__26 -> T__'60'__50 -> T__'60'__50
du_'8804''45''60''45'trans_1844 Any
v7 Any
v8)
                                (Integer -> Any
forall a b. a -> b
coe Integer
v3) (Integer -> Any
forall a b. a -> b
coe Integer
v0) (Integer -> Any
forall a b. a -> b
coe Integer
v0)
                                ((T_IsPreorder_70 -> Any -> T__IsRelatedTo__70) -> Any -> Any -> Any
forall a b. a -> b
coe
                                   T_IsPreorder_70 -> Any -> T__IsRelatedTo__70
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du__'8718'_346
                                   (T_IsPreorder_70 -> Any
forall a b. a -> b
coe T_IsPreorder_70
d_'8804''45'isPreorder_1656) (Integer -> Any
forall a b. a -> b
coe Integer
v0))
                                ((T__'8804'__18 -> T__'8804'__26) -> T__'8804'__18 -> Any
forall a b. a -> b
coe
                                   T__'8804'__18 -> T__'8804'__26
MAlonzo.Code.Data.Integer.Base.C_'43''8804''43'_48
                                   (Integer -> T__'8804'__18
MAlonzo.Code.Data.Nat.Properties.d_n'8804'1'43'n_1724
                                      (Integer -> Integer
forall a b. a -> b
coe Integer
v3))))
                             ((Integer -> Integer -> T__'8804'__26) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> T__'8804'__26
d_m'8854'n'8804'm_2774 (Integer -> Any
forall a b. a -> b
coe Integer
v3) (Integer -> Any
forall a b. a -> b
coe Integer
v2)))))
-- Data.Integer.Properties.m⊖n<1+m
d_m'8854'n'60'1'43'm_2792 ::
  Integer -> Integer -> MAlonzo.Code.Data.Integer.Base.T__'60'__50
d_m'8854'n'60'1'43'm_2792 :: Integer -> Integer -> T__'60'__50
d_m'8854'n'60'1'43'm_2792 Integer
v0 Integer
v1
  = (T__'8804'__26 -> T__'60'__50 -> T__'60'__50)
-> Any -> Any -> T__'60'__50
forall a b. a -> b
coe
      T__'8804'__26 -> T__'60'__50 -> T__'60'__50
du_'8804''45''60''45'trans_1844
      ((Integer -> Integer -> T__'8804'__26) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> T__'8804'__26
d_m'8854'n'8804'm_2774 (Integer -> Any
forall a b. a -> b
coe Integer
v0) (Integer -> Any
forall a b. a -> b
coe Integer
v1))
      ((T__'8804'__18 -> T__'60'__50) -> Any -> Any
forall a b. a -> b
coe
         T__'8804'__18 -> T__'60'__50
MAlonzo.Code.Data.Integer.Base.C_'43''60''43'_72
         ((Integer -> T__'8804'__18 -> T__'8804'__18) -> Any -> Any -> Any
forall a b. a -> b
coe
            Integer -> T__'8804'__18 -> T__'8804'__18
MAlonzo.Code.Data.Nat.Properties.du_m'60'n'43'm_2498 (Integer -> Any
forall a b. a -> b
coe Integer
v0)
            ((T__'8804'__18 -> T__'8804'__18) -> Any -> Any
forall a b. a -> b
coe
               T__'8804'__18 -> T__'8804'__18
MAlonzo.Code.Data.Nat.Base.C_s'8804's_30
               (T__'8804'__18 -> Any
forall a b. a -> b
coe T__'8804'__18
MAlonzo.Code.Data.Nat.Base.C_z'8804'n_22))))
-- Data.Integer.Properties.m⊖1+n<m
d_m'8854'1'43'n'60'm_2802 ::
  Integer -> Integer -> MAlonzo.Code.Data.Integer.Base.T__'60'__50
d_m'8854'1'43'n'60'm_2802 :: Integer -> Integer -> T__'60'__50
d_m'8854'1'43'n'60'm_2802 Integer
v0 Integer
v1
  = case Integer -> Integer
forall a b. a -> b
coe Integer
v0 of
      Integer
0 -> T__'60'__50 -> T__'60'__50
forall a b. a -> b
coe T__'60'__50
MAlonzo.Code.Data.Integer.Base.C_'45''60''43'_64
      Integer
_ -> let v2 :: Integer
v2 = Integer -> Integer -> Integer
subInt (Integer -> Integer
forall a b. a -> b
coe Integer
v0) (Integer -> Integer
forall a b. a -> b
coe (Integer
1 :: Integer)) in
           Any -> T__'60'__50
forall a b. a -> b
coe
             ((T__IsRelatedTo__70 -> Any) -> Any -> Any
forall a b. a -> b
coe
                T__IsRelatedTo__70 -> Any
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_begin'45'strict__176
                (((Any -> Any -> Any -> Any -> Any -> Any)
 -> T_Σ_14
 -> (Any -> Any -> Any -> Any -> Any -> Any)
 -> Any
 -> Any
 -> Any
 -> T__IsRelatedTo__70
 -> Any
 -> T__IsRelatedTo__70)
-> (Any -> Any -> Any -> Any -> Any -> Any)
-> Any
-> (Any -> Any -> Any -> Any -> Any -> Any)
-> Any
-> Any
-> Any
-> Any
-> Any
-> Any
forall a b. a -> b
coe
                   (Any -> Any -> Any -> Any -> Any -> Any)
-> T_Σ_14
-> (Any -> Any -> Any -> Any -> Any -> Any)
-> Any
-> Any
-> Any
-> T__IsRelatedTo__70
-> Any
-> T__IsRelatedTo__70
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_step'45''60'_202
                   (\ Any
v3 Any
v4 Any
v5 Any
v6 Any
v7 -> (Integer -> Integer -> T__'60'__50 -> T__'60'__50 -> T__'60'__50)
-> Any -> Any -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> T__'60'__50 -> T__'60'__50 -> T__'60'__50
du_'60''45'trans_1872 Any
v3 Any
v4 Any
v6 Any
v7)
                   (T_Σ_14 -> Any
forall a b. a -> b
coe
                      T_Σ_14
MAlonzo.Code.Relation.Binary.PropositionalEquality.Core.du_resp'8322'_144)
                   (\ Any
v3 Any
v4 Any
v5 Any
v6 Any
v7 -> (T__'60'__50 -> T__'8804'__26 -> T__'60'__50) -> Any -> Any -> Any
forall a b. a -> b
coe T__'60'__50 -> T__'8804'__26 -> T__'60'__50
du_'60''45''8804''45'trans_1858 Any
v6 Any
v7)
                   ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe
                      Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'8854'__224 (Integer -> Any
forall a b. a -> b
coe Integer
v2) (Integer -> Any
forall a b. a -> b
coe Integer
v1))
                   (Integer -> Any
forall a b. a -> b
coe Integer
v0) (Integer -> Any
forall a b. a -> b
coe Integer
v0)
                   ((T_IsPreorder_70 -> Any -> T__IsRelatedTo__70) -> Any -> Any -> Any
forall a b. a -> b
coe
                      T_IsPreorder_70 -> Any -> T__IsRelatedTo__70
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du__'8718'_346
                      (T_IsPreorder_70 -> Any
forall a b. a -> b
coe T_IsPreorder_70
d_'8804''45'isPreorder_1656) (Integer -> Any
forall a b. a -> b
coe Integer
v0))
                   ((Integer -> Integer -> T__'60'__50) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> T__'60'__50
d_m'8854'n'60'1'43'm_2792 (Integer -> Any
forall a b. a -> b
coe Integer
v2) (Integer -> Any
forall a b. a -> b
coe Integer
v1))))
-- Data.Integer.Properties.-1+m<n⊖m
d_'45'1'43'm'60'n'8854'm_2818 ::
  Integer -> Integer -> MAlonzo.Code.Data.Integer.Base.T__'60'__50
d_'45'1'43'm'60'n'8854'm_2818 :: Integer -> Integer -> T__'60'__50
d_'45'1'43'm'60'n'8854'm_2818 Integer
v0 Integer
v1
  = case Integer -> Integer
forall a b. a -> b
coe Integer
v0 of
      Integer
0 -> T__'60'__50 -> T__'60'__50
forall a b. a -> b
coe T__'60'__50
MAlonzo.Code.Data.Integer.Base.C_'45''60''43'_64
      Integer
_ -> let v2 :: Integer
v2 = Integer -> Integer -> Integer
subInt (Integer -> Integer
forall a b. a -> b
coe Integer
v0) (Integer -> Integer
forall a b. a -> b
coe (Integer
1 :: Integer)) in
           Any -> T__'60'__50
forall a b. a -> b
coe
             (case Integer -> Integer
forall a b. a -> b
coe Integer
v1 of
                Integer
0 -> (T__'8804'__18 -> T__'60'__50) -> T__'8804'__18 -> Any
forall a b. a -> b
coe
                       T__'8804'__18 -> T__'60'__50
MAlonzo.Code.Data.Integer.Base.C_'45''60''45'_58
                       (Integer -> T__'8804'__18
MAlonzo.Code.Data.Nat.Properties.d_'8804''45'refl_1634 (Integer -> Integer
forall a b. a -> b
coe Integer
v0))
                Integer
_ -> let v3 :: Integer
v3 = Integer -> Integer -> Integer
subInt (Integer -> Integer
forall a b. a -> b
coe Integer
v1) (Integer -> Integer
forall a b. a -> b
coe (Integer
1 :: Integer)) in
                     Any -> Any
forall a b. a -> b
coe
                       ((T__IsRelatedTo__70 -> Any) -> Any -> Any
forall a b. a -> b
coe
                          T__IsRelatedTo__70 -> Any
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_begin'45'strict__176
                          (((Any -> Any -> Any -> Any -> Any -> Any)
 -> T_Σ_14
 -> (Any -> Any -> Any -> Any -> Any -> Any)
 -> Any
 -> Any
 -> Any
 -> T__IsRelatedTo__70
 -> Any
 -> T__IsRelatedTo__70)
-> (Any -> Any -> Any -> Any -> Any -> Any)
-> Any
-> (Any -> Any -> Any -> Any -> Any -> Any)
-> Any
-> Any
-> Any
-> Any
-> Any
-> Any
forall a b. a -> b
coe
                             (Any -> Any -> Any -> Any -> Any -> Any)
-> T_Σ_14
-> (Any -> Any -> Any -> Any -> Any -> Any)
-> Any
-> Any
-> Any
-> T__IsRelatedTo__70
-> Any
-> T__IsRelatedTo__70
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_step'45''60'_202
                             (\ Any
v4 Any
v5 Any
v6 Any
v7 Any
v8 -> (Integer -> Integer -> T__'60'__50 -> T__'60'__50 -> T__'60'__50)
-> Any -> Any -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> T__'60'__50 -> T__'60'__50 -> T__'60'__50
du_'60''45'trans_1872 Any
v4 Any
v5 Any
v7 Any
v8)
                             (T_Σ_14 -> Any
forall a b. a -> b
coe
                                T_Σ_14
MAlonzo.Code.Relation.Binary.PropositionalEquality.Core.du_resp'8322'_144)
                             (\ Any
v4 Any
v5 Any
v6 Any
v7 Any
v8 -> (T__'60'__50 -> T__'8804'__26 -> T__'60'__50) -> Any -> Any -> Any
forall a b. a -> b
coe T__'60'__50 -> T__'8804'__26 -> T__'60'__50
du_'60''45''8804''45'trans_1858 Any
v7 Any
v8)
                             ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> Integer
subInt (Integer -> Any
forall a b. a -> b
coe (-Integer
1 :: Integer)) (Integer -> Any
forall a b. a -> b
coe Integer
v0))
                             ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> Integer
subInt (Integer -> Any
forall a b. a -> b
coe (Integer
0 :: Integer)) (Integer -> Any
forall a b. a -> b
coe Integer
v0))
                             ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe
                                Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'8854'__224 (Integer -> Any
forall a b. a -> b
coe Integer
v1) (Integer -> Any
forall a b. a -> b
coe Integer
v0))
                             (((Any -> Any -> Any -> Any -> Any -> Any)
 -> T_Σ_14
 -> (Any -> Any -> Any -> Any -> Any -> Any)
 -> Any
 -> Any
 -> Any
 -> T__IsRelatedTo__70
 -> Any
 -> T__IsRelatedTo__70)
-> (Any -> Any -> Any -> Any -> Any -> Any)
-> Any
-> (Any -> Any -> Any -> Any -> Any -> Any)
-> Any
-> Any
-> Any
-> Any
-> Any
-> Any
forall a b. a -> b
coe
                                (Any -> Any -> Any -> Any -> Any -> Any)
-> T_Σ_14
-> (Any -> Any -> Any -> Any -> Any -> Any)
-> Any
-> Any
-> Any
-> T__IsRelatedTo__70
-> Any
-> T__IsRelatedTo__70
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_step'45''60'_202
                                (\ Any
v4 Any
v5 Any
v6 Any
v7 Any
v8 -> (Integer -> Integer -> T__'60'__50 -> T__'60'__50 -> T__'60'__50)
-> Any -> Any -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> T__'60'__50 -> T__'60'__50 -> T__'60'__50
du_'60''45'trans_1872 Any
v4 Any
v5 Any
v7 Any
v8)
                                (T_Σ_14 -> Any
forall a b. a -> b
coe
                                   T_Σ_14
MAlonzo.Code.Relation.Binary.PropositionalEquality.Core.du_resp'8322'_144)
                                (\ Any
v4 Any
v5 Any
v6 Any
v7 Any
v8 -> (T__'60'__50 -> T__'8804'__26 -> T__'60'__50) -> Any -> Any -> Any
forall a b. a -> b
coe T__'60'__50 -> T__'8804'__26 -> T__'60'__50
du_'60''45''8804''45'trans_1858 Any
v7 Any
v8)
                                ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> Integer
subInt (Integer -> Any
forall a b. a -> b
coe (Integer
0 :: Integer)) (Integer -> Any
forall a b. a -> b
coe Integer
v0))
                                ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe
                                   Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'8854'__224 (Integer -> Any
forall a b. a -> b
coe Integer
v3) (Integer -> Any
forall a b. a -> b
coe Integer
v2))
                                ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe
                                   Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'8854'__224 (Integer -> Any
forall a b. a -> b
coe Integer
v1) (Integer -> Any
forall a b. a -> b
coe Integer
v0))
                                ((T_IsPreorder_70 -> Any -> T__IsRelatedTo__70) -> Any -> Any -> Any
forall a b. a -> b
coe
                                   T_IsPreorder_70 -> Any -> T__IsRelatedTo__70
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du__'8718'_346
                                   (T_IsPreorder_70 -> Any
forall a b. a -> b
coe T_IsPreorder_70
d_'8804''45'isPreorder_1656)
                                   ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe
                                      Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'8854'__224 (Integer -> Any
forall a b. a -> b
coe Integer
v1)
                                      (Integer -> Any
forall a b. a -> b
coe Integer
v0)))
                                ((Integer -> Integer -> T__'60'__50) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> T__'60'__50
d_'45'1'43'm'60'n'8854'm_2818 (Integer -> Any
forall a b. a -> b
coe Integer
v2) (Integer -> Any
forall a b. a -> b
coe Integer
v3)))
                             ((T__'8804'__18 -> T__'60'__50) -> T__'8804'__18 -> Any
forall a b. a -> b
coe
                                T__'8804'__18 -> T__'60'__50
MAlonzo.Code.Data.Integer.Base.C_'45''60''45'_58
                                (Integer -> T__'8804'__18
MAlonzo.Code.Data.Nat.Properties.d_'8804''45'refl_1634
                                   (Integer -> Integer
forall a b. a -> b
coe Integer
v0))))))
-- Data.Integer.Properties.-[1+m]≤n⊖m+1
d_'45''91'1'43'm'93''8804'n'8854'm'43'1_2836 ::
  Integer -> Integer -> MAlonzo.Code.Data.Integer.Base.T__'8804'__26
d_'45''91'1'43'm'93''8804'n'8854'm'43'1_2836 :: Integer -> Integer -> T__'8804'__26
d_'45''91'1'43'm'93''8804'n'8854'm'43'1_2836 Integer
v0 Integer
v1
  = case Integer -> Integer
forall a b. a -> b
coe Integer
v1 of
      Integer
0 -> (Integer -> T__'8804'__26) -> Any -> T__'8804'__26
forall a b. a -> b
coe
             Integer -> T__'8804'__26
d_'8804''45'refl_1584 ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> Integer
subInt (Integer -> Any
forall a b. a -> b
coe (-Integer
1 :: Integer)) (Integer -> Any
forall a b. a -> b
coe Integer
v0))
      Integer
_ -> let v2 :: Integer
v2 = Integer -> Integer -> Integer
subInt (Integer -> Integer
forall a b. a -> b
coe Integer
v1) (Integer -> Integer
forall a b. a -> b
coe (Integer
1 :: Integer)) in
           Any -> T__'8804'__26
forall a b. a -> b
coe
             ((T_IsPreorder_70
 -> (Any -> Any -> Any -> Any)
 -> Any
 -> Any
 -> T__IsRelatedTo__70
 -> Any)
-> Any -> Any -> Any -> Any -> Any -> Any
forall a b. a -> b
coe
                T_IsPreorder_70
-> (Any -> Any -> Any -> Any)
-> Any
-> Any
-> T__IsRelatedTo__70
-> Any
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_begin__160
                (T_IsPreorder_70 -> Any
forall a b. a -> b
coe T_IsPreorder_70
d_'8804''45'isPreorder_1656) ((Integer -> Integer -> T__'60'__50 -> T__'8804'__26) -> Any
forall a b. a -> b
coe Integer -> Integer -> T__'60'__50 -> T__'8804'__26
d_'60''8658''8804'_1724)
                ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> Integer
subInt (Integer -> Any
forall a b. a -> b
coe (-Integer
1 :: Integer)) (Integer -> Any
forall a b. a -> b
coe Integer
v0))
                ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe
                   Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'8854'__224 (Integer -> Any
forall a b. a -> b
coe Integer
v1)
                   ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> Integer
addInt (Integer -> Any
forall a b. a -> b
coe (Integer
1 :: Integer)) (Integer -> Any
forall a b. a -> b
coe Integer
v0)))
                ((T_IsPreorder_70
 -> (Any -> Any -> Any -> Any -> Any -> Any)
 -> Any
 -> Any
 -> Any
 -> T__IsRelatedTo__70
 -> Any
 -> T__IsRelatedTo__70)
-> Any
-> (Any -> Any -> Any -> Any -> Any -> Any)
-> Any
-> Any
-> Any
-> Any
-> Any
-> Any
forall a b. a -> b
coe
                   T_IsPreorder_70
-> (Any -> Any -> Any -> Any -> Any -> Any)
-> Any
-> Any
-> Any
-> T__IsRelatedTo__70
-> Any
-> T__IsRelatedTo__70
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_step'45''8804'_228
                   (T_IsPreorder_70 -> Any
forall a b. a -> b
coe T_IsPreorder_70
d_'8804''45'isPreorder_1656)
                   (\ Any
v3 Any
v4 Any
v5 Any
v6 Any
v7 -> (T__'8804'__26 -> T__'60'__50 -> T__'60'__50) -> Any -> Any -> Any
forall a b. a -> b
coe T__'8804'__26 -> T__'60'__50 -> T__'60'__50
du_'8804''45''60''45'trans_1844 Any
v6 Any
v7)
                   ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> Integer
subInt (Integer -> Any
forall a b. a -> b
coe (-Integer
1 :: Integer)) (Integer -> Any
forall a b. a -> b
coe Integer
v0))
                   ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe
                      Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'8854'__224 (Integer -> Any
forall a b. a -> b
coe Integer
v2) (Integer -> Any
forall a b. a -> b
coe Integer
v0))
                   ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe
                      Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'8854'__224 (Integer -> Any
forall a b. a -> b
coe Integer
v1)
                      ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> Integer
addInt (Integer -> Any
forall a b. a -> b
coe (Integer
1 :: Integer)) (Integer -> Any
forall a b. a -> b
coe Integer
v0)))
                   ((T_IsPreorder_70 -> Any -> T__IsRelatedTo__70) -> Any -> Any -> Any
forall a b. a -> b
coe
                      T_IsPreorder_70 -> Any -> T__IsRelatedTo__70
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du__'8718'_346
                      (T_IsPreorder_70 -> Any
forall a b. a -> b
coe T_IsPreorder_70
d_'8804''45'isPreorder_1656)
                      ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe
                         Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'8854'__224 (Integer -> Any
forall a b. a -> b
coe Integer
v1)
                         ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> Integer
addInt (Integer -> Any
forall a b. a -> b
coe (Integer
1 :: Integer)) (Integer -> Any
forall a b. a -> b
coe Integer
v0))))
                   ((Integer -> Integer -> T__'60'__50 -> T__'8804'__26)
-> Any -> Any -> Any -> Any
forall a b. a -> b
coe
                      Integer -> Integer -> T__'60'__50 -> T__'8804'__26
d_'60''8658''8804'_1724 ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> Integer
subInt (Integer -> Any
forall a b. a -> b
coe (-Integer
1 :: Integer)) (Integer -> Any
forall a b. a -> b
coe Integer
v0))
                      ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe
                         Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'8854'__224 (Integer -> Any
forall a b. a -> b
coe Integer
v2) (Integer -> Any
forall a b. a -> b
coe Integer
v0))
                      ((Integer -> Integer -> T__'60'__50) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> T__'60'__50
d_'45'1'43'm'60'n'8854'm_2818 (Integer -> Any
forall a b. a -> b
coe Integer
v0) (Integer -> Any
forall a b. a -> b
coe Integer
v2)))))
-- Data.Integer.Properties.-1+m≤n⊖m
d_'45'1'43'm'8804'n'8854'm_2852 ::
  Integer -> Integer -> MAlonzo.Code.Data.Integer.Base.T__'8804'__26
d_'45'1'43'm'8804'n'8854'm_2852 :: Integer -> Integer -> T__'8804'__26
d_'45'1'43'm'8804'n'8854'm_2852 Integer
v0 Integer
v1
  = (Integer -> Integer -> T__'60'__50 -> T__'8804'__26)
-> Any -> Any -> Any -> T__'8804'__26
forall a b. a -> b
coe
      Integer -> Integer -> T__'60'__50 -> T__'8804'__26
d_'60''8658''8804'_1724 ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> Integer
subInt (Integer -> Any
forall a b. a -> b
coe (-Integer
1 :: Integer)) (Integer -> Any
forall a b. a -> b
coe Integer
v0))
      ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe
         Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'8854'__224 (Integer -> Any
forall a b. a -> b
coe Integer
v1) (Integer -> Any
forall a b. a -> b
coe Integer
v0))
      ((Integer -> Integer -> T__'60'__50) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> T__'60'__50
d_'45'1'43'm'60'n'8854'm_2818 (Integer -> Any
forall a b. a -> b
coe Integer
v0) (Integer -> Any
forall a b. a -> b
coe Integer
v1))
-- Data.Integer.Properties.0⊖m≤+
d_0'8854'm'8804''43'_2862 ::
  Integer -> Integer -> MAlonzo.Code.Data.Integer.Base.T__'8804'__26
d_0'8854'm'8804''43'_2862 :: Integer -> Integer -> T__'8804'__26
d_0'8854'm'8804''43'_2862 Integer
v0 ~Integer
v1 = Integer -> T__'8804'__26
du_0'8854'm'8804''43'_2862 Integer
v0
du_0'8854'm'8804''43'_2862 ::
  Integer -> MAlonzo.Code.Data.Integer.Base.T__'8804'__26
du_0'8854'm'8804''43'_2862 :: Integer -> T__'8804'__26
du_0'8854'm'8804''43'_2862 Integer
v0
  = case Integer -> Integer
forall a b. a -> b
coe Integer
v0 of
      Integer
0 -> (T__'8804'__18 -> T__'8804'__26) -> Any -> T__'8804'__26
forall a b. a -> b
coe
             T__'8804'__18 -> T__'8804'__26
MAlonzo.Code.Data.Integer.Base.C_'43''8804''43'_48
             (T__'8804'__18 -> Any
forall a b. a -> b
coe T__'8804'__18
MAlonzo.Code.Data.Nat.Base.C_z'8804'n_22)
      Integer
_ -> T__'8804'__26 -> T__'8804'__26
forall a b. a -> b
coe T__'8804'__26
MAlonzo.Code.Data.Integer.Base.C_'45''8804''43'_40
-- Data.Integer.Properties.sign-⊖-<
d_sign'45''8854''45''60'_2870 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__18 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_sign'45''8854''45''60'_2870 :: Integer -> Integer -> T__'8804'__18 -> T__'8801'__12
d_sign'45''8854''45''60'_2870 = Integer -> Integer -> T__'8804'__18 -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.sign-⊖-≰
d_sign'45''8854''45''8816'_2886 ::
  Integer ->
  Integer ->
  (MAlonzo.Code.Data.Nat.Base.T__'8804'__18 ->
   MAlonzo.Code.Data.Empty.T_'8869'_4) ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_sign'45''8854''45''8816'_2886 :: Integer
-> Integer -> (T__'8804'__18 -> T_'8869'_4) -> T__'8801'__12
d_sign'45''8854''45''8816'_2886 = Integer
-> Integer -> (T__'8804'__18 -> T_'8869'_4) -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.⊖-monoʳ-≥-≤
d_'8854''45'mono'691''45''8805''45''8804'_2892 ::
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__18 ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26
d_'8854''45'mono'691''45''8805''45''8804'_2892 :: Integer -> Integer -> Integer -> T__'8804'__18 -> T__'8804'__26
d_'8854''45'mono'691''45''8805''45''8804'_2892 Integer
v0 Integer
v1 Integer
v2 T__'8804'__18
v3
  = case Integer -> Integer
forall a b. a -> b
coe Integer
v0 of
      Integer
0 -> case T__'8804'__18 -> T__'8804'__18
forall a b. a -> b
coe T__'8804'__18
v3 of
             T__'8804'__18
MAlonzo.Code.Data.Nat.Base.C_z'8804'n_22
               -> (Integer -> T__'8804'__26) -> Any -> T__'8804'__26
forall a b. a -> b
coe Integer -> T__'8804'__26
du_0'8854'm'8804''43'_2862 (Integer -> Any
forall a b. a -> b
coe Integer
v1)
             MAlonzo.Code.Data.Nat.Base.C_s'8804's_30 T__'8804'__18
v6
               -> (T__'8804'__18 -> T__'8804'__26) -> T__'8804'__18 -> T__'8804'__26
forall a b. a -> b
coe T__'8804'__18 -> T__'8804'__26
MAlonzo.Code.Data.Integer.Base.C_'45''8804''45'_34 T__'8804'__18
v6
             T__'8804'__18
_ -> T__'8804'__26
forall a. a
MAlonzo.RTE.mazUnreachableError
      Integer
_ -> let v4 :: Integer
v4 = Integer -> Integer -> Integer
subInt (Integer -> Integer
forall a b. a -> b
coe Integer
v0) (Integer -> Integer
forall a b. a -> b
coe (Integer
1 :: Integer)) in
           Any -> T__'8804'__26
forall a b. a -> b
coe
             (case Integer -> Integer
forall a b. a -> b
coe Integer
v1 of
                Integer
0 -> (Any -> Any -> Any) -> Any -> Any -> Any
forall a b. a -> b
coe
                       Any -> Any -> Any
forall a b. a -> b -> b
seq (T__'8804'__18 -> Any
forall a b. a -> b
coe T__'8804'__18
v3)
                       ((Integer -> T__'8804'__26) -> Any -> Any
forall a b. a -> b
coe
                          Integer -> T__'8804'__26
d_'8804''45'refl_1584
                          (((Any -> Any) -> (Any -> Any -> Any) -> Any -> Any -> Any)
-> (Integer -> Integer)
-> (Any -> Any -> Any)
-> Integer
-> Integer
-> Any
forall a b. a -> b
coe
                             (Any -> Any) -> (Any -> Any -> Any) -> Any -> Any -> Any
MAlonzo.Code.Function.Base.du__'45''10216'_'8739'_302
                             (Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'8854'__224 (Integer -> Integer
forall a b. a -> b
coe Integer
v0))
                             (\ Any
v5 Any
v6 -> Any
v5) (Integer
0 :: Integer) (Integer
0 :: Integer)))
                Integer
_ -> let v5 :: Integer
v5 = Integer -> Integer -> Integer
subInt (Integer -> Integer
forall a b. a -> b
coe Integer
v1) (Integer -> Integer
forall a b. a -> b
coe (Integer
1 :: Integer)) in
                     Any -> Any
forall a b. a -> b
coe
                       (case T__'8804'__18 -> T__'8804'__18
forall a b. a -> b
coe T__'8804'__18
v3 of
                          T__'8804'__18
MAlonzo.Code.Data.Nat.Base.C_z'8804'n_22
                            -> (T_IsPreorder_70
 -> (Any -> Any -> Any -> Any)
 -> Any
 -> Any
 -> T__IsRelatedTo__70
 -> Any)
-> Any -> Any -> Any -> Any -> Any -> Any
forall a b. a -> b
coe
                                 T_IsPreorder_70
-> (Any -> Any -> Any -> Any)
-> Any
-> Any
-> T__IsRelatedTo__70
-> Any
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_begin__160
                                 (T_IsPreorder_70 -> Any
forall a b. a -> b
coe T_IsPreorder_70
d_'8804''45'isPreorder_1656) ((Integer -> Integer -> T__'60'__50 -> T__'8804'__26) -> Any
forall a b. a -> b
coe Integer -> Integer -> T__'60'__50 -> T__'8804'__26
d_'60''8658''8804'_1724)
                                 (((Any -> Any) -> (Any -> Any -> Any) -> Any -> Any -> Any)
-> (Integer -> Integer)
-> (Any -> Any -> Any)
-> Integer
-> Integer
-> Any
forall a b. a -> b
coe
                                    (Any -> Any) -> (Any -> Any -> Any) -> Any -> Any -> Any
MAlonzo.Code.Function.Base.du__'45''10216'_'8739'_302
                                    (Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'8854'__224 (Integer -> Integer
forall a b. a -> b
coe Integer
v0))
                                    (\ Any
v7 Any
v8 -> Any
v7) Integer
v1 (Integer
0 :: Integer))
                                 (((Any -> Any -> Any) -> (Any -> Any) -> Any -> Any -> Any)
-> (Any -> Any -> Any)
-> (Integer -> Integer)
-> Integer
-> Integer
-> Any
forall a b. a -> b
coe
                                    (Any -> Any -> Any) -> (Any -> Any) -> Any -> Any -> Any
MAlonzo.Code.Function.Base.du_'8739'_'10217''45'__308
                                    (\ Any
v7 Any
v8 -> Any
v8)
                                    (Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'8854'__224 (Integer -> Integer
forall a b. a -> b
coe Integer
v0)) Integer
v1
                                    (Integer
0 :: Integer))
                                 ((T_IsPreorder_70
 -> (Any -> Any -> Any -> Any -> Any -> Any)
 -> Any
 -> Any
 -> Any
 -> T__IsRelatedTo__70
 -> Any
 -> T__IsRelatedTo__70)
-> Any
-> (Any -> Any -> Any -> Any -> Any -> Any)
-> Any
-> Any
-> Any
-> Any
-> Any
-> Any
forall a b. a -> b
coe
                                    T_IsPreorder_70
-> (Any -> Any -> Any -> Any -> Any -> Any)
-> Any
-> Any
-> Any
-> T__IsRelatedTo__70
-> Any
-> T__IsRelatedTo__70
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_step'45''8804'_228
                                    (T_IsPreorder_70 -> Any
forall a b. a -> b
coe T_IsPreorder_70
d_'8804''45'isPreorder_1656)
                                    (\ Any
v7 Any
v8 Any
v9 Any
v10 Any
v11 ->
                                       (T__'8804'__26 -> T__'60'__50 -> T__'60'__50) -> Any -> Any -> Any
forall a b. a -> b
coe T__'8804'__26 -> T__'60'__50 -> T__'60'__50
du_'8804''45''60''45'trans_1844 Any
v10 Any
v11)
                                    ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe
                                       Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'8854'__224 (Integer -> Any
forall a b. a -> b
coe Integer
v4)
                                       (Integer -> Any
forall a b. a -> b
coe Integer
v5))
                                    (Integer -> Any
forall a b. a -> b
coe Integer
v0)
                                    (((Any -> Any -> Any) -> (Any -> Any) -> Any -> Any -> Any)
-> (Any -> Any -> Any)
-> (Integer -> Integer)
-> Integer
-> Integer
-> Any
forall a b. a -> b
coe
                                       (Any -> Any -> Any) -> (Any -> Any) -> Any -> Any -> Any
MAlonzo.Code.Function.Base.du_'8739'_'10217''45'__308
                                       (\ Any
v7 Any
v8 -> Any
v8)
                                       (Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'8854'__224 (Integer -> Integer
forall a b. a -> b
coe Integer
v0)) Integer
v1
                                       (Integer
0 :: Integer))
                                    ((T_IsPreorder_70 -> Any -> T__IsRelatedTo__70) -> Any -> Any -> Any
forall a b. a -> b
coe
                                       T_IsPreorder_70 -> Any -> T__IsRelatedTo__70
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du__'8718'_346
                                       (T_IsPreorder_70 -> Any
forall a b. a -> b
coe T_IsPreorder_70
d_'8804''45'isPreorder_1656) (Integer -> Any
forall a b. a -> b
coe Integer
v0))
                                    ((Integer -> Integer -> T__'60'__50 -> T__'8804'__26)
-> Any -> Any -> Any -> Any
forall a b. a -> b
coe
                                       Integer -> Integer -> T__'60'__50 -> T__'8804'__26
d_'60''8658''8804'_1724
                                       ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe
                                          Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'8854'__224 (Integer -> Any
forall a b. a -> b
coe Integer
v4)
                                          (Integer -> Any
forall a b. a -> b
coe Integer
v5))
                                       (Integer -> Any
forall a b. a -> b
coe Integer
v0) ((Integer -> Integer -> T__'60'__50) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> T__'60'__50
d_m'8854'n'60'1'43'm_2792 (Integer -> Any
forall a b. a -> b
coe Integer
v4) (Integer -> Any
forall a b. a -> b
coe Integer
v5))))
                          MAlonzo.Code.Data.Nat.Base.C_s'8804's_30 T__'8804'__18
v8
                            -> let v9 :: Integer
v9 = Integer -> Integer -> Integer
subInt (Integer -> Integer
forall a b. a -> b
coe Integer
v2) (Integer -> Integer
forall a b. a -> b
coe (Integer
1 :: Integer)) in
                               Any -> Any
forall a b. a -> b
coe
                                 ((T_IsPreorder_70
 -> (Any -> Any -> Any -> Any)
 -> Any
 -> Any
 -> T__IsRelatedTo__70
 -> Any)
-> Any -> Any -> Any -> Any -> Any -> Any
forall a b. a -> b
coe
                                    T_IsPreorder_70
-> (Any -> Any -> Any -> Any)
-> Any
-> Any
-> T__IsRelatedTo__70
-> Any
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_begin__160
                                    (T_IsPreorder_70 -> Any
forall a b. a -> b
coe T_IsPreorder_70
d_'8804''45'isPreorder_1656) ((Integer -> Integer -> T__'60'__50 -> T__'8804'__26) -> Any
forall a b. a -> b
coe Integer -> Integer -> T__'60'__50 -> T__'8804'__26
d_'60''8658''8804'_1724)
                                    (((Any -> Any) -> (Any -> Any -> Any) -> Any -> Any -> Any)
-> (Integer -> Integer)
-> (Any -> Any -> Any)
-> Integer
-> Integer
-> Any
forall a b. a -> b
coe
                                       (Any -> Any) -> (Any -> Any -> Any) -> Any -> Any -> Any
MAlonzo.Code.Function.Base.du__'45''10216'_'8739'_302
                                       (Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'8854'__224 (Integer -> Integer
forall a b. a -> b
coe Integer
v0))
                                       (\ Any
v10 Any
v11 -> Any
v10) Integer
v1 Integer
v2)
                                    (((Any -> Any -> Any) -> (Any -> Any) -> Any -> Any -> Any)
-> (Any -> Any -> Any)
-> (Integer -> Integer)
-> Integer
-> Integer
-> Any
forall a b. a -> b
coe
                                       (Any -> Any -> Any) -> (Any -> Any) -> Any -> Any -> Any
MAlonzo.Code.Function.Base.du_'8739'_'10217''45'__308
                                       (\ Any
v10 Any
v11 -> Any
v11)
                                       (Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'8854'__224 (Integer -> Integer
forall a b. a -> b
coe Integer
v0)) Integer
v1
                                       Integer
v2)
                                    ((T_IsPreorder_70
 -> (Any -> Any -> Any -> Any -> Any -> Any)
 -> Any
 -> Any
 -> Any
 -> T__IsRelatedTo__70
 -> Any
 -> T__IsRelatedTo__70)
-> Any
-> (Any -> Any -> Any -> Any -> Any -> Any)
-> Any
-> Any
-> Any
-> Any
-> Any
-> Any
forall a b. a -> b
coe
                                       T_IsPreorder_70
-> (Any -> Any -> Any -> Any -> Any -> Any)
-> Any
-> Any
-> Any
-> T__IsRelatedTo__70
-> Any
-> T__IsRelatedTo__70
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_step'45''8804'_228
                                       (T_IsPreorder_70 -> Any
forall a b. a -> b
coe T_IsPreorder_70
d_'8804''45'isPreorder_1656)
                                       (\ Any
v10 Any
v11 Any
v12 Any
v13 Any
v14 ->
                                          (T__'8804'__26 -> T__'60'__50 -> T__'60'__50) -> Any -> Any -> Any
forall a b. a -> b
coe T__'8804'__26 -> T__'60'__50 -> T__'60'__50
du_'8804''45''60''45'trans_1844 Any
v13 Any
v14)
                                       ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe
                                          Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'8854'__224 (Integer -> Any
forall a b. a -> b
coe Integer
v4)
                                          (Integer -> Any
forall a b. a -> b
coe Integer
v5))
                                       ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe
                                          Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'8854'__224 (Integer -> Any
forall a b. a -> b
coe Integer
v4)
                                          (Integer -> Any
forall a b. a -> b
coe Integer
v9))
                                       (((Any -> Any -> Any) -> (Any -> Any) -> Any -> Any -> Any)
-> (Any -> Any -> Any)
-> (Integer -> Integer)
-> Integer
-> Integer
-> Any
forall a b. a -> b
coe
                                          (Any -> Any -> Any) -> (Any -> Any) -> Any -> Any -> Any
MAlonzo.Code.Function.Base.du_'8739'_'10217''45'__308
                                          (\ Any
v10 Any
v11 -> Any
v11)
                                          (Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'8854'__224 (Integer -> Integer
forall a b. a -> b
coe Integer
v0))
                                          Integer
v1 Integer
v2)
                                       ((T_IsPreorder_70 -> Any -> T__IsRelatedTo__70) -> Any -> Any -> Any
forall a b. a -> b
coe
                                          T_IsPreorder_70 -> Any -> T__IsRelatedTo__70
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du__'8718'_346
                                          (T_IsPreorder_70 -> Any
forall a b. a -> b
coe T_IsPreorder_70
d_'8804''45'isPreorder_1656)
                                          ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe
                                             Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'8854'__224 (Integer -> Any
forall a b. a -> b
coe Integer
v0)
                                             (Integer -> Any
forall a b. a -> b
coe Integer
v2)))
                                       ((Integer -> Integer -> Integer -> T__'8804'__18 -> T__'8804'__26)
-> Any -> Any -> Any -> Any -> Any
forall a b. a -> b
coe
                                          Integer -> Integer -> Integer -> T__'8804'__18 -> T__'8804'__26
d_'8854''45'mono'691''45''8805''45''8804'_2892 (Integer -> Any
forall a b. a -> b
coe Integer
v4)
                                          (Integer -> Any
forall a b. a -> b
coe Integer
v5) (Integer -> Any
forall a b. a -> b
coe Integer
v9) (T__'8804'__18 -> Any
forall a b. a -> b
coe T__'8804'__18
v8))))
                          T__'8804'__18
_ -> Any
forall a. a
MAlonzo.RTE.mazUnreachableError))
-- Data.Integer.Properties.⊖-monoˡ-≤
d_'8854''45'mono'737''45''8804'_2924 ::
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__18 ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26
d_'8854''45'mono'737''45''8804'_2924 :: Integer -> Integer -> Integer -> T__'8804'__18 -> T__'8804'__26
d_'8854''45'mono'737''45''8804'_2924 Integer
v0 Integer
v1 Integer
v2 T__'8804'__18
v3
  = case Integer -> Integer
forall a b. a -> b
coe Integer
v0 of
      Integer
0 -> (T__'8804'__18 -> T__'8804'__26) -> T__'8804'__18 -> T__'8804'__26
forall a b. a -> b
coe T__'8804'__18 -> T__'8804'__26
MAlonzo.Code.Data.Integer.Base.C_'43''8804''43'_48 T__'8804'__18
v3
      Integer
_ -> let v4 :: Integer
v4 = Integer -> Integer -> Integer
subInt (Integer -> Integer
forall a b. a -> b
coe Integer
v0) (Integer -> Integer
forall a b. a -> b
coe (Integer
1 :: Integer)) in
           Any -> T__'8804'__26
forall a b. a -> b
coe
             (case Integer -> Integer
forall a b. a -> b
coe Integer
v2 of
                Integer
0 -> (Any -> Any -> Any) -> Any -> Any -> Any
forall a b. a -> b
coe
                       Any -> Any -> Any
forall a b. a -> b -> b
seq (T__'8804'__18 -> Any
forall a b. a -> b
coe T__'8804'__18
v3)
                       ((Integer -> T__'8804'__26) -> Any -> Any
forall a b. a -> b
coe
                          Integer -> T__'8804'__26
d_'8804''45'refl_1584
                          (((Any -> Any) -> (Any -> Any -> Any) -> Any -> Any -> Any)
-> (Any -> Integer)
-> (Any -> Any -> Any)
-> Integer
-> Integer
-> Any
forall a b. a -> b
coe
                             (Any -> Any) -> (Any -> Any -> Any) -> Any -> Any -> Any
MAlonzo.Code.Function.Base.du__'45''10216'_'8739'_302
                             (\ Any
v5 ->
                                Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'8854'__224 (Any -> Integer
forall a b. a -> b
coe Any
v5) (Integer -> Integer
forall a b. a -> b
coe Integer
v0))
                             (\ Any
v5 Any
v6 -> Any
v5) (Integer
0 :: Integer) (Integer
0 :: Integer)))
                Integer
_ -> let v5 :: Integer
v5 = Integer -> Integer -> Integer
subInt (Integer -> Integer
forall a b. a -> b
coe Integer
v2) (Integer -> Integer
forall a b. a -> b
coe (Integer
1 :: Integer)) in
                     Any -> Any
forall a b. a -> b
coe
                       (case T__'8804'__18 -> T__'8804'__18
forall a b. a -> b
coe T__'8804'__18
v3 of
                          T__'8804'__18
MAlonzo.Code.Data.Nat.Base.C_z'8804'n_22
                            -> (T_IsPreorder_70
 -> (Any -> Any -> Any -> Any)
 -> Any
 -> Any
 -> T__IsRelatedTo__70
 -> Any)
-> Any -> Any -> Any -> Any -> Any -> Any
forall a b. a -> b
coe
                                 T_IsPreorder_70
-> (Any -> Any -> Any -> Any)
-> Any
-> Any
-> T__IsRelatedTo__70
-> Any
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_begin__160
                                 (T_IsPreorder_70 -> Any
forall a b. a -> b
coe T_IsPreorder_70
d_'8804''45'isPreorder_1656) ((Integer -> Integer -> T__'60'__50 -> T__'8804'__26) -> Any
forall a b. a -> b
coe Integer -> Integer -> T__'60'__50 -> T__'8804'__26
d_'60''8658''8804'_1724)
                                 (((Any -> Any) -> (Any -> Any -> Any) -> Any -> Any -> Any)
-> (Any -> Integer)
-> (Any -> Any -> Any)
-> Integer
-> Integer
-> Any
forall a b. a -> b
coe
                                    (Any -> Any) -> (Any -> Any -> Any) -> Any -> Any -> Any
MAlonzo.Code.Function.Base.du__'45''10216'_'8739'_302
                                    (\ Any
v7 ->
                                       Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'8854'__224
                                         (Any -> Integer
forall a b. a -> b
coe Any
v7) (Integer -> Integer
forall a b. a -> b
coe Integer
v0))
                                    (\ Any
v7 Any
v8 -> Any
v7) (Integer
0 :: Integer) Integer
v2)
                                 (((Any -> Any -> Any) -> (Any -> Any) -> Any -> Any -> Any)
-> (Any -> Any -> Any)
-> (Any -> Integer)
-> Integer
-> Integer
-> Any
forall a b. a -> b
coe
                                    (Any -> Any -> Any) -> (Any -> Any) -> Any -> Any -> Any
MAlonzo.Code.Function.Base.du_'8739'_'10217''45'__308
                                    (\ Any
v7 Any
v8 -> Any
v8)
                                    (\ Any
v7 ->
                                       Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'8854'__224
                                         (Any -> Integer
forall a b. a -> b
coe Any
v7) (Integer -> Integer
forall a b. a -> b
coe Integer
v0))
                                    (Integer
0 :: Integer) Integer
v2)
                                 ((T_IsPreorder_70
 -> (Any -> Any -> Any -> Any -> Any -> Any)
 -> Any
 -> Any
 -> Any
 -> T__IsRelatedTo__70
 -> Any
 -> T__IsRelatedTo__70)
-> Any
-> (Any -> Any -> Any -> Any -> Any -> Any)
-> Any
-> Any
-> Any
-> Any
-> Any
-> Any
forall a b. a -> b
coe
                                    T_IsPreorder_70
-> (Any -> Any -> Any -> Any -> Any -> Any)
-> Any
-> Any
-> Any
-> T__IsRelatedTo__70
-> Any
-> T__IsRelatedTo__70
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_step'45''8804'_228
                                    (T_IsPreorder_70 -> Any
forall a b. a -> b
coe T_IsPreorder_70
d_'8804''45'isPreorder_1656)
                                    (\ Any
v7 Any
v8 Any
v9 Any
v10 Any
v11 ->
                                       (T__'8804'__26 -> T__'60'__50 -> T__'60'__50) -> Any -> Any -> Any
forall a b. a -> b
coe T__'8804'__26 -> T__'60'__50 -> T__'60'__50
du_'8804''45''60''45'trans_1844 Any
v10 Any
v11)
                                    ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe
                                       Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'8854'__224
                                       (Integer -> Any
forall a b. a -> b
coe (Integer
0 :: Integer)) (Integer -> Any
forall a b. a -> b
coe Integer
v0))
                                    ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe
                                       Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'8854'__224
                                       (Integer -> Any
forall a b. a -> b
coe (Integer
0 :: Integer)) (Integer -> Any
forall a b. a -> b
coe Integer
v4))
                                    (((Any -> Any -> Any) -> (Any -> Any) -> Any -> Any -> Any)
-> (Any -> Any -> Any)
-> (Any -> Integer)
-> Integer
-> Integer
-> Any
forall a b. a -> b
coe
                                       (Any -> Any -> Any) -> (Any -> Any) -> Any -> Any -> Any
MAlonzo.Code.Function.Base.du_'8739'_'10217''45'__308
                                       (\ Any
v7 Any
v8 -> Any
v8)
                                       (\ Any
v7 ->
                                          Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'8854'__224
                                            (Any -> Integer
forall a b. a -> b
coe Any
v7) (Integer -> Integer
forall a b. a -> b
coe Integer
v0))
                                       (Integer
0 :: Integer) Integer
v2)
                                    ((T_IsPreorder_70
 -> (Any -> Any -> Any -> Any -> Any -> Any)
 -> Any
 -> Any
 -> Any
 -> T__IsRelatedTo__70
 -> Any
 -> T__IsRelatedTo__70)
-> Any
-> (Any -> Any -> Any -> Any -> Any -> Any)
-> Any
-> Any
-> Any
-> Any
-> Any
-> Any
forall a b. a -> b
coe
                                       T_IsPreorder_70
-> (Any -> Any -> Any -> Any -> Any -> Any)
-> Any
-> Any
-> Any
-> T__IsRelatedTo__70
-> Any
-> T__IsRelatedTo__70
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_step'45''8804'_228
                                       (T_IsPreorder_70 -> Any
forall a b. a -> b
coe T_IsPreorder_70
d_'8804''45'isPreorder_1656)
                                       (\ Any
v7 Any
v8 Any
v9 Any
v10 Any
v11 ->
                                          (T__'8804'__26 -> T__'60'__50 -> T__'60'__50) -> Any -> Any -> Any
forall a b. a -> b
coe T__'8804'__26 -> T__'60'__50 -> T__'60'__50
du_'8804''45''60''45'trans_1844 Any
v10 Any
v11)
                                       ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe
                                          Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'8854'__224
                                          (Integer -> Any
forall a b. a -> b
coe (Integer
0 :: Integer)) (Integer -> Any
forall a b. a -> b
coe Integer
v4))
                                       ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe
                                          Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'8854'__224 (Integer -> Any
forall a b. a -> b
coe Integer
v5)
                                          (Integer -> Any
forall a b. a -> b
coe Integer
v4))
                                       (((Any -> Any -> Any) -> (Any -> Any) -> Any -> Any -> Any)
-> (Any -> Any -> Any)
-> (Any -> Integer)
-> Integer
-> Integer
-> Any
forall a b. a -> b
coe
                                          (Any -> Any -> Any) -> (Any -> Any) -> Any -> Any -> Any
MAlonzo.Code.Function.Base.du_'8739'_'10217''45'__308
                                          (\ Any
v7 Any
v8 -> Any
v8)
                                          (\ Any
v7 ->
                                             Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'8854'__224
                                               (Any -> Integer
forall a b. a -> b
coe Any
v7) (Integer -> Integer
forall a b. a -> b
coe Integer
v0))
                                          (Integer
0 :: Integer) Integer
v2)
                                       ((T_IsPreorder_70 -> Any -> T__IsRelatedTo__70) -> Any -> Any -> Any
forall a b. a -> b
coe
                                          T_IsPreorder_70 -> Any -> T__IsRelatedTo__70
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du__'8718'_346
                                          (T_IsPreorder_70 -> Any
forall a b. a -> b
coe T_IsPreorder_70
d_'8804''45'isPreorder_1656)
                                          ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe
                                             Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'8854'__224 (Integer -> Any
forall a b. a -> b
coe Integer
v2)
                                             (Integer -> Any
forall a b. a -> b
coe Integer
v0)))
                                       ((Integer -> Integer -> Integer -> T__'8804'__18 -> T__'8804'__26)
-> Any -> Any -> Any -> Any -> Any
forall a b. a -> b
coe
                                          Integer -> Integer -> Integer -> T__'8804'__18 -> T__'8804'__26
d_'8854''45'mono'737''45''8804'_2924 (Integer -> Any
forall a b. a -> b
coe Integer
v4)
                                          (Integer -> Any
forall a b. a -> b
coe (Integer
0 :: Integer)) (Integer -> Any
forall a b. a -> b
coe Integer
v5)
                                          (T__'8804'__18 -> Any
forall a b. a -> b
coe T__'8804'__18
MAlonzo.Code.Data.Nat.Base.C_z'8804'n_22)))
                                    ((Integer -> Integer -> Integer -> T__'8804'__18 -> T__'8804'__26)
-> Any -> Any -> Any -> Any -> Any
forall a b. a -> b
coe
                                       Integer -> Integer -> Integer -> T__'8804'__18 -> T__'8804'__26
d_'8854''45'mono'691''45''8805''45''8804'_2892
                                       (Integer -> Any
forall a b. a -> b
coe (Integer
0 :: Integer)) (Integer -> Any
forall a b. a -> b
coe Integer
v0) (Integer -> Any
forall a b. a -> b
coe Integer
v4)
                                       ((Integer -> T__'8804'__18) -> Any -> Any
forall a b. a -> b
coe
                                          Integer -> T__'8804'__18
MAlonzo.Code.Data.Nat.Properties.d_n'8804'1'43'n_1724
                                          (Integer -> Any
forall a b. a -> b
coe Integer
v4))))
                          MAlonzo.Code.Data.Nat.Base.C_s'8804's_30 T__'8804'__18
v8
                            -> let v9 :: Integer
v9 = Integer -> Integer -> Integer
subInt (Integer -> Integer
forall a b. a -> b
coe Integer
v1) (Integer -> Integer
forall a b. a -> b
coe (Integer
1 :: Integer)) in
                               Any -> Any
forall a b. a -> b
coe
                                 ((T_IsPreorder_70
 -> (Any -> Any -> Any -> Any)
 -> Any
 -> Any
 -> T__IsRelatedTo__70
 -> Any)
-> Any -> Any -> Any -> Any -> Any -> Any
forall a b. a -> b
coe
                                    T_IsPreorder_70
-> (Any -> Any -> Any -> Any)
-> Any
-> Any
-> T__IsRelatedTo__70
-> Any
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_begin__160
                                    (T_IsPreorder_70 -> Any
forall a b. a -> b
coe T_IsPreorder_70
d_'8804''45'isPreorder_1656) ((Integer -> Integer -> T__'60'__50 -> T__'8804'__26) -> Any
forall a b. a -> b
coe Integer -> Integer -> T__'60'__50 -> T__'8804'__26
d_'60''8658''8804'_1724)
                                    (((Any -> Any) -> (Any -> Any -> Any) -> Any -> Any -> Any)
-> (Any -> Integer)
-> (Any -> Any -> Any)
-> Integer
-> Integer
-> Any
forall a b. a -> b
coe
                                       (Any -> Any) -> (Any -> Any -> Any) -> Any -> Any -> Any
MAlonzo.Code.Function.Base.du__'45''10216'_'8739'_302
                                       (\ Any
v10 ->
                                          Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'8854'__224
                                            (Any -> Integer
forall a b. a -> b
coe Any
v10) (Integer -> Integer
forall a b. a -> b
coe Integer
v0))
                                       (\ Any
v10 Any
v11 -> Any
v10) Integer
v1 Integer
v2)
                                    (((Any -> Any -> Any) -> (Any -> Any) -> Any -> Any -> Any)
-> (Any -> Any -> Any)
-> (Any -> Integer)
-> Integer
-> Integer
-> Any
forall a b. a -> b
coe
                                       (Any -> Any -> Any) -> (Any -> Any) -> Any -> Any -> Any
MAlonzo.Code.Function.Base.du_'8739'_'10217''45'__308
                                       (\ Any
v10 Any
v11 -> Any
v11)
                                       (\ Any
v10 ->
                                          Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'8854'__224
                                            (Any -> Integer
forall a b. a -> b
coe Any
v10) (Integer -> Integer
forall a b. a -> b
coe Integer
v0))
                                       Integer
v1 Integer
v2)
                                    ((T_IsPreorder_70
 -> (Any -> Any -> Any -> Any -> Any -> Any)
 -> Any
 -> Any
 -> Any
 -> T__IsRelatedTo__70
 -> Any
 -> T__IsRelatedTo__70)
-> Any
-> (Any -> Any -> Any -> Any -> Any -> Any)
-> Any
-> Any
-> Any
-> Any
-> Any
-> Any
forall a b. a -> b
coe
                                       T_IsPreorder_70
-> (Any -> Any -> Any -> Any -> Any -> Any)
-> Any
-> Any
-> Any
-> T__IsRelatedTo__70
-> Any
-> T__IsRelatedTo__70
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_step'45''8804'_228
                                       (T_IsPreorder_70 -> Any
forall a b. a -> b
coe T_IsPreorder_70
d_'8804''45'isPreorder_1656)
                                       (\ Any
v10 Any
v11 Any
v12 Any
v13 Any
v14 ->
                                          (T__'8804'__26 -> T__'60'__50 -> T__'60'__50) -> Any -> Any -> Any
forall a b. a -> b
coe T__'8804'__26 -> T__'60'__50 -> T__'60'__50
du_'8804''45''60''45'trans_1844 Any
v13 Any
v14)
                                       ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe
                                          Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'8854'__224 (Integer -> Any
forall a b. a -> b
coe Integer
v9)
                                          (Integer -> Any
forall a b. a -> b
coe Integer
v4))
                                       ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe
                                          Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'8854'__224 (Integer -> Any
forall a b. a -> b
coe Integer
v5)
                                          (Integer -> Any
forall a b. a -> b
coe Integer
v4))
                                       (((Any -> Any -> Any) -> (Any -> Any) -> Any -> Any -> Any)
-> (Any -> Any -> Any)
-> (Any -> Integer)
-> Integer
-> Integer
-> Any
forall a b. a -> b
coe
                                          (Any -> Any -> Any) -> (Any -> Any) -> Any -> Any -> Any
MAlonzo.Code.Function.Base.du_'8739'_'10217''45'__308
                                          (\ Any
v10 Any
v11 -> Any
v11)
                                          (\ Any
v10 ->
                                             Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'8854'__224
                                               (Any -> Integer
forall a b. a -> b
coe Any
v10) (Integer -> Integer
forall a b. a -> b
coe Integer
v0))
                                          Integer
v1 Integer
v2)
                                       ((T_IsPreorder_70 -> Any -> T__IsRelatedTo__70) -> Any -> Any -> Any
forall a b. a -> b
coe
                                          T_IsPreorder_70 -> Any -> T__IsRelatedTo__70
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du__'8718'_346
                                          (T_IsPreorder_70 -> Any
forall a b. a -> b
coe T_IsPreorder_70
d_'8804''45'isPreorder_1656)
                                          ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe
                                             Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'8854'__224 (Integer -> Any
forall a b. a -> b
coe Integer
v2)
                                             (Integer -> Any
forall a b. a -> b
coe Integer
v0)))
                                       ((Integer -> Integer -> Integer -> T__'8804'__18 -> T__'8804'__26)
-> Any -> Any -> Any -> Any -> Any
forall a b. a -> b
coe
                                          Integer -> Integer -> Integer -> T__'8804'__18 -> T__'8804'__26
d_'8854''45'mono'737''45''8804'_2924 (Integer -> Any
forall a b. a -> b
coe Integer
v4) (Integer -> Any
forall a b. a -> b
coe Integer
v9)
                                          (Integer -> Any
forall a b. a -> b
coe Integer
v5) (T__'8804'__18 -> Any
forall a b. a -> b
coe T__'8804'__18
v8))))
                          T__'8804'__18
_ -> Any
forall a. a
MAlonzo.RTE.mazUnreachableError))
-- Data.Integer.Properties.⊖-monoʳ->-<
d_'8854''45'mono'691''45''62''45''60'_2954 ::
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__18 ->
  MAlonzo.Code.Data.Integer.Base.T__'60'__50
d_'8854''45'mono'691''45''62''45''60'_2954 :: Integer -> Integer -> Integer -> T__'8804'__18 -> T__'60'__50
d_'8854''45'mono'691''45''62''45''60'_2954 Integer
v0 Integer
v1 Integer
v2 T__'8804'__18
v3
  = case Integer -> Integer
forall a b. a -> b
coe Integer
v0 of
      Integer
0 -> case T__'8804'__18 -> T__'8804'__18
forall a b. a -> b
coe T__'8804'__18
v3 of
             MAlonzo.Code.Data.Nat.Base.C_s'8804's_30 T__'8804'__18
v6
               -> case T__'8804'__18 -> T__'8804'__18
forall a b. a -> b
coe T__'8804'__18
v6 of
                    T__'8804'__18
MAlonzo.Code.Data.Nat.Base.C_z'8804'n_22
                      -> T__'60'__50 -> T__'60'__50
forall a b. a -> b
coe T__'60'__50
MAlonzo.Code.Data.Integer.Base.C_'45''60''43'_64
                    MAlonzo.Code.Data.Nat.Base.C_s'8804's_30 T__'8804'__18
v9
                      -> (T__'8804'__18 -> T__'60'__50) -> Any -> T__'60'__50
forall a b. a -> b
coe
                           T__'8804'__18 -> T__'60'__50
MAlonzo.Code.Data.Integer.Base.C_'45''60''45'_58
                           ((T__'8804'__18 -> T__'8804'__18) -> T__'8804'__18 -> Any
forall a b. a -> b
coe T__'8804'__18 -> T__'8804'__18
MAlonzo.Code.Data.Nat.Base.C_s'8804's_30 T__'8804'__18
v9)
                    T__'8804'__18
_ -> T__'60'__50
forall a. a
MAlonzo.RTE.mazUnreachableError
             T__'8804'__18
_ -> T__'60'__50
forall a. a
MAlonzo.RTE.mazUnreachableError
      Integer
_ -> let v4 :: Integer
v4 = Integer -> Integer -> Integer
subInt (Integer -> Integer
forall a b. a -> b
coe Integer
v0) (Integer -> Integer
forall a b. a -> b
coe (Integer
1 :: Integer)) in
           Any -> T__'60'__50
forall a b. a -> b
coe
             (let v5 :: Integer
v5 = Integer -> Integer -> Integer
subInt (Integer -> Integer
forall a b. a -> b
