content: {-# 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 Data.Text qualified
  import MAlonzo.Code.Agda.Builtin.Bool qualified
  import MAlonzo.Code.Agda.Builtin.Equality qualified
  import MAlonzo.Code.Agda.Builtin.Sigma qualified
  import MAlonzo.Code.Agda.Builtin.Unit qualified
  import MAlonzo.Code.Agda.Primitive qualified
  import MAlonzo.Code.Algebra.Bundles qualified
  import MAlonzo.Code.Algebra.Construct.NaturalChoice.Base qualified
  import MAlonzo.Code.Algebra.Construct.NaturalChoice.MinMaxOp qualified
  import MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp qualified
  import MAlonzo.Code.Algebra.Lattice.Bundles qualified
  import MAlonzo.Code.Algebra.Lattice.Construct.NaturalChoice.MinMaxOp qualified
  import MAlonzo.Code.Algebra.Lattice.Construct.NaturalChoice.MinOp qualified
  import MAlonzo.Code.Algebra.Lattice.Structures qualified
  import MAlonzo.Code.Algebra.Morphism.Structures qualified
  import MAlonzo.Code.Algebra.Structures qualified
  import MAlonzo.Code.Data.Integer.Base qualified
  import MAlonzo.Code.Data.Irrelevant qualified
  import MAlonzo.Code.Data.Nat.Base qualified
  import MAlonzo.Code.Data.Nat.Properties qualified
  import MAlonzo.Code.Data.Sign.Base qualified
  import MAlonzo.Code.Data.Sum.Base qualified
  import MAlonzo.Code.Function.Base qualified
  import MAlonzo.Code.Relation.Binary.Bundles qualified
  import MAlonzo.Code.Relation.Binary.Construct.Flip.EqAndOrd qualified
  import MAlonzo.Code.Relation.Binary.Definitions qualified
  import MAlonzo.Code.Relation.Binary.Morphism.Structures qualified
  import MAlonzo.Code.Relation.Binary.PropositionalEquality.Core qualified
  import MAlonzo.Code.Relation.Binary.PropositionalEquality.Properties qualified
  import MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple qualified
  import MAlonzo.Code.Relation.Binary.Reasoning.Syntax qualified
  import MAlonzo.Code.Relation.Binary.Structures qualified
  import MAlonzo.Code.Relation.Nullary.Decidable.Core qualified
  import MAlonzo.Code.Relation.Nullary.Negation.Core qualified
  import MAlonzo.Code.Relation.Nullary.Reflects qualified
  import MAlonzo.RTE (AgdaAny, add64, addInt, coe, eq64, eqInt, erased, geqInt, lt64, ltInt, mul64,
                      mulInt, quot64, quotInt, rem64, remInt, sub64, subInt, word64FromNat,
                      word64ToNat)
  import MAlonzo.RTE qualified
  
  -- Data.Integer.Properties._._DistributesOver_
  d__DistributesOver__10 ::
    (Integer -> Integer -> Integer) ->
    (Integer -> Integer -> Integer) -> ()
  d__DistributesOver__10 = erased
  -- Data.Integer.Properties._._DistributesOverʳ_
  d__DistributesOver'691'__12 ::
    (Integer -> Integer -> Integer) ->
    (Integer -> Integer -> Integer) -> ()
  d__DistributesOver'691'__12 = erased
  -- Data.Integer.Properties._._DistributesOverˡ_
  d__DistributesOver'737'__14 ::
    (Integer -> Integer -> Integer) ->
    (Integer -> Integer -> Integer) -> ()
  d__DistributesOver'737'__14 = erased
  -- Data.Integer.Properties._.Associative
  d_Associative_30 :: (Integer -> Integer -> Integer) -> ()
  d_Associative_30 = erased
  -- Data.Integer.Properties._.Commutative
  d_Commutative_34 :: (Integer -> Integer -> Integer) -> ()
  d_Commutative_34 = erased
  -- Data.Integer.Properties._.Identity
  d_Identity_50 :: Integer -> (Integer -> Integer -> Integer) -> ()
  d_Identity_50 = erased
  -- Data.Integer.Properties._.Inverse
  d_Inverse_54 ::
    Integer ->
    (Integer -> Integer) -> (Integer -> Integer -> Integer) -> ()
  d_Inverse_54 = erased
  -- Data.Integer.Properties._.LeftIdentity
  d_LeftIdentity_76 ::
    Integer -> (Integer -> Integer -> Integer) -> ()
  d_LeftIdentity_76 = erased
  -- Data.Integer.Properties._.LeftInverse
  d_LeftInverse_78 ::
    Integer ->
    (Integer -> Integer) -> (Integer -> Integer -> Integer) -> ()
  d_LeftInverse_78 = erased
  -- Data.Integer.Properties._.LeftZero
  d_LeftZero_84 :: Integer -> (Integer -> Integer -> Integer) -> ()
  d_LeftZero_84 = erased
  -- Data.Integer.Properties._.RightIdentity
  d_RightIdentity_106 ::
    Integer -> (Integer -> Integer -> Integer) -> ()
  d_RightIdentity_106 = erased
  -- Data.Integer.Properties._.RightInverse
  d_RightInverse_108 ::
    Integer ->
    (Integer -> Integer) -> (Integer -> Integer -> Integer) -> ()
  d_RightInverse_108 = erased
  -- Data.Integer.Properties._.RightZero
  d_RightZero_114 :: Integer -> (Integer -> Integer -> Integer) -> ()
  d_RightZero_114 = erased
  -- Data.Integer.Properties._.Zero
  d_Zero_134 :: Integer -> (Integer -> Integer -> Integer) -> ()
  d_Zero_134 = erased
  -- Data.Integer.Properties._.IsAbelianGroup
  d_IsAbelianGroup_138 a0 a1 a2 = ()
  -- Data.Integer.Properties._.IsCommutativeMonoid
  d_IsCommutativeMonoid_150 a0 a1 = ()
  -- Data.Integer.Properties._.IsCommutativeRing
  d_IsCommutativeRing_152 a0 a1 a2 a3 a4 = ()
  -- Data.Integer.Properties._.IsCommutativeSemigroup
  d_IsCommutativeSemigroup_154 a0 = ()
  -- Data.Integer.Properties._.IsCommutativeSemiring
  d_IsCommutativeSemiring_156 a0 a1 a2 a3 = ()
  -- Data.Integer.Properties._.IsGroup
  d_IsGroup_162 a0 a1 a2 = ()
  -- Data.Integer.Properties._.IsMagma
  d_IsMagma_182 a0 = ()
  -- Data.Integer.Properties._.IsMonoid
  d_IsMonoid_188 a0 a1 = ()
  -- Data.Integer.Properties._.IsRing
  d_IsRing_204 a0 a1 a2 a3 a4 = ()
  -- Data.Integer.Properties._.IsSemigroup
  d_IsSemigroup_210 a0 = ()
  -- Data.Integer.Properties._.IsSemiring
  d_IsSemiring_214 a0 a1 a2 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 = 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 v0
    = coe MAlonzo.Code.Algebra.Structures.d_isGroup_1144 (coe 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 = 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 v0
    = coe MAlonzo.Code.Algebra.Structures.d_isMonoid_746 (coe 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 = 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 v0
    = coe MAlonzo.Code.Algebra.Structures.d_isRing_2812 (coe 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 = 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 v0
    = coe MAlonzo.Code.Algebra.Structures.d_isSemigroup_556 (coe 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 = 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 v0
    = coe MAlonzo.Code.Algebra.Structures.d_isSemiring_1692 (coe 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 v0
    = coe MAlonzo.Code.Algebra.Structures.d_inverse_1052 (coe 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 v0
    = coe MAlonzo.Code.Algebra.Structures.d_isMonoid_1050 (coe 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 = 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 v0
    = coe MAlonzo.Code.Algebra.Structures.d_isEquivalence_184 (coe 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 = 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 v0
    = coe MAlonzo.Code.Algebra.Structures.d_identity_698 (coe 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 v0
    = coe MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (coe 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 = 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 = 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 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_'42''45'identity_2678 (coe 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 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2672
        (coe 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 v0
    = coe MAlonzo.Code.Algebra.Structures.d_distrib_2680 (coe 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 = 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 v0
    = coe MAlonzo.Code.Algebra.Structures.d_isMagma_480 (coe 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 v0
    = coe
        MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
        (coe 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 v0
    = coe MAlonzo.Code.Algebra.Structures.d_zero_1586 (coe v0)
  -- Data.Integer.Properties.ℤtoℕ.Homomorphic₀
  d_Homomorphic'8320'_2652 ::
    (Integer -> Integer) -> Integer -> Integer -> ()
  d_Homomorphic'8320'_2652 = erased
  -- Data.Integer.Properties.ℤtoℕ.Homomorphic₁
  d_Homomorphic'8321'_2654 ::
    (Integer -> Integer) ->
    (Integer -> Integer) -> (Integer -> Integer) -> ()
  d_Homomorphic'8321'_2654 = erased
  -- Data.Integer.Properties.ℤtoℕ.Homomorphic₂
  d_Homomorphic'8322'_2656 ::
    (Integer -> Integer) ->
    (Integer -> Integer -> Integer) ->
    (Integer -> Integer -> Integer) -> ()
  d_Homomorphic'8322'_2656 = erased
  -- Data.Integer.Properties.ℤtoℕ.Morphism
  d_Morphism_2658 :: ()
  d_Morphism_2658 = erased
  -- Data.Integer.Properties.ℕtoℤ.Homomorphic₀
  d_Homomorphic'8320'_2662 ::
    (Integer -> Integer) -> Integer -> Integer -> ()
  d_Homomorphic'8320'_2662 = erased
  -- Data.Integer.Properties.ℕtoℤ.Homomorphic₁
  d_Homomorphic'8321'_2664 ::
    (Integer -> Integer) ->
    (Integer -> Integer) -> (Integer -> Integer) -> ()
  d_Homomorphic'8321'_2664 = erased
  -- Data.Integer.Properties.ℕtoℤ.Homomorphic₂
  d_Homomorphic'8322'_2666 ::
    (Integer -> Integer) ->
    (Integer -> Integer -> Integer) ->
    (Integer -> Integer -> Integer) -> ()
  d_Homomorphic'8322'_2666 = erased
  -- Data.Integer.Properties.ℕtoℤ.Morphism
  d_Morphism_2668 :: ()
  d_Morphism_2668 = 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 = 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 = 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 = erased
  -- Data.Integer.Properties._≟_
  d__'8799'__2692 ::
    Integer ->
    Integer -> MAlonzo.Code.Relation.Nullary.Decidable.Core.T_Dec_20
  d__'8799'__2692 v0 v1
    = case coe v0 of
        _ | coe geqInt (coe v0) (coe (0 :: Integer)) ->
            case coe v1 of
              _ | coe geqInt (coe v1) (coe (0 :: Integer)) ->
                  coe
                    MAlonzo.Code.Relation.Nullary.Decidable.Core.du_map'8242'_168
                    erased erased
                    (coe
                       MAlonzo.Code.Data.Nat.Properties.d__'8799'__2688 (coe v0) (coe v1))
              _ -> coe
                     MAlonzo.Code.Relation.Nullary.Decidable.Core.C__because__32
                     (coe MAlonzo.Code.Agda.Builtin.Bool.C_false_8)
                     (coe MAlonzo.Code.Relation.Nullary.Reflects.C_of'8319'_26)
        _ -> let v2 = subInt (coe (-1 :: Integer)) (coe v0) in
             coe
               (case coe v1 of
                  _ | coe geqInt (coe v1) (coe (0 :: Integer)) ->
                      coe
                        MAlonzo.Code.Relation.Nullary.Decidable.Core.C__because__32
                        (coe MAlonzo.Code.Agda.Builtin.Bool.C_false_8)
                        (coe MAlonzo.Code.Relation.Nullary.Reflects.C_of'8319'_26)
                  _ -> let v3 = subInt (coe (-1 :: Integer)) (coe v1) in
                       coe
                         (coe
                            MAlonzo.Code.Relation.Nullary.Decidable.Core.du_map'8242'_168
                            erased erased
                            (coe
                               MAlonzo.Code.Data.Nat.Properties.d__'8799'__2688 (coe v2)
                               (coe v3))))
  -- Data.Integer.Properties.≡-setoid
  d_'8801''45'setoid_2710 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
  d_'8801''45'setoid_2710
    = coe
        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
    = coe
        MAlonzo.Code.Relation.Binary.PropositionalEquality.Properties.du_decSetoid_406
        (coe 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 ~v0 ~v1 v2
    = du_drop'8255''43''8804''43'_2714 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 v0
    = case coe v0 of
        MAlonzo.Code.Data.Integer.Base.C_'43''8804''43'_48 v3 -> coe v3
        _                                                     -> 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 ~v0 ~v1 v2
    = du_drop'8255''45''8804''45'_2718 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 v0
    = case coe v0 of
        MAlonzo.Code.Data.Integer.Base.C_'45''8804''45'_34 v3 -> coe v3
        _                                                     -> 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 v0 ~v1 ~v2
    = du_'8804''45'reflexive_2722 v0
  du_'8804''45'reflexive_2722 ::
    Integer -> MAlonzo.Code.Data.Integer.Base.T__'8804'__26
  du_'8804''45'reflexive_2722 v0
    = case coe v0 of
        _ | coe geqInt (coe v0) (coe (0 :: Integer)) ->
            coe
              MAlonzo.Code.Data.Integer.Base.C_'43''8804''43'_48
              (MAlonzo.Code.Data.Nat.Properties.d_'8804''45'refl_2776 (coe v0))
        _ -> let v1 = subInt (coe (-1 :: Integer)) (coe v0) in
             coe
               (coe
                  MAlonzo.Code.Data.Integer.Base.C_'45''8804''45'_34
                  (MAlonzo.Code.Data.Nat.Properties.d_'8804''45'refl_2776 (coe v1)))
  -- Data.Integer.Properties.≤-refl
  d_'8804''45'refl_2728 ::
    Integer -> MAlonzo.Code.Data.Integer.Base.T__'8804'__26
  d_'8804''45'refl_2728 v0 = coe du_'8804''45'reflexive_2722 (coe 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 ~v0 ~v1 ~v2 v3 v4
    = du_'8804''45'trans_2730 v3 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 v0 v1
    = case coe v0 of
        MAlonzo.Code.Data.Integer.Base.C_'45''8804''45'_34 v4
          -> case coe v1 of
               MAlonzo.Code.Data.Integer.Base.C_'45''8804''45'_34 v7
                 -> coe
                      MAlonzo.Code.Data.Integer.Base.C_'45''8804''45'_34
                      (coe
                         MAlonzo.Code.Data.Nat.Properties.du_'8804''45'trans_2784 (coe v7)
                         (coe v4))
               MAlonzo.Code.Data.Integer.Base.C_'45''8804''43'_40
                 -> coe MAlonzo.Code.Data.Integer.Base.C_'45''8804''43'_40
               _ -> MAlonzo.RTE.mazUnreachableError
        MAlonzo.Code.Data.Integer.Base.C_'45''8804''43'_40
          -> coe
               seq (coe v1)
               (coe MAlonzo.Code.Data.Integer.Base.C_'45''8804''43'_40)
        MAlonzo.Code.Data.Integer.Base.C_'43''8804''43'_48 v4
          -> case coe v1 of
               MAlonzo.Code.Data.Integer.Base.C_'43''8804''43'_48 v7
                 -> coe
                      MAlonzo.Code.Data.Integer.Base.C_'43''8804''43'_48
                      (coe
                         MAlonzo.Code.Data.Nat.Properties.du_'8804''45'trans_2784 (coe v4)
                         (coe v7))
               _ -> MAlonzo.RTE.mazUnreachableError
        _ -> 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 = 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 v0 v1
    = case coe v0 of
        _ | coe geqInt (coe v0) (coe (0 :: Integer)) ->
            case coe v1 of
              _ | coe geqInt (coe v1) (coe (0 :: Integer)) ->
                  coe
                    MAlonzo.Code.Data.Sum.Base.du_map_84
                    (coe MAlonzo.Code.Data.Integer.Base.C_'43''8804''43'_48)
                    (coe MAlonzo.Code.Data.Integer.Base.C_'43''8804''43'_48)
                    (MAlonzo.Code.Data.Nat.Properties.d_'8804''45'total_2790
                       (coe v0) (coe v1))
              _ -> coe
                     MAlonzo.Code.Data.Sum.Base.C_inj'8322'_42
                     (coe MAlonzo.Code.Data.Integer.Base.C_'45''8804''43'_40)
        _ -> let v2 = subInt (coe (-1 :: Integer)) (coe v0) in
             coe
               (case coe v1 of
                  _ | coe geqInt (coe v1) (coe (0 :: Integer)) ->
                      coe
                        MAlonzo.Code.Data.Sum.Base.C_inj'8321'_38
                        (coe MAlonzo.Code.Data.Integer.Base.C_'45''8804''43'_40)
                  _ -> let v3 = subInt (coe (-1 :: Integer)) (coe v1) in
                       coe
                         (coe
                            MAlonzo.Code.Data.Sum.Base.du_map_84
                            (coe MAlonzo.Code.Data.Integer.Base.C_'45''8804''45'_34)
                            (coe MAlonzo.Code.Data.Integer.Base.C_'45''8804''45'_34)
                            (MAlonzo.Code.Data.Nat.Properties.d_'8804''45'total_2790
                               (coe v3) (coe v2))))
  -- Data.Integer.Properties._≤?_
  d__'8804''63'__2772 ::
    Integer ->
    Integer -> MAlonzo.Code.Relation.Nullary.Decidable.Core.T_Dec_20
  d__'8804''63'__2772 v0 v1
    = case coe v0 of
        _ | coe geqInt (coe v0) (coe (0 :: Integer)) ->
            case coe v1 of
              _ | coe geqInt (coe v1) (coe (0 :: Integer)) ->
                  coe
                    MAlonzo.Code.Relation.Nullary.Decidable.Core.du_map'8242'_168
                    (coe MAlonzo.Code.Data.Integer.Base.C_'43''8804''43'_48)
                    (coe du_drop'8255''43''8804''43'_2714)
                    (coe
                       MAlonzo.Code.Data.Nat.Properties.d__'8804''63'__2802 (coe v0)
