{-# 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.Lattice.Bundles
import qualified MAlonzo.Code.Algebra.Lattice.Construct.NaturalChoice.MinMaxOp
import qualified MAlonzo.Code.Algebra.Lattice.Construct.NaturalChoice.MinOp
import qualified MAlonzo.Code.Algebra.Lattice.Structures
import qualified MAlonzo.Code.Algebra.Morphism.Structures
import qualified MAlonzo.Code.Algebra.Structures
import qualified MAlonzo.Code.Data.Integer.Base
import qualified MAlonzo.Code.Data.Irrelevant
import qualified MAlonzo.Code.Data.Nat.Base
import qualified MAlonzo.Code.Data.Nat.Properties
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.Flip.EqAndOrd
import qualified MAlonzo.Code.Relation.Binary.Definitions
import qualified MAlonzo.Code.Relation.Binary.Morphism.Structures
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.Reasoning.Syntax
import qualified MAlonzo.Code.Relation.Binary.Structures
import qualified MAlonzo.Code.Relation.Nullary.Decidable.Core
import qualified MAlonzo.Code.Relation.Nullary.Negation.Core
import qualified MAlonzo.Code.Relation.Nullary.Reflects

-- 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_30 :: (Integer -> Integer -> Integer) -> ()
d_Associative_30 :: (Integer -> Integer -> Integer) -> ()
d_Associative_30 = (Integer -> Integer -> Integer) -> ()
forall a. a
erased
-- Data.Integer.Properties._.Commutative
d_Commutative_34 :: (Integer -> Integer -> Integer) -> ()
d_Commutative_34 :: (Integer -> Integer -> Integer) -> ()
d_Commutative_34 = (Integer -> Integer -> Integer) -> ()
forall a. a
erased
-- Data.Integer.Properties._.Identity
d_Identity_50 :: Integer -> (Integer -> Integer -> Integer) -> ()
d_Identity_50 :: Integer -> (Integer -> Integer -> Integer) -> ()
d_Identity_50 = Integer -> (Integer -> Integer -> Integer) -> ()
forall a. a
erased
-- Data.Integer.Properties._.Inverse
d_Inverse_54 ::
  Integer ->
  (Integer -> Integer) -> (Integer -> Integer -> Integer) -> ()
d_Inverse_54 :: Integer
-> (Integer -> Integer) -> (Integer -> Integer -> Integer) -> ()
d_Inverse_54 = Integer
-> (Integer -> Integer) -> (Integer -> Integer -> Integer) -> ()
forall a. a
erased
-- Data.Integer.Properties._.LeftIdentity
d_LeftIdentity_76 ::
  Integer -> (Integer -> Integer -> Integer) -> ()
d_LeftIdentity_76 :: Integer -> (Integer -> Integer -> Integer) -> ()
d_LeftIdentity_76 = Integer -> (Integer -> Integer -> Integer) -> ()
forall a. a
erased
-- Data.Integer.Properties._.LeftInverse
d_LeftInverse_78 ::
  Integer ->
  (Integer -> Integer) -> (Integer -> Integer -> Integer) -> ()
d_LeftInverse_78 :: Integer
-> (Integer -> Integer) -> (Integer -> Integer -> Integer) -> ()
d_LeftInverse_78 = Integer
-> (Integer -> Integer) -> (Integer -> Integer -> Integer) -> ()
forall a. a
erased
-- Data.Integer.Properties._.LeftZero
d_LeftZero_84 :: Integer -> (Integer -> Integer -> Integer) -> ()
d_LeftZero_84 :: Integer -> (Integer -> Integer -> Integer) -> ()
d_LeftZero_84 = Integer -> (Integer -> Integer -> Integer) -> ()
forall a. a
erased
-- Data.Integer.Properties._.RightIdentity
d_RightIdentity_106 ::
  Integer -> (Integer -> Integer -> Integer) -> ()
d_RightIdentity_106 :: Integer -> (Integer -> Integer -> Integer) -> ()
d_RightIdentity_106 = Integer -> (Integer -> Integer -> Integer) -> ()
forall a. a
erased
-- Data.Integer.Properties._.RightInverse
d_RightInverse_108 ::
  Integer ->
  (Integer -> Integer) -> (Integer -> Integer -> Integer) -> ()
d_RightInverse_108 :: Integer
-> (Integer -> Integer) -> (Integer -> Integer -> Integer) -> ()
d_RightInverse_108 = Integer
-> (Integer -> Integer) -> (Integer -> Integer -> Integer) -> ()
forall a. a
erased
-- Data.Integer.Properties._.RightZero
d_RightZero_114 :: Integer -> (Integer -> Integer -> Integer) -> ()
d_RightZero_114 :: Integer -> (Integer -> Integer -> Integer) -> ()
d_RightZero_114 = Integer -> (Integer -> Integer -> Integer) -> ()
forall a. a
erased
-- Data.Integer.Properties._.Zero
d_Zero_134 :: Integer -> (Integer -> Integer -> Integer) -> ()
d_Zero_134 :: Integer -> (Integer -> Integer -> Integer) -> ()
d_Zero_134 = Integer -> (Integer -> Integer -> Integer) -> ()
forall a. a
erased
-- Data.Integer.Properties._.IsAbelianGroup
d_IsAbelianGroup_138 :: p -> p -> p -> ()
d_IsAbelianGroup_138 p
a0 p
a1 p
a2 = ()
-- Data.Integer.Properties._.IsCommutativeMonoid
d_IsCommutativeMonoid_150 :: p -> p -> ()
d_IsCommutativeMonoid_150 p
a0 p
a1 = ()
-- Data.Integer.Properties._.IsCommutativeRing
d_IsCommutativeRing_152 :: p -> p -> p -> p -> p -> ()
d_IsCommutativeRing_152 p
a0 p
a1 p
a2 p
a3 p
a4 = ()
-- Data.Integer.Properties._.IsCommutativeSemigroup
d_IsCommutativeSemigroup_154 :: p -> ()
d_IsCommutativeSemigroup_154 p
a0 = ()
-- Data.Integer.Properties._.IsCommutativeSemiring
d_IsCommutativeSemiring_156 :: p -> p -> p -> p -> ()
d_IsCommutativeSemiring_156 p
a0 p
a1 p
a2 p
a3 = ()
-- Data.Integer.Properties._.IsGroup
d_IsGroup_162 :: p -> p -> p -> ()
d_IsGroup_162 p
a0 p
a1 p
a2 = ()
-- Data.Integer.Properties._.IsMagma
d_IsMagma_182 :: p -> ()
d_IsMagma_182 p
a0 = ()
-- Data.Integer.Properties._.IsMonoid
d_IsMonoid_188 :: p -> p -> ()
d_IsMonoid_188 p
a0 p
a1 = ()
-- Data.Integer.Properties._.IsRing
d_IsRing_204 :: p -> p -> p -> p -> p -> ()
d_IsRing_204 p
a0 p
a1 p
a2 p
a3 p
a4 = ()
-- Data.Integer.Properties._.IsSemigroup
d_IsSemigroup_210 :: p -> ()
d_IsSemigroup_210 p
a0 = ()
-- Data.Integer.Properties._.IsSemiring
d_IsSemiring_214 :: p -> p -> p -> p -> ()
d_IsSemiring_214 p
a0 p
a1 p
a2 p
a3 = ()
-- Data.Integer.Properties._.IsAbelianGroup.comm
d_comm_230 ::
  MAlonzo.Code.Algebra.Structures.T_IsAbelianGroup_1132 ->
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_comm_230 :: T_IsAbelianGroup_1132 -> Integer -> Integer -> T__'8801'__12
d_comm_230 = T_IsAbelianGroup_1132 -> Integer -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties._.IsAbelianGroup.isGroup
d_isGroup_252 ::
  MAlonzo.Code.Algebra.Structures.T_IsAbelianGroup_1132 ->
  MAlonzo.Code.Algebra.Structures.T_IsGroup_1036
d_isGroup_252 :: T_IsAbelianGroup_1132 -> T_IsGroup_1036
d_isGroup_252 T_IsAbelianGroup_1132
v0
  = (T_IsAbelianGroup_1132 -> T_IsGroup_1036) -> Any -> T_IsGroup_1036
forall a b. a -> b
coe T_IsAbelianGroup_1132 -> T_IsGroup_1036
MAlonzo.Code.Algebra.Structures.d_isGroup_1144 (T_IsAbelianGroup_1132 -> Any
forall a b. a -> b
coe T_IsAbelianGroup_1132
v0)
-- Data.Integer.Properties._.IsCommutativeMonoid.comm
d_comm_520 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMonoid_736 ->
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_comm_520 :: T_IsCommutativeMonoid_736 -> Integer -> Integer -> T__'8801'__12
d_comm_520 = T_IsCommutativeMonoid_736 -> Integer -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties._.IsCommutativeMonoid.isMonoid
d_isMonoid_536 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMonoid_736 ->
  MAlonzo.Code.Algebra.Structures.T_IsMonoid_686
d_isMonoid_536 :: T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_536 T_IsCommutativeMonoid_736
v0
  = (T_IsCommutativeMonoid_736 -> T_IsMonoid_686)
-> Any -> T_IsMonoid_686
forall a b. a -> b
coe T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746 (T_IsCommutativeMonoid_736 -> Any
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v0)
-- Data.Integer.Properties._.IsCommutativeRing.*-comm
d_'42''45'comm_566 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeRing_2796 ->
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'42''45'comm_566 :: T_IsCommutativeRing_2796 -> Integer -> Integer -> T__'8801'__12
d_'42''45'comm_566 = T_IsCommutativeRing_2796 -> Integer -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties._.IsCommutativeRing.isRing
d_isRing_654 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeRing_2796 ->
  MAlonzo.Code.Algebra.Structures.T_IsRing_2650
d_isRing_654 :: T_IsCommutativeRing_2796 -> T_IsRing_2650
d_isRing_654 T_IsCommutativeRing_2796
v0
  = (T_IsCommutativeRing_2796 -> T_IsRing_2650) -> Any -> T_IsRing_2650
forall a b. a -> b
coe T_IsCommutativeRing_2796 -> T_IsRing_2650
MAlonzo.Code.Algebra.Structures.d_isRing_2812 (T_IsCommutativeRing_2796 -> Any
forall a b. a -> b
coe T_IsCommutativeRing_2796
v0)
-- Data.Integer.Properties._.IsCommutativeSemigroup.comm
d_comm_688 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_548 ->
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_comm_688 :: T_IsCommutativeSemigroup_548 -> Integer -> Integer -> T__'8801'__12
d_comm_688 = T_IsCommutativeSemigroup_548 -> Integer -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties._.IsCommutativeSemigroup.isSemigroup
d_isSemigroup_698 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_548 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_472
d_isSemigroup_698 :: T_IsCommutativeSemigroup_548 -> T_IsSemigroup_472
d_isSemigroup_698 T_IsCommutativeSemigroup_548
v0
  = (T_IsCommutativeSemigroup_548 -> T_IsSemigroup_472)
-> Any -> T_IsSemigroup_472
forall a b. a -> b
coe T_IsCommutativeSemigroup_548 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_556 (T_IsCommutativeSemigroup_548 -> Any
forall a b. a -> b
coe T_IsCommutativeSemigroup_548
v0)
-- Data.Integer.Properties._.IsCommutativeSemiring.*-comm
d_'42''45'comm_720 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiring_1678 ->
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'42''45'comm_720 :: T_IsCommutativeSemiring_1678 -> Integer -> Integer -> T__'8801'__12
d_'42''45'comm_720 = T_IsCommutativeSemiring_1678 -> Integer -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties._.IsCommutativeSemiring.isSemiring
d_isSemiring_790 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiring_1678 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemiring_1570
d_isSemiring_790 :: T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570
d_isSemiring_790 T_IsCommutativeSemiring_1678
v0
  = (T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570)
-> Any -> T_IsSemiring_1570
forall a b. a -> b
coe T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570
MAlonzo.Code.Algebra.Structures.d_isSemiring_1692 (T_IsCommutativeSemiring_1678 -> Any
forall a b. a -> b
coe T_IsCommutativeSemiring_1678
v0)
-- Data.Integer.Properties._.IsGroup.inverse
d_inverse_918 ::
  MAlonzo.Code.Algebra.Structures.T_IsGroup_1036 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_inverse_918 :: T_IsGroup_1036 -> T_Σ_14
d_inverse_918 T_IsGroup_1036
v0
  = (T_IsGroup_1036 -> T_Σ_14) -> Any -> T_Σ_14
forall a b. a -> b
coe T_IsGroup_1036 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_inverse_1052 (T_IsGroup_1036 -> Any
forall a b. a -> b
coe T_IsGroup_1036
v0)
-- Data.Integer.Properties._.IsGroup.isMonoid
d_isMonoid_932 ::
  MAlonzo.Code.Algebra.Structures.T_IsGroup_1036 ->
  MAlonzo.Code.Algebra.Structures.T_IsMonoid_686
d_isMonoid_932 :: T_IsGroup_1036 -> T_IsMonoid_686
d_isMonoid_932 T_IsGroup_1036
v0
  = (T_IsGroup_1036 -> T_IsMonoid_686) -> Any -> T_IsMonoid_686
forall a b. a -> b
coe T_IsGroup_1036 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_1050 (T_IsGroup_1036 -> Any
forall a b. a -> b
coe T_IsGroup_1036
v0)
-- Data.Integer.Properties._.IsGroup.⁻¹-cong
d_'8315''185''45'cong_954 ::
  MAlonzo.Code.Algebra.Structures.T_IsGroup_1036 ->
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8315''185''45'cong_954 :: T_IsGroup_1036
-> Integer -> Integer -> T__'8801'__12 -> T__'8801'__12
d_'8315''185''45'cong_954 = T_IsGroup_1036
-> Integer -> Integer -> T__'8801'__12 -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties._.IsMagma.isEquivalence
d_isEquivalence_1482 ::
  MAlonzo.Code.Algebra.Structures.T_IsMagma_176 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_1482 :: T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_1482 T_IsMagma_176
v0
  = (T_IsMagma_176 -> T_IsEquivalence_26) -> Any -> T_IsEquivalence_26
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184 (T_IsMagma_176 -> Any
forall a b. a -> b
coe T_IsMagma_176
v0)
-- Data.Integer.Properties._.IsMagma.∙-cong
d_'8729''45'cong_1496 ::
  MAlonzo.Code.Algebra.Structures.T_IsMagma_176 ->
  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_1496 :: T_IsMagma_176
-> Integer
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong_1496 = T_IsMagma_176
-> Integer
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties._.IsMonoid.identity
d_identity_1592 ::
  MAlonzo.Code.Algebra.Structures.T_IsMonoid_686 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_identity_1592 :: T_IsMonoid_686 -> T_Σ_14
d_identity_1592 T_IsMonoid_686
v0
  = (T_IsMonoid_686 -> T_Σ_14) -> Any -> T_Σ_14
forall a b. a -> b
coe T_IsMonoid_686 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_identity_698 (T_IsMonoid_686 -> Any
forall a b. a -> b
coe T_IsMonoid_686
v0)
-- Data.Integer.Properties._.IsMonoid.isSemigroup
d_isSemigroup_1604 ::
  MAlonzo.Code.Algebra.Structures.T_IsMonoid_686 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_472
d_isSemigroup_1604 :: T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_1604 T_IsMonoid_686
v0
  = (T_IsMonoid_686 -> T_IsSemigroup_472) -> Any -> T_IsSemigroup_472
forall a b. a -> b
coe T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (T_IsMonoid_686 -> Any
forall a b. a -> b
coe T_IsMonoid_686
v0)
-- Data.Integer.Properties._.IsRing.*-assoc
d_'42''45'assoc_2110 ::
  MAlonzo.Code.Algebra.Structures.T_IsRing_2650 ->
  Integer ->
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'42''45'assoc_2110 :: T_IsRing_2650 -> Integer -> Integer -> Integer -> T__'8801'__12
d_'42''45'assoc_2110 = T_IsRing_2650 -> Integer -> Integer -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties._.IsRing.*-cong
d_'42''45'cong_2112 ::
  MAlonzo.Code.Algebra.Structures.T_IsRing_2650 ->
  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_'42''45'cong_2112 :: T_IsRing_2650
-> Integer
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
d_'42''45'cong_2112 = T_IsRing_2650
-> Integer
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties._.IsRing.*-identity
d_'42''45'identity_2118 ::
  MAlonzo.Code.Algebra.Structures.T_IsRing_2650 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'42''45'identity_2118 :: T_IsRing_2650 -> T_Σ_14
d_'42''45'identity_2118 T_IsRing_2650
v0
  = (T_IsRing_2650 -> T_Σ_14) -> Any -> T_Σ_14
forall a b. a -> b
coe
      T_IsRing_2650 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_'42''45'identity_2678 (T_IsRing_2650 -> Any
forall a b. a -> b
coe T_IsRing_2650
v0)
-- Data.Integer.Properties._.IsRing.+-isAbelianGroup
d_'43''45'isAbelianGroup_2146 ::
  MAlonzo.Code.Algebra.Structures.T_IsRing_2650 ->
  MAlonzo.Code.Algebra.Structures.T_IsAbelianGroup_1132
d_'43''45'isAbelianGroup_2146 :: T_IsRing_2650 -> T_IsAbelianGroup_1132
d_'43''45'isAbelianGroup_2146 T_IsRing_2650
v0
  = (T_IsRing_2650 -> T_IsAbelianGroup_1132)
-> Any -> T_IsAbelianGroup_1132
forall a b. a -> b
coe
      T_IsRing_2650 -> T_IsAbelianGroup_1132
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2672
      (T_IsRing_2650 -> Any
forall a b. a -> b
coe T_IsRing_2650
v0)
-- Data.Integer.Properties._.IsRing.distrib
d_distrib_2176 ::
  MAlonzo.Code.Algebra.Structures.T_IsRing_2650 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_distrib_2176 :: T_IsRing_2650 -> T_Σ_14
d_distrib_2176 T_IsRing_2650
v0
  = (T_IsRing_2650 -> T_Σ_14) -> Any -> T_Σ_14
forall a b. a -> b
coe T_IsRing_2650 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_distrib_2680 (T_IsRing_2650 -> Any
forall a b. a -> b
coe T_IsRing_2650
v0)
-- Data.Integer.Properties._.IsSemigroup.assoc
d_assoc_2336 ::
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_472 ->
  Integer ->
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_assoc_2336 :: T_IsSemigroup_472 -> Integer -> Integer -> Integer -> T__'8801'__12
d_assoc_2336 = T_IsSemigroup_472 -> Integer -> Integer -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties._.IsSemigroup.isMagma
d_isMagma_2340 ::
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_472 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_176
d_isMagma_2340 :: T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_2340 T_IsSemigroup_472
v0
  = (T_IsSemigroup_472 -> T_IsMagma_176) -> Any -> T_IsMagma_176
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (T_IsSemigroup_472 -> Any
forall a b. a -> b
coe T_IsSemigroup_472
v0)
-- Data.Integer.Properties._.IsSemiring.isSemiringWithoutAnnihilatingZero
d_isSemiringWithoutAnnihilatingZero_2454 ::
  MAlonzo.Code.Algebra.Structures.T_IsSemiring_1570 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_2454 :: T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_2454 T_IsSemiring_1570
v0
  = (T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> Any -> T_IsSemiringWithoutAnnihilatingZero_1468
forall a b. a -> b
coe
      T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
      (T_IsSemiring_1570 -> Any
forall a b. a -> b
coe T_IsSemiring_1570
v0)
-- Data.Integer.Properties._.IsSemiring.zero
d_zero_2468 ::
  MAlonzo.Code.Algebra.Structures.T_IsSemiring_1570 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_zero_2468 :: T_IsSemiring_1570 -> T_Σ_14
d_zero_2468 T_IsSemiring_1570
v0
  = (T_IsSemiring_1570 -> T_Σ_14) -> Any -> T_Σ_14
forall a b. a -> b
coe T_IsSemiring_1570 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_zero_1586 (T_IsSemiring_1570 -> Any
forall a b. a -> b
coe T_IsSemiring_1570
v0)
-- Data.Integer.Properties.ℤtoℕ.Homomorphic₀
d_Homomorphic'8320'_2652 ::
  (Integer -> Integer) -> Integer -> Integer -> ()
d_Homomorphic'8320'_2652 :: (Integer -> Integer) -> Integer -> Integer -> ()
d_Homomorphic'8320'_2652 = (Integer -> Integer) -> Integer -> Integer -> ()
forall a. a
erased
-- Data.Integer.Properties.ℤtoℕ.Homomorphic₁
d_Homomorphic'8321'_2654 ::
  (Integer -> Integer) ->
  (Integer -> Integer) -> (Integer -> Integer) -> ()
d_Homomorphic'8321'_2654 :: (Integer -> Integer)
-> (Integer -> Integer) -> (Integer -> Integer) -> ()
d_Homomorphic'8321'_2654 = (Integer -> Integer)
-> (Integer -> Integer) -> (Integer -> Integer) -> ()
forall a. a
erased
-- Data.Integer.Properties.ℤtoℕ.Homomorphic₂
d_Homomorphic'8322'_2656 ::
  (Integer -> Integer) ->
  (Integer -> Integer -> Integer) ->
  (Integer -> Integer -> Integer) -> ()
d_Homomorphic'8322'_2656 :: (Integer -> Integer)
-> (Integer -> Integer -> Integer)
-> (Integer -> Integer -> Integer)
-> ()
d_Homomorphic'8322'_2656 = (Integer -> Integer)
-> (Integer -> Integer -> Integer)
-> (Integer -> Integer -> Integer)
-> ()
forall a. a
erased
-- Data.Integer.Properties.ℤtoℕ.Morphism
d_Morphism_2658 :: ()
d_Morphism_2658 :: ()
d_Morphism_2658 = ()
forall a. a
erased
-- Data.Integer.Properties.ℕtoℤ.Homomorphic₀
d_Homomorphic'8320'_2662 ::
  (Integer -> Integer) -> Integer -> Integer -> ()
d_Homomorphic'8320'_2662 :: (Integer -> Integer) -> Integer -> Integer -> ()
d_Homomorphic'8320'_2662 = (Integer -> Integer) -> Integer -> Integer -> ()
forall a. a
erased
-- Data.Integer.Properties.ℕtoℤ.Homomorphic₁
d_Homomorphic'8321'_2664 ::
  (Integer -> Integer) ->
  (Integer -> Integer) -> (Integer -> Integer) -> ()
d_Homomorphic'8321'_2664 :: (Integer -> Integer)
-> (Integer -> Integer) -> (Integer -> Integer) -> ()
d_Homomorphic'8321'_2664 = (Integer -> Integer)
-> (Integer -> Integer) -> (Integer -> Integer) -> ()
forall a. a
erased
-- Data.Integer.Properties.ℕtoℤ.Homomorphic₂
d_Homomorphic'8322'_2666 ::
  (Integer -> Integer) ->
  (Integer -> Integer -> Integer) ->
  (Integer -> Integer -> Integer) -> ()
d_Homomorphic'8322'_2666 :: (Integer -> Integer)
-> (Integer -> Integer -> Integer)
-> (Integer -> Integer -> Integer)
-> ()
d_Homomorphic'8322'_2666 = (Integer -> Integer)
-> (Integer -> Integer -> Integer)
-> (Integer -> Integer -> Integer)
-> ()
forall a. a
erased
-- Data.Integer.Properties.ℕtoℤ.Morphism
d_Morphism_2668 :: ()
d_Morphism_2668 :: ()
d_Morphism_2668 = ()
forall a. a
erased
-- Data.Integer.Properties.+-injective
d_'43''45'injective_2686 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'43''45'injective_2686 :: Integer -> Integer -> T__'8801'__12 -> T__'8801'__12
d_'43''45'injective_2686 = Integer -> Integer -> T__'8801'__12 -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.-[1+-injective
d_'45''91'1'43''45'injective_2688 ::
  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_2688 :: Integer -> Integer -> T__'8801'__12 -> T__'8801'__12
d_'45''91'1'43''45'injective_2688 = Integer -> Integer -> T__'8801'__12 -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.+[1+-injective
d_'43''91'1'43''45'injective_2690 ::
  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_2690 :: Integer -> Integer -> T__'8801'__12 -> T__'8801'__12
d_'43''91'1'43''45'injective_2690 = Integer -> Integer -> T__'8801'__12 -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties._≟_
d__'8799'__2692 ::
  Integer ->
  Integer -> MAlonzo.Code.Relation.Nullary.Decidable.Core.T_Dec_20
d__'8799'__2692 :: Integer -> Integer -> T_Dec_20
d__'8799'__2692 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_Dec_20 -> T_Dec_20)
-> Any -> Any -> Any -> T_Dec_20
forall a b. a -> b
coe
                  (Any -> Any) -> (Any -> Any) -> T_Dec_20 -> T_Dec_20
MAlonzo.Code.Relation.Nullary.Decidable.Core.du_map'8242'_168
                  Any
forall a. a
erased Any
forall a. a
erased
                  ((Integer -> Integer -> T_Dec_20) -> Any -> Any -> Any
forall a b. a -> b
coe
                     Integer -> Integer -> T_Dec_20
MAlonzo.Code.Data.Nat.Properties.d__'8799'__2688 (Integer -> Any
forall a b. a -> b
coe Integer
v0) (Integer -> Any
forall a b. a -> b
coe Integer
v1))
            Any
_ -> (Bool -> T_Reflects_16 -> T_Dec_20) -> Any -> Any -> T_Dec_20
forall a b. a -> b
coe
                   Bool -> T_Reflects_16 -> T_Dec_20
MAlonzo.Code.Relation.Nullary.Decidable.Core.C__because__32
                   (Bool -> Any
forall a b. a -> b
coe Bool
MAlonzo.Code.Agda.Builtin.Bool.C_false_8)
                   (T_Reflects_16 -> Any
forall a b. a -> b
coe T_Reflects_16
MAlonzo.Code.Relation.Nullary.Reflects.C_of'8319'_26)
      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_20
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_16 -> T_Dec_20) -> Any -> Any -> Any
forall a b. a -> b
coe
                      Bool -> T_Reflects_16 -> T_Dec_20
MAlonzo.Code.Relation.Nullary.Decidable.Core.C__because__32
                      (Bool -> Any
forall a b. a -> b
coe Bool
MAlonzo.Code.Agda.Builtin.Bool.C_false_8)
                      (T_Reflects_16 -> Any
forall a b. a -> b
coe T_Reflects_16
MAlonzo.Code.Relation.Nullary.Reflects.C_of'8319'_26)
                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_Dec_20 -> T_Dec_20)
-> Any -> Any -> Any -> Any
forall a b. a -> b
coe
                          (Any -> Any) -> (Any -> Any) -> T_Dec_20 -> T_Dec_20
MAlonzo.Code.Relation.Nullary.Decidable.Core.du_map'8242'_168
                          Any
forall a. a
erased Any
forall a. a
erased
                          ((Integer -> Integer -> T_Dec_20) -> Any -> Any -> Any
forall a b. a -> b
coe
                             Integer -> Integer -> T_Dec_20
MAlonzo.Code.Data.Nat.Properties.d__'8799'__2688 (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_2710 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_'8801''45'setoid_2710 :: T_Setoid_44
d_'8801''45'setoid_2710
  = T_Setoid_44 -> T_Setoid_44
forall a b. a -> b
coe
      T_Setoid_44
MAlonzo.Code.Relation.Binary.PropositionalEquality.Properties.du_setoid_402
-- Data.Integer.Properties.≡-decSetoid
d_'8801''45'decSetoid_2712 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_DecSetoid_84
d_'8801''45'decSetoid_2712 :: T_DecSetoid_84
d_'8801''45'decSetoid_2712
  = ((Any -> Any -> T_Dec_20) -> T_DecSetoid_84)
-> Any -> T_DecSetoid_84
forall a b. a -> b
coe
      (Any -> Any -> T_Dec_20) -> T_DecSetoid_84
MAlonzo.Code.Relation.Binary.PropositionalEquality.Properties.du_decSetoid_406
      ((Integer -> Integer -> T_Dec_20) -> Any
forall a b. a -> b
coe Integer -> Integer -> T_Dec_20
d__'8799'__2692)
-- Data.Integer.Properties.drop‿+≤+
d_drop'8255''43''8804''43'_2714 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_drop'8255''43''8804''43'_2714 :: Integer -> Integer -> T__'8804'__26 -> T__'8804'__22
d_drop'8255''43''8804''43'_2714 ~Integer
v0 ~Integer
v1 T__'8804'__26
v2
  = T__'8804'__26 -> T__'8804'__22
du_drop'8255''43''8804''43'_2714 T__'8804'__26
v2
du_drop'8255''43''8804''43'_2714 ::
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
du_drop'8255''43''8804''43'_2714 :: T__'8804'__26 -> T__'8804'__22
du_drop'8255''43''8804''43'_2714 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'__22
v3 -> T__'8804'__22 -> T__'8804'__22
forall a b. a -> b
coe T__'8804'__22
v3
      T__'8804'__26
_ -> T__'8804'__22
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Data.Integer.Properties.drop‿-≤-
d_drop'8255''45''8804''45'_2718 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_drop'8255''45''8804''45'_2718 :: Integer -> Integer -> T__'8804'__26 -> T__'8804'__22
d_drop'8255''45''8804''45'_2718 ~Integer
v0 ~Integer
v1 T__'8804'__26
v2
  = T__'8804'__26 -> T__'8804'__22
du_drop'8255''45''8804''45'_2718 T__'8804'__26
v2
du_drop'8255''45''8804''45'_2718 ::
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
du_drop'8255''45''8804''45'_2718 :: T__'8804'__26 -> T__'8804'__22
du_drop'8255''45''8804''45'_2718 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'__22
v3 -> T__'8804'__22 -> T__'8804'__22
forall a b. a -> b
coe T__'8804'__22
v3
      T__'8804'__26
_ -> T__'8804'__22
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Data.Integer.Properties.≤-reflexive
d_'8804''45'reflexive_2722 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26
d_'8804''45'reflexive_2722 :: Integer -> Integer -> T__'8801'__12 -> T__'8804'__26
d_'8804''45'reflexive_2722 Integer
v0 ~Integer
v1 ~T__'8801'__12
v2
  = Integer -> T__'8804'__26
du_'8804''45'reflexive_2722 Integer
v0
du_'8804''45'reflexive_2722 ::
  Integer -> MAlonzo.Code.Data.Integer.Base.T__'8804'__26
du_'8804''45'reflexive_2722 :: Integer -> T__'8804'__26
du_'8804''45'reflexive_2722 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'__22 -> T__'8804'__26) -> T__'8804'__22 -> T__'8804'__26
forall a b. a -> b
coe
            T__'8804'__22 -> T__'8804'__26
MAlonzo.Code.Data.Integer.Base.C_'43''8804''43'_48
            (Integer -> T__'8804'__22
MAlonzo.Code.Data.Nat.Properties.d_'8804''45'refl_2776 (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'__22 -> T__'8804'__26) -> T__'8804'__22 -> Any
forall a b. a -> b
coe
                T__'8804'__22 -> T__'8804'__26
MAlonzo.Code.Data.Integer.Base.C_'45''8804''45'_34
                (Integer -> T__'8804'__22
MAlonzo.Code.Data.Nat.Properties.d_'8804''45'refl_2776 (Integer -> Integer
forall a b. a -> b
coe Integer
v1)))
-- Data.Integer.Properties.≤-refl
d_'8804''45'refl_2728 ::
  Integer -> MAlonzo.Code.Data.Integer.Base.T__'8804'__26
d_'8804''45'refl_2728 :: Integer -> T__'8804'__26
d_'8804''45'refl_2728 Integer
v0 = (Integer -> T__'8804'__26) -> Any -> T__'8804'__26
forall a b. a -> b
coe Integer -> T__'8804'__26
du_'8804''45'reflexive_2722 (Integer -> Any
forall a b. a -> b
coe Integer
v0)
-- Data.Integer.Properties.≤-trans
d_'8804''45'trans_2730 ::
  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_2730 :: Integer
-> Integer
-> Integer
-> T__'8804'__26
-> T__'8804'__26
-> T__'8804'__26
d_'8804''45'trans_2730 ~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_2730 T__'8804'__26
v3 T__'8804'__26
v4
du_'8804''45'trans_2730 ::
  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_2730 :: T__'8804'__26 -> T__'8804'__26 -> T__'8804'__26
du_'8804''45'trans_2730 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'__22
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'__22
v7
               -> (T__'8804'__22 -> T__'8804'__26) -> Any -> T__'8804'__26
forall a b. a -> b
coe
                    T__'8804'__22 -> T__'8804'__26
MAlonzo.Code.Data.Integer.Base.C_'45''8804''45'_34
                    ((T__'8804'__22 -> T__'8804'__22 -> T__'8804'__22)
-> Any -> Any -> Any
forall a b. a -> b
coe
                       T__'8804'__22 -> T__'8804'__22 -> T__'8804'__22
MAlonzo.Code.Data.Nat.Properties.du_'8804''45'trans_2784 (T__'8804'__22 -> Any
forall a b. a -> b
coe T__'8804'__22
v7)
                       (T__'8804'__22 -> Any
forall a b. a -> b
coe T__'8804'__22
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'__22
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'__22
v7
               -> (T__'8804'__22 -> T__'8804'__26) -> Any -> T__'8804'__26
forall a b. a -> b
coe
                    T__'8804'__22 -> T__'8804'__26
MAlonzo.Code.Data.Integer.Base.C_'43''8804''43'_48
                    ((T__'8804'__22 -> T__'8804'__22 -> T__'8804'__22)
-> Any -> Any -> Any
forall a b. a -> b
coe
                       T__'8804'__22 -> T__'8804'__22 -> T__'8804'__22
MAlonzo.Code.Data.Nat.Properties.du_'8804''45'trans_2784 (T__'8804'__22 -> Any
forall a b. a -> b
coe T__'8804'__22
v4)
                       (T__'8804'__22 -> Any
forall a b. a -> b
coe T__'8804'__22
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_2744 ::
  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_2744 :: Integer
-> Integer -> T__'8804'__26 -> T__'8804'__26 -> T__'8801'__12
d_'8804''45'antisym_2744 = Integer
-> Integer -> T__'8804'__26 -> T__'8804'__26 -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.≤-total
d_'8804''45'total_2754 ::
  Integer -> Integer -> MAlonzo.Code.Data.Sum.Base.T__'8846'__30
d_'8804''45'total_2754 :: Integer -> Integer -> T__'8846'__30
d_'8804''45'total_2754 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'__22 -> T__'8804'__26) -> Any
forall a b. a -> b
coe T__'8804'__22 -> T__'8804'__26
MAlonzo.Code.Data.Integer.Base.C_'43''8804''43'_48)
                  ((T__'8804'__22 -> T__'8804'__26) -> Any
forall a b. a -> b
coe T__'8804'__22 -> 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_2790
                     (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'__22 -> T__'8804'__26) -> Any
forall a b. a -> b
coe T__'8804'__22 -> T__'8804'__26
MAlonzo.Code.Data.Integer.Base.C_'45''8804''45'_34)
                          ((T__'8804'__22 -> T__'8804'__26) -> Any
forall a b. a -> b
coe T__'8804'__22 -> 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_2790
                             (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'__2772 ::
  Integer ->
  Integer -> MAlonzo.Code.Relation.Nullary.Decidable.Core.T_Dec_20
d__'8804''63'__2772 :: Integer -> Integer -> T_Dec_20
d__'8804''63'__2772 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_Dec_20 -> T_Dec_20)
-> Any -> Any -> Any -> T_Dec_20
forall a b. a -> b
coe
                  (Any -> Any) -> (Any -> Any) -> T_Dec_20 -> T_Dec_20
MAlonzo.Code.Relation.Nullary.Decidable.Core.du_map'8242'_168
                  ((T__'8804'__22 -> T__'8804'__26) -> Any
forall a b. a -> b
coe T__'8804'__22 -> T__'8804'__26
MAlonzo.Code.Data.Integer.Base.C_'43''8804''43'_48)
                  ((T__'8804'__26 -> T__'8804'__22) -> Any
forall a b. a -> b
coe T__'8804'__26 -> T__'8804'__22
du_drop'8255''43''8804''43'_2714)
                  ((Integer -> Integer -> T_Dec_20) -> Any -> Any -> Any
forall a b. a -> b
coe
                     Integer -> Integer -> T_Dec_20
MAlonzo.Code.Data.Nat.Properties.d__'8804''63'__2802 (Integer -> Any
forall a b. a -> b
coe Integer
v0)
                     (Integer -> Any
forall a b. a -> b
coe Integer
v1))
            Any
_ -> (Bool -> T_Reflects_16 -> T_Dec_20) -> Any -> Any -> T_Dec_20
forall a b. a -> b
coe
                   Bool -> T_Reflects_16 -> T_Dec_20
MAlonzo.Code.Relation.Nullary.Decidable.Core.C__because__32
                   (Bool -> Any
forall a b. a -> b
coe Bool
MAlonzo.Code.Agda.Builtin.Bool.C_false_8)
                   (T_Reflects_16 -> Any
forall a b. a -> b
coe T_Reflects_16
MAlonzo.Code.Relation.Nullary.Reflects.C_of'8319'_26)
      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_20
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_16 -> T_Dec_20) -> Any -> Any -> Any
forall a b. a -> b
coe
                      Bool -> T_Reflects_16 -> T_Dec_20
MAlonzo.Code.Relation.Nullary.Decidable.Core.C__because__32
                      (Bool -> Any
forall a b. a -> b
coe Bool
MAlonzo.Code.Agda.Builtin.Bool.C_true_10)
                      ((Any -> T_Reflects_16) -> Any -> Any
forall a b. a -> b
coe
                         Any -> T_Reflects_16
MAlonzo.Code.Relation.Nullary.Reflects.C_of'696'_22
                         (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_Dec_20 -> T_Dec_20)
-> Any -> Any -> Any -> Any
forall a b. a -> b
coe
                          (Any -> Any) -> (Any -> Any) -> T_Dec_20 -> T_Dec_20
MAlonzo.Code.Relation.Nullary.Decidable.Core.du_map'8242'_168
                          ((T__'8804'__22 -> T__'8804'__26) -> Any
forall a b. a -> b
coe T__'8804'__22 -> T__'8804'__26
MAlonzo.Code.Data.Integer.Base.C_'45''8804''45'_34)
                          ((T__'8804'__26 -> T__'8804'__22) -> Any
forall a b. a -> b
coe T__'8804'__26 -> T__'8804'__22
du_drop'8255''45''8804''45'_2718)
                          ((Integer -> Integer -> T_Dec_20) -> Any -> Any -> Any
forall a b. a -> b
coe
                             Integer -> Integer -> T_Dec_20
MAlonzo.Code.Data.Nat.Properties.d__'8804''63'__2802 (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_2790 ::
  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_2790 :: Integer
-> Integer -> T__'8804'__26 -> T__'8804'__26 -> T__'8801'__12
d_'8804''45'irrelevant_2790 = Integer
-> Integer -> T__'8804'__26 -> T__'8804'__26 -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.≤-isPreorder
d_'8804''45'isPreorder_2800 ::
  MAlonzo.Code.Relation.Binary.Structures.T_IsPreorder_70
d_'8804''45'isPreorder_2800 :: T_IsPreorder_70
d_'8804''45'isPreorder_2800
  = (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_4003
      (T_IsEquivalence_26 -> Any
forall a b. a -> b
coe
         T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.PropositionalEquality.Properties.du_isEquivalence_396)
      (\ 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_2722 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_2730 Any
v3 Any
v4)
-- Data.Integer.Properties.≤-isTotalPreorder
d_'8804''45'isTotalPreorder_2802 ::
  MAlonzo.Code.Relation.Binary.Structures.T_IsTotalPreorder_124
d_'8804''45'isTotalPreorder_2802 :: T_IsTotalPreorder_124
d_'8804''45'isTotalPreorder_2802
  = (T_IsPreorder_70
 -> (Any -> Any -> T__'8846'__30) -> T_IsTotalPreorder_124)
-> Any -> Any -> T_IsTotalPreorder_124
forall a b. a -> b
coe
      T_IsPreorder_70
-> (Any -> Any -> T__'8846'__30) -> T_IsTotalPreorder_124
MAlonzo.Code.Relation.Binary.Structures.C_IsTotalPreorder'46'constructor_8325
      (T_IsPreorder_70 -> Any
forall a b. a -> b
coe T_IsPreorder_70
d_'8804''45'isPreorder_2800) ((Integer -> Integer -> T__'8846'__30) -> Any
forall a b. a -> b
coe Integer -> Integer -> T__'8846'__30
d_'8804''45'total_2754)
-- Data.Integer.Properties.≤-isPartialOrder
d_'8804''45'isPartialOrder_2804 ::
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialOrder_174
d_'8804''45'isPartialOrder_2804 :: T_IsPartialOrder_174
d_'8804''45'isPartialOrder_2804
  = (T_IsPreorder_70
 -> (Any -> Any -> Any -> Any -> Any) -> T_IsPartialOrder_174)
-> Any -> Any -> T_IsPartialOrder_174
forall a b. a -> b
coe
      T_IsPreorder_70
-> (Any -> Any -> Any -> Any -> Any) -> T_IsPartialOrder_174
MAlonzo.Code.Relation.Binary.Structures.C_IsPartialOrder'46'constructor_9853
      (T_IsPreorder_70 -> Any
forall a b. a -> b
coe T_IsPreorder_70
d_'8804''45'isPreorder_2800) Any
forall a. a
erased
-- Data.Integer.Properties.≤-isTotalOrder
d_'8804''45'isTotalOrder_2806 ::
  MAlonzo.Code.Relation.Binary.Structures.T_IsTotalOrder_404
d_'8804''45'isTotalOrder_2806 :: T_IsTotalOrder_404
d_'8804''45'isTotalOrder_2806
  = (T_IsPartialOrder_174
 -> (Any -> Any -> T__'8846'__30) -> T_IsTotalOrder_404)
-> Any -> Any -> T_IsTotalOrder_404
forall a b. a -> b
coe
      T_IsPartialOrder_174
-> (Any -> Any -> T__'8846'__30) -> T_IsTotalOrder_404
MAlonzo.Code.Relation.Binary.Structures.C_IsTotalOrder'46'constructor_20555
      (T_IsPartialOrder_174 -> Any
forall a b. a -> b
coe T_IsPartialOrder_174
d_'8804''45'isPartialOrder_2804) ((Integer -> Integer -> T__'8846'__30) -> Any
forall a b. a -> b
coe Integer -> Integer -> T__'8846'__30
d_'8804''45'total_2754)
-- Data.Integer.Properties.≤-isDecTotalOrder
d_'8804''45'isDecTotalOrder_2808 ::
  MAlonzo.Code.Relation.Binary.Structures.T_IsDecTotalOrder_460
d_'8804''45'isDecTotalOrder_2808 :: T_IsDecTotalOrder_460
d_'8804''45'isDecTotalOrder_2808
  = (T_IsTotalOrder_404
 -> (Any -> Any -> T_Dec_20)
 -> (Any -> Any -> T_Dec_20)
 -> T_IsDecTotalOrder_460)
-> Any -> Any -> Any -> T_IsDecTotalOrder_460
forall a b. a -> b
coe
      T_IsTotalOrder_404
-> (Any -> Any -> T_Dec_20)
-> (Any -> Any -> T_Dec_20)
-> T_IsDecTotalOrder_460
MAlonzo.Code.Relation.Binary.Structures.C_IsDecTotalOrder'46'constructor_22695
      (T_IsTotalOrder_404 -> Any
forall a b. a -> b
coe T_IsTotalOrder_404
d_'8804''45'isTotalOrder_2806) ((Integer -> Integer -> T_Dec_20) -> Any
forall a b. a -> b
coe Integer -> Integer -> T_Dec_20
d__'8799'__2692)
      ((Integer -> Integer -> T_Dec_20) -> Any
forall a b. a -> b
coe Integer -> Integer -> T_Dec_20
d__'8804''63'__2772)
-- Data.Integer.Properties.≤-preorder
d_'8804''45'preorder_2810 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Preorder_132
d_'8804''45'preorder_2810 :: T_Preorder_132
d_'8804''45'preorder_2810
  = (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_2267
      T_IsPreorder_70
d_'8804''45'isPreorder_2800
-- Data.Integer.Properties.≤-totalPreorder
d_'8804''45'totalPreorder_2812 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_222
d_'8804''45'totalPreorder_2812 :: T_TotalPreorder_222
d_'8804''45'totalPreorder_2812
  = (T_IsTotalPreorder_124 -> T_TotalPreorder_222)
-> T_IsTotalPreorder_124 -> T_TotalPreorder_222
forall a b. a -> b
coe
      T_IsTotalPreorder_124 -> T_TotalPreorder_222
MAlonzo.Code.Relation.Binary.Bundles.C_TotalPreorder'46'constructor_4573
      T_IsTotalPreorder_124
d_'8804''45'isTotalPreorder_2802
-- Data.Integer.Properties.≤-poset
d_'8804''45'poset_2814 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Poset_314
d_'8804''45'poset_2814 :: T_Poset_314
d_'8804''45'poset_2814
  = (T_IsPartialOrder_174 -> T_Poset_314)
-> T_IsPartialOrder_174 -> T_Poset_314
forall a b. a -> b
coe
      T_IsPartialOrder_174 -> T_Poset_314
MAlonzo.Code.Relation.Binary.Bundles.C_Poset'46'constructor_6389
      T_IsPartialOrder_174
d_'8804''45'isPartialOrder_2804
-- Data.Integer.Properties.≤-totalOrder
d_'8804''45'totalOrder_2816 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_TotalOrder_764
d_'8804''45'totalOrder_2816 :: T_TotalOrder_764
d_'8804''45'totalOrder_2816
  = (T_IsTotalOrder_404 -> T_TotalOrder_764)
-> T_IsTotalOrder_404 -> T_TotalOrder_764
forall a b. a -> b
coe
      T_IsTotalOrder_404 -> T_TotalOrder_764
MAlonzo.Code.Relation.Binary.Bundles.C_TotalOrder'46'constructor_15747
      T_IsTotalOrder_404
d_'8804''45'isTotalOrder_2806
-- Data.Integer.Properties.≤-decTotalOrder
d_'8804''45'decTotalOrder_2818 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_DecTotalOrder_866
d_'8804''45'decTotalOrder_2818 :: T_DecTotalOrder_866
d_'8804''45'decTotalOrder_2818
  = (T_IsDecTotalOrder_460 -> T_DecTotalOrder_866)
-> T_IsDecTotalOrder_460 -> T_DecTotalOrder_866
forall a b. a -> b
coe
      T_IsDecTotalOrder_460 -> T_DecTotalOrder_866
MAlonzo.Code.Relation.Binary.Bundles.C_DecTotalOrder'46'constructor_17849
      T_IsDecTotalOrder_460
d_'8804''45'isDecTotalOrder_2808
-- Data.Integer.Properties.≤ᵇ⇒≤
d_'8804''7495''8658''8804'_2820 ::
  Integer ->
  Integer -> AgdaAny -> MAlonzo.Code.Data.Integer.Base.T__'8804'__26
d_'8804''7495''8658''8804'_2820 :: Integer -> Integer -> Any -> T__'8804'__26
d_'8804''7495''8658''8804'_2820 Integer
v0 Integer
v1 ~Any
v2
  = Integer -> Integer -> T__'8804'__26
du_'8804''7495''8658''8804'_2820 Integer
v0 Integer
v1
du_'8804''7495''8658''8804'_2820 ::
  Integer -> Integer -> MAlonzo.Code.Data.Integer.Base.T__'8804'__26
du_'8804''7495''8658''8804'_2820 :: Integer -> Integer -> T__'8804'__26
du_'8804''7495''8658''8804'_2820 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'__22 -> T__'8804'__26) -> Any -> T__'8804'__26
forall a b. a -> b
coe
            T__'8804'__22 -> T__'8804'__26
MAlonzo.Code.Data.Integer.Base.C_'43''8804''43'_48
            ((Integer -> T__'8804'__22) -> Any -> Any
forall a b. a -> b
coe
               Integer -> T__'8804'__22
MAlonzo.Code.Data.Nat.Properties.du_'8804''7495''8658''8804'_2746
               (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'__22 -> T__'8804'__26) -> Any -> Any
forall a b. a -> b
coe
                       T__'8804'__22 -> T__'8804'__26
MAlonzo.Code.Data.Integer.Base.C_'45''8804''45'_34
                       ((Integer -> T__'8804'__22) -> Any -> Any
forall a b. a -> b
coe
                          Integer -> T__'8804'__22
MAlonzo.Code.Data.Nat.Properties.du_'8804''7495''8658''8804'_2746
                          (Integer -> Any
forall a b. a -> b
coe Integer
v2)))
-- Data.Integer.Properties.≤⇒≤ᵇ
d_'8804''8658''8804''7495'_2828 ::
  Integer ->
  Integer -> MAlonzo.Code.Data.Integer.Base.T__'8804'__26 -> AgdaAny
d_'8804''8658''8804''7495'_2828 :: Integer -> Integer -> T__'8804'__26 -> Any
d_'8804''8658''8804''7495'_2828 ~Integer
v0 ~Integer
v1 T__'8804'__26
v2
  = T__'8804'__26 -> Any
du_'8804''8658''8804''7495'_2828 T__'8804'__26
v2
du_'8804''8658''8804''7495'_2828 ::
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26 -> AgdaAny
du_'8804''8658''8804''7495'_2828 :: T__'8804'__26 -> Any
du_'8804''8658''8804''7495'_2828 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'__22
v3
        -> (T__'8804'__22 -> Any) -> Any -> Any
forall a b. a -> b
coe
             T__'8804'__22 -> Any
MAlonzo.Code.Data.Nat.Properties.du_'8804''8658''8804''7495'_2758
             (T__'8804'__22 -> Any
forall a b. a -> b
coe T__'8804'__22
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'__22
v3
        -> (T__'8804'__22 -> Any) -> Any -> Any
forall a b. a -> b
coe
             T__'8804'__22 -> Any
MAlonzo.Code.Data.Nat.Properties.du_'8804''8658''8804''7495'_2758
             (T__'8804'__22 -> Any
forall a b. a -> b
coe T__'8804'__22
v3)
      T__'8804'__26
_ -> Any
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Data.Integer.Properties.drop‿+<+
d_drop'8255''43''60''43'_2834 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Integer.Base.T__'60'__50 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_drop'8255''43''60''43'_2834 :: Integer -> Integer -> T__'60'__50 -> T__'8804'__22
d_drop'8255''43''60''43'_2834 ~Integer
v0 ~Integer
v1 T__'60'__50
v2
  = T__'60'__50 -> T__'8804'__22
du_drop'8255''43''60''43'_2834 T__'60'__50
v2
du_drop'8255''43''60''43'_2834 ::
  MAlonzo.Code.Data.Integer.Base.T__'60'__50 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
du_drop'8255''43''60''43'_2834 :: T__'60'__50 -> T__'8804'__22
du_drop'8255''43''60''43'_2834 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'__22
v3 -> T__'8804'__22 -> T__'8804'__22
forall a b. a -> b
coe T__'8804'__22
v3
      T__'60'__50
_ -> T__'8804'__22
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Data.Integer.Properties.drop‿-<-
d_drop'8255''45''60''45'_2838 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Integer.Base.T__'60'__50 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_drop'8255''45''60''45'_2838 :: Integer -> Integer -> T__'60'__50 -> T__'8804'__22
d_drop'8255''45''60''45'_2838 ~Integer
v0 ~Integer
v1 T__'60'__50
v2
  = T__'60'__50 -> T__'8804'__22
du_drop'8255''45''60''45'_2838 T__'60'__50
v2
du_drop'8255''45''60''45'_2838 ::
  MAlonzo.Code.Data.Integer.Base.T__'60'__50 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
du_drop'8255''45''60''45'_2838 :: T__'60'__50 -> T__'8804'__22
du_drop'8255''45''60''45'_2838 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'__22
v3 -> T__'8804'__22 -> T__'8804'__22
forall a b. a -> b
coe T__'8804'__22
v3
      T__'60'__50
_ -> T__'8804'__22
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Data.Integer.Properties.+≮0
d_'43''8814'0_2842 ::
  Integer ->
  MAlonzo.Code.Data.Integer.Base.T__'60'__50 ->
  MAlonzo.Code.Data.Irrelevant.T_Irrelevant_20
d_'43''8814'0_2842 :: Integer -> T__'60'__50 -> T_Irrelevant_20
d_'43''8814'0_2842 = Integer -> T__'60'__50 -> T_Irrelevant_20
forall a. a
erased
-- Data.Integer.Properties.+≮-
d_'43''8814''45'_2844 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Integer.Base.T__'60'__50 ->
  MAlonzo.Code.Data.Irrelevant.T_Irrelevant_20
d_'43''8814''45'_2844 :: Integer -> Integer -> T__'60'__50 -> T_Irrelevant_20
d_'43''8814''45'_2844 = Integer -> Integer -> T__'60'__50 -> T_Irrelevant_20
forall a. a
erased
-- Data.Integer.Properties.<⇒≤
d_'60''8658''8804'_2846 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Integer.Base.T__'60'__50 ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26
d_'60''8658''8804'_2846 :: Integer -> Integer -> T__'60'__50 -> T__'8804'__26
d_'60''8658''8804'_2846 ~Integer
v0 ~Integer
v1 T__'60'__50
v2 = T__'60'__50 -> T__'8804'__26
du_'60''8658''8804'_2846 T__'60'__50
v2
du_'60''8658''8804'_2846 ::
  MAlonzo.Code.Data.Integer.Base.T__'60'__50 ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26
du_'60''8658''8804'_2846 :: T__'60'__50 -> T__'8804'__26
du_'60''8658''8804'_2846 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'__22
v3
        -> (T__'8804'__22 -> T__'8804'__26) -> Any -> T__'8804'__26
forall a b. a -> b
coe
             T__'8804'__22 -> T__'8804'__26
MAlonzo.Code.Data.Integer.Base.C_'45''8804''45'_34
             ((T__'8804'__22 -> T__'8804'__22) -> Any -> Any
forall a b. a -> b
coe
                T__'8804'__22 -> T__'8804'__22
MAlonzo.Code.Data.Nat.Properties.du_'60''8658''8804'_2854 (T__'8804'__22 -> Any
forall a b. a -> b
coe T__'8804'__22
v3))
      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'__22
v3
        -> (T__'8804'__22 -> T__'8804'__26) -> Any -> T__'8804'__26
forall a b. a -> b
coe
             T__'8804'__22 -> T__'8804'__26
MAlonzo.Code.Data.Integer.Base.C_'43''8804''43'_48
             ((T__'8804'__22 -> T__'8804'__22) -> Any -> Any
forall a b. a -> b
coe
                T__'8804'__22 -> T__'8804'__22
MAlonzo.Code.Data.Nat.Properties.du_'60''8658''8804'_2854 (T__'8804'__22 -> Any
forall a b. a -> b
coe T__'8804'__22
v3))
      T__'60'__50
_ -> T__'8804'__26
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Data.Integer.Properties.<⇒≢
d_'60''8658''8802'_2852 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Integer.Base.T__'60'__50 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Data.Irrelevant.T_Irrelevant_20
d_'60''8658''8802'_2852 :: Integer
-> Integer -> T__'60'__50 -> T__'8801'__12 -> T_Irrelevant_20
d_'60''8658''8802'_2852 = Integer
-> Integer -> T__'60'__50 -> T__'8801'__12 -> T_Irrelevant_20
forall a. a
erased
-- Data.Integer.Properties.<⇒≱
d_'60''8658''8817'_2858 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Integer.Base.T__'60'__50 ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26 ->
  MAlonzo.Code.Data.Irrelevant.T_Irrelevant_20
d_'60''8658''8817'_2858 :: Integer
-> Integer -> T__'60'__50 -> T__'8804'__26 -> T_Irrelevant_20
d_'60''8658''8817'_2858 = Integer
-> Integer -> T__'60'__50 -> T__'8804'__26 -> T_Irrelevant_20
forall a. a
erased
-- Data.Integer.Properties.≤⇒≯
d_'8804''8658''8815'_2864 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26 ->
  MAlonzo.Code.Data.Integer.Base.T__'60'__50 ->
  MAlonzo.Code.Data.Irrelevant.T_Irrelevant_20
d_'8804''8658''8815'_2864 :: Integer
-> Integer -> T__'8804'__26 -> T__'60'__50 -> T_Irrelevant_20
d_'8804''8658''8815'_2864 = Integer
-> Integer -> T__'8804'__26 -> T__'60'__50 -> T_Irrelevant_20
forall a. a
erased
-- Data.Integer.Properties.≰⇒>
d_'8816''8658''62'_2874 ::
  Integer ->
  Integer ->
  (MAlonzo.Code.Data.Integer.Base.T__'8804'__26 ->
   MAlonzo.Code.Data.Irrelevant.T_Irrelevant_20) ->
  MAlonzo.Code.Data.Integer.Base.T__'60'__50
d_'8816''8658''62'_2874 :: Integer
-> Integer -> (T__'8804'__26 -> T_Irrelevant_20) -> T__'60'__50
d_'8816''8658''62'_2874 Integer
v0 Integer
v1 ~T__'8804'__26 -> T_Irrelevant_20
v2 = Integer -> Integer -> T__'60'__50
du_'8816''8658''62'_2874 Integer
v0 Integer
v1
du_'8816''8658''62'_2874 ::
  Integer -> Integer -> MAlonzo.Code.Data.Integer.Base.T__'60'__50
du_'8816''8658''62'_2874 :: Integer -> Integer -> T__'60'__50
du_'8816''8658''62'_2874 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'__22 -> T__'60'__50) -> Any -> T__'60'__50
forall a b. a -> b
coe
                  T__'8804'__22 -> T__'60'__50
MAlonzo.Code.Data.Integer.Base.C_'43''60''43'_72
                  ((Integer -> Integer -> T__'8804'__22) -> Any -> Any -> Any
forall a b. a -> b
coe
                     Integer -> Integer -> T__'8804'__22
MAlonzo.Code.Data.Nat.Properties.du_'8816''8658''62'_2888 (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 -> T_Irrelevant_20) -> Any) -> Any -> Any
forall a b. a -> b
coe
                      (Any -> T_Irrelevant_20) -> Any
MAlonzo.Code.Relation.Nullary.Negation.Core.du_contradiction_44
                      Any
forall a. a
erased
                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'__22 -> T__'60'__50) -> Any -> Any
forall a b. a -> b
coe
                          T__'8804'__22 -> T__'60'__50
MAlonzo.Code.Data.Integer.Base.C_'45''60''45'_58
                          ((Integer -> Integer -> T__'8804'__22) -> Any -> Any -> Any
forall a b. a -> b
coe
                             Integer -> Integer -> T__'8804'__22
MAlonzo.Code.Data.Nat.Properties.du_'8816''8658''62'_2888 (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'_2900 ::
  Integer ->
  Integer ->
  (MAlonzo.Code.Data.Integer.Base.T__'60'__50 ->
   MAlonzo.Code.Data.Irrelevant.T_Irrelevant_20) ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26
d_'8814''8658''8805'_2900 :: Integer
-> Integer -> (T__'60'__50 -> T_Irrelevant_20) -> T__'8804'__26
d_'8814''8658''8805'_2900 Integer
v0 Integer
v1 ~T__'60'__50 -> T_Irrelevant_20
v2
  = Integer -> Integer -> T__'8804'__26
du_'8814''8658''8805'_2900 Integer
v0 Integer
v1
du_'8814''8658''8805'_2900 ::
  Integer -> Integer -> MAlonzo.Code.Data.Integer.Base.T__'8804'__26
du_'8814''8658''8805'_2900 :: Integer -> Integer -> T__'8804'__26
du_'8814''8658''8805'_2900 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'__22 -> T__'8804'__26) -> Any -> T__'8804'__26
forall a b. a -> b
coe
                  T__'8804'__22 -> T__'8804'__26
MAlonzo.Code.Data.Integer.Base.C_'43''8804''43'_48
                  ((Integer -> Integer -> T__'8804'__22) -> Any -> Any -> Any
forall a b. a -> b
coe
                     Integer -> Integer -> T__'8804'__22
MAlonzo.Code.Data.Nat.Properties.du_'8814''8658''8805'_2902
                     (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 -> T_Irrelevant_20) -> Any) -> Any -> Any
forall a b. a -> b
coe
                      (Any -> T_Irrelevant_20) -> Any
MAlonzo.Code.Relation.Nullary.Negation.Core.du_contradiction_44
                      Any
forall a. a
erased
                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'__22 -> T__'8804'__26) -> Any -> Any
forall a b. a -> b
coe
                          T__'8804'__22 -> T__'8804'__26
MAlonzo.Code.Data.Integer.Base.C_'45''8804''45'_34
                          ((Integer -> Integer -> T__'8804'__22) -> Any -> Any -> Any
forall a b. a -> b
coe
                             Integer -> Integer -> T__'8804'__22
MAlonzo.Code.Data.Nat.Properties.du_'8814''8658''8805'_2902
                             (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'_2926 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Integer.Base.T__'60'__50 ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26 ->
  MAlonzo.Code.Data.Irrelevant.T_Irrelevant_20
d_'62''8658''8816'_2926 :: Integer
-> Integer -> T__'60'__50 -> T__'8804'__26 -> T_Irrelevant_20
d_'62''8658''8816'_2926 = Integer
-> Integer -> T__'60'__50 -> T__'8804'__26 -> T_Irrelevant_20
forall a. a
erased
-- Data.Integer.Properties.≤∧≢⇒<
d_'8804''8743''8802''8658''60'_2928 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26 ->
  (MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
   MAlonzo.Code.Data.Irrelevant.T_Irrelevant_20) ->
  MAlonzo.Code.Data.Integer.Base.T__'60'__50
d_'8804''8743''8802''8658''60'_2928 :: Integer
-> Integer
-> T__'8804'__26
-> (T__'8801'__12 -> T_Irrelevant_20)
-> T__'60'__50
d_'8804''8743''8802''8658''60'_2928 Integer
v0 Integer
v1 T__'8804'__26
v2 ~T__'8801'__12 -> T_Irrelevant_20
v3
  = Integer -> Integer -> T__'8804'__26 -> T__'60'__50
du_'8804''8743''8802''8658''60'_2928 Integer
v0 Integer
v1 T__'8804'__26
v2
du_'8804''8743''8802''8658''60'_2928 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26 ->
  MAlonzo.Code.Data.Integer.Base.T__'60'__50
du_'8804''8743''8802''8658''60'_2928 :: Integer -> Integer -> T__'8804'__26 -> T__'60'__50
du_'8804''8743''8802''8658''60'_2928 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'__22
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'__22 -> T__'60'__50) -> Any -> Any
forall a b. a -> b
coe
                T__'8804'__22 -> T__'60'__50
MAlonzo.Code.Data.Integer.Base.C_'45''60''45'_58
                ((Integer -> T__'8804'__22 -> T__'8804'__22) -> Any -> Any -> Any
forall a b. a -> b
coe
                   Integer -> T__'8804'__22 -> T__'8804'__22
MAlonzo.Code.Data.Nat.Properties.du_'8804''8743''8802''8658''60'_2918
                   (Integer -> Any
forall a b. a -> b
coe Integer
v6) (T__'8804'__22 -> Any
forall a b. a -> b
coe T__'8804'__22
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'__22
v5
        -> (T__'8804'__22 -> T__'60'__50) -> Any -> T__'60'__50
forall a b. a -> b
coe
             T__'8804'__22 -> T__'60'__50
MAlonzo.Code.Data.Integer.Base.C_'43''60''43'_72
             ((Integer -> T__'8804'__22 -> T__'8804'__22) -> Any -> Any -> Any
forall a b. a -> b
coe
                Integer -> T__'8804'__22 -> T__'8804'__22
MAlonzo.Code.Data.Nat.Properties.du_'8804''8743''8802''8658''60'_2918
                (Integer -> Any
forall a b. a -> b
coe Integer
v1) (T__'8804'__22 -> Any
forall a b. a -> b
coe T__'8804'__22
v5))
      T__'8804'__26
_ -> T__'60'__50
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Data.Integer.Properties.≤∧≮⇒≡
d_'8804''8743''8814''8658''8801'_2940 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26 ->
  (MAlonzo.Code.Data.Integer.Base.T__'60'__50 ->
   MAlonzo.Code.Data.Irrelevant.T_Irrelevant_20) ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8804''8743''8814''8658''8801'_2940 :: Integer
-> Integer
-> T__'8804'__26
-> (T__'60'__50 -> T_Irrelevant_20)
-> T__'8801'__12
d_'8804''8743''8814''8658''8801'_2940 = Integer
-> Integer
-> T__'8804'__26
-> (T__'60'__50 -> T_Irrelevant_20)
-> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.<-irrefl
d_'60''45'irrefl_2946 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Data.Integer.Base.T__'60'__50 ->
  MAlonzo.Code.Data.Irrelevant.T_Irrelevant_20
d_'60''45'irrefl_2946 :: Integer
-> Integer -> T__'8801'__12 -> T__'60'__50 -> T_Irrelevant_20
d_'60''45'irrefl_2946 = Integer
-> Integer -> T__'8801'__12 -> T__'60'__50 -> T_Irrelevant_20
forall a. a
erased
-- Data.Integer.Properties.<-asym
d_'60''45'asym_2952 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Integer.Base.T__'60'__50 ->
  MAlonzo.Code.Data.Integer.Base.T__'60'__50 ->
  MAlonzo.Code.Data.Irrelevant.T_Irrelevant_20
d_'60''45'asym_2952 :: Integer -> Integer -> T__'60'__50 -> T__'60'__50 -> T_Irrelevant_20
d_'60''45'asym_2952 = Integer -> Integer -> T__'60'__50 -> T__'60'__50 -> T_Irrelevant_20
forall a. a
erased
-- Data.Integer.Properties.≤-<-trans
d_'8804''45''60''45'trans_2958 ::
  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_2958 :: Integer
-> Integer
-> Integer
-> T__'8804'__26
-> T__'60'__50
-> T__'60'__50
d_'8804''45''60''45'trans_2958 ~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_2958 T__'8804'__26
v3 T__'60'__50
v4
du_'8804''45''60''45'trans_2958 ::
  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_2958 :: T__'8804'__26 -> T__'60'__50 -> T__'60'__50
du_'8804''45''60''45'trans_2958 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'__22
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'__22
v7
               -> (T__'8804'__22 -> T__'60'__50) -> Any -> T__'60'__50
forall a b. a -> b
coe
                    T__'8804'__22 -> T__'60'__50
MAlonzo.Code.Data.Integer.Base.C_'45''60''45'_58
                    ((T__'8804'__22 -> T__'8804'__22 -> T__'8804'__22)
-> Any -> Any -> Any
forall a b. a -> b
coe
                       T__'8804'__22 -> T__'8804'__22 -> T__'8804'__22
MAlonzo.Code.Data.Nat.Properties.du_'60''45''8804''45'trans_2992
                       (T__'8804'__22 -> Any
forall a b. a -> b
coe T__'8804'__22
v7) (T__'8804'__22 -> Any
forall a b. a -> b
coe T__'8804'__22
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'__22
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'__22
v7
               -> (T__'8804'__22 -> T__'60'__50) -> Any -> T__'60'__50
forall a b. a -> b
coe
                    T__'8804'__22 -> T__'60'__50
MAlonzo.Code.Data.Integer.Base.C_'43''60''43'_72
                    ((T__'8804'__22 -> T__'8804'__22 -> T__'8804'__22)
-> Any -> Any -> Any
forall a b. a -> b
coe
                       T__'8804'__22 -> T__'8804'__22 -> T__'8804'__22
MAlonzo.Code.Data.Nat.Properties.du_'8804''45''60''45'trans_2986
                       (T__'8804'__22 -> Any
forall a b. a -> b
coe T__'8804'__22
v4) (T__'8804'__22 -> Any
forall a b. a -> b
coe T__'8804'__22
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_2972 ::
  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_2972 :: Integer
-> Integer
-> Integer
-> T__'60'__50
-> T__'8804'__26
-> T__'60'__50
d_'60''45''8804''45'trans_2972 ~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_2972 T__'60'__50
v3 T__'8804'__26
v4
du_'60''45''8804''45'trans_2972 ::
  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_2972 :: T__'60'__50 -> T__'8804'__26 -> T__'60'__50
du_'60''45''8804''45'trans_2972 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'__22
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'__22
v7
               -> (T__'8804'__22 -> T__'60'__50) -> Any -> T__'60'__50
forall a b. a -> b
coe
                    T__'8804'__22 -> T__'60'__50
MAlonzo.Code.Data.Integer.Base.C_'45''60''45'_58
                    ((T__'8804'__22 -> T__'8804'__22 -> T__'8804'__22)
-> Any -> Any -> Any
forall a b. a -> b
coe
                       T__'8804'__22 -> T__'8804'__22 -> T__'8804'__22
MAlonzo.Code.Data.Nat.Properties.du_'8804''45''60''45'trans_2986
                       (T__'8804'__22 -> Any
forall a b. a -> b
coe T__'8804'__22
v7) (T__'8804'__22 -> Any
forall a b. a -> b
coe T__'8804'__22
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'__22
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'__22
v7
               -> (T__'8804'__22 -> T__'60'__50) -> Any -> T__'60'__50
forall a b. a -> b
coe
                    T__'8804'__22 -> T__'60'__50
MAlonzo.Code.Data.Integer.Base.C_'43''60''43'_72
                    ((T__'8804'__22 -> T__'8804'__22 -> T__'8804'__22)
-> Any -> Any -> Any
forall a b. a -> b
coe
                       T__'8804'__22 -> T__'8804'__22 -> T__'8804'__22
MAlonzo.Code.Data.Nat.Properties.du_'60''45''8804''45'trans_2992
                       (T__'8804'__22 -> Any
forall a b. a -> b
coe T__'8804'__22
v4) (T__'8804'__22 -> Any
forall a b. a -> b
coe T__'8804'__22
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_2986 ::
  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_2986 :: Integer
-> Integer -> Integer -> T__'60'__50 -> T__'60'__50 -> T__'60'__50
d_'60''45'trans_2986 ~Integer
v0 ~Integer
v1 ~Integer
v2 T__'60'__50
v3 T__'60'__50
v4
  = T__'60'__50 -> T__'60'__50 -> T__'60'__50
du_'60''45'trans_2986 T__'60'__50
v3 T__'60'__50
v4
du_'60''45'trans_2986 ::
  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_2986 :: T__'60'__50 -> T__'60'__50 -> T__'60'__50
du_'60''45'trans_2986 T__'60'__50
v0 T__'60'__50
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_2958
      ((T__'60'__50 -> T__'8804'__26) -> Any -> Any
forall a b. a -> b
coe T__'60'__50 -> T__'8804'__26
du_'60''8658''8804'_2846 (T__'60'__50 -> Any
forall a b. a -> b
coe T__'60'__50
v0)) (T__'60'__50 -> Any
forall a b. a -> b
coe T__'60'__50
v1)
-- Data.Integer.Properties.<-cmp
d_'60''45'cmp_2992 ::
  Integer ->
  Integer -> MAlonzo.Code.Relation.Binary.Definitions.T_Tri_158
d_'60''45'cmp_2992 :: Integer -> Integer -> T_Tri_158
d_'60''45'cmp_2992 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_158) -> Any -> t
forall a b. a -> b
coe
                    Any -> T_Tri_158
MAlonzo.Code.Relation.Binary.Definitions.C_tri'62'_188
                    (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_158
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_158) -> Any -> Any
forall a b. a -> b
coe
                             Any -> T_Tri_158
MAlonzo.Code.Relation.Binary.Definitions.C_tri'8776'_180 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_158) -> Any -> Any
forall a b. a -> b
coe
                            Any -> T_Tri_158
MAlonzo.Code.Relation.Binary.Definitions.C_tri'60'_172
                            ((T__'8804'__22 -> T__'60'__50) -> Any -> Any
forall a b. a -> b
coe
                               T__'8804'__22 -> T__'60'__50
MAlonzo.Code.Data.Integer.Base.C_'43''60''43'_72
                               ((T__'8804'__22 -> T__'8804'__22) -> Any -> Any
forall a b. a -> b
coe
                                  T__'8804'__22 -> T__'8804'__22
MAlonzo.Code.Data.Nat.Base.C_s'8804's_34
                                  (T__'8804'__22 -> Any
forall a b. a -> b
coe T__'8804'__22
MAlonzo.Code.Data.Nat.Base.C_z'8804'n_26)))
                      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_158) -> Any -> Any
forall a b. a -> b
coe
                                Any -> T_Tri_158
MAlonzo.Code.Relation.Binary.Definitions.C_tri'62'_188
                                ((T__'8804'__22 -> T__'60'__50) -> Any -> Any
forall a b. a -> b
coe
                                   T__'8804'__22 -> T__'60'__50
MAlonzo.Code.Data.Integer.Base.C_'43''60''43'_72
                                   ((T__'8804'__22 -> T__'8804'__22) -> Any -> Any
forall a b. a -> b
coe
                                      T__'8804'__22 -> T__'8804'__22
MAlonzo.Code.Data.Nat.Base.C_s'8804's_34
                                      (T__'8804'__22 -> Any
forall a b. a -> b
coe T__'8804'__22
MAlonzo.Code.Data.Nat.Base.C_z'8804'n_26)))
                         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) -> (Any -> Any) -> T_Dec_20 -> T_Dec_20)
-> Any -> (Any -> Any) -> Any -> t
forall a b. a -> b
coe
                                          (Any -> Any) -> (Any -> Any) -> T_Dec_20 -> T_Dec_20
MAlonzo.Code.Relation.Nullary.Decidable.Core.du_map'8242'_168
                                          Any
forall a. a
erased
                                          (\ Any
v5 ->
                                             (Integer -> Any) -> Any -> Any
forall a b. a -> b
coe
                                               Integer -> Any
MAlonzo.Code.Data.Nat.Properties.du_'8801''8658''8801''7495'_2678
                                               (Integer -> Any
forall a b. a -> b
coe Integer
v3))
                                          ((Bool -> T_Reflects_16 -> T_Dec_20) -> Any -> Any -> Any
forall a b. a -> b
coe
                                             Bool -> T_Reflects_16 -> T_Dec_20
MAlonzo.Code.Relation.Nullary.Decidable.Core.C__because__32
                                             ((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))
                                             ((Bool -> T_Reflects_16) -> Any -> Any
forall a b. a -> b
coe
                                                Bool -> T_Reflects_16
MAlonzo.Code.Relation.Nullary.Reflects.d_T'45'reflects_66
                                                ((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
                                  (case Any -> T_Dec_20
forall a b. a -> b
coe Any
forall a. a
v5 of
                                     MAlonzo.Code.Relation.Nullary.Decidable.Core.C__because__32 Bool
v6 T_Reflects_16
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_16 -> Any
forall a b. a -> b
coe T_Reflects_16
v7)
                                                   ((Any -> T_Tri_158) -> Any -> Any
forall a b. a -> b
coe
                                                      Any -> T_Tri_158
MAlonzo.Code.Relation.Binary.Definitions.C_tri'8776'_180
                                                      Any
forall a. a
erased)
                                            else (let v8 :: b
v8
                                                        = Any -> b -> b
forall a b. a -> b -> b
seq
                                                            (T_Reflects_16 -> Any
forall a b. a -> b
coe T_Reflects_16
v7)
                                                            (let v8 :: Bool
v8 = 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 -> b
forall a b. a -> b
coe
                                                               (if Bool -> Bool
forall a b. a -> b
coe Bool
v8
                                                                  then (Any -> Any -> Any) -> Any -> Any -> Any
forall a b. a -> b
coe
                                                                         Any -> Any -> Any
forall a b. a -> b -> b
seq
                                                                         ((Bool -> T_Reflects_16) -> Any -> Any
forall a b. a -> b
coe
                                                                            Bool -> T_Reflects_16
MAlonzo.Code.Relation.Nullary.Reflects.d_T'45'reflects_66
                                                                            (Bool -> Any
forall a b. a -> b
coe Bool
v8))
                                                                         ((Any -> T_Tri_158) -> Any -> Any
forall a b. a -> b
coe
                                                                            Any -> T_Tri_158
MAlonzo.Code.Relation.Binary.Definitions.C_tri'60'_172
                                                                            ((Integer -> T__'8804'__22) -> Any -> Any
forall a b. a -> b
coe
                                                                               Integer -> T__'8804'__22
MAlonzo.Code.Data.Nat.Properties.du_'60''7495''8658''60'_2716
                                                                               (Integer -> Any
forall a b. a -> b
coe Integer
v3)))
                                                                  else (Any -> Any -> Any) -> Any -> Any -> Any
forall a b. a -> b
coe
                                                                         Any -> Any -> Any
forall a b. a -> b -> b
seq
                                                                         ((Bool -> T_Reflects_16) -> Any -> Any
forall a b. a -> b
coe
                                                                            Bool -> T_Reflects_16
MAlonzo.Code.Relation.Nullary.Reflects.d_T'45'reflects_66
                                                                            (Bool -> Any
forall a b. a -> b
coe Bool
v8))
                                                                         ((Any -> T_Tri_158) -> Any -> Any
forall a b. a -> b
coe
                                                                            Any -> T_Tri_158
MAlonzo.Code.Relation.Binary.Definitions.C_tri'62'_188
                                                                            ((Integer -> T__'8804'__22 -> T__'8804'__22) -> Any -> Any -> Any
forall a b. a -> b
coe
                                                                               Integer -> T__'8804'__22 -> T__'8804'__22
MAlonzo.Code.Data.Nat.Properties.du_'8804''8743''8802''8658''60'_2918
                                                                               (Integer -> Any
forall a b. a -> b
coe Integer
v3)
                                                                               ((Integer -> Integer -> T__'8804'__22) -> Any -> Any -> Any
forall a b. a -> b
coe
                                                                                  Integer -> Integer -> T__'8804'__22
MAlonzo.Code.Data.Nat.Properties.du_'8814''8658''8805'_2902
                                                                                  (Integer -> Any
forall a b. a -> b
coe Integer
v3)
                                                                                  (Integer -> Any
forall a b. a -> b
coe Integer
v4)))))) in
                                                  Any -> Any
forall a b. a -> b
coe
                                                    (case Any -> T_Tri_158
forall a b. a -> b
coe Any
forall a. a
v8 of
                                                       MAlonzo.Code.Relation.Binary.Definitions.C_tri'60'_172 Any
v9
                                                         -> (Any -> T_Tri_158) -> Any -> Any
forall a b. a -> b
coe
                                                              Any -> T_Tri_158
MAlonzo.Code.Relation.Binary.Definitions.C_tri'60'_172
                                                              ((T__'8804'__22 -> T__'60'__50) -> Any -> Any
forall a b. a -> b
coe
                                                                 T__'8804'__22 -> T__'60'__50
MAlonzo.Code.Data.Integer.Base.C_'43''60''43'_72
                                                                 ((T__'8804'__22 -> T__'8804'__22) -> Any -> Any
forall a b. a -> b
coe
                                                                    T__'8804'__22 -> T__'8804'__22
MAlonzo.Code.Data.Nat.Base.C_s'8804's_34
                                                                    Any
v9))
                                                       MAlonzo.Code.Relation.Binary.Definitions.C_tri'8776'_180 Any
v10
                                                         -> (Any -> T_Tri_158) -> Any -> Any
forall a b. a -> b
coe
                                                              Any -> T_Tri_158
MAlonzo.Code.Relation.Binary.Definitions.C_tri'8776'_180
                                                              Any
forall a. a
erased
                                                       MAlonzo.Code.Relation.Binary.Definitions.C_tri'62'_188 Any
v11
                                                         -> (Any -> T_Tri_158) -> Any -> Any
forall a b. a -> b
coe
                                                              Any -> T_Tri_158
MAlonzo.Code.Relation.Binary.Definitions.C_tri'62'_188
                                                              ((T__'8804'__22 -> T__'60'__50) -> Any -> Any
forall a b. a -> b
coe
                                                                 T__'8804'__22 -> T__'60'__50
MAlonzo.Code.Data.Integer.Base.C_'43''60''43'_72
                                                                 ((T__'8804'__22 -> T__'8804'__22) -> Any -> Any
forall a b. a -> b
coe
                                                                    T__'8804'__22 -> T__'8804'__22
MAlonzo.Code.Data.Nat.Base.C_s'8804's_34
                                                                    Any
v11))
                                                       T_Tri_158
_ -> Any
forall a. a
MAlonzo.RTE.mazUnreachableError))
                                     T_Dec_20
_ -> Any
forall a. a
MAlonzo.RTE.mazUnreachableError))
                         Integer
_ -> (Any -> T_Tri_158) -> Any -> Any
forall a b. a -> b
coe
                                Any -> T_Tri_158
MAlonzo.Code.Relation.Binary.Definitions.C_tri'62'_188
                                (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_158
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_158) -> Any -> Any
forall a b. a -> b
coe
                      Any -> T_Tri_158
MAlonzo.Code.Relation.Binary.Definitions.C_tri'60'_172
                      (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) -> (Any -> Any) -> T_Dec_20 -> T_Dec_20)
-> Any -> (Any -> Any) -> Any -> t
forall a b. a -> b
coe
                                  (Any -> Any) -> (Any -> Any) -> T_Dec_20 -> T_Dec_20
MAlonzo.Code.Relation.Nullary.Decidable.Core.du_map'8242'_168
                                  Any
forall a. a
erased
                                  (\ Any
v4 ->
                                     (Integer -> Any) -> Any -> Any
forall a b. a -> b
coe
                                       Integer -> Any
MAlonzo.Code.Data.Nat.Properties.du_'8801''8658''8801''7495'_2678
                                       (Integer -> Any
forall a b. a -> b
coe Integer
v2))
                                  ((Bool -> T_Reflects_16 -> T_Dec_20) -> Any -> Any -> Any
forall a b. a -> b
coe
                                     Bool -> T_Reflects_16 -> T_Dec_20
MAlonzo.Code.Relation.Nullary.Decidable.Core.C__because__32
                                     ((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))
                                     ((Bool -> T_Reflects_16) -> Any -> Any
forall a b. a -> b
coe
                                        Bool -> T_Reflects_16
MAlonzo.Code.Relation.Nullary.Reflects.d_T'45'reflects_66
                                        ((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
                          (case Any -> T_Dec_20
forall a b. a -> b
coe Any
forall a. a
v4 of
                             MAlonzo.Code.Relation.Nullary.Decidable.Core.C__because__32 Bool
v5 T_Reflects_16
v6
                               -> if Bool -> Bool
forall a b. a -> b
coe Bool
v5
                                    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_16 -> Any
forall a b. a -> b
coe T_Reflects_16
v6)
                                           ((Any -> T_Tri_158) -> Any -> Any
forall a b. a -> b
coe
                                              Any -> T_Tri_158
MAlonzo.Code.Relation.Binary.Definitions.C_tri'8776'_180
                                              Any
forall a. a
erased)
                                    else (let v7 :: b
v7
                                                = Any -> b -> b
forall a b. a -> b -> b
seq
                                                    (T_Reflects_16 -> Any
forall a b. a -> b
coe T_Reflects_16
v6)
                                                    (let v7 :: Bool
v7 = Integer -> Integer -> Bool
ltInt (Integer -> Integer
forall a b. a -> b
coe Integer
v1) (Integer -> Integer
forall a b. a -> b
coe Integer
v0) in
                                                     Any -> b
forall a b. a -> b
coe
                                                       (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
                                                                 ((Bool -> T_Reflects_16) -> Any -> Any
forall a b. a -> b
coe
                                                                    Bool -> T_Reflects_16
MAlonzo.Code.Relation.Nullary.Reflects.d_T'45'reflects_66
                                                                    (Bool -> Any
forall a b. a -> b
coe Bool
v7))
                                                                 ((Any -> T_Tri_158) -> Any -> Any
forall a b. a -> b
coe
                                                                    Any -> T_Tri_158
MAlonzo.Code.Relation.Binary.Definitions.C_tri'60'_172
                                                                    ((Integer -> T__'8804'__22) -> Any -> Any
forall a b. a -> b
coe
                                                                       Integer -> T__'8804'__22
MAlonzo.Code.Data.Nat.Properties.du_'60''7495''8658''60'_2716
                                                                       (Integer -> Any
forall a b. a -> b
coe Integer
v2)))
                                                          else (Any -> Any -> Any) -> Any -> Any -> Any
forall a b. a -> b
coe
                                                                 Any -> Any -> Any
forall a b. a -> b -> b
seq
                                                                 ((Bool -> T_Reflects_16) -> Any -> Any
forall a b. a -> b
coe
                                                                    Bool -> T_Reflects_16
MAlonzo.Code.Relation.Nullary.Reflects.d_T'45'reflects_66
                                                                    (Bool -> Any
forall a b. a -> b
coe Bool
v7))
                                                                 ((Any -> T_Tri_158) -> Any -> Any
forall a b. a -> b
coe
                                                                    Any -> T_Tri_158
MAlonzo.Code.Relation.Binary.Definitions.C_tri'62'_188
                                                                    ((Integer -> T__'8804'__22 -> T__'8804'__22) -> Any -> Any -> Any
forall a b. a -> b
coe
                                                                       Integer -> T__'8804'__22 -> T__'8804'__22
MAlonzo.Code.Data.Nat.Properties.du_'8804''8743''8802''8658''60'_2918
                                                                       (Integer -> Any
forall a b. a -> b
coe Integer
v2)
                                                                       ((Integer -> Integer -> T__'8804'__22) -> Any -> Any -> Any
forall a b. a -> b
coe
                                                                          Integer -> Integer -> T__'8804'__22
MAlonzo.Code.Data.Nat.Properties.du_'8814''8658''8805'_2902
                                                                          (Integer -> Any
forall a b. a -> b
coe Integer
v2) (Integer -> Any
forall a b. a -> b
coe Integer
v3)))))) in
                                          Any -> Any
forall a b. a -> b
coe
                                            (case Any -> T_Tri_158
forall a b. a -> b
coe Any
forall a. a
v7 of
                                               MAlonzo.Code.Relation.Binary.Definitions.C_tri'60'_172 Any
v8
                                                 -> (Any -> T_Tri_158) -> Any -> Any
forall a b. a -> b
coe
                                                      Any -> T_Tri_158
MAlonzo.Code.Relation.Binary.Definitions.C_tri'62'_188
                                                      ((T__'8804'__22 -> T__'60'__50) -> Any -> Any
forall a b. a -> b
coe
                                                         T__'8804'__22 -> T__'60'__50
MAlonzo.Code.Data.Integer.Base.C_'45''60''45'_58
                                                         Any
v8)
                                               MAlonzo.Code.Relation.Binary.Definitions.C_tri'8776'_180 Any
v9
                                                 -> (Any -> T_Tri_158) -> Any -> Any
forall a b. a -> b
coe
                                                      Any -> T_Tri_158
MAlonzo.Code.Relation.Binary.Definitions.C_tri'8776'_180
                                                      Any
forall a. a
erased
                                               MAlonzo.Code.Relation.Binary.Definitions.C_tri'62'_188 Any
v10
                                                 -> (Any -> T_Tri_158) -> Any -> Any
forall a b. a -> b
coe
                                                      Any -> T_Tri_158
MAlonzo.Code.Relation.Binary.Definitions.C_tri'60'_172
                                                      ((T__'8804'__22 -> T__'60'__50) -> Any -> Any
forall a b. a -> b
coe
                                                         T__'8804'__22 -> T__'60'__50
MAlonzo.Code.Data.Integer.Base.C_'45''60''45'_58
                                                         Any
v10)
                                               T_Tri_158
_ -> Any
forall a. a
MAlonzo.RTE.mazUnreachableError))
                             T_Dec_20
_ -> Any
forall a. a
MAlonzo.RTE.mazUnreachableError)))
-- Data.Integer.Properties._<?_
d__'60''63'__3082 ::
  Integer ->
  Integer -> MAlonzo.Code.Relation.Nullary.Decidable.Core.T_Dec_20
d__'60''63'__3082 :: Integer -> Integer -> T_Dec_20
d__'60''63'__3082 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_Dec_20 -> T_Dec_20)
-> Any -> Any -> Any -> T_Dec_20
forall a b. a -> b
coe
                  (Any -> Any) -> (Any -> Any) -> T_Dec_20 -> T_Dec_20
MAlonzo.Code.Relation.Nullary.Decidable.Core.du_map'8242'_168
                  ((T__'8804'__22 -> T__'60'__50) -> Any
forall a b. a -> b
coe T__'8804'__22 -> T__'60'__50
MAlonzo.Code.Data.Integer.Base.C_'43''60''43'_72)
                  ((T__'60'__50 -> T__'8804'__22) -> Any
forall a b. a -> b
coe T__'60'__50 -> T__'8804'__22
du_drop'8255''43''60''43'_2834)
                  ((Integer -> Integer -> T_Dec_20) -> Any -> Any -> Any
forall a b. a -> b
coe
                     Integer -> Integer -> T_Dec_20
MAlonzo.Code.Data.Nat.Properties.d__'60''63'__3030 (Integer -> Any
forall a b. a -> b
coe Integer
v0)
                     (Integer -> Any
forall a b. a -> b
coe Integer
v1))
            Any
_ -> (Bool -> T_Reflects_16 -> T_Dec_20) -> Any -> Any -> T_Dec_20
forall a b. a -> b
coe
                   Bool -> T_Reflects_16 -> T_Dec_20
MAlonzo.Code.Relation.Nullary.Decidable.Core.C__because__32
                   (Bool -> Any
forall a b. a -> b
coe Bool
MAlonzo.Code.Agda.Builtin.Bool.C_false_8)
                   (T_Reflects_16 -> Any
forall a b. a -> b
coe T_Reflects_16
MAlonzo.Code.Relation.Nullary.Reflects.C_of'8319'_26)
      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_20
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_16 -> T_Dec_20) -> Any -> Any -> Any
forall a b. a -> b
coe
                      Bool -> T_Reflects_16 -> T_Dec_20
MAlonzo.Code.Relation.Nullary.Decidable.Core.C__because__32
                      (Bool -> Any
forall a b. a -> b
coe Bool
MAlonzo.Code.Agda.Builtin.Bool.C_true_10)
                      ((Any -> T_Reflects_16) -> Any -> Any
forall a b. a -> b
coe
                         Any -> T_Reflects_16
MAlonzo.Code.Relation.Nullary.Reflects.C_of'696'_22
                         (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) -> (Any -> Any) -> T_Dec_20 -> T_Dec_20)
-> Any -> Any -> Any -> Any
forall a b. a -> b
coe
                          (Any -> Any) -> (Any -> Any) -> T_Dec_20 -> T_Dec_20
MAlonzo.Code.Relation.Nullary.Decidable.Core.du_map'8242'_168
                          ((T__'8804'__22 -> T__'60'__50) -> Any
forall a b. a -> b
coe T__'8804'__22 -> T__'60'__50
MAlonzo.Code.Data.Integer.Base.C_'45''60''45'_58)
                          ((T__'60'__50 -> T__'8804'__22) -> Any
forall a b. a -> b
coe T__'60'__50 -> T__'8804'__22
du_drop'8255''45''60''45'_2838)
                          ((Integer -> Integer -> T_Dec_20) -> Any -> Any -> Any
forall a b. a -> b
coe
                             Integer -> Integer -> T_Dec_20
MAlonzo.Code.Data.Nat.Properties.d__'60''63'__3030 (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_3100 ::
  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_3100 :: Integer -> Integer -> T__'60'__50 -> T__'60'__50 -> T__'8801'__12
d_'60''45'irrelevant_3100 = Integer -> Integer -> T__'60'__50 -> T__'60'__50 -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.<-isStrictPartialOrder
d_'60''45'isStrictPartialOrder_3110 ::
  MAlonzo.Code.Relation.Binary.Structures.T_IsStrictPartialOrder_290
d_'60''45'isStrictPartialOrder_3110 :: T_IsStrictPartialOrder_290
d_'60''45'isStrictPartialOrder_3110
  = (T_IsEquivalence_26
 -> (Any -> Any -> Any -> Any -> Any -> Any)
 -> T_Σ_14
 -> T_IsStrictPartialOrder_290)
-> Any
-> (Any -> Any -> Any -> Any -> Any -> Any)
-> Any
-> T_IsStrictPartialOrder_290
forall a b. a -> b
coe
      T_IsEquivalence_26
-> (Any -> Any -> Any -> Any -> Any -> Any)
-> T_Σ_14
-> T_IsStrictPartialOrder_290
MAlonzo.Code.Relation.Binary.Structures.C_IsStrictPartialOrder'46'constructor_14045
      (T_IsEquivalence_26 -> Any
forall a b. a -> b
coe
         T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.PropositionalEquality.Properties.du_isEquivalence_396)
      (\ Any
v0 Any
v1 Any
v2 Any
v3 Any
v4 -> (T__'60'__50 -> T__'60'__50 -> T__'60'__50) -> Any -> Any -> Any
forall a b. a -> b
coe T__'60'__50 -> T__'60'__50 -> T__'60'__50
du_'60''45'trans_2986 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_3116 ::
  MAlonzo.Code.Relation.Binary.Structures.T_IsStrictTotalOrder_534
d_'60''45'isStrictTotalOrder_3116 :: T_IsStrictTotalOrder_534
d_'60''45'isStrictTotalOrder_3116
  = (T_IsStrictPartialOrder_290
 -> (Any -> Any -> T_Tri_158) -> T_IsStrictTotalOrder_534)
-> Any -> Any -> T_IsStrictTotalOrder_534
forall a b. a -> b
coe
      T_IsStrictPartialOrder_290
-> (Any -> Any -> T_Tri_158) -> T_IsStrictTotalOrder_534
MAlonzo.Code.Relation.Binary.Structures.C_IsStrictTotalOrder'46'constructor_24953
      (T_IsStrictPartialOrder_290 -> Any
forall a b. a -> b
coe T_IsStrictPartialOrder_290
d_'60''45'isStrictPartialOrder_3110) ((Integer -> Integer -> T_Tri_158) -> Any
forall a b. a -> b
coe Integer -> Integer -> T_Tri_158
d_'60''45'cmp_2992)
-- Data.Integer.Properties.<-strictPartialOrder
d_'60''45'strictPartialOrder_3118 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_StrictPartialOrder_556
d_'60''45'strictPartialOrder_3118 :: T_StrictPartialOrder_556
d_'60''45'strictPartialOrder_3118
  = (T_IsStrictPartialOrder_290 -> T_StrictPartialOrder_556)
-> T_IsStrictPartialOrder_290 -> T_StrictPartialOrder_556
forall a b. a -> b
coe
      T_IsStrictPartialOrder_290 -> T_StrictPartialOrder_556
MAlonzo.Code.Relation.Binary.Bundles.C_StrictPartialOrder'46'constructor_11097
      T_IsStrictPartialOrder_290
d_'60''45'isStrictPartialOrder_3110
-- Data.Integer.Properties.<-strictTotalOrder
d_'60''45'strictTotalOrder_3120 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_StrictTotalOrder_1036
d_'60''45'strictTotalOrder_3120 :: T_StrictTotalOrder_1036
d_'60''45'strictTotalOrder_3120
  = (T_IsStrictTotalOrder_534 -> T_StrictTotalOrder_1036)
-> T_IsStrictTotalOrder_534 -> T_StrictTotalOrder_1036
forall a b. a -> b
coe
      T_IsStrictTotalOrder_534 -> T_StrictTotalOrder_1036
MAlonzo.Code.Relation.Binary.Bundles.C_StrictTotalOrder'46'constructor_21059
      T_IsStrictTotalOrder_534
d_'60''45'isStrictTotalOrder_3116
-- Data.Integer.Properties.i≮i
d_i'8814'i_3122 ::
  Integer ->
  MAlonzo.Code.Data.Integer.Base.T__'60'__50 ->
  MAlonzo.Code.Data.Irrelevant.T_Irrelevant_20
d_i'8814'i_3122 :: Integer -> T__'60'__50 -> T_Irrelevant_20
d_i'8814'i_3122 = Integer -> T__'60'__50 -> T_Irrelevant_20
forall a. a
erased
-- Data.Integer.Properties.>-irrefl
d_'62''45'irrefl_3124 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Data.Integer.Base.T__'60'__50 ->
  MAlonzo.Code.Data.Irrelevant.T_Irrelevant_20
d_'62''45'irrefl_3124 :: Integer
-> Integer -> T__'8801'__12 -> T__'60'__50 -> T_Irrelevant_20
d_'62''45'irrefl_3124 = Integer
-> Integer -> T__'8801'__12 -> T__'60'__50 -> T_Irrelevant_20
forall a. a
erased
-- Data.Integer.Properties.≤-Reasoning._._IsRelatedTo_
d__IsRelatedTo__3130 :: p -> p -> ()
d__IsRelatedTo__3130 p
a0 p
a1 = ()
-- Data.Integer.Properties.≤-Reasoning._._∎
d__'8718'_3132 ::
  Integer ->
  MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.T__IsRelatedTo__78
d__'8718'_3132 :: Integer -> T__IsRelatedTo__78
d__'8718'_3132
  = let v0 :: T_IsPreorder_70
v0 = T_IsPreorder_70
d_'8804''45'isPreorder_2800 in
    Any -> Integer -> T__IsRelatedTo__78
forall a b. a -> b
coe
      (((Any -> Any) -> Any -> Any) -> Any -> Any
forall a b. a -> b
coe
         (Any -> Any) -> Any -> Any
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du__'8718'_492
         ((T_IsPreorder_70 -> Any -> T__IsRelatedTo__78) -> Any -> Any
forall a b. a -> b
coe
            T_IsPreorder_70 -> Any -> T__IsRelatedTo__78
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_stop_166
            (T_IsPreorder_70 -> Any
forall a b. a -> b
coe T_IsPreorder_70
v0)))
-- Data.Integer.Properties.≤-Reasoning._.<-go
d_'60''45'go_3134 ::
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Integer.Base.T__'60'__50 ->
  MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.T__IsRelatedTo__78 ->
  MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.T__IsRelatedTo__78
d_'60''45'go_3134 :: Integer
-> Integer
-> Integer
-> T__'60'__50
-> T__IsRelatedTo__78
-> T__IsRelatedTo__78
d_'60''45'go_3134
  = ((Any -> Any -> Any -> Any -> Any -> Any)
 -> T_Σ_14
 -> (Any -> Any -> Any -> Any -> Any -> Any)
 -> Any
 -> Any
 -> Any
 -> Any
 -> T__IsRelatedTo__78
 -> T__IsRelatedTo__78)
-> (Any -> Any -> Any -> Any -> Any -> Any)
-> Any
-> (Any -> Any -> Any -> Any -> Any -> Any)
-> Integer
-> Integer
-> Integer
-> T__'60'__50
-> T__IsRelatedTo__78
-> T__IsRelatedTo__78
forall a b. a -> b
coe
      (Any -> Any -> Any -> Any -> Any -> Any)
-> T_Σ_14
-> (Any -> Any -> Any -> Any -> Any -> Any)
-> Any
-> Any
-> Any
-> Any
-> T__IsRelatedTo__78
-> T__IsRelatedTo__78
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_'60''45'go_152
      (\ Any
v0 Any
v1 Any
v2 Any
v3 Any
v4 -> (T__'60'__50 -> T__'60'__50 -> T__'60'__50) -> Any -> Any -> Any
forall a b. a -> b
coe T__'60'__50 -> T__'60'__50 -> T__'60'__50
du_'60''45'trans_2986 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'_160)
      (\ 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_2972 Any
v3 Any
v4)
-- Data.Integer.Properties.≤-Reasoning._.IsEquality
d_IsEquality_3136 :: p -> p -> p -> ()
d_IsEquality_3136 p
a0 p
a1 p
a2 = ()
-- Data.Integer.Properties.≤-Reasoning._.IsEquality?