coe Integer
v1) (Integer -> Integer
forall a b. a -> b
coe (Integer
1 :: Integer)) in
              Any -> Any
forall a b. a -> b
coe
                (case T__'8804'__18 -> T__'8804'__18
forall a b. a -> b
coe T__'8804'__18
v3 of
                   MAlonzo.Code.Data.Nat.Base.C_s'8804's_30 T__'8804'__18
v8
                     -> case T__'8804'__18 -> T__'8804'__18
forall a b. a -> b
coe T__'8804'__18
v8 of
                          T__'8804'__18
MAlonzo.Code.Data.Nat.Base.C_z'8804'n_22
                            -> (T__IsRelatedTo__70 -> Any) -> Any -> Any
forall a b. a -> b
coe
                                 T__IsRelatedTo__70 -> Any
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_begin'45'strict__176
                                 (((Any -> Any -> Any -> Any -> Any -> Any)
 -> T_Σ_14
 -> (Any -> Any -> Any -> Any -> Any -> Any)
 -> Any
 -> Any
 -> Any
 -> T__IsRelatedTo__70
 -> Any
 -> T__IsRelatedTo__70)
-> (Any -> Any -> Any -> Any -> Any -> Any)
-> Any
-> (Any -> Any -> Any -> Any -> Any -> Any)
-> Any
-> Any
-> Any
-> Any
-> Any
-> Any
forall a b. a -> b
coe
                                    (Any -> Any -> Any -> Any -> Any -> Any)
-> T_Σ_14
-> (Any -> Any -> Any -> Any -> Any -> Any)
-> Any
-> Any
-> Any
-> T__IsRelatedTo__70
-> Any
-> T__IsRelatedTo__70
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_step'45''60'_202
                                    (\ Any
v10 Any
v11 Any
v12 Any
v13 Any
v14 ->
                                       (Integer -> Integer -> T__'60'__50 -> T__'60'__50 -> T__'60'__50)
-> Any -> Any -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> T__'60'__50 -> T__'60'__50 -> T__'60'__50
du_'60''45'trans_1872 Any
v10 Any
v11 Any
v13 Any
v14)
                                    (T_Σ_14 -> Any
forall a b. a -> b
coe
                                       T_Σ_14
MAlonzo.Code.Relation.Binary.PropositionalEquality.Core.du_resp'8322'_144)
                                    (\ Any
v10 Any
v11 Any
v12 Any
v13 Any
v14 ->
                                       (T__'60'__50 -> T__'8804'__26 -> T__'60'__50) -> Any -> Any -> Any
forall a b. a -> b
coe T__'60'__50 -> T__'8804'__26 -> T__'60'__50
du_'60''45''8804''45'trans_1858 Any
v13 Any
v14)
                                    ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe
                                       Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'8854'__224 (Integer -> Any
forall a b. a -> b
coe Integer
v4)
                                       (Integer -> Any
forall a b. a -> b
coe Integer
v5))
                                    (Integer -> Any
forall a b. a -> b
coe Integer
v0) (Integer -> Any
forall a b. a -> b
coe Integer
v0)
                                    ((T_IsPreorder_70 -> Any -> T__IsRelatedTo__70) -> Any -> Any -> Any
forall a b. a -> b
coe
                                       T_IsPreorder_70 -> Any -> T__IsRelatedTo__70
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du__'8718'_346
                                       (T_IsPreorder_70 -> Any
forall a b. a -> b
coe T_IsPreorder_70
d_'8804''45'isPreorder_1656) (Integer -> Any
forall a b. a -> b
coe Integer
v0))
                                    ((Integer -> Integer -> T__'60'__50) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> T__'60'__50
d_m'8854'n'60'1'43'm_2792 (Integer -> Any
forall a b. a -> b
coe Integer
v4) (Integer -> Any
forall a b. a -> b
coe Integer
v5)))
                          MAlonzo.Code.Data.Nat.Base.C_s'8804's_30 T__'8804'__18
v11
                            -> let v12 :: Integer
v12 = Integer -> Integer -> Integer
subInt (Integer -> Integer
forall a b. a -> b
coe Integer
v2) (Integer -> Integer
forall a b. a -> b
coe (Integer
1 :: Integer)) in
                               Any -> Any
forall a b. a -> b
coe
                                 ((T__IsRelatedTo__70 -> Any) -> Any -> Any
forall a b. a -> b
coe
                                    T__IsRelatedTo__70 -> Any
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_begin'45'strict__176
                                    (((Any -> Any -> Any -> Any -> Any -> Any)
 -> T_Σ_14
 -> (Any -> Any -> Any -> Any -> Any -> Any)
 -> Any
 -> Any
 -> Any
 -> T__IsRelatedTo__70
 -> Any
 -> T__IsRelatedTo__70)
-> (Any -> Any -> Any -> Any -> Any -> Any)
-> Any
-> (Any -> Any -> Any -> Any -> Any -> Any)
-> Any
-> Any
-> Any
-> Any
-> Any
-> Any
forall a b. a -> b
coe
                                       (Any -> Any -> Any -> Any -> Any -> Any)
-> T_Σ_14
-> (Any -> Any -> Any -> Any -> Any -> Any)
-> Any
-> Any
-> Any
-> T__IsRelatedTo__70
-> Any
-> T__IsRelatedTo__70
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_step'45''60'_202
                                       (\ Any
v13 Any
v14 Any
v15 Any
v16 Any
v17 ->
                                          (Integer -> Integer -> T__'60'__50 -> T__'60'__50 -> T__'60'__50)
-> Any -> Any -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> T__'60'__50 -> T__'60'__50 -> T__'60'__50
du_'60''45'trans_1872 Any
v13 Any
v14 Any
v16 Any
v17)
                                       (T_Σ_14 -> Any
forall a b. a -> b
coe
                                          T_Σ_14
MAlonzo.Code.Relation.Binary.PropositionalEquality.Core.du_resp'8322'_144)
                                       (\ Any
v13 Any
v14 Any
v15 Any
v16 Any
v17 ->
                                          (T__'60'__50 -> T__'8804'__26 -> T__'60'__50) -> Any -> Any -> Any
forall a b. a -> b
coe T__'60'__50 -> T__'8804'__26 -> T__'60'__50
du_'60''45''8804''45'trans_1858 Any
v16 Any
v17)
                                       ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe
                                          Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'8854'__224 (Integer -> Any
forall a b. a -> b
coe Integer
v4)
                                          ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> Integer
subInt (Integer -> Any
forall a b. a -> b
coe Integer
v1) (Integer -> Any
forall a b. a -> b
coe (Integer
1 :: Integer))))
                                       ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe
                                          Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'8854'__224 (Integer -> Any
forall a b. a -> b
coe Integer
v4)
                                          (Integer -> Any
forall a b. a -> b
coe Integer
v12))
                                       ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe
                                          Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'8854'__224 (Integer -> Any
forall a b. a -> b
coe Integer
v0)
                                          (Integer -> Any
forall a b. a -> b
coe Integer
v2))
                                       ((T_IsPreorder_70 -> Any -> T__IsRelatedTo__70) -> Any -> Any -> Any
forall a b. a -> b
coe
                                          T_IsPreorder_70 -> Any -> T__IsRelatedTo__70
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du__'8718'_346
                                          (T_IsPreorder_70 -> Any
forall a b. a -> b
coe T_IsPreorder_70
d_'8804''45'isPreorder_1656)
                                          ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe
                                             Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'8854'__224 (Integer -> Any
forall a b. a -> b
coe Integer
v0)
                                             (Integer -> Any
forall a b. a -> b
coe Integer
v2)))
                                       ((Integer -> Integer -> Integer -> T__'8804'__18 -> T__'60'__50)
-> Any -> Any -> Any -> Any -> Any
forall a b. a -> b
coe
                                          Integer -> Integer -> Integer -> T__'8804'__18 -> T__'60'__50
d_'8854''45'mono'691''45''62''45''60'_2954 (Integer -> Any
forall a b. a -> b
coe Integer
v4)
                                          ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> Integer
subInt (Integer -> Any
forall a b. a -> b
coe Integer
v1) (Integer -> Any
forall a b. a -> b
coe (Integer
1 :: Integer))) (Integer -> Any
forall a b. a -> b
coe Integer
v12)
                                          ((T__'8804'__18 -> T__'8804'__18) -> T__'8804'__18 -> Any
forall a b. a -> b
coe T__'8804'__18 -> T__'8804'__18
MAlonzo.Code.Data.Nat.Base.C_s'8804's_30 T__'8804'__18
v11))))
                          T__'8804'__18
_ -> Any
forall a. a
MAlonzo.RTE.mazUnreachableError
                   T__'8804'__18
_ -> Any
forall a. a
MAlonzo.RTE.mazUnreachableError))
-- Data.Integer.Properties.⊖-monoˡ-<
d_'8854''45'mono'737''45''60'_2982 ::
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__18 ->
  MAlonzo.Code.Data.Integer.Base.T__'60'__50
d_'8854''45'mono'737''45''60'_2982 :: Integer -> Integer -> Integer -> T__'8804'__18 -> T__'60'__50
d_'8854''45'mono'737''45''60'_2982 Integer
v0 Integer
v1 Integer
v2 T__'8804'__18
v3
  = case Integer -> Integer
forall a b. a -> b
coe Integer
v0 of
      Integer
0 -> (T__'8804'__18 -> T__'60'__50) -> T__'8804'__18 -> T__'60'__50
forall a b. a -> b
coe T__'8804'__18 -> T__'60'__50
MAlonzo.Code.Data.Integer.Base.C_'43''60''43'_72 T__'8804'__18
v3
      Integer
_ -> let v4 :: Integer
v4 = Integer -> Integer -> Integer
subInt (Integer -> Integer
forall a b. a -> b
coe Integer
v0) (Integer -> Integer
forall a b. a -> b
coe (Integer
1 :: Integer)) in
           Any -> T__'60'__50
forall a b. a -> b
coe
             (case T__'8804'__18 -> T__'8804'__18
forall a b. a -> b
coe T__'8804'__18
v3 of
                MAlonzo.Code.Data.Nat.Base.C_s'8804's_30 T__'8804'__18
v7
                  -> let v8 :: Integer
v8 = Integer -> Integer -> Integer
subInt (Integer -> Integer
forall a b. a -> b
coe Integer
v2) (Integer -> Integer
forall a b. a -> b
coe (Integer
1 :: Integer)) in
                     Any -> Any
forall a b. a -> b
coe
                       (case T__'8804'__18 -> T__'8804'__18
forall a b. a -> b
coe T__'8804'__18
v7 of
                          T__'8804'__18
MAlonzo.Code.Data.Nat.Base.C_z'8804'n_22
                            -> (T__IsRelatedTo__70 -> Any) -> Any -> Any
forall a b. a -> b
coe
                                 T__IsRelatedTo__70 -> Any
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_begin'45'strict__176
                                 (((Any -> Any -> Any -> Any -> Any -> Any)
 -> T_Σ_14
 -> (Any -> Any -> Any -> Any -> Any -> Any)
 -> Any
 -> Any
 -> Any
 -> T__IsRelatedTo__70
 -> Any
 -> T__IsRelatedTo__70)
-> (Any -> Any -> Any -> Any -> Any -> Any)
-> Any
-> (Any -> Any -> Any -> Any -> Any -> Any)
-> Any
-> Any
-> Any
-> Any
-> Any
-> Any
forall a b. a -> b
coe
                                    (Any -> Any -> Any -> Any -> Any -> Any)
-> T_Σ_14
-> (Any -> Any -> Any -> Any -> Any -> Any)
-> Any
-> Any
-> Any
-> T__IsRelatedTo__70
-> Any
-> T__IsRelatedTo__70
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_step'45''60'_202
                                    (\ Any
v10 Any
v11 Any
v12 Any
v13 Any
v14 ->
                                       (Integer -> Integer -> T__'60'__50 -> T__'60'__50 -> T__'60'__50)
-> Any -> Any -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> T__'60'__50 -> T__'60'__50 -> T__'60'__50
du_'60''45'trans_1872 Any
v10 Any
v11 Any
v13 Any
v14)
                                    (T_Σ_14 -> Any
forall a b. a -> b
coe
                                       T_Σ_14
MAlonzo.Code.Relation.Binary.PropositionalEquality.Core.du_resp'8322'_144)
                                    (\ Any
v10 Any
v11 Any
v12 Any
v13 Any
v14 ->
                                       (T__'60'__50 -> T__'8804'__26 -> T__'60'__50) -> Any -> Any -> Any
forall a b. a -> b
coe T__'60'__50 -> T__'8804'__26 -> T__'60'__50
du_'60''45''8804''45'trans_1858 Any
v13 Any
v14)
                                    ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> Integer
subInt (Integer -> Any
forall a b. a -> b
coe (Integer
0 :: Integer)) (Integer -> Any
forall a b. a -> b
coe Integer
v0))
                                    ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe
                                       Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'8854'__224 (Integer -> Any
forall a b. a -> b
coe Integer
v8)
                                       (Integer -> Any
forall a b. a -> b
coe Integer
v4))
                                    ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe
                                       Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'8854'__224 (Integer -> Any
forall a b. a -> b
coe Integer
v2)
                                       (Integer -> Any
forall a b. a -> b
coe Integer
v0))
                                    ((T_IsPreorder_70 -> Any -> T__IsRelatedTo__70) -> Any -> Any -> Any
forall a b. a -> b
coe
                                       T_IsPreorder_70 -> Any -> T__IsRelatedTo__70
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du__'8718'_346
                                       (T_IsPreorder_70 -> Any
forall a b. a -> b
coe T_IsPreorder_70
d_'8804''45'isPreorder_1656)
                                       ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe
                                          Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'8854'__224 (Integer -> Any
forall a b. a -> b
coe Integer
v2)
                                          (Integer -> Any
forall a b. a -> b
coe Integer
v0)))
                                    ((Integer -> Integer -> T__'60'__50) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> T__'60'__50
d_'45'1'43'm'60'n'8854'm_2818 (Integer -> Any
forall a b. a -> b
coe Integer
v4) (Integer -> Any
forall a b. a -> b
coe Integer
v8)))
                          MAlonzo.Code.Data.Nat.Base.C_s'8804's_30 T__'8804'__18
v11
                            -> let v12 :: Integer
v12 = Integer -> Integer -> Integer
subInt (Integer -> Integer
forall a b. a -> b
coe Integer
v1) (Integer -> Integer
forall a b. a -> b
coe (Integer
1 :: Integer)) in
                               Any -> Any
forall a b. a -> b
coe
                                 ((T__IsRelatedTo__70 -> Any) -> Any -> Any
forall a b. a -> b
coe
                                    T__IsRelatedTo__70 -> Any
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_begin'45'strict__176
                                    (((Any -> Any -> Any -> Any -> Any -> Any)
 -> T_Σ_14
 -> (Any -> Any -> Any -> Any -> Any -> Any)
 -> Any
 -> Any
 -> Any
 -> T__IsRelatedTo__70
 -> Any
 -> T__IsRelatedTo__70)
-> (Any -> Any -> Any -> Any -> Any -> Any)
-> Any
-> (Any -> Any -> Any -> Any -> Any -> Any)
-> Any
-> Any
-> Any
-> Any
-> Any
-> Any
forall a b. a -> b
coe
                                       (Any -> Any -> Any -> Any -> Any -> Any)
-> T_Σ_14
-> (Any -> Any -> Any -> Any -> Any -> Any)
-> Any
-> Any
-> Any
-> T__IsRelatedTo__70
-> Any
-> T__IsRelatedTo__70
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_step'45''60'_202
                                       (\ Any
v13 Any
v14 Any
v15 Any
v16 Any
v17 ->
                                          (Integer -> Integer -> T__'60'__50 -> T__'60'__50 -> T__'60'__50)
-> Any -> Any -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> T__'60'__50 -> T__'60'__50 -> T__'60'__50
du_'60''45'trans_1872 Any
v13 Any
v14 Any
v16 Any
v17)
                                       (T_Σ_14 -> Any
forall a b. a -> b
coe
                                          T_Σ_14
MAlonzo.Code.Relation.Binary.PropositionalEquality.Core.du_resp'8322'_144)
                                       (\ Any
v13 Any
v14 Any
v15 Any
v16 Any
v17 ->
                                          (T__'60'__50 -> T__'8804'__26 -> T__'60'__50) -> Any -> Any -> Any
forall a b. a -> b
coe T__'60'__50 -> T__'8804'__26 -> T__'60'__50
du_'60''45''8804''45'trans_1858 Any
v16 Any
v17)
                                       ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe
                                          Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'8854'__224 (Integer -> Any
forall a b. a -> b
coe Integer
v12)
                                          (Integer -> Any
forall a b. a -> b
coe Integer
v4))
                                       ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe
                                          Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'8854'__224
                                          ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> Integer
subInt (Integer -> Any
forall a b. a -> b
coe Integer
v2) (Integer -> Any
forall a b. a -> b
coe (Integer
1 :: Integer))) (Integer -> Any
forall a b. a -> b
coe Integer
v4))
                                       ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe
                                          Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'8854'__224 (Integer -> Any
forall a b. a -> b
coe Integer
v2)
                                          (Integer -> Any
forall a b. a -> b
coe Integer
v0))
                                       ((T_IsPreorder_70 -> Any -> T__IsRelatedTo__70) -> Any -> Any -> Any
forall a b. a -> b
coe
                                          T_IsPreorder_70 -> Any -> T__IsRelatedTo__70
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du__'8718'_346
                                          (T_IsPreorder_70 -> Any
forall a b. a -> b
coe T_IsPreorder_70
d_'8804''45'isPreorder_1656)
                                          ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe
                                             Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'8854'__224 (Integer -> Any
forall a b. a -> b
coe Integer
v2)
                                             (Integer -> Any
forall a b. a -> b
coe Integer
v0)))
                                       ((Integer -> Integer -> Integer -> T__'8804'__18 -> T__'60'__50)
-> Any -> Any -> Any -> Any -> Any
forall a b. a -> b
coe
                                          Integer -> Integer -> Integer -> T__'8804'__18 -> T__'60'__50
d_'8854''45'mono'737''45''60'_2982 (Integer -> Any
forall a b. a -> b
coe Integer
v4) (Integer -> Any
forall a b. a -> b
coe Integer
v12)
                                          ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> Integer
subInt (Integer -> Any
forall a b. a -> b
coe Integer
v2) (Integer -> Any
forall a b. a -> b
coe (Integer
1 :: Integer)))
                                          ((T__'8804'__18 -> T__'8804'__18) -> T__'8804'__18 -> Any
forall a b. a -> b
coe T__'8804'__18 -> T__'8804'__18
MAlonzo.Code.Data.Nat.Base.C_s'8804's_30 T__'8804'__18
v11))))
                          T__'8804'__18
_ -> Any
forall a. a
MAlonzo.RTE.mazUnreachableError)
                T__'8804'__18
_ -> Any
forall a. a
MAlonzo.RTE.mazUnreachableError)
-- Data.Integer.Properties.+-comm
d_'43''45'comm_3006 ::
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'43''45'comm_3006 :: Integer -> Integer -> T__'8801'__12
d_'43''45'comm_3006 = Integer -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.+-identityˡ
d_'43''45'identity'737'_3016 ::
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'43''45'identity'737'_3016 :: Integer -> T__'8801'__12
d_'43''45'identity'737'_3016 = Integer -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.+-identityʳ
d_'43''45'identity'691'_3018 ::
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'43''45'identity'691'_3018 :: Integer -> T__'8801'__12
d_'43''45'identity'691'_3018 = Integer -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.+-identity
d_'43''45'identity_3020 :: MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'43''45'identity_3020 :: T_Σ_14
d_'43''45'identity_3020
  = (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.Integer.Properties.distribˡ-⊖-+-pos
d_distrib'737''45''8854''45''43''45'pos_3028 ::
  Integer ->
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_distrib'737''45''8854''45''43''45'pos_3028 :: Integer -> Integer -> Integer -> T__'8801'__12
d_distrib'737''45''8854''45''43''45'pos_3028 = Integer -> Integer -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.distribˡ-⊖-+-neg
d_distrib'737''45''8854''45''43''45'neg_3048 ::
  Integer ->
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_distrib'737''45''8854''45''43''45'neg_3048 :: Integer -> Integer -> Integer -> T__'8801'__12
d_distrib'737''45''8854''45''43''45'neg_3048 = Integer -> Integer -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.distribʳ-⊖-+-pos
d_distrib'691''45''8854''45''43''45'pos_3068 ::
  Integer ->
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_distrib'691''45''8854''45''43''45'pos_3068 :: Integer -> Integer -> Integer -> T__'8801'__12
d_distrib'691''45''8854''45''43''45'pos_3068 = Integer -> Integer -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.distribʳ-⊖-+-neg
d_distrib'691''45''8854''45''43''45'neg_3088 ::
  Integer ->
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_distrib'691''45''8854''45''43''45'neg_3088 :: Integer -> Integer -> Integer -> T__'8801'__12
d_distrib'691''45''8854''45''43''45'neg_3088 = Integer -> Integer -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.+-assoc
d_'43''45'assoc_3102 ::
  Integer ->
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'43''45'assoc_3102 :: Integer -> Integer -> Integer -> T__'8801'__12
d_'43''45'assoc_3102 = Integer -> Integer -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.+-inverseˡ
d_'43''45'inverse'737'_3282 ::
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'43''45'inverse'737'_3282 :: Integer -> T__'8801'__12
d_'43''45'inverse'737'_3282 = Integer -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.+-inverseʳ
d_'43''45'inverse'691'_3288 ::
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'43''45'inverse'691'_3288 :: Integer -> T__'8801'__12
d_'43''45'inverse'691'_3288 = Integer -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.+-inverse
d_'43''45'inverse_3290 :: MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'43''45'inverse_3290 :: T_Σ_14
d_'43''45'inverse_3290
  = (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.Integer.Properties.+-isMagma
d_'43''45'isMagma_3292 ::
  MAlonzo.Code.Algebra.Structures.T_IsMagma_86
d_'43''45'isMagma_3292 :: T_IsMagma_86
d_'43''45'isMagma_3292
  = (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.Integer.Properties.+-isSemigroup
d_'43''45'isSemigroup_3294 ::
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_194
d_'43''45'isSemigroup_3294 :: T_IsSemigroup_194
d_'43''45'isSemigroup_3294
  = (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_'43''45'isMagma_3292) Any
forall a. a
erased
-- Data.Integer.Properties.+-isCommutativeSemigroup
d_'43''45'isCommutativeSemigroup_3296 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_270
d_'43''45'isCommutativeSemigroup_3296 :: T_IsCommutativeSemigroup_270
d_'43''45'isCommutativeSemigroup_3296
  = (T_IsSemigroup_194
 -> (Any -> Any -> Any) -> T_IsCommutativeSemigroup_270)
-> Any -> Any -> T_IsCommutativeSemigroup_270
forall a b. a -> b
coe
      T_IsSemigroup_194
-> (Any -> Any -> Any) -> T_IsCommutativeSemigroup_270
MAlonzo.Code.Algebra.Structures.C_IsCommutativeSemigroup'46'constructor_5673
      (T_IsSemigroup_194 -> Any
forall a b. a -> b
coe T_IsSemigroup_194
d_'43''45'isSemigroup_3294) Any
forall a. a
erased
-- Data.Integer.Properties.+-0-isMonoid
d_'43''45'0'45'isMonoid_3298 ::
  MAlonzo.Code.Algebra.Structures.T_IsMonoid_358
d_'43''45'0'45'isMonoid_3298 :: T_IsMonoid_358
d_'43''45'0'45'isMonoid_3298
  = (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_'43''45'isSemigroup_3294) (T_Σ_14 -> Any
forall a b. a -> b
coe T_Σ_14
d_'43''45'identity_3020)
-- Data.Integer.Properties.+-0-isCommutativeMonoid
d_'43''45'0'45'isCommutativeMonoid_3300 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMonoid_406
d_'43''45'0'45'isCommutativeMonoid_3300 :: T_IsCommutativeMonoid_406
d_'43''45'0'45'isCommutativeMonoid_3300
  = (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_'43''45'0'45'isMonoid_3298) Any
forall a. a
erased
-- Data.Integer.Properties.+-0-isGroup
d_'43''45'0'45'isGroup_3302 ::
  MAlonzo.Code.Algebra.Structures.T_IsGroup_580
d_'43''45'0'45'isGroup_3302 :: T_IsGroup_580
d_'43''45'0'45'isGroup_3302
  = (T_IsMonoid_358
 -> T_Σ_14 -> (Any -> Any -> Any -> Any) -> T_IsGroup_580)
-> Any -> Any -> Any -> T_IsGroup_580
forall a b. a -> b
coe
      T_IsMonoid_358
-> T_Σ_14 -> (Any -> Any -> Any -> Any) -> T_IsGroup_580
MAlonzo.Code.Algebra.Structures.C_IsGroup'46'constructor_12945
      (T_IsMonoid_358 -> Any
forall a b. a -> b
coe T_IsMonoid_358
d_'43''45'0'45'isMonoid_3298) (T_Σ_14 -> Any
forall a b. a -> b
coe T_Σ_14
d_'43''45'inverse_3290)
      Any
forall a. a
erased
-- Data.Integer.Properties.+-isAbelianGroup
d_'43''45'isAbelianGroup_3304 ::
  MAlonzo.Code.Algebra.Structures.T_IsAbelianGroup_662
d_'43''45'isAbelianGroup_3304 :: T_IsAbelianGroup_662
d_'43''45'isAbelianGroup_3304
  = (T_IsGroup_580 -> (Any -> Any -> Any) -> T_IsAbelianGroup_662)
-> Any -> Any -> T_IsAbelianGroup_662
forall a b. a -> b
coe
      T_IsGroup_580 -> (Any -> Any -> Any) -> T_IsAbelianGroup_662
MAlonzo.Code.Algebra.Structures.C_IsAbelianGroup'46'constructor_17421
      (T_IsGroup_580 -> Any
forall a b. a -> b
coe T_IsGroup_580
d_'43''45'0'45'isGroup_3302) Any
forall a. a
erased
-- Data.Integer.Properties.+-magma
d_'43''45'magma_3306 :: MAlonzo.Code.Algebra.Bundles.T_Magma_36
d_'43''45'magma_3306 :: T_Magma_36
d_'43''45'magma_3306
  = ((Any -> Any -> Any) -> T_IsMagma_86 -> T_Magma_36)
-> (Integer -> Integer -> Integer) -> 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
      Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'43'__242 T_IsMagma_86
d_'43''45'isMagma_3292
-- Data.Integer.Properties.+-semigroup
d_'43''45'semigroup_3308 ::
  MAlonzo.Code.Algebra.Bundles.T_Semigroup_206
d_'43''45'semigroup_3308 :: T_Semigroup_206
d_'43''45'semigroup_3308
  = ((Any -> Any -> Any) -> T_IsSemigroup_194 -> T_Semigroup_206)
-> (Integer -> Integer -> Integer)
-> 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
      Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'43'__242
      T_IsSemigroup_194
d_'43''45'isSemigroup_3294
-- Data.Integer.Properties.+-commutativeSemigroup
d_'43''45'commutativeSemigroup_3310 ::
  MAlonzo.Code.Algebra.Bundles.T_CommutativeSemigroup_332
d_'43''45'commutativeSemigroup_3310 :: T_CommutativeSemigroup_332
d_'43''45'commutativeSemigroup_3310
  = ((Any -> Any -> Any)
 -> T_IsCommutativeSemigroup_270 -> T_CommutativeSemigroup_332)
-> (Integer -> Integer -> Integer)
-> T_IsCommutativeSemigroup_270
-> T_CommutativeSemigroup_332
forall a b. a -> b
coe
      (Any -> Any -> Any)
-> T_IsCommutativeSemigroup_270 -> T_CommutativeSemigroup_332
MAlonzo.Code.Algebra.Bundles.C_CommutativeSemigroup'46'constructor_5887
      Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'43'__242
      T_IsCommutativeSemigroup_270
d_'43''45'isCommutativeSemigroup_3296
-- Data.Integer.Properties.+-0-monoid
d_'43''45'0'45'monoid_3312 ::
  MAlonzo.Code.Algebra.Bundles.T_Monoid_506
d_'43''45'0'45'monoid_3312 :: T_Monoid_506
d_'43''45'0'45'monoid_3312
  = ((Any -> Any -> Any) -> Any -> T_IsMonoid_358 -> T_Monoid_506)
-> (Integer -> Integer -> Integer)
-> Integer
-> T_IsMonoid_358
-> T_Monoid_506
forall a b. a -> b
coe
      (Any -> Any -> Any) -> Any -> T_IsMonoid_358 -> T_Monoid_506
MAlonzo.Code.Algebra.Bundles.C_Monoid'46'constructor_8851
      Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'43'__242 (Integer
0 :: Integer)
      T_IsMonoid_358
d_'43''45'0'45'isMonoid_3298
-- Data.Integer.Properties.+-0-commutativeMonoid
d_'43''45'0'45'commutativeMonoid_3314 ::
  MAlonzo.Code.Algebra.Bundles.T_CommutativeMonoid_582
d_'43''45'0'45'commutativeMonoid_3314 :: T_CommutativeMonoid_582
d_'43''45'0'45'commutativeMonoid_3314
  = ((Any -> Any -> Any)
 -> Any -> T_IsCommutativeMonoid_406 -> T_CommutativeMonoid_582)
-> (Integer -> Integer -> Integer)
-> Integer
-> 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
      Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'43'__242 (Integer
0 :: Integer)
      T_IsCommutativeMonoid_406
d_'43''45'0'45'isCommutativeMonoid_3300
-- Data.Integer.Properties.+-0-abelianGroup
d_'43''45'0'45'abelianGroup_3316 ::
  MAlonzo.Code.Algebra.Bundles.T_AbelianGroup_990
d_'43''45'0'45'abelianGroup_3316 :: T_AbelianGroup_990
d_'43''45'0'45'abelianGroup_3316
  = ((Any -> Any -> Any)
 -> Any
 -> (Any -> Any)
 -> T_IsAbelianGroup_662
 -> T_AbelianGroup_990)
-> (Integer -> Integer -> Integer)
-> Integer
-> (Integer -> Integer)
-> T_IsAbelianGroup_662
-> T_AbelianGroup_990
forall a b. a -> b
coe
      (Any -> Any -> Any)
-> Any
-> (Any -> Any)
-> T_IsAbelianGroup_662
-> T_AbelianGroup_990
MAlonzo.Code.Algebra.Bundles.C_AbelianGroup'46'constructor_16529
      Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'43'__242 (Integer
0 :: Integer)
      Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d_'45'__218
      T_IsAbelianGroup_662
d_'43''45'isAbelianGroup_3304
-- Data.Integer.Properties.pos-+-commute
d_pos'45''43''45'commute_3318 ::
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_pos'45''43''45'commute_3318 :: Integer -> Integer -> T__'8801'__12
d_pos'45''43''45'commute_3318 = Integer -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.neg-distrib-+
d_neg'45'distrib'45''43'_3330 ::
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_neg'45'distrib'45''43'_3330 :: Integer -> Integer -> T__'8801'__12
d_neg'45'distrib'45''43'_3330 = Integer -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.◃-distrib-+
d_'9667''45'distrib'45''43'_3360 ::
  MAlonzo.Code.Data.Sign.Base.T_Sign_6 ->
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'9667''45'distrib'45''43'_3360 :: T_Sign_6 -> Integer -> Integer -> T__'8801'__12
d_'9667''45'distrib'45''43'_3360 = T_Sign_6 -> Integer -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.+-pos-monoʳ-≤
d_'43''45'pos'45'mono'691''45''8804'_3380 ::
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26 ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26
d_'43''45'pos'45'mono'691''45''8804'_3380 :: Integer -> Integer -> Integer -> T__'8804'__26 -> T__'8804'__26
d_'43''45'pos'45'mono'691''45''8804'_3380 Integer
v0 Integer
v1 Integer
v2 T__'8804'__26
v3
  = case T__'8804'__26 -> T__'8804'__26
forall a b. a -> b
coe T__'8804'__26
v3 of
      MAlonzo.Code.Data.Integer.Base.C_'45''8804''45'_34 T__'8804'__18
v6
        -> (Integer -> Integer -> Integer -> T__'8804'__18 -> T__'8804'__26)
-> Any -> Any -> Any -> Any -> T__'8804'__26
forall a b. a -> b
coe
             Integer -> Integer -> Integer -> T__'8804'__18 -> T__'8804'__26
d_'8854''45'mono'691''45''8805''45''8804'_2892 (Integer -> Any
forall a b. a -> b
coe Integer
v0)
             ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> Integer
subInt (Integer -> Any
forall a b. a -> b
coe (Integer
0 :: Integer)) (Integer -> Any
forall a b. a -> b
coe Integer
v1))
             ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> Integer
subInt (Integer -> Any
forall a b. a -> b
coe (Integer
0 :: Integer)) (Integer -> Any
forall a b. a -> b
coe Integer
v2))
             ((T__'8804'__18 -> T__'8804'__18) -> T__'8804'__18 -> Any
forall a b. a -> b
coe T__'8804'__18 -> T__'8804'__18
MAlonzo.Code.Data.Nat.Base.C_s'8804's_30 T__'8804'__18
v6)
      T__'8804'__26
MAlonzo.Code.Data.Integer.Base.C_'45''8804''43'_40
        -> (T__'8804'__26 -> T__'8804'__26 -> T__'8804'__26)
-> Any -> Any -> T__'8804'__26
forall a b. a -> b
coe
             T__'8804'__26 -> T__'8804'__26 -> T__'8804'__26
du_'8804''45'trans_1586
             ((Integer -> Integer -> T__'8804'__26) -> Any -> Any -> Any
forall a b. a -> b
coe
                Integer -> Integer -> T__'8804'__26
d_m'8854'n'8804'm_2774 (Integer -> Any
forall a b. a -> b
coe Integer
v0)
                ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> Integer
subInt (Integer -> Any
forall a b. a -> b
coe (Integer
0 :: Integer)) (Integer -> Any
forall a b. a -> b
coe Integer
v1)))
             ((T__'8804'__18 -> T__'8804'__26) -> Any -> Any
forall a b. a -> b
coe
                T__'8804'__18 -> T__'8804'__26
MAlonzo.Code.Data.Integer.Base.C_'43''8804''43'_48
                ((Integer -> T__'8804'__18) -> Any -> Any
forall a b. a -> b
coe
                   Integer -> T__'8804'__18
MAlonzo.Code.Data.Nat.Properties.du_m'8804'm'43'n_2316 (Integer -> Any
forall a b. a -> b
coe Integer
v0)))
      MAlonzo.Code.Data.Integer.Base.C_'43''8804''43'_48 T__'8804'__18
v6
        -> (T__'8804'__18 -> T__'8804'__26) -> Any -> T__'8804'__26
forall a b. a -> b
coe
             T__'8804'__18 -> T__'8804'__26
MAlonzo.Code.Data.Integer.Base.C_'43''8804''43'_48
             ((Integer -> Integer -> T__'8804'__18 -> T__'8804'__18)
-> Any -> Any -> Any -> Any
forall a b. a -> b
coe
                Integer -> Integer -> T__'8804'__18 -> T__'8804'__18
MAlonzo.Code.Data.Nat.Properties.du_'43''45'mono'691''45''8804'_2422
                (Integer -> Any
forall a b. a -> b
coe Integer
v0) (Integer -> Any
forall a b. a -> b
coe Integer
v2) (T__'8804'__18 -> Any
forall a b. a -> b
coe T__'8804'__18
v6))
      T__'8804'__26
_ -> T__'8804'__26
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Data.Integer.Properties.+-neg-monoʳ-≤
d_'43''45'neg'45'mono'691''45''8804'_3396 ::
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26 ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26
d_'43''45'neg'45'mono'691''45''8804'_3396 :: Integer -> Integer -> Integer -> T__'8804'__26 -> T__'8804'__26
d_'43''45'neg'45'mono'691''45''8804'_3396 Integer
v0 Integer
v1 Integer
v2 T__'8804'__26
v3
  = case T__'8804'__26 -> T__'8804'__26
forall a b. a -> b
coe T__'8804'__26
v3 of
      MAlonzo.Code.Data.Integer.Base.C_'45''8804''45'_34 T__'8804'__18
v6
        -> let v7 :: Integer
v7 = Integer -> Integer -> Integer
subInt (Integer -> Integer
forall a b. a -> b
coe (-Integer
1 :: Integer)) (Integer -> Integer
forall a b. a -> b
coe Integer
v1) in
           Any -> T__'8804'__26
forall a b. a -> b
coe
             ((T__'8804'__18 -> T__'8804'__26) -> Any -> Any
forall a b. a -> b
coe
                T__'8804'__18 -> T__'8804'__26
MAlonzo.Code.Data.Integer.Base.C_'45''8804''45'_34
                ((Integer -> Integer -> T__'8804'__18 -> T__'8804'__18)
-> Any -> Any -> Any -> Any
forall a b. a -> b
coe
                   Integer -> Integer -> T__'8804'__18 -> T__'8804'__18
MAlonzo.Code.Data.Nat.Properties.du_'43''45'mono'691''45''8804'_2422
                   ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> Integer
addInt (Integer -> Any
forall a b. a -> b
coe (Integer
1 :: Integer)) (Integer -> Any
forall a b. a -> b
coe Integer
v0)) (Integer -> Any
forall a b. a -> b
coe Integer
v7) (T__'8804'__18 -> Any
forall a b. a -> b
coe T__'8804'__18
v6)))
      T__'8804'__26
MAlonzo.Code.Data.Integer.Base.C_'45''8804''43'_40
        -> (T__'8804'__26 -> T__'8804'__26 -> T__'8804'__26)
-> Any -> Any -> T__'8804'__26
forall a b. a -> b
coe
             T__'8804'__26 -> T__'8804'__26 -> T__'8804'__26
du_'8804''45'trans_1586
             ((T__'8804'__18 -> T__'8804'__26) -> Any -> Any
forall a b. a -> b
coe
                T__'8804'__18 -> T__'8804'__26
MAlonzo.Code.Data.Integer.Base.C_'45''8804''45'_34
                ((Integer -> T__'8804'__18) -> Any -> Any
forall a b. a -> b
coe
                   Integer -> T__'8804'__18
MAlonzo.Code.Data.Nat.Properties.du_m'8804'm'43'n_2316
                   ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> Integer
addInt (Integer -> Any
forall a b. a -> b
coe (Integer
1 :: Integer)) (Integer -> Any
forall a b. a -> b
coe Integer
v0))))
             ((Integer -> Integer -> T__'8804'__26) -> Any -> Any -> Any
forall a b. a -> b
coe
                Integer -> Integer -> T__'8804'__26
d_'45'1'43'm'8804'n'8854'm_2852
                ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> Integer
addInt (Integer -> Any
forall a b. a -> b
coe (Integer
1 :: Integer)) (Integer -> Any
forall a b. a -> b
coe Integer
v0)) (Integer -> Any
forall a b. a -> b
coe Integer
v2))
      MAlonzo.Code.Data.Integer.Base.C_'43''8804''43'_48 T__'8804'__18
v6
        -> (Integer -> Integer -> Integer -> T__'8804'__18 -> T__'8804'__26)
-> Any -> Any -> Any -> Any -> T__'8804'__26
forall a b. a -> b
coe
             Integer -> Integer -> Integer -> T__'8804'__18 -> T__'8804'__26
d_'8854''45'mono'737''45''8804'_2924
             ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> Integer
addInt (Integer -> Any
forall a b. a -> b
coe (Integer
1 :: Integer)) (Integer -> Any
forall a b. a -> b
coe Integer
v0)) (Integer -> Any
forall a b. a -> b
coe Integer
v1) (Integer -> Any
forall a b. a -> b
coe Integer
v2)
             (T__'8804'__18 -> Any
forall a b. a -> b
coe T__'8804'__18
v6)
      T__'8804'__26
_ -> T__'8804'__26
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Data.Integer.Properties.+-monoʳ-≤
d_'43''45'mono'691''45''8804'_3412 ::
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26 ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26
d_'43''45'mono'691''45''8804'_3412 :: Integer -> Integer -> Integer -> T__'8804'__26 -> T__'8804'__26
d_'43''45'mono'691''45''8804'_3412 Integer
v0 Integer
v1 Integer
v2
  = case Integer -> Any
forall a b. a -> b
coe Integer
v0 of
      Any
_ | (Integer -> Integer -> Bool) -> Any -> Any -> Bool
forall a b. a -> b
coe Integer -> Integer -> Bool
geqInt (Integer -> Any
forall a b. a -> b
coe Integer
v0) (Integer -> Any
forall a b. a -> b
coe (Integer
0 :: Integer)) ->
          (Integer -> Integer -> Integer -> T__'8804'__26 -> T__'8804'__26)
-> Any -> Any -> Any -> T__'8804'__26 -> T__'8804'__26
forall a b. a -> b
coe
            Integer -> Integer -> Integer -> T__'8804'__26 -> T__'8804'__26
d_'43''45'pos'45'mono'691''45''8804'_3380 (Integer -> Any
forall a b. a -> b
coe Integer
v0) (Integer -> Any
forall a b. a -> b
coe Integer
v1)
            (Integer -> Any
forall a b. a -> b
coe Integer
v2)
      Any
_ -> let v3 :: Integer
v3 = Integer -> Integer -> Integer
subInt (Integer -> Integer
forall a b. a -> b
coe (-Integer
1 :: Integer)) (Integer -> Integer
forall a b. a -> b
coe Integer
v0) in
           Any -> T__'8804'__26 -> T__'8804'__26
forall a b. a -> b
coe
             ((Integer -> Integer -> Integer -> T__'8804'__26 -> T__'8804'__26)
-> Any -> Any -> Any -> Any
forall a b. a -> b
coe
                Integer -> Integer -> Integer -> T__'8804'__26 -> T__'8804'__26
d_'43''45'neg'45'mono'691''45''8804'_3396 (Integer -> Any
forall a b. a -> b
coe Integer
v3) (Integer -> Any
forall a b. a -> b
coe Integer
v1)
                (Integer -> Any
forall a b. a -> b
coe Integer
v2))
-- Data.Integer.Properties.+-monoˡ-≤
d_'43''45'mono'737''45''8804'_3422 ::
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26 ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26
d_'43''45'mono'737''45''8804'_3422 :: Integer -> Integer -> Integer -> T__'8804'__26 -> T__'8804'__26
d_'43''45'mono'737''45''8804'_3422 Integer
v0 Integer
v1 Integer
v2 T__'8804'__26
v3
  = (Integer -> Integer -> Integer -> T__'8804'__26 -> T__'8804'__26)
-> Integer -> Integer -> Integer -> T__'8804'__26 -> T__'8804'__26
forall a b. a -> b
coe Integer -> Integer -> Integer -> T__'8804'__26 -> T__'8804'__26
d_'43''45'mono'691''45''8804'_3412 Integer
v0 Integer
v1 Integer
v2 T__'8804'__26
v3
-- Data.Integer.Properties.+-mono-≤
d_'43''45'mono'45''8804'_3440 ::
  Integer ->
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26 ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26 ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26
d_'43''45'mono'45''8804'_3440 :: Integer
-> Integer
-> Integer
-> Integer
-> T__'8804'__26
-> T__'8804'__26
-> T__'8804'__26
d_'43''45'mono'45''8804'_3440 Integer
v0 Integer
v1 Integer
v2 Integer
v3 T__'8804'__26
v4 T__'8804'__26
v5
  = (T_IsPreorder_70
 -> (Any -> Any -> Any -> Any)
 -> Any
 -> Any
 -> T__IsRelatedTo__70
 -> Any)
-> Any -> Any -> Any -> Any -> Any -> T__'8804'__26
forall a b. a -> b
coe
      T_IsPreorder_70
-> (Any -> Any -> Any -> Any)
-> Any
-> Any
-> T__IsRelatedTo__70
-> Any
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_begin__160
      (T_IsPreorder_70 -> Any
forall a b. a -> b
coe T_IsPreorder_70
d_'8804''45'isPreorder_1656) ((Integer -> Integer -> T__'60'__50 -> T__'8804'__26) -> Any
forall a b. a -> b
coe Integer -> Integer -> T__'60'__50 -> T__'8804'__26
d_'60''8658''8804'_1724)
      ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'43'__242 (Integer -> Any
forall a b. a -> b
coe Integer
v0) (Integer -> Any
forall a b. a -> b
coe Integer
v2))
      ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'43'__242 (Integer -> Any
forall a b. a -> b
coe Integer
v1) (Integer -> Any
forall a b. a -> b
coe Integer
v3))
      ((T_IsPreorder_70
 -> (Any -> Any -> Any -> Any -> Any -> Any)
 -> Any
 -> Any
 -> Any
 -> T__IsRelatedTo__70
 -> Any
 -> T__IsRelatedTo__70)
-> Any
-> (Any -> Any -> Any -> Any -> Any -> Any)
-> Any
-> Any
-> Any
-> Any
-> Any
-> Any
forall a b. a -> b
coe
         T_IsPreorder_70
-> (Any -> Any -> Any -> Any -> Any -> Any)
-> Any
-> Any
-> Any
-> T__IsRelatedTo__70
-> Any
-> T__IsRelatedTo__70
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_step'45''8804'_228
         (T_IsPreorder_70 -> Any
forall a b. a -> b
coe T_IsPreorder_70
d_'8804''45'isPreorder_1656)
         (\ Any
v6 Any
v7 Any
v8 Any
v9 Any
v10 -> (T__'8804'__26 -> T__'60'__50 -> T__'60'__50) -> Any -> Any -> Any
forall a b. a -> b
coe T__'8804'__26 -> T__'60'__50 -> T__'60'__50
du_'8804''45''60''45'trans_1844 Any
v9 Any
v10)
         ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'43'__242 (Integer -> Any
forall a b. a -> b
coe Integer
v0) (Integer -> Any
forall a b. a -> b
coe Integer
v2))
         ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'43'__242 (Integer -> Any
forall a b. a -> b
coe Integer
v1) (Integer -> Any
forall a b. a -> b
coe Integer
v2))
         ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'43'__242 (Integer -> Any
forall a b. a -> b
coe Integer
v1) (Integer -> Any
forall a b. a -> b
coe Integer
v3))
         ((T_IsPreorder_70
 -> (Any -> Any -> Any -> Any -> Any -> Any)
 -> Any
 -> Any
 -> Any
 -> T__IsRelatedTo__70
 -> Any
 -> T__IsRelatedTo__70)
-> Any
-> (Any -> Any -> Any -> Any -> Any -> Any)
-> Any
-> Any
-> Any
-> Any
-> Any
-> Any
forall a b. a -> b
coe
            T_IsPreorder_70
-> (Any -> Any -> Any -> Any -> Any -> Any)
-> Any
-> Any
-> Any
-> T__IsRelatedTo__70
-> Any
-> T__IsRelatedTo__70
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_step'45''8804'_228
            (T_IsPreorder_70 -> Any
forall a b. a -> b
coe T_IsPreorder_70
d_'8804''45'isPreorder_1656)
            (\ Any
v6 Any
v7 Any
v8 Any
v9 Any
v10 -> (T__'8804'__26 -> T__'60'__50 -> T__'60'__50) -> Any -> Any -> Any
forall a b. a -> b
coe T__'8804'__26 -> T__'60'__50 -> T__'60'__50
du_'8804''45''60''45'trans_1844 Any
v9 Any
v10)
            ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'43'__242 (Integer -> Any
forall a b. a -> b
coe Integer
v1) (Integer -> Any
forall a b. a -> b
coe Integer
v2))
            ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'43'__242 (Integer -> Any
forall a b. a -> b
coe Integer
v1) (Integer -> Any
forall a b. a -> b
coe Integer
v3))
            ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'43'__242 (Integer -> Any
forall a b. a -> b
coe Integer
v1) (Integer -> Any
forall a b. a -> b
coe Integer
v3))
            ((T_IsPreorder_70 -> Any -> T__IsRelatedTo__70) -> Any -> Any -> Any
forall a b. a -> b
coe
               T_IsPreorder_70 -> Any -> T__IsRelatedTo__70
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du__'8718'_346
               (T_IsPreorder_70 -> Any
forall a b. a -> b
coe T_IsPreorder_70
d_'8804''45'isPreorder_1656)
               ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe
                  Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'43'__242 (Integer -> Any
forall a b. a -> b
coe Integer
v1) (Integer -> Any
forall a b. a -> b
coe Integer
v3)))
            ((Integer -> Integer -> Integer -> T__'8804'__26 -> T__'8804'__26)
-> Integer -> Integer -> Integer -> T__'8804'__26 -> Any
forall a b. a -> b
coe Integer -> Integer -> Integer -> T__'8804'__26 -> T__'8804'__26
d_'43''45'mono'691''45''8804'_3412 Integer
v1 Integer
v2 Integer
v3 T__'8804'__26
v5))
         ((Integer -> Integer -> Integer -> T__'8804'__26 -> T__'8804'__26)
-> Any -> Any -> Any -> Any -> Any
forall a b. a -> b
coe
            Integer -> Integer -> Integer -> T__'8804'__26 -> T__'8804'__26
d_'43''45'mono'737''45''8804'_3422 (Integer -> Any
forall a b. a -> b
coe Integer
v2) (Integer -> Any
forall a b. a -> b
coe Integer
v0) (Integer -> Any
forall a b. a -> b
coe Integer
v1)
            (T__'8804'__26 -> Any
forall a b. a -> b
coe T__'8804'__26
v4)))
-- Data.Integer.Properties.≤-steps
d_'8804''45'steps_3464 ::
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26 ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26
d_'8804''45'steps_3464 :: Integer -> Integer -> Integer -> T__'8804'__26 -> T__'8804'__26
d_'8804''45'steps_3464 Integer
v0 Integer
v1 Integer
v2 T__'8804'__26
v3
  = (Integer
 -> Integer
 -> Integer
 -> Integer
 -> T__'8804'__26
 -> T__'8804'__26
 -> T__'8804'__26)
-> Any -> Any -> Any -> Any -> Any -> Any -> T__'8804'__26
forall a b. a -> b
coe
      Integer
-> Integer
-> Integer
-> Integer
-> T__'8804'__26
-> T__'8804'__26
-> T__'8804'__26
d_'43''45'mono'45''8804'_3440 (Integer -> Any
forall a b. a -> b
coe (Integer
0 :: Integer)) (Integer -> Any
forall a b. a -> b
coe Integer
v2)
      (Integer -> Any
forall a b. a -> b
coe Integer
v0) (Integer -> Any
forall a b. a -> b
coe Integer
v1)
      ((T__'8804'__18 -> T__'8804'__26) -> Any -> Any
forall a b. a -> b
coe
         T__'8804'__18 -> T__'8804'__26
MAlonzo.Code.Data.Integer.Base.C_'43''8804''43'_48
         (T__'8804'__18 -> Any
forall a b. a -> b
coe T__'8804'__18
MAlonzo.Code.Data.Nat.Base.C_z'8804'n_22))
      (T__'8804'__26 -> Any
forall a b. a -> b
coe T__'8804'__26
v3)
-- Data.Integer.Properties.m≤m+n
d_m'8804'm'43'n_3476 ::
  Integer -> Integer -> MAlonzo.Code.Data.Integer.Base.T__'8804'__26
d_m'8804'm'43'n_3476 :: Integer -> Integer -> T__'8804'__26
d_m'8804'm'43'n_3476 Integer
v0 Integer
v1
  = (T_IsPreorder_70
 -> (Any -> Any -> Any -> Any)
 -> Any
 -> Any
 -> T__IsRelatedTo__70
 -> Any)
-> Any -> Any -> Any -> Any -> Any -> T__'8804'__26
forall a b. a -> b
coe
      T_IsPreorder_70
-> (Any -> Any -> Any -> Any)
-> Any
-> Any
-> T__IsRelatedTo__70
-> Any
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_begin__160
      (T_IsPreorder_70 -> Any
forall a b. a -> b
coe T_IsPreorder_70
d_'8804''45'isPreorder_1656) ((Integer -> Integer -> T__'60'__50 -> T__'8804'__26) -> Any
forall a b. a -> b
coe Integer -> Integer -> T__'60'__50 -> T__'8804'__26
d_'60''8658''8804'_1724)
      (Integer -> Any
forall a b. a -> b
coe Integer
v0)
      ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'43'__242 (Integer -> Any
forall a b. a -> b
coe Integer
v0) (Integer -> Any
forall a b. a -> b
coe Integer
v1))
      ((T_IsPreorder_70
 -> (Any -> Any -> Any -> Any -> Any -> Any)
 -> Any
 -> Any
 -> Any
 -> T__IsRelatedTo__70
 -> Any
 -> T__IsRelatedTo__70)
-> Any
-> (Any -> Any -> Any -> Any -> Any -> Any)
-> Any
-> Any
-> Any
-> Any
-> Any
-> Any
forall a b. a -> b
coe
         T_IsPreorder_70
-> (Any -> Any -> Any -> Any -> Any -> Any)
-> Any
-> Any
-> Any
-> T__IsRelatedTo__70
-> Any
-> T__IsRelatedTo__70
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_step'45''8804'_228
         (T_IsPreorder_70 -> Any
forall a b. a -> b
coe T_IsPreorder_70
d_'8804''45'isPreorder_1656)
         (\ Any
v2 Any
v3 Any
v4 Any
v5 Any
v6 -> (T__'8804'__26 -> T__'60'__50 -> T__'60'__50) -> Any -> Any -> Any
forall a b. a -> b
coe T__'8804'__26 -> T__'60'__50 -> T__'60'__50
du_'8804''45''60''45'trans_1844 Any
v5 Any
v6)
         ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe
            Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'43'__242 (Integer -> Any
forall a b. a -> b
coe Integer
v0)
            (Integer -> Any
forall a b. a -> b
coe (Integer
0 :: Integer)))
         ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'43'__242 (Integer -> Any
forall a b. a -> b
coe Integer
v0) (Integer -> Any
forall a b. a -> b
coe Integer
v1))
         ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'43'__242 (Integer -> Any
forall a b. a -> b
coe Integer
v0) (Integer -> Any
forall a b. a -> b
coe Integer
v1))
         ((T_IsPreorder_70 -> Any -> T__IsRelatedTo__70) -> Any -> Any -> Any
forall a b. a -> b
coe
            T_IsPreorder_70 -> Any -> T__IsRelatedTo__70
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du__'8718'_346
            (T_IsPreorder_70 -> Any
forall a b. a -> b
coe T_IsPreorder_70
d_'8804''45'isPreorder_1656)
            ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe
               Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'43'__242 (Integer -> Any
forall a b. a -> b
coe Integer
v0) (Integer -> Any
forall a b. a -> b
coe Integer
v1)))
         ((Integer -> Integer -> Integer -> T__'8804'__26 -> T__'8804'__26)
-> Integer -> Integer -> Integer -> Any -> Any
forall a b. a -> b
coe
            Integer -> Integer -> Integer -> T__'8804'__26 -> T__'8804'__26
d_'43''45'mono'691''45''8804'_3412 Integer
v0 (Integer
0 :: Integer) Integer
v1
            ((T__'8804'__18 -> T__'8804'__26) -> Any -> Any
forall a b. a -> b
coe
               T__'8804'__18 -> T__'8804'__26
MAlonzo.Code.Data.Integer.Base.C_'43''8804''43'_48
               (T__'8804'__18 -> Any
forall a b. a -> b
coe T__'8804'__18
MAlonzo.Code.Data.Nat.Base.C_z'8804'n_22))))
-- Data.Integer.Properties.n≤m+n
d_n'8804'm'43'n_3490 ::
  Integer -> Integer -> MAlonzo.Code.Data.Integer.Base.T__'8804'__26
d_n'8804'm'43'n_3490 :: Integer -> Integer -> T__'8804'__26
d_n'8804'm'43'n_3490 Integer
v0 Integer
v1
  = (Integer -> Integer -> T__'8804'__26)
-> Any -> Any -> T__'8804'__26
forall a b. a -> b
coe Integer -> Integer -> T__'8804'__26
d_m'8804'm'43'n_3476 (Integer -> Any
forall a b. a -> b
coe Integer
v1) (Integer -> Any
forall a b. a -> b
coe Integer
v0)
-- Data.Integer.Properties.+-monoʳ-<
d_'43''45'mono'691''45''60'_3502 ::
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Integer.Base.T__'60'__50 ->
  MAlonzo.Code.Data.Integer.Base.T__'60'__50
d_'43''45'mono'691''45''60'_3502 :: Integer -> Integer -> Integer -> T__'60'__50 -> T__'60'__50
d_'43''45'mono'691''45''60'_3502 Integer
v0 Integer
v1 Integer
v2 T__'60'__50
v3
  = case Integer -> Any
forall a b. a -> b
coe Integer
v0 of
      Any
_ | (Integer -> Integer -> Bool) -> Any -> Any -> Bool
forall a b. a -> b
coe Integer -> Integer -> Bool
geqInt (Integer -> Any
forall a b. a -> b
coe Integer
v0) (Integer -> Any
forall a b. a -> b
coe (Integer
0 :: Integer)) ->
          case T__'60'__50 -> T__'60'__50
forall a b. a -> b
coe T__'60'__50
v3 of
            MAlonzo.Code.Data.Integer.Base.C_'45''60''45'_58 T__'8804'__18
v6
              -> (Integer -> Integer -> Integer -> T__'8804'__18 -> T__'60'__50)
-> Any -> Any -> Any -> Any -> T__'60'__50
forall a b. a -> b
coe
                   Integer -> Integer -> Integer -> T__'8804'__18 -> T__'60'__50
d_'8854''45'mono'691''45''62''45''60'_2954 (Integer -> Any
forall a b. a -> b
coe Integer
v0)
                   ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> Integer
subInt (Integer -> Any
forall a b. a -> b
coe (Integer
0 :: Integer)) (Integer -> Any
forall a b. a -> b
coe Integer
v1))
                   ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> Integer
subInt (Integer -> Any
forall a b. a -> b
coe (Integer
0 :: Integer)) (Integer -> Any
forall a b. a -> b
coe Integer
v2))
                   ((T__'8804'__18 -> T__'8804'__18) -> T__'8804'__18 -> Any
forall a b. a -> b
coe T__'8804'__18 -> T__'8804'__18
MAlonzo.Code.Data.Nat.Base.C_s'8804's_30 T__'8804'__18
v6)
            T__'60'__50
MAlonzo.Code.Data.Integer.Base.C_'45''60''43'_64
              -> let v6 :: Integer
v6 = Integer -> Integer -> Integer
subInt (Integer -> Integer
forall a b. a -> b
coe (-Integer
1 :: Integer)) (Integer -> Integer
forall a b. a -> b
coe Integer
v1) in
                 Any -> T__'60'__50
forall a b. a -> b
coe
                   ((T__'60'__50 -> T__'8804'__26 -> T__'60'__50) -> Any -> Any -> Any
forall a b. a -> b
coe
                      T__'60'__50 -> T__'8804'__26 -> T__'60'__50
du_'60''45''8804''45'trans_1858
                      ((Integer -> Integer -> T__'60'__50) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> T__'60'__50
d_m'8854'1'43'n'60'm_2802 (Integer -> Any
forall a b. a -> b
coe Integer
v0) (Integer -> Any
forall a b. a -> b
coe Integer
v6))
                      ((T__'8804'__18 -> T__'8804'__26) -> Any -> Any
forall a b. a -> b
coe
                         T__'8804'__18 -> T__'8804'__26
MAlonzo.Code.Data.Integer.Base.C_'43''8804''43'_48
                         ((Integer -> T__'8804'__18) -> Any -> Any
forall a b. a -> b
coe
                            Integer -> T__'8804'__18
MAlonzo.Code.Data.Nat.Properties.du_m'8804'm'43'n_2316 (Integer -> Any
forall a b. a -> b
coe Integer
v0))))
            MAlonzo.Code.Data.Integer.Base.C_'43''60''43'_72 T__'8804'__18
v6
              -> (T__'8804'__18 -> T__'60'__50) -> Any -> T__'60'__50
forall a b. a -> b
coe
                   T__'8804'__18 -> T__'60'__50
MAlonzo.Code.Data.Integer.Base.C_'43''60''43'_72
                   ((Integer -> T__'8804'__18 -> T__'8804'__18) -> Any -> Any -> Any
forall a b. a -> b
coe
                      Integer -> T__'8804'__18 -> T__'8804'__18
MAlonzo.Code.Data.Nat.Properties.du_'43''45'mono'691''45''60'_2464
                      (Integer -> Any
forall a b. a -> b
coe Integer
v0) (T__'8804'__18 -> Any
forall a b. a -> b
coe T__'8804'__18
v6))
            T__'60'__50
_ -> T__'60'__50
forall a. a
MAlonzo.RTE.mazUnreachableError
      Any
_ -> let v4 :: Integer
v4 = Integer -> Integer -> Integer
subInt (Integer -> Integer
forall a b. a -> b
coe (-Integer
1 :: Integer)) (Integer -> Integer
forall a b. a -> b
coe Integer
v0) in
           Any -> T__'60'__50
forall a b. a -> b
coe
             (case T__'60'__50 -> T__'60'__50
forall a b. a -> b
coe T__'60'__50
v3 of
                MAlonzo.Code.Data.Integer.Base.C_'45''60''45'_58 T__'8804'__18
v7
                  -> (T__'8804'__18 -> T__'60'__50) -> Any -> Any
forall a b. a -> b
coe
                       T__'8804'__18 -> T__'60'__50
MAlonzo.Code.Data.Integer.Base.C_'45''60''45'_58
                       ((Integer -> T__'8804'__18 -> T__'8804'__18) -> Any -> Any -> Any
forall a b. a -> b
coe
                          Integer -> T__'8804'__18 -> T__'8804'__18
MAlonzo.Code.Data.Nat.Properties.du_'43''45'mono'691''45''60'_2464
                          ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> Integer
subInt (Integer -> Any
forall a b. a -> b
coe (Integer
0 :: Integer)) (Integer -> Any
forall a b. a -> b
coe Integer
v0)) (T__'8804'__18 -> Any
forall a b. a -> b
coe T__'8804'__18
v7))
                T__'60'__50
MAlonzo.Code.Data.Integer.Base.C_'45''60''43'_64
                  -> (T__'60'__50 -> T__'8804'__26 -> T__'60'__50) -> Any -> Any -> Any
forall a b. a -> b
coe
                       T__'60'__50 -> T__'8804'__26 -> T__'60'__50
du_'60''45''8804''45'trans_1858
                       ((T__'8804'__18 -> T__'60'__50) -> Any -> Any
forall a b. a -> b
coe
                          T__'8804'__18 -> T__'60'__50
MAlonzo.Code.Data.Integer.Base.C_'45''60''45'_58
                          ((Integer -> T__'8804'__18) -> Any -> Any
forall a b. a -> b
coe
                             Integer -> T__'8804'__18
MAlonzo.Code.Data.Nat.Properties.du_m'8804'm'43'n_2316
                             ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> Integer
subInt (Integer -> Any
forall a b. a -> b
coe (Integer
0 :: Integer)) (Integer -> Any
forall a b. a -> b
coe Integer
v0))))
                       ((Integer -> Integer -> T__'8804'__26) -> Any -> Any -> Any
forall a b. a -> b
coe
                          Integer -> Integer -> T__'8804'__26
d_'45''91'1'43'm'93''8804'n'8854'm'43'1_2836 (Integer -> Any
forall a b. a -> b
coe Integer
v4) (Integer -> Any
forall a b. a -> b
coe Integer
v2))
                MAlonzo.Code.Data.Integer.Base.C_'43''60''43'_72 T__'8804'__18
v7
                  -> (Integer -> Integer -> Integer -> T__'8804'__18 -> T__'60'__50)
-> Any -> Any -> Any -> Any -> Any
forall a b. a -> b
coe
                       Integer -> Integer -> Integer -> T__'8804'__18 -> T__'60'__50