                       (coe v1))
              _ -> coe
                     MAlonzo.Code.Relation.Nullary.Decidable.Core.C__because__32
                     (coe MAlonzo.Code.Agda.Builtin.Bool.C_false_8)
                     (coe MAlonzo.Code.Relation.Nullary.Reflects.C_of'8319'_26)
        _ -> let v2 = subInt (coe (-1 :: Integer)) (coe v0) in
             coe
               (case coe v1 of
                  _ | coe geqInt (coe v1) (coe (0 :: Integer)) ->
                      coe
                        MAlonzo.Code.Relation.Nullary.Decidable.Core.C__because__32
                        (coe MAlonzo.Code.Agda.Builtin.Bool.C_true_10)
                        (coe
                           MAlonzo.Code.Relation.Nullary.Reflects.C_of'696'_22
                           (coe MAlonzo.Code.Data.Integer.Base.C_'45''8804''43'_40))
                  _ -> let v3 = subInt (coe (-1 :: Integer)) (coe v1) in
                       coe
                         (coe
                            MAlonzo.Code.Relation.Nullary.Decidable.Core.du_map'8242'_168
                            (coe MAlonzo.Code.Data.Integer.Base.C_'45''8804''45'_34)
                            (coe du_drop'8255''45''8804''45'_2718)
                            (coe
                               MAlonzo.Code.Data.Nat.Properties.d__'8804''63'__2802 (coe v3)
                               (coe 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 = erased
  -- Data.Integer.Properties.≤-isPreorder
  d_'8804''45'isPreorder_2800 ::
    MAlonzo.Code.Relation.Binary.Structures.T_IsPreorder_70
  d_'8804''45'isPreorder_2800
    = coe
        MAlonzo.Code.Relation.Binary.Structures.C_IsPreorder'46'constructor_4003
        (coe
           MAlonzo.Code.Relation.Binary.PropositionalEquality.Properties.du_isEquivalence_396)
        (\ v0 v1 v2 -> coe du_'8804''45'reflexive_2722 v0)
        (\ v0 v1 v2 v3 v4 -> coe du_'8804''45'trans_2730 v3 v4)
  -- Data.Integer.Properties.≤-isTotalPreorder
  d_'8804''45'isTotalPreorder_2802 ::
    MAlonzo.Code.Relation.Binary.Structures.T_IsTotalPreorder_124
  d_'8804''45'isTotalPreorder_2802
    = coe
        MAlonzo.Code.Relation.Binary.Structures.C_IsTotalPreorder'46'constructor_8325
        (coe d_'8804''45'isPreorder_2800) (coe 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
    = coe
        MAlonzo.Code.Relation.Binary.Structures.C_IsPartialOrder'46'constructor_9853
        (coe d_'8804''45'isPreorder_2800) erased
  -- Data.Integer.Properties.≤-isTotalOrder
  d_'8804''45'isTotalOrder_2806 ::
    MAlonzo.Code.Relation.Binary.Structures.T_IsTotalOrder_404
  d_'8804''45'isTotalOrder_2806
    = coe
        MAlonzo.Code.Relation.Binary.Structures.C_IsTotalOrder'46'constructor_20555
        (coe d_'8804''45'isPartialOrder_2804) (coe 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
    = coe
        MAlonzo.Code.Relation.Binary.Structures.C_IsDecTotalOrder'46'constructor_22695
        (coe d_'8804''45'isTotalOrder_2806) (coe d__'8799'__2692)
        (coe 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
    = coe
        MAlonzo.Code.Relation.Binary.Bundles.C_Preorder'46'constructor_2267
        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
    = coe
        MAlonzo.Code.Relation.Binary.Bundles.C_TotalPreorder'46'constructor_4573
        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
    = coe
        MAlonzo.Code.Relation.Binary.Bundles.C_Poset'46'constructor_6389
        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
    = coe
        MAlonzo.Code.Relation.Binary.Bundles.C_TotalOrder'46'constructor_15747
        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
    = coe
        MAlonzo.Code.Relation.Binary.Bundles.C_DecTotalOrder'46'constructor_17849
        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 v0 v1 ~v2
    = du_'8804''7495''8658''8804'_2820 v0 v1
  du_'8804''7495''8658''8804'_2820 ::
    Integer -> Integer -> MAlonzo.Code.Data.Integer.Base.T__'8804'__26
  du_'8804''7495''8658''8804'_2820 v0 v1
    = case coe v0 of
        _ | coe geqInt (coe v0) (coe (0 :: Integer)) ->
            coe
              MAlonzo.Code.Data.Integer.Base.C_'43''8804''43'_48
              (coe
                 MAlonzo.Code.Data.Nat.Properties.du_'8804''7495''8658''8804'_2746
                 (coe v0))
        _ -> case coe v1 of
               _ | coe geqInt (coe v1) (coe (0 :: Integer)) ->
                   coe MAlonzo.Code.Data.Integer.Base.C_'45''8804''43'_40
               _ -> let v2 = subInt (coe (-1 :: Integer)) (coe v1) in
                    coe
                      (coe
                         MAlonzo.Code.Data.Integer.Base.C_'45''8804''45'_34
                         (coe
                            MAlonzo.Code.Data.Nat.Properties.du_'8804''7495''8658''8804'_2746
                            (coe 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 ~v0 ~v1 v2
    = du_'8804''8658''8804''7495'_2828 v2
  du_'8804''8658''8804''7495'_2828 ::
    MAlonzo.Code.Data.Integer.Base.T__'8804'__26 -> AgdaAny
  du_'8804''8658''8804''7495'_2828 v0
    = case coe v0 of
        MAlonzo.Code.Data.Integer.Base.C_'45''8804''45'_34 v3
          -> coe
               MAlonzo.Code.Data.Nat.Properties.du_'8804''8658''8804''7495'_2758
               (coe v3)
        MAlonzo.Code.Data.Integer.Base.C_'45''8804''43'_40
          -> coe MAlonzo.Code.Agda.Builtin.Unit.C_tt_8
        MAlonzo.Code.Data.Integer.Base.C_'43''8804''43'_48 v3
          -> coe
               MAlonzo.Code.Data.Nat.Properties.du_'8804''8658''8804''7495'_2758
               (coe v3)
        _ -> 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 ~v0 ~v1 v2
    = du_drop'8255''43''60''43'_2834 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 v0
    = case coe v0 of
        MAlonzo.Code.Data.Integer.Base.C_'43''60''43'_72 v3 -> coe v3
        _                                                   -> 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 ~v0 ~v1 v2
    = du_drop'8255''45''60''45'_2838 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 v0
    = case coe v0 of
        MAlonzo.Code.Data.Integer.Base.C_'45''60''45'_58 v3 -> coe v3
        _                                                   -> 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 = 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 = 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 ~v0 ~v1 v2 = du_'60''8658''8804'_2846 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 v0
    = case coe v0 of
        MAlonzo.Code.Data.Integer.Base.C_'45''60''45'_58 v3
          -> coe
               MAlonzo.Code.Data.Integer.Base.C_'45''8804''45'_34
               (coe
                  MAlonzo.Code.Data.Nat.Properties.du_'60''8658''8804'_2854 (coe v3))
        MAlonzo.Code.Data.Integer.Base.C_'45''60''43'_64
          -> coe MAlonzo.Code.Data.Integer.Base.C_'45''8804''43'_40
        MAlonzo.Code.Data.Integer.Base.C_'43''60''43'_72 v3
          -> coe
               MAlonzo.Code.Data.Integer.Base.C_'43''8804''43'_48
               (coe
                  MAlonzo.Code.Data.Nat.Properties.du_'60''8658''8804'_2854 (coe v3))
        _ -> 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 = 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 = 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 = 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 v0 v1 ~v2 = du_'8816''8658''62'_2874 v0 v1
  du_'8816''8658''62'_2874 ::
    Integer -> Integer -> MAlonzo.Code.Data.Integer.Base.T__'60'__50
  du_'8816''8658''62'_2874 v0 v1
    = case coe v0 of
        _ | coe geqInt (coe v0) (coe (0 :: Integer)) ->
            case coe v1 of
              _ | coe geqInt (coe v1) (coe (0 :: Integer)) ->
                  coe
                    MAlonzo.Code.Data.Integer.Base.C_'43''60''43'_72
                    (coe
                       MAlonzo.Code.Data.Nat.Properties.du_'8816''8658''62'_2888 (coe v0)
                       (coe v1))
              _ -> coe MAlonzo.Code.Data.Integer.Base.C_'45''60''43'_64
        _ -> let v2 = subInt (coe (-1 :: Integer)) (coe v0) in
             coe
               (case coe v1 of
                  _ | coe geqInt (coe v1) (coe (0 :: Integer)) ->
                      coe
                        MAlonzo.Code.Relation.Nullary.Negation.Core.du_contradiction_44
                        erased
                  _ -> let v3 = subInt (coe (-1 :: Integer)) (coe v1) in
                       coe
                         (coe
                            MAlonzo.Code.Data.Integer.Base.C_'45''60''45'_58
                            (coe
                               MAlonzo.Code.Data.Nat.Properties.du_'8816''8658''62'_2888 (coe v3)
                               (coe 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 v0 v1 ~v2
    = du_'8814''8658''8805'_2900 v0 v1
  du_'8814''8658''8805'_2900 ::
    Integer -> Integer -> MAlonzo.Code.Data.Integer.Base.T__'8804'__26
  du_'8814''8658''8805'_2900 v0 v1
    = case coe v0 of
        _ | coe geqInt (coe v0) (coe (0 :: Integer)) ->
            case coe v1 of
              _ | coe geqInt (coe v1) (coe (0 :: Integer)) ->
                  coe
                    MAlonzo.Code.Data.Integer.Base.C_'43''8804''43'_48
                    (coe
                       MAlonzo.Code.Data.Nat.Properties.du_'8814''8658''8805'_2902
                       (coe v0) (coe v1))
              _ -> coe MAlonzo.Code.Data.Integer.Base.C_'45''8804''43'_40
        _ -> let v2 = subInt (coe (-1 :: Integer)) (coe v0) in
             coe
               (case coe v1 of
                  _ | coe geqInt (coe v1) (coe (0 :: Integer)) ->
                      coe
                        MAlonzo.Code.Relation.Nullary.Negation.Core.du_contradiction_44
                        erased
                  _ -> let v3 = subInt (coe (-1 :: Integer)) (coe v1) in
                       coe
                         (coe
                            MAlonzo.Code.Data.Integer.Base.C_'45''8804''45'_34
                            (coe
                               MAlonzo.Code.Data.Nat.Properties.du_'8814''8658''8805'_2902
                               (coe v3) (coe 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 = 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 v0 v1 v2 ~v3
    = du_'8804''8743''8802''8658''60'_2928 v0 v1 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 v0 v1 v2
    = case coe v2 of
        MAlonzo.Code.Data.Integer.Base.C_'45''8804''45'_34 v5
          -> let v6 = subInt (coe (-1 :: Integer)) (coe v0) in
             coe
               (coe
                  MAlonzo.Code.Data.Integer.Base.C_'45''60''45'_58
                  (coe
                     MAlonzo.Code.Data.Nat.Properties.du_'8804''8743''8802''8658''60'_2918
                     (coe v6) (coe v5)))
        MAlonzo.Code.Data.Integer.Base.C_'45''8804''43'_40
          -> coe MAlonzo.Code.Data.Integer.Base.C_'45''60''43'_64
        MAlonzo.Code.Data.Integer.Base.C_'43''8804''43'_48 v5
          -> coe
               MAlonzo.Code.Data.Integer.Base.C_'43''60''43'_72
               (coe
                  MAlonzo.Code.Data.Nat.Properties.du_'8804''8743''8802''8658''60'_2918
                  (coe v1) (coe v5))
        _ -> 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 = 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 = 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 = 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 ~v0 ~v1 ~v2 v3 v4
    = du_'8804''45''60''45'trans_2958 v3 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 v0 v1
    = case coe v0 of
        MAlonzo.Code.Data.Integer.Base.C_'45''8804''45'_34 v4
          -> case coe v1 of
               MAlonzo.Code.Data.Integer.Base.C_'45''60''45'_58 v7
                 -> coe
                      MAlonzo.Code.Data.Integer.Base.C_'45''60''45'_58
                      (coe
                         MAlonzo.Code.Data.Nat.Properties.du_'60''45''8804''45'trans_2992
                         (coe v7) (coe v4))
               MAlonzo.Code.Data.Integer.Base.C_'45''60''43'_64
                 -> coe MAlonzo.Code.Data.Integer.Base.C_'45''60''43'_64
               _ -> MAlonzo.RTE.mazUnreachableError
        MAlonzo.Code.Data.Integer.Base.C_'45''8804''43'_40
          -> coe
               seq (coe v1) (coe MAlonzo.Code.Data.Integer.Base.C_'45''60''43'_64)
        MAlonzo.Code.Data.Integer.Base.C_'43''8804''43'_48 v4
          -> case coe v1 of
               MAlonzo.Code.Data.Integer.Base.C_'43''60''43'_72 v7
                 -> coe
                      MAlonzo.Code.Data.Integer.Base.C_'43''60''43'_72
                      (coe
                         MAlonzo.Code.Data.Nat.Properties.du_'8804''45''60''45'trans_2986
                         (coe v4) (coe v7))
               _ -> MAlonzo.RTE.mazUnreachableError
        _ -> 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 ~v0 ~v1 ~v2 v3 v4
    = du_'60''45''8804''45'trans_2972 v3 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 v0 v1
    = case coe v0 of
        MAlonzo.Code.Data.Integer.Base.C_'45''60''45'_58 v4
          -> case coe v1 of
               MAlonzo.Code.Data.Integer.Base.C_'45''8804''45'_34 v7
                 -> coe
                      MAlonzo.Code.Data.Integer.Base.C_'45''60''45'_58
                      (coe
                         MAlonzo.Code.Data.Nat.Properties.du_'8804''45''60''45'trans_2986
                         (coe v7) (coe v4))
               MAlonzo.Code.Data.Integer.Base.C_'45''8804''43'_40
                 -> coe MAlonzo.Code.Data.Integer.Base.C_'45''60''43'_64
               _ -> MAlonzo.RTE.mazUnreachableError
        MAlonzo.Code.Data.Integer.Base.C_'45''60''43'_64
          -> coe
               seq (coe v1) (coe MAlonzo.Code.Data.Integer.Base.C_'45''60''43'_64)
        MAlonzo.Code.Data.Integer.Base.C_'43''60''43'_72 v4
          -> case coe v1 of
               MAlonzo.Code.Data.Integer.Base.C_'43''8804''43'_48 v7
                 -> coe
                      MAlonzo.Code.Data.Integer.Base.C_'43''60''43'_72
                      (coe
                         MAlonzo.Code.Data.Nat.Properties.du_'60''45''8804''45'trans_2992
                         (coe v4) (coe v7))
               _ -> MAlonzo.RTE.mazUnreachableError
        _ -> 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 ~v0 ~v1 ~v2 v3 v4
    = du_'60''45'trans_2986 v3 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 v0 v1
    = coe
        du_'8804''45''60''45'trans_2958
        (coe du_'60''8658''8804'_2846 (coe v0)) (coe 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 v0 v1
    = case coe v0 of
        _ | coe geqInt (coe v0) (coe (0 :: Integer)) ->
            let v2
                  = coe
                      MAlonzo.Code.Relation.Binary.Definitions.C_tri'62'_188
                      (coe MAlonzo.Code.Data.Integer.Base.C_'45''60''43'_64) in
            coe
              (case coe v0 of
                 0 -> case coe v1 of
                        0 -> coe
                               MAlonzo.Code.Relation.Binary.Definitions.C_tri'8776'_180 erased
                        _ | coe geqInt (coe v1) (coe (1 :: Integer)) ->
                            coe
                              MAlonzo.Code.Relation.Binary.Definitions.C_tri'60'_172
                              (coe
                                 MAlonzo.Code.Data.Integer.Base.C_'43''60''43'_72
                                 (coe
                                    MAlonzo.Code.Data.Nat.Base.C_s'8804's_34
                                    (coe MAlonzo.Code.Data.Nat.Base.C_z'8804'n_26)))
                        _ -> coe v2
                 _ -> let v3 = subInt (coe v0) (coe (1 :: Integer)) in
                      coe
                        (case coe v1 of
                           0 -> coe
                                  MAlonzo.Code.Relation.Binary.Definitions.C_tri'62'_188
                                  (coe
                                     MAlonzo.Code.Data.Integer.Base.C_'43''60''43'_72
                                     (coe
                                        MAlonzo.Code.Data.Nat.Base.C_s'8804's_34
                                        (coe MAlonzo.Code.Data.Nat.Base.C_z'8804'n_26)))
                           _ | coe geqInt (coe v1) (coe (1 :: Integer)) ->
                               let v4 = subInt (coe v1) (coe (1 :: Integer)) in
                               coe
                                 (let v5
                                        = coe
                                            MAlonzo.Code.Relation.Nullary.Decidable.Core.du_map'8242'_168
                                            erased
                                            (\ v5 ->
                                               coe
                                                 MAlonzo.Code.Data.Nat.Properties.du_'8801''8658''8801''7495'_2678