d_IsEquality'63'_3138 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.T__IsRelatedTo__78 ->
  MAlonzo.Code.Relation.Nullary.Decidable.Core.T_Dec_20
d_IsEquality'63'_3138 :: Integer -> Integer -> T__IsRelatedTo__78 -> T_Dec_20
d_IsEquality'63'_3138 Integer
v0 Integer
v1 T__IsRelatedTo__78
v2
  = (T__IsRelatedTo__78 -> T_Dec_20) -> T__IsRelatedTo__78 -> T_Dec_20
forall a b. a -> b
coe
      T__IsRelatedTo__78 -> T_Dec_20
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_IsEquality'63'_224
      T__IsRelatedTo__78
v2
-- Data.Integer.Properties.≤-Reasoning._.IsStrict
d_IsStrict_3140 :: p -> p -> p -> ()
d_IsStrict_3140 p
a0 p
a1 p
a2 = ()
-- Data.Integer.Properties.≤-Reasoning._.IsStrict?
d_IsStrict'63'_3142 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.T__IsRelatedTo__78 ->
  MAlonzo.Code.Relation.Nullary.Decidable.Core.T_Dec_20
d_IsStrict'63'_3142 :: Integer -> Integer -> T__IsRelatedTo__78 -> T_Dec_20
d_IsStrict'63'_3142 Integer
v0 Integer
v1 T__IsRelatedTo__78
v2
  = (T__IsRelatedTo__78 -> T_Dec_20) -> T__IsRelatedTo__78 -> T_Dec_20
forall a b. a -> b
coe
      T__IsRelatedTo__78 -> T_Dec_20
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_IsStrict'63'_188
      T__IsRelatedTo__78
v2
-- Data.Integer.Properties.≤-Reasoning._.begin_
d_begin__3144 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.T__IsRelatedTo__78 ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26
d_begin__3144 :: Integer -> Integer -> T__IsRelatedTo__78 -> T__'8804'__26
d_begin__3144
  = let v0 :: T_IsPreorder_70
v0 = T_IsPreorder_70
d_'8804''45'isPreorder_2800 in
    Any -> Integer -> Integer -> T__IsRelatedTo__78 -> T__'8804'__26
forall a b. a -> b
coe
      (let v1 :: p -> p -> t -> t
v1 = \ p
v1 p
v2 t
v3 -> (T__'60'__50 -> T__'8804'__26) -> t -> t
forall a b. a -> b
coe T__'60'__50 -> T__'8804'__26
du_'60''8658''8804'_2846 t
v3 in
       Any -> Any
forall a b. a -> b
coe
         (((Any -> Any -> Any -> Any) -> Any -> Any -> Any -> Any)
-> Any -> Any
forall a b. a -> b
coe
            (Any -> Any -> Any -> Any) -> Any -> Any -> Any -> Any
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_begin__46
            ((T_IsPreorder_70
 -> (Any -> Any -> Any -> Any)
 -> Any
 -> Any
 -> T__IsRelatedTo__78
 -> Any)
-> Any -> Any -> Any
forall a b. a -> b
coe
               T_IsPreorder_70
-> (Any -> Any -> Any -> Any)
-> Any
-> Any
-> T__IsRelatedTo__78
-> Any
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_start_96
               (T_IsPreorder_70 -> Any
forall a b. a -> b
coe T_IsPreorder_70
v0) ((Any -> Any -> Any -> Any) -> Any
forall a b. a -> b
coe Any -> Any -> Any -> Any
forall {p} {p} {t} {t}. p -> p -> t -> t
v1))))
-- Data.Integer.Properties.≤-Reasoning._.begin-contradiction_
d_begin'45'contradiction__3146 ::
  Integer ->
  MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.T__IsRelatedTo__78 ->
  AgdaAny -> MAlonzo.Code.Agda.Primitive.T_Level_18 -> () -> AgdaAny
d_begin'45'contradiction__3146 :: Integer -> T__IsRelatedTo__78 -> Any -> () -> () -> Any
d_begin'45'contradiction__3146 Integer
v0 T__IsRelatedTo__78
v1 Any
v2 ()
v3 ()
v4
  = Any -> Any
forall a b. a -> b
coe
      Any
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_begin'45'contradiction__246
-- Data.Integer.Properties.≤-Reasoning._.begin_
d_begin__3148 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.T__IsRelatedTo__78 ->
  AgdaAny -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_begin__3148 :: Integer -> Integer -> T__IsRelatedTo__78 -> Any -> T__'8801'__12
d_begin__3148 = Integer -> Integer -> T__IsRelatedTo__78 -> Any -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.≤-Reasoning._.begin_
d_begin__3150 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.T__IsRelatedTo__78 ->
  AgdaAny -> MAlonzo.Code.Data.Integer.Base.T__'60'__50
d_begin__3150 :: Integer -> Integer -> T__IsRelatedTo__78 -> Any -> T__'60'__50
d_begin__3150
  = let v0 :: b
v0
          = T_SubRelation_60 -> b
forall a b. a -> b
coe
              T_SubRelation_60
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_strictRelation_202 in
    (Any -> Any -> Any -> Any -> Any)
-> Integer -> Integer -> T__IsRelatedTo__78 -> Any -> T__'60'__50
forall a b. a -> b
coe
      (\ Any
v1 Any
v2 Any
v3 Any
v4 ->
         (T_SubRelation_60 -> Any -> Any -> Any -> Any)
-> Any -> Any -> Any -> Any -> Any
forall a b. a -> b
coe
           T_SubRelation_60 -> Any -> Any -> Any -> Any
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_begin__126
           (Any -> Any
forall a b. a -> b
coe Any
forall a. a
v0) Any
v1 Any
v2 Any
v3)
-- Data.Integer.Properties.≤-Reasoning._.eqRelation
d_eqRelation_3152 ::
  MAlonzo.Code.Relation.Binary.Reasoning.Syntax.T_SubRelation_60
d_eqRelation_3152 :: T_SubRelation_60
d_eqRelation_3152
  = T_SubRelation_60 -> T_SubRelation_60
forall a b. a -> b
coe
      T_SubRelation_60
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_eqRelation_238
-- Data.Integer.Properties.≤-Reasoning._.extractEquality
d_extractEquality_3156 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.T__IsRelatedTo__78 ->
  MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.T_IsEquality_208 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_extractEquality_3156 :: Integer
-> Integer
-> T__IsRelatedTo__78
-> T_IsEquality_208
-> T__'8801'__12
d_extractEquality_3156 = Integer
-> Integer
-> T__IsRelatedTo__78
-> T_IsEquality_208
-> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.≤-Reasoning._.extractStrict
d_extractStrict_3158 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.T__IsRelatedTo__78 ->
  MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.T_IsStrict_172 ->
  MAlonzo.Code.Data.Integer.Base.T__'60'__50
d_extractStrict_3158 :: Integer
-> Integer -> T__IsRelatedTo__78 -> T_IsStrict_172 -> T__'60'__50
d_extractStrict_3158 Integer
v0 Integer
v1 T__IsRelatedTo__78
v2 T_IsStrict_172
v3
  = (T__IsRelatedTo__78 -> T_IsStrict_172 -> Any)
-> T__IsRelatedTo__78 -> T_IsStrict_172 -> T__'60'__50
forall a b. a -> b
coe
      T__IsRelatedTo__78 -> T_IsStrict_172 -> Any
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_extractStrict_198
      T__IsRelatedTo__78
v2 T_IsStrict_172
v3
-- Data.Integer.Properties.≤-Reasoning._.start
d_start_3166 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.T__IsRelatedTo__78 ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26
d_start_3166 :: Integer -> Integer -> T__IsRelatedTo__78 -> T__'8804'__26
d_start_3166
  = (T_IsPreorder_70
 -> (Any -> Any -> Any -> Any)
 -> Any
 -> Any
 -> T__IsRelatedTo__78
 -> Any)
-> Any
-> (Any -> Any -> Any -> Any)
-> Integer
-> Integer
-> T__IsRelatedTo__78
-> T__'8804'__26
forall a b. a -> b
coe
      T_IsPreorder_70
-> (Any -> Any -> Any -> Any)
-> Any
-> Any
-> T__IsRelatedTo__78
-> Any
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_start_96
      (T_IsPreorder_70 -> Any
forall a b. a -> b
coe T_IsPreorder_70
d_'8804''45'isPreorder_2800)
      (\ Any
v0 Any
v1 Any
v2 -> (T__'60'__50 -> T__'8804'__26) -> Any -> Any
forall a b. a -> b
coe T__'60'__50 -> T__'8804'__26
du_'60''8658''8804'_2846 Any
v2)
-- Data.Integer.Properties.≤-Reasoning._.step-<
d_step'45''60'_3168 ::
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.T__IsRelatedTo__78 ->
  MAlonzo.Code.Data.Integer.Base.T__'60'__50 ->
  MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.T__IsRelatedTo__78
d_step'45''60'_3168 :: Integer
-> Integer
-> Integer
-> T__IsRelatedTo__78
-> T__'60'__50
-> T__IsRelatedTo__78
d_step'45''60'_3168
  = let v0 :: p -> p -> p -> t -> t -> t
v0 = \ p
v0 p
v1 p
v2 t
v3 t
v4 -> (T__'60'__50 -> T__'60'__50 -> T__'60'__50) -> t -> t -> t
forall a b. a -> b
coe T__'60'__50 -> T__'60'__50 -> T__'60'__50
du_'60''45'trans_2986 t
v3 t
v4 in
    Any
-> Integer
-> Integer
-> Integer
-> T__IsRelatedTo__78
-> T__'60'__50
-> T__IsRelatedTo__78
forall a b. a -> b
coe
      (let v1 :: b
v1
             = T_Σ_14 -> b
forall a b. a -> b
coe
                 T_Σ_14
MAlonzo.Code.Relation.Binary.PropositionalEquality.Core.du_resp'8322'_160 in
       Any -> Any
forall a b. a -> b
coe
         (let v2 :: p -> p -> p -> t -> t -> t
v2
                = \ p
v2 p
v3 p
v4 t
v5 t
v6 -> (T__'60'__50 -> T__'8804'__26 -> T__'60'__50) -> t -> t -> t
forall a b. a -> b
coe T__'60'__50 -> T__'8804'__26 -> T__'60'__50
du_'60''45''8804''45'trans_2972 t
v5 t
v6 in
          Any -> Any
forall a b. a -> b
coe
            (((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)
-> Any -> Any -> Any -> Any -> Any -> Any
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''60'_312
               (((Any -> Any -> Any -> Any -> Any -> Any)
 -> T_Σ_14
 -> (Any -> Any -> Any -> Any -> Any -> Any)
 -> Any
 -> Any
 -> Any
 -> Any
 -> T__IsRelatedTo__78
 -> T__IsRelatedTo__78)
-> 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
-> Any
-> T__IsRelatedTo__78
-> T__IsRelatedTo__78
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_'60''45'go_152
                  ((Any -> Any -> Any -> Any -> Any -> Any) -> Any
forall a b. a -> b
coe Any -> Any -> Any -> Any -> Any -> Any
forall {p} {p} {p} {t} {t} {t}. p -> p -> p -> t -> t -> t
v0) (Any -> Any
forall a b. a -> b
coe Any
forall a. a
v1) ((Any -> Any -> Any -> Any -> Any -> Any) -> Any
forall a b. a -> b
coe Any -> Any -> Any -> Any -> Any -> Any
forall {p} {p} {p} {t} {t} {t}. p -> p -> p -> t -> t -> t
v2)))))
-- Data.Integer.Properties.≤-Reasoning._.step-≡
d_step'45''8801'_3170 ::
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.T__IsRelatedTo__78 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.T__IsRelatedTo__78
d_step'45''8801'_3170 :: Integer
-> Integer
-> Integer
-> T__IsRelatedTo__78
-> T__'8801'__12
-> T__IsRelatedTo__78
d_step'45''8801'_3170
  = ((Any -> Any -> Any -> T__'8801'__12 -> Any -> Any)
 -> Any -> Any -> Any -> Any -> T__'8801'__12 -> Any)
-> Any
-> Integer
-> Integer
-> Integer
-> T__IsRelatedTo__78
-> T__'8801'__12
-> T__IsRelatedTo__78
forall a b. a -> b
coe
      (Any -> Any -> Any -> T__'8801'__12 -> Any -> Any)
-> Any -> Any -> Any -> Any -> T__'8801'__12 -> Any
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8801'_450
      ((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.≤-Reasoning._.step-≡-∣
d_step'45''8801''45''8739'_3172 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.T__IsRelatedTo__78 ->
  MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.T__IsRelatedTo__78
d_step'45''8801''45''8739'_3172 :: Integer -> Integer -> T__IsRelatedTo__78 -> T__IsRelatedTo__78
d_step'45''8801''45''8739'_3172 ~Integer
v0 ~Integer
v1 T__IsRelatedTo__78
v2
  = T__IsRelatedTo__78 -> T__IsRelatedTo__78
du_step'45''8801''45''8739'_3172 T__IsRelatedTo__78
v2
du_step'45''8801''45''8739'_3172 ::
  MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.T__IsRelatedTo__78 ->
  MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.T__IsRelatedTo__78
du_step'45''8801''45''8739'_3172 :: T__IsRelatedTo__78 -> T__IsRelatedTo__78
du_step'45''8801''45''8739'_3172 T__IsRelatedTo__78
v0 = T__IsRelatedTo__78 -> T__IsRelatedTo__78
forall a b. a -> b
coe T__IsRelatedTo__78
v0
-- Data.Integer.Properties.≤-Reasoning._.step-≡-⟨
d_step'45''8801''45''10216'_3174 ::
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.T__IsRelatedTo__78 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.T__IsRelatedTo__78
d_step'45''8801''45''10216'_3174 :: Integer
-> Integer
-> Integer
-> T__IsRelatedTo__78
-> T__'8801'__12
-> T__IsRelatedTo__78
d_step'45''8801''45''10216'_3174
  = ((Any -> Any -> Any -> T__'8801'__12 -> Any -> Any)
 -> Any -> Any -> Any -> Any -> T__'8801'__12 -> Any)
-> Any
-> Integer
-> Integer
-> Integer
-> T__IsRelatedTo__78
-> T__'8801'__12
-> T__IsRelatedTo__78
forall a b. a -> b
coe
      (Any -> Any -> Any -> T__'8801'__12 -> Any -> Any)
-> Any -> Any -> Any -> Any -> T__'8801'__12 -> Any
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8801''45''10216'_448
      ((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.≤-Reasoning._.step-≡-⟩
d_step'45''8801''45''10217'_3176 ::
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.T__IsRelatedTo__78 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.T__IsRelatedTo__78
d_step'45''8801''45''10217'_3176 :: Integer
-> Integer
-> Integer
-> T__IsRelatedTo__78
-> T__'8801'__12
-> T__IsRelatedTo__78
d_step'45''8801''45''10217'_3176
  = ((Any -> Any -> Any -> T__'8801'__12 -> Any -> Any)
 -> Any -> Any -> Any -> Any -> T__'8801'__12 -> Any)
-> Any
-> Integer
-> Integer
-> Integer
-> T__IsRelatedTo__78
-> T__'8801'__12
-> T__IsRelatedTo__78
forall a b. a -> b
coe
      (Any -> Any -> Any -> T__'8801'__12 -> Any -> Any)
-> Any -> Any -> Any -> Any -> T__'8801'__12 -> Any
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8801''45''10217'_436
      ((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.≤-Reasoning._.step-≡˘
d_step'45''8801''728'_3178 ::
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.T__IsRelatedTo__78 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.T__IsRelatedTo__78
d_step'45''8801''728'_3178 :: Integer
-> Integer
-> Integer
-> T__IsRelatedTo__78
-> T__'8801'__12
-> T__IsRelatedTo__78
d_step'45''8801''728'_3178
  = ((Any -> Any -> Any -> T__'8801'__12 -> Any -> Any)
 -> Any -> Any -> Any -> Any -> T__'8801'__12 -> Any)
-> Any
-> Integer
-> Integer
-> Integer
-> T__IsRelatedTo__78
-> T__'8801'__12
-> T__IsRelatedTo__78
forall a b. a -> b
coe
      (Any -> Any -> Any -> T__'8801'__12 -> Any -> Any)
-> Any -> Any -> Any -> Any -> T__'8801'__12 -> Any
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8801''728'_452
      ((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.≤-Reasoning._.step-≤
d_step'45''8804'_3180 ::
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.T__IsRelatedTo__78 ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26 ->
  MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.T__IsRelatedTo__78
d_step'45''8804'_3180 :: Integer
-> Integer
-> Integer
-> T__IsRelatedTo__78
-> T__'8804'__26
-> T__IsRelatedTo__78
d_step'45''8804'_3180
  = let v0 :: T_IsPreorder_70
v0 = T_IsPreorder_70
d_'8804''45'isPreorder_2800 in
    Any
-> Integer
-> Integer
-> Integer
-> T__IsRelatedTo__78
-> T__'8804'__26
-> T__IsRelatedTo__78
forall a b. a -> b
coe
      (let v1 :: p -> p -> p -> t -> t -> t
v1
             = \ p
v1 p
v2 p
v3 t
v4 t
v5 -> (T__'8804'__26 -> T__'60'__50 -> T__'60'__50) -> t -> t -> t
forall a b. a -> b
coe T__'8804'__26 -> T__'60'__50 -> T__'60'__50
du_'8804''45''60''45'trans_2958 t
v4 t
v5 in
       Any -> Any
forall a b. a -> b
coe
         (((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)
-> Any -> Any -> Any -> Any -> Any -> Any
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8804'_308
            ((T_IsPreorder_70
 -> (Any -> Any -> Any -> Any -> Any -> Any)
 -> Any
 -> Any
 -> Any
 -> Any
 -> T__IsRelatedTo__78
 -> T__IsRelatedTo__78)
-> Any -> Any -> Any
forall a b. a -> b
coe
               T_IsPreorder_70
-> (Any -> Any -> Any -> Any -> Any -> Any)
-> Any
-> Any
-> Any
-> Any
-> T__IsRelatedTo__78
-> T__IsRelatedTo__78
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_'8804''45'go_138
               (T_IsPreorder_70 -> Any
forall a b. a -> b
coe T_IsPreorder_70
v0) ((Any -> Any -> Any -> Any -> Any -> Any) -> Any
forall a b. a -> b
coe Any -> Any -> Any -> Any -> Any -> Any
forall {p} {p} {p} {t} {t} {t}. p -> p -> p -> t -> t -> t
v1))))
-- Data.Integer.Properties.≤-Reasoning._.stop
d_stop_3182 ::
  Integer ->
  MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.T__IsRelatedTo__78
d_stop_3182 :: Integer -> T__IsRelatedTo__78
d_stop_3182
  = (T_IsPreorder_70 -> Any -> T__IsRelatedTo__78)
-> Any -> Integer -> T__IsRelatedTo__78
forall a b. a -> b
coe
      T_IsPreorder_70 -> Any -> T__IsRelatedTo__78
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_stop_166
      (T_IsPreorder_70 -> Any
forall a b. a -> b
coe T_IsPreorder_70
d_'8804''45'isPreorder_2800)
-- Data.Integer.Properties.≤-Reasoning._.strictRelation
d_strictRelation_3186 ::
  MAlonzo.Code.Relation.Binary.Reasoning.Syntax.T_SubRelation_60
d_strictRelation_3186 :: T_SubRelation_60
d_strictRelation_3186
  = T_SubRelation_60 -> T_SubRelation_60
forall a b. a -> b
coe
      T_SubRelation_60
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_strictRelation_202
-- Data.Integer.Properties.≤-Reasoning._.≈-go
d_'8776''45'go_3188 ::
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.T__IsRelatedTo__78 ->
  MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.T__IsRelatedTo__78
d_'8776''45'go_3188 :: Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__IsRelatedTo__78
-> T__IsRelatedTo__78
d_'8776''45'go_3188
  = (T_IsPreorder_70
 -> T_Σ_14
 -> Any
 -> Any
 -> Any
 -> Any
 -> T__IsRelatedTo__78
 -> T__IsRelatedTo__78)
-> Any
-> Any
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__IsRelatedTo__78
-> T__IsRelatedTo__78
forall a b. a -> b
coe
      T_IsPreorder_70
-> T_Σ_14
-> Any
-> Any
-> Any
-> Any
-> T__IsRelatedTo__78
-> T__IsRelatedTo__78
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_'8776''45'go_124
      (T_IsPreorder_70 -> Any
forall a b. a -> b
coe T_IsPreorder_70
d_'8804''45'isPreorder_2800)
      (T_Σ_14 -> Any
forall a b. a -> b
coe
         T_Σ_14
MAlonzo.Code.Relation.Binary.PropositionalEquality.Core.du_resp'8322'_160)
-- Data.Integer.Properties.≤-Reasoning._.≡-go
d_'8801''45'go_3190 ::
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.T__IsRelatedTo__78 ->
  MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.T__IsRelatedTo__78
d_'8801''45'go_3190 :: Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__IsRelatedTo__78
-> T__IsRelatedTo__78
d_'8801''45'go_3190 ~Integer
v0 ~Integer
v1 ~Integer
v2 ~T__'8801'__12
v3 T__IsRelatedTo__78
v4 = T__IsRelatedTo__78 -> T__IsRelatedTo__78
du_'8801''45'go_3190 T__IsRelatedTo__78
v4
du_'8801''45'go_3190 ::
  MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.T__IsRelatedTo__78 ->
  MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.T__IsRelatedTo__78
du_'8801''45'go_3190 :: T__IsRelatedTo__78 -> T__IsRelatedTo__78
du_'8801''45'go_3190 T__IsRelatedTo__78
v0 = T__IsRelatedTo__78 -> T__IsRelatedTo__78
forall a b. a -> b
coe T__IsRelatedTo__78
v0
-- Data.Integer.Properties.≤-Reasoning._.≤-go
d_'8804''45'go_3192 ::
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26 ->
  MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.T__IsRelatedTo__78 ->
  MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.T__IsRelatedTo__78
d_'8804''45'go_3192 :: Integer
-> Integer
-> Integer
-> T__'8804'__26
-> T__IsRelatedTo__78
-> T__IsRelatedTo__78
d_'8804''45'go_3192
  = (T_IsPreorder_70
 -> (Any -> Any -> Any -> Any -> Any -> Any)
 -> Any
 -> Any
 -> Any
 -> Any
 -> T__IsRelatedTo__78
 -> T__IsRelatedTo__78)
-> Any
-> (Any -> Any -> Any -> Any -> Any -> Any)
-> Integer
-> Integer
-> Integer
-> T__'8804'__26
-> T__IsRelatedTo__78
-> T__IsRelatedTo__78
forall a b. a -> b
coe
      T_IsPreorder_70
-> (Any -> Any -> Any -> Any -> Any -> Any)
-> Any
-> Any
-> Any
-> Any
-> T__IsRelatedTo__78
-> T__IsRelatedTo__78
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_'8804''45'go_138
      (T_IsPreorder_70 -> Any
forall a b. a -> b
coe T_IsPreorder_70
d_'8804''45'isPreorder_2800)
      (\ 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_2958 Any
v3 Any
v4)
-- Data.Integer.Properties.positive⁻¹
d_positive'8315''185'_3212 ::
  Integer ->
  MAlonzo.Code.Data.Integer.Base.T_Positive_134 ->
  MAlonzo.Code.Data.Integer.Base.T__'60'__50
d_positive'8315''185'_3212 :: Integer -> T_Positive_134 -> T__'60'__50
d_positive'8315''185'_3212 ~Integer
v0 ~T_Positive_134
v1 = T__'60'__50
du_positive'8315''185'_3212
du_positive'8315''185'_3212 ::
  MAlonzo.Code.Data.Integer.Base.T__'60'__50
du_positive'8315''185'_3212 :: T__'60'__50
du_positive'8315''185'_3212
  = (T__'8804'__22 -> T__'60'__50) -> Any -> T__'60'__50
forall a b. a -> b
coe
      T__'8804'__22 -> T__'60'__50
MAlonzo.Code.Data.Integer.Base.C_'43''60''43'_72
      ((T__'8804'__22 -> T__'8804'__22) -> Any -> Any
forall a b. a -> b
coe
         T__'8804'__22 -> T__'8804'__22
MAlonzo.Code.Data.Nat.Base.C_s'8804's_34
         (T__'8804'__22 -> Any
forall a b. a -> b
coe T__'8804'__22
MAlonzo.Code.Data.Nat.Base.C_z'8804'n_26))
-- Data.Integer.Properties.negative⁻¹
d_negative'8315''185'_3218 ::
  Integer ->
  MAlonzo.Code.Data.Integer.Base.T_Negative_164 ->
  MAlonzo.Code.Data.Integer.Base.T__'60'__50
d_negative'8315''185'_3218 :: Integer -> T_Negative_164 -> T__'60'__50
d_negative'8315''185'_3218 ~Integer
v0 ~T_Negative_164
v1 = T__'60'__50
du_negative'8315''185'_3218
du_negative'8315''185'_3218 ::
  MAlonzo.Code.Data.Integer.Base.T__'60'__50
du_negative'8315''185'_3218 :: T__'60'__50
du_negative'8315''185'_3218
  = 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'_3224 ::
  Integer ->
  MAlonzo.Code.Data.Integer.Base.T_NonPositive_154 ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26
d_nonPositive'8315''185'_3224 :: Integer -> T_NonPositive_154 -> T__'8804'__26
d_nonPositive'8315''185'_3224 Integer
v0 ~T_NonPositive_154
v1
  = Integer -> T__'8804'__26
du_nonPositive'8315''185'_3224 Integer
v0
du_nonPositive'8315''185'_3224 ::
  Integer -> MAlonzo.Code.Data.Integer.Base.T__'8804'__26
du_nonPositive'8315''185'_3224 :: Integer -> T__'8804'__26
du_nonPositive'8315''185'_3224 Integer
v0
  = case Integer -> Integer
forall a b. a -> b
coe Integer
v0 of
      Integer
0 -> (T__'8804'__22 -> T__'8804'__26) -> Any -> T__'8804'__26
forall a b. a -> b
coe
             T__'8804'__22 -> T__'8804'__26
MAlonzo.Code.Data.Integer.Base.C_'43''8804''43'_48
             (T__'8804'__22 -> Any
forall a b. a -> b
coe T__'8804'__22
MAlonzo.Code.Data.Nat.Base.C_z'8804'n_26)
      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.nonNegative⁻¹
d_nonNegative'8315''185'_3230 ::
  Integer ->
  MAlonzo.Code.Data.Integer.Base.T_NonNegative_144 ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26
d_nonNegative'8315''185'_3230 :: Integer -> T_NonNegative_144 -> T__'8804'__26
d_nonNegative'8315''185'_3230 ~Integer
v0 ~T_NonNegative_144
v1
  = T__'8804'__26
du_nonNegative'8315''185'_3230
du_nonNegative'8315''185'_3230 ::
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26
du_nonNegative'8315''185'_3230 :: T__'8804'__26
du_nonNegative'8315''185'_3230
  = (T__'8804'__22 -> T__'8804'__26) -> Any -> T__'8804'__26
forall a b. a -> b
coe
      T__'8804'__22 -> T__'8804'__26
MAlonzo.Code.Data.Integer.Base.C_'43''8804''43'_48
      (T__'8804'__22 -> Any
forall a b. a -> b
coe T__'8804'__22
MAlonzo.Code.Data.Nat.Base.C_z'8804'n_26)
-- Data.Integer.Properties.negative<positive
d_negative'60'positive_3238 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Integer.Base.T_Negative_164 ->
  MAlonzo.Code.Data.Integer.Base.T_Positive_134 ->
  MAlonzo.Code.Data.Integer.Base.T__'60'__50
d_negative'60'positive_3238 :: Integer
-> Integer -> T_Negative_164 -> T_Positive_134 -> T__'60'__50
d_negative'60'positive_3238 ~Integer
v0 ~Integer
v1 ~T_Negative_164
v2 ~T_Positive_134
v3
  = T__'60'__50
du_negative'60'positive_3238
du_negative'60'positive_3238 ::
  MAlonzo.Code.Data.Integer.Base.T__'60'__50
du_negative'60'positive_3238 :: T__'60'__50
du_negative'60'positive_3238
  = (T__'60'__50 -> T__'60'__50 -> T__'60'__50)
-> Any -> Any -> T__'60'__50
forall a b. a -> b
coe
      T__'60'__50 -> T__'60'__50 -> T__'60'__50
du_'60''45'trans_2986 (T__'60'__50 -> Any
forall a b. a -> b
coe T__'60'__50
du_negative'8315''185'_3218)
      (T__'60'__50 -> Any
forall a b. a -> b
coe T__'60'__50
du_positive'8315''185'_3212)
-- Data.Integer.Properties.neg-involutive
d_neg'45'involutive_3246 ::
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_neg'45'involutive_3246 :: Integer -> T__'8801'__12
d_neg'45'involutive_3246 = Integer -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.neg-injective
d_neg'45'injective_3252 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_neg'45'injective_3252 :: Integer -> Integer -> T__'8801'__12 -> T__'8801'__12
d_neg'45'injective_3252 = Integer -> Integer -> T__'8801'__12 -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.neg-≤-pos
d_neg'45''8804''45'pos_3268 ::
  Integer -> Integer -> MAlonzo.Code.Data.Integer.Base.T__'8804'__26
d_neg'45''8804''45'pos_3268 :: Integer -> Integer -> T__'8804'__26
d_neg'45''8804''45'pos_3268 Integer
v0 ~Integer
v1
  = Integer -> T__'8804'__26
du_neg'45''8804''45'pos_3268 Integer
v0
du_neg'45''8804''45'pos_3268 ::
  Integer -> MAlonzo.Code.Data.Integer.Base.T__'8804'__26
du_neg'45''8804''45'pos_3268 :: Integer -> T__'8804'__26
du_neg'45''8804''45'pos_3268 Integer
v0
  = case Integer -> Integer
forall a b. a -> b
coe Integer
v0 of
      Integer
0 -> (T__'8804'__22 -> T__'8804'__26) -> Any -> T__'8804'__26
forall a b. a -> b
coe
             T__'8804'__22 -> T__'8804'__26
MAlonzo.Code.Data.Integer.Base.C_'43''8804''43'_48
             (T__'8804'__22 -> Any
forall a b. a -> b
coe T__'8804'__22
MAlonzo.Code.Data.Nat.Base.C_z'8804'n_26)
      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''8804'_3272 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26 ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26
d_neg'45'mono'45''8804'_3272 :: Integer -> Integer -> T__'8804'__26 -> T__'8804'__26
d_neg'45'mono'45''8804'_3272 ~Integer
v0 Integer
v1 T__'8804'__26
v2
  = Integer -> T__'8804'__26 -> T__'8804'__26
du_neg'45'mono'45''8804'_3272 Integer
v1 T__'8804'__26
v2
du_neg'45'mono'45''8804'_3272 ::
  Integer ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26 ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26
du_neg'45'mono'45''8804'_3272 :: Integer -> T__'8804'__26 -> T__'8804'__26
du_neg'45'mono'45''8804'_3272 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'__22
v4
        -> (T__'8804'__22 -> T__'8804'__26) -> Any -> T__'8804'__26
forall a b. a -> b
coe
             T__'8804'__22 -> T__'8804'__26
MAlonzo.Code.Data.Integer.Base.C_'43''8804''43'_48
             ((T__'8804'__22 -> T__'8804'__22) -> T__'8804'__22 -> Any
forall a b. a -> b
coe T__'8804'__22 -> T__'8804'__22
MAlonzo.Code.Data.Nat.Base.C_s'8804's_34 T__'8804'__22
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_3268 (Integer -> Any
forall a b. a -> b
coe Integer
v0)
      MAlonzo.Code.Data.Integer.Base.C_'43''8804''43'_48 T__'8804'__22
v4
        -> case T__'8804'__22 -> T__'8804'__22
forall a b. a -> b
coe T__'8804'__22
v4 of
             T__'8804'__22
MAlonzo.Code.Data.Nat.Base.C_z'8804'n_26
               -> (Integer -> T__'8804'__26) -> Any -> T__'8804'__26
forall a b. a -> b
coe Integer -> T__'8804'__26
du_neg'45''8804''45'pos_3268 (Integer -> Any
forall a b. a -> b
coe Integer
v0)
             MAlonzo.Code.Data.Nat.Base.C_s'8804's_34 T__'8804'__22
v7
               -> (T__'8804'__22 -> T__'8804'__26) -> T__'8804'__22 -> T__'8804'__26
forall a b. a -> b
coe T__'8804'__22 -> T__'8804'__26
MAlonzo.Code.Data.Integer.Base.C_'45''8804''45'_34 T__'8804'__22
v7
             T__'8804'__22
_ -> 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'_3278 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26 ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26
d_neg'45'cancel'45''8804'_3278 :: Integer -> Integer -> T__'8804'__26 -> T__'8804'__26
d_neg'45'cancel'45''8804'_3278 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'__22 -> T__'8804'__26) -> Any -> T__'8804'__26
forall a b. a -> b
coe
                    T__'8804'__22 -> T__'8804'__26
MAlonzo.Code.Data.Integer.Base.C_'43''8804''43'_48
                    (T__'8804'__22 -> Any
forall a b. a -> b
coe T__'8804'__22
MAlonzo.Code.Data.Nat.Base.C_z'8804'n_26)
             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'__22 -> T__'8804'__26) -> Any -> Any
forall a b. a -> b
coe
                      T__'8804'__22 -> T__'8804'__26
MAlonzo.Code.Data.Integer.Base.C_'43''8804''43'_48
                      (T__'8804'__22 -> Any
forall a b. a -> b
coe T__'8804'__22
MAlonzo.Code.Data.Nat.Base.C_z'8804'n_26))
            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'__22
v5
                    -> (T__'8804'__22 -> T__'8804'__26) -> Any -> T__'8804'__26
forall a b. a -> b
coe
                         T__'8804'__22 -> T__'8804'__26
MAlonzo.Code.Data.Integer.Base.C_'43''8804''43'_48
                         ((T__'8804'__22 -> T__'8804'__22) -> T__'8804'__22 -> Any
forall a b. a -> b
coe T__'8804'__22 -> T__'8804'__22
MAlonzo.Code.Data.Nat.Base.C_s'8804's_34 T__'8804'__22
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'__22
v5
               -> case T__'8804'__22 -> T__'8804'__22
forall a b. a -> b
coe T__'8804'__22
v5 of
                    MAlonzo.Code.Data.Nat.Base.C_s'8804's_34 T__'8804'__22
v8
                      -> (T__'8804'__22 -> T__'8804'__26) -> T__'8804'__22 -> T__'8804'__26
forall a b. a -> b
coe T__'8804'__22 -> T__'8804'__26
MAlonzo.Code.Data.Integer.Base.C_'45''8804''45'_34 T__'8804'__22
v8
                    T__'8804'__22
_ -> 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-mono-<
d_neg'45'mono'45''60'_3302 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Integer.Base.T__'60'__50 ->
  MAlonzo.Code.Data.Integer.Base.T__'60'__50
d_neg'45'mono'45''60'_3302 :: Integer -> Integer -> T__'60'__50 -> T__'60'__50
d_neg'45'mono'45''60'_3302 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'__22
v5
              -> (T__'8804'__22 -> T__'60'__50) -> Any -> T__'60'__50
forall a b. a -> b
coe
                   T__'8804'__22 -> T__'60'__50
MAlonzo.Code.Data.Integer.Base.C_'45''60''45'_58
                   ((T__'8804'__22 -> T__'8804'__22) -> Any -> Any
forall a b. a -> b
coe T__'8804'__22 -> T__'8804'__22
MAlonzo.Code.Data.Nat.Base.du_s'60's'8315''185'_70 (T__'8804'__22 -> Any
forall a b. a -> b
coe T__'8804'__22
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'__22 -> T__'60'__50) -> Any -> Any
forall a b. a -> b
coe
                       T__'8804'__22 -> T__'60'__50
MAlonzo.Code.Data.Integer.Base.C_'43''60''43'_72
                       ((T__'8804'__22 -> T__'8804'__22) -> Any -> Any
forall a b. a -> b
coe
                          T__'8804'__22 -> T__'8804'__22
MAlonzo.Code.Data.Nat.Base.C_s'8804's_34
                          (T__'8804'__22 -> Any
forall a b. a -> b
coe T__'8804'__22
MAlonzo.Code.Data.Nat.Base.C_z'8804'n_26)))
             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'__22
v5
                      -> (T__'8804'__22 -> T__'60'__50) -> Any -> T__'60'__50
forall a b. a -> b
coe
                           T__'8804'__22 -> T__'60'__50
MAlonzo.Code.Data.Integer.Base.C_'43''60''43'_72
                           ((T__'8804'__22 -> T__'8804'__22) -> T__'8804'__22 -> Any
forall a b. a -> b
coe T__'8804'__22 -> T__'8804'__22
MAlonzo.Code.Data.Nat.Base.C_s'8804's_34 T__'8804'__22
v5)
                    T__'60'__50
_ -> T__'60'__50
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Data.Integer.Properties.neg-cancel-<
d_neg'45'cancel'45''60'_3316 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Integer.Base.T__'60'__50 ->
  MAlonzo.Code.Data.Integer.Base.T__'60'__50
d_neg'45'cancel'45''60'_3316 :: Integer -> Integer -> T__'60'__50 -> T__'60'__50
d_neg'45'cancel'45''60'_3316 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'__22 -> T__'60'__50) -> Any -> Any
forall a b. a -> b
coe
                      T__'8804'__22 -> T__'60'__50
MAlonzo.Code.Data.Integer.Base.C_'43''60''43'_72
                      ((T__'8804'__22 -> T__'8804'__22) -> Any -> Any
forall a b. a -> b
coe
                         T__'8804'__22 -> T__'8804'__22
MAlonzo.Code.Data.Nat.Base.C_s'8804's_34
                         (T__'8804'__22 -> Any
forall a b. a -> b
coe T__'8804'__22
MAlonzo.Code.Data.Nat.Base.C_z'8804'n_26)))
            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'__22
v5
                    -> (T__'8804'__22 -> T__'60'__50) -> Any -> T__'60'__50
forall a b. a -> b
coe
                         T__'8804'__22 -> T__'60'__50
MAlonzo.Code.Data.Integer.Base.C_'43''60''43'_72
                         ((T__'8804'__22 -> T__'8804'__22) -> T__'8804'__22 -> Any
forall a b. a -> b
coe T__'8804'__22 -> T__'8804'__22
MAlonzo.Code.Data.Nat.Base.C_s'8804's_34 T__'8804'__22
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'__22
v5
               -> (T__'8804'__22 -> T__'60'__50) -> Any -> T__'60'__50
forall a b. a -> b
coe
                    T__'8804'__22 -> T__'60'__50
MAlonzo.Code.Data.Integer.Base.C_'45''60''45'_58
                    ((T__'8804'__22 -> T__'8804'__22) -> Any -> Any
forall a b. a -> b
coe T__'8804'__22 -> T__'8804'__22
MAlonzo.Code.Data.Nat.Base.du_s'60's'8315''185'_70 (T__'8804'__22 -> Any
forall a b. a -> b
coe T__'8804'__22
v5))
             T__'60'__50
_ -> T__'60'__50
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Data.Integer.Properties.∣i∣≡0⇒i≡0
d_'8739'i'8739''8801'0'8658'i'8801'0_3340 ::
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8739'i'8739''8801'0'8658'i'8801'0_3340 :: Integer -> T__'8801'__12 -> T__'8801'__12
d_'8739'i'8739''8801'0'8658'i'8801'0_3340 = Integer -> T__'8801'__12 -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.∣-i∣≡∣i∣
d_'8739''45'i'8739''8801''8739'i'8739'_3344 ::
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8739''45'i'8739''8801''8739'i'8739'_3344 :: Integer -> T__'8801'__12
d_'8739''45'i'8739''8801''8739'i'8739'_3344 = Integer -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.0≤i⇒+∣i∣≡i
d_0'8804'i'8658''43''8739'i'8739''8801'i_3350 ::
  Integer ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_0'8804'i'8658''43''8739'i'8739''8801'i_3350 :: Integer -> T__'8804'__26 -> T__'8801'__12
d_0'8804'i'8658''43''8739'i'8739''8801'i_3350 = Integer -> T__'8804'__26 -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.+∣i∣≡i⇒0≤i
d_'43''8739'i'8739''8801'i'8658'0'8804'i_3352 ::
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26
d_'43''8739'i'8739''8801'i'8658'0'8804'i_3352 :: Integer -> T__'8801'__12 -> T__'8804'__26
d_'43''8739'i'8739''8801'i'8658'0'8804'i_3352 ~Integer
v0 ~T__'8801'__12
v1
  = T__'8804'__26
du_'43''8739'i'8739''8801'i'8658'0'8804'i_3352
du_'43''8739'i'8739''8801'i'8658'0'8804'i_3352 ::
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26
du_'43''8739'i'8739''8801'i'8658'0'8804'i_3352 :: T__'8804'__26
du_'43''8739'i'8739''8801'i'8658'0'8804'i_3352
  = (T__'8804'__22 -> T__'8804'__26) -> Any -> T__'8804'__26
forall a b. a -> b
coe
      T__'8804'__22 -> T__'8804'__26
MAlonzo.Code.Data.Integer.Base.C_'43''8804''43'_48
      (T__'8804'__22 -> Any
forall a b. a -> b
coe T__'8804'__22
MAlonzo.Code.Data.Nat.Base.C_z'8804'n_26)
-- Data.Integer.Properties.+∣i∣≡i⊎+∣i∣≡-i
d_'43''8739'i'8739''8801'i'8846''43''8739'i'8739''8801''45'i_3358 ::
  Integer -> MAlonzo.Code.Data.Sum.Base.T__'8846'__30
d_'43''8739'i'8739''8801'i'8846''43''8739'i'8739''8801''45'i_3358 :: Integer -> T__'8846'__30
d_'43''8739'i'8739''8801'i'8846''43''8739'i'8739''8801''45'i_3358 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_3368 ::
  Integer -> Integer -> MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_'8739'm'8861'n'8739''8804'm'8852'n_3368 :: Integer -> Integer -> T__'8804'__22
d_'8739'm'8861'n'8739''8804'm'8852'n_3368 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'__22
forall a b. a -> b
coe
      (if Bool -> Bool
forall a b. a -> b
coe Bool
v2
         then ((Any -> Any -> Any -> Any) -> Any -> Any -> Any -> Any)
-> Any -> Integer -> Integer -> Any -> Any
forall a b. a -> b
coe
                (Any -> Any -> Any -> Any) -> Any -> Any -> Any -> Any
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_begin__46
                ((T_IsPreorder_70
 -> (Any -> Any -> Any -> Any)
 -> Any
 -> Any
 -> T__IsRelatedTo__78
 -> Any)
-> Any -> (Any -> Any -> Any -> Any) -> Any
forall a b. a -> b
coe
                   T_IsPreorder_70
-> (Any -> Any -> Any -> Any)
-> Any
-> Any
-> T__IsRelatedTo__78
-> Any
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_start_96
                   (T_IsPreorder_70 -> Any
forall a b. a -> b
coe T_IsPreorder_70
MAlonzo.Code.Data.Nat.Properties.d_'8804''45'isPreorder_2810)
                   (\ Any
v3 Any
v4 Any
v5 ->
                      (T__'8804'__22 -> T__'8804'__22) -> Any -> Any
forall a b. a -> b
coe T__'8804'__22 -> T__'8804'__22
MAlonzo.Code.Data.Nat.Properties.du_'60''8658''8804'_2854 Any
v5))
                (Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d_'8739'_'8739'_18
                   ((Integer -> Integer) -> Any -> Integer
forall a b. a -> b
coe
                      Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d_'45'__252
                      ((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
MAlonzo.Code.Data.Nat.Base.d__'8852'__204 (Integer -> Integer
forall a b. a -> b
coe Integer
v0) (Integer -> Integer
forall a b. a -> b
coe Integer
v1))
                (((Any -> Any -> Any -> T__'8801'__12 -> Any -> Any)
 -> Any -> Any -> Any -> Any -> T__'8801'__12 -> Any)
-> (Any -> Any -> Any -> Any -> Any -> Any)
-> Integer
-> Integer
-> Integer
-> Any
-> Any
-> Any
forall a b. a -> b
coe
                   (Any -> Any -> Any -> T__'8801'__12 -> Any -> Any)
-> Any -> Any -> Any -> Any -> T__'8801'__12 -> Any
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8801''45''10217'_436
                   (\ Any
v3 Any
v4 Any
v5 Any
v6 Any
v7 -> Any
v7)
                   (Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d_'8739'_'8739'_18
                      ((Integer -> Integer) -> Any -> Integer
forall a b. a -> b
coe
                         Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d_'45'__252
                         ((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
MAlonzo.Code.Data.Integer.Base.d_'8739'_'8739'_18
                      ((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
v1) (Integer -> Any
forall a b. a -> b
coe Integer
v0)))
                   (Integer -> Integer -> Integer
MAlonzo.Code.Data.Nat.Base.d__'8852'__204 (Integer -> Integer
forall a b. a -> b
coe Integer
v0) (Integer -> Integer
forall a b. a -> b
coe Integer
v1))
                   (((Any -> Any -> Any -> Any -> Any -> Any)
 -> Any -> Any -> Any -> Any -> Any -> Any)
-> Any
-> Integer
-> Integer
-> Integer
-> Any
-> T__'8804'__22
-> Any
forall a b. a -> b
coe
                      (Any -> Any -> Any -> Any -> Any -> Any)
-> Any -> Any -> Any -> Any -> Any -> Any
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8804'_308
                      ((T_IsPreorder_70
 -> (Any -> Any -> Any -> Any -> Any -> Any)
 -> Any
 -> Any
 -> Any
 -> Any
 -> T__IsRelatedTo__78
 -> T__IsRelatedTo__78)
-> 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
-> Any
-> T__IsRelatedTo__78
-> T__IsRelatedTo__78
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_'8804''45'go_138
                         (T_IsPreorder_70 -> Any
forall a b. a -> b
coe T_IsPreorder_70
MAlonzo.Code.Data.Nat.Properties.d_'8804''45'isPreorder_2810)
                         (\ Any
v3 Any
v4 Any
v5 Any
v6 Any
v7 ->
                            (T__'8804'__22 -> T__'8804'__22 -> T__'8804'__22)
-> Any -> Any -> Any
forall a b. a -> b
coe
                              T__'8804'__22 -> T__'8804'__22 -> T__'8804'__22
MAlonzo.Code.Data.Nat.Properties.du_'8804''45''60''45'trans_2986 Any
v6
                              Any
v7))
                      (Integer -> Integer -> Integer
subInt (Integer -> Integer
forall a b. a -> b
coe Integer
v1) (Integer -> Integer
forall a b. a -> b
coe Integer
v0)) Integer
v1
                      (Integer -> Integer -> Integer
MAlonzo.Code.Data.Nat.Base.d__'8852'__204 (Integer -> Integer
forall a b. a -> b
coe Integer
v0) (Integer -> Integer
forall a b. a -> b
coe Integer
v1))
                      (((Any -> Any -> Any -> Any -> Any -> Any)
 -> Any -> Any -> Any -> Any -> Any -> Any)
-> Any -> Integer -> Integer -> Integer -> Any -> Any -> Any
forall a b. a -> b
coe
                         (Any -> Any -> Any -> Any -> Any -> Any)
-> Any -> Any -> Any -> Any -> Any -> Any
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8804'_308
                         ((T_IsPreorder_70
 -> (Any -> Any -> Any -> Any -> Any -> Any)
 -> Any
 -> Any
 -> Any
 -> Any
 -> T__IsRelatedTo__78
 -> T__IsRelatedTo__78)
-> 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
-> Any
-> T__IsRelatedTo__78
-> T__IsRelatedTo__78
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_'8804''45'go_138
                            (T_IsPreorder_70 -> Any
forall a b. a -> b
coe T_IsPreorder_70
MAlonzo.Code.Data.Nat.Properties.d_'8804''45'isPreorder_2810)
                            (\ Any
v3 Any
v4 Any
v5 Any
v6 Any
v7 ->
                               (T__'8804'__22 -> T__'8804'__22 -> T__'8804'__22)
-> Any -> Any -> Any
forall a b. a -> b
coe
                                 T__'8804'__22 -> T__'8804'__22 -> T__'8804'__22
MAlonzo.Code.Data.Nat.Properties.du_'8804''45''60''45'trans_2986 Any
v6
                                 Any
v7))
                         Integer
v1 (Integer -> Integer -> Integer
MAlonzo.Code.Data.Nat.Base.d__'8852'__204 (Integer -> Integer
forall a b. a -> b
coe Integer
v0) (Integer -> Integer
forall a b. a -> b
coe Integer
v1))
                         (Integer -> Integer -> Integer
MAlonzo.Code.Data.Nat.Base.d__'8852'__204 (Integer -> Integer
forall a b. a -> b
coe Integer
v0) (Integer -> Integer
forall a b. a -> b
coe Integer
v1))
                         (((Any -> Any) -> Any -> Any) -> Any -> Any -> Any
forall a b. a -> b
coe
                            (Any -> Any) -> Any -> Any
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du__'8718'_492
                            ((T_IsPreorder_70 -> Any -> T__IsRelatedTo__78) -> Any -> Any
forall a b. a -> b
coe
                               T_IsPreorder_70 -> Any -> T__IsRelatedTo__78
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_stop_166
                               (T_IsPreorder_70 -> Any
forall a b. a -> b
coe T_IsPreorder_70
MAlonzo.Code.Data.Nat.Properties.d_'8804''45'isPreorder_2810))
                            ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> Integer
MAlonzo.Code.Data.Nat.Base.d__'8852'__204 (Integer -> Any
forall a b. a -> b
coe Integer
v0) (Integer -> Any
forall a b. a -> b
coe Integer
v1)))
                         (let v3 :: T_TotalPreorder_222
v3
                                = T_TotalPreorder_222
MAlonzo.Code.Data.Nat.Properties.d_'8804''45'totalPreorder_2822 in
                          Any -> Any
forall a b. a -> b
coe
                            (let v4 :: T_MaxOperator_128
v4
                                   = T_MaxOperator_128
MAlonzo.Code.Data.Nat.Properties.d_'8852''45'operator_4440 in
                             Any -> Any
forall a b. a -> b
coe
                               ((T_TotalPreorder_222 -> T_MinOperator_98 -> Any -> Any -> Any)
-> Any -> Any -> Any -> Any -> Any
forall a b. a -> b
coe
                                  T_TotalPreorder_222 -> T_MinOperator_98 -> Any -> Any -> Any
MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_x'8851'y'8804'y_2834
                                  ((T_TotalPreorder_222 -> T_TotalPreorder_222) -> Any -> Any
forall a b. a -> b
coe
                                     T_TotalPreorder_222 -> T_TotalPreorder_222
MAlonzo.Code.Relation.Binary.Construct.Flip.EqAndOrd.du_totalPreorder_746
                                     (T_TotalPreorder_222 -> Any
forall a b. a -> b
coe T_TotalPreorder_222
v3))
                                  ((T_MaxOperator_128 -> T_MinOperator_98) -> Any -> Any
forall a b. a -> b
coe
                                     T_MaxOperator_128 -> T_MinOperator_98
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.du_MaxOp'8658'MinOp_174
                                     (T_MaxOperator_128 -> Any
forall a b. a -> b
coe T_MaxOperator_128
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'__22
MAlonzo.Code.Data.Nat.Properties.d_m'8760'n'8804'm_5042
                         (Integer -> Integer
forall a b. a -> b
coe Integer
v1) (Integer -> Integer
forall a b. a -> b
coe Integer
v0)))
                   Any
forall a. a
erased)
         else ((Any -> Any -> Any -> Any) -> Any -> Any -> Any -> Any)
-> Any -> Integer -> Integer -> Any -> Any
forall a b. a -> b
coe
                (Any -> Any -> Any -> Any) -> Any -> Any -> Any -> Any
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_begin__46
                ((T_IsPreorder_70
 -> (Any -> Any -> Any -> Any)
 -> Any
 -> Any
 -> T__IsRelatedTo__78
 -> Any)
-> Any -> (Any -> Any -> Any -> Any) -> Any
forall a b. a -> b
coe
                   T_IsPreorder_70
-> (Any -> Any -> Any -> Any)
-> Any
-> Any
-> T__IsRelatedTo__78
-> Any
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_start_96
                   (T_IsPreorder_70 -> Any
forall a b. a -> b
coe T_IsPreorder_70
MAlonzo.Code.Data.Nat.Properties.d_'8804''45'isPreorder_2810)
                   (\ Any
v3 Any
v4 Any
v5 ->
                      (T__'8804'__22 -> T__'8804'__22) -> Any -> Any
forall a b. a -> b
coe T__'8804'__22 -> T__'8804'__22
MAlonzo.Code.Data.Nat.Properties.du_'60''8658''8804'_2854 Any
v5))
                (Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d_'8739'_'8739'_18
                   ((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
v0) (Integer -> Any
forall a b. a -> b
coe Integer
v1)))
                (Integer -> Integer -> Integer
MAlonzo.Code.Data.Nat.Base.d__'8852'__204 (Integer -> Integer
forall a b. a -> b
coe Integer
v0) (Integer -> Integer
forall a b. a -> b
coe Integer
v1))
                (((Any -> Any -> Any -> Any -> Any -> Any)
 -> Any -> Any -> Any -> Any -> Any -> Any)
-> Any
-> Integer
-> Integer
-> Integer
-> Any
-> T__'8804'__22
-> Any
forall a b. a -> b
coe
                   (Any -> Any -> Any -> Any -> Any -> Any)
-> Any -> Any -> Any -> Any -> Any -> Any
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8804'_308
                   ((T_IsPreorder_70
 -> (Any -> Any -> Any -> Any -> Any -> Any)
 -> Any
 -> Any
 -> Any
 -> Any
 -> T__IsRelatedTo__78
 -> T__IsRelatedTo__78)
-> 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
-> Any
-> T__IsRelatedTo__78
-> T__IsRelatedTo__78
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_'8804''45'go_138
                      (T_IsPreorder_70 -> Any
forall a b. a -> b
coe T_IsPreorder_70
MAlonzo.Code.Data.Nat.Properties.d_'8804''45'isPreorder_2810)
                      (\ Any
v3 Any
v4 Any
v5 Any
v6 Any
v7 ->
                         (T__'8804'__22 -> T__'8804'__22 -> T__'8804'__22)
-> Any -> Any -> Any
forall a b. a -> b
coe
                           T__'8804'__22 -> T__'8804'__22 -> T__'8804'__22
MAlonzo.Code.Data.Nat.Properties.du_'8804''45''60''45'trans_2986 Any
v6
                           Any
v7))
                   (Integer -> Integer -> Integer
subInt (Integer -> Integer
forall a b. a -> b
coe Integer
v0) (Integer -> Integer
forall a b. a -> b
coe Integer
v1)) Integer
v0
                   (Integer -> Integer -> Integer
MAlonzo.Code.Data.Nat.Base.d__'8852'__204 (Integer -> Integer
forall a b. a -> b
coe Integer
v0) (Integer -> Integer
forall a b. a -> b
coe Integer
v1))
                   (((Any -> Any -> Any -> Any -> Any -> Any)
 -> Any -> Any -> Any -> Any -> Any -> Any)
-> Any -> Integer -> Integer -> Integer -> Any -> Any -> Any
forall a b. a -> b
coe
                      (Any -> Any -> Any -> Any -> Any -> Any)
-> Any -> Any -> Any -> Any -> Any -> Any
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8804'_308
                      ((T_IsPreorder_70
 -> (Any -> Any -> Any -> Any -> Any -> Any)
 -> Any
 -> Any
 -> Any
 -> Any
 -> T__IsRelatedTo__78
 -> T__IsRelatedTo__78)
-> 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
-> Any
-> T__IsRelatedTo__78
-> T__IsRelatedTo__78
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_'8804''45'go_138
                         (T_IsPreorder_70 -> Any
forall a b. a -> b
coe T_IsPreorder_70
MAlonzo.Code.Data.Nat.Properties.d_'8804''45'isPreorder_2810)
                         (\ Any
v3 Any
v4 Any
v5 Any
v6 Any
v7 ->
                            (T__'8804'__22 -> T__'8804'__22 -> T__'8804'__22)
-> Any -> Any -> Any
forall a b. a -> b
coe
                              T__'8804'__22 -> T__'8804'__22 -> T__'8804'__22
MAlonzo.Code.Data.Nat.Properties.du_'8804''45''60''45'trans_2986 Any
v6
                              Any
v7))
                      Integer
v0 (Integer -> Integer -> Integer
MAlonzo.Code.Data.Nat.Base.d__'8852'__204 (Integer -> Integer
forall a b. a -> b
coe Integer
v0) (Integer -> Integer
forall a b. a -> b
coe Integer
v1))
                      (Integer -> Integer -> Integer
MAlonzo.Code.Data.Nat.Base.d__'8852'__204 (Integer -> Integer
forall a b. a -> b
coe Integer
v0) (Integer -> Integer
forall a b. a -> b
coe Integer
v1))
                      (((Any -> Any) -> Any -> Any) -> Any -> Any -> Any
forall a b. a -> b
coe
                         (Any -> Any) -> Any -> Any
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du__'8718'_492
                         ((T_IsPreorder_70 -> Any -> T__IsRelatedTo__78) -> Any -> Any
forall a b. a -> b
coe
                            T_IsPreorder_70 -> Any -> T__IsRelatedTo__78
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_stop_166
                            (T_IsPreorder_70 -> Any
forall a b. a -> b
coe T_IsPreorder_70
MAlonzo.Code.Data.Nat.Properties.d_'8804''45'isPreorder_2810))
                         ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> Integer
MAlonzo.Code.Data.Nat.Base.d__'8852'__204 (Integer -> Any
forall a b. a -> b
coe Integer
v0) (Integer -> Any
forall a b. a -> b
coe Integer
v1)))
                      (let v3 :: T_TotalPreorder_222
v3
                             = T_TotalPreorder_222
MAlonzo.Code.Data.Nat.Properties.d_'8804''45'totalPreorder_2822 in
                       Any -> Any
forall a b. a -> b
coe
                         (let v4 :: T_MaxOperator_128
v4
                                = T_MaxOperator_128
MAlonzo.Code.Data.Nat.Properties.d_'8852''45'operator_4440 in
                          Any -> Any
forall a b. a -> b
coe
                            ((T_TotalPreorder_222 -> T_MinOperator_98 -> Any -> Any -> Any)
-> Any -> Any -> Any -> Any -> Any
forall a b. a -> b
coe
                               T_TotalPreorder_222 -> T_MinOperator_98 -> Any -> Any -> Any
MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_x'8851'y'8804'x_2808
                               ((T_TotalPreorder_222 -> T_TotalPreorder_222) -> Any -> Any
forall a b. a -> b
coe
                                  T_TotalPreorder_222 -> T_TotalPreorder_222
MAlonzo.Code.Relation.Binary.Construct.Flip.EqAndOrd.du_totalPreorder_746
                                  (T_TotalPreorder_222 -> Any
forall a b. a -> b
coe T_TotalPreorder_222
v3))
                               ((T_MaxOperator_128 -> T_MinOperator_98) -> Any -> Any
forall a b. a -> b
coe
                                  T_MaxOperator_128 -> T_MinOperator_98
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.du_MaxOp'8658'MinOp_174
                                  (T_MaxOperator_128 -> Any
forall a b. a -> b
coe T_MaxOperator_128
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'__22
MAlonzo.Code.Data.Nat.Properties.d_m'8760'n'8804'm_5042
                      (Integer -> Integer
forall a b. a -> b
coe Integer
v0) (Integer -> Integer
forall a b. a -> b
coe Integer
v1))))
-- Data.Integer.Properties.∣i+j∣≤∣i∣+∣j∣
d_'8739'i'43'j'8739''8804''8739'i'8739''43''8739'j'8739'_3398 ::
  Integer -> Integer -> MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_'8739'i'43'j'8739''8804''8739'i'8739''43''8739'j'8739'_3398 :: Integer -> Integer -> T__'8804'__22
d_'8739'i'43'j'8739''8804''8739'i'8739''43''8739'j'8739'_3398 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'__22
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'__22) -> Any -> Any
forall a b. a -> b
coe
                Integer -> T__'8804'__22
MAlonzo.Code.Data.Nat.Properties.d_'8804''45'refl_2776
                ((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'__276 (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'__22) -> Any -> T__'8804'__22
forall a b. a -> b
coe
                  Integer -> T__'8804'__22
MAlonzo.Code.Data.Nat.Properties.d_'8804''45'refl_2776
                  ((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'__276 (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)
-> Any -> Integer -> Integer -> Any -> T__'8804'__22
forall a b. a -> b
coe
                   (Any -> Any -> Any -> Any) -> Any -> Any -> Any -> Any
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_begin__46
                   ((T_IsPreorder_70
 -> (Any -> Any -> Any -> Any)
 -> Any
 -> Any
 -> T__IsRelatedTo__78
 -> Any)
-> Any -> (Any -> Any -> Any -> Any) -> Any
forall a b. a -> b
coe
                      T_IsPreorder_70
-> (Any -> Any -> Any -> Any)
-> Any
-> Any
-> T__IsRelatedTo__78
-> Any
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_start_96
                      (T_IsPreorder_70 -> Any
forall a b. a -> b
coe T_IsPreorder_70
MAlonzo.Code.Data.Nat.Properties.d_'8804''45'isPreorder_2810)
                      (\ Any
v2 Any
v3 Any
v4 ->
                         (T__'8804'__22 -> T__'8804'__22) -> Any -> Any
forall a b. a -> b
coe T__'8804'__22 -> T__'8804'__22
MAlonzo.Code.Data.Nat.Properties.du_'60''8658''8804'_2854 Any
v4))
                   (Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d_'8739'_'8739'_18
                      ((Integer -> Integer -> Integer) -> Any -> Any -> Integer
forall a b. a -> b
coe
                         Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'43'__276 (Integer -> Any
forall a b. a -> b
coe Integer
v0) (Integer -> Any
forall a b. a -> b
coe Integer
v1)))
                   (Integer -> Integer -> Integer
addInt
                      ((Integer -> Integer) -> Any -> Integer
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 -> Integer
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)))
                   (((Any -> Any -> Any -> Any -> Any -> Any)
 -> Any -> Any -> Any -> Any -> Any -> Any)
-> Any
-> Integer
-> Integer
-> Integer
-> Any
-> T__'8804'__22
-> Any
forall a b. a -> b
coe
                      (Any -> Any -> Any -> Any -> Any -> Any)
-> Any -> Any -> Any -> Any -> Any -> Any
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8804'_308
                      ((T_IsPreorder_70
 -> (Any -> Any -> Any -> Any -> Any -> Any)
 -> Any
 -> Any
 -> Any
 -> Any
 -> T__IsRelatedTo__78
 -> T__IsRelatedTo__78)
-> 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
-> Any
-> T__IsRelatedTo__78
-> T__IsRelatedTo__78
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_'8804''45'go_138
                         (T_IsPreorder_70 -> Any
forall a b. a -> b
coe T_IsPreorder_70
MAlonzo.Code.Data.Nat.Properties.d_'8804''45'isPreorder_2810)
                         (\ Any
v2 Any
v3 Any
v4 Any
v5 Any
v6 ->
                            (T__'8804'__22 -> T__'8804'__22 -> T__'8804'__22)
-> Any -> Any -> Any
forall a b. a -> b
coe
                              T__'8804'__22 -> T__'8804'__22 -> T__'8804'__22
MAlonzo.Code.Data.Nat.Properties.du_'8804''45''60''45'trans_2986 Any
v5
                              Any
v6))
                      (Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d_'8739'_'8739'_18
                         ((Integer -> Integer -> Integer) -> Any -> Any -> Integer
forall a b. a -> b
coe
                            Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'8854'__258 (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
MAlonzo.Code.Data.Nat.Base.d__'8852'__204
                         (Integer -> Integer
forall a b. a -> b
coe Integer
v0) ((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
v1)))
                      (Integer -> Integer -> Integer
addInt
                         ((Integer -> Integer) -> Any -> Integer
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 -> Integer
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)))
                      (((Any -> Any -> Any -> Any -> Any -> Any)
 -> Any -> Any -> Any -> Any -> Any -> Any)
-> Any
-> Integer
-> Integer
-> Integer
-> Any
-> T__'8804'__22
-> Any
forall a b. a -> b
coe
                         (Any -> Any -> Any -> Any -> Any -> Any)
-> Any -> Any -> Any -> Any -> Any -> Any
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8804'_308
                         ((T_IsPreorder_70
 -> (Any -> Any -> Any -> Any -> Any -> Any)
 -> Any
 -> Any
 -> Any
 -> Any
 -> T__IsRelatedTo__78
 -> T__IsRelatedTo__78)
-> 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
-> Any
-> T__IsRelatedTo__78
-> T__IsRelatedTo__78
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_'8804''45'go_138
                            (T_IsPreorder_70 -> Any
forall a b. a -> b
coe T_IsPreorder_70
MAlonzo.Code.Data.Nat.Properties.d_'8804''45'isPreorder_2810)
                            (\ Any
v2 Any
v3 Any
v4 Any
v5 Any
v6 ->
                               (T__'8804'__22 -> T__'8804'__22 -> T__'8804'__22)
-> Any -> Any -> Any
forall a b. a -> b
coe
                                 T__'8804'__22 -> T__'8804'__22 -> T__'8804'__22
MAlonzo.Code.Data.Nat.Properties.du_'8804''45''60''45'trans_2986 Any
v5
                                 Any
v6))
                         (Integer -> Integer -> Integer
MAlonzo.Code.Data.Nat.Base.d__'8852'__204
                            (Integer -> Integer
forall a b. a -> b
coe Integer
v0) ((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
v1)))
                         (Integer -> Integer -> Integer
subInt (Integer -> Integer
forall a b. a -> b
coe Integer
v0) (Integer -> Integer
forall a b. a -> b
coe Integer
v1))
                         (Integer -> Integer -> Integer
addInt
                            ((Integer -> Integer) -> Any -> Integer
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 -> Integer
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)))
                         (((Any -> Any) -> Any -> Any) -> Any -> Any -> Any
forall a b. a -> b
coe
                            (Any -> Any) -> Any -> Any
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du__'8718'_492
                            ((T_IsPreorder_70 -> Any -> T__IsRelatedTo__78) -> Any -> Any
forall a b. a -> b
coe
                               T_IsPreorder_70 -> Any -> T__IsRelatedTo__78
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_stop_166
                               (T_IsPreorder_70 -> Any
forall a b. a -> b
coe T_IsPreorder_70
MAlonzo.Code.Data.Nat.Properties.d_'8804''45'isPreorder_2810))
                            ((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'__22
MAlonzo.Code.Data.Nat.Properties.d_m'8852'n'8804'm'43'n_4830
                            (Integer -> Integer
forall a b. a -> b
coe Integer
v0) ((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
v1))))
                      (Integer -> Integer -> T__'8804'__22
d_'8739'm'8861'n'8739''8804'm'8852'n_3368
                         (Integer -> Integer
forall a b. a -> b
coe Integer
v0) ((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
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)) ->
                 ((Any -> Any -> Any -> Any) -> Any -> Any -> Any -> Any)
-> Any -> Integer -> Integer -> Any -> T__'8804'__22
forall a b. a -> b
coe
                   (Any -> Any -> Any -> Any) -> Any -> Any -> Any -> Any
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_begin__46
                   ((T_IsPreorder_70
 -> (Any -> Any -> Any -> Any)
 -> Any
 -> Any
 -> T__IsRelatedTo__78
 -> Any)
-> Any -> (Any -> Any -> Any -> Any) -> Any
forall a b. a -> b
coe
                      T_IsPreorder_70
-> (Any -> Any -> Any -> Any)
-> Any
-> Any
-> T__IsRelatedTo__78
-> Any
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_start_96
                      (T_IsPreorder_70 -> Any
forall a b. a -> b
coe T_IsPreorder_70
MAlonzo.Code.Data.Nat.Properties.d_'8804''45'isPreorder_2810)
                      (\ Any
v2 Any
v3 Any
v4 ->
                         (T__'8804'__22 -> T__'8804'__22) -> Any -> Any
forall a b. a -> b
coe T__'8804'__22 -> T__'8804'__22
MAlonzo.Code.Data.Nat.Properties.du_'60''8658''8804'_2854 Any
v4))
                   (Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d_'8739'_'8739'_18
                      ((Integer -> Integer -> Integer) -> Any -> Any -> Integer
forall a b. a -> b
coe
                         Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'43'__276 (Integer -> Any
forall a b. a -> b
coe Integer
v0) (Integer -> Any
forall a b. a -> b
coe Integer
v1)))
                   (Integer -> Integer -> Integer
addInt
                      ((Integer -> Integer) -> Any -> Integer
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 -> Integer
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)))
                   (((Any -> Any -> Any -> Any -> Any -> Any)
 -> Any -> Any -> Any -> Any -> Any -> Any)
-> Any
-> Integer
-> Integer
-> Integer
-> Any
-> T__'8804'__22
-> Any
forall a b. a -> b
coe
                      (Any -> Any -> Any -> Any -> Any -> Any)
-> Any -> Any -> Any -> Any -> Any -> Any
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8804'_308
                      ((T_IsPreorder_70
 -> (Any -> Any -> Any -> Any -> Any -> Any)
 -> Any
 -> Any
 -> Any
 -> Any
 -> T__IsRelatedTo__78
 -> T__IsRelatedTo__78)
-> 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
-> Any
-> T__IsRelatedTo__78
-> T__IsRelatedTo__78
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_'8804''45'go_138
                         (T_IsPreorder_70 -> Any
forall a b. a -> b
coe T_IsPreorder_70
MAlonzo.Code.Data.Nat.Properties.d_'8804''45'isPreorder_2810)
                         (\ Any
v2 Any
v3 Any
v4 Any
v5 Any
v6 ->
                            (T__'8804'__22 -> T__'8804'__22 -> T__'8804'__22)
-> Any -> Any -> Any
forall a b. a -> b
coe
                              T__'8804'__22 -> T__'8804'__22 -> T__'8804'__22
MAlonzo.Code.Data.Nat.Properties.du_'8804''45''60''45'trans_2986 Any
v5
                              Any
v6))
                      (Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d_'8739'_'8739'_18
                         ((Integer -> Integer -> Integer) -> Any -> Any -> Integer
forall a b. a -> b
coe
                            Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'8854'__258 (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
MAlonzo.Code.Data.Nat.Base.d__'8852'__204
                         (Integer -> Integer
forall a b. a -> b
coe Integer
v1) ((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)))
                      (Integer -> Integer -> Integer
addInt
                         ((Integer -> Integer) -> Any -> Integer
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 -> Integer
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)))
                      (((Any -> Any -> Any -> Any -> Any -> Any)
 -> Any -> Any -> Any -> Any -> Any -> Any)
-> Any
-> Integer
-> Integer
-> Integer
-> Any
-> T__'8804'__22
-> Any
forall a b. a -> b
coe
                         (Any -> Any -> Any -> Any -> Any -> Any)
-> Any -> Any -> Any -> Any -> Any -> Any
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8804'_308
                         ((T_IsPreorder_70
 -> (Any -> Any -> Any -> Any -> Any -> Any)
 -> Any
 -> Any
 -> Any
 -> Any
 -> T__IsRelatedTo__78
 -> T__IsRelatedTo__78)
-> 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
-> Any
-> T__IsRelatedTo__78
-> T__IsRelatedTo__78
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_'8804''45'go_138
                            (T_IsPreorder_70 -> Any
forall a b. a -> b
coe T_IsPreorder_70
MAlonzo.Code.Data.Nat.Properties.d_'8804''45'isPreorder_2810)
                            (\ Any
v2 Any
v3 Any
v4 Any
v5 Any
v6 ->
                               (T__'8804'__22 -> T__'8804'__22 -> T__'8804'__22)
-> Any -> Any -> Any
forall a b. a -> b
coe
                                 T__'8804'__22 -> T__'8804'__22 -> T__'8804'__22
MAlonzo.Code.Data.Nat.Properties.du_'8804''45''60''45'trans_2986 Any
v5
                                 Any
v6))
                         (Integer -> Integer -> Integer
MAlonzo.Code.Data.Nat.Base.d__'8852'__204
                            (Integer -> Integer
forall a b. a -> b
coe Integer
v1) ((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)))
                         (Integer -> Integer -> Integer
subInt (Integer -> Integer
forall a b. a -> b
coe Integer
v1) (Integer -> Integer
forall a b. a -> b
coe Integer
v0))
                         (Integer -> Integer -> Integer
addInt
                            ((Integer -> Integer) -> Any -> Integer
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 -> Integer
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)))
                         (((Any -> Any -> Any -> T__'8801'__12 -> Any -> Any)
 -> Any -> Any -> Any -> Any -> T__'8801'__12 -> Any)
-> (Any -> Any -> Any -> Any -> Any -> Any)
-> Integer
-> Integer
-> Integer
-> Any
-> Any
-> Any
forall a b. a -> b
coe
                            (Any -> Any -> Any -> T__'8801'__12 -> Any -> Any)
-> Any -> Any -> Any -> Any -> T__'8801'__12 -> Any
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8801''45''10217'_436
                            (\ Any
v2 Any
v3 Any
v4 Any
v5 Any
v6 -> Any
v6) (Integer -> Integer -> Integer
subInt (Integer -> Integer
forall a b. a -> b
coe Integer
v1) (Integer -> Integer
forall a b. a -> b
coe Integer
v0))
                            (Integer -> Integer -> Integer
subInt (Integer -> Integer
forall a b. a -> b
coe Integer
v1) (Integer -> Integer
forall a b. a -> b
coe Integer
v0))
                            (Integer -> Integer -> Integer
addInt
                               ((Integer -> Integer) -> Any -> Integer
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 -> Integer
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)))
                            (((Any -> Any) -> Any -> Any) -> Any -> Any -> Any
forall a b. a -> b
coe
                               (Any -> Any) -> Any -> Any
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du__'8718'_492
                               ((T_IsPreorder_70 -> Any -> T__IsRelatedTo__78) -> Any -> Any
forall a b. a -> b
coe
                                  T_IsPreorder_70 -> Any -> T__IsRelatedTo__78
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_stop_166
                                  (T_IsPreorder_70 -> Any
forall a b. a -> b
coe
                                     T_IsPreorder_70
MAlonzo.Code.Data.Nat.Properties.d_'8804''45'isPreorder_2810))
                               ((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)))
                            Any
forall a. a
erased)
                         (Integer -> Integer -> T__'8804'__22
MAlonzo.Code.Data.Nat.Properties.d_m'8852'n'8804'm'43'n_4830
                            (Integer -> Integer
forall a b. a -> b
coe Integer
v1) ((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))))
                      (Integer -> Integer -> T__'8804'__22
d_'8739'm'8861'n'8739''8804'm'8852'n_3368
                         (Integer -> Integer
forall a b. a -> b
coe Integer
v1) ((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))))
             Any
_ -> (Integer -> T__'8804'__22) -> Any -> T__'8804'__22
forall a b. a -> b
coe
                    Integer -> T__'8804'__22
MAlonzo.Code.Data.Nat.Properties.d_'8804''45'refl_2776
                    ((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.∣i-j∣≤∣i∣+∣j∣
d_'8739'i'45'j'8739''8804''8739'i'8739''43''8739'j'8739'_3436 ::
  Integer -> Integer -> MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_'8739'i'45'j'8739''8804''8739'i'8739''43''8739'j'8739'_3436 :: Integer -> Integer -> T__'8804'__22
d_'8739'i'45'j'8739''8804''8739'i'8739''43''8739'j'8739'_3436 Integer
v0 Integer
v1
  = ((Any -> Any -> Any -> Any) -> Any -> Any -> Any -> Any)
-> Any -> Integer -> Integer -> Any -> T__'8804'__22
forall a b. a -> b
coe
      (Any -> Any -> Any -> Any) -> Any -> Any -> Any -> Any
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_begin__46
      ((T_IsPreorder_70
 -> (Any -> Any -> Any -> Any)
 -> Any
 -> Any
 -> T__IsRelatedTo__78
 -> Any)
-> Any -> (Any -> Any -> Any -> Any) -> Any
forall a b. a -> b
coe
         T_IsPreorder_70
-> (Any -> Any -> Any -> Any)
-> Any
-> Any
-> T__IsRelatedTo__78
-> Any
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_start_96
         (T_IsPreorder_70 -> Any
forall a b. a -> b
coe T_IsPreorder_70
MAlonzo.Code.Data.Nat.Properties.d_'8804''45'isPreorder_2810)
         (\ Any
v2 Any
v3 Any
v4 ->
            (T__'8804'__22 -> T__'8804'__22) -> Any -> Any
forall a b. a -> b
coe T__'8804'__22 -> T__'8804'__22
MAlonzo.Code.Data.Nat.Properties.du_'60''8658''8804'_2854 Any
v4))
      (Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d_'8739'_'8739'_18
         ((Integer -> Integer -> Integer) -> Any -> Any -> Integer
forall a b. a -> b
coe
            Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'45'__294 (Integer -> Any
forall a b. a -> b
coe Integer
v0) (Integer -> Any
forall a b. a -> b
coe Integer
v1)))
      (Integer -> Integer -> Integer
addInt
         ((Integer -> Integer) -> Any -> Integer
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 -> Integer
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)))
      (((Any -> Any -> Any -> Any -> Any -> Any)
 -> Any -> Any -> Any -> Any -> Any -> Any)
-> Any
-> Integer
-> Integer
-> Integer
-> Any
-> T__'8804'__22
-> Any
forall a b. a -> b
coe
         (Any -> Any -> Any -> Any -> Any -> Any)
-> Any -> Any -> Any -> Any -> Any -> Any
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8804'_308
         ((T_IsPreorder_70
 -> (Any -> Any -> Any -> Any -> Any -> Any)
 -> Any
 -> Any
 -> Any
 -> Any
 -> T__IsRelatedTo__78
 -> T__IsRelatedTo__78)
-> 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
-> Any
-> T__IsRelatedTo__78
-> T__IsRelatedTo__78
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_'8804''45'go_138
            (T_IsPreorder_70 -> Any
forall a b. a -> b
coe T_IsPreorder_70
MAlonzo.Code.Data.Nat.Properties.d_'8804''45'isPreorder_2810)
            (\ Any
v2 Any
v3 Any
v4 Any
v5 Any
v6 ->
               (T__'8804'__22 -> T__'8804'__22 -> T__'8804'__22)
-> Any -> Any -> Any
forall a b. a -> b
coe
                 T__'8804'__22 -> T__'8804'__22 -> T__'8804'__22
MAlonzo.Code.Data.Nat.Properties.du_'8804''45''60''45'trans_2986 Any
v5
                 Any
v6))
         (Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d_'8739'_'8739'_18
            ((Integer -> Integer -> Integer) -> Any -> Any -> Integer
forall a b. a -> b
coe
               Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'45'__294 (Integer -> Any
forall a b. a -> b
coe Integer
v0) (Integer -> Any
forall a b. a -> b
coe Integer
v1)))
         (Integer -> Integer -> Integer
addInt
            ((Integer -> Integer) -> Any -> Integer
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'__252 (Integer -> Any
forall a b. a -> b
coe Integer
v1)))
            ((Integer -> Integer) -> Any -> Integer