d_'8854''45'mono'737''45''60'_2982
                       ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> Integer
subInt (Integer -> Any
forall a b. a -> b
coe (Integer
0 :: Integer)) (Integer -> Any
forall a b. a -> b
coe Integer
v0)) (Integer -> Any
forall a b. a -> b
coe Integer
v1) (Integer -> Any
forall a b. a -> b
coe Integer
v2)
                       (T__'8804'__18 -> Any
forall a b. a -> b
coe T__'8804'__18
v7)
                T__'60'__50
_ -> Any
forall a. a
MAlonzo.RTE.mazUnreachableError)
-- Data.Integer.Properties.+-monoˡ-<
d_'43''45'mono'737''45''60'_3530 ::
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Integer.Base.T__'60'__50 ->
  MAlonzo.Code.Data.Integer.Base.T__'60'__50
d_'43''45'mono'737''45''60'_3530 :: Integer -> Integer -> Integer -> T__'60'__50 -> T__'60'__50
d_'43''45'mono'737''45''60'_3530 Integer
v0 Integer
v1 Integer
v2 T__'60'__50
v3
  = (Integer -> Integer -> Integer -> T__'60'__50 -> T__'60'__50)
-> Any -> Any -> Any -> Any -> T__'60'__50
forall a b. a -> b
coe
      Integer -> Integer -> Integer -> T__'60'__50 -> T__'60'__50
d_'43''45'mono'691''45''60'_3502 (Integer -> Any
forall a b. a -> b
coe Integer
v0) (Integer -> Any
forall a b. a -> b
coe Integer
v1) (Integer -> Any
forall a b. a -> b
coe Integer
v2)
      (T__'60'__50 -> Any
forall a b. a -> b
coe T__'60'__50
v3)
-- Data.Integer.Properties.+-mono-<
d_'43''45'mono'45''60'_3548 ::
  Integer ->
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Integer.Base.T__'60'__50 ->
  MAlonzo.Code.Data.Integer.Base.T__'60'__50 ->
  MAlonzo.Code.Data.Integer.Base.T__'60'__50
d_'43''45'mono'45''60'_3548 :: Integer
-> Integer
-> Integer
-> Integer
-> T__'60'__50
-> T__'60'__50
-> T__'60'__50
d_'43''45'mono'45''60'_3548 Integer
v0 Integer
v1 Integer
v2 Integer
v3 T__'60'__50
v4 T__'60'__50
v5
  = (T__IsRelatedTo__70 -> Any) -> Any -> T__'60'__50
forall a b. a -> b
coe
      T__IsRelatedTo__70 -> Any
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_begin'45'strict__176
      (((Any -> Any -> Any -> Any -> Any -> Any)
 -> T_Σ_14
 -> (Any -> Any -> Any -> Any -> Any -> Any)
 -> Any
 -> Any
 -> Any
 -> T__IsRelatedTo__70
 -> Any
 -> T__IsRelatedTo__70)
-> (Any -> Any -> Any -> Any -> Any -> Any)
-> Any
-> (Any -> Any -> Any -> Any -> Any -> Any)
-> Any
-> Any
-> Any
-> Any
-> Any
-> Any
forall a b. a -> b
coe
         (Any -> Any -> Any -> Any -> Any -> Any)
-> T_Σ_14
-> (Any -> Any -> Any -> Any -> Any -> Any)
-> Any
-> Any
-> Any
-> T__IsRelatedTo__70
-> Any
-> T__IsRelatedTo__70
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_step'45''60'_202
         (\ Any
v6 Any
v7 Any
v8 Any
v9 Any
v10 -> (Integer -> Integer -> T__'60'__50 -> T__'60'__50 -> T__'60'__50)
-> Any -> Any -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> T__'60'__50 -> T__'60'__50 -> T__'60'__50
du_'60''45'trans_1872 Any
v6 Any
v7 Any
v9 Any
v10)
         (T_Σ_14 -> Any
forall a b. a -> b
coe
            T_Σ_14
MAlonzo.Code.Relation.Binary.PropositionalEquality.Core.du_resp'8322'_144)
         (\ Any
v6 Any
v7 Any
v8 Any
v9 Any
v10 -> (T__'60'__50 -> T__'8804'__26 -> T__'60'__50) -> Any -> Any -> Any
forall a b. a -> b
coe T__'60'__50 -> T__'8804'__26 -> T__'60'__50
du_'60''45''8804''45'trans_1858 Any
v9 Any
v10)
         ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'43'__242 (Integer -> Any
forall a b. a -> b
coe Integer
v0) (Integer -> Any
forall a b. a -> b
coe Integer
v2))
         ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'43'__242 (Integer -> Any
forall a b. a -> b
coe Integer
v1) (Integer -> Any
forall a b. a -> b
coe Integer
v2))
         ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'43'__242 (Integer -> Any
forall a b. a -> b
coe Integer
v1) (Integer -> Any
forall a b. a -> b
coe Integer
v3))
         (((Any -> Any -> Any -> Any -> Any -> Any)
 -> T_Σ_14
 -> (Any -> Any -> Any -> Any -> Any -> Any)
 -> Any
 -> Any
 -> Any
 -> T__IsRelatedTo__70
 -> Any
 -> T__IsRelatedTo__70)
-> (Any -> Any -> Any -> Any -> Any -> Any)
-> Any
-> (Any -> Any -> Any -> Any -> Any -> Any)
-> Any
-> Any
-> Any
-> Any
-> Any
-> Any
forall a b. a -> b
coe
            (Any -> Any -> Any -> Any -> Any -> Any)
-> T_Σ_14
-> (Any -> Any -> Any -> Any -> Any -> Any)
-> Any
-> Any
-> Any
-> T__IsRelatedTo__70
-> Any
-> T__IsRelatedTo__70
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_step'45''60'_202
            (\ Any
v6 Any
v7 Any
v8 Any
v9 Any
v10 -> (Integer -> Integer -> T__'60'__50 -> T__'60'__50 -> T__'60'__50)
-> Any -> Any -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> T__'60'__50 -> T__'60'__50 -> T__'60'__50
du_'60''45'trans_1872 Any
v6 Any
v7 Any
v9 Any
v10)
            (T_Σ_14 -> Any
forall a b. a -> b
coe
               T_Σ_14
MAlonzo.Code.Relation.Binary.PropositionalEquality.Core.du_resp'8322'_144)
            (\ Any
v6 Any
v7 Any
v8 Any
v9 Any
v10 -> (T__'60'__50 -> T__'8804'__26 -> T__'60'__50) -> Any -> Any -> Any
forall a b. a -> b
coe T__'60'__50 -> T__'8804'__26 -> T__'60'__50
du_'60''45''8804''45'trans_1858 Any
v9 Any
v10)
            ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'43'__242 (Integer -> Any
forall a b. a -> b
coe Integer
v1) (Integer -> Any
forall a b. a -> b
coe Integer
v2))
            ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'43'__242 (Integer -> Any
forall a b. a -> b
coe Integer
v1) (Integer -> Any
forall a b. a -> b
coe Integer
v3))
            ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'43'__242 (Integer -> Any
forall a b. a -> b
coe Integer
v1) (Integer -> Any
forall a b. a -> b
coe Integer
v3))
            ((T_IsPreorder_70 -> Any -> T__IsRelatedTo__70) -> Any -> Any -> Any
forall a b. a -> b
coe
               T_IsPreorder_70 -> Any -> T__IsRelatedTo__70
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du__'8718'_346
               (T_IsPreorder_70 -> Any
forall a b. a -> b
coe T_IsPreorder_70
d_'8804''45'isPreorder_1656)
               ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe
                  Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'43'__242 (Integer -> Any
forall a b. a -> b
coe Integer
v1) (Integer -> Any
forall a b. a -> b
coe Integer
v3)))
            ((Integer -> Integer -> Integer -> T__'60'__50 -> T__'60'__50)
-> Any -> Any -> Any -> Any -> Any
forall a b. a -> b
coe
               Integer -> Integer -> Integer -> T__'60'__50 -> T__'60'__50
d_'43''45'mono'691''45''60'_3502 (Integer -> Any
forall a b. a -> b
coe Integer
v1) (Integer -> Any
forall a b. a -> b
coe Integer
v2) (Integer -> Any
forall a b. a -> b
coe Integer
v3)
               (T__'60'__50 -> Any
forall a b. a -> b
coe T__'60'__50
v5)))
         ((Integer -> Integer -> Integer -> T__'60'__50 -> T__'60'__50)
-> Any -> Any -> Any -> Any -> Any
forall a b. a -> b
coe
            Integer -> Integer -> Integer -> T__'60'__50 -> T__'60'__50
d_'43''45'mono'737''45''60'_3530 (Integer -> Any
forall a b. a -> b
coe Integer
v2) (Integer -> Any
forall a b. a -> b
coe Integer
v0) (Integer -> Any
forall a b. a -> b
coe Integer
v1)
            (T__'60'__50 -> Any
forall a b. a -> b
coe T__'60'__50
v4)))
-- Data.Integer.Properties.+-mono-≤-<
d_'43''45'mono'45''8804''45''60'_3566 ::
  Integer ->
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26 ->
  MAlonzo.Code.Data.Integer.Base.T__'60'__50 ->
  MAlonzo.Code.Data.Integer.Base.T__'60'__50
d_'43''45'mono'45''8804''45''60'_3566 :: Integer
-> Integer
-> Integer
-> Integer
-> T__'8804'__26
-> T__'60'__50
-> T__'60'__50
d_'43''45'mono'45''8804''45''60'_3566 Integer
v0 Integer
v1 Integer
v2 Integer
v3 T__'8804'__26
v4 T__'60'__50
v5
  = (T__'8804'__26 -> T__'60'__50 -> T__'60'__50)
-> Any -> Any -> T__'60'__50
forall a b. a -> b
coe
      T__'8804'__26 -> T__'60'__50 -> T__'60'__50
du_'8804''45''60''45'trans_1844
      ((Integer -> Integer -> Integer -> T__'8804'__26 -> T__'8804'__26)
-> Any -> Any -> Any -> Any -> Any
forall a b. a -> b
coe
         Integer -> Integer -> Integer -> T__'8804'__26 -> T__'8804'__26
d_'43''45'mono'737''45''8804'_3422 (Integer -> Any
forall a b. a -> b
coe Integer
v2) (Integer -> Any
forall a b. a -> b
coe Integer
v0) (Integer -> Any
forall a b. a -> b
coe Integer
v1)
         (T__'8804'__26 -> Any
forall a b. a -> b
coe T__'8804'__26
v4))
      ((Integer -> Integer -> Integer -> T__'60'__50 -> T__'60'__50)
-> Any -> Any -> Any -> Any -> Any
forall a b. a -> b
coe
         Integer -> Integer -> Integer -> T__'60'__50 -> T__'60'__50
d_'43''45'mono'691''45''60'_3502 (Integer -> Any
forall a b. a -> b
coe Integer
v1) (Integer -> Any
forall a b. a -> b
coe Integer
v2) (Integer -> Any
forall a b. a -> b
coe Integer
v3)
         (T__'60'__50 -> Any
forall a b. a -> b
coe T__'60'__50
v5))
-- Data.Integer.Properties.+-mono-<-≤
d_'43''45'mono'45''60''45''8804'_3578 ::
  Integer ->
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Integer.Base.T__'60'__50 ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26 ->
  MAlonzo.Code.Data.Integer.Base.T__'60'__50
d_'43''45'mono'45''60''45''8804'_3578 :: Integer
-> Integer
-> Integer
-> Integer
-> T__'60'__50
-> T__'8804'__26
-> T__'60'__50
d_'43''45'mono'45''60''45''8804'_3578 Integer
v0 Integer
v1 Integer
v2 Integer
v3 T__'60'__50
v4 T__'8804'__26
v5
  = (T__'60'__50 -> T__'8804'__26 -> T__'60'__50)
-> Any -> Any -> T__'60'__50
forall a b. a -> b
coe
      T__'60'__50 -> T__'8804'__26 -> T__'60'__50
du_'60''45''8804''45'trans_1858
      ((Integer -> Integer -> Integer -> T__'60'__50 -> T__'60'__50)
-> Any -> Any -> Any -> Any -> Any
forall a b. a -> b
coe
         Integer -> Integer -> Integer -> T__'60'__50 -> T__'60'__50
d_'43''45'mono'737''45''60'_3530 (Integer -> Any
forall a b. a -> b
coe Integer
v2) (Integer -> Any
forall a b. a -> b
coe Integer
v0) (Integer -> Any
forall a b. a -> b
coe Integer
v1)
         (T__'60'__50 -> Any
forall a b. a -> b
coe T__'60'__50
v4))
      ((Integer -> Integer -> Integer -> T__'8804'__26 -> T__'8804'__26)
-> Integer -> Integer -> Integer -> T__'8804'__26 -> Any
forall a b. a -> b
coe Integer -> Integer -> Integer -> T__'8804'__26 -> T__'8804'__26
d_'43''45'mono'691''45''8804'_3412 Integer
v1 Integer
v2 Integer
v3 T__'8804'__26
v5)
-- Data.Integer.Properties.neg-minus-pos
d_neg'45'minus'45'pos_3594 ::
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_neg'45'minus'45'pos_3594 :: Integer -> Integer -> T__'8801'__12
d_neg'45'minus'45'pos_3594 = Integer -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.+-minus-telescope
d_'43''45'minus'45'telescope_3610 ::
  Integer ->
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'43''45'minus'45'telescope_3610 :: Integer -> Integer -> Integer -> T__'8801'__12
d_'43''45'minus'45'telescope_3610 = Integer -> Integer -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.[+m]-[+n]≡m⊖n
d_'91''43'm'93''45''91''43'n'93''8801'm'8854'n_3632 ::
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'91''43'm'93''45''91''43'n'93''8801'm'8854'n_3632 :: Integer -> Integer -> T__'8801'__12
d_'91''43'm'93''45''91''43'n'93''8801'm'8854'n_3632 = Integer -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.∣m-n∣≡∣n-m∣
d_'8739'm'45'n'8739''8801''8739'n'45'm'8739'_3646 ::
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8739'm'45'n'8739''8801''8739'n'45'm'8739'_3646 :: Integer -> Integer -> T__'8801'__12
d_'8739'm'45'n'8739''8801''8739'n'45'm'8739'_3646 = Integer -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.m≡n⇒m-n≡0
d_m'8801'n'8658'm'45'n'8801'0_3680 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_m'8801'n'8658'm'45'n'8801'0_3680 :: Integer -> Integer -> T__'8801'__12 -> T__'8801'__12
d_m'8801'n'8658'm'45'n'8801'0_3680 = Integer -> Integer -> T__'8801'__12 -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.m-n≡0⇒m≡n
d_m'45'n'8801'0'8658'm'8801'n_3688 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_m'45'n'8801'0'8658'm'8801'n_3688 :: Integer -> Integer -> T__'8801'__12 -> T__'8801'__12
d_m'45'n'8801'0'8658'm'8801'n_3688 = Integer -> Integer -> T__'8801'__12 -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.≤-steps-neg
d_'8804''45'steps'45'neg_3708 ::
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26 ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26
d_'8804''45'steps'45'neg_3708 :: Integer -> Integer -> Integer -> T__'8804'__26 -> T__'8804'__26
d_'8804''45'steps'45'neg_3708 Integer
v0 ~Integer
v1 Integer
v2 T__'8804'__26
v3
  = Integer -> Integer -> T__'8804'__26 -> T__'8804'__26
du_'8804''45'steps'45'neg_3708 Integer
v0 Integer
v2 T__'8804'__26
v3
du_'8804''45'steps'45'neg_3708 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26 ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26
du_'8804''45'steps'45'neg_3708 :: Integer -> Integer -> T__'8804'__26 -> T__'8804'__26
du_'8804''45'steps'45'neg_3708 Integer
v0 Integer
v1 T__'8804'__26
v2
  = case Integer -> Integer
forall a b. a -> b
coe Integer
v1 of
      Integer
0 -> T__'8804'__26 -> T__'8804'__26
forall a b. a -> b
coe T__'8804'__26
v2
      Integer
_ -> let v3 :: Integer
v3 = Integer -> Integer -> Integer
subInt (Integer -> Integer
forall a b. a -> b
coe Integer
v1) (Integer -> Integer
forall a b. a -> b
coe (Integer
1 :: Integer)) in
           Any -> T__'8804'__26
forall a b. a -> b
coe
             (case Integer -> Any
forall a b. a -> b
coe Integer
v0 of
                Any
_ | (Integer -> Integer -> Bool) -> Any -> Any -> Bool
forall a b. a -> b
coe Integer -> Integer -> Bool
geqInt (Integer -> Any
forall a b. a -> b
coe Integer
v0) (Integer -> Any
forall a b. a -> b
coe (Integer
0 :: Integer)) ->
                    (T__'8804'__26 -> T__'8804'__26 -> T__'8804'__26)
-> Any -> Any -> Any
forall a b. a -> b
coe
                      T__'8804'__26 -> T__'8804'__26 -> T__'8804'__26
du_'8804''45'trans_1586
                      ((Integer -> Integer -> T__'8804'__26) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> T__'8804'__26
d_m'8854'n'8804'm_2774 (Integer -> Any
forall a b. a -> b
coe Integer
v0) (Integer -> Any
forall a b. a -> b
coe Integer
v1)) (T__'8804'__26 -> Any
forall a b. a -> b
coe T__'8804'__26
v2)
                Any
_ -> let v4 :: Integer
v4 = Integer -> Integer -> Integer
subInt (Integer -> Integer
forall a b. a -> b
coe (-Integer
1 :: Integer)) (Integer -> Integer
forall a b. a -> b
coe Integer
v0) in
                     Any -> Any
forall a b. a -> b
coe
                       ((T__'8804'__26 -> T__'8804'__26 -> T__'8804'__26)
-> Any -> Any -> Any
forall a b. a -> b
coe
                          T__'8804'__26 -> T__'8804'__26 -> T__'8804'__26
du_'8804''45'trans_1586
                          ((T__'8804'__18 -> T__'8804'__26) -> Any -> Any
forall a b. a -> b
coe
                             T__'8804'__18 -> T__'8804'__26
MAlonzo.Code.Data.Integer.Base.C_'45''8804''45'_34
                             ((T__'8804'__18 -> T__'8804'__18 -> T__'8804'__18)
-> Any -> Any -> Any
forall a b. a -> b
coe
                                T__'8804'__18 -> T__'8804'__18 -> T__'8804'__18
MAlonzo.Code.Data.Nat.Properties.du_'8804''45'trans_1642
                                ((Integer -> T__'8804'__18) -> Any -> Any
forall a b. a -> b
coe
                                   Integer -> T__'8804'__18
MAlonzo.Code.Data.Nat.Properties.du_m'8804'm'43'n_2316 (Integer -> Any
forall a b. a -> b
coe Integer
v4))
                                ((Integer -> T__'8804'__18) -> Any -> Any
forall a b. a -> b
coe
                                   Integer -> T__'8804'__18
MAlonzo.Code.Data.Nat.Properties.d_n'8804'1'43'n_1724
                                   ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> Integer
addInt (Integer -> Any
forall a b. a -> b
coe Integer
v4) (Integer -> Any
forall a b. a -> b
coe Integer
v3)))))
                          (T__'8804'__26 -> Any
forall a b. a -> b
coe T__'8804'__26
v2)))
-- Data.Integer.Properties.neg-mono-≤
d_neg'45'mono'45''8804'_3730 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26 ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26
d_neg'45'mono'45''8804'_3730 :: Integer -> Integer -> T__'8804'__26 -> T__'8804'__26
d_neg'45'mono'45''8804'_3730 ~Integer
v0 Integer
v1 T__'8804'__26
v2
  = Integer -> T__'8804'__26 -> T__'8804'__26
du_neg'45'mono'45''8804'_3730 Integer
v1 T__'8804'__26
v2
du_neg'45'mono'45''8804'_3730 ::
  Integer ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26 ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26
du_neg'45'mono'45''8804'_3730 :: Integer -> T__'8804'__26 -> T__'8804'__26
du_neg'45'mono'45''8804'_3730 Integer
v0 T__'8804'__26
v1
  = case T__'8804'__26 -> T__'8804'__26
forall a b. a -> b
coe T__'8804'__26
v1 of
      MAlonzo.Code.Data.Integer.Base.C_'45''8804''45'_34 T__'8804'__18
v4
        -> (T__'8804'__18 -> T__'8804'__26) -> Any -> T__'8804'__26
forall a b. a -> b
coe
             T__'8804'__18 -> T__'8804'__26
MAlonzo.Code.Data.Integer.Base.C_'43''8804''43'_48
             ((T__'8804'__18 -> T__'8804'__18) -> T__'8804'__18 -> Any
forall a b. a -> b
coe T__'8804'__18 -> T__'8804'__18
MAlonzo.Code.Data.Nat.Base.C_s'8804's_30 T__'8804'__18
v4)
      T__'8804'__26
MAlonzo.Code.Data.Integer.Base.C_'45''8804''43'_40
        -> (Integer -> T__'8804'__26) -> Any -> T__'8804'__26
forall a b. a -> b
coe Integer -> T__'8804'__26
du_neg'45''8804''45'pos_2140 (Integer -> Any
forall a b. a -> b
coe Integer
v0)
      MAlonzo.Code.Data.Integer.Base.C_'43''8804''43'_48 T__'8804'__18
v4
        -> case T__'8804'__18 -> T__'8804'__18
forall a b. a -> b
coe T__'8804'__18
v4 of
             T__'8804'__18
MAlonzo.Code.Data.Nat.Base.C_z'8804'n_22
               -> (Integer -> T__'8804'__26) -> Any -> T__'8804'__26
forall a b. a -> b
coe Integer -> T__'8804'__26
du_neg'45''8804''45'pos_2140 (Integer -> Any
forall a b. a -> b
coe Integer
v0)
             MAlonzo.Code.Data.Nat.Base.C_s'8804's_30 T__'8804'__18
v7
               -> (T__'8804'__18 -> T__'8804'__26) -> T__'8804'__18 -> T__'8804'__26
forall a b. a -> b
coe T__'8804'__18 -> T__'8804'__26
MAlonzo.Code.Data.Integer.Base.C_'45''8804''45'_34 T__'8804'__18
v7
             T__'8804'__18
_ -> T__'8804'__26
forall a. a
MAlonzo.RTE.mazUnreachableError
      T__'8804'__26
_ -> T__'8804'__26
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Data.Integer.Properties.neg-cancel-≤
d_neg'45'cancel'45''8804'_3740 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26 ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26
d_neg'45'cancel'45''8804'_3740 :: Integer -> Integer -> T__'8804'__26 -> T__'8804'__26
d_neg'45'cancel'45''8804'_3740 Integer
v0 Integer
v1 T__'8804'__26
v2
  = case Integer -> Integer
forall a b. a -> b
coe Integer
v0 of
      Integer
0 -> case Integer -> Integer
forall a b. a -> b
coe Integer
v1 of
             Integer
0 -> (T__'8804'__18 -> T__'8804'__26) -> Any -> T__'8804'__26
forall a b. a -> b
coe
                    T__'8804'__18 -> T__'8804'__26
MAlonzo.Code.Data.Integer.Base.C_'43''8804''43'_48
                    (T__'8804'__18 -> Any
forall a b. a -> b
coe T__'8804'__18
MAlonzo.Code.Data.Nat.Base.C_z'8804'n_22)
             Integer
_ -> T__'8804'__26 -> T__'8804'__26
forall a b. a -> b
coe T__'8804'__26
MAlonzo.Code.Data.Integer.Base.C_'45''8804''43'_40
      Integer
_ | (Integer -> Integer -> Bool) -> Any -> Any -> Bool
forall a b. a -> b
coe Integer -> Integer -> Bool
geqInt (Integer -> Any
forall a b. a -> b
coe Integer
v0) (Integer -> Any
forall a b. a -> b
coe (Integer
1 :: Integer)) ->
          case Integer -> Integer
forall a b. a -> b
coe Integer
v1 of
            Integer
0 -> (Any -> Any -> Any) -> Any -> Any -> T__'8804'__26
forall a b. a -> b
coe
                   Any -> Any -> Any
forall a b. a -> b -> b
seq (T__'8804'__26 -> Any
forall a b. a -> b
coe T__'8804'__26
v2)
                   ((T__'8804'__18 -> T__'8804'__26) -> Any -> Any
forall a b. a -> b
coe
                      T__'8804'__18 -> T__'8804'__26
MAlonzo.Code.Data.Integer.Base.C_'43''8804''43'_48
                      (T__'8804'__18 -> Any
forall a b. a -> b
coe T__'8804'__18
MAlonzo.Code.Data.Nat.Base.C_z'8804'n_22))
            Integer
_ | (Integer -> Integer -> Bool) -> Any -> Any -> Bool
forall a b. a -> b
coe Integer -> Integer -> Bool
geqInt (Integer -> Any
forall a b. a -> b
coe Integer
v1) (Integer -> Any
forall a b. a -> b
coe (Integer
1 :: Integer)) ->
                case T__'8804'__26 -> T__'8804'__26
forall a b. a -> b
coe T__'8804'__26
v2 of
                  MAlonzo.Code.Data.Integer.Base.C_'45''8804''45'_34 T__'8804'__18
v5
                    -> (T__'8804'__18 -> T__'8804'__26) -> Any -> T__'8804'__26
forall a b. a -> b
coe
                         T__'8804'__18 -> T__'8804'__26
MAlonzo.Code.Data.Integer.Base.C_'43''8804''43'_48
                         ((T__'8804'__18 -> T__'8804'__18) -> T__'8804'__18 -> Any
forall a b. a -> b
coe T__'8804'__18 -> T__'8804'__18
MAlonzo.Code.Data.Nat.Base.C_s'8804's_30 T__'8804'__18
v5)
                  T__'8804'__26
_ -> T__'8804'__26
forall a. a
MAlonzo.RTE.mazUnreachableError
            Integer
_ -> (Any -> Any -> Any) -> Any -> Any -> T__'8804'__26
forall a b. a -> b
coe
                   Any -> Any -> Any
forall a b. a -> b -> b
seq (T__'8804'__26 -> Any
forall a b. a -> b
coe T__'8804'__26
v2)
                   (T__'8804'__26 -> Any
forall a b. a -> b
coe T__'8804'__26
MAlonzo.Code.Data.Integer.Base.C_'45''8804''43'_40)
      Integer
_ -> case T__'8804'__26 -> T__'8804'__26
forall a b. a -> b
coe T__'8804'__26
v2 of
             MAlonzo.Code.Data.Integer.Base.C_'43''8804''43'_48 T__'8804'__18
v5
               -> case T__'8804'__18 -> T__'8804'__18
forall a b. a -> b
coe T__'8804'__18
v5 of
                    MAlonzo.Code.Data.Nat.Base.C_s'8804's_30 T__'8804'__18
v8
                      -> (T__'8804'__18 -> T__'8804'__26) -> T__'8804'__18 -> T__'8804'__26
forall a b. a -> b
coe T__'8804'__18 -> T__'8804'__26
MAlonzo.Code.Data.Integer.Base.C_'45''8804''45'_34 T__'8804'__18
v8
                    T__'8804'__18
_ -> T__'8804'__26
forall a. a
MAlonzo.RTE.mazUnreachableError
             T__'8804'__26
_ -> T__'8804'__26
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Data.Integer.Properties.m-n≤m
d_m'45'n'8804'm_3768 ::
  Integer -> Integer -> MAlonzo.Code.Data.Integer.Base.T__'8804'__26
d_m'45'n'8804'm_3768 :: Integer -> Integer -> T__'8804'__26
d_m'45'n'8804'm_3768 Integer
v0 Integer
v1
  = (Integer -> Integer -> T__'8804'__26 -> T__'8804'__26)
-> Any -> Any -> Any -> T__'8804'__26
forall a b. a -> b
coe
      Integer -> Integer -> T__'8804'__26 -> T__'8804'__26
du_'8804''45'steps'45'neg_3708 (Integer -> Any
forall a b. a -> b
coe Integer
v0) (Integer -> Any
forall a b. a -> b
coe Integer
v1)
      ((Integer -> T__'8804'__26) -> Any -> Any
forall a b. a -> b
coe Integer -> T__'8804'__26
d_'8804''45'refl_1584 (Integer -> Any
forall a b. a -> b
coe Integer
v0))
-- Data.Integer.Properties.m≤n⇒m-n≤0
d_m'8804'n'8658'm'45'n'8804'0_3778 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26 ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26
d_m'8804'n'8658'm'45'n'8804'0_3778 :: Integer -> Integer -> T__'8804'__26 -> T__'8804'__26
d_m'8804'n'8658'm'45'n'8804'0_3778 Integer
v0 Integer
v1 T__'8804'__26
v2
  = case T__'8804'__26 -> T__'8804'__26
forall a b. a -> b
coe T__'8804'__26
v2 of
      MAlonzo.Code.Data.Integer.Base.C_'45''8804''45'_34 T__'8804'__18
v5
        -> let v6 :: Integer
v6 = Integer -> Integer -> Integer
subInt (Integer -> Integer
forall a b. a -> b
coe (-Integer
1 :: Integer)) (Integer -> Integer
forall a b. a -> b
coe Integer
v0) in
           Any -> T__'8804'__26
forall a b. a -> b
coe
             (let v7 :: Integer
v7 = Integer -> Integer -> Integer
subInt (Integer -> Integer
forall a b. a -> b
coe (-Integer
1 :: Integer)) (Integer -> Integer
forall a b. a -> b
coe Integer
v1) in
              Any -> Any
forall a b. a -> b
coe
                ((T_IsPreorder_70
 -> (Any -> Any -> Any -> Any)
 -> Any
 -> Any
 -> T__IsRelatedTo__70
 -> Any)
-> Any -> Any -> Any -> Any -> Any -> Any
forall a b. a -> b
coe
                   T_IsPreorder_70
-> (Any -> Any -> Any -> Any)
-> Any
-> Any
-> T__IsRelatedTo__70
-> Any
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_begin__160
                   (T_IsPreorder_70 -> Any
forall a b. a -> b
coe T_IsPreorder_70
d_'8804''45'isPreorder_1656) ((Integer -> Integer -> T__'60'__50 -> T__'8804'__26) -> Any
forall a b. a -> b
coe Integer -> Integer -> T__'60'__50 -> T__'8804'__26
d_'60''8658''8804'_1724)
                   ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'45'__260 (Integer -> Any
forall a b. a -> b
coe Integer
v0) (Integer -> Any
forall a b. a -> b
coe Integer
v1))
                   (Integer -> Any
forall a b. a -> b
coe (Integer
0 :: Integer))
                   ((T_IsPreorder_70
 -> (Any -> Any -> Any -> Any -> Any -> Any)
 -> Any
 -> Any
 -> Any
 -> T__IsRelatedTo__70
 -> Any
 -> T__IsRelatedTo__70)
-> Any
-> (Any -> Any -> Any -> Any -> Any -> Any)
-> Any
-> Any
-> Any
-> Any
-> Any
-> Any
forall a b. a -> b
coe
                      T_IsPreorder_70
-> (Any -> Any -> Any -> Any -> Any -> Any)
-> Any
-> Any
-> Any
-> T__IsRelatedTo__70
-> Any
-> T__IsRelatedTo__70
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_step'45''8804'_228
                      (T_IsPreorder_70 -> Any
forall a b. a -> b
coe T_IsPreorder_70
d_'8804''45'isPreorder_1656)
                      (\ Any
v8 Any
v9 Any
v10 Any
v11 Any
v12 ->
                         (T__'8804'__26 -> T__'60'__50 -> T__'60'__50) -> Any -> Any -> Any
forall a b. a -> b
coe T__'8804'__26 -> T__'60'__50 -> T__'60'__50
du_'8804''45''60''45'trans_1844 Any
v11 Any
v12)
                      ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe
                         Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'8854'__224 (Integer -> Any
forall a b. a -> b
coe Integer
v7) (Integer -> Any
forall a b. a -> b
coe Integer
v6))
                      ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe
                         Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'8854'__224 (Integer -> Any
forall a b. a -> b
coe Integer
v7) (Integer -> Any
forall a b. a -> b
coe Integer
v7))
                      (Integer -> Any
forall a b. a -> b
coe (Integer
0 :: Integer))
                      ((T_IsPreorder_70 -> Any -> T__IsRelatedTo__70) -> Any -> Any -> Any
forall a b. a -> b
coe
                         T_IsPreorder_70 -> Any -> T__IsRelatedTo__70
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du__'8718'_346
                         (T_IsPreorder_70 -> Any
forall a b. a -> b
coe T_IsPreorder_70
d_'8804''45'isPreorder_1656) (Integer -> Any
forall a b. a -> b
coe (Integer
0 :: Integer)))
                      ((Integer -> Integer -> Integer -> T__'8804'__18 -> T__'8804'__26)
-> Any -> Any -> Any -> Any -> Any
forall a b. a -> b
coe
                         Integer -> Integer -> Integer -> T__'8804'__18 -> T__'8804'__26
d_'8854''45'mono'691''45''8805''45''8804'_2892 (Integer -> Any
forall a b. a -> b
coe Integer
v7) (Integer -> Any
forall a b. a -> b
coe Integer
v6)
                         (Integer -> Any
forall a b. a -> b
coe Integer
v7) (T__'8804'__18 -> Any
forall a b. a -> b
coe T__'8804'__18
v5)))))
      T__'8804'__26
MAlonzo.Code.Data.Integer.Base.C_'45''8804''43'_40
        -> (Integer -> Integer -> T__'8804'__26 -> T__'8804'__26)
-> Any -> Any -> Any -> T__'8804'__26
forall a b. a -> b
coe
             Integer -> Integer -> T__'8804'__26 -> T__'8804'__26
du_'8804''45'steps'45'neg_3708 (Integer -> Any
forall a b. a -> b
coe Integer
v0) (Integer -> Any
forall a b. a -> b
coe Integer
v1)
             (T__'8804'__26 -> Any
forall a b. a -> b
coe T__'8804'__26
MAlonzo.Code.Data.Integer.Base.C_'45''8804''43'_40)
      MAlonzo.Code.Data.Integer.Base.C_'43''8804''43'_48 T__'8804'__18
v5
        -> case T__'8804'__18 -> T__'8804'__18
forall a b. a -> b
coe T__'8804'__18
v5 of
             T__'8804'__18
MAlonzo.Code.Data.Nat.Base.C_z'8804'n_22
               -> case Integer -> Integer
forall a b. a -> b
coe Integer
v1 of
                    Integer
0 -> (T__'8804'__18 -> T__'8804'__26) -> Any -> T__'8804'__26
forall a b. a -> b
coe
                           T__'8804'__18 -> T__'8804'__26
MAlonzo.Code.Data.Integer.Base.C_'43''8804''43'_48
                           (T__'8804'__18 -> Any
forall a b. a -> b
coe T__'8804'__18
MAlonzo.Code.Data.Nat.Base.C_z'8804'n_22)
                    Integer
_ -> T__'8804'__26 -> T__'8804'__26
forall a b. a -> b
coe T__'8804'__26
MAlonzo.Code.Data.Integer.Base.C_'45''8804''43'_40
             MAlonzo.Code.Data.Nat.Base.C_s'8804's_30 T__'8804'__18
v8
               -> let v9 :: Integer
v9 = Integer -> Integer -> Integer
subInt (Integer -> Integer
forall a b. a -> b
coe Integer
v0) (Integer -> Integer
forall a b. a -> b
coe (Integer
1 :: Integer)) in
                  Any -> T__'8804'__26
forall a b. a -> b
coe
                    (let v10 :: Integer
v10 = Integer -> Integer -> Integer
subInt (Integer -> Integer
forall a b. a -> b
coe Integer
v1) (Integer -> Integer
forall a b. a -> b
coe (Integer
1 :: Integer)) in
                     Any -> Any
forall a b. a -> b
coe
                       ((T_IsPreorder_70
 -> (Any -> Any -> Any -> Any)
 -> Any
 -> Any
 -> T__IsRelatedTo__70
 -> Any)
-> Any -> Any -> Any -> Any -> Any -> Any
forall a b. a -> b
coe
                          T_IsPreorder_70
-> (Any -> Any -> Any -> Any)
-> Any
-> Any
-> T__IsRelatedTo__70
-> Any
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_begin__160
                          (T_IsPreorder_70 -> Any
forall a b. a -> b
coe T_IsPreorder_70
d_'8804''45'isPreorder_1656) ((Integer -> Integer -> T__'60'__50 -> T__'8804'__26) -> Any
forall a b. a -> b
coe Integer -> Integer -> T__'60'__50 -> T__'8804'__26
d_'60''8658''8804'_1724)
                          ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'45'__260 (Integer -> Any
forall a b. a -> b
coe Integer
v0) (Integer -> Any
forall a b. a -> b
coe Integer
v1))
                          (Integer -> Any
forall a b. a -> b
coe (Integer
0 :: Integer))
                          ((T_IsPreorder_70
 -> (Any -> Any -> Any -> Any -> Any -> Any)
 -> Any
 -> Any
 -> Any
 -> T__IsRelatedTo__70
 -> Any
 -> T__IsRelatedTo__70)
-> Any
-> (Any -> Any -> Any -> Any -> Any -> Any)
-> Any
-> Any
-> Any
-> Any
-> Any
-> Any
forall a b. a -> b
coe
                             T_IsPreorder_70
-> (Any -> Any -> Any -> Any -> Any -> Any)
-> Any
-> Any
-> Any
-> T__IsRelatedTo__70
-> Any
-> T__IsRelatedTo__70
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_step'45''8804'_228
                             (T_IsPreorder_70 -> Any
forall a b. a -> b
coe T_IsPreorder_70
d_'8804''45'isPreorder_1656)
                             (\ Any
v11 Any
v12 Any
v13 Any
v14 Any
v15 ->
                                (T__'8804'__26 -> T__'60'__50 -> T__'60'__50) -> Any -> Any -> Any
forall a b. a -> b
coe T__'8804'__26 -> T__'60'__50 -> T__'60'__50
du_'8804''45''60''45'trans_1844 Any
v14 Any
v15)
                             ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe
                                Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'8854'__224 (Integer -> Any
forall a b. a -> b
coe Integer
v9) (Integer -> Any
forall a b. a -> b
coe Integer
v10))
                             ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe
                                Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'8854'__224 (Integer -> Any
forall a b. a -> b
coe Integer
v9) (Integer -> Any
forall a b. a -> b
coe Integer
v9))
                             (Integer -> Any
forall a b. a -> b
coe (Integer
0 :: Integer))
                             ((T_IsPreorder_70 -> Any -> T__IsRelatedTo__70) -> Any -> Any -> Any
forall a b. a -> b
coe
                                T_IsPreorder_70 -> Any -> T__IsRelatedTo__70
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du__'8718'_346
                                (T_IsPreorder_70 -> Any
forall a b. a -> b
coe T_IsPreorder_70
d_'8804''45'isPreorder_1656) (Integer -> Any
forall a b. a -> b
coe (Integer
0 :: Integer)))
                             ((Integer -> Integer -> Integer -> T__'8804'__18 -> T__'8804'__26)
-> Any -> Any -> Any -> Any -> Any
forall a b. a -> b
coe
                                Integer -> Integer -> Integer -> T__'8804'__18 -> T__'8804'__26
d_'8854''45'mono'691''45''8805''45''8804'_2892 (Integer -> Any
forall a b. a -> b
coe Integer
v9) (Integer -> Any
forall a b. a -> b
coe Integer
v10)
                                (Integer -> Any
forall a b. a -> b
coe Integer
v9) (T__'8804'__18 -> Any
forall a b. a -> b
coe T__'8804'__18
v8)))))
             T__'8804'__18
_ -> T__'8804'__26
forall a. a
MAlonzo.RTE.mazUnreachableError
      T__'8804'__26
_ -> T__'8804'__26
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Data.Integer.Properties.m-n≤0⇒m≤n
d_m'45'n'8804'0'8658'm'8804'n_3808 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26 ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26
d_m'45'n'8804'0'8658'm'8804'n_3808 :: Integer -> Integer -> T__'8804'__26 -> T__'8804'__26
d_m'45'n'8804'0'8658'm'8804'n_3808 Integer
v0 Integer
v1 T__'8804'__26
v2
  = (T_IsPreorder_70
 -> (Any -> Any -> Any -> Any)
 -> Any
 -> Any
 -> T__IsRelatedTo__70
 -> Any)
-> Any -> Any -> Any -> Any -> Any -> T__'8804'__26
forall a b. a -> b
coe
      T_IsPreorder_70
-> (Any -> Any -> Any -> Any)
-> Any
-> Any
-> T__IsRelatedTo__70
-> Any
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_begin__160
      (T_IsPreorder_70 -> Any
forall a b. a -> b
coe T_IsPreorder_70
d_'8804''45'isPreorder_1656) ((Integer -> Integer -> T__'60'__50 -> T__'8804'__26) -> Any
forall a b. a -> b
coe Integer -> Integer -> T__'60'__50 -> T__'8804'__26
d_'60''8658''8804'_1724)
      (Integer -> Any
forall a b. a -> b
coe Integer
v0) (Integer -> Any
forall a b. a -> b
coe Integer
v1)
      ((T_IsPreorder_70
 -> (Any -> Any -> Any -> Any -> Any -> Any)
 -> Any
 -> Any
 -> Any
 -> T__IsRelatedTo__70
 -> Any
 -> T__IsRelatedTo__70)
-> Any
-> (Any -> Any -> Any -> Any -> Any -> Any)
-> Any
-> Any
-> Any
-> Any
-> Any
-> Any
forall a b. a -> b
coe
         T_IsPreorder_70
-> (Any -> Any -> Any -> Any -> Any -> Any)
-> Any
-> Any
-> Any
-> T__IsRelatedTo__70
-> Any
-> T__IsRelatedTo__70
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_step'45''8804'_228
         (T_IsPreorder_70 -> Any
forall a b. a -> b
coe T_IsPreorder_70
d_'8804''45'isPreorder_1656)
         (\ Any
v3 Any
v4 Any
v5 Any
v6 Any
v7 -> (T__'8804'__26 -> T__'60'__50 -> T__'60'__50) -> Any -> Any -> Any
forall a b. a -> b
coe T__'8804'__26 -> T__'60'__50 -> T__'60'__50
du_'8804''45''60''45'trans_1844 Any
v6 Any
v7)
         ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe
            Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'43'__242
            ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'45'__260 (Integer -> Any
forall a b. a -> b
coe Integer
v0) (Integer -> Any
forall a b. a -> b
coe Integer
v1))
            (Integer -> Any
forall a b. a -> b
coe Integer
v1))
         ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe
            Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'43'__242 (Integer -> Any
forall a b. a -> b
coe (Integer
0 :: Integer))
            (Integer -> Any
forall a b. a -> b
coe Integer
v1))
         (Integer -> Any
forall a b. a -> b
coe Integer
v1)
         ((T_IsPreorder_70 -> Any -> T__IsRelatedTo__70) -> Any -> Any -> Any
forall a b. a -> b
coe
            T_IsPreorder_70 -> Any -> T__IsRelatedTo__70
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du__'8718'_346
            (T_IsPreorder_70 -> Any
forall a b. a -> b
coe T_IsPreorder_70
d_'8804''45'isPreorder_1656) (Integer -> Any
forall a b. a -> b
coe Integer
v1))
         ((Integer -> Integer -> Integer -> T__'8804'__26 -> T__'8804'__26)
-> Any -> Any -> Any -> Any -> Any
forall a b. a -> b
coe
            Integer -> Integer -> Integer -> T__'8804'__26 -> T__'8804'__26
d_'43''45'mono'737''45''8804'_3422 (Integer -> Any
forall a b. a -> b
coe Integer
v1)
            ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'45'__260 (Integer -> Any
forall a b. a -> b
coe Integer
v0) (Integer -> Any
forall a b. a -> b
coe Integer
v1))
            (Integer -> Any
forall a b. a -> b
coe (Integer
0 :: Integer)) (T__'8804'__26 -> Any
forall a b. a -> b
coe T__'8804'__26
v2)))
-- Data.Integer.Properties.m≤n⇒0≤n-m
d_m'8804'n'8658'0'8804'n'45'm_3824 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26 ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26
d_m'8804'n'8658'0'8804'n'45'm_3824 :: Integer -> Integer -> T__'8804'__26 -> T__'8804'__26
d_m'8804'n'8658'0'8804'n'45'm_3824 Integer
v0 Integer
v1 T__'8804'__26
v2
  = (T_IsPreorder_70
 -> (Any -> Any -> Any -> Any)
 -> Any
 -> Any
 -> T__IsRelatedTo__70
 -> Any)
-> Any -> Any -> Any -> Any -> Any -> T__'8804'__26
forall a b. a -> b
coe
      T_IsPreorder_70
-> (Any -> Any -> Any -> Any)
-> Any
-> Any
-> T__IsRelatedTo__70
-> Any
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_begin__160
      (T_IsPreorder_70 -> Any
forall a b. a -> b
coe T_IsPreorder_70
d_'8804''45'isPreorder_1656) ((Integer -> Integer -> T__'60'__50 -> T__'8804'__26) -> Any
forall a b. a -> b
coe Integer -> Integer -> T__'60'__50 -> T__'8804'__26
d_'60''8658''8804'_1724)
      (Integer -> Any
forall a b. a -> b
coe (Integer
0 :: Integer))
      ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'45'__260 (Integer -> Any
forall a b. a -> b
coe Integer
v1) (Integer -> Any
forall a b. a -> b
coe Integer
v0))
      ((T_IsPreorder_70
 -> (Any -> Any -> Any -> Any -> Any -> Any)
 -> Any
 -> Any
 -> Any
 -> T__IsRelatedTo__70
 -> Any
 -> T__IsRelatedTo__70)
-> Any
-> (Any -> Any -> Any -> Any -> Any -> Any)
-> Any
-> Any
-> Any
-> Any
-> Any
-> Any
forall a b. a -> b
coe
         T_IsPreorder_70
-> (Any -> Any -> Any -> Any -> Any -> Any)
-> Any
-> Any
-> Any
-> T__IsRelatedTo__70
-> Any
-> T__IsRelatedTo__70
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_step'45''8804'_228
         (T_IsPreorder_70 -> Any
forall a b. a -> b
coe T_IsPreorder_70
d_'8804''45'isPreorder_1656)
         (\ Any
v3 Any
v4 Any
v5 Any
v6 Any
v7 -> (T__'8804'__26 -> T__'60'__50 -> T__'60'__50) -> Any -> Any -> Any
forall a b. a -> b
coe T__'8804'__26 -> T__'60'__50 -> T__'60'__50
du_'8804''45''60''45'trans_1844 Any
v6 Any
v7)
         ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'45'__260 (Integer -> Any
forall a b. a -> b
coe Integer
v0) (Integer -> Any
forall a b. a -> b
coe Integer
v0))
         ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'45'__260 (Integer -> Any
forall a b. a -> b
coe Integer
v1) (Integer -> Any
forall a b. a -> b
coe Integer
v0))
         ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'45'__260 (Integer -> Any
forall a b. a -> b
coe Integer
v1) (Integer -> Any
forall a b. a -> b
coe Integer
v0))
         ((T_IsPreorder_70 -> Any -> T__IsRelatedTo__70) -> Any -> Any -> Any
forall a b. a -> b
coe
            T_IsPreorder_70 -> Any -> T__IsRelatedTo__70
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du__'8718'_346
            (T_IsPreorder_70 -> Any
forall a b. a -> b
coe T_IsPreorder_70
d_'8804''45'isPreorder_1656)
            ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe
               Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'45'__260 (Integer -> Any
forall a b. a -> b
coe Integer
v1) (Integer -> Any
forall a b. a -> b
coe Integer
v0)))
         ((Integer -> Integer -> Integer -> T__'8804'__26 -> T__'8804'__26)
-> Any -> Any -> Any -> Any -> Any
forall a b. a -> b
coe
            Integer -> Integer -> Integer -> T__'8804'__26 -> T__'8804'__26
d_'43''45'mono'737''45''8804'_3422
            ((Integer -> Integer) -> Any -> Any
forall a b. a -> b
coe Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d_'45'__218 (Integer -> Any
forall a b. a -> b
coe Integer
v0)) (Integer -> Any
forall a b. a -> b
coe Integer
v0)
            (Integer -> Any
forall a b. a -> b
coe Integer
v1) (T__'8804'__26 -> Any
forall a b. a -> b
coe T__'8804'__26
v2)))
-- Data.Integer.Properties.0≤n-m⇒m≤n
d_0'8804'n'45'm'8658'm'8804'n_3840 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26 ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26
d_0'8804'n'45'm'8658'm'8804'n_3840 :: Integer -> Integer -> T__'8804'__26 -> T__'8804'__26
d_0'8804'n'45'm'8658'm'8804'n_3840 Integer
v0 Integer
v1 T__'8804'__26
v2
  = (T_IsPreorder_70
 -> (Any -> Any -> Any -> Any)
 -> Any
 -> Any
 -> T__IsRelatedTo__70
 -> Any)
-> Any -> Any -> Any -> Any -> Any -> T__'8804'__26
forall a b. a -> b
coe
      T_IsPreorder_70
-> (Any -> Any -> Any -> Any)
-> Any
-> Any
-> T__IsRelatedTo__70
-> Any
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_begin__160
      (T_IsPreorder_70 -> Any
forall a b. a -> b
coe T_IsPreorder_70
d_'8804''45'isPreorder_1656) ((Integer -> Integer -> T__'60'__50 -> T__'8804'__26) -> Any
forall a b. a -> b
coe Integer -> Integer -> T__'60'__50 -> T__'8804'__26
d_'60''8658''8804'_1724)
      (Integer -> Any
forall a b. a -> b
coe Integer
v0) (Integer -> Any
forall a b. a -> b
coe Integer
v1)
      ((T_IsPreorder_70
 -> (Any -> Any -> Any -> Any -> Any -> Any)
 -> Any
 -> Any
 -> Any
 -> T__IsRelatedTo__70
 -> Any
 -> T__IsRelatedTo__70)
-> Any
-> (Any -> Any -> Any -> Any -> Any -> Any)
-> Any
-> Any
-> Any
-> Any
-> Any
-> Any
forall a b. a -> b
coe
         T_IsPreorder_70
-> (Any -> Any -> Any -> Any -> Any -> Any)
-> Any
-> Any
-> Any
-> T__IsRelatedTo__70
-> Any
-> T__IsRelatedTo__70
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_step'45''8804'_228
         (T_IsPreorder_70 -> Any
forall a b. a -> b
coe T_IsPreorder_70
d_'8804''45'isPreorder_1656)
         (\ Any
v3 Any
v4 Any
v5 Any
v6 Any
v7 -> (T__'8804'__26 -> T__'60'__50 -> T__'60'__50) -> Any -> Any -> Any
forall a b. a -> b
coe T__'8804'__26 -> T__'60'__50 -> T__'60'__50
du_'8804''45''60''45'trans_1844 Any
v6 Any
v7)
         ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe
            Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'43'__242 (Integer -> Any
forall a b. a -> b
coe (Integer
0 :: Integer))
            (Integer -> Any
forall a b. a -> b
coe Integer
v0))
         ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe
            Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'43'__242
            ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'45'__260 (Integer -> Any
forall a b. a -> b
coe Integer
v1) (Integer -> Any
forall a b. a -> b
coe Integer
v0))
            (Integer -> Any
forall a b. a -> b
coe Integer
v0))
         (Integer -> Any
forall a b. a -> b
coe Integer
v1)
         ((T_IsPreorder_70 -> Any -> T__IsRelatedTo__70) -> Any -> Any -> Any
forall a b. a -> b
coe
            T_IsPreorder_70 -> Any -> T__IsRelatedTo__70
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du__'8718'_346
            (T_IsPreorder_70 -> Any
forall a b. a -> b
coe T_IsPreorder_70
d_'8804''45'isPreorder_1656) (Integer -> Any
forall a b. a -> b
coe Integer
v1))
         ((Integer -> Integer -> Integer -> T__'8804'__26 -> T__'8804'__26)
-> Any -> Any -> Any -> Any -> Any
forall a b. a -> b
coe
            Integer -> Integer -> Integer -> T__'8804'__26 -> T__'8804'__26
d_'43''45'mono'737''45''8804'_3422 (Integer -> Any
forall a b. a -> b
coe Integer
v0) (Integer -> Any
forall a b. a -> b
coe (Integer
0 :: Integer))
            ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'45'__260 (Integer -> Any
forall a b. a -> b
coe Integer
v1) (Integer -> Any
forall a b. a -> b
coe Integer
v0))
            (T__'8804'__26 -> Any
forall a b. a -> b
coe T__'8804'__26
v2)))
-- Data.Integer.Properties.≤-step
d_'8804''45'step_3856 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26 ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26
d_'8804''45'step_3856 :: Integer -> Integer -> T__'8804'__26 -> T__'8804'__26
d_'8804''45'step_3856 Integer
v0 Integer
v1
  = (Integer -> Integer -> Integer -> T__'8804'__26 -> T__'8804'__26)
-> Any -> Any -> Any -> T__'8804'__26 -> T__'8804'__26
forall a b. a -> b
coe Integer -> Integer -> Integer -> T__'8804'__26 -> T__'8804'__26
d_'8804''45'steps_3464 (Integer -> Any
forall a b. a -> b
coe Integer
v0) (Integer -> Any
forall a b. a -> b
coe Integer
v1) (Integer -> Any
forall a b. a -> b
coe (Integer
1 :: Integer))
-- Data.Integer.Properties.n≤1+n
d_n'8804'1'43'n_3860 ::
  Integer -> MAlonzo.Code.Data.Integer.Base.T__'8804'__26
d_n'8804'1'43'n_3860 :: Integer -> T__'8804'__26
d_n'8804'1'43'n_3860 Integer
v0
  = (Integer -> Integer -> Integer -> T__'8804'__26 -> T__'8804'__26)
-> Any -> Any -> Any -> Any -> T__'8804'__26
forall a b. a -> b
coe
      Integer -> Integer -> Integer -> T__'8804'__26 -> T__'8804'__26
d_'8804''45'steps_3464 (Integer -> Any
forall a b. a -> b
coe Integer
v0) (Integer -> Any
forall a b. a -> b
coe Integer
v0) (Integer -> Any
forall a b. a -> b
coe (Integer
1 :: Integer))
      ((Integer -> T__'8804'__26) -> Any -> Any
forall a b. a -> b
coe Integer -> T__'8804'__26
d_'8804''45'refl_1584 (Integer -> Any
forall a b. a -> b
coe Integer
v0))
-- Data.Integer.Properties.suc-+
d_suc'45''43'_3868 ::
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_suc'45''43'_3868 :: Integer -> Integer -> T__'8801'__12
d_suc'45''43'_3868 = Integer -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.n≢1+n
d_n'8802'1'43'n_3880 ::
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Data.Empty.T_'8869'_4
d_n'8802'1'43'n_3880 :: Integer -> T__'8801'__12 -> T_'8869'_4
d_n'8802'1'43'n_3880 = Integer -> T__'8801'__12 -> T_'8869'_4
forall a. a
erased
-- Data.Integer.Properties.1-[1+n]≡-n
d_1'45''91'1'43'n'93''8801''45'n_3886 ::
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_1'45''91'1'43'n'93''8801''45'n_3886 :: Integer -> T__'8801'__12
d_1'45''91'1'43'n'93''8801''45'n_3886 = Integer -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.suc-mono
d_suc'45'mono_3890 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26 ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26
d_suc'45'mono_3890 :: Integer -> Integer -> T__'8804'__26 -> T__'8804'__26
d_suc'45'mono_3890 Integer
v0 Integer
v1 T__'8804'__26
v2
  = case T__'8804'__26 -> T__'8804'__26
forall a b. a -> b
coe T__'8804'__26
v2 of
      MAlonzo.Code.Data.Integer.Base.C_'45''8804''45'_34 T__'8804'__18
v5
        -> (Integer -> Integer -> Integer -> T__'8804'__18 -> T__'8804'__26)
-> Any -> Any -> Any -> Any -> T__'8804'__26
forall a b. a -> b
coe
             Integer -> Integer -> Integer -> T__'8804'__18 -> T__'8804'__26
d_'8854''45'mono'691''45''8805''45''8804'_2892 (Integer -> Any
forall a b. a -> b
coe (Integer
1 :: Integer))
             ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> Integer
subInt (Integer -> Any
forall a b. a -> b
coe (Integer
0 :: Integer)) (Integer -> Any
forall a b. a -> b
coe Integer
v0))
             ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> Integer
subInt (Integer -> Any
forall a b. a -> b
coe (Integer
0 :: Integer)) (Integer -> Any
forall a b. a -> b
coe Integer
v1))
             ((T__'8804'__18 -> T__'8804'__18) -> T__'8804'__18 -> Any
forall a b. a -> b
coe T__'8804'__18 -> T__'8804'__18
MAlonzo.Code.Data.Nat.Base.C_s'8804's_30 T__'8804'__18
v5)
      T__'8804'__26
MAlonzo.Code.Data.Integer.Base.C_'45''8804''43'_40
        -> let v5 :: Integer
v5 = Integer -> Integer -> Integer
subInt (Integer -> Integer
forall a b. a -> b
coe (-Integer
1 :: Integer)) (Integer -> Integer
forall a b. a -> b
coe Integer
v0) in
           Any -> T__'8804'__26
forall a b. a -> b
coe
             ((T_IsPreorder_70
 -> (Any -> Any -> Any -> Any)
 -> Any
 -> Any
 -> T__IsRelatedTo__70
 -> Any)
-> Any -> Any -> Any -> Any -> Any -> Any
forall a b. a -> b
coe
                T_IsPreorder_70
-> (Any -> Any -> Any -> Any)
-> Any
-> Any
-> T__IsRelatedTo__70
-> Any
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_begin__160
                (T_IsPreorder_70 -> Any
forall a b. a -> b
coe T_IsPreorder_70
d_'8804''45'isPreorder_1656) ((Integer -> Integer -> T__'60'__50 -> T__'8804'__26) -> Any
forall a b. a -> b
coe Integer -> Integer -> T__'60'__50 -> T__'8804'__26
d_'60''8658''8804'_1724)
                (((Any -> Any) -> (Any -> Any -> Any) -> Any -> Any -> Any)
-> (Integer -> Integer)
-> (Any -> Any -> Any)
-> Integer
-> Integer
-> Any
forall a b. a -> b
coe
                   (Any -> Any) -> (Any -> Any -> Any) -> Any -> Any -> Any
MAlonzo.Code.Function.Base.du__'45''10216'_'8739'_302
                   Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d_suc_266 (\ Any
v6 Any
v7 -> Any
v6) Integer
v0 Integer
v1)
                (((Any -> Any -> Any) -> (Any -> Any) -> Any -> Any -> Any)
-> (Any -> Any -> Any)
-> (Integer -> Integer)
-> Integer
-> Integer
-> Any
forall a b. a -> b
coe
                   (Any -> Any -> Any) -> (Any -> Any) -> Any -> Any -> Any
MAlonzo.Code.Function.Base.du_'8739'_'10217''45'__308
                   (\ Any
v6 Any
v7 -> Any
v7) Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d_suc_266 Integer
v0 Integer
v1)
                ((T_IsPreorder_70
 -> (Any -> Any -> Any -> Any -> Any -> Any)
 -> Any
 -> Any
 -> Any
 -> T__IsRelatedTo__70
 -> Any
 -> T__IsRelatedTo__70)
-> Any
-> (Any -> Any -> Any -> Any -> Any -> Any)
-> Any
-> Any
-> Any
-> Any
-> Any
-> Any
forall a b. a -> b
coe
                   T_IsPreorder_70
-> (Any -> Any -> Any -> Any -> Any -> Any)
-> Any
-> Any
-> Any
-> T__IsRelatedTo__70
-> Any
-> T__IsRelatedTo__70
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_step'45''8804'_228
                   (T_IsPreorder_70 -> Any
forall a b. a -> b
coe T_IsPreorder_70
d_'8804''45'isPreorder_1656)
                   (\ Any
v6 Any
v7 Any
v8 Any
v9 Any
v10 -> (T__'8804'__26 -> T__'60'__50 -> T__'60'__50) -> Any -> Any -> Any
forall a b. a -> b
coe T__'8804'__26 -> T__'60'__50 -> T__'60'__50
du_'8804''45''60''45'trans_1844 Any
v9 Any
v10)
                   ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe
                      Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'8854'__224 (Integer -> Any
forall a b. a -> b
coe (Integer
0 :: Integer))
                      (Integer -> Any
forall a b. a -> b
coe Integer
v5))
                   ((Integer -> Integer) -> Any -> Any
forall a b. a -> b
coe Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d_suc_266 (Integer -> Any
forall a b. a -> b
coe Integer
v1))
                   (((Any -> Any -> Any) -> (Any -> Any) -> Any -> Any -> Any)
-> (Any -> Any -> Any)
-> (Integer -> Integer)
-> Integer
-> Integer
-> Any
forall a b. a -> b
coe
                      (Any -> Any -> Any) -> (Any -> Any) -> Any -> Any -> Any
MAlonzo.Code.Function.Base.du_'8739'_'10217''45'__308
                      (\ Any
v6 Any
v7 -> Any
v7) Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d_suc_266 Integer
v0 Integer
v1)
                   ((T_IsPreorder_70 -> Any -> T__IsRelatedTo__70) -> Any -> Any -> Any
forall a b. a -> b
coe
                      T_IsPreorder_70 -> Any -> T__IsRelatedTo__70
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du__'8718'_346
                      (T_IsPreorder_70 -> Any
forall a b. a -> b
coe T_IsPreorder_70
d_'8804''45'isPreorder_1656)
                      ((Integer -> Integer) -> Any -> Any
forall a b. a -> b
coe Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d_suc_266 (Integer -> Any
forall a b. a -> b
coe Integer
v1)))
                   ((Integer -> T__'8804'__26) -> Any -> Any
forall a b. a -> b
coe Integer -> T__'8804'__26
du_0'8854'm'8804''43'_2862 (Integer -> Any
forall a b. a -> b
coe Integer
v5))))
      MAlonzo.Code.Data.Integer.Base.C_'43''8804''43'_48 T__'8804'__18
v5
        -> (T__'8804'__18 -> T__'8804'__26) -> Any -> T__'8804'__26
forall a b. a -> b
coe
             T__'8804'__18 -> T__'8804'__26
MAlonzo.Code.Data.Integer.Base.C_'43''8804''43'_48
             ((T__'8804'__18 -> T__'8804'__18) -> T__'8804'__18 -> Any
forall a b. a -> b
coe T__'8804'__18 -> T__'8804'__18
MAlonzo.Code.Data.Nat.Base.C_s'8804's_30 T__'8804'__18
v5)
      T__'8804'__26
_ -> T__'8804'__26
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Data.Integer.Properties.suc[i]≤j⇒i<j
d_suc'91'i'93''8804'j'8658'i'60'j_3908 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26 ->
  MAlonzo.Code.Data.Integer.Base.T__'60'__50
d_suc'91'i'93''8804'j'8658'i'60'j_3908 :: Integer -> Integer -> T__'8804'__26 -> T__'60'__50
d_suc'91'i'93''8804'j'8658'i'60'j_3908 Integer
v0 Integer
v1 T__'8804'__26
v2
  = case Integer -> Integer
forall a b. a -> b
coe Integer
v0 of
      Integer
_ | (Integer -> Integer -> Bool) -> Any -> Any -> Bool
forall a b. a -> b
coe Integer -> Integer -> Bool
geqInt (Integer -> Any
forall a b. a -> b
coe Integer
v0) (Integer -> Any
forall a b. a -> b
coe (Integer
0 :: Integer)) ->
          case T__'8804'__26 -> T__'8804'__26
forall a b. a -> b
coe T__'8804'__26
v2 of
            MAlonzo.Code.Data.Integer.Base.C_'43''8804''43'_48 T__'8804'__18
v5
              -> (T__'8804'__18 -> T__'60'__50) -> T__'8804'__18 -> T__'60'__50
forall a b. a -> b
coe T__'8804'__18 -> T__'60'__50
MAlonzo.Code.Data.Integer.Base.C_'43''60''43'_72 T__'8804'__18
v5
            T__'8804'__26
_ -> T__'60'__50
forall a. a
MAlonzo.RTE.mazUnreachableError
      -1 -> T__'60'__50 -> T__'60'__50
forall a b. a -> b
coe T__'60'__50
MAlonzo.Code.Data.Integer.Base.C_'45''60''43'_64
      Integer
_ -> case Integer -> Any
forall a b. a -> b
coe Integer
v1 of
             Any
_ | (Integer -> Integer -> Bool) -> Any -> Any -> Bool
forall a b. a -> b
coe Integer -> Integer -> Bool
geqInt (Integer -> Any
forall a b. a -> b
coe Integer
v1) (Integer -> Any
forall a b. a -> b
coe (Integer
0 :: Integer)) ->
                 (Any -> Any -> Any) -> Any -> Any -> T__'60'__50
forall a b. a -> b
coe
                   Any -> Any -> Any
forall a b. a -> b -> b
seq (T__'8804'__26 -> Any
forall a b. a -> b
coe T__'8804'__26
v2) (T__'60'__50 -> Any
forall a b. a -> b
coe T__'60'__50
MAlonzo.Code.Data.Integer.Base.C_'45''60''43'_64)
             Any
_ -> case T__'8804'__26 -> T__'8804'__26
forall a b. a -> b
coe T__'8804'__26
v2 of
                    MAlonzo.Code.Data.Integer.Base.C_'45''8804''45'_34 T__'8804'__18
v5
                      -> (T__'8804'__18 -> T__'60'__50) -> Any -> T__'60'__50
forall a b. a -> b
coe
                           T__'8804'__18 -> T__'60'__50
MAlonzo.Code.Data.Integer.Base.C_'45''60''45'_58
                           ((T__'8804'__18 -> T__'8804'__18) -> T__'8804'__18 -> Any
forall a b. a -> b
coe T__'8804'__18 -> T__'8804'__18
MAlonzo.Code.Data.Nat.Base.C_s'8804's_30 T__'8804'__18
v5)
                    T__'8804'__26
_ -> T__'60'__50
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Data.Integer.Properties.i<j⇒suc[i]≤j
d_i'60'j'8658'suc'91'i'93''8804'j_3932 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Integer.Base.T__'60'__50 ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26
d_i'60'j'8658'suc'91'i'93''8804'j_3932 :: Integer -> Integer -> T__'60'__50 -> T__'8804'__26
d_i'60'j'8658'suc'91'i'93''8804'j_3932 Integer
v0 Integer
v1 T__'60'__50
v2
  = case Integer -> Integer
forall a b. a -> b
coe Integer
v0 of
      Integer
_ | (Integer -> Integer -> Bool) -> Any -> Any -> Bool
forall a b. a -> b
coe Integer -> Integer -> Bool
geqInt (Integer -> Any
forall a b. a -> b
coe Integer
v0) (Integer -> Any
forall a b. a -> b
coe (Integer
0 :: Integer)) ->
          case T__'60'__50 -> T__'60'__50
forall a b. a -> b
coe T__'60'__50
v2 of
            MAlonzo.Code.Data.Integer.Base.C_'43''60''43'_72 T__'8804'__18
v5
              -> (T__'8804'__18 -> T__'8804'__26) -> T__'8804'__18 -> T__'8804'__26
forall a b. a -> b
coe T__'8804'__18 -> T__'8804'__26
MAlonzo.Code.Data.Integer.Base.C_'43''8804''43'_48 T__'8804'__18
v5
            T__'60'__50
_ -> T__'8804'__26
forall a. a
MAlonzo.RTE.mazUnreachableError
      -1
        -> (Any -> Any -> Any) -> Any -> Any -> T__'8804'__26
forall a b. a -> b
coe
             Any -> Any -> Any
forall a b. a -> b -> b
seq (T__'60'__50 -> Any
forall a b. a -> b
coe T__'60'__50
v2)
             ((T__'8804'__18 -> T__'8804'__26) -> Any -> Any
forall a b. a -> b
coe
                T__'8804'__18 -> T__'8804'__26
MAlonzo.Code.Data.Integer.Base.C_'43''8804''43'_48
                (T__'8804'__18 -> Any
forall a b. a -> b
coe T__'8804'__18
MAlonzo.Code.Data.Nat.Base.C_z'8804'n_22))
      Integer
_ -> case Integer -> Any
forall a b. a -> b
coe Integer
v1 of
             Any
_ | (Integer -> Integer -> Bool) -> Any -> Any -> Bool
forall a b. a -> b
coe Integer -> Integer -> Bool
geqInt (Integer -> Any
forall a b. a -> b
coe Integer
v1) (Integer -> Any
forall a b. a -> b
coe (Integer
0 :: Integer)) ->