                                                 (coe v3))
                                            (coe
                                               MAlonzo.Code.Relation.Nullary.Decidable.Core.C__because__32
                                               (coe eqInt (coe v0) (coe v1))
                                               (coe
                                                  MAlonzo.Code.Relation.Nullary.Reflects.d_T'45'reflects_66
                                                  (coe eqInt (coe v0) (coe v1)))) in
                                  coe
                                    (case coe v5 of
                                       MAlonzo.Code.Relation.Nullary.Decidable.Core.C__because__32 v6 v7
                                         -> if coe v6
                                              then coe
                                                     seq (coe v7)
                                                     (coe
                                                        MAlonzo.Code.Relation.Binary.Definitions.C_tri'8776'_180
                                                        erased)
                                              else (let v8
                                                          = seq
                                                              (coe v7)
                                                              (let v8 = ltInt (coe v0) (coe v1) in
                                                               coe
                                                                 (if coe v8
                                                                    then coe
                                                                           seq
                                                                           (coe
                                                                              MAlonzo.Code.Relation.Nullary.Reflects.d_T'45'reflects_66
                                                                              (coe v8))
                                                                           (coe
                                                                              MAlonzo.Code.Relation.Binary.Definitions.C_tri'60'_172
                                                                              (coe
                                                                                 MAlonzo.Code.Data.Nat.Properties.du_'60''7495''8658''60'_2716
                                                                                 (coe v3)))
                                                                    else coe
                                                                           seq
                                                                           (coe
                                                                              MAlonzo.Code.Relation.Nullary.Reflects.d_T'45'reflects_66
                                                                              (coe v8))
                                                                           (coe
                                                                              MAlonzo.Code.Relation.Binary.Definitions.C_tri'62'_188
                                                                              (coe
                                                                                 MAlonzo.Code.Data.Nat.Properties.du_'8804''8743''8802''8658''60'_2918
                                                                                 (coe v3)
                                                                                 (coe
                                                                                    MAlonzo.Code.Data.Nat.Properties.du_'8814''8658''8805'_2902
                                                                                    (coe v3)
                                                                                    (coe v4)))))) in
                                                    coe
                                                      (case coe v8 of
                                                         MAlonzo.Code.Relation.Binary.Definitions.C_tri'60'_172 v9
                                                           -> coe
                                                                MAlonzo.Code.Relation.Binary.Definitions.C_tri'60'_172
                                                                (coe
                                                                   MAlonzo.Code.Data.Integer.Base.C_'43''60''43'_72
                                                                   (coe
                                                                      MAlonzo.Code.Data.Nat.Base.C_s'8804's_34
                                                                      v9))
                                                         MAlonzo.Code.Relation.Binary.Definitions.C_tri'8776'_180 v10
                                                           -> coe
                                                                MAlonzo.Code.Relation.Binary.Definitions.C_tri'8776'_180
                                                                erased
                                                         MAlonzo.Code.Relation.Binary.Definitions.C_tri'62'_188 v11
                                                           -> coe
                                                                MAlonzo.Code.Relation.Binary.Definitions.C_tri'62'_188
                                                                (coe
                                                                   MAlonzo.Code.Data.Integer.Base.C_'43''60''43'_72
                                                                   (coe
                                                                      MAlonzo.Code.Data.Nat.Base.C_s'8804's_34
                                                                      v11))
                                                         _ -> MAlonzo.RTE.mazUnreachableError))
                                       _ -> MAlonzo.RTE.mazUnreachableError))
                           _ -> coe
                                  MAlonzo.Code.Relation.Binary.Definitions.C_tri'62'_188
                                  (coe MAlonzo.Code.Data.Integer.Base.C_'45''60''43'_64)))
        _ -> let v2 = subInt (coe (-1 :: Integer)) (coe v0) in
             coe
               (case coe v1 of
                  _ | coe geqInt (coe v1) (coe (0 :: Integer)) ->
                      coe
                        MAlonzo.Code.Relation.Binary.Definitions.C_tri'60'_172
                        (coe MAlonzo.Code.Data.Integer.Base.C_'45''60''43'_64)
                  _ -> let v3 = subInt (coe (-1 :: Integer)) (coe v1) in
                       coe
                         (let v4
                                = coe
                                    MAlonzo.Code.Relation.Nullary.Decidable.Core.du_map'8242'_168
                                    erased
                                    (\ v4 ->
                                       coe
                                         MAlonzo.Code.Data.Nat.Properties.du_'8801''8658''8801''7495'_2678
                                         (coe v2))
                                    (coe
                                       MAlonzo.Code.Relation.Nullary.Decidable.Core.C__because__32
                                       (coe eqInt (coe v0) (coe v1))
                                       (coe
                                          MAlonzo.Code.Relation.Nullary.Reflects.d_T'45'reflects_66
                                          (coe eqInt (coe v0) (coe v1)))) in
                          coe
                            (case coe v4 of
                               MAlonzo.Code.Relation.Nullary.Decidable.Core.C__because__32 v5 v6
                                 -> if coe v5
                                      then coe
                                             seq (coe v6)
                                             (coe
                                                MAlonzo.Code.Relation.Binary.Definitions.C_tri'8776'_180
                                                erased)
                                      else (let v7
                                                  = seq
                                                      (coe v6)
                                                      (let v7 = ltInt (coe v1) (coe v0) in
                                                       coe
                                                         (if coe v7
                                                            then coe
                                                                   seq
                                                                   (coe
                                                                      MAlonzo.Code.Relation.Nullary.Reflects.d_T'45'reflects_66
                                                                      (coe v7))
                                                                   (coe
                                                                      MAlonzo.Code.Relation.Binary.Definitions.C_tri'60'_172
                                                                      (coe
                                                                         MAlonzo.Code.Data.Nat.Properties.du_'60''7495''8658''60'_2716
                                                                         (coe v2)))
                                                            else coe
                                                                   seq
                                                                   (coe
                                                                      MAlonzo.Code.Relation.Nullary.Reflects.d_T'45'reflects_66
                                                                      (coe v7))
                                                                   (coe
                                                                      MAlonzo.Code.Relation.Binary.Definitions.C_tri'62'_188
                                                                      (coe
                                                                         MAlonzo.Code.Data.Nat.Properties.du_'8804''8743''8802''8658''60'_2918
                                                                         (coe v2)
                                                                         (coe
                                                                            MAlonzo.Code.Data.Nat.Properties.du_'8814''8658''8805'_2902
                                                                            (coe v2) (coe v3)))))) in
                                            coe
                                              (case coe v7 of
                                                 MAlonzo.Code.Relation.Binary.Definitions.C_tri'60'_172 v8
                                                   -> coe
                                                        MAlonzo.Code.Relation.Binary.Definitions.C_tri'62'_188
                                                        (coe
                                                           MAlonzo.Code.Data.Integer.Base.C_'45''60''45'_58
                                                           v8)
                                                 MAlonzo.Code.Relation.Binary.Definitions.C_tri'8776'_180 v9
                                                   -> coe
                                                        MAlonzo.Code.Relation.Binary.Definitions.C_tri'8776'_180
                                                        erased
                                                 MAlonzo.Code.Relation.Binary.Definitions.C_tri'62'_188 v10
                                                   -> coe
                                                        MAlonzo.Code.Relation.Binary.Definitions.C_tri'60'_172
                                                        (coe
                                                           MAlonzo.Code.Data.Integer.Base.C_'45''60''45'_58
                                                           v10)
                                                 _ -> MAlonzo.RTE.mazUnreachableError))
                               _ -> 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 v0 v1
    = case coe v0 of
        _ | coe geqInt (coe v0) (coe (0 :: Integer)) ->
            case coe v1 of
              _ | coe geqInt (coe v1) (coe (0 :: Integer)) ->
                  coe
                    MAlonzo.Code.Relation.Nullary.Decidable.Core.du_map'8242'_168
                    (coe MAlonzo.Code.Data.Integer.Base.C_'43''60''43'_72)
                    (coe du_drop'8255''43''60''43'_2834)
                    (coe
                       MAlonzo.Code.Data.Nat.Properties.d__'60''63'__3030 (coe v0)
                       (coe v1))
              _ -> coe
                     MAlonzo.Code.Relation.Nullary.Decidable.Core.C__because__32
                     (coe MAlonzo.Code.Agda.Builtin.Bool.C_false_8)
                     (coe MAlonzo.Code.Relation.Nullary.Reflects.C_of'8319'_26)
        _ -> let v2 = subInt (coe (-1 :: Integer)) (coe v0) in
             coe
               (case coe v1 of
                  _ | coe geqInt (coe v1) (coe (0 :: Integer)) ->
                      coe
                        MAlonzo.Code.Relation.Nullary.Decidable.Core.C__because__32
                        (coe MAlonzo.Code.Agda.Builtin.Bool.C_true_10)
                        (coe
                           MAlonzo.Code.Relation.Nullary.Reflects.C_of'696'_22
                           (coe MAlonzo.Code.Data.Integer.Base.C_'45''60''43'_64))
                  _ -> let v3 = subInt (coe (-1 :: Integer)) (coe v1) in
                       coe
                         (coe
                            MAlonzo.Code.Relation.Nullary.Decidable.Core.du_map'8242'_168
                            (coe MAlonzo.Code.Data.Integer.Base.C_'45''60''45'_58)
                            (coe du_drop'8255''45''60''45'_2838)
                            (coe
                               MAlonzo.Code.Data.Nat.Properties.d__'60''63'__3030 (coe v3)
                               (coe 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 = erased
  -- Data.Integer.Properties.<-isStrictPartialOrder
  d_'60''45'isStrictPartialOrder_3110 ::
    MAlonzo.Code.Relation.Binary.Structures.T_IsStrictPartialOrder_290
  d_'60''45'isStrictPartialOrder_3110
    = coe
        MAlonzo.Code.Relation.Binary.Structures.C_IsStrictPartialOrder'46'constructor_14045
        (coe
           MAlonzo.Code.Relation.Binary.PropositionalEquality.Properties.du_isEquivalence_396)
        (\ v0 v1 v2 v3 v4 -> coe du_'60''45'trans_2986 v3 v4)
        (coe
           MAlonzo.Code.Agda.Builtin.Sigma.C__'44'__32
           (coe (\ v0 v1 v2 v3 v4 -> v4)) (coe (\ v0 v1 v2 v3 v4 -> v4)))
  -- Data.Integer.Properties.<-isStrictTotalOrder
  d_'60''45'isStrictTotalOrder_3116 ::
    MAlonzo.Code.Relation.Binary.Structures.T_IsStrictTotalOrder_534
  d_'60''45'isStrictTotalOrder_3116
    = coe
        MAlonzo.Code.Relation.Binary.Structures.C_IsStrictTotalOrder'46'constructor_24953
        (coe d_'60''45'isStrictPartialOrder_3110) (coe 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
    = coe
        MAlonzo.Code.Relation.Binary.Bundles.C_StrictPartialOrder'46'constructor_11097
        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
    = coe
        MAlonzo.Code.Relation.Binary.Bundles.C_StrictTotalOrder'46'constructor_21059
        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 = 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 = erased
  -- Data.Integer.Properties.≤-Reasoning._._IsRelatedTo_
  d__IsRelatedTo__3130 a0 a1 = ()
  -- Data.Integer.Properties.≤-Reasoning._._∎
  d__'8718'_3132 ::
    Integer ->
    MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.T__IsRelatedTo__78
  d__'8718'_3132
    = let v0 = d_'8804''45'isPreorder_2800 in
      coe
        (coe
           MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du__'8718'_492
           (coe
              MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_stop_166
              (coe 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
    = coe
        MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_'60''45'go_152
        (\ v0 v1 v2 v3 v4 -> coe du_'60''45'trans_2986 v3 v4)
        (coe
           MAlonzo.Code.Relation.Binary.PropositionalEquality.Core.du_resp'8322'_160)
        (\ v0 v1 v2 v3 v4 -> coe du_'60''45''8804''45'trans_2972 v3 v4)
  -- Data.Integer.Properties.≤-Reasoning._.IsEquality
  d_IsEquality_3136 a0 a1 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 v0 v1 v2
    = coe
        MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_IsEquality'63'_224
        v2
  -- Data.Integer.Properties.≤-Reasoning._.IsStrict
  d_IsStrict_3140 a0 a1 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 v0 v1 v2
    = coe
        MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_IsStrict'63'_188
        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
    = let v0 = d_'8804''45'isPreorder_2800 in
      coe
        (let v1 = \ v1 v2 v3 -> coe du_'60''8658''8804'_2846 v3 in
         coe
           (coe
              MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_begin__46
              (coe
                 MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_start_96
                 (coe v0) (coe 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 v0 v1 v2 v3 v4
    = coe
        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 = 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
    = let v0
            = coe
                MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_strictRelation_202 in
      coe
        (\ v1 v2 v3 v4 ->
           coe
             MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_begin__126
             (coe v0) v1 v2 v3)
  -- Data.Integer.Properties.≤-Reasoning._.eqRelation
  d_eqRelation_3152 ::
    MAlonzo.Code.Relation.Binary.Reasoning.Syntax.T_SubRelation_60
  d_eqRelation_3152
    = coe
        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 = 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 v0 v1 v2 v3
    = coe
        MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_extractStrict_198
        v2 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
    = coe
        MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_start_96
        (coe d_'8804''45'isPreorder_2800)
        (\ v0 v1 v2 -> coe du_'60''8658''8804'_2846 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
    = let v0 = \ v0 v1 v2 v3 v4 -> coe du_'60''45'trans_2986 v3 v4 in
      coe
        (let v1
               = coe
                   MAlonzo.Code.Relation.Binary.PropositionalEquality.Core.du_resp'8322'_160 in
         coe
           (let v2
                  = \ v2 v3 v4 v5 v6 -> coe du_'60''45''8804''45'trans_2972 v5 v6 in
            coe
              (coe
                 MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''60'_312
                 (coe
                    MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_'60''45'go_152
                    (coe v0) (coe v1) (coe 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
    = coe
        MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8801'_450
        (coe (\ v0 v1 v2 v3 v4 -> 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 ~v0 ~v1 v2
    = du_step'45''8801''45''8739'_3172 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 v0 = coe 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
    = coe
        MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8801''45''10216'_448
        (coe (\ v0 v1 v2 v3 v4 -> 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
    = coe
        MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8801''45''10217'_436
        (coe (\ v0 v1 v2 v3 v4 -> 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
    = coe
        MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8801''728'_452
        (coe (\ v0 v1 v2 v3 v4 -> 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
    = let v0 = d_'8804''45'isPreorder_2800 in
      coe
        (let v1
               = \ v1 v2 v3 v4 v5 -> coe du_'8804''45''60''45'trans_2958 v4 v5 in
         coe
           (coe
              MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8804'_308
              (coe
                 MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_'8804''45'go_138
                 (coe v0) (coe v1))))
  -- Data.Integer.Properties.≤-Reasoning._.stop
  d_stop_3182 ::
    Integer ->
    MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.T__IsRelatedTo__78
  d_stop_3182
    = coe
        MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_stop_166
        (coe 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
    = coe
        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
    = coe
        MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_'8776''45'go_124
        (coe d_'8804''45'isPreorder_2800)
        (coe
           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 ~v0 ~v1 ~v2 ~v3 v4 = du_'8801''45'go_3190 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 v0 = coe 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
    = coe
        MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_'8804''45'go_138
        (coe d_'8804''45'isPreorder_2800)
        (\ v0 v1 v2 v3 v4 -> coe du_'8804''45''60''45'trans_2958 v3 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 ~v0 ~v1 = du_positive'8315''185'_3212
  du_positive'8315''185'_3212 ::
    MAlonzo.Code.Data.Integer.Base.T__'60'__50
  du_positive'8315''185'_3212
    = coe
        MAlonzo.Code.Data.Integer.Base.C_'43''60''43'_72
        (coe
           MAlonzo.Code.Data.Nat.Base.C_s'8804's_34
           (coe 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 ~v0 ~v1 = du_negative'8315''185'_3218
  du_negative'8315''185'_3218 ::
    MAlonzo.Code.Data.Integer.Base.T__'60'__50
  du_negative'8315''185'_3218
    = coe 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 v0 ~v1
    = du_nonPositive'8315''185'_3224 v0
  du_nonPositive'8315''185'_3224 ::
    Integer -> MAlonzo.Code.Data.Integer.Base.T__'8804'__26
  du_nonPositive'8315''185'_3224 v0
    = case coe v0 of
        0 -> coe
               MAlonzo.Code.Data.Integer.Base.C_'43''8804''43'_48
               (coe MAlonzo.Code.Data.Nat.Base.C_z'8804'n_26)
        _ -> coe 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 ~v0 ~v1
    = du_nonNegative'8315''185'_3230
  du_nonNegative'8315''185'_3230 ::
    MAlonzo.Code.Data.Integer.Base.T__'8804'__26
  du_nonNegative'8315''185'_3230
    = coe
        MAlonzo.Code.Data.Integer.Base.C_'43''8804''43'_48
        (coe 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 ~v0 ~v1 ~v2 ~v3
    = du_negative'60'positive_3238
  du_negative'60'positive_3238 ::
    MAlonzo.Code.Data.Integer.Base.T__'60'__50
  du_negative'60'positive_3238
    = coe
        du_'60''45'trans_2986 (coe du_negative'8315''185'_3218)
        (coe 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 = 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 = 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 v0 ~v1
    = du_neg'45''8804''45'pos_3268 v0
  du_neg'45''8804''45'pos_3268 ::
    Integer -> MAlonzo.Code.Data.Integer.Base.T__'8804'__26
  du_neg'45''8804''45'pos_3268 v0
    = case coe v0 of
        0 -> coe
               MAlonzo.Code.Data.Integer.Base.C_'43''8804''43'_48
               (coe MAlonzo.Code.Data.Nat.Base.C_z'8804'n_26)
        _ -> coe 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 ~v0 v1 v2
    = du_neg'45'mono'45''8804'_3272 v1 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 v0 v1
    = case coe v1 of
        MAlonzo.Code.Data.Integer.Base.C_'45''8804''45'_34 v4
          -> coe
               MAlonzo.Code.Data.Integer.Base.C_'43''8804''43'_48
               (coe MAlonzo.Code.Data.Nat.Base.C_s'8804's_34 v4)
        MAlonzo.Code.Data.Integer.Base.C_'45''8804''43'_40
          -> coe du_neg'45''8804''45'pos_3268 (coe v0)
        MAlonzo.Code.Data.Integer.Base.C_'43''8804''43'_48 v4
          -> case coe v4 of
               MAlonzo.Code.Data.Nat.Base.C_z'8804'n_26
                 -> coe du_neg'45''8804''45'pos_3268 (coe v0)
               MAlonzo.Code.Data.Nat.Base.C_s'8804's_34 v7
                 -> coe MAlonzo.Code.Data.Integer.Base.C_'45''8804''45'_34 v7
               _ -> MAlonzo.RTE.mazUnreachableError
        _ -> 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 v0 v1 v2
    = case coe v0 of
        0 -> case coe v1 of
               0 -> coe
                      MAlonzo.Code.Data.Integer.Base.C_'43''8804''43'_48
                      (coe MAlonzo.Code.Data.Nat.Base.C_z'8804'n_26)
               _ -> coe MAlonzo.Code.Data.Integer.Base.C_'45''8804''43'_40
        _ | coe geqInt (coe v0) (coe (1 :: Integer)) ->
            case coe v1 of
              0 -> coe
                     seq (coe v2)
                     (coe
                        MAlonzo.Code.Data.Integer.Base.C_'43''8804''43'_48
                        (coe MAlonzo.Code.Data.Nat.Base.C_z'8804'n_26))
              _ | coe geqInt (coe v1) (coe (1 :: Integer)) ->
                  case coe v2 of
                    MAlonzo.Code.Data.Integer.Base.C_'45''8804''45'_34 v5
                      -> coe
                           MAlonzo.Code.Data.Integer.Base.C_'43''8804''43'_48
                           (coe MAlonzo.Code.Data.Nat.Base.C_s'8804's_34 v5)
                    _ -> MAlonzo.RTE.mazUnreachableError
              _ -> coe
                     seq (coe v2)
                     (coe MAlonzo.Code.Data.Integer.Base.C_'45''8804''43'_40)
        _ -> case coe v2 of
               MAlonzo.Code.Data.Integer.Base.C_'43''8804''43'_48 v5
                 -> case coe v5 of
                      MAlonzo.Code.Data.Nat.Base.C_s'8804's_34 v8
                        -> coe MAlonzo.Code.Data.Integer.Base.C_'45''8804''45'_34 v8
                      _ -> MAlonzo.RTE.mazUnreachableError
               _ -> 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 v0 v1 v2
    = case coe v0 of
        0 -> coe
               seq (coe v2) (coe MAlonzo.Code.Data.Integer.Base.C_'45''60''43'_64)
        _ | coe geqInt (coe v0) (coe (1 :: Integer)) ->
            case coe v2 of
              MAlonzo.Code.Data.Integer.Base.C_'43''60''43'_72 v5
                -> coe
                     MAlonzo.Code.Data.Integer.Base.C_'45''60''45'_58
                     (coe MAlonzo.Code.Data.Nat.Base.du_s'60's'8315''185'_70 (coe v5))
              _ -> MAlonzo.RTE.mazUnreachableError
        _ -> case coe v1 of
               0 -> coe
                      seq (coe v2)
                      (coe
                         MAlonzo.Code.Data.Integer.Base.C_'43''60''43'_72
                         (coe
                            MAlonzo.Code.Data.Nat.Base.C_s'8804's_34
                            (coe MAlonzo.Code.Data.Nat.Base.C_z'8804'n_26)))
               _ | coe geqInt (coe v1) (coe (1 :: Integer)) ->
                   coe
                     seq (coe v2) (coe MAlonzo.Code.Data.Integer.Base.C_'45''60''43'_64)
               _ -> case coe v2 of
                      MAlonzo.Code.Data.Integer.Base.C_'45''60''45'_58 v5
                        -> coe
                             MAlonzo.Code.Data.Integer.Base.C_'43''60''43'_72
                             (coe MAlonzo.Code.Data.Nat.Base.C_s'8804's_34 v5)
                      _ -> 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 v0 v1 v2
    = case coe v0 of
        0 -> coe MAlonzo.Code.Data.Integer.Base.C_'45''60''43'_64
        _ | coe geqInt (coe v0) (coe (1 :: Integer)) ->
            case coe v1 of
              0 -> coe
                     seq (coe v2)
                     (coe
                        MAlonzo.Code.Data.Integer.Base.C_'43''60''43'_72
                        (coe
                           MAlonzo.Code.Data.Nat.Base.C_s'8804's_34
                           (coe MAlonzo.Code.Data.Nat.Base.C_z'8804'n_26)))
              _ | coe geqInt (coe v1) (coe (1 :: Integer)) ->
                  case coe v2 of
                    MAlonzo.Code.Data.Integer.Base.C_'45''60''45'_58 v5
                      -> coe
                           MAlonzo.Code.Data.Integer.Base.C_'43''60''43'_72
                           (coe MAlonzo.Code.Data.Nat.Base.C_s'8804's_34 v5)
                    _ -> MAlonzo.RTE.mazUnreachableError
              _ -> coe
                     seq (coe v2) (coe MAlonzo.Code.Data.Integer.Base.C_'45''60''43'_64)
        _ -> case coe v2 of
               MAlonzo.Code.Data.Integer.Base.C_'43''60''43'_72 v5
                 -> coe
                      MAlonzo.Code.Data.Integer.Base.C_'45''60''45'_58
                      (coe MAlonzo.Code.Data.Nat.Base.du_s'60's'8315''185'_70 (coe v5))
               _ -> 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 = 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 = 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 = 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 ~v0 ~v1
    = 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
    = coe
        MAlonzo.Code.Data.Integer.Base.C_'43''8804''43'_48
        (coe 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 v0
    = case coe v0 of
        _ | coe geqInt (coe v0) (coe (0 :: Integer)) ->
            coe MAlonzo.Code.Data.Sum.Base.C_inj'8321'_38 erased
        _ -> coe MAlonzo.Code.Data.Sum.Base.C_inj'8322'_42 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 v0 v1
    = let v2 = ltInt (coe v0) (coe v1) in
      coe
        (if coe v2
           then coe
                  MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_begin__46
                  (coe
                     MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_start_96
                     (coe MAlonzo.Code.Data.Nat.Properties.d_'8804''45'isPreorder_2810)
                     (\ v3 v4 v5 ->
                        coe MAlonzo.Code.Data.Nat.Properties.du_'60''8658''8804'_2854 v5))
                  (MAlonzo.Code.Data.Integer.Base.d_'8739'_'8739'_18
                     (coe
                        MAlonzo.Code.Data.Integer.Base.d_'45'__252
                        (coe subInt (coe v1) (coe v0))))
                  (MAlonzo.Code.Data.Nat.Base.d__'8852'__204 (coe v0) (coe v1))
                  (coe
                     MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8801''45''10217'_436
                     (\ v3 v4 v5 v6 v7 -> v7)
                     (MAlonzo.Code.Data.Integer.Base.d_'8739'_'8739'_18
                        (coe
                           MAlonzo.Code.Data.Integer.Base.d_'45'__252
                           (coe subInt (coe v1) (coe v0))))
                     (MAlonzo.Code.Data.Integer.Base.d_'8739'_'8739'_18
                        (coe subInt (coe v1) (coe v0)))
                     (MAlonzo.Code.Data.Nat.Base.d__'8852'__204 (coe v0) (coe v1))
                     (coe
                        MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8804'_308
                        (coe
                           MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_'8804''45'go_138
                           (coe MAlonzo.Code.Data.Nat.Properties.d_'8804''45'isPreorder_2810)
                           (\ v3 v4 v5 v6 v7 ->
                              coe
                                MAlonzo.Code.Data.Nat.Properties.du_'8804''45''60''45'trans_2986 v6
                                v7))
                        (subInt (coe v1) (coe v0)) v1
                        (MAlonzo.Code.Data.Nat.Base.d__'8852'__204 (coe v0) (coe v1))
                        (coe
                           MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8804'_308
                           (coe
                              MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_'8804''45'go_138
                              (coe MAlonzo.Code.Data.Nat.Properties.d_'8804''45'isPreorder_2810)
                              (\ v3 v4 v5 v6 v7 ->
                                 coe
                                   MAlonzo.Code.Data.Nat.Properties.du_'8804''45''60''45'trans_2986 v6
                                   v7))
                           v1 (MAlonzo.Code.Data.Nat.Base.d__'8852'__204 (coe v0) (coe v1))
                           (MAlonzo.Code.Data.Nat.Base.d__'8852'__204 (coe v0) (coe v1))
                           (coe
                              MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du__'8718'_492
                              (coe
                                 MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_stop_166
                                 (coe MAlonzo.Code.Data.Nat.Properties.d_'8804''45'isPreorder_2810))
                              (coe MAlonzo.Code.Data.Nat.Base.d__'8852'__204 (coe v0) (coe v1)))
                           (let v3
                                  = MAlonzo.Code.Data.Nat.Properties.d_'8804''45'totalPreorder_2822 in
                            coe
                              (let v4
                                     = MAlonzo.Code.Data.Nat.Properties.d_'8852''45'operator_4440 in
                               coe
                                 (coe
                                    MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_x'8851'y'8804'y_2834
                                    (coe
                                       MAlonzo.Code.Relation.Binary.Construct.Flip.EqAndOrd.du_totalPreorder_746