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
addInt
            ((Integer -> Integer) -> Any -> Integer
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 -> Integer
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)))
         (((Any -> Any -> Any -> T__'8801'__12 -> Any -> Any)
 -> Any -> Any -> Any -> Any -> T__'8801'__12 -> Any)
-> (Any -> Any -> Any -> Any -> Any -> Any)
-> Integer
-> Integer
-> Integer
-> Any
-> Any
-> Any
forall a b. a -> b
coe
            (Any -> Any -> Any -> T__'8801'__12 -> Any -> Any)
-> Any -> Any -> Any -> Any -> T__'8801'__12 -> Any
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8801''45''10217'_436
            (\ Any
v2 Any
v3 Any
v4 Any
v5 Any
v6 -> Any
v6)
            (Integer -> Integer -> Integer
addInt
               ((Integer -> Integer) -> Any -> Integer
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'__252 (Integer -> Any
forall a b. a -> b
coe Integer
v1)))
               ((Integer -> Integer) -> Any -> Integer
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
addInt
               ((Integer -> Integer) -> Any -> Integer
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 -> Integer
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 -> Integer
addInt
               ((Integer -> Integer) -> Any -> Integer
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 -> Integer
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)))
            (((Any -> Any) -> Any -> Any) -> Any -> Any -> Any
forall a b. a -> b
coe
               (Any -> Any) -> Any -> Any
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du__'8718'_492
               ((T_IsPreorder_70 -> Any -> T__IsRelatedTo__78) -> Any -> Any
forall a b. a -> b
coe
                  T_IsPreorder_70 -> Any -> T__IsRelatedTo__78
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_stop_166
                  (T_IsPreorder_70 -> Any
forall a b. a -> b
coe T_IsPreorder_70
MAlonzo.Code.Data.Nat.Properties.d_'8804''45'isPreorder_2810))
               ((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))))
            Any
forall a. a
erased)
         (Integer -> Integer -> T__'8804'__22
d_'8739'i'43'j'8739''8804''8739'i'8739''43''8739'j'8739'_3398
            (Integer -> Integer
forall a b. a -> b
coe Integer
v0)
            ((Integer -> Integer) -> Any -> Integer
forall a b. a -> b
coe Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d_'45'__252 (Integer -> Any
forall a b. a -> b
coe Integer
v1))))
-- Data.Integer.Properties.◃-nonZero
d_'9667''45'nonZero_3454 ::
  MAlonzo.Code.Data.Sign.Base.T_Sign_6 ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T_NonZero_112 ->
  MAlonzo.Code.Data.Nat.Base.T_NonZero_112
d_'9667''45'nonZero_3454 :: T_Sign_6 -> Integer -> T_NonZero_112 -> T_NonZero_112
d_'9667''45'nonZero_3454 T_Sign_6
v0 ~Integer
v1 ~T_NonZero_112
v2 = T_Sign_6 -> T_NonZero_112
du_'9667''45'nonZero_3454 T_Sign_6
v0
du_'9667''45'nonZero_3454 ::
  MAlonzo.Code.Data.Sign.Base.T_Sign_6 ->
  MAlonzo.Code.Data.Nat.Base.T_NonZero_112
du_'9667''45'nonZero_3454 :: T_Sign_6 -> T_NonZero_112
du_'9667''45'nonZero_3454 T_Sign_6
v0
  = (Any -> Any -> Any) -> Any -> Any -> T_NonZero_112
forall a b. a -> b
coe
      Any -> Any -> Any
forall a b. a -> b -> b
seq (T_Sign_6 -> Any
forall a b. a -> b
coe T_Sign_6
v0)
      ((Any -> T_NonZero_112) -> Any -> Any
forall a b. a -> b
coe
         Any -> T_NonZero_112
MAlonzo.Code.Data.Nat.Base.C_NonZero'46'constructor_3575
         (() -> Any
forall a b. a -> b
coe ()
MAlonzo.Code.Agda.Builtin.Unit.C_tt_8))
-- Data.Integer.Properties.◃-inverse
d_'9667''45'inverse_3458 ::
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'9667''45'inverse_3458 :: Integer -> T__'8801'__12
d_'9667''45'inverse_3458 = Integer -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.◃-cong
d_'9667''45'cong_3464 ::
  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_3464 :: Integer
-> Integer -> T__'8801'__12 -> T__'8801'__12 -> T__'8801'__12
d_'9667''45'cong_3464 = 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_3480 ::
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'43''9667'n'8801''43'n_3480 :: Integer -> T__'8801'__12
d_'43''9667'n'8801''43'n_3480 = Integer -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.-◃n≡-n
d_'45''9667'n'8801''45'n_3484 ::
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'45''9667'n'8801''45'n_3484 :: Integer -> T__'8801'__12
d_'45''9667'n'8801''45'n_3484 = Integer -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.sign-◃
d_sign'45''9667'_3492 ::
  MAlonzo.Code.Data.Sign.Base.T_Sign_6 ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T_NonZero_112 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_sign'45''9667'_3492 :: T_Sign_6 -> Integer -> T_NonZero_112 -> T__'8801'__12
d_sign'45''9667'_3492 = T_Sign_6 -> Integer -> T_NonZero_112 -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.abs-◃
d_abs'45''9667'_3498 ::
  MAlonzo.Code.Data.Sign.Base.T_Sign_6 ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_abs'45''9667'_3498 :: T_Sign_6 -> Integer -> T__'8801'__12
d_abs'45''9667'_3498 = T_Sign_6 -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.signᵢ◃∣i∣≡i
d_sign'7522''9667''8739'i'8739''8801'i_3506 ::
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_sign'7522''9667''8739'i'8739''8801'i_3506 :: Integer -> T__'8801'__12
d_sign'7522''9667''8739'i'8739''8801'i_3506 = Integer -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.sign-cong
d_sign'45'cong_3516 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Sign.Base.T_Sign_6 ->
  MAlonzo.Code.Data.Sign.Base.T_Sign_6 ->
  MAlonzo.Code.Data.Nat.Base.T_NonZero_112 ->
  MAlonzo.Code.Data.Nat.Base.T_NonZero_112 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_sign'45'cong_3516 :: Integer
-> Integer
-> T_Sign_6
-> T_Sign_6
-> T_NonZero_112
-> T_NonZero_112
-> T__'8801'__12
-> T__'8801'__12
d_sign'45'cong_3516 = Integer
-> Integer
-> T_Sign_6
-> T_Sign_6
-> T_NonZero_112
-> T_NonZero_112
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.sign-cong′
d_sign'45'cong'8242'_3532 ::
  MAlonzo.Code.Data.Sign.Base.T_Sign_6 ->
  Integer ->
  MAlonzo.Code.Data.Sign.Base.T_Sign_6 ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Data.Sum.Base.T__'8846'__30
d_sign'45'cong'8242'_3532 :: T_Sign_6
-> Integer -> T_Sign_6 -> Integer -> T__'8801'__12 -> T__'8846'__30
d_sign'45'cong'8242'_3532 T_Sign_6
v0 Integer
v1 ~T_Sign_6
v2 ~Integer
v3 ~T__'8801'__12
v4
  = T_Sign_6 -> Integer -> T__'8846'__30
du_sign'45'cong'8242'_3532 T_Sign_6
v0 Integer
v1
du_sign'45'cong'8242'_3532 ::
  MAlonzo.Code.Data.Sign.Base.T_Sign_6 ->
  Integer -> MAlonzo.Code.Data.Sum.Base.T__'8846'__30
du_sign'45'cong'8242'_3532 :: T_Sign_6 -> Integer -> T__'8846'__30
du_sign'45'cong'8242'_3532 T_Sign_6
v0 Integer
v1
  = case Integer -> Integer
forall a b. a -> b
coe Integer
v1 of
      Integer
0 -> (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 -> 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
forall a. a
erased Any
forall a. a
erased)
      Integer
_ -> let v2 :: t
v2
                 = (Any -> T__'8846'__30) -> Any -> t
forall a b. a -> b
coe Any -> T__'8846'__30
MAlonzo.Code.Data.Sum.Base.C_inj'8321'_38 Any
forall a. a
erased in
           Any -> T__'8846'__30
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 (T_Sign_6 -> Any
forall a b. a -> b
coe T_Sign_6
v0) (Any -> Any
forall a b. a -> b
coe Any
forall a. a
v2))
-- Data.Integer.Properties.abs-cong
d_abs'45'cong_3566 ::
  MAlonzo.Code.Data.Sign.Base.T_Sign_6 ->
  Integer ->
  MAlonzo.Code.Data.Sign.Base.T_Sign_6 ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_abs'45'cong_3566 :: T_Sign_6
-> Integer -> T_Sign_6 -> Integer -> T__'8801'__12 -> T__'8801'__12
d_abs'45'cong_3566 = T_Sign_6
-> Integer -> T_Sign_6 -> 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_3590 ::
  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_3590 :: 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_3590
  = T_Sign_6 -> T_Sign_6 -> Integer -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.+◃-mono-<
d_'43''9667''45'mono'45''60'_3600 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Integer.Base.T__'60'__50
d_'43''9667''45'mono'45''60'_3600 :: Integer -> Integer -> T__'8804'__22 -> T__'60'__50
d_'43''9667''45'mono'45''60'_3600 Integer
v0 ~Integer
v1 T__'8804'__22
v2
  = Integer -> T__'8804'__22 -> T__'60'__50
du_'43''9667''45'mono'45''60'_3600 Integer
v0 T__'8804'__22
v2
du_'43''9667''45'mono'45''60'_3600 ::
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Integer.Base.T__'60'__50
du_'43''9667''45'mono'45''60'_3600 :: Integer -> T__'8804'__22 -> T__'60'__50
du_'43''9667''45'mono'45''60'_3600 Integer
v0 T__'8804'__22
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'__22 -> T__'60'__50) -> T__'8804'__22 -> Any
forall a b. a -> b
coe T__'8804'__22 -> T__'60'__50
MAlonzo.Code.Data.Integer.Base.C_'43''60''43'_72 T__'8804'__22
v1)
-- Data.Integer.Properties.+◃-cancel-<
d_'43''9667''45'cancel'45''60'_3612 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Integer.Base.T__'60'__50 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_'43''9667''45'cancel'45''60'_3612 :: Integer -> Integer -> T__'60'__50 -> T__'8804'__22
d_'43''9667''45'cancel'45''60'_3612 Integer
v0 ~Integer
v1 T__'60'__50
v2
  = Integer -> T__'60'__50 -> T__'8804'__22
du_'43''9667''45'cancel'45''60'_3612 Integer
v0 T__'60'__50
v2
du_'43''9667''45'cancel'45''60'_3612 ::
  Integer ->
  MAlonzo.Code.Data.Integer.Base.T__'60'__50 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
du_'43''9667''45'cancel'45''60'_3612 :: Integer -> T__'60'__50 -> T__'8804'__22
du_'43''9667''45'cancel'45''60'_3612 Integer
v0 T__'60'__50
v1
  = (Any -> Any -> Any) -> Any -> Any -> T__'8804'__22
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'__22
v4 -> T__'8804'__22 -> Any
forall a b. a -> b
coe T__'8804'__22
v4
         T__'60'__50
_ -> Any
forall a. a
MAlonzo.RTE.mazUnreachableError)
-- Data.Integer.Properties.neg◃-cancel-<
d_neg'9667''45'cancel'45''60'_3626 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Integer.Base.T__'60'__50 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_neg'9667''45'cancel'45''60'_3626 :: Integer -> Integer -> T__'60'__50 -> T__'8804'__22
d_neg'9667''45'cancel'45''60'_3626 ~Integer
v0 Integer
v1 T__'60'__50
v2
  = Integer -> T__'60'__50 -> T__'8804'__22
du_neg'9667''45'cancel'45''60'_3626 Integer
v1 T__'60'__50
v2
du_neg'9667''45'cancel'45''60'_3626 ::
  Integer ->
  MAlonzo.Code.Data.Integer.Base.T__'60'__50 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
du_neg'9667''45'cancel'45''60'_3626 :: Integer -> T__'60'__50 -> T__'8804'__22
du_neg'9667''45'cancel'45''60'_3626 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'__22
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'__22 -> T__'8804'__22) -> Any -> Any
forall a b. a -> b
coe
                T__'8804'__22 -> T__'8804'__22
MAlonzo.Code.Data.Nat.Base.C_s'8804's_34
                (T__'8804'__22 -> Any
forall a b. a -> b
coe T__'8804'__22
MAlonzo.Code.Data.Nat.Base.C_z'8804'n_26))
      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'__22
v4
               -> (T__'8804'__22 -> T__'8804'__22) -> T__'8804'__22 -> T__'8804'__22
forall a b. a -> b
coe T__'8804'__22 -> T__'8804'__22
MAlonzo.Code.Data.Nat.Base.C_s'8804's_34 T__'8804'__22
v4
             T__'60'__50
_ -> T__'8804'__22
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Data.Integer.Properties.-◃<+◃
d_'45''9667''60''43''9667'_3642 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T_NonZero_112 ->
  MAlonzo.Code.Data.Integer.Base.T__'60'__50
d_'45''9667''60''43''9667'_3642 :: Integer -> Integer -> T_NonZero_112 -> T__'60'__50
d_'45''9667''60''43''9667'_3642 ~Integer
v0 Integer
v1 ~T_NonZero_112
v2
  = Integer -> T__'60'__50
du_'45''9667''60''43''9667'_3642 Integer
v1
du_'45''9667''60''43''9667'_3642 ::
  Integer -> MAlonzo.Code.Data.Integer.Base.T__'60'__50
du_'45''9667''60''43''9667'_3642 :: Integer -> T__'60'__50
du_'45''9667''60''43''9667'_3642 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'_3644 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Integer.Base.T__'60'__50 ->
  MAlonzo.Code.Data.Irrelevant.T_Irrelevant_20
d_'43''9667''8814''45''9667'_3644 :: Integer -> Integer -> T__'60'__50 -> T_Irrelevant_20
d_'43''9667''8814''45''9667'_3644 = Integer -> Integer -> T__'60'__50 -> T_Irrelevant_20
forall a. a
erased
-- Data.Integer.Properties.n⊖n≡0
d_n'8854'n'8801'0_3650 ::
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_n'8854'n'8801'0_3650 :: Integer -> T__'8801'__12
d_n'8854'n'8801'0_3650 = 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_3668 ::
  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_3668 :: Integer -> Integer -> T__'8801'__12
d_'91'1'43'm'93''8854''91'1'43'n'93''8801'm'8854'n_3668 = Integer -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.⊖-swap
d_'8854''45'swap_3690 ::
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8854''45'swap_3690 :: Integer -> Integer -> T__'8801'__12
d_'8854''45'swap_3690 = Integer -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.⊖-≥
d_'8854''45''8805'_3704 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8854''45''8805'_3704 :: Integer -> Integer -> T__'8804'__22 -> T__'8801'__12
d_'8854''45''8805'_3704 = Integer -> Integer -> T__'8804'__22 -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.≤-⊖
d_'8804''45''8854'_3732 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8804''45''8854'_3732 :: Integer -> Integer -> T__'8804'__22 -> T__'8801'__12
d_'8804''45''8854'_3732 = Integer -> Integer -> T__'8804'__22 -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.⊖-≤
d_'8854''45''8804'_3746 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8854''45''8804'_3746 :: Integer -> Integer -> T__'8804'__22 -> T__'8801'__12
d_'8854''45''8804'_3746 = Integer -> Integer -> T__'8804'__22 -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.⊖-<
d_'8854''45''60'_3782 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8854''45''60'_3782 :: Integer -> Integer -> T__'8804'__22 -> T__'8801'__12
d_'8854''45''60'_3782 = Integer -> Integer -> T__'8804'__22 -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.⊖-≰
d_'8854''45''8816'_3784 ::
  Integer ->
  Integer ->
  (MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
   MAlonzo.Code.Data.Irrelevant.T_Irrelevant_20) ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8854''45''8816'_3784 :: Integer
-> Integer -> (T__'8804'__22 -> T_Irrelevant_20) -> T__'8801'__12
d_'8854''45''8816'_3784 = Integer
-> Integer -> (T__'8804'__22 -> T_Irrelevant_20) -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.∣⊖∣-≤
d_'8739''8854''8739''45''8804'_3786 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8739''8854''8739''45''8804'_3786 :: Integer -> Integer -> T__'8804'__22 -> T__'8801'__12
d_'8739''8854''8739''45''8804'_3786 = Integer -> Integer -> T__'8804'__22 -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.∣⊖∣-<
d_'8739''8854''8739''45''60'_3798 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8739''8854''8739''45''60'_3798 :: Integer -> Integer -> T__'8804'__22 -> T__'8801'__12
d_'8739''8854''8739''45''60'_3798 = Integer -> Integer -> T__'8804'__22 -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.∣⊖∣-≰
d_'8739''8854''8739''45''8816'_3810 ::
  Integer ->
  Integer ->
  (MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
   MAlonzo.Code.Data.Irrelevant.T_Irrelevant_20) ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8739''8854''8739''45''8816'_3810 :: Integer
-> Integer -> (T__'8804'__22 -> T_Irrelevant_20) -> T__'8801'__12
d_'8739''8854''8739''45''8816'_3810 = Integer
-> Integer -> (T__'8804'__22 -> T_Irrelevant_20) -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.-m+n≡n⊖m
d_'45'm'43'n'8801'n'8854'm_3816 ::
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'45'm'43'n'8801'n'8854'm_3816 :: Integer -> Integer -> T__'8801'__12
d_'45'm'43'n'8801'n'8854'm_3816 = Integer -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.m-n≡m⊖n
d_m'45'n'8801'm'8854'n_3828 ::
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_m'45'n'8801'm'8854'n_3828 :: Integer -> Integer -> T__'8801'__12
d_m'45'n'8801'm'8854'n_3828 = 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_3842 ::
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'45''91'n'8854'm'93''8801''45'm'43'n_3842 :: Integer -> Integer -> T__'8801'__12
d_'45''91'n'8854'm'93''8801''45'm'43'n_3842 = 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'_3876 ::
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8739'm'8854'n'8739''8801''8739'n'8854'm'8739'_3876 :: Integer -> Integer -> T__'8801'__12
d_'8739'm'8854'n'8739''8801''8739'n'8854'm'8739'_3876 = Integer -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.+-cancelˡ-⊖
d_'43''45'cancel'737''45''8854'_3892 ::
  Integer ->
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'43''45'cancel'737''45''8854'_3892 :: Integer -> Integer -> Integer -> T__'8801'__12
d_'43''45'cancel'737''45''8854'_3892 = Integer -> Integer -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.m⊖n≤m
d_m'8854'n'8804'm_3912 ::
  Integer -> Integer -> MAlonzo.Code.Data.Integer.Base.T__'8804'__26
d_m'8854'n'8804'm_3912 :: Integer -> Integer -> T__'8804'__26
d_m'8854'n'8804'm_3912 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_2728
             ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe
                Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'8854'__258 (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
                       (((Any -> Any -> Any -> Any) -> Any -> Any -> Any -> Any)
-> Any -> Integer -> Integer -> Any -> Any
forall a b. a -> b
coe
                          (Any -> Any -> Any -> Any) -> Any -> Any -> Any -> Any
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_begin__46
                          ((T_IsPreorder_70
 -> (Any -> Any -> Any -> Any)
 -> Any
 -> Any
 -> T__IsRelatedTo__78
 -> Any)
-> Any -> (Any -> Any -> Any -> Any) -> Any
forall a b. a -> b
coe
                             T_IsPreorder_70
-> (Any -> Any -> Any -> Any)
-> Any
-> Any
-> T__IsRelatedTo__78
-> Any
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_start_96
                             (T_IsPreorder_70 -> Any
forall a b. a -> b
coe T_IsPreorder_70
d_'8804''45'isPreorder_2800)
                             (\ Any
v4 Any
v5 Any
v6 -> (T__'60'__50 -> T__'8804'__26) -> Any -> Any
forall a b. a -> b
coe T__'60'__50 -> T__'8804'__26
du_'60''8658''8804'_2846 Any
v6))
                          (Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'8854'__258 (Integer -> Integer
forall a b. a -> b
coe Integer
v0) (Integer -> Integer
forall a b. a -> b
coe Integer
v1))
                          Integer
v0
                          (((Any -> Any -> Any -> T__'8801'__12 -> Any -> Any)
 -> Any -> Any -> Any -> Any -> T__'8801'__12 -> Any)
-> (Any -> Any -> Any -> Any -> Any -> Any)
-> Integer
-> Integer
-> Integer
-> Any
-> Any
-> Any
forall a b. a -> b
coe
                             (Any -> Any -> Any -> T__'8801'__12 -> Any -> Any)
-> Any -> Any -> Any -> Any -> T__'8801'__12 -> Any
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8801''45''10217'_436
                             (\ Any
v4 Any
v5 Any
v6 Any
v7 Any
v8 -> Any
v8)
                             (Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'8854'__258 (Integer -> Integer
forall a b. a -> b
coe Integer
v0) (Integer -> Integer
forall a b. a -> b
coe Integer
v1))
                             (Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'8854'__258 (Integer -> Integer
forall a b. a -> b
coe Integer
v3) (Integer -> Integer
forall a b. a -> b
coe Integer
v2))
                             Integer
v0
                             (((Any -> Any -> Any -> Any -> Any -> Any)
 -> Any -> Any -> Any -> Any -> Any -> Any)
-> Any
-> Integer
-> Integer
-> Integer
-> Any
-> T__'8804'__26
-> Any
forall a b. a -> b
coe
                                (Any -> Any -> Any -> Any -> Any -> Any)
-> Any -> Any -> Any -> Any -> Any -> Any
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8804'_308
                                ((T_IsPreorder_70
 -> (Any -> Any -> Any -> Any -> Any -> Any)
 -> Any
 -> Any
 -> Any
 -> Any
 -> T__IsRelatedTo__78
 -> T__IsRelatedTo__78)
-> 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
-> Any
-> T__IsRelatedTo__78
-> T__IsRelatedTo__78
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_'8804''45'go_138
                                   (T_IsPreorder_70 -> Any
forall a b. a -> b
coe T_IsPreorder_70
d_'8804''45'isPreorder_2800)
                                   (\ 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_2958 Any
v7 Any
v8))
                                (Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'8854'__258 (Integer -> Integer
forall a b. a -> b
coe Integer
v3) (Integer -> Integer
forall a b. a -> b
coe Integer
v2))
                                Integer
v3 Integer
v0
                                (((Any -> Any -> Any -> Any -> Any -> Any)
 -> Any -> Any -> Any -> Any -> Any -> Any)
-> Any -> Integer -> Integer -> Integer -> Any -> Any -> Any
forall a b. a -> b
coe
                                   (Any -> Any -> Any -> Any -> Any -> Any)
-> Any -> Any -> Any -> Any -> Any -> Any
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8804'_308
                                   ((T_IsPreorder_70
 -> (Any -> Any -> Any -> Any -> Any -> Any)
 -> Any
 -> Any
 -> Any
 -> Any
 -> T__IsRelatedTo__78
 -> T__IsRelatedTo__78)
-> 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
-> Any
-> T__IsRelatedTo__78
-> T__IsRelatedTo__78
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_'8804''45'go_138
                                      (T_IsPreorder_70 -> Any
forall a b. a -> b
coe T_IsPreorder_70
d_'8804''45'isPreorder_2800)
                                      (\ 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_2958 Any
v7 Any
v8))
                                   Integer
v3 Integer
v0 Integer
v0
                                   (((Any -> Any) -> Any -> Any) -> Any -> Any -> Any
forall a b. a -> b
coe
                                      (Any -> Any) -> Any -> Any
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du__'8718'_492
                                      ((T_IsPreorder_70 -> Any -> T__IsRelatedTo__78) -> Any -> Any
forall a b. a -> b
coe
                                         T_IsPreorder_70 -> Any -> T__IsRelatedTo__78
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_stop_166
                                         (T_IsPreorder_70 -> Any
forall a b. a -> b
coe T_IsPreorder_70
d_'8804''45'isPreorder_2800))
                                      (Integer -> Any
forall a b. a -> b
coe Integer
v0))
                                   ((T__'8804'__22 -> T__'8804'__26) -> T__'8804'__22 -> Any
forall a b. a -> b
coe
                                      T__'8804'__22 -> T__'8804'__26
MAlonzo.Code.Data.Integer.Base.C_'43''8804''43'_48
                                      (Integer -> T__'8804'__22
MAlonzo.Code.Data.Nat.Properties.d_n'8804'1'43'n_2844
                                         (Integer -> Integer
forall a b. a -> b
coe Integer
v3))))
                                (Integer -> Integer -> T__'8804'__26
d_m'8854'n'8804'm_3912 (Integer -> Integer
forall a b. a -> b
coe Integer
v3) (Integer -> Integer
forall a b. a -> b
coe Integer
v2)))
                             Any
forall a. a
erased)))
-- Data.Integer.Properties.m⊖n<1+m
d_m'8854'n'60'1'43'm_3930 ::
  Integer -> Integer -> MAlonzo.Code.Data.Integer.Base.T__'60'__50
d_m'8854'n'60'1'43'm_3930 :: Integer -> Integer -> T__'60'__50
d_m'8854'n'60'1'43'm_3930 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_2958
      ((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_3912 (Integer -> Any
forall a b. a -> b
coe Integer
v0) (Integer -> Any
forall a b. a -> b
coe Integer
v1))
      ((T__'8804'__22 -> T__'60'__50) -> Any -> Any
forall a b. a -> b
coe
         T__'8804'__22 -> T__'60'__50
MAlonzo.Code.Data.Integer.Base.C_'43''60''43'_72
         ((Integer -> T__'8804'__22 -> T__'8804'__22) -> Any -> Any -> Any
forall a b. a -> b
coe
            Integer -> T__'8804'__22 -> T__'8804'__22
MAlonzo.Code.Data.Nat.Properties.du_m'60'n'43'm_3630 (Integer -> Any
forall a b. a -> b
coe Integer
v0)
            ((T__'8804'__22 -> T__'8804'__22) -> Any -> Any
forall a b. a -> b
coe
               T__'8804'__22 -> T__'8804'__22
MAlonzo.Code.Data.Nat.Base.C_s'8804's_34
               (T__'8804'__22 -> Any
forall a b. a -> b
coe T__'8804'__22
MAlonzo.Code.Data.Nat.Base.C_z'8804'n_26))))
-- Data.Integer.Properties.m⊖1+n<m
d_m'8854'1'43'n'60'm_3942 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T_NonZero_112 ->
  MAlonzo.Code.Data.Integer.Base.T__'60'__50
d_m'8854'1'43'n'60'm_3942 :: Integer -> Integer -> T_NonZero_112 -> T__'60'__50
d_m'8854'1'43'n'60'm_3942 Integer
v0 Integer
v1 ~T_NonZero_112
v2
  = Integer -> Integer -> T__'60'__50
du_m'8854'1'43'n'60'm_3942 Integer
v0 Integer
v1
du_m'8854'1'43'n'60'm_3942 ::
  Integer -> Integer -> MAlonzo.Code.Data.Integer.Base.T__'60'__50
du_m'8854'1'43'n'60'm_3942 :: Integer -> Integer -> T__'60'__50
du_m'8854'1'43'n'60'm_3942 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
             (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
                (let v4 :: b
v4
                       = T_SubRelation_60 -> b
forall a b. a -> b
coe
                           T_SubRelation_60
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_strictRelation_202 in
                 Any -> Any
forall a b. a -> b
coe
                   ((T_SubRelation_60 -> Any -> Any -> Any -> Any)
-> Any -> Any -> Any -> Any -> Any
forall a b. a -> b
coe
                      T_SubRelation_60 -> Any -> Any -> Any -> Any
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_begin__126
                      (Any -> Any
forall a b. a -> b
coe Any
forall a. a
v4)
                      ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe
                         Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'8854'__258 (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)
                      (((Any -> Any -> Any -> T__'8801'__12 -> Any -> Any)
 -> Any -> Any -> Any -> Any -> T__'8801'__12 -> Any)
-> (Any -> Any -> Any -> Any -> Any -> Any)
-> Integer
-> Integer
-> Integer
-> Any
-> Any
-> Any
forall a b. a -> b
coe
                         (Any -> Any -> Any -> T__'8801'__12 -> Any -> Any)
-> Any -> Any -> Any -> Any -> T__'8801'__12 -> Any
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8801''45''10217'_436
                         (\ Any
v5 Any
v6 Any
v7 Any
v8 Any
v9 -> Any
v9)
                         (Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'8854'__258 (Integer -> Integer
forall a b. a -> b
coe Integer
v0) (Integer -> Integer
forall a b. a -> b
coe Integer
v1))
                         (Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'8854'__258 (Integer -> Integer
forall a b. a -> b
coe Integer
v2) (Integer -> Integer
forall a b. a -> b
coe Integer
v3))
                         Integer
v0
                         (((Any -> Any -> Any -> Any -> Any -> Any)
 -> Any -> Any -> Any -> Any -> Any -> Any)
-> Any
-> Integer
-> Integer
-> Integer
-> Any
-> T__'60'__50
-> Any
forall a b. a -> b
coe
                            (Any -> Any -> Any -> Any -> Any -> Any)
-> Any -> Any -> Any -> Any -> Any -> Any
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''60'_312
                            (((Any -> Any -> Any -> Any -> Any -> Any)
 -> T_Σ_14
 -> (Any -> Any -> Any -> Any -> Any -> Any)
 -> Any
 -> Any
 -> Any
 -> Any
 -> T__IsRelatedTo__78
 -> T__IsRelatedTo__78)
-> (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
-> Any
-> T__IsRelatedTo__78
-> T__IsRelatedTo__78
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_'60''45'go_152
                               (\ Any
v5 Any
v6 Any
v7 Any
v8 Any
v9 -> (T__'60'__50 -> T__'60'__50 -> T__'60'__50) -> Any -> Any -> Any
forall a b. a -> b
coe T__'60'__50 -> T__'60'__50 -> T__'60'__50
du_'60''45'trans_2986 Any
v8 Any
v9)
                               (T_Σ_14 -> Any
forall a b. a -> b
coe
                                  T_Σ_14
MAlonzo.Code.Relation.Binary.PropositionalEquality.Core.du_resp'8322'_160)
                               (\ Any
v5 Any
v6 Any
v7 Any
v8 Any
v9 -> (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_2972 Any
v8 Any
v9))
                            (Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'8854'__258 (Integer -> Integer
forall a b. a -> b
coe Integer
v2) (Integer -> Integer
forall a b. a -> b
coe Integer
v3))
                            Integer
v0 Integer
v0
                            (((Any -> Any) -> Any -> Any) -> Any -> Any -> Any
forall a b. a -> b
coe
                               (Any -> Any) -> Any -> Any
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du__'8718'_492
                               ((T_IsPreorder_70 -> Any -> T__IsRelatedTo__78) -> Any -> Any
forall a b. a -> b
coe
                                  T_IsPreorder_70 -> Any -> T__IsRelatedTo__78
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_stop_166
                                  (T_IsPreorder_70 -> Any
forall a b. a -> b
coe T_IsPreorder_70
d_'8804''45'isPreorder_2800))
                               (Integer -> Any
forall a b. a -> b
coe Integer
v0))
                            (Integer -> Integer -> T__'60'__50
d_m'8854'n'60'1'43'm_3930 (Integer -> Integer
forall a b. a -> b
coe Integer
v2) (Integer -> Integer
forall a b. a -> b
coe Integer
v3)))
                         Any
forall a. a
erased))))
-- Data.Integer.Properties.-1+m<n⊖m
d_'45'1'43'm'60'n'8854'm_3958 ::
  Integer -> Integer -> MAlonzo.Code.Data.Integer.Base.T__'60'__50
d_'45'1'43'm'60'n'8854'm_3958 :: Integer -> Integer -> T__'60'__50
d_'45'1'43'm'60'n'8854'm_3958 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'__22 -> T__'60'__50) -> T__'8804'__22 -> Any
forall a b. a -> b
coe
                       T__'8804'__22 -> T__'60'__50
MAlonzo.Code.Data.Integer.Base.C_'45''60''45'_58
                       (Integer -> T__'8804'__22
MAlonzo.Code.Data.Nat.Properties.d_'8804''45'refl_2776 (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
                       (let v4 :: b
v4
                              = T_SubRelation_60 -> b
forall a b. a -> b
coe
                                  T_SubRelation_60
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_strictRelation_202 in
                        Any -> Any
forall a b. a -> b
coe
                          ((T_SubRelation_60 -> Any -> Any -> Any -> Any)
-> Any -> Any -> Any -> Any -> Any
forall a b. a -> b
coe
                             T_SubRelation_60 -> Any -> Any -> Any -> Any
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_begin__126
                             (Any -> Any
forall a b. a -> b
coe Any
forall a. a
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
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'__258 (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)
 -> Any -> Any -> Any -> Any -> Any -> Any)
-> Any -> Integer -> Integer -> Integer -> Any -> Any -> Any
forall a b. a -> b
coe
                                (Any -> Any -> Any -> Any -> Any -> Any)
-> Any -> Any -> Any -> Any -> Any -> Any
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''60'_312
                                (((Any -> Any -> Any -> Any -> Any -> Any)
 -> T_Σ_14
 -> (Any -> Any -> Any -> Any -> Any -> Any)
 -> Any
 -> Any
 -> Any
 -> Any
 -> T__IsRelatedTo__78
 -> T__IsRelatedTo__78)
-> (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
-> Any
-> T__IsRelatedTo__78
-> T__IsRelatedTo__78
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_'60''45'go_152
                                   (\ Any
v5 Any
v6 Any
v7 Any
v8 Any
v9 -> (T__'60'__50 -> T__'60'__50 -> T__'60'__50) -> Any -> Any -> Any
forall a b. a -> b
coe T__'60'__50 -> T__'60'__50 -> T__'60'__50
du_'60''45'trans_2986 Any
v8 Any
v9)
                                   (T_Σ_14 -> Any
forall a b. a -> b
coe
                                      T_Σ_14
MAlonzo.Code.Relation.Binary.PropositionalEquality.Core.du_resp'8322'_160)
                                   (\ Any
v5 Any
v6 Any
v7 Any
v8 Any
v9 -> (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_2972 Any
v8 Any
v9))
                                (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))
                                (Integer -> Integer -> Integer
subInt (Integer -> Integer
forall a b. a -> b
coe (Integer
0 :: Integer)) (Integer -> Integer
forall a b. a -> b
coe Integer
v0))
                                (Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'8854'__258 (Integer -> Integer
forall a b. a -> b
coe Integer
v1) (Integer -> Integer
forall a b. a -> b
coe Integer
v0))
                                (((Any -> Any -> Any -> Any -> Any -> Any)
 -> Any -> Any -> Any -> Any -> Any -> Any)
-> Any
-> Integer
-> Integer
-> Integer
-> Any
-> T__'60'__50
-> Any
forall a b. a -> b
coe
                                   (Any -> Any -> Any -> Any -> Any -> Any)
-> Any -> Any -> Any -> Any -> Any -> Any
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''60'_312
                                   (((Any -> Any -> Any -> Any -> Any -> Any)
 -> T_Σ_14
 -> (Any -> Any -> Any -> Any -> Any -> Any)
 -> Any
 -> Any
 -> Any
 -> Any
 -> T__IsRelatedTo__78
 -> T__IsRelatedTo__78)
-> (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
-> Any
-> T__IsRelatedTo__78
-> T__IsRelatedTo__78
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_'60''45'go_152
                                      (\ Any
v5 Any
v6 Any
v7 Any
v8 Any
v9 -> (T__'60'__50 -> T__'60'__50 -> T__'60'__50) -> Any -> Any -> Any
forall a b. a -> b
coe T__'60'__50 -> T__'60'__50 -> T__'60'__50
du_'60''45'trans_2986 Any
v8 Any
v9)
                                      (T_Σ_14 -> Any
forall a b. a -> b
coe
                                         T_Σ_14
MAlonzo.Code.Relation.Binary.PropositionalEquality.Core.du_resp'8322'_160)
                                      (\ Any
v5 Any
v6 Any
v7 Any
v8 Any
v9 ->
                                         (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_2972 Any
v8 Any
v9))
                                   (Integer -> Integer -> Integer
subInt (Integer -> Integer
forall a b. a -> b
coe (Integer
0 :: Integer)) (Integer -> Integer
forall a b. a -> b
coe Integer
v0))
                                   (Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'8854'__258 (Integer -> Integer
forall a b. a -> b
coe Integer
v3) (Integer -> Integer
forall a b. a -> b
coe Integer
v2))
                                   (Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'8854'__258 (Integer -> Integer
forall a b. a -> b
coe Integer
v1) (Integer -> Integer
forall a b. a -> b
coe Integer
v0))
                                   (((Any -> Any -> Any -> T__'8801'__12 -> Any -> Any)
 -> Any -> Any -> Any -> Any -> T__'8801'__12 -> Any)
-> (Any -> Any -> Any -> Any -> Any -> Any)
-> Integer
-> Integer
-> Integer
-> Any
-> Any
-> Any
forall a b. a -> b
coe
                                      (Any -> Any -> Any -> T__'8801'__12 -> Any -> Any)
-> Any -> Any -> Any -> Any -> T__'8801'__12 -> Any
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8801''45''10216'_448
                                      (\ Any
v5 Any
v6 Any
v7 Any
v8 Any
v9 -> Any
v9)
                                      (Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'8854'__258
                                         (Integer -> Integer
forall a b. a -> b
coe Integer
v3) (Integer -> Integer
forall a b. a -> b
coe Integer
v2))
                                      (Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'8854'__258
                                         (Integer -> Integer
forall a b. a -> b
coe Integer
v1) (Integer -> Integer
forall a b. a -> b
coe Integer
v0))
                                      (Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'8854'__258
                                         (Integer -> Integer
forall a b. a -> b
coe Integer
v1) (Integer -> Integer
forall a b. a -> b
coe Integer
v0))
                                      (((Any -> Any) -> Any -> Any) -> Any -> Any -> Any
forall a b. a -> b
coe
                                         (Any -> Any) -> Any -> Any
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du__'8718'_492
                                         ((T_IsPreorder_70 -> Any -> T__IsRelatedTo__78) -> Any -> Any
forall a b. a -> b
coe
                                            T_IsPreorder_70 -> Any -> T__IsRelatedTo__78
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_stop_166
                                            (T_IsPreorder_70 -> Any
forall a b. a -> b
coe T_IsPreorder_70
d_'8804''45'isPreorder_2800))
                                         ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe
                                            Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'8854'__258 (Integer -> Any
forall a b. a -> b
coe Integer
v1)
                                            (Integer -> Any
forall a b. a -> b
coe Integer
v0)))
                                      Any
forall a. a
erased)
                                   (Integer -> Integer -> T__'60'__50
d_'45'1'43'm'60'n'8854'm_3958 (Integer -> Integer
forall a b. a -> b
coe Integer
v2) (Integer -> Integer
forall a b. a -> b
coe Integer
v3)))
                                ((T__'8804'__22 -> T__'60'__50) -> T__'8804'__22 -> Any
forall a b. a -> b
coe
                                   T__'8804'__22 -> T__'60'__50
MAlonzo.Code.Data.Integer.Base.C_'45''60''45'_58
                                   (Integer -> T__'8804'__22
MAlonzo.Code.Data.Nat.Properties.d_'8804''45'refl_2776
                                      (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_3976 ::
  Integer -> Integer -> MAlonzo.Code.Data.Integer.Base.T__'8804'__26
d_'45''91'1'43'm'93''8804'n'8854'm'43'1_3976 :: Integer -> Integer -> T__'8804'__26
d_'45''91'1'43'm'93''8804'n'8854'm'43'1_3976 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_2728 ((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
             (((Any -> Any -> Any -> Any) -> Any -> Any -> Any -> Any)
-> Any -> Integer -> Integer -> Any -> Any
forall a b. a -> b
coe
                (Any -> Any -> Any -> Any) -> Any -> Any -> Any -> Any
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_begin__46
                ((T_IsPreorder_70
 -> (Any -> Any -> Any -> Any)
 -> Any
 -> Any
 -> T__IsRelatedTo__78
 -> Any)
-> Any -> (Any -> Any -> Any -> Any) -> Any
forall a b. a -> b
coe
                   T_IsPreorder_70
-> (Any -> Any -> Any -> Any)
-> Any
-> Any
-> T__IsRelatedTo__78
-> Any
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_start_96
                   (T_IsPreorder_70 -> Any
forall a b. a -> b
coe T_IsPreorder_70
d_'8804''45'isPreorder_2800)
                   (\ Any
v3 Any
v4 Any
v5 -> (T__'60'__50 -> T__'8804'__26) -> Any -> Any
forall a b. a -> b
coe T__'60'__50 -> T__'8804'__26
du_'60''8658''8804'_2846 Any
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))
                (Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'8854'__258
                   (Integer -> Integer
forall a b. a -> b
coe Integer
v1) ((Integer -> Integer -> Integer) -> Any -> Any -> Integer
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)))
                (((Any -> Any -> Any -> Any -> Any -> Any)
 -> Any -> Any -> Any -> Any -> Any -> Any)
-> Any -> Integer -> Integer -> Integer -> Any -> Any -> Any
forall a b. a -> b
coe
                   (Any -> Any -> Any -> Any -> Any -> Any)
-> Any -> Any -> Any -> Any -> Any -> Any
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8804'_308
                   ((T_IsPreorder_70
 -> (Any -> Any -> Any -> Any -> Any -> Any)
 -> Any
 -> Any
 -> Any
 -> Any
 -> T__IsRelatedTo__78
 -> T__IsRelatedTo__78)
-> 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
-> Any
-> T__IsRelatedTo__78
-> T__IsRelatedTo__78
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_'8804''45'go_138
                      (T_IsPreorder_70 -> Any
forall a b. a -> b
coe T_IsPreorder_70
d_'8804''45'isPreorder_2800)
                      (\ 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_2958 Any
v6 Any
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
v0))
                   (Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'8854'__258 (Integer -> Integer
forall a b. a -> b
coe Integer
v2) (Integer -> Integer
forall a b. a -> b
coe Integer
v0))
                   (Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'8854'__258
                      (Integer -> Integer
forall a b. a -> b
coe Integer
v1) ((Integer -> Integer -> Integer) -> Any -> Any -> Integer
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)))
                   (((Any -> Any -> Any -> T__'8801'__12 -> Any -> Any)
 -> Any -> Any -> Any -> Any -> T__'8801'__12 -> Any)
-> (Any -> Any -> Any -> Any -> Any -> Any)
-> Integer
-> Integer
-> Integer
-> Any
-> Any
-> Any
forall a b. a -> b
coe
                      (Any -> Any -> Any -> T__'8801'__12 -> Any -> Any)
-> Any -> Any -> Any -> Any -> T__'8801'__12 -> Any
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8801''45''10216'_448
                      (\ Any
v3 Any
v4 Any
v5 Any
v6 Any
v7 -> Any
v7)
                      (Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'8854'__258 (Integer -> Integer
forall a b. a -> b
coe Integer
v2) (Integer -> Integer
forall a b. a -> b
coe Integer
v0))
                      (Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'8854'__258
                         (Integer -> Integer
forall a b. a -> b
coe Integer
v1) ((Integer -> Integer -> Integer) -> Any -> Any -> Integer
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 -> Integer
MAlonzo.Code.Data.Integer.Base.d__'8854'__258
                         (Integer -> Integer
forall a b. a -> b
coe Integer
v1) ((Integer -> Integer -> Integer) -> Any -> Any -> Integer
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)))
                      (((Any -> Any) -> Any -> Any) -> Any -> Any -> Any
forall a b. a -> b
coe
                         (Any -> Any) -> Any -> Any
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du__'8718'_492
                         ((T_IsPreorder_70 -> Any -> T__IsRelatedTo__78) -> Any -> Any
forall a b. a -> b
coe
                            T_IsPreorder_70 -> Any -> T__IsRelatedTo__78
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_stop_166
                            (T_IsPreorder_70 -> Any
forall a b. a -> b
coe T_IsPreorder_70
d_'8804''45'isPreorder_2800))
                         ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe
                            Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'8854'__258 (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))))
                      Any
forall a. a
erased)
                   ((T__'60'__50 -> T__'8804'__26) -> Any -> Any
forall a b. a -> b
coe
                      T__'60'__50 -> T__'8804'__26
du_'60''8658''8804'_2846
                      ((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_3958 (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_3992 ::
  Integer -> Integer -> MAlonzo.Code.Data.Integer.Base.T__'8804'__26
d_'45'1'43'm'8804'n'8854'm_3992 :: Integer -> Integer -> T__'8804'__26
d_'45'1'43'm'8804'n'8854'm_3992 Integer
v0 Integer
v1
  = (T__'60'__50 -> T__'8804'__26) -> Any -> T__'8804'__26
forall a b. a -> b
coe
      T__'60'__50 -> T__'8804'__26
du_'60''8658''8804'_2846
      ((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_3958 (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'_4002 ::
  Integer -> Integer -> MAlonzo.Code.Data.Integer.Base.T__'8804'__26
d_0'8854'm'8804''43'_4002 :: Integer -> Integer -> T__'8804'__26
d_0'8854'm'8804''43'_4002 Integer
v0 ~Integer
v1 = Integer -> T__'8804'__26
du_0'8854'm'8804''43'_4002 Integer
v0
du_0'8854'm'8804''43'_4002 ::
  Integer -> MAlonzo.Code.Data.Integer.Base.T__'8804'__26
du_0'8854'm'8804''43'_4002 :: Integer -> T__'8804'__26
du_0'8854'm'8804''43'_4002 Integer
v0
  = case Integer -> Integer
forall a b. a -> b
coe Integer
v0 of
      Integer
0 -> (T__'8804'__22 -> T__'8804'__26) -> Any -> T__'8804'__26
forall a b. a -> b
coe
             T__'8804'__22 -> T__'8804'__26
MAlonzo.Code.Data.Integer.Base.C_'43''8804''43'_48
             (T__'8804'__22 -> Any
forall a b. a -> b
coe T__'8804'__22
MAlonzo.Code.Data.Nat.Base.C_z'8804'n_26)
      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'_4006 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_sign'45''8854''45''60'_4006 :: Integer -> Integer -> T__'8804'__22 -> T__'8801'__12
d_sign'45''8854''45''60'_4006 = Integer -> Integer -> T__'8804'__22 -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.sign-⊖-≰
d_sign'45''8854''45''8816'_4018 ::
  Integer ->
  Integer ->
  (MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
   MAlonzo.Code.Data.Irrelevant.T_Irrelevant_20) ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_sign'45''8854''45''8816'_4018 :: Integer
-> Integer -> (T__'8804'__22 -> T_Irrelevant_20) -> T__'8801'__12
d_sign'45''8854''45''8816'_4018 = Integer
-> Integer -> (T__'8804'__22 -> T_Irrelevant_20) -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.⊖-monoʳ-≥-≤
d_'8854''45'mono'691''45''8805''45''8804'_4024 ::
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26
d_'8854''45'mono'691''45''8805''45''8804'_4024 :: Integer -> Integer -> Integer -> T__'8804'__22 -> T__'8804'__26
d_'8854''45'mono'691''45''8805''45''8804'_4024 Integer
v0 Integer
v1 Integer
v2 T__'8804'__22
v3
  = case Integer -> Integer
forall a b. a -> b
coe Integer
v0 of
      Integer
0 -> case T__'8804'__22 -> T__'8804'__22
forall a b. a -> b
coe T__'8804'__22
v3 of
             T__'8804'__22
MAlonzo.Code.Data.Nat.Base.C_z'8804'n_26
               -> (Integer -> T__'8804'__26) -> Any -> T__'8804'__26
forall a b. a -> b
coe Integer -> T__'8804'__26
du_0'8854'm'8804''43'_4002 (Integer -> Any
forall a b. a -> b
coe Integer
v1)
             MAlonzo.Code.Data.Nat.Base.C_s'8804's_34 T__'8804'__22
v6
               -> (T__'8804'__22 -> T__'8804'__26) -> T__'8804'__22 -> T__'8804'__26
forall a b. a -> b
coe T__'8804'__22 -> T__'8804'__26
MAlonzo.Code.Data.Integer.Base.C_'45''8804''45'_34 T__'8804'__22
v6
             T__'8804'__22
_ -> 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'__22 -> Any
forall a b. a -> b
coe T__'8804'__22
v3)
                       ((Integer -> T__'8804'__26) -> Any -> Any
forall a b. a -> b
coe
                          Integer -> T__'8804'__26
d_'8804''45'refl_2728
                          (((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'_292
                             (Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'8854'__258 (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'__22 -> T__'8804'__22
forall a b. a -> b
coe T__'8804'__22
v3 of
                          T__'8804'__22
MAlonzo.Code.Data.Nat.Base.C_z'8804'n_26
                            -> ((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 -> Any -> Any
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_begin__46
                                 ((T_IsPreorder_70
 -> (Any -> Any -> Any -> Any)
 -> Any
 -> Any
 -> T__IsRelatedTo__78
 -> Any)
-> Any -> (Any -> Any -> Any -> Any) -> Any
forall a b. a -> b
coe
                                    T_IsPreorder_70
-> (Any -> Any -> Any -> Any)
-> Any
-> Any
-> T__IsRelatedTo__78
-> Any
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_start_96
                                    (T_IsPreorder_70 -> Any
forall a b. a -> b
coe T_IsPreorder_70
d_'8804''45'isPreorder_2800)
                                    (\ Any
v7 Any
v8 Any
v9 -> (T__'60'__50 -> T__'8804'__26) -> Any -> Any
forall a b. a -> b
coe T__'60'__50 -> T__'8804'__26
du_'60''8658''8804'_2846 Any
v9))
                                 (((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'_292
                                    (Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'8854'__258 (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'__298
                                    (\ Any
v7 Any
v8 -> Any
v8)
                                    (Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'8854'__258 (Integer -> Integer
forall a b. a -> b
coe Integer
v0)) Integer
v1
                                    (Integer
0 :: Integer))
                                 (((Any -> Any -> Any -> T__'8801'__12 -> Any -> Any)
 -> Any -> Any -> Any -> Any -> T__'8801'__12 -> Any)
-> (Any -> Any -> Any -> Any -> Any -> Any)
-> Integer
-> Integer
-> Any
-> Any
-> Any
-> Any
forall a b. a -> b
coe
                                    (Any -> Any -> Any -> T__'8801'__12 -> Any -> Any)
-> Any -> Any -> Any -> Any -> T__'8801'__12 -> Any
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8801''45''10217'_436
                                    (\ Any
v7 Any
v8 Any
v9 Any
v10 Any
v11 -> Any
v11)
                                    (Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'8854'__258
                                       (Integer -> Integer
forall a b. a -> b
coe Integer
v0) (Integer -> Integer
forall a b. a -> b
coe Integer
v1))
                                    (Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'8854'__258
                                       (Integer -> Integer
forall a b. a -> b
coe Integer
v4) (Integer -> Integer
forall a b. a -> b
coe Integer
v5))
                                    (((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'__298
                                       (\ Any
v7 Any
v8 -> Any
v8)
                                       (Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'8854'__258 (Integer -> Integer
forall a b. a -> b
coe Integer
v0)) Integer
v1
                                       (Integer
0 :: Integer))
                                    (((Any -> Any -> Any -> Any -> Any -> Any)
 -> Any -> Any -> Any -> Any -> Any -> Any)
-> Any -> Integer -> Integer -> Any -> Any -> T__'60'__50 -> Any
forall a b. a -> b
coe
                                       (Any -> Any -> Any -> Any -> Any -> Any)
-> Any -> Any -> Any -> Any -> Any -> Any
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''60'_312
                                       (((Any -> Any -> Any -> Any -> Any -> Any)
 -> T_Σ_14
 -> (Any -> Any -> Any -> Any -> Any -> Any)
 -> Any
 -> Any
 -> Any
 -> Any
 -> T__IsRelatedTo__78
 -> T__IsRelatedTo__78)
-> (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
-> Any
-> T__IsRelatedTo__78
-> T__IsRelatedTo__78
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_'60''45'go_152
                                          (\ Any
v7 Any
v8 Any
v9 Any
v10 Any
v11 -> (T__'60'__50 -> T__'60'__50 -> T__'60'__50) -> Any -> Any -> Any
forall a b. a -> b
coe T__'60'__50 -> T__'60'__50 -> T__'60'__50
du_'60''45'trans_2986 Any
v10 Any
v11)
                                          (T_Σ_14 -> Any
forall a b. a -> b
coe
                                             T_Σ_14
MAlonzo.Code.Relation.Binary.PropositionalEquality.Core.du_resp'8322'_160)
                                          (\ Any
v7 Any
v8 Any
v9 Any
v10 Any
v11 ->
                                             (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_2972 Any
v10 Any
v11))
                                       (Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'8854'__258
                                          (Integer -> Integer
forall a b. a -> b
coe Integer
v4) (Integer -> Integer
forall a b. a -> b
coe Integer
v5))
                                       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'__298
                                          (\ Any
v7 Any
v8 -> Any
v8)
                                          (Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'8854'__258 (Integer -> Integer
forall a b. a -> b
coe Integer
v0))
                                          Integer
v1 (Integer
0 :: Integer))
                                       (((Any -> Any) -> Any -> Any) -> Any -> Any -> Any
forall a b. a -> b
coe
                                          (Any -> Any) -> Any -> Any
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du__'8718'_492
                                          ((T_IsPreorder_70 -> Any -> T__IsRelatedTo__78) -> Any -> Any
forall a b. a -> b
coe
                                             T_IsPreorder_70 -> Any -> T__IsRelatedTo__78
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_stop_166
                                             (T_IsPreorder_70 -> Any
forall a b. a -> b
coe T_IsPreorder_70
d_'8804''45'isPreorder_2800))
                                          (Integer -> Any
forall a b. a -> b
coe Integer
v0))
                                       (Integer -> Integer -> T__'60'__50
d_m'8854'n'60'1'43'm_3930 (Integer -> Integer
forall a b. a -> b
coe Integer
v4) (Integer -> Integer
forall a b. a -> b
coe Integer
v5)))
                                    Any
forall a. a
erased)
                          MAlonzo.Code.Data.Nat.Base.C_s'8804's_34 T__'8804'__22
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
                                 (((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 -> Any -> Any
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_begin__46
                                    ((T_IsPreorder_70
 -> (Any -> Any -> Any -> Any)
 -> Any
 -> Any
 -> T__IsRelatedTo__78
 -> Any)
-> Any -> (Any -> Any -> Any -> Any) -> Any
forall a b. a -> b
coe
                                       T_IsPreorder_70
-> (Any -> Any -> Any -> Any)
-> Any
-> Any
-> T__IsRelatedTo__78
-> Any
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_start_96
                                       (T_IsPreorder_70 -> Any
forall a b. a -> b
coe T_IsPreorder_70
d_'8804''45'isPreorder_2800)
                                       (\ Any
v10 Any
v11 Any
v12 -> (T__'60'__50 -> T__'8804'__26) -> Any -> Any
forall a b. a -> b
coe T__'60'__50 -> T__'8804'__26
du_'60''8658''8804'_2846 Any
v12))
                                    (((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'_292
                                       (Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'8854'__258 (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'__298
                                       (\ Any
v10 Any
v11 -> Any
v11)
                                       (Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'8854'__258 (Integer -> Integer
forall a b. a -> b
coe Integer
v0)) Integer
v1
                                       Integer
v2)
                                    (((Any -> Any -> Any -> T__'8801'__12 -> Any -> Any)
 -> Any -> Any -> Any -> Any -> T__'8801'__12 -> Any)
-> (Any -> Any -> Any -> Any -> Any -> Any)
-> Integer
-> Integer
-> Any
-> Any
-> Any
-> Any
forall a b. a -> b
coe
                                       (Any -> Any -> Any -> T__'8801'__12 -> Any -> Any)
-> Any -> Any -> Any -> Any -> T__'8801'__12 -> Any
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8801''45''10217'_436
                                       (\ Any
v10 Any
v11 Any
v12 Any
v13 Any
v14 -> Any
v14)
                                       (Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'8854'__258
                                          (Integer -> Integer
forall a b. a -> b
coe Integer
v0) (Integer -> Integer
forall a b. a -> b
coe Integer
v1))
                                       (Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'8854'__258
                                          (Integer -> Integer
forall a b. a -> b
coe Integer
v4) (Integer -> Integer
forall a b. a -> b
coe Integer
v5))
                                       (((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'__298
                                          (\ Any
v10 Any
v11 -> Any
v11)
                                          (Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'8854'__258 (Integer -> Integer
forall a b. a -> b
coe Integer
v0))
                                          Integer
v1 Integer
v2)
                                       (((Any -> Any -> Any -> Any -> Any -> Any)
 -> Any -> Any -> Any -> Any -> Any -> Any)
-> Any -> Integer -> Integer -> Any -> Any -> T__'8804'__26 -> Any
forall a b. a -> b
coe
                                          (Any -> Any -> Any -> Any -> Any -> Any)
-> Any -> Any -> Any -> Any -> Any -> Any
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8804'_308
                                          ((T_IsPreorder_70
 -> (Any -> Any -> Any -> Any -> Any -> Any)
 -> Any
 -> Any
 -> Any
 -> Any
 -> T__IsRelatedTo__78
 -> T__IsRelatedTo__78)
-> 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
-> Any
-> T__IsRelatedTo__78
-> T__IsRelatedTo__78
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_'8804''45'go_138
                                             (T_IsPreorder_70 -> Any
forall a b. a -> b
coe T_IsPreorder_70
d_'8804''45'isPreorder_2800)
                                             (\ 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_2958 Any
v13 Any
v14))
                                          (Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'8854'__258
                                             (Integer -> Integer
forall a b. a -> b
coe Integer
v4) (Integer -> Integer
forall a b. a -> b
coe Integer
v5))
                                          (Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'8854'__258
                                             (Integer -> Integer
forall a b. a -> b
coe Integer
v4) (Integer -> Integer
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'__298
                                             (\ Any
v10 Any
v11 -> Any
v11)
                                             (Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'8854'__258
                                                (Integer -> Integer
forall a b. a -> b
coe Integer
v0))
                                             Integer
v1 Integer
v2)
                                          (((Any -> Any -> Any -> T__'8801'__12 -> Any -> Any)
 -> Any -> Any -> Any -> Any -> T__'8801'__12 -> Any)
-> (Any -> Any -> Any -> Any -> Any -> Any)
-> Integer
-> Integer
-> Any
-> Any
-> Any
-> Any
forall a b. a -> b
coe
                                             (Any -> Any -> Any -> T__'8801'__12 -> Any -> Any)
-> Any -> Any -> Any -> Any -> T__'8801'__12 -> Any
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8801''45''10216'_448
                                             (\ Any
v10 Any
v11 Any
v12 Any
v13 Any
v14 -> Any
v14)
                                             (Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'8854'__258
                                                (Integer -> Integer
forall a b. a -> b
coe Integer
v4) (Integer -> Integer
forall a b. a -> b
coe Integer
v9))
                                             (Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'8854'__258
                                                (Integer -> Integer
forall a b. a -> b
coe Integer
v0) (Integer -> Integer
forall a b. a -> b
coe 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'__298
                                                (\ Any
v10 Any
v11 -> Any
v11)
                                                (Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'8854'__258
                                                   (Integer -> Integer
forall a b. a -> b
coe Integer
v0))
                                                Integer
v1 Integer
v2)
                                             (((Any -> Any) -> Any -> Any) -> Any -> Any -> Any
forall a b. a -> b
coe
                                                (Any -> Any) -> Any -> Any
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du__'8718'_492
                                                ((T_IsPreorder_70 -> Any -> T__IsRelatedTo__78) -> Any -> Any
forall a b. a -> b
coe
                                                   T_IsPreorder_70 -> Any -> T__IsRelatedTo__78
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_stop_166
                                                   (T_IsPreorder_70 -> Any
forall a b. a -> b
coe T_IsPreorder_70
d_'8804''45'isPreorder_2800))
                                                ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe
                                                   Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'8854'__258
                                                   (Integer -> Any
forall a b. a -> b
coe Integer
v0) (Integer -> Any
forall a b. a -> b
coe Integer
v2)))
                                             Any
forall a. a
erased)
                                          (Integer -> Integer -> Integer -> T__'8804'__22 -> T__'8804'__26
d_'8854''45'mono'691''45''8805''45''8804'_4024
                                             (Integer -> Integer
forall a b. a -> b
coe Integer
v4) (Integer -> Integer
forall a b. a -> b
coe Integer
v5) (Integer -> Integer
forall a b. a -> b
coe Integer
v9) (T__'8804'__22 -> T__'8804'__22
forall a b. a -> b
coe T__'8804'__22
v8)))
                                       Any
forall a. a
erased))
                          T__'8804'__22
_ -> Any
forall a. a
MAlonzo.RTE.mazUnreachableError))
-- Data.Integer.Properties.⊖-monoˡ-≤
d_'8854''45'mono'737''45''8804'_4056 ::
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26
d_'8854''45'mono'737''45''8804'_4056 :: Integer -> Integer -> Integer -> T__'8804'__22 -> T__'8804'__26
d_'8854''45'mono'737''45''8804'_4056 Integer
v0 Integer
v1 Integer
v2 T__'8804'__22
v3
  = case Integer -> Integer
forall a b. a -> b
coe Integer
v0 of
      Integer
0 -> (T__'8804'__22 -> T__'8804'__26) -> T__'8804'__22 -> T__'8804'__26
forall a b. a -> b
coe T__'8804'__22 -> T__'8804'__26
MAlonzo.Code.Data.Integer.Base.C_'43''8804''43'_48 T__'8804'__22
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'__22 -> Any
forall a b. a -> b
coe T__'8804'__22
v3)
                       ((Integer -> T__'8804'__26) -> Any -> Any
forall a b. a -> b
coe
                          Integer -> T__'8804'__26
d_'8804''45'refl_2728
                          (((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'_292
                             (\ Any
v5 ->
                                Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'8854'__258 (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'__22 -> T__'8804'__22
forall a b. a -> b
coe T__'8804'__22
v3 of
                          T__'8804'__22
MAlonzo.Code.Data.Nat.Base.C_z'8804'n_26
                            -> ((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 -> Any -> Any
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_begin__46
                                 ((T_IsPreorder_70
 -> (Any -> Any -> Any -> Any)
 -> Any
 -> Any
 -> T__IsRelatedTo__78
 -> Any)
-> Any -> (Any -> Any -> Any -> Any) -> Any
forall a b. a -> b
coe
                                    T_IsPreorder_70
-> (Any -> Any -> Any -> Any)
-> Any
-> Any
-> T__IsRelatedTo__78
-> Any
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_start_96
                                    (T_IsPreorder_70 -> Any
forall a b. a -> b
coe T_IsPreorder_70
d_'8804''45'isPreorder_2800)
                                    (\ Any
v7 Any
v8 Any
v9 -> (T__'60'__50 -> T__'8804'__26) -> Any -> Any
forall a b. a -> b
coe T__'60'__50 -> T__'8804'__26
du_'60''8658''8804'_2846 Any
v9))
                                 (((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'_292
                                    (\ Any
v7 ->
                                       Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'8854'__258
                                         (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'__298
                                    (\ Any
v7 Any
v8 -> Any
v8)
                                    (\ Any
v7 ->
                                       Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'8854'__258
                                         (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)
                                 (((Any -> Any -> Any -> Any -> Any -> Any)
 -> Any -> Any -> Any -> Any -> Any -> Any)
-> Any -> Integer -> Integer -> Any -> Any -> T__'8804'__26 -> Any
forall a b. a -> b
coe
                                    (Any -> Any -> Any -> Any -> Any -> Any)
-> Any -> Any -> Any -> Any -> Any -> Any
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8804'_308
                                    ((T_IsPreorder_70
 -> (Any -> Any -> Any -> Any -> Any -> Any)
 -> Any
 -> Any
 -> Any
 -> Any
 -> T__IsRelatedTo__78
 -> T__IsRelatedTo__78)
-> 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
-> Any
-> T__IsRelatedTo__78
-> T__IsRelatedTo__78
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_'8804''45'go_138
                                       (T_IsPreorder_70 -> Any
forall a b. a -> b
coe T_IsPreorder_70
d_'8804''45'isPreorder_2800)
                                       (\ 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_2958 Any
v10 Any
v11))
                                    (Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'8854'__258
                                       (Integer -> Integer
forall a b. a -> b
coe (Integer
0 :: Integer)) (Integer -> Integer
forall a b. a -> b
coe Integer
v0))
                                    (Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'8854'__258
                                       (Integer -> Integer
forall a b. a -> b
coe (Integer
0 :: Integer)) (Integer -> Integer
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'__298
                                       (\ Any
v7 Any
v8 -> Any
v8)
                                       (\ Any
v7 ->
                                          Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'8854'__258
                                            (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)
                                    (((Any -> Any -> Any -> Any -> Any -> Any)
 -> Any -> Any -> Any -> Any -> Any -> Any)
-> Any -> Integer -> Integer -> Any -> Any -> T__'8804'__26 -> Any
forall a b. a -> b
coe
                                       (Any -> Any -> Any -> Any -> Any -> Any)
-> Any -> Any -> Any -> Any -> Any -> Any
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8804'_308
                                       ((T_IsPreorder_70
 -> (Any -> Any -> Any -> Any -> Any -> Any)
 -> Any
 -> Any
 -> Any
 -> Any
 -> T__IsRelatedTo__78
 -> T__IsRelatedTo__78)
-> 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
-> Any
-> T__IsRelatedTo__78
-> T__IsRelatedTo__78
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_'8804''45'go_138
                                          (T_IsPreorder_70 -> Any
forall a b. a -> b
coe T_IsPreorder_70
d_'8804''45'isPreorder_2800)
                                          (\ 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_2958 Any
v10 Any
v11))
                                       (Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'8854'__258
                                          (Integer -> Integer
forall a b. a -> b
coe (Integer
0 :: Integer)) (Integer -> Integer
forall a b. a -> b
coe Integer
v4))
                                       (Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'8854'__258
                                          (Integer -> Integer
forall a b. a -> b
coe Integer
v5) (Integer -> Integer
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'__298
                                          (\ Any
v7 Any
v8 -> Any
v8)
                                          (\ Any
v7 ->
                                             Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'8854'__258
                                               (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)
                                       (((Any -> Any -> Any -> T__'8801'__12 -> Any -> Any)
 -> Any -> Any -> Any -> Any -> T__'8801'__12 -> Any)
-> (Any -> Any -> Any -> Any -> Any -> Any)
-> Integer
-> Integer
-> Any
-> Any
-> Any
-> Any
forall a b. a -> b
coe
                                          (Any -> Any -> Any -> T__'8801'__12 -> Any -> Any)
-> Any -> Any -> Any -> Any -> T__'8801'__12 -> Any
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8801''45''10216'_448
                                          (\ Any
v7 Any
v8 Any
v9 Any
v10 Any
v11 -> Any
v11)
                                          (Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'8854'__258
                                             (Integer -> Integer
forall a b. a -> b
coe Integer
v5) (Integer -> Integer
forall a b. a -> b
coe Integer
v4))
                                          (Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'8854'__258
                                             (Integer -> Integer
forall a b. a -> b
coe Integer
v2) (Integer -> Integer
forall a b. a -> b
coe Integer
v0))
                                          (((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'__298
                                             (\ Any
v7 Any
v8 -> Any
v8)
                                             (\ Any
v7 ->
                                                Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'8854'__258
                                                  (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)
                                          (((Any -> Any) -> Any -> Any) -> Any -> Any -> Any
forall a b. a -> b
coe
                                             (Any -> Any) -> Any -> Any
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du__'8718'_492
                                             ((T_IsPreorder_70 -> Any -> T__IsRelatedTo__78) -> Any -> Any
forall a b. a -> b
coe
                                                T_IsPreorder_70 -> Any -> T__IsRelatedTo__78
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_stop_166
                                                (T_IsPreorder_70 -> Any
forall a b. a -> b
coe T_IsPreorder_70
d_'8804''45'isPreorder_2800))
                                             ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe
                                                Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'8854'__258
                                                (Integer -> Any
forall a b. a -> b
coe Integer
v2) (Integer -> Any
forall a b. a -> b
coe Integer
v0)))
                                          Any
forall a. a
erased)
                                       (Integer -> Integer -> Integer -> T__'8804'__22 -> T__'8804'__26