                 (Any -> Any -> Any) -> Any -> Any -> T__'8804'__26
forall a b. a -> b
coe
                   Any -> Any -> Any
forall a b. a -> b -> b
seq (T__'60'__50 -> Any
forall a b. a -> b
coe T__'60'__50
v2)
                   (T__'8804'__26 -> Any
forall a b. a -> b
coe T__'8804'__26
MAlonzo.Code.Data.Integer.Base.C_'45''8804''43'_40)
             Any
_ -> case T__'60'__50 -> T__'60'__50
forall a b. a -> b
coe T__'60'__50
v2 of
                    MAlonzo.Code.Data.Integer.Base.C_'45''60''45'_58 T__'8804'__18
v5
                      -> (T__'8804'__18 -> T__'8804'__26) -> Any -> T__'8804'__26
forall a b. a -> b
coe
                           T__'8804'__18 -> T__'8804'__26
MAlonzo.Code.Data.Integer.Base.C_'45''8804''45'_34
                           ((T__'8804'__18 -> T__'8804'__18) -> Any -> Any
forall a b. a -> b
coe
                              T__'8804'__18 -> T__'8804'__18
MAlonzo.Code.Data.Nat.Properties.Core.du_'8804''45'pred_12
                              (T__'8804'__18 -> Any
forall a b. a -> b
coe T__'8804'__18
v5))
                    T__'60'__50
_ -> T__'8804'__26
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Data.Integer.Properties.suc-pred
d_suc'45'pred_3944 ::
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_suc'45'pred_3944 :: Integer -> T__'8801'__12
d_suc'45'pred_3944 = Integer -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.pred-suc
d_pred'45'suc_3954 ::
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_pred'45'suc_3954 :: Integer -> T__'8801'__12
d_pred'45'suc_3954 = Integer -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.+-pred
d_'43''45'pred_3966 ::
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'43''45'pred_3966 :: Integer -> Integer -> T__'8801'__12
d_'43''45'pred_3966 = Integer -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.pred-+
d_pred'45''43'_3982 ::
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_pred'45''43'_3982 :: Integer -> Integer -> T__'8801'__12
d_pred'45''43'_3982 = Integer -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.neg-suc
d_neg'45'suc_3994 ::
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_neg'45'suc_3994 :: Integer -> T__'8801'__12
d_neg'45'suc_3994 = Integer -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.minus-suc
d_minus'45'suc_4002 ::
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_minus'45'suc_4002 :: Integer -> Integer -> T__'8801'__12
d_minus'45'suc_4002 = Integer -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.m≤pred[n]⇒m<n
d_m'8804'pred'91'n'93''8658'm'60'n_4016 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26 ->
  MAlonzo.Code.Data.Integer.Base.T__'60'__50
d_m'8804'pred'91'n'93''8658'm'60'n_4016 :: Integer -> Integer -> T__'8804'__26 -> T__'60'__50
d_m'8804'pred'91'n'93''8658'm'60'n_4016 ~Integer
v0 Integer
v1 T__'8804'__26
v2
  = Integer -> T__'8804'__26 -> T__'60'__50
du_m'8804'pred'91'n'93''8658'm'60'n_4016 Integer
v1 T__'8804'__26
v2
du_m'8804'pred'91'n'93''8658'm'60'n_4016 ::
  Integer ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26 ->
  MAlonzo.Code.Data.Integer.Base.T__'60'__50
du_m'8804'pred'91'n'93''8658'm'60'n_4016 :: Integer -> T__'8804'__26 -> T__'60'__50
du_m'8804'pred'91'n'93''8658'm'60'n_4016 Integer
v0 T__'8804'__26
v1
  = case Integer -> Any
forall a b. a -> b
coe Integer
v0 of
      Any
_ | (Integer -> Integer -> Bool) -> Any -> Any -> Bool
forall a b. a -> b
coe Integer -> Integer -> Bool
geqInt (Integer -> Any
forall a b. a -> b
coe Integer
v0) (Integer -> Any
forall a b. a -> b
coe (Integer
0 :: Integer)) ->
          (T__'8804'__26 -> T__'60'__50 -> T__'60'__50)
-> Any -> Any -> T__'60'__50
forall a b. a -> b
coe
            T__'8804'__26 -> T__'60'__50 -> T__'60'__50
du_'8804''45''60''45'trans_1844 (T__'8804'__26 -> Any
forall a b. a -> b
coe T__'8804'__26
v1)
            ((Integer -> Integer -> T__'60'__50) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> T__'60'__50
d_m'8854'1'43'n'60'm_2802 (Integer -> Any
forall a b. a -> b
coe Integer
v0) (Integer -> Any
forall a b. a -> b
coe (Integer
0 :: Integer)))
      Any
_ -> (T__'8804'__26 -> T__'60'__50 -> T__'60'__50)
-> Any -> Any -> T__'60'__50
forall a b. a -> b
coe
             T__'8804'__26 -> T__'60'__50 -> T__'60'__50
du_'8804''45''60''45'trans_1844 (T__'8804'__26 -> Any
forall a b. a -> b
coe T__'8804'__26
v1)
             ((T__'8804'__18 -> T__'60'__50) -> T__'8804'__18 -> Any
forall a b. a -> b
coe
                T__'8804'__18 -> T__'60'__50
MAlonzo.Code.Data.Integer.Base.C_'45''60''45'_58
                (Integer -> T__'8804'__18
MAlonzo.Code.Data.Nat.Properties.d_'8804''45'refl_1634
                   ((Integer -> Integer -> Integer) -> Any -> Any -> Integer
forall a b. a -> b
coe Integer -> Integer -> Integer
subInt (Integer -> Any
forall a b. a -> b
coe (Integer
0 :: Integer)) (Integer -> Any
forall a b. a -> b
coe Integer
v0))))
-- Data.Integer.Properties.m<n⇒m≤pred[n]
d_m'60'n'8658'm'8804'pred'91'n'93'_4034 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Integer.Base.T__'60'__50 ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26
d_m'60'n'8658'm'8804'pred'91'n'93'_4034 :: Integer -> Integer -> T__'60'__50 -> T__'8804'__26
d_m'60'n'8658'm'8804'pred'91'n'93'_4034 ~Integer
v0 Integer
v1 T__'60'__50
v2
  = Integer -> T__'60'__50 -> T__'8804'__26
du_m'60'n'8658'm'8804'pred'91'n'93'_4034 Integer
v1 T__'60'__50
v2
du_m'60'n'8658'm'8804'pred'91'n'93'_4034 ::
  Integer ->
  MAlonzo.Code.Data.Integer.Base.T__'60'__50 ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26
du_m'60'n'8658'm'8804'pred'91'n'93'_4034 :: Integer -> T__'60'__50 -> T__'8804'__26
du_m'60'n'8658'm'8804'pred'91'n'93'_4034 Integer
v0 T__'60'__50
v1
  = case Integer -> Integer
forall a b. a -> b
coe Integer
v0 of
      Integer
0 -> (Any -> Any -> Any) -> Any -> Any -> T__'8804'__26
forall a b. a -> b
coe
             Any -> Any -> Any
forall a b. a -> b -> b
seq (T__'60'__50 -> Any
forall a b. a -> b
coe T__'60'__50
v1)
             ((T__'8804'__18 -> T__'8804'__26) -> Any -> Any
forall a b. a -> b
coe
                T__'8804'__18 -> T__'8804'__26
MAlonzo.Code.Data.Integer.Base.C_'45''8804''45'_34
                (T__'8804'__18 -> Any
forall a b. a -> b
coe T__'8804'__18
MAlonzo.Code.Data.Nat.Base.C_z'8804'n_22))
      Integer
_ | (Integer -> Integer -> Bool) -> Any -> Any -> Bool
forall a b. a -> b
coe Integer -> Integer -> Bool
geqInt (Integer -> Any
forall a b. a -> b
coe Integer
v0) (Integer -> Any
forall a b. a -> b
coe (Integer
1 :: Integer)) ->
          case T__'60'__50 -> T__'60'__50
forall a b. a -> b
coe T__'60'__50
v1 of
            T__'60'__50
MAlonzo.Code.Data.Integer.Base.C_'45''60''43'_64
              -> T__'8804'__26 -> T__'8804'__26
forall a b. a -> b
coe T__'8804'__26
MAlonzo.Code.Data.Integer.Base.C_'45''8804''43'_40
            MAlonzo.Code.Data.Integer.Base.C_'43''60''43'_72 T__'8804'__18
v4
              -> (T__'8804'__18 -> T__'8804'__26) -> Any -> T__'8804'__26
forall a b. a -> b
coe
                   T__'8804'__18 -> T__'8804'__26
MAlonzo.Code.Data.Integer.Base.C_'43''8804''43'_48
                   ((T__'8804'__18 -> T__'8804'__18) -> Any -> Any
forall a b. a -> b
coe
                      T__'8804'__18 -> T__'8804'__18
MAlonzo.Code.Data.Nat.Properties.Core.du_'8804''45'pred_12
                      (T__'8804'__18 -> Any
forall a b. a -> b
coe T__'8804'__18
v4))
            T__'60'__50
_ -> T__'8804'__26
forall a. a
MAlonzo.RTE.mazUnreachableError
      Integer
_ -> case T__'60'__50 -> T__'60'__50
forall a b. a -> b
coe T__'60'__50
v1 of
             MAlonzo.Code.Data.Integer.Base.C_'45''60''45'_58 T__'8804'__18
v4
               -> (T__'8804'__18 -> T__'8804'__26) -> T__'8804'__18 -> T__'8804'__26
forall a b. a -> b
coe T__'8804'__18 -> T__'8804'__26
MAlonzo.Code.Data.Integer.Base.C_'45''8804''45'_34 T__'8804'__18
v4
             T__'60'__50
_ -> T__'8804'__26
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Data.Integer.Properties.≤-step-neg
d_'8804''45'step'45'neg_4050 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26 ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26
d_'8804''45'step'45'neg_4050 :: Integer -> Integer -> T__'8804'__26 -> T__'8804'__26
d_'8804''45'step'45'neg_4050 ~Integer
v0 ~Integer
v1 T__'8804'__26
v2
  = T__'8804'__26 -> T__'8804'__26
du_'8804''45'step'45'neg_4050 T__'8804'__26
v2
du_'8804''45'step'45'neg_4050 ::
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26 ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26
du_'8804''45'step'45'neg_4050 :: T__'8804'__26 -> T__'8804'__26
du_'8804''45'step'45'neg_4050 T__'8804'__26
v0
  = case T__'8804'__26 -> T__'8804'__26
forall a b. a -> b
coe T__'8804'__26
v0 of
      MAlonzo.Code.Data.Integer.Base.C_'45''8804''45'_34 T__'8804'__18
v3
        -> (T__'8804'__18 -> T__'8804'__26) -> T__'8804'__18 -> T__'8804'__26
forall a b. a -> b
coe T__'8804'__18 -> T__'8804'__26
MAlonzo.Code.Data.Integer.Base.C_'45''8804''45'_34 T__'8804'__18
v3
      T__'8804'__26
MAlonzo.Code.Data.Integer.Base.C_'45''8804''43'_40
        -> T__'8804'__26 -> T__'8804'__26
forall a b. a -> b
coe T__'8804'__26
MAlonzo.Code.Data.Integer.Base.C_'45''8804''43'_40
      MAlonzo.Code.Data.Integer.Base.C_'43''8804''43'_48 T__'8804'__18
v3
        -> case T__'8804'__18 -> T__'8804'__18
forall a b. a -> b
coe T__'8804'__18
v3 of
             T__'8804'__18
MAlonzo.Code.Data.Nat.Base.C_z'8804'n_22
               -> T__'8804'__26 -> T__'8804'__26
forall a b. a -> b
coe T__'8804'__26
MAlonzo.Code.Data.Integer.Base.C_'45''8804''43'_40
             MAlonzo.Code.Data.Nat.Base.C_s'8804's_30 T__'8804'__18
v6
               -> (T__'8804'__18 -> T__'8804'__26) -> T__'8804'__18 -> T__'8804'__26
forall a b. a -> b
coe T__'8804'__18 -> T__'8804'__26
MAlonzo.Code.Data.Integer.Base.C_'43''8804''43'_48 T__'8804'__18
v6
             T__'8804'__18
_ -> T__'8804'__26
forall a. a
MAlonzo.RTE.mazUnreachableError
      T__'8804'__26
_ -> T__'8804'__26
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Data.Integer.Properties.pred-mono
d_pred'45'mono_4056 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26 ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26
d_pred'45'mono_4056 :: Integer -> Integer -> T__'8804'__26 -> T__'8804'__26
d_pred'45'mono_4056 Integer
v0 Integer
v1 T__'8804'__26
v2
  = case T__'8804'__26 -> T__'8804'__26
forall a b. a -> b
coe T__'8804'__26
v2 of
      MAlonzo.Code.Data.Integer.Base.C_'45''8804''45'_34 T__'8804'__18
v5
        -> (T__'8804'__18 -> T__'8804'__26) -> Any -> T__'8804'__26
forall a b. a -> b
coe
             T__'8804'__18 -> T__'8804'__26
MAlonzo.Code.Data.Integer.Base.C_'45''8804''45'_34
             ((T__'8804'__18 -> T__'8804'__18) -> T__'8804'__18 -> Any
forall a b. a -> b
coe T__'8804'__18 -> T__'8804'__18
MAlonzo.Code.Data.Nat.Base.C_s'8804's_30 T__'8804'__18
v5)
      T__'8804'__26
MAlonzo.Code.Data.Integer.Base.C_'45''8804''43'_40
        -> case Integer -> Integer
forall a b. a -> b
coe Integer
v1 of
             Integer
0 -> (T__'8804'__18 -> T__'8804'__26) -> Any -> T__'8804'__26
forall a b. a -> b
coe
                    T__'8804'__18 -> T__'8804'__26
MAlonzo.Code.Data.Integer.Base.C_'45''8804''45'_34
                    (T__'8804'__18 -> Any
forall a b. a -> b
coe T__'8804'__18
MAlonzo.Code.Data.Nat.Base.C_z'8804'n_22)
             Integer
_ -> T__'8804'__26 -> T__'8804'__26
forall a b. a -> b
coe T__'8804'__26
MAlonzo.Code.Data.Integer.Base.C_'45''8804''43'_40
      MAlonzo.Code.Data.Integer.Base.C_'43''8804''43'_48 T__'8804'__18
v5
        -> (Integer -> Integer -> Integer -> T__'8804'__18 -> T__'8804'__26)
-> Any -> Any -> Any -> Any -> T__'8804'__26
forall a b. a -> b
coe
             Integer -> Integer -> Integer -> T__'8804'__18 -> T__'8804'__26
d_'8854''45'mono'737''45''8804'_2924 (Integer -> Any
forall a b. a -> b
coe (Integer
1 :: Integer)) (Integer -> Any
forall a b. a -> b
coe Integer
v0)
             (Integer -> Any
forall a b. a -> b
coe Integer
v1) (T__'8804'__18 -> Any
forall a b. a -> b
coe T__'8804'__18
v5)
      T__'8804'__26
_ -> T__'8804'__26
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Data.Integer.Properties.*-comm
d_'42''45'comm_4064 ::
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'42''45'comm_4064 :: Integer -> Integer -> T__'8801'__12
d_'42''45'comm_4064 = Integer -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.*-identityˡ
d_'42''45'identity'737'_4098 ::
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'42''45'identity'737'_4098 :: Integer -> T__'8801'__12
d_'42''45'identity'737'_4098 = Integer -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.*-identityʳ
d_'42''45'identity'691'_4112 ::
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'42''45'identity'691'_4112 :: Integer -> T__'8801'__12
d_'42''45'identity'691'_4112 = Integer -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.*-identity
d_'42''45'identity_4114 :: MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'42''45'identity_4114 :: T_Σ_14
d_'42''45'identity_4114
  = (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.Integer.Properties.*-zeroˡ
d_'42''45'zero'737'_4116 ::
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'42''45'zero'737'_4116 :: Integer -> T__'8801'__12
d_'42''45'zero'737'_4116 = Integer -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.*-zeroʳ
d_'42''45'zero'691'_4120 ::
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'42''45'zero'691'_4120 :: Integer -> T__'8801'__12
d_'42''45'zero'691'_4120 = Integer -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.*-zero
d_'42''45'zero_4122 :: MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'42''45'zero_4122 :: T_Σ_14
d_'42''45'zero_4122
  = (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.Integer.Properties.lemma
d_lemma_4130 ::
  Integer ->
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_lemma_4130 :: Integer -> Integer -> Integer -> T__'8801'__12
d_lemma_4130 = Integer -> Integer -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.*-assoc
d_'42''45'assoc_4138 ::
  Integer ->
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'42''45'assoc_4138 :: Integer -> Integer -> Integer -> T__'8801'__12
d_'42''45'assoc_4138 = Integer -> Integer -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.distrib-lemma
d_distrib'45'lemma_4218 ::
  Integer ->
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_distrib'45'lemma_4218 :: Integer -> Integer -> Integer -> T__'8801'__12
d_distrib'45'lemma_4218 = Integer -> Integer -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.*-distribʳ-+
d_'42''45'distrib'691''45''43'_4294 ::
  Integer ->
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'42''45'distrib'691''45''43'_4294 :: Integer -> Integer -> Integer -> T__'8801'__12
d_'42''45'distrib'691''45''43'_4294 = Integer -> Integer -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.*-distribˡ-+
d_'42''45'distrib'737''45''43'_4584 ::
  Integer ->
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'42''45'distrib'737''45''43'_4584 :: Integer -> Integer -> Integer -> T__'8801'__12
d_'42''45'distrib'737''45''43'_4584 = Integer -> Integer -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.*-distrib-+
d_'42''45'distrib'45''43'_4586 ::
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'42''45'distrib'45''43'_4586 :: T_Σ_14
d_'42''45'distrib'45''43'_4586
  = (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.Integer.Properties.*-isMagma
d_'42''45'isMagma_4588 ::
  MAlonzo.Code.Algebra.Structures.T_IsMagma_86
d_'42''45'isMagma_4588 :: T_IsMagma_86
d_'42''45'isMagma_4588
  = (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.Integer.Properties.*-isSemigroup
d_'42''45'isSemigroup_4590 ::
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_194
d_'42''45'isSemigroup_4590 :: T_IsSemigroup_194
d_'42''45'isSemigroup_4590
  = (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_'42''45'isMagma_4588) Any
forall a. a
erased
-- Data.Integer.Properties.*-isCommutativeSemigroup
d_'42''45'isCommutativeSemigroup_4592 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_270
d_'42''45'isCommutativeSemigroup_4592 :: T_IsCommutativeSemigroup_270
d_'42''45'isCommutativeSemigroup_4592
  = (T_IsSemigroup_194
 -> (Any -> Any -> Any) -> T_IsCommutativeSemigroup_270)
-> Any -> Any -> T_IsCommutativeSemigroup_270
forall a b. a -> b
coe
      T_IsSemigroup_194
-> (Any -> Any -> Any) -> T_IsCommutativeSemigroup_270
MAlonzo.Code.Algebra.Structures.C_IsCommutativeSemigroup'46'constructor_5673
      (T_IsSemigroup_194 -> Any
forall a b. a -> b
coe T_IsSemigroup_194
d_'42''45'isSemigroup_4590) Any
forall a. a
erased
-- Data.Integer.Properties.*-1-isMonoid
d_'42''45'1'45'isMonoid_4594 ::
  MAlonzo.Code.Algebra.Structures.T_IsMonoid_358
d_'42''45'1'45'isMonoid_4594 :: T_IsMonoid_358
d_'42''45'1'45'isMonoid_4594
  = (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_'42''45'isSemigroup_4590) (T_Σ_14 -> Any
forall a b. a -> b
coe T_Σ_14
d_'42''45'identity_4114)
-- Data.Integer.Properties.*-1-isCommutativeMonoid
d_'42''45'1'45'isCommutativeMonoid_4596 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMonoid_406
d_'42''45'1'45'isCommutativeMonoid_4596 :: T_IsCommutativeMonoid_406
d_'42''45'1'45'isCommutativeMonoid_4596
  = (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_'42''45'1'45'isMonoid_4594) Any
forall a. a
erased
-- Data.Integer.Properties.+-*-isSemiring
d_'43''45''42''45'isSemiring_4598 ::
  MAlonzo.Code.Algebra.Structures.T_IsSemiring_1238
d_'43''45''42''45'isSemiring_4598 :: T_IsSemiring_1238
d_'43''45''42''45'isSemiring_4598
  = (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_'43''45'0'45'isCommutativeMonoid_3300)
         (T_IsMonoid_358 -> Any
forall a b. a -> b
coe T_IsMonoid_358
d_'42''45'1'45'isMonoid_4594)
         (T_Σ_14 -> Any
forall a b. a -> b
coe T_Σ_14
d_'42''45'distrib'45''43'_4586))
      (T_Σ_14 -> Any
forall a b. a -> b
coe T_Σ_14
d_'42''45'zero_4122)
-- Data.Integer.Properties.+-*-isCommutativeSemiring
d_'43''45''42''45'isCommutativeSemiring_4600 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiring_1344
d_'43''45''42''45'isCommutativeSemiring_4600 :: T_IsCommutativeSemiring_1344
d_'43''45''42''45'isCommutativeSemiring_4600
  = (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_'43''45''42''45'isSemiring_4598) Any
forall a. a
erased
-- Data.Integer.Properties.+-*-isRing
d_'43''45''42''45'isRing_4602 ::
  MAlonzo.Code.Algebra.Structures.T_IsRing_1584
d_'43''45''42''45'isRing_4602 :: T_IsRing_1584
d_'43''45''42''45'isRing_4602
  = (T_IsAbelianGroup_662
 -> T_IsMonoid_358 -> T_Σ_14 -> T_Σ_14 -> T_IsRing_1584)
-> Any -> Any -> Any -> Any -> T_IsRing_1584
forall a b. a -> b
coe
      T_IsAbelianGroup_662
-> T_IsMonoid_358 -> T_Σ_14 -> T_Σ_14 -> T_IsRing_1584
MAlonzo.Code.Algebra.Structures.C_IsRing'46'constructor_48413
      (T_IsAbelianGroup_662 -> Any
forall a b. a -> b
coe T_IsAbelianGroup_662
d_'43''45'isAbelianGroup_3304)
      (T_IsMonoid_358 -> Any
forall a b. a -> b
coe T_IsMonoid_358
d_'42''45'1'45'isMonoid_4594)
      (T_Σ_14 -> Any
forall a b. a -> b
coe T_Σ_14
d_'42''45'distrib'45''43'_4586) (T_Σ_14 -> Any
forall a b. a -> b
coe T_Σ_14
d_'42''45'zero_4122)
-- Data.Integer.Properties.+-*-isCommutativeRing
d_'43''45''42''45'isCommutativeRing_4604 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeRing_1720
d_'43''45''42''45'isCommutativeRing_4604 :: T_IsCommutativeRing_1720
d_'43''45''42''45'isCommutativeRing_4604
  = (T_IsRing_1584 -> (Any -> Any -> Any) -> T_IsCommutativeRing_1720)
-> Any -> Any -> T_IsCommutativeRing_1720
forall a b. a -> b
coe
      T_IsRing_1584 -> (Any -> Any -> Any) -> T_IsCommutativeRing_1720
MAlonzo.Code.Algebra.Structures.C_IsCommutativeRing'46'constructor_54081
      (T_IsRing_1584 -> Any
forall a b. a -> b
coe T_IsRing_1584
d_'43''45''42''45'isRing_4602) Any
forall a. a
erased
-- Data.Integer.Properties.*-magma
d_'42''45'magma_4606 :: MAlonzo.Code.Algebra.Bundles.T_Magma_36
d_'42''45'magma_4606 :: T_Magma_36
d_'42''45'magma_4606
  = ((Any -> Any -> Any) -> T_IsMagma_86 -> T_Magma_36)
-> (Integer -> Integer -> Integer) -> 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
      Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'42'__274 T_IsMagma_86
d_'42''45'isMagma_4588
-- Data.Integer.Properties.*-semigroup
d_'42''45'semigroup_4608 ::
  MAlonzo.Code.Algebra.Bundles.T_Semigroup_206
d_'42''45'semigroup_4608 :: T_Semigroup_206
d_'42''45'semigroup_4608
  = ((Any -> Any -> Any) -> T_IsSemigroup_194 -> T_Semigroup_206)
-> (Integer -> Integer -> Integer)
-> 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
      Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'42'__274
      T_IsSemigroup_194
d_'42''45'isSemigroup_4590
-- Data.Integer.Properties.*-commutativeSemigroup
d_'42''45'commutativeSemigroup_4610 ::
  MAlonzo.Code.Algebra.Bundles.T_CommutativeSemigroup_332
d_'42''45'commutativeSemigroup_4610 :: T_CommutativeSemigroup_332
d_'42''45'commutativeSemigroup_4610
  = ((Any -> Any -> Any)
 -> T_IsCommutativeSemigroup_270 -> T_CommutativeSemigroup_332)
-> (Integer -> Integer -> Integer)
-> T_IsCommutativeSemigroup_270
-> T_CommutativeSemigroup_332
forall a b. a -> b
coe
      (Any -> Any -> Any)
-> T_IsCommutativeSemigroup_270 -> T_CommutativeSemigroup_332
MAlonzo.Code.Algebra.Bundles.C_CommutativeSemigroup'46'constructor_5887
      Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'42'__274
      T_IsCommutativeSemigroup_270
d_'42''45'isCommutativeSemigroup_4592
-- Data.Integer.Properties.*-1-monoid
d_'42''45'1'45'monoid_4612 ::
  MAlonzo.Code.Algebra.Bundles.T_Monoid_506
d_'42''45'1'45'monoid_4612 :: T_Monoid_506
d_'42''45'1'45'monoid_4612
  = ((Any -> Any -> Any) -> Any -> T_IsMonoid_358 -> T_Monoid_506)
-> (Integer -> Integer -> Integer)
-> Integer
-> T_IsMonoid_358
-> T_Monoid_506
forall a b. a -> b
coe
      (Any -> Any -> Any) -> Any -> T_IsMonoid_358 -> T_Monoid_506
MAlonzo.Code.Algebra.Bundles.C_Monoid'46'constructor_8851
      Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'42'__274 (Integer
1 :: Integer)
      T_IsMonoid_358
d_'42''45'1'45'isMonoid_4594
-- Data.Integer.Properties.*-1-commutativeMonoid
d_'42''45'1'45'commutativeMonoid_4614 ::
  MAlonzo.Code.Algebra.Bundles.T_CommutativeMonoid_582
d_'42''45'1'45'commutativeMonoid_4614 :: T_CommutativeMonoid_582
d_'42''45'1'45'commutativeMonoid_4614
  = ((Any -> Any -> Any)
 -> Any -> T_IsCommutativeMonoid_406 -> T_CommutativeMonoid_582)
-> (Integer -> Integer -> Integer)
-> Integer
-> 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
      Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'42'__274 (Integer
1 :: Integer)
      T_IsCommutativeMonoid_406
d_'42''45'1'45'isCommutativeMonoid_4596
-- Data.Integer.Properties.+-*-semiring
d_'43''45''42''45'semiring_4616 ::
  MAlonzo.Code.Algebra.Bundles.T_Semiring_1932
d_'43''45''42''45'semiring_4616 :: T_Semiring_1932
d_'43''45''42''45'semiring_4616
  = ((Any -> Any -> Any)
 -> (Any -> Any -> Any)
 -> Any
 -> Any
 -> T_IsSemiring_1238
 -> T_Semiring_1932)
-> (Integer -> Integer -> Integer)
-> (Integer -> Integer -> Integer)
-> Integer
-> Integer
-> T_IsSemiring_1238
-> T_Semiring_1932
forall a b. a -> b
coe
      (Any -> Any -> Any)
-> (Any -> Any -> Any)
-> Any
-> Any
-> T_IsSemiring_1238
-> T_Semiring_1932
MAlonzo.Code.Algebra.Bundles.C_Semiring'46'constructor_33613
      Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'43'__242
      Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'42'__274 (Integer
0 :: Integer)
      (Integer
1 :: Integer) T_IsSemiring_1238
d_'43''45''42''45'isSemiring_4598
-- Data.Integer.Properties.+-*-commutativeSemiring
d_'43''45''42''45'commutativeSemiring_4618 ::
  MAlonzo.Code.Algebra.Bundles.T_CommutativeSemiring_2094
d_'43''45''42''45'commutativeSemiring_4618 :: T_CommutativeSemiring_2094
d_'43''45''42''45'commutativeSemiring_4618
  = ((Any -> Any -> Any)
 -> (Any -> Any -> Any)
 -> Any
 -> Any
 -> T_IsCommutativeSemiring_1344
 -> T_CommutativeSemiring_2094)
-> (Integer -> Integer -> Integer)
-> (Integer -> Integer -> Integer)
-> Integer
-> Integer
-> 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
      Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'43'__242
      Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'42'__274 (Integer
0 :: Integer)
      (Integer
1 :: Integer) T_IsCommutativeSemiring_1344
d_'43''45''42''45'isCommutativeSemiring_4600
-- Data.Integer.Properties.+-*-ring
d_'43''45''42''45'ring_4620 ::
  MAlonzo.Code.Algebra.Bundles.T_Ring_2514
d_'43''45''42''45'ring_4620 :: T_Ring_2514
d_'43''45''42''45'ring_4620
  = ((Any -> Any -> Any)
 -> (Any -> Any -> Any)
 -> (Any -> Any)
 -> Any
 -> Any
 -> T_IsRing_1584
 -> T_Ring_2514)
-> (Integer -> Integer -> Integer)
-> (Integer -> Integer -> Integer)
-> (Integer -> Integer)
-> Integer
-> Integer
-> T_IsRing_1584
-> T_Ring_2514
forall a b. a -> b
coe
      (Any -> Any -> Any)
-> (Any -> Any -> Any)
-> (Any -> Any)
-> Any
-> Any
-> T_IsRing_1584
-> T_Ring_2514
MAlonzo.Code.Algebra.Bundles.C_Ring'46'constructor_43513
      Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'43'__242
      Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'42'__274
      Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d_'45'__218 (Integer
0 :: Integer)
      (Integer
1 :: Integer) T_IsRing_1584
d_'43''45''42''45'isRing_4602
-- Data.Integer.Properties.+-*-commutativeRing
d_'43''45''42''45'commutativeRing_4622 ::
  MAlonzo.Code.Algebra.Bundles.T_CommutativeRing_2704
d_'43''45''42''45'commutativeRing_4622 :: T_CommutativeRing_2704
d_'43''45''42''45'commutativeRing_4622
  = ((Any -> Any -> Any)
 -> (Any -> Any -> Any)
 -> (Any -> Any)
 -> Any
 -> Any
 -> T_IsCommutativeRing_1720
 -> T_CommutativeRing_2704)
-> (Integer -> Integer -> Integer)
-> (Integer -> Integer -> Integer)
-> (Integer -> Integer)
-> Integer
-> Integer
-> T_IsCommutativeRing_1720
-> T_CommutativeRing_2704
forall a b. a -> b
coe
      (Any -> Any -> Any)
-> (Any -> Any -> Any)
-> (Any -> Any)
-> Any
-> Any
-> T_IsCommutativeRing_1720
-> T_CommutativeRing_2704
MAlonzo.Code.Algebra.Bundles.C_CommutativeRing'46'constructor_47013
      Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'43'__242
      Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'42'__274
      Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d_'45'__218 (Integer
0 :: Integer)
      (Integer
1 :: Integer) T_IsCommutativeRing_1720
d_'43''45''42''45'isCommutativeRing_4604
-- Data.Integer.Properties.abs-*-commute
d_abs'45''42''45'commute_4624 ::
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_abs'45''42''45'commute_4624 :: Integer -> Integer -> T__'8801'__12
d_abs'45''42''45'commute_4624 = Integer -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.*-cancelʳ-≡
d_'42''45'cancel'691''45''8801'_4636 ::
  Integer ->
  Integer ->
  Integer ->
  (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'691''45''8801'_4636 :: Integer
-> Integer
-> Integer
-> (T__'8801'__12 -> T_'8869'_4)
-> T__'8801'__12
-> T__'8801'__12
d_'42''45'cancel'691''45''8801'_4636 = Integer
-> Integer
-> Integer
-> (T__'8801'__12 -> T_'8869'_4)
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties._.sign-i≡sign-j
d_sign'45'i'8801'sign'45'j_4698 ::
  MAlonzo.Code.Data.Sign.Base.T_Sign_6 ->
  Integer ->
  Integer ->
  Integer ->
  (MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
   MAlonzo.Code.Data.Empty.T_'8869'_4) ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_sign'45'i'8801'sign'45'j_4698 :: T_Sign_6
-> Integer
-> Integer
-> Integer
-> (T__'8801'__12 -> T_'8869'_4)
-> T__'8801'__12
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8801'__12
d_sign'45'i'8801'sign'45'j_4698 = T_Sign_6
-> Integer
-> Integer
-> Integer
-> (T__'8801'__12 -> T_'8869'_4)
-> T__'8801'__12
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.*-cancelˡ-≡
d_'42''45'cancel'737''45''8801'_4810 ::
  Integer ->
  Integer ->
  Integer ->
  (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''8801'_4810 :: Integer
-> Integer
-> Integer
-> (T__'8801'__12 -> T_'8869'_4)
-> T__'8801'__12
-> T__'8801'__12
d_'42''45'cancel'737''45''8801'_4810 = Integer
-> Integer
-> Integer
-> (T__'8801'__12 -> T_'8869'_4)
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.suc-*
d_suc'45''42'_4830 ::
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_suc'45''42'_4830 :: Integer -> Integer -> T__'8801'__12
d_suc'45''42'_4830 = Integer -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.*-suc
d_'42''45'suc_4846 ::
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'42''45'suc_4846 :: Integer -> Integer -> T__'8801'__12
d_'42''45'suc_4846 = Integer -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.-1*n≡-n
d_'45'1'42'n'8801''45'n_4860 ::
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'45'1'42'n'8801''45'n_4860 :: Integer -> T__'8801'__12
d_'45'1'42'n'8801''45'n_4860 = Integer -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.m*n≡0⇒m≡0∨n≡0
d_m'42'n'8801'0'8658'm'8801'0'8744'n'8801'0_4872 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Data.Sum.Base.T__'8846'__30
d_m'42'n'8801'0'8658'm'8801'0'8744'n'8801'0_4872 :: Integer -> Integer -> T__'8801'__12 -> T__'8846'__30
d_m'42'n'8801'0'8658'm'8801'0'8744'n'8801'0_4872 Integer
v0 ~Integer
v1 ~T__'8801'__12
v2
  = Integer -> T__'8846'__30
du_m'42'n'8801'0'8658'm'8801'0'8744'n'8801'0_4872 Integer
v0
du_m'42'n'8801'0'8658'm'8801'0'8744'n'8801'0_4872 ::
  Integer -> MAlonzo.Code.Data.Sum.Base.T__'8846'__30
du_m'42'n'8801'0'8658'm'8801'0'8744'n'8801'0_4872 :: Integer -> T__'8846'__30
du_m'42'n'8801'0'8658'm'8801'0'8744'n'8801'0_4872 Integer
v0
  = (Integer -> T__'8846'__30) -> Any -> T__'8846'__30
forall a b. a -> b
coe
      Integer -> T__'8846'__30
MAlonzo.Code.Data.Nat.Properties.du_m'42'n'8801'0'8658'm'8801'0'8744'n'8801'0_2682
      ((Integer -> Integer) -> Any -> Any
forall a b. a -> b
coe Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d_'8739'_'8739'_18 (Integer -> Any
forall a b. a -> b
coe Integer
v0))
-- Data.Integer.Properties.pos-distrib-*
d_pos'45'distrib'45''42'_4898 ::
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_pos'45'distrib'45''42'_4898 :: Integer -> Integer -> T__'8801'__12
d_pos'45'distrib'45''42'_4898 = Integer -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.neg-distribˡ-*
d_neg'45'distrib'737''45''42'_4912 ::
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_neg'45'distrib'737''45''42'_4912 :: Integer -> Integer -> T__'8801'__12
d_neg'45'distrib'737''45''42'_4912 = Integer -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.neg-distribʳ-*
d_neg'45'distrib'691''45''42'_4928 ::
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_neg'45'distrib'691''45''42'_4928 :: Integer -> Integer -> T__'8801'__12
d_neg'45'distrib'691''45''42'_4928 = Integer -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.◃-distrib-*
d_'9667''45'distrib'45''42'_4946 ::
  MAlonzo.Code.Data.Sign.Base.T_Sign_6 ->
  MAlonzo.Code.Data.Sign.Base.T_Sign_6 ->
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'9667''45'distrib'45''42'_4946 :: T_Sign_6 -> T_Sign_6 -> Integer -> Integer -> T__'8801'__12
d_'9667''45'distrib'45''42'_4946 = T_Sign_6 -> T_Sign_6 -> Integer -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.*-cancelʳ-≤-pos
d_'42''45'cancel'691''45''8804''45'pos_4978 ::
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26 ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26
d_'42''45'cancel'691''45''8804''45'pos_4978 :: Integer -> Integer -> Integer -> T__'8804'__26 -> T__'8804'__26
d_'42''45'cancel'691''45''8804''45'pos_4978 Integer
v0 Integer
v1 ~Integer
v2 T__'8804'__26
v3
  = Integer -> Integer -> T__'8804'__26 -> T__'8804'__26
du_'42''45'cancel'691''45''8804''45'pos_4978 Integer
v0 Integer
v1 T__'8804'__26
v3
du_'42''45'cancel'691''45''8804''45'pos_4978 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26 ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26
du_'42''45'cancel'691''45''8804''45'pos_4978 :: Integer -> Integer -> T__'8804'__26 -> T__'8804'__26
du_'42''45'cancel'691''45''8804''45'pos_4978 Integer
v0 Integer
v1 T__'8804'__26
v2
  = case Integer -> Integer
forall a b. a -> b
coe Integer
v0 of
      Integer
0 -> (Any -> Any -> Any) -> Any -> Any -> T__'8804'__26
forall a b. a -> b
coe
             Any -> Any -> Any
forall a b. a -> b -> b
seq (Integer -> Any
forall a b. a -> b
coe Integer
v1)
             ((T__'8804'__18 -> T__'8804'__26) -> Any -> Any
forall a b. a -> b
coe
                T__'8804'__18 -> T__'8804'__26
MAlonzo.Code.Data.Integer.Base.C_'43''8804''43'_48
                (T__'8804'__18 -> Any
forall a b. a -> b
coe T__'8804'__18
MAlonzo.Code.Data.Nat.Base.C_z'8804'n_22))
      Integer
_ | (Integer -> Integer -> Bool) -> Any -> Any -> Bool
forall a b. a -> b
coe Integer -> Integer -> Bool
geqInt (Integer -> Any
forall a b. a -> b
coe Integer
v0) (Integer -> Any
forall a b. a -> b
coe (Integer
1 :: Integer)) ->
          (Any -> Any -> Any) -> Any -> Any -> T__'8804'__26
forall a b. a -> b
coe
            Any -> Any -> Any
forall a b. a -> b -> b
seq (T__'8804'__26 -> Any
forall a b. a -> b
coe T__'8804'__26
v2)
            ((T__'8804'__18 -> T__'8804'__26) -> Any -> Any
forall a b. a -> b
coe
               T__'8804'__18 -> T__'8804'__26
MAlonzo.Code.Data.Integer.Base.C_'43''8804''43'_48
               ((Integer -> T__'8804'__18) -> Any -> Any
forall a b. a -> b
coe
                  Integer -> T__'8804'__18
MAlonzo.Code.Data.Nat.Properties.du_'42''45'cancel'691''45''8804'_2792
                  (Integer -> Any
forall a b. a -> b
coe Integer
v0)))
      Integer
_ -> case Integer -> Any
forall a b. a -> b
coe Integer
v1 of
             Any
_ | (Integer -> Integer -> Bool) -> Any -> Any -> Bool
forall a b. a -> b
coe Integer -> Integer -> Bool
geqInt (Integer -> Any
forall a b. a -> b
coe Integer
v1) (Integer -> Any
forall a b. a -> b
coe (Integer
0 :: Integer)) ->
                 T__'8804'__26 -> T__'8804'__26
forall a b. a -> b
coe T__'8804'__26
MAlonzo.Code.Data.Integer.Base.C_'45''8804''43'_40
             Any
_ -> (Any -> Any -> Any) -> Any -> Any -> T__'8804'__26
forall a b. a -> b
coe
                    Any -> Any -> Any
forall a b. a -> b -> b
seq (T__'8804'__26 -> Any
forall a b. a -> b
coe T__'8804'__26
v2)
                    ((T__'8804'__18 -> T__'8804'__26) -> Any -> Any
forall a b. a -> b
coe
                       T__'8804'__18 -> T__'8804'__26
MAlonzo.Code.Data.Integer.Base.C_'45''8804''45'_34
                       ((T__'8804'__18 -> T__'8804'__18) -> Any -> Any
forall a b. a -> b
coe
                          T__'8804'__18 -> T__'8804'__18
MAlonzo.Code.Data.Nat.Properties.Core.du_'8804''45'pred_12
                          ((Integer -> T__'8804'__18) -> Any -> Any
forall a b. a -> b
coe
                             Integer -> T__'8804'__18
MAlonzo.Code.Data.Nat.Properties.du_'42''45'cancel'691''45''8804'_2792
                             ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> Integer
subInt (Integer -> Any
forall a b. a -> b
coe (Integer
0 :: Integer)) (Integer -> Any
forall a b. a -> b
coe Integer
v1)))))
-- Data.Integer.Properties.*-cancelˡ-≤-pos
d_'42''45'cancel'737''45''8804''45'pos_5002 ::
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26 ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26
d_'42''45'cancel'737''45''8804''45'pos_5002 :: Integer -> Integer -> Integer -> T__'8804'__26 -> T__'8804'__26
d_'42''45'cancel'737''45''8804''45'pos_5002 ~Integer
v0 Integer
v1 Integer
v2
  = Integer -> Integer -> T__'8804'__26 -> T__'8804'__26
du_'42''45'cancel'737''45''8804''45'pos_5002 Integer
v1 Integer
v2
du_'42''45'cancel'737''45''8804''45'pos_5002 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26 ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26
du_'42''45'cancel'737''45''8804''45'pos_5002 :: Integer -> Integer -> T__'8804'__26 -> T__'8804'__26
du_'42''45'cancel'737''45''8804''45'pos_5002 Integer
v0 Integer
v1
  = (Integer -> Integer -> T__'8804'__26 -> T__'8804'__26)
-> Any -> Any -> T__'8804'__26 -> T__'8804'__26
forall a b. a -> b
coe
      Integer -> Integer -> T__'8804'__26 -> T__'8804'__26
du_'42''45'cancel'691''45''8804''45'pos_4978 (Integer -> Any
forall a b. a -> b
coe Integer
v0) (Integer -> Any
forall a b. a -> b
coe Integer
v1)
-- Data.Integer.Properties.*-monoʳ-≤-pos
d_'42''45'mono'691''45''8804''45'pos_5022 ::
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26 ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26
d_'42''45'mono'691''45''8804''45'pos_5022 :: Integer -> Integer -> Integer -> T__'8804'__26 -> T__'8804'__26
d_'42''45'mono'691''45''8804''45'pos_5022 Integer
v0 Integer
v1 Integer
v2 T__'8804'__26
v3
  = case T__'8804'__26 -> T__'8804'__26
forall a b. a -> b
coe T__'8804'__26
v3 of
      MAlonzo.Code.Data.Integer.Base.C_'45''8804''45'_34 T__'8804'__18
v6
        -> (T__'8804'__18 -> T__'8804'__26) -> Any -> T__'8804'__26
forall a b. a -> b
coe
             T__'8804'__18 -> T__'8804'__26
MAlonzo.Code.Data.Integer.Base.C_'45''8804''45'_34
             ((T__'8804'__18 -> T__'8804'__18) -> Any -> Any
forall a b. a -> b
coe
                T__'8804'__18 -> T__'8804'__18
MAlonzo.Code.Data.Nat.Properties.Core.du_'8804''45'pred_12
                ((Integer
 -> Integer -> T__'8804'__18 -> T__'8804'__18 -> T__'8804'__18)
-> Any -> Any -> Any -> Any -> Any
forall a b. a -> b
coe
                   Integer
-> Integer -> T__'8804'__18 -> T__'8804'__18 -> T__'8804'__18
MAlonzo.Code.Data.Nat.Properties.du_'42''45'mono'45''8804'_2824
                   ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> Integer
subInt (Integer -> Any
forall a b. a -> b
coe (Integer
0 :: Integer)) (Integer -> Any
forall a b. a -> b
coe Integer
v1))
                   ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> Integer
addInt (Integer -> Any
forall a b. a -> b
coe (Integer
1 :: Integer)) (Integer -> Any
forall a b. a -> b
coe Integer
v0))
                   ((T__'8804'__18 -> T__'8804'__18) -> T__'8804'__18 -> Any
forall a b. a -> b
coe T__'8804'__18 -> T__'8804'__18
MAlonzo.Code.Data.Nat.Base.C_s'8804's_30 T__'8804'__18
v6)
                   ((Integer -> T__'8804'__18) -> Any -> Any
forall a b. a -> b
coe
                      Integer -> T__'8804'__18
MAlonzo.Code.Data.Nat.Properties.d_'8804''45'refl_1634
                      ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> Integer
addInt (Integer -> Any
forall a b. a -> b
coe (Integer
1 :: Integer)) (Integer -> Any
forall a b. a -> b
coe Integer
v0)))))
      T__'8804'__26
MAlonzo.Code.Data.Integer.Base.C_'45''8804''43'_40
        -> T__'8804'__26 -> T__'8804'__26
forall a b. a -> b
coe T__'8804'__26
MAlonzo.Code.Data.Integer.Base.C_'45''8804''43'_40
      MAlonzo.Code.Data.Integer.Base.C_'43''8804''43'_48 T__'8804'__18
v6
        -> case Integer -> Integer
forall a b. a -> b
coe Integer
v1 of
             Integer
0 -> case Integer -> Integer
forall a b. a -> b
coe Integer
v2 of
                    Integer
0 -> (T__'8804'__18 -> T__'8804'__26) -> T__'8804'__18 -> T__'8804'__26
forall a b. a -> b
coe T__'8804'__18 -> T__'8804'__26
MAlonzo.Code.Data.Integer.Base.C_'43''8804''43'_48 T__'8804'__18
v6
                    Integer
_ -> (T__'8804'__18 -> T__'8804'__26) -> Any -> T__'8804'__26
forall a b. a -> b
coe
                           T__'8804'__18 -> T__'8804'__26
MAlonzo.Code.Data.Integer.Base.C_'43''8804''43'_48
                           (T__'8804'__18 -> Any
forall a b. a -> b
coe T__'8804'__18
MAlonzo.Code.Data.Nat.Base.C_z'8804'n_22)
             Integer
_ -> (T__'8804'__18 -> T__'8804'__26) -> Any -> T__'8804'__26
forall a b. a -> b
coe
                    T__'8804'__18 -> T__'8804'__26
MAlonzo.Code.Data.Integer.Base.C_'43''8804''43'_48
                    ((Integer
 -> Integer -> T__'8804'__18 -> T__'8804'__18 -> T__'8804'__18)
-> Any -> Any -> Any -> Any -> Any
forall a b. a -> b
coe
                       Integer
-> Integer -> T__'8804'__18 -> T__'8804'__18 -> T__'8804'__18
MAlonzo.Code.Data.Nat.Properties.du_'42''45'mono'45''8804'_2824
                       (Integer -> Any
forall a b. a -> b
coe Integer
v2) ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> Integer
addInt (Integer -> Any
forall a b. a -> b
coe (Integer
1 :: Integer)) (Integer -> Any
forall a b. a -> b
coe Integer
v0)) (T__'8804'__18 -> Any
forall a b. a -> b
coe T__'8804'__18
v6)
                       ((Integer -> T__'8804'__18) -> Any -> Any
forall a b. a -> b
coe
                          Integer -> T__'8804'__18
MAlonzo.Code.Data.Nat.Properties.d_'8804''45'refl_1634
                          ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> Integer
addInt (Integer -> Any
forall a b. a -> b
coe (Integer
1 :: Integer)) (Integer -> Any
forall a b. a -> b
coe Integer
v0))))
      T__'8804'__26
_ -> T__'8804'__26
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Data.Integer.Properties.*-monoʳ-≤-nonNeg
d_'42''45'mono'691''45''8804''45'nonNeg_5044 ::
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26 ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26
d_'42''45'mono'691''45''8804''45'nonNeg_5044 :: Integer -> Integer -> Integer -> T__'8804'__26 -> T__'8804'__26
d_'42''45'mono'691''45''8804''45'nonNeg_5044 Integer
v0 Integer
v1 Integer
v2
  = case Integer -> Integer
forall a b. a -> b
coe Integer
v0 of
      Integer
0 -> (Any -> Any) -> T__'8804'__26 -> T__'8804'__26
forall a b. a -> b
coe
             (\ Any
v3 ->
                (T__'8804'__18 -> T__'8804'__26) -> Any -> Any
forall a b. a -> b
coe
                  T__'8804'__18 -> T__'8804'__26
MAlonzo.Code.Data.Integer.Base.C_'43''8804''43'_48
                  (T__'8804'__18 -> Any
forall a b. a -> b
coe T__'8804'__18
MAlonzo.Code.Data.Nat.Base.C_z'8804'n_22))
      Integer
_ -> let v3 :: Integer
v3 = Integer -> Integer -> Integer
subInt (Integer -> Integer
forall a b. a -> b
coe Integer
v0) (Integer -> Integer
forall a b. a -> b
coe (Integer
1 :: Integer)) in
           Any -> T__'8804'__26 -> T__'8804'__26
forall a b. a -> b
coe
             ((Integer -> Integer -> Integer -> T__'8804'__26 -> T__'8804'__26)
-> Any -> Any -> Any -> Any
forall a b. a -> b
coe
                Integer -> Integer -> Integer -> T__'8804'__26 -> T__'8804'__26
d_'42''45'mono'691''45''8804''45'pos_5022 (Integer -> Any
forall a b. a -> b
coe Integer
v3) (Integer -> Any
forall a b. a -> b
coe Integer
v1)
                (Integer -> Any
forall a b. a -> b
coe Integer
v2))
-- Data.Integer.Properties.*-monoˡ-≤-nonNeg
d_'42''45'mono'737''45''8804''45'nonNeg_5066 ::
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26 ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26
d_'42''45'mono'737''45''8804''45'nonNeg_5066 :: Integer -> Integer -> Integer -> T__'8804'__26 -> T__'8804'__26
d_'42''45'mono'737''45''8804''45'nonNeg_5066 Integer
v0 Integer
v1 Integer
v2 T__'8804'__26
v3
  = (Integer -> Integer -> Integer -> T__'8804'__26 -> T__'8804'__26)
-> Integer -> Integer -> Integer -> T__'8804'__26 -> T__'8804'__26
forall a b. a -> b
coe Integer -> Integer -> Integer -> T__'8804'__26 -> T__'8804'__26
d_'42''45'mono'691''45''8804''45'nonNeg_5044 Integer
v0 Integer
v1 Integer
v2 T__'8804'__26
v3
-- Data.Integer.Properties.*-monoˡ-≤-pos
d_'42''45'mono'737''45''8804''45'pos_5088 ::
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26 ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26
d_'42''45'mono'737''45''8804''45'pos_5088 :: Integer -> Integer -> Integer -> T__'8804'__26 -> T__'8804'__26
d_'42''45'mono'737''45''8804''45'pos_5088 Integer
v0 Integer
v1 Integer
v2
  = (Integer -> Integer -> Integer -> T__'8804'__26 -> T__'8804'__26)
-> Any -> Any -> Any -> T__'8804'__26 -> T__'8804'__26
forall a b. a -> b
coe
      Integer -> Integer -> Integer -> T__'8804'__26 -> T__'8804'__26
d_'42''45'mono'737''45''8804''45'nonNeg_5066
      ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> Integer
addInt (Integer -> Any
forall a b. a -> b
coe (Integer
1 :: Integer)) (Integer -> Any
forall a b. a -> b
coe Integer
v0)) (Integer -> Any
forall a b. a -> b
coe Integer
v1) (Integer -> Any
forall a b. a -> b
coe Integer
v2)
-- Data.Integer.Properties.*-cancelˡ-≤-neg
d_'42''45'cancel'737''45''8804''45'neg_5098 ::
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26 ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26
d_'42''45'cancel'737''45''8804''45'neg_5098 :: Integer -> Integer -> Integer -> T__'8804'__26 -> T__'8804'__26
d_'42''45'cancel'737''45''8804''45'neg_5098 Integer
v0 Integer
v1 Integer
v2 T__'8804'__26
v3
  = (Integer -> Integer -> T__'8804'__26 -> T__'8804'__26)
-> Any -> Any -> Any -> T__'8804'__26
forall a b. a -> b
coe
      Integer -> Integer -> T__'8804'__26 -> T__'8804'__26
d_neg'45'cancel'45''8804'_3740 (Integer -> Any
forall a b. a -> b
coe Integer
v1) (Integer -> Any
forall a b. a -> b
coe Integer
v2)
      ((Integer -> Integer -> T__'8804'__26 -> T__'8804'__26)
-> Integer -> Integer -> Any -> Any
forall a b. a -> b
coe
         Integer -> Integer -> T__'8804'__26 -> T__'8804'__26
du_'42''45'cancel'737''45''8804''45'pos_5002
         (Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d_'45'__218 (Integer -> Integer
forall a b. a -> b
coe Integer
v1))
         (Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d_'45'__218 (Integer -> Integer
forall a b. a -> b
coe Integer
v2))
         ((T_IsPreorder_70
 -> (Any -> Any -> Any -> Any)
 -> Any
 -> Any
 -> T__IsRelatedTo__70
 -> Any)
-> Any -> Any -> Any -> Any -> Any -> Any
forall a b. a -> b
coe
            T_IsPreorder_70
-> (Any -> Any -> Any -> Any)
-> Any
-> Any
-> T__IsRelatedTo__70
-> Any
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_begin__160
            (T_IsPreorder_70 -> Any
forall a b. a -> b
coe T_IsPreorder_70
d_'8804''45'isPreorder_1656) ((Integer -> Integer -> T__'60'__50 -> T__'8804'__26) -> Any
forall a b. a -> b
coe Integer -> Integer -> T__'60'__50 -> T__'8804'__26
d_'60''8658''8804'_1724)
            ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe
               Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'42'__274
               ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> Integer
addInt (Integer -> Any
forall a b. a -> b
coe (Integer
1 :: Integer)) (Integer -> Any
forall a b. a -> b
coe Integer
v0))
               ((Integer -> Integer) -> Any -> Any
forall a b. a -> b
coe Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d_'45'__218 (Integer -> Any
forall a b. a -> b
coe Integer
v1)))
            ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe
               Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'42'__274
               ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> Integer
addInt (Integer -> Any
forall a b. a -> b
coe (Integer
1 :: Integer)) (Integer -> Any
forall a b. a -> b
coe Integer
v0))
               ((Integer -> Integer) -> Any -> Any
forall a b. a -> b
coe Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d_'45'__218 (Integer -> Any
forall a b. a -> b
coe Integer
v2)))
            ((T_IsPreorder_70
 -> (Any -> Any -> Any -> Any -> Any -> Any)
 -> Any
 -> Any
 -> Any
 -> T__IsRelatedTo__70
 -> Any
 -> T__IsRelatedTo__70)
-> Any
-> (Any -> Any -> Any -> Any -> Any -> Any)
-> Any
-> Any
-> Any
-> Any
-> Any
-> Any
forall a b. a -> b
coe
               T_IsPreorder_70
-> (Any -> Any -> Any -> Any -> Any -> Any)
-> Any
-> Any
-> Any
-> T__IsRelatedTo__70
-> Any
-> T__IsRelatedTo__70
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_step'45''8804'_228
               (T_IsPreorder_70 -> Any
forall a b. a -> b
coe T_IsPreorder_70
d_'8804''45'isPreorder_1656)
               (\ Any
v4 Any
v5 Any
v6 Any
v7 Any
v8 -> (T__'8804'__26 -> T__'60'__50 -> T__'60'__50) -> Any -> Any -> Any
forall a b. a -> b
coe T__'8804'__26 -> T__'60'__50 -> T__'60'__50
du_'8804''45''60''45'trans_1844 Any
v7 Any
v8)
               ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe
                  Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'42'__274
                  ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> Integer
subInt (Integer -> Any
forall a b. a -> b
coe (-Integer
1 :: Integer)) (Integer -> Any
forall a b. a -> b
coe Integer
v0)) (Integer -> Any
forall a b. a -> b
coe Integer
v1))
               ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe
                  Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'42'__274
                  ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> Integer
subInt (Integer -> Any
forall a b. a -> b
coe (-Integer
1 :: Integer)) (Integer -> Any
forall a b. a -> b
coe Integer
v0)) (Integer -> Any
forall a b. a -> b
coe Integer
v2))
               ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe
                  Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'42'__274
                  ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> Integer
addInt (Integer -> Any
forall a b. a -> b
coe (Integer
1 :: Integer)) (Integer -> Any
forall a b. a -> b
coe Integer
v0))
                  ((Integer -> Integer) -> Any -> Any
forall a b. a -> b
coe Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d_'45'__218 (Integer -> Any
forall a b. a -> b
coe Integer
v2)))
               ((T_IsPreorder_70 -> Any -> T__IsRelatedTo__70) -> Any -> Any -> Any
forall a b. a -> b
coe
                  T_IsPreorder_70 -> Any -> T__IsRelatedTo__70
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du__'8718'_346
                  (T_IsPreorder_70 -> Any
forall a b. a -> b
coe T_IsPreorder_70
d_'8804''45'isPreorder_1656)
                  ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe
                     Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'42'__274
                     ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> Integer
addInt (Integer -> Any
forall a b. a -> b
coe (Integer
1 :: Integer)) (Integer -> Any
forall a b. a -> b
coe Integer
v0))
                     ((Integer -> Integer) -> Any -> Any
forall a b. a -> b
coe Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d_'45'__218 (Integer -> Any
forall a b. a -> b
coe Integer
v2))))
               (T__'8804'__26 -> Any
forall a b. a -> b
coe T__'8804'__26
v3))))
-- Data.Integer.Properties.*-cancelʳ-≤-neg
d_'42''45'cancel'691''45''8804''45'neg_5118 ::
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26 ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26
d_'42''45'cancel'691''45''8804''45'neg_5118 :: Integer -> Integer -> Integer -> T__'8804'__26 -> T__'8804'__26
d_'42''45'cancel'691''45''8804''45'neg_5118 Integer
v0 Integer
v1 Integer
v2 T__'8804'__26
v3
  = (Integer -> Integer -> T__'8804'__26 -> T__'8804'__26)
-> Any -> Any -> Any -> T__'8804'__26
forall a b. a -> b
coe
      Integer -> Integer -> T__'8804'__26 -> T__'8804'__26
d_neg'45'cancel'45''8804'_3740 (Integer -> Any
forall a b. a -> b
coe Integer
v0) (Integer -> Any
forall a b. a -> b
coe Integer
v1)
      ((Integer -> Integer -> T__'8804'__26 -> T__'8804'__26)
-> Any -> Any -> Any -> Any
forall a b. a -> b
coe
         Integer -> Integer -> T__'8804'__26 -> T__'8804'__26
du_'42''45'cancel'691''45''8804''45'pos_4978
         ((Integer -> Integer) -> Any -> Any
forall a b. a -> b
coe Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d_'45'__218 (Integer -> Any
forall a b. a -> b
coe Integer
v0))
         ((Integer -> Integer) -> Any -> Any
forall a b. a -> b
coe Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d_'45'__218 (Integer -> Any
forall a b. a -> b
coe Integer
v1))
         ((T_IsPreorder_70
 -> (Any -> Any -> Any -> Any)
 -> Any
 -> Any
 -> T__IsRelatedTo__70
 -> Any)
-> Any -> Any -> Any -> Any -> Any -> Any
forall a b. a -> b
coe
            T_IsPreorder_70
-> (Any -> Any -> Any -> Any)
-> Any
-> Any
-> T__IsRelatedTo__70
-> Any
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_begin__160
            (T_IsPreorder_70 -> Any
forall a b. a -> b
coe T_IsPreorder_70
d_'8804''45'isPreorder_1656) ((Integer -> Integer -> T__'60'__50 -> T__'8804'__26) -> Any
forall a b. a -> b
coe Integer -> Integer -> T__'60'__50 -> T__'8804'__26
d_'60''8658''8804'_1724)
            ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe
               Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'42'__274
               ((Integer -> Integer) -> Any -> Any
forall a b. a -> b
coe Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d_'45'__218 (Integer -> Any
forall a b. a -> b
coe Integer
v0))
               ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> Integer
addInt (Integer -> Any
forall a b. a -> b
coe (Integer
1 :: Integer)) (Integer -> Any
forall a b. a -> b
coe Integer
v2)))
            ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe
               Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'42'__274
               ((Integer -> Integer) -> Any -> Any
forall a b. a -> b
coe Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d_'45'__218 (Integer -> Any
forall a b. a -> b
coe Integer
v1))
               ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> Integer
addInt (Integer -> Any
forall a b. a -> b
coe (Integer
1 :: Integer)) (Integer -> Any
forall a b. a -> b
coe Integer
v2)))
            ((T_IsPreorder_70
 -> (Any -> Any -> Any -> Any -> Any -> Any)
 -> Any
 -> Any
 -> Any
 -> T__IsRelatedTo__70
 -> Any
 -> T__IsRelatedTo__70)
-> Any
-> (Any -> Any -> Any -> Any -> Any -> Any)
-> Any
-> Any
-> Any
-> Any
-> Any
-> Any
forall a b. a -> b
coe
               T_IsPreorder_70
-> (Any -> Any -> Any -> Any -> Any -> Any)
-> Any
-> Any
-> Any
-> T__IsRelatedTo__70
-> Any
-> T__IsRelatedTo__70
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_step'45''8804'_228
               (T_IsPreorder_70 -> Any
forall a b. a -> b
coe T_IsPreorder_70
d_'8804''45'isPreorder_1656)
               (\ Any
v4 Any
v5 Any
v6 Any
v7 Any
v8 -> (T__'8804'__26 -> T__'60'__50 -> T__'60'__50) -> Any -> Any -> Any
forall a b. a -> b
coe T__'8804'__26 -> T__'60'__50 -> T__'60'__50
du_'8804''45''60''45'trans_1844 Any
v7 Any
v8)
               ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe
                  Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'42'__274 (Integer -> Any
forall a b. a -> b
coe Integer
v0)
                  ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> Integer
subInt (Integer -> Any
forall a b. a -> b
coe (-Integer
1 :: Integer)) (Integer -> Any
forall a b. a -> b
coe Integer
v2)))
               ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe
                  Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'42'__274 (Integer -> Any
forall a b. a -> b
coe Integer
v1)
                  ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> Integer
subInt (Integer -> Any
forall a b. a -> b
coe (-Integer
1 :: Integer)) (Integer -> Any
forall a b. a -> b
coe Integer
v2)))
               ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe
                  Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'42'__274
                  ((Integer -> Integer) -> Any -> Any
forall a b. a -> b
coe Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d_'45'__218 (Integer -> Any
forall a b. a -> b
coe Integer
v1))
                  ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> Integer
addInt (Integer -> Any
forall a b. a -> b
coe (Integer
1 :: Integer)) (Integer -> Any
forall a b. a -> b
coe Integer
v2)))
               ((T_IsPreorder_70 -> Any -> T__IsRelatedTo__70) -> Any -> Any -> Any
forall a b. a -> b
coe
                  T_IsPreorder_70 -> Any -> T__IsRelatedTo__70
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du__'8718'_346
                  (T_IsPreorder_70 -> Any
forall a b. a -> b
coe T_IsPreorder_70
d_'8804''45'isPreorder_1656)
                  ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe
                     Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'42'__274
                     ((Integer -> Integer) -> Any -> Any
forall a b. a -> b
coe Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d_'45'__218 (Integer -> Any
forall a b. a -> b
coe Integer
v1))
                     ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> Integer
addInt (Integer -> Any
forall a b. a -> b
coe (Integer
1 :: Integer)) (Integer -> Any
forall a b. a -> b
coe Integer
v2))))
               (T__'8804'__26 -> Any
forall a b. a -> b
coe T__'8804'__26
v3))))
-- Data.Integer.Properties.*-monoˡ-≤-nonPos
d_'42''45'mono'737''45''8804''45'nonPos_5136 ::
  Integer ->
  AgdaAny ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26 ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26
d_'42''45'mono'737''45''8804''45'nonPos_5136 :: Integer
-> Any -> Integer -> Integer -> T__'8804'__26 -> T__'8804'__26