                                       (coe v3))
                                    (coe
                                       MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.du_MaxOp'8658'MinOp_174
                                       (coe v4))
                                    (coe v0) (coe v1)))))
                        (MAlonzo.Code.Data.Nat.Properties.d_m'8760'n'8804'm_5042
                           (coe v1) (coe v0)))
                     erased)
           else coe
                  MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_begin__46
                  (coe
                     MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_start_96
                     (coe MAlonzo.Code.Data.Nat.Properties.d_'8804''45'isPreorder_2810)
                     (\ v3 v4 v5 ->
                        coe MAlonzo.Code.Data.Nat.Properties.du_'60''8658''8804'_2854 v5))
                  (MAlonzo.Code.Data.Integer.Base.d_'8739'_'8739'_18
                     (coe subInt (coe v0) (coe v1)))
                  (MAlonzo.Code.Data.Nat.Base.d__'8852'__204 (coe v0) (coe v1))
                  (coe
                     MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8804'_308
                     (coe
                        MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_'8804''45'go_138
                        (coe MAlonzo.Code.Data.Nat.Properties.d_'8804''45'isPreorder_2810)
                        (\ v3 v4 v5 v6 v7 ->
                           coe
                             MAlonzo.Code.Data.Nat.Properties.du_'8804''45''60''45'trans_2986 v6
                             v7))
                     (subInt (coe v0) (coe v1)) v0
                     (MAlonzo.Code.Data.Nat.Base.d__'8852'__204 (coe v0) (coe v1))
                     (coe
                        MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8804'_308
                        (coe
                           MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_'8804''45'go_138
                           (coe MAlonzo.Code.Data.Nat.Properties.d_'8804''45'isPreorder_2810)
                           (\ v3 v4 v5 v6 v7 ->
                              coe
                                MAlonzo.Code.Data.Nat.Properties.du_'8804''45''60''45'trans_2986 v6
                                v7))
                        v0 (MAlonzo.Code.Data.Nat.Base.d__'8852'__204 (coe v0) (coe v1))
                        (MAlonzo.Code.Data.Nat.Base.d__'8852'__204 (coe v0) (coe v1))
                        (coe
                           MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du__'8718'_492
                           (coe
                              MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_stop_166
                              (coe MAlonzo.Code.Data.Nat.Properties.d_'8804''45'isPreorder_2810))
                           (coe MAlonzo.Code.Data.Nat.Base.d__'8852'__204 (coe v0) (coe v1)))
                        (let v3
                               = MAlonzo.Code.Data.Nat.Properties.d_'8804''45'totalPreorder_2822 in
                         coe
                           (let v4
                                  = MAlonzo.Code.Data.Nat.Properties.d_'8852''45'operator_4440 in
                            coe
                              (coe
                                 MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_x'8851'y'8804'x_2808
                                 (coe
                                    MAlonzo.Code.Relation.Binary.Construct.Flip.EqAndOrd.du_totalPreorder_746
                                    (coe v3))
                                 (coe
                                    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.du_MaxOp'8658'MinOp_174
                                    (coe v4))
                                 (coe v0) (coe v1)))))
                     (MAlonzo.Code.Data.Nat.Properties.d_m'8760'n'8804'm_5042
                        (coe v0) (coe 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 v0 v1
    = case coe v0 of
        0 -> coe
               seq (coe v1)
               (coe
                  MAlonzo.Code.Data.Nat.Properties.d_'8804''45'refl_2776
                  (coe
                     MAlonzo.Code.Data.Integer.Base.d_'8739'_'8739'_18
                     (coe
                        MAlonzo.Code.Data.Integer.Base.d__'43'__276 (coe (0 :: Integer))
                        (coe v1))))
        _ | coe geqInt (coe v0) (coe (1 :: Integer)) ->
            case coe v1 of
              _ | coe geqInt (coe v1) (coe (0 :: Integer)) ->
                  coe
                    MAlonzo.Code.Data.Nat.Properties.d_'8804''45'refl_2776
                    (coe
                       MAlonzo.Code.Data.Integer.Base.d_'8739'_'8739'_18
                       (coe
                          MAlonzo.Code.Data.Integer.Base.d__'43'__276 (coe v0) (coe v1)))
              _ -> coe
                     MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_begin__46
                     (coe
                        MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_start_96
                        (coe MAlonzo.Code.Data.Nat.Properties.d_'8804''45'isPreorder_2810)
                        (\ v2 v3 v4 ->
                           coe MAlonzo.Code.Data.Nat.Properties.du_'60''8658''8804'_2854 v4))
                     (MAlonzo.Code.Data.Integer.Base.d_'8739'_'8739'_18
                        (coe
                           MAlonzo.Code.Data.Integer.Base.d__'43'__276 (coe v0) (coe v1)))
                     (addInt
                        (coe MAlonzo.Code.Data.Integer.Base.d_'8739'_'8739'_18 (coe v0))
                        (coe MAlonzo.Code.Data.Integer.Base.d_'8739'_'8739'_18 (coe v1)))
                     (coe
                        MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8804'_308
                        (coe
                           MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_'8804''45'go_138
                           (coe MAlonzo.Code.Data.Nat.Properties.d_'8804''45'isPreorder_2810)
                           (\ v2 v3 v4 v5 v6 ->
                              coe
                                MAlonzo.Code.Data.Nat.Properties.du_'8804''45''60''45'trans_2986 v5
                                v6))
                        (MAlonzo.Code.Data.Integer.Base.d_'8739'_'8739'_18
                           (coe
                              MAlonzo.Code.Data.Integer.Base.d__'8854'__258 (coe v0)
                              (coe subInt (coe (0 :: Integer)) (coe v1))))
                        (MAlonzo.Code.Data.Nat.Base.d__'8852'__204
                           (coe v0) (coe subInt (coe (0 :: Integer)) (coe v1)))
                        (addInt
                           (coe MAlonzo.Code.Data.Integer.Base.d_'8739'_'8739'_18 (coe v0))
                           (coe MAlonzo.Code.Data.Integer.Base.d_'8739'_'8739'_18 (coe v1)))
                        (coe
                           MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8804'_308
                           (coe
                              MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_'8804''45'go_138
                              (coe MAlonzo.Code.Data.Nat.Properties.d_'8804''45'isPreorder_2810)
                              (\ v2 v3 v4 v5 v6 ->
                                 coe
                                   MAlonzo.Code.Data.Nat.Properties.du_'8804''45''60''45'trans_2986 v5
                                   v6))
                           (MAlonzo.Code.Data.Nat.Base.d__'8852'__204
                              (coe v0) (coe subInt (coe (0 :: Integer)) (coe v1)))
                           (subInt (coe v0) (coe v1))
                           (addInt
                              (coe MAlonzo.Code.Data.Integer.Base.d_'8739'_'8739'_18 (coe v0))
                              (coe MAlonzo.Code.Data.Integer.Base.d_'8739'_'8739'_18 (coe v1)))
                           (coe
                              MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du__'8718'_492
                              (coe
                                 MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_stop_166
                                 (coe MAlonzo.Code.Data.Nat.Properties.d_'8804''45'isPreorder_2810))
                              (coe subInt (coe v0) (coe v1)))
                           (MAlonzo.Code.Data.Nat.Properties.d_m'8852'n'8804'm'43'n_4830
                              (coe v0) (coe subInt (coe (0 :: Integer)) (coe v1))))
                        (d_'8739'm'8861'n'8739''8804'm'8852'n_3368
                           (coe v0) (coe subInt (coe (0 :: Integer)) (coe v1))))
        _ -> case coe v1 of
               _ | coe geqInt (coe v1) (coe (0 :: Integer)) ->
                   coe
                     MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_begin__46
                     (coe
                        MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_start_96
                        (coe MAlonzo.Code.Data.Nat.Properties.d_'8804''45'isPreorder_2810)
                        (\ v2 v3 v4 ->
                           coe MAlonzo.Code.Data.Nat.Properties.du_'60''8658''8804'_2854 v4))
                     (MAlonzo.Code.Data.Integer.Base.d_'8739'_'8739'_18
                        (coe
                           MAlonzo.Code.Data.Integer.Base.d__'43'__276 (coe v0) (coe v1)))
                     (addInt
                        (coe MAlonzo.Code.Data.Integer.Base.d_'8739'_'8739'_18 (coe v0))
                        (coe MAlonzo.Code.Data.Integer.Base.d_'8739'_'8739'_18 (coe v1)))
                     (coe
                        MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8804'_308
                        (coe
                           MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_'8804''45'go_138
                           (coe MAlonzo.Code.Data.Nat.Properties.d_'8804''45'isPreorder_2810)
                           (\ v2 v3 v4 v5 v6 ->
                              coe
                                MAlonzo.Code.Data.Nat.Properties.du_'8804''45''60''45'trans_2986 v5
                                v6))
                        (MAlonzo.Code.Data.Integer.Base.d_'8739'_'8739'_18
                           (coe
                              MAlonzo.Code.Data.Integer.Base.d__'8854'__258 (coe v1)
                              (coe subInt (coe (0 :: Integer)) (coe v0))))
                        (MAlonzo.Code.Data.Nat.Base.d__'8852'__204
                           (coe v1) (coe subInt (coe (0 :: Integer)) (coe v0)))
                        (addInt
                           (coe MAlonzo.Code.Data.Integer.Base.d_'8739'_'8739'_18 (coe v0))
                           (coe MAlonzo.Code.Data.Integer.Base.d_'8739'_'8739'_18 (coe v1)))
                        (coe
                           MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8804'_308
                           (coe
                              MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_'8804''45'go_138
                              (coe MAlonzo.Code.Data.Nat.Properties.d_'8804''45'isPreorder_2810)
                              (\ v2 v3 v4 v5 v6 ->
                                 coe
                                   MAlonzo.Code.Data.Nat.Properties.du_'8804''45''60''45'trans_2986 v5
                                   v6))
                           (MAlonzo.Code.Data.Nat.Base.d__'8852'__204
                              (coe v1) (coe subInt (coe (0 :: Integer)) (coe v0)))
                           (subInt (coe v1) (coe v0))
                           (addInt
                              (coe MAlonzo.Code.Data.Integer.Base.d_'8739'_'8739'_18 (coe v0))
                              (coe MAlonzo.Code.Data.Integer.Base.d_'8739'_'8739'_18 (coe v1)))
                           (coe
                              MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8801''45''10217'_436
                              (\ v2 v3 v4 v5 v6 -> v6) (subInt (coe v1) (coe v0))
                              (subInt (coe v1) (coe v0))
                              (addInt
                                 (coe MAlonzo.Code.Data.Integer.Base.d_'8739'_'8739'_18 (coe v0))
                                 (coe MAlonzo.Code.Data.Integer.Base.d_'8739'_'8739'_18 (coe v1)))
                              (coe
                                 MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du__'8718'_492
                                 (coe
                                    MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_stop_166
                                    (coe
                                       MAlonzo.Code.Data.Nat.Properties.d_'8804''45'isPreorder_2810))
                                 (coe subInt (coe v1) (coe v0)))
                              erased)
                           (MAlonzo.Code.Data.Nat.Properties.d_m'8852'n'8804'm'43'n_4830
                              (coe v1) (coe subInt (coe (0 :: Integer)) (coe v0))))
                        (d_'8739'm'8861'n'8739''8804'm'8852'n_3368
                           (coe v1) (coe subInt (coe (0 :: Integer)) (coe v0))))
               _ -> coe
                      MAlonzo.Code.Data.Nat.Properties.d_'8804''45'refl_2776
                      (coe subInt (coe subInt (coe (0 :: Integer)) (coe v0)) (coe 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 v0 v1
    = coe
        MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_begin__46
        (coe
           MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_start_96
           (coe MAlonzo.Code.Data.Nat.Properties.d_'8804''45'isPreorder_2810)
           (\ v2 v3 v4 ->
              coe MAlonzo.Code.Data.Nat.Properties.du_'60''8658''8804'_2854 v4))
        (MAlonzo.Code.Data.Integer.Base.d_'8739'_'8739'_18
           (coe
              MAlonzo.Code.Data.Integer.Base.d__'45'__294 (coe v0) (coe v1)))
        (addInt
           (coe MAlonzo.Code.Data.Integer.Base.d_'8739'_'8739'_18 (coe v0))
           (coe MAlonzo.Code.Data.Integer.Base.d_'8739'_'8739'_18 (coe v1)))
        (coe
           MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8804'_308
           (coe
              MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_'8804''45'go_138
              (coe MAlonzo.Code.Data.Nat.Properties.d_'8804''45'isPreorder_2810)
              (\ v2 v3 v4 v5 v6 ->
                 coe
                   MAlonzo.Code.Data.Nat.Properties.du_'8804''45''60''45'trans_2986 v5
                   v6))
           (MAlonzo.Code.Data.Integer.Base.d_'8739'_'8739'_18
              (coe
                 MAlonzo.Code.Data.Integer.Base.d__'45'__294 (coe v0) (coe v1)))
           (addInt
              (coe
                 MAlonzo.Code.Data.Integer.Base.d_'8739'_'8739'_18
                 (coe MAlonzo.Code.Data.Integer.Base.d_'45'__252 (coe v1)))
              (coe MAlonzo.Code.Data.Integer.Base.d_'8739'_'8739'_18 (coe v0)))
           (addInt
              (coe MAlonzo.Code.Data.Integer.Base.d_'8739'_'8739'_18 (coe v0))
              (coe MAlonzo.Code.Data.Integer.Base.d_'8739'_'8739'_18 (coe v1)))
           (coe
              MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8801''45''10217'_436
              (\ v2 v3 v4 v5 v6 -> v6)
              (addInt
                 (coe
                    MAlonzo.Code.Data.Integer.Base.d_'8739'_'8739'_18
                    (coe MAlonzo.Code.Data.Integer.Base.d_'45'__252 (coe v1)))
                 (coe MAlonzo.Code.Data.Integer.Base.d_'8739'_'8739'_18 (coe v0)))
              (addInt
                 (coe MAlonzo.Code.Data.Integer.Base.d_'8739'_'8739'_18 (coe v0))
                 (coe MAlonzo.Code.Data.Integer.Base.d_'8739'_'8739'_18 (coe v1)))
              (addInt
                 (coe MAlonzo.Code.Data.Integer.Base.d_'8739'_'8739'_18 (coe v0))
                 (coe MAlonzo.Code.Data.Integer.Base.d_'8739'_'8739'_18 (coe v1)))
              (coe
                 MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du__'8718'_492
                 (coe
                    MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_stop_166
                    (coe MAlonzo.Code.Data.Nat.Properties.d_'8804''45'isPreorder_2810))
                 (coe
                    addInt
                    (coe MAlonzo.Code.Data.Integer.Base.d_'8739'_'8739'_18 (coe v0))
                    (coe MAlonzo.Code.Data.Integer.Base.d_'8739'_'8739'_18 (coe v1))))
              erased)
           (d_'8739'i'43'j'8739''8804''8739'i'8739''43''8739'j'8739'_3398
              (coe v0)
              (coe MAlonzo.Code.Data.Integer.Base.d_'45'__252 (coe 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 v0 ~v1 ~v2 = du_'9667''45'nonZero_3454 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 v0
    = coe
        seq (coe v0)