d_'8854''45'mono'737''45''8804'_4056
                                          (Integer -> Integer
forall a b. a -> b
coe Integer
v4) (Integer -> Integer
forall a b. a -> b
coe (Integer
0 :: Integer)) (Integer -> Integer
forall a b. a -> b
coe Integer
v5)
                                          (T__'8804'__22 -> T__'8804'__22
forall a b. a -> b
coe T__'8804'__22
MAlonzo.Code.Data.Nat.Base.C_z'8804'n_26)))
                                    (Integer -> Integer -> Integer -> T__'8804'__22 -> T__'8804'__26
d_'8854''45'mono'691''45''8805''45''8804'_4024
                                       (Integer -> Integer
forall a b. a -> b
coe (Integer
0 :: Integer)) (Integer -> Integer
forall a b. a -> b
coe Integer
v0) (Integer -> Integer
forall a b. a -> b
coe Integer
v4)
                                       ((Integer -> T__'8804'__22) -> Any -> T__'8804'__22
forall a b. a -> b
coe
                                          Integer -> T__'8804'__22
MAlonzo.Code.Data.Nat.Properties.d_n'8804'1'43'n_2844
                                          (Integer -> Any
forall a b. a -> b
coe Integer
v4))))
                          MAlonzo.Code.Data.Nat.Base.C_s'8804's_34 T__'8804'__22
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
                                 (((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 -> Any -> Any
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_begin__46
                                    ((T_IsPreorder_70
 -> (Any -> Any -> Any -> Any)
 -> Any
 -> Any
 -> T__IsRelatedTo__78
 -> Any)
-> Any -> (Any -> Any -> Any -> Any) -> Any
forall a b. a -> b
coe
                                       T_IsPreorder_70
-> (Any -> Any -> Any -> Any)
-> Any
-> Any
-> T__IsRelatedTo__78
-> Any
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_start_96
                                       (T_IsPreorder_70 -> Any
forall a b. a -> b
coe T_IsPreorder_70
d_'8804''45'isPreorder_2800)
                                       (\ Any
v10 Any
v11 Any
v12 -> (T__'60'__50 -> T__'8804'__26) -> Any -> Any
forall a b. a -> b
coe T__'60'__50 -> T__'8804'__26
du_'60''8658''8804'_2846 Any
v12))
                                    (((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'_292
                                       (\ Any
v10 ->
                                          Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'8854'__258
                                            (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'__298
                                       (\ Any
v10 Any
v11 -> Any
v11)
                                       (\ Any
v10 ->
                                          Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'8854'__258
                                            (Any -> Integer
forall a b. a -> b
coe Any
v10) (Integer -> Integer
forall a b. a -> b
coe Integer
v0))
                                       Integer
v1 Integer
v2)
                                    (((Any -> Any -> Any -> T__'8801'__12 -> Any -> Any)
 -> Any -> Any -> Any -> Any -> T__'8801'__12 -> Any)
-> (Any -> Any -> Any -> Any -> Any -> Any)
-> Integer
-> Integer
-> Any
-> Any
-> Any
-> Any
forall a b. a -> b
coe
                                       (Any -> Any -> Any -> T__'8801'__12 -> Any -> Any)
-> Any -> Any -> Any -> Any -> T__'8801'__12 -> Any
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8801''45''10217'_436
                                       (\ Any
v10 Any
v11 Any
v12 Any
v13 Any
v14 -> Any
v14)
                                       (Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'8854'__258
                                          (Integer -> Integer
forall a b. a -> b
coe Integer
v1) (Integer -> Integer
forall a b. a -> b
coe Integer
v0))
                                       (Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'8854'__258
                                          (Integer -> Integer
forall a b. a -> b
coe Integer
v9) (Integer -> Integer
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'__298
                                          (\ Any
v10 Any
v11 -> Any
v11)
                                          (\ Any
v10 ->
                                             Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'8854'__258
                                               (Any -> Integer
forall a b. a -> b
coe Any
v10) (Integer -> Integer
forall a b. a -> b
coe Integer
v0))
                                          Integer
v1 Integer
v2)
                                       (((Any -> Any -> Any -> Any -> Any -> Any)
 -> Any -> Any -> Any -> Any -> Any -> Any)
-> Any -> Integer -> Integer -> Any -> Any -> T__'8804'__26 -> Any
forall a b. a -> b
coe
                                          (Any -> Any -> Any -> Any -> Any -> Any)
-> Any -> Any -> Any -> Any -> Any -> Any
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8804'_308
                                          ((T_IsPreorder_70
 -> (Any -> Any -> Any -> Any -> Any -> Any)
 -> Any
 -> Any
 -> Any
 -> Any
 -> T__IsRelatedTo__78
 -> T__IsRelatedTo__78)
-> 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
-> Any
-> T__IsRelatedTo__78
-> T__IsRelatedTo__78
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_'8804''45'go_138
                                             (T_IsPreorder_70 -> Any
forall a b. a -> b
coe T_IsPreorder_70
d_'8804''45'isPreorder_2800)
                                             (\ 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_2958 Any
v13 Any
v14))
                                          (Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'8854'__258
                                             (Integer -> Integer
forall a b. a -> b
coe Integer
v9) (Integer -> Integer
forall a b. a -> b
coe Integer
v4))
                                          (Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'8854'__258
                                             (Integer -> Integer
forall a b. a -> b
coe Integer
v5) (Integer -> Integer
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'__298
                                             (\ Any
v10 Any
v11 -> Any
v11)
                                             (\ Any
v10 ->
                                                Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'8854'__258
                                                  (Any -> Integer
forall a b. a -> b
coe Any
v10) (Integer -> Integer
forall a b. a -> b
coe Integer
v0))
                                             Integer
v1 Integer
v2)
                                          (((Any -> Any -> Any -> T__'8801'__12 -> Any -> Any)
 -> Any -> Any -> Any -> Any -> T__'8801'__12 -> Any)
-> (Any -> Any -> Any -> Any -> Any -> Any)
-> Integer
-> Integer
-> Any
-> Any
-> Any
-> Any
forall a b. a -> b
coe
                                             (Any -> Any -> Any -> T__'8801'__12 -> Any -> Any)
-> Any -> Any -> Any -> Any -> T__'8801'__12 -> Any
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8801''45''10216'_448
                                             (\ Any
v10 Any
v11 Any
v12 Any
v13 Any
v14 -> Any
v14)
                                             (Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'8854'__258
                                                (Integer -> Integer
forall a b. a -> b
coe Integer
v5) (Integer -> Integer
forall a b. a -> b
coe Integer
v4))
                                             (Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'8854'__258
                                                (Integer -> Integer
forall a b. a -> b
coe Integer
v2) (Integer -> Integer
forall a b. a -> b
coe Integer
v0))
                                             (((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'__298
                                                (\ Any
v10 Any
v11 -> Any
v11)
                                                (\ Any
v10 ->
                                                   Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'8854'__258
                                                     (Any -> Integer
forall a b. a -> b
coe Any
v10) (Integer -> Integer
forall a b. a -> b
coe Integer
v0))
                                                Integer
v1 Integer
v2)
                                             (((Any -> Any) -> Any -> Any) -> Any -> Any -> Any
forall a b. a -> b
coe
                                                (Any -> Any) -> Any -> Any
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du__'8718'_492
                                                ((T_IsPreorder_70 -> Any -> T__IsRelatedTo__78) -> Any -> Any
forall a b. a -> b
coe
                                                   T_IsPreorder_70 -> Any -> T__IsRelatedTo__78
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_stop_166
                                                   (T_IsPreorder_70 -> Any
forall a b. a -> b
coe T_IsPreorder_70
d_'8804''45'isPreorder_2800))
                                                ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe
                                                   Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'8854'__258
                                                   (Integer -> Any
forall a b. a -> b
coe Integer
v2) (Integer -> Any
forall a b. a -> b
coe Integer
v0)))
                                             Any
forall a. a
erased)
                                          (Integer -> Integer -> Integer -> T__'8804'__22 -> T__'8804'__26
d_'8854''45'mono'737''45''8804'_4056
                                             (Integer -> Integer
forall a b. a -> b
coe Integer
v4) (Integer -> Integer
forall a b. a -> b
coe Integer
v9) (Integer -> Integer
forall a b. a -> b
coe Integer
v5) (T__'8804'__22 -> T__'8804'__22
forall a b. a -> b
coe T__'8804'__22
v8)))
                                       Any
forall a. a
erased))
                          T__'8804'__22
_ -> Any
forall a. a
MAlonzo.RTE.mazUnreachableError))
-- Data.Integer.Properties.⊖-monoʳ->-<
d_'8854''45'mono'691''45''62''45''60'_4086 ::
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Integer.Base.T__'60'__50
d_'8854''45'mono'691''45''62''45''60'_4086 :: Integer -> Integer -> Integer -> T__'8804'__22 -> T__'60'__50
d_'8854''45'mono'691''45''62''45''60'_4086 Integer
v0 Integer
v1 Integer
v2 T__'8804'__22
v3
  = case Integer -> Integer
forall a b. a -> b
coe Integer
v0 of
      Integer
0 -> case T__'8804'__22 -> T__'8804'__22
forall a b. a -> b
coe T__'8804'__22
v3 of
             MAlonzo.Code.Data.Nat.Base.C_s'8804's_34 T__'8804'__22
v6
               -> case T__'8804'__22 -> T__'8804'__22
forall a b. a -> b
coe T__'8804'__22
v6 of
                    T__'8804'__22
MAlonzo.Code.Data.Nat.Base.C_z'8804'n_26
                      -> 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_34 T__'8804'__22
v9
                      -> (T__'8804'__22 -> T__'60'__50) -> Any -> T__'60'__50
forall a b. a -> b
coe
                           T__'8804'__22 -> T__'60'__50
MAlonzo.Code.Data.Integer.Base.C_'45''60''45'_58
                           ((T__'8804'__22 -> T__'8804'__22) -> T__'8804'__22 -> Any
forall a b. a -> b
coe T__'8804'__22 -> T__'8804'__22
MAlonzo.Code.Data.Nat.Base.C_s'8804's_34 T__'8804'__22
v9)
                    T__'8804'__22
_ -> T__'60'__50
forall a. a
MAlonzo.RTE.mazUnreachableError
             T__'8804'__22
_ -> 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'__22 -> T__'8804'__22
forall a b. a -> b
coe T__'8804'__22
v3 of
                   MAlonzo.Code.Data.Nat.Base.C_s'8804's_34 T__'8804'__22
v8
                     -> case T__'8804'__22 -> T__'8804'__22
forall a b. a -> b
coe T__'8804'__22
v8 of
                          T__'8804'__22
MAlonzo.Code.Data.Nat.Base.C_z'8804'n_26
                            -> let v10 :: b
v10
                                     = T_SubRelation_60 -> b
forall a b. a -> b
coe
                                         T_SubRelation_60
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_strictRelation_202 in
                               Any -> Any
forall a b. a -> b
coe
                                 ((T_SubRelation_60 -> Any -> Any -> Any -> Any)
-> Any -> Any -> Any -> Any -> Any
forall a b. a -> b
coe
                                    T_SubRelation_60 -> Any -> Any -> Any -> Any
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_begin__126
                                    (Any -> Any
forall a b. a -> b
coe Any
forall a. a
v10)
                                    ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe
                                       Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'8854'__258 (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)
                                    (((Any -> Any -> Any -> T__'8801'__12 -> Any -> Any)
 -> Any -> Any -> Any -> Any -> T__'8801'__12 -> Any)
-> (Any -> Any -> Any -> Any -> Any -> Any)
-> Integer
-> Integer
-> Integer
-> Any
-> Any
-> Any
forall a b. a -> b
coe
                                       (Any -> Any -> Any -> T__'8801'__12 -> Any -> Any)
-> Any -> Any -> Any -> Any -> T__'8801'__12 -> Any
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8801''45''10217'_436
                                       (\ Any
v11 Any
v12 Any
v13 Any
v14 Any
v15 -> Any
v15)
                                       (Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'8854'__258
                                          (Integer -> Integer
forall a b. a -> b
coe Integer
v0) (Integer -> Integer
forall a b. a -> b
coe Integer
v1))
                                       (Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'8854'__258
                                          (Integer -> Integer
forall a b. a -> b
coe Integer
v4) (Integer -> Integer
forall a b. a -> b
coe Integer
v5))
                                       Integer
v0
                                       (((Any -> Any -> Any -> Any -> Any -> Any)
 -> Any -> Any -> Any -> Any -> Any -> Any)
-> Any
-> Integer
-> Integer
-> Integer
-> Any
-> T__'60'__50
-> Any
forall a b. a -> b
coe
                                          (Any -> Any -> Any -> Any -> Any -> Any)
-> Any -> Any -> Any -> Any -> Any -> Any
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''60'_312
                                          (((Any -> Any -> Any -> Any -> Any -> Any)
 -> T_Σ_14
 -> (Any -> Any -> Any -> Any -> Any -> Any)
 -> Any
 -> Any
 -> Any
 -> Any
 -> T__IsRelatedTo__78
 -> T__IsRelatedTo__78)
-> (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
-> Any
-> T__IsRelatedTo__78
-> T__IsRelatedTo__78
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_'60''45'go_152
                                             (\ Any
v11 Any
v12 Any
v13 Any
v14 Any
v15 ->
                                                (T__'60'__50 -> T__'60'__50 -> T__'60'__50) -> Any -> Any -> Any
forall a b. a -> b
coe T__'60'__50 -> T__'60'__50 -> T__'60'__50
du_'60''45'trans_2986 Any
v14 Any
v15)
                                             (T_Σ_14 -> Any
forall a b. a -> b
coe
                                                T_Σ_14
MAlonzo.Code.Relation.Binary.PropositionalEquality.Core.du_resp'8322'_160)
                                             (\ Any
v11 Any
v12 Any
v13 Any
v14 Any
v15 ->
                                                (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_2972 Any
v14 Any
v15))
                                          (Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'8854'__258
                                             (Integer -> Integer
forall a b. a -> b
coe Integer
v4) (Integer -> Integer
forall a b. a -> b
coe Integer
v5))
                                          Integer
v0 Integer
v0
                                          (((Any -> Any) -> Any -> Any) -> Any -> Any -> Any
forall a b. a -> b
coe
                                             (Any -> Any) -> Any -> Any
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du__'8718'_492
                                             ((T_IsPreorder_70 -> Any -> T__IsRelatedTo__78) -> Any -> Any
forall a b. a -> b
coe
                                                T_IsPreorder_70 -> Any -> T__IsRelatedTo__78
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_stop_166
                                                (T_IsPreorder_70 -> Any
forall a b. a -> b
coe T_IsPreorder_70
d_'8804''45'isPreorder_2800))
                                             (Integer -> Any
forall a b. a -> b
coe Integer
v0))
                                          (Integer -> Integer -> T__'60'__50
d_m'8854'n'60'1'43'm_3930 (Integer -> Integer
forall a b. a -> b
coe Integer
v4) (Integer -> Integer
forall a b. a -> b
coe Integer
v5)))
                                       Any
forall a. a
erased))
                          MAlonzo.Code.Data.Nat.Base.C_s'8804's_34 T__'8804'__22
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
                                 (let v13 :: b
v13
                                        = T_SubRelation_60 -> b
forall a b. a -> b
coe
                                            T_SubRelation_60
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_strictRelation_202 in
                                  Any -> Any
forall a b. a -> b
coe
                                    ((T_SubRelation_60 -> Any -> Any -> Any -> Any)
-> Any -> Any -> Any -> Any -> Any
forall a b. a -> b
coe
                                       T_SubRelation_60 -> Any -> Any -> Any -> Any
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_begin__126
                                       (Any -> Any
forall a b. a -> b
coe Any
forall a. a
v13)
                                       ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe
                                          Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'8854'__258 (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__'8854'__258 (Integer -> Any
forall a b. a -> b
coe Integer
v0)
                                          (Integer -> Any
forall a b. a -> b
coe Integer
v2))
                                       (((Any -> Any -> Any -> T__'8801'__12 -> Any -> Any)
 -> Any -> Any -> Any -> Any -> T__'8801'__12 -> Any)
-> (Any -> Any -> Any -> Any -> Any -> Any)
-> Integer
-> Integer
-> Integer
-> Any
-> Any
-> Any
forall a b. a -> b
coe
                                          (Any -> Any -> Any -> T__'8801'__12 -> Any -> Any)
-> Any -> Any -> Any -> Any -> T__'8801'__12 -> Any
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8801''45''10217'_436
                                          (\ Any
v14 Any
v15 Any
v16 Any
v17 Any
v18 -> Any
v18)
                                          (Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'8854'__258
                                             (Integer -> Integer
forall a b. a -> b
coe Integer
v0) (Integer -> Integer
forall a b. a -> b
coe Integer
v1))
                                          (Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'8854'__258
                                             (Integer -> Integer
forall a b. a -> b
coe Integer
v4) ((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
v1) (Integer -> Any
forall a b. a -> b
coe (Integer
1 :: Integer))))
                                          (Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'8854'__258
                                             (Integer -> Integer
forall a b. a -> b
coe Integer
v0) (Integer -> Integer
forall a b. a -> b
coe Integer
v2))
                                          (((Any -> Any -> Any -> Any -> Any -> Any)
 -> Any -> Any -> Any -> Any -> Any -> Any)
-> Any
-> Integer
-> Integer
-> Integer
-> Any
-> T__'60'__50
-> Any
forall a b. a -> b
coe
                                             (Any -> Any -> Any -> Any -> Any -> Any)
-> Any -> Any -> Any -> Any -> Any -> Any
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''60'_312
                                             (((Any -> Any -> Any -> Any -> Any -> Any)
 -> T_Σ_14
 -> (Any -> Any -> Any -> Any -> Any -> Any)
 -> Any
 -> Any
 -> Any
 -> Any
 -> T__IsRelatedTo__78
 -> T__IsRelatedTo__78)
-> (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
-> Any
-> T__IsRelatedTo__78
-> T__IsRelatedTo__78
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_'60''45'go_152
                                                (\ Any
v14 Any
v15 Any
v16 Any
v17 Any
v18 ->
                                                   (T__'60'__50 -> T__'60'__50 -> T__'60'__50) -> Any -> Any -> Any
forall a b. a -> b
coe T__'60'__50 -> T__'60'__50 -> T__'60'__50
du_'60''45'trans_2986 Any
v17 Any
v18)
                                                (T_Σ_14 -> Any
forall a b. a -> b
coe
                                                   T_Σ_14
MAlonzo.Code.Relation.Binary.PropositionalEquality.Core.du_resp'8322'_160)
                                                (\ Any
v14 Any
v15 Any
v16 Any
v17 Any
v18 ->
                                                   (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_2972 Any
v17 Any
v18))
                                             (Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'8854'__258
                                                (Integer -> Integer
forall a b. a -> b
coe Integer
v4) ((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
v1) (Integer -> Any
forall a b. a -> b
coe (Integer
1 :: Integer))))
                                             (Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'8854'__258
                                                (Integer -> Integer
forall a b. a -> b
coe Integer
v4) (Integer -> Integer
forall a b. a -> b
coe Integer
v12))
                                             (Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'8854'__258
                                                (Integer -> Integer
forall a b. a -> b
coe Integer
v0) (Integer -> Integer
forall a b. a -> b
coe Integer
v2))
                                             (((Any -> Any -> Any -> T__'8801'__12 -> Any -> Any)
 -> Any -> Any -> Any -> Any -> T__'8801'__12 -> Any)
-> (Any -> Any -> Any -> Any -> Any -> Any)
-> Integer
-> Integer
-> Integer
-> Any
-> Any
-> Any
forall a b. a -> b
coe
                                                (Any -> Any -> Any -> T__'8801'__12 -> Any -> Any)
-> Any -> Any -> Any -> Any -> T__'8801'__12 -> Any
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8801''45''10216'_448
                                                (\ Any
v14 Any
v15 Any
v16 Any
v17 Any
v18 -> Any
v18)
                                                (Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'8854'__258
                                                   (Integer -> Integer
forall a b. a -> b
coe Integer
v4) (Integer -> Integer
forall a b. a -> b
coe Integer
v12))
                                                (Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'8854'__258
                                                   (Integer -> Integer
forall a b. a -> b
coe Integer
v0) (Integer -> Integer
forall a b. a -> b
coe Integer
v2))
                                                (Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'8854'__258
                                                   (Integer -> Integer
forall a b. a -> b
coe Integer
v0) (Integer -> Integer
forall a b. a -> b
coe Integer
v2))
                                                (((Any -> Any) -> Any -> Any) -> Any -> Any -> Any
forall a b. a -> b
coe
                                                   (Any -> Any) -> Any -> Any
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du__'8718'_492
                                                   ((T_IsPreorder_70 -> Any -> T__IsRelatedTo__78) -> Any -> Any
forall a b. a -> b
coe
                                                      T_IsPreorder_70 -> Any -> T__IsRelatedTo__78
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_stop_166
                                                      (T_IsPreorder_70 -> Any
forall a b. a -> b
coe T_IsPreorder_70
d_'8804''45'isPreorder_2800))
                                                   ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe
                                                      Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'8854'__258
                                                      (Integer -> Any
forall a b. a -> b
coe Integer
v0) (Integer -> Any
forall a b. a -> b
coe Integer
v2)))
                                                Any
forall a. a
erased)
                                             (Integer -> Integer -> Integer -> T__'8804'__22 -> T__'60'__50
d_'8854''45'mono'691''45''62''45''60'_4086
                                                (Integer -> Integer
forall a b. a -> b
coe Integer
v4) ((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
v1) (Integer -> Any
forall a b. a -> b
coe (Integer
1 :: Integer)))
                                                (Integer -> Integer
forall a b. a -> b
coe Integer
v12)
                                                ((T__'8804'__22 -> T__'8804'__22) -> T__'8804'__22 -> T__'8804'__22
forall a b. a -> b
coe T__'8804'__22 -> T__'8804'__22
MAlonzo.Code.Data.Nat.Base.C_s'8804's_34 T__'8804'__22
v11)))
                                          Any
forall a. a
erased)))
                          T__'8804'__22
_ -> Any
forall a. a
MAlonzo.RTE.mazUnreachableError
                   T__'8804'__22
_ -> Any
forall a. a
MAlonzo.RTE.mazUnreachableError))
-- Data.Integer.Properties.⊖-monoˡ-<
d_'8854''45'mono'737''45''60'_4114 ::
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Integer.Base.T__'60'__50
d_'8854''45'mono'737''45''60'_4114 :: Integer -> Integer -> Integer -> T__'8804'__22 -> T__'60'__50
d_'8854''45'mono'737''45''60'_4114 Integer
v0 Integer
v1 Integer
v2 T__'8804'__22
v3
  = case Integer -> Integer
forall a b. a -> b
coe Integer
v0 of
      Integer
0 -> (T__'8804'__22 -> T__'60'__50) -> T__'8804'__22 -> T__'60'__50
forall a b. a -> b
coe T__'8804'__22 -> T__'60'__50
MAlonzo.Code.Data.Integer.Base.C_'43''60''43'_72 T__'8804'__22
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
             (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'__22 -> T__'8804'__22
forall a b. a -> b
coe T__'8804'__22
v3 of
                   MAlonzo.Code.Data.Nat.Base.C_s'8804's_34 T__'8804'__22
v8
                     -> case T__'8804'__22 -> T__'8804'__22
forall a b. a -> b
coe T__'8804'__22
v8 of
                          T__'8804'__22
MAlonzo.Code.Data.Nat.Base.C_z'8804'n_26
                            -> let v10 :: b
v10
                                     = T_SubRelation_60 -> b
forall a b. a -> b
coe
                                         T_SubRelation_60
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_strictRelation_202 in
                               Any -> Any
forall a b. a -> b
coe
                                 ((T_SubRelation_60 -> Any -> Any -> Any -> Any)
-> Any -> Any -> Any -> Any -> Any
forall a b. a -> b
coe
                                    T_SubRelation_60 -> Any -> Any -> Any -> Any
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_begin__126
                                    (Any -> Any
forall a b. a -> b
coe Any
forall a. a
v10) ((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'__258 (Integer -> Any
forall a b. a -> b
coe Integer
v2)
                                       (Integer -> Any
forall a b. a -> b
coe Integer
v0))
                                    (((Any -> Any -> Any -> Any -> Any -> Any)
 -> Any -> Any -> Any -> Any -> Any -> Any)
-> Any
-> Integer
-> Integer
-> Integer
-> Any
-> T__'60'__50
-> Any
forall a b. a -> b
coe
                                       (Any -> Any -> Any -> Any -> Any -> Any)
-> Any -> Any -> Any -> Any -> Any -> Any
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''60'_312
                                       (((Any -> Any -> Any -> Any -> Any -> Any)
 -> T_Σ_14
 -> (Any -> Any -> Any -> Any -> Any -> Any)
 -> Any
 -> Any
 -> Any
 -> Any
 -> T__IsRelatedTo__78
 -> T__IsRelatedTo__78)
-> (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
-> Any
-> T__IsRelatedTo__78
-> T__IsRelatedTo__78
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_'60''45'go_152
                                          (\ Any
v11 Any
v12 Any
v13 Any
v14 Any
v15 ->
                                             (T__'60'__50 -> T__'60'__50 -> T__'60'__50) -> Any -> Any -> Any
forall a b. a -> b
coe T__'60'__50 -> T__'60'__50 -> T__'60'__50
du_'60''45'trans_2986 Any
v14 Any
v15)
                                          (T_Σ_14 -> Any
forall a b. a -> b
coe
                                             T_Σ_14
MAlonzo.Code.Relation.Binary.PropositionalEquality.Core.du_resp'8322'_160)
                                          (\ Any
v11 Any
v12 Any
v13 Any
v14 Any
v15 ->
                                             (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_2972 Any
v14 Any
v15))
                                       (Integer -> Integer -> Integer
subInt (Integer -> Integer
forall a b. a -> b
coe (Integer
0 :: Integer)) (Integer -> Integer
forall a b. a -> b
coe Integer
v0))
                                       (Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'8854'__258
                                          (Integer -> Integer
forall a b. a -> b
coe Integer
v5) (Integer -> Integer
forall a b. a -> b
coe Integer
v4))
                                       (Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'8854'__258
                                          (Integer -> Integer
forall a b. a -> b
coe Integer
v2) (Integer -> Integer
forall a b. a -> b
coe Integer
v0))
                                       (((Any -> Any -> Any -> T__'8801'__12 -> Any -> Any)
 -> Any -> Any -> Any -> Any -> T__'8801'__12 -> Any)
-> (Any -> Any -> Any -> Any -> Any -> Any)
-> Integer
-> Integer
-> Integer
-> Any
-> Any
-> Any
forall a b. a -> b
coe
                                          (Any -> Any -> Any -> T__'8801'__12 -> Any -> Any)
-> Any -> Any -> Any -> Any -> T__'8801'__12 -> Any
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8801''45''10216'_448
                                          (\ Any
v11 Any
v12 Any
v13 Any
v14 Any
v15 -> Any
v15)
                                          (Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'8854'__258
                                             (Integer -> Integer
forall a b. a -> b
coe Integer
v5) (Integer -> Integer
forall a b. a -> b
coe Integer
v4))
                                          (Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'8854'__258
                                             (Integer -> Integer
forall a b. a -> b
coe Integer
v2) (Integer -> Integer
forall a b. a -> b
coe Integer
v0))
                                          (Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'8854'__258
                                             (Integer -> Integer
forall a b. a -> b
coe Integer
v2) (Integer -> Integer
forall a b. a -> b
coe Integer
v0))
                                          (((Any -> Any) -> Any -> Any) -> Any -> Any -> Any
forall a b. a -> b
coe
                                             (Any -> Any) -> Any -> Any
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du__'8718'_492
                                             ((T_IsPreorder_70 -> Any -> T__IsRelatedTo__78) -> Any -> Any
forall a b. a -> b
coe
                                                T_IsPreorder_70 -> Any -> T__IsRelatedTo__78
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_stop_166
                                                (T_IsPreorder_70 -> Any
forall a b. a -> b
coe T_IsPreorder_70
d_'8804''45'isPreorder_2800))
                                             ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe
                                                Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'8854'__258
                                                (Integer -> Any
forall a b. a -> b
coe Integer
v2) (Integer -> Any
forall a b. a -> b
coe Integer
v0)))
                                          Any
forall a. a
erased)
                                       (Integer -> Integer -> T__'60'__50
d_'45'1'43'm'60'n'8854'm_3958 (Integer -> Integer
forall a b. a -> b
coe Integer
v4) (Integer -> Integer
forall a b. a -> b
coe Integer
v5))))
                          MAlonzo.Code.Data.Nat.Base.C_s'8804's_34 T__'8804'__22
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
                                 (let v13 :: b
v13
                                        = T_SubRelation_60 -> b
forall a b. a -> b
coe
                                            T_SubRelation_60
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_strictRelation_202 in
                                  Any -> Any
forall a b. a -> b
coe
                                    ((T_SubRelation_60 -> Any -> Any -> Any -> Any)
-> Any -> Any -> Any -> Any -> Any
forall a b. a -> b
coe
                                       T_SubRelation_60 -> Any -> Any -> Any -> Any
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_begin__126
                                       (Any -> Any
forall a b. a -> b
coe Any
forall a. a
v13)
                                       ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe
                                          Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'8854'__258 (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__'8854'__258 (Integer -> Any
forall a b. a -> b
coe Integer
v2)
                                          (Integer -> Any
forall a b. a -> b
coe Integer
v0))
                                       (((Any -> Any -> Any -> T__'8801'__12 -> Any -> Any)
 -> Any -> Any -> Any -> Any -> T__'8801'__12 -> Any)
-> (Any -> Any -> Any -> Any -> Any -> Any)
-> Integer
-> Integer
-> Integer
-> Any
-> Any
-> Any
forall a b. a -> b
coe
                                          (Any -> Any -> Any -> T__'8801'__12 -> Any -> Any)
-> Any -> Any -> Any -> Any -> T__'8801'__12 -> Any
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8801''45''10217'_436
                                          (\ Any
v14 Any
v15 Any
v16 Any
v17 Any
v18 -> Any
v18)
                                          (Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'8854'__258
                                             (Integer -> Integer
forall a b. a -> b
coe Integer
v1) (Integer -> Integer
forall a b. a -> b
coe Integer
v0))
                                          (Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'8854'__258
                                             (Integer -> Integer
forall a b. a -> b
coe Integer
v12) (Integer -> Integer
forall a b. a -> b
coe Integer
v4))
                                          (Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'8854'__258
                                             (Integer -> Integer
forall a b. a -> b
coe Integer
v2) (Integer -> Integer
forall a b. a -> b
coe Integer
v0))
                                          (((Any -> Any -> Any -> Any -> Any -> Any)
 -> Any -> Any -> Any -> Any -> Any -> Any)
-> Any
-> Integer
-> Integer
-> Integer
-> Any
-> T__'60'__50
-> Any
forall a b. a -> b
coe
                                             (Any -> Any -> Any -> Any -> Any -> Any)
-> Any -> Any -> Any -> Any -> Any -> Any
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''60'_312
                                             (((Any -> Any -> Any -> Any -> Any -> Any)
 -> T_Σ_14
 -> (Any -> Any -> Any -> Any -> Any -> Any)
 -> Any
 -> Any
 -> Any
 -> Any
 -> T__IsRelatedTo__78
 -> T__IsRelatedTo__78)
-> (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
-> Any
-> T__IsRelatedTo__78
-> T__IsRelatedTo__78
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_'60''45'go_152
                                                (\ Any
v14 Any
v15 Any
v16 Any
v17 Any
v18 ->
                                                   (T__'60'__50 -> T__'60'__50 -> T__'60'__50) -> Any -> Any -> Any
forall a b. a -> b
coe T__'60'__50 -> T__'60'__50 -> T__'60'__50
du_'60''45'trans_2986 Any
v17 Any
v18)
                                                (T_Σ_14 -> Any
forall a b. a -> b
coe
                                                   T_Σ_14
MAlonzo.Code.Relation.Binary.PropositionalEquality.Core.du_resp'8322'_160)
                                                (\ Any
v14 Any
v15 Any
v16 Any
v17 Any
v18 ->
                                                   (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_2972 Any
v17 Any
v18))
                                             (Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'8854'__258
                                                (Integer -> Integer
forall a b. a -> b
coe Integer
v12) (Integer -> Integer
forall a b. a -> b
coe Integer
v4))
                                             (Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'8854'__258
                                                ((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
v2) (Integer -> Any
forall a b. a -> b
coe (Integer
1 :: Integer))) (Integer -> Integer
forall a b. a -> b
coe Integer
v4))
                                             (Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'8854'__258
                                                (Integer -> Integer
forall a b. a -> b
coe Integer
v2) (Integer -> Integer
forall a b. a -> b
coe Integer
v0))
                                             (((Any -> Any -> Any -> T__'8801'__12 -> Any -> Any)
 -> Any -> Any -> Any -> Any -> T__'8801'__12 -> Any)
-> (Any -> Any -> Any -> Any -> Any -> Any)
-> Integer
-> Integer
-> Integer
-> Any
-> Any
-> Any
forall a b. a -> b
coe
                                                (Any -> Any -> Any -> T__'8801'__12 -> Any -> Any)
-> Any -> Any -> Any -> Any -> T__'8801'__12 -> Any
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8801''45''10216'_448
                                                (\ Any
v14 Any
v15 Any
v16 Any
v17 Any
v18 -> Any
v18)
                                                (Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'8854'__258
                                                   ((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
v2) (Integer -> Any
forall a b. a -> b
coe (Integer
1 :: Integer)))
                                                   (Integer -> Integer
forall a b. a -> b
coe Integer
v4))
                                                (Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'8854'__258
                                                   (Integer -> Integer
forall a b. a -> b
coe Integer
v2) (Integer -> Integer
forall a b. a -> b
coe Integer
v0))
                                                (Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'8854'__258
                                                   (Integer -> Integer
forall a b. a -> b
coe Integer
v2) (Integer -> Integer
forall a b. a -> b
coe Integer
v0))
                                                (((Any -> Any) -> Any -> Any) -> Any -> Any -> Any
forall a b. a -> b
coe
                                                   (Any -> Any) -> Any -> Any
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du__'8718'_492
                                                   ((T_IsPreorder_70 -> Any -> T__IsRelatedTo__78) -> Any -> Any
forall a b. a -> b
coe
                                                      T_IsPreorder_70 -> Any -> T__IsRelatedTo__78
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_stop_166
                                                      (T_IsPreorder_70 -> Any
forall a b. a -> b
coe T_IsPreorder_70
d_'8804''45'isPreorder_2800))
                                                   ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe
                                                      Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'8854'__258
                                                      (Integer -> Any
forall a b. a -> b
coe Integer
v2) (Integer -> Any
forall a b. a -> b
coe Integer
v0)))
                                                Any
forall a. a
erased)
                                             (Integer -> Integer -> Integer -> T__'8804'__22 -> T__'60'__50
d_'8854''45'mono'737''45''60'_4114
                                                (Integer -> Integer
forall a b. a -> b
coe Integer
v4) (Integer -> Integer
forall a b. a -> b
coe Integer
v12)
                                                ((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
v2) (Integer -> Any
forall a b. a -> b
coe (Integer
1 :: Integer)))
                                                ((T__'8804'__22 -> T__'8804'__22) -> T__'8804'__22 -> T__'8804'__22
forall a b. a -> b
coe T__'8804'__22 -> T__'8804'__22
MAlonzo.Code.Data.Nat.Base.C_s'8804's_34 T__'8804'__22
v11)))
                                          Any
forall a. a
erased)))
                          T__'8804'__22
_ -> Any
forall a. a
MAlonzo.RTE.mazUnreachableError
                   T__'8804'__22
_ -> Any
forall a. a
MAlonzo.RTE.mazUnreachableError))
-- Data.Integer.Properties.+-comm
d_'43''45'comm_4138 ::
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'43''45'comm_4138 :: Integer -> Integer -> T__'8801'__12
d_'43''45'comm_4138 = Integer -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.+-identityˡ
d_'43''45'identity'737'_4148 ::
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'43''45'identity'737'_4148 :: Integer -> T__'8801'__12
d_'43''45'identity'737'_4148 = Integer -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.+-identityʳ
d_'43''45'identity'691'_4150 ::
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'43''45'identity'691'_4150 :: Integer -> T__'8801'__12
d_'43''45'identity'691'_4150 = Integer -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.+-identity
d_'43''45'identity_4152 :: MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'43''45'identity_4152 :: T_Σ_14
d_'43''45'identity_4152
  = (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_4160 ::
  Integer ->
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_distrib'737''45''8854''45''43''45'pos_4160 :: Integer -> Integer -> Integer -> T__'8801'__12
d_distrib'737''45''8854''45''43''45'pos_4160 = Integer -> Integer -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.distribˡ-⊖-+-neg
d_distrib'737''45''8854''45''43''45'neg_4180 ::
  Integer ->
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_distrib'737''45''8854''45''43''45'neg_4180 :: Integer -> Integer -> Integer -> T__'8801'__12
d_distrib'737''45''8854''45''43''45'neg_4180 = Integer -> Integer -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.distribʳ-⊖-+-pos
d_distrib'691''45''8854''45''43''45'pos_4200 ::
  Integer ->
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_distrib'691''45''8854''45''43''45'pos_4200 :: Integer -> Integer -> Integer -> T__'8801'__12
d_distrib'691''45''8854''45''43''45'pos_4200 = Integer -> Integer -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.distribʳ-⊖-+-neg
d_distrib'691''45''8854''45''43''45'neg_4220 ::
  Integer ->
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_distrib'691''45''8854''45''43''45'neg_4220 :: Integer -> Integer -> Integer -> T__'8801'__12
d_distrib'691''45''8854''45''43''45'neg_4220 = Integer -> Integer -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.+-assoc
d_'43''45'assoc_4234 ::
  Integer ->
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'43''45'assoc_4234 :: Integer -> Integer -> Integer -> T__'8801'__12
d_'43''45'assoc_4234 = Integer -> Integer -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.+-inverseˡ
d_'43''45'inverse'737'_4414 ::
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'43''45'inverse'737'_4414 :: Integer -> T__'8801'__12
d_'43''45'inverse'737'_4414 = Integer -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.+-inverseʳ
d_'43''45'inverse'691'_4420 ::
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'43''45'inverse'691'_4420 :: Integer -> T__'8801'__12
d_'43''45'inverse'691'_4420 = Integer -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.+-inverse
d_'43''45'inverse_4422 :: MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'43''45'inverse_4422 :: T_Σ_14
d_'43''45'inverse_4422
  = (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_4424 ::
  MAlonzo.Code.Algebra.Structures.T_IsMagma_176
d_'43''45'isMagma_4424 :: T_IsMagma_176
d_'43''45'isMagma_4424
  = (T_IsEquivalence_26
 -> (Any -> Any -> Any -> Any -> Any -> Any -> Any)
 -> T_IsMagma_176)
-> Any -> Any -> T_IsMagma_176
forall a b. a -> b
coe
      T_IsEquivalence_26
-> (Any -> Any -> Any -> Any -> Any -> Any -> Any) -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.C_IsMagma'46'constructor_1867
      (T_IsEquivalence_26 -> Any
forall a b. a -> b
coe
         T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.PropositionalEquality.Properties.du_isEquivalence_396)
      Any
forall a. a
erased
-- Data.Integer.Properties.+-isSemigroup
d_'43''45'isSemigroup_4426 ::
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_472
d_'43''45'isSemigroup_4426 :: T_IsSemigroup_472
d_'43''45'isSemigroup_4426
  = (T_IsMagma_176 -> (Any -> Any -> Any -> Any) -> T_IsSemigroup_472)
-> Any -> Any -> T_IsSemigroup_472
forall a b. a -> b
coe
      T_IsMagma_176 -> (Any -> Any -> Any -> Any) -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.C_IsSemigroup'46'constructor_10417
      (T_IsMagma_176 -> Any
forall a b. a -> b
coe T_IsMagma_176
d_'43''45'isMagma_4424) Any
forall a. a
erased
-- Data.Integer.Properties.+-isCommutativeSemigroup
d_'43''45'isCommutativeSemigroup_4428 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_548
d_'43''45'isCommutativeSemigroup_4428 :: T_IsCommutativeSemigroup_548
d_'43''45'isCommutativeSemigroup_4428
  = (T_IsSemigroup_472
 -> (Any -> Any -> Any) -> T_IsCommutativeSemigroup_548)
-> Any -> Any -> T_IsCommutativeSemigroup_548
forall a b. a -> b
coe
      T_IsSemigroup_472
-> (Any -> Any -> Any) -> T_IsCommutativeSemigroup_548
MAlonzo.Code.Algebra.Structures.C_IsCommutativeSemigroup'46'constructor_12093
      (T_IsSemigroup_472 -> Any
forall a b. a -> b
coe T_IsSemigroup_472
d_'43''45'isSemigroup_4426) Any
forall a. a
erased
-- Data.Integer.Properties.+-0-isMonoid
d_'43''45'0'45'isMonoid_4430 ::
  MAlonzo.Code.Algebra.Structures.T_IsMonoid_686
d_'43''45'0'45'isMonoid_4430 :: T_IsMonoid_686
d_'43''45'0'45'isMonoid_4430
  = (T_IsSemigroup_472 -> T_Σ_14 -> T_IsMonoid_686)
-> Any -> Any -> T_IsMonoid_686
forall a b. a -> b
coe
      T_IsSemigroup_472 -> T_Σ_14 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.C_IsMonoid'46'constructor_15873
      (T_IsSemigroup_472 -> Any
forall a b. a -> b
coe T_IsSemigroup_472
d_'43''45'isSemigroup_4426) (T_Σ_14 -> Any
forall a b. a -> b
coe T_Σ_14
d_'43''45'identity_4152)
-- Data.Integer.Properties.+-0-isCommutativeMonoid
d_'43''45'0'45'isCommutativeMonoid_4432 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMonoid_736
d_'43''45'0'45'isCommutativeMonoid_4432 :: T_IsCommutativeMonoid_736
d_'43''45'0'45'isCommutativeMonoid_4432
  = (T_IsMonoid_686
 -> (Any -> Any -> Any) -> T_IsCommutativeMonoid_736)
-> Any -> Any -> T_IsCommutativeMonoid_736
forall a b. a -> b
coe
      T_IsMonoid_686 -> (Any -> Any -> Any) -> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.C_IsCommutativeMonoid'46'constructor_17695
      (T_IsMonoid_686 -> Any
forall a b. a -> b
coe T_IsMonoid_686
d_'43''45'0'45'isMonoid_4430) Any
forall a. a
erased
-- Data.Integer.Properties.+-0-isGroup
d_'43''45'0'45'isGroup_4434 ::
  MAlonzo.Code.Algebra.Structures.T_IsGroup_1036
d_'43''45'0'45'isGroup_4434 :: T_IsGroup_1036
d_'43''45'0'45'isGroup_4434
  = (T_IsMonoid_686
 -> T_Σ_14 -> (Any -> Any -> Any -> Any) -> T_IsGroup_1036)
-> Any -> Any -> Any -> T_IsGroup_1036
forall a b. a -> b
coe
      T_IsMonoid_686
-> T_Σ_14 -> (Any -> Any -> Any -> Any) -> T_IsGroup_1036
MAlonzo.Code.Algebra.Structures.C_IsGroup'46'constructor_26963
      (T_IsMonoid_686 -> Any
forall a b. a -> b
coe T_IsMonoid_686
d_'43''45'0'45'isMonoid_4430) (T_Σ_14 -> Any
forall a b. a -> b
coe T_Σ_14
d_'43''45'inverse_4422)
      Any
forall a. a
erased
-- Data.Integer.Properties.+-0-isAbelianGroup
d_'43''45'0'45'isAbelianGroup_4436 ::
  MAlonzo.Code.Algebra.Structures.T_IsAbelianGroup_1132
d_'43''45'0'45'isAbelianGroup_4436 :: T_IsAbelianGroup_1132
d_'43''45'0'45'isAbelianGroup_4436
  = (T_IsGroup_1036 -> (Any -> Any -> Any) -> T_IsAbelianGroup_1132)
-> Any -> Any -> T_IsAbelianGroup_1132
forall a b. a -> b
coe
      T_IsGroup_1036 -> (Any -> Any -> Any) -> T_IsAbelianGroup_1132
MAlonzo.Code.Algebra.Structures.C_IsAbelianGroup'46'constructor_32441
      (T_IsGroup_1036 -> Any
forall a b. a -> b
coe T_IsGroup_1036
d_'43''45'0'45'isGroup_4434) Any
forall a. a
erased
-- Data.Integer.Properties.+-magma
d_'43''45'magma_4438 :: MAlonzo.Code.Algebra.Bundles.T_Magma_68
d_'43''45'magma_4438 :: T_Magma_68
d_'43''45'magma_4438
  = ((Any -> Any -> Any) -> T_IsMagma_176 -> T_Magma_68)
-> (Integer -> Integer -> Integer) -> T_IsMagma_176 -> T_Magma_68
forall a b. a -> b
coe
      (Any -> Any -> Any) -> T_IsMagma_176 -> T_Magma_68
MAlonzo.Code.Algebra.Bundles.C_Magma'46'constructor_1279
      Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'43'__276 T_IsMagma_176
d_'43''45'isMagma_4424
-- Data.Integer.Properties.+-semigroup
d_'43''45'semigroup_4440 ::
  MAlonzo.Code.Algebra.Bundles.T_Semigroup_536
d_'43''45'semigroup_4440 :: T_Semigroup_536
d_'43''45'semigroup_4440
  = ((Any -> Any -> Any) -> T_IsSemigroup_472 -> T_Semigroup_536)
-> (Integer -> Integer -> Integer)
-> T_IsSemigroup_472
-> T_Semigroup_536
forall a b. a -> b
coe
      (Any -> Any -> Any) -> T_IsSemigroup_472 -> T_Semigroup_536
MAlonzo.Code.Algebra.Bundles.C_Semigroup'46'constructor_9793
      Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'43'__276
      T_IsSemigroup_472
d_'43''45'isSemigroup_4426
-- Data.Integer.Properties.+-commutativeSemigroup
d_'43''45'commutativeSemigroup_4442 ::
  MAlonzo.Code.Algebra.Bundles.T_CommutativeSemigroup_662
d_'43''45'commutativeSemigroup_4442 :: T_CommutativeSemigroup_662
d_'43''45'commutativeSemigroup_4442
  = ((Any -> Any -> Any)
 -> T_IsCommutativeSemigroup_548 -> T_CommutativeSemigroup_662)
-> (Integer -> Integer -> Integer)
-> T_IsCommutativeSemigroup_548
-> T_CommutativeSemigroup_662
forall a b. a -> b
coe
      (Any -> Any -> Any)
-> T_IsCommutativeSemigroup_548 -> T_CommutativeSemigroup_662
MAlonzo.Code.Algebra.Bundles.C_CommutativeSemigroup'46'constructor_12035
      Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'43'__276
      T_IsCommutativeSemigroup_548
d_'43''45'isCommutativeSemigroup_4428
-- Data.Integer.Properties.+-0-monoid
d_'43''45'0'45'monoid_4444 ::
  MAlonzo.Code.Algebra.Bundles.T_Monoid_882
d_'43''45'0'45'monoid_4444 :: T_Monoid_882
d_'43''45'0'45'monoid_4444
  = ((Any -> Any -> Any) -> Any -> T_IsMonoid_686 -> T_Monoid_882)
-> (Integer -> Integer -> Integer)
-> Integer
-> T_IsMonoid_686
-> T_Monoid_882
forall a b. a -> b
coe
      (Any -> Any -> Any) -> Any -> T_IsMonoid_686 -> T_Monoid_882
MAlonzo.Code.Algebra.Bundles.C_Monoid'46'constructor_16157
      Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'43'__276 (Integer
0 :: Integer)
      T_IsMonoid_686
d_'43''45'0'45'isMonoid_4430
-- Data.Integer.Properties.+-0-commutativeMonoid
d_'43''45'0'45'commutativeMonoid_4446 ::
  MAlonzo.Code.Algebra.Bundles.T_CommutativeMonoid_962
d_'43''45'0'45'commutativeMonoid_4446 :: T_CommutativeMonoid_962
d_'43''45'0'45'commutativeMonoid_4446
  = ((Any -> Any -> Any)
 -> Any -> T_IsCommutativeMonoid_736 -> T_CommutativeMonoid_962)
-> (Integer -> Integer -> Integer)
-> Integer
-> T_IsCommutativeMonoid_736
-> T_CommutativeMonoid_962
forall a b. a -> b
coe
      (Any -> Any -> Any)
-> Any -> T_IsCommutativeMonoid_736 -> T_CommutativeMonoid_962
MAlonzo.Code.Algebra.Bundles.C_CommutativeMonoid'46'constructor_17931
      Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'43'__276 (Integer
0 :: Integer)
      T_IsCommutativeMonoid_736
d_'43''45'0'45'isCommutativeMonoid_4432
-- Data.Integer.Properties.+-0-abelianGroup
d_'43''45'0'45'abelianGroup_4448 ::
  MAlonzo.Code.Algebra.Bundles.T_AbelianGroup_1636
d_'43''45'0'45'abelianGroup_4448 :: T_AbelianGroup_1636
d_'43''45'0'45'abelianGroup_4448
  = ((Any -> Any -> Any)
 -> Any
 -> (Any -> Any)
 -> T_IsAbelianGroup_1132
 -> T_AbelianGroup_1636)
-> (Integer -> Integer -> Integer)
-> Integer
-> (Integer -> Integer)
-> T_IsAbelianGroup_1132
-> T_AbelianGroup_1636
forall a b. a -> b
coe
      (Any -> Any -> Any)
-> Any
-> (Any -> Any)
-> T_IsAbelianGroup_1132
-> T_AbelianGroup_1636
MAlonzo.Code.Algebra.Bundles.C_AbelianGroup'46'constructor_29855
      Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'43'__276 (Integer
0 :: Integer)
      Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d_'45'__252
      T_IsAbelianGroup_1132
d_'43''45'0'45'isAbelianGroup_4436
-- Data.Integer.Properties.pos-+
d_pos'45''43'_4450 ::
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_pos'45''43'_4450 :: Integer -> Integer -> T__'8801'__12
d_pos'45''43'_4450 = Integer -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.neg-distrib-+
d_neg'45'distrib'45''43'_4462 ::
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_neg'45'distrib'45''43'_4462 :: Integer -> Integer -> T__'8801'__12
d_neg'45'distrib'45''43'_4462 = Integer -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.◃-distrib-+
d_'9667''45'distrib'45''43'_4490 ::
  MAlonzo.Code.Data.Sign.Base.T_Sign_6 ->
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'9667''45'distrib'45''43'_4490 :: T_Sign_6 -> Integer -> Integer -> T__'8801'__12
d_'9667''45'distrib'45''43'_4490 = T_Sign_6 -> Integer -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.+-monoʳ-≤
d_'43''45'mono'691''45''8804'_4510 ::
  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'_4510 :: Integer -> Integer -> Integer -> T__'8804'__26 -> T__'8804'__26
d_'43''45'mono'691''45''8804'_4510 Integer
v0 Integer
v1 Integer
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
v3 of
            MAlonzo.Code.Data.Integer.Base.C_'45''8804''45'_34 T__'8804'__22
v6
              -> (Integer -> Integer -> Integer -> T__'8804'__22 -> T__'8804'__26)
-> Any -> Any -> Any -> Any -> T__'8804'__26
forall a b. a -> b
coe
                   Integer -> Integer -> Integer -> T__'8804'__22 -> T__'8804'__26
d_'8854''45'mono'691''45''8805''45''8804'_4024 (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'__22 -> T__'8804'__22) -> T__'8804'__22 -> Any
forall a b. a -> b
coe T__'8804'__22 -> T__'8804'__22
MAlonzo.Code.Data.Nat.Base.C_s'8804's_34 T__'8804'__22
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_2730
                   ((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_3912 (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'__22 -> T__'8804'__26) -> Any -> Any
forall a b. a -> b
coe
                      T__'8804'__22 -> T__'8804'__26
MAlonzo.Code.Data.Integer.Base.C_'43''8804''43'_48
                      ((Integer -> T__'8804'__22) -> Any -> Any
forall a b. a -> b
coe
                         Integer -> T__'8804'__22
MAlonzo.Code.Data.Nat.Properties.du_m'8804'm'43'n_3482 (Integer -> Any
forall a b. a -> b
coe Integer
v0)))
            MAlonzo.Code.Data.Integer.Base.C_'43''8804''43'_48 T__'8804'__22
v6
              -> (T__'8804'__22 -> T__'8804'__26) -> Any -> T__'8804'__26
forall a b. a -> b
coe
                   T__'8804'__22 -> T__'8804'__26
MAlonzo.Code.Data.Integer.Base.C_'43''8804''43'_48
                   ((Integer -> Integer -> T__'8804'__22 -> T__'8804'__22)
-> Any -> Any -> Any -> Any
forall a b. a -> b
coe
                      Integer -> Integer -> T__'8804'__22 -> T__'8804'__22
MAlonzo.Code.Data.Nat.Properties.du_'43''45'mono'691''45''8804'_3554
                      (Integer -> Any
forall a b. a -> b
coe Integer
v0) (Integer -> Any
forall a b. a -> b
coe Integer
v2) (T__'8804'__22 -> Any
forall a b. a -> b
coe T__'8804'__22
v6))
            T__'8804'__26
_ -> T__'8804'__26
forall a. a
MAlonzo.RTE.mazUnreachableError
      Any
_ -> 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'__22
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'__22 -> T__'8804'__26) -> Any -> Any
forall a b. a -> b
coe
                       T__'8804'__22 -> T__'8804'__26
MAlonzo.Code.Data.Integer.Base.C_'45''8804''45'_34
                       ((Integer -> Integer -> T__'8804'__22 -> T__'8804'__22)
-> Any -> Any -> Any -> Any
forall a b. a -> b
coe
                          Integer -> Integer -> T__'8804'__22 -> T__'8804'__22
MAlonzo.Code.Data.Nat.Properties.du_'43''45'mono'691''45''8804'_3554
                          ((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
v7) (T__'8804'__22 -> Any
forall a b. a -> b
coe T__'8804'__22
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_2730
                    ((T__'8804'__22 -> T__'8804'__26) -> Any -> Any
forall a b. a -> b
coe
                       T__'8804'__22 -> T__'8804'__26
MAlonzo.Code.Data.Integer.Base.C_'45''8804''45'_34
                       ((Integer -> T__'8804'__22) -> Any -> Any
forall a b. a -> b
coe
                          Integer -> T__'8804'__22
MAlonzo.Code.Data.Nat.Properties.du_m'8804'm'43'n_3482
                          ((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_'45'1'43'm'8804'n'8854'm_3992
                       ((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
v2))
             MAlonzo.Code.Data.Integer.Base.C_'43''8804''43'_48 T__'8804'__22
v6
               -> (Integer -> Integer -> Integer -> T__'8804'__22 -> T__'8804'__26)
-> Any -> Any -> Any -> Any -> T__'8804'__26
forall a b. a -> b
coe
                    Integer -> Integer -> Integer -> T__'8804'__22 -> T__'8804'__26
d_'8854''45'mono'737''45''8804'_4056
                    ((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'__22 -> Any
forall a b. a -> b
coe T__'8804'__22
v6)
             T__'8804'__26
_ -> T__'8804'__26
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Data.Integer.Properties.+-monoˡ-≤
d_'43''45'mono'737''45''8804'_4540 ::
  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'_4540 :: Integer -> Integer -> Integer -> T__'8804'__26 -> T__'8804'__26
d_'43''45'mono'737''45''8804'_4540 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_'43''45'mono'691''45''8804'_4510 (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.+-mono-≤
d_'43''45'mono'45''8804'_4556 ::
  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'_4556 :: Integer
-> Integer
-> Integer
-> Integer
-> T__'8804'__26
-> T__'8804'__26
-> T__'8804'__26
d_'43''45'mono'45''8804'_4556 Integer
v0 Integer
v1 Integer
v2 Integer
v3 T__'8804'__26
v4 T__'8804'__26
v5
  = ((Any -> Any -> Any -> Any) -> Any -> Any -> Any -> Any)
-> Any -> Integer -> Integer -> Any -> T__'8804'__26
forall a b. a -> b
coe
      (Any -> Any -> Any -> Any) -> Any -> Any -> Any -> Any
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_begin__46
      ((T_IsPreorder_70
 -> (Any -> Any -> Any -> Any)
 -> Any
 -> Any
 -> T__IsRelatedTo__78
 -> Any)
-> Any -> (Any -> Any -> Any -> Any) -> Any
forall a b. a -> b
coe
         T_IsPreorder_70
-> (Any -> Any -> Any -> Any)
-> Any
-> Any
-> T__IsRelatedTo__78
-> Any
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_start_96
         (T_IsPreorder_70 -> Any
forall a b. a -> b
coe T_IsPreorder_70
d_'8804''45'isPreorder_2800)
         (\ Any
v6 Any
v7 Any
v8 -> (T__'60'__50 -> T__'8804'__26) -> Any -> Any
forall a b. a -> b
coe T__'60'__50 -> T__'8804'__26
du_'60''8658''8804'_2846 Any
v8))
      (Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'43'__276 (Integer -> Integer
forall a b. a -> b
coe Integer
v0) (Integer -> Integer
forall a b. a -> b
coe Integer
v2))
      (Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'43'__276 (Integer -> Integer
forall a b. a -> b
coe Integer
v1) (Integer -> Integer
forall a b. a -> b
coe Integer
v3))
      (((Any -> Any -> Any -> Any -> Any -> Any)
 -> Any -> Any -> Any -> Any -> Any -> Any)
-> Any -> Integer -> Integer -> Integer -> Any -> Any -> Any
forall a b. a -> b
coe
         (Any -> Any -> Any -> Any -> Any -> Any)
-> Any -> Any -> Any -> Any -> Any -> Any
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8804'_308
         ((T_IsPreorder_70
 -> (Any -> Any -> Any -> Any -> Any -> Any)
 -> Any
 -> Any
 -> Any
 -> Any
 -> T__IsRelatedTo__78
 -> T__IsRelatedTo__78)
-> 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
-> Any
-> T__IsRelatedTo__78
-> T__IsRelatedTo__78
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_'8804''45'go_138
            (T_IsPreorder_70 -> Any
forall a b. a -> b
coe T_IsPreorder_70
d_'8804''45'isPreorder_2800)
            (\ 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_2958 Any
v9 Any
v10))
         (Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'43'__276 (Integer -> Integer
forall a b. a -> b
coe Integer
v0) (Integer -> Integer
forall a b. a -> b
coe Integer
v2))
         (Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'43'__276 (Integer -> Integer
forall a b. a -> b
coe Integer
v1) (Integer -> Integer
forall a b. a -> b
coe Integer
v2))
         (Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'43'__276 (Integer -> Integer
forall a b. a -> b
coe Integer
v1) (Integer -> Integer
forall a b. a -> b
coe Integer
v3))
         (((Any -> Any -> Any -> Any -> Any -> Any)
 -> Any -> Any -> Any -> Any -> Any -> Any)
-> Any
-> Integer
-> Integer
-> Integer
-> Any
-> T__'8804'__26
-> Any
forall a b. a -> b
coe
            (Any -> Any -> Any -> Any -> Any -> Any)
-> Any -> Any -> Any -> Any -> Any -> Any
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8804'_308
            ((T_IsPreorder_70
 -> (Any -> Any -> Any -> Any -> Any -> Any)
 -> Any
 -> Any
 -> Any
 -> Any
 -> T__IsRelatedTo__78
 -> T__IsRelatedTo__78)
-> 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
-> Any
-> T__IsRelatedTo__78
-> T__IsRelatedTo__78
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_'8804''45'go_138
               (T_IsPreorder_70 -> Any
forall a b. a -> b
coe T_IsPreorder_70
d_'8804''45'isPreorder_2800)
               (\ 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_2958 Any
v9 Any
v10))
            (Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'43'__276 (Integer -> Integer
forall a b. a -> b
coe Integer
v1) (Integer -> Integer
forall a b. a -> b
coe Integer
v2))
            (Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'43'__276 (Integer -> Integer
forall a b. a -> b
coe Integer
v1) (Integer -> Integer
forall a b. a -> b
coe Integer
v3))
            (Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'43'__276 (Integer -> Integer
forall a b. a -> b
coe Integer
v1) (Integer -> Integer
forall a b. a -> b
coe Integer
v3))
            (((Any -> Any) -> Any -> Any) -> Any -> Any -> Any
forall a b. a -> b
coe
               (Any -> Any) -> Any -> Any
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du__'8718'_492
               ((T_IsPreorder_70 -> Any -> T__IsRelatedTo__78) -> Any -> Any
forall a b. a -> b
coe
                  T_IsPreorder_70 -> Any -> T__IsRelatedTo__78
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_stop_166
                  (T_IsPreorder_70 -> Any
forall a b. a -> b
coe T_IsPreorder_70
d_'8804''45'isPreorder_2800))
               ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe
                  Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'43'__276 (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
d_'43''45'mono'691''45''8804'_4510
               (Integer -> Integer
forall a b. a -> b
coe Integer
v1) (Integer -> Integer
forall a b. a -> b
coe Integer
v2) (Integer -> Integer
forall a b. a -> b
coe Integer
v3) (T__'8804'__26 -> T__'8804'__26
forall a b. a -> b
coe T__'8804'__26
v5)))
         ((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'737''45''8804'_4540 Integer
v2 Integer
v0 Integer
v1 T__'8804'__26
v4))
-- Data.Integer.Properties.i≤j⇒i≤k+j
d_i'8804'j'8658'i'8804'k'43'j_4578 ::
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Integer.Base.T_NonNegative_144 ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26 ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26
d_i'8804'j'8658'i'8804'k'43'j_4578 :: Integer
-> Integer
-> Integer
-> T_NonNegative_144
-> T__'8804'__26
-> T__'8804'__26
d_i'8804'j'8658'i'8804'k'43'j_4578 Integer
v0 Integer
v1 Integer
v2 ~T_NonNegative_144
v3 T__'8804'__26
v4
  = Integer -> Integer -> Integer -> T__'8804'__26 -> T__'8804'__26
du_i'8804'j'8658'i'8804'k'43'j_4578 Integer
v0 Integer
v1 Integer
v2 T__'8804'__26
v4
du_i'8804'j'8658'i'8804'k'43'j_4578 ::
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26 ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26
du_i'8804'j'8658'i'8804'k'43'j_4578 :: Integer -> Integer -> Integer -> T__'8804'__26 -> T__'8804'__26
du_i'8804'j'8658'i'8804'k'43'j_4578 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'_4556 (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'__22 -> T__'8804'__26) -> Any -> Any
forall a b. a -> b
coe
         T__'8804'__22 -> T__'8804'__26
MAlonzo.Code.Data.Integer.Base.C_'43''8804''43'_48
         (T__'8804'__22 -> Any
forall a b. a -> b
coe T__'8804'__22
MAlonzo.Code.Data.Nat.Base.C_z'8804'n_26))
      (T__'8804'__26 -> Any
forall a b. a -> b
coe T__'8804'__26
v3)
-- Data.Integer.Properties.i≤j+i
d_i'8804'j'43'i_4592 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Integer.Base.T_NonNegative_144 ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26
d_i'8804'j'43'i_4592 :: Integer -> Integer -> T_NonNegative_144 -> T__'8804'__26
d_i'8804'j'43'i_4592 Integer
v0 Integer
v1 ~T_NonNegative_144
v2 = Integer -> Integer -> T__'8804'__26
du_i'8804'j'43'i_4592 Integer
v0 Integer
v1
du_i'8804'j'43'i_4592 ::
  Integer -> Integer -> MAlonzo.Code.Data.Integer.Base.T__'8804'__26
du_i'8804'j'43'i_4592 :: Integer -> Integer -> T__'8804'__26
du_i'8804'j'43'i_4592 Integer
v0 Integer
v1
  = (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
du_i'8804'j'8658'i'8804'k'43'j_4578 (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)
      ((Integer -> T__'8804'__26) -> Any -> Any
forall a b. a -> b
coe Integer -> T__'8804'__26
d_'8804''45'refl_2728 (Integer -> Any
forall a b. a -> b
coe Integer
v0))
-- Data.Integer.Properties.i≤i+j
d_i'8804'i'43'j_4604 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Integer.Base.T_NonNegative_144 ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26
d_i'8804'i'43'j_4604 :: Integer -> Integer -> T_NonNegative_144 -> T__'8804'__26
d_i'8804'i'43'j_4604 Integer
v0 Integer
v1 ~T_NonNegative_144
v2 = Integer -> Integer -> T__'8804'__26
du_i'8804'i'43'j_4604 Integer
v0 Integer
v1
du_i'8804'i'43'j_4604 ::
  Integer -> Integer -> MAlonzo.Code.Data.Integer.Base.T__'8804'__26
du_i'8804'i'43'j_4604 :: Integer -> Integer -> T__'8804'__26
du_i'8804'i'43'j_4604 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
du_i'8804'j'43'i_4592 (Integer -> Any
forall a b. a -> b
coe Integer
v0) (Integer -> Any
forall a b. a -> b
coe Integer
v1)
-- Data.Integer.Properties.+-monoʳ-<
d_'43''45'mono'691''45''60'_4616 ::
  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'_4616 :: Integer -> Integer -> Integer -> T__'60'__50 -> T__'60'__50
d_'43''45'mono'691''45''60'_4616 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'__22
v6
              -> (Integer -> Integer -> Integer -> T__'8804'__22 -> T__'60'__50)
-> Any -> Any -> Any -> Any -> T__'60'__50
forall a b. a -> b
coe
                   Integer -> Integer -> Integer -> T__'8804'__22 -> T__'60'__50
d_'8854''45'mono'691''45''62''45''60'_4086 (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'__22 -> T__'8804'__22) -> T__'8804'__22 -> Any
forall a b. a -> b
coe T__'8804'__22 -> T__'8804'__22
MAlonzo.Code.Data.Nat.Base.C_s'8804's_34 T__'8804'__22
v6)
            T__'60'__50
MAlonzo.Code.Data.Integer.Base.C_'45''60''43'_64
              -> (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_2972
                   ((Integer -> Integer -> T__'60'__50) -> Any -> Any -> Any
forall a b. a -> b
coe
                      Integer -> Integer -> T__'60'__50
du_m'8854'1'43'n'60'm_3942 (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'__22 -> T__'8804'__26) -> Any -> Any
forall a b. a -> b
coe
                      T__'8804'__22 -> T__'8804'__26
MAlonzo.Code.Data.Integer.Base.C_'43''8804''43'_48
                      ((Integer -> T__'8804'__22) -> Any -> Any
forall a b. a -> b
coe
                         Integer -> T__'8804'__22
MAlonzo.Code.Data.Nat.Properties.du_m'8804'm'43'n_3482 (Integer -> Any
forall a b. a -> b
coe Integer
v0)))
            MAlonzo.Code.Data.Integer.Base.C_'43''60''43'_72 T__'8804'__22
v6
              -> (T__'8804'__22 -> T__'60'__50) -> Any -> T__'60'__50
forall a b. a -> b
coe
                   T__'8804'__22 -> T__'60'__50
MAlonzo.Code.Data.Integer.Base.C_'43''60''43'_72
                   ((Integer -> T__'8804'__22 -> T__'8804'__22) -> Any -> Any -> Any
forall a b. a -> b
coe
                      Integer -> T__'8804'__22 -> T__'8804'__22
MAlonzo.Code.Data.Nat.Properties.du_'43''45'mono'691''45''60'_3596
                      (Integer -> Any
forall a b. a -> b
coe Integer
v0) (T__'8804'__22 -> Any
forall a b. a -> b
coe T__'8804'__22
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'__22
v7
                  -> (T__'8804'__22 -> T__'60'__50) -> Any -> Any
forall a b. a -> b
coe
                       T__'8804'__22 -> T__'60'__50
MAlonzo.Code.Data.Integer.Base.C_'45''60''45'_58
                       ((Integer -> T__'8804'__22 -> T__'8804'__22) -> Any -> Any -> Any
forall a b. a -> b
coe
                          Integer -> T__'8804'__22 -> T__'8804'__22
MAlonzo.Code.Data.Nat.Properties.du_'43''45'mono'691''45''60'_3596
                          ((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'__22 -> Any
forall a b. a -> b
coe T__'8804'__22
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_2972
                       ((T__'8804'__22 -> T__'60'__50) -> Any -> Any
forall a b. a -> b
coe
                          T__'8804'__22 -> T__'60'__50
MAlonzo.Code.Data.Integer.Base.C_'45''60''45'_58
                          ((Integer -> T__'8804'__22) -> Any -> Any
forall a b. a -> b
coe
                             Integer -> T__'8804'__22
MAlonzo.Code.Data.Nat.Properties.du_m'8804'm'43'n_3482
                             ((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_3976 (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'__22
v7
                  -> (Integer -> Integer -> Integer -> T__'8804'__22 -> T__'60'__50)
-> Any -> Any -> Any -> Any -> Any
forall a b. a -> b
coe
                       Integer -> Integer -> Integer -> T__'8804'__22 -> T__'60'__50
d_'8854''45'mono'737''45''60'_4114
                       ((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'__22 -> Any