d_'42''45'mono'737''45''8804''45'nonPos_5136 Integer
v0 ~Any
v1 Integer
v2 Integer
v3 T__'8804'__26
v4
  = Integer -> Integer -> Integer -> T__'8804'__26 -> T__'8804'__26
du_'42''45'mono'737''45''8804''45'nonPos_5136 Integer
v0 Integer
v2 Integer
v3 T__'8804'__26
v4
du_'42''45'mono'737''45''8804''45'nonPos_5136 ::
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26 ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26
du_'42''45'mono'737''45''8804''45'nonPos_5136 :: Integer -> Integer -> Integer -> T__'8804'__26 -> T__'8804'__26
du_'42''45'mono'737''45''8804''45'nonPos_5136 Integer
v0 Integer
v1 Integer
v2 T__'8804'__26
v3
  = case Integer -> Integer
forall a b. a -> b
coe Integer
v0 of
      Integer
0 -> (T__'8804'__18 -> T__'8804'__26) -> Any -> T__'8804'__26
forall a b. a -> b
coe
             T__'8804'__18 -> T__'8804'__26
MAlonzo.Code.Data.Integer.Base.C_'43''8804''43'_48
             (T__'8804'__18 -> Any
forall a b. a -> b
coe T__'8804'__18
MAlonzo.Code.Data.Nat.Base.C_z'8804'n_22)
      Integer
_ -> let v4 :: Integer
v4 = Integer -> Integer -> Integer
subInt (Integer -> Integer
forall a b. a -> b
coe (-Integer
1 :: Integer)) (Integer -> Integer
forall a b. a -> b
coe Integer
v0) in
           Any -> T__'8804'__26
forall a b. a -> b
coe
             ((T_IsPreorder_70
 -> (Any -> Any -> Any -> Any)
 -> Any
 -> Any
 -> T__IsRelatedTo__70
 -> Any)
-> Any -> Any -> Any -> Any -> Any -> Any
forall a b. a -> b
coe
                T_IsPreorder_70
-> (Any -> Any -> Any -> Any)
-> Any
-> Any
-> T__IsRelatedTo__70
-> Any
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_begin__160
                (T_IsPreorder_70 -> Any
forall a b. a -> b
coe T_IsPreorder_70
d_'8804''45'isPreorder_1656) ((Integer -> Integer -> T__'60'__50 -> T__'8804'__26) -> Any
forall a b. a -> b
coe Integer -> Integer -> T__'60'__50 -> T__'8804'__26
d_'60''8658''8804'_1724)
                (((Any -> Any -> Any) -> (Any -> Any) -> Any -> Any -> Any)
-> (Any -> Any -> Any)
-> (Integer -> Integer)
-> Integer
-> Integer
-> Any
forall a b. a -> b
coe
                   (Any -> Any -> Any) -> (Any -> Any) -> Any -> Any -> Any
MAlonzo.Code.Function.Base.du_'8739'_'10217''45'__308
                   (\ Any
v5 Any
v6 -> Any
v6)
                   (Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'42'__274 (Integer -> Integer
forall a b. a -> b
coe Integer
v0)) Integer
v1 Integer
v2)
                (((Any -> Any) -> (Any -> Any -> Any) -> Any -> Any -> Any)
-> (Integer -> Integer)
-> (Any -> Any -> Any)
-> Integer
-> Integer
-> Any
forall a b. a -> b
coe
                   (Any -> Any) -> (Any -> Any -> Any) -> Any -> Any -> Any
MAlonzo.Code.Function.Base.du__'45''10216'_'8739'_302
                   (Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'42'__274 (Integer -> Integer
forall a b. a -> b
coe Integer
v0))
                   (\ Any
v5 Any
v6 -> Any
v5) Integer
v1 Integer
v2)
                ((T_IsPreorder_70
 -> (Any -> Any -> Any -> Any -> Any -> Any)
 -> Any
 -> Any
 -> Any
 -> T__IsRelatedTo__70
 -> Any
 -> T__IsRelatedTo__70)
-> Any
-> (Any -> Any -> Any -> Any -> Any -> Any)
-> Any
-> Any
-> Any
-> Any
-> Any
-> Any
forall a b. a -> b
coe
                   T_IsPreorder_70
-> (Any -> Any -> Any -> Any -> Any -> Any)
-> Any
-> Any
-> Any
-> T__IsRelatedTo__70
-> Any
-> T__IsRelatedTo__70
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_step'45''8804'_228
                   (T_IsPreorder_70 -> Any
forall a b. a -> b
coe T_IsPreorder_70
d_'8804''45'isPreorder_1656)
                   (\ Any
v5 Any
v6 Any
v7 Any
v8 Any
v9 -> (T__'8804'__26 -> T__'60'__50 -> T__'60'__50) -> Any -> Any -> Any
forall a b. a -> b
coe T__'8804'__26 -> T__'60'__50 -> T__'60'__50
du_'8804''45''60''45'trans_1844 Any
v8 Any
v9)
                   ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe
                      Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'42'__274
                      ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> Integer
subInt (Integer -> Any
forall a b. a -> b
coe (Integer
0 :: Integer)) (Integer -> Any
forall a b. a -> b
coe Integer
v0))
                      ((Integer -> Integer) -> Any -> Any
forall a b. a -> b
coe Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d_'45'__218 (Integer -> Any
forall a b. a -> b
coe Integer
v2)))
                   ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe
                      Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'42'__274
                      ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> Integer
subInt (Integer -> Any
forall a b. a -> b
coe (Integer
0 :: Integer)) (Integer -> Any
forall a b. a -> b
coe Integer
v0))
                      ((Integer -> Integer) -> Any -> Any
forall a b. a -> b
coe Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d_'45'__218 (Integer -> Any
forall a b. a -> b
coe Integer
v1)))
                   (((Any -> Any) -> (Any -> Any -> Any) -> Any -> Any -> Any)
-> (Integer -> Integer)
-> (Any -> Any -> Any)
-> Integer
-> Integer
-> Any
forall a b. a -> b
coe
                      (Any -> Any) -> (Any -> Any -> Any) -> Any -> Any -> Any
MAlonzo.Code.Function.Base.du__'45''10216'_'8739'_302
                      (Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'42'__274 (Integer -> Integer
forall a b. a -> b
coe Integer
v0))
                      (\ Any
v5 Any
v6 -> Any
v5) Integer
v1 Integer
v2)
                   ((T_IsPreorder_70 -> Any -> T__IsRelatedTo__70) -> Any -> Any -> Any
forall a b. a -> b
coe
                      T_IsPreorder_70 -> Any -> T__IsRelatedTo__70
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du__'8718'_346
                      (T_IsPreorder_70 -> Any
forall a b. a -> b
coe T_IsPreorder_70
d_'8804''45'isPreorder_1656)
                      ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe
                         Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'42'__274 (Integer -> Any
forall a b. a -> b
coe Integer
v0) (Integer -> Any
forall a b. a -> b
coe Integer
v1)))
                   ((Integer -> Integer -> Integer -> T__'8804'__26 -> T__'8804'__26)
-> Integer -> Any -> Any -> Any -> Any
forall a b. a -> b
coe
                      Integer -> Integer -> Integer -> T__'8804'__26 -> T__'8804'__26
d_'42''45'mono'737''45''8804''45'pos_5088 Integer
v4
                      (((Any -> Any -> Any) -> (Any -> Any) -> Any -> Any -> Any)
-> (Any -> Any -> Any)
-> (Integer -> Integer)
-> Integer
-> Integer
-> Any
forall a b. a -> b
coe
                         (Any -> Any -> Any) -> (Any -> Any) -> Any -> Any -> Any
MAlonzo.Code.Function.Base.du_'8739'_'10217''45'__308
                         (\ Any
v5 Any
v6 -> Any
v6) Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d_'45'__218 Integer
v1 Integer
v2)
                      (((Any -> Any) -> (Any -> Any -> Any) -> Any -> Any -> Any)
-> (Integer -> Integer)
-> (Any -> Any -> Any)
-> Integer
-> Integer
-> Any
forall a b. a -> b
coe
                         (Any -> Any) -> (Any -> Any -> Any) -> Any -> Any -> Any
MAlonzo.Code.Function.Base.du__'45''10216'_'8739'_302
                         Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d_'45'__218 (\ Any
v5 Any
v6 -> Any
v5) Integer
v1 Integer
v2)
                      ((Integer -> T__'8804'__26 -> T__'8804'__26) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> T__'8804'__26 -> T__'8804'__26
du_neg'45'mono'45''8804'_3730 (Integer -> Any
forall a b. a -> b
coe Integer
v2) (T__'8804'__26 -> Any
forall a b. a -> b
coe T__'8804'__26
v3)))))
-- Data.Integer.Properties.*-monoʳ-≤-nonPos
d_'42''45'mono'691''45''8804''45'nonPos_5164 ::
  Integer ->
  AgdaAny ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26 ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26
d_'42''45'mono'691''45''8804''45'nonPos_5164 :: Integer
-> Any -> Integer -> Integer -> T__'8804'__26 -> T__'8804'__26
d_'42''45'mono'691''45''8804''45'nonPos_5164 Integer
v0 ~Any
v1 Integer
v2 Integer
v3 T__'8804'__26
v4
  = Integer -> Integer -> Integer -> T__'8804'__26 -> T__'8804'__26
du_'42''45'mono'691''45''8804''45'nonPos_5164 Integer
v0 Integer
v2 Integer
v3 T__'8804'__26
v4
du_'42''45'mono'691''45''8804''45'nonPos_5164 ::
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26 ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26
du_'42''45'mono'691''45''8804''45'nonPos_5164 :: Integer -> Integer -> Integer -> T__'8804'__26 -> T__'8804'__26
du_'42''45'mono'691''45''8804''45'nonPos_5164 Integer
v0 Integer
v1 Integer
v2 T__'8804'__26
v3
  = (T_IsPreorder_70
 -> (Any -> Any -> Any -> Any)
 -> Any
 -> Any
 -> T__IsRelatedTo__70
 -> Any)
-> Any -> Any -> Any -> Any -> Any -> T__'8804'__26
forall a b. a -> b
coe
      T_IsPreorder_70
-> (Any -> Any -> Any -> Any)
-> Any
-> Any
-> T__IsRelatedTo__70
-> Any
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_begin__160
      (T_IsPreorder_70 -> Any
forall a b. a -> b
coe T_IsPreorder_70
d_'8804''45'isPreorder_1656) ((Integer -> Integer -> T__'60'__50 -> T__'8804'__26) -> Any
forall a b. a -> b
coe Integer -> Integer -> T__'60'__50 -> T__'8804'__26
d_'60''8658''8804'_1724)
      (((Any -> Any -> Any) -> (Any -> Any) -> Any -> Any -> Any)
-> (Any -> Any -> Any)
-> (Any -> Integer)
-> Integer
-> Integer
-> Any
forall a b. a -> b
coe
         (Any -> Any -> Any) -> (Any -> Any) -> Any -> Any -> Any
MAlonzo.Code.Function.Base.du_'8739'_'10217''45'__308
         (\ Any
v4 Any
v5 -> Any
v5)
         (\ Any
v4 ->
            Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'42'__274 (Any -> Integer
forall a b. a -> b
coe Any
v4) (Integer -> Integer
forall a b. a -> b
coe Integer
v0))
         Integer
v1 Integer
v2)
      (((Any -> Any) -> (Any -> Any -> Any) -> Any -> Any -> Any)
-> (Any -> Integer)
-> (Any -> Any -> Any)
-> Integer
-> Integer
-> Any
forall a b. a -> b
coe
         (Any -> Any) -> (Any -> Any -> Any) -> Any -> Any -> Any
MAlonzo.Code.Function.Base.du__'45''10216'_'8739'_302
         (\ Any
v4 ->
            Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'42'__274 (Any -> Integer
forall a b. a -> b
coe Any
v4) (Integer -> Integer
forall a b. a -> b
coe Integer
v0))
         (\ Any
v4 Any
v5 -> Any
v4) Integer
v1 Integer
v2)
      ((T_IsPreorder_70
 -> (Any -> Any -> Any -> Any -> Any -> Any)
 -> Any
 -> Any
 -> Any
 -> T__IsRelatedTo__70
 -> Any
 -> T__IsRelatedTo__70)
-> Any
-> (Any -> Any -> Any -> Any -> Any -> Any)
-> Any
-> Any
-> Any
-> Any
-> Any
-> Any
forall a b. a -> b
coe
         T_IsPreorder_70
-> (Any -> Any -> Any -> Any -> Any -> Any)
-> Any
-> Any
-> Any
-> T__IsRelatedTo__70
-> Any
-> T__IsRelatedTo__70
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_step'45''8804'_228
         (T_IsPreorder_70 -> Any
forall a b. a -> b
coe T_IsPreorder_70
d_'8804''45'isPreorder_1656)
         (\ Any
v4 Any
v5 Any
v6 Any
v7 Any
v8 -> (T__'8804'__26 -> T__'60'__50 -> T__'60'__50) -> Any -> Any -> Any
forall a b. a -> b
coe T__'8804'__26 -> T__'60'__50 -> T__'60'__50
du_'8804''45''60''45'trans_1844 Any
v7 Any
v8)
         ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'42'__274 (Integer -> Any
forall a b. a -> b
coe Integer
v0) (Integer -> Any
forall a b. a -> b
coe Integer
v2))
         ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'42'__274 (Integer -> Any
forall a b. a -> b
coe Integer
v0) (Integer -> Any
forall a b. a -> b
coe Integer
v1))
         (((Any -> Any) -> (Any -> Any -> Any) -> Any -> Any -> Any)
-> (Any -> Integer)
-> (Any -> Any -> Any)
-> Integer
-> Integer
-> Any
forall a b. a -> b
coe
            (Any -> Any) -> (Any -> Any -> Any) -> Any -> Any -> Any
MAlonzo.Code.Function.Base.du__'45''10216'_'8739'_302
            (\ Any
v4 ->
               Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'42'__274 (Any -> Integer
forall a b. a -> b
coe Any
v4) (Integer -> Integer
forall a b. a -> b
coe Integer
v0))
            (\ Any
v4 Any
v5 -> Any
v4) Integer
v1 Integer
v2)
         ((T_IsPreorder_70 -> Any -> T__IsRelatedTo__70) -> Any -> Any -> Any
forall a b. a -> b
coe
            T_IsPreorder_70 -> Any -> T__IsRelatedTo__70
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du__'8718'_346
            (T_IsPreorder_70 -> Any
forall a b. a -> b
coe T_IsPreorder_70
d_'8804''45'isPreorder_1656)
            ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe
               Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'42'__274 (Integer -> Any
forall a b. a -> b
coe Integer
v1) (Integer -> Any
forall a b. a -> b
coe Integer
v0)))
         ((Integer -> Integer -> Integer -> T__'8804'__26 -> T__'8804'__26)
-> Any -> Any -> Any -> Any -> Any
forall a b. a -> b
coe
            Integer -> Integer -> Integer -> T__'8804'__26 -> T__'8804'__26
du_'42''45'mono'737''45''8804''45'nonPos_5136 (Integer -> Any
forall a b. a -> b
coe Integer
v0) (Integer -> Any
forall a b. a -> b
coe Integer
v1)
            (Integer -> Any
forall a b. a -> b
coe Integer
v2) (T__'8804'__26 -> Any
forall a b. a -> b
coe T__'8804'__26
v3)))
-- Data.Integer.Properties.*-monoˡ-≤-neg
d_'42''45'mono'737''45''8804''45'neg_5184 ::
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26 ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26
d_'42''45'mono'737''45''8804''45'neg_5184 :: Integer -> Integer -> Integer -> T__'8804'__26 -> T__'8804'__26
d_'42''45'mono'737''45''8804''45'neg_5184 Integer
v0 Integer
v1 Integer
v2
  = (Integer -> Integer -> Integer -> T__'8804'__26 -> T__'8804'__26)
-> Any -> Any -> Any -> T__'8804'__26 -> T__'8804'__26
forall a b. a -> b
coe
      Integer -> Integer -> Integer -> T__'8804'__26 -> T__'8804'__26
du_'42''45'mono'737''45''8804''45'nonPos_5136
      ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> Integer
subInt (Integer -> Any
forall a b. a -> b
coe (-Integer
1 :: Integer)) (Integer -> Any
forall a b. a -> b
coe Integer
v0)) (Integer -> Any
forall a b. a -> b
coe Integer
v1) (Integer -> Any
forall a b. a -> b
coe Integer
v2)
-- Data.Integer.Properties.*-monoʳ-≤-neg
d_'42''45'mono'691''45''8804''45'neg_5192 ::
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26 ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26
d_'42''45'mono'691''45''8804''45'neg_5192 :: Integer -> Integer -> Integer -> T__'8804'__26 -> T__'8804'__26
d_'42''45'mono'691''45''8804''45'neg_5192 Integer
v0 Integer
v1 Integer
v2
  = (Integer -> Integer -> Integer -> T__'8804'__26 -> T__'8804'__26)
-> Any -> Any -> Any -> T__'8804'__26 -> T__'8804'__26
forall a b. a -> b
coe
      Integer -> Integer -> Integer -> T__'8804'__26 -> T__'8804'__26
du_'42''45'mono'691''45''8804''45'nonPos_5164
      ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> Integer
subInt (Integer -> Any
forall a b. a -> b
coe (-Integer
1 :: Integer)) (Integer -> Any
forall a b. a -> b
coe Integer
v0)) (Integer -> Any
forall a b. a -> b
coe Integer
v1) (Integer -> Any
forall a b. a -> b
coe Integer
v2)
-- Data.Integer.Properties.*-monoˡ-<-pos
d_'42''45'mono'737''45''60''45'pos_5200 ::
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Integer.Base.T__'60'__50 ->
  MAlonzo.Code.Data.Integer.Base.T__'60'__50
d_'42''45'mono'737''45''60''45'pos_5200 :: Integer -> Integer -> Integer -> T__'60'__50 -> T__'60'__50
d_'42''45'mono'737''45''60''45'pos_5200 Integer
v0 Integer
v1 Integer
v2 T__'60'__50
v3
  = case Integer -> Any
forall a b. a -> b
coe Integer
v1 of
      Any
_ | (Integer -> Integer -> Bool) -> Any -> Any -> Bool
forall a b. a -> b
coe Integer -> Integer -> Bool
geqInt (Integer -> Any
forall a b. a -> b
coe Integer
v1) (Integer -> Any
forall a b. a -> b
coe (Integer
0 :: Integer)) ->
          case T__'60'__50 -> T__'60'__50
forall a b. a -> b
coe T__'60'__50
v3 of
            MAlonzo.Code.Data.Integer.Base.C_'43''60''43'_72 T__'8804'__18
v6
              -> (Integer -> T__'8804'__18 -> T__'60'__50)
-> Any -> Any -> T__'60'__50
forall a b. a -> b
coe
                   Integer -> T__'8804'__18 -> T__'60'__50
du_'43''9667''45'mono'45''60'_2448
                   ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> Integer
addInt ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> Integer
mulInt (Integer -> Any
forall a b. a -> b
coe Integer
v0) (Integer -> Any
forall a b. a -> b
coe Integer
v1)) (Integer -> Any
forall a b. a -> b
coe Integer
v1))
                   ((T__'8804'__18 -> T__'8804'__18 -> T__'8804'__18)
-> Any -> Any -> Any
forall a b. a -> b
coe
                      T__'8804'__18 -> T__'8804'__18 -> T__'8804'__18
MAlonzo.Code.Data.Nat.Properties.du_'43''45'mono'45''60''45''8804'_2428
                      (T__'8804'__18 -> Any
forall a b. a -> b
coe T__'8804'__18
v6)
                      ((Integer -> Integer -> T__'8804'__18 -> T__'8804'__18)
-> Any -> Any -> Any -> Any
forall a b. a -> b
coe
                         Integer -> Integer -> T__'8804'__18 -> T__'8804'__18
MAlonzo.Code.Data.Nat.Properties.du_'42''45'mono'691''45''8804'_2844
                         (Integer -> Any
forall a b. a -> b
coe Integer
v0) (Integer -> Any
forall a b. a -> b
coe Integer
v2)
                         ((Integer -> T__'8804'__18 -> T__'8804'__18) -> Any -> Any -> Any
forall a b. a -> b
coe
                            Integer -> T__'8804'__18 -> T__'8804'__18
MAlonzo.Code.Data.Nat.Properties.du_'60''8658''8804'_1736 (Integer -> Any
forall a b. a -> b
coe Integer
v2)
                            (T__'8804'__18 -> Any
forall a b. a -> b
coe T__'8804'__18
v6))))
            T__'60'__50
_ -> T__'60'__50
forall a. a
MAlonzo.RTE.mazUnreachableError
      Any
_ -> case Integer -> Any
forall a b. a -> b
coe Integer
v2 of
             Any
_ | (Integer -> Integer -> Bool) -> Any -> Any -> Bool
forall a b. a -> b
coe Integer -> Integer -> Bool
geqInt (Integer -> Any
forall a b. a -> b
coe Integer
v2) (Integer -> Any
forall a b. a -> b
coe (Integer
0 :: Integer)) ->
                 (Integer -> T__'60'__50) -> Any -> T__'60'__50
forall a b. a -> b
coe
                   Integer -> T__'60'__50
du_'45''9667''60''43''9667'_2498
                   ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> Integer
mulInt ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> Integer
addInt (Integer -> Any
forall a b. a -> b
coe (Integer
1 :: Integer)) (Integer -> Any
forall a b. a -> b
coe Integer
v0)) (Integer -> Any
forall a b. a -> b
coe Integer
v2))
             Any
_ -> case T__'60'__50 -> T__'60'__50
forall a b. a -> b
coe T__'60'__50
v3 of
                    MAlonzo.Code.Data.Integer.Base.C_'45''60''45'_58 T__'8804'__18
v6
                      -> (T__'8804'__18 -> T__'60'__50) -> Any -> T__'60'__50
forall a b. a -> b
coe
                           T__'8804'__18 -> T__'60'__50
MAlonzo.Code.Data.Integer.Base.C_'45''60''45'_58
                           ((T__'8804'__18 -> T__'8804'__18 -> T__'8804'__18)
-> Any -> Any -> Any
forall a b. a -> b
coe
                              T__'8804'__18 -> T__'8804'__18 -> T__'8804'__18
MAlonzo.Code.Data.Nat.Properties.du_'43''45'mono'45''60''45''8804'_2428
                              (T__'8804'__18 -> Any
forall a b. a -> b
coe T__'8804'__18
v6)
                              ((Integer -> Integer -> T__'8804'__18 -> T__'8804'__18)
-> Any -> Any -> Any -> Any
forall a b. a -> b
coe
                                 Integer -> Integer -> T__'8804'__18 -> T__'8804'__18
MAlonzo.Code.Data.Nat.Properties.du_'42''45'mono'691''45''8804'_2844
                                 (Integer -> Any
forall a b. a -> b
coe Integer
v0) ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> Integer
subInt (Integer -> Any
forall a b. a -> b
coe (Integer
0 :: Integer)) (Integer -> Any
forall a b. a -> b
coe Integer
v1))
                                 ((Integer -> T__'8804'__18 -> T__'8804'__18) -> Any -> Any -> Any
forall a b. a -> b
coe
                                    Integer -> T__'8804'__18 -> T__'8804'__18
MAlonzo.Code.Data.Nat.Properties.du_'60''8658''8804'_1736
                                    ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> Integer
subInt (Integer -> Any
forall a b. a -> b
coe (Integer
0 :: Integer)) (Integer -> Any
forall a b. a -> b
coe Integer
v1))
                                    ((T__'8804'__18 -> T__'8804'__18) -> T__'8804'__18 -> Any
forall a b. a -> b
coe T__'8804'__18 -> T__'8804'__18
MAlonzo.Code.Data.Nat.Base.C_s'8804's_30 T__'8804'__18
v6))))
                    T__'60'__50
_ -> T__'60'__50
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Data.Integer.Properties.*-monoʳ-<-pos
d_'42''45'mono'691''45''60''45'pos_5230 ::
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Integer.Base.T__'60'__50 ->
  MAlonzo.Code.Data.Integer.Base.T__'60'__50
d_'42''45'mono'691''45''60''45'pos_5230 :: Integer -> Integer -> Integer -> T__'60'__50 -> T__'60'__50
d_'42''45'mono'691''45''60''45'pos_5230 Integer
v0 Integer
v1 Integer
v2
  = (Integer -> Integer -> Integer -> T__'60'__50 -> T__'60'__50)
-> Any -> Any -> Any -> T__'60'__50 -> T__'60'__50
forall a b. a -> b
coe
      Integer -> Integer -> Integer -> T__'60'__50 -> T__'60'__50
d_'42''45'mono'737''45''60''45'pos_5200 (Integer -> Any
forall a b. a -> b
coe Integer
v0) (Integer -> Any
forall a b. a -> b
coe Integer
v1) (Integer -> Any
forall a b. a -> b
coe Integer
v2)
-- Data.Integer.Properties.*-cancelˡ-<-nonNeg
d_'42''45'cancel'737''45''60''45'nonNeg_5252 ::
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Integer.Base.T__'60'__50 ->
  MAlonzo.Code.Data.Integer.Base.T__'60'__50
d_'42''45'cancel'737''45''60''45'nonNeg_5252 :: Integer -> Integer -> Integer -> T__'60'__50 -> T__'60'__50
d_'42''45'cancel'737''45''60''45'nonNeg_5252 Integer
v0 Integer
v1 Integer
v2 T__'60'__50
v3
  = case Integer -> Any
forall a b. a -> b
coe Integer
v1 of
      Any
_ | (Integer -> Integer -> Bool) -> Any -> Any -> Bool
forall a b. a -> b
coe Integer -> Integer -> Bool
geqInt (Integer -> Any
forall a b. a -> b
coe Integer
v1) (Integer -> Any
forall a b. a -> b
coe (Integer
0 :: Integer)) ->
          case Integer -> Any
forall a b. a -> b
coe Integer
v2 of
            Any
_ | (Integer -> Integer -> Bool) -> Any -> Any -> Bool
forall a b. a -> b
coe Integer -> Integer -> Bool
geqInt (Integer -> Any
forall a b. a -> b
coe Integer
v2) (Integer -> Any
forall a b. a -> b
coe (Integer
0 :: Integer)) ->
                (T__'8804'__18 -> T__'60'__50) -> Any -> T__'60'__50
forall a b. a -> b
coe
                  T__'8804'__18 -> T__'60'__50
MAlonzo.Code.Data.Integer.Base.C_'43''60''43'_72
                  ((Integer -> Integer -> Integer -> T__'8804'__18 -> T__'8804'__18)
-> Integer -> Integer -> Integer -> Any -> Any
forall a b. a -> b
coe
                     Integer -> Integer -> Integer -> T__'8804'__18 -> T__'8804'__18
MAlonzo.Code.Data.Nat.Properties.d_'42''45'cancel'737''45''60'_2936
                     Integer
v0 (Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d_'8739'_'8739'_18 (Integer -> Integer
forall a b. a -> b
coe Integer
v1))
                     (Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d_'8739'_'8739'_18 (Integer -> Integer
forall a b. a -> b
coe Integer
v2))
                     ((Integer -> T__'60'__50 -> T__'8804'__18) -> Any -> Any -> Any
forall a b. a -> b
coe
                        Integer -> T__'60'__50 -> T__'8804'__18
du_'43''9667''45'cancel'45''60'_2464
                        ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe
                           Integer -> Integer -> Integer
mulInt (Integer -> Any
forall a b. a -> b
coe Integer
v0)
                           ((Integer -> Integer) -> Any -> Any
forall a b. a -> b
coe Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d_'8739'_'8739'_18 (Integer -> Any
forall a b. a -> b
coe Integer
v1)))
                        (T__'60'__50 -> Any
forall a b. a -> b
coe T__'60'__50
v3)))
            Any
_ -> Any -> T__'60'__50
forall a b. a -> b
coe
                   Any
MAlonzo.Code.Relation.Nullary.Negation.Core.du_contradiction_24
      Any
_ -> case Integer -> Any
forall a b. a -> b
coe Integer
v2 of
             Any
_ | (Integer -> Integer -> Bool) -> Any -> Any -> Bool
forall a b. a -> b
coe Integer -> Integer -> Bool
geqInt (Integer -> Any
forall a b. a -> b
coe Integer
v2) (Integer -> Any
forall a b. a -> b
coe (Integer
0 :: Integer)) ->
                 T__'60'__50 -> T__'60'__50
forall a b. a -> b
coe T__'60'__50
MAlonzo.Code.Data.Integer.Base.C_'45''60''43'_64
             Any
_ -> (T__'8804'__18 -> T__'60'__50) -> Any -> T__'60'__50
forall a b. a -> b
coe
                    T__'8804'__18 -> T__'60'__50
MAlonzo.Code.Data.Integer.Base.C_'45''60''45'_58
                    ((T__'8804'__18 -> T__'8804'__18) -> Any -> Any
forall a b. a -> b
coe
                       T__'8804'__18 -> T__'8804'__18
MAlonzo.Code.Data.Nat.Properties.Core.du_'8804''45'pred_12
                       ((Integer -> Integer -> Integer -> T__'8804'__18 -> T__'8804'__18)
-> Integer -> Integer -> Integer -> Any -> Any
forall a b. a -> b
coe
                          Integer -> Integer -> Integer -> T__'8804'__18 -> T__'8804'__18
MAlonzo.Code.Data.Nat.Properties.d_'42''45'cancel'737''45''60'_2936
                          Integer
v0 (Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d_'8739'_'8739'_18 (Integer -> Integer
forall a b. a -> b
coe Integer
v2))
                          (Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d_'8739'_'8739'_18 (Integer -> Integer
forall a b. a -> b
coe Integer
v1))
                          ((Integer -> T__'60'__50 -> T__'8804'__18) -> Any -> Any -> Any
forall a b. a -> b
coe
                             Integer -> T__'60'__50 -> T__'8804'__18
du_neg'9667''45'cancel'45''60'_2482
                             ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe
                                Integer -> Integer -> Integer
mulInt (Integer -> Any
forall a b. a -> b
coe Integer
v0)
                                ((Integer -> Integer) -> Any -> Any
forall a b. a -> b
coe Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d_'8739'_'8739'_18 (Integer -> Any
forall a b. a -> b
coe Integer
v2)))
                             (T__'60'__50 -> Any
forall a b. a -> b
coe T__'60'__50
v3))))
-- Data.Integer.Properties.*-cancelʳ-<-nonNeg
d_'42''45'cancel'691''45''60''45'nonNeg_5292 ::
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Integer.Base.T__'60'__50 ->
  MAlonzo.Code.Data.Integer.Base.T__'60'__50
d_'42''45'cancel'691''45''60''45'nonNeg_5292 :: Integer -> Integer -> Integer -> T__'60'__50 -> T__'60'__50
d_'42''45'cancel'691''45''60''45'nonNeg_5292 Integer
v0 Integer
v1 Integer
v2
  = (Integer -> Integer -> Integer -> T__'60'__50 -> T__'60'__50)
-> Any -> Any -> Any -> T__'60'__50 -> T__'60'__50
forall a b. a -> b
coe
      Integer -> Integer -> Integer -> T__'60'__50 -> T__'60'__50
d_'42''45'cancel'737''45''60''45'nonNeg_5252 (Integer -> Any
forall a b. a -> b
coe Integer
v2) (Integer -> Any
forall a b. a -> b
coe Integer
v0)
      (Integer -> Any
forall a b. a -> b
coe Integer
v1)
-- Data.Integer.Properties.*-monoˡ-<-neg
d_'42''45'mono'737''45''60''45'neg_5312 ::
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Integer.Base.T__'60'__50 ->
  MAlonzo.Code.Data.Integer.Base.T__'60'__50
d_'42''45'mono'737''45''60''45'neg_5312 :: Integer -> Integer -> Integer -> T__'60'__50 -> T__'60'__50
d_'42''45'mono'737''45''60''45'neg_5312 Integer
v0 Integer
v1 Integer
v2 T__'60'__50
v3
  = (T__IsRelatedTo__70 -> Any) -> Any -> T__'60'__50
forall a b. a -> b
coe
      T__IsRelatedTo__70 -> Any
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_begin'45'strict__176
      (((Any -> Any -> Any -> Any -> Any -> Any)
 -> T_Σ_14
 -> (Any -> Any -> Any -> Any -> Any -> Any)
 -> Any
 -> Any
 -> Any
 -> T__IsRelatedTo__70
 -> Any
 -> T__IsRelatedTo__70)
-> (Any -> Any -> Any -> Any -> Any -> Any)
-> Any
-> (Any -> Any -> Any -> Any -> Any -> Any)
-> Any
-> Any
-> Any
-> Any
-> Any
-> Any
forall a b. a -> b
coe
         (Any -> Any -> Any -> Any -> Any -> Any)
-> T_Σ_14
-> (Any -> Any -> Any -> Any -> Any -> Any)
-> Any
-> Any
-> Any
-> T__IsRelatedTo__70
-> Any
-> T__IsRelatedTo__70
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_step'45''60'_202
         (\ Any
v4 Any
v5 Any
v6 Any
v7 Any
v8 -> (Integer -> Integer -> T__'60'__50 -> T__'60'__50 -> T__'60'__50)
-> Any -> Any -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> T__'60'__50 -> T__'60'__50 -> T__'60'__50
du_'60''45'trans_1872 Any
v4 Any
v5 Any
v7 Any
v8)
         (T_Σ_14 -> Any
forall a b. a -> b
coe
            T_Σ_14
MAlonzo.Code.Relation.Binary.PropositionalEquality.Core.du_resp'8322'_144)
         (\ Any
v4 Any
v5 Any
v6 Any
v7 Any
v8 -> (T__'60'__50 -> T__'8804'__26 -> T__'60'__50) -> Any -> Any -> Any
forall a b. a -> b
coe T__'60'__50 -> T__'8804'__26 -> T__'60'__50
du_'60''45''8804''45'trans_1858 Any
v7 Any
v8)
         ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe
            Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'42'__274
            ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> Integer
addInt (Integer -> Any
forall a b. a -> b
coe (Integer
1 :: Integer)) (Integer -> Any
forall a b. a -> b
coe Integer
v0))
            ((Integer -> Integer) -> Any -> Any
forall a b. a -> b
coe Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d_'45'__218 (Integer -> Any
forall a b. a -> b
coe Integer
v2)))
         ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe
            Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'42'__274
            ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> Integer
addInt (Integer -> Any
forall a b. a -> b
coe (Integer
1 :: Integer)) (Integer -> Any
forall a b. a -> b
coe Integer
v0))
            ((Integer -> Integer) -> Any -> Any
forall a b. a -> b
coe Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d_'45'__218 (Integer -> Any
forall a b. a -> b
coe Integer
v1)))
         ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe
            Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'42'__274
            ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> Integer
subInt (Integer -> Any
forall a b. a -> b
coe (-Integer
1 :: Integer)) (Integer -> Any
forall a b. a -> b
coe Integer
v0)) (Integer -> Any
forall a b. a -> b
coe Integer
v1))
         ((T_IsPreorder_70 -> Any -> T__IsRelatedTo__70) -> Any -> Any -> Any
forall a b. a -> b
coe
            T_IsPreorder_70 -> Any -> T__IsRelatedTo__70
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du__'8718'_346
            (T_IsPreorder_70 -> Any
forall a b. a -> b
coe T_IsPreorder_70
d_'8804''45'isPreorder_1656)
            ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe
               Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'42'__274
               ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> Integer
subInt (Integer -> Any
forall a b. a -> b
coe (-Integer
1 :: Integer)) (Integer -> Any
forall a b. a -> b
coe Integer
v0)) (Integer -> Any
forall a b. a -> b
coe Integer
v1)))
         ((Integer -> Integer -> Integer -> T__'60'__50 -> T__'60'__50)
-> Any -> Any -> Any -> Any -> Any
forall a b. a -> b
coe
            Integer -> Integer -> Integer -> T__'60'__50 -> T__'60'__50
d_'42''45'mono'737''45''60''45'pos_5200 (Integer -> Any
forall a b. a -> b
coe Integer
v0)
            (((Any -> Any -> Any) -> (Any -> Any) -> Any -> Any -> Any)
-> (Any -> Any -> Any)
-> (Integer -> Integer)
-> Integer
-> Integer
-> Any
forall a b. a -> b
coe
               (Any -> Any -> Any) -> (Any -> Any) -> Any -> Any -> Any
MAlonzo.Code.Function.Base.du_'8739'_'10217''45'__308
               (\ Any
v4 Any
v5 -> Any
v5) Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d_'45'__218 Integer
v1 Integer
v2)
            (((Any -> Any) -> (Any -> Any -> Any) -> Any -> Any -> Any)
-> (Integer -> Integer)
-> (Any -> Any -> Any)
-> Integer
-> Integer
-> Any
forall a b. a -> b
coe
               (Any -> Any) -> (Any -> Any -> Any) -> Any -> Any -> Any
MAlonzo.Code.Function.Base.du__'45''10216'_'8739'_302
               Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d_'45'__218 (\ Any
v4 Any
v5 -> Any
v4) Integer
v1 Integer
v2)
            ((Integer -> Integer -> T__'60'__50 -> T__'60'__50)
-> Any -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> T__'60'__50 -> T__'60'__50
d_neg'45'mono'45''60'_2144 (Integer -> Any
forall a b. a -> b
coe Integer
v1) (Integer -> Any
forall a b. a -> b
coe Integer
v2) (T__'60'__50 -> Any
forall a b. a -> b
coe T__'60'__50
v3))))
-- Data.Integer.Properties.*-monoʳ-<-neg
d_'42''45'mono'691''45''60''45'neg_5330 ::
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Integer.Base.T__'60'__50 ->
  MAlonzo.Code.Data.Integer.Base.T__'60'__50
d_'42''45'mono'691''45''60''45'neg_5330 :: Integer -> Integer -> Integer -> T__'60'__50 -> T__'60'__50
d_'42''45'mono'691''45''60''45'neg_5330 Integer
v0 Integer
v1 Integer
v2 T__'60'__50
v3
  = (T__IsRelatedTo__70 -> Any) -> Any -> T__'60'__50
forall a b. a -> b
coe
      T__IsRelatedTo__70 -> Any
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_begin'45'strict__176
      (((Any -> Any -> Any -> Any -> Any -> Any)
 -> T_Σ_14
 -> (Any -> Any -> Any -> Any -> Any -> Any)
 -> Any
 -> Any
 -> Any
 -> T__IsRelatedTo__70
 -> Any
 -> T__IsRelatedTo__70)
-> (Any -> Any -> Any -> Any -> Any -> Any)
-> Any
-> (Any -> Any -> Any -> Any -> Any -> Any)
-> Any
-> Any
-> Any
-> Any
-> Any
-> Any
forall a b. a -> b
coe
         (Any -> Any -> Any -> Any -> Any -> Any)
-> T_Σ_14
-> (Any -> Any -> Any -> Any -> Any -> Any)
-> Any
-> Any
-> Any
-> T__IsRelatedTo__70
-> Any
-> T__IsRelatedTo__70
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_step'45''60'_202
         (\ Any
v4 Any
v5 Any
v6 Any
v7 Any
v8 -> (Integer -> Integer -> T__'60'__50 -> T__'60'__50 -> T__'60'__50)
-> Any -> Any -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> T__'60'__50 -> T__'60'__50 -> T__'60'__50
du_'60''45'trans_1872 Any
v4 Any
v5 Any
v7 Any
v8)
         (T_Σ_14 -> Any
forall a b. a -> b
coe
            T_Σ_14
MAlonzo.Code.Relation.Binary.PropositionalEquality.Core.du_resp'8322'_144)
         (\ Any
v4 Any
v5 Any
v6 Any
v7 Any
v8 -> (T__'60'__50 -> T__'8804'__26 -> T__'60'__50) -> Any -> Any -> Any
forall a b. a -> b
coe T__'60'__50 -> T__'8804'__26 -> T__'60'__50
du_'60''45''8804''45'trans_1858 Any
v7 Any
v8)
         ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe
            Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'42'__274
            ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> Integer
subInt (Integer -> Any
forall a b. a -> b
coe (-Integer
1 :: Integer)) (Integer -> Any
forall a b. a -> b
coe Integer
v0)) (Integer -> Any
forall a b. a -> b
coe Integer
v2))
         ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe
            Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'42'__274
            ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> Integer
subInt (Integer -> Any
forall a b. a -> b
coe (-Integer
1 :: Integer)) (Integer -> Any
forall a b. a -> b
coe Integer
v0)) (Integer -> Any
forall a b. a -> b
coe Integer
v1))
         ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe
            Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'42'__274 (Integer -> Any
forall a b. a -> b
coe Integer
v1)
            ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> Integer
subInt (Integer -> Any
forall a b. a -> b
coe (-Integer
1 :: Integer)) (Integer -> Any
forall a b. a -> b
coe Integer
v0)))
         ((T_IsPreorder_70 -> Any -> T__IsRelatedTo__70) -> Any -> Any -> Any
forall a b. a -> b
coe
            T_IsPreorder_70 -> Any -> T__IsRelatedTo__70
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du__'8718'_346
            (T_IsPreorder_70 -> Any
forall a b. a -> b
coe T_IsPreorder_70
d_'8804''45'isPreorder_1656)
            ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe
               Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'42'__274 (Integer -> Any
forall a b. a -> b
coe Integer
v1)
               ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> Integer
subInt (Integer -> Any
forall a b. a -> b
coe (-Integer
1 :: Integer)) (Integer -> Any
forall a b. a -> b
coe Integer
v0))))
         ((Integer -> Integer -> Integer -> T__'60'__50 -> T__'60'__50)
-> Any -> Any -> Any -> Any -> Any
forall a b. a -> b
coe
            Integer -> Integer -> Integer -> T__'60'__50 -> T__'60'__50
d_'42''45'mono'737''45''60''45'neg_5312 (Integer -> Any
forall a b. a -> b
coe Integer
v0) (Integer -> Any
forall a b. a -> b
coe Integer
v1) (Integer -> Any
forall a b. a -> b
coe Integer
v2)
            (T__'60'__50 -> Any
forall a b. a -> b
coe T__'60'__50
v3)))
-- Data.Integer.Properties.*-cancelˡ-<-neg
d_'42''45'cancel'737''45''60''45'neg_5350 ::
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Integer.Base.T__'60'__50 ->
  MAlonzo.Code.Data.Integer.Base.T__'60'__50
d_'42''45'cancel'737''45''60''45'neg_5350 :: Integer -> Integer -> Integer -> T__'60'__50 -> T__'60'__50
d_'42''45'cancel'737''45''60''45'neg_5350 Integer
v0 Integer
v1 Integer
v2 T__'60'__50
v3
  = (Integer -> Integer -> T__'60'__50 -> T__'60'__50)
-> Any -> Any -> Any -> T__'60'__50
forall a b. a -> b
coe
      Integer -> Integer -> T__'60'__50 -> T__'60'__50
d_neg'45'cancel'45''60'_2162 (Integer -> Any
forall a b. a -> b
coe Integer
v1) (Integer -> Any
forall a b. a -> b
coe Integer
v2)
      ((Integer -> Integer -> Integer -> T__'60'__50 -> T__'60'__50)
-> Any -> Any -> Any -> Any -> Any
forall a b. a -> b
coe
         Integer -> Integer -> Integer -> T__'60'__50 -> T__'60'__50
d_'42''45'cancel'737''45''60''45'nonNeg_5252
         ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> Integer
addInt (Integer -> Any
forall a b. a -> b
coe (Integer
1 :: Integer)) (Integer -> Any
forall a b. a -> b
coe Integer
v0))
         ((Integer -> Integer) -> Any -> Any
forall a b. a -> b
coe Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d_'45'__218 (Integer -> Any
forall a b. a -> b
coe Integer
v1))
         ((Integer -> Integer) -> Any -> Any
forall a b. a -> b
coe Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d_'45'__218 (Integer -> Any
forall a b. a -> b
coe Integer
v2))
         ((T__IsRelatedTo__70 -> Any) -> Any -> Any
forall a b. a -> b
coe
            T__IsRelatedTo__70 -> Any
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_begin'45'strict__176
            (((Any -> Any -> Any -> Any -> Any -> Any)
 -> T_Σ_14
 -> (Any -> Any -> Any -> Any -> Any -> Any)
 -> Any
 -> Any
 -> Any
 -> T__IsRelatedTo__70
 -> Any
 -> T__IsRelatedTo__70)
-> (Any -> Any -> Any -> Any -> Any -> Any)
-> Any
-> (Any -> Any -> Any -> Any -> Any -> Any)
-> Any
-> Any
-> Any
-> Any
-> Any
-> Any
forall a b. a -> b
coe
               (Any -> Any -> Any -> Any -> Any -> Any)
-> T_Σ_14
-> (Any -> Any -> Any -> Any -> Any -> Any)
-> Any
-> Any
-> Any
-> T__IsRelatedTo__70
-> Any
-> T__IsRelatedTo__70
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_step'45''60'_202
               (\ Any
v4 Any
v5 Any
v6 Any
v7 Any
v8 -> (Integer -> Integer -> T__'60'__50 -> T__'60'__50 -> T__'60'__50)
-> Any -> Any -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> T__'60'__50 -> T__'60'__50 -> T__'60'__50
du_'60''45'trans_1872 Any
v4 Any
v5 Any
v7 Any
v8)
               (T_Σ_14 -> Any
forall a b. a -> b
coe
                  T_Σ_14
MAlonzo.Code.Relation.Binary.PropositionalEquality.Core.du_resp'8322'_144)
               (\ Any
v4 Any
v5 Any
v6 Any
v7 Any
v8 -> (T__'60'__50 -> T__'8804'__26 -> T__'60'__50) -> Any -> Any -> Any
forall a b. a -> b
coe T__'60'__50 -> T__'8804'__26 -> T__'60'__50
du_'60''45''8804''45'trans_1858 Any
v7 Any
v8)
               ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe
                  Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'42'__274
                  ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> Integer
subInt (Integer -> Any
forall a b. a -> b
coe (-Integer
1 :: Integer)) (Integer -> Any
forall a b. a -> b
coe Integer
v0)) (Integer -> Any
forall a b. a -> b
coe Integer
v1))
               ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe
                  Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'42'__274
                  ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> Integer
subInt (Integer -> Any
forall a b. a -> b
coe (-Integer
1 :: Integer)) (Integer -> Any
forall a b. a -> b
coe Integer
v0)) (Integer -> Any
forall a b. a -> b
coe Integer
v2))
               ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe
                  Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'42'__274
                  ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> Integer
addInt (Integer -> Any
forall a b. a -> b
coe (Integer
1 :: Integer)) (Integer -> Any
forall a b. a -> b
coe Integer
v0))
                  ((Integer -> Integer) -> Any -> Any
forall a b. a -> b
coe Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d_'45'__218 (Integer -> Any
forall a b. a -> b
coe Integer
v2)))
               ((T_IsPreorder_70 -> Any -> T__IsRelatedTo__70) -> Any -> Any -> Any
forall a b. a -> b
coe
                  T_IsPreorder_70 -> Any -> T__IsRelatedTo__70
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du__'8718'_346
                  (T_IsPreorder_70 -> Any
forall a b. a -> b
coe T_IsPreorder_70
d_'8804''45'isPreorder_1656)
                  ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe
                     Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'42'__274
                     ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> Integer
addInt (Integer -> Any
forall a b. a -> b
coe (Integer
1 :: Integer)) (Integer -> Any
forall a b. a -> b
coe Integer
v0))
                     ((Integer -> Integer) -> Any -> Any
forall a b. a -> b
coe Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d_'45'__218 (Integer -> Any
forall a b. a -> b
coe Integer
v2))))
               (T__'60'__50 -> Any
forall a b. a -> b
coe T__'60'__50
v3))))
-- Data.Integer.Properties.*-cancelˡ-<-nonPos
d_'42''45'cancel'737''45''60''45'nonPos_5370 ::
  Integer ->
  Integer ->
  Integer ->
  AgdaAny ->
  MAlonzo.Code.Data.Integer.Base.T__'60'__50 ->
  MAlonzo.Code.Data.Integer.Base.T__'60'__50
d_'42''45'cancel'737''45''60''45'nonPos_5370 :: Integer -> Integer -> Integer -> Any -> T__'60'__50 -> T__'60'__50
d_'42''45'cancel'737''45''60''45'nonPos_5370 Integer
v0 Integer
v1 Integer
v2 ~Any
v3 T__'60'__50
v4
  = Integer -> Integer -> Integer -> T__'60'__50 -> T__'60'__50
du_'42''45'cancel'737''45''60''45'nonPos_5370 Integer
v0 Integer
v1 Integer
v2 T__'60'__50
v4
du_'42''45'cancel'737''45''60''45'nonPos_5370 ::
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Integer.Base.T__'60'__50 ->
  MAlonzo.Code.Data.Integer.Base.T__'60'__50
du_'42''45'cancel'737''45''60''45'nonPos_5370 :: Integer -> Integer -> Integer -> T__'60'__50 -> T__'60'__50
du_'42''45'cancel'737''45''60''45'nonPos_5370 Integer
v0 Integer
v1 Integer
v2 T__'60'__50
v3
  = let v4 :: Integer
v4 = Integer -> Integer -> Integer
subInt (Integer -> Integer
forall a b. a -> b
coe (-Integer
1 :: Integer)) (Integer -> Integer
forall a b. a -> b
coe Integer
v0) in
    Any -> T__'60'__50
forall a b. a -> b
coe
      ((Integer -> Integer -> Integer -> T__'60'__50 -> T__'60'__50)
-> Any -> Any -> Any -> Any -> Any
forall a b. a -> b
coe
         Integer -> Integer -> Integer -> T__'60'__50 -> T__'60'__50
d_'42''45'cancel'737''45''60''45'neg_5350 (Integer -> Any
forall a b. a -> b
coe Integer
v4) (Integer -> Any
forall a b. a -> b
coe Integer
v1)
         (Integer -> Any
forall a b. a -> b
coe Integer
v2) (T__'60'__50 -> Any
forall a b. a -> b
coe T__'60'__50
v3))
-- Data.Integer.Properties.*-cancelʳ-<-neg
d_'42''45'cancel'691''45''60''45'neg_5394 ::
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Integer.Base.T__'60'__50 ->
  MAlonzo.Code.Data.Integer.Base.T__'60'__50
d_'42''45'cancel'691''45''60''45'neg_5394 :: Integer -> Integer -> Integer -> T__'60'__50 -> T__'60'__50
d_'42''45'cancel'691''45''60''45'neg_5394 Integer
v0 Integer
v1 Integer
v2 T__'60'__50
v3
  = (Integer -> Integer -> Integer -> T__'60'__50 -> T__'60'__50)
-> Any -> Any -> Any -> Any -> T__'60'__50
forall a b. a -> b
coe
      Integer -> Integer -> Integer -> T__'60'__50 -> T__'60'__50
d_'42''45'cancel'737''45''60''45'neg_5350 (Integer -> Any
forall a b. a -> b
coe Integer
v0) (Integer -> Any
forall a b. a -> b
coe Integer
v1)
      (Integer -> Any
forall a b. a -> b
coe Integer
v2)
      ((T__IsRelatedTo__70 -> Any) -> Any -> Any
forall a b. a -> b
coe
         T__IsRelatedTo__70 -> Any
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_begin'45'strict__176
         (((Any -> Any -> Any -> Any -> Any -> Any)
 -> T_Σ_14
 -> (Any -> Any -> Any -> Any -> Any -> Any)
 -> Any
 -> Any
 -> Any
 -> T__IsRelatedTo__70
 -> Any
 -> T__IsRelatedTo__70)
-> (Any -> Any -> Any -> Any -> Any -> Any)
-> Any
-> (Any -> Any -> Any -> Any -> Any -> Any)
-> Any
-> Any
-> Any
-> Any
-> Any
-> Any
forall a b. a -> b
coe
            (Any -> Any -> Any -> Any -> Any -> Any)
-> T_Σ_14
-> (Any -> Any -> Any -> Any -> Any -> Any)
-> Any
-> Any
-> Any
-> T__IsRelatedTo__70
-> Any
-> T__IsRelatedTo__70
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_step'45''60'_202
            (\ Any
v4 Any
v5 Any
v6 Any
v7 Any
v8 -> (Integer -> Integer -> T__'60'__50 -> T__'60'__50 -> T__'60'__50)
-> Any -> Any -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> T__'60'__50 -> T__'60'__50 -> T__'60'__50
du_'60''45'trans_1872 Any
v4 Any
v5 Any
v7 Any
v8)
            (T_Σ_14 -> Any
forall a b. a -> b
coe
               T_Σ_14
MAlonzo.Code.Relation.Binary.PropositionalEquality.Core.du_resp'8322'_144)
            (\ Any
v4 Any
v5 Any
v6 Any
v7 Any
v8 -> (T__'60'__50 -> T__'8804'__26 -> T__'60'__50) -> Any -> Any -> Any
forall a b. a -> b
coe T__'60'__50 -> T__'8804'__26 -> T__'60'__50
du_'60''45''8804''45'trans_1858 Any
v7 Any
v8)
            ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe
               Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'42'__274 (Integer -> Any
forall a b. a -> b
coe Integer
v1)
               ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> Integer
subInt (Integer -> Any
forall a b. a -> b
coe (-Integer
1 :: Integer)) (Integer -> Any
forall a b. a -> b
coe Integer
v0)))
            ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe
               Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'42'__274 (Integer -> Any
forall a b. a -> b
coe Integer
v2)
               ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> Integer
subInt (Integer -> Any
forall a b. a -> b
coe (-Integer
1 :: Integer)) (Integer -> Any
forall a b. a -> b
coe Integer
v0)))
            ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe
               Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'42'__274
               ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> Integer
subInt (Integer -> Any
forall a b. a -> b
coe (-Integer
1 :: Integer)) (Integer -> Any
forall a b. a -> b
coe Integer
v0)) (Integer -> Any
forall a b. a -> b
coe Integer
v2))
            ((T_IsPreorder_70 -> Any -> T__IsRelatedTo__70) -> Any -> Any -> Any
forall a b. a -> b
coe
               T_IsPreorder_70 -> Any -> T__IsRelatedTo__70
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du__'8718'_346
               (T_IsPreorder_70 -> Any
forall a b. a -> b
coe T_IsPreorder_70
d_'8804''45'isPreorder_1656)
               ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe
                  Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'42'__274
                  ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> Integer
subInt (Integer -> Any
forall a b. a -> b
coe (-Integer
1 :: Integer)) (Integer -> Any
forall a b. a -> b
coe Integer
v0)) (Integer -> Any
forall a b. a -> b
coe Integer
v2)))
            (T__'60'__50 -> Any
forall a b. a -> b
coe T__'60'__50
v3)))
-- Data.Integer.Properties.*-cancelʳ-<-nonPos
d_'42''45'cancel'691''45''60''45'nonPos_5414 ::
  Integer ->
  Integer ->
  Integer ->
  AgdaAny ->
  MAlonzo.Code.Data.Integer.Base.T__'60'__50 ->
  MAlonzo.Code.Data.Integer.Base.T__'60'__50
d_'42''45'cancel'691''45''60''45'nonPos_5414 :: Integer -> Integer -> Integer -> Any -> T__'60'__50 -> T__'60'__50
d_'42''45'cancel'691''45''60''45'nonPos_5414 Integer
v0 Integer
v1 Integer
v2 ~Any
v3 T__'60'__50
v4
  = Integer -> Integer -> Integer -> T__'60'__50 -> T__'60'__50
du_'42''45'cancel'691''45''60''45'nonPos_5414 Integer
v0 Integer
v1 Integer
v2 T__'60'__50
v4
du_'42''45'cancel'691''45''60''45'nonPos_5414 ::
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Integer.Base.T__'60'__50 ->
  MAlonzo.Code.Data.Integer.Base.T__'60'__50
du_'42''45'cancel'691''45''60''45'nonPos_5414 :: Integer -> Integer -> Integer -> T__'60'__50 -> T__'60'__50
du_'42''45'cancel'691''45''60''45'nonPos_5414 Integer
v0 Integer
v1 Integer
v2 T__'60'__50
v3
  = case Integer -> Integer
forall a b. a -> b
coe Integer
v0 of
      Integer
0 -> Any -> T__'60'__50
forall a b. a -> b
coe
             Any
MAlonzo.Code.Relation.Nullary.Negation.Core.du_contradiction_24
      Integer
_ -> let v4 :: Integer
v4 = Integer -> Integer -> Integer
subInt (Integer -> Integer
forall a b. a -> b
coe (-Integer
1 :: Integer)) (Integer -> Integer
forall a b. a -> b
coe Integer
v0) in
           Any -> T__'60'__50
forall a b. a -> b
coe
             ((Integer -> Integer -> Integer -> T__'60'__50 -> T__'60'__50)
-> Any -> Any -> Any -> Any -> Any
forall a b. a -> b
coe
                Integer -> Integer -> Integer -> T__'60'__50 -> T__'60'__50
d_'42''45'cancel'691''45''60''45'neg_5394 (Integer -> Any
forall a b. a -> b
coe Integer
v4) (Integer -> Any
forall a b. a -> b
coe Integer
v1)
                (Integer -> Any
forall a b. a -> b
coe Integer
v2) (T__'60'__50 -> Any
forall a b. a -> b
coe T__'60'__50
v3))
-- Data.Integer.Properties.∣m*n∣≡∣m∣*∣n∣
d_'8739'm'42'n'8739''8801''8739'm'8739''42''8739'n'8739'_5442 ::
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8739'm'42'n'8739''8801''8739'm'8739''42''8739'n'8739'_5442 :: Integer -> Integer -> T__'8801'__12
d_'8739'm'42'n'8739''8801''8739'm'8739''42''8739'n'8739'_5442
  = Integer -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.i≤j⇒i⊓j≡i
d_i'8804'j'8658'i'8851'j'8801'i_5480 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_i'8804'j'8658'i'8851'j'8801'i_5480 :: Integer -> Integer -> T__'8804'__26 -> T__'8801'__12
d_i'8804'j'8658'i'8851'j'8801'i_5480 = Integer -> Integer -> T__'8804'__26 -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.i≥j⇒i⊓j≡j
d_i'8805'j'8658'i'8851'j'8801'j_5490 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_i'8805'j'8658'i'8851'j'8801'j_5490 :: Integer -> Integer -> T__'8804'__26 -> T__'8801'__12
d_i'8805'j'8658'i'8851'j'8801'j_5490 = Integer -> Integer -> T__'8804'__26 -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.i≤j⇒i⊔j≡j
d_i'8804'j'8658'i'8852'j'8801'j_5500 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_i'8804'j'8658'i'8852'j'8801'j_5500 :: Integer -> Integer -> T__'8804'__26 -> T__'8801'__12
d_i'8804'j'8658'i'8852'j'8801'j_5500 = Integer -> Integer -> T__'8804'__26 -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.i≥j⇒i⊔j≡i
d_i'8805'j'8658'i'8852'j'8801'i_5510 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_i'8805'j'8658'i'8852'j'8801'i_5510 :: Integer -> Integer -> T__'8804'__26 -> T__'8801'__12
d_i'8805'j'8658'i'8852'j'8801'i_5510 = Integer -> Integer -> T__'8804'__26 -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.⊓-operator
d_'8851''45'operator_5516 ::
  MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_84
d_'8851''45'operator_5516 :: T_MinOperator_84
d_'8851''45'operator_5516
  = ((Any -> Any -> Any)
 -> (Any -> Any -> Any -> Any)
 -> (Any -> Any -> Any -> Any)
 -> T_MinOperator_84)
-> Any -> Any -> Any -> T_MinOperator_84
forall a b. a -> b
coe
      (Any -> Any -> Any)
-> (Any -> Any -> Any -> Any)
-> (Any -> Any -> Any -> Any)
-> T_MinOperator_84
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.C_MinOperator'46'constructor_983
      ((Integer -> Integer -> Integer) -> Any
forall a b. a -> b
coe Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'8851'__298) Any
forall a. a
erased Any
forall a. a
erased
-- Data.Integer.Properties.⊔-operator
d_'8852''45'operator_5518 ::
  MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MaxOperator_114
d_'8852''45'operator_5518 :: T_MaxOperator_114
d_'8852''45'operator_5518
  = ((Any -> Any -> Any)
 -> (Any -> Any -> Any -> Any)
 -> (Any -> Any -> Any -> Any)
 -> T_MaxOperator_114)
-> Any -> Any -> Any -> T_MaxOperator_114
forall a b. a -> b
coe
      (Any -> Any -> Any)
-> (Any -> Any -> Any -> Any)
-> (Any -> Any -> Any -> Any)
-> T_MaxOperator_114
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.C_MaxOperator'46'constructor_1521
      ((Integer -> Integer -> Integer) -> Any
forall a b. a -> b
coe Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'8852'__280) Any
forall a. a
erased Any
forall a. a
erased
-- Data.Integer.Properties.⊓-⊔-properties.antimono-≤-distrib-⊓
d_antimono'45''8804''45'distrib'45''8851'_5522 ::
  (Integer -> Integer) ->
  (Integer ->
   Integer ->
   MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
   MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12) ->
  (Integer ->
   Integer ->
   MAlonzo.Code.Data.Integer.Base.T__'8804'__26 ->
   MAlonzo.Code.Data.Integer.Base.T__'8804'__26) ->
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_antimono'45''8804''45'distrib'45''8851'_5522 :: (Integer -> Integer)
-> (Integer -> Integer -> T__'8801'__12 -> T__'8801'__12)
-> (Integer -> Integer -> T__'8804'__26 -> T__'8804'__26)
-> Integer
-> Integer
-> T__'8801'__12
d_antimono'45''8804''45'distrib'45''8851'_5522 = (Integer -> Integer)
-> (Integer -> Integer -> T__'8801'__12 -> T__'8801'__12)
-> (Integer -> Integer -> T__'8804'__26 -> T__'8804'__26)
-> Integer
-> Integer
-> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.⊓-⊔-properties.antimono-≤-distrib-⊔
d_antimono'45''8804''45'distrib'45''8852'_5524 ::
  (Integer -> Integer) ->
  (Integer ->
   Integer ->
   MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
   MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12) ->
  (Integer ->
   Integer ->
   MAlonzo.Code.Data.Integer.Base.T__'8804'__26 ->
   MAlonzo.Code.Data.Integer.Base.T__'8804'__26) ->
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_antimono'45''8804''45'distrib'45''8852'_5524 :: (Integer -> Integer)
-> (Integer -> Integer -> T__'8801'__12 -> T__'8801'__12)
-> (Integer -> Integer -> T__'8804'__26 -> T__'8804'__26)
-> Integer
-> Integer
-> T__'8801'__12
d_antimono'45''8804''45'distrib'45''8852'_5524 = (Integer -> Integer)
-> (Integer -> Integer -> T__'8801'__12 -> T__'8801'__12)
-> (Integer -> Integer -> T__'8804'__26 -> T__'8804'__26)
-> Integer
-> Integer
-> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.⊓-⊔-properties.mono-≤-distrib-⊓
d_mono'45''8804''45'distrib'45''8851'_5526 ::
  (Integer -> Integer) ->
  (Integer ->
   Integer ->
   MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
   MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12) ->
  (Integer ->
   Integer ->
   MAlonzo.Code.Data.Integer.Base.T__'8804'__26 ->
   MAlonzo.Code.Data.Integer.Base.T__'8804'__26) ->
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_mono'45''8804''45'distrib'45''8851'_5526 :: (Integer -> Integer)
-> (Integer -> Integer -> T__'8801'__12 -> T__'8801'__12)
-> (Integer -> Integer -> T__'8804'__26 -> T__'8804'__26)
-> Integer
-> Integer
-> T__'8801'__12
d_mono'45''8804''45'distrib'45''8851'_5526 = (Integer -> Integer)
-> (Integer -> Integer -> T__'8801'__12 -> T__'8801'__12)
-> (Integer -> Integer -> T__'8804'__26 -> T__'8804'__26)
-> Integer
-> Integer
-> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.⊓-⊔-properties.mono-≤-distrib-⊔
d_mono'45''8804''45'distrib'45''8852'_5528 ::
  (Integer -> Integer) ->
  (Integer ->
   Integer ->
   MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
   MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12) ->
  (Integer ->
   Integer ->
   MAlonzo.Code.Data.Integer.Base.T__'8804'__26 ->
   MAlonzo.Code.Data.Integer.Base.T__'8804'__26) ->
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_mono'45''8804''45'distrib'45''8852'_5528 :: (Integer -> Integer)
-> (Integer -> Integer -> T__'8801'__12 -> T__'8801'__12)
-> (Integer -> Integer -> T__'8804'__26 -> T__'8804'__26)
-> Integer
-> Integer
-> T__'8801'__12
d_mono'45''8804''45'distrib'45''8852'_5528 = (Integer -> Integer)
-> (Integer -> Integer -> T__'8801'__12 -> T__'8801'__12)
-> (Integer -> Integer -> T__'8804'__26 -> T__'8804'__26)
-> Integer
-> Integer
-> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.⊓-⊔-properties.x⊓y≤x
d_x'8851'y'8804'x_5530 ::
  Integer -> Integer -> MAlonzo.Code.Data.Integer.Base.T__'8804'__26
d_x'8851'y'8804'x_5530 :: Integer -> Integer -> T__'8804'__26
d_x'8851'y'8804'x_5530
  = let v0 :: T_TotalPreorder_204
v0 = T_TotalPreorder_204
d_'8804''45'totalPreorder_1668 in
    Any -> Integer -> Integer -> T__'8804'__26
forall a b. a -> b
coe
      (let v1 :: T_MaxOperator_114
v1 = T_MaxOperator_114
d_'8852''45'operator_5518 in
       Any -> Any
forall a b. a -> b
coe
         ((T_TotalPreorder_204 -> T_MinOperator_84 -> Any -> Any -> Any)
-> Any -> Any -> Any
forall a b. a -> b
coe
            T_TotalPreorder_204 -> T_MinOperator_84 -> Any -> Any -> Any
MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_x'8851'y'8804'x_1626
            ((T_TotalPreorder_204 -> T_TotalPreorder_204) -> Any -> Any
forall a b. a -> b
coe
               T_TotalPreorder_204 -> T_TotalPreorder_204
MAlonzo.Code.Relation.Binary.Construct.Converse.du_totalPreorder_718
               (T_TotalPreorder_204 -> Any
forall a b. a -> b
coe T_TotalPreorder_204
v0))
            ((T_MaxOperator_114 -> T_MinOperator_84) -> Any -> Any
forall a b. a -> b
coe
               T_MaxOperator_114 -> T_MinOperator_84
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.du_MaxOp'8658'MinOp_160
               (T_MaxOperator_114 -> Any
forall a b. a -> b
coe T_MaxOperator_114
v1))))
-- Data.Integer.Properties.⊓-⊔-properties.x≤y⇒x⊓z≤y
d_x'8804'y'8658'x'8851'z'8804'y_5532 ::
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26 ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26
d_x'8804'y'8658'x'8851'z'8804'y_5532 :: Integer -> Integer -> Integer -> T__'8804'__26 -> T__'8804'__26
d_x'8804'y'8658'x'8851'z'8804'y_5532
  = let v0 :: T_TotalPreorder_204
v0 = T_TotalPreorder_204
d_'8804''45'totalPreorder_1668 in
    Any
-> Integer -> Integer -> Integer -> T__'8804'__26 -> T__'8804'__26
forall a b. a -> b
coe
      (let v1 :: T_MaxOperator_114
v1 = T_MaxOperator_114
d_'8852''45'operator_5518 in
       Any -> Any
forall a b. a -> b
coe
         ((T_TotalPreorder_204
 -> T_MinOperator_84 -> Any -> Any -> Any -> Any -> Any)
-> Any -> Any -> Any
forall a b. a -> b
coe
            T_TotalPreorder_204
-> T_MinOperator_84 -> Any -> Any -> Any -> Any -> Any
MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_x'8804'y'8658'x'8851'z'8804'y_1982
            ((T_TotalPreorder_204 -> T_TotalPreorder_204) -> Any -> Any
forall a b. a -> b
coe
               T_TotalPreorder_204 -> T_TotalPreorder_204
MAlonzo.Code.Relation.Binary.Construct.Converse.du_totalPreorder_718
               (T_TotalPreorder_204 -> Any
forall a b. a -> b
coe T_TotalPreorder_204
v0))
            ((T_MaxOperator_114 -> T_MinOperator_84) -> Any -> Any
forall a b. a -> b
coe
               T_MaxOperator_114 -> T_MinOperator_84
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.du_MaxOp'8658'MinOp_160
               (T_MaxOperator_114 -> Any
forall a b. a -> b
coe T_MaxOperator_114
v1))))
-- Data.Integer.Properties.⊓-⊔-properties.x≤y⇒z⊓x≤y
d_x'8804'y'8658'z'8851'x'8804'y_5534 ::
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26 ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26
d_x'8804'y'8658'z'8851'x'8804'y_5534 :: Integer -> Integer -> Integer -> T__'8804'__26 -> T__'8804'__26
d_x'8804'y'8658'z'8851'x'8804'y_5534
  = let v0 :: T_TotalPreorder_204
v0 = T_TotalPreorder_204
d_'8804''45'totalPreorder_1668 in
    Any
-> Integer -> Integer -> Integer -> T__'8804'__26 -> T__'8804'__26
forall a b. a -> b
coe
      (let v1 :: T_MaxOperator_114
v1 = T_MaxOperator_114
d_'8852''45'operator_5518 in
       Any -> Any
forall a b. a -> b
coe
         ((T_TotalPreorder_204
 -> T_MinOperator_84 -> Any -> Any -> Any -> Any -> Any)
-> Any -> Any -> Any
forall a b. a -> b
coe
            T_TotalPreorder_204
-> T_MinOperator_84 -> Any -> Any -> Any -> Any -> Any
MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_x'8804'y'8658'z'8851'x'8804'y_1994
            ((T_TotalPreorder_204 -> T_TotalPreorder_204) -> Any -> Any
forall a b. a -> b
coe
               T_TotalPreorder_204 -> T_TotalPreorder_204
MAlonzo.Code.Relation.Binary.Construct.Converse.du_totalPreorder_718
               (T_TotalPreorder_204 -> Any
forall a b. a -> b
coe T_TotalPreorder_204
v0))
            ((T_MaxOperator_114 -> T_MinOperator_84) -> Any -> Any
forall a b. a -> b
coe
               T_MaxOperator_114 -> T_MinOperator_84
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.du_MaxOp'8658'MinOp_160
               (T_MaxOperator_114 -> Any
forall a b. a -> b
coe T_MaxOperator_114
v1))))
-- Data.Integer.Properties.⊓-⊔-properties.x≤y⇒x⊓z≤y
d_x'8804'y'8658'x'8851'z'8804'y_5536 ::
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26 ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26
d_x'8804'y'8658'x'8851'z'8804'y_5536 :: Integer -> Integer -> Integer -> T__'8804'__26 -> T__'8804'__26
d_x'8804'y'8658'x'8851'z'8804'y_5536
  = let v0 :: T_TotalPreorder_204
v0 = T_TotalPreorder_204
d_'8804''45'totalPreorder_1668 in
    Any
-> Integer -> Integer -> Integer -> T__'8804'__26 -> T__'8804'__26
forall a b. a -> b
coe
      (let v1 :: T_MinOperator_84
v1 = T_MinOperator_84
d_'8851''45'operator_5516 in
       Any -> Any
forall a b. a -> b
coe
         ((T_TotalPreorder_204
 -> T_MinOperator_84 -> Any -> Any -> Any -> Any -> Any)
-> Any -> Any -> Any
forall a b. a -> b
coe
            T_TotalPreorder_204
-> T_MinOperator_84 -> Any -> Any -> Any -> Any -> Any
MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_x'8804'y'8658'x'8851'z'8804'y_1982
            (T_TotalPreorder_204 -> Any
forall a b. a -> b
coe T_TotalPreorder_204
v0) (T_MinOperator_84 -> Any
forall a b. a -> b
coe T_MinOperator_84
v1)))
-- Data.Integer.Properties.⊓-⊔-properties.x≤y⇒z⊓x≤y
d_x'8804'y'8658'z'8851'x'8804'y_5538 ::
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26 ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26
d_x'8804'y'8658'z'8851'x'8804'y_5538 :: Integer -> Integer -> Integer -> T__'8804'__26 -> T__'8804'__26
d_x'8804'y'8658'z'8851'x'8804'y_5538
  = let v0 :: T_TotalPreorder_204
v0 = T_TotalPreorder_204
d_'8804''45'totalPreorder_1668 in
    Any
-> Integer -> Integer -> Integer -> T__'8804'__26 -> T__'8804'__26
forall a b. a -> b
coe
      (let v1 :: T_MinOperator_84
v1 = T_MinOperator_84
d_'8851''45'operator_5516 in
       Any -> Any
forall a b. a -> b
coe
         ((T_TotalPreorder_204
 -> T_MinOperator_84 -> Any -> Any -> Any -> Any -> Any)
-> Any -> Any -> Any
forall a b. a -> b
coe
            T_TotalPreorder_204
-> T_MinOperator_84 -> Any -> Any -> Any -> Any -> Any
MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_x'8804'y'8658'z'8851'x'8804'y_1994
            (T_TotalPreorder_204 -> Any
forall a b. a -> b
coe T_TotalPreorder_204
v0) (T_MinOperator_84 -> Any
forall a b. a -> b
coe T_MinOperator_84
v1)))
-- Data.Integer.Properties.⊓-⊔-properties.x≤y⊓z⇒x≤y
d_x'8804'y'8851'z'8658'x'8804'y_5540 ::
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26 ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26
d_x'8804'y'8851'z'8658'x'8804'y_5540 :: Integer -> Integer -> Integer -> T__'8804'__26 -> T__'8804'__26
d_x'8804'y'8851'z'8658'x'8804'y_5540
  = let v0 :: T_TotalPreorder_204
v0 = T_TotalPreorder_204
d_'8804''45'totalPreorder_1668 in
    Any
-> Integer -> Integer -> Integer -> T__'8804'__26 -> T__'8804'__26
forall a b. a -> b
coe
      (let v1 :: T_MinOperator_84
v1 = T_MinOperator_84
d_'8851''45'operator_5516 in
       Any -> Any
forall a b. a -> b
coe
         ((T_TotalPreorder_204
 -> T_MinOperator_84 -> Any -> Any -> Any -> Any -> Any)
-> Any -> Any -> Any
forall a b. a -> b
coe
            T_TotalPreorder_204
-> T_MinOperator_84 -> Any -> Any -> Any -> Any -> Any
MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_x'8804'y'8851'z'8658'x'8804'y_2006
            (T_TotalPreorder_204 -> Any
forall a b. a -> b
coe T_TotalPreorder_204
v0) (T_MinOperator_84 -> Any
forall a b. a -> b
coe T_MinOperator_84
v1)))
-- Data.Integer.Properties.⊓-⊔-properties.x≤y⊓z⇒x≤z
d_x'8804'y'8851'z'8658'x'8804'z_5542 ::
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26 ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26
d_x'8804'y'8851'z'8658'x'8804'z_5542 :: Integer -> Integer -> Integer -> T__'8804'__26 -> T__'8804'__26
d_x'8804'y'8851'z'8658'x'8804'z_5542
  = let v0 :: T_TotalPreorder_204
v0 = T_TotalPreorder_204
d_'8804''45'totalPreorder_1668 in
    Any
-> Integer -> Integer -> Integer -> T__'8804'__26 -> T__'8804'__26
forall a b. a -> b
coe
      (let v1 :: T_MinOperator_84
v1 = T_MinOperator_84
d_'8851''45'operator_5516 in
       Any -> Any
forall a b. a -> b
coe
         ((T_TotalPreorder_204
 -> T_MinOperator_84 -> Any -> Any -> Any -> Any -> Any)
-> Any -> Any -> Any
forall a b. a -> b
coe
            T_TotalPreorder_204
-> T_MinOperator_84 -> Any -> Any -> Any -> Any -> Any
MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_x'8804'y'8851'z'8658'x'8804'z_2020
            (T_TotalPreorder_204 -> Any
forall a b. a -> b
coe T_TotalPreorder_204
v0) (T_MinOperator_84 -> Any
forall a b. a -> b
coe T_MinOperator_84
v1)))
-- Data.Integer.Properties.⊓-⊔-properties.x⊓y≤y
d_x'8851'y'8804'y_5544 ::
  Integer -> Integer -> MAlonzo.Code.Data.Integer.Base.T__'8804'__26
d_x'8851'y'8804'y_5544 :: Integer -> Integer -> T__'8804'__26
d_x'8851'y'8804'y_5544
  = let v0 :: T_TotalPreorder_204
v0 = T_TotalPreorder_204
d_'8804''45'totalPreorder_1668 in
    Any -> Integer -> Integer -> T__'8804'__26
forall a b. a -> b
coe
      (let v1 :: T_MaxOperator_114
v1 = T_MaxOperator_114
d_'8852''45'operator_5518 in
       Any -> Any
forall a b. a -> b
coe
         ((T_TotalPreorder_204 -> T_MinOperator_84 -> Any -> Any -> Any)
-> Any -> Any -> Any
forall a b. a -> b
coe
            T_TotalPreorder_204 -> T_MinOperator_84 -> Any -> Any -> Any
MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_x'8851'y'8804'y_1652
            ((T_TotalPreorder_204 -> T_TotalPreorder_204) -> Any -> Any
forall a b. a -> b
coe
               T_TotalPreorder_204 -> T_TotalPreorder_204
MAlonzo.Code.Relation.Binary.Construct.Converse.du_totalPreorder_718
               (T_TotalPreorder_204 -> Any
forall a b. a -> b
coe T_TotalPreorder_204
v0))
            ((T_MaxOperator_114 -> T_MinOperator_84) -> Any -> Any
forall a b. a -> b
coe
               T_MaxOperator_114 -> T_MinOperator_84
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.du_MaxOp'8658'MinOp_160
               (T_MaxOperator_114 -> Any
forall a b. a -> b
coe T_MaxOperator_114
v1))))
-- Data.Integer.Properties.⊓-⊔-properties.x⊓y≈x⇒x≤y
d_x'8851'y'8776'x'8658'x'8804'y_5546 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26
d_x'8851'y'8776'x'8658'x'8804'y_5546 :: Integer -> Integer -> T__'8801'__12 -> T__'8804'__26
d_x'8851'y'8776'x'8658'x'8804'y_5546
  = let v0 :: T_TotalPreorder_204
v0 = T_TotalPreorder_204
d_'8804''45'totalPreorder_1668 in
    Any -> Integer -> Integer -> T__'8801'__12 -> T__'8804'__26
forall a b. a -> b
coe
      (let v1 :: T_MinOperator_84
v1 = T_MinOperator_84
d_'8851''45'operator_5516 in
       Any -> Any
forall a b. a -> b
coe
         ((T_TotalPreorder_204
 -> T_MinOperator_84 -> Any -> Any -> Any -> Any)
-> Any -> Any -> Any
forall a b. a -> b
coe
            T_TotalPreorder_204 -> T_MinOperator_84 -> Any -> Any -> Any -> Any
MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_x'8851'y'8776'x'8658'x'8804'y_1890
            (T_TotalPreorder_204 -> Any
forall a b. a -> b
coe T_TotalPreorder_204
v0) (T_MinOperator_84 -> Any
forall a b. a -> b
coe T_MinOperator_84
v1)))
-- Data.Integer.Properties.⊓-⊔-properties.x⊓y≈y⇒y≤x
d_x'8851'y'8776'y'8658'y'8804'x_5548 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26
d_x'8851'y'8776'y'8658'y'8804'x_5548 :: Integer -> Integer -> T__'8801'__12 -> T__'8804'__26
d_x'8851'y'8776'y'8658'y'8804'x_5548
  = let v0 :: T_TotalPreorder_204
v0 = T_TotalPreorder_204
d_'8804''45'totalPreorder_1668 in
    Any -> Integer -> Integer -> T__'8801'__12 -> T__'8804'__26
forall a b. a -> b
coe
      (let v1 :: T_MinOperator_84
v1 = T_MinOperator_84
d_'8851''45'operator_5516 in
       Any -> Any
forall a b. a -> b
coe
         ((T_TotalPreorder_204
 -> T_MinOperator_84 -> Any -> Any -> Any -> Any)
-> Any -> Any -> Any
forall a b. a -> b
coe
            T_TotalPreorder_204 -> T_MinOperator_84 -> Any -> Any -> Any -> Any
MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_x'8851'y'8776'y'8658'y'8804'x_1922
            (T_TotalPreorder_204 -> Any
forall a b. a -> b
coe T_TotalPreorder_204
v0) (T_MinOperator_84 -> Any
forall a b. a -> b
coe T_MinOperator_84
v1)))
-- Data.Integer.Properties.⊓-⊔-properties.x⊓y≤x
d_x'8851'y'8804'x_5550 ::
  Integer -> Integer -> MAlonzo.Code.Data.Integer.Base.T__'8804'__26
d_x'8851'y'8804'x_5550 :: Integer -> Integer -> T__'8804'__26
d_x'8851'y'8804'x_5550
  = let v0 :: T_TotalPreorder_204
v0 = T_TotalPreorder_204
d_'8804''45'totalPreorder_1668 in
    Any -> Integer -> Integer -> T__'8804'__26
forall a b. a -> b
coe
      (let v1 :: T_MinOperator_84
v1 = T_MinOperator_84
d_'8851''45'operator_5516 in
       Any -> Any
forall a b. a -> b
coe
         ((T_TotalPreorder_204 -> T_MinOperator_84 -> Any -> Any -> Any)
-> Any -> Any -> Any
forall a b. a -> b
coe
            T_TotalPreorder_204 -> T_MinOperator_84 -> Any -> Any -> Any
MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_x'8851'y'8804'x_1626
            (T_TotalPreorder_204 -> Any
forall a b. a -> b
coe T_TotalPreorder_204
v0) (T_MinOperator_84 -> Any
forall a b. a -> b
coe T_MinOperator_84
v1)))
-- Data.Integer.Properties.⊓-⊔-properties.x⊓y≤x⊔y
d_x'8851'y'8804'x'8852'y_5552 ::
  Integer -> Integer -> MAlonzo.Code.Data.Integer.Base.T__'8804'__26
d_x'8851'y'8804'x'8852'y_5552 :: Integer -> Integer -> T__'8804'__26
d_x'8851'y'8804'x'8852'y_5552
  = (T_TotalPreorder_204
 -> T_MinOperator_84 -> T_MaxOperator_114 -> Any -> Any -> Any)
-> Any -> Any -> Any -> Integer -> Integer -> T__'8804'__26
forall a b. a -> b
coe
      T_TotalPreorder_204
-> T_MinOperator_84 -> T_MaxOperator_114 -> Any -> Any -> Any
MAlonzo.Code.Algebra.Construct.NaturalChoice.MinMaxOp.du_x'8851'y'8804'x'8852'y_2072
      (T_TotalPreorder_204 -> Any
forall a b. a -> b
coe T_TotalPreorder_204
d_'8804''45'totalPreorder_1668)
      (T_MinOperator_84 -> Any
forall a b. a -> b
coe T_MinOperator_84
d_'8851''45'operator_5516) (T_MaxOperator_114 -> Any
forall a b. a -> b
coe T_MaxOperator_114
d_'8852''45'operator_5518)
-- Data.Integer.Properties.⊓-⊔-properties.x⊓y≤y
d_x'8851'y'8804'y_5554 ::
  Integer -> Integer -> MAlonzo.Code.Data.Integer.Base.T__'8804'__26
d_x'8851'y'8804'y_5554 :: Integer -> Integer -> T__'8804'__26
d_x'8851'y'8804'y_5554
  = let v0 :: T_TotalPreorder_204
v0 = T_TotalPreorder_204
d_'8804''45'totalPreorder_1668 in
    Any -> Integer -> Integer -> T__'8804'__26
forall a b. a -> b
coe
      (let v1 :: T_MinOperator_84
v1 = T_MinOperator_84
d_'8851''45'operator_5516 in
       Any -> Any
forall a b. a -> b
coe
         ((T_TotalPreorder_204 -> T_MinOperator_84 -> Any -> Any -> Any)
-> Any -> Any -> Any
forall a b. a -> b
coe
            T_TotalPreorder_204 -> T_MinOperator_84 -> Any -> Any -> Any
MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_x'8851'y'8804'y_1652
            (T_TotalPreorder_204 -> Any
forall a b. a -> b
coe T_TotalPreorder_204
v0) (T_MinOperator_84 -> Any
forall a b. a -> b
coe T_MinOperator_84
v1)))
-- Data.Integer.Properties.⊓-⊔-properties.x⊓y≈x⇒x≤y
d_x'8851'y'8776'x'8658'x'8804'y_5556 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26
d_x'8851'y'8776'x'8658'x'8804'y_5556 :: Integer -> Integer -> T__'8801'__12 -> T__'8804'__26
d_x'8851'y'8776'x'8658'x'8804'y_5556
  = let v0 :: T_TotalPreorder_204
v0 = T_TotalPreorder_204
d_'8804''45'totalPreorder_1668 in
    Any -> Integer -> Integer -> T__'8801'__12 -> T__'8804'__26
forall a b. a -> b
coe
      (let v1 :: T_MaxOperator_114
v1 = T_MaxOperator_114
d_'8852''45'operator_5518 in
       Any -> Any
forall a b. a -> b
coe
         ((T_TotalPreorder_204
 -> T_MinOperator_84 -> Any -> Any -> Any -> Any)
-> Any -> Any -> Any
forall a b. a -> b
coe
            T_TotalPreorder_204 -> T_MinOperator_84 -> Any -> Any -> Any -> Any
MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_x'8851'y'8776'x'8658'x'8804'y_1890
            ((T_TotalPreorder_204 -> T_TotalPreorder_204) -> Any -> Any
forall a b. a -> b
coe
               T_TotalPreorder_204 -> T_TotalPreorder_204
MAlonzo.Code.Relation.Binary.Construct.Converse.du_totalPreorder_718
               (T_TotalPreorder_204 -> Any
forall a b. a -> b
coe T_TotalPreorder_204
v0))
            ((T_MaxOperator_114 -> T_MinOperator_84) -> Any -> Any
forall a b. a -> b
coe
               T_MaxOperator_114 -> T_MinOperator_84
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.du_MaxOp'8658'MinOp_160
               (T_MaxOperator_114 -> Any
forall a b. a -> b
coe T_MaxOperator_114
v1))))
-- Data.Integer.Properties.⊓-⊔-properties.x⊓y≈y⇒y≤x
d_x'8851'y'8776'y'8658'y'8804'x_5558 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26
d_x'8851'y'8776'y'8658'y'8804'x_5558 :: Integer -> Integer -> T__'8801'__12 -> T__'8804'__26
d_x'8851'y'8776'y'8658'y'8804'x_5558
  = let v0 :: T_TotalPreorder_204
v0 = T_TotalPreorder_204
d_'8804''45'totalPreorder_1668 in
    Any -> Integer -> Integer -> T__'8801'__12 -> T__'8804'__26
forall a b. a -> b
coe
      (let v1 :: T_MaxOperator_114
v1 = T_MaxOperator_114
d_'8852''45'operator_5518 in
       Any -> Any
forall a b. a -> b
coe
         ((T_TotalPreorder_204
 -> T_MinOperator_84 -> Any -> Any -> Any -> Any)
-> Any -> Any -> Any
forall a b. a -> b
coe
            T_TotalPreorder_204 -> T_MinOperator_84 -> Any -> Any -> Any -> Any
MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_x'8851'y'8776'y'8658'y'8804'x_1922
            ((T_TotalPreorder_204 -> T_TotalPreorder_204) -> Any -> Any
forall a b. a -> b
coe
               T_TotalPreorder_204 -> T_TotalPreorder_204
MAlonzo.Code.Relation.Binary.Construct.Converse.du_totalPreorder_718
               (T_TotalPreorder_204 -> Any
forall a b. a -> b
coe T_TotalPreorder_204
v0))
            ((T_MaxOperator_114 -> T_MinOperator_84) -> Any -> Any
forall a b. a -> b
coe
               T_MaxOperator_114 -> T_MinOperator_84
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.du_MaxOp'8658'MinOp_160
               (T_MaxOperator_114 -> Any
forall a b. a -> b
coe T_MaxOperator_114
v1))))
-- Data.Integer.Properties.⊓-⊔-properties.x≤y⊓z⇒x≤y
d_x'8804'y'8851'z'8658'x'8804'y_5560 ::
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26 ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26
d_x'8804'y'8851'z'8658'x'8804'y_5560 :: Integer -> Integer -> Integer -> T__'8804'__26 -> T__'8804'__26
d_x'8804'y'8851'z'8658'x'8804'y_5560
  = let v0 :: T_TotalPreorder_204
v0 = T_TotalPreorder_204
d_'8804''45'totalPreorder_1668 in
    Any
-> Integer -> Integer -> Integer -> T__'8804'__26 -> T__'8804'__26
forall a b. a -> b
coe
      (let v1 :: T_MaxOperator_114
v1 = T_MaxOperator_114
d_'8852''45'operator_5518 in
       Any -> Any
forall a b. a -> b
coe
         ((T_TotalPreorder_204
 -> T_MinOperator_84 -> Any -> Any -> Any -> Any -> Any)
-> Any -> Any -> Any
forall a b. a -> b
coe
            T_TotalPreorder_204
-> T_MinOperator_84 -> Any -> Any -> Any -> Any -> Any
MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_x'8804'y'8851'z'8658'x'8804'y_2006
            ((T_TotalPreorder_204 -> T_TotalPreorder_204) -> Any -> Any
forall a b. a -> b
coe
               T_TotalPreorder_204 -> T_TotalPreorder_204
MAlonzo.Code.Relation.Binary.Construct.Converse.du_totalPreorder_718
               (T_TotalPreorder_204 -> Any
forall a b. a -> b
coe T_TotalPreorder_204
v0))
            ((T_MaxOperator_114 -> T_MinOperator_84) -> Any -> Any
forall a b. a -> b
coe
               T_MaxOperator_114 -> T_MinOperator_84
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.du_MaxOp'8658'MinOp_160
               (T_MaxOperator_114 -> Any
forall a b. a -> b
coe T_MaxOperator_114
v1))))
-- Data.Integer.Properties.⊓-⊔-properties.x≤y⊓z⇒x≤z
d_x'8804'y'8851'z'8658'x'8804'z_5562 ::
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26 ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26
d_x'8804'y'8851'z'8658'x'8804'z_5562 :: Integer -> Integer -> Integer -> T__'8804'__26 -> T__'8804'__26
d_x'8804'y'8851'z'8658'x'8804'z_5562
  = let v0 :: T_TotalPreorder_204
v0 = T_TotalPreorder_204
d_'8804''45'totalPreorder_1668 in
    Any
-> Integer -> Integer -> Integer -> T__'8804'__26 -> T__'8804'__26
forall a b. a -> b
coe
      (let v1 :: T_MaxOperator_114
v1 = T_MaxOperator_114
d_'8852''45'operator_5518 in
       Any -> Any
forall a b. a -> b
coe
         ((T_TotalPreorder_204
 -> T_MinOperator_84 -> Any -> Any -> Any -> Any -> Any)
-> Any -> Any -> Any
forall a b. a -> b
coe
            T_TotalPreorder_204
-> T_MinOperator_84 -> Any -> Any -> Any -> Any -> Any
MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_x'8804'y'8851'z'8658'x'8804'z_2020
            ((T_TotalPreorder_204 -> T_TotalPreorder_204) -> Any -> Any
forall a b. a -> b
coe
               T_TotalPreorder_204 -> T_TotalPreorder_204
MAlonzo.Code.Relation.Binary.Construct.Converse.du_totalPreorder_718
               (T_TotalPreorder_204 -> Any
forall a b. a -> b
coe T_TotalPreorder_204
v0))
            ((T_MaxOperator_114 -> T_MinOperator_84) -> Any -> Any
forall a b. a -> b
coe
               T_MaxOperator_114 -> T_MinOperator_84
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.du_MaxOp'8658'MinOp_160
               (T_MaxOperator_114 -> Any
forall a b. a -> b
coe T_MaxOperator_114
v1))))
-- Data.Integer.Properties.⊓-⊔-properties.⊓-absorbs-⊔
d_'8851''45'absorbs'45''8852'_5564 ::
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8851''45'absorbs'45''8852'_5564 :: Integer -> Integer -> T__'8801'__12
d_'8851''45'absorbs'45''8852'_5564 = Integer -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.⊓-⊔-properties.⊓-assoc
d_'8851''45'assoc_5566 ::
  Integer ->
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8851''45'assoc_5566 :: Integer -> Integer -> Integer -> T__'8801'__12
d_'8851''45'assoc_5566 = Integer -> Integer -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.⊓-⊔-properties.⊓-band
d_'8851''45'band_5568 :: MAlonzo.Code.Algebra.Bundles.T_Band_266
d_'8851''45'band_5568 :: T_Band_266
d_'8851''45'band_5568
  = let v0 :: T_TotalPreorder_204
v0 = T_TotalPreorder_204
d_'8804''45'totalPreorder_1668 in
    Any -> T_Band_266
forall a b. a -> b
coe
      (let v1 :: T_MinOperator_84
v1 = T_MinOperator_84
d_'8851''45'operator_5516 in
       Any -> Any
forall a b. a -> b
coe
         ((T_TotalPreorder_204 -> T_MinOperator_84 -> T_Band_266)
-> Any -> Any -> Any
forall a b. a -> b
coe
            T_TotalPreorder_204 -> T_MinOperator_84 -> T_Band_266
MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_'8851''45'band_1872
            (T_TotalPreorder_204 -> Any
forall a b. a -> b
coe T_TotalPreorder_204
v0) (T_MinOperator_84 -> Any
forall a b. a -> b
coe T_MinOperator_84
v1)))
-- Data.Integer.Properties.⊓-⊔-properties.⊓-comm
d_'8851''45'comm_5570 ::
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8851''45'comm_5570 :: Integer -> Integer -> T__'8801'__12
d_'8851''45'comm_5570 = Integer -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.⊓-⊔-properties.⊓-commutativeSemigroup
d_'8851''45'commutativeSemigroup_5572 ::
  MAlonzo.Code.Algebra.Bundles.T_CommutativeSemigroup_332
d_'8851''45'commutativeSemigroup_5572 :: T_CommutativeSemigroup_332
d_'8851''45'commutativeSemigroup_5572
  = let v0 :: T_TotalPreorder_204
v0 = T_TotalPreorder_204
d_'8804''45'totalPreorder_1668 in
    Any -> T_CommutativeSemigroup_332
forall a b. a -> b
coe
      (let v1 :: T_MinOperator_84
v1 = T_MinOperator_84
d_'8851''45'operator_5516 in
       Any -> Any
forall a b. a -> b
coe
         ((T_TotalPreorder_204
 -> T_MinOperator_84 -> T_CommutativeSemigroup_332)
-> Any -> Any -> Any
forall a b. a -> b
coe
            T_TotalPreorder_204
-> T_MinOperator_84 -> T_CommutativeSemigroup_332
MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_'8851''45'commutativeSemigroup_1874
            (T_TotalPreorder_204 -> Any
forall a b. a -> b
coe T_TotalPreorder_204
v0) (T_MinOperator_84 -> Any
forall a b. a -> b
coe T_MinOperator_84
v1)))
-- Data.Integer.Properties.⊓-⊔-properties.⊓-distrib-⊔
d_'8851''45'distrib'45''8852'_5580 ::
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'8851''45'distrib'45''8852'_5580 :: T_Σ_14
d_'8851''45'distrib'45''8852'_5580
  = (T_TotalPreorder_204
 -> T_MinOperator_84 -> T_MaxOperator_114 -> T_Σ_14)
-> Any -> Any -> Any -> T_Σ_14
forall a b. a -> b
coe
      T_TotalPreorder_204
-> T_MinOperator_84 -> T_MaxOperator_114 -> T_Σ_14
MAlonzo.Code.Algebra.Construct.NaturalChoice.MinMaxOp.du_'8851''45'distrib'45''8852'_1876
      (T_TotalPreorder_204 -> Any
forall a b. a -> b
coe T_TotalPreorder_204
d_'8804''45'totalPreorder_1668)
      (T_MinOperator_84 -> Any
forall a b. a -> b
coe T_MinOperator_84
d_'8851''45'operator_5516) (T_MaxOperator_114 -> Any
forall a b. a -> b
coe T_MaxOperator_114
d_'8852''45'operator_5518)
-- Data.Integer.Properties.⊓-⊔-properties.⊓-distribʳ-⊔
d_'8851''45'distrib'691''45''8852'_5582 ::
  Integer ->
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8851''45'distrib'691''45''8852'_5582 :: Integer -> Integer -> Integer -> T__'8801'__12
d_'8851''45'distrib'691''45''8852'_5582 = Integer -> Integer -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.⊓-⊔-properties.⊓-distribˡ-⊔
d_'8851''45'distrib'737''45''8852'_5584 ::
  Integer ->
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8851''45'distrib'737''45''8852'_5584 :: Integer -> Integer -> Integer -> T__'8801'__12
d_'8851''45'distrib'737''45''8852'_5584 = Integer -> Integer -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.⊓-⊔-properties.⊓-glb
d_'8851''45'glb_5586 ::
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26 ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26 ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26
d_'8851''45'glb_5586 :: Integer
-> Integer
-> Integer
-> T__'8804'__26
-> T__'8804'__26
-> T__'8804'__26
d_'8851''45'glb_5586
  = let v0 :: T_TotalPreorder_204
v0 = T_TotalPreorder_204
d_'8804''45'totalPreorder_1668 in
    Any
-> Integer
-> Integer
-> Integer
-> T__'8804'__26
-> T__'8804'__26
-> T__'8804'__26
forall a b. a -> b
coe
      (let v1 :: T_MinOperator_84
v1 = T_MinOperator_84
d_'8851''45'operator_5516 in
       Any -> Any
forall a b. a -> b
coe
         ((T_TotalPreorder_204
 -> T_MinOperator_84 -> Any -> Any -> Any -> Any -> Any -> Any)
-> Any -> Any -> Any
forall a b. a -> b
coe
            T_TotalPreorder_204
-> T_MinOperator_84 -> Any -> Any -> Any -> Any -> Any -> Any
MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_'8851''45'glb_2100
            (T_TotalPreorder_204 -> Any
forall a b. a -> b
coe T_TotalPreorder_204
v0) (T_MinOperator_84 -> Any
forall a b. a -> b
coe T_MinOperator_84
v1)))
-- Data.Integer.Properties.⊓-⊔-properties.⊓-idem
d_'8851''45'idem_5588 ::
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8851''45'idem_5588 :: Integer -> T__'8801'__12
d_'8851''45'idem_5588 = Integer -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.⊓-⊔-properties.⊓-isBand
d_'8851''45'isBand_5596 ::
  MAlonzo.Code.Algebra.Structures.T_IsBand_230
d_'8851''45'isBand_5596 :: T_IsBand_230
d_'8851''45'isBand_5596
  = let v0 :: T_TotalPreorder_204
v0 = T_TotalPreorder_204
d_'8804''45'totalPreorder_1668 in
    Any -> T_IsBand_230
forall a b. a -> b
coe
      (let v1 :: T_MinOperator_84
v1 = T_MinOperator_84
d_'8851''45'operator_5516 in
       Any -> Any
forall a b. a -> b
coe
         ((T_TotalPreorder_204 -> T_MinOperator_84 -> T_IsBand_230)
-> Any -> Any -> Any
forall a b. a -> b
coe
            T_TotalPreorder_204 -> T_MinOperator_84 -> T_IsBand_230
MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_'8851''45'isBand_1852
            (T_TotalPreorder_204 -> Any
forall a b. a -> b
coe T_TotalPreorder_204
v0) (T_MinOperator_84 -> Any
forall a b. a -> b
coe T_MinOperator_84
v1)))
-- Data.Integer.Properties.⊓-⊔-properties.⊓-isCommutativeSemigroup
d_'8851''45'isCommutativeSemigroup_5598 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_270
d_'8851''45'isCommutativeSemigroup_5598 :: T_IsCommutativeSemigroup_270
d_'8851''45'isCommutativeSemigroup_5598
  = let v0 :: T_TotalPreorder_204
v0 = T_TotalPreorder_204
d_'8804''45'totalPreorder_1668 in
    Any -> T_IsCommutativeSemigroup_270
forall a b. a -> b
coe
      (let v1 :: T_MinOperator_84
v1 = T_MinOperator_84
d_'8851''45'operator_5516 in
       Any -> Any
forall a b. a -> b
coe
         ((T_TotalPreorder_204
 -> T_MinOperator_84 -> T_IsCommutativeSemigroup_270)
-> Any -> Any -> Any
forall a b. a -> b
coe
            T_TotalPreorder_204
-> T_MinOperator_84 -> T_IsCommutativeSemigroup_270
MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_'8851''45'isCommutativeSemigroup_1854
            (T_TotalPreorder_204 -> Any
forall a b. a -> b
coe T_TotalPreorder_204
v0) (T_MinOperator_84 -> Any
forall a b. a -> b
coe T_MinOperator_84
v1)))
-- Data.Integer.Properties.⊓-⊔-properties.⊓-isMagma
d_'8851''45'isMagma_5600 ::
  MAlonzo.Code.Algebra.Structures.T_IsMagma_86
d_'8851''45'isMagma_5600 :: T_IsMagma_86
d_'8851''45'isMagma_5600
  = let v0 :: T_TotalPreorder_204
v0 = T_TotalPreorder_204
d_'8804''45'totalPreorder_1668 in
    Any -> T_IsMagma_86
forall a b. a -> b
coe
      (let v1 :: T_MinOperator_84
v1 = T_MinOperator_84
d_'8851''45'operator_5516 in
       Any -> Any
forall a b. a -> b
coe
         ((T_TotalPreorder_204 -> T_MinOperator_84 -> T_IsMagma_86)
-> Any -> Any -> Any
forall a b. a -> b
coe
            T_TotalPreorder_204 -> T_MinOperator_84 -> T_IsMagma_86
MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_'8851''45'isMagma_1848
            (T_TotalPreorder_204 -> Any
forall a b. a -> b
coe T_TotalPreorder_204
v0) (T_MinOperator_84 -> Any
forall a b. a -> b
coe T_MinOperator_84
v1)))
-- Data.Integer.Properties.⊓-⊔-properties.⊓-isSelectiveMagma
d_'8851''45'isSelectiveMagma_5604 ::
  MAlonzo.Code.Algebra.Structures.T_IsSelectiveMagma_158
d_'8851''45'isSelectiveMagma_5604 :: T_IsSelectiveMagma_158
d_'8851''45'isSelectiveMagma_5604
  = let v0 :: T_TotalPreorder_204
v0 = T_TotalPreorder_204
d_'8804''45'totalPreorder_1668 in
    Any -> T_IsSelectiveMagma_158
forall a b. a -> b
coe
      (let v1 :: T_MinOperator_84
v1 = T_MinOperator_84
d_'8851''45'operator_5516 in
       Any -> Any
forall a b. a -> b
coe
         ((T_TotalPreorder_204 -> T_MinOperator_84 -> T_IsSelectiveMagma_158)
-> Any -> Any -> Any
forall a b. a -> b
coe
            T_TotalPreorder_204 -> T_MinOperator_84 -> T_IsSelectiveMagma_158
MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_'8851''45'isSelectiveMagma_1858
            (T_TotalPreorder_204 -> Any
forall a b. a -> b
coe T_TotalPreorder_204
v0) (T_MinOperator_84 -> Any
forall a b. a -> b
coe T_MinOperator_84
v1)))
-- Data.Integer.Properties.⊓-⊔-properties.⊓-isSemigroup
d_'8851''45'isSemigroup_5606 ::
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_194
d_'8851''45'isSemigroup_5606 :: T_IsSemigroup_194
d_'8851''45'isSemigroup_5606
  = let v0 :: T_TotalPreorder_204
v0 = T_TotalPreorder_204
d_'8804''45'totalPreorder_1668 in
    Any -> T_IsSemigroup_194
forall a b. a -> b
coe
      (let v1 :: T_MinOperator_84
v1 = T_MinOperator_84
d_'8851''45'operator_5516 in
       Any -> Any
forall a b. a -> b
coe
         ((T_TotalPreorder_204 -> T_MinOperator_84 -> T_IsSemigroup_194)
-> Any -> Any -> Any
forall a b. a -> b
coe
            T_TotalPreorder_204 -> T_MinOperator_84 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_'8851''45'isSemigroup_1850
            (T_TotalPreorder_204 -> Any
forall a b. a -> b
coe T_TotalPreorder_204
v0) (T_MinOperator_84 -> Any
forall a b. a -> b
coe T_MinOperator_84
v1)))
-- Data.Integer.Properties.⊓-⊔-properties.⊓-isSemilattice
d_'8851''45'isSemilattice_5608 ::
  MAlonzo.Code.Algebra.Structures.T_IsSemilattice_312
d_'8851''45'isSemilattice_5608 :: T_IsSemilattice_312
d_'8851''45'isSemilattice_5608
  = let v0 :: T_TotalPreorder_204
v0 = T_TotalPreorder_204
d_'8804''45'totalPreorder_1668 in
    Any -> T_IsSemilattice_312
forall a b. a -> b
coe
      (let v1 :: T_MinOperator_84
v1 = T_MinOperator_84
d_'8851''45'operator_5516 in
       Any -> Any
forall a b. a -> b
coe
         ((T_TotalPreorder_204 -> T_MinOperator_84 -> T_IsSemilattice_312)
-> Any -> Any -> Any
forall a b. a -> b
coe
            T_TotalPreorder_204 -> T_MinOperator_84 -> T_IsSemilattice_312
MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_'8851''45'isSemilattice_1856
            (T_TotalPreorder_204 -> Any
forall a b. a -> b
coe T_TotalPreorder_204
v0) (T_MinOperator_84 -> Any
forall a b. a -> b
coe T_MinOperator_84
v1)))
-- Data.Integer.Properties.⊓-⊔-properties.⊓-magma
d_'8851''45'magma_5610 :: MAlonzo.Code.Algebra.Bundles.T_Magma_36
d_'8851''45'magma_5610 :: T_Magma_36
d_'8851''45'magma_5610
  = let v0 :: T_TotalPreorder_204
v0 = T_TotalPreorder_204
d_'8804''45'totalPreorder_1668 in
    Any -> T_Magma_36
forall a b. a -> b
coe
      (let v1 :: T_MinOperator_84
v1 = T_MinOperator_84
d_'8851''45'operator_5516 in
       Any -> Any
forall a b. a -> b
coe
         ((T_TotalPreorder_204 -> T_MinOperator_84 -> T_Magma_36)
-> Any -> Any -> Any
forall a b. a -> b
coe
            T_TotalPreorder_204 -> T_MinOperator_84 -> T_Magma_36
MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_'8851''45'magma_1868
            (T_TotalPreorder_204 -> Any
forall a b. a -> b
coe T_TotalPreorder_204
v0) (T_MinOperator_84 -> Any
forall a b. a -> b
coe T_MinOperator_84
v1)))
-- Data.Integer.Properties.⊓-⊔-properties.⊓-mono-≤
d_'8851''45'mono'45''8804'_5612 ::
  Integer ->
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26 ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26 ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26
d_'8851''45'mono'45''8804'_5612 :: Integer
-> Integer
-> Integer
-> Integer
-> T__'8804'__26
-> T__'8804'__26
-> T__'8804'__26
d_'8851''45'mono'45''8804'_5612
  = let v0 :: T_TotalPreorder_204
v0 = T_TotalPreorder_204
d_'8804''45'totalPreorder_1668 in
    Any
-> Integer
-> Integer
-> Integer
-> Integer
-> T__'8804'__26
-> T__'8804'__26
-> T__'8804'__26
forall a b. a -> b
coe
      (let v1 :: T_MinOperator_84
v1 = T_MinOperator_84
d_'8851''45'operator_5516 in
       Any -> Any
forall a b. a -> b
coe
         ((T_TotalPreorder_204
 -> T_MinOperator_84
 -> Any
 -> Any
 -> Any
 -> Any
 -> Any
 -> Any
 -> Any)
-> Any -> Any -> Any
forall a b. a -> b
coe
            T_TotalPreorder_204
-> T_MinOperator_84
-> Any
-> Any
-> Any
-> Any
-> Any
-> Any
-> Any
MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_'8851''45'mono'45''8804'_2028
            (T_TotalPreorder_204 -> Any
forall a b. a -> b
coe T_TotalPreorder_204
v0) (T_MinOperator_84 -> Any
forall a b. a -> b
coe T_MinOperator_84
v1)))
-- Data.Integer.Properties.⊓-⊔-properties.⊓-monoʳ-≤
d_'8851''45'mono'691''45''8804'_5616 ::
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26 ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26
d_'8851''45'mono'691''45''8804'_5616 :: Integer -> Integer -> Integer -> T__'8804'__26 -> T__'8804'__26
d_'8851''45'mono'691''45''8804'_5616
  = let v0 :: T_TotalPreorder_204
v0 = T_TotalPreorder_204
d_'8804''45'totalPreorder_1668 in
    Any
-> Integer -> Integer -> Integer -> T__'8804'__26 -> T__'8804'__26
forall a b. a -> b
coe
      (let v1 :: T_MinOperator_84
v1 = T_MinOperator_84
d_'8851''45'operator_5516 in
       Any -> Any
forall a b. a -> b
coe
         ((T_TotalPreorder_204
 -> T_MinOperator_84 -> Any -> Any -> Any -> Any -> Any)
-> Any -> Any -> Any
forall a b. a -> b
coe
            T_TotalPreorder_204
-> T_MinOperator_84 -> Any -> Any -> Any -> Any -> Any
MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_'8851''45'mono'691''45''8804'_2088
            (T_TotalPreorder_204 -> Any
forall a b. a -> b
coe T_TotalPreorder_204
v0) (T_MinOperator_84 -> Any
forall a b. a -> b
coe T_MinOperator_84
v1)))
-- Data.Integer.Properties.⊓-⊔-properties.⊓-monoˡ-≤
d_'8851''45'mono'737''45''8804'_5618 ::
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26 ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26
d_'8851''45'mono'737''45''8804'_5618 :: Integer -> Integer -> Integer -> T__'8804'__26 -> T__'8804'__26
d_'8851''45'mono'737''45''8804'_5618
  = let v0 :: T_TotalPreorder_204
v0 = T_TotalPreorder_204
d_'8804''45'totalPreorder_1668 in
    Any
-> Integer -> Integer -> Integer -> T__'8804'__26 -> T__'8804'__26
forall a b. a -> b
coe
      (let v1 :: T_MinOperator_84
v1 = T_MinOperator_84
d_'8851''45'operator_5516 in
       Any -> Any
forall a b. a -> b
coe
         ((T_TotalPreorder_204
 -> T_MinOperator_84 -> Any -> Any -> Any -> Any -> Any)
-> Any -> Any -> Any
forall a b. a -> b
coe
            T_TotalPreorder_204
-> T_MinOperator_84 -> Any -> Any -> Any -> Any -> Any
MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_'8851''45'mono'737''45''8804'_2078
            (T_TotalPreorder_204 -> Any
forall a b. a -> b
coe T_TotalPreorder_204
v0) (T_MinOperator_84 -> Any
forall a b. a -> b
coe T_MinOperator_84
v1)))
-- Data.Integer.Properties.⊓-⊔-properties.⊓-sel
d_'8851''45'sel_5622 ::
  Integer -> Integer -> MAlonzo.Code.Data.Sum.Base.T__'8846'__30
d_'8851''45'sel_5622 :: Integer -> Integer -> T__'8846'__30
d_'8851''45'sel_5622
  = let v0 :: T_TotalPreorder_204
v0 = T_TotalPreorder_204
d_'8804''45'totalPreorder_1668 in
    Any -> Integer -> Integer -> T__'8846'__30
forall a b. a -> b
coe
      (let v1 :: T_MinOperator_84
v1 = T_MinOperator_84
d_'8851''45'operator_5516 in
       Any -> Any
forall a b. a -> b
coe
         ((T_TotalPreorder_204
 -> T_MinOperator_84 -> Any -> Any -> T__'8846'__30)
-> Any -> Any -> Any
forall a b. a -> b
coe
            T_TotalPreorder_204
-> T_MinOperator_84 -> Any -> Any -> T__'8846'__30
MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_'8851''45'sel_1806
            (T_TotalPreorder_204 -> Any
forall a b. a -> b
coe T_TotalPreorder_204
v0) (T_MinOperator_84 -> Any
forall a b. a -> b
coe T_MinOperator_84
v1)))
-- Data.Integer.Properties.⊓-⊔-properties.⊓-selectiveMagma
d_'8851''45'selectiveMagma_5624 ::
  MAlonzo.Code.Algebra.Bundles.T_SelectiveMagma_90
d_'8851''45'selectiveMagma_5624 :: T_SelectiveMagma_90
d_'8851''45'selectiveMagma_5624
  = let v0 :: T_TotalPreorder_204
v0 = T_TotalPreorder_204
d_'8804''45'totalPreorder_1668 in
    Any -> T_SelectiveMagma_90
forall a b. a -> b
coe
      (let v1 :: T_MinOperator_84
v1 = T_MinOperator_84
d_'8851''45'operator_5516 in
       Any -> Any
forall a b. a -> b
coe
         ((T_TotalPreorder_204 -> T_MinOperator_84 -> T_SelectiveMagma_90)
-> Any -> Any -> Any
forall a b. a -> b
coe
            T_TotalPreorder_204 -> T_MinOperator_84 -> T_SelectiveMagma_90
MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_'8851''45'selectiveMagma_1878
            (T_TotalPreorder_204 -> Any
forall a b. a -> b
coe T_TotalPreorder_204
v0) (T_MinOperator_84 -> Any
forall a b. a -> b
coe T_MinOperator_84
v1)))
-- Data.Integer.Properties.⊓-⊔-properties.⊓-semigroup
d_'8851''45'semigroup_5626 ::
  MAlonzo.Code.Algebra.Bundles.T_Semigroup_206
d_'8851''45'semigroup_5626 :: T_Semigroup_206
d_'8851''45'semigroup_5626
  = let v0 :: T_TotalPreorder_204
v0 = T_TotalPreorder_204
d_'8804''45'totalPreorder_1668 in
    Any -> T_Semigroup_206
forall a b. a -> b
coe
      (let v1 :: T_MinOperator_84
v1 = T_MinOperator_84
d_'8851''45'operator_5516 in
       Any -> Any
forall a b. a -> b
coe
         ((T_TotalPreorder_204 -> T_MinOperator_84 -> T_Semigroup_206)
-> Any -> Any -> Any
forall a b. a -> b
coe
            T_TotalPreorder_204 -> T_MinOperator_84 -> T_Semigroup_206
MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_'8851''45'semigroup_1870
            (T_TotalPreorder_204 -> Any
forall a b. a -> b
coe T_TotalPreorder_204
v0) (T_MinOperator_84 -> Any
forall a b. a -> b
coe T_MinOperator_84
v1)))
-- Data.Integer.Properties.⊓-⊔-properties.⊓-semilattice
d_'8851''45'semilattice_5628 ::
  MAlonzo.Code.Algebra.Bundles.T_Semilattice_402
d_'8851''45'semilattice_5628 :: T_Semilattice_402
d_'8851''45'semilattice_5628
  = let v0 :: T_TotalPreorder_204
v0 = T_TotalPreorder_204
d_'8804''45'totalPreorder_1668 in
    Any -> T_Semilattice_402
forall a b. a -> b
coe
      (let v1 :: T_MinOperator_84
v1 = T_MinOperator_84
d_'8851''45'operator_5516 in
       Any -> Any
forall a b. a -> b
coe
         ((T_TotalPreorder_204 -> T_MinOperator_84 -> T_Semilattice_402)
-> Any -> Any -> Any
forall a b. a -> b
coe
            T_TotalPreorder_204 -> T_MinOperator_84 -> T_Semilattice_402
MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_'8851''45'semilattice_1876
            (T_TotalPreorder_204 -> Any
forall a b. a -> b
coe T_TotalPreorder_204
v0) (T_MinOperator_84 -> Any
forall a b. a -> b
coe T_MinOperator_84
v1)))
-- Data.Integer.Properties.⊓-⊔-properties.⊓-triangulate
d_'8851''45'triangulate_5630 ::
  Integer ->
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8851''45'triangulate_5630 :: Integer -> Integer -> Integer -> T__'8801'__12
d_'8851''45'triangulate_5630 = Integer -> Integer -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.⊓-⊔-properties.⊓-⊔-absorptive
d_'8851''45''8852''45'absorptive_5638 ::
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'8851''45''8852''45'absorptive_5638 :: T_Σ_14
d_'8851''45''8852''45'absorptive_5638
  = (T_TotalPreorder_204
 -> T_MinOperator_84 -> T_MaxOperator_114 -> T_Σ_14)
-> Any -> Any -> Any -> T_Σ_14
forall a b. a -> b
coe
      T_TotalPreorder_204
-> T_MinOperator_84 -> T_MaxOperator_114 -> T_Σ_14
MAlonzo.Code.Algebra.Construct.NaturalChoice.MinMaxOp.du_'8851''45''8852''45'absorptive_1956
      (T_TotalPreorder_204 -> Any
forall a b. a -> b
coe T_TotalPreorder_204
d_'8804''45'totalPreorder_1668)
      (T_MinOperator_84 -> Any
forall a b. a -> b
coe T_MinOperator_84
d_'8851''45'operator_5516) (T_MaxOperator_114 -> Any
forall a b. a -> b
coe T_MaxOperator_114
d_'8852''45'operator_5518)
-- Data.Integer.Properties.⊓-⊔-properties.⊓-⊔-distributiveLattice
d_'8851''45''8852''45'distributiveLattice_5640 ::
  MAlonzo.Code.Algebra.Bundles.T_DistributiveLattice_1228
d_'8851''45''8852''45'distributiveLattice_5640 :: T_DistributiveLattice_1228
d_'8851''45''8852''45'distributiveLattice_5640
  = (T_TotalPreorder_204
 -> T_MinOperator_84
 -> T_MaxOperator_114
 -> T_DistributiveLattice_1228)
-> Any -> Any -> Any -> T_DistributiveLattice_1228
forall a b. a -> b
coe
      T_TotalPreorder_204
-> T_MinOperator_84
-> T_MaxOperator_114
-> T_DistributiveLattice_1228
MAlonzo.Code.Algebra.Construct.NaturalChoice.MinMaxOp.du_'8851''45''8852''45'distributiveLattice_1972
      (T_TotalPreorder_204 -> Any
forall a b. a -> b
coe T_TotalPreorder_204
d_'8804''45'totalPreorder_1668)
      (T_MinOperator_84 -> Any
forall a b. a -> b
coe T_MinOperator_84
d_'8851''45'operator_5516) (T_MaxOperator_114 -> Any
forall a b. a -> b
coe T_MaxOperator_114
d_'8852''45'operator_5518)
-- Data.Integer.Properties.⊓-⊔-properties.⊓-⊔-isDistributiveLattice
d_'8851''45''8852''45'isDistributiveLattice_5642 ::
  MAlonzo.Code.Algebra.Structures.T_IsDistributiveLattice_814
d_'8851''45''8852''45'isDistributiveLattice_5642 :: T_IsDistributiveLattice_814
d_'8851''45''8852''45'isDistributiveLattice_5642
  = (T_TotalPreorder_204
 -> T_MinOperator_84
 -> T_MaxOperator_114
 -> T_IsDistributiveLattice_814)
-> Any -> Any -> Any -> T_IsDistributiveLattice_814
forall a b. a -> b
coe
      T_TotalPreorder_204
-> T_MinOperator_84
-> T_MaxOperator_114
-> T_IsDistributiveLattice_814
MAlonzo.Code.Algebra.Construct.NaturalChoice.MinMaxOp.du_'8851''45''8852''45'isDistributiveLattice_1962
      (T_TotalPreorder_204 -> Any
forall a b. a -> b
coe T_TotalPreorder_204
d_'8804''45'totalPreorder_1668)
      (T_MinOperator_84 -> Any
forall a b. a -> b
coe T_MinOperator_84
d_'8851''45'operator_5516) (T_MaxOperator_114 -> Any
forall a b. a -> b
coe T_MaxOperator_114
d_'8852''45'operator_5518)
-- Data.Integer.Properties.⊓-⊔-properties.⊓-⊔-isLattice
d_'8851''45''8852''45'isLattice_5644 ::
  MAlonzo.Code.Algebra.Structures.T_IsLattice_740
d_'8851''45''8852''45'isLattice_5644 :: T_IsLattice_740
d_'8851''45''8852''45'isLattice_5644
  = (T_TotalPreorder_204
 -> T_MinOperator_84 -> T_MaxOperator_114 -> T_IsLattice_740)
-> Any -> Any -> Any -> T_IsLattice_740
forall a b. a -> b
coe
      T_TotalPreorder_204
-> T_MinOperator_84 -> T_MaxOperator_114 -> T_IsLattice_740
MAlonzo.Code.Algebra.Construct.NaturalChoice.MinMaxOp.du_'8851''45''8852''45'isLattice_1960
      (T_TotalPreorder_204 -> Any
forall a b. a -> b
coe T_TotalPreorder_204
d_'8804''45'totalPreorder_1668)
      (T_MinOperator_84 -> Any
forall a b. a -> b
coe T_MinOperator_84
d_'8851''45'operator_5516) (T_MaxOperator_114 -> Any
forall a b. a -> b
coe T_MaxOperator_114
d_'8852''45'operator_5518)
-- Data.Integer.Properties.⊓-⊔-properties.⊓-⊔-lattice
d_'8851''45''8852''45'lattice_5646 ::
  MAlonzo.Code.Algebra.Bundles.T_Lattice_1144
d_'8851''45''8852''45'lattice_5646 :: T_Lattice_1144
d_'8851''45''8852''45'lattice_5646
  = (T_TotalPreorder_204
 -> T_MinOperator_84 -> T_MaxOperator_114 -> T_Lattice_1144)
-> Any -> Any -> Any -> T_Lattice_1144
forall a b. a -> b
coe
      T_TotalPreorder_204
-> T_MinOperator_84 -> T_MaxOperator_114 -> T_Lattice_1144
MAlonzo.Code.Algebra.Construct.NaturalChoice.MinMaxOp.du_'8851''45''8852''45'lattice_1968
      (T_TotalPreorder_204 -> Any
forall a b. a -> b
coe T_TotalPreorder_204
d_'8804''45'totalPreorder_1668)
      (T_MinOperator_84 -> Any
forall a b. a -> b
coe T_MinOperator_84
d_'8851''45'operator_5516) (T_MaxOperator_114 -> Any
forall a b. a -> b
coe T_MaxOperator_114
d_'8852''45'operator_5518)
-- Data.Integer.Properties.⊓-⊔-properties.⊔-absorbs-⊓
d_'8852''45'absorbs'45''8851'_5648 ::
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8852''45'absorbs'45''8851'_5648 :: Integer -> Integer -> T__'8801'__12
d_'8852''45'absorbs'45''8851'_5648 = Integer -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.⊓-⊔-properties.⊓-assoc
d_'8851''45'assoc_5650 ::
  Integer ->
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8851''45'assoc_5650 :: Integer -> Integer -> Integer -> T__'8801'__12
d_'8851''45'assoc_5650 = Integer -> Integer -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.⊓-⊔-properties.⊓-band
d_'8851''45'band_5652 :: MAlonzo.Code.Algebra.Bundles.T_Band_266
d_'8851''45'band_5652 :: T_Band_266
d_'8851''45'band_5652
  = let v0 :: T_TotalPreorder_204
v0 = T_TotalPreorder_204
d_'8804''45'totalPreorder_1668 in
    Any -> T_Band_266
forall a b. a -> b
coe
      (let v1 :: T_MaxOperator_114
v1 = T_MaxOperator_114
d_'8852''45'operator_5518 in
       Any -> Any
forall a b. a -> b
coe
         ((T_TotalPreorder_204 -> T_MinOperator_84 -> T_Band_266)
-> Any -> Any -> Any
forall a b. a -> b
coe
            T_TotalPreorder_204 -> T_MinOperator_84 -> T_Band_266
MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_'8851''45'band_1872
            ((T_TotalPreorder_204 -> T_TotalPreorder_204) -> Any -> Any
forall a b. a -> b
coe
               T_TotalPreorder_204 -> T_TotalPreorder_204
MAlonzo.Code.Relation.Binary.Construct.Converse.du_totalPreorder_718
               (T_TotalPreorder_204 -> Any
forall a b. a -> b
coe T_TotalPreorder_204
v0))
            ((T_MaxOperator_114 -> T_MinOperator_84) -> Any -> Any
forall a b. a -> b
coe
               T_MaxOperator_114 -> T_MinOperator_84
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.du_MaxOp'8658'MinOp_160
               (T_MaxOperator_114 -> Any
forall a b. a -> b
coe T_MaxOperator_114
v1))))
-- Data.Integer.Properties.⊓-⊔-properties.⊓-comm
d_'8851''45'comm_5654 ::
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8851''45'comm_5654 :: Integer -> Integer -> T__'8801'__12
d_'8851''45'comm_5654 = Integer -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.⊓-⊔-properties.⊓-commutativeSemigroup
d_'8851''45'commutativeSemigroup_5656 ::
  MAlonzo.Code.Algebra.Bundles.T_CommutativeSemigroup_332
d_'8851''45'commutativeSemigroup_5656 :: T_CommutativeSemigroup_332
d_'8851''45'commutativeSemigroup_5656
  = let v0 :: T_TotalPreorder_204
v0 = T_TotalPreorder_204
d_'8804''45'totalPreorder_1668 in
    Any -> T_CommutativeSemigroup_332
forall a b. a -> b
coe
      (let v1 :: T_MaxOperator_114
v1 = T_MaxOperator_114
d_'8852''45'operator_5518 in
       Any -> Any
forall a b. a -> b
coe
         ((T_TotalPreorder_204
 -> T_MinOperator_84 -> T_CommutativeSemigroup_332)
-> Any -> Any -> Any
forall a b. a -> b
coe
            T_TotalPreorder_204
-> T_MinOperator_84 -> T_CommutativeSemigroup_332
MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_'8851''45'commutativeSemigroup_1874
            ((T_TotalPreorder_204 -> T_TotalPreorder_204) -> Any -> Any
forall a b. a -> b
coe
               T_TotalPreorder_204 -> T_TotalPreorder_204
MAlonzo.Code.Relation.Binary.Construct.Converse.du_totalPreorder_718
               (T_TotalPreorder_204 -> Any
forall a b. a -> b
coe T_TotalPreorder_204
v0))
            ((T_MaxOperator_114 -> T_MinOperator_84) -> Any -> Any
forall a b. a -> b
coe
               T_MaxOperator_114 -> T_MinOperator_84
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.du_MaxOp'8658'MinOp_160
               (T_MaxOperator_114 -> Any
forall a b. a -> b
coe T_MaxOperator_114
v1))))
-- Data.Integer.Properties.⊓-⊔-properties.⊔-distrib-⊓
d_'8852''45'distrib'45''8851'_5664 ::
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'8852''45'distrib'45''8851'_5664 :: T_Σ_14
d_'8852''45'distrib'45''8851'_5664
  = (T_TotalPreorder_204
 -> T_MinOperator_84 -> T_MaxOperator_114 -> T_Σ_14)
-> Any -> Any -> Any -> T_Σ_14
forall a b. a -> b
coe
      T_TotalPreorder_204
-> T_MinOperator_84 -> T_MaxOperator_114 -> T_Σ_14
MAlonzo.Code.Algebra.Construct.NaturalChoice.MinMaxOp.du_'8852''45'distrib'45''8851'_1908
      (T_TotalPreorder_204 -> Any
forall a b. a -> b
coe T_TotalPreorder_204
d_'8804''45'totalPreorder_1668)
      (T_MinOperator_84 -> Any
forall a b. a -> b
coe T_MinOperator_84
d_'8851''45'operator_5516) (T_MaxOperator_114 -> Any
forall a b. a -> b
coe T_MaxOperator_114
d_'8852''45'operator_5518)
-- Data.Integer.Properties.⊓-⊔-properties.⊔-distribʳ-⊓
d_'8852''45'distrib'691''45''8851'_5666 ::
  Integer ->
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8852''45'distrib'691''45''8851'_5666 :: Integer -> Integer -> Integer -> T__'8801'__12
d_'8852''45'distrib'691''45''8851'_5666 = Integer -> Integer -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.⊓-⊔-properties.⊔-distribˡ-⊓
d_'8852''45'distrib'737''45''8851'_5668 ::
  Integer ->
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8852''45'distrib'737''45''8851'_5668 :: Integer -> Integer -> Integer -> T__'8801'__12
d_'8852''45'distrib'737''45''8851'_5668 = Integer -> Integer -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.⊓-⊔-properties.⊓-idem
d_'8851''45'idem_5670 ::
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8851''45'idem_5670 :: Integer -> T__'8801'__12
d_'8851''45'idem_5670 = Integer -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.⊓-⊔-properties.⊓-isBand
d_'8851''45'isBand_5678 ::
  MAlonzo.Code.Algebra.Structures.T_IsBand_230
d_'8851''45'isBand_5678 :: T_IsBand_230
d_'8851''45'isBand_5678
  = let v0 :: T_TotalPreorder_204
v0 = T_TotalPreorder_204
d_'8804''45'totalPreorder_1668 in
    Any -> T_IsBand_230
forall a b. a -> b
coe
      (let v1 :: T_MaxOperator_114
v1 = T_MaxOperator_114
d_'8852''45'operator_5518 in
       Any -> Any
forall a b. a -> b
coe
         ((T_TotalPreorder_204 -> T_MinOperator_84 -> T_IsBand_230)
-> Any -> Any -> Any
forall a b. a -> b
coe
            T_TotalPreorder_204 -> T_MinOperator_84 -> T_IsBand_230
MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_'8851''45'isBand_1852
            ((T_TotalPreorder_204 -> T_TotalPreorder_204) -> Any -> Any
forall a b. a -> b
coe
               T_TotalPreorder_204 -> T_TotalPreorder_204
MAlonzo.Code.Relation.Binary.Construct.Converse.du_totalPreorder_718
               (T_TotalPreorder_204 -> Any
forall a b. a -> b
coe T_TotalPreorder_204
v0))
            ((T_MaxOperator_114 -> T_MinOperator_84) -> Any -> Any
forall a b. a -> b
coe
               T_MaxOperator_114 -> T_MinOperator_84
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.du_MaxOp'8658'MinOp_160
               (T_MaxOperator_114 -> Any
forall a b. a -> b
coe T_MaxOperator_114
v1))))
-- Data.Integer.Properties.⊓-⊔-properties.⊓-isCommutativeSemigroup
d_'8851''45'isCommutativeSemigroup_5680 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_270
d_'8851''45'isCommutativeSemigroup_5680 :: T_IsCommutativeSemigroup_270
d_'8851''45'isCommutativeSemigroup_5680
  = let v0 :: T_TotalPreorder_204
v0 = T_TotalPreorder_204
d_'8804''45'totalPreorder_1668 in
    Any -> T_IsCommutativeSemigroup_270
forall a b. a -> b
coe
      (let v1 :: T_MaxOperator_114
v1 = T_MaxOperator_114
d_'8852''45'operator_5518 in
       Any -> Any
forall a b. a -> b
coe
         ((T_TotalPreorder_204
 -> T_MinOperator_84 -> T_IsCommutativeSemigroup_270)
-> Any -> Any -> Any
forall a b. a -> b
coe
            T_TotalPreorder_204
-> T_MinOperator_84 -> T_IsCommutativeSemigroup_270
MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_'8851''45'isCommutativeSemigroup_1854
            ((T_TotalPreorder_204 -> T_TotalPreorder_204) -> Any -> Any
forall a b. a -> b
coe
               T_TotalPreorder_204 -> T_TotalPreorder_204
MAlonzo.Code.Relation.Binary.Construct.Converse.du_totalPreorder_718
               (T_TotalPreorder_204 -> Any
forall a b. a -> b
coe T_TotalPreorder_204
v0))
            ((T_MaxOperator_114 -> T_MinOperator_84) -> Any -> Any
forall a b. a -> b
coe
               T_MaxOperator_114 -> T_MinOperator_84
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.du_MaxOp'8658'MinOp_160
               (T_MaxOperator_114 -> Any
forall a b. a -> b
coe T_MaxOperator_114
v1))))
-- Data.Integer.Properties.⊓-⊔-properties.⊓-isMagma
d_'8851''45'isMagma_5682 ::
  MAlonzo.Code.Algebra.Structures.T_IsMagma_86
d_'8851''45'isMagma_5682 :: T_IsMagma_86
d_'8851''45'isMagma_5682
  = let v0 :: T_TotalPreorder_204
v0 = T_TotalPreorder_204
d_'8804''45'totalPreorder_1668 in
    Any -> T_IsMagma_86
forall a b. a -> b
coe
      (let v1 :: T_MaxOperator_114
v1 = T_MaxOperator_114
d_'8852''45'operator_5518 in
       Any -> Any
forall a b. a -> b
coe
         ((T_TotalPreorder_204 -> T_MinOperator_84 -> T_IsMagma_86)
-> Any -> Any -> Any
forall a b. a -> b
coe
            T_TotalPreorder_204 -> T_MinOperator_84 -> T_IsMagma_86
MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_'8851''45'isMagma_1848
            ((T_TotalPreorder_204 -> T_TotalPreorder_204) -> Any -> Any
forall a b. a -> b
coe
               T_TotalPreorder_204 -> T_TotalPreorder_204
MAlonzo.Code.Relation.Binary.Construct.Converse.du_totalPreorder_718
               (T_TotalPreorder_204 -> Any
forall a b. a -> b
coe T_TotalPreorder_204
v0))
            ((T_MaxOperator_114 -> T_MinOperator_84) -> Any -> Any
forall a b. a -> b
coe
               T_MaxOperator_114 -> T_MinOperator_84
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.du_MaxOp'8658'MinOp_160
               (T_MaxOperator_114 -> Any
forall a b. a -> b
coe T_MaxOperator_114
v1))))
-- Data.Integer.Properties.⊓-⊔-properties.⊓-isSelectiveMagma
d_'8851''45'isSelectiveMagma_5686 ::
  MAlonzo.Code.Algebra.Structures.T_IsSelectiveMagma_158
d_'8851''45'isSelectiveMagma_5686 :: T_IsSelectiveMagma_158
d_'8851''45'isSelectiveMagma_5686
  = let v0 :: T_TotalPreorder_204
v0 = T_TotalPreorder_204
d_'8804''45'totalPreorder_1668 in
    Any -> T_IsSelectiveMagma_158
forall a b. a -> b
coe
      (let v1 :: T_MaxOperator_114
v1 = T_MaxOperator_114
d_'8852''45'operator_5518 in
       Any -> Any
forall a b. a -> b
coe
         ((T_TotalPreorder_204 -> T_MinOperator_84 -> T_IsSelectiveMagma_158)
-> Any -> Any -> Any
forall a b. a -> b
coe
            T_TotalPreorder_204 -> T_MinOperator_84 -> T_IsSelectiveMagma_158
MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_'8851''45'isSelectiveMagma_1858
            ((T_TotalPreorder_204 -> T_TotalPreorder_204) -> Any -> Any
forall a b. a -> b
coe
               T_TotalPreorder_204 -> T_TotalPreorder_204
MAlonzo.Code.Relation.Binary.Construct.Converse.du_totalPreorder_718
               (T_TotalPreorder_204 -> Any
forall a b. a -> b
coe T_TotalPreorder_204
v0))
            ((T_MaxOperator_114 -> T_MinOperator_84) -> Any -> Any
forall a b. a -> b
coe
               T_MaxOperator_114 -> T_MinOperator_84
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.du_MaxOp'8658'MinOp_160
               (T_MaxOperator_114 -> Any
forall a b. a -> b