        (coe
           MAlonzo.Code.Data.Nat.Base.C_NonZero'46'constructor_3575
           (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 = 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 = 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 = 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 = 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 = 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 = 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 = 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 = 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 v0 v1 ~v2 ~v3 ~v4
    = du_sign'45'cong'8242'_3532 v0 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 v0 v1
    = case coe v1 of
        0 -> coe
               MAlonzo.Code.Data.Sum.Base.C_inj'8322'_42
               (coe MAlonzo.Code.Agda.Builtin.Sigma.C__'44'__32 erased erased)
        _ -> let v2
                   = coe MAlonzo.Code.Data.Sum.Base.C_inj'8321'_38 erased in
             coe (coe seq (coe v0) (coe 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 = 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
    = 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 v0 ~v1 v2
    = du_'43''9667''45'mono'45''60'_3600 v0 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 v0 v1
    = coe
        seq (coe v0)
        (coe MAlonzo.Code.Data.Integer.Base.C_'43''60''43'_72 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 v0 ~v1 v2
    = du_'43''9667''45'cancel'45''60'_3612 v0 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 v0 v1
    = coe
        seq (coe v0)
        (case coe v1 of
           MAlonzo.Code.Data.Integer.Base.C_'43''60''43'_72 v4 -> coe v4
           _                                                   -> 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 ~v0 v1 v2
    = du_neg'9667''45'cancel'45''60'_3626 v1 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 v0 v1
    = case coe v0 of
        0 -> coe
               seq (coe v1)
               (coe
                  MAlonzo.Code.Data.Nat.Base.C_s'8804's_34
                  (coe MAlonzo.Code.Data.Nat.Base.C_z'8804'n_26))
        _ -> case coe v1 of
               MAlonzo.Code.Data.Integer.Base.C_'45''60''45'_58 v4
                 -> coe MAlonzo.Code.Data.Nat.Base.C_s'8804's_34 v4
               _ -> 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 ~v0 v1 ~v2
    = du_'45''9667''60''43''9667'_3642 v1
  du_'45''9667''60''43''9667'_3642 ::
    Integer -> MAlonzo.Code.Data.Integer.Base.T__'60'__50
  du_'45''9667''60''43''9667'_3642 v0
    = coe
        seq (coe v0) (coe 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 = 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 = 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 = 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 = 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 = 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 = 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 = 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 = 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 = 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 = 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 = 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 = 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 = 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 = 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 = 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 = 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 = 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 v0 v1
    = case coe v1 of
        0 -> coe
               d_'8804''45'refl_2728
               (coe
                  MAlonzo.Code.Data.Integer.Base.d__'8854'__258 (coe v0)
                  (coe (0 :: Integer)))
        _ -> let v2 = subInt (coe v1) (coe (1 :: Integer)) in
             coe
               (case coe v0 of
                  0 -> coe MAlonzo.Code.Data.Integer.Base.C_'45''8804''43'_40
                  _ -> let v3 = subInt (coe v0) (coe (1 :: Integer)) in
                       coe
                         (coe
                            MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_begin__46
                            (coe
                               MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_start_96
                               (coe d_'8804''45'isPreorder_2800)
                               (\ v4 v5 v6 -> coe du_'60''8658''8804'_2846 v6))
                            (MAlonzo.Code.Data.Integer.Base.d__'8854'__258 (coe v0) (coe v1))
                            v0
                            (coe
                               MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8801''45''10217'_436
                               (\ v4 v5 v6 v7 v8 -> v8)
                               (MAlonzo.Code.Data.Integer.Base.d__'8854'__258 (coe v0) (coe v1))
                               (MAlonzo.Code.Data.Integer.Base.d__'8854'__258 (coe v3) (coe v2))
                               v0
                               (coe
                                  MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8804'_308
                                  (coe
                                     MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_'8804''45'go_138
                                     (coe d_'8804''45'isPreorder_2800)
                                     (\ v4 v5 v6 v7 v8 -> coe du_'8804''45''60''45'trans_2958 v7 v8))
                                  (MAlonzo.Code.Data.Integer.Base.d__'8854'__258 (coe v3) (coe v2))
                                  v3 v0
                                  (coe
                                     MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8804'_308
                                     (coe
                                        MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_'8804''45'go_138
                                        (coe d_'8804''45'isPreorder_2800)
                                        (\ v4 v5 v6 v7 v8 ->
                                           coe du_'8804''45''60''45'trans_2958 v7 v8))
                                     v3 v0 v0
                                     (coe
                                        MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du__'8718'_492
                                        (coe
                                           MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_stop_166
                                           (coe d_'8804''45'isPreorder_2800))
                                        (coe v0))
                                     (coe
                                        MAlonzo.Code.Data.Integer.Base.C_'43''8804''43'_48
                                        (MAlonzo.Code.Data.Nat.Properties.d_n'8804'1'43'n_2844
                                           (coe v3))))
                                  (d_m'8854'n'8804'm_3912 (coe v3) (coe v2)))
                               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 v0 v1
    = coe
        du_'8804''45''60''45'trans_2958
        (coe d_m'8854'n'8804'm_3912 (coe v0) (coe v1))
        (coe
           MAlonzo.Code.Data.Integer.Base.C_'43''60''43'_72
           (coe
              MAlonzo.Code.Data.Nat.Properties.du_m'60'n'43'm_3630 (coe v0)
              (coe
                 MAlonzo.Code.Data.Nat.Base.C_s'8804's_34
                 (coe 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 v0 v1 ~v2
    = du_m'8854'1'43'n'60'm_3942 v0 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 v0 v1
    = case coe v0 of
        0 -> coe MAlonzo.Code.Data.Integer.Base.C_'45''60''43'_64
        _ -> let v2 = subInt (coe v0) (coe (1 :: Integer)) in
             coe
               (let v3 = subInt (coe v1) (coe (1 :: Integer)) in
                coe
                  (let v4
                         = coe
                             MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_strictRelation_202 in
                   coe
                     (coe
                        MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_begin__126
                        (coe v4)
                        (coe
                           MAlonzo.Code.Data.Integer.Base.d__'8854'__258 (coe v0) (coe v1))
                        (coe v0)
                        (coe
                           MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8801''45''10217'_436
                           (\ v5 v6 v7 v8 v9 -> v9)
                           (MAlonzo.Code.Data.Integer.Base.d__'8854'__258 (coe v0) (coe v1))
                           (MAlonzo.Code.Data.Integer.Base.d__'8854'__258 (coe v2) (coe v3))
                           v0
                           (coe
                              MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''60'_312
                              (coe
                                 MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_'60''45'go_152
                                 (\ v5 v6 v7 v8 v9 -> coe du_'60''45'trans_2986 v8 v9)
                                 (coe
                                    MAlonzo.Code.Relation.Binary.PropositionalEquality.Core.du_resp'8322'_160)
                                 (\ v5 v6 v7 v8 v9 -> coe du_'60''45''8804''45'trans_2972 v8 v9))
                              (MAlonzo.Code.Data.Integer.Base.d__'8854'__258 (coe v2) (coe v3))
                              v0 v0
                              (coe
                                 MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du__'8718'_492
                                 (coe
                                    MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_stop_166
                                    (coe d_'8804''45'isPreorder_2800))
                                 (coe v0))
                              (d_m'8854'n'60'1'43'm_3930 (coe v2) (coe v3)))
                           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 v0 v1
    = case coe v0 of
        0 -> coe MAlonzo.Code.Data.Integer.Base.C_'45''60''43'_64
        _ -> let v2 = subInt (coe v0) (coe (1 :: Integer)) in
             coe
               (case coe v1 of
                  0 -> coe
                         MAlonzo.Code.Data.Integer.Base.C_'45''60''45'_58
                         (MAlonzo.Code.Data.Nat.Properties.d_'8804''45'refl_2776 (coe v0))
                  _ -> let v3 = subInt (coe v1) (coe (1 :: Integer)) in
                       coe
                         (let v4
                                = coe
                                    MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_strictRelation_202 in
                          coe
                            (coe
                               MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_begin__126
                               (coe v4) (coe subInt (coe (-1 :: Integer)) (coe v0))
                               (coe
                                  MAlonzo.Code.Data.Integer.Base.d__'8854'__258 (coe v1) (coe v0))
                               (coe
                                  MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''60'_312
                                  (coe
                                     MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_'60''45'go_152
                                     (\ v5 v6 v7 v8 v9 -> coe du_'60''45'trans_2986 v8 v9)
                                     (coe
                                        MAlonzo.Code.Relation.Binary.PropositionalEquality.Core.du_resp'8322'_160)
                                     (\ v5 v6 v7 v8 v9 -> coe du_'60''45''8804''45'trans_2972 v8 v9))
                                  (subInt (coe (-1 :: Integer)) (coe v0))
                                  (subInt (coe (0 :: Integer)) (coe v0))
                                  (MAlonzo.Code.Data.Integer.Base.d__'8854'__258 (coe v1) (coe v0))
                                  (coe
                                     MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''60'_312
                                     (coe
                                        MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_'60''45'go_152
                                        (\ v5 v6 v7 v8 v9 -> coe du_'60''45'trans_2986 v8 v9)
                                        (coe
                                           MAlonzo.Code.Relation.Binary.PropositionalEquality.Core.du_resp'8322'_160)
                                        (\ v5 v6 v7 v8 v9 ->
                                           coe du_'60''45''8804''45'trans_2972 v8 v9))
                                     (subInt (coe (0 :: Integer)) (coe v0))
                                     (MAlonzo.Code.Data.Integer.Base.d__'8854'__258 (coe v3) (coe v2))
                                     (MAlonzo.Code.Data.Integer.Base.d__'8854'__258 (coe v1) (coe v0))
                                     (coe
                                        MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8801''45''10216'_448
                                        (\ v5 v6 v7 v8 v9 -> v9)
                                        (MAlonzo.Code.Data.Integer.Base.d__'8854'__258
                                           (coe v3) (coe v2))
                                        (MAlonzo.Code.Data.Integer.Base.d__'8854'__258
                                           (coe v1) (coe v0))
                                        (MAlonzo.Code.Data.Integer.Base.d__'8854'__258
                                           (coe v1) (coe v0))
                                        (coe
                                           MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du__'8718'_492
                                           (coe
                                              MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_stop_166
                                              (coe d_'8804''45'isPreorder_2800))
                                           (coe
                                              MAlonzo.Code.Data.Integer.Base.d__'8854'__258 (coe v1)
                                              (coe v0)))
                                        erased)
                                     (d_'45'1'43'm'60'n'8854'm_3958 (coe v2) (coe v3)))
                                  (coe
                                     MAlonzo.Code.Data.Integer.Base.C_'45''60''45'_58
                                     (MAlonzo.Code.Data.Nat.Properties.d_'8804''45'refl_2776
                                        (coe 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 v0 v1
    = case coe v1 of
        0 -> coe
               d_'8804''45'refl_2728 (coe subInt (coe (-1 :: Integer)) (coe v0))
        _ -> let v2 = subInt (coe v1) (coe (1 :: Integer)) in
             coe
               (coe
                  MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_begin__46
                  (coe
                     MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_start_96
                     (coe d_'8804''45'isPreorder_2800)
                     (\ v3 v4 v5 -> coe du_'60''8658''8804'_2846 v5))
                  (subInt (coe (-1 :: Integer)) (coe v0))
                  (MAlonzo.Code.Data.Integer.Base.d__'8854'__258
                     (coe v1) (coe addInt (coe (1 :: Integer)) (coe v0)))
                  (coe
                     MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8804'_308
                     (coe
                        MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_'8804''45'go_138
                        (coe d_'8804''45'isPreorder_2800)
                        (\ v3 v4 v5 v6 v7 -> coe du_'8804''45''60''45'trans_2958 v6 v7))
                     (subInt (coe (-1 :: Integer)) (coe v0))
                     (MAlonzo.Code.Data.Integer.Base.d__'8854'__258 (coe v2) (coe v0))
                     (MAlonzo.Code.Data.Integer.Base.d__'8854'__258
                        (coe v1) (coe addInt (coe (1 :: Integer)) (coe v0)))
                     (coe
                        MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8801''45''10216'_448
                        (\ v3 v4 v5 v6 v7 -> v7)
                        (MAlonzo.Code.Data.Integer.Base.d__'8854'__258 (coe v2) (coe v0))
                        (MAlonzo.Code.Data.Integer.Base.d__'8854'__258
                           (coe v1) (coe addInt (coe (1 :: Integer)) (coe v0)))
                        (MAlonzo.Code.Data.Integer.Base.d__'8854'__258
                           (coe v1) (coe addInt (coe (1 :: Integer)) (coe v0)))
                        (coe
                           MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du__'8718'_492
                           (coe