forall a b. a -> b
coe T__'8804'__22
v7)
                T__'60'__50
_ -> Any
forall a. a
MAlonzo.RTE.mazUnreachableError)
-- Data.Integer.Properties.+-monoˡ-<
d_'43''45'mono'737''45''60'_4644 ::
  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'_4644 :: Integer -> Integer -> Integer -> T__'60'__50 -> T__'60'__50
d_'43''45'mono'737''45''60'_4644 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_'43''45'mono'691''45''60'_4616 (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.+-mono-<
d_'43''45'mono'45''60'_4660 ::
  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'_4660 :: Integer
-> Integer
-> Integer
-> Integer
-> T__'60'__50
-> T__'60'__50
-> T__'60'__50
d_'43''45'mono'45''60'_4660 Integer
v0 Integer
v1 Integer
v2 Integer
v3 T__'60'__50
v4 T__'60'__50
v5
  = let v6 :: b
v6
          = T_SubRelation_60 -> b
forall a b. a -> b
coe
              T_SubRelation_60
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_strictRelation_202 in
    Any -> T__'60'__50
forall a b. a -> b
coe
      ((T_SubRelation_60 -> Any -> Any -> Any -> Any)
-> Any -> Any -> Any -> Any -> Any
forall a b. a -> b
coe
         T_SubRelation_60 -> Any -> Any -> Any -> Any
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_begin__126
         (Any -> Any
forall a b. a -> b
coe Any
forall a. a
v6)
         ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'43'__276 (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'__276 (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)
 -> Any -> Any -> Any -> Any -> Any -> Any)
-> Any -> Integer -> Integer -> Integer -> Any -> Any -> Any
forall a b. a -> b
coe
            (Any -> Any -> Any -> Any -> Any -> Any)
-> Any -> Any -> Any -> Any -> Any -> Any
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''60'_312
            (((Any -> Any -> Any -> Any -> Any -> Any)
 -> T_Σ_14
 -> (Any -> Any -> Any -> Any -> Any -> Any)
 -> Any
 -> Any
 -> Any
 -> Any
 -> T__IsRelatedTo__78
 -> T__IsRelatedTo__78)
-> (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
-> Any
-> T__IsRelatedTo__78
-> T__IsRelatedTo__78
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_'60''45'go_152
               (\ Any
v7 Any
v8 Any
v9 Any
v10 Any
v11 -> (T__'60'__50 -> T__'60'__50 -> T__'60'__50) -> Any -> Any -> Any
forall a b. a -> b
coe T__'60'__50 -> T__'60'__50 -> T__'60'__50
du_'60''45'trans_2986 Any
v10 Any
v11)
               (T_Σ_14 -> Any
forall a b. a -> b
coe
                  T_Σ_14
MAlonzo.Code.Relation.Binary.PropositionalEquality.Core.du_resp'8322'_160)
               (\ Any
v7 Any
v8 Any
v9 Any
v10 Any
v11 ->
                  (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_2972 Any
v10 Any
v11))
            (Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'43'__276 (Integer -> Integer
forall a b. a -> b
coe Integer
v0) (Integer -> Integer
forall a b. a -> b
coe Integer
v2))
            (Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'43'__276 (Integer -> Integer
forall a b. a -> b
coe Integer
v1) (Integer -> Integer
forall a b. a -> b
coe Integer
v2))
            (Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'43'__276 (Integer -> Integer
forall a b. a -> b
coe Integer
v1) (Integer -> Integer
forall a b. a -> b
coe Integer
v3))
            (((Any -> Any -> Any -> Any -> Any -> Any)
 -> Any -> Any -> Any -> Any -> Any -> Any)
-> Any
-> Integer
-> Integer
-> Integer
-> Any
-> T__'60'__50
-> Any
forall a b. a -> b
coe
               (Any -> Any -> Any -> Any -> Any -> Any)
-> Any -> Any -> Any -> Any -> Any -> Any
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''60'_312
               (((Any -> Any -> Any -> Any -> Any -> Any)
 -> T_Σ_14
 -> (Any -> Any -> Any -> Any -> Any -> Any)
 -> Any
 -> Any
 -> Any
 -> Any
 -> T__IsRelatedTo__78
 -> T__IsRelatedTo__78)
-> (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
-> Any
-> T__IsRelatedTo__78
-> T__IsRelatedTo__78
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_'60''45'go_152
                  (\ Any
v7 Any
v8 Any
v9 Any
v10 Any
v11 -> (T__'60'__50 -> T__'60'__50 -> T__'60'__50) -> Any -> Any -> Any
forall a b. a -> b
coe T__'60'__50 -> T__'60'__50 -> T__'60'__50
du_'60''45'trans_2986 Any
v10 Any
v11)
                  (T_Σ_14 -> Any
forall a b. a -> b
coe
                     T_Σ_14
MAlonzo.Code.Relation.Binary.PropositionalEquality.Core.du_resp'8322'_160)
                  (\ Any
v7 Any
v8 Any
v9 Any
v10 Any
v11 ->
                     (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_2972 Any
v10 Any
v11))
               (Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'43'__276 (Integer -> Integer
forall a b. a -> b
coe Integer
v1) (Integer -> Integer
forall a b. a -> b
coe Integer
v2))
               (Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'43'__276 (Integer -> Integer
forall a b. a -> b
coe Integer
v1) (Integer -> Integer
forall a b. a -> b
coe Integer
v3))
               (Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'43'__276 (Integer -> Integer
forall a b. a -> b
coe Integer
v1) (Integer -> Integer
forall a b. a -> b
coe Integer
v3))
               (((Any -> Any) -> Any -> Any) -> Any -> Any -> Any
forall a b. a -> b
coe
                  (Any -> Any) -> Any -> Any
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du__'8718'_492
                  ((T_IsPreorder_70 -> Any -> T__IsRelatedTo__78) -> Any -> Any
forall a b. a -> b
coe
                     T_IsPreorder_70 -> Any -> T__IsRelatedTo__78
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_stop_166
                     (T_IsPreorder_70 -> Any
forall a b. a -> b
coe T_IsPreorder_70
d_'8804''45'isPreorder_2800))
                  ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe
                     Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'43'__276 (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
d_'43''45'mono'691''45''60'_4616
                  (Integer -> Integer
forall a b. a -> b
coe Integer
v1) (Integer -> Integer
forall a b. a -> b
coe Integer
v2) (Integer -> Integer
forall a b. a -> b
coe Integer
v3) (T__'60'__50 -> T__'60'__50
forall a b. a -> b
coe T__'60'__50
v5)))
            ((Integer -> Integer -> Integer -> T__'60'__50 -> T__'60'__50)
-> Integer -> Integer -> Integer -> T__'60'__50 -> Any
forall a b. a -> b
coe Integer -> Integer -> Integer -> T__'60'__50 -> T__'60'__50
d_'43''45'mono'737''45''60'_4644 Integer
v2 Integer
v0 Integer
v1 T__'60'__50
v4)))
-- Data.Integer.Properties.+-mono-≤-<
d_'43''45'mono'45''8804''45''60'_4678 ::
  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'_4678 :: Integer
-> Integer
-> Integer
-> Integer
-> T__'8804'__26
-> T__'60'__50
-> T__'60'__50
d_'43''45'mono'45''8804''45''60'_4678 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_2958
      ((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'737''45''8804'_4540 Integer
v2 Integer
v0 Integer
v1 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'_4616 (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'_4690 ::
  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'_4690 :: Integer
-> Integer
-> Integer
-> Integer
-> T__'60'__50
-> T__'8804'__26
-> T__'60'__50
d_'43''45'mono'45''60''45''8804'_4690 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_2972
      ((Integer -> Integer -> Integer -> T__'60'__50 -> T__'60'__50)
-> Integer -> Integer -> Integer -> T__'60'__50 -> Any
forall a b. a -> b
coe Integer -> Integer -> Integer -> T__'60'__50 -> T__'60'__50
d_'43''45'mono'737''45''60'_4644 Integer
v2 Integer
v0 Integer
v1 T__'60'__50
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''8804'_4510 (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.neg-minus-pos
d_neg'45'minus'45'pos_4706 ::
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_neg'45'minus'45'pos_4706 :: Integer -> Integer -> T__'8801'__12
d_neg'45'minus'45'pos_4706 = Integer -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.+-minus-telescope
d_'43''45'minus'45'telescope_4722 ::
  Integer ->
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'43''45'minus'45'telescope_4722 :: Integer -> Integer -> Integer -> T__'8801'__12
d_'43''45'minus'45'telescope_4722 = 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_4744 ::
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'91''43'm'93''45''91''43'n'93''8801'm'8854'n_4744 :: Integer -> Integer -> T__'8801'__12
d_'91''43'm'93''45''91''43'n'93''8801'm'8854'n_4744 = Integer -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.∣i-j∣≡∣j-i∣
d_'8739'i'45'j'8739''8801''8739'j'45'i'8739'_4758 ::
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8739'i'45'j'8739''8801''8739'j'45'i'8739'_4758 :: Integer -> Integer -> T__'8801'__12
d_'8739'i'45'j'8739''8801''8739'j'45'i'8739'_4758 = Integer -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.∣-∣-≤
d_'8739''45''8739''45''8804'_4788 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8739''45''8739''45''8804'_4788 :: Integer -> Integer -> T__'8804'__26 -> T__'8801'__12
d_'8739''45''8739''45''8804'_4788 = Integer -> Integer -> T__'8804'__26 -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.i≡j⇒i-j≡0
d_i'8801'j'8658'i'45'j'8801'0_4826 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_i'8801'j'8658'i'45'j'8801'0_4826 :: Integer -> Integer -> T__'8801'__12 -> T__'8801'__12
d_i'8801'j'8658'i'45'j'8801'0_4826 = Integer -> Integer -> T__'8801'__12 -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.i-j≡0⇒i≡j
d_i'45'j'8801'0'8658'i'8801'j_4834 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_i'45'j'8801'0'8658'i'8801'j_4834 :: Integer -> Integer -> T__'8801'__12 -> T__'8801'__12
d_i'45'j'8801'0'8658'i'8801'j_4834 = Integer -> Integer -> T__'8801'__12 -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.i≤j⇒i-k≤j
d_i'8804'j'8658'i'45'k'8804'j_4852 ::
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Integer.Base.T_NonNegative_144 ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26 ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26
d_i'8804'j'8658'i'45'k'8804'j_4852 :: Integer
-> Integer
-> Integer
-> T_NonNegative_144
-> T__'8804'__26
-> T__'8804'__26
d_i'8804'j'8658'i'45'k'8804'j_4852 Integer
v0 ~Integer
v1 Integer
v2 ~T_NonNegative_144
v3 T__'8804'__26
v4
  = Integer -> Integer -> T__'8804'__26 -> T__'8804'__26
du_i'8804'j'8658'i'45'k'8804'j_4852 Integer
v0 Integer
v2 T__'8804'__26
v4
du_i'8804'j'8658'i'45'k'8804'j_4852 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26 ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26
du_i'8804'j'8658'i'45'k'8804'j_4852 :: Integer -> Integer -> T__'8804'__26 -> T__'8804'__26
du_i'8804'j'8658'i'45'k'8804'j_4852 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_2730
                      ((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_3912 (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_2730
                          ((T__'8804'__22 -> T__'8804'__26) -> Any -> Any
forall a b. a -> b
coe
                             T__'8804'__22 -> T__'8804'__26
MAlonzo.Code.Data.Integer.Base.C_'45''8804''45'_34
                             ((T__'8804'__22 -> T__'8804'__22 -> T__'8804'__22)
-> Any -> Any -> Any
forall a b. a -> b
coe
                                T__'8804'__22 -> T__'8804'__22 -> T__'8804'__22
MAlonzo.Code.Data.Nat.Properties.du_'8804''45'trans_2784
                                ((Integer -> T__'8804'__22) -> Any -> Any
forall a b. a -> b
coe
                                   Integer -> T__'8804'__22
MAlonzo.Code.Data.Nat.Properties.du_m'8804'm'43'n_3482 (Integer -> Any
forall a b. a -> b
coe Integer
v4))
                                ((Integer -> T__'8804'__22) -> Any -> Any
forall a b. a -> b
coe
                                   Integer -> T__'8804'__22
MAlonzo.Code.Data.Nat.Properties.d_n'8804'1'43'n_2844
                                   ((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.i-j≤i
d_i'45'j'8804'i_4880 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Integer.Base.T_NonNegative_144 ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26
d_i'45'j'8804'i_4880 :: Integer -> Integer -> T_NonNegative_144 -> T__'8804'__26
d_i'45'j'8804'i_4880 Integer
v0 Integer
v1 ~T_NonNegative_144
v2 = Integer -> Integer -> T__'8804'__26
du_i'45'j'8804'i_4880 Integer
v0 Integer
v1
du_i'45'j'8804'i_4880 ::
  Integer -> Integer -> MAlonzo.Code.Data.Integer.Base.T__'8804'__26
du_i'45'j'8804'i_4880 :: Integer -> Integer -> T__'8804'__26
du_i'45'j'8804'i_4880 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_i'8804'j'8658'i'45'k'8804'j_4852 (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_2728 (Integer -> Any
forall a b. a -> b
coe Integer
v0))
-- Data.Integer.Properties.i≤j⇒i-j≤0
d_i'8804'j'8658'i'45'j'8804'0_4886 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26 ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26
d_i'8804'j'8658'i'45'j'8804'0_4886 :: Integer -> Integer -> T__'8804'__26 -> T__'8804'__26
d_i'8804'j'8658'i'45'j'8804'0_4886 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'__22
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
                (((Any -> Any -> Any -> Any) -> Any -> Any -> Any -> Any)
-> Any -> Integer -> Integer -> Any -> Any
forall a b. a -> b
coe
                   (Any -> Any -> Any -> Any) -> Any -> Any -> Any -> Any
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_begin__46
                   ((T_IsPreorder_70
 -> (Any -> Any -> Any -> Any)
 -> Any
 -> Any
 -> T__IsRelatedTo__78
 -> Any)
-> Any -> (Any -> Any -> Any -> Any) -> Any
forall a b. a -> b
coe
                      T_IsPreorder_70
-> (Any -> Any -> Any -> Any)
-> Any
-> Any
-> T__IsRelatedTo__78
-> Any
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_start_96
                      (T_IsPreorder_70 -> Any
forall a b. a -> b
coe T_IsPreorder_70
d_'8804''45'isPreorder_2800)
                      (\ Any
v8 Any
v9 Any
v10 -> (T__'60'__50 -> T__'8804'__26) -> Any -> Any
forall a b. a -> b
coe T__'60'__50 -> T__'8804'__26
du_'60''8658''8804'_2846 Any
v10))
                   (Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'45'__294 (Integer -> Integer
forall a b. a -> b
coe Integer
v0) (Integer -> Integer
forall a b. a -> b
coe Integer
v1))
                   Integer
MAlonzo.Code.Data.Integer.Base.d_0ℤ_12
                   (((Any -> Any -> Any -> T__'8801'__12 -> Any -> Any)
 -> Any -> Any -> Any -> Any -> T__'8801'__12 -> Any)
-> (Any -> Any -> Any -> Any -> Any -> Any)
-> Integer
-> Integer
-> Integer
-> Any
-> Any
-> Any
forall a b. a -> b
coe
                      (Any -> Any -> Any -> T__'8801'__12 -> Any -> Any)
-> Any -> Any -> Any -> Any -> T__'8801'__12 -> Any
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8801''45''10217'_436
                      (\ Any
v8 Any
v9 Any
v10 Any
v11 Any
v12 -> Any
v12)
                      (Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'8854'__258
                         ((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
v1))
                         ((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)))
                      (Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'8854'__258 (Integer -> Integer
forall a b. a -> b
coe Integer
v7) (Integer -> Integer
forall a b. a -> b
coe Integer
v6))
                      Integer
MAlonzo.Code.Data.Integer.Base.d_0ℤ_12
                      (((Any -> Any -> Any -> Any -> Any -> Any)
 -> Any -> Any -> Any -> Any -> Any -> Any)
-> Any
-> Integer
-> Integer
-> Integer
-> Any
-> T__'8804'__26
-> Any
forall a b. a -> b
coe
                         (Any -> Any -> Any -> Any -> Any -> Any)
-> Any -> Any -> Any -> Any -> Any -> Any
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8804'_308
                         ((T_IsPreorder_70
 -> (Any -> Any -> Any -> Any -> Any -> Any)
 -> Any
 -> Any
 -> Any
 -> Any
 -> T__IsRelatedTo__78
 -> T__IsRelatedTo__78)
-> 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
-> Any
-> T__IsRelatedTo__78
-> T__IsRelatedTo__78
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_'8804''45'go_138
                            (T_IsPreorder_70 -> Any
forall a b. a -> b
coe T_IsPreorder_70
d_'8804''45'isPreorder_2800)
                            (\ 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_2958 Any
v11 Any
v12))
                         (Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'8854'__258 (Integer -> Integer
forall a b. a -> b
coe Integer
v7) (Integer -> Integer
forall a b. a -> b
coe Integer
v6))
                         (Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'8854'__258 (Integer -> Integer
forall a b. a -> b
coe Integer
v7) (Integer -> Integer
forall a b. a -> b
coe Integer
v7))
                         Integer
MAlonzo.Code.Data.Integer.Base.d_0ℤ_12
                         (((Any -> Any -> Any -> T__'8801'__12 -> Any -> Any)
 -> Any -> Any -> Any -> Any -> T__'8801'__12 -> Any)
-> (Any -> Any -> Any -> Any -> Any -> Any)
-> Integer
-> Integer
-> Integer
-> Any
-> Any
-> Any
forall a b. a -> b
coe
                            (Any -> Any -> Any -> T__'8801'__12 -> Any -> Any)
-> Any -> Any -> Any -> Any -> T__'8801'__12 -> Any
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8801''45''10217'_436
                            (\ Any
v8 Any
v9 Any
v10 Any
v11 Any
v12 -> Any
v12)
                            (Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'8854'__258 (Integer -> Integer
forall a b. a -> b
coe Integer
v7) (Integer -> Integer
forall a b. a -> b
coe Integer
v7))
                            Integer
MAlonzo.Code.Data.Integer.Base.d_0ℤ_12
                            Integer
MAlonzo.Code.Data.Integer.Base.d_0ℤ_12
                            (((Any -> Any) -> Any -> Any) -> Any -> Any -> Any
forall a b. a -> b
coe
                               (Any -> Any) -> Any -> Any
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du__'8718'_492
                               ((T_IsPreorder_70 -> Any -> T__IsRelatedTo__78) -> Any -> Any
forall a b. a -> b
coe
                                  T_IsPreorder_70 -> Any -> T__IsRelatedTo__78
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_stop_166
                                  (T_IsPreorder_70 -> Any
forall a b. a -> b
coe T_IsPreorder_70
d_'8804''45'isPreorder_2800))
                               (Integer -> Any
forall a b. a -> b
coe Integer
MAlonzo.Code.Data.Integer.Base.d_0ℤ_12))
                            Any
forall a. a
erased)
                         (Integer -> Integer -> Integer -> T__'8804'__22 -> T__'8804'__26
d_'8854''45'mono'691''45''8805''45''8804'_4024
                            (Integer -> Integer
forall a b. a -> b
coe Integer
v7) (Integer -> Integer
forall a b. a -> b
coe Integer
v6) (Integer -> Integer
forall a b. a -> b
coe Integer
v7) (T__'8804'__22 -> T__'8804'__22
forall a b. a -> b
coe T__'8804'__22
v5)))
                      Any
forall a. a
erased)))
      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_i'8804'j'8658'i'45'k'8804'j_4852 (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'__22
v5
        -> 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'__22 -> Any
forall a b. a -> b
coe T__'8804'__22
v5)
                    ((T__'8804'__22 -> T__'8804'__26) -> Any -> Any
forall a b. a -> b
coe
                       T__'8804'__22 -> T__'8804'__26
MAlonzo.Code.Data.Integer.Base.C_'43''8804''43'_48
                       (T__'8804'__22 -> Any
forall a b. a -> b
coe T__'8804'__22
MAlonzo.Code.Data.Nat.Base.C_z'8804'n_26))
             Integer
_ -> let v6 :: Integer
v6 = 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 T__'8804'__22 -> T__'8804'__22
forall a b. a -> b
coe T__'8804'__22
v5 of
                       T__'8804'__22
MAlonzo.Code.Data.Nat.Base.C_z'8804'n_26
                         -> 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.Nat.Base.C_s'8804's_34 T__'8804'__22
v9
                         -> let v10 :: Integer
v10 = 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
                              (((Any -> Any -> Any -> Any) -> Any -> Any -> Any -> Any)
-> Any -> Integer -> Integer -> Any -> Any
forall a b. a -> b
coe
                                 (Any -> Any -> Any -> Any) -> Any -> Any -> Any -> Any
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_begin__46
                                 ((T_IsPreorder_70
 -> (Any -> Any -> Any -> Any)
 -> Any
 -> Any
 -> T__IsRelatedTo__78
 -> Any)
-> Any -> (Any -> Any -> Any -> Any) -> Any
forall a b. a -> b
coe
                                    T_IsPreorder_70
-> (Any -> Any -> Any -> Any)
-> Any
-> Any
-> T__IsRelatedTo__78
-> Any
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_start_96
                                    (T_IsPreorder_70 -> Any
forall a b. a -> b
coe T_IsPreorder_70
d_'8804''45'isPreorder_2800)
                                    (\ Any
v11 Any
v12 Any
v13 -> (T__'60'__50 -> T__'8804'__26) -> Any -> Any
forall a b. a -> b
coe T__'60'__50 -> T__'8804'__26
du_'60''8658''8804'_2846 Any
v13))
                                 (Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'45'__294 (Integer -> Integer
forall a b. a -> b
coe Integer
v0) (Integer -> Integer
forall a b. a -> b
coe Integer
v1))
                                 Integer
MAlonzo.Code.Data.Integer.Base.d_0ℤ_12
                                 (((Any -> Any -> Any -> T__'8801'__12 -> Any -> Any)
 -> Any -> Any -> Any -> Any -> T__'8801'__12 -> Any)
-> (Any -> Any -> Any -> Any -> Any -> Any)
-> Integer
-> Integer
-> Integer
-> Any
-> Any
-> Any
forall a b. a -> b
coe
                                    (Any -> Any -> Any -> T__'8801'__12 -> Any -> Any)
-> Any -> Any -> Any -> Any -> T__'8801'__12 -> Any
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8801''45''10217'_436
                                    (\ Any
v11 Any
v12 Any
v13 Any
v14 Any
v15 -> Any
v15)
                                    (Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'8854'__258
                                       (Integer -> Integer
forall a b. a -> b
coe Integer
v0) (Integer -> Integer
forall a b. a -> b
coe Integer
v1))
                                    (Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'8854'__258
                                       (Integer -> Integer
forall a b. a -> b
coe Integer
v10) (Integer -> Integer
forall a b. a -> b
coe Integer
v6))
                                    Integer
MAlonzo.Code.Data.Integer.Base.d_0ℤ_12
                                    (((Any -> Any -> Any -> Any -> Any -> Any)
 -> Any -> Any -> Any -> Any -> Any -> Any)
-> Any
-> Integer
-> Integer
-> Integer
-> Any
-> T__'8804'__26
-> Any
forall a b. a -> b
coe
                                       (Any -> Any -> Any -> Any -> Any -> Any)
-> Any -> Any -> Any -> Any -> Any -> Any
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8804'_308
                                       ((T_IsPreorder_70
 -> (Any -> Any -> Any -> Any -> Any -> Any)
 -> Any
 -> Any
 -> Any
 -> Any
 -> T__IsRelatedTo__78
 -> T__IsRelatedTo__78)
-> 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
-> Any
-> T__IsRelatedTo__78
-> T__IsRelatedTo__78
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_'8804''45'go_138
                                          (T_IsPreorder_70 -> Any
forall a b. a -> b
coe T_IsPreorder_70
d_'8804''45'isPreorder_2800)
                                          (\ 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_2958 Any
v14 Any
v15))
                                       (Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'8854'__258
                                          (Integer -> Integer
forall a b. a -> b
coe Integer
v10) (Integer -> Integer
forall a b. a -> b
coe Integer
v6))
                                       (Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'8854'__258
                                          (Integer -> Integer
forall a b. a -> b
coe Integer
v10) (Integer -> Integer
forall a b. a -> b
coe Integer
v10))
                                       Integer
MAlonzo.Code.Data.Integer.Base.d_0ℤ_12
                                       (((Any -> Any -> Any -> T__'8801'__12 -> Any -> Any)
 -> Any -> Any -> Any -> Any -> T__'8801'__12 -> Any)
-> (Any -> Any -> Any -> Any -> Any -> Any)
-> Integer
-> Integer
-> Integer
-> Any
-> Any
-> Any
forall a b. a -> b
coe
                                          (Any -> Any -> Any -> T__'8801'__12 -> Any -> Any)
-> Any -> Any -> Any -> Any -> T__'8801'__12 -> Any
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8801''45''10217'_436
                                          (\ Any
v11 Any
v12 Any
v13 Any
v14 Any
v15 -> Any
v15)
                                          (Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'8854'__258
                                             (Integer -> Integer
forall a b. a -> b
coe Integer
v10) (Integer -> Integer
forall a b. a -> b
coe Integer
v10))
                                          Integer
MAlonzo.Code.Data.Integer.Base.d_0ℤ_12
                                          Integer
MAlonzo.Code.Data.Integer.Base.d_0ℤ_12
                                          (((Any -> Any) -> Any -> Any) -> Any -> Any -> Any
forall a b. a -> b
coe
                                             (Any -> Any) -> Any -> Any
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du__'8718'_492
                                             ((T_IsPreorder_70 -> Any -> T__IsRelatedTo__78) -> Any -> Any
forall a b. a -> b
coe
                                                T_IsPreorder_70 -> Any -> T__IsRelatedTo__78
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_stop_166
                                                (T_IsPreorder_70 -> Any
forall a b. a -> b
coe T_IsPreorder_70
d_'8804''45'isPreorder_2800))
                                             (Integer -> Any
forall a b. a -> b
coe Integer
MAlonzo.Code.Data.Integer.Base.d_0ℤ_12))
                                          Any
forall a. a
erased)
                                       (Integer -> Integer -> Integer -> T__'8804'__22 -> T__'8804'__26
d_'8854''45'mono'691''45''8805''45''8804'_4024
                                          (Integer -> Integer
forall a b. a -> b
coe Integer
v10) (Integer -> Integer
forall a b. a -> b
coe Integer
v6) (Integer -> Integer
forall a b. a -> b
coe Integer
v10) (T__'8804'__22 -> T__'8804'__22
forall a b. a -> b
coe T__'8804'__22
v9)))
                                    Any
forall a. a
erased))
                       T__'8804'__22
_ -> Any
forall a. a
MAlonzo.RTE.mazUnreachableError)
      T__'8804'__26
_ -> T__'8804'__26
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Data.Integer.Properties.i-j≤0⇒i≤j
d_i'45'j'8804'0'8658'i'8804'j_4912 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26 ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26
d_i'45'j'8804'0'8658'i'8804'j_4912 :: Integer -> Integer -> T__'8804'__26 -> T__'8804'__26
d_i'45'j'8804'0'8658'i'8804'j_4912 Integer
v0 Integer
v1 T__'8804'__26
v2
  = ((Any -> Any -> Any -> Any) -> Any -> Any -> Any -> Any)
-> Any -> Integer -> Integer -> Any -> T__'8804'__26
forall a b. a -> b
coe
      (Any -> Any -> Any -> Any) -> Any -> Any -> Any -> Any
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_begin__46
      ((T_IsPreorder_70
 -> (Any -> Any -> Any -> Any)
 -> Any
 -> Any
 -> T__IsRelatedTo__78
 -> Any)
-> Any -> (Any -> Any -> Any -> Any) -> Any
forall a b. a -> b
coe
         T_IsPreorder_70
-> (Any -> Any -> Any -> Any)
-> Any
-> Any
-> T__IsRelatedTo__78
-> Any
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_start_96
         (T_IsPreorder_70 -> Any
forall a b. a -> b
coe T_IsPreorder_70
d_'8804''45'isPreorder_2800)
         (\ Any
v3 Any
v4 Any
v5 -> (T__'60'__50 -> T__'8804'__26) -> Any -> Any
forall a b. a -> b
coe T__'60'__50 -> T__'8804'__26
du_'60''8658''8804'_2846 Any
v5))
      Integer
v0 Integer
v1
      (((Any -> Any -> Any -> T__'8801'__12 -> Any -> Any)
 -> Any -> Any -> Any -> Any -> T__'8801'__12 -> Any)
-> (Any -> Any -> Any -> Any -> Any -> Any)
-> Integer
-> Integer
-> Integer
-> Any
-> Any
-> Any
forall a b. a -> b
coe
         (Any -> Any -> Any -> T__'8801'__12 -> Any -> Any)
-> Any -> Any -> Any -> Any -> T__'8801'__12 -> Any
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8801''45''10216'_448
         (\ Any
v3 Any
v4 Any
v5 Any
v6 Any
v7 -> Any
v7) Integer
v0
         (Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'43'__276
            (Integer -> Integer
forall a b. a -> b
coe Integer
v0) (Integer -> Integer
forall a b. a -> b
coe Integer
MAlonzo.Code.Data.Integer.Base.d_0ℤ_12))
         Integer
v1
         (((Any -> Any -> Any -> T__'8801'__12 -> Any -> Any)
 -> Any -> Any -> Any -> Any -> T__'8801'__12 -> Any)
-> (Any -> Any -> Any -> Any -> Any -> Any)
-> Integer
-> Integer
-> Integer
-> Any
-> Any
-> Any
forall a b. a -> b
coe
            (Any -> Any -> Any -> T__'8801'__12 -> Any -> Any)
-> Any -> Any -> Any -> Any -> T__'8801'__12 -> Any
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8801''45''10216'_448
            (\ Any
v3 Any
v4 Any
v5 Any
v6 Any
v7 -> Any
v7)
            (Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'43'__276
               (Integer -> Integer
forall a b. a -> b
coe Integer
v0) (Integer -> Integer
forall a b. a -> b
coe Integer
MAlonzo.Code.Data.Integer.Base.d_0ℤ_12))
            (Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'43'__276
               (Integer -> Integer
forall a b. a -> b
coe Integer
v0)
               ((Integer -> Integer -> Integer) -> Any -> Any -> Integer
forall a b. a -> b
coe
                  Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'43'__276
                  ((Integer -> Integer) -> Any -> Any
forall a b. a -> b
coe Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d_'45'__252 (Integer -> Any
forall a b. a -> b
coe Integer
v1))
                  (Integer -> Any
forall a b. a -> b
coe Integer
v1)))
            Integer
v1
            (((Any -> Any -> Any -> T__'8801'__12 -> Any -> Any)
 -> Any -> Any -> Any -> Any -> T__'8801'__12 -> Any)
-> (Any -> Any -> Any -> Any -> Any -> Any)
-> Integer
-> Integer
-> Integer
-> Any
-> Any
-> Any
forall a b. a -> b
coe
               (Any -> Any -> Any -> T__'8801'__12 -> Any -> Any)
-> Any -> Any -> Any -> Any -> T__'8801'__12 -> Any
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8801''45''10216'_448
               (\ Any
v3 Any
v4 Any
v5 Any
v6 Any
v7 -> Any
v7)
               (Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'43'__276
                  (Integer -> Integer
forall a b. a -> b
coe Integer
v0)
                  ((Integer -> Integer -> Integer) -> Any -> Any -> Integer
forall a b. a -> b
coe
                     Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'43'__276
                     ((Integer -> Integer) -> Any -> Any
forall a b. a -> b
coe Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d_'45'__252 (Integer -> Any
forall a b. a -> b
coe Integer
v1))
                     (Integer -> Any
forall a b. a -> b
coe Integer
v1)))
               (Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'43'__276
                  ((Integer -> Integer -> Integer) -> Any -> Any -> Integer
forall a b. a -> b
coe Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'45'__294 (Integer -> Any
forall a b. a -> b
coe Integer
v0) (Integer -> Any
forall a b. a -> b
coe Integer
v1))
                  (Integer -> Integer
forall a b. a -> b
coe Integer
v1))
               Integer
v1
               (((Any -> Any -> Any -> Any -> Any -> Any)
 -> Any -> Any -> Any -> Any -> Any -> Any)
-> Any -> Integer -> Integer -> Integer -> Any -> Any -> Any
forall a b. a -> b
coe
                  (Any -> Any -> Any -> Any -> Any -> Any)
-> Any -> Any -> Any -> Any -> Any -> Any
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8804'_308
                  ((T_IsPreorder_70
 -> (Any -> Any -> Any -> Any -> Any -> Any)
 -> Any
 -> Any
 -> Any
 -> Any
 -> T__IsRelatedTo__78
 -> T__IsRelatedTo__78)
-> 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
-> Any
-> T__IsRelatedTo__78
-> T__IsRelatedTo__78
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_'8804''45'go_138
                     (T_IsPreorder_70 -> Any
forall a b. a -> b
coe T_IsPreorder_70
d_'8804''45'isPreorder_2800)
                     (\ 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_2958 Any
v6 Any
v7))
                  (Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'43'__276
                     ((Integer -> Integer -> Integer) -> Any -> Any -> Integer
forall a b. a -> b
coe Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'45'__294 (Integer -> Any
forall a b. a -> b
coe Integer
v0) (Integer -> Any
forall a b. a -> b
coe Integer
v1))
                     (Integer -> Integer
forall a b. a -> b
coe Integer
v1))
                  (Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'43'__276
                     (Integer -> Integer
forall a b. a -> b
coe Integer
MAlonzo.Code.Data.Integer.Base.d_0ℤ_12) (Integer -> Integer
forall a b. a -> b
coe Integer
v1))
                  Integer
v1
                  (((Any -> Any -> Any -> T__'8801'__12 -> Any -> Any)
 -> Any -> Any -> Any -> Any -> T__'8801'__12 -> Any)
-> (Any -> Any -> Any -> Any -> Any -> Any)
-> Integer
-> Integer
-> Integer
-> Any
-> Any
-> Any
forall a b. a -> b
coe
                     (Any -> Any -> Any -> T__'8801'__12 -> Any -> Any)
-> Any -> Any -> Any -> Any -> T__'8801'__12 -> Any
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8801''45''10217'_436
                     (\ Any
v3 Any
v4 Any
v5 Any
v6 Any
v7 -> Any
v7)
                     (Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'43'__276
                        (Integer -> Integer
forall a b. a -> b
coe Integer
MAlonzo.Code.Data.Integer.Base.d_0ℤ_12) (Integer -> Integer
forall a b. a -> b
coe Integer
v1))
                     Integer
v1 Integer
v1
                     (((Any -> Any) -> Any -> Any) -> Any -> Any -> Any
forall a b. a -> b
coe
                        (Any -> Any) -> Any -> Any
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du__'8718'_492
                        ((T_IsPreorder_70 -> Any -> T__IsRelatedTo__78) -> Any -> Any
forall a b. a -> b
coe
                           T_IsPreorder_70 -> Any -> T__IsRelatedTo__78
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_stop_166
                           (T_IsPreorder_70 -> Any
forall a b. a -> b
coe T_IsPreorder_70
d_'8804''45'isPreorder_2800))
                        (Integer -> Any
forall a b. a -> b
coe Integer
v1))
                     Any
forall a. a
erased)
                  ((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'737''45''8804'_4540 Integer
v1
                     (Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'45'__294 (Integer -> Integer
forall a b. a -> b
coe Integer
v0) (Integer -> Integer
forall a b. a -> b
coe Integer
v1))
                     Integer
MAlonzo.Code.Data.Integer.Base.d_0ℤ_12 T__'8804'__26
v2))
               Any
forall a. a
erased)
            Any
forall a. a
erased)
         Any
forall a. a
erased)
-- Data.Integer.Properties.i≤j⇒0≤j-i
d_i'8804'j'8658'0'8804'j'45'i_4924 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26 ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26
d_i'8804'j'8658'0'8804'j'45'i_4924 :: Integer -> Integer -> T__'8804'__26 -> T__'8804'__26
d_i'8804'j'8658'0'8804'j'45'i_4924 Integer
v0 Integer
v1 T__'8804'__26
v2
  = ((Any -> Any -> Any -> Any) -> Any -> Any -> Any -> Any)
-> Any -> Integer -> Integer -> Any -> T__'8804'__26
forall a b. a -> b
coe
      (Any -> Any -> Any -> Any) -> Any -> Any -> Any -> Any
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_begin__46
      ((T_IsPreorder_70
 -> (Any -> Any -> Any -> Any)
 -> Any
 -> Any
 -> T__IsRelatedTo__78
 -> Any)
-> Any -> (Any -> Any -> Any -> Any) -> Any
forall a b. a -> b
coe
         T_IsPreorder_70
-> (Any -> Any -> Any -> Any)
-> Any
-> Any
-> T__IsRelatedTo__78
-> Any
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_start_96
         (T_IsPreorder_70 -> Any
forall a b. a -> b
coe T_IsPreorder_70
d_'8804''45'isPreorder_2800)
         (\ Any
v3 Any
v4 Any
v5 -> (T__'60'__50 -> T__'8804'__26) -> Any -> Any
forall a b. a -> b
coe T__'60'__50 -> T__'8804'__26
du_'60''8658''8804'_2846 Any
v5))
      Integer
MAlonzo.Code.Data.Integer.Base.d_0ℤ_12
      (Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'45'__294 (Integer -> Integer
forall a b. a -> b
coe Integer
v1) (Integer -> Integer
forall a b. a -> b
coe Integer
v0))
      (((Any -> Any -> Any -> T__'8801'__12 -> Any -> Any)
 -> Any -> Any -> Any -> Any -> T__'8801'__12 -> Any)
-> (Any -> Any -> Any -> Any -> Any -> Any)
-> Integer
-> Integer
-> Integer
-> Any
-> Any
-> Any
forall a b. a -> b
coe
         (Any -> Any -> Any -> T__'8801'__12 -> Any -> Any)
-> Any -> Any -> Any -> Any -> T__'8801'__12 -> Any
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8801''45''10216'_448
         (\ Any
v3 Any
v4 Any
v5 Any
v6 Any
v7 -> Any
v7) Integer
MAlonzo.Code.Data.Integer.Base.d_0ℤ_12
         (Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'45'__294 (Integer -> Integer
forall a b. a -> b
coe Integer
v0) (Integer -> Integer
forall a b. a -> b
coe Integer
v0))
         (Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'45'__294 (Integer -> Integer
forall a b. a -> b
coe Integer
v1) (Integer -> Integer
forall a b. a -> b
coe Integer
v0))
         (((Any -> Any -> Any -> Any -> Any -> Any)
 -> Any -> Any -> Any -> Any -> Any -> Any)
-> Any -> Integer -> Integer -> Integer -> Any -> Any -> Any
forall a b. a -> b
coe
            (Any -> Any -> Any -> Any -> Any -> Any)
-> Any -> Any -> Any -> Any -> Any -> Any
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8804'_308
            ((T_IsPreorder_70
 -> (Any -> Any -> Any -> Any -> Any -> Any)
 -> Any
 -> Any
 -> Any
 -> Any
 -> T__IsRelatedTo__78
 -> T__IsRelatedTo__78)
-> 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
-> Any
-> T__IsRelatedTo__78
-> T__IsRelatedTo__78
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_'8804''45'go_138
               (T_IsPreorder_70 -> Any
forall a b. a -> b
coe T_IsPreorder_70
d_'8804''45'isPreorder_2800)
               (\ 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_2958 Any
v6 Any
v7))
            (Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'45'__294 (Integer -> Integer
forall a b. a -> b
coe Integer
v0) (Integer -> Integer
forall a b. a -> b
coe Integer
v0))
            (Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'45'__294 (Integer -> Integer
forall a b. a -> b
coe Integer
v1) (Integer -> Integer
forall a b. a -> b
coe Integer
v0))
            (Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'45'__294 (Integer -> Integer
forall a b. a -> b
coe Integer
v1) (Integer -> Integer
forall a b. a -> b
coe Integer
v0))
            (((Any -> Any) -> Any -> Any) -> Any -> Any -> Any
forall a b. a -> b
coe
               (Any -> Any) -> Any -> Any
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du__'8718'_492
               ((T_IsPreorder_70 -> Any -> T__IsRelatedTo__78) -> Any -> Any
forall a b. a -> b
coe
                  T_IsPreorder_70 -> Any -> T__IsRelatedTo__78
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_stop_166
                  (T_IsPreorder_70 -> Any
forall a b. a -> b
coe T_IsPreorder_70
d_'8804''45'isPreorder_2800))
               ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe
                  Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'45'__294 (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)
-> 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'737''45''8804'_4540
               (Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d_'45'__252 (Integer -> Integer
forall a b. a -> b
coe Integer
v0)) Integer
v0 Integer
v1 T__'8804'__26
v2))
         Any
forall a. a
erased)
-- Data.Integer.Properties.0≤i-j⇒j≤i
d_0'8804'i'45'j'8658'j'8804'i_4936 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26 ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26
d_0'8804'i'45'j'8658'j'8804'i_4936 :: Integer -> Integer -> T__'8804'__26 -> T__'8804'__26
d_0'8804'i'45'j'8658'j'8804'i_4936 Integer
v0 Integer
v1 T__'8804'__26
v2
  = ((Any -> Any -> Any -> Any) -> Any -> Any -> Any -> Any)
-> Any -> Integer -> Integer -> Any -> T__'8804'__26
forall a b. a -> b
coe
      (Any -> Any -> Any -> Any) -> Any -> Any -> Any -> Any
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_begin__46
      ((T_IsPreorder_70
 -> (Any -> Any -> Any -> Any)
 -> Any
 -> Any
 -> T__IsRelatedTo__78
 -> Any)
-> Any -> (Any -> Any -> Any -> Any) -> Any
forall a b. a -> b
coe
         T_IsPreorder_70
-> (Any -> Any -> Any -> Any)
-> Any
-> Any
-> T__IsRelatedTo__78
-> Any
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_start_96
         (T_IsPreorder_70 -> Any
forall a b. a -> b
coe T_IsPreorder_70
d_'8804''45'isPreorder_2800)
         (\ Any
v3 Any
v4 Any
v5 -> (T__'60'__50 -> T__'8804'__26) -> Any -> Any
forall a b. a -> b
coe T__'60'__50 -> T__'8804'__26
du_'60''8658''8804'_2846 Any
v5))
      Integer
v1 Integer
v0
      (((Any -> Any -> Any -> T__'8801'__12 -> Any -> Any)
 -> Any -> Any -> Any -> Any -> T__'8801'__12 -> Any)
-> (Any -> Any -> Any -> Any -> Any -> Any)
-> Integer
-> Integer
-> Integer
-> Any
-> Any
-> Any
forall a b. a -> b
coe
         (Any -> Any -> Any -> T__'8801'__12 -> Any -> Any)
-> Any -> Any -> Any -> Any -> T__'8801'__12 -> Any
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8801''45''10216'_448
         (\ Any
v3 Any
v4 Any
v5 Any
v6 Any
v7 -> Any
v7) Integer
v1
         (Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'43'__276
            (Integer -> Integer
forall a b. a -> b
coe Integer
MAlonzo.Code.Data.Integer.Base.d_0ℤ_12) (Integer -> Integer
forall a b. a -> b
coe Integer
v1))
         Integer
v0
         (((Any -> Any -> Any -> Any -> Any -> Any)
 -> Any -> Any -> Any -> Any -> Any -> Any)
-> Any -> Integer -> Integer -> Integer -> Any -> Any -> Any
forall a b. a -> b
coe
            (Any -> Any -> Any -> Any -> Any -> Any)
-> Any -> Any -> Any -> Any -> Any -> Any
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8804'_308
            ((T_IsPreorder_70
 -> (Any -> Any -> Any -> Any -> Any -> Any)
 -> Any
 -> Any
 -> Any
 -> Any
 -> T__IsRelatedTo__78
 -> T__IsRelatedTo__78)
-> 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
-> Any
-> T__IsRelatedTo__78
-> T__IsRelatedTo__78
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_'8804''45'go_138
               (T_IsPreorder_70 -> Any
forall a b. a -> b
coe T_IsPreorder_70
d_'8804''45'isPreorder_2800)
               (\ 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_2958 Any
v6 Any
v7))
            (Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'43'__276
               (Integer -> Integer
forall a b. a -> b
coe Integer
MAlonzo.Code.Data.Integer.Base.d_0ℤ_12) (Integer -> Integer
forall a b. a -> b
coe Integer
v1))
            (Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'43'__276
               ((Integer -> Integer -> Integer) -> Any -> Any -> Integer
forall a b. a -> b
coe Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'45'__294 (Integer -> Any
forall a b. a -> b
coe Integer
v0) (Integer -> Any
forall a b. a -> b
coe Integer
v1))
               (Integer -> Integer
forall a b. a -> b
coe Integer
v1))
            Integer
v0
            (((Any -> Any -> Any -> T__'8801'__12 -> Any -> Any)
 -> Any -> Any -> Any -> Any -> T__'8801'__12 -> Any)
-> (Any -> Any -> Any -> Any -> Any -> Any)
-> Integer
-> Integer
-> Integer
-> Any
-> Any
-> Any
forall a b. a -> b
coe
               (Any -> Any -> Any -> T__'8801'__12 -> Any -> Any)
-> Any -> Any -> Any -> Any -> T__'8801'__12 -> Any
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8801''45''10217'_436
               (\ Any
v3 Any
v4 Any
v5 Any
v6 Any
v7 -> Any
v7)
               (Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'43'__276
                  ((Integer -> Integer -> Integer) -> Any -> Any -> Integer
forall a b. a -> b
coe Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'45'__294 (Integer -> Any
forall a b. a -> b
coe Integer
v0) (Integer -> Any
forall a b. a -> b
coe Integer
v1))
                  (Integer -> Integer
forall a b. a -> b
coe Integer
v1))
               (Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'43'__276
                  (Integer -> Integer
forall a b. a -> b
coe Integer
v0)
                  ((Integer -> Integer -> Integer) -> Any -> Any -> Integer
forall a b. a -> b
coe
                     Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'43'__276
                     ((Integer -> Integer) -> Any -> Any
forall a b. a -> b
coe Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d_'45'__252 (Integer -> Any
forall a b. a -> b
coe Integer
v1))
                     (Integer -> Any
forall a b. a -> b
coe Integer
v1)))
               Integer
v0
               (((Any -> Any -> Any -> T__'8801'__12 -> Any -> Any)
 -> Any -> Any -> Any -> Any -> T__'8801'__12 -> Any)
-> (Any -> Any -> Any -> Any -> Any -> Any)
-> Integer
-> Integer
-> Integer
-> Any
-> Any
-> Any
forall a b. a -> b
coe
                  (Any -> Any -> Any -> T__'8801'__12 -> Any -> Any)
-> Any -> Any -> Any -> Any -> T__'8801'__12 -> Any
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8801''45''10217'_436
                  (\ Any
v3 Any
v4 Any
v5 Any
v6 Any
v7 -> Any
v7)
                  (Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'43'__276
                     (Integer -> Integer
forall a b. a -> b
coe Integer
v0)
                     ((Integer -> Integer -> Integer) -> Any -> Any -> Integer
forall a b. a -> b
coe
                        Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'43'__276
                        ((Integer -> Integer) -> Any -> Any
forall a b. a -> b
coe Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d_'45'__252 (Integer -> Any
forall a b. a -> b
coe Integer
v1))
                        (Integer -> Any
forall a b. a -> b
coe Integer
v1)))
                  (Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'43'__276
                     (Integer -> Integer
forall a b. a -> b
coe Integer
v0) (Integer -> Integer
forall a b. a -> b
coe Integer
MAlonzo.Code.Data.Integer.Base.d_0ℤ_12))
                  Integer
v0
                  (((Any -> Any -> Any -> T__'8801'__12 -> Any -> Any)
 -> Any -> Any -> Any -> Any -> T__'8801'__12 -> Any)
-> (Any -> Any -> Any -> Any -> Any -> Any)
-> Integer
-> Integer
-> Integer
-> Any
-> Any
-> Any
forall a b. a -> b
coe
                     (Any -> Any -> Any -> T__'8801'__12 -> Any -> Any)
-> Any -> Any -> Any -> Any -> T__'8801'__12 -> Any
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8801''45''10217'_436
                     (\ Any
v3 Any
v4 Any
v5 Any
v6 Any
v7 -> Any
v7)
                     (Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'43'__276
                        (Integer -> Integer
forall a b. a -> b
coe Integer
v0) (Integer -> Integer
forall a b. a -> b
coe Integer
MAlonzo.Code.Data.Integer.Base.d_0ℤ_12))
                     Integer
v0 Integer
v0
                     (((Any -> Any) -> Any -> Any) -> Any -> Any -> Any
forall a b. a -> b
coe
                        (Any -> Any) -> Any -> Any
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du__'8718'_492
                        ((T_IsPreorder_70 -> Any -> T__IsRelatedTo__78) -> Any -> Any
forall a b. a -> b
coe
                           T_IsPreorder_70 -> Any -> T__IsRelatedTo__78
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_stop_166
                           (T_IsPreorder_70 -> Any
forall a b. a -> b
coe T_IsPreorder_70
d_'8804''45'isPreorder_2800))
                        (Integer -> Any
forall a b. a -> b
coe Integer
v0))
                     Any
forall a. a
erased)
                  Any
forall a. a
erased)
               Any
forall a. a
erased)
            ((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'737''45''8804'_4540 Integer
v1
               Integer
MAlonzo.Code.Data.Integer.Base.d_0ℤ_12
               (Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'45'__294 (Integer -> Integer
forall a b. a -> b
coe Integer
v0) (Integer -> Integer
forall a b. a -> b
coe Integer
v1))
               T__'8804'__26
v2))
         Any
forall a. a
erased)
-- Data.Integer.Properties.i≤j⇒i≤1+j
d_i'8804'j'8658'i'8804'1'43'j_4948 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26 ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26
d_i'8804'j'8658'i'8804'1'43'j_4948 :: Integer -> Integer -> T__'8804'__26 -> T__'8804'__26
d_i'8804'j'8658'i'8804'1'43'j_4948 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
du_i'8804'j'8658'i'8804'k'43'j_4578 (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.i≤suc[i]
d_i'8804'suc'91'i'93'_4952 ::
  Integer -> MAlonzo.Code.Data.Integer.Base.T__'8804'__26
d_i'8804'suc'91'i'93'_4952 :: Integer -> T__'8804'__26
d_i'8804'suc'91'i'93'_4952 Integer
v0
  = (Integer -> Integer -> T__'8804'__26)
-> Any -> Any -> T__'8804'__26
forall a b. a -> b
coe Integer -> Integer -> T__'8804'__26
du_i'8804'j'43'i_4592 (Integer -> Any
forall a b. a -> b
coe Integer
v0) (Integer -> Any
forall a b. a -> b
coe (Integer
1 :: Integer))
-- Data.Integer.Properties.suc-+
d_suc'45''43'_4960 ::
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_suc'45''43'_4960 :: Integer -> Integer -> T__'8801'__12
d_suc'45''43'_4960 = Integer -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.i≢suc[i]
d_i'8802'suc'91'i'93'_4970 ::
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Data.Irrelevant.T_Irrelevant_20
d_i'8802'suc'91'i'93'_4970 :: Integer -> T__'8801'__12 -> T_Irrelevant_20
d_i'8802'suc'91'i'93'_4970 = Integer -> T__'8801'__12 -> T_Irrelevant_20
forall a. a
erased
-- Data.Integer.Properties.1-[1+n]≡-n
d_1'45''91'1'43'n'93''8801''45'n_4976 ::
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_1'45''91'1'43'n'93''8801''45'n_4976 :: Integer -> T__'8801'__12
d_1'45''91'1'43'n'93''8801''45'n_4976 = Integer -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.suc-mono
d_suc'45'mono_4980 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26 ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26
d_suc'45'mono_4980 :: Integer -> Integer -> T__'8804'__26 -> T__'8804'__26
d_suc'45'mono_4980 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'__22
v5
        -> (Integer -> Integer -> Integer -> T__'8804'__22 -> T__'8804'__26)
-> Any -> Any -> Any -> Any -> T__'8804'__26
forall a b. a -> b
coe
             Integer -> Integer -> Integer -> T__'8804'__22 -> T__'8804'__26
d_'8854''45'mono'691''45''8805''45''8804'_4024 (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'__22 -> T__'8804'__22) -> T__'8804'__22 -> Any
forall a b. a -> b
coe T__'8804'__22 -> T__'8804'__22
MAlonzo.Code.Data.Nat.Base.C_s'8804's_34 T__'8804'__22
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
             (((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 -> Any -> Any
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_begin__46
                ((T_IsPreorder_70
 -> (Any -> Any -> Any -> Any)
 -> Any
 -> Any
 -> T__IsRelatedTo__78
 -> Any)
-> Any -> (Any -> Any -> Any -> Any) -> Any
forall a b. a -> b
coe
                   T_IsPreorder_70
-> (Any -> Any -> Any -> Any)
-> Any
-> Any
-> T__IsRelatedTo__78
-> Any
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_start_96
                   (T_IsPreorder_70 -> Any
forall a b. a -> b
coe T_IsPreorder_70
d_'8804''45'isPreorder_2800)
                   (\ Any
v6 Any
v7 Any
v8 -> (T__'60'__50 -> T__'8804'__26) -> Any -> Any
forall a b. a -> b
coe T__'60'__50 -> T__'8804'__26
du_'60''8658''8804'_2846 Any
v8))
                (((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'_292
                   Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d_suc_300 (\ 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'__298
                   (\ Any
v6 Any
v7 -> Any
v7) Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d_suc_300 Integer
v0 Integer
v1)
                (((Any -> Any -> Any -> T__'8801'__12 -> Any -> Any)
 -> Any -> Any -> Any -> Any -> T__'8801'__12 -> Any)
-> (Any -> Any -> Any -> Any -> Any -> Any)
-> Integer
-> Integer
-> Any
-> Any
-> Any
-> Any
forall a b. a -> b
coe
                   (Any -> Any -> Any -> T__'8801'__12 -> Any -> Any)
-> Any -> Any -> Any -> Any -> T__'8801'__12 -> Any
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8801''45''10217'_436
                   (\ Any
v6 Any
v7 Any
v8 Any
v9 Any
v10 -> Any
v10)
                   (Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'8854'__258
                      (Integer -> Integer
forall a b. a -> b
coe (Integer
1 :: Integer)) ((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)))
                   (Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'8854'__258
                      (Integer -> Integer
forall a b. a -> b
coe (Integer
0 :: Integer)) (Integer -> Integer
forall a b. a -> b
coe Integer
v5))
                   (((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'__298
                      (\ Any
v6 Any
v7 -> Any
v7) Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d_suc_300 Integer
v0 Integer
v1)
                   (((Any -> Any -> Any -> Any -> Any -> Any)
 -> Any -> Any -> Any -> Any -> Any -> Any)
-> Any -> Integer -> Integer -> Any -> Any -> Any -> Any
forall a b. a -> b
coe
                      (Any -> Any -> Any -> Any -> Any -> Any)
-> Any -> Any -> Any -> Any -> Any -> Any
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8804'_308
                      ((T_IsPreorder_70
 -> (Any -> Any -> Any -> Any -> Any -> Any)
 -> Any
 -> Any
 -> Any
 -> Any
 -> T__IsRelatedTo__78
 -> T__IsRelatedTo__78)
-> 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
-> Any
-> T__IsRelatedTo__78
-> T__IsRelatedTo__78
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_'8804''45'go_138
                         (T_IsPreorder_70 -> Any
forall a b. a -> b
coe T_IsPreorder_70
d_'8804''45'isPreorder_2800)
                         (\ 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_2958 Any
v9 Any
v10))
                      (Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'8854'__258
                         (Integer -> Integer
forall a b. a -> b
coe (Integer
0 :: Integer)) (Integer -> Integer
forall a b. a -> b
coe Integer
v5))
                      (Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d_suc_300 (Integer -> Integer
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'__298
                         (\ Any
v6 Any
v7 -> Any
v7) Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d_suc_300 Integer
v0 Integer
v1)
                      (((Any -> Any) -> Any -> Any) -> Any -> Any -> Any
forall a b. a -> b
coe
                         (Any -> Any) -> Any -> Any
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du__'8718'_492
                         ((T_IsPreorder_70 -> Any -> T__IsRelatedTo__78) -> Any -> Any
forall a b. a -> b
coe
                            T_IsPreorder_70 -> Any -> T__IsRelatedTo__78
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_stop_166
                            (T_IsPreorder_70 -> Any
forall a b. a -> b
coe T_IsPreorder_70
d_'8804''45'isPreorder_2800))
                         ((Integer -> Integer) -> Any -> Any
forall a b. a -> b
coe Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d_suc_300 (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'_4002 (Integer -> Any
forall a b. a -> b
coe Integer
v5)))
                   Any
forall a. a
erased))
      MAlonzo.Code.Data.Integer.Base.C_'43''8804''43'_48 T__'8804'__22
v5
        -> (T__'8804'__22 -> T__'8804'__26) -> Any -> T__'8804'__26
forall a b. a -> b
coe
             T__'8804'__22 -> T__'8804'__26
MAlonzo.Code.Data.Integer.Base.C_'43''8804''43'_48
             ((T__'8804'__22 -> T__'8804'__22) -> T__'8804'__22 -> Any
forall a b. a -> b
coe T__'8804'__22 -> T__'8804'__22
MAlonzo.Code.Data.Nat.Base.C_s'8804's_34 T__'8804'__22
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_4994 ::
  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_4994 :: Integer -> Integer -> T__'8804'__26 -> T__'60'__50
d_suc'91'i'93''8804'j'8658'i'60'j_4994 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'__22
v5
              -> (T__'8804'__22 -> T__'60'__50) -> T__'8804'__22 -> T__'60'__50
forall a b. a -> b
coe T__'8804'__22 -> T__'60'__50
MAlonzo.Code.Data.Integer.Base.C_'43''60''43'_72 T__'8804'__22
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'__22
v5
                      -> (T__'8804'__22 -> T__'60'__50) -> Any -> T__'60'__50
forall a b. a -> b
coe
                           T__'8804'__22 -> T__'60'__50
MAlonzo.Code.Data.Integer.Base.C_'45''60''45'_58
                           ((T__'8804'__22 -> T__'8804'__22) -> T__'8804'__22 -> Any
forall a b. a -> b
coe T__'8804'__22 -> T__'8804'__22
MAlonzo.Code.Data.Nat.Base.C_s'8804's_34 T__'8804'__22
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_5014 ::
  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_5014 :: Integer -> Integer -> T__'60'__50 -> T__'8804'__26
d_i'60'j'8658'suc'91'i'93''8804'j_5014 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'__22
v5
              -> (T__'8804'__22 -> T__'8804'__26) -> T__'8804'__22 -> T__'8804'__26
forall a b. a -> b
coe T__'8804'__22 -> T__'8804'__26
MAlonzo.Code.Data.Integer.Base.C_'43''8804''43'_48 T__'8804'__22
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'__22 -> T__'8804'__26) -> Any -> Any
forall a b. a -> b
coe
                T__'8804'__22 -> T__'8804'__26
MAlonzo.Code.Data.Integer.Base.C_'43''8804''43'_48
                (T__'8804'__22 -> Any
forall a b. a -> b
coe T__'8804'__22
MAlonzo.Code.Data.Nat.Base.C_z'8804'n_26))
      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'__22
v5
                      -> (T__'8804'__22 -> T__'8804'__26) -> Any -> T__'8804'__26
forall a b. a -> b
coe
                           T__'8804'__22 -> T__'8804'__26
MAlonzo.Code.Data.Integer.Base.C_'45''8804''45'_34
                           ((T__'8804'__22 -> T__'8804'__22) -> Any -> Any
forall a b. a -> b
coe T__'8804'__22 -> T__'8804'__22
MAlonzo.Code.Data.Nat.Base.du_s'8804's'8315''185'_62 (T__'8804'__22 -> Any
forall a b. a -> b
coe T__'8804'__22
v5))
                    T__'60'__50
_ -> T__'8804'__26
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Data.Integer.Properties.suc-pred
d_suc'45'pred_5026 ::
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_suc'45'pred_5026 :: Integer -> T__'8801'__12
d_suc'45'pred_5026 = Integer -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.pred-suc
d_pred'45'suc_5036 ::
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_pred'45'suc_5036 :: Integer -> T__'8801'__12
d_pred'45'suc_5036 = Integer -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.+-pred
d_'43''45'pred_5048 ::
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'43''45'pred_5048 :: Integer -> Integer -> T__'8801'__12
d_'43''45'pred_5048 = Integer -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.pred-+
d_pred'45''43'_5064 ::
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_pred'45''43'_5064 :: Integer -> Integer -> T__'8801'__12
d_pred'45''43'_5064 = Integer -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.neg-suc
d_neg'45'suc_5076 ::
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_neg'45'suc_5076 :: Integer -> T__'8801'__12
d_neg'45'suc_5076 = Integer -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.minus-suc
d_minus'45'suc_5084 ::
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_minus'45'suc_5084 :: Integer -> Integer -> T__'8801'__12
d_minus'45'suc_5084 = Integer -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.i≤pred[j]⇒i<j
d_i'8804'pred'91'j'93''8658'i'60'j_5094 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26 ->
  MAlonzo.Code.Data.Integer.Base.T__'60'__50
d_i'8804'pred'91'j'93''8658'i'60'j_5094 :: Integer -> Integer -> T__'8804'__26 -> T__'60'__50
d_i'8804'pred'91'j'93''8658'i'60'j_5094 ~Integer
v0 Integer
v1 T__'8804'__26
v2
  = Integer -> T__'8804'__26 -> T__'60'__50
du_i'8804'pred'91'j'93''8658'i'60'j_5094 Integer
v1 T__'8804'__26
v2
du_i'8804'pred'91'j'93''8658'i'60'j_5094 ::
  Integer ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26 ->
  MAlonzo.Code.Data.Integer.Base.T__'60'__50
du_i'8804'pred'91'j'93''8658'i'60'j_5094 :: Integer -> T__'8804'__26 -> T__'60'__50
du_i'8804'pred'91'j'93''8658'i'60'j_5094 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_2958 (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
du_m'8854'1'43'n'60'm_3942 (Integer -> Any
forall a b. a -> b
coe Integer
v0) (Integer -> Any
forall a b. a -> b
coe (Integer
1 :: 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_2958 (T__'8804'__26 -> Any
forall a b. a -> b
coe T__'8804'__26
v1)
             ((T__'8804'__22 -> T__'60'__50) -> T__'8804'__22 -> Any
forall a b. a -> b
coe
                T__'8804'__22 -> T__'60'__50
MAlonzo.Code.Data.Integer.Base.C_'45''60''45'_58
                (Integer -> T__'8804'__22
MAlonzo.Code.Data.Nat.Properties.d_'8804''45'refl_2776
                   ((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.i<j⇒i≤pred[j]
d_i'60'j'8658'i'8804'pred'91'j'93'_5104 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Integer.Base.T__'60'__50 ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26
d_i'60'j'8658'i'8804'pred'91'j'93'_5104 :: Integer -> Integer -> T__'60'__50 -> T__'8804'__26
d_i'60'j'8658'i'8804'pred'91'j'93'_5104 ~Integer
v0 Integer
v1 T__'60'__50
v2
  = Integer -> T__'60'__50 -> T__'8804'__26
du_i'60'j'8658'i'8804'pred'91'j'93'_5104 Integer
v1 T__'60'__50
v2
du_i'60'j'8658'i'8804'pred'91'j'93'_5104 ::
  Integer ->
  MAlonzo.Code.Data.Integer.Base.T__'60'__50 ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26
du_i'60'j'8658'i'8804'pred'91'j'93'_5104 :: Integer -> T__'60'__50 -> T__'8804'__26
du_i'60'j'8658'i'8804'pred'91'j'93'_5104 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'__22 -> T__'8804'__26) -> Any -> Any
forall a b. a -> b
coe
                T__'8804'__22 -> T__'8804'__26
MAlonzo.Code.Data.Integer.Base.C_'45''8804''45'_34
                (T__'8804'__22 -> Any
forall a b. a -> b
coe T__'8804'__22
MAlonzo.Code.Data.Nat.Base.C_z'8804'n_26))
      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'__22
v4
              -> (T__'8804'__22 -> T__'8804'__26) -> Any -> T__'8804'__26
forall a b. a -> b
coe
                   T__'8804'__22 -> T__'8804'__26
MAlonzo.Code.Data.Integer.Base.C_'43''8804''43'_48
                   ((T__'8804'__22 -> T__'8804'__22) -> Any -> Any
forall a b. a -> b
coe T__'8804'__22 -> T__'8804'__22
MAlonzo.Code.Data.Nat.Base.du_s'8804's'8315''185'_62 (T__'8804'__22 -> Any
forall a b. a -> b
coe T__'8804'__22
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'__22
v4
               -> (T__'8804'__22 -> T__'8804'__26) -> T__'8804'__22 -> T__'8804'__26
forall a b. a -> b
coe T__'8804'__22 -> T__'8804'__26
MAlonzo.Code.Data.Integer.Base.C_'45''8804''45'_34 T__'8804'__22
v4
             T__'60'__50
_ -> T__'8804'__26
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Data.Integer.Properties.i≤j⇒pred[i]≤j
d_i'8804'j'8658'pred'91'i'93''8804'j_5116 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26 ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26
d_i'8804'j'8658'pred'91'i'93''8804'j_5116 :: Integer -> Integer -> T__'8804'__26 -> T__'8804'__26
d_i'8804'j'8658'pred'91'i'93''8804'j_5116 ~Integer
v0 ~Integer
v1 T__'8804'__26
v2
  = T__'8804'__26 -> T__'8804'__26
du_i'8804'j'8658'pred'91'i'93''8804'j_5116 T__'8804'__26
v2
du_i'8804'j'8658'pred'91'i'93''8804'j_5116 ::
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26 ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26
du_i'8804'j'8658'pred'91'i'93''8804'j_5116 :: T__'8804'__26 -> T__'8804'__26
du_i'8804'j'8658'pred'91'i'93''8804'j_5116 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'__22
v3
        -> (T__'8804'__22 -> T__'8804'__26) -> T__'8804'__22 -> T__'8804'__26
forall a b. a -> b
coe T__'8804'__22 -> T__'8804'__26
MAlonzo.Code.Data.Integer.Base.C_'45''8804''45'_34 T__'8804'__22
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'__22
v3
        -> case T__'8804'__22 -> T__'8804'__22
forall a b. a -> b
coe T__'8804'__22
v3 of
             T__'8804'__22
MAlonzo.Code.Data.Nat.Base.C_z'8804'n_26
               -> 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_34 T__'8804'__22
v6
               -> (T__'8804'__22 -> T__'8804'__26) -> T__'8804'__22 -> T__'8804'__26
forall a b. a -> b
coe T__'8804'__22 -> T__'8804'__26
MAlonzo.Code.Data.Integer.Base.C_'43''8804''43'_48 T__'8804'__22
v6
             T__'8804'__22
_ -> 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_5122 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26 ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26
d_pred'45'mono_5122 :: Integer -> Integer -> T__'8804'__26 -> T__'8804'__26
d_pred'45'mono_5122 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'__22
v5
        -> (T__'8804'__22 -> T__'8804'__26) -> Any -> T__'8804'__26
forall a b. a -> b
coe
             T__'8804'__22 -> T__'8804'__26
MAlonzo.Code.Data.Integer.Base.C_'45''8804''45'_34
             ((T__'8804'__22 -> T__'8804'__22) -> T__'8804'__22 -> Any
forall a b. a -> b
coe T__'8804'__22 -> T__'8804'__22
MAlonzo.Code.Data.Nat.Base.C_s'8804's_34 T__'8804'__22
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'__22 -> T__'8804'__26) -> Any -> T__'8804'__26
forall a b. a -> b
coe
                    T__'8804'__22 -> T__'8804'__26
MAlonzo.Code.Data.Integer.Base.C_'45''8804''45'_34
                    (T__'8804'__22 -> Any
forall a b. a -> b
coe T__'8804'__22
MAlonzo.Code.Data.Nat.Base.C_z'8804'n_26)
             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'__22
v5
        -> (Integer -> Integer -> Integer -> T__'8804'__22 -> T__'8804'__26)
-> Any -> Any -> Any -> Any -> T__'8804'__26
forall a b. a -> b
coe
             Integer -> Integer -> Integer -> T__'8804'__22 -> T__'8804'__26
d_'8854''45'mono'737''45''8804'_4056 (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'__22 -> Any
forall a b. a -> b
coe T__'8804'__22
v5)
      T__'8804'__26
_ -> T__'8804'__26
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Data.Integer.Properties.*-comm
d_'42''45'comm_5130 ::
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'42''45'comm_5130 :: Integer -> Integer -> T__'8801'__12
d_'42''45'comm_5130 = Integer -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.*-identityˡ
d_'42''45'identity'737'_5164 ::
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'42''45'identity'737'_5164 :: Integer -> T__'8801'__12
d_'42''45'identity'737'_5164 = Integer -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.*-identityʳ
d_'42''45'identity'691'_5178 ::
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'42''45'identity'691'_5178 :: Integer -> T__'8801'__12
d_'42''45'identity'691'_5178 = Integer -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.*-identity
d_'42''45'identity_5180 :: MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'42''45'identity_5180 :: T_Σ_14
d_'42''45'identity_5180
  = (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'_5182 ::
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'42''45'zero'737'_5182 :: Integer -> T__'8801'__12
d_'42''45'zero'737'_5182 = Integer -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.*-zeroʳ
d_'42''45'zero'691'_5184 ::
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'42''45'zero'691'_5184 :: Integer -> T__'8801'__12
d_'42''45'zero'691'_5184 = Integer -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.*-zero
d_'42''45'zero_5186 :: MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'42''45'zero_5186 :: T_Σ_14
d_'42''45'zero_5186
  = (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.*-assoc
d_'42''45'assoc_5188 ::
  Integer ->
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'42''45'assoc_5188 :: Integer -> Integer -> Integer -> T__'8801'__12
d_'42''45'assoc_5188 = Integer -> Integer -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.distrib-lemma
d_distrib'45'lemma_5266 ::
  Integer ->
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_distrib'45'lemma_5266 :: Integer -> Integer -> Integer -> T__'8801'__12
d_distrib'45'lemma_5266 = Integer -> Integer -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.*-distribʳ-+
d_'42''45'distrib'691''45''43'_5342 ::
  Integer ->
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'42''45'distrib'691''45''43'_5342 :: Integer -> Integer -> Integer -> T__'8801'__12
d_'42''45'distrib'691''45''43'_5342 = Integer -> Integer -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.*-distribˡ-+
d_'42''45'distrib'737''45''43'_5608 ::
  Integer ->
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'42''45'distrib'737''45''43'_5608 :: Integer -> Integer -> Integer -> T__'8801'__12
d_'42''45'distrib'737''45''43'_5608 = Integer -> Integer -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.*-distrib-+
d_'42''45'distrib'45''43'_5610 ::
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'42''45'distrib'45''43'_5610 :: T_Σ_14
d_'42''45'distrib'45''43'_5610
  = (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_5612 ::
  MAlonzo.Code.Algebra.Structures.T_IsMagma_176
d_'42''45'isMagma_5612 :: T_IsMagma_176
d_'42''45'isMagma_5612
  = (T_IsEquivalence_26
 -> (Any -> Any -> Any -> Any -> Any -> Any -> Any)
 -> T_IsMagma_176)
-> Any -> Any -> T_IsMagma_176
forall a b. a -> b
coe
      T_IsEquivalence_26
-> (Any -> Any -> Any -> Any -> Any -> Any -> Any) -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.C_IsMagma'46'constructor_1867
      (T_IsEquivalence_26 -> Any
forall a b. a -> b
coe
         T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.PropositionalEquality.Properties.du_isEquivalence_396)
      Any
forall a. a
erased
-- Data.Integer.Properties.*-isSemigroup
d_'42''45'isSemigroup_5614 ::
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_472
d_'42''45'isSemigroup_5614 :: T_IsSemigroup_472
d_'42''45'isSemigroup_5614
  = (T_IsMagma_176 -> (Any -> Any -> Any -> Any) -> T_IsSemigroup_472)
-> Any -> Any -> T_IsSemigroup_472
forall a b. a -> b
coe
      T_IsMagma_176 -> (Any -> Any -> Any -> Any) -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.C_IsSemigroup'46'constructor_10417
      (T_IsMagma_176 -> Any
forall a b. a -> b
coe T_IsMagma_176
d_'42''45'isMagma_5612) Any
forall a. a
erased
-- Data.Integer.Properties.*-isCommutativeSemigroup
d_'42''45'isCommutativeSemigroup_5616 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_548
d_'42''45'isCommutativeSemigroup_5616 :: T_IsCommutativeSemigroup_548
d_'42''45'isCommutativeSemigroup_5616
  = (T_IsSemigroup_472
 -> (Any -> Any -> Any) -> T_IsCommutativeSemigroup_548)
-> Any -> Any -> T_IsCommutativeSemigroup_548
forall a b. a -> b
coe
      T_IsSemigroup_472