coe T_MaxOperator_114
v1))))
-- Data.Integer.Properties.⊓-⊔-properties.⊓-isSemigroup
d_'8851''45'isSemigroup_5688 ::
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_194
d_'8851''45'isSemigroup_5688 :: T_IsSemigroup_194
d_'8851''45'isSemigroup_5688
  = let v0 :: T_TotalPreorder_204
v0 = T_TotalPreorder_204
d_'8804''45'totalPreorder_1668 in
    Any -> T_IsSemigroup_194
forall a b. a -> b
coe
      (let v1 :: T_MaxOperator_114
v1 = T_MaxOperator_114
d_'8852''45'operator_5518 in
       Any -> Any
forall a b. a -> b
coe
         ((T_TotalPreorder_204 -> T_MinOperator_84 -> T_IsSemigroup_194)
-> Any -> Any -> Any
forall a b. a -> b
coe
            T_TotalPreorder_204 -> T_MinOperator_84 -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_'8851''45'isSemigroup_1850
            ((T_TotalPreorder_204 -> T_TotalPreorder_204) -> Any -> Any
forall a b. a -> b
coe
               T_TotalPreorder_204 -> T_TotalPreorder_204
MAlonzo.Code.Relation.Binary.Construct.Converse.du_totalPreorder_718
               (T_TotalPreorder_204 -> Any
forall a b. a -> b
coe T_TotalPreorder_204
v0))
            ((T_MaxOperator_114 -> T_MinOperator_84) -> Any -> Any
forall a b. a -> b
coe
               T_MaxOperator_114 -> T_MinOperator_84
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.du_MaxOp'8658'MinOp_160
               (T_MaxOperator_114 -> Any
forall a b. a -> b
coe T_MaxOperator_114
v1))))
-- Data.Integer.Properties.⊓-⊔-properties.⊓-isSemilattice
d_'8851''45'isSemilattice_5690 ::
  MAlonzo.Code.Algebra.Structures.T_IsSemilattice_312
d_'8851''45'isSemilattice_5690 :: T_IsSemilattice_312
d_'8851''45'isSemilattice_5690
  = let v0 :: T_TotalPreorder_204
v0 = T_TotalPreorder_204
d_'8804''45'totalPreorder_1668 in
    Any -> T_IsSemilattice_312
forall a b. a -> b
coe
      (let v1 :: T_MaxOperator_114
v1 = T_MaxOperator_114
d_'8852''45'operator_5518 in
       Any -> Any
forall a b. a -> b
coe
         ((T_TotalPreorder_204 -> T_MinOperator_84 -> T_IsSemilattice_312)
-> Any -> Any -> Any
forall a b. a -> b
coe
            T_TotalPreorder_204 -> T_MinOperator_84 -> T_IsSemilattice_312
MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_'8851''45'isSemilattice_1856
            ((T_TotalPreorder_204 -> T_TotalPreorder_204) -> Any -> Any
forall a b. a -> b
coe
               T_TotalPreorder_204 -> T_TotalPreorder_204
MAlonzo.Code.Relation.Binary.Construct.Converse.du_totalPreorder_718
               (T_TotalPreorder_204 -> Any
forall a b. a -> b
coe T_TotalPreorder_204
v0))
            ((T_MaxOperator_114 -> T_MinOperator_84) -> Any -> Any
forall a b. a -> b
coe
               T_MaxOperator_114 -> T_MinOperator_84
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.du_MaxOp'8658'MinOp_160
               (T_MaxOperator_114 -> Any
forall a b. a -> b
coe T_MaxOperator_114
v1))))
-- Data.Integer.Properties.⊓-⊔-properties.⊓-glb
d_'8851''45'glb_5692 ::
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26 ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26 ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26
d_'8851''45'glb_5692 :: Integer
-> Integer
-> Integer
-> T__'8804'__26
-> T__'8804'__26
-> T__'8804'__26
d_'8851''45'glb_5692
  = let v0 :: T_TotalPreorder_204
v0 = T_TotalPreorder_204
d_'8804''45'totalPreorder_1668 in
    Any
-> Integer
-> Integer
-> Integer
-> T__'8804'__26
-> T__'8804'__26
-> T__'8804'__26
forall a b. a -> b
coe
      (let v1 :: T_MaxOperator_114
v1 = T_MaxOperator_114
d_'8852''45'operator_5518 in
       Any -> Any
forall a b. a -> b
coe
         ((T_TotalPreorder_204
 -> T_MinOperator_84 -> Any -> Any -> Any -> Any -> Any -> Any)
-> Any -> Any -> Any
forall a b. a -> b
coe
            T_TotalPreorder_204
-> T_MinOperator_84 -> Any -> Any -> Any -> Any -> Any -> Any
MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_'8851''45'glb_2100
            ((T_TotalPreorder_204 -> T_TotalPreorder_204) -> Any -> Any
forall a b. a -> b
coe
               T_TotalPreorder_204 -> T_TotalPreorder_204
MAlonzo.Code.Relation.Binary.Construct.Converse.du_totalPreorder_718
               (T_TotalPreorder_204 -> Any
forall a b. a -> b
coe T_TotalPreorder_204
v0))
            ((T_MaxOperator_114 -> T_MinOperator_84) -> Any -> Any
forall a b. a -> b
coe
               T_MaxOperator_114 -> T_MinOperator_84
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.du_MaxOp'8658'MinOp_160
               (T_MaxOperator_114 -> Any
forall a b. a -> b
coe T_MaxOperator_114
v1))))
-- Data.Integer.Properties.⊓-⊔-properties.⊓-magma
d_'8851''45'magma_5694 :: MAlonzo.Code.Algebra.Bundles.T_Magma_36
d_'8851''45'magma_5694 :: T_Magma_36
d_'8851''45'magma_5694
  = let v0 :: T_TotalPreorder_204
v0 = T_TotalPreorder_204
d_'8804''45'totalPreorder_1668 in
    Any -> T_Magma_36
forall a b. a -> b
coe
      (let v1 :: T_MaxOperator_114
v1 = T_MaxOperator_114
d_'8852''45'operator_5518 in
       Any -> Any
forall a b. a -> b
coe
         ((T_TotalPreorder_204 -> T_MinOperator_84 -> T_Magma_36)
-> Any -> Any -> Any
forall a b. a -> b
coe
            T_TotalPreorder_204 -> T_MinOperator_84 -> T_Magma_36
MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_'8851''45'magma_1868
            ((T_TotalPreorder_204 -> T_TotalPreorder_204) -> Any -> Any
forall a b. a -> b
coe
               T_TotalPreorder_204 -> T_TotalPreorder_204
MAlonzo.Code.Relation.Binary.Construct.Converse.du_totalPreorder_718
               (T_TotalPreorder_204 -> Any
forall a b. a -> b
coe T_TotalPreorder_204
v0))
            ((T_MaxOperator_114 -> T_MinOperator_84) -> Any -> Any
forall a b. a -> b
coe
               T_MaxOperator_114 -> T_MinOperator_84
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.du_MaxOp'8658'MinOp_160
               (T_MaxOperator_114 -> Any
forall a b. a -> b
coe T_MaxOperator_114
v1))))
-- Data.Integer.Properties.⊓-⊔-properties.⊓-mono-≤
d_'8851''45'mono'45''8804'_5696 ::
  Integer ->
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26 ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26 ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26
d_'8851''45'mono'45''8804'_5696 :: Integer
-> Integer
-> Integer
-> Integer
-> T__'8804'__26
-> T__'8804'__26
-> T__'8804'__26
d_'8851''45'mono'45''8804'_5696
  = let v0 :: T_TotalPreorder_204
v0 = T_TotalPreorder_204
d_'8804''45'totalPreorder_1668 in
    Any
-> Integer
-> Integer
-> Integer
-> Integer
-> T__'8804'__26
-> T__'8804'__26
-> T__'8804'__26
forall a b. a -> b
coe
      (let v1 :: T_MaxOperator_114
v1 = T_MaxOperator_114
d_'8852''45'operator_5518 in
       Any -> Any
forall a b. a -> b
coe
         ((T_TotalPreorder_204
 -> T_MinOperator_84
 -> Any
 -> Any
 -> Any
 -> Any
 -> Any
 -> Any
 -> Any)
-> Any -> Any -> Any
forall a b. a -> b
coe
            T_TotalPreorder_204
-> T_MinOperator_84
-> Any
-> Any
-> Any
-> Any
-> Any
-> Any
-> Any
MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_'8851''45'mono'45''8804'_2028
            ((T_TotalPreorder_204 -> T_TotalPreorder_204) -> Any -> Any
forall a b. a -> b
coe
               T_TotalPreorder_204 -> T_TotalPreorder_204
MAlonzo.Code.Relation.Binary.Construct.Converse.du_totalPreorder_718
               (T_TotalPreorder_204 -> Any
forall a b. a -> b
coe T_TotalPreorder_204
v0))
            ((T_MaxOperator_114 -> T_MinOperator_84) -> Any -> Any
forall a b. a -> b
coe
               T_MaxOperator_114 -> T_MinOperator_84
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.du_MaxOp'8658'MinOp_160
               (T_MaxOperator_114 -> Any
forall a b. a -> b
coe T_MaxOperator_114
v1))))
-- Data.Integer.Properties.⊓-⊔-properties.⊓-monoʳ-≤
d_'8851''45'mono'691''45''8804'_5700 ::
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26 ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26
d_'8851''45'mono'691''45''8804'_5700 :: Integer -> Integer -> Integer -> T__'8804'__26 -> T__'8804'__26
d_'8851''45'mono'691''45''8804'_5700
  = let v0 :: T_TotalPreorder_204
v0 = T_TotalPreorder_204
d_'8804''45'totalPreorder_1668 in
    Any
-> Integer -> Integer -> Integer -> T__'8804'__26 -> T__'8804'__26
forall a b. a -> b
coe
      (let v1 :: T_MaxOperator_114
v1 = T_MaxOperator_114
d_'8852''45'operator_5518 in
       Any -> Any
forall a b. a -> b
coe
         ((T_TotalPreorder_204
 -> T_MinOperator_84 -> Any -> Any -> Any -> Any -> Any)
-> Any -> Any -> Any
forall a b. a -> b
coe
            T_TotalPreorder_204
-> T_MinOperator_84 -> Any -> Any -> Any -> Any -> Any
MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_'8851''45'mono'691''45''8804'_2088
            ((T_TotalPreorder_204 -> T_TotalPreorder_204) -> Any -> Any
forall a b. a -> b
coe
               T_TotalPreorder_204 -> T_TotalPreorder_204
MAlonzo.Code.Relation.Binary.Construct.Converse.du_totalPreorder_718
               (T_TotalPreorder_204 -> Any
forall a b. a -> b
coe T_TotalPreorder_204
v0))
            ((T_MaxOperator_114 -> T_MinOperator_84) -> Any -> Any
forall a b. a -> b
coe
               T_MaxOperator_114 -> T_MinOperator_84
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.du_MaxOp'8658'MinOp_160
               (T_MaxOperator_114 -> Any
forall a b. a -> b
coe T_MaxOperator_114
v1))))
-- Data.Integer.Properties.⊓-⊔-properties.⊓-monoˡ-≤
d_'8851''45'mono'737''45''8804'_5702 ::
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26 ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26
d_'8851''45'mono'737''45''8804'_5702 :: Integer -> Integer -> Integer -> T__'8804'__26 -> T__'8804'__26
d_'8851''45'mono'737''45''8804'_5702
  = let v0 :: T_TotalPreorder_204
v0 = T_TotalPreorder_204
d_'8804''45'totalPreorder_1668 in
    Any
-> Integer -> Integer -> Integer -> T__'8804'__26 -> T__'8804'__26
forall a b. a -> b
coe
      (let v1 :: T_MaxOperator_114
v1 = T_MaxOperator_114
d_'8852''45'operator_5518 in
       Any -> Any
forall a b. a -> b
coe
         ((T_TotalPreorder_204
 -> T_MinOperator_84 -> Any -> Any -> Any -> Any -> Any)
-> Any -> Any -> Any
forall a b. a -> b
coe
            T_TotalPreorder_204
-> T_MinOperator_84 -> Any -> Any -> Any -> Any -> Any
MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_'8851''45'mono'737''45''8804'_2078
            ((T_TotalPreorder_204 -> T_TotalPreorder_204) -> Any -> Any
forall a b. a -> b
coe
               T_TotalPreorder_204 -> T_TotalPreorder_204
MAlonzo.Code.Relation.Binary.Construct.Converse.du_totalPreorder_718
               (T_TotalPreorder_204 -> Any
forall a b. a -> b
coe T_TotalPreorder_204
v0))
            ((T_MaxOperator_114 -> T_MinOperator_84) -> Any -> Any
forall a b. a -> b
coe
               T_MaxOperator_114 -> T_MinOperator_84
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.du_MaxOp'8658'MinOp_160
               (T_MaxOperator_114 -> Any
forall a b. a -> b
coe T_MaxOperator_114
v1))))
-- Data.Integer.Properties.⊓-⊔-properties.⊓-sel
d_'8851''45'sel_5704 ::
  Integer -> Integer -> MAlonzo.Code.Data.Sum.Base.T__'8846'__30
d_'8851''45'sel_5704 :: Integer -> Integer -> T__'8846'__30
d_'8851''45'sel_5704
  = let v0 :: T_TotalPreorder_204
v0 = T_TotalPreorder_204
d_'8804''45'totalPreorder_1668 in
    Any -> Integer -> Integer -> T__'8846'__30
forall a b. a -> b
coe
      (let v1 :: T_MaxOperator_114
v1 = T_MaxOperator_114
d_'8852''45'operator_5518 in
       Any -> Any
forall a b. a -> b
coe
         ((T_TotalPreorder_204
 -> T_MinOperator_84 -> Any -> Any -> T__'8846'__30)
-> Any -> Any -> Any
forall a b. a -> b
coe
            T_TotalPreorder_204
-> T_MinOperator_84 -> Any -> Any -> T__'8846'__30
MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_'8851''45'sel_1806
            ((T_TotalPreorder_204 -> T_TotalPreorder_204) -> Any -> Any
forall a b. a -> b
coe
               T_TotalPreorder_204 -> T_TotalPreorder_204
MAlonzo.Code.Relation.Binary.Construct.Converse.du_totalPreorder_718
               (T_TotalPreorder_204 -> Any
forall a b. a -> b
coe T_TotalPreorder_204
v0))
            ((T_MaxOperator_114 -> T_MinOperator_84) -> Any -> Any
forall a b. a -> b
coe
               T_MaxOperator_114 -> T_MinOperator_84
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.du_MaxOp'8658'MinOp_160
               (T_MaxOperator_114 -> Any
forall a b. a -> b
coe T_MaxOperator_114
v1))))
-- Data.Integer.Properties.⊓-⊔-properties.⊓-selectiveMagma
d_'8851''45'selectiveMagma_5706 ::
  MAlonzo.Code.Algebra.Bundles.T_SelectiveMagma_90
d_'8851''45'selectiveMagma_5706 :: T_SelectiveMagma_90
d_'8851''45'selectiveMagma_5706
  = let v0 :: T_TotalPreorder_204
v0 = T_TotalPreorder_204
d_'8804''45'totalPreorder_1668 in
    Any -> T_SelectiveMagma_90
forall a b. a -> b
coe
      (let v1 :: T_MaxOperator_114
v1 = T_MaxOperator_114
d_'8852''45'operator_5518 in
       Any -> Any
forall a b. a -> b
coe
         ((T_TotalPreorder_204 -> T_MinOperator_84 -> T_SelectiveMagma_90)
-> Any -> Any -> Any
forall a b. a -> b
coe
            T_TotalPreorder_204 -> T_MinOperator_84 -> T_SelectiveMagma_90
MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_'8851''45'selectiveMagma_1878
            ((T_TotalPreorder_204 -> T_TotalPreorder_204) -> Any -> Any
forall a b. a -> b
coe
               T_TotalPreorder_204 -> T_TotalPreorder_204
MAlonzo.Code.Relation.Binary.Construct.Converse.du_totalPreorder_718
               (T_TotalPreorder_204 -> Any
forall a b. a -> b
coe T_TotalPreorder_204
v0))
            ((T_MaxOperator_114 -> T_MinOperator_84) -> Any -> Any
forall a b. a -> b
coe
               T_MaxOperator_114 -> T_MinOperator_84
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.du_MaxOp'8658'MinOp_160
               (T_MaxOperator_114 -> Any
forall a b. a -> b
coe T_MaxOperator_114
v1))))
-- Data.Integer.Properties.⊓-⊔-properties.⊓-semigroup
d_'8851''45'semigroup_5708 ::
  MAlonzo.Code.Algebra.Bundles.T_Semigroup_206
d_'8851''45'semigroup_5708 :: T_Semigroup_206
d_'8851''45'semigroup_5708
  = let v0 :: T_TotalPreorder_204
v0 = T_TotalPreorder_204
d_'8804''45'totalPreorder_1668 in
    Any -> T_Semigroup_206
forall a b. a -> b
coe
      (let v1 :: T_MaxOperator_114
v1 = T_MaxOperator_114
d_'8852''45'operator_5518 in
       Any -> Any
forall a b. a -> b
coe
         ((T_TotalPreorder_204 -> T_MinOperator_84 -> T_Semigroup_206)
-> Any -> Any -> Any
forall a b. a -> b
coe
            T_TotalPreorder_204 -> T_MinOperator_84 -> T_Semigroup_206
MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_'8851''45'semigroup_1870
            ((T_TotalPreorder_204 -> T_TotalPreorder_204) -> Any -> Any
forall a b. a -> b
coe
               T_TotalPreorder_204 -> T_TotalPreorder_204
MAlonzo.Code.Relation.Binary.Construct.Converse.du_totalPreorder_718
               (T_TotalPreorder_204 -> Any
forall a b. a -> b
coe T_TotalPreorder_204
v0))
            ((T_MaxOperator_114 -> T_MinOperator_84) -> Any -> Any
forall a b. a -> b
coe
               T_MaxOperator_114 -> T_MinOperator_84
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.du_MaxOp'8658'MinOp_160
               (T_MaxOperator_114 -> Any
forall a b. a -> b
coe T_MaxOperator_114
v1))))
-- Data.Integer.Properties.⊓-⊔-properties.⊓-semilattice
d_'8851''45'semilattice_5710 ::
  MAlonzo.Code.Algebra.Bundles.T_Semilattice_402
d_'8851''45'semilattice_5710 :: T_Semilattice_402
d_'8851''45'semilattice_5710
  = let v0 :: T_TotalPreorder_204
v0 = T_TotalPreorder_204
d_'8804''45'totalPreorder_1668 in
    Any -> T_Semilattice_402
forall a b. a -> b
coe
      (let v1 :: T_MaxOperator_114
v1 = T_MaxOperator_114
d_'8852''45'operator_5518 in
       Any -> Any
forall a b. a -> b
coe
         ((T_TotalPreorder_204 -> T_MinOperator_84 -> T_Semilattice_402)
-> Any -> Any -> Any
forall a b. a -> b
coe
            T_TotalPreorder_204 -> T_MinOperator_84 -> T_Semilattice_402
MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_'8851''45'semilattice_1876
            ((T_TotalPreorder_204 -> T_TotalPreorder_204) -> Any -> Any
forall a b. a -> b
coe
               T_TotalPreorder_204 -> T_TotalPreorder_204
MAlonzo.Code.Relation.Binary.Construct.Converse.du_totalPreorder_718
               (T_TotalPreorder_204 -> Any
forall a b. a -> b
coe T_TotalPreorder_204
v0))
            ((T_MaxOperator_114 -> T_MinOperator_84) -> Any -> Any
forall a b. a -> b
coe
               T_MaxOperator_114 -> T_MinOperator_84
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.du_MaxOp'8658'MinOp_160
               (T_MaxOperator_114 -> Any
forall a b. a -> b
coe T_MaxOperator_114
v1))))
-- Data.Integer.Properties.⊓-⊔-properties.⊓-triangulate
d_'8851''45'triangulate_5712 ::
  Integer ->
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8851''45'triangulate_5712 :: Integer -> Integer -> Integer -> T__'8801'__12
d_'8851''45'triangulate_5712 = Integer -> Integer -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.⊓-⊔-properties.⊔-⊓-absorptive
d_'8852''45''8851''45'absorptive_5720 ::
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'8852''45''8851''45'absorptive_5720 :: T_Σ_14
d_'8852''45''8851''45'absorptive_5720
  = (T_TotalPreorder_204
 -> T_MinOperator_84 -> T_MaxOperator_114 -> T_Σ_14)
-> Any -> Any -> Any -> T_Σ_14
forall a b. a -> b
coe
      T_TotalPreorder_204
-> T_MinOperator_84 -> T_MaxOperator_114 -> T_Σ_14
MAlonzo.Code.Algebra.Construct.NaturalChoice.MinMaxOp.du_'8852''45''8851''45'absorptive_1954
      (T_TotalPreorder_204 -> Any
forall a b. a -> b
coe T_TotalPreorder_204
d_'8804''45'totalPreorder_1668)
      (T_MinOperator_84 -> Any
forall a b. a -> b
coe T_MinOperator_84
d_'8851''45'operator_5516) (T_MaxOperator_114 -> Any
forall a b. a -> b
coe T_MaxOperator_114
d_'8852''45'operator_5518)
-- Data.Integer.Properties.⊓-⊔-properties.⊔-⊓-distributiveLattice
d_'8852''45''8851''45'distributiveLattice_5722 ::
  MAlonzo.Code.Algebra.Bundles.T_DistributiveLattice_1228
d_'8852''45''8851''45'distributiveLattice_5722 :: T_DistributiveLattice_1228
d_'8852''45''8851''45'distributiveLattice_5722
  = (T_TotalPreorder_204
 -> T_MinOperator_84
 -> T_MaxOperator_114
 -> T_DistributiveLattice_1228)
-> Any -> Any -> Any -> T_DistributiveLattice_1228
forall a b. a -> b
coe
      T_TotalPreorder_204
-> T_MinOperator_84
-> T_MaxOperator_114
-> T_DistributiveLattice_1228
MAlonzo.Code.Algebra.Construct.NaturalChoice.MinMaxOp.du_'8852''45''8851''45'distributiveLattice_1970
      (T_TotalPreorder_204 -> Any
forall a b. a -> b
coe T_TotalPreorder_204
d_'8804''45'totalPreorder_1668)
      (T_MinOperator_84 -> Any
forall a b. a -> b
coe T_MinOperator_84
d_'8851''45'operator_5516) (T_MaxOperator_114 -> Any
forall a b. a -> b
coe T_MaxOperator_114
d_'8852''45'operator_5518)
-- Data.Integer.Properties.⊓-⊔-properties.⊔-⊓-isDistributiveLattice
d_'8852''45''8851''45'isDistributiveLattice_5724 ::
  MAlonzo.Code.Algebra.Structures.T_IsDistributiveLattice_814
d_'8852''45''8851''45'isDistributiveLattice_5724 :: T_IsDistributiveLattice_814
d_'8852''45''8851''45'isDistributiveLattice_5724
  = (T_TotalPreorder_204
 -> T_MinOperator_84
 -> T_MaxOperator_114
 -> T_IsDistributiveLattice_814)
-> Any -> Any -> Any -> T_IsDistributiveLattice_814
forall a b. a -> b
coe
      T_TotalPreorder_204
-> T_MinOperator_84
-> T_MaxOperator_114
-> T_IsDistributiveLattice_814
MAlonzo.Code.Algebra.Construct.NaturalChoice.MinMaxOp.du_'8852''45''8851''45'isDistributiveLattice_1964
      (T_TotalPreorder_204 -> Any
forall a b. a -> b
coe T_TotalPreorder_204
d_'8804''45'totalPreorder_1668)
      (T_MinOperator_84 -> Any
forall a b. a -> b
coe T_MinOperator_84
d_'8851''45'operator_5516) (T_MaxOperator_114 -> Any
forall a b. a -> b
coe T_MaxOperator_114
d_'8852''45'operator_5518)
-- Data.Integer.Properties.⊓-⊔-properties.⊔-⊓-isLattice
d_'8852''45''8851''45'isLattice_5726 ::
  MAlonzo.Code.Algebra.Structures.T_IsLattice_740
d_'8852''45''8851''45'isLattice_5726 :: T_IsLattice_740
d_'8852''45''8851''45'isLattice_5726
  = (T_TotalPreorder_204
 -> T_MinOperator_84 -> T_MaxOperator_114 -> T_IsLattice_740)
-> Any -> Any -> Any -> T_IsLattice_740
forall a b. a -> b
coe
      T_TotalPreorder_204
-> T_MinOperator_84 -> T_MaxOperator_114 -> T_IsLattice_740
MAlonzo.Code.Algebra.Construct.NaturalChoice.MinMaxOp.du_'8852''45''8851''45'isLattice_1958
      (T_TotalPreorder_204 -> Any
forall a b. a -> b
coe T_TotalPreorder_204
d_'8804''45'totalPreorder_1668)
      (T_MinOperator_84 -> Any
forall a b. a -> b
coe T_MinOperator_84
d_'8851''45'operator_5516) (T_MaxOperator_114 -> Any
forall a b. a -> b
coe T_MaxOperator_114
d_'8852''45'operator_5518)
-- Data.Integer.Properties.⊓-⊔-properties.⊔-⊓-lattice
d_'8852''45''8851''45'lattice_5728 ::
  MAlonzo.Code.Algebra.Bundles.T_Lattice_1144
d_'8852''45''8851''45'lattice_5728 :: T_Lattice_1144
d_'8852''45''8851''45'lattice_5728
  = (T_TotalPreorder_204
 -> T_MinOperator_84 -> T_MaxOperator_114 -> T_Lattice_1144)
-> Any -> Any -> Any -> T_Lattice_1144
forall a b. a -> b
coe
      T_TotalPreorder_204
-> T_MinOperator_84 -> T_MaxOperator_114 -> T_Lattice_1144
MAlonzo.Code.Algebra.Construct.NaturalChoice.MinMaxOp.du_'8852''45''8851''45'lattice_1966
      (T_TotalPreorder_204 -> Any
forall a b. a -> b
coe T_TotalPreorder_204
d_'8804''45'totalPreorder_1668)
      (T_MinOperator_84 -> Any
forall a b. a -> b
coe T_MinOperator_84
d_'8851''45'operator_5516) (T_MaxOperator_114 -> Any
forall a b. a -> b
coe T_MaxOperator_114
d_'8852''45'operator_5518)
-- Data.Integer.Properties.mono-≤-distrib-⊔
d_mono'45''8804''45'distrib'45''8852'_5736 ::
  (Integer -> Integer) ->
  (Integer ->
   Integer ->
   MAlonzo.Code.Data.Integer.Base.T__'8804'__26 ->
   MAlonzo.Code.Data.Integer.Base.T__'8804'__26) ->
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_mono'45''8804''45'distrib'45''8852'_5736 :: (Integer -> Integer)
-> (Integer -> Integer -> T__'8804'__26 -> T__'8804'__26)
-> Integer
-> Integer
-> T__'8801'__12
d_mono'45''8804''45'distrib'45''8852'_5736 = (Integer -> Integer)
-> (Integer -> Integer -> T__'8804'__26 -> T__'8804'__26)
-> Integer
-> Integer
-> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.mono-≤-distrib-⊓
d_mono'45''8804''45'distrib'45''8851'_5746 ::
  (Integer -> Integer) ->
  (Integer ->
   Integer ->
   MAlonzo.Code.Data.Integer.Base.T__'8804'__26 ->
   MAlonzo.Code.Data.Integer.Base.T__'8804'__26) ->
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_mono'45''8804''45'distrib'45''8851'_5746 :: (Integer -> Integer)
-> (Integer -> Integer -> T__'8804'__26 -> T__'8804'__26)
-> Integer
-> Integer
-> T__'8801'__12
d_mono'45''8804''45'distrib'45''8851'_5746 = (Integer -> Integer)
-> (Integer -> Integer -> T__'8804'__26 -> T__'8804'__26)
-> Integer
-> Integer
-> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.antimono-≤-distrib-⊓
d_antimono'45''8804''45'distrib'45''8851'_5756 ::
  (Integer -> Integer) ->
  (Integer ->
   Integer ->
   MAlonzo.Code.Data.Integer.Base.T__'8804'__26 ->
   MAlonzo.Code.Data.Integer.Base.T__'8804'__26) ->
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_antimono'45''8804''45'distrib'45''8851'_5756 :: (Integer -> Integer)
-> (Integer -> Integer -> T__'8804'__26 -> T__'8804'__26)
-> Integer
-> Integer
-> T__'8801'__12
d_antimono'45''8804''45'distrib'45''8851'_5756 = (Integer -> Integer)
-> (Integer -> Integer -> T__'8804'__26 -> T__'8804'__26)
-> Integer
-> Integer
-> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.antimono-≤-distrib-⊔
d_antimono'45''8804''45'distrib'45''8852'_5766 ::
  (Integer -> Integer) ->
  (Integer ->
   Integer ->
   MAlonzo.Code.Data.Integer.Base.T__'8804'__26 ->
   MAlonzo.Code.Data.Integer.Base.T__'8804'__26) ->
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_antimono'45''8804''45'distrib'45''8852'_5766 :: (Integer -> Integer)
-> (Integer -> Integer -> T__'8804'__26 -> T__'8804'__26)
-> Integer
-> Integer
-> T__'8801'__12
d_antimono'45''8804''45'distrib'45''8852'_5766 = (Integer -> Integer)
-> (Integer -> Integer -> T__'8804'__26 -> T__'8804'__26)
-> Integer
-> Integer
-> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.mono-<-distrib-⊓
d_mono'45''60''45'distrib'45''8851'_5776 ::
  (Integer -> Integer) ->
  (Integer ->
   Integer ->
   MAlonzo.Code.Data.Integer.Base.T__'60'__50 ->
   MAlonzo.Code.Data.Integer.Base.T__'60'__50) ->
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_mono'45''60''45'distrib'45''8851'_5776 :: (Integer -> Integer)
-> (Integer -> Integer -> T__'60'__50 -> T__'60'__50)
-> Integer
-> Integer
-> T__'8801'__12
d_mono'45''60''45'distrib'45''8851'_5776 = (Integer -> Integer)
-> (Integer -> Integer -> T__'60'__50 -> T__'60'__50)
-> Integer
-> Integer
-> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.mono-<-distrib-⊔
d_mono'45''60''45'distrib'45''8852'_5824 ::
  (Integer -> Integer) ->
  (Integer ->
   Integer ->
   MAlonzo.Code.Data.Integer.Base.T__'60'__50 ->
   MAlonzo.Code.Data.Integer.Base.T__'60'__50) ->
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_mono'45''60''45'distrib'45''8852'_5824 :: (Integer -> Integer)
-> (Integer -> Integer -> T__'60'__50 -> T__'60'__50)
-> Integer
-> Integer
-> T__'8801'__12
d_mono'45''60''45'distrib'45''8852'_5824 = (Integer -> Integer)
-> (Integer -> Integer -> T__'60'__50 -> T__'60'__50)
-> Integer
-> Integer
-> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.antimono-<-distrib-⊔
d_antimono'45''60''45'distrib'45''8852'_5872 ::
  (Integer -> Integer) ->
  (Integer ->
   Integer ->
   MAlonzo.Code.Data.Integer.Base.T__'60'__50 ->
   MAlonzo.Code.Data.Integer.Base.T__'60'__50) ->
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_antimono'45''60''45'distrib'45''8852'_5872 :: (Integer -> Integer)
-> (Integer -> Integer -> T__'60'__50 -> T__'60'__50)
-> Integer
-> Integer
-> T__'8801'__12
d_antimono'45''60''45'distrib'45''8852'_5872 = (Integer -> Integer)
-> (Integer -> Integer -> T__'60'__50 -> T__'60'__50)
-> Integer
-> Integer
-> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.antimono-<-distrib-⊓
d_antimono'45''60''45'distrib'45''8851'_5920 ::
  (Integer -> Integer) ->
  (Integer ->
   Integer ->
   MAlonzo.Code.Data.Integer.Base.T__'60'__50 ->
   MAlonzo.Code.Data.Integer.Base.T__'60'__50) ->
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_antimono'45''60''45'distrib'45''8851'_5920 :: (Integer -> Integer)
-> (Integer -> Integer -> T__'60'__50 -> T__'60'__50)
-> Integer
-> Integer
-> T__'8801'__12
d_antimono'45''60''45'distrib'45''8851'_5920 = (Integer -> Integer)
-> (Integer -> Integer -> T__'60'__50 -> T__'60'__50)
-> Integer
-> Integer
-> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.neg-distrib-⊔-⊓
d_neg'45'distrib'45''8852''45''8851'_5966 ::
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_neg'45'distrib'45''8852''45''8851'_5966 :: Integer -> Integer -> T__'8801'__12
d_neg'45'distrib'45''8852''45''8851'_5966 = Integer -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.neg-distrib-⊓-⊔
d_neg'45'distrib'45''8851''45''8852'_5972 ::
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_neg'45'distrib'45''8851''45''8852'_5972 :: Integer -> Integer -> T__'8801'__12
d_neg'45'distrib'45''8851''45''8852'_5972 = Integer -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.*-distribˡ-⊓-nonNeg
d_'42''45'distrib'737''45''8851''45'nonNeg_5980 ::
  Integer ->
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'42''45'distrib'737''45''8851''45'nonNeg_5980 :: Integer -> Integer -> Integer -> T__'8801'__12
d_'42''45'distrib'737''45''8851''45'nonNeg_5980 = Integer -> Integer -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.*-distribʳ-⊓-nonNeg
d_'42''45'distrib'691''45''8851''45'nonNeg_5990 ::
  Integer ->
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'42''45'distrib'691''45''8851''45'nonNeg_5990 :: Integer -> Integer -> Integer -> T__'8801'__12
d_'42''45'distrib'691''45''8851''45'nonNeg_5990 = Integer -> Integer -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.*-distribˡ-⊓-nonPos
d_'42''45'distrib'737''45''8851''45'nonPos_6008 ::
  Integer ->
  AgdaAny ->
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'42''45'distrib'737''45''8851''45'nonPos_6008 :: Integer -> Any -> Integer -> Integer -> T__'8801'__12
d_'42''45'distrib'737''45''8851''45'nonPos_6008 = Integer -> Any -> Integer -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.*-distribʳ-⊓-nonPos
d_'42''45'distrib'691''45''8851''45'nonPos_6026 ::
  Integer ->
  AgdaAny ->
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'42''45'distrib'691''45''8851''45'nonPos_6026 :: Integer -> Any -> Integer -> Integer -> T__'8801'__12
d_'42''45'distrib'691''45''8851''45'nonPos_6026 = Integer -> Any -> Integer -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.*-distribˡ-⊔-nonNeg
d_'42''45'distrib'737''45''8852''45'nonNeg_6046 ::
  Integer ->
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'42''45'distrib'737''45''8852''45'nonNeg_6046 :: Integer -> Integer -> Integer -> T__'8801'__12
d_'42''45'distrib'737''45''8852''45'nonNeg_6046 = Integer -> Integer -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.*-distribʳ-⊔-nonNeg
d_'42''45'distrib'691''45''8852''45'nonNeg_6060 ::
  Integer ->
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'42''45'distrib'691''45''8852''45'nonNeg_6060 :: Integer -> Integer -> Integer -> T__'8801'__12
d_'42''45'distrib'691''45''8852''45'nonNeg_6060 = Integer -> Integer -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.*-distribˡ-⊔-nonPos
d_'42''45'distrib'737''45''8852''45'nonPos_6078 ::
  Integer ->
  AgdaAny ->
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'42''45'distrib'737''45''8852''45'nonPos_6078 :: Integer -> Any -> Integer -> Integer -> T__'8801'__12
d_'42''45'distrib'737''45''8852''45'nonPos_6078 = Integer -> Any -> Integer -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.*-distribʳ-⊔-nonPos
d_'42''45'distrib'691''45''8852''45'nonPos_6096 ::
  Integer ->
  AgdaAny ->
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'42''45'distrib'691''45''8852''45'nonPos_6096 :: Integer -> Any -> Integer -> Integer -> T__'8801'__12
d_'42''45'distrib'691''45''8852''45'nonPos_6096 = Integer -> Any -> Integer -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.inverseˡ
d_inverse'737'_6110 ::
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_inverse'737'_6110 :: Integer -> T__'8801'__12
d_inverse'737'_6110 = Integer -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.inverseʳ
d_inverse'691'_6112 ::
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_inverse'691'_6112 :: Integer -> T__'8801'__12
d_inverse'691'_6112 = Integer -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.distribʳ
d_distrib'691'_6114 ::
  Integer ->
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_distrib'691'_6114 :: Integer -> Integer -> Integer -> T__'8801'__12
d_distrib'691'_6114 = Integer -> Integer -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.isCommutativeSemiring
d_isCommutativeSemiring_6116 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiring_1344
d_isCommutativeSemiring_6116 :: T_IsCommutativeSemiring_1344
d_isCommutativeSemiring_6116
  = T_IsCommutativeSemiring_1344 -> T_IsCommutativeSemiring_1344
forall a b. a -> b
coe T_IsCommutativeSemiring_1344
d_'43''45''42''45'isCommutativeSemiring_4600
-- Data.Integer.Properties.commutativeRing
d_commutativeRing_6118 ::
  MAlonzo.Code.Algebra.Bundles.T_CommutativeRing_2704
d_commutativeRing_6118 :: T_CommutativeRing_2704
d_commutativeRing_6118 = T_CommutativeRing_2704 -> T_CommutativeRing_2704
forall a b. a -> b
coe T_CommutativeRing_2704
d_'43''45''42''45'commutativeRing_4622
-- Data.Integer.Properties.*-+-right-mono
d_'42''45''43''45'right'45'mono_6120 ::
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26 ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26
d_'42''45''43''45'right'45'mono_6120 :: Integer -> Integer -> Integer -> T__'8804'__26 -> T__'8804'__26
d_'42''45''43''45'right'45'mono_6120
  = (Integer -> Integer -> Integer -> T__'8804'__26 -> T__'8804'__26)
-> Integer -> Integer -> Integer -> T__'8804'__26 -> T__'8804'__26
forall a b. a -> b
coe Integer -> Integer -> Integer -> T__'8804'__26 -> T__'8804'__26
d_'42''45'mono'691''45''8804''45'pos_5022
-- Data.Integer.Properties.cancel-*-+-right-≤
d_cancel'45''42''45''43''45'right'45''8804'_6122 ::
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26 ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26
d_cancel'45''42''45''43''45'right'45''8804'_6122 :: Integer -> Integer -> Integer -> T__'8804'__26 -> T__'8804'__26
d_cancel'45''42''45''43''45'right'45''8804'_6122 Integer
v0 Integer
v1 Integer
v2 T__'8804'__26
v3
  = (Integer -> Integer -> T__'8804'__26 -> T__'8804'__26)
-> Integer -> Integer -> T__'8804'__26 -> T__'8804'__26
forall a b. a -> b
coe Integer -> Integer -> T__'8804'__26 -> T__'8804'__26
du_'42''45'cancel'691''45''8804''45'pos_4978 Integer
v0 Integer
v1 T__'8804'__26
v3
-- Data.Integer.Properties.cancel-*-right
d_cancel'45''42''45'right_6124 ::
  Integer ->
  Integer ->
  Integer ->
  (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_cancel'45''42''45'right_6124 :: Integer
-> Integer
-> Integer
-> (T__'8801'__12 -> T_'8869'_4)
-> T__'8801'__12
-> T__'8801'__12
d_cancel'45''42''45'right_6124 = Integer
-> Integer
-> Integer
-> (T__'8801'__12 -> T_'8869'_4)
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.doubleNeg
d_doubleNeg_6126 ::
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_doubleNeg_6126 :: Integer -> T__'8801'__12
d_doubleNeg_6126 = Integer -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.-‿involutive
d_'45''8255'involutive_6128 ::
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'45''8255'involutive_6128 :: Integer -> T__'8801'__12
d_'45''8255'involutive_6128 = Integer -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.+-⊖-left-cancel
d_'43''45''8854''45'left'45'cancel_6130 ::
  Integer ->
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'43''45''8854''45'left'45'cancel_6130 :: Integer -> Integer -> Integer -> T__'8801'__12
d_'43''45''8854''45'left'45'cancel_6130 = Integer -> Integer -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.≰→>
d_'8816''8594''62'_6132 ::
  Integer ->
  Integer ->
  (MAlonzo.Code.Data.Integer.Base.T__'8804'__26 ->
   MAlonzo.Code.Data.Empty.T_'8869'_4) ->
  MAlonzo.Code.Data.Integer.Base.T__'60'__50
d_'8816''8594''62'_6132 :: Integer -> Integer -> (T__'8804'__26 -> T_'8869'_4) -> T__'60'__50
d_'8816''8594''62'_6132 Integer
v0 Integer
v1 T__'8804'__26 -> T_'8869'_4
v2
  = (Integer -> Integer -> T__'60'__50)
-> Integer -> Integer -> T__'60'__50
forall a b. a -> b
coe Integer -> Integer -> T__'60'__50
du_'8816''8658''62'_1752 Integer
v0 Integer
v1
-- Data.Integer.Properties.≤-irrelevance
d_'8804''45'irrelevance_6134 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26 ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8804''45'irrelevance_6134 :: Integer
-> Integer -> T__'8804'__26 -> T__'8804'__26 -> T__'8801'__12
d_'8804''45'irrelevance_6134 = Integer
-> Integer -> T__'8804'__26 -> T__'8804'__26 -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.<-irrelevance
d_'60''45'irrelevance_6136 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Integer.Base.T__'60'__50 ->
  MAlonzo.Code.Data.Integer.Base.T__'60'__50 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'60''45'irrelevance_6136 :: Integer -> Integer -> T__'60'__50 -> T__'60'__50 -> T__'8801'__12
d_'60''45'irrelevance_6136 = Integer -> Integer -> T__'60'__50 -> T__'60'__50 -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.-<′+
d_'45''60''8242''43'_6142 ::
  Integer -> Integer -> MAlonzo.Code.Data.Integer.Base.T__'8804'__26
d_'45''60''8242''43'_6142 :: Integer -> Integer -> T__'8804'__26
d_'45''60''8242''43'_6142 Integer
v0 ~Integer
v1 = Integer -> T__'8804'__26
du_'45''60''8242''43'_6142 Integer
v0
du_'45''60''8242''43'_6142 ::
  Integer -> MAlonzo.Code.Data.Integer.Base.T__'8804'__26
du_'45''60''8242''43'_6142 :: Integer -> T__'8804'__26
du_'45''60''8242''43'_6142 Integer
v0
  = case Integer -> Integer
forall a b. a -> b
coe Integer
v0 of
      Integer
0 -> (T__'8804'__18 -> T__'8804'__26) -> Any -> T__'8804'__26
forall a b. a -> b
coe
             T__'8804'__18 -> T__'8804'__26
MAlonzo.Code.Data.Integer.Base.C_'43''8804''43'_48
             (T__'8804'__18 -> Any
forall a b. a -> b
coe T__'8804'__18
MAlonzo.Code.Data.Nat.Base.C_z'8804'n_22)
      Integer
_ -> T__'8804'__26 -> T__'8804'__26
forall a b. a -> b
coe T__'8804'__26
MAlonzo.Code.Data.Integer.Base.C_'45''8804''43'_40
-- Data.Integer.Properties.<′-irrefl
d_'60''8242''45'irrefl_6144 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26 ->
  MAlonzo.Code.Data.Empty.T_'8869'_4
d_'60''8242''45'irrefl_6144 :: Integer -> Integer -> T__'8801'__12 -> T__'8804'__26 -> T_'8869'_4
d_'60''8242''45'irrefl_6144 = Integer -> Integer -> T__'8801'__12 -> T__'8804'__26 -> T_'8869'_4
forall a. a
erased
-- Data.Integer.Properties.>′-irrefl
d_'62''8242''45'irrefl_6154 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26 ->
  MAlonzo.Code.Data.Empty.T_'8869'_4
d_'62''8242''45'irrefl_6154 :: Integer -> Integer -> T__'8801'__12 -> T__'8804'__26 -> T_'8869'_4
d_'62''8242''45'irrefl_6154 = Integer -> Integer -> T__'8801'__12 -> T__'8804'__26 -> T_'8869'_4
forall a. a
erased
-- Data.Integer.Properties.<′-asym
d_'60''8242''45'asym_6156 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26 ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26 ->
  MAlonzo.Code.Data.Empty.T_'8869'_4
d_'60''8242''45'asym_6156 :: Integer -> Integer -> T__'8804'__26 -> T__'8804'__26 -> T_'8869'_4
d_'60''8242''45'asym_6156 = Integer -> Integer -> T__'8804'__26 -> T__'8804'__26 -> T_'8869'_4
forall a. a
erased
-- Data.Integer.Properties.≤-<′-trans
d_'8804''45''60''8242''45'trans_6174 ::
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26 ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26 ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26
d_'8804''45''60''8242''45'trans_6174 :: Integer
-> Integer
-> Integer
-> T__'8804'__26
-> T__'8804'__26
-> T__'8804'__26
d_'8804''45''60''8242''45'trans_6174 Integer
v0 Integer
v1 ~Integer
v2 T__'8804'__26
v3 T__'8804'__26
v4
  = Integer
-> Integer -> T__'8804'__26 -> T__'8804'__26 -> T__'8804'__26
du_'8804''45''60''8242''45'trans_6174 Integer
v0 Integer
v1 T__'8804'__26
v3 T__'8804'__26
v4
du_'8804''45''60''8242''45'trans_6174 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26 ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26 ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26
du_'8804''45''60''8242''45'trans_6174 :: Integer
-> Integer -> T__'8804'__26 -> T__'8804'__26 -> T__'8804'__26
du_'8804''45''60''8242''45'trans_6174 Integer
v0 Integer
v1 T__'8804'__26
v2 T__'8804'__26
v3
  = case Integer -> Any
forall a b. a -> b
coe Integer
v0 of
      Any
_ | (Integer -> Integer -> Bool) -> Any -> Any -> Bool
forall a b. a -> b
coe Integer -> Integer -> Bool
geqInt (Integer -> Any
forall a b. a -> b
coe Integer
v0) (Integer -> Any
forall a b. a -> b
coe (Integer
0 :: Integer)) ->
          case T__'8804'__26 -> T__'8804'__26
forall a b. a -> b
coe T__'8804'__26
v2 of
            MAlonzo.Code.Data.Integer.Base.C_'43''8804''43'_48 T__'8804'__18
v6
              -> case T__'8804'__26 -> T__'8804'__26
forall a b. a -> b
coe T__'8804'__26
v3 of
                   MAlonzo.Code.Data.Integer.Base.C_'43''8804''43'_48 T__'8804'__18
v9
                     -> (T__'8804'__18 -> T__'8804'__26) -> Any -> T__'8804'__26
forall a b. a -> b
coe
                          T__'8804'__18 -> T__'8804'__26
MAlonzo.Code.Data.Integer.Base.C_'43''8804''43'_48
                          ((T__'8804'__18 -> T__'8804'__18 -> T__'8804'__18)
-> Any -> Any -> Any
forall a b. a -> b
coe
                             T__'8804'__18 -> T__'8804'__18 -> T__'8804'__18
MAlonzo.Code.Data.Nat.Properties.du_'8804''45'trans_1642
                             ((T__'8804'__18 -> T__'8804'__18) -> T__'8804'__18 -> Any
forall a b. a -> b
coe T__'8804'__18 -> T__'8804'__18
MAlonzo.Code.Data.Nat.Base.C_s'8804's_30 T__'8804'__18
v6) (T__'8804'__18 -> Any
forall a b. a -> b
coe T__'8804'__18
v9))
                   T__'8804'__26
_ -> T__'8804'__26
forall a. a
MAlonzo.RTE.mazUnreachableError
            T__'8804'__26
_ -> T__'8804'__26
forall a. a
MAlonzo.RTE.mazUnreachableError
      Any
_ -> let v4 :: Integer
v4 = Integer -> Integer -> Integer
subInt (Integer -> Integer
forall a b. a -> b
coe (-Integer
1 :: Integer)) (Integer -> Integer
forall a b. a -> b
coe Integer
v0) in
           Any -> T__'8804'__26
forall a b. a -> b
coe
             (case Integer -> Any
forall a b. a -> b
coe Integer
v1 of
                Any
_ | (Integer -> Integer -> Bool) -> Any -> Any -> Bool
forall a b. a -> b
coe Integer -> Integer -> Bool
geqInt (Integer -> Any
forall a b. a -> b
coe Integer
v1) (Integer -> Any
forall a b. a -> b
coe (Integer
0 :: Integer)) ->
                    (Any -> Any -> Any) -> Any -> Any -> Any
forall a b. a -> b
coe
                      Any -> Any -> Any
forall a b. a -> b -> b
seq (T__'8804'__26 -> Any
forall a b. a -> b
coe T__'8804'__26
v2)
                      ((Any -> Any -> Any) -> Any -> Any -> Any
forall a b. a -> b
coe Any -> Any -> Any
forall a b. a -> b -> b
seq (T__'8804'__26 -> Any
forall a b. a -> b
coe T__'8804'__26
v3) ((Integer -> T__'8804'__26) -> Any -> Any
forall a b. a -> b
coe Integer -> T__'8804'__26
du_'45''60''8242''43'_6142 (Integer -> Any
forall a b. a -> b
coe Integer
v4)))
                Any
_ -> case T__'8804'__26 -> T__'8804'__26
forall a b. a -> b
coe T__'8804'__26
v2 of
                       MAlonzo.Code.Data.Integer.Base.C_'45''8804''45'_34 T__'8804'__18
v7
                         -> (T__'8804'__26 -> T__'8804'__26 -> T__'8804'__26)
-> Any -> Any -> Any
forall a b. a -> b
coe
                              T__'8804'__26 -> T__'8804'__26 -> T__'8804'__26
du_'8804''45'trans_1586
                              ((Integer -> Integer -> Integer -> T__'8804'__18 -> T__'8804'__26)
-> Any -> Any -> Any -> Any -> Any
forall a b. a -> b
coe
                                 Integer -> Integer -> Integer -> T__'8804'__18 -> T__'8804'__26
d_'8854''45'mono'691''45''8805''45''8804'_2892 (Integer -> Any
forall a b. a -> b
coe (Integer
1 :: Integer))
                                 ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> Integer
subInt (Integer -> Any
forall a b. a -> b
coe (Integer
0 :: Integer)) (Integer -> Any
forall a b. a -> b
coe Integer
v0))
                                 ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> Integer
subInt (Integer -> Any
forall a b. a -> b
coe (Integer
0 :: Integer)) (Integer -> Any
forall a b. a -> b
coe Integer
v1))
                                 ((T__'8804'__18 -> T__'8804'__18) -> T__'8804'__18 -> Any
forall a b. a -> b
coe T__'8804'__18 -> T__'8804'__18
MAlonzo.Code.Data.Nat.Base.C_s'8804's_30 T__'8804'__18
v7))
                              (T__'8804'__26 -> Any
forall a b. a -> b
coe T__'8804'__26
v3)
                       T__'8804'__26
_ -> Any
forall a. a
MAlonzo.RTE.mazUnreachableError)
-- Data.Integer.Properties.<′-≤-trans
d_'60''8242''45''8804''45'trans_6202 ::
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26 ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26 ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26
d_'60''8242''45''8804''45'trans_6202 :: Integer
-> Integer
-> Integer
-> T__'8804'__26
-> T__'8804'__26
-> T__'8804'__26
d_'60''8242''45''8804''45'trans_6202 ~Integer
v0 ~Integer
v1 ~Integer
v2
  = T__'8804'__26 -> T__'8804'__26 -> T__'8804'__26
du_'60''8242''45''8804''45'trans_6202
du_'60''8242''45''8804''45'trans_6202 ::
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26 ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26 ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26
du_'60''8242''45''8804''45'trans_6202 :: T__'8804'__26 -> T__'8804'__26 -> T__'8804'__26
du_'60''8242''45''8804''45'trans_6202 = (T__'8804'__26 -> T__'8804'__26 -> T__'8804'__26)
-> T__'8804'__26 -> T__'8804'__26 -> T__'8804'__26
forall a b. a -> b
coe T__'8804'__26 -> T__'8804'__26 -> T__'8804'__26
du_'8804''45'trans_1586
-- Data.Integer.Properties.<′⇒≤
d_'60''8242''8658''8804'_6208 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26 ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26
d_'60''8242''8658''8804'_6208 :: Integer -> Integer -> T__'8804'__26 -> T__'8804'__26
d_'60''8242''8658''8804'_6208 Integer
v0 ~Integer
v1 T__'8804'__26
v2
  = Integer -> T__'8804'__26 -> T__'8804'__26
du_'60''8242''8658''8804'_6208 Integer
v0 T__'8804'__26
v2
du_'60''8242''8658''8804'_6208 ::
  Integer ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26 ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26
du_'60''8242''8658''8804'_6208 :: Integer -> T__'8804'__26 -> T__'8804'__26
du_'60''8242''8658''8804'_6208 Integer
v0 T__'8804'__26
v1
  = (T__'8804'__26 -> T__'8804'__26 -> T__'8804'__26)
-> Any -> Any -> T__'8804'__26
forall a b. a -> b
coe
      T__'8804'__26 -> T__'8804'__26 -> T__'8804'__26
du_'8804''45'trans_1586 ((Integer -> T__'8804'__26) -> Any -> Any
forall a b. a -> b
coe Integer -> T__'8804'__26
d_n'8804'1'43'n_3860 (Integer -> Any
forall a b. a -> b
coe Integer
v0))
      (T__'8804'__26 -> Any
forall a b. a -> b
coe T__'8804'__26
v1)
-- Data.Integer.Properties.<′-trans
d_'60''8242''45'trans_6212 ::
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26 ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26 ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26
d_'60''8242''45'trans_6212 :: Integer
-> Integer
-> Integer
-> T__'8804'__26
-> T__'8804'__26
-> T__'8804'__26
d_'60''8242''45'trans_6212 Integer
v0 Integer
v1 ~Integer
v2 T__'8804'__26
v3 T__'8804'__26
v4
  = Integer
-> Integer -> T__'8804'__26 -> T__'8804'__26 -> T__'8804'__26
du_'60''8242''45'trans_6212 Integer
v0 Integer
v1 T__'8804'__26
v3 T__'8804'__26
v4
du_'60''8242''45'trans_6212 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26 ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26 ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26
du_'60''8242''45'trans_6212 :: Integer
-> Integer -> T__'8804'__26 -> T__'8804'__26 -> T__'8804'__26
du_'60''8242''45'trans_6212 Integer
v0 Integer
v1 T__'8804'__26
v2 T__'8804'__26
v3
  = (Integer
 -> Integer -> T__'8804'__26 -> T__'8804'__26 -> T__'8804'__26)
-> Any -> Any -> Any -> Any -> T__'8804'__26
forall a b. a -> b
coe
      Integer
-> Integer -> T__'8804'__26 -> T__'8804'__26 -> T__'8804'__26
du_'8804''45''60''8242''45'trans_6174 (Integer -> Any
forall a b. a -> b
coe Integer
v0) (Integer -> Any
forall a b. a -> b
coe Integer
v1)
      ((Integer -> T__'8804'__26 -> T__'8804'__26) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> T__'8804'__26 -> T__'8804'__26
du_'60''8242''8658''8804'_6208 (Integer -> Any
forall a b. a -> b
coe Integer
v0) (T__'8804'__26 -> Any
forall a b. a -> b
coe T__'8804'__26
v2)) (T__'8804'__26 -> Any
forall a b. a -> b
coe T__'8804'__26
v3)
-- Data.Integer.Properties.<′-cmp
d_'60''8242''45'cmp_6224 ::
  Integer ->
  Integer -> MAlonzo.Code.Relation.Binary.Definitions.T_Tri_136
d_'60''8242''45'cmp_6224 :: Integer -> Integer -> T_Tri_136
d_'60''8242''45'cmp_6224 Integer
v0 Integer
v1
  = case Integer -> Integer
forall a b. a -> b
coe Integer
v0 of
      Integer
_ | (Integer -> Integer -> Bool) -> Any -> Any -> Bool
forall a b. a -> b
coe Integer -> Integer -> Bool
geqInt (Integer -> Any
forall a b. a -> b
coe Integer
v0) (Integer -> Any
forall a b. a -> b
coe (Integer
0 :: Integer)) ->
          case Integer -> Integer
forall a b. a -> b
coe Integer
v1 of
            Integer
_ | (Integer -> Integer -> Bool) -> Any -> Any -> Bool
forall a b. a -> b
coe Integer -> Integer -> Bool
geqInt (Integer -> Any
forall a b. a -> b
coe Integer
v1) (Integer -> Any
forall a b. a -> b
coe (Integer
0 :: Integer)) ->
                let v2 :: t
v2
                      = ((Any -> Any) -> T_Dec_32 -> T_Dec_32) -> Any -> Any -> t
forall a b. a -> b
coe
                          (Any -> Any) -> T_Dec_32 -> T_Dec_32
MAlonzo.Code.Relation.Nullary.Decidable.Core.du_map'8242'_168
                          Any
forall a. a
erased
                          ((Bool -> T_Dec_32) -> Any -> Any
forall a b. a -> b
coe
                             Bool -> T_Dec_32
MAlonzo.Code.Data.Bool.Properties.d_T'63'_2210
                             ((Integer -> Integer -> Bool) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> Bool
eqInt (Integer -> Any
forall a b. a -> b
coe Integer
v0) (Integer -> Any
forall a b. a -> b
coe Integer
v1))) in
                Any -> T_Tri_136
forall a b. a -> b
coe
                  (let v3 :: T_Dec_32
v3
                         = Bool -> T_Dec_32
MAlonzo.Code.Data.Bool.Properties.d_T'63'_2210
                             ((Integer -> Integer -> Bool) -> Any -> Any -> Bool
forall a b. a -> b
coe Integer -> Integer -> Bool
ltInt (Integer -> Any
forall a b. a -> b
coe Integer
v0) (Integer -> Any
forall a b. a -> b
coe Integer
v1)) in
                   Any -> Any
forall a b. a -> b
coe
                     (case Any -> T_Dec_32
forall a b. a -> b
coe Any
forall a. a
v2 of
                        MAlonzo.Code.Relation.Nullary.C__because__46 Bool
v4 T_Reflects_14
v5
                          -> if Bool -> Bool
forall a b. a -> b
coe Bool
v4
                               then (Any -> Any -> Any) -> Any -> Any -> Any
forall a b. a -> b
coe
                                      Any -> Any -> Any
forall a b. a -> b -> b
seq (T_Reflects_14 -> Any
forall a b. a -> b
coe T_Reflects_14
v5)
                                      ((Any -> T_Tri_136) -> Any -> Any
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 (let v6 :: b
v6
                                           = Any -> b -> b
forall a b. a -> b -> b
seq
                                               (T_Reflects_14 -> Any
forall a b. a -> b
coe T_Reflects_14
v5)
                                               (case T_Dec_32 -> T_Dec_32
forall a b. a -> b
coe T_Dec_32
v3 of
                                                  MAlonzo.Code.Relation.Nullary.C__because__46 Bool
v6 T_Reflects_14
v7
                                                    -> if Bool -> Bool
forall a b. a -> b
coe Bool
v6
                                                         then (Any -> Any -> Any) -> Any -> Any -> b
forall a b. a -> b
coe
                                                                Any -> Any -> Any
forall a b. a -> b -> b
seq (T_Reflects_14 -> Any
forall a b. a -> b
coe T_Reflects_14
v7)
                                                                ((Any -> T_Tri_136) -> Any -> Any
forall a b. a -> b
coe
                                                                   Any -> T_Tri_136
MAlonzo.Code.Relation.Binary.Definitions.C_tri'60'_150
                                                                   ((Integer -> T__'8804'__18) -> Any -> Any
forall a b. a -> b
coe
                                                                      Integer -> T__'8804'__18
MAlonzo.Code.Data.Nat.Properties.du_'60''7495''8658''60'_1566
                                                                      (Integer -> Any
forall a b. a -> b
coe Integer
v0)))
                                                         else (Any -> Any -> Any) -> Any -> Any -> b
forall a b. a -> b
coe
                                                                Any -> Any -> Any
forall a b. a -> b -> b
seq (T_Reflects_14 -> Any
forall a b. a -> b
coe T_Reflects_14
v7)
                                                                ((Any -> T_Tri_136) -> Any -> Any
forall a b. a -> b
coe
                                                                   Any -> T_Tri_136
MAlonzo.Code.Relation.Binary.Definitions.C_tri'62'_166
                                                                   ((Integer -> T__'8804'__18 -> T__'8804'__18) -> Any -> Any -> Any
forall a b. a -> b
coe
                                                                      Integer -> T__'8804'__18 -> T__'8804'__18
MAlonzo.Code.Data.Nat.Properties.du_'8804''8743''8802''8658''60'_1800
                                                                      (Integer -> Any
forall a b. a -> b
coe Integer
v0)
                                                                      ((Integer -> Integer -> T__'8804'__18) -> Any -> Any -> Any
forall a b. a -> b
coe
                                                                         Integer -> Integer -> T__'8804'__18
MAlonzo.Code.Data.Nat.Properties.du_'8814''8658''8805'_1784
                                                                         (Integer -> Any
forall a b. a -> b
coe Integer
v0) (Integer -> Any
forall a b. a -> b
coe Integer
v1))))
                                                  T_Dec_32
_ -> b
forall a. a
MAlonzo.RTE.mazUnreachableError) in
                                     Any -> Any
forall a b. a -> b
coe
                                       (case Any -> T_Tri_136
forall a b. a -> b
coe Any
forall a. a
v6 of
                                          MAlonzo.Code.Relation.Binary.Definitions.C_tri'60'_150 Any
v7
                                            -> (Any -> T_Tri_136) -> Any -> Any
forall a b. a -> b
coe
                                                 Any -> T_Tri_136
MAlonzo.Code.Relation.Binary.Definitions.C_tri'60'_150
                                                 ((T__'8804'__18 -> T__'8804'__26) -> Any -> Any
forall a b. a -> b
coe
                                                    T__'8804'__18 -> T__'8804'__26
MAlonzo.Code.Data.Integer.Base.C_'43''8804''43'_48
                                                    Any
v7)
                                          MAlonzo.Code.Relation.Binary.Definitions.C_tri'8776'_158 Any
v8
                                            -> (Any -> T_Tri_136) -> Any -> Any
forall a b. a -> b
coe
                                                 Any -> T_Tri_136
MAlonzo.Code.Relation.Binary.Definitions.C_tri'8776'_158
                                                 Any
forall a. a
erased
                                          MAlonzo.Code.Relation.Binary.Definitions.C_tri'62'_166 Any
v9
                                            -> (Any -> T_Tri_136) -> Any -> Any
forall a b. a -> b
coe
                                                 Any -> T_Tri_136
MAlonzo.Code.Relation.Binary.Definitions.C_tri'62'_166
                                                 ((T__'8804'__18 -> T__'8804'__26) -> Any -> Any
forall a b. a -> b
coe
                                                    T__'8804'__18 -> T__'8804'__26
MAlonzo.Code.Data.Integer.Base.C_'43''8804''43'_48
                                                    Any
v9)
                                          T_Tri_136
_ -> Any
forall a. a
MAlonzo.RTE.mazUnreachableError))
                        T_Dec_32
_ -> Any
forall a. a
MAlonzo.RTE.mazUnreachableError))
            -1
              -> (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
                   ((T__'8804'__18 -> T__'8804'__26) -> Any -> Any
forall a b. a -> b
coe
                      T__'8804'__18 -> T__'8804'__26
MAlonzo.Code.Data.Integer.Base.C_'43''8804''43'_48
                      (T__'8804'__18 -> Any
forall a b. a -> b
coe T__'8804'__18
MAlonzo.Code.Data.Nat.Base.C_z'8804'n_22))
            Integer
_ -> (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
                   (T__'8804'__26 -> Any
forall a b. a -> b
coe T__'8804'__26
MAlonzo.Code.Data.Integer.Base.C_'45''8804''43'_40)
      -1
        -> case Integer -> Integer
forall a b. a -> b
coe Integer
v1 of
             Integer
_ | (Integer -> Integer -> Bool) -> Any -> Any -> Bool
forall a b. a -> b
coe Integer -> Integer -> Bool
geqInt (Integer -> Any
forall a b. a -> b
coe Integer
v1) (Integer -> Any
forall a b. a -> b
coe (Integer
0 :: Integer)) ->
                 (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
                   ((T__'8804'__18 -> T__'8804'__26) -> Any -> Any
forall a b. a -> b
coe
                      T__'8804'__18 -> T__'8804'__26
MAlonzo.Code.Data.Integer.Base.C_'43''8804''43'_48
                      (T__'8804'__18 -> Any
forall a b. a -> b
coe T__'8804'__18
MAlonzo.Code.Data.Nat.Base.C_z'8804'n_22))
             -1
               -> (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
             Integer
_ -> (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
                    ((T__'8804'__18 -> T__'8804'__26) -> Any -> Any
forall a b. a -> b
coe
                       T__'8804'__18 -> T__'8804'__26
MAlonzo.Code.Data.Integer.Base.C_'45''8804''45'_34
                       (T__'8804'__18 -> Any
forall a b. a -> b
coe T__'8804'__18
MAlonzo.Code.Data.Nat.Base.C_z'8804'n_22))
      Integer
_ -> case Integer -> Integer
forall a b. a -> b
coe Integer
v1 of
             Integer
_ | (Integer -> Integer -> Bool) -> Any -> Any -> Bool
forall a b. a -> b
coe Integer -> Integer -> Bool
geqInt (Integer -> Any
forall a b. a -> b
coe Integer
v1) (Integer -> Any
forall a b. a -> b
coe (Integer