                              MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_stop_166
                              (coe d_'8804''45'isPreorder_2800))
                           (coe
                              MAlonzo.Code.Data.Integer.Base.d__'8854'__258 (coe v1)
                              (coe addInt (coe (1 :: Integer)) (coe v0))))
                        erased)
                     (coe
                        du_'60''8658''8804'_2846
                        (coe d_'45'1'43'm'60'n'8854'm_3958 (coe v0) (coe 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 v0 v1
    = coe
        du_'60''8658''8804'_2846
        (coe d_'45'1'43'm'60'n'8854'm_3958 (coe v0) (coe 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 v0 ~v1 = du_0'8854'm'8804''43'_4002 v0
  du_0'8854'm'8804''43'_4002 ::
    Integer -> MAlonzo.Code.Data.Integer.Base.T__'8804'__26
  du_0'8854'm'8804''43'_4002 v0
    = case coe v0 of
        0 -> coe
               MAlonzo.Code.Data.Integer.Base.C_'43''8804''43'_48
               (coe MAlonzo.Code.Data.Nat.Base.C_z'8804'n_26)
        _ -> coe 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 = 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 = 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 v0 v1 v2 v3
    = case coe v0 of
        0 -> case coe v3 of
               MAlonzo.Code.Data.Nat.Base.C_z'8804'n_26
                 -> coe du_0'8854'm'8804''43'_4002 (coe v1)
               MAlonzo.Code.Data.Nat.Base.C_s'8804's_34 v6
                 -> coe MAlonzo.Code.Data.Integer.Base.C_'45''8804''45'_34 v6
               _ -> MAlonzo.RTE.mazUnreachableError
        _ -> let v4 = subInt (coe v0) (coe (1 :: Integer)) in
             coe
               (case coe v1 of
                  0 -> coe
                         seq (coe v3)
                         (coe
                            d_'8804''45'refl_2728
                            (coe
                               MAlonzo.Code.Function.Base.du__'45''10216'_'8739'_292
                               (MAlonzo.Code.Data.Integer.Base.d__'8854'__258 (coe v0))
                               (\ v5 v6 -> v5) (0 :: Integer) (0 :: Integer)))
                  _ -> let v5 = subInt (coe v1) (coe (1 :: Integer)) in
                       coe
                         (case coe v3 of
                            MAlonzo.Code.Data.Nat.Base.C_z'8804'n_26
                              -> coe
                                   MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_begin__46
                                   (coe
                                      MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_start_96
                                      (coe d_'8804''45'isPreorder_2800)
                                      (\ v7 v8 v9 -> coe du_'60''8658''8804'_2846 v9))
                                   (coe
                                      MAlonzo.Code.Function.Base.du__'45''10216'_'8739'_292
                                      (MAlonzo.Code.Data.Integer.Base.d__'8854'__258 (coe v0))
                                      (\ v7 v8 -> v7) v1 (0 :: Integer))
                                   (coe
                                      MAlonzo.Code.Function.Base.du_'8739'_'10217''45'__298
                                      (\ v7 v8 -> v8)
                                      (MAlonzo.Code.Data.Integer.Base.d__'8854'__258 (coe v0)) v1
                                      (0 :: Integer))
                                   (coe
                                      MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8801''45''10217'_436
                                      (\ v7 v8 v9 v10 v11 -> v11)
                                      (MAlonzo.Code.Data.Integer.Base.d__'8854'__258
                                         (coe v0) (coe v1))
                                      (MAlonzo.Code.Data.Integer.Base.d__'8854'__258
                                         (coe v4) (coe v5))
                                      (coe
                                         MAlonzo.Code.Function.Base.du_'8739'_'10217''45'__298
                                         (\ v7 v8 -> v8)
                                         (MAlonzo.Code.Data.Integer.Base.d__'8854'__258 (coe v0)) v1
                                         (0 :: Integer))
                                      (coe
                                         MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''60'_312
                                         (coe
                                            MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_'60''45'go_152
                                            (\ v7 v8 v9 v10 v11 -> coe du_'60''45'trans_2986 v10 v11)
                                            (coe
                                               MAlonzo.Code.Relation.Binary.PropositionalEquality.Core.du_resp'8322'_160)
                                            (\ v7 v8 v9 v10 v11 ->
                                               coe du_'60''45''8804''45'trans_2972 v10 v11))
                                         (MAlonzo.Code.Data.Integer.Base.d__'8854'__258
                                            (coe v4) (coe v5))
                                         v0
                                         (coe
                                            MAlonzo.Code.Function.Base.du_'8739'_'10217''45'__298
                                            (\ v7 v8 -> v8)
                                            (MAlonzo.Code.Data.Integer.Base.d__'8854'__258 (coe v0))
                                            v1 (0 :: Integer))
                                         (coe
                                            MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du__'8718'_492
                                            (coe
                                               MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_stop_166
                                               (coe d_'8804''45'isPreorder_2800))
                                            (coe v0))
                                         (d_m'8854'n'60'1'43'm_3930 (coe v4) (coe v5)))
                                      erased)
                            MAlonzo.Code.Data.Nat.Base.C_s'8804's_34 v8
                              -> let v9 = subInt (coe v2) (coe (1 :: Integer)) in
                                 coe
                                   (coe
                                      MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_begin__46
                                      (coe
                                         MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_start_96
                                         (coe d_'8804''45'isPreorder_2800)
                                         (\ v10 v11 v12 -> coe du_'60''8658''8804'_2846 v12))
                                      (coe
                                         MAlonzo.Code.Function.Base.du__'45''10216'_'8739'_292
                                         (MAlonzo.Code.Data.Integer.Base.d__'8854'__258 (coe v0))
                                         (\ v10 v11 -> v10) v1 v2)
                                      (coe
                                         MAlonzo.Code.Function.Base.du_'8739'_'10217''45'__298
                                         (\ v10 v11 -> v11)
                                         (MAlonzo.Code.Data.Integer.Base.d__'8854'__258 (coe v0)) v1
                                         v2)
                                      (coe
                                         MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8801''45''10217'_436
                                         (\ v10 v11 v12 v13 v14 -> v14)
                                         (MAlonzo.Code.Data.Integer.Base.d__'8854'__258
                                            (coe v0) (coe v1))
                                         (MAlonzo.Code.Data.Integer.Base.d__'8854'__258
                                            (coe v4) (coe v5))
                                         (coe
                                            MAlonzo.Code.Function.Base.du_'8739'_'10217''45'__298
                                            (\ v10 v11 -> v11)
                                            (MAlonzo.Code.Data.Integer.Base.d__'8854'__258 (coe v0))
                                            v1 v2)
                                         (coe
                                            MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8804'_308
                                            (coe
                                               MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_'8804''45'go_138
                                               (coe d_'8804''45'isPreorder_2800)
                                               (\ v10 v11 v12 v13 v14 ->
                                                  coe du_'8804''45''60''45'trans_2958 v13 v14))
                                            (MAlonzo.Code.Data.Integer.Base.d__'8854'__258
                                               (coe v4) (coe v5))
                                            (MAlonzo.Code.Data.Integer.Base.d__'8854'__258
                                               (coe v4) (coe v9))
                                            (coe
                                               MAlonzo.Code.Function.Base.du_'8739'_'10217''45'__298
                                               (\ v10 v11 -> v11)
                                               (MAlonzo.Code.Data.Integer.Base.d__'8854'__258
                                                  (coe v0))
                                               v1 v2)
                                            (coe
                                               MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8801''45''10216'_448
                                               (\ v10 v11 v12 v13 v14 -> v14)
                                               (MAlonzo.Code.Data.Integer.Base.d__'8854'__258
                                                  (coe v4) (coe v9))
                                               (MAlonzo.Code.Data.Integer.Base.d__'8854'__258
                                                  (coe v0) (coe v2))
                                               (coe
                                                  MAlonzo.Code.Function.Base.du_'8739'_'10217''45'__298
                                                  (\ v10 v11 -> v11)
                                                  (MAlonzo.Code.Data.Integer.Base.d__'8854'__258
                                                     (coe v0))
                                                  v1 v2)
                                               (coe
                                                  MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du__'8718'_492
                                                  (coe
                                                     MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_stop_166
                                                     (coe d_'8804''45'isPreorder_2800))
                                                  (coe
                                                     MAlonzo.Code.Data.Integer.Base.d__'8854'__258
                                                     (coe v0) (coe v2)))
                                               erased)
                                            (d_'8854''45'mono'691''45''8805''45''8804'_4024
                                               (coe v4) (coe v5) (coe v9) (coe v8)))
                                         erased))
                            _ -> 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 v0 v1 v2 v3
    = case coe v0 of
        0 -> coe MAlonzo.Code.Data.Integer.Base.C_'43''8804''43'_48 v3
        _ -> let v4 = subInt (coe v0) (coe (1 :: Integer)) in
             coe
               (case coe v2 of
                  0 -> coe
                         seq (coe v3)
                         (coe
                            d_'8804''45'refl_2728
                            (coe
                               MAlonzo.Code.Function.Base.du__'45''10216'_'8739'_292
                               (\ v5 ->
                                  MAlonzo.Code.Data.Integer.Base.d__'8854'__258 (coe v5) (coe v0))
                               (\ v5 v6 -> v5) (0 :: Integer) (0 :: Integer)))
                  _ -> let v5 = subInt (coe v2) (coe (1 :: Integer)) in
                       coe
                         (case coe v3 of
                            MAlonzo.Code.Data.Nat.Base.C_z'8804'n_26
                              -> coe
                                   MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_begin__46
                                   (coe
                                      MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_start_96
                                      (coe d_'8804''45'isPreorder_2800)
                                      (\ v7 v8 v9 -> coe du_'60''8658''8804'_2846 v9))
                                   (coe
                                      MAlonzo.Code.Function.Base.du__'45''10216'_'8739'_292
                                      (\ v7 ->
                                         MAlonzo.Code.Data.Integer.Base.d__'8854'__258
                                           (coe v7) (coe v0))
                                      (\ v7 v8 -> v7) (0 :: Integer) v2)
                                   (coe
                                      MAlonzo.Code.Function.Base.du_'8739'_'10217''45'__298
                                      (\ v7 v8 -> v8)
                                      (\ v7 ->
                                         MAlonzo.Code.Data.Integer.Base.d__'8854'__258
                                           (coe v7) (coe v0))
                                      (0 :: Integer) v2)
                                   (coe
                                      MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8804'_308
                                      (coe
                                         MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_'8804''45'go_138
                                         (coe d_'8804''45'isPreorder_2800)
                                         (\ v7 v8 v9 v10 v11 ->
                                            coe du_'8804''45''60''45'trans_2958 v10 v11))
                                      (MAlonzo.Code.Data.Integer.Base.d__'8854'__258
                                         (coe (0 :: Integer)) (coe v0))
                                      (MAlonzo.Code.Data.Integer.Base.d__'8854'__258
                                         (coe (0 :: Integer)) (coe v4))
                                      (coe
                                         MAlonzo.Code.Function.Base.du_'8739'_'10217''45'__298
                                         (\ v7 v8 -> v8)
                                         (\ v7 ->
                                            MAlonzo.Code.Data.Integer.Base.d__'8854'__258
                                              (coe v7) (coe v0))
                                         (0 :: Integer) v2)
                                      (coe
                                         MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8804'_308
                                         (coe
                                            MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_'8804''45'go_138
                                            (coe d_'8804''45'isPreorder_2800)
                                            (\ v7 v8 v9 v10 v11 ->
                                               coe du_'8804''45''60''45'trans_2958 v10 v11))
                                         (MAlonzo.Code.Data.Integer.Base.d__'8854'__258
                                            (coe (0 :: Integer)) (coe v4))
                                         (MAlonzo.Code.Data.Integer.Base.d__'8854'__258
                                            (coe v5) (coe v4))
                                         (coe
                                            MAlonzo.Code.Function.Base.du_'8739'_'10217''45'__298
                                            (\ v7 v8 -> v8)
                                            (\ v7 ->
                                               MAlonzo.Code.Data.Integer.Base.d__'8854'__258
                                                 (coe v7) (coe v0))
                                            (0 :: Integer) v2)
                                         (coe
                                            MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8801''45''10216'_448
                                            (\ v7 v8 v9 v10 v11 -> v11)
                                            (MAlonzo.Code.Data.Integer.Base.d__'8854'__258