-> (Any -> Any -> Any) -> T_IsCommutativeSemigroup_548
MAlonzo.Code.Algebra.Structures.C_IsCommutativeSemigroup'46'constructor_12093
      (T_IsSemigroup_472 -> Any
forall a b. a -> b
coe T_IsSemigroup_472
d_'42''45'isSemigroup_5614) Any
forall a. a
erased
-- Data.Integer.Properties.*-1-isMonoid
d_'42''45'1'45'isMonoid_5618 ::
  MAlonzo.Code.Algebra.Structures.T_IsMonoid_686
d_'42''45'1'45'isMonoid_5618 :: T_IsMonoid_686
d_'42''45'1'45'isMonoid_5618
  = (T_IsSemigroup_472 -> T_Σ_14 -> T_IsMonoid_686)
-> Any -> Any -> T_IsMonoid_686
forall a b. a -> b
coe
      T_IsSemigroup_472 -> T_Σ_14 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.C_IsMonoid'46'constructor_15873
      (T_IsSemigroup_472 -> Any
forall a b. a -> b
coe T_IsSemigroup_472
d_'42''45'isSemigroup_5614) (T_Σ_14 -> Any
forall a b. a -> b
coe T_Σ_14
d_'42''45'identity_5180)
-- Data.Integer.Properties.*-1-isCommutativeMonoid
d_'42''45'1'45'isCommutativeMonoid_5620 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMonoid_736
d_'42''45'1'45'isCommutativeMonoid_5620 :: T_IsCommutativeMonoid_736
d_'42''45'1'45'isCommutativeMonoid_5620
  = (T_IsMonoid_686
 -> (Any -> Any -> Any) -> T_IsCommutativeMonoid_736)
-> Any -> Any -> T_IsCommutativeMonoid_736
forall a b. a -> b
coe
      T_IsMonoid_686 -> (Any -> Any -> Any) -> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.C_IsCommutativeMonoid'46'constructor_17695
      (T_IsMonoid_686 -> Any
forall a b. a -> b
coe T_IsMonoid_686
d_'42''45'1'45'isMonoid_5618) Any
forall a. a
erased
-- Data.Integer.Properties.+-*-isSemiring
d_'43''45''42''45'isSemiring_5622 ::
  MAlonzo.Code.Algebra.Structures.T_IsSemiring_1570
d_'43''45''42''45'isSemiring_5622 :: T_IsSemiring_1570
d_'43''45''42''45'isSemiring_5622
  = (T_IsSemiringWithoutAnnihilatingZero_1468
 -> T_Σ_14 -> T_IsSemiring_1570)
-> Any -> Any -> T_IsSemiring_1570
forall a b. a -> b
coe
      T_IsSemiringWithoutAnnihilatingZero_1468
-> T_Σ_14 -> T_IsSemiring_1570
MAlonzo.Code.Algebra.Structures.C_IsSemiring'46'constructor_48071
      ((T_IsCommutativeMonoid_736
 -> (Any -> Any -> Any -> Any -> Any -> Any -> Any)
 -> (Any -> Any -> Any -> Any)
 -> T_Σ_14
 -> T_Σ_14
 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> Any -> Any -> Any -> Any -> Any -> Any
forall a b. a -> b
coe
         T_IsCommutativeMonoid_736
-> (Any -> Any -> Any -> Any -> Any -> Any -> Any)
-> (Any -> Any -> Any -> Any)
-> T_Σ_14
-> T_Σ_14
-> T_IsSemiringWithoutAnnihilatingZero_1468
MAlonzo.Code.Algebra.Structures.C_IsSemiringWithoutAnnihilatingZero'46'constructor_43811
         (T_IsCommutativeMonoid_736 -> Any
forall a b. a -> b
coe T_IsCommutativeMonoid_736
d_'43''45'0'45'isCommutativeMonoid_4432) Any
forall a. a
erased Any
forall a. a
erased
         (T_Σ_14 -> Any
forall a b. a -> b
coe T_Σ_14
d_'42''45'identity_5180) (T_Σ_14 -> Any
forall a b. a -> b
coe T_Σ_14
d_'42''45'distrib'45''43'_5610))
      (T_Σ_14 -> Any
forall a b. a -> b
coe T_Σ_14
d_'42''45'zero_5186)
-- Data.Integer.Properties.+-*-isCommutativeSemiring
d_'43''45''42''45'isCommutativeSemiring_5624 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiring_1678
d_'43''45''42''45'isCommutativeSemiring_5624 :: T_IsCommutativeSemiring_1678
d_'43''45''42''45'isCommutativeSemiring_5624
  = (T_IsSemiring_1570
 -> (Any -> Any -> Any) -> T_IsCommutativeSemiring_1678)
-> Any -> Any -> T_IsCommutativeSemiring_1678
forall a b. a -> b
coe
      T_IsSemiring_1570
-> (Any -> Any -> Any) -> T_IsCommutativeSemiring_1678
MAlonzo.Code.Algebra.Structures.C_IsCommutativeSemiring'46'constructor_51895
      (T_IsSemiring_1570 -> Any
forall a b. a -> b
coe T_IsSemiring_1570
d_'43''45''42''45'isSemiring_5622) Any
forall a. a
erased
-- Data.Integer.Properties.+-*-isRing
d_'43''45''42''45'isRing_5626 ::
  MAlonzo.Code.Algebra.Structures.T_IsRing_2650
d_'43''45''42''45'isRing_5626 :: T_IsRing_2650
d_'43''45''42''45'isRing_5626
  = (T_IsAbelianGroup_1132
 -> (Any -> Any -> Any -> Any -> Any -> Any -> Any)
 -> (Any -> Any -> Any -> Any)
 -> T_Σ_14
 -> T_Σ_14
 -> T_IsRing_2650)
-> Any -> Any -> Any -> Any -> Any -> T_IsRing_2650
forall a b. a -> b
coe
      T_IsAbelianGroup_1132
-> (Any -> Any -> Any -> Any -> Any -> Any -> Any)
-> (Any -> Any -> Any -> Any)
-> T_Σ_14
-> T_Σ_14
-> T_IsRing_2650
MAlonzo.Code.Algebra.Structures.C_IsRing'46'constructor_95033
      (T_IsAbelianGroup_1132 -> Any
forall a b. a -> b
coe T_IsAbelianGroup_1132
d_'43''45'0'45'isAbelianGroup_4436) Any
forall a. a
erased Any
forall a. a
erased
      (T_Σ_14 -> Any
forall a b. a -> b
coe T_Σ_14
d_'42''45'identity_5180) (T_Σ_14 -> Any
forall a b. a -> b
coe T_Σ_14
d_'42''45'distrib'45''43'_5610)
-- Data.Integer.Properties.+-*-isCommutativeRing
d_'43''45''42''45'isCommutativeRing_5628 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeRing_2796
d_'43''45''42''45'isCommutativeRing_5628 :: T_IsCommutativeRing_2796
d_'43''45''42''45'isCommutativeRing_5628
  = (T_IsRing_2650 -> (Any -> Any -> Any) -> T_IsCommutativeRing_2796)
-> Any -> Any -> T_IsCommutativeRing_2796
forall a b. a -> b
coe
      T_IsRing_2650 -> (Any -> Any -> Any) -> T_IsCommutativeRing_2796
MAlonzo.Code.Algebra.Structures.C_IsCommutativeRing'46'constructor_100945
      (T_IsRing_2650 -> Any
forall a b. a -> b
coe T_IsRing_2650
d_'43''45''42''45'isRing_5626) Any
forall a. a
erased
-- Data.Integer.Properties.*-magma
d_'42''45'magma_5630 :: MAlonzo.Code.Algebra.Bundles.T_Magma_68
d_'42''45'magma_5630 :: T_Magma_68
d_'42''45'magma_5630
  = ((Any -> Any -> Any) -> T_IsMagma_176 -> T_Magma_68)
-> (Integer -> Integer -> Integer) -> T_IsMagma_176 -> T_Magma_68
forall a b. a -> b
coe
      (Any -> Any -> Any) -> T_IsMagma_176 -> T_Magma_68
MAlonzo.Code.Algebra.Bundles.C_Magma'46'constructor_1279
      Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'42'__308 T_IsMagma_176
d_'42''45'isMagma_5612
-- Data.Integer.Properties.*-semigroup
d_'42''45'semigroup_5632 ::
  MAlonzo.Code.Algebra.Bundles.T_Semigroup_536
d_'42''45'semigroup_5632 :: T_Semigroup_536
d_'42''45'semigroup_5632
  = ((Any -> Any -> Any) -> T_IsSemigroup_472 -> T_Semigroup_536)
-> (Integer -> Integer -> Integer)
-> T_IsSemigroup_472
-> T_Semigroup_536
forall a b. a -> b
coe
      (Any -> Any -> Any) -> T_IsSemigroup_472 -> T_Semigroup_536
MAlonzo.Code.Algebra.Bundles.C_Semigroup'46'constructor_9793
      Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'42'__308
      T_IsSemigroup_472
d_'42''45'isSemigroup_5614
-- Data.Integer.Properties.*-commutativeSemigroup
d_'42''45'commutativeSemigroup_5634 ::
  MAlonzo.Code.Algebra.Bundles.T_CommutativeSemigroup_662
d_'42''45'commutativeSemigroup_5634 :: T_CommutativeSemigroup_662
d_'42''45'commutativeSemigroup_5634
  = ((Any -> Any -> Any)
 -> T_IsCommutativeSemigroup_548 -> T_CommutativeSemigroup_662)
-> (Integer -> Integer -> Integer)
-> T_IsCommutativeSemigroup_548
-> T_CommutativeSemigroup_662
forall a b. a -> b
coe
      (Any -> Any -> Any)
-> T_IsCommutativeSemigroup_548 -> T_CommutativeSemigroup_662
MAlonzo.Code.Algebra.Bundles.C_CommutativeSemigroup'46'constructor_12035
      Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'42'__308
      T_IsCommutativeSemigroup_548
d_'42''45'isCommutativeSemigroup_5616
-- Data.Integer.Properties.*-1-monoid
d_'42''45'1'45'monoid_5636 ::
  MAlonzo.Code.Algebra.Bundles.T_Monoid_882
d_'42''45'1'45'monoid_5636 :: T_Monoid_882
d_'42''45'1'45'monoid_5636
  = ((Any -> Any -> Any) -> Any -> T_IsMonoid_686 -> T_Monoid_882)
-> (Integer -> Integer -> Integer)
-> Integer
-> T_IsMonoid_686
-> T_Monoid_882
forall a b. a -> b
coe
      (Any -> Any -> Any) -> Any -> T_IsMonoid_686 -> T_Monoid_882
MAlonzo.Code.Algebra.Bundles.C_Monoid'46'constructor_16157
      Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'42'__308
      Integer
MAlonzo.Code.Data.Integer.Base.d_1ℤ_16 T_IsMonoid_686
d_'42''45'1'45'isMonoid_5618
-- Data.Integer.Properties.*-1-commutativeMonoid
d_'42''45'1'45'commutativeMonoid_5638 ::
  MAlonzo.Code.Algebra.Bundles.T_CommutativeMonoid_962
d_'42''45'1'45'commutativeMonoid_5638 :: T_CommutativeMonoid_962
d_'42''45'1'45'commutativeMonoid_5638
  = ((Any -> Any -> Any)
 -> Any -> T_IsCommutativeMonoid_736 -> T_CommutativeMonoid_962)
-> (Integer -> Integer -> Integer)
-> Integer
-> T_IsCommutativeMonoid_736
-> T_CommutativeMonoid_962
forall a b. a -> b
coe
      (Any -> Any -> Any)
-> Any -> T_IsCommutativeMonoid_736 -> T_CommutativeMonoid_962
MAlonzo.Code.Algebra.Bundles.C_CommutativeMonoid'46'constructor_17931
      Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'42'__308
      Integer
MAlonzo.Code.Data.Integer.Base.d_1ℤ_16
      T_IsCommutativeMonoid_736
d_'42''45'1'45'isCommutativeMonoid_5620
-- Data.Integer.Properties.+-*-semiring
d_'43''45''42''45'semiring_5640 ::
  MAlonzo.Code.Algebra.Bundles.T_Semiring_2280
d_'43''45''42''45'semiring_5640 :: T_Semiring_2280
d_'43''45''42''45'semiring_5640
  = ((Any -> Any -> Any)
 -> (Any -> Any -> Any)
 -> Any
 -> Any
 -> T_IsSemiring_1570
 -> T_Semiring_2280)
-> (Integer -> Integer -> Integer)
-> (Integer -> Integer -> Integer)
-> Integer
-> Integer
-> T_IsSemiring_1570
-> T_Semiring_2280
forall a b. a -> b
coe
      (Any -> Any -> Any)
-> (Any -> Any -> Any)
-> Any
-> Any
-> T_IsSemiring_1570
-> T_Semiring_2280
MAlonzo.Code.Algebra.Bundles.C_Semiring'46'constructor_41765
      Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'43'__276
      Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'42'__308
      Integer
MAlonzo.Code.Data.Integer.Base.d_0ℤ_12
      Integer
MAlonzo.Code.Data.Integer.Base.d_1ℤ_16
      T_IsSemiring_1570
d_'43''45''42''45'isSemiring_5622
-- Data.Integer.Properties.+-*-commutativeSemiring
d_'43''45''42''45'commutativeSemiring_5642 ::
  MAlonzo.Code.Algebra.Bundles.T_CommutativeSemiring_2446
d_'43''45''42''45'commutativeSemiring_5642 :: T_CommutativeSemiring_2446
d_'43''45''42''45'commutativeSemiring_5642
  = ((Any -> Any -> Any)
 -> (Any -> Any -> Any)
 -> Any
 -> Any
 -> T_IsCommutativeSemiring_1678
 -> T_CommutativeSemiring_2446)
-> (Integer -> Integer -> Integer)
-> (Integer -> Integer -> Integer)
-> Integer
-> Integer
-> T_IsCommutativeSemiring_1678
-> T_CommutativeSemiring_2446
forall a b. a -> b
coe
      (Any -> Any -> Any)
-> (Any -> Any -> Any)
-> Any
-> Any
-> T_IsCommutativeSemiring_1678
-> T_CommutativeSemiring_2446
MAlonzo.Code.Algebra.Bundles.C_CommutativeSemiring'46'constructor_44731
      Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'43'__276
      Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'42'__308
      Integer
MAlonzo.Code.Data.Integer.Base.d_0ℤ_12
      Integer
MAlonzo.Code.Data.Integer.Base.d_1ℤ_16
      T_IsCommutativeSemiring_1678
d_'43''45''42''45'isCommutativeSemiring_5624
-- Data.Integer.Properties.+-*-ring
d_'43''45''42''45'ring_5644 ::
  MAlonzo.Code.Algebra.Bundles.T_Ring_3800
d_'43''45''42''45'ring_5644 :: T_Ring_3800
d_'43''45''42''45'ring_5644
  = ((Any -> Any -> Any)
 -> (Any -> Any -> Any)
 -> (Any -> Any)
 -> Any
 -> Any
 -> T_IsRing_2650
 -> T_Ring_3800)
-> (Integer -> Integer -> Integer)
-> (Integer -> Integer -> Integer)
-> (Integer -> Integer)
-> Integer
-> Integer
-> T_IsRing_2650
-> T_Ring_3800
forall a b. a -> b
coe
      (Any -> Any -> Any)
-> (Any -> Any -> Any)
-> (Any -> Any)
-> Any
-> Any
-> T_IsRing_2650
-> T_Ring_3800
MAlonzo.Code.Algebra.Bundles.C_Ring'46'constructor_68489
      Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'43'__276
      Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'42'__308
      Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d_'45'__252
      Integer
MAlonzo.Code.Data.Integer.Base.d_0ℤ_12
      Integer
MAlonzo.Code.Data.Integer.Base.d_1ℤ_16
      T_IsRing_2650
d_'43''45''42''45'isRing_5626
-- Data.Integer.Properties.+-*-commutativeRing
d_'43''45''42''45'commutativeRing_5646 ::
  MAlonzo.Code.Algebra.Bundles.T_CommutativeRing_4016
d_'43''45''42''45'commutativeRing_5646 :: T_CommutativeRing_4016
d_'43''45''42''45'commutativeRing_5646
  = ((Any -> Any -> Any)
 -> (Any -> Any -> Any)
 -> (Any -> Any)
 -> Any
 -> Any
 -> T_IsCommutativeRing_2796
 -> T_CommutativeRing_4016)
-> (Integer -> Integer -> Integer)
-> (Integer -> Integer -> Integer)
-> (Integer -> Integer)
-> Integer
-> Integer
-> T_IsCommutativeRing_2796
-> T_CommutativeRing_4016
forall a b. a -> b
coe
      (Any -> Any -> Any)
-> (Any -> Any -> Any)
-> (Any -> Any)
-> Any
-> Any
-> T_IsCommutativeRing_2796
-> T_CommutativeRing_4016
MAlonzo.Code.Algebra.Bundles.C_CommutativeRing'46'constructor_72553
      Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'43'__276
      Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'42'__308
      Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d_'45'__252
      Integer
MAlonzo.Code.Data.Integer.Base.d_0ℤ_12
      Integer
MAlonzo.Code.Data.Integer.Base.d_1ℤ_16
      T_IsCommutativeRing_2796
d_'43''45''42''45'isCommutativeRing_5628
-- Data.Integer.Properties.abs-*
d_abs'45''42'_5648 ::
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_abs'45''42'_5648 :: Integer -> Integer -> T__'8801'__12
d_abs'45''42'_5648 = Integer -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.sign-*
d_sign'45''42'_5658 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T_NonZero_112 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_sign'45''42'_5658 :: Integer -> Integer -> T_NonZero_112 -> T__'8801'__12
d_sign'45''42'_5658 = Integer -> Integer -> T_NonZero_112 -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.*-cancelʳ-≡
d_'42''45'cancel'691''45''8801'_5676 ::
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T_NonZero_112 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'42''45'cancel'691''45''8801'_5676 :: Integer
-> Integer
-> Integer
-> T_NonZero_112
-> T__'8801'__12
-> T__'8801'__12
d_'42''45'cancel'691''45''8801'_5676 = Integer
-> Integer
-> Integer
-> T_NonZero_112
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.*-cancelˡ-≡
d_'42''45'cancel'737''45''8801'_5720 ::
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T_NonZero_112 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'42''45'cancel'737''45''8801'_5720 :: Integer
-> Integer
-> Integer
-> T_NonZero_112
-> T__'8801'__12
-> T__'8801'__12
d_'42''45'cancel'737''45''8801'_5720 = Integer
-> Integer
-> Integer
-> T_NonZero_112
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.suc-*
d_suc'45''42'_5740 ::
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_suc'45''42'_5740 :: Integer -> Integer -> T__'8801'__12
d_suc'45''42'_5740 = Integer -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.*-suc
d_'42''45'suc_5756 ::
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'42''45'suc_5756 :: Integer -> Integer -> T__'8801'__12
d_'42''45'suc_5756 = Integer -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.-1*i≡-i
d_'45'1'42'i'8801''45'i_5770 ::
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'45'1'42'i'8801''45'i_5770 :: Integer -> T__'8801'__12
d_'45'1'42'i'8801''45'i_5770 = Integer -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.i*j≡0⇒i≡0∨j≡0
d_i'42'j'8801'0'8658'i'8801'0'8744'j'8801'0_5780 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Data.Sum.Base.T__'8846'__30
d_i'42'j'8801'0'8658'i'8801'0'8744'j'8801'0_5780 :: Integer -> Integer -> T__'8801'__12 -> T__'8846'__30
d_i'42'j'8801'0'8658'i'8801'0'8744'j'8801'0_5780 Integer
v0 ~Integer
v1 ~T__'8801'__12
v2
  = Integer -> T__'8846'__30
du_i'42'j'8801'0'8658'i'8801'0'8744'j'8801'0_5780 Integer
v0
du_i'42'j'8801'0'8658'i'8801'0'8744'j'8801'0_5780 ::
  Integer -> MAlonzo.Code.Data.Sum.Base.T__'8846'__30
du_i'42'j'8801'0'8658'i'8801'0'8744'j'8801'0_5780 :: Integer -> T__'8846'__30
du_i'42'j'8801'0'8658'i'8801'0'8744'j'8801'0_5780 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_3822
      ((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.i*j≢0
d_i'42'j'8802'0_5810 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T_NonZero_112 ->
  MAlonzo.Code.Data.Nat.Base.T_NonZero_112 ->
  MAlonzo.Code.Data.Nat.Base.T_NonZero_112
d_i'42'j'8802'0_5810 :: Integer
-> Integer -> T_NonZero_112 -> T_NonZero_112 -> T_NonZero_112
d_i'42'j'8802'0_5810 ~Integer
v0 ~Integer
v1 ~T_NonZero_112
v2 ~T_NonZero_112
v3 = T_NonZero_112
du_i'42'j'8802'0_5810
du_i'42'j'8802'0_5810 :: MAlonzo.Code.Data.Nat.Base.T_NonZero_112
du_i'42'j'8802'0_5810 :: T_NonZero_112
du_i'42'j'8802'0_5810
  = T_NonZero_112 -> T_NonZero_112
forall a b. a -> b
coe T_NonZero_112
MAlonzo.Code.Data.Nat.Properties.du_m'42'n'8802'0_3840
-- Data.Integer.Properties.^-identityʳ
d_'94''45'identity'691'_5822 ::
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'94''45'identity'691'_5822 :: Integer -> T__'8801'__12
d_'94''45'identity'691'_5822 = Integer -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.^-zeroˡ
d_'94''45'zero'737'_5826 ::
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'94''45'zero'737'_5826 :: Integer -> T__'8801'__12
d_'94''45'zero'737'_5826 = Integer -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.^-distribˡ-+-*
d_'94''45'distrib'737''45''43''45''42'_5840 ::
  Integer ->
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'94''45'distrib'737''45''43''45''42'_5840 :: Integer -> Integer -> Integer -> T__'8801'__12
d_'94''45'distrib'737''45''43''45''42'_5840 = Integer -> Integer -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.^-isMagmaHomomorphism
d_'94''45'isMagmaHomomorphism_5862 ::
  Integer ->
  MAlonzo.Code.Algebra.Morphism.Structures.T_IsMagmaHomomorphism_176
d_'94''45'isMagmaHomomorphism_5862 :: Integer -> T_IsMagmaHomomorphism_176
d_'94''45'isMagmaHomomorphism_5862 ~Integer
v0
  = T_IsMagmaHomomorphism_176
du_'94''45'isMagmaHomomorphism_5862
du_'94''45'isMagmaHomomorphism_5862 ::
  MAlonzo.Code.Algebra.Morphism.Structures.T_IsMagmaHomomorphism_176
du_'94''45'isMagmaHomomorphism_5862 :: T_IsMagmaHomomorphism_176
du_'94''45'isMagmaHomomorphism_5862
  = (T_IsRelHomomorphism_42
 -> (Any -> Any -> Any) -> T_IsMagmaHomomorphism_176)
-> Any -> Any -> T_IsMagmaHomomorphism_176
forall a b. a -> b
coe
      T_IsRelHomomorphism_42
-> (Any -> Any -> Any) -> T_IsMagmaHomomorphism_176
MAlonzo.Code.Algebra.Morphism.Structures.C_IsMagmaHomomorphism'46'constructor_4629
      (((Any -> Any -> Any -> Any) -> T_IsRelHomomorphism_42)
-> Any -> Any
forall a b. a -> b
coe
         (Any -> Any -> Any -> Any) -> T_IsRelHomomorphism_42
MAlonzo.Code.Relation.Binary.Morphism.Structures.C_IsRelHomomorphism'46'constructor_587
         Any
forall a. a
erased)
      Any
forall a. a
erased
-- Data.Integer.Properties.^-isMonoidHomomorphism
d_'94''45'isMonoidHomomorphism_5872 ::
  Integer ->
  MAlonzo.Code.Algebra.Morphism.Structures.T_IsMonoidHomomorphism_350
d_'94''45'isMonoidHomomorphism_5872 :: Integer -> T_IsMonoidHomomorphism_350
d_'94''45'isMonoidHomomorphism_5872 ~Integer
v0
  = T_IsMonoidHomomorphism_350
du_'94''45'isMonoidHomomorphism_5872
du_'94''45'isMonoidHomomorphism_5872 ::
  MAlonzo.Code.Algebra.Morphism.Structures.T_IsMonoidHomomorphism_350
du_'94''45'isMonoidHomomorphism_5872 :: T_IsMonoidHomomorphism_350
du_'94''45'isMonoidHomomorphism_5872
  = (T_IsMagmaHomomorphism_176 -> Any -> T_IsMonoidHomomorphism_350)
-> Any -> Any -> T_IsMonoidHomomorphism_350
forall a b. a -> b
coe
      T_IsMagmaHomomorphism_176 -> Any -> T_IsMonoidHomomorphism_350
MAlonzo.Code.Algebra.Morphism.Structures.C_IsMonoidHomomorphism'46'constructor_9411
      (T_IsMagmaHomomorphism_176 -> Any
forall a b. a -> b
coe T_IsMagmaHomomorphism_176
du_'94''45'isMagmaHomomorphism_5862) Any
forall a. a
erased
-- Data.Integer.Properties.^-*-assoc
d_'94''45''42''45'assoc_5882 ::
  Integer ->
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'94''45''42''45'assoc_5882 :: Integer -> Integer -> Integer -> T__'8801'__12
d_'94''45''42''45'assoc_5882 = Integer -> Integer -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.i^n≡0⇒i≡0
d_i'94'n'8801'0'8658'i'8801'0_5908 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_i'94'n'8801'0'8658'i'8801'0_5908 :: Integer -> Integer -> T__'8801'__12 -> T__'8801'__12
d_i'94'n'8801'0'8658'i'8801'0_5908 = Integer -> Integer -> T__'8801'__12 -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.pos-*
d_pos'45''42'_5916 ::
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_pos'45''42'_5916 :: Integer -> Integer -> T__'8801'__12
d_pos'45''42'_5916 = Integer -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.neg-distribˡ-*
d_neg'45'distrib'737''45''42'_5930 ::
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_neg'45'distrib'737''45''42'_5930 :: Integer -> Integer -> T__'8801'__12
d_neg'45'distrib'737''45''42'_5930 = Integer -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.neg-distribʳ-*
d_neg'45'distrib'691''45''42'_5946 ::
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_neg'45'distrib'691''45''42'_5946 :: Integer -> Integer -> T__'8801'__12
d_neg'45'distrib'691''45''42'_5946 = Integer -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.◃-distrib-*
d_'9667''45'distrib'45''42'_5964 ::
  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'_5964 :: T_Sign_6 -> T_Sign_6 -> Integer -> Integer -> T__'8801'__12
d_'9667''45'distrib'45''42'_5964 = 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_5998 ::
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Integer.Base.T_Positive_134 ->
  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_5998 :: Integer
-> Integer
-> Integer
-> T_Positive_134
-> T__'8804'__26
-> T__'8804'__26
d_'42''45'cancel'691''45''8804''45'pos_5998 Integer
v0 Integer
v1 ~Integer
v2 ~T_Positive_134
v3 T__'8804'__26
v4
  = Integer -> Integer -> T__'8804'__26 -> T__'8804'__26
du_'42''45'cancel'691''45''8804''45'pos_5998 Integer
v0 Integer
v1 T__'8804'__26
v4
du_'42''45'cancel'691''45''8804''45'pos_5998 ::
  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_5998 :: Integer -> Integer -> T__'8804'__26 -> T__'8804'__26
du_'42''45'cancel'691''45''8804''45'pos_5998 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'__22 -> T__'8804'__26) -> Any -> Any
forall a b. a -> b
coe
                T__'8804'__22 -> T__'8804'__26
MAlonzo.Code.Data.Integer.Base.C_'43''8804''43'_48
                (T__'8804'__22 -> Any
forall a b. a -> b
coe T__'8804'__22
MAlonzo.Code.Data.Nat.Base.C_z'8804'n_26))
      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'__22 -> T__'8804'__26) -> Any -> Any
forall a b. a -> b
coe
               T__'8804'__22 -> T__'8804'__26
MAlonzo.Code.Data.Integer.Base.C_'43''8804''43'_48
               ((Integer -> T__'8804'__22) -> Any -> Any
forall a b. a -> b
coe
                  Integer -> T__'8804'__22
MAlonzo.Code.Data.Nat.Properties.du_'42''45'cancel'691''45''8804'_4030
                  (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'__22 -> T__'8804'__26) -> Any -> Any
forall a b. a -> b
coe
                       T__'8804'__22 -> T__'8804'__26
MAlonzo.Code.Data.Integer.Base.C_'45''8804''45'_34
                       ((T__'8804'__22 -> T__'8804'__22) -> Any -> Any
forall a b. a -> b
coe
                          T__'8804'__22 -> T__'8804'__22
MAlonzo.Code.Data.Nat.Base.du_s'8804's'8315''185'_62
                          ((Integer -> T__'8804'__22) -> Any -> Any
forall a b. a -> b
coe
                             Integer -> T__'8804'__22
MAlonzo.Code.Data.Nat.Properties.du_'42''45'cancel'691''45''8804'_4030
                             ((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_6032 ::
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Integer.Base.T_Positive_134 ->
  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_6032 :: Integer
-> Integer
-> Integer
-> T_Positive_134
-> T__'8804'__26
-> T__'8804'__26
d_'42''45'cancel'737''45''8804''45'pos_6032 Integer
v0 Integer
v1 ~Integer
v2 ~T_Positive_134
v3
  = Integer -> Integer -> T__'8804'__26 -> T__'8804'__26
du_'42''45'cancel'737''45''8804''45'pos_6032 Integer
v0 Integer
v1
du_'42''45'cancel'737''45''8804''45'pos_6032 ::
  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_6032 :: Integer -> Integer -> T__'8804'__26 -> T__'8804'__26
du_'42''45'cancel'737''45''8804''45'pos_6032 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_5998 (Integer -> Any
forall a b. a -> b
coe Integer
v0) (Integer -> Any
forall a b. a -> b
coe Integer
v1)
-- Data.Integer.Properties.*-monoʳ-≤-nonNeg
d_'42''45'mono'691''45''8804''45'nonNeg_6054 ::
  Integer ->
  MAlonzo.Code.Data.Integer.Base.T_NonNegative_144 ->
  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_6054 :: Integer
-> T_NonNegative_144
-> Integer
-> Integer
-> T__'8804'__26
-> T__'8804'__26
d_'42''45'mono'691''45''8804''45'nonNeg_6054 Integer
v0 ~T_NonNegative_144
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'nonNeg_6054 Integer
v0 Integer
v2 Integer
v3 T__'8804'__26
v4
du_'42''45'mono'691''45''8804''45'nonNeg_6054 ::
  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'nonNeg_6054 :: Integer -> Integer -> Integer -> T__'8804'__26 -> T__'8804'__26
du_'42''45'mono'691''45''8804''45'nonNeg_6054 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'__22 -> T__'8804'__26) -> Any -> T__'8804'__26
forall a b. a -> b
coe
             T__'8804'__22 -> T__'8804'__26
MAlonzo.Code.Data.Integer.Base.C_'43''8804''43'_48
             (T__'8804'__22 -> Any
forall a b. a -> b
coe T__'8804'__22
MAlonzo.Code.Data.Nat.Base.C_z'8804'n_26)
      Integer
_ -> 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'__22
v6
               -> (T__'8804'__22 -> T__'8804'__26) -> Any -> T__'8804'__26
forall a b. a -> b
coe
                    T__'8804'__22 -> T__'8804'__26
MAlonzo.Code.Data.Integer.Base.C_'45''8804''45'_34
                    ((T__'8804'__22 -> T__'8804'__22) -> Any -> Any
forall a b. a -> b
coe
                       T__'8804'__22 -> T__'8804'__22
MAlonzo.Code.Data.Nat.Base.du_s'8804's'8315''185'_62
                       ((Integer
 -> Integer -> T__'8804'__22 -> T__'8804'__22 -> T__'8804'__22)
-> Any -> Any -> Any -> Any -> Any
forall a b. a -> b
coe
                          Integer
-> Integer -> T__'8804'__22 -> T__'8804'__22 -> T__'8804'__22
MAlonzo.Code.Data.Nat.Properties.du_'42''45'mono'45''8804'_4060
                          ((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 -> Any
forall a b. a -> b
coe Integer
v0)
                          ((T__'8804'__22 -> T__'8804'__22) -> T__'8804'__22 -> Any
forall a b. a -> b
coe T__'8804'__22 -> T__'8804'__22
MAlonzo.Code.Data.Nat.Base.C_s'8804's_34 T__'8804'__22
v6)
                          ((Integer -> T__'8804'__22) -> Any -> Any
forall a b. a -> b
coe
                             Integer -> T__'8804'__22
MAlonzo.Code.Data.Nat.Properties.d_'8804''45'refl_2776 (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'__22
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'__22 -> T__'8804'__26) -> T__'8804'__22 -> T__'8804'__26
forall a b. a -> b
coe T__'8804'__22 -> T__'8804'__26
MAlonzo.Code.Data.Integer.Base.C_'43''8804''43'_48 T__'8804'__22
v6
                           Integer
_ -> (T__'8804'__22 -> T__'8804'__26) -> Any -> T__'8804'__26
forall a b. a -> b
coe
                                  T__'8804'__22 -> T__'8804'__26
MAlonzo.Code.Data.Integer.Base.C_'43''8804''43'_48
                                  (T__'8804'__22 -> Any
forall a b. a -> b
coe T__'8804'__22
MAlonzo.Code.Data.Nat.Base.C_z'8804'n_26)
                    Integer
_ -> (T__'8804'__22 -> T__'8804'__26) -> Any -> T__'8804'__26
forall a b. a -> b
coe
                           T__'8804'__22 -> T__'8804'__26
MAlonzo.Code.Data.Integer.Base.C_'43''8804''43'_48
                           ((Integer -> Integer -> T__'8804'__22 -> T__'8804'__22)
-> Any -> Any -> Any -> Any
forall a b. a -> b
coe
                              Integer -> Integer -> T__'8804'__22 -> T__'8804'__22
MAlonzo.Code.Data.Nat.Properties.du_'42''45'mono'737''45''8804'_4070
                              (Integer -> Any
forall a b. a -> b
coe Integer
v0) (Integer -> Any
forall a b. a -> b
coe Integer
v2) (T__'8804'__22 -> Any
forall a b. a -> b
coe T__'8804'__22
v6))
             T__'8804'__26
_ -> T__'8804'__26
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Data.Integer.Properties.*-monoˡ-≤-nonNeg
d_'42''45'mono'737''45''8804''45'nonNeg_6096 ::
  Integer ->
  MAlonzo.Code.Data.Integer.Base.T_NonNegative_144 ->
  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_6096 :: Integer
-> T_NonNegative_144
-> Integer
-> Integer
-> T__'8804'__26
-> T__'8804'__26
d_'42''45'mono'737''45''8804''45'nonNeg_6096 Integer
v0 ~T_NonNegative_144
v1 Integer
v2 Integer
v3
  = Integer -> Integer -> Integer -> T__'8804'__26 -> T__'8804'__26
du_'42''45'mono'737''45''8804''45'nonNeg_6096 Integer
v0 Integer
v2 Integer
v3
du_'42''45'mono'737''45''8804''45'nonNeg_6096 ::
  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'nonNeg_6096 :: Integer -> Integer -> Integer -> T__'8804'__26 -> T__'8804'__26
du_'42''45'mono'737''45''8804''45'nonNeg_6096 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'nonNeg_6054 (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_6120 ::
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Integer.Base.T_Negative_164 ->
  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_6120 :: Integer
-> Integer
-> Integer
-> T_Negative_164
-> T__'8804'__26
-> T__'8804'__26
d_'42''45'cancel'737''45''8804''45'neg_6120 Integer
v0 Integer
v1 Integer
v2 ~T_Negative_164
v3 T__'8804'__26
v4
  = Integer -> Integer -> Integer -> T__'8804'__26 -> T__'8804'__26
du_'42''45'cancel'737''45''8804''45'neg_6120 Integer
v0 Integer
v1 Integer
v2 T__'8804'__26
v4
du_'42''45'cancel'737''45''8804''45'neg_6120 ::
  Integer ->
  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'neg_6120 :: Integer -> Integer -> Integer -> T__'8804'__26 -> T__'8804'__26
du_'42''45'cancel'737''45''8804''45'neg_6120 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'_3278 (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_6032
         (Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d_'45'__252 (Integer -> Integer
forall a b. a -> b
coe Integer
v1))
         (Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d_'45'__252 (Integer -> Integer
forall a b. a -> b
coe Integer
v2))
         (((Any -> Any -> Any -> Any) -> Any -> Any -> Any -> Any)
-> Any -> Integer -> Integer -> Any -> Any
forall a b. a -> b
coe
            (Any -> Any -> Any -> Any) -> Any -> Any -> Any -> Any
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_begin__46
            ((T_IsPreorder_70
 -> (Any -> Any -> Any -> Any)
 -> Any
 -> Any
 -> T__IsRelatedTo__78
 -> Any)
-> Any -> (Any -> Any -> Any -> Any) -> Any
forall a b. a -> b
coe
               T_IsPreorder_70
-> (Any -> Any -> Any -> Any)
-> Any
-> Any
-> T__IsRelatedTo__78
-> Any
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_start_96
               (T_IsPreorder_70 -> Any
forall a b. a -> b
coe T_IsPreorder_70
d_'8804''45'isPreorder_2800)
               (\ Any
v4 Any
v5 Any
v6 -> (T__'60'__50 -> T__'8804'__26) -> Any -> Any
forall a b. a -> b
coe T__'60'__50 -> T__'8804'__26
du_'60''8658''8804'_2846 Any
v6))
            (Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'42'__308
               ((Integer -> Integer) -> Any -> Integer
forall a b. a -> b
coe Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d_'45'__252 (Integer -> Any
forall a b. a -> b
coe Integer
v0))
               ((Integer -> Integer) -> Any -> Integer
forall a b. a -> b
coe Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d_'45'__252 (Integer -> Any
forall a b. a -> b
coe Integer
v1)))
            (Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'42'__308
               ((Integer -> Integer) -> Any -> Integer
forall a b. a -> b
coe Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d_'45'__252 (Integer -> Any
forall a b. a -> b
coe Integer
v0))
               ((Integer -> Integer) -> Any -> Integer
forall a b. a -> b
coe Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d_'45'__252 (Integer -> Any
forall a b. a -> b
coe Integer
v2)))
            (((Any -> Any -> Any -> T__'8801'__12 -> Any -> Any)
 -> Any -> Any -> Any -> Any -> T__'8801'__12 -> Any)
-> (Any -> Any -> Any -> Any -> Any -> Any)
-> Integer
-> Integer
-> Integer
-> Any
-> Any
-> Any
forall a b. a -> b
coe
               (Any -> Any -> Any -> T__'8801'__12 -> Any -> Any)
-> Any -> Any -> Any -> Any -> T__'8801'__12 -> Any
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8801''45''10216'_448
               (\ Any
v4 Any
v5 Any
v6 Any
v7 Any
v8 -> Any
v8)
               (Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'42'__308
                  ((Integer -> Integer) -> Any -> Integer
forall a b. a -> b
coe Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d_'45'__252 (Integer -> Any
forall a b. a -> b
coe Integer
v0))
                  ((Integer -> Integer) -> Any -> Integer
forall a b. a -> b
coe Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d_'45'__252 (Integer -> Any
forall a b. a -> b
coe Integer
v1)))
               (Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d_'45'__252
                  ((Integer -> Integer -> Integer) -> Any -> Any -> Integer
forall a b. a -> b
coe
                     Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'42'__308
                     ((Integer -> Integer) -> Any -> Any
forall a b. a -> b
coe Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d_'45'__252 (Integer -> Any
forall a b. a -> b
coe Integer
v0))
                     (Integer -> Any
forall a b. a -> b
coe Integer
v1)))
               (Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'42'__308
                  ((Integer -> Integer) -> Any -> Integer
forall a b. a -> b
coe Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d_'45'__252 (Integer -> Any
forall a b. a -> b
coe Integer
v0))
                  ((Integer -> Integer) -> Any -> Integer
forall a b. a -> b
coe Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d_'45'__252 (Integer -> Any
forall a b. a -> b
coe Integer
v2)))
               (((Any -> Any -> Any -> T__'8801'__12 -> Any -> Any)
 -> Any -> Any -> Any -> Any -> T__'8801'__12 -> Any)
-> (Any -> Any -> Any -> Any -> Any -> Any)
-> Integer
-> Integer
-> Integer
-> Any
-> Any
-> Any
forall a b. a -> b
coe
                  (Any -> Any -> Any -> T__'8801'__12 -> Any -> Any)
-> Any -> Any -> Any -> Any -> T__'8801'__12 -> Any
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8801''45''10217'_436
                  (\ Any
v4 Any
v5 Any
v6 Any
v7 Any
v8 -> Any
v8)
                  (Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d_'45'__252
                     ((Integer -> Integer -> Integer) -> Any -> Any -> Integer
forall a b. a -> b
coe
                        Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'42'__308
                        ((Integer -> Integer) -> Any -> Any
forall a b. a -> b
coe Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d_'45'__252 (Integer -> Any
forall a b. a -> b
coe Integer
v0))
                        (Integer -> Any
forall a b. a -> b
coe Integer
v1)))
                  (Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'42'__308 (Integer -> Integer
forall a b. a -> b
coe Integer
v0) (Integer -> Integer
forall a b. a -> b
coe Integer
v1))
                  (Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'42'__308
                     ((Integer -> Integer) -> Any -> Integer
forall a b. a -> b
coe Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d_'45'__252 (Integer -> Any
forall a b. a -> b
coe Integer
v0))
                     ((Integer -> Integer) -> Any -> Integer
forall a b. a -> b
coe Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d_'45'__252 (Integer -> Any
forall a b. a -> b
coe Integer
v2)))
                  (((Any -> Any -> Any -> Any -> Any -> Any)
 -> Any -> Any -> Any -> Any -> Any -> Any)
-> Any
-> Integer
-> Integer
-> Integer
-> Any
-> T__'8804'__26
-> Any
forall a b. a -> b
coe
                     (Any -> Any -> Any -> Any -> Any -> Any)
-> Any -> Any -> Any -> Any -> Any -> Any
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8804'_308
                     ((T_IsPreorder_70
 -> (Any -> Any -> Any -> Any -> Any -> Any)
 -> Any
 -> Any
 -> Any
 -> Any
 -> T__IsRelatedTo__78
 -> T__IsRelatedTo__78)
-> 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
-> Any
-> T__IsRelatedTo__78
-> T__IsRelatedTo__78
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_'8804''45'go_138
                        (T_IsPreorder_70 -> Any
forall a b. a -> b
coe T_IsPreorder_70
d_'8804''45'isPreorder_2800)
                        (\ 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_2958 Any
v7 Any
v8))
                     (Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'42'__308 (Integer -> Integer
forall a b. a -> b
coe Integer
v0) (Integer -> Integer
forall a b. a -> b
coe Integer
v1))
                     (Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'42'__308 (Integer -> Integer
forall a b. a -> b
coe Integer
v0) (Integer -> Integer
forall a b. a -> b
coe Integer
v2))
                     (Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'42'__308
                        ((Integer -> Integer) -> Any -> Integer
forall a b. a -> b
coe Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d_'45'__252 (Integer -> Any
forall a b. a -> b
coe Integer
v0))
                        ((Integer -> Integer) -> Any -> Integer
forall a b. a -> b
coe Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d_'45'__252 (Integer -> Any
forall a b. a -> b
coe Integer
v2)))
                     (((Any -> Any -> Any -> T__'8801'__12 -> Any -> Any)
 -> Any -> Any -> Any -> Any -> T__'8801'__12 -> Any)
-> (Any -> Any -> Any -> Any -> Any -> Any)
-> Integer
-> Integer
-> Integer
-> Any
-> Any
-> Any
forall a b. a -> b
coe
                        (Any -> Any -> Any -> T__'8801'__12 -> Any -> Any)
-> Any -> Any -> Any -> Any -> T__'8801'__12 -> Any
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8801''45''10216'_448
                        (\ Any
v4 Any
v5 Any
v6 Any
v7 Any
v8 -> Any
v8)
                        (Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'42'__308 (Integer -> Integer
forall a b. a -> b
coe Integer
v0) (Integer -> Integer
forall a b. a -> b
coe Integer
v2))
                        (Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d_'45'__252
                           ((Integer -> Integer -> Integer) -> Any -> Any -> Integer
forall a b. a -> b
coe
                              Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'42'__308
                              ((Integer -> Integer) -> Any -> Any
forall a b. a -> b
coe Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d_'45'__252 (Integer -> Any
forall a b. a -> b
coe Integer
v0))
                              (Integer -> Any
forall a b. a -> b
coe Integer
v2)))
                        (Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'42'__308
                           ((Integer -> Integer) -> Any -> Integer
forall a b. a -> b
coe Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d_'45'__252 (Integer -> Any
forall a b. a -> b
coe Integer
v0))
                           ((Integer -> Integer) -> Any -> Integer
forall a b. a -> b
coe Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d_'45'__252 (Integer -> Any
forall a b. a -> b
coe Integer
v2)))
                        (((Any -> Any -> Any -> T__'8801'__12 -> Any -> Any)
 -> Any -> Any -> Any -> Any -> T__'8801'__12 -> Any)
-> (Any -> Any -> Any -> Any -> Any -> Any)
-> Integer
-> Integer
-> Integer
-> Any
-> Any
-> Any
forall a b. a -> b
coe
                           (Any -> Any -> Any -> T__'8801'__12 -> Any -> Any)
-> Any -> Any -> Any -> Any -> T__'8801'__12 -> Any
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8801''45''10217'_436
                           (\ Any
v4 Any
v5 Any
v6 Any
v7 Any
v8 -> Any
v8)
                           (Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d_'45'__252
                              ((Integer -> Integer -> Integer) -> Any -> Any -> Integer
forall a b. a -> b
coe
                                 Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'42'__308
                                 ((Integer -> Integer) -> Any -> Any
forall a b. a -> b
coe Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d_'45'__252 (Integer -> Any
forall a b. a -> b
coe Integer
v0))
                                 (Integer -> Any
forall a b. a -> b
coe Integer
v2)))
                           (Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'42'__308
                              ((Integer -> Integer) -> Any -> Integer
forall a b. a -> b
coe Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d_'45'__252 (Integer -> Any
forall a b. a -> b
coe Integer
v0))
                              ((Integer -> Integer) -> Any -> Integer
forall a b. a -> b
coe Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d_'45'__252 (Integer -> Any
forall a b. a -> b
coe Integer
v2)))
                           (Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'42'__308
                              ((Integer -> Integer) -> Any -> Integer
forall a b. a -> b
coe Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d_'45'__252 (Integer -> Any
forall a b. a -> b
coe Integer
v0))
                              ((Integer -> Integer) -> Any -> Integer
forall a b. a -> b
coe Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d_'45'__252 (Integer -> Any
forall a b. a -> b
coe Integer
v2)))
                           (((Any -> Any) -> Any -> Any) -> Any -> Any -> Any
forall a b. a -> b
coe
                              (Any -> Any) -> Any -> Any
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du__'8718'_492
                              ((T_IsPreorder_70 -> Any -> T__IsRelatedTo__78) -> Any -> Any
forall a b. a -> b
coe
                                 T_IsPreorder_70 -> Any -> T__IsRelatedTo__78
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_stop_166
                                 (T_IsPreorder_70 -> Any
forall a b. a -> b
coe T_IsPreorder_70
d_'8804''45'isPreorder_2800))
                              ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe
                                 Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'42'__308
                                 ((Integer -> Integer) -> Any -> Any
forall a b. a -> b
coe Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d_'45'__252 (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'__252 (Integer -> Any
forall a b. a -> b
coe Integer
v2))))
                           Any
forall a. a
erased)
                        Any
forall a. a
erased)
                     T__'8804'__26
v3)
                  Any
forall a. a
erased)
               Any
forall a. a
erased)))
-- Data.Integer.Properties.*-cancelʳ-≤-neg
d_'42''45'cancel'691''45''8804''45'neg_6142 ::
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Integer.Base.T_Negative_164 ->
  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_6142 :: Integer
-> Integer
-> Integer
-> T_Negative_164
-> T__'8804'__26
-> T__'8804'__26
d_'42''45'cancel'691''45''8804''45'neg_6142 Integer
v0 Integer
v1 Integer
v2 ~T_Negative_164
v3
  = Integer -> Integer -> Integer -> T__'8804'__26 -> T__'8804'__26
du_'42''45'cancel'691''45''8804''45'neg_6142 Integer
v0 Integer
v1 Integer
v2
du_'42''45'cancel'691''45''8804''45'neg_6142 ::
  Integer ->
  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'neg_6142 :: Integer -> Integer -> Integer -> T__'8804'__26 -> T__'8804'__26
du_'42''45'cancel'691''45''8804''45'neg_6142 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'cancel'737''45''8804''45'neg_6120 (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-≤-nonPos
d_'42''45'mono'737''45''8804''45'nonPos_6164 ::
  Integer ->
  MAlonzo.Code.Data.Integer.Base.T_NonPositive_154 ->
  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_6164 :: Integer
-> T_NonPositive_154
-> Integer
-> Integer
-> T__'8804'__26
-> T__'8804'__26
d_'42''45'mono'737''45''8804''45'nonPos_6164 Integer
v0 ~T_NonPositive_154
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_6164 Integer
v0 Integer
v2 Integer
v3 T__'8804'__26
v4
du_'42''45'mono'737''45''8804''45'nonPos_6164 ::
  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_6164 :: Integer -> Integer -> Integer -> T__'8804'__26 -> T__'8804'__26
du_'42''45'mono'737''45''8804''45'nonPos_6164 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'__22 -> T__'8804'__26) -> Any -> T__'8804'__26
forall a b. a -> b
coe
             T__'8804'__22 -> T__'8804'__26
MAlonzo.Code.Data.Integer.Base.C_'43''8804''43'_48
             (T__'8804'__22 -> Any
forall a b. a -> b
coe T__'8804'__22
MAlonzo.Code.Data.Nat.Base.C_z'8804'n_26)
      Integer
_ -> ((Any -> Any -> Any -> Any) -> Any -> Any -> Any -> Any)
-> Any -> Any -> Any -> Any -> T__'8804'__26
forall a b. a -> b
coe
             (Any -> Any -> Any -> Any) -> Any -> Any -> Any -> Any
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_begin__46
             ((T_IsPreorder_70
 -> (Any -> Any -> Any -> Any)
 -> Any
 -> Any
 -> T__IsRelatedTo__78
 -> Any)
-> Any -> (Any -> Any -> Any -> Any) -> Any
forall a b. a -> b
coe
                T_IsPreorder_70
-> (Any -> Any -> Any -> Any)
-> Any
-> Any
-> T__IsRelatedTo__78
-> Any
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_start_96
                (T_IsPreorder_70 -> Any
forall a b. a -> b
coe T_IsPreorder_70
d_'8804''45'isPreorder_2800)
                (\ Any
v4 Any
v5 Any
v6 -> (T__'60'__50 -> T__'8804'__26) -> Any -> Any
forall a b. a -> b
coe T__'60'__50 -> T__'8804'__26
du_'60''8658''8804'_2846 Any
v6))
             (((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'__298
                (\ Any
v4 Any
v5 -> Any
v5)
                (Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'42'__308 (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'_292
                (Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'42'__308 (Integer -> Integer
forall a b. a -> b
coe Integer
v0))
                (\ Any
v4 Any
v5 -> Any
v4) Integer
v1 Integer
v2)
             (((Any -> Any -> Any -> T__'8801'__12 -> Any -> Any)
 -> Any -> Any -> Any -> Any -> T__'8801'__12 -> Any)
-> (Any -> Any -> Any -> Any -> Any -> Any)
-> Integer
-> Integer
-> Any
-> Any
-> Any
-> Any
forall a b. a -> b
coe
                (Any -> Any -> Any -> T__'8801'__12 -> Any -> Any)
-> Any -> Any -> Any -> Any -> T__'8801'__12 -> Any
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8801''45''10216'_448
                (\ Any
v4 Any
v5 Any
v6 Any
v7 Any
v8 -> Any
v8)
                (Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'42'__308 (Integer -> Integer
forall a b. a -> b
coe Integer
v0) (Integer -> Integer
forall a b. a -> b
coe Integer
v2))
                (Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d_'45'__252
                   ((Integer -> Integer -> Integer) -> Any -> Any -> Integer
forall a b. a -> b
coe
                      Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'42'__308
                      ((Integer -> Integer) -> Any -> Any
forall a b. a -> b
coe Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d_'45'__252 (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)
-> (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'_292
                   (Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'42'__308 (Integer -> Integer
forall a b. a -> b
coe Integer
v0))
                   (\ Any
v4 Any
v5 -> Any
v4) Integer
v1 Integer
v2)
                (((Any -> Any -> Any -> T__'8801'__12 -> Any -> Any)
 -> Any -> Any -> Any -> Any -> T__'8801'__12 -> Any)
-> (Any -> Any -> Any -> Any -> Any -> Any)
-> Integer
-> Integer
-> Any
-> Any
-> Any
-> Any
forall a b. a -> b
coe
                   (Any -> Any -> Any -> T__'8801'__12 -> Any -> Any)
-> Any -> Any -> Any -> Any -> T__'8801'__12 -> Any
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8801''45''10217'_436
                   (\ Any
v4 Any
v5 Any
v6 Any
v7 Any
v8 -> Any
v8)
                   (Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d_'45'__252
                      ((Integer -> Integer -> Integer) -> Any -> Any -> Integer
forall a b. a -> b
coe
                         Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'42'__308
                         ((Integer -> Integer) -> Any -> Any
forall a b. a -> b
coe Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d_'45'__252 (Integer -> Any
forall a b. a -> b
coe Integer
v0))
                         (Integer -> Any
forall a b. a -> b
coe Integer
v2)))
                   (Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'42'__308
                      ((Integer -> Integer) -> Any -> Integer
forall a b. a -> b
coe Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d_'45'__252 (Integer -> Any
forall a b. a -> b
coe Integer
v0))
                      ((Integer -> Integer) -> Any -> Integer
forall a b. a -> b
coe Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d_'45'__252 (Integer -> Any
forall a b. a -> b
coe 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'_292
                      (Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'42'__308 (Integer -> Integer
forall a b. a -> b
coe Integer
v0))
                      (\ Any
v4 Any
v5 -> Any
v4) Integer
v1 Integer
v2)
                   (((Any -> Any -> Any -> Any -> Any -> Any)
 -> Any -> Any -> Any -> Any -> Any -> Any)
-> Any -> Integer -> Integer -> Any -> Any -> Any -> Any
forall a b. a -> b
coe
                      (Any -> Any -> Any -> Any -> Any -> Any)
-> Any -> Any -> Any -> Any -> Any -> Any
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8804'_308
                      ((T_IsPreorder_70
 -> (Any -> Any -> Any -> Any -> Any -> Any)
 -> Any
 -> Any
 -> Any
 -> Any
 -> T__IsRelatedTo__78
 -> T__IsRelatedTo__78)
-> 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
-> Any
-> T__IsRelatedTo__78
-> T__IsRelatedTo__78
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_'8804''45'go_138
                         (T_IsPreorder_70 -> Any
forall a b. a -> b
coe T_IsPreorder_70
d_'8804''45'isPreorder_2800)
                         (\ 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_2958 Any
v7 Any
v8))
                      (Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'42'__308
                         ((Integer -> Integer) -> Any -> Integer
forall a b. a -> b
coe Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d_'45'__252 (Integer -> Any
forall a b. a -> b
coe Integer
v0))
                         ((Integer -> Integer) -> Any -> Integer
forall a b. a -> b
coe Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d_'45'__252 (Integer -> Any
forall a b. a -> b
coe Integer
v2)))
                      (Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'42'__308
                         ((Integer -> Integer) -> Any -> Integer
forall a b. a -> b
coe Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d_'45'__252 (Integer -> Any
forall a b. a -> b
coe Integer
v0))
                         ((Integer -> Integer) -> Any -> Integer
forall a b. a -> b
coe Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d_'45'__252 (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'_292
                         (Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'42'__308 (Integer -> Integer
forall a b. a -> b
coe Integer
v0))
                         (\ Any
v4 Any
v5 -> Any
v4) Integer
v1 Integer
v2)
                      (((Any -> Any -> Any -> T__'8801'__12 -> Any -> Any)
 -> Any -> Any -> Any -> Any -> T__'8801'__12 -> Any)
-> (Any -> Any -> Any -> Any -> Any -> Any)
-> Integer
-> Integer
-> Any
-> Any
-> Any
-> Any
forall a b. a -> b
coe
                         (Any -> Any -> Any -> T__'8801'__12 -> Any -> Any)
-> Any -> Any -> Any -> Any -> T__'8801'__12 -> Any
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8801''45''10216'_448
                         (\ Any
v4 Any
v5 Any
v6 Any
v7 Any
v8 -> Any
v8)
                         (Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'42'__308
                            ((Integer -> Integer) -> Any -> Integer
forall a b. a -> b
coe Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d_'45'__252 (Integer -> Any
forall a b. a -> b
coe Integer
v0))
                            ((Integer -> Integer) -> Any -> Integer
forall a b. a -> b
coe Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d_'45'__252 (Integer -> Any
forall a b. a -> b
coe Integer
v1)))
                         (Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d_'45'__252
                            ((Integer -> Integer -> Integer) -> Any -> Any -> Integer
forall a b. a -> b
coe
                               Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'42'__308
                               ((Integer -> Integer) -> Any -> Any
forall a b. a -> b
coe Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d_'45'__252 (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)
-> (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'_292
                            (Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'42'__308 (Integer -> Integer
forall a b. a -> b
coe Integer
v0))
                            (\ Any
v4 Any
v5 -> Any
v4) Integer
v1 Integer
v2)
                         (((Any -> Any -> Any -> T__'8801'__12 -> Any -> Any)
 -> Any -> Any -> Any -> Any -> T__'8801'__12 -> Any)
-> (Any -> Any -> Any -> Any -> Any -> Any)
-> Integer
-> Integer
-> Any
-> Any
-> Any
-> Any
forall a b. a -> b
coe
                            (Any -> Any -> Any -> T__'8801'__12 -> Any -> Any)
-> Any -> Any -> Any -> Any -> T__'8801'__12 -> Any
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8801''45''10217'_436
                            (\ Any
v4 Any
v5 Any
v6 Any
v7 Any
v8 -> Any
v8)
                            (Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d_'45'__252
                               ((Integer -> Integer -> Integer) -> Any -> Any -> Integer
forall a b. a -> b
coe
                                  Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'42'__308
                                  ((Integer -> Integer) -> Any -> Any
forall a b. a -> b
coe Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d_'45'__252 (Integer -> Any
forall a b. a -> b
coe Integer
v0))
                                  (Integer -> Any
forall a b. a -> b
coe Integer
v1)))
                            (Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'42'__308 (Integer -> Integer
forall a b. a -> b
coe Integer
v0) (Integer -> Integer
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'_292
                               (Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'42'__308 (Integer -> Integer
forall a b. a -> b
coe Integer
v0))
                               (\ Any
v4 Any
v5 -> Any
v4) Integer
v1 Integer
v2)
                            (((Any -> Any) -> Any -> Any) -> Any -> Any -> Any
forall a b. a -> b
coe
                               (Any -> Any) -> Any -> Any
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du__'8718'_492
                               ((T_IsPreorder_70 -> Any -> T__IsRelatedTo__78) -> Any -> Any
forall a b. a -> b
coe
                                  T_IsPreorder_70 -> Any -> T__IsRelatedTo__78
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_stop_166
                                  (T_IsPreorder_70 -> Any
forall a b. a -> b
coe T_IsPreorder_70
d_'8804''45'isPreorder_2800))
                               ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe
                                  Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'42'__308 (Integer -> Any
forall a b. a -> b
coe Integer
v0) (Integer -> Any
forall a b. a -> b
coe Integer
v1)))
                            Any
forall a. a
erased)
                         Any
forall a. a
erased)
                      ((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
du_'42''45'mono'737''45''8804''45'nonNeg_6096
                         (Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d_'45'__252 (Integer -> Integer
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'__298
                            (\ Any
v4 Any
v5 -> Any
v5) Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d_'45'__252 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'_292
                            Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d_'45'__252 (\ Any
v4 Any
v5 -> Any
v4) 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'_3272 (Integer -> Any
forall a b. a -> b
coe Integer
v2) (T__'8804'__26 -> Any
forall a b. a -> b
coe T__'8804'__26
v3))))
                   Any
forall a. a
erased)
                Any
forall a. a
erased)
-- Data.Integer.Properties.*-monoʳ-≤-nonPos
d_'42''45'mono'691''45''8804''45'nonPos_6192 ::
  Integer ->
  MAlonzo.Code.Data.Integer.Base.T_NonPositive_154 ->
  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_6192 :: Integer
-> T_NonPositive_154
-> Integer
-> Integer
-> T__'8804'__26
-> T__'8804'__26
d_'42''45'mono'691''45''8804''45'nonPos_6192 Integer
v0 ~T_NonPositive_154
v1 Integer
v2 Integer
v3
  = Integer -> Integer -> Integer -> T__'8804'__26 -> T__'8804'__26
du_'42''45'mono'691''45''8804''45'nonPos_6192 Integer
v0 Integer
v2 Integer
v3
du_'42''45'mono'691''45''8804''45'nonPos_6192 ::
  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_6192 :: Integer -> Integer -> Integer -> T__'8804'__26 -> T__'8804'__26
du_'42''45'mono'691''45''8804''45'nonPos_6192 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_6164 (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_6214 ::
  Integer ->
  MAlonzo.Code.Data.Integer.Base.T_Positive_134 ->
  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_6214 :: Integer
-> T_Positive_134
-> Integer
-> Integer
-> T__'60'__50
-> T__'60'__50
d_'42''45'mono'737''45''60''45'pos_6214 Integer
v0 ~T_Positive_134
v1 Integer
v2 Integer
v3 T__'60'__50
v4
  = Integer -> Integer -> Integer -> T__'60'__50 -> T__'60'__50
du_'42''45'mono'737''45''60''45'pos_6214 Integer
v0 Integer
v2 Integer
v3 T__'60'__50
v4
du_'42''45'mono'737''45''60''45'pos_6214 ::
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Integer.Base.T__'60'__50 ->
  MAlonzo.Code.Data.Integer.Base.T__'60'__50
du_'42''45'mono'737''45''60''45'pos_6214 :: Integer -> Integer -> Integer -> T__'60'__50 -> T__'60'__50
du_'42''45'mono'737''45''60''45'pos_6214 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
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 -> 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'__22
v7
                 -> (Integer -> T__'8804'__22 -> T__'60'__50) -> Any -> Any -> Any
forall a b. a -> b
coe
                      Integer -> T__'8804'__22 -> T__'60'__50
du_'43''9667''45'mono'45''60'_3600
                      ((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
v1) ((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
v4) (Integer -> Any
forall a b. a -> b
coe Integer
v1)))
                      ((T__'8804'__22 -> T__'8804'__22 -> T__'8804'__22)
-> Any -> Any -> Any
forall a b. a -> b
coe
                         T__'8804'__22 -> T__'8804'__22 -> T__'8804'__22
MAlonzo.Code.Data.Nat.Properties.du_'43''45'mono'45''60''45''8804'_3560
                         (T__'8804'__22 -> Any
forall a b. a -> b
coe T__'8804'__22
v7)
                         ((Integer -> Integer -> T__'8804'__22 -> T__'8804'__22)
-> Any -> Any -> Any -> Any
forall a b. a -> b
coe
                            Integer -> Integer -> T__'8804'__22 -> T__'8804'__22
MAlonzo.Code.Data.Nat.Properties.du_'42''45'mono'691''45''8804'_4080
                            (Integer -> Any
forall a b. a -> b
coe Integer
v4) (Integer -> Any
forall a b. a -> b
coe Integer
v2)
                            ((T__'8804'__22 -> T__'8804'__22) -> Any -> Any
forall a b. a -> b
coe
                               T__'8804'__22 -> T__'8804'__22
MAlonzo.Code.Data.Nat.Properties.du_'60''8658''8804'_2854
                               (T__'8804'__22 -> Any
forall a b. a -> b
coe T__'8804'__22
v7))))
               T__'60'__50
_ -> Any
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 -> Any
forall a b. a -> b
coe Integer -> T__'60'__50
du_'45''9667''60''43''9667'_3642 ((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
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'__22
v7
                         -> (T__'8804'__22 -> T__'60'__50) -> Any -> Any
forall a b. a -> b
coe
                              T__'8804'__22 -> T__'60'__50
MAlonzo.Code.Data.Integer.Base.C_'45''60''45'_58
                              ((T__'8804'__22 -> T__'8804'__22 -> T__'8804'__22)
-> Any -> Any -> Any
forall a b. a -> b
coe
                                 T__'8804'__22 -> T__'8804'__22 -> T__'8804'__22
MAlonzo.Code.Data.Nat.Properties.du_'43''45'mono'45''60''45''8804'_3560
                                 (T__'8804'__22 -> Any
forall a b. a -> b
coe T__'8804'__22
v7)
                                 ((Integer -> Integer -> T__'8804'__22 -> T__'8804'__22)
-> Any -> Any -> Any -> Any
forall a b. a -> b
coe
                                    Integer -> Integer -> T__'8804'__22 -> T__'8804'__22
MAlonzo.Code.Data.Nat.Properties.du_'42''45'mono'691''45''8804'_4080
                                    (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
0 :: Integer)) (Integer -> Any
forall a b. a -> b
coe Integer
v1))
                                    ((T__'8804'__22 -> T__'8804'__22) -> Any -> Any
forall a b. a -> b
coe
                                       T__'8804'__22 -> T__'8804'__22
MAlonzo.Code.Data.Nat.Properties.du_'60''8658''8804'_2854
                                       ((T__'8804'__22 -> T__'8804'__22) -> T__'8804'__22 -> Any
forall a b. a -> b
coe T__'8804'__22 -> T__'8804'__22
MAlonzo.Code.Data.Nat.Base.C_s'8804's_34 T__'8804'__22
v7))))
                       T__'60'__50
_ -> Any
forall a. a
MAlonzo.RTE.mazUnreachableError)
-- Data.Integer.Properties.*-monoʳ-<-pos
d_'42''45'mono'691''45''60''45'pos_6246 ::
  Integer ->
  MAlonzo.Code.Data.Integer.Base.T_Positive_134 ->
  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_6246 :: Integer
-> T_Positive_134
-> Integer
-> Integer
-> T__'60'__50
-> T__'60'__50
d_'42''45'mono'691''45''60''45'pos_6246 Integer
v0 ~T_Positive_134
v1 Integer
v2 Integer
v3
  = Integer -> Integer -> Integer -> T__'60'__50 -> T__'60'__50
du_'42''45'mono'691''45''60''45'pos_6246 Integer
v0 Integer
v2 Integer
v3
du_'42''45'mono'691''45''60''45'pos_6246 ::
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Integer.Base.T__'60'__50 ->
  MAlonzo.Code.Data.Integer.Base.T__'60'__50
du_'42''45'mono'691''45''60''45'pos_6246 :: Integer -> Integer -> Integer -> T__'60'__50 -> T__'60'__50
du_'42''45'mono'691''45''60''45'pos_6246 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
du_'42''45'mono'737''45''60''45'pos_6214 (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_6266 ::
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Integer.Base.T_NonNegative_144 ->
  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_6266 :: Integer
-> Integer
-> Integer
-> T_NonNegative_144
-> T__'60'__50
-> T__'60'__50
d_'42''45'cancel'737''45''60''45'nonNeg_6266 Integer
v0 Integer
v1 Integer
v2 ~T_NonNegative_144
v3 T__'60'__50
v4
  = Integer -> Integer -> Integer -> T__'60'__50 -> T__'60'__50
du_'42''45'cancel'737''45''60''45'nonNeg_6266 Integer
v0 Integer
v1 Integer
v2 T__'60'__50
v4
du_'42''45'cancel'737''45''60''45'nonNeg_6266 ::
  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'nonNeg_6266 :: Integer -> Integer -> Integer -> T__'60'__50 -> T__'60'__50
du_'42''45'cancel'737''45''60''45'nonNeg_6266 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 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'__22 -> T__'60'__50) -> Any -> T__'60'__50
forall a b. a -> b
coe
                  T__'8804'__22 -> T__'60'__50
MAlonzo.Code.Data.Integer.Base.C_'43''60''43'_72
                  ((Integer -> Integer -> Integer -> T__'8804'__22 -> T__'8804'__22)
-> Integer -> Integer -> Integer -> Any -> Any
forall a b. a -> b
coe
                     Integer -> Integer -> Integer -> T__'8804'__22 -> T__'8804'__22
MAlonzo.Code.Data.Nat.Properties.d_'42''45'cancel'737''45''60'_4208
                     Integer
v2 (Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d_'8739'_'8739'_18 (Integer -> Integer
forall a b. a -> b
coe Integer
v0))
                     (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'__22) -> Any -> Any -> Any
forall a b. a -> b
coe
                        Integer -> T__'60'__50 -> T__'8804'__22
du_'43''9667''45'cancel'45''60'_3612
                        ((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
v2)
                           ((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)))
                        (T__'60'__50 -> Any
forall a b. a -> b
coe T__'60'__50
v3)))
            Any
_ -> ((Any -> T_Irrelevant_20) -> Any) -> Any -> T__'60'__50
forall a b. a -> b
coe
                   (Any -> T_Irrelevant_20) -> Any
MAlonzo.Code.Relation.Nullary.Negation.Core.du_contradiction_44
                   Any
forall a. a
erased
      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__'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'__22 -> T__'60'__50) -> Any -> T__'60'__50
forall a b. a -> b
coe
                    T__'8804'__22 -> T__'60'__50
MAlonzo.Code.Data.Integer.Base.C_'45''60''45'_58
                    ((T__'8804'__22 -> T__'8804'__22) -> Any -> Any
forall a b. a -> b
coe
                       T__'8804'__22 -> T__'8804'__22
MAlonzo.Code.Data.Nat.Base.du_s'60's'8315''185'_70
                       ((Integer -> Integer -> Integer -> T__'8804'__22 -> T__'8804'__22)
-> Integer -> Integer -> Integer -> Any -> Any
forall a b. a -> b
coe
                          Integer -> Integer -> Integer -> T__'8804'__22 -> T__'8804'__22
MAlonzo.Code.Data.Nat.Properties.d_'42''45'cancel'737''45''60'_4208
                          Integer
v2 (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
v0))
                          ((Integer -> T__'60'__50 -> T__'8804'__22) -> Any -> Any -> Any
forall a b. a -> b
coe
                             Integer -> T__'60'__50 -> T__'8804'__22
du_neg'9667''45'cancel'45''60'_3626
                             ((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
v2)
                                ((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))))
-- Data.Integer.Properties.*-cancelʳ-<-nonNeg
d_'42''45'cancel'691''45''60''45'nonNeg_6304 ::
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Integer.Base.T_NonNegative_144 ->
  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_6304 :: Integer
-> Integer
-> Integer
-> T_NonNegative_144
-> T__'60'__50
-> T__'60'__50
d_'42''45'cancel'691''45''60''45'nonNeg_6304 Integer
v0 Integer
v1 Integer
v2 ~T_NonNegative_144
v3
  = Integer -> Integer -> Integer -> T__'60'__50 -> T__'60'__50
du_'42''45'cancel'691''45''60''45'nonNeg_6304 Integer
v0 Integer
v1 Integer
v2
du_'42''45'cancel'691''45''60''45'nonNeg_6304 ::
  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'nonNeg_6304 :: Integer -> Integer -> Integer -> T__'60'__50 -> T__'60'__50
du_'42''45'cancel'691''45''60''45'nonNeg_6304 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
du_'42''45'cancel'737''45''60''45'nonNeg_6266 (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-<-neg
d_'42''45'mono'737''45''60''45'neg_6326 ::
  Integer ->
  MAlonzo.Code.Data.Integer.Base.T_Negative_164 ->
  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_6326 :: Integer
-> T_Negative_164
-> Integer
-> Integer
-> T__'60'__50
-> T__'60'__50
d_'42''45'mono'737''45''60''45'neg_6326 Integer
v0 ~T_Negative_164
v1 Integer
v2 Integer
v3 T__'60'__50
v4
  = Integer -> Integer -> Integer -> T__'60'__50 -> T__'60'__50
du_'42''45'mono'737''45''60''45'neg_6326 Integer
v0 Integer
v2 Integer
v3 T__'60'__50
v4
du_'42''45'mono'737''45''60''45'neg_6326 ::
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Integer.Base.T__'60'__50 ->
  MAlonzo.Code.Data.Integer.Base.T__'60'__50
du_'42''45'mono'737''45''60''45'neg_6326 :: Integer -> Integer -> Integer -> T__'60'__50 -> T__'60'__50
du_'42''45'mono'737''45''60''45'neg_6326 Integer
v0 Integer
v1 Integer
v2 T__'60'__50
v3
  = let v4 :: b
v4
          = T_SubRelation_60 -> b
forall a b. a -> b
coe
              T_SubRelation_60
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_strictRelation_202 in
    Any -> T__'60'__50
forall a b. a -> b
coe
      ((T_SubRelation_60 -> Any -> Any -> Any -> Any)
-> Any -> Any -> Any -> Any -> Any
forall a b. a -> b
coe
         T_SubRelation_60 -> Any -> Any -> Any -> Any
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_begin__126
         (Any -> Any
forall a b. a -> b
coe Any
forall a. a
v4)
         ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'42'__308 (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'__308 (Integer -> Any
forall a b. a -> b
coe Integer
v0) (Integer -> Any
forall a b. a -> b
coe Integer
v1))
         (((Any -> Any -> Any -> T__'8801'__12 -> Any -> Any)
 -> Any -> Any -> Any -> Any -> T__'8801'__12 -> Any)
-> (Any -> Any -> Any -> Any -> Any -> Any)
-> Integer
-> Integer
-> Integer
-> Any
-> Any
-> Any
forall a b. a -> b
coe
            (Any -> Any -> Any -> T__'8801'__12 -> Any -> Any)
-> Any -> Any -> Any -> Any -> T__'8801'__12 -> Any
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8801''45''10216'_448
            (\ Any
v5 Any
v6 Any
v7 Any
v8 Any
v9 -> Any
v9)
            (Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'42'__308 (Integer -> Integer
forall a b. a -> b
coe Integer
v0) (Integer -> Integer
forall a b. a -> b
coe Integer
v2))
            (Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d_'45'__252
               ((Integer -> Integer -> Integer) -> Any -> Any -> Integer
forall a b. a -> b
coe
                  Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'42'__308
                  ((Integer -> Integer) -> Any -> Any
forall a b. a -> b
coe Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d_'45'__252 (Integer -> Any
forall a b. a -> b
coe Integer
v0))
                  (Integer -> Any
forall a b. a -> b
coe Integer
v2)))
            (Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'42'__308 (Integer -> Integer
forall a b. a -> b
coe Integer
v0) (Integer -> Integer
forall a b. a -> b
coe Integer
v1))
            (((Any -> Any -> Any -> T__'8801'__12 -> Any -> Any)
 -> Any -> Any -> Any -> Any -> T__'8801'__12 -> Any)
-> (Any -> Any -> Any -> Any -> Any -> Any)
-> Integer
-> Integer
-> Integer
-> Any
-> Any
-> Any
forall a b. a -> b
coe
               (Any -> Any -> Any -> T__'8801'__12 -> Any -> Any)
-> Any -> Any -> Any -> Any -> T__'8801'__12 -> Any
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8801''45''10217'_436
               (\ Any
v5 Any
v6 Any
v7 Any
v8 Any
v9 -> Any
v9)
               (Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d_'45'__252
                  ((Integer -> Integer -> Integer) -> Any -> Any -> Integer
forall a b. a -> b
coe
                     Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'42'__308