0 :: Integer)) ->
                 (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
                   (T__'8804'__26 -> Any
forall a b. a -> b
coe T__'8804'__26
MAlonzo.Code.Data.Integer.Base.C_'45''8804''43'_40)
             -1
               -> (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
                    ((T__'8804'__18 -> T__'8804'__26) -> Any -> Any
forall a b. a -> b
coe
                       T__'8804'__18 -> T__'8804'__26
MAlonzo.Code.Data.Integer.Base.C_'45''8804''45'_34
                       (T__'8804'__18 -> Any
forall a b. a -> b
coe T__'8804'__18
MAlonzo.Code.Data.Nat.Base.C_z'8804'n_22))
             Integer
_ -> let v2 :: Integer
v2 = Integer -> Integer -> Integer
subInt (Integer -> Integer
forall a b. a -> b
coe (-Integer
1 :: Integer)) (Integer -> Integer
forall a b. a -> b
coe Integer
v0) in
                  Any -> T_Tri_136
forall a b. a -> b
coe
                    (let v3 :: Integer
v3 = Integer -> Integer -> Integer
subInt (Integer -> Integer
forall a b. a -> b
coe (-Integer
1 :: Integer)) (Integer -> Integer
forall a b. a -> b
coe Integer
v1) in
                     Any -> Any
forall a b. a -> b
coe
                       (let v4 :: t
v4
                              = ((Any -> Any) -> T_Dec_32 -> T_Dec_32) -> Any -> Any -> t
forall a b. a -> b
coe
                                  (Any -> Any) -> T_Dec_32 -> T_Dec_32
MAlonzo.Code.Relation.Nullary.Decidable.Core.du_map'8242'_168
                                  Any
forall a. a
erased
                                  ((Bool -> T_Dec_32) -> Any -> Any
forall a b. a -> b
coe
                                     Bool -> T_Dec_32
MAlonzo.Code.Data.Bool.Properties.d_T'63'_2210
                                     ((Integer -> Integer -> Bool) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> Bool
eqInt (Integer -> Any
forall a b. a -> b
coe Integer
v0) (Integer -> Any
forall a b. a -> b
coe Integer
v1))) in
                        Any -> Any
forall a b. a -> b
coe
                          (let v5 :: T_Dec_32
v5
                                 = Bool -> T_Dec_32
MAlonzo.Code.Data.Bool.Properties.d_T'63'_2210
                                     ((Integer -> Integer -> Bool) -> Any -> Any -> Bool
forall a b. a -> b
coe Integer -> Integer -> Bool
ltInt (Integer -> Any
forall a b. a -> b
coe Integer
v1) (Integer -> Any
forall a b. a -> b
coe Integer
v0)) in
                           Any -> Any
forall a b. a -> b
coe
                             (case Any -> T_Dec_32
forall a b. a -> b
coe Any
forall a. a
v4 of
                                MAlonzo.Code.Relation.Nullary.C__because__46 Bool
v6 T_Reflects_14
v7
                                  -> if Bool -> Bool
forall a b. a -> b
coe Bool
v6
                                       then (Any -> Any -> Any) -> Any -> Any -> Any
forall a b. a -> b
coe
                                              Any -> Any -> Any
forall a b. a -> b -> b
seq (T_Reflects_14 -> Any
forall a b. a -> b
coe T_Reflects_14
v7)
                                              ((Any -> T_Tri_136) -> Any -> Any
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 (let v8 :: b
v8
                                                   = Any -> b -> b
forall a b. a -> b -> b
seq
                                                       (T_Reflects_14 -> Any
forall a b. a -> b
coe T_Reflects_14
v7)
                                                       (case T_Dec_32 -> T_Dec_32
forall a b. a -> b
coe T_Dec_32
v5 of
                                                          MAlonzo.Code.Relation.Nullary.C__because__46 Bool
v8 T_Reflects_14
v9
                                                            -> if Bool -> Bool
forall a b. a -> b
coe Bool
v8
                                                                 then (Any -> Any -> Any) -> Any -> Any -> b
forall a b. a -> b
coe
                                                                        Any -> Any -> Any
forall a b. a -> b -> b
seq (T_Reflects_14 -> Any
forall a b. a -> b
coe T_Reflects_14
v9)
                                                                        ((Any -> T_Tri_136) -> Any -> Any
forall a b. a -> b
coe
                                                                           Any -> T_Tri_136
MAlonzo.Code.Relation.Binary.Definitions.C_tri'60'_150
                                                                           ((Integer -> T__'8804'__18) -> Any -> Any
forall a b. a -> b
coe
                                                                              Integer -> T__'8804'__18
MAlonzo.Code.Data.Nat.Properties.du_'60''7495''8658''60'_1566
                                                                              (Integer -> Any
forall a b. a -> b
coe Integer
v2)))
                                                                 else (Any -> Any -> Any) -> Any -> Any -> b
forall a b. a -> b
coe
                                                                        Any -> Any -> Any
forall a b. a -> b -> b
seq (T_Reflects_14 -> Any
forall a b. a -> b
coe T_Reflects_14
v9)
                                                                        ((Any -> T_Tri_136) -> Any -> Any
forall a b. a -> b
coe
                                                                           Any -> T_Tri_136
MAlonzo.Code.Relation.Binary.Definitions.C_tri'62'_166
                                                                           ((Integer -> T__'8804'__18 -> T__'8804'__18) -> Any -> Any -> Any
forall a b. a -> b
coe
                                                                              Integer -> T__'8804'__18 -> T__'8804'__18
MAlonzo.Code.Data.Nat.Properties.du_'8804''8743''8802''8658''60'_1800
                                                                              (Integer -> Any
forall a b. a -> b
coe Integer
v2)
                                                                              ((Integer -> Integer -> T__'8804'__18) -> Any -> Any -> Any
forall a b. a -> b
coe
                                                                                 Integer -> Integer -> T__'8804'__18
MAlonzo.Code.Data.Nat.Properties.du_'8814''8658''8805'_1784
                                                                                 (Integer -> Any
forall a b. a -> b
coe Integer
v2)
                                                                                 (Integer -> Any
forall a b. a -> b
coe Integer
v3))))
                                                          T_Dec_32
_ -> b
forall a. a
MAlonzo.RTE.mazUnreachableError) in
                                             Any -> Any
forall a b. a -> b
coe
                                               (case Any -> T_Tri_136
forall a b. a -> b
coe Any
forall a. a
v8 of
                                                  MAlonzo.Code.Relation.Binary.Definitions.C_tri'60'_150 Any
v9
                                                    -> (Any -> T_Tri_136) -> Any -> Any
forall a b. a -> b
coe
                                                         Any -> T_Tri_136
MAlonzo.Code.Relation.Binary.Definitions.C_tri'62'_166
                                                         ((T__'8804'__18 -> T__'8804'__26) -> Any -> Any
forall a b. a -> b
coe
                                                            T__'8804'__18 -> T__'8804'__26
MAlonzo.Code.Data.Integer.Base.C_'45''8804''45'_34
                                                            ((T__'8804'__18 -> T__'8804'__18) -> Any -> Any
forall a b. a -> b
coe
                                                               T__'8804'__18 -> T__'8804'__18
MAlonzo.Code.Data.Nat.Properties.Core.du_'8804''45'pred_12
                                                               (Any -> Any
forall a b. a -> b
coe Any
v9)))
                                                  MAlonzo.Code.Relation.Binary.Definitions.C_tri'8776'_158 Any
v10
                                                    -> (Any -> T_Tri_136) -> Any -> Any
forall a b. a -> b
coe
                                                         Any -> T_Tri_136
MAlonzo.Code.Relation.Binary.Definitions.C_tri'8776'_158
                                                         Any
forall a. a
erased
                                                  MAlonzo.Code.Relation.Binary.Definitions.C_tri'62'_166 Any
v11
                                                    -> (Any -> T_Tri_136) -> Any -> Any
forall a b. a -> b
coe
                                                         Any -> T_Tri_136
MAlonzo.Code.Relation.Binary.Definitions.C_tri'60'_150
                                                         ((T__'8804'__18 -> T__'8804'__26) -> Any -> Any
forall a b. a -> b
coe
                                                            T__'8804'__18 -> T__'8804'__26
MAlonzo.Code.Data.Integer.Base.C_'45''8804''45'_34
                                                            ((T__'8804'__18 -> T__'8804'__18) -> Any -> Any
forall a b. a -> b
coe
                                                               T__'8804'__18 -> T__'8804'__18
MAlonzo.Code.Data.Nat.Properties.Core.du_'8804''45'pred_12
                                                               (Any -> Any
forall a b. a -> b
coe Any
v11)))
                                                  T_Tri_136
_ -> Any
forall a. a
MAlonzo.RTE.mazUnreachableError))
                                T_Dec_32
_ -> Any
forall a. a
MAlonzo.RTE.mazUnreachableError))))
-- Data.Integer.Properties.<′-isStrictPartialOrder
d_'60''8242''45'isStrictPartialOrder_6318 ::
  MAlonzo.Code.Relation.Binary.Structures.T_IsStrictPartialOrder_266
d_'60''8242''45'isStrictPartialOrder_6318 :: T_IsStrictPartialOrder_266
d_'60''8242''45'isStrictPartialOrder_6318
  = (T_IsEquivalence_26
 -> (Any -> Any -> Any -> Any -> Any -> Any)
 -> T_Σ_14
 -> T_IsStrictPartialOrder_266)
-> Any
-> (Any -> Any -> Any -> Any -> Any -> Any)
-> Any
-> 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
v0 Any
v1 Any
v2 Any
v3 Any
v4 -> (Integer
 -> Integer -> T__'8804'__26 -> T__'8804'__26 -> T__'8804'__26)
-> Any -> Any -> Any -> Any -> Any
forall a b. a -> b
coe Integer
-> Integer -> T__'8804'__26 -> T__'8804'__26 -> T__'8804'__26
du_'60''8242''45'trans_6212 Any
v0 Any
v1 Any
v3 Any
v4)
      ((Any -> Any -> T_Σ_14) -> Any -> Any -> Any
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.Integer.Properties.<′-strictPartialOrder
d_'60''8242''45'strictPartialOrder_6328 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_StrictPartialOrder_472
d_'60''8242''45'strictPartialOrder_6328 :: T_StrictPartialOrder_472
d_'60''8242''45'strictPartialOrder_6328
  = (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''8242''45'isStrictPartialOrder_6318
-- Data.Integer.Properties.<′-isStrictTotalOrder
d_'60''8242''45'isStrictTotalOrder_6330 ::
  MAlonzo.Code.Relation.Binary.Structures.T_IsStrictTotalOrder_502
d_'60''8242''45'isStrictTotalOrder_6330 :: T_IsStrictTotalOrder_502
d_'60''8242''45'isStrictTotalOrder_6330
  = (T_IsEquivalence_26
 -> (Any -> Any -> Any -> Any -> Any -> Any)
 -> (Any -> Any -> T_Tri_136)
 -> T_IsStrictTotalOrder_502)
-> Any
-> (Any -> Any -> Any -> Any -> 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
v0 Any
v1 Any
v2 Any
v3 Any
v4 -> (Integer
 -> Integer -> T__'8804'__26 -> T__'8804'__26 -> T__'8804'__26)
-> Any -> Any -> Any -> Any -> Any
forall a b. a -> b
coe Integer
-> Integer -> T__'8804'__26 -> T__'8804'__26 -> T__'8804'__26
du_'60''8242''45'trans_6212 Any
v0 Any
v1 Any
v3 Any
v4)
      ((Integer -> Integer -> T_Tri_136) -> Any
forall a b. a -> b
coe Integer -> Integer -> T_Tri_136
d_'60''8242''45'cmp_6224)
-- Data.Integer.Properties.<′-strictTotalOrder
d_'60''8242''45'strictTotalOrder_6334 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_StrictTotalOrder_864
d_'60''8242''45'strictTotalOrder_6334 :: T_StrictTotalOrder_864
d_'60''8242''45'strictTotalOrder_6334
  = (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''8242''45'isStrictTotalOrder_6330
-- Data.Integer.Properties.n≮′n
d_n'8814''8242'n_6338 ::
  Integer ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26 ->
  MAlonzo.Code.Data.Empty.T_'8869'_4
d_n'8814''8242'n_6338 :: Integer -> T__'8804'__26 -> T_'8869'_4
d_n'8814''8242'n_6338 = Integer -> T__'8804'__26 -> T_'8869'_4
forall a. a
erased
-- Data.Integer.Properties.>′⇒≰′
d_'62''8242''8658''8816''8242'_6352 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26 ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26 ->
  MAlonzo.Code.Data.Empty.T_'8869'_4
d_'62''8242''8658''8816''8242'_6352 :: Integer -> Integer -> T__'8804'__26 -> T__'8804'__26 -> T_'8869'_4
d_'62''8242''8658''8816''8242'_6352 = Integer -> Integer -> T__'8804'__26 -> T__'8804'__26 -> T_'8869'_4
forall a. a
erased
-- Data.Integer.Properties.≰⇒>′
d_'8816''8658''62''8242'_6364 ::
  Integer ->
  Integer ->
  (MAlonzo.Code.Data.Integer.Base.T__'8804'__26 ->
   MAlonzo.Code.Data.Empty.T_'8869'_4) ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26
d_'8816''8658''62''8242'_6364 :: Integer
-> Integer -> (T__'8804'__26 -> T_'8869'_4) -> T__'8804'__26
d_'8816''8658''62''8242'_6364 Integer
v0 Integer
v1 ~T__'8804'__26 -> T_'8869'_4
v2
  = Integer -> Integer -> T__'8804'__26
du_'8816''8658''62''8242'_6364 Integer
v0 Integer
v1
du_'8816''8658''62''8242'_6364 ::
  Integer -> Integer -> MAlonzo.Code.Data.Integer.Base.T__'8804'__26
du_'8816''8658''62''8242'_6364 :: Integer -> Integer -> T__'8804'__26
du_'8816''8658''62''8242'_6364 Integer
v0 Integer
v1
  = case Integer -> Any
forall a b. a -> b
coe Integer
v0 of
      Any
_ | (Integer -> Integer -> Bool) -> Any -> Any -> Bool
forall a b. a -> b
coe Integer -> Integer -> Bool
geqInt (Integer -> Any
forall a b. a -> b
coe Integer
v0) (Integer -> Any
forall a b. a -> b
coe (Integer
0 :: Integer)) ->
          case Integer -> Any
forall a b. a -> b
coe Integer
v1 of
            Any
_ | (Integer -> Integer -> Bool) -> Any -> Any -> Bool
forall a b. a -> b
coe Integer -> Integer -> Bool
geqInt (Integer -> Any
forall a b. a -> b
coe Integer
v1) (Integer -> Any
forall a b. a -> b
coe (Integer
0 :: Integer)) ->
                (T__'8804'__18 -> T__'8804'__26) -> Any -> T__'8804'__26
forall a b. a -> b
coe
                  T__'8804'__18 -> T__'8804'__26
MAlonzo.Code.Data.Integer.Base.C_'43''8804''43'_48
                  ((Integer -> Integer -> T__'8804'__18) -> Any -> Any -> Any
forall a b. a -> b
coe
                     Integer -> Integer -> T__'8804'__18
MAlonzo.Code.Data.Nat.Properties.du_'8816''8658''62'_1770 (Integer -> Any
forall a b. a -> b
coe Integer
v0)
                     (Integer -> Any
forall a b. a -> b
coe Integer
v1))
            Any
_ -> let v2 :: Integer
v2 = Integer -> Integer -> Integer
subInt (Integer -> Integer
forall a b. a -> b
coe (-Integer
1 :: Integer)) (Integer -> Integer
forall a b. a -> b
coe Integer
v1) in
                 Any -> T__'8804'__26
forall a b. a -> b
coe ((Integer -> T__'8804'__26) -> Any -> Any
forall a b. a -> b
coe Integer -> T__'8804'__26
du_'45''60''8242''43'_6142 (Integer -> Any
forall a b. a -> b
coe Integer
v2))
      Any
_ -> let v2 :: Integer
v2 = Integer -> Integer -> Integer
subInt (Integer -> Integer
forall a b. a -> b
coe (-Integer
1 :: Integer)) (Integer -> Integer
forall a b. a -> b
coe Integer
v0) in
           Any -> T__'8804'__26
forall a b. a -> b
coe
             (case Integer -> Any
forall a b. a -> b
coe Integer
v1 of
                Any
_ | (Integer -> Integer -> Bool) -> Any -> Any -> Bool
forall a b. a -> b
coe Integer -> Integer -> Bool
geqInt (Integer -> Any
forall a b. a -> b
coe Integer
v1) (Integer -> Any
forall a b. a -> b
coe (Integer
0 :: Integer)) ->
                    Any -> Any
forall a b. a -> b
coe Any
MAlonzo.Code.Relation.Nullary.Negation.Core.du_contradiction_24
                Any
_ -> let v3 :: Integer
v3 = Integer -> Integer -> Integer
subInt (Integer -> Integer
forall a b. a -> b
coe (-Integer
1 :: Integer)) (Integer -> Integer
forall a b. a -> b
coe Integer
v1) in
                     Any -> Any
forall a b. a -> b
coe
                       (let v4 :: b
v4
                              = let v4 :: Integer
v4 = Integer -> Integer -> Integer
subInt (Integer -> Integer
forall a b. a -> b
coe (-Integer
2 :: Integer)) (Integer -> Integer
forall a b. a -> b
coe Integer
v1) in
                                Any -> b
forall a b. a -> b
coe
                                  (let v5 :: t
v5
                                         = ((Any -> Any) -> T_Dec_32 -> T_Dec_32) -> (Any -> Any) -> Any -> t
forall a b. a -> b
coe
                                             (Any -> Any) -> T_Dec_32 -> T_Dec_32
MAlonzo.Code.Relation.Nullary.Decidable.Core.du_map'8242'_168
                                             (\ Any
v5 ->
                                                (Integer -> T__'8804'__18) -> Any -> Any
forall a b. a -> b
coe
                                                  Integer -> T__'8804'__18
MAlonzo.Code.Data.Nat.Properties.du_'8804''7495''8658''8804'_1600
                                                  (Integer -> Any
forall a b. a -> b
coe Integer
v2))
                                             ((Bool -> T_Dec_32) -> Any -> Any
forall a b. a -> b
coe
                                                Bool -> T_Dec_32
MAlonzo.Code.Data.Bool.Properties.d_T'63'_2210
                                                ((Integer -> Integer -> Bool) -> Any -> Any -> Any
forall a b. a -> b
coe
                                                   Integer -> Integer -> Bool
MAlonzo.Code.Data.Nat.Base.d__'8804''7495'__10
                                                   (Integer -> Any
forall a b. a -> b
coe Integer
v2) (Integer -> Any
forall a b. a -> b
coe Integer
v4))) in
                                   Any -> Any
forall a b. a -> b
coe
                                     (case Any -> T_Dec_32
forall a b. a -> b
coe Any
forall a. a
v5 of
                                        MAlonzo.Code.Relation.Nullary.C__because__46 Bool
v6 T_Reflects_14
v7
                                          -> if Bool -> Bool
forall a b. a -> b
coe Bool
v6
                                               then case T_Reflects_14 -> T_Reflects_14
forall a b. a -> b
coe T_Reflects_14
v7 of
                                                      MAlonzo.Code.Relation.Nullary.C_of'696'_22 Any
v8
                                                        -> (T__'8804'__18 -> T__'8804'__26) -> Any -> Any
forall a b. a -> b
coe
                                                             T__'8804'__18 -> T__'8804'__26
MAlonzo.Code.Data.Integer.Base.C_'45''8804''45'_34
                                                             Any
v8
                                                      T_Reflects_14
_ -> Any
forall a. a
MAlonzo.RTE.mazUnreachableError
                                               else (Any -> Any -> Any) -> Any -> Any -> Any
forall a b. a -> b
coe
                                                      Any -> Any -> Any
forall a b. a -> b -> b
seq (T_Reflects_14 -> Any
forall a b. a -> b
coe T_Reflects_14
v7)
                                                      (Any -> Any
forall a b. a -> b
coe
                                                         Any
MAlonzo.Code.Relation.Nullary.Negation.Core.du_contradiction_24)
                                        T_Dec_32
_ -> Any
forall a. a
MAlonzo.RTE.mazUnreachableError)) in
                        Any -> Any
forall a b. a -> b
coe
                          ((Any -> Any -> Any) -> Any -> Any -> Any
forall a b. a -> b
coe
                             Any -> Any -> Any
forall a b. a -> b -> b
seq (Integer -> Any
forall a b. a -> b
coe Integer
v2)
                             (case Integer -> Integer
forall a b. a -> b
coe Integer
v3 of
                                Integer
0 -> Any -> Any
forall a b. a -> b
coe
                                       Any
MAlonzo.Code.Relation.Nullary.Negation.Core.du_contradiction_24
                                Integer
_ -> Any -> Any
forall a b. a -> b
coe Any
forall a. a
v4))))
-- Data.Integer.Properties.<′-irrelevant
d_'60''8242''45'irrelevant_6410 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26 ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'60''8242''45'irrelevant_6410 :: Integer
-> Integer -> T__'8804'__26 -> T__'8804'__26 -> T__'8801'__12
d_'60''8242''45'irrelevant_6410 = Integer
-> Integer -> T__'8804'__26 -> T__'8804'__26 -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.+-monoˡ-<′
d_'43''45'mono'737''45''60''8242'_6416 ::
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26 ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26
d_'43''45'mono'737''45''60''8242'_6416 :: Integer -> Integer -> Integer -> T__'8804'__26 -> T__'8804'__26
d_'43''45'mono'737''45''60''8242'_6416 Integer
v0 Integer
v1 Integer
v2 T__'8804'__26
v3
  = (Integer -> Integer -> Integer -> T__'8804'__26 -> T__'8804'__26)
-> Any -> Any -> Any -> Any -> T__'8804'__26
forall a b. a -> b
coe
      Integer -> Integer -> Integer -> T__'8804'__26 -> T__'8804'__26
d_'43''45'mono'737''45''8804'_3422 (Integer -> Any
forall a b. a -> b
coe Integer
v0)
      ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe
         Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'43'__242 (Integer -> Any
forall a b. a -> b
coe (Integer
1 :: Integer))
         (Integer -> Any
forall a b. a -> b
coe Integer
v1))
      (Integer -> Any
forall a b. a -> b
coe Integer
v2) (T__'8804'__26 -> Any
forall a b. a -> b
coe T__'8804'__26
v3)
-- Data.Integer.Properties.+-monoʳ-<′
d_'43''45'mono'691''45''60''8242'_6432 ::
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26 ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26
d_'43''45'mono'691''45''60''8242'_6432 :: Integer -> Integer -> Integer -> T__'8804'__26 -> T__'8804'__26
d_'43''45'mono'691''45''60''8242'_6432 Integer
v0 Integer
v1 Integer
v2 T__'8804'__26
v3
  = (Integer -> Integer -> Integer -> T__'8804'__26 -> T__'8804'__26)
-> Any -> Any -> Any -> Any -> T__'8804'__26
forall a b. a -> b
coe
      Integer -> Integer -> Integer -> T__'8804'__26 -> T__'8804'__26
d_'43''45'mono'737''45''60''8242'_6416 (Integer -> Any
forall a b. a -> b
coe Integer
v0) (Integer -> Any
forall a b. a -> b
coe Integer
v1) (Integer -> Any
forall a b. a -> b
coe Integer
v2)
      (T__'8804'__26 -> Any
forall a b. a -> b
coe T__'8804'__26
v3)
-- Data.Integer.Properties.+-mono-<′
d_'43''45'mono'45''60''8242'_6450 ::
  Integer ->
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26 ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26 ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26
d_'43''45'mono'45''60''8242'_6450 :: Integer
-> Integer
-> Integer
-> Integer
-> T__'8804'__26
-> T__'8804'__26
-> T__'8804'__26
d_'43''45'mono'45''60''8242'_6450 Integer
v0 Integer
v1 Integer
v2 Integer
v3 T__'8804'__26
v4 T__'8804'__26
v5
  = (T_IsPreorder_70
 -> (Any -> Any -> Any -> Any)
 -> Any
 -> Any
 -> T__IsRelatedTo__70
 -> Any)
-> Any -> Any -> Any -> Any -> Any -> T__'8804'__26
forall a b. a -> b
coe
      T_IsPreorder_70
-> (Any -> Any -> Any -> Any)
-> Any
-> Any
-> T__IsRelatedTo__70
-> Any
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_begin__160
      (T_IsPreorder_70 -> Any
forall a b. a -> b
coe T_IsPreorder_70
d_'8804''45'isPreorder_1656) ((Integer -> Integer -> T__'60'__50 -> T__'8804'__26) -> Any
forall a b. a -> b
coe Integer -> Integer -> T__'60'__50 -> T__'8804'__26
d_'60''8658''8804'_1724)
      ((Integer -> Integer) -> Any -> Any
forall a b. a -> b
coe
         Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d_suc_266
         ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe
            Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'43'__242 (Integer -> Any
forall a b. a -> b
coe Integer
v0) (Integer -> Any
forall a b. a -> b
coe Integer
v2)))
      ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'43'__242 (Integer -> Any
forall a b. a -> b
coe Integer
v1) (Integer -> Any
forall a b. a -> b
coe Integer
v3))
      ((T_IsPreorder_70
 -> (Any -> Any -> Any -> Any -> Any -> Any)
 -> Any
 -> Any
 -> Any
 -> T__IsRelatedTo__70
 -> Any
 -> T__IsRelatedTo__70)
-> Any
-> (Any -> Any -> Any -> Any -> Any -> Any)
-> Any
-> Any
-> Any
-> Any
-> Any
-> Any
forall a b. a -> b
coe
         T_IsPreorder_70
-> (Any -> Any -> Any -> Any -> Any -> Any)
-> Any
-> Any
-> Any
-> T__IsRelatedTo__70
-> Any
-> T__IsRelatedTo__70
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_step'45''8804'_228
         (T_IsPreorder_70 -> Any
forall a b. a -> b
coe T_IsPreorder_70
d_'8804''45'isPreorder_1656)
         (\ Any
v6 Any
v7 Any
v8 Any
v9 Any
v10 -> (T__'8804'__26 -> T__'60'__50 -> T__'60'__50) -> Any -> Any -> Any
forall a b. a -> b
coe T__'8804'__26 -> T__'60'__50 -> T__'60'__50
du_'8804''45''60''45'trans_1844 Any
v9 Any
v10)
         ((Integer -> Integer) -> Any -> Any
forall a b. a -> b
coe
            Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d_suc_266
            ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe
               Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'43'__242 (Integer -> Any
forall a b. a -> b
coe Integer
v0) (Integer -> Any
forall a b. a -> b
coe Integer
v2)))
         ((Integer -> Integer) -> Any -> Any
forall a b. a -> b
coe
            Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d_suc_266
            ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe
               Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'43'__242 (Integer -> Any
forall a b. a -> b
coe Integer
v1) (Integer -> Any
forall a b. a -> b
coe Integer
v2)))
         ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'43'__242 (Integer -> Any
forall a b. a -> b
coe Integer
v1) (Integer -> Any
forall a b. a -> b
coe Integer
v3))
         ((T_IsPreorder_70
 -> (Any -> Any -> Any -> Any -> Any -> Any)
 -> Any
 -> Any
 -> Any
 -> T__IsRelatedTo__70
 -> Any
 -> T__IsRelatedTo__70)
-> Any
-> (Any -> Any -> Any -> Any -> Any -> Any)
-> Any
-> Any
-> Any
-> Any
-> Any
-> Any
forall a b. a -> b
coe
            T_IsPreorder_70
-> (Any -> Any -> Any -> Any -> Any -> Any)
-> Any
-> Any
-> Any
-> T__IsRelatedTo__70
-> Any
-> T__IsRelatedTo__70
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_step'45''8804'_228
            (T_IsPreorder_70 -> Any
forall a b. a -> b
coe T_IsPreorder_70
d_'8804''45'isPreorder_1656)
            (\ Any
v6 Any
v7 Any
v8 Any
v9 Any
v10 -> (T__'8804'__26 -> T__'60'__50 -> T__'60'__50) -> Any -> Any -> Any
forall a b. a -> b
coe T__'8804'__26 -> T__'60'__50 -> T__'60'__50
du_'8804''45''60''45'trans_1844 Any
v9 Any
v10)
            ((Integer -> Integer) -> Any -> Any
forall a b. a -> b
coe
               Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d_suc_266
               ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe
                  Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'43'__242 (Integer -> Any
forall a b. a -> b
coe Integer
v1) (Integer -> Any
forall a b. a -> b
coe Integer
v2)))
            ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'43'__242 (Integer -> Any
forall a b. a -> b
coe Integer
v1) (Integer -> Any
forall a b. a -> b
coe Integer
v3))
            ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'43'__242 (Integer -> Any
forall a b. a -> b
coe Integer
v1) (Integer -> Any
forall a b. a -> b
coe Integer
v3))
            ((T_IsPreorder_70 -> Any -> T__IsRelatedTo__70) -> Any -> Any -> Any
forall a b. a -> b
coe
               T_IsPreorder_70 -> Any -> T__IsRelatedTo__70
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du__'8718'_346
               (T_IsPreorder_70 -> Any
forall a b. a -> b
coe T_IsPreorder_70
d_'8804''45'isPreorder_1656)
               ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe
                  Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'43'__242 (Integer -> Any
forall a b. a -> b
coe Integer
v1) (Integer -> Any
forall a b. a -> b
coe Integer
v3)))
            ((Integer -> Integer -> Integer -> T__'8804'__26 -> T__'8804'__26)
-> Any -> Any -> Any -> Any -> Any
forall a b. a -> b
coe
               Integer -> Integer -> Integer -> T__'8804'__26 -> T__'8804'__26
d_'43''45'mono'691''45''60''8242'_6432 (Integer -> Any
forall a b. a -> b
coe Integer
v1) (Integer -> Any
forall a b. a -> b
coe Integer
v2) (Integer -> Any
forall a b. a -> b
coe Integer
v3)
               (T__'8804'__26 -> Any
forall a b. a -> b
coe T__'8804'__26
v5)))
         ((Integer -> Integer -> T__'8804'__26 -> T__'8804'__26)
-> Any -> Any -> Any -> Any
forall a b. a -> b
coe
            Integer -> Integer -> T__'8804'__26 -> T__'8804'__26
d_suc'45'mono_3890
            ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'43'__242 (Integer -> Any
forall a b. a -> b
coe Integer
v0) (Integer -> Any
forall a b. a -> b
coe Integer
v2))
            (((Any -> Any -> Any) -> (Any -> Any) -> Any -> Any -> Any)
-> (Any -> Any -> Any)
-> (Any -> Integer)
-> Integer
-> Integer
-> Any
forall a b. a -> b
coe
               (Any -> Any -> Any) -> (Any -> Any) -> Any -> Any -> Any
MAlonzo.Code.Function.Base.du_'8739'_'10217''45'__308
               (\ Any
v6 Any
v7 -> Any
v7)
               (\ Any
v6 ->
                  Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'43'__242 (Any -> Integer
forall a b. a -> b
coe Any
v6) (Integer -> Integer
forall a b. a -> b
coe Integer
v2))
               Integer
v0 Integer
v1)
            ((Integer -> T__'8804'__26 -> T__'8804'__26) -> Any -> Any -> Any
forall a b. a -> b
coe
               Integer -> T__'8804'__26 -> T__'8804'__26
du_'60''8242''8658''8804'_6208
               ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'43'__242 (Integer -> Any
forall a b. a -> b
coe Integer
v0) (Integer -> Any
forall a b. a -> b
coe Integer
v2))
               ((Integer -> Integer -> Integer -> T__'8804'__26 -> T__'8804'__26)
-> Any -> Any -> Any -> Any -> Any
forall a b. a -> b
coe
                  Integer -> Integer -> Integer -> T__'8804'__26 -> T__'8804'__26
d_'43''45'mono'737''45''60''8242'_6416 (Integer -> Any
forall a b. a -> b
coe Integer
v2) (Integer -> Any
forall a b. a -> b
coe Integer
v0) (Integer -> Any
forall a b. a -> b
coe Integer
v1)
                  (T__'8804'__26 -> Any
forall a b. a -> b
coe T__'8804'__26
v4)))))
-- Data.Integer.Properties.+-mono-≤-<′
d_'43''45'mono'45''8804''45''60''8242'_6468 ::
  Integer ->
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26 ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26 ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26
d_'43''45'mono'45''8804''45''60''8242'_6468 :: Integer
-> Integer
-> Integer
-> Integer
-> T__'8804'__26
-> T__'8804'__26
-> T__'8804'__26
d_'43''45'mono'45''8804''45''60''8242'_6468 Integer
v0 Integer
v1 Integer
v2 Integer
v3 T__'8804'__26
v4 T__'8804'__26
v5
  = (Integer
 -> Integer -> T__'8804'__26 -> T__'8804'__26 -> T__'8804'__26)
-> Any -> Any -> Any -> Any -> T__'8804'__26
forall a b. a -> b
coe
      Integer
-> Integer -> T__'8804'__26 -> T__'8804'__26 -> T__'8804'__26
du_'8804''45''60''8242''45'trans_6174
      (((Any -> Any) -> (Any -> Any -> Any) -> Any -> Any -> Any)
-> (Any -> Integer)
-> (Any -> Any -> Any)
-> Integer
-> Integer
-> Any
forall a b. a -> b
coe
         (Any -> Any) -> (Any -> Any -> Any) -> Any -> Any -> Any
MAlonzo.Code.Function.Base.du__'45''10216'_'8739'_302
         (\ Any
v6 ->
            Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'43'__242 (Any -> Integer
forall a b. a -> b
coe Any
v6) (Integer -> Integer
forall a b. a -> b
coe Integer
v2))
         (\ Any
v6 Any
v7 -> Any
v6) Integer
v0 Integer
v1)
      (((Any -> Any -> Any) -> (Any -> Any) -> Any -> Any -> Any)
-> (Any -> Any -> Any)
-> (Any -> Integer)
-> Integer
-> Integer
-> Any
forall a b. a -> b
coe
         (Any -> Any -> Any) -> (Any -> Any) -> Any -> Any -> Any
MAlonzo.Code.Function.Base.du_'8739'_'10217''45'__308
         (\ Any
v6 Any
v7 -> Any
v7)
         (\ Any
v6 ->
            Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'43'__242 (Any -> Integer
forall a b. a -> b
coe Any
v6) (Integer -> Integer
forall a b. a -> b
coe Integer
v2))
         Integer
v0 Integer
v1)
      ((Integer -> Integer -> Integer -> T__'8804'__26 -> T__'8804'__26)
-> Any -> Any -> Any -> Any -> Any
forall a b. a -> b
coe
         Integer -> Integer -> Integer -> T__'8804'__26 -> T__'8804'__26
d_'43''45'mono'737''45''8804'_3422 (Integer -> Any
forall a b. a -> b
coe Integer
v2) (Integer -> Any
forall a b. a -> b
coe Integer
v0) (Integer -> Any
forall a b. a -> b
coe Integer
v1)
         (T__'8804'__26 -> Any
forall a b. a -> b
coe T__'8804'__26
v4))
      ((Integer -> Integer -> Integer -> T__'8804'__26 -> T__'8804'__26)
-> Any -> Any -> Any -> Any -> Any
forall a b. a -> b
coe
         Integer -> Integer -> Integer -> T__'8804'__26 -> T__'8804'__26
d_'43''45'mono'691''45''60''8242'_6432 (Integer -> Any
forall a b. a -> b
coe Integer
v1) (Integer -> Any
forall a b. a -> b
coe Integer
v2) (Integer -> Any
forall a b. a -> b
coe Integer
v3)
         (T__'8804'__26 -> Any
forall a b. a -> b
coe T__'8804'__26
v5))
-- Data.Integer.Properties.+-mono-<′-≤
d_'43''45'mono'45''60''8242''45''8804'_6482 ::
  Integer ->
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26 ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26 ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26
d_'43''45'mono'45''60''8242''45''8804'_6482 :: Integer
-> Integer
-> Integer
-> Integer
-> T__'8804'__26
-> T__'8804'__26
-> T__'8804'__26
d_'43''45'mono'45''60''8242''45''8804'_6482 Integer
v0 Integer
v1 Integer
v2 Integer
v3 T__'8804'__26
v4 T__'8804'__26
v5
  = (T__'8804'__26 -> T__'8804'__26 -> T__'8804'__26)
-> T__'8804'__26 -> Any -> T__'8804'__26
forall a b. a -> b
coe
      T__'8804'__26 -> T__'8804'__26 -> T__'8804'__26
du_'60''8242''45''8804''45'trans_6202
      (Integer -> Integer -> Integer -> T__'8804'__26 -> T__'8804'__26
d_'43''45'mono'737''45''60''8242'_6416
         (Integer -> Integer
forall a b. a -> b
coe Integer
v2) (Integer -> Integer
forall a b. a -> b
coe Integer
v0) (Integer -> Integer
forall a b. a -> b
coe Integer
v1) (T__'8804'__26 -> T__'8804'__26
forall a b. a -> b
coe T__'8804'__26
v4))
      ((Integer -> Integer -> Integer -> T__'8804'__26 -> T__'8804'__26)
-> Integer -> Integer -> Integer -> T__'8804'__26 -> Any
forall a b. a -> b
coe Integer -> Integer -> Integer -> T__'8804'__26 -> T__'8804'__26
d_'43''45'mono'691''45''8804'_3412 Integer
v1 Integer
v2 Integer
v3 T__'8804'__26
v5)
-- Data.Integer.Properties.m≤pred[n]⇒m<′n
d_m'8804'pred'91'n'93''8658'm'60''8242'n_6500 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26 ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26
d_m'8804'pred'91'n'93''8658'm'60''8242'n_6500 :: Integer -> Integer -> T__'8804'__26 -> T__'8804'__26
d_m'8804'pred'91'n'93''8658'm'60''8242'n_6500 Integer
v0 Integer
v1 T__'8804'__26
v2
  = (T_IsPreorder_70
 -> (Any -> Any -> Any -> Any)
 -> Any
 -> Any
 -> T__IsRelatedTo__70
 -> Any)
-> Any -> Any -> Any -> Any -> Any -> T__'8804'__26
forall a b. a -> b
coe
      T_IsPreorder_70
-> (Any -> Any -> Any -> Any)
-> Any
-> Any
-> T__IsRelatedTo__70
-> Any
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_begin__160
      (T_IsPreorder_70 -> Any
forall a b. a -> b
coe T_IsPreorder_70
d_'8804''45'isPreorder_1656) ((Integer -> Integer -> T__'60'__50 -> T__'8804'__26) -> Any
forall a b. a -> b
coe Integer -> Integer -> T__'60'__50 -> T__'8804'__26
d_'60''8658''8804'_1724)
      ((Integer -> Integer) -> Any -> Any
forall a b. a -> b
coe Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d_suc_266 (Integer -> Any
forall a b. a -> b
coe Integer
v0)) (Integer -> Any
forall a b. a -> b
coe Integer
v1)
      ((T_IsPreorder_70
 -> (Any -> Any -> Any -> Any -> Any -> Any)
 -> Any
 -> Any
 -> Any
 -> T__IsRelatedTo__70
 -> Any
 -> T__IsRelatedTo__70)
-> Any
-> (Any -> Any -> Any -> Any -> Any -> Any)
-> Any
-> Any
-> Any
-> Any
-> Any
-> Any
forall a b. a -> b
coe
         T_IsPreorder_70
-> (Any -> Any -> Any -> Any -> Any -> Any)
-> Any
-> Any
-> Any
-> T__IsRelatedTo__70
-> Any
-> T__IsRelatedTo__70
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_step'45''8804'_228
         (T_IsPreorder_70 -> Any
forall a b. a -> b
coe T_IsPreorder_70
d_'8804''45'isPreorder_1656)
         (\ Any
v3 Any
v4 Any
v5 Any
v6 Any
v7 -> (T__'8804'__26 -> T__'60'__50 -> T__'60'__50) -> Any -> Any -> Any
forall a b. a -> b
coe T__'8804'__26 -> T__'60'__50 -> T__'60'__50
du_'8804''45''60''45'trans_1844 Any
v6 Any
v7)
         ((Integer -> Integer) -> Any -> Any
forall a b. a -> b
coe Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d_suc_266 (Integer -> Any
forall a b. a -> b
coe Integer
v0))
         ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe
            Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'43'__242 (Integer -> Any
forall a b. a -> b
coe (Integer
1 :: Integer))
            ((Integer -> Integer) -> Any -> Any
forall a b. a -> b
coe Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d_pred_270 (Integer -> Any
forall a b. a -> b
coe Integer
v1)))
         (Integer -> Any
forall a b. a -> b
coe Integer
v1)
         ((T_IsPreorder_70 -> Any -> T__IsRelatedTo__70) -> Any -> Any -> Any
forall a b. a -> b
coe
            T_IsPreorder_70 -> Any -> T__IsRelatedTo__70
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du__'8718'_346
            (T_IsPreorder_70 -> Any
forall a b. a -> b
coe T_IsPreorder_70
d_'8804''45'isPreorder_1656) (Integer -> Any
forall a b. a -> b
coe Integer
v1))
         ((Integer -> Integer -> Integer -> T__'8804'__26 -> T__'8804'__26)
-> Integer -> Integer -> Integer -> T__'8804'__26 -> Any
forall a b. a -> b
coe
            Integer -> Integer -> Integer -> T__'8804'__26 -> T__'8804'__26
d_'43''45'mono'691''45''8804'_3412 (Integer
1 :: Integer) Integer
v0
            (Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d_pred_270 (Integer -> Integer
forall a b. a -> b
coe Integer
v1)) T__'8804'__26
v2))
-- Data.Integer.Properties.m<′n⇒m≤pred[n]
d_m'60''8242'n'8658'm'8804'pred'91'n'93'_6518 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26 ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26
d_m'60''8242'n'8658'm'8804'pred'91'n'93'_6518 :: Integer -> Integer -> T__'8804'__26 -> T__'8804'__26
d_m'60''8242'n'8658'm'8804'pred'91'n'93'_6518 Integer
v0 Integer
v1 T__'8804'__26
v2
  = (T_IsPreorder_70
 -> (Any -> Any -> Any -> Any)
 -> Any
 -> Any
 -> T__IsRelatedTo__70
 -> Any)
-> Any -> Any -> Any -> Any -> Any -> T__'8804'__26
forall a b. a -> b
coe
      T_IsPreorder_70
-> (Any -> Any -> Any -> Any)
-> Any
-> Any
-> T__IsRelatedTo__70
-> Any
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_begin__160
      (T_IsPreorder_70 -> Any
forall a b. a -> b
coe T_IsPreorder_70
d_'8804''45'isPreorder_1656) ((Integer -> Integer -> T__'60'__50 -> T__'8804'__26) -> Any
forall a b. a -> b
coe Integer -> Integer -> T__'60'__50 -> T__'8804'__26
d_'60''8658''8804'_1724)
      (Integer -> Any
forall a b. a -> b
coe Integer
v0) ((Integer -> Integer) -> Any -> Any
forall a b. a -> b
coe Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d_pred_270 (Integer -> Any
forall a b. a -> b
coe Integer
v1))
      ((T_IsPreorder_70
 -> (Any -> Any -> Any -> Any -> Any -> Any)
 -> Any
 -> Any
 -> Any
 -> T__IsRelatedTo__70
 -> Any
 -> T__IsRelatedTo__70)
-> Any
-> (Any -> Any -> Any -> Any -> Any -> Any)
-> Any
-> Any
-> Any
-> Any
-> Any
-> Any
forall a b. a -> b
coe
         T_IsPreorder_70
-> (Any -> Any -> Any -> Any -> Any -> Any)
-> Any
-> Any
-> Any
-> T__IsRelatedTo__70
-> Any
-> T__IsRelatedTo__70
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_step'45''8804'_228
         (T_IsPreorder_70 -> Any
forall a b. a -> b
coe T_IsPreorder_70
d_'8804''45'isPreorder_1656)
         (\ Any
v3 Any
v4 Any
v5 Any
v6 Any
v7 -> (T__'8804'__26 -> T__'60'__50 -> T__'60'__50) -> Any -> Any -> Any
forall a b. a -> b
coe T__'8804'__26 -> T__'60'__50 -> T__'60'__50
du_'8804''45''60''45'trans_1844 Any
v6 Any
v7)
         ((Integer -> Integer) -> Any -> Any
forall a b. a -> b
coe
            Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d_pred_270
            ((Integer -> Integer) -> Any -> Any
forall a b. a -> b
coe Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d_suc_266 (Integer -> Any
forall a b. a -> b
coe Integer
v0)))
         ((Integer -> Integer) -> Any -> Any
forall a b. a -> b
coe Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d_pred_270 (Integer -> Any
forall a b. a -> b
coe Integer
v1))
         ((Integer -> Integer) -> Any -> Any
forall a b. a -> b
coe Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d_pred_270 (Integer -> Any
forall a b. a -> b
coe Integer
v1))
         ((T_IsPreorder_70 -> Any -> T__IsRelatedTo__70) -> Any -> Any -> Any
forall a b. a -> b
coe
            T_IsPreorder_70 -> Any -> T__IsRelatedTo__70
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du__'8718'_346
            (T_IsPreorder_70 -> Any
forall a b. a -> b
coe T_IsPreorder_70
d_'8804''45'isPreorder_1656)
            ((Integer -> Integer) -> Any -> Any
forall a b. a -> b
coe Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d_pred_270 (Integer -> Any
forall a b. a -> b
coe Integer
v1)))
         ((Integer -> Integer -> T__'8804'__26 -> T__'8804'__26)
-> Any -> Any -> Any -> Any
forall a b. a -> b
coe
            Integer -> Integer -> T__'8804'__26 -> T__'8804'__26
d_pred'45'mono_4056
            ((Integer -> Integer) -> Any -> Any
forall a b. a -> b
coe Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d_suc_266 (Integer -> Any
forall a b. a -> b
coe Integer
v0)) (Integer -> Any
forall a b. a -> b
coe Integer
v1)
            (T__'8804'__26 -> Any
forall a b. a -> b
coe T__'8804'__26
v2)))
-- Data.Integer.Properties.[1+m]*n≡n+m*n
d_'91'1'43'm'93''42'n'8801'n'43'm'42'n_6530 ::
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'91'1'43'm'93''42'n'8801'n'43'm'42'n_6530 :: Integer -> Integer -> T__'8801'__12
d_'91'1'43'm'93''42'n'8801'n'43'm'42'n_6530 = Integer -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.neg-mono-<->
d_neg'45'mono'45''60''45''62'_6532 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Integer.Base.T__'60'__50 ->
  MAlonzo.Code.Data.Integer.Base.T__'60'__50
d_neg'45'mono'45''60''45''62'_6532 :: Integer -> Integer -> T__'60'__50 -> T__'60'__50
d_neg'45'mono'45''60''45''62'_6532 = (Integer -> Integer -> T__'60'__50 -> T__'60'__50)
-> Integer -> Integer -> T__'60'__50 -> T__'60'__50
forall a b. a -> b
coe Integer -> Integer -> T__'60'__50 -> T__'60'__50
d_neg'45'mono'45''60'_2144
-- Data.Integer.Properties.neg-mono-≤-≥
d_neg'45'mono'45''8804''45''8805'_6534 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26 ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26
d_neg'45'mono'45''8804''45''8805'_6534 :: Integer -> Integer -> T__'8804'__26 -> T__'8804'__26
d_neg'45'mono'45''8804''45''8805'_6534 Integer
v0 Integer
v1 T__'8804'__26
v2
  = (Integer -> T__'8804'__26 -> T__'8804'__26)
-> Integer -> T__'8804'__26 -> T__'8804'__26
forall a b. a -> b
coe Integer -> T__'8804'__26 -> T__'8804'__26
du_neg'45'mono'45''8804'_3730 Integer
v1 T__'8804'__26
v2
-- Data.Integer.Properties.*-monoʳ-≤-non-neg
d_'42''45'mono'691''45''8804''45'non'45'neg_6536 ::
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26 ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26
d_'42''45'mono'691''45''8804''45'non'45'neg_6536 :: Integer -> Integer -> Integer -> T__'8804'__26 -> T__'8804'__26
d_'42''45'mono'691''45''8804''45'non'45'neg_6536
  = (Integer -> Integer -> Integer -> T__'8804'__26 -> T__'8804'__26)
-> Integer -> Integer -> Integer -> T__'8804'__26 -> T__'8804'__26
forall a b. a -> b
coe Integer -> Integer -> Integer -> T__'8804'__26 -> T__'8804'__26
d_'42''45'mono'691''45''8804''45'nonNeg_5044
-- Data.Integer.Properties.*-monoˡ-≤-non-neg
d_'42''45'mono'737''45''8804''45'non'45'neg_6538 ::
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26 ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26
d_'42''45'mono'737''45''8804''45'non'45'neg_6538 :: Integer -> Integer -> Integer -> T__'8804'__26 -> T__'8804'__26
d_'42''45'mono'737''45''8804''45'non'45'neg_6538
  = (Integer -> Integer -> Integer -> T__'8804'__26 -> T__'8804'__26)
-> Integer -> Integer -> Integer -> T__'8804'__26 -> T__'8804'__26
forall a b. a -> b
coe Integer -> Integer -> Integer -> T__'8804'__26 -> T__'8804'__26
d_'42''45'mono'737''45''8804''45'nonNeg_5066
-- Data.Integer.Properties.*-cancelˡ-<-non-neg
d_'42''45'cancel'737''45''60''45'non'45'neg_6540 ::
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Integer.Base.T__'60'__50 ->
  MAlonzo.Code.Data.Integer.Base.T__'60'__50
d_'42''45'cancel'737''45''60''45'non'45'neg_6540 :: Integer -> Integer -> Integer -> T__'60'__50 -> T__'60'__50
d_'42''45'cancel'737''45''60''45'non'45'neg_6540
  = (Integer -> Integer -> Integer -> T__'60'__50 -> T__'60'__50)
-> Integer -> Integer -> Integer -> T__'60'__50 -> T__'60'__50
forall a b. a -> b
coe Integer -> Integer -> Integer -> T__'60'__50 -> T__'60'__50
d_'42''45'cancel'737''45''60''45'nonNeg_5252
-- Data.Integer.Properties.*-cancelʳ-<-non-neg
d_'42''45'cancel'691''45''60''45'non'45'neg_6542 ::
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Integer.Base.T__'60'__50 ->
  MAlonzo.Code.Data.Integer.Base.T__'60'__50
d_'42''45'cancel'691''45''60''45'non'45'neg_6542 :: Integer -> Integer -> Integer -> T__'60'__50 -> T__'60'__50
d_'42''45'cancel'691''45''60''45'non'45'neg_6542
  = (Integer -> Integer -> Integer -> T__'60'__50 -> T__'60'__50)
-> Integer -> Integer -> Integer -> T__'60'__50 -> T__'60'__50
forall a b. a -> b
coe Integer -> Integer -> Integer -> T__'60'__50 -> T__'60'__50
d_'42''45'cancel'691''45''60''45'nonNeg_5292
-- Data.Integer.Properties.m≤n⇒m⊓n≡m
d_m'8804'n'8658'm'8851'n'8801'm_6544 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_m'8804'n'8658'm'8851'n'8801'm_6544 :: Integer -> Integer -> T__'8804'__26 -> T__'8801'__12
d_m'8804'n'8658'm'8851'n'8801'm_6544 = Integer -> Integer -> T__'8804'__26 -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.m⊓n≡m⇒m≤n
d_m'8851'n'8801'm'8658'm'8804'n_6546 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26
d_m'8851'n'8801'm'8658'm'8804'n_6546 :: Integer -> Integer -> T__'8801'__12 -> T__'8804'__26
d_m'8851'n'8801'm'8658'm'8804'n_6546
  = let v0 :: T_TotalPreorder_204
v0 = T_TotalPreorder_204
d_'8804''45'totalPreorder_1668 in
    Any -> Integer -> Integer -> T__'8801'__12 -> T__'8804'__26
forall a b. a -> b
coe
      (let v1 :: T_MinOperator_84
v1 = T_MinOperator_84
d_'8851''45'operator_5516 in
       Any -> Any
forall a b. a -> b
coe
         ((T_TotalPreorder_204
 -> T_MinOperator_84 -> Any -> Any -> Any -> Any)
-> Any -> Any -> Any
forall a b. a -> b
coe
            T_TotalPreorder_204 -> T_MinOperator_84 -> Any -> Any -> Any -> Any
MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_x'8851'y'8776'x'8658'x'8804'y_1890
            (T_TotalPreorder_204 -> Any
forall a b. a -> b
coe T_TotalPreorder_204
v0) (T_MinOperator_84 -> Any
forall a b. a -> b
coe T_MinOperator_84
v1)))
-- Data.Integer.Properties.m≥n⇒m⊓n≡n
d_m'8805'n'8658'm'8851'n'8801'n_6548 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_m'8805'n'8658'm'8851'n'8801'n_6548 :: Integer -> Integer -> T__'8804'__26 -> T__'8801'__12
d_m'8805'n'8658'm'8851'n'8801'n_6548 = Integer -> Integer -> T__'8804'__26 -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.m⊓n≡n⇒m≥n
d_m'8851'n'8801'n'8658'm'8805'n_6550 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26
d_m'8851'n'8801'n'8658'm'8805'n_6550 :: Integer -> Integer -> T__'8801'__12 -> T__'8804'__26
d_m'8851'n'8801'n'8658'm'8805'n_6550
  = let v0 :: T_TotalPreorder_204
v0 = T_TotalPreorder_204
d_'8804''45'totalPreorder_1668 in
    Any -> Integer -> Integer -> T__'8801'__12 -> T__'8804'__26
forall a b. a -> b
coe
      (let v1 :: T_MinOperator_84
v1 = T_MinOperator_84
d_'8851''45'operator_5516 in
       Any -> Any
forall a b. a -> b
coe
         ((T_TotalPreorder_204
 -> T_MinOperator_84 -> Any -> Any -> Any -> Any)
-> Any -> Any -> Any
forall a b. a -> b
coe
            T_TotalPreorder_204 -> T_MinOperator_84 -> Any -> Any -> Any -> Any
MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_x'8851'y'8776'y'8658'y'8804'x_1922
            (T_TotalPreorder_204 -> Any
forall a b. a -> b
coe T_TotalPreorder_204
v0) (T_MinOperator_84 -> Any
forall a b. a -> b
coe T_MinOperator_84
v1)))
-- Data.Integer.Properties.m⊓n≤n
d_m'8851'n'8804'n_6552 ::
  Integer -> Integer -> MAlonzo.Code.Data.Integer.Base.T__'8804'__26
d_m'8851'n'8804'n_6552 :: Integer -> Integer -> T__'8804'__26
d_m'8851'n'8804'n_6552
  = let v0 :: T_TotalPreorder_204
v0 = T_TotalPreorder_204
d_'8804''45'totalPreorder_1668 in
    Any -> Integer -> Integer -> T__'8804'__26
forall a b. a -> b
coe
      (let v1 :: T_MinOperator_84
v1 = T_MinOperator_84
d_'8851''45'operator_5516 in
       Any -> Any
forall a b. a -> b
coe
         ((T_TotalPreorder_204 -> T_MinOperator_84 -> Any -> Any -> Any)
-> Any -> Any -> Any
forall a b. a -> b
coe
            T_TotalPreorder_204 -> T_MinOperator_84 -> Any -> Any -> Any
MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_x'8851'y'8804'y_1652
            (T_TotalPreorder_204 -> Any
forall a b. a -> b
coe T_TotalPreorder_204
v0) (T_MinOperator_84 -> Any
forall a b. a -> b
coe T_MinOperator_84
v1)))
-- Data.Integer.Properties.m⊓n≤m
d_m'8851'n'8804'm_6554 ::
  Integer -> Integer -> MAlonzo.Code.Data.Integer.Base.T__'8804'__26
d_m'8851'n'8804'm_6554 :: Integer -> Integer -> T__'8804'__26
d_m'8851'n'8804'm_6554
  = let v0 :: T_TotalPreorder_204
v0 = T_TotalPreorder_204
d_'8804''45'totalPreorder_1668 in
    Any -> Integer -> Integer -> T__'8804'__26
forall a b. a -> b
coe
      (let v1 :: T_MinOperator_84
v1 = T_MinOperator_84
d_'8851''45'operator_5516 in
       Any -> Any
forall a b. a -> b
coe
         ((T_TotalPreorder_204 -> T_MinOperator_84 -> Any -> Any -> Any)
-> Any -> Any -> Any
forall a b. a -> b
coe
            T_TotalPreorder_204 -> T_MinOperator_84 -> Any -> Any -> Any
MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_x'8851'y'8804'x_1626
            (T_TotalPreorder_204 -> Any
forall a b. a -> b
coe T_TotalPreorder_204
v0) (T_MinOperator_84 -> Any
forall a b. a -> b
coe T_MinOperator_84
v1)))
-- Data.Integer.Properties.m≤n⇒m⊔n≡n
d_m'8804'n'8658'm'8852'n'8801'n_6556 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_m'8804'n'8658'm'8852'n'8801'n_6556 :: Integer -> Integer -> T__'8804'__26 -> T__'8801'__12
d_m'8804'n'8658'm'8852'n'8801'n_6556 = Integer -> Integer -> T__'8804'__26 -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.m⊔n≡n⇒m≤n
d_m'8852'n'8801'n'8658'm'8804'n_6558 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26
d_m'8852'n'8801'n'8658'm'8804'n_6558 :: Integer -> Integer -> T__'8801'__12 -> T__'8804'__26
d_m'8852'n'8801'n'8658'm'8804'n_6558
  = let v0 :: T_TotalPreorder_204
v0 = T_TotalPreorder_204
d_'8804''45'totalPreorder_1668 in
    Any -> Integer -> Integer -> T__'8801'__12 -> T__'8804'__26
forall a b. a -> b
coe
      (let v1 :: T_MaxOperator_114
v1 = T_MaxOperator_114
d_'8852''45'operator_5518 in
       Any -> Any
forall a b. a -> b
coe
         ((T_TotalPreorder_204
 -> T_MinOperator_84 -> Any -> Any -> Any -> Any)
-> Any -> Any -> Any
forall a b. a -> b
coe
            T_TotalPreorder_204 -> T_MinOperator_84 -> Any -> Any -> Any -> Any
MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_x'8851'y'8776'y'8658'y'8804'x_1922
            ((T_TotalPreorder_204 -> T_TotalPreorder_204) -> Any -> Any
forall a b. a -> b
coe
               T_TotalPreorder_204 -> T_TotalPreorder_204
MAlonzo.Code.Relation.Binary.Construct.Converse.du_totalPreorder_718
               (T_TotalPreorder_204 -> Any
forall a b. a -> b
coe T_TotalPreorder_204
v0))
            ((T_MaxOperator_114 -> T_MinOperator_84) -> Any -> Any
forall a b. a -> b
coe
               T_MaxOperator_114 -> T_MinOperator_84
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.du_MaxOp'8658'MinOp_160
               (T_MaxOperator_114 -> Any
forall a b. a -> b
coe T_MaxOperator_114
v1))))
-- Data.Integer.Properties.m≥n⇒m⊔n≡m
d_m'8805'n'8658'm'8852'n'8801'm_6560 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_m'8805'n'8658'm'8852'n'8801'm_6560 :: Integer -> Integer -> T__'8804'__26 -> T__'8801'__12
d_m'8805'n'8658'm'8852'n'8801'm_6560 = Integer -> Integer -> T__'8804'__26 -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.m⊔n≡m⇒m≥n
d_m'8852'n'8801'm'8658'm'8805'n_6562 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26
d_m'8852'n'8801'm'8658'm'8805'n_6562 :: Integer -> Integer -> T__'8801'__12 -> T__'8804'__26
d_m'8852'n'8801'm'8658'm'8805'n_6562
  = let v0 :: T_TotalPreorder_204
v0 = T_TotalPreorder_204
d_'8804''45'totalPreorder_1668 in
    Any -> Integer -> Integer -> T__'8801'__12 -> T__'8804'__26
forall a b. a -> b
coe
      (let v1 :: T_MaxOperator_114
v1 = T_MaxOperator_114
d_'8852''45'operator_5518 in
       Any -> Any
forall a b. a -> b
coe
         ((T_TotalPreorder_204
 -> T_MinOperator_84 -> Any -> Any -> Any -> Any)
-> Any -> Any -> Any
forall a b. a -> b
coe
            T_TotalPreorder_204 -> T_MinOperator_84 -> Any -> Any -> Any -> Any
MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_x'8851'y'8776'x'8658'x'8804'y_1890
            ((T_TotalPreorder_204 -> T_TotalPreorder_204) -> Any -> Any
forall a b. a -> b
coe
               T_TotalPreorder_204 -> T_TotalPreorder_204
MAlonzo.Code.Relation.Binary.Construct.Converse.du_totalPreorder_718
               (T_TotalPreorder_204 -> Any
forall a b. a -> b
coe T_TotalPreorder_204
v0))
            ((T_MaxOperator_114 -> T_MinOperator_84) -> Any -> Any
forall a b. a -> b
coe
               T_MaxOperator_114 -> T_MinOperator_84
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.du_MaxOp'8658'MinOp_160
               (T_MaxOperator_114 -> Any
forall a b. a -> b
coe T_MaxOperator_114
v1))))
-- Data.Integer.Properties.m≤m⊔n
d_m'8804'm'8852'n_6564 ::
  Integer -> Integer -> MAlonzo.Code.Data.Integer.Base.T__'8804'__26
d_m'8804'm'8852'n_6564 :: Integer -> Integer -> T__'8804'__26
d_m'8804'm'8852'n_6564
  = let v0 :: T_TotalPreorder_204
v0 = T_TotalPreorder_204
d_'8804''45'totalPreorder_1668 in
    Any -> Integer -> Integer -> T__'8804'__26
forall a b. a -> b
coe
      (let v1 :: T_MaxOperator_114
v1 = T_MaxOperator_114
d_'8852''45'operator_5518 in
       Any -> Any
forall a b. a -> b
coe
         ((T_TotalPreorder_204 -> T_MinOperator_84 -> Any -> Any -> Any)
-> Any -> Any -> Any
forall a b. a -> b
coe
            T_TotalPreorder_204 -> T_MinOperator_84 -> Any -> Any -> Any
MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_x'8851'y'8804'x_1626
            ((T_TotalPreorder_204 -> T_TotalPreorder_204) -> Any -> Any
forall a b. a -> b
coe
               T_TotalPreorder_204 -> T_TotalPreorder_204
MAlonzo.Code.Relation.Binary.Construct.Converse.du_totalPreorder_718
               (T_TotalPreorder_204 -> Any
forall a b. a -> b
coe T_TotalPreorder_204
v0))
            ((T_MaxOperator_114 -> T_MinOperator_84) -> Any -> Any
forall a b. a -> b
coe
               T_MaxOperator_114 -> T_MinOperator_84
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.du_MaxOp'8658'MinOp_160
               (T_MaxOperator_114 -> Any
forall a b. a -> b
coe T_MaxOperator_114
v1))))
-- Data.Integer.Properties.n≤m⊔n
d_n'8804'm'8852'n_6566 ::
  Integer -> Integer -> MAlonzo.Code.Data.Integer.Base.T__'8804'__26
d_n'8804'm'8852'n_6566 :: Integer -> Integer -> T__'8804'__26
d_n'8804'm'8852'n_6566
  = let v0 :: T_TotalPreorder_204
v0 = T_TotalPreorder_204
d_'8804''45'totalPreorder_1668 in
    Any -> Integer -> Integer -> T__'8804'__26
forall a b. a -> b
coe
      (let v1 :: T_MaxOperator_114
v1 = T_MaxOperator_114
d_'8852''45'operator_5518 in
       Any -> Any
forall a b. a -> b
coe
         ((T_TotalPreorder_204 -> T_MinOperator_84 -> Any -> Any -> Any)
-> Any -> Any -> Any
forall a b. a -> b
coe
            T_TotalPreorder_204 -> T_MinOperator_84 -> Any -> Any -> Any
MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_x'8851'y'8804'y_1652
            ((T_TotalPreorder_204 -> T_TotalPreorder_204) -> Any -> Any
forall a b. a -> b
coe
               T_TotalPreorder_204 -> T_TotalPreorder_204
MAlonzo.Code.Relation.Binary.Construct.Converse.du_totalPreorder_718
               (T_TotalPreorder_204 -> Any
forall a b. a -> b
coe T_TotalPreorder_204
v0))
            ((T_MaxOperator_114 -> T_MinOperator_84) -> Any -> Any
forall a b. a -> b
coe
               T_MaxOperator_114 -> T_MinOperator_84
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.du_MaxOp'8658'MinOp_160
               (T_MaxOperator_114 -> Any
forall a b. a -> b
coe T_MaxOperator_114
v1))))