                     ((Integer -> Integer) -> Any -> Any
forall a b. a -> b
coe Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d_'45'__252 (Integer -> Any
forall a b. a -> b
coe Integer
v0))
                     (Integer -> Any
forall a b. a -> b
coe Integer
v2)))
               (Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'42'__308
                  ((Integer -> Integer) -> Any -> Integer
forall a b. a -> b
coe Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d_'45'__252 (Integer -> Any
forall a b. a -> b
coe Integer
v0))
                  ((Integer -> Integer) -> Any -> Integer
forall a b. a -> b
coe Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d_'45'__252 (Integer -> Any
forall a b. a -> b
coe Integer
v2)))
               (Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'42'__308 (Integer -> Integer
forall a b. a -> b
coe Integer
v0) (Integer -> Integer
forall a b. a -> b
coe Integer
v1))
               (((Any -> Any -> Any -> Any -> Any -> Any)
 -> Any -> Any -> Any -> Any -> Any -> Any)
-> Any -> Integer -> Integer -> Integer -> Any -> Any -> Any
forall a b. a -> b
coe
                  (Any -> Any -> Any -> Any -> Any -> Any)
-> Any -> Any -> Any -> Any -> Any -> Any
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''60'_312
                  (((Any -> Any -> Any -> Any -> Any -> Any)
 -> T_Σ_14
 -> (Any -> Any -> Any -> Any -> Any -> Any)
 -> Any
 -> Any
 -> Any
 -> Any
 -> T__IsRelatedTo__78
 -> T__IsRelatedTo__78)
-> (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
-> Any
-> T__IsRelatedTo__78
-> T__IsRelatedTo__78
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_'60''45'go_152
                     (\ Any
v5 Any
v6 Any
v7 Any
v8 Any
v9 -> (T__'60'__50 -> T__'60'__50 -> T__'60'__50) -> Any -> Any -> Any
forall a b. a -> b
coe T__'60'__50 -> T__'60'__50 -> T__'60'__50
du_'60''45'trans_2986 Any
v8 Any
v9)
                     (T_Σ_14 -> Any
forall a b. a -> b
coe
                        T_Σ_14
MAlonzo.Code.Relation.Binary.PropositionalEquality.Core.du_resp'8322'_160)
                     (\ Any
v5 Any
v6 Any
v7 Any
v8 Any
v9 -> (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_2972 Any
v8 Any
v9))
                  (Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'42'__308
                     ((Integer -> Integer) -> Any -> Integer
forall a b. a -> b
coe Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d_'45'__252 (Integer -> Any
forall a b. a -> b
coe Integer
v0))
                     ((Integer -> Integer) -> Any -> Integer
forall a b. a -> b
coe Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d_'45'__252 (Integer -> Any
forall a b. a -> b
coe Integer
v2)))
                  (Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'42'__308
                     ((Integer -> Integer) -> Any -> Integer
forall a b. a -> b
coe Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d_'45'__252 (Integer -> Any
forall a b. a -> b
coe Integer
v0))
                     ((Integer -> Integer) -> Any -> Integer
forall a b. a -> b
coe Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d_'45'__252 (Integer -> Any
forall a b. a -> b
coe Integer
v1)))
                  (Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'42'__308 (Integer -> Integer
forall a b. a -> b
coe Integer
v0) (Integer -> Integer
forall a b. a -> b
coe Integer
v1))
                  (((Any -> Any -> Any -> T__'8801'__12 -> Any -> Any)
 -> Any -> Any -> Any -> Any -> T__'8801'__12 -> Any)
-> (Any -> Any -> Any -> Any -> Any -> Any)
-> Integer
-> Integer
-> Integer
-> Any
-> Any
-> Any
forall a b. a -> b
coe
                     (Any -> Any -> Any -> T__'8801'__12 -> Any -> Any)
-> Any -> Any -> Any -> Any -> T__'8801'__12 -> Any
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8801''45''10216'_448
                     (\ Any
v5 Any
v6 Any
v7 Any
v8 Any
v9 -> Any
v9)
                     (Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'42'__308
                        ((Integer -> Integer) -> Any -> Integer
forall a b. a -> b
coe Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d_'45'__252 (Integer -> Any
forall a b. a -> b
coe Integer
v0))
                        ((Integer -> Integer) -> Any -> Integer
forall a b. a -> b
coe Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d_'45'__252 (Integer -> Any
forall a b. a -> b
coe Integer
v1)))
                     (Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d_'45'__252
                        ((Integer -> Integer -> Integer) -> Any -> Any -> Integer
forall a b. a -> b
coe
                           Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'42'__308
                           ((Integer -> Integer) -> Any -> Any
forall a b. a -> b
coe Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d_'45'__252 (Integer -> Any
forall a b. a -> b
coe Integer
v0))
                           (Integer -> Any
forall a b. a -> b
coe Integer
v1)))
                     (Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'42'__308 (Integer -> Integer
forall a b. a -> b
coe Integer
v0) (Integer -> Integer
forall a b. a -> b
coe Integer
v1))
                     (((Any -> Any -> Any -> T__'8801'__12 -> Any -> Any)
 -> Any -> Any -> Any -> Any -> T__'8801'__12 -> Any)
-> (Any -> Any -> Any -> Any -> Any -> Any)
-> Integer
-> Integer
-> Integer
-> Any
-> Any
-> Any
forall a b. a -> b
coe
                        (Any -> Any -> Any -> T__'8801'__12 -> Any -> Any)
-> Any -> Any -> Any -> Any -> T__'8801'__12 -> Any
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8801''45''10217'_436
                        (\ Any
v5 Any
v6 Any
v7 Any
v8 Any
v9 -> Any
v9)
                        (Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d_'45'__252
                           ((Integer -> Integer -> Integer) -> Any -> Any -> Integer
forall a b. a -> b
coe
                              Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'42'__308
                              ((Integer -> Integer) -> Any -> Any
forall a b. a -> b
coe Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d_'45'__252 (Integer -> Any
forall a b. a -> b
coe Integer
v0))
                              (Integer -> Any
forall a b. a -> b
coe Integer
v1)))
                        (Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'42'__308 (Integer -> Integer
forall a b. a -> b
coe Integer
v0) (Integer -> Integer
forall a b. a -> b
coe Integer
v1))
                        (Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'42'__308 (Integer -> Integer
forall a b. a -> b
coe Integer
v0) (Integer -> Integer
forall a b. a -> b
coe Integer
v1))
                        (((Any -> Any) -> Any -> Any) -> Any -> Any -> Any
forall a b. a -> b
coe
                           (Any -> Any) -> Any -> Any
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du__'8718'_492
                           ((T_IsPreorder_70 -> Any -> T__IsRelatedTo__78) -> Any -> Any
forall a b. a -> b
coe
                              T_IsPreorder_70 -> Any -> T__IsRelatedTo__78
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_stop_166
                              (T_IsPreorder_70 -> Any
forall a b. a -> b
coe T_IsPreorder_70
d_'8804''45'isPreorder_2800))
                           ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe
                              Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'42'__308 (Integer -> Any
forall a b. a -> b
coe Integer
v0) (Integer -> Any
forall a b. a -> b
coe Integer
v1)))
                        Any
forall a. a
erased)
                     Any
forall a. a
erased)
                  ((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
du_'42''45'mono'737''45''60''45'pos_6214
                     ((Integer -> Integer) -> Any -> Any
forall a b. a -> b
coe Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d_'45'__252 (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'__298
                        (\ Any
v5 Any
v6 -> Any
v6) Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d_'45'__252 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'_292
                        Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d_'45'__252 (\ Any
v5 Any
v6 -> Any
v5) 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'_3302 (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))))
               Any
forall a. a
erased)
            Any
forall a. a
erased))
-- Data.Integer.Properties.*-monoʳ-<-neg
d_'42''45'mono'691''45''60''45'neg_6346 ::
  Integer ->
  MAlonzo.Code.Data.Integer.Base.T_Negative_164 ->
  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_6346 :: Integer
-> T_Negative_164
-> Integer
-> Integer
-> T__'60'__50
-> T__'60'__50
d_'42''45'mono'691''45''60''45'neg_6346 Integer
v0 ~T_Negative_164
v1 Integer
v2 Integer
v3
  = Integer -> Integer -> Integer -> T__'60'__50 -> T__'60'__50
du_'42''45'mono'691''45''60''45'neg_6346 Integer
v0 Integer
v2 Integer
v3
du_'42''45'mono'691''45''60''45'neg_6346 ::
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Integer.Base.T__'60'__50 ->
  MAlonzo.Code.Data.Integer.Base.T__'60'__50
du_'42''45'mono'691''45''60''45'neg_6346 :: Integer -> Integer -> Integer -> T__'60'__50 -> T__'60'__50
du_'42''45'mono'691''45''60''45'neg_6346 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
du_'42''45'mono'737''45''60''45'neg_6326 (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-<-nonPos
d_'42''45'cancel'737''45''60''45'nonPos_6366 ::
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Integer.Base.T_NonPositive_154 ->
  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_6366 :: Integer
-> Integer
-> Integer
-> T_NonPositive_154
-> T__'60'__50
-> T__'60'__50
d_'42''45'cancel'737''45''60''45'nonPos_6366 Integer
v0 Integer
v1 Integer
v2 ~T_NonPositive_154
v3 T__'60'__50
v4
  = Integer -> Integer -> Integer -> T__'60'__50 -> T__'60'__50
du_'42''45'cancel'737''45''60''45'nonPos_6366 Integer
v0 Integer
v1 Integer
v2 T__'60'__50
v4
du_'42''45'cancel'737''45''60''45'nonPos_6366 ::
  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_6366 :: Integer -> Integer -> Integer -> T__'60'__50 -> T__'60'__50
du_'42''45'cancel'737''45''60''45'nonPos_6366 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'_3316 (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
du_'42''45'cancel'737''45''60''45'nonNeg_6266
         ((Integer -> Integer) -> Any -> Any
forall a b. a -> b
coe Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d_'45'__252 (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'__252 (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'__252 (Integer -> Any
forall a b. a -> b
coe Integer
v2))
         (let v4 :: b
v4
                = T_SubRelation_60 -> b
forall a b. a -> b
coe
                    T_SubRelation_60
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_strictRelation_202 in
          Any -> Any
forall a b. a -> b
coe
            ((T_SubRelation_60 -> Any -> Any -> Any -> Any)
-> Any -> Any -> Any -> Any -> Any
forall a b. a -> b
coe
               T_SubRelation_60 -> Any -> Any -> Any -> Any
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_begin__126
               (Any -> Any
forall a b. a -> b
coe Any
forall a. a
v4)
               ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe
                  Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'42'__308
                  ((Integer -> Integer) -> Any -> Any
forall a b. a -> b
coe Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d_'45'__252 (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_'45'__252 (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'__308
                  ((Integer -> Integer) -> Any -> Any
forall a b. a -> b
coe Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d_'45'__252 (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_'45'__252 (Integer -> Any
forall a b. a -> b
coe Integer
v1)))
               (((Any -> Any -> Any -> T__'8801'__12 -> Any -> Any)
 -> Any -> Any -> Any -> Any -> T__'8801'__12 -> Any)
-> (Any -> Any -> Any -> Any -> Any -> Any)
-> Integer
-> Integer
-> Integer
-> Any
-> Any
-> Any
forall a b. a -> b
coe
                  (Any -> Any -> Any -> T__'8801'__12 -> Any -> Any)
-> Any -> Any -> Any -> Any -> T__'8801'__12 -> Any
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8801''45''10216'_448
                  (\ Any
v5 Any
v6 Any
v7 Any
v8 Any
v9 -> Any
v9)
                  (Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'42'__308
                     ((Integer -> Integer) -> Any -> Integer
forall a b. a -> b
coe Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d_'45'__252 (Integer -> Any
forall a b. a -> b
coe Integer
v2))
                     ((Integer -> Integer) -> Any -> Integer
forall a b. a -> b
coe Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d_'45'__252 (Integer -> Any
forall a b. a -> b
coe Integer
v0)))
                  (Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d_'45'__252
                     ((Integer -> Integer -> Integer) -> Any -> Any -> Integer
forall a b. a -> b
coe
                        Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'42'__308
                        ((Integer -> Integer) -> Any -> Any
forall a b. a -> b
coe Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d_'45'__252 (Integer -> Any
forall a b. a -> b
coe Integer
v2))
                        (Integer -> Any
forall a b. a -> b
coe Integer
v0)))
                  (Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'42'__308
                     ((Integer -> Integer) -> Any -> Integer
forall a b. a -> b
coe Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d_'45'__252 (Integer -> Any
forall a b. a -> b
coe Integer
v2))
                     ((Integer -> Integer) -> Any -> Integer
forall a b. a -> b
coe Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d_'45'__252 (Integer -> Any
forall a b. a -> b
coe Integer
v1)))
                  (((Any -> Any -> Any -> T__'8801'__12 -> Any -> Any)
 -> Any -> Any -> Any -> Any -> T__'8801'__12 -> Any)
-> (Any -> Any -> Any -> Any -> Any -> Any)
-> Integer
-> Integer
-> Integer
-> Any
-> Any
-> Any
forall a b. a -> b
coe
                     (Any -> Any -> Any -> T__'8801'__12 -> Any -> Any)
-> Any -> Any -> Any -> Any -> T__'8801'__12 -> Any
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8801''45''10217'_436
                     (\ Any
v5 Any
v6 Any
v7 Any
v8 Any
v9 -> Any
v9)
                     (Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d_'45'__252
                        ((Integer -> Integer -> Integer) -> Any -> Any -> Integer
forall a b. a -> b
coe
                           Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'42'__308
                           ((Integer -> Integer) -> Any -> Any
forall a b. a -> b
coe Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d_'45'__252 (Integer -> Any
forall a b. a -> b
coe Integer
v2))
                           (Integer -> Any
forall a b. a -> b
coe Integer
v0)))
                     (Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'42'__308 (Integer -> Integer
forall a b. a -> b
coe Integer
v2) (Integer -> Integer
forall a b. a -> b
coe Integer
v0))
                     (Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'42'__308
                        ((Integer -> Integer) -> Any -> Integer
forall a b. a -> b
coe Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d_'45'__252 (Integer -> Any
forall a b. a -> b
coe Integer
v2))
                        ((Integer -> Integer) -> Any -> Integer
forall a b. a -> b
coe Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d_'45'__252 (Integer -> Any
forall a b. a -> b
coe Integer
v1)))
                     (((Any -> Any -> Any -> Any -> Any -> Any)
 -> Any -> Any -> Any -> Any -> Any -> Any)
-> Any
-> Integer
-> Integer
-> Integer
-> Any
-> T__'60'__50
-> Any
forall a b. a -> b
coe
                        (Any -> Any -> Any -> Any -> Any -> Any)
-> Any -> Any -> Any -> Any -> Any -> Any
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''60'_312
                        (((Any -> Any -> Any -> Any -> Any -> Any)
 -> T_Σ_14
 -> (Any -> Any -> Any -> Any -> Any -> Any)
 -> Any
 -> Any
 -> Any
 -> Any
 -> T__IsRelatedTo__78
 -> T__IsRelatedTo__78)
-> (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
-> Any
-> T__IsRelatedTo__78
-> T__IsRelatedTo__78
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_'60''45'go_152
                           (\ Any
v5 Any
v6 Any
v7 Any
v8 Any
v9 -> (T__'60'__50 -> T__'60'__50 -> T__'60'__50) -> Any -> Any -> Any
forall a b. a -> b
coe T__'60'__50 -> T__'60'__50 -> T__'60'__50
du_'60''45'trans_2986 Any
v8 Any
v9)
                           (T_Σ_14 -> Any
forall a b. a -> b
coe
                              T_Σ_14
MAlonzo.Code.Relation.Binary.PropositionalEquality.Core.du_resp'8322'_160)
                           (\ Any
v5 Any
v6 Any
v7 Any
v8 Any
v9 -> (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_2972 Any
v8 Any
v9))
                        (Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'42'__308 (Integer -> Integer
forall a b. a -> b
coe Integer
v2) (Integer -> Integer
forall a b. a -> b
coe Integer
v0))
                        (Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'42'__308 (Integer -> Integer
forall a b. a -> b
coe Integer
v2) (Integer -> Integer
forall a b. a -> b
coe Integer
v1))
                        (Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'42'__308
                           ((Integer -> Integer) -> Any -> Integer
forall a b. a -> b
coe Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d_'45'__252 (Integer -> Any
forall a b. a -> b
coe Integer
v2))
                           ((Integer -> Integer) -> Any -> Integer
forall a b. a -> b
coe Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d_'45'__252 (Integer -> Any
forall a b. a -> b
coe Integer
v1)))
                        (((Any -> Any -> Any -> T__'8801'__12 -> Any -> Any)
 -> Any -> Any -> Any -> Any -> T__'8801'__12 -> Any)
-> (Any -> Any -> Any -> Any -> Any -> Any)
-> Integer
-> Integer
-> Integer
-> Any
-> Any
-> Any
forall a b. a -> b
coe
                           (Any -> Any -> Any -> T__'8801'__12 -> Any -> Any)
-> Any -> Any -> Any -> Any -> T__'8801'__12 -> Any
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8801''45''10216'_448
                           (\ Any
v5 Any
v6 Any
v7 Any
v8 Any
v9 -> Any
v9)
                           (Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'42'__308 (Integer -> Integer
forall a b. a -> b
coe Integer
v2) (Integer -> Integer
forall a b. a -> b
coe Integer
v1))
                           (Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d_'45'__252
                              ((Integer -> Integer -> Integer) -> Any -> Any -> Integer
forall a b. a -> b
coe
                                 Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'42'__308
                                 ((Integer -> Integer) -> Any -> Any
forall a b. a -> b
coe Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d_'45'__252 (Integer -> Any
forall a b. a -> b
coe Integer
v2))
                                 (Integer -> Any
forall a b. a -> b
coe Integer
v1)))
                           (Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'42'__308
                              ((Integer -> Integer) -> Any -> Integer
forall a b. a -> b
coe Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d_'45'__252 (Integer -> Any
forall a b. a -> b
coe Integer
v2))
                              ((Integer -> Integer) -> Any -> Integer
forall a b. a -> b
coe Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d_'45'__252 (Integer -> Any
forall a b. a -> b
coe Integer
v1)))
                           (((Any -> Any -> Any -> T__'8801'__12 -> Any -> Any)
 -> Any -> Any -> Any -> Any -> T__'8801'__12 -> Any)
-> (Any -> Any -> Any -> Any -> Any -> Any)
-> Integer
-> Integer
-> Integer
-> Any
-> Any
-> Any
forall a b. a -> b
coe
                              (Any -> Any -> Any -> T__'8801'__12 -> Any -> Any)
-> Any -> Any -> Any -> Any -> T__'8801'__12 -> Any
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8801''45''10217'_436
                              (\ Any
v5 Any
v6 Any
v7 Any
v8 Any
v9 -> Any
v9)
                              (Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d_'45'__252
                                 ((Integer -> Integer -> Integer) -> Any -> Any -> Integer
forall a b. a -> b
coe
                                    Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'42'__308
                                    ((Integer -> Integer) -> Any -> Any
forall a b. a -> b
coe Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d_'45'__252 (Integer -> Any
forall a b. a -> b
coe Integer
v2))
                                    (Integer -> Any
forall a b. a -> b
coe Integer
v1)))
                              (Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'42'__308
                                 ((Integer -> Integer) -> Any -> Integer
forall a b. a -> b
coe Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d_'45'__252 (Integer -> Any
forall a b. a -> b
coe Integer
v2))
                                 ((Integer -> Integer) -> Any -> Integer
forall a b. a -> b
coe Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d_'45'__252 (Integer -> Any
forall a b. a -> b
coe Integer
v1)))
                              (Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'42'__308
                                 ((Integer -> Integer) -> Any -> Integer
forall a b. a -> b
coe Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d_'45'__252 (Integer -> Any
forall a b. a -> b
coe Integer
v2))
                                 ((Integer -> Integer) -> Any -> Integer
forall a b. a -> b
coe Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d_'45'__252 (Integer -> Any
forall a b. a -> b
coe Integer
v1)))
                              (((Any -> Any) -> Any -> Any) -> Any -> Any -> Any
forall a b. a -> b
coe
                                 (Any -> Any) -> Any -> Any
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du__'8718'_492
                                 ((T_IsPreorder_70 -> Any -> T__IsRelatedTo__78) -> Any -> Any
forall a b. a -> b
coe
                                    T_IsPreorder_70 -> Any -> T__IsRelatedTo__78
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_stop_166
                                    (T_IsPreorder_70 -> Any
forall a b. a -> b
coe T_IsPreorder_70
d_'8804''45'isPreorder_2800))
                                 ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe
                                    Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'42'__308
                                    ((Integer -> Integer) -> Any -> Any
forall a b. a -> b
coe Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d_'45'__252 (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_'45'__252 (Integer -> Any
forall a b. a -> b
coe Integer
v1))))
                              Any
forall a. a
erased)
                           Any
forall a. a
erased)
                        T__'60'__50
v3)
                     Any
forall a. a
erased)
                  Any
forall a. a
erased))))
-- Data.Integer.Properties.*-cancelʳ-<-nonPos
d_'42''45'cancel'691''45''60''45'nonPos_6388 ::
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Integer.Base.T_NonPositive_154 ->
  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_6388 :: Integer
-> Integer
-> Integer
-> T_NonPositive_154
-> T__'60'__50
-> T__'60'__50
d_'42''45'cancel'691''45''60''45'nonPos_6388 Integer
v0 Integer
v1 Integer
v2 ~T_NonPositive_154
v3
  = Integer -> Integer -> Integer -> T__'60'__50 -> T__'60'__50
du_'42''45'cancel'691''45''60''45'nonPos_6388 Integer
v0 Integer
v1 Integer
v2
du_'42''45'cancel'691''45''60''45'nonPos_6388 ::
  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_6388 :: Integer -> Integer -> Integer -> T__'60'__50 -> T__'60'__50
du_'42''45'cancel'691''45''60''45'nonPos_6388 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
du_'42''45'cancel'737''45''60''45'nonPos_6366 (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''60''45'neg_6406 ::
  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_6406 :: Integer -> Integer -> Integer -> T__'60'__50 -> T__'60'__50
d_'42''45'cancel'737''45''60''45'neg_6406 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
du_'42''45'cancel'737''45''60''45'nonPos_6366 (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
subInt (Integer -> Any
forall a b. a -> b
coe (-Integer
1 :: Integer)) (Integer -> Any
forall a b. a -> b
coe Integer
v2))
-- Data.Integer.Properties.*-cancelʳ-<-neg
d_'42''45'cancel'691''45''60''45'neg_6416 ::
  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_6416 :: Integer -> Integer -> Integer -> T__'60'__50 -> T__'60'__50
d_'42''45'cancel'691''45''60''45'neg_6416 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
du_'42''45'cancel'691''45''60''45'nonPos_6388 (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
subInt (Integer -> Any
forall a b. a -> b
coe (-Integer
1 :: Integer)) (Integer -> Any
forall a b. a -> b
coe Integer
v2))
-- Data.Integer.Properties.∣i*j∣≡∣i∣*∣j∣
d_'8739'i'42'j'8739''8801''8739'i'8739''42''8739'j'8739'_6428 ::
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8739'i'42'j'8739''8801''8739'i'8739''42''8739'j'8739'_6428 :: Integer -> Integer -> T__'8801'__12
d_'8739'i'42'j'8739''8801''8739'i'8739''42''8739'j'8739'_6428
  = 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_6430 ::
  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_6430 :: Integer -> Integer -> T__'8804'__26 -> T__'8801'__12
d_i'8804'j'8658'i'8851'j'8801'i_6430 = 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_6436 ::
  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_6436 :: Integer -> Integer -> T__'8804'__26 -> T__'8801'__12
d_i'8805'j'8658'i'8851'j'8801'j_6436 = 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_6442 ::
  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_6442 :: Integer -> Integer -> T__'8804'__26 -> T__'8801'__12
d_i'8804'j'8658'i'8852'j'8801'j_6442 = 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_6448 ::
  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_6448 :: Integer -> Integer -> T__'8804'__26 -> T__'8801'__12
d_i'8805'j'8658'i'8852'j'8801'i_6448 = Integer -> Integer -> T__'8804'__26 -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.⊓-operator
d_'8851''45'operator_6454 ::
  MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98
d_'8851''45'operator_6454 :: T_MinOperator_98
d_'8851''45'operator_6454
  = ((Any -> Any -> Any)
 -> (Any -> Any -> Any -> Any)
 -> (Any -> Any -> Any -> Any)
 -> T_MinOperator_98)
-> Any -> Any -> Any -> T_MinOperator_98
forall a b. a -> b
coe
      (Any -> Any -> Any)
-> (Any -> Any -> Any -> Any)
-> (Any -> Any -> Any -> Any)
-> T_MinOperator_98
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.C_MinOperator'46'constructor_1121
      ((Integer -> Integer -> Integer) -> Any
forall a b. a -> b
coe Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'8851'__340) Any
forall a. a
erased Any
forall a. a
erased
-- Data.Integer.Properties.⊔-operator
d_'8852''45'operator_6456 ::
  MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MaxOperator_128
d_'8852''45'operator_6456 :: T_MaxOperator_128
d_'8852''45'operator_6456
  = ((Any -> Any -> Any)
 -> (Any -> Any -> Any -> Any)
 -> (Any -> Any -> Any -> Any)
 -> T_MaxOperator_128)
-> Any -> Any -> Any -> T_MaxOperator_128
forall a b. a -> b
coe
      (Any -> Any -> Any)
-> (Any -> Any -> Any -> Any)
-> (Any -> Any -> Any -> Any)
-> T_MaxOperator_128
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.C_MaxOperator'46'constructor_1665
      ((Integer -> Integer -> Integer) -> Any
forall a b. a -> b
coe Integer -> Integer -> Integer
MAlonzo.Code.Data.Integer.Base.d__'8852'__322) Any
forall a. a
erased Any
forall a. a
erased
-- Data.Integer.Properties.⊓-⊔-properties.x⊓y≤x
d_x'8851'y'8804'x_6468 ::
  Integer -> Integer -> MAlonzo.Code.Data.Integer.Base.T__'8804'__26
d_x'8851'y'8804'x_6468 :: Integer -> Integer -> T__'8804'__26
d_x'8851'y'8804'x_6468
  = let v0 :: T_TotalPreorder_222
v0 = T_TotalPreorder_222
d_'8804''45'totalPreorder_2812 in
    Any -> Integer -> Integer -> T__'8804'__26
forall a b. a -> b
coe
      (let v1 :: T_MaxOperator_128
v1 = T_MaxOperator_128
d_'8852''45'operator_6456 in
       Any -> Any
forall a b. a -> b
coe
         ((T_TotalPreorder_222 -> T_MinOperator_98 -> Any -> Any -> Any)
-> Any -> Any -> Any
forall a b. a -> b
coe
            T_TotalPreorder_222 -> T_MinOperator_98 -> Any -> Any -> Any
MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_x'8851'y'8804'x_2808
            ((T_TotalPreorder_222 -> T_TotalPreorder_222) -> Any -> Any
forall a b. a -> b
coe
               T_TotalPreorder_222 -> T_TotalPreorder_222
MAlonzo.Code.Relation.Binary.Construct.Flip.EqAndOrd.du_totalPreorder_746
               (T_TotalPreorder_222 -> Any
forall a b. a -> b
coe T_TotalPreorder_222
v0))
            ((T_MaxOperator_128 -> T_MinOperator_98) -> Any -> Any
forall a b. a -> b
coe
               T_MaxOperator_128 -> T_MinOperator_98
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.du_MaxOp'8658'MinOp_174
               (T_MaxOperator_128 -> Any
forall a b. a -> b
coe T_MaxOperator_128
v1))))
-- Data.Integer.Properties.⊓-⊔-properties.x≤y⇒x⊓z≤y
d_x'8804'y'8658'x'8851'z'8804'y_6470 ::
  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_6470 :: Integer -> Integer -> Integer -> T__'8804'__26 -> T__'8804'__26
d_x'8804'y'8658'x'8851'z'8804'y_6470
  = let v0 :: T_TotalPreorder_222
v0 = T_TotalPreorder_222
d_'8804''45'totalPreorder_2812 in
    Any
-> Integer -> Integer -> Integer -> T__'8804'__26 -> T__'8804'__26
forall a b. a -> b
coe
      (let v1 :: T_MaxOperator_128
v1 = T_MaxOperator_128
d_'8852''45'operator_6456 in
       Any -> Any
forall a b. a -> b
coe
         ((T_TotalPreorder_222
 -> T_MinOperator_98 -> Any -> Any -> Any -> Any -> Any)
-> Any -> Any -> Any
forall a b. a -> b
coe
            T_TotalPreorder_222
-> T_MinOperator_98 -> Any -> Any -> Any -> Any -> Any
MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_x'8804'y'8658'x'8851'z'8804'y_3160
            ((T_TotalPreorder_222 -> T_TotalPreorder_222) -> Any -> Any
forall a b. a -> b
coe
               T_TotalPreorder_222 -> T_TotalPreorder_222
MAlonzo.Code.Relation.Binary.Construct.Flip.EqAndOrd.du_totalPreorder_746
               (T_TotalPreorder_222 -> Any
forall a b. a -> b
coe T_TotalPreorder_222
v0))
            ((T_MaxOperator_128 -> T_MinOperator_98) -> Any -> Any
forall a b. a -> b
coe
               T_MaxOperator_128 -> T_MinOperator_98
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.du_MaxOp'8658'MinOp_174
               (T_MaxOperator_128 -> Any
forall a b. a -> b
coe T_MaxOperator_128
v1))))
-- Data.Integer.Properties.⊓-⊔-properties.x≤y⇒z⊓x≤y
d_x'8804'y'8658'z'8851'x'8804'y_6472 ::
  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_6472 :: Integer -> Integer -> Integer -> T__'8804'__26 -> T__'8804'__26
d_x'8804'y'8658'z'8851'x'8804'y_6472
  = let v0 :: T_TotalPreorder_222
v0 = T_TotalPreorder_222
d_'8804''45'totalPreorder_2812 in
    Any
-> Integer -> Integer -> Integer -> T__'8804'__26 -> T__'8804'__26
forall a b. a -> b
coe
      (let v1 :: T_MaxOperator_128
v1 = T_MaxOperator_128
d_'8852''45'operator_6456 in
       Any -> Any
forall a b. a -> b
coe
         ((T_TotalPreorder_222
 -> T_MinOperator_98 -> Any -> Any -> Any -> Any -> Any)
-> Any -> Any -> Any
forall a b. a -> b
coe
            T_TotalPreorder_222
-> T_MinOperator_98 -> Any -> Any -> Any -> Any -> Any
MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_x'8804'y'8658'z'8851'x'8804'y_3172
            ((T_TotalPreorder_222 -> T_TotalPreorder_222) -> Any -> Any
forall a b. a -> b
coe
               T_TotalPreorder_222 -> T_TotalPreorder_222
MAlonzo.Code.Relation.Binary.Construct.Flip.EqAndOrd.du_totalPreorder_746
               (T_TotalPreorder_222 -> Any
forall a b. a -> b
coe T_TotalPreorder_222
v0))
            ((T_MaxOperator_128 -> T_MinOperator_98) -> Any -> Any
forall a b. a -> b
coe
               T_MaxOperator_128 -> T_MinOperator_98
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.du_MaxOp'8658'MinOp_174
               (T_MaxOperator_128 -> Any
forall a b. a -> b
coe T_MaxOperator_128
v1))))
-- Data.Integer.Properties.⊓-⊔-properties.x≤y⇒x⊓z≤y
d_x'8804'y'8658'x'8851'z'8804'y_6474 ::
  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_6474 :: Integer -> Integer -> Integer -> T__'8804'__26 -> T__'8804'__26
d_x'8804'y'8658'x'8851'z'8804'y_6474
  = let v0 :: T_TotalPreorder_222
v0 = T_TotalPreorder_222
d_'8804''45'totalPreorder_2812 in
    Any
-> Integer -> Integer -> Integer -> T__'8804'__26 -> T__'8804'__26
forall a b. a -> b
coe
      (let v1 :: T_MinOperator_98
v1 = T_MinOperator_98
d_'8851''45'operator_6454 in
       Any -> Any
forall a b. a -> b
coe
         ((T_TotalPreorder_222
 -> T_MinOperator_98 -> Any -> Any -> Any -> Any -> Any)
-> Any -> Any -> Any
forall a b. a -> b
coe
            T_TotalPreorder_222
-> T_MinOperator_98 -> Any -> Any -> Any -> Any -> Any
MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_x'8804'y'8658'x'8851'z'8804'y_3160
            (T_TotalPreorder_222 -> Any
forall a b. a -> b
coe T_TotalPreorder_222
v0) (T_MinOperator_98 -> Any
forall a b. a -> b
coe T_MinOperator_98
v1)))
-- Data.Integer.Properties.⊓-⊔-properties.x≤y⇒z⊓x≤y
d_x'8804'y'8658'z'8851'x'8804'y_6476 ::
  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_6476 :: Integer -> Integer -> Integer -> T__'8804'__26 -> T__'8804'__26
d_x'8804'y'8658'z'8851'x'8804'y_6476
  = let v0 :: T_TotalPreorder_222
v0 = T_TotalPreorder_222
d_'8804''45'totalPreorder_2812 in
    Any
-> Integer -> Integer -> Integer -> T__'8804'__26 -> T__'8804'__26
forall a b. a -> b
coe
      (let v1 :: T_MinOperator_98
v1 = T_MinOperator_98
d_'8851''45'operator_6454 in
       Any -> Any
forall a b. a -> b
coe
         ((T_TotalPreorder_222
 -> T_MinOperator_98 -> Any -> Any -> Any -> Any -> Any)
-> Any -> Any -> Any
forall a b. a -> b
coe
            T_TotalPreorder_222
-> T_MinOperator_98 -> Any -> Any -> Any -> Any -> Any
MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_x'8804'y'8658'z'8851'x'8804'y_3172
            (T_TotalPreorder_222 -> Any
forall a b. a -> b
coe T_TotalPreorder_222
v0) (T_MinOperator_98 -> Any
forall a b. a -> b
coe T_MinOperator_98
v1)))
-- Data.Integer.Properties.⊓-⊔-properties.x≤y⊓z⇒x≤y
d_x'8804'y'8851'z'8658'x'8804'y_6478 ::
  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_6478 :: Integer -> Integer -> Integer -> T__'8804'__26 -> T__'8804'__26
d_x'8804'y'8851'z'8658'x'8804'y_6478
  = let v0 :: T_TotalPreorder_222
v0 = T_TotalPreorder_222
d_'8804''45'totalPreorder_2812 in
    Any
-> Integer -> Integer -> Integer -> T__'8804'__26 -> T__'8804'__26
forall a b. a -> b
coe
      (let v1 :: T_MinOperator_98
v1 = T_MinOperator_98
d_'8851''45'operator_6454 in
       Any -> Any
forall a b. a -> b
coe
         ((T_TotalPreorder_222
 -> T_MinOperator_98 -> Any -> Any -> Any -> Any -> Any)
-> Any -> Any -> Any
forall a b. a -> b
coe
            T_TotalPreorder_222
-> T_MinOperator_98 -> Any -> Any -> Any -> Any -> Any
MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_x'8804'y'8851'z'8658'x'8804'y_3184
            (T_TotalPreorder_222 -> Any
forall a b. a -> b
coe T_TotalPreorder_222
v0) (T_MinOperator_98 -> Any
forall a b. a -> b
coe T_MinOperator_98
v1)))
-- Data.Integer.Properties.⊓-⊔-properties.x≤y⊓z⇒x≤z
d_x'8804'y'8851'z'8658'x'8804'z_6480 ::
  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_6480 :: Integer -> Integer -> Integer -> T__'8804'__26 -> T__'8804'__26
d_x'8804'y'8851'z'8658'x'8804'z_6480
  = let v0 :: T_TotalPreorder_222
v0 = T_TotalPreorder_222
d_'8804''45'totalPreorder_2812 in
    Any
-> Integer -> Integer -> Integer -> T__'8804'__26 -> T__'8804'__26
forall a b. a -> b
coe
      (let v1 :: T_MinOperator_98
v1 = T_MinOperator_98
d_'8851''45'operator_6454 in
       Any -> Any
forall a b. a -> b
coe
         ((T_TotalPreorder_222
 -> T_MinOperator_98 -> Any -> Any -> Any -> Any -> Any)
-> Any -> Any -> Any
forall a b. a -> b
coe
            T_TotalPreorder_222
-> T_MinOperator_98 -> Any -> Any -> Any -> Any -> Any
MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_x'8804'y'8851'z'8658'x'8804'z_3198
            (T_TotalPreorder_222 -> Any
forall a b. a -> b
coe T_TotalPreorder_222
v0) (T_MinOperator_98 -> Any
forall a b. a -> b
coe T_MinOperator_98
v1)))
-- Data.Integer.Properties.⊓-⊔-properties.x⊓y≤y
d_x'8851'y'8804'y_6482 ::
  Integer -> Integer -> MAlonzo.Code.Data.Integer.Base.T__'8804'__26
d_x'8851'y'8804'y_6482 :: Integer -> Integer -> T__'8804'__26
d_x'8851'y'8804'y_6482
  = let v0 :: T_TotalPreorder_222
v0 = T_TotalPreorder_222
d_'8804''45'totalPreorder_2812 in
    Any -> Integer -> Integer -> T__'8804'__26
forall a b. a -> b
coe
      (let v1 :: T_MaxOperator_128
v1 = T_MaxOperator_128
d_'8852''45'operator_6456 in
       Any -> Any
forall a b. a -> b
coe
         ((T_TotalPreorder_222 -> T_MinOperator_98 -> Any -> Any -> Any)
-> Any -> Any -> Any
forall a b. a -> b
coe
            T_TotalPreorder_222 -> T_MinOperator_98 -> Any -> Any -> Any
MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_x'8851'y'8804'y_2834
            ((T_TotalPreorder_222 -> T_TotalPreorder_222) -> Any -> Any
forall a b. a -> b
coe
               T_TotalPreorder_222 -> T_TotalPreorder_222
MAlonzo.Code.Relation.Binary.Construct.Flip.EqAndOrd.du_totalPreorder_746
               (T_TotalPreorder_222 -> Any
forall a b. a -> b
coe T_TotalPreorder_222
v0))
            ((T_MaxOperator_128 -> T_MinOperator_98) -> Any -> Any
forall a b. a -> b
coe
               T_MaxOperator_128 -> T_MinOperator_98
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.du_MaxOp'8658'MinOp_174
               (T_MaxOperator_128 -> Any
forall a b. a -> b
coe T_MaxOperator_128
v1))))
-- Data.Integer.Properties.⊓-⊔-properties.x⊓y≈x⇒x≤y
d_x'8851'y'8776'x'8658'x'8804'y_6484 ::
  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_6484 :: Integer -> Integer -> T__'8801'__12 -> T__'8804'__26
d_x'8851'y'8776'x'8658'x'8804'y_6484
  = let v0 :: T_TotalPreorder_222
v0 = T_TotalPreorder_222
d_'8804''45'totalPreorder_2812 in
    Any -> Integer -> Integer -> T__'8801'__12 -> T__'8804'__26
forall a b. a -> b
coe
      (let v1 :: T_MinOperator_98
v1 = T_MinOperator_98
d_'8851''45'operator_6454 in
       Any -> Any
forall a b. a -> b
coe
         ((T_TotalPreorder_222
 -> T_MinOperator_98 -> Any -> Any -> Any -> Any)
-> Any -> Any -> Any
forall a b. a -> b
coe
            T_TotalPreorder_222 -> T_MinOperator_98 -> Any -> Any -> Any -> Any
MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_x'8851'y'8776'x'8658'x'8804'y_3068
            (T_TotalPreorder_222 -> Any
forall a b. a -> b
coe T_TotalPreorder_222
v0) (T_MinOperator_98 -> Any
forall a b. a -> b
coe T_MinOperator_98
v1)))
-- Data.Integer.Properties.⊓-⊔-properties.x⊓y≈y⇒y≤x
d_x'8851'y'8776'y'8658'y'8804'x_6486 ::
  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_6486 :: Integer -> Integer -> T__'8801'__12 -> T__'8804'__26
d_x'8851'y'8776'y'8658'y'8804'x_6486
  = let v0 :: T_TotalPreorder_222
v0 = T_TotalPreorder_222
d_'8804''45'totalPreorder_2812 in
    Any -> Integer -> Integer -> T__'8801'__12 -> T__'8804'__26
forall a b. a -> b
coe
      (let v1 :: T_MinOperator_98
v1 = T_MinOperator_98
d_'8851''45'operator_6454 in
       Any -> Any
forall a b. a -> b
coe
         ((T_TotalPreorder_222
 -> T_MinOperator_98 -> Any -> Any -> Any -> Any)
-> Any -> Any -> Any
forall a b. a -> b
coe
            T_TotalPreorder_222 -> T_MinOperator_98 -> Any -> Any -> Any -> Any
MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_x'8851'y'8776'y'8658'y'8804'x_3100
            (T_TotalPreorder_222 -> Any
forall a b. a -> b
coe T_TotalPreorder_222
v0) (T_MinOperator_98 -> Any
forall a b. a -> b
coe T_MinOperator_98
v1)))
-- Data.Integer.Properties.⊓-⊔-properties.x⊓y≤x
d_x'8851'y'8804'x_6488 ::
  Integer -> Integer -> MAlonzo.Code.Data.Integer.Base.T__'8804'__26
d_x'8851'y'8804'x_6488 :: Integer -> Integer -> T__'8804'__26
d_x'8851'y'8804'x_6488
  = let v0 :: T_TotalPreorder_222
v0 = T_TotalPreorder_222
d_'8804''45'totalPreorder_2812 in
    Any -> Integer -> Integer -> T__'8804'__26
forall a b. a -> b
coe
      (let v1 :: T_MinOperator_98
v1 = T_MinOperator_98
d_'8851''45'operator_6454 in
       Any -> Any
forall a b. a -> b
coe
         ((T_TotalPreorder_222 -> T_MinOperator_98 -> Any -> Any -> Any)
-> Any -> Any -> Any
forall a b. a -> b
coe
            T_TotalPreorder_222 -> T_MinOperator_98 -> Any -> Any -> Any
MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_x'8851'y'8804'x_2808
            (T_TotalPreorder_222 -> Any
forall a b. a -> b
coe T_TotalPreorder_222
v0) (T_MinOperator_98 -> Any
forall a b. a -> b
coe T_MinOperator_98
v1)))
-- Data.Integer.Properties.⊓-⊔-properties.x⊓y≤x⊔y
d_x'8851'y'8804'x'8852'y_6490 ::
  Integer -> Integer -> MAlonzo.Code.Data.Integer.Base.T__'8804'__26
d_x'8851'y'8804'x'8852'y_6490 :: Integer -> Integer -> T__'8804'__26
d_x'8851'y'8804'x'8852'y_6490
  = (T_TotalPreorder_222
 -> T_MinOperator_98 -> T_MaxOperator_128 -> Any -> Any -> Any)
-> Any -> Any -> Any -> Integer -> Integer -> T__'8804'__26
forall a b. a -> b
coe
      T_TotalPreorder_222
-> T_MinOperator_98 -> T_MaxOperator_128 -> Any -> Any -> Any
MAlonzo.Code.Algebra.Construct.NaturalChoice.MinMaxOp.du_x'8851'y'8804'x'8852'y_3318
      (T_TotalPreorder_222 -> Any
forall a b. a -> b
coe T_TotalPreorder_222
d_'8804''45'totalPreorder_2812)
      (T_MinOperator_98 -> Any
forall a b. a -> b
coe T_MinOperator_98
d_'8851''45'operator_6454) (T_MaxOperator_128 -> Any
forall a b. a -> b
coe T_MaxOperator_128
d_'8852''45'operator_6456)
-- Data.Integer.Properties.⊓-⊔-properties.x⊓y≤y
d_x'8851'y'8804'y_6492 ::
  Integer -> Integer -> MAlonzo.Code.Data.Integer.Base.T__'8804'__26
d_x'8851'y'8804'y_6492 :: Integer -> Integer -> T__'8804'__26
d_x'8851'y'8804'y_6492
  = let v0 :: T_TotalPreorder_222
v0 = T_TotalPreorder_222
d_'8804''45'totalPreorder_2812 in
    Any -> Integer -> Integer -> T__'8804'__26
forall a b. a -> b
coe
      (let v1 :: T_MinOperator_98
v1 = T_MinOperator_98
d_'8851''45'operator_6454 in
       Any -> Any
forall a b. a -> b
coe
         ((T_TotalPreorder_222 -> T_MinOperator_98 -> Any -> Any -> Any)
-> Any -> Any -> Any
forall a b. a -> b
coe
            T_TotalPreorder_222 -> T_MinOperator_98 -> Any -> Any -> Any
MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_x'8851'y'8804'y_2834
            (T_TotalPreorder_222 -> Any
forall a b. a -> b
coe T_TotalPreorder_222
v0) (T_MinOperator_98 -> Any
forall a b. a -> b
coe T_MinOperator_98
v1)))
-- Data.Integer.Properties.⊓-⊔-properties.x⊓y≈x⇒x≤y
d_x'8851'y'8776'x'8658'x'8804'y_6494 ::
  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_6494 :: Integer -> Integer -> T__'8801'__12 -> T__'8804'__26
d_x'8851'y'8776'x'8658'x'8804'y_6494
  = let v0 :: T_TotalPreorder_222
v0 = T_TotalPreorder_222
d_'8804''45'totalPreorder_2812 in
    Any -> Integer -> Integer -> T__'8801'__12 -> T__'8804'__26
forall a b. a -> b
coe
      (let v1 :: T_MaxOperator_128
v1 = T_MaxOperator_128
d_'8852''45'operator_6456 in
       Any -> Any
forall a b. a -> b
coe
         ((T_TotalPreorder_222
 -> T_MinOperator_98 -> Any -> Any -> Any -> Any)
-> Any -> Any -> Any
forall a b. a -> b
coe
            T_TotalPreorder_222 -> T_MinOperator_98 -> Any -> Any -> Any -> Any
MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_x'8851'y'8776'x'8658'x'8804'y_3068
            ((T_TotalPreorder_222 -> T_TotalPreorder_222) -> Any -> Any
forall a b. a -> b
coe
               T_TotalPreorder_222 -> T_TotalPreorder_222
MAlonzo.Code.Relation.Binary.Construct.Flip.EqAndOrd.du_totalPreorder_746
               (T_TotalPreorder_222 -> Any
forall a b. a -> b
coe T_TotalPreorder_222
v0))
            ((T_MaxOperator_128 -> T_MinOperator_98) -> Any -> Any
forall a b. a -> b
coe
               T_MaxOperator_128 -> T_MinOperator_98
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.du_MaxOp'8658'MinOp_174
               (T_MaxOperator_128 -> Any
forall a b. a -> b
coe T_MaxOperator_128
v1))))
-- Data.Integer.Properties.⊓-⊔-properties.x⊓y≈y⇒y≤x
d_x'8851'y'8776'y'8658'y'8804'x_6496 ::
  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_6496 :: Integer -> Integer -> T__'8801'__12 -> T__'8804'__26
d_x'8851'y'8776'y'8658'y'8804'x_6496
  = let v0 :: T_TotalPreorder_222
v0 = T_TotalPreorder_222
d_'8804''45'totalPreorder_2812 in
    Any -> Integer -> Integer -> T__'8801'__12 -> T__'8804'__26
forall a b. a -> b
coe
      (let v1 :: T_MaxOperator_128
v1 = T_MaxOperator_128
d_'8852''45'operator_6456 in
       Any -> Any
forall a b. a -> b
coe
         ((T_TotalPreorder_222
 -> T_MinOperator_98 -> Any -> Any -> Any -> Any)
-> Any -> Any -> Any
forall a b. a -> b
coe
            T_TotalPreorder_222 -> T_MinOperator_98 -> Any -> Any -> Any -> Any
MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_x'8851'y'8776'y'8658'y'8804'x_3100
            ((T_TotalPreorder_222 -> T_TotalPreorder_222) -> Any -> Any
forall a b. a -> b
coe
               T_TotalPreorder_222 -> T_TotalPreorder_222
MAlonzo.Code.Relation.Binary.Construct.Flip.EqAndOrd.du_totalPreorder_746
               (T_TotalPreorder_222 -> Any
forall a b. a -> b
coe T_TotalPreorder_222
v0))
            ((T_MaxOperator_128 -> T_MinOperator_98) -> Any -> Any
forall a b. a -> b
coe
               T_MaxOperator_128 -> T_MinOperator_98
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.du_MaxOp'8658'MinOp_174
               (T_MaxOperator_128 -> Any
forall a b. a -> b
coe T_MaxOperator_128
v1))))
-- Data.Integer.Properties.⊓-⊔-properties.x≤y⊓z⇒x≤y
d_x'8804'y'8851'z'8658'x'8804'y_6498 ::
  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_6498 :: Integer -> Integer -> Integer -> T__'8804'__26 -> T__'8804'__26
d_x'8804'y'8851'z'8658'x'8804'y_6498
  = let v0 :: T_TotalPreorder_222
v0 = T_TotalPreorder_222
d_'8804''45'totalPreorder_2812 in
    Any
-> Integer -> Integer -> Integer -> T__'8804'__26 -> T__'8804'__26
forall a b. a -> b
coe
      (let v1 :: T_MaxOperator_128
v1 = T_MaxOperator_128
d_'8852''45'operator_6456 in
       Any -> Any
forall a b. a -> b
coe
         ((T_TotalPreorder_222
 -> T_MinOperator_98 -> Any -> Any -> Any -> Any -> Any)
-> Any -> Any -> Any
forall a b. a -> b
coe
            T_TotalPreorder_222
-> T_MinOperator_98 -> Any -> Any -> Any -> Any -> Any
MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_x'8804'y'8851'z'8658'x'8804'y_3184
            ((T_TotalPreorder_222 -> T_TotalPreorder_222) -> Any -> Any
forall a b. a -> b
coe
               T_TotalPreorder_222 -> T_TotalPreorder_222
MAlonzo.Code.Relation.Binary.Construct.Flip.EqAndOrd.du_totalPreorder_746
               (T_TotalPreorder_222 -> Any
forall a b. a -> b
coe T_TotalPreorder_222
v0))
            ((T_MaxOperator_128 -> T_MinOperator_98) -> Any -> Any
forall a b. a -> b
coe
               T_MaxOperator_128 -> T_MinOperator_98
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.du_MaxOp'8658'MinOp_174
               (T_MaxOperator_128 -> Any
forall a b. a -> b
coe T_MaxOperator_128
v1))))
-- Data.Integer.Properties.⊓-⊔-properties.x≤y⊓z⇒x≤z
d_x'8804'y'8851'z'8658'x'8804'z_6500 ::
  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_6500 :: Integer -> Integer -> Integer -> T__'8804'__26 -> T__'8804'__26
d_x'8804'y'8851'z'8658'x'8804'z_6500
  = let v0 :: T_TotalPreorder_222
v0 = T_TotalPreorder_222
d_'8804''45'totalPreorder_2812 in
    Any
-> Integer -> Integer -> Integer -> T__'8804'__26 -> T__'8804'__26
forall a b. a -> b
coe
      (let v1 :: T_MaxOperator_128
v1 = T_MaxOperator_128
d_'8852''45'operator_6456 in
       Any -> Any
forall a b. a -> b
coe
         ((T_TotalPreorder_222
 -> T_MinOperator_98 -> Any -> Any -> Any -> Any -> Any)
-> Any -> Any -> Any
forall a b. a -> b
coe
            T_TotalPreorder_222
-> T_MinOperator_98 -> Any -> Any -> Any -> Any -> Any
MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_x'8804'y'8851'z'8658'x'8804'z_3198
            ((T_TotalPreorder_222 -> T_TotalPreorder_222) -> Any -> Any
forall a b. a -> b
coe
               T_TotalPreorder_222 -> T_TotalPreorder_222
MAlonzo.Code.Relation.Binary.Construct.Flip.EqAndOrd.du_totalPreorder_746
               (T_TotalPreorder_222 -> Any
forall a b. a -> b
coe T_TotalPreorder_222
v0))
            ((T_MaxOperator_128 -> T_MinOperator_98) -> Any -> Any
forall a b. a -> b
coe
               T_MaxOperator_128 -> T_MinOperator_98
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.du_MaxOp'8658'MinOp_174
               (T_MaxOperator_128 -> Any
forall a b. a -> b
coe T_MaxOperator_128
v1))))
-- Data.Integer.Properties.⊓-⊔-properties.⊓-absorbs-⊔
d_'8851''45'absorbs'45''8852'_6502 ::
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8851''45'absorbs'45''8852'_6502 :: Integer -> Integer -> T__'8801'__12
d_'8851''45'absorbs'45''8852'_6502 = Integer -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.⊓-⊔-properties.⊓-assoc
d_'8851''45'assoc_6504 ::
  Integer ->
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8851''45'assoc_6504 :: Integer -> Integer -> Integer -> T__'8801'__12
d_'8851''45'assoc_6504 = Integer -> Integer -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.⊓-⊔-properties.⊓-band
d_'8851''45'band_6506 :: MAlonzo.Code.Algebra.Bundles.T_Band_596
d_'8851''45'band_6506 :: T_Band_596
d_'8851''45'band_6506
  = let v0 :: T_TotalPreorder_222
v0 = T_TotalPreorder_222
d_'8804''45'totalPreorder_2812 in
    Any -> T_Band_596
forall a b. a -> b
coe
      (let v1 :: T_MinOperator_98
v1 = T_MinOperator_98
d_'8851''45'operator_6454 in
       Any -> Any
forall a b. a -> b
coe
         ((T_TotalPreorder_222 -> T_MinOperator_98 -> T_Band_596)
-> Any -> Any -> Any
forall a b. a -> b
coe
            T_TotalPreorder_222 -> T_MinOperator_98 -> T_Band_596
MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_'8851''45'band_3052
            (T_TotalPreorder_222 -> Any
forall a b. a -> b
coe T_TotalPreorder_222
v0) (T_MinOperator_98 -> Any
forall a b. a -> b
coe T_MinOperator_98
v1)))
-- Data.Integer.Properties.⊓-⊔-properties.⊓-comm
d_'8851''45'comm_6508 ::
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8851''45'comm_6508 :: Integer -> Integer -> T__'8801'__12
d_'8851''45'comm_6508 = Integer -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.⊓-⊔-properties.⊓-commutativeSemigroup
d_'8851''45'commutativeSemigroup_6510 ::
  MAlonzo.Code.Algebra.Bundles.T_CommutativeSemigroup_662
d_'8851''45'commutativeSemigroup_6510 :: T_CommutativeSemigroup_662
d_'8851''45'commutativeSemigroup_6510
  = let v0 :: T_TotalPreorder_222
v0 = T_TotalPreorder_222
d_'8804''45'totalPreorder_2812 in
    Any -> T_CommutativeSemigroup_662
forall a b. a -> b
coe
      (let v1 :: T_MinOperator_98
v1 = T_MinOperator_98
d_'8851''45'operator_6454 in
       Any -> Any
forall a b. a -> b
coe
         ((T_TotalPreorder_222
 -> T_MinOperator_98 -> T_CommutativeSemigroup_662)
-> Any -> Any -> Any
forall a b. a -> b
coe
            T_TotalPreorder_222
-> T_MinOperator_98 -> T_CommutativeSemigroup_662
MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_'8851''45'commutativeSemigroup_3054
            (T_TotalPreorder_222 -> Any
forall a b. a -> b
coe T_TotalPreorder_222
v0) (T_MinOperator_98 -> Any
forall a b. a -> b
coe T_MinOperator_98
v1)))
-- Data.Integer.Properties.⊓-⊔-properties.⊓-distrib-⊔
d_'8851''45'distrib'45''8852'_6518 ::
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'8851''45'distrib'45''8852'_6518 :: T_Σ_14
d_'8851''45'distrib'45''8852'_6518
  = (T_TotalPreorder_222
 -> T_MinOperator_98 -> T_MaxOperator_128 -> T_Σ_14)
-> Any -> Any -> Any -> T_Σ_14
forall a b. a -> b
coe
      T_TotalPreorder_222
-> T_MinOperator_98 -> T_MaxOperator_128 -> T_Σ_14
MAlonzo.Code.Algebra.Construct.NaturalChoice.MinMaxOp.du_'8851''45'distrib'45''8852'_3138
      (T_TotalPreorder_222 -> Any
forall a b. a -> b
coe T_TotalPreorder_222
d_'8804''45'totalPreorder_2812)
      (T_MinOperator_98 -> Any
forall a b. a -> b
coe T_MinOperator_98
d_'8851''45'operator_6454) (T_MaxOperator_128 -> Any
forall a b. a -> b
coe T_MaxOperator_128
d_'8852''45'operator_6456)
-- Data.Integer.Properties.⊓-⊔-properties.⊓-distribʳ-⊔
d_'8851''45'distrib'691''45''8852'_6520 ::
  Integer ->
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8851''45'distrib'691''45''8852'_6520 :: Integer -> Integer -> Integer -> T__'8801'__12
d_'8851''45'distrib'691''45''8852'_6520 = Integer -> Integer -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.⊓-⊔-properties.⊓-distribˡ-⊔
d_'8851''45'distrib'737''45''8852'_6522 ::
  Integer ->
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8851''45'distrib'737''45''8852'_6522 :: Integer -> Integer -> Integer -> T__'8801'__12
d_'8851''45'distrib'737''45''8852'_6522 = Integer -> Integer -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.⊓-⊔-properties.⊓-glb
d_'8851''45'glb_6524 ::
  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_6524 :: Integer
-> Integer
-> Integer
-> T__'8804'__26
-> T__'8804'__26
-> T__'8804'__26
d_'8851''45'glb_6524
  = let v0 :: T_TotalPreorder_222
v0 = T_TotalPreorder_222
d_'8804''45'totalPreorder_2812 in
    Any
-> Integer
-> Integer
-> Integer
-> T__'8804'__26
-> T__'8804'__26
-> T__'8804'__26
forall a b. a -> b
coe
      (let v1 :: T_MinOperator_98
v1 = T_MinOperator_98
d_'8851''45'operator_6454 in
       Any -> Any
forall a b. a -> b
coe
         ((T_TotalPreorder_222
 -> T_MinOperator_98 -> Any -> Any -> Any -> Any -> Any -> Any)
-> Any -> Any -> Any
forall a b. a -> b
coe
            T_TotalPreorder_222
-> T_MinOperator_98 -> Any -> Any -> Any -> Any -> Any -> Any
MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_'8851''45'glb_3278
            (T_TotalPreorder_222 -> Any
forall a b. a -> b
coe T_TotalPreorder_222
v0) (T_MinOperator_98 -> Any
forall a b. a -> b
coe T_MinOperator_98
v1)))
-- Data.Integer.Properties.⊓-⊔-properties.⊓-idem
d_'8851''45'idem_6526 ::
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8851''45'idem_6526 :: Integer -> T__'8801'__12
d_'8851''45'idem_6526 = Integer -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.⊓-⊔-properties.⊓-isBand
d_'8851''45'isBand_6534 ::
  MAlonzo.Code.Algebra.Structures.T_IsBand_508
d_'8851''45'isBand_6534 :: T_IsBand_508
d_'8851''45'isBand_6534
  = let v0 :: T_TotalPreorder_222
v0 = T_TotalPreorder_222
d_'8804''45'totalPreorder_2812 in
    Any -> T_IsBand_508
forall a b. a -> b
coe
      (let v1 :: T_MinOperator_98
v1 = T_MinOperator_98
d_'8851''45'operator_6454 in
       Any -> Any
forall a b. a -> b
coe
         ((T_TotalPreorder_222 -> T_MinOperator_98 -> T_IsBand_508)
-> Any -> Any -> Any
forall a b. a -> b
coe
            T_TotalPreorder_222 -> T_MinOperator_98 -> T_IsBand_508
MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_'8851''45'isBand_3034
            (T_TotalPreorder_222 -> Any
forall a b. a -> b
coe T_TotalPreorder_222
v0) (T_MinOperator_98 -> Any
forall a b. a -> b
coe T_MinOperator_98
v1)))
-- Data.Integer.Properties.⊓-⊔-properties.⊓-isCommutativeSemigroup
d_'8851''45'isCommutativeSemigroup_6536 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_548
d_'8851''45'isCommutativeSemigroup_6536 :: T_IsCommutativeSemigroup_548
d_'8851''45'isCommutativeSemigroup_6536
  = let v0 :: T_TotalPreorder_222
v0 = T_TotalPreorder_222
d_'8804''45'totalPreorder_2812 in
    Any -> T_IsCommutativeSemigroup_548
forall a b. a -> b
coe
      (let v1 :: T_MinOperator_98
v1 = T_MinOperator_98
d_'8851''45'operator_6454 in
       Any -> Any
forall a b. a -> b
coe
         ((T_TotalPreorder_222
 -> T_MinOperator_98 -> T_IsCommutativeSemigroup_548)
-> Any -> Any -> Any
forall a b. a -> b
coe
            T_TotalPreorder_222
-> T_MinOperator_98 -> T_IsCommutativeSemigroup_548
MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_'8851''45'isCommutativeSemigroup_3036
            (T_TotalPreorder_222 -> Any
forall a b. a -> b
coe T_TotalPreorder_222
v0) (T_MinOperator_98 -> Any
forall a b. a -> b
coe T_MinOperator_98
v1)))
-- Data.Integer.Properties.⊓-⊔-properties.⊓-isMagma
d_'8851''45'isMagma_6538 ::
  MAlonzo.Code.Algebra.Structures.T_IsMagma_176
d_'8851''45'isMagma_6538 :: T_IsMagma_176
d_'8851''45'isMagma_6538
  = let v0 :: T_TotalPreorder_222
v0 = T_TotalPreorder_222
d_'8804''45'totalPreorder_2812 in
    Any -> T_IsMagma_176
forall a b. a -> b
coe
      (let v1 :: T_MinOperator_98
v1 = T_MinOperator_98
d_'8851''45'operator_6454 in
       Any -> Any
forall a b. a -> b
coe
         ((T_TotalPreorder_222 -> T_MinOperator_98 -> T_IsMagma_176)
-> Any -> Any -> Any
forall a b. a -> b
coe
            T_TotalPreorder_222 -> T_MinOperator_98 -> T_IsMagma_176
MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_'8851''45'isMagma_3030
            (T_TotalPreorder_222 -> Any
forall a b. a -> b
coe T_TotalPreorder_222
v0) (T_MinOperator_98 -> Any
forall a b. a -> b
coe T_MinOperator_98
v1)))
-- Data.Integer.Properties.⊓-⊔-properties.⊓-isSelectiveMagma
d_'8851''45'isSelectiveMagma_6542 ::
  MAlonzo.Code.Algebra.Structures.T_IsSelectiveMagma_436
d_'8851''45'isSelectiveMagma_6542 :: T_IsSelectiveMagma_436
d_'8851''45'isSelectiveMagma_6542
  = let v0 :: T_TotalPreorder_222
v0 = T_TotalPreorder_222
d_'8804''45'totalPreorder_2812 in
    Any -> T_IsSelectiveMagma_436
forall a b. a -> b
coe
      (let v1 :: T_MinOperator_98
v1 = T_MinOperator_98
d_'8851''45'operator_6454 in
       Any -> Any
forall a b. a -> b
coe
         ((T_TotalPreorder_222 -> T_MinOperator_98 -> T_IsSelectiveMagma_436)
-> Any -> Any -> Any
forall a b. a -> b
coe
            T_TotalPreorder_222 -> T_MinOperator_98 -> T_IsSelectiveMagma_436
MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_'8851''45'isSelectiveMagma_3038
            (T_TotalPreorder_222 -> Any
forall a b. a -> b
coe T_TotalPreorder_222
v0) (T_MinOperator_98 -> Any
forall a b. a -> b
coe T_MinOperator_98
v1)))
-- Data.Integer.Properties.⊓-⊔-properties.⊓-isSemigroup
d_'8851''45'isSemigroup_6544 ::
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_472
d_'8851''45'isSemigroup_6544 :: T_IsSemigroup_472
d_'8851''45'isSemigroup_6544
  = let v0 :: T_TotalPreorder_222
v0 = T_TotalPreorder_222
d_'8804''45'totalPreorder_2812 in
    Any -> T_IsSemigroup_472
forall a b. a -> b
coe
      (let v1 :: T_MinOperator_98
v1 = T_MinOperator_98
d_'8851''45'operator_6454 in
       Any -> Any
forall a b. a -> b
coe
         ((T_TotalPreorder_222 -> T_MinOperator_98 -> T_IsSemigroup_472)
-> Any -> Any -> Any
forall a b. a -> b
coe
            T_TotalPreorder_222 -> T_MinOperator_98 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_'8851''45'isSemigroup_3032
            (T_TotalPreorder_222 -> Any
forall a b. a -> b
coe T_TotalPreorder_222
v0) (T_MinOperator_98 -> Any
forall a b. a -> b
coe T_MinOperator_98
v1)))
-- Data.Integer.Properties.⊓-⊔-properties.⊓-magma
d_'8851''45'magma_6546 :: MAlonzo.Code.Algebra.Bundles.T_Magma_68
d_'8851''45'magma_6546 :: T_Magma_68
d_'8851''45'magma_6546
  = let v0 :: T_TotalPreorder_222
v0 = T_TotalPreorder_222
d_'8804''45'totalPreorder_2812 in
    Any -> T_Magma_68
forall a b. a -> b
coe
      (let v1 :: T_MinOperator_98
v1 = T_MinOperator_98
d_'8851''45'operator_6454 in
       Any -> Any
forall a b. a -> b
coe
         ((T_TotalPreorder_222 -> T_MinOperator_98 -> T_Magma_68)
-> Any -> Any -> Any
forall a b. a -> b
coe
            T_TotalPreorder_222 -> T_MinOperator_98 -> T_Magma_68
MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_'8851''45'magma_3048
            (T_TotalPreorder_222 -> Any
forall a b. a -> b
coe T_TotalPreorder_222
v0) (T_MinOperator_98 -> Any
forall a b. a -> b
coe T_MinOperator_98
v1)))
-- Data.Integer.Properties.⊓-⊔-properties.⊓-mono-≤
d_'8851''45'mono'45''8804'_6548 ::
  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'_6548 :: Integer
-> Integer
-> Integer
-> Integer
-> T__'8804'__26
-> T__'8804'__26
-> T__'8804'__26
d_'8851''45'mono'45''8804'_6548
  = let v0 :: T_TotalPreorder_222
v0 = T_TotalPreorder_222
d_'8804''45'totalPreorder_2812 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_98
v1 = T_MinOperator_98
d_'8851''45'operator_6454 in
       Any -> Any
forall a b. a -> b
coe
         ((T_TotalPreorder_222
 -> T_MinOperator_98
 -> Any
 -> Any
 -> Any
 -> Any
 -> Any
 -> Any
 -> Any)
-> Any -> Any -> Any
forall a b. a -> b
coe
            T_TotalPreorder_222
-> T_MinOperator_98
-> Any
-> Any
-> Any
-> Any
-> Any
-> Any
-> Any
MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_'8851''45'mono'45''8804'_3206
            (T_TotalPreorder_222 -> Any
forall a b. a -> b
coe T_TotalPreorder_222
v0) (T_MinOperator_98 -> Any
forall a b. a -> b
coe T_MinOperator_98
v1)))
-- Data.Integer.Properties.⊓-⊔-properties.⊓-monoʳ-≤
d_'8851''45'mono'691''45''8804'_6552 ::
  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'_6552 :: Integer -> Integer -> Integer -> T__'8804'__26 -> T__'8804'__26
d_'8851''45'mono'691''45''8804'_6552
  = let v0 :: T_TotalPreorder_222
v0 = T_TotalPreorder_222
d_'8804''45'totalPreorder_2812 in
    Any
-> Integer -> Integer -> Integer -> T__'8804'__26 -> T__'8804'__26
forall a b. a -> b
coe
      (let v1 :: T_MinOperator_98
v1 = T_MinOperator_98
d_'8851''45'operator_6454 in
       Any -> Any
forall a b. a -> b
coe
         ((T_TotalPreorder_222
 -> T_MinOperator_98 -> Any -> Any -> Any -> Any -> Any)
-> Any -> Any -> Any
forall a b. a -> b
coe
            T_TotalPreorder_222
-> T_MinOperator_98 -> Any -> Any -> Any -> Any -> Any
MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_'8851''45'mono'691''45''8804'_3266
            (T_TotalPreorder_222 -> Any
forall a b. a -> b
coe T_TotalPreorder_222
v0) (T_MinOperator_98 -> Any
forall a b. a -> b
coe T_MinOperator_98
v1)))
-- Data.Integer.Properties.⊓-⊔-properties.⊓-monoˡ-≤
d_'8851''45'mono'737''45''8804'_6554 ::
  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'_6554 :: Integer -> Integer -> Integer -> T__'8804'__26 -> T__'8804'__26
d_'8851''45'mono'737''45''8804'_6554
  = let v0 :: T_TotalPreorder_222
v0 = T_TotalPreorder_222
d_'8804''45'totalPreorder_2812 in
    Any
-> Integer -> Integer -> Integer -> T__'8804'__26 -> T__'8804'__26
forall a b. a -> b
coe
      (let v1 :: T_MinOperator_98
v1 = T_MinOperator_98
d_'8851''45'operator_6454 in
       Any -> Any
forall a b. a -> b
coe
         ((T_TotalPreorder_222
 -> T_MinOperator_98 -> Any -> Any -> Any -> Any -> Any)
-> Any -> Any -> Any
forall a b. a -> b
coe
            T_TotalPreorder_222
-> T_MinOperator_98 -> Any -> Any -> Any -> Any -> Any
MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_'8851''45'mono'737''45''8804'_3256
            (T_TotalPreorder_222 -> Any
forall a b. a -> b
coe T_TotalPreorder_222
v0) (T_MinOperator_98 -> Any
forall a b. a -> b
coe T_MinOperator_98
v1)))
-- Data.Integer.Properties.⊓-⊔-properties.⊓-sel
d_'8851''45'sel_6558 ::
  Integer -> Integer -> MAlonzo.Code.Data.Sum.Base.T__'8846'__30
d_'8851''45'sel_6558 :: Integer -> Integer -> T__'8846'__30
d_'8851''45'sel_6558
  = let v0 :: T_TotalPreorder_222
v0 = T_TotalPreorder_222
d_'8804''45'totalPreorder_2812 in
    Any -> Integer -> Integer -> T__'8846'__30
forall a b. a -> b
coe
      (let v1 :: T_MinOperator_98
v1 = T_MinOperator_98
d_'8851''45'operator_6454 in
       Any -> Any
forall a b. a -> b
coe
         ((T_TotalPreorder_222
 -> T_MinOperator_98 -> Any -> Any -> T__'8846'__30)
-> Any -> Any -> Any
forall a b. a -> b
coe
            T_TotalPreorder_222
-> T_MinOperator_98 -> Any -> Any -> T__'8846'__30
MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_'8851''45'sel_2988
            (T_TotalPreorder_222 -> Any
forall a b. a -> b
coe T_TotalPreorder_222
v0) (T_MinOperator_98 -> Any
forall a b. a -> b
coe T_MinOperator_98
v1)))
-- Data.Integer.Properties.⊓-⊔-properties.⊓-selectiveMagma
d_'8851''45'selectiveMagma_6560 ::
  MAlonzo.Code.Algebra.Bundles.T_SelectiveMagma_122
d_'8851''45'selectiveMagma_6560 :: T_SelectiveMagma_122
d_'8851''45'selectiveMagma_6560
  = let v0 :: T_TotalPreorder_222
v0 = T_TotalPreorder_222
d_'8804''45'totalPreorder_2812 in
    Any -> T_SelectiveMagma_122
forall a b. a -> b
coe
      (let v1 :: T_MinOperator_98
v1 = T_MinOperator_98
d_'8851''45'operator_6454 in
       Any -> Any
forall a b. a -> b
coe
         ((T_TotalPreorder_222 -> T_MinOperator_98 -> T_SelectiveMagma_122)
-> Any -> Any -> Any
forall a b. a -> b
coe
            T_TotalPreorder_222 -> T_MinOperator_98 -> T_SelectiveMagma_122
MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_'8851''45'selectiveMagma_3056
            (T_TotalPreorder_222 -> Any
forall a b. a -> b
coe T_TotalPreorder_222
v0) (T_MinOperator_98 -> Any
forall a b. a -> b
coe T_MinOperator_98
v1)))
-- Data.Integer.Properties.⊓-⊔-properties.⊓-semigroup
d_'8851''45'semigroup_6562 ::
  MAlonzo.Code.Algebra.Bundles.T_Semigroup_536
d_'8851''45'semigroup_6562 :: T_Semigroup_536
d_'8851''45'semigroup_6562
  = let v0 :: T_TotalPreorder_222
v0 = T_TotalPreorder_222
d_'8804''45'totalPreorder_2812 in
    Any -> T_Semigroup_536
forall a b. a -> b
coe
      (let v1 :: T_MinOperator_98
v1 = T_MinOperator_98
d_'8851''45'operator_6454 in
       Any -> Any
forall a b. a -> b
coe
         ((T_TotalPreorder_222 -> T_MinOperator_98 -> T_Semigroup_536)
-> Any -> Any -> Any
forall a b. a -> b
coe
            T_TotalPreorder_222 -> T_MinOperator_98 -> T_Semigroup_536
MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_'8851''45'semigroup_3050
            (T_TotalPreorder_222 -> Any
forall a b. a -> b
coe T_TotalPreorder_222
v0) (T_MinOperator_98 -> Any
forall a b. a -> b
coe T_MinOperator_98
v1)))
-- Data.Integer.Properties.⊓-⊔-properties.⊓-triangulate
d_'8851''45'triangulate_6564 ::
  Integer ->
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8851''45'triangulate_6564 :: Integer -> Integer -> Integer -> T__'8801'__12
d_'8851''45'triangulate_6564 = Integer -> Integer -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.⊓-⊔-properties.⊓-⊔-absorptive
d_'8851''45''8852''45'absorptive_6572 ::
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'8851''45''8852''45'absorptive_6572 :: T_Σ_14
d_'8851''45''8852''45'absorptive_6572
  = (T_TotalPreorder_222
 -> T_MinOperator_98 -> T_MaxOperator_128 -> T_Σ_14)
-> Any -> Any -> Any -> T_Σ_14
forall a b. a -> b
coe
      T_TotalPreorder_222
-> T_MinOperator_98 -> T_MaxOperator_128 -> T_Σ_14
MAlonzo.Code.Algebra.Construct.NaturalChoice.MinMaxOp.du_'8851''45''8852''45'absorptive_3218
      (T_TotalPreorder_222 -> Any
forall a b. a -> b
coe T_TotalPreorder_222
d_'8804''45'totalPreorder_2812)
      (T_MinOperator_98 -> Any
forall a b. a -> b
coe T_MinOperator_98
d_'8851''45'operator_6454) (T_MaxOperator_128 -> Any
forall a b. a -> b
coe T_MaxOperator_128
d_'8852''45'operator_6456)
-- Data.Integer.Properties.⊓-⊔-properties.⊔-absorbs-⊓
d_'8852''45'absorbs'45''8851'_6574 ::
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8852''45'absorbs'45''8851'_6574 :: Integer -> Integer -> T__'8801'__12
d_'8852''45'absorbs'45''8851'_6574 = Integer -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.⊓-⊔-properties.⊓-assoc
d_'8851''45'assoc_6576 ::
  Integer ->
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8851''45'assoc_6576 :: Integer -> Integer -> Integer -> T__'8801'__12
d_'8851''45'assoc_6576 = Integer -> Integer -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.⊓-⊔-properties.⊓-band
d_'8851''45'band_6578 :: MAlonzo.Code.Algebra.Bundles.T_Band_596
d_'8851''45'band_6578 :: T_Band_596
d_'8851''45'band_6578
  = let v0 :: T_TotalPreorder_222
v0 = T_TotalPreorder_222
d_'8804''45'totalPreorder_2812 in
    Any -> T_Band_596
forall a b. a -> b
coe
      (let v1 :: T_MaxOperator_128
v1 = T_MaxOperator_128
d_'8852''45'operator_6456 in
       Any -> Any
forall a b. a -> b
coe
         ((T_TotalPreorder_222 -> T_MinOperator_98 -> T_Band_596)
-> Any -> Any -> Any
forall a b. a -> b
coe
            T_TotalPreorder_222 -> T_MinOperator_98 -> T_Band_596
MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_'8851''45'band_3052
            ((T_TotalPreorder_222 -> T_TotalPreorder_222) -> Any -> Any
forall a b. a -> b
coe
               T_TotalPreorder_222 -> T_TotalPreorder_222
MAlonzo.Code.Relation.Binary.Construct.Flip.EqAndOrd.du_totalPreorder_746
               (T_TotalPreorder_222 -> Any
forall a b. a -> b
coe T_TotalPreorder_222
v0))
            ((T_MaxOperator_128 -> T_MinOperator_98) -> Any -> Any
forall a b. a -> b
coe
               T_MaxOperator_128 -> T_MinOperator_98
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.du_MaxOp'8658'MinOp_174
               (T_MaxOperator_128 -> Any
forall a b. a -> b
coe T_MaxOperator_128
v1))))
-- Data.Integer.Properties.⊓-⊔-properties.⊓-comm
d_'8851''45'comm_6580 ::
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8851''45'comm_6580 :: Integer -> Integer -> T__'8801'__12
d_'8851''45'comm_6580 = Integer -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.⊓-⊔-properties.⊓-commutativeSemigroup
d_'8851''45'commutativeSemigroup_6582 ::
  MAlonzo.Code.Algebra.Bundles.T_CommutativeSemigroup_662
d_'8851''45'commutativeSemigroup_6582 :: T_CommutativeSemigroup_662
d_'8851''45'commutativeSemigroup_6582
  = let v0 :: T_TotalPreorder_222
v0 = T_TotalPreorder_222
d_'8804''45'totalPreorder_2812 in
    Any -> T_CommutativeSemigroup_662
forall a b. a -> b
coe
      (let v1 :: T_MaxOperator_128
v1 = T_MaxOperator_128
d_'8852''45'operator_6456 in
       Any -> Any
forall a b. a -> b
coe
         ((T_TotalPreorder_222
 -> T_MinOperator_98 -> T_CommutativeSemigroup_662)
-> Any -> Any -> Any
forall a b. a -> b
coe
            T_TotalPreorder_222
-> T_MinOperator_98 -> T_CommutativeSemigroup_662
MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_'8851''45'commutativeSemigroup_3054
            ((T_TotalPreorder_222 -> T_TotalPreorder_222) -> Any -> Any
forall a b. a -> b
coe
               T_TotalPreorder_222 -> T_TotalPreorder_222
MAlonzo.Code.Relation.Binary.Construct.Flip.EqAndOrd.du_totalPreorder_746
               (T_TotalPreorder_222 -> Any
forall a b. a -> b
coe T_TotalPreorder_222
v0))
            ((T_MaxOperator_128 -> T_MinOperator_98) -> Any -> Any
forall a b. a -> b
coe
               T_MaxOperator_128 -> T_MinOperator_98
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.du_MaxOp'8658'MinOp_174
               (T_MaxOperator_128 -> Any
forall a b. a -> b
coe T_MaxOperator_128
v1))))
-- Data.Integer.Properties.⊓-⊔-properties.⊔-distrib-⊓
d_'8852''45'distrib'45''8851'_6590 ::
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'8852''45'distrib'45''8851'_6590 :: T_Σ_14
d_'8852''45'distrib'45''8851'_6590
  = (T_TotalPreorder_222
 -> T_MinOperator_98 -> T_MaxOperator_128 -> T_Σ_14)
-> Any -> Any -> Any -> T_Σ_14
forall a b. a -> b
coe
      T_TotalPreorder_222
-> T_MinOperator_98 -> T_MaxOperator_128 -> T_Σ_14
MAlonzo.Code.Algebra.Construct.NaturalChoice.MinMaxOp.du_'8852''45'distrib'45''8851'_3170
      (T_TotalPreorder_222 -> Any
forall a b. a -> b
coe T_TotalPreorder_222
d_'8804''45'totalPreorder_2812)
      (T_MinOperator_98 -> Any
forall a b. a -> b
coe T_MinOperator_98
d_'8851''45'operator_6454) (T_MaxOperator_128 -> Any
forall a b. a -> b
coe T_MaxOperator_128
d_'8852''45'operator_6456)
-- Data.Integer.Properties.⊓-⊔-properties.⊔-distribʳ-⊓
d_'8852''45'distrib'691''45''8851'_6592 ::
  Integer ->
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8852''45'distrib'691''45''8851'_6592 :: Integer -> Integer -> Integer -> T__'8801'__12
d_'8852''45'distrib'691''45''8851'_6592 = Integer -> Integer -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.⊓-⊔-properties.⊔-distribˡ-⊓
d_'8852''45'distrib'737''45''8851'_6594 ::
  Integer ->
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8852''45'distrib'737''45''8851'_6594 :: Integer -> Integer -> Integer -> T__'8801'__12
d_'8852''45'distrib'737''45''8851'_6594 = Integer -> Integer -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.⊓-⊔-properties.⊓-idem
d_'8851''45'idem_6596 ::
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8851''45'idem_6596 :: Integer -> T__'8801'__12
d_'8851''45'idem_6596 = Integer -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.⊓-⊔-properties.⊓-isBand
d_'8851''45'isBand_6604 ::
  MAlonzo.Code.Algebra.Structures.T_IsBand_508
d_'8851''45'isBand_6604 :: T_IsBand_508
d_'8851''45'isBand_6604
  = let v0 :: T_TotalPreorder_222
v0 = T_TotalPreorder_222
d_'8804''45'totalPreorder_2812 in
    Any -> T_IsBand_508
forall a b. a -> b
coe
      (let v1 :: T_MaxOperator_128
v1 = T_MaxOperator_128
d_'8852''45'operator_6456 in
       Any -> Any
forall a b. a -> b
coe
         ((T_TotalPreorder_222 -> T_MinOperator_98 -> T_IsBand_508)
-> Any -> Any -> Any
forall a b. a -> b
coe
            T_TotalPreorder_222 -> T_MinOperator_98 -> T_IsBand_508
MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_'8851''45'isBand_3034
            ((T_TotalPreorder_222 -> T_TotalPreorder_222) -> Any -> Any
forall a b. a -> b
coe
               T_TotalPreorder_222 -> T_TotalPreorder_222
MAlonzo.Code.Relation.Binary.Construct.Flip.EqAndOrd.du_totalPreorder_746
               (T_TotalPreorder_222 -> Any
forall a b. a -> b
coe T_TotalPreorder_222
v0))
            ((T_MaxOperator_128 -> T_MinOperator_98) -> Any -> Any
forall a b. a -> b
coe
               T_MaxOperator_128 -> T_MinOperator_98
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.du_MaxOp'8658'MinOp_174
               (T_MaxOperator_128 -> Any
forall a b. a -> b
coe T_MaxOperator_128
v1))))
-- Data.Integer.Properties.⊓-⊔-properties.⊓-isCommutativeSemigroup
d_'8851''45'isCommutativeSemigroup_6606 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_548
d_'8851''45'isCommutativeSemigroup_6606 :: T_IsCommutativeSemigroup_548
d_'8851''45'isCommutativeSemigroup_6606
  = let v0 :: T_TotalPreorder_222
v0 = T_TotalPreorder_222
d_'8804''45'totalPreorder_2812 in
    Any -> T_IsCommutativeSemigroup_548
forall a b. a -> b
coe
      (let v1 :: T_MaxOperator_128
v1 = T_MaxOperator_128
d_'8852''45'operator_6456 in
       Any -> Any
forall a b. a -> b
coe
         ((T_TotalPreorder_222
 -> T_MinOperator_98 -> T_IsCommutativeSemigroup_548)
-> Any -> Any -> Any
forall a b. a -> b
coe
            T_TotalPreorder_222
-> T_MinOperator_98 -> T_IsCommutativeSemigroup_548
MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_'8851''45'isCommutativeSemigroup_3036
            ((T_TotalPreorder_222 -> T_TotalPreorder_222) -> Any -> Any
forall a b. a -> b
coe
               T_TotalPreorder_222 -> T_TotalPreorder_222
MAlonzo.Code.Relation.Binary.Construct.Flip.EqAndOrd.du_totalPreorder_746
               (T_TotalPreorder_222 -> Any
forall a b. a -> b
coe T_TotalPreorder_222
v0))
            ((T_MaxOperator_128 -> T_MinOperator_98) -> Any -> Any
forall a b. a -> b
coe
               T_MaxOperator_128 -> T_MinOperator_98
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.du_MaxOp'8658'MinOp_174
               (T_MaxOperator_128 -> Any
forall a b. a -> b
coe T_MaxOperator_128
v1))))
-- Data.Integer.Properties.⊓-⊔-properties.⊓-isMagma
d_'8851''45'isMagma_6608 ::
  MAlonzo.Code.Algebra.Structures.T_IsMagma_176
d_'8851''45'isMagma_6608 :: T_IsMagma_176
d_'8851''45'isMagma_6608
  = let v0 :: T_TotalPreorder_222
v0 = T_TotalPreorder_222
d_'8804''45'totalPreorder_2812 in
    Any -> T_IsMagma_176
forall a b. a -> b
coe
      (let v1 :: T_MaxOperator_128
v1 = T_MaxOperator_128
d_'8852''45'operator_6456 in
       Any -> Any
forall a b. a -> b
coe
         ((T_TotalPreorder_222 -> T_MinOperator_98 -> T_IsMagma_176)
-> Any -> Any -> Any
forall a b. a -> b
coe
            T_TotalPreorder_222 -> T_MinOperator_98 -> T_IsMagma_176
MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_'8851''45'isMagma_3030
            ((T_TotalPreorder_222 -> T_TotalPreorder_222) -> Any -> Any
forall a b. a -> b
coe
               T_TotalPreorder_222 -> T_TotalPreorder_222
MAlonzo.Code.Relation.Binary.Construct.Flip.EqAndOrd.du_totalPreorder_746
               (T_TotalPreorder_222 -> Any
forall a b. a -> b
coe T_TotalPreorder_222
v0))
            ((T_MaxOperator_128 -> T_MinOperator_98) -> Any -> Any
forall a b. a -> b
coe
               T_MaxOperator_128 -> T_MinOperator_98
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.du_MaxOp'8658'MinOp_174
               (T_MaxOperator_128 -> Any
forall a b. a -> b
coe T_MaxOperator_128
v1))))
-- Data.Integer.Properties.⊓-⊔-properties.⊓-isSelectiveMagma
d_'8851''45'isSelectiveMagma_6612 ::
  MAlonzo.Code.Algebra.Structures.T_IsSelectiveMagma_436
d_'8851''45'isSelectiveMagma_6612 :: T_IsSelectiveMagma_436
d_'8851''45'isSelectiveMagma_6612
  = let v0 :: T_TotalPreorder_222
v0 = T_TotalPreorder_222
d_'8804''45'totalPreorder_2812 in
    Any -> T_IsSelectiveMagma_436
forall a b. a -> b
coe
      (let v1 :: T_MaxOperator_128
v1 = T_MaxOperator_128
d_'8852''45'operator_6456 in
       Any -> Any
forall a b. a -> b
coe
         ((T_TotalPreorder_222 -> T_MinOperator_98 -> T_IsSelectiveMagma_436)
-> Any -> Any -> Any
forall a b. a -> b
coe
            T_TotalPreorder_222 -> T_MinOperator_98 -> T_IsSelectiveMagma_436
MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_'8851''45'isSelectiveMagma_3038
            ((T_TotalPreorder_222 -> T_TotalPreorder_222) -> Any -> Any
forall a b. a -> b
coe
               T_TotalPreorder_222 -> T_TotalPreorder_222
MAlonzo.Code.Relation.Binary.Construct.Flip.EqAndOrd.du_totalPreorder_746
               (T_TotalPreorder_222 -> Any
forall a b. a -> b
coe T_TotalPreorder_222
v0))
            ((T_MaxOperator_128 -> T_MinOperator_98) -> Any -> Any
forall a b. a -> b
coe
               T_MaxOperator_128 -> T_MinOperator_98
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.du_MaxOp'8658'MinOp_174
               (T_MaxOperator_128 -> Any
forall a b. a -> b
coe T_MaxOperator_128
v1))))
-- Data.Integer.Properties.⊓-⊔-properties.⊓-isSemigroup
d_'8851''45'isSemigroup_6614 ::
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_472
d_'8851''45'isSemigroup_6614 :: T_IsSemigroup_472
d_'8851''45'isSemigroup_6614
  = let v0 :: T_TotalPreorder_222
v0 = T_TotalPreorder_222
d_'8804''45'totalPreorder_2812 in
    Any -> T_IsSemigroup_472
forall a b. a -> b
coe
      (let v1 :: T_MaxOperator_128
v1 = T_MaxOperator_128
d_'8852''45'operator_6456 in
       Any -> Any
forall a b. a -> b
coe
         ((T_TotalPreorder_222 -> T_MinOperator_98 -> T_IsSemigroup_472)
-> Any -> Any -> Any
forall a b. a -> b
coe
            T_TotalPreorder_222 -> T_MinOperator_98 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_'8851''45'isSemigroup_3032
            ((T_TotalPreorder_222 -> T_TotalPreorder_222) -> Any -> Any
forall a b. a -> b
coe
               T_TotalPreorder_222 -> T_TotalPreorder_222
MAlonzo.Code.Relation.Binary.Construct.Flip.EqAndOrd.du_totalPreorder_746
               (T_TotalPreorder_222 -> Any
forall a b. a -> b
coe T_TotalPreorder_222
v0))
            ((T_MaxOperator_128 -> T_MinOperator_98) -> Any -> Any
forall a b. a -> b
coe
               T_MaxOperator_128 -> T_MinOperator_98
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.du_MaxOp'8658'MinOp_174
               (T_MaxOperator_128 -> Any
forall a b. a -> b
coe T_MaxOperator_128
v1))))
-- Data.Integer.Properties.⊓-⊔-properties.⊓-glb
d_'8851''45'glb_6616 ::
  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_6616 :: Integer
-> Integer
-> Integer
-> T__'8804'__26
-> T__'8804'__26
-> T__'8804'__26
d_'8851''45'glb_6616
  = let v0 :: T_TotalPreorder_222
v0 = T_TotalPreorder_222
d_'8804''45'totalPreorder_2812 in
    Any
-> Integer
-> Integer
-> Integer
-> T__'8804'__26
-> T__'8804'__26
-> T__'8804'__26
forall a b. a -> b
coe
      (let v1 :: T_MaxOperator_128
v1 = T_MaxOperator_128
d_'8852''45'operator_6456 in
       Any -> Any
forall a b. a -> b
coe
         ((T_TotalPreorder_222
 -> T_MinOperator_98 -> Any -> Any -> Any -> Any -> Any -> Any)
-> Any -> Any -> Any
forall a b. a -> b
coe
            T_TotalPreorder_222
-> T_MinOperator_98 -> Any -> Any -> Any -> Any -> Any -> Any
MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_'8851''45'glb_3278
            ((T_TotalPreorder_222 -> T_TotalPreorder_222) -> Any -> Any
forall a b. a -> b
coe
               T_TotalPreorder_222 -> T_TotalPreorder_222
MAlonzo.Code.Relation.Binary.Construct.Flip.EqAndOrd.du_totalPreorder_746
               (T_TotalPreorder_222 -> Any
forall a b. a -> b
coe T_TotalPreorder_222
v0))
            ((T_MaxOperator_128 -> T_MinOperator_98) -> Any -> Any
forall a b. a -> b
coe
               T_MaxOperator_128 -> T_MinOperator_98
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.du_MaxOp'8658'MinOp_174
               (T_MaxOperator_128 -> Any
forall a b. a -> b
coe T_MaxOperator_128
v1))))
-- Data.Integer.Properties.⊓-⊔-properties.⊓-magma
d_'8851''45'magma_6618 :: MAlonzo.Code.Algebra.Bundles.T_Magma_68
d_'8851''45'magma_6618 :: T_Magma_68
d_'8851''45'magma_6618
  = let v0 :: T_TotalPreorder_222
v0 = T_TotalPreorder_222
d_'8804''45'totalPreorder_2812 in
    Any -> T_Magma_68
forall a b. a -> b
coe
      (let v1 :: T_MaxOperator_128
v1 = T_MaxOperator_128
d_'8852''45'operator_6456 in
       Any -> Any
forall a b. a -> b
coe
         ((T_TotalPreorder_222 -> T_MinOperator_98 -> T_Magma_68)
-> Any -> Any -> Any
forall a b. a -> b
coe
            T_TotalPreorder_222 -> T_MinOperator_98 -> T_Magma_68
MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_'8851''45'magma_3048
            ((T_TotalPreorder_222 -> T_TotalPreorder_222) -> Any -> Any
forall a b. a -> b
coe
               T_TotalPreorder_222 -> T_TotalPreorder_222
MAlonzo.Code.Relation.Binary.Construct.Flip.EqAndOrd.du_totalPreorder_746
               (T_TotalPreorder_222 -> Any
forall a b. a -> b
coe T_TotalPreorder_222
v0))
            ((T_MaxOperator_128 -> T_MinOperator_98) -> Any -> Any
forall a b. a -> b
coe
               T_MaxOperator_128 -> T_MinOperator_98
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.du_MaxOp'8658'MinOp_174
               (T_MaxOperator_128 -> Any
forall a b. a -> b
coe T_MaxOperator_128
v1))))
-- Data.Integer.Properties.⊓-⊔-properties.⊓-mono-≤
d_'8851''45'mono'45''8804'_6620 ::
  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'_6620 :: Integer
-> Integer
-> Integer
-> Integer
-> T__'8804'__26
-> T__'8804'__26
-> T__'8804'__26
d_'8851''45'mono'45''8804'_6620
  = let v0 :: T_TotalPreorder_222
v0 = T_TotalPreorder_222
d_'8804''45'totalPreorder_2812 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_128
v1 = T_MaxOperator_128
d_'8852''45'operator_6456 in
       Any -> Any
forall a b. a -> b
coe
         ((T_TotalPreorder_222
 -> T_MinOperator_98
 -> Any
 -> Any
 -> Any
 -> Any
 -> Any
 -> Any
 -> Any)
-> Any -> Any -> Any
forall a b. a -> b
coe
            T_TotalPreorder_222
-> T_MinOperator_98
-> Any
-> Any
-> Any
-> Any
-> Any
-> Any
-> Any
MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_'8851''45'mono'45''8804'_3206
            ((T_TotalPreorder_222 -> T_TotalPreorder_222) -> Any -> Any
forall a b. a -> b
coe
               T_TotalPreorder_222 -> T_TotalPreorder_222
MAlonzo.Code.Relation.Binary.Construct.Flip.EqAndOrd.du_totalPreorder_746
               (T_TotalPreorder_222 -> Any
forall a b. a -> b
coe T_TotalPreorder_222
v0))
            ((T_MaxOperator_128 -> T_MinOperator_98) -> Any -> Any
forall a b. a -> b
coe
               T_MaxOperator_128 -> T_MinOperator_98
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.du_MaxOp'8658'MinOp_174
               (T_MaxOperator_128 -> Any
forall a b. a -> b
coe T_MaxOperator_128
v1))))
-- Data.Integer.Properties.⊓-⊔-properties.⊓-monoʳ-≤
d_'8851''45'mono'691''45''8804'_6624 ::
  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'_6624 :: Integer -> Integer -> Integer -> T__'8804'__26 -> T__'8804'__26
d_'8851''45'mono'691''45''8804'_6624
  = let v0 :: T_TotalPreorder_222
v0 = T_TotalPreorder_222
d_'8804''45'totalPreorder_2812 in
    Any
-> Integer -> Integer -> Integer -> T__'8804'__26 -> T__'8804'__26
forall a b. a -> b
coe
      (let v1 :: T_MaxOperator_128
v1 = T_MaxOperator_128
d_'8852''45'operator_6456 in
       Any -> Any
forall a b. a -> b
coe
         ((T_TotalPreorder_222
 -> T_MinOperator_98 -> Any -> Any -> Any -> Any -> Any)
-> Any -> Any -> Any
forall a b. a -> b
coe
            T_TotalPreorder_222
-> T_MinOperator_98 -> Any -> Any -> Any -> Any -> Any
MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_'8851''45'mono'691''45''8804'_3266
            ((T_TotalPreorder_222 -> T_TotalPreorder_222) -> Any -> Any
forall a b. a -> b
coe
               T_TotalPreorder_222 -> T_TotalPreorder_222
MAlonzo.Code.Relation.Binary.Construct.Flip.EqAndOrd.du_totalPreorder_746
               (T_TotalPreorder_222 -> Any
forall a b. a -> b
coe T_TotalPreorder_222
v0))
            ((T_MaxOperator_128 -> T_MinOperator_98) -> Any -> Any
forall a b. a -> b
coe
               T_MaxOperator_128 -> T_MinOperator_98
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.du_MaxOp'8658'MinOp_174
               (T_MaxOperator_128 -> Any
forall a b. a -> b
coe T_MaxOperator_128
v1))))
-- Data.Integer.Properties.⊓-⊔-properties.⊓-monoˡ-≤
d_'8851''45'mono'737''45''8804'_6626 ::
  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'_6626 :: Integer -> Integer -> Integer -> T__'8804'__26 -> T__'8804'__26
d_'8851''45'mono'737''45''8804'_6626
  = let v0 :: T_TotalPreorder_222
v0 = T_TotalPreorder_222
d_'8804''45'totalPreorder_2812 in
    Any
-> Integer -> Integer -> Integer -> T__'8804'__26 -> T__'8804'__26
forall a b. a -> b
coe
      (let v1 :: T_MaxOperator_128
v1 = T_MaxOperator_128
d_'8852''45'operator_6456 in
       Any -> Any
forall a b. a -> b
coe
         ((T_TotalPreorder_222
 -> T_MinOperator_98 -> Any -> Any -> Any -> Any -> Any)
-> Any -> Any -> Any
forall a b. a -> b
coe
            T_TotalPreorder_222
-> T_MinOperator_98 -> Any -> Any -> Any -> Any -> Any
MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_'8851''45'mono'737''45''8804'_3256
            ((T_TotalPreorder_222 -> T_TotalPreorder_222) -> Any -> Any
forall a b. a -> b
coe
               T_TotalPreorder_222 -> T_TotalPreorder_222
MAlonzo.Code.Relation.Binary.Construct.Flip.EqAndOrd.du_totalPreorder_746
               (T_TotalPreorder_222 -> Any
forall a b. a -> b
coe T_TotalPreorder_222
v0))
            ((T_MaxOperator_128 -> T_MinOperator_98) -> Any -> Any
forall a b. a -> b
coe
               T_MaxOperator_128 -> T_MinOperator_98
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.du_MaxOp'8658'MinOp_174
               (T_MaxOperator_128 -> Any
forall a b. a -> b
coe T_MaxOperator_128
v1))))
-- Data.Integer.Properties.⊓-⊔-properties.⊓-sel
d_'8851''45'sel_6628 ::
  Integer -> Integer -> MAlonzo.Code.Data.Sum.Base.T__'8846'__30
d_'8851''45'sel_6628 :: Integer -> Integer -> T__'8846'__30
d_'8851''45'sel_6628
  = let v0 :: T_TotalPreorder_222
v0 = T_TotalPreorder_222
d_'8804''45'totalPreorder_2812 in
    Any -> Integer -> Integer -> T__'8846'__30
forall a b. a -> b
coe
      (let v1 :: T_MaxOperator_128
v1 = T_MaxOperator_128
d_'8852''45'operator_6456 in
       Any -> Any
forall a b. a -> b
coe
         ((T_TotalPreorder_222
 -> T_MinOperator_98 -> Any -> Any -> T__'8846'__30)
-> Any -> Any -> Any
forall a b. a -> b
coe
            T_TotalPreorder_222
-> T_MinOperator_98 -> Any -> Any -> T__'8846'__30
MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_'8851''45'sel_2988
            ((T_TotalPreorder_222 -> T_TotalPreorder_222) -> Any -> Any
forall a b. a -> b
coe
               T_TotalPreorder_222 -> T_TotalPreorder_222
MAlonzo.Code.Relation.Binary.Construct.Flip.EqAndOrd.du_totalPreorder_746
               (T_TotalPreorder_222 -> Any
forall a b. a -> b
coe T_TotalPreorder_222
v0))
            ((T_MaxOperator_128 -> T_MinOperator_98) -> Any -> Any
forall a b. a -> b
coe
               T_MaxOperator_128 -> T_MinOperator_98
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.du_MaxOp'8658'MinOp_174
               (T_MaxOperator_128 -> Any
forall a b. a -> b
coe T_MaxOperator_128
v1))))
-- Data.Integer.Properties.⊓-⊔-properties.⊓-selectiveMagma
d_'8851''45'selectiveMagma_6630 ::
  MAlonzo.Code.Algebra.Bundles.T_SelectiveMagma_122
d_'8851''45'selectiveMagma_6630 :: T_SelectiveMagma_122
d_'8851''45'selectiveMagma_6630
  = let v0 :: T_TotalPreorder_222
v0 = T_TotalPreorder_222
d_'8804''45'totalPreorder_2812 in
    Any -> T_SelectiveMagma_122
forall a b. a -> b
coe
      (let v1 :: T_MaxOperator_128
v1 = T_MaxOperator_128
d_'8852''45'operator_6456 in
       Any -> Any
forall a b. a -> b
coe
         ((T_TotalPreorder_222 -> T_MinOperator_98 -> T_SelectiveMagma_122)
-> Any -> Any -> Any
forall a b. a -> b
coe
            T_TotalPreorder_222 -> T_MinOperator_98 -> T_SelectiveMagma_122
MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_'8851''45'selectiveMagma_3056
            ((T_TotalPreorder_222 -> T_TotalPreorder_222) -> Any -> Any
forall a b. a -> b
coe
               T_TotalPreorder_222 -> T_TotalPreorder_222
MAlonzo.Code.Relation.Binary.Construct.Flip.EqAndOrd.du_totalPreorder_746
               (T_TotalPreorder_222 -> Any
forall a b. a -> b
coe T_TotalPreorder_222
v0))
            ((T_MaxOperator_128 -> T_MinOperator_98) -> Any -> Any
forall a b. a -> b
coe
               T_MaxOperator_128 -> T_MinOperator_98
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.du_MaxOp'8658'MinOp_174
               (T_MaxOperator_128 -> Any
forall a b. a -> b
coe T_MaxOperator_128
v1))))
-- Data.Integer.Properties.⊓-⊔-properties.⊓-semigroup
d_'8851''45'semigroup_6632 ::
  MAlonzo.Code.Algebra.Bundles.T_Semigroup_536
d_'8851''45'semigroup_6632 :: T_Semigroup_536
d_'8851''45'semigroup_6632
  = let v0 :: T_TotalPreorder_222
v0 = T_TotalPreorder_222
d_'8804''45'totalPreorder_2812 in
    Any -> T_Semigroup_536
forall a b. a -> b
coe
      (let v1 :: T_MaxOperator_128
v1 = T_MaxOperator_128
d_'8852''45'operator_6456 in
       Any -> Any
forall a b. a -> b
coe
         ((T_TotalPreorder_222 -> T_MinOperator_98 -> T_Semigroup_536)
-> Any -> Any -> Any
forall a b. a -> b
coe
            T_TotalPreorder_222 -> T_MinOperator_98 -> T_Semigroup_536
MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_'8851''45'semigroup_3050
            ((T_TotalPreorder_222 -> T_TotalPreorder_222) -> Any -> Any
forall a b. a -> b
coe
               T_TotalPreorder_222 -> T_TotalPreorder_222
MAlonzo.Code.Relation.Binary.Construct.Flip.EqAndOrd.du_totalPreorder_746
               (T_TotalPreorder_222 -> Any
forall a b. a -> b
coe T_TotalPreorder_222
v0))
            ((T_MaxOperator_128 -> T_MinOperator_98) -> Any -> Any
forall a b. a -> b
coe
               T_MaxOperator_128 -> T_MinOperator_98
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.du_MaxOp'8658'MinOp_174
               (T_MaxOperator_128 -> Any
forall a b. a -> b
coe T_MaxOperator_128
v1))))
-- Data.Integer.Properties.⊓-⊔-properties.⊓-triangulate
d_'8851''45'triangulate_6634 ::
  Integer ->
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8851''45'triangulate_6634 :: Integer -> Integer -> Integer -> T__'8801'__12
d_'8851''45'triangulate_6634 = Integer -> Integer -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.⊓-⊔-properties.⊔-⊓-absorptive
d_'8852''45''8851''45'absorptive_6642 ::
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'8852''45''8851''45'absorptive_6642 :: T_Σ_14
d_'8852''45''8851''45'absorptive_6642
  = (T_TotalPreorder_222
 -> T_MinOperator_98 -> T_MaxOperator_128 -> T_Σ_14)
-> Any -> Any -> Any -> T_Σ_14
forall a b. a -> b
coe
      T_TotalPreorder_222
-> T_MinOperator_98 -> T_MaxOperator_128 -> T_Σ_14
MAlonzo.Code.Algebra.Construct.NaturalChoice.MinMaxOp.du_'8852''45''8851''45'absorptive_3216
      (T_TotalPreorder_222 -> Any
forall a b. a -> b
coe T_TotalPreorder_222
d_'8804''45'totalPreorder_2812)
      (T_MinOperator_98 -> Any
forall a b. a -> b
coe T_MinOperator_98
d_'8851''45'operator_6454) (T_MaxOperator_128 -> Any
forall a b. a -> b
coe T_MaxOperator_128
d_'8852''45'operator_6456)
-- Data.Integer.Properties.⊓-⊔-latticeProperties.⊓-isSemilattice
d_'8851''45'isSemilattice_6646 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_590
d_'8851''45'isSemilattice_6646 :: T_IsCommutativeBand_590
d_'8851''45'isSemilattice_6646
  = let v0 :: T_TotalPreorder_222
v0 = T_TotalPreorder_222
d_'8804''45'totalPreorder_2812 in
    Any -> T_IsCommutativeBand_590
forall a b. a -> b
coe
      (let v1 :: T_MinOperator_98
v1 = T_MinOperator_98
d_'8851''45'operator_6454 in
       Any -> Any
forall a b. a -> b
coe
         ((T_TotalPreorder_222
 -> T_MinOperator_98 -> T_IsCommutativeBand_590)
-> Any -> Any -> Any
forall a b. a -> b
coe
            T_TotalPreorder_222 -> T_MinOperator_98 -> T_IsCommutativeBand_590
MAlonzo.Code.Algebra.Lattice.Construct.NaturalChoice.MinOp.du_'8851''45'isSemilattice_602
            (T_TotalPreorder_222 -> Any
forall a b. a -> b
coe T_TotalPreorder_222
v0) (T_MinOperator_98 -> Any
forall a b. a -> b
coe T_MinOperator_98
v1)))
-- Data.Integer.Properties.⊓-⊔-latticeProperties.⊓-semilattice
d_'8851''45'semilattice_6648 ::
  MAlonzo.Code.Algebra.Lattice.Bundles.T_Semilattice_10
d_'8851''45'semilattice_6648 :: T_Semilattice_10
d_'8851''45'semilattice_6648
  = let v0 :: T_TotalPreorder_222
v0 = T_TotalPreorder_222
d_'8804''45'totalPreorder_2812 in
    Any -> T_Semilattice_10
forall a b. a -> b
coe
      (let v1 :: T_MinOperator_98
v1 = T_MinOperator_98
d_'8851''45'operator_6454 in
       Any -> Any
forall a b. a -> b
coe
         ((T_TotalPreorder_222 -> T_MinOperator_98 -> T_Semilattice_10)
-> Any -> Any -> Any
forall a b. a -> b
coe
            T_TotalPreorder_222 -> T_MinOperator_98 -> T_Semilattice_10
MAlonzo.Code.Algebra.Lattice.Construct.NaturalChoice.MinOp.du_'8851''45'semilattice_604
            (T_TotalPreorder_222 -> Any
forall a b. a -> b
coe T_TotalPreorder_222
v0) (T_MinOperator_98 -> Any
forall a b. a -> b
coe T_MinOperator_98
v1)))
-- Data.Integer.Properties.⊓-⊔-latticeProperties.⊓-⊔-distributiveLattice
d_'8851''45''8852''45'distributiveLattice_6650 ::
  MAlonzo.Code.Algebra.Lattice.Bundles.T_DistributiveLattice_584
d_'8851''45''8852''45'distributiveLattice_6650 :: T_DistributiveLattice_584
d_'8851''45''8852''45'distributiveLattice_6650
  = (T_TotalPreorder_222
 -> T_MinOperator_98
 -> T_MaxOperator_128
 -> T_DistributiveLattice_584)
-> Any -> Any -> Any -> T_DistributiveLattice_584
forall a b. a -> b
coe
      T_TotalPreorder_222
-> T_MinOperator_98
-> T_MaxOperator_128
-> T_DistributiveLattice_584
MAlonzo.Code.Algebra.Lattice.Construct.NaturalChoice.MinMaxOp.du_'8851''45''8852''45'distributiveLattice_808
      (T_TotalPreorder_222 -> Any
forall a b. a -> b
coe T_TotalPreorder_222
d_'8804''45'totalPreorder_2812)
      (T_MinOperator_98 -> Any
forall a b. a -> b
coe T_MinOperator_98
d_'8851''45'operator_6454) (T_MaxOperator_128 -> Any
forall a b. a -> b
coe T_MaxOperator_128
d_'8852''45'operator_6456)
-- Data.Integer.Properties.⊓-⊔-latticeProperties.⊓-⊔-isDistributiveLattice
d_'8851''45''8852''45'isDistributiveLattice_6652 ::
  MAlonzo.Code.Algebra.Lattice.Structures.T_IsDistributiveLattice_3036
d_'8851''45''8852''45'isDistributiveLattice_6652 :: T_IsDistributiveLattice_3036
d_'8851''45''8852''45'isDistributiveLattice_6652
  = (T_TotalPreorder_222
 -> T_MinOperator_98
 -> T_MaxOperator_128
 -> T_IsDistributiveLattice_3036)
-> Any -> Any -> Any -> T_IsDistributiveLattice_3036
forall a b. a -> b
coe
      T_TotalPreorder_222
-> T_MinOperator_98
-> T_MaxOperator_128
-> T_IsDistributiveLattice_3036
MAlonzo.Code.Algebra.Lattice.Construct.NaturalChoice.MinMaxOp.du_'8851''45''8852''45'isDistributiveLattice_798
      (T_TotalPreorder_222 -> Any
forall a b. a -> b
coe T_TotalPreorder_222
d_'8804''45'totalPreorder_2812)
      (T_MinOperator_98 -> Any
forall a b. a -> b
coe T_MinOperator_98
d_'8851''45'operator_6454) (T_MaxOperator_128 -> Any
forall a b. a -> b
coe T_MaxOperator_128
d_'8852''45'operator_6456)
-- Data.Integer.Properties.⊓-⊔-latticeProperties.⊓-⊔-isLattice
d_'8851''45''8852''45'isLattice_6654 ::
  MAlonzo.Code.Algebra.Lattice.Structures.T_IsLattice_2962
d_'8851''45''8852''45'isLattice_6654 :: T_IsLattice_2962
d_'8851''45''8852''45'isLattice_6654
  = (T_TotalPreorder_222
 -> T_MinOperator_98 -> T_MaxOperator_128 -> T_IsLattice_2962)
-> Any -> Any -> Any -> T_IsLattice_2962
forall a b. a -> b
coe
      T_TotalPreorder_222
-> T_MinOperator_98 -> T_MaxOperator_128 -> T_IsLattice_2962
MAlonzo.Code.Algebra.Lattice.Construct.NaturalChoice.MinMaxOp.du_'8851''45''8852''45'isLattice_796
      (T_TotalPreorder_222 -> Any
forall a b. a -> b
coe T_TotalPreorder_222
d_'8804''45'totalPreorder_2812)
      (T_MinOperator_98 -> Any
forall a b. a -> b
coe T_MinOperator_98
d_'8851''45'operator_6454) (T_MaxOperator_128 -> Any
forall a b. a -> b
coe T_MaxOperator_128
d_'8852''45'operator_6456)
-- Data.Integer.Properties.⊓-⊔-latticeProperties.⊓-⊔-lattice
d_'8851''45''8852''45'lattice_6656 ::
  MAlonzo.Code.Algebra.Lattice.Bundles.T_Lattice_500
d_'8851''45''8852''45'lattice_6656 :: T_Lattice_500
d_'8851''45''8852''45'lattice_6656
  = (T_TotalPreorder_222
 -> T_MinOperator_98 -> T_MaxOperator_128 -> T_Lattice_500)
-> Any -> Any -> Any -> T_Lattice_500
forall a b. a -> b
coe
      T_TotalPreorder_222
-> T_MinOperator_98 -> T_MaxOperator_128 -> T_Lattice_500
MAlonzo.Code.Algebra.Lattice.Construct.NaturalChoice.MinMaxOp.du_'8851''45''8852''45'lattice_804
      (T_TotalPreorder_222 -> Any
forall a b. a -> b
coe T_TotalPreorder_222
d_'8804''45'totalPreorder_2812)
      (T_MinOperator_98 -> Any
forall a b. a -> b
coe T_MinOperator_98
d_'8851''45'operator_6454) (T_MaxOperator_128 -> Any
forall a b. a -> b
coe T_MaxOperator_128
d_'8852''45'operator_6456)
-- Data.Integer.Properties.⊓-⊔-latticeProperties.⊓-isSemilattice
d_'8851''45'isSemilattice_6658 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_590
d_'8851''45'isSemilattice_6658 :: T_IsCommutativeBand_590
d_'8851''45'isSemilattice_6658
  = let v0 :: T_TotalPreorder_222
v0 = T_TotalPreorder_222
d_'8804''45'totalPreorder_2812 in
    Any -> T_IsCommutativeBand_590
forall a b. a -> b
coe
      (let v1 :: T_MaxOperator_128
v1 = T_MaxOperator_128
d_'8852''45'operator_6456 in
       Any -> Any
forall a b. a -> b
coe
         ((T_TotalPreorder_222
 -> T_MinOperator_98 -> T_IsCommutativeBand_590)
-> Any -> Any -> Any
forall a b. a -> b
coe
            T_TotalPreorder_222 -> T_MinOperator_98 -> T_IsCommutativeBand_590
MAlonzo.Code.Algebra.Lattice.Construct.NaturalChoice.MinOp.du_'8851''45'isSemilattice_602
            ((T_TotalPreorder_222 -> T_TotalPreorder_222) -> Any -> Any
forall a b. a -> b
coe
               T_TotalPreorder_222 -> T_TotalPreorder_222
MAlonzo.Code.Relation.Binary.Construct.Flip.EqAndOrd.du_totalPreorder_746
               (T_TotalPreorder_222 -> Any
forall a b. a -> b
coe T_TotalPreorder_222
v0))
            ((T_MaxOperator_128 -> T_MinOperator_98) -> Any -> Any
forall a b. a -> b
coe
               T_MaxOperator_128 -> T_MinOperator_98
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.du_MaxOp'8658'MinOp_174
               (T_MaxOperator_128 -> Any
forall a b. a -> b
coe T_MaxOperator_128
v1))))
-- Data.Integer.Properties.⊓-⊔-latticeProperties.⊓-semilattice
d_'8851''45'semilattice_6660 ::
  MAlonzo.Code.Algebra.Lattice.Bundles.T_Semilattice_10
d_'8851''45'semilattice_6660 :: T_Semilattice_10
d_'8851''45'semilattice_6660
  = let v0 :: T_TotalPreorder_222
v0 = T_TotalPreorder_222
d_'8804''45'totalPreorder_2812 in
    Any -> T_Semilattice_10
forall a b. a -> b
coe
      (let v1 :: T_MaxOperator_128
v1 = T_MaxOperator_128
d_'8852''45'operator_6456 in
       Any -> Any
forall a b. a -> b
coe
         ((T_TotalPreorder_222 -> T_MinOperator_98 -> T_Semilattice_10)
-> Any -> Any -> Any
forall a b. a -> b
coe
            T_TotalPreorder_222 -> T_MinOperator_98 -> T_Semilattice_10
MAlonzo.Code.Algebra.Lattice.Construct.NaturalChoice.MinOp.du_'8851''45'semilattice_604
            ((T_TotalPreorder_222 -> T_TotalPreorder_222) -> Any -> Any
forall a b. a -> b
coe
               T_TotalPreorder_222 -> T_TotalPreorder_222
MAlonzo.Code.Relation.Binary.Construct.Flip.EqAndOrd.du_totalPreorder_746
               (T_TotalPreorder_222 -> Any
forall a b. a -> b
coe T_TotalPreorder_222
v0))
            ((T_MaxOperator_128 -> T_MinOperator_98) -> Any -> Any
forall a b. a -> b
coe
               T_MaxOperator_128 -> T_MinOperator_98
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.du_MaxOp'8658'MinOp_174
               (T_MaxOperator_128 -> Any
forall a b. a -> b
coe T_MaxOperator_128
v1))))
-- Data.Integer.Properties.⊓-⊔-latticeProperties.⊔-⊓-distributiveLattice
d_'8852''45''8851''45'distributiveLattice_6662 ::
  MAlonzo.Code.Algebra.Lattice.Bundles.T_DistributiveLattice_584
d_'8852''45''8851''45'distributiveLattice_6662 :: T_DistributiveLattice_584
d_'8852''45''8851''45'distributiveLattice_6662
  = (T_TotalPreorder_222
 -> T_MinOperator_98
 -> T_MaxOperator_128
 -> T_DistributiveLattice_584)
-> Any -> Any -> Any -> T_DistributiveLattice_584
forall a b. a -> b
coe
      T_TotalPreorder_222
-> T_MinOperator_98
-> T_MaxOperator_128
-> T_DistributiveLattice_584
MAlonzo.Code.Algebra.Lattice.Construct.NaturalChoice.MinMaxOp.du_'8852''45''8851''45'distributiveLattice_806
      (T_TotalPreorder_222 -> Any
forall a b. a -> b
coe T_TotalPreorder_222
d_'8804''45'totalPreorder_2812)
      (T_MinOperator_98 -> Any
forall a b. a -> b
coe T_MinOperator_98
d_'8851''45'operator_6454) (T_MaxOperator_128 -> Any
forall a b. a -> b
coe T_MaxOperator_128
d_'8852''45'operator_6456)
-- Data.Integer.Properties.⊓-⊔-latticeProperties.⊔-⊓-isDistributiveLattice
d_'8852''45''8851''45'isDistributiveLattice_6664 ::
  MAlonzo.Code.Algebra.Lattice.Structures.T_IsDistributiveLattice_3036
d_'8852''45''8851''45'isDistributiveLattice_6664 :: T_IsDistributiveLattice_3036
d_'8852''45''8851''45'isDistributiveLattice_6664
  = (T_TotalPreorder_222
 -> T_MinOperator_98
 -> T_MaxOperator_128
 -> T_IsDistributiveLattice_3036)
-> Any -> Any -> Any -> T_IsDistributiveLattice_3036
forall a b. a -> b
coe
      T_TotalPreorder_222
-> T_MinOperator_98
-> T_MaxOperator_128
-> T_IsDistributiveLattice_3036
MAlonzo.Code.Algebra.Lattice.Construct.NaturalChoice.MinMaxOp.du_'8852''45''8851''45'isDistributiveLattice_800
      (T_TotalPreorder_222 -> Any
forall a b. a -> b
coe T_TotalPreorder_222
d_'8804''45'totalPreorder_2812)
      (T_MinOperator_98 -> Any
forall a b. a -> b
coe T_MinOperator_98
d_'8851''45'operator_6454) (T_MaxOperator_128 -> Any
forall a b. a -> b
coe T_MaxOperator_128
d_'8852''45'operator_6456)
-- Data.Integer.Properties.⊓-⊔-latticeProperties.⊔-⊓-isLattice
d_'8852''45''8851''45'isLattice_6666 ::
  MAlonzo.Code.Algebra.Lattice.Structures.T_IsLattice_2962
d_'8852''45''8851''45'isLattice_6666 :: T_IsLattice_2962
d_'8852''45''8851''45'isLattice_6666
  = (T_TotalPreorder_222
 -> T_MinOperator_98 -> T_MaxOperator_128 -> T_IsLattice_2962)
-> Any -> Any -> Any -> T_IsLattice_2962
forall a b. a -> b
coe
      T_TotalPreorder_222
-> T_MinOperator_98 -> T_MaxOperator_128 -> T_IsLattice_2962
MAlonzo.Code.Algebra.Lattice.Construct.NaturalChoice.MinMaxOp.du_'8852''45''8851''45'isLattice_794
      (T_TotalPreorder_222 -> Any
forall a b. a -> b
coe T_TotalPreorder_222
d_'8804''45'totalPreorder_2812)
      (T_MinOperator_98 -> Any
forall a b. a -> b
coe T_MinOperator_98
d_'8851''45'operator_6454) (T_MaxOperator_128 -> Any
forall a b. a -> b
coe T_MaxOperator_128
d_'8852''45'operator_6456)
-- Data.Integer.Properties.⊓-⊔-latticeProperties.⊔-⊓-lattice
d_'8852''45''8851''45'lattice_6668 ::
  MAlonzo.Code.Algebra.Lattice.Bundles.T_Lattice_500
d_'8852''45''8851''45'lattice_6668 :: T_Lattice_500
d_'8852''45''8851''45'lattice_6668
  = (T_TotalPreorder_222
 -> T_MinOperator_98 -> T_MaxOperator_128 -> T_Lattice_500)
-> Any -> Any -> Any -> T_Lattice_500
forall a b. a -> b
coe
      T_TotalPreorder_222
-> T_MinOperator_98 -> T_MaxOperator_128 -> T_Lattice_500
MAlonzo.Code.Algebra.Lattice.Construct.NaturalChoice.MinMaxOp.du_'8852''45''8851''45'lattice_802
      (T_TotalPreorder_222 -> Any
forall a b. a -> b
coe T_TotalPreorder_222
d_'8804''45'totalPreorder_2812)
      (T_MinOperator_98 -> Any
forall a b. a -> b
coe T_MinOperator_98
d_'8851''45'operator_6454) (T_MaxOperator_128 -> Any
forall a b. a -> b
coe T_MaxOperator_128
d_'8852''45'operator_6456)
-- Data.Integer.Properties.mono-≤-distrib-⊔
d_mono'45''8804''45'distrib'45''8852'_6676 ::
  (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'_6676 :: (Integer -> Integer)
-> (Integer -> Integer -> T__'8804'__26 -> T__'8804'__26)
-> Integer
-> Integer
-> T__'8801'__12
d_mono'45''8804''45'distrib'45''8852'_6676 = (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'_6686 ::
  (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'_6686 :: (Integer -> Integer)
-> (Integer -> Integer -> T__'8804'__26 -> T__'8804'__26)
-> Integer
-> Integer
-> T__'8801'__12
d_mono'45''8804''45'distrib'45''8851'_6686 = (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'_6696 ::
  (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'_6696 :: (Integer -> Integer)
-> (Integer -> Integer -> T__'8804'__26 -> T__'8804'__26)
-> Integer
-> Integer
-> T__'8801'__12
d_antimono'45''8804''45'distrib'45''8851'_6696 = (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'_6706 ::
  (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'_6706 :: (Integer -> Integer)
-> (Integer -> Integer -> T__'8804'__26 -> T__'8804'__26)
-> Integer
-> Integer
-> T__'8801'__12
d_antimono'45''8804''45'distrib'45''8852'_6706 = (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'_6716 ::
  (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'_6716 :: (Integer -> Integer)
-> (Integer -> Integer -> T__'60'__50 -> T__'60'__50)
-> Integer
-> Integer
-> T__'8801'__12
d_mono'45''60''45'distrib'45''8851'_6716 = (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'_6764 ::
  (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'_6764 :: (Integer -> Integer)
-> (Integer -> Integer -> T__'60'__50 -> T__'60'__50)
-> Integer
-> Integer
-> T__'8801'__12
d_mono'45''60''45'distrib'45''8852'_6764 = (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'_6812 ::
  (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'_6812 :: (Integer -> Integer)
-> (Integer -> Integer -> T__'60'__50 -> T__'60'__50)
-> Integer
-> Integer
-> T__'8801'__12
d_antimono'45''60''45'distrib'45''8852'_6812 = (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'_6860 ::
  (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'_6860 :: (Integer -> Integer)
-> (Integer -> Integer -> T__'60'__50 -> T__'60'__50)
-> Integer
-> Integer
-> T__'8801'__12
d_antimono'45''60''45'distrib'45''8851'_6860 = (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'_6906 ::
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_neg'45'distrib'45''8852''45''8851'_6906 :: Integer -> Integer -> T__'8801'__12
d_neg'45'distrib'45''8852''45''8851'_6906 = Integer -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.neg-distrib-⊓-⊔
d_neg'45'distrib'45''8851''45''8852'_6912 ::
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_neg'45'distrib'45''8851''45''8852'_6912 :: Integer -> Integer -> T__'8801'__12
d_neg'45'distrib'45''8851''45''8852'_6912 = Integer -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.*-distribˡ-⊓-nonNeg
d_'42''45'distrib'737''45''8851''45'nonNeg_6922 ::
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Integer.Base.T_NonNegative_144 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'42''45'distrib'737''45''8851''45'nonNeg_6922 :: Integer -> Integer -> Integer -> T_NonNegative_144 -> T__'8801'__12
d_'42''45'distrib'737''45''8851''45'nonNeg_6922 = Integer -> Integer -> Integer -> T_NonNegative_144 -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.*-distribʳ-⊓-nonNeg
d_'42''45'distrib'691''45''8851''45'nonNeg_6938 ::
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Integer.Base.T_NonNegative_144 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'42''45'distrib'691''45''8851''45'nonNeg_6938 :: Integer -> Integer -> Integer -> T_NonNegative_144 -> T__'8801'__12
d_'42''45'distrib'691''45''8851''45'nonNeg_6938 = Integer -> Integer -> Integer -> T_NonNegative_144 -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.*-distribˡ-⊓-nonPos
d_'42''45'distrib'737''45''8851''45'nonPos_6954 ::
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Integer.Base.T_NonPositive_154 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'42''45'distrib'737''45''8851''45'nonPos_6954 :: Integer -> Integer -> Integer -> T_NonPositive_154 -> T__'8801'__12
d_'42''45'distrib'737''45''8851''45'nonPos_6954 = Integer -> Integer -> Integer -> T_NonPositive_154 -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.*-distribʳ-⊓-nonPos
d_'42''45'distrib'691''45''8851''45'nonPos_6970 ::
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Integer.Base.T_NonPositive_154 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'42''45'distrib'691''45''8851''45'nonPos_6970 :: Integer -> Integer -> Integer -> T_NonPositive_154 -> T__'8801'__12
d_'42''45'distrib'691''45''8851''45'nonPos_6970 = Integer -> Integer -> Integer -> T_NonPositive_154 -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.*-distribˡ-⊔-nonNeg
d_'42''45'distrib'737''45''8852''45'nonNeg_6986 ::
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Integer.Base.T_NonNegative_144 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'42''45'distrib'737''45''8852''45'nonNeg_6986 :: Integer -> Integer -> Integer -> T_NonNegative_144 -> T__'8801'__12
d_'42''45'distrib'737''45''8852''45'nonNeg_6986 = Integer -> Integer -> Integer -> T_NonNegative_144 -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.*-distribʳ-⊔-nonNeg
d_'42''45'distrib'691''45''8852''45'nonNeg_7002 ::
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Integer.Base.T_NonNegative_144 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'42''45'distrib'691''45''8852''45'nonNeg_7002 :: Integer -> Integer -> Integer -> T_NonNegative_144 -> T__'8801'__12
d_'42''45'distrib'691''45''8852''45'nonNeg_7002 = Integer -> Integer -> Integer -> T_NonNegative_144 -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.*-distribˡ-⊔-nonPos
d_'42''45'distrib'737''45''8852''45'nonPos_7018 ::
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Integer.Base.T_NonPositive_154 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'42''45'distrib'737''45''8852''45'nonPos_7018 :: Integer -> Integer -> Integer -> T_NonPositive_154 -> T__'8801'__12
d_'42''45'distrib'737''45''8852''45'nonPos_7018 = Integer -> Integer -> Integer -> T_NonPositive_154 -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.*-distribʳ-⊔-nonPos
d_'42''45'distrib'691''45''8852''45'nonPos_7034 ::
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Integer.Base.T_NonPositive_154 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'42''45'distrib'691''45''8852''45'nonPos_7034 :: Integer -> Integer -> Integer -> T_NonPositive_154 -> T__'8801'__12
d_'42''45'distrib'691''45''8852''45'nonPos_7034 = Integer -> Integer -> Integer -> T_NonPositive_154 -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.neg-mono-<->
d_neg'45'mono'45''60''45''62'_7042 ::
  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'_7042 :: Integer -> Integer -> T__'60'__50 -> T__'60'__50
d_neg'45'mono'45''60''45''62'_7042 = (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'_3302
-- Data.Integer.Properties.neg-mono-≤-≥
d_neg'45'mono'45''8804''45''8805'_7044 ::
  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'_7044 :: Integer -> Integer -> T__'8804'__26 -> T__'8804'__26
d_neg'45'mono'45''8804''45''8805'_7044 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'_3272 Integer
v1 T__'8804'__26
v2
-- Data.Integer.Properties.*-monoʳ-≤-non-neg
d_'42''45'mono'691''45''8804''45'non'45'neg_7046 ::
  Integer ->
  MAlonzo.Code.Data.Integer.Base.T_NonNegative_144 ->
  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_7046 :: Integer
-> T_NonNegative_144
-> Integer
-> Integer
-> T__'8804'__26
-> T__'8804'__26
d_'42''45'mono'691''45''8804''45'non'45'neg_7046 Integer
v0 T_NonNegative_144
v1 Integer
v2 Integer
v3 T__'8804'__26
v4
  = (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
du_'42''45'mono'691''45''8804''45'nonNeg_6054 Integer
v0 Integer
v2 Integer
v3 T__'8804'__26
v4
-- Data.Integer.Properties.*-monoˡ-≤-non-neg
d_'42''45'mono'737''45''8804''45'non'45'neg_7048 ::
  Integer ->
  MAlonzo.Code.Data.Integer.Base.T_NonNegative_144 ->
  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_7048 :: Integer
-> T_NonNegative_144
-> Integer
-> Integer
-> T__'8804'__26
-> T__'8804'__26
d_'42''45'mono'737''45''8804''45'non'45'neg_7048 Integer
v0 T_NonNegative_144
v1 Integer
v2 Integer
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
du_'42''45'mono'737''45''8804''45'nonNeg_6096 Integer
v0 Integer
v2 Integer
v3
-- Data.Integer.Properties.*-cancelˡ-<-non-neg
d_'42''45'cancel'737''45''60''45'non'45'neg_7050 ::
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Integer.Base.T_NonNegative_144 ->
  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_7050 :: Integer
-> Integer
-> Integer
-> T_NonNegative_144
-> T__'60'__50
-> T__'60'__50
d_'42''45'cancel'737''45''60''45'non'45'neg_7050 Integer
v0 Integer
v1 Integer
v2 T_NonNegative_144
v3 T__'60'__50
v4
  = (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
du_'42''45'cancel'737''45''60''45'nonNeg_6266 Integer
v0 Integer
v1 Integer
v2 T__'60'__50
v4
-- Data.Integer.Properties.*-cancelʳ-<-non-neg
d_'42''45'cancel'691''45''60''45'non'45'neg_7052 ::
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Integer.Base.T_NonNegative_144 ->
  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_7052 :: Integer
-> Integer
-> Integer
-> T_NonNegative_144
-> T__'60'__50
-> T__'60'__50
d_'42''45'cancel'691''45''60''45'non'45'neg_7052 Integer
v0 Integer
v1 Integer
v2 T_NonNegative_144
v3
  = (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
du_'42''45'cancel'691''45''60''45'nonNeg_6304 Integer
v0 Integer
v1 Integer
v2
-- Data.Integer.Properties.m≤n⇒m⊓n≡m
d_m'8804'n'8658'm'8851'n'8801'm_7054 ::
  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_7054 :: Integer -> Integer -> T__'8804'__26 -> T__'8801'__12
d_m'8804'n'8658'm'8851'n'8801'm_7054 = 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_7056 ::
  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_7056 :: Integer -> Integer -> T__'8801'__12 -> T__'8804'__26
d_m'8851'n'8801'm'8658'm'8804'n_7056
  = let v0 :: T_TotalPreorder_222
v0 = T_TotalPreorder_222
d_'8804''45'totalPreorder_2812 in
    Any -> Integer -> Integer -> T__'8801'__12 -> T__'8804'__26
forall a b. a -> b
coe
      (let v1 :: T_MinOperator_98
v1 = T_MinOperator_98
d_'8851''45'operator_6454 in
       Any -> Any
forall a b. a -> b
coe
         ((T_TotalPreorder_222
 -> T_MinOperator_98 -> Any -> Any -> Any -> Any)
-> Any -> Any -> Any
forall a b. a -> b
coe
            T_TotalPreorder_222 -> T_MinOperator_98 -> Any -> Any -> Any -> Any
MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_x'8851'y'8776'x'8658'x'8804'y_3068
            (T_TotalPreorder_222 -> Any
forall a b. a -> b
coe T_TotalPreorder_222
v0) (T_MinOperator_98 -> Any
forall a b. a -> b
coe T_MinOperator_98
v1)))
-- Data.Integer.Properties.m≥n⇒m⊓n≡n
d_m'8805'n'8658'm'8851'n'8801'n_7058 ::
  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_7058 :: Integer -> Integer -> T__'8804'__26 -> T__'8801'__12
d_m'8805'n'8658'm'8851'n'8801'n_7058 = 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_7060 ::
  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_7060 :: Integer -> Integer -> T__'8801'__12 -> T__'8804'__26
d_m'8851'n'8801'n'8658'm'8805'n_7060
  = let v0 :: T_TotalPreorder_222
v0 = T_TotalPreorder_222
d_'8804''45'totalPreorder_2812 in
    Any -> Integer -> Integer -> T__'8801'__12 -> T__'8804'__26
forall a b. a -> b
coe
      (let v1 :: T_MinOperator_98
v1 = T_MinOperator_98
d_'8851''45'operator_6454 in
       Any -> Any
forall a b. a -> b
coe
         ((T_TotalPreorder_222
 -> T_MinOperator_98 -> Any -> Any -> Any -> Any)
-> Any -> Any -> Any
forall a b. a -> b
coe
            T_TotalPreorder_222 -> T_MinOperator_98 -> Any -> Any -> Any -> Any
MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_x'8851'y'8776'y'8658'y'8804'x_3100
            (T_TotalPreorder_222 -> Any
forall a b. a -> b
coe T_TotalPreorder_222
v0) (T_MinOperator_98 -> Any
forall a b. a -> b
coe T_MinOperator_98
v1)))
-- Data.Integer.Properties.m⊓n≤n
d_m'8851'n'8804'n_7062 ::
  Integer -> Integer -> MAlonzo.Code.Data.Integer.Base.T__'8804'__26
d_m'8851'n'8804'n_7062 :: Integer -> Integer -> T__'8804'__26
d_m'8851'n'8804'n_7062
  = let v0 :: T_TotalPreorder_222
v0 = T_TotalPreorder_222
d_'8804''45'totalPreorder_2812 in
    Any -> Integer -> Integer -> T__'8804'__26
forall a b. a -> b
coe
      (let v1 :: T_MinOperator_98
v1 = T_MinOperator_98
d_'8851''45'operator_6454 in
       Any -> Any
forall a b. a -> b
coe
         ((T_TotalPreorder_222 -> T_MinOperator_98 -> Any -> Any -> Any)
-> Any -> Any -> Any
forall a b. a -> b
coe
            T_TotalPreorder_222 -> T_MinOperator_98 -> Any -> Any -> Any
MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_x'8851'y'8804'y_2834
            (T_TotalPreorder_222 -> Any
forall a b. a -> b
coe T_TotalPreorder_222
v0) (T_MinOperator_98 -> Any
forall a b. a -> b
coe T_MinOperator_98
v1)))
-- Data.Integer.Properties.m⊓n≤m
d_m'8851'n'8804'm_7064 ::
  Integer -> Integer -> MAlonzo.Code.Data.Integer.Base.T__'8804'__26
d_m'8851'n'8804'm_7064 :: Integer -> Integer -> T__'8804'__26
d_m'8851'n'8804'm_7064
  = let v0 :: T_TotalPreorder_222
v0 = T_TotalPreorder_222
d_'8804''45'totalPreorder_2812 in
    Any -> Integer -> Integer -> T__'8804'__26
forall a b. a -> b
coe
      (let v1 :: T_MinOperator_98
v1 = T_MinOperator_98
d_'8851''45'operator_6454 in
       Any -> Any
forall a b. a -> b
coe
         ((T_TotalPreorder_222 -> T_MinOperator_98 -> Any -> Any -> Any)
-> Any -> Any -> Any
forall a b. a -> b
coe
            T_TotalPreorder_222 -> T_MinOperator_98 -> Any -> Any -> Any
MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_x'8851'y'8804'x_2808
            (T_TotalPreorder_222 -> Any
forall a b. a -> b
coe T_TotalPreorder_222
v0) (T_MinOperator_98 -> Any
forall a b. a -> b
coe T_MinOperator_98
v1)))
-- Data.Integer.Properties.m≤n⇒m⊔n≡n
d_m'8804'n'8658'm'8852'n'8801'n_7066 ::
  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_7066 :: Integer -> Integer -> T__'8804'__26 -> T__'8801'__12
d_m'8804'n'8658'm'8852'n'8801'n_7066 = 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_7068 ::
  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_7068 :: Integer -> Integer -> T__'8801'__12 -> T__'8804'__26
d_m'8852'n'8801'n'8658'm'8804'n_7068
  = let v0 :: T_TotalPreorder_222
v0 = T_TotalPreorder_222
d_'8804''45'totalPreorder_2812 in
    Any -> Integer -> Integer -> T__'8801'__12 -> T__'8804'__26
forall a b. a -> b
coe
      (let v1 :: T_MaxOperator_128
v1 = T_MaxOperator_128
d_'8852''45'operator_6456 in
       Any -> Any
forall a b. a -> b
coe
         ((T_TotalPreorder_222
 -> T_MinOperator_98 -> Any -> Any -> Any -> Any)
-> Any -> Any -> Any
forall a b. a -> b
coe
            T_TotalPreorder_222 -> T_MinOperator_98 -> Any -> Any -> Any -> Any
MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_x'8851'y'8776'y'8658'y'8804'x_3100
            ((T_TotalPreorder_222 -> T_TotalPreorder_222) -> Any -> Any
forall a b. a -> b
coe
               T_TotalPreorder_222 -> T_TotalPreorder_222
MAlonzo.Code.Relation.Binary.Construct.Flip.EqAndOrd.du_totalPreorder_746
               (T_TotalPreorder_222 -> Any
forall a b. a -> b
coe T_TotalPreorder_222
v0))
            ((T_MaxOperator_128 -> T_MinOperator_98) -> Any -> Any
forall a b. a -> b
coe
               T_MaxOperator_128 -> T_MinOperator_98
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.du_MaxOp'8658'MinOp_174
               (T_MaxOperator_128 -> Any
forall a b. a -> b
coe T_MaxOperator_128
v1))))
-- Data.Integer.Properties.m≥n⇒m⊔n≡m
d_m'8805'n'8658'm'8852'n'8801'm_7070 ::
  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_7070 :: Integer -> Integer -> T__'8804'__26 -> T__'8801'__12
d_m'8805'n'8658'm'8852'n'8801'm_7070 = 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_7072 ::
  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_7072 :: Integer -> Integer -> T__'8801'__12 -> T__'8804'__26
d_m'8852'n'8801'm'8658'm'8805'n_7072
  = let v0 :: T_TotalPreorder_222
v0 = T_TotalPreorder_222
d_'8804''45'totalPreorder_2812 in
    Any -> Integer -> Integer -> T__'8801'__12 -> T__'8804'__26
forall a b. a -> b
coe
      (let v1 :: T_MaxOperator_128
v1 = T_MaxOperator_128
d_'8852''45'operator_6456 in
       Any -> Any
forall a b. a -> b
coe
         ((T_TotalPreorder_222
 -> T_MinOperator_98 -> Any -> Any -> Any -> Any)
-> Any -> Any -> Any
forall a b. a -> b
coe
            T_TotalPreorder_222 -> T_MinOperator_98 -> Any -> Any -> Any -> Any
MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_x'8851'y'8776'x'8658'x'8804'y_3068
            ((T_TotalPreorder_222 -> T_TotalPreorder_222) -> Any -> Any
forall a b. a -> b
coe
               T_TotalPreorder_222 -> T_TotalPreorder_222
MAlonzo.Code.Relation.Binary.Construct.Flip.EqAndOrd.du_totalPreorder_746
               (T_TotalPreorder_222 -> Any
forall a b. a -> b
coe T_TotalPreorder_222
v0))
            ((T_MaxOperator_128 -> T_MinOperator_98) -> Any -> Any
forall a b. a -> b
coe
               T_MaxOperator_128 -> T_MinOperator_98
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.du_MaxOp'8658'MinOp_174
               (T_MaxOperator_128 -> Any
forall a b. a -> b
coe T_MaxOperator_128
v1))))
-- Data.Integer.Properties.m≤m⊔n
d_m'8804'm'8852'n_7074 ::
  Integer -> Integer -> MAlonzo.Code.Data.Integer.Base.T__'8804'__26
d_m'8804'm'8852'n_7074 :: Integer -> Integer -> T__'8804'__26
d_m'8804'm'8852'n_7074
  = let v0 :: T_TotalPreorder_222
v0 = T_TotalPreorder_222
d_'8804''45'totalPreorder_2812 in
    Any -> Integer -> Integer -> T__'8804'__26
forall a b. a -> b
coe
      (let v1 :: T_MaxOperator_128
v1 = T_MaxOperator_128
d_'8852''45'operator_6456 in
       Any -> Any
forall a b. a -> b
coe
         ((T_TotalPreorder_222 -> T_MinOperator_98 -> Any -> Any -> Any)
-> Any -> Any -> Any
forall a b. a -> b
coe
            T_TotalPreorder_222 -> T_MinOperator_98 -> Any -> Any -> Any
MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_x'8851'y'8804'x_2808
            ((T_TotalPreorder_222 -> T_TotalPreorder_222) -> Any -> Any
forall a b. a -> b
coe
               T_TotalPreorder_222 -> T_TotalPreorder_222
MAlonzo.Code.Relation.Binary.Construct.Flip.EqAndOrd.du_totalPreorder_746
               (T_TotalPreorder_222 -> Any
forall a b. a -> b
coe T_TotalPreorder_222
v0))
            ((T_MaxOperator_128 -> T_MinOperator_98) -> Any -> Any
forall a b. a -> b
coe
               T_MaxOperator_128 -> T_MinOperator_98
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.du_MaxOp'8658'MinOp_174
               (T_MaxOperator_128 -> Any
forall a b. a -> b
coe T_MaxOperator_128
v1))))
-- Data.Integer.Properties.n≤m⊔n
d_n'8804'm'8852'n_7076 ::
  Integer -> Integer -> MAlonzo.Code.Data.Integer.Base.T__'8804'__26
d_n'8804'm'8852'n_7076 :: Integer -> Integer -> T__'8804'__26
d_n'8804'm'8852'n_7076
  = let v0 :: T_TotalPreorder_222
v0 = T_TotalPreorder_222
d_'8804''45'totalPreorder_2812 in
    Any -> Integer -> Integer -> T__'8804'__26
forall a b. a -> b
coe
      (let v1 :: T_MaxOperator_128
v1 = T_MaxOperator_128
d_'8852''45'operator_6456 in
       Any -> Any
forall a b. a -> b
coe
         ((T_TotalPreorder_222 -> T_MinOperator_98 -> Any -> Any -> Any)
-> Any -> Any -> Any
forall a b. a -> b
coe
            T_TotalPreorder_222 -> T_MinOperator_98 -> Any -> Any -> Any
MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_x'8851'y'8804'y_2834
            ((T_TotalPreorder_222 -> T_TotalPreorder_222) -> Any -> Any
forall a b. a -> b
coe
               T_TotalPreorder_222 -> T_TotalPreorder_222
MAlonzo.Code.Relation.Binary.Construct.Flip.EqAndOrd.du_totalPreorder_746
               (T_TotalPreorder_222 -> Any
forall a b. a -> b
coe T_TotalPreorder_222
v0))
            ((T_MaxOperator_128 -> T_MinOperator_98) -> Any -> Any
forall a b. a -> b
coe
               T_MaxOperator_128 -> T_MinOperator_98
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.du_MaxOp'8658'MinOp_174
               (T_MaxOperator_128 -> Any
forall a b. a -> b
coe T_MaxOperator_128
v1))))
-- Data.Integer.Properties.+-pos-monoʳ-≤
d_'43''45'pos'45'mono'691''45''8804'_7080 ::
  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'_7080 :: Integer -> Integer -> Integer -> T__'8804'__26 -> T__'8804'__26
d_'43''45'pos'45'mono'691''45''8804'_7080 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'__22
v6
        -> (Integer -> Integer -> Integer -> T__'8804'__22 -> T__'8804'__26)
-> Any -> Any -> Any -> Any -> T__'8804'__26
forall a b. a -> b
coe
             Integer -> Integer -> Integer -> T__'8804'__22 -> T__'8804'__26
d_'8854''45'mono'691''45''8805''45''8804'_4024 (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'__22 -> T__'8804'__22) -> T__'8804'__22 -> Any
forall a b. a -> b
coe T__'8804'__22 -> T__'8804'__22
MAlonzo.Code.Data.Nat.Base.C_s'8804's_34 T__'8804'__22
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_2730
             ((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_3912 (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'__22 -> T__'8804'__26) -> Any -> Any
forall a b. a -> b
coe
                T__'8804'__22 -> T__'8804'__26
MAlonzo.Code.Data.Integer.Base.C_'43''8804''43'_48
                ((Integer -> T__'8804'__22) -> Any -> Any
forall a b. a -> b
coe
                   Integer -> T__'8804'__22
MAlonzo.Code.Data.Nat.Properties.du_m'8804'm'43'n_3482 (Integer -> Any
forall a b. a -> b
coe Integer
v0)))
      MAlonzo.Code.Data.Integer.Base.C_'43''8804''43'_48 T__'8804'__22
v6
        -> (T__'8804'__22 -> T__'8804'__26) -> Any -> T__'8804'__26
forall a b. a -> b
coe
             T__'8804'__22 -> T__'8804'__26
MAlonzo.Code.Data.Integer.Base.C_'43''8804''43'_48
             ((Integer -> Integer -> T__'8804'__22 -> T__'8804'__22)
-> Any -> Any -> Any -> Any
forall a b. a -> b
coe
                Integer -> Integer -> T__'8804'__22 -> T__'8804'__22
MAlonzo.Code.Data.Nat.Properties.du_'43''45'mono'691''45''8804'_3554
                (Integer -> Any
forall a b. a -> b
coe Integer
v0) (Integer -> Any
forall a b. a -> b
coe Integer
v2) (T__'8804'__22 -> Any
forall a b. a -> b
coe T__'8804'__22
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'_7096 ::
  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'_7096 :: Integer -> Integer -> Integer -> T__'8804'__26 -> T__'8804'__26
d_'43''45'neg'45'mono'691''45''8804'_7096 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'__22
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'__22 -> T__'8804'__26) -> Any -> Any
forall a b. a -> b
coe
                T__'8804'__22 -> T__'8804'__26
MAlonzo.Code.Data.Integer.Base.C_'45''8804''45'_34
                ((Integer -> Integer -> T__'8804'__22 -> T__'8804'__22)
-> Any -> Any -> Any -> Any
forall a b. a -> b
coe
                   Integer -> Integer -> T__'8804'__22 -> T__'8804'__22
MAlonzo.Code.Data.Nat.Properties.du_'43''45'mono'691''45''8804'_3554
                   ((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'__22 -> Any
forall a b. a -> b
coe T__'8804'__22
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_2730
             ((T__'8804'__22 -> T__'8804'__26) -> Any -> Any
forall a b. a -> b
coe
                T__'8804'__22 -> T__'8804'__26
MAlonzo.Code.Data.Integer.Base.C_'45''8804''45'_34
                ((Integer -> T__'8804'__22) -> Any -> Any
forall a b. a -> b
coe
                   Integer -> T__'8804'__22
MAlonzo.Code.Data.Nat.Properties.du_m'8804'm'43'n_3482
                   ((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_3992
                ((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'__22
v6
        -> (Integer -> Integer -> Integer -> T__'8804'__22 -> T__'8804'__26)
-> Any -> Any -> Any -> Any -> T__'8804'__26
forall a b. a -> b
coe
             Integer -> Integer -> Integer -> T__'8804'__22 -> T__'8804'__26
d_'8854''45'mono'737''45''8804'_4056
             ((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'__22 -> Any
forall a b. a -> b
coe T__'8804'__22
v6)
      T__'8804'__26
_ -> T__'8804'__26
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Data.Integer.Properties.n≮n
d_n'8814'n_7110 ::
  Integer ->
  MAlonzo.Code.Data.Integer.Base.T__'60'__50 ->
  MAlonzo.Code.Data.Irrelevant.T_Irrelevant_20
d_n'8814'n_7110 :: Integer -> T__'60'__50 -> T_Irrelevant_20
d_n'8814'n_7110 = Integer -> T__'60'__50 -> T_Irrelevant_20
forall a. a
erased
-- Data.Integer.Properties.∣n∣≡0⇒n≡0
d_'8739'n'8739''8801'0'8658'n'8801'0_7112 ::
  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_7112 :: Integer -> T__'8801'__12 -> T__'8801'__12
d_'8739'n'8739''8801'0'8658'n'8801'0_7112 = 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'_7114 ::
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8739''45'n'8739''8801''8739'n'8739'_7114 :: Integer -> T__'8801'__12
d_'8739''45'n'8739''8801''8739'n'8739'_7114 = 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_7116 ::
  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_7116 :: Integer -> T__'8804'__26 -> T__'8801'__12
d_0'8804'n'8658''43''8739'n'8739''8801'n_7116 = 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_7118 ::
  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_7118 :: Integer -> T__'8801'__12 -> T__'8804'__26
d_'43''8739'n'8739''8801'n'8658'0'8804'n_7118 Integer
v0 T__'8801'__12
v1
  = T__'8804'__26 -> T__'8804'__26
forall a b. a -> b
coe T__'8804'__26
du_'43''8739'i'8739''8801'i'8658'0'8804'i_3352
-- Data.Integer.Properties.+∣n∣≡n⊎+∣n∣≡-n
d_'43''8739'n'8739''8801'n'8846''43''8739'n'8739''8801''45'n_7120 ::
  Integer -> MAlonzo.Code.Data.Sum.Base.T__'8846'__30
d_'43''8739'n'8739''8801'n'8846''43''8739'n'8739''8801''45'n_7120 :: Integer -> T__'8846'__30
d_'43''8739'n'8739''8801'n'8846''43''8739'n'8739''8801''45'n_7120
  = (Integer -> T__'8846'__30) -> Integer -> T__'8846'__30
forall a b. a -> b
coe
      Integer -> T__'8846'__30
d_'43''8739'i'8739''8801'i'8846''43''8739'i'8739''8801''45'i_3358
-- Data.Integer.Properties.∣m+n∣≤∣m∣+∣n∣
d_'8739'm'43'n'8739''8804''8739'm'8739''43''8739'n'8739'_7122 ::
  Integer -> Integer -> MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_'8739'm'43'n'8739''8804''8739'm'8739''43''8739'n'8739'_7122 :: Integer -> Integer -> T__'8804'__22
d_'8739'm'43'n'8739''8804''8739'm'8739''43''8739'n'8739'_7122
  = (Integer -> Integer -> T__'8804'__22)
-> Integer -> Integer -> T__'8804'__22
forall a b. a -> b
coe Integer -> Integer -> T__'8804'__22
d_'8739'i'43'j'8739''8804''8739'i'8739''43''8739'j'8739'_3398
-- Data.Integer.Properties.∣m-n∣≤∣m∣+∣n∣
d_'8739'm'45'n'8739''8804''8739'm'8739''43''8739'n'8739'_7124 ::
  Integer -> Integer -> MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_'8739'm'45'n'8739''8804''8739'm'8739''43''8739'n'8739'_7124 :: Integer -> Integer -> T__'8804'__22
d_'8739'm'45'n'8739''8804''8739'm'8739''43''8739'n'8739'_7124
  = (Integer -> Integer -> T__'8804'__22)
-> Integer -> Integer -> T__'8804'__22
forall a b. a -> b
coe Integer -> Integer -> T__'8804'__22
d_'8739'i'45'j'8739''8804''8739'i'8739''43''8739'j'8739'_3436
-- Data.Integer.Properties.signₙ◃∣n∣≡n
d_sign'8345''9667''8739'n'8739''8801'n_7126 ::
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_sign'8345''9667''8739'n'8739''8801'n_7126 :: Integer -> T__'8801'__12
d_sign'8345''9667''8739'n'8739''8801'n_7126 = Integer -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.◃-≡
d_'9667''45''8801'_7128 ::
  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'_7128 :: Integer
-> Integer -> T__'8801'__12 -> T__'8801'__12 -> T__'8801'__12
d_'9667''45''8801'_7128 = Integer
-> Integer -> T__'8801'__12 -> T__'8801'__12 -> 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'_7130 ::
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8739'm'45'n'8739''8801''8739'n'45'm'8739'_7130 :: Integer -> Integer -> T__'8801'__12
d_'8739'm'45'n'8739''8801''8739'n'45'm'8739'_7130 = 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_7132 ::
  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_7132 :: Integer -> Integer -> T__'8801'__12 -> T__'8801'__12
d_m'8801'n'8658'm'45'n'8801'0_7132 = 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_7134 ::
  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_7134 :: Integer -> Integer -> T__'8801'__12 -> T__'8801'__12
d_m'45'n'8801'0'8658'm'8801'n_7134 = Integer -> Integer -> T__'8801'__12 -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.≤-steps
d_'8804''45'steps_7136 ::
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Integer.Base.T_NonNegative_144 ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26 ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26
d_'8804''45'steps_7136 :: Integer
-> Integer
-> Integer
-> T_NonNegative_144
-> T__'8804'__26
-> T__'8804'__26
d_'8804''45'steps_7136 Integer
v0 Integer
v1 Integer
v2 T_NonNegative_144
v3 T__'8804'__26
v4
  = (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
du_i'8804'j'8658'i'8804'k'43'j_4578 Integer
v0 Integer
v1 Integer
v2 T__'8804'__26
v4
-- Data.Integer.Properties.≤-steps-neg
d_'8804''45'steps'45'neg_7138 ::
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Integer.Base.T_NonNegative_144 ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26 ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26
d_'8804''45'steps'45'neg_7138 :: Integer
-> Integer
-> Integer
-> T_NonNegative_144
-> T__'8804'__26
-> T__'8804'__26
d_'8804''45'steps'45'neg_7138 Integer
v0 Integer
v1 Integer
v2 T_NonNegative_144
v3 T__'8804'__26
v4
  = (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_i'8804'j'8658'i'45'k'8804'j_4852 Integer
v0 Integer
v2 T__'8804'__26
v4
-- Data.Integer.Properties.≤-step
d_'8804''45'step_7140 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26 ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26
d_'8804''45'step_7140 :: Integer -> Integer -> T__'8804'__26 -> T__'8804'__26
d_'8804''45'step_7140 = (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
d_i'8804'j'8658'i'8804'1'43'j_4948
-- Data.Integer.Properties.≤-step-neg
d_'8804''45'step'45'neg_7142 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26 ->
  MAlonzo.Code.Data.Integer.Base.T__'8804'__26
d_'8804''45'step'45'neg_7142 :: Integer -> Integer -> T__'8804'__26 -> T__'8804'__26
d_'8804''45'step'45'neg_7142 Integer
v0 Integer
v1 T__'8804'__26
v2
  = (T__'8804'__26 -> T__'8804'__26) -> T__'8804'__26 -> T__'8804'__26
forall a b. a -> b
coe T__'8804'__26 -> T__'8804'__26
du_i'8804'j'8658'pred'91'i'93''8804'j_5116 T__'8804'__26
v2
-- Data.Integer.Properties.m≤n⇒m-n≤0
d_m'8804'n'8658'm'45'n'8804'0_7144 ::
  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_7144 :: Integer -> Integer -> T__'8804'__26 -> T__'8804'__26
d_m'8804'n'8658'm'45'n'8804'0_7144
  = (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
d_i'8804'j'8658'i'45'j'8804'0_4886
-- Data.Integer.Properties.m-n≤0⇒m≤n
d_m'45'n'8804'0'8658'm'8804'n_7146 ::
  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_7146 :: Integer -> Integer -> T__'8804'__26 -> T__'8804'__26
d_m'45'n'8804'0'8658'm'8804'n_7146
  = (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
d_i'45'j'8804'0'8658'i'8804'j_4912
-- Data.Integer.Properties.m≤n⇒0≤n-m
d_m'8804'n'8658'0'8804'n'45'm_7148 ::
  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_7148 :: Integer -> Integer -> T__'8804'__26 -> T__'8804'__26
d_m'8804'n'8658'0'8804'n'45'm_7148
  = (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
d_i'8804'j'8658'0'8804'j'45'i_4924
-- Data.Integer.Properties.0≤n-m⇒m≤n
d_0'8804'n'45'm'8658'm'8804'n_7150 ::
  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_7150 :: Integer -> Integer -> T__'8804'__26 -> T__'8804'__26
d_0'8804'n'45'm'8658'm'8804'n_7150
  = (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
d_0'8804'i'45'j'8658'j'8804'i_4936
-- Data.Integer.Properties.n≤1+n
d_n'8804'1'43'n_7152 ::
  Integer -> MAlonzo.Code.Data.Integer.Base.T__'8804'__26
d_n'8804'1'43'n_7152 :: Integer -> T__'8804'__26
d_n'8804'1'43'n_7152 = (Integer -> T__'8804'__26) -> Integer -> T__'8804'__26
forall a b. a -> b
coe Integer -> T__'8804'__26
d_i'8804'suc'91'i'93'_4952
-- Data.Integer.Properties.n≢1+n
d_n'8802'1'43'n_7154 ::
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Data.Irrelevant.T_Irrelevant_20
d_n'8802'1'43'n_7154 :: Integer -> T__'8801'__12 -> T_Irrelevant_20
d_n'8802'1'43'n_7154 = Integer -> T__'8801'__12 -> T_Irrelevant_20
forall a. a
erased
-- Data.Integer.Properties.m≤pred[n]⇒m<n
d_m'8804'pred'91'n'93''8658'm'60'n_7156 ::
  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_7156 :: Integer -> Integer -> T__'8804'__26 -> T__'60'__50
d_m'8804'pred'91'n'93''8658'm'60'n_7156 Integer
v0 Integer
v1 T__'8804'__26
v2
  = (Integer -> T__'8804'__26 -> T__'60'__50)
-> Integer -> T__'8804'__26 -> T__'60'__50
forall a b. a -> b
coe Integer -> T__'8804'__26 -> T__'60'__50
du_i'8804'pred'91'j'93''8658'i'60'j_5094 Integer
v1 T__'8804'__26
v2
-- Data.Integer.Properties.m<n⇒m≤pred[n]
d_m'60'n'8658'm'8804'pred'91'n'93'_7158 ::
  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'_7158 :: Integer -> Integer -> T__'60'__50 -> T__'8804'__26
d_m'60'n'8658'm'8804'pred'91'n'93'_7158 Integer
v0 Integer
v1 T__'60'__50
v2
  = (Integer -> T__'60'__50 -> T__'8804'__26)
-> Integer -> T__'60'__50 -> T__'8804'__26
forall a b. a -> b
coe Integer -> T__'60'__50 -> T__'8804'__26
du_i'60'j'8658'i'8804'pred'91'j'93'_5104 Integer
v1 T__'60'__50
v2
-- Data.Integer.Properties.-1*n≡-n
d_'45'1'42'n'8801''45'n_7160 ::
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'45'1'42'n'8801''45'n_7160 :: Integer -> T__'8801'__12
d_'45'1'42'n'8801''45'n_7160 = 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_7162 ::
  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_7162 :: Integer -> Integer -> T__'8801'__12 -> T__'8846'__30
d_m'42'n'8801'0'8658'm'8801'0'8744'n'8801'0_7162 Integer
v0 Integer
v1 T__'8801'__12
v2
  = (Integer -> T__'8846'__30) -> Integer -> T__'8846'__30
forall a b. a -> b
coe Integer -> T__'8846'__30
du_i'42'j'8801'0'8658'i'8801'0'8744'j'8801'0_5780 Integer
v0
-- Data.Integer.Properties.∣m*n∣≡∣m∣*∣n∣
d_'8739'm'42'n'8739''8801''8739'm'8739''42''8739'n'8739'_7164 ::
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8739'm'42'n'8739''8801''8739'm'8739''42''8739'n'8739'_7164 :: Integer -> Integer -> T__'8801'__12
d_'8739'm'42'n'8739''8801''8739'm'8739''42''8739'n'8739'_7164
  = Integer -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.n≤m+n
d_n'8804'm'43'n_7168 ::
  Integer -> Integer -> MAlonzo.Code.Data.Integer.Base.T__'8804'__26
d_n'8804'm'43'n_7168 :: Integer -> Integer -> T__'8804'__26
d_n'8804'm'43'n_7168 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
du_i'8804'j'43'i_4592 (Integer -> Any
forall a b. a -> b
coe Integer
v0) (Integer -> Any
forall a b. a -> b
coe Integer
v1)
-- Data.Integer.Properties.m≤m+n
d_m'8804'm'43'n_7176 ::
  Integer -> Integer -> MAlonzo.Code.Data.Integer.Base.T__'8804'__26
d_m'8804'm'43'n_7176 :: Integer -> Integer -> T__'8804'__26
d_m'8804'm'43'n_7176 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
du_i'8804'i'43'j_4604 (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
d_m'45'n'8804'm_7186 ::
  Integer -> Integer -> MAlonzo.Code.Data.Integer.Base.T__'8804'__26
d_m'45'n'8804'm_7186 :: Integer -> Integer -> T__'8804'__26
d_m'45'n'8804'm_7186 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
du_i'45'j'8804'i_4880 (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_7196 ::
  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_7196 :: Integer -> Integer -> Integer -> T__'8804'__26 -> T__'8804'__26
d_'42''45'mono'691''45''8804''45'pos_7196 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'nonNeg_6054
      ((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.*-monoˡ-≤-pos
d_'42''45'mono'737''45''8804''45'pos_7204 ::
  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_7204 :: Integer -> Integer -> Integer -> T__'8804'__26 -> T__'8804'__26
d_'42''45'mono'737''45''8804''45'pos_7204 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'nonNeg_6096
      ((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.*-monoˡ-≤-neg
d_'42''45'mono'737''45''8804''45'neg_7212 ::
  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_7212 :: Integer -> Integer -> Integer -> T__'8804'__26 -> T__'8804'__26
d_'42''45'mono'737''45''8804''45'neg_7212 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_6164
      ((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_7220 ::
  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_7220 :: Integer -> Integer -> Integer -> T__'8804'__26 -> T__'8804'__26
d_'42''45'mono'691''45''8804''45'neg_7220 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_6192
      ((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.pos-+-commute
d_pos'45''43''45'commute_7224 ::
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_pos'45''43''45'commute_7224 :: Integer -> Integer -> T__'8801'__12
d_pos'45''43''45'commute_7224 = Integer -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.abs-*-commute
d_abs'45''42''45'commute_7226 ::
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_abs'45''42''45'commute_7226 :: Integer -> Integer -> T__'8801'__12
d_abs'45''42''45'commute_7226 = Integer -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.pos-distrib-*
d_pos'45'distrib'45''42'_7232 ::
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_pos'45'distrib'45''42'_7232 :: Integer -> Integer -> T__'8801'__12
d_pos'45'distrib'45''42'_7232 = Integer -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Integer.Properties.+-isAbelianGroup
d_'43''45'isAbelianGroup_7238 ::
  MAlonzo.Code.Algebra.Structures.T_IsAbelianGroup_1132
d_'43''45'isAbelianGroup_7238 :: T_IsAbelianGroup_1132
d_'43''45'isAbelianGroup_7238
  = T_IsAbelianGroup_1132 -> T_IsAbelianGroup_1132
forall a b. a -> b
coe T_IsAbelianGroup_1132
d_'43''45'0'45'isAbelianGroup_4436