                                               (coe v5) (coe v4))
                                            (MAlonzo.Code.Data.Integer.Base.d__'8854'__258
                                               (coe v2) (coe v0))
                                            (coe
                                               MAlonzo.Code.Function.Base.du_'8739'_'10217''45'__298
                                               (\ v7 v8 -> v8)
                                               (\ v7 ->
                                                  MAlonzo.Code.Data.Integer.Base.d__'8854'__258
                                                    (coe v7) (coe v0))
                                               (0 :: Integer) v2)
                                            (coe
                                               MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du__'8718'_492
                                               (coe
                                                  MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_stop_166
                                                  (coe d_'8804''45'isPreorder_2800))
                                               (coe
                                                  MAlonzo.Code.Data.Integer.Base.d__'8854'__258
                                                  (coe v2) (coe v0)))
                                            erased)
                                         (d_'8854''45'mono'737''45''8804'_4056
                                            (coe v4) (coe (0 :: Integer)) (coe v5)
                                            (coe MAlonzo.Code.Data.Nat.Base.C_z'8804'n_26)))
                                      (d_'8854''45'mono'691''45''8805''45''8804'_4024
                                         (coe (0 :: Integer)) (coe v0) (coe v4)
                                         (coe
                                            MAlonzo.Code.Data.Nat.Properties.d_n'8804'1'43'n_2844
                                            (coe v4))))
                            MAlonzo.Code.Data.Nat.Base.C_s'8804's_34 v8
                              -> let v9 = subInt (coe v1) (coe (1 :: Integer)) in
                                 coe
                                   (coe
                                      MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_begin__46
                                      (coe
                                         MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_start_96
                                         (coe d_'8804''45'isPreorder_2800)
                                         (\ v10 v11 v12 -> coe du_'60''8658''8804'_2846 v12))
                                      (coe
                                         MAlonzo.Code.Function.Base.du__'45''10216'_'8739'_292
                                         (\ v10 ->
                                            MAlonzo.Code.Data.Integer.Base.d__'8854'__258
                                              (coe v10) (coe v0))
                                         (\ v10 v11 -> v10) v1 v2)
                                      (coe
                                         MAlonzo.Code.Function.Base.du_'8739'_'10217''45'__298
                                         (\ v10 v11 -> v11)
                                         (\ v10 ->
                                            MAlonzo.Code.Data.Integer.Base.d__'8854'__258
                                              (coe v10) (coe v0))
                                         v1 v2)
                                      (coe
                                         MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8801''45''10217'_436
                                         (\ v10 v11 v12 v13 v14 -> v14)
                                         (MAlonzo.Code.Data.Integer.Base.d__'8854'__258
                                            (coe v1) (coe v0))
                                         (MAlonzo.Code.Data.Integer.Base.d__'8854'__258
                                            (coe v9) (coe v4))
                                         (coe
                                            MAlonzo.Code.Function.Base.du_'8739'_'10217''45'__298
                                            (\ v10 v11 -> v11)
                                            (\ v10 ->
                                               MAlonzo.Code.Data.Integer.Base.d__'8854'__258
                                                 (coe v10) (coe v0))
                                            v1 v2)
                                         (coe
                                            MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8804'_308
                                            (coe
                                               MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_'8804''45'go_138
                                               (coe d_'8804''45'isPreorder_2800)
                                               (\ v10 v11 v12 v13 v14 ->
                                                  coe du_'8804''45''60''45'trans_2958 v13 v14))
                                            (MAlonzo.Code.Data.Integer.Base.d__'8854'__258
                                               (coe v9) (coe v4))
                                            (MAlonzo.Code.Data.Integer.Base.d__'8854'__258
                                               (coe v5) (coe v4))
                                            (coe
                                               MAlonzo.Code.Function.Base.du_'8739'_'10217''45'__298
                                               (\ v10 v11 -> v11)
                                               (\ v10 ->
                                                  MAlonzo.Code.Data.Integer.Base.d__'8854'__258
                                                    (coe v10) (coe v0))
                                               v1 v2)
                                            (coe
                                               MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8801''45''10216'_448
                                               (\ v10 v11 v12 v13 v14 -> v14)
                                               (MAlonzo.Code.Data.Integer.Base.d__'8854'__258
                                                  (coe v5) (coe v4))
                                               (MAlonzo.Code.Data.Integer.Base.d__'8854'__258
                                                  (coe v2) (coe v0))
                                               (coe
                                                  MAlonzo.Code.Function.Base.du_'8739'_'10217''45'__298
                                                  (\ v10 v11 -> v11)
                                                  (\ v10 ->
                                                     MAlonzo.Code.Data.Integer.Base.d__'8854'__258
                                                       (coe v10) (coe v0))
                                                  v1 v2)
                                               (coe
                                                  MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du__'8718'_492
                                                  (coe
                                                     MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_stop_166
                                                     (coe d_'8804''45'isPreorder_2800))
                                                  (coe
                                                     MAlonzo.Code.Data.Integer.Base.d__'8854'__258
                                                     (coe v2) (coe v0)))
                                               erased)
                                            (d_'8854''45'mono'737''45''8804'_4056
                                               (coe v4) (coe v9) (coe v5) (coe v8)))
                                         erased))
                            _ -> 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 v0 v1 v2 v3
    = case coe v0 of
        0 -> case coe v3 of
               MAlonzo.Code.Data.Nat.Base.C_s'8804's_34 v6
                 -> case coe v6 of
                      MAlonzo.Code.Data.Nat.Base.C_z'8804'n_26
                        -> coe MAlonzo.Code.Data.Integer.Base.C_'45''60''43'_64
                      MAlonzo.Code.Data.Nat.Base.C_s'8804's_34 v9
                        -> coe
                             MAlonzo.Code.Data.Integer.Base.C_'45''60''45'_58
                             (coe MAlonzo.Code.Data.Nat.Base.C_s'8804's_34 v9)
                      _ -> MAlonzo.RTE.mazUnreachableError
               _ -> MAlonzo.RTE.mazUnreachableError
        _ -> let v4 = subInt (coe v0) (coe (1 :: Integer)) in
             coe
               (let v5 = subInt (coe v1) (coe (1 :: Integer)) in
                coe
                  (case coe v3 of
                     MAlonzo.Code.Data.Nat.Base.C_s'8804's_34 v8
                       -> case coe v8 of
                            MAlonzo.Code.Data.Nat.Base.C_z'8804'n_26
                              -> let v10
                                       = coe
                                           MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_strictRelation_202 in
                                 coe
                                   (coe
                                      MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_begin__126
                                      (coe v10)
                                      (coe
                                         MAlonzo.Code.Data.Integer.Base.d__'8854'__258 (coe v0)
                                         (coe v1))
                                      (coe v0)
                                      (coe
                                         MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8801''45''10217'_436
                                         (\ v11 v12 v13 v14 v15 -> v15)
                                         (MAlonzo.Code.Data.Integer.Base.d__'8854'__258
                                            (coe v0) (coe v1))
                                         (MAlonzo.Code.Data.Integer.Base.d__'8854'__258
                                            (coe v4) (coe v5))
                                         v0
                                         (coe
                                            MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''60'_312
                                            (coe
                                               MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_'60''45'go_152
                                               (\ v11 v12 v13 v14 v15 ->
                                                  coe du_'60''45'trans_2986 v14 v15)
                                               (coe
                                                  MAlonzo.Code.Relation.Binary.PropositionalEquality.Core.du_resp'8322'_160)
                                               (\ v11 v12 v13 v14 v15 ->
                                                  coe du_'60''45''8804''45'trans_2972 v14 v15))
                                            (MAlonzo.Code.Data.Integer.Base.d__'8854'__258
                                               (coe v4) (coe v5))
                                            v0 v0
                                            (coe
                                               MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du__'8718'_492
                                               (coe
                                                  MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_stop_166
                                                  (coe d_'8804''45'isPreorder_2800))
                                               (coe v0))
                                            (d_m'8854'n'60'1'43'm_3930 (coe v4) (coe v5)))
                                         erased))
                            MAlonzo.Code.Data.Nat.Base.C_s'8804's_34 v11
                              -> let v12 = subInt (coe v2) (coe (1 :: Integer)) in
                                 coe
                                   (let v13
                                          = coe
                                              MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_strictRelation_202 in
                                    coe
                                      (coe
                                         MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_begin__126
                                         (coe v13)
                                         (coe
                                            MAlonzo.Code.Data.Integer.Base.d__'8854'__258 (coe v0)
                                            (coe v1))
                                         (coe
                                            MAlonzo.Code.Data.Integer.Base.d__'8854'__258 (coe v0)
                                            (coe v2))
                                         (coe
                                            MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8801''45''10217'_436
                                            (\ v14 v15 v16 v17 v18 -> v18)
                                            (MAlonzo.Code.Data.Integer.Base.d__'8854'__258
                                               (coe v0) (coe v1))
                                            (MAlonzo.Code.Data.Integer.Base.d__'8854'__258
                                               (coe v4) (coe subInt (coe v1) (coe (1 :: Integer))))
                                            (MAlonzo.Code.Data.Integer.Base.d__'8854'__258
                                               (coe v0) (coe v2))
                                            (coe
                                               MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''60'_312
                                               (coe
                                                  MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_'60''45'go_152
                                                  (\ v14 v15 v16 v17 v18 ->
                                                     coe du_'60''45'trans_2986 v17 v18)
                                                  (coe
                                                     MAlonzo.Code.Relation.Binary.PropositionalEquality.Core.du_resp'8322'_160)
                                                  (\ v14 v15 v16 v17 v18 ->
                                                     coe du_'60''45''8804''45'trans_2972 v17 v18))
                                               (MAlonzo.Code.Data.Integer.Base.d__'8854'__258
                                                  (coe v4) (coe subInt (coe v1) (coe (1 :: Integer))))
                                               (MAlonzo.Code.Data.Integer.Base.d__'8854'__258
                                                  (coe v4) (coe v12))
                                               (MAlonzo.Code.Data.Integer.Base.d__'8854'__258
                                                  (coe v0) (coe v2))
                                               (coe
                                                  MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8801''45''10216'_448
                                                  (\ v14 v15 v16 v17 v18 -> v18)
                                                  (MAlonzo.Code.Data.Integer.Base.d__'8854'__258
                                                     (coe v4) (coe v12))
                                                  (MAlonzo.Code.Data.Integer.Base.d__'8854'__258
                                                     (coe v0) (coe v2))
                                                  (MAlonzo.Code.Data.Integer.Base.d__'8854'__258
                                                     (coe v0) (coe v2))
                                                  (coe
                                                     MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du__'8718'_492
                                                     (coe
                                                        MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_stop_166
                                                        (coe d_'8804''45'isPreorder_2800))
                                                     (coe
                                                        MAlonzo.Code.Data.Integer.Base.d__'8854'__258
                                                        (coe v0) (coe v2)))
                                                  erased)
                                               (d_'8854''45'mono'691''45''62''45''60'_4086
                                                  (coe v4) (coe subInt (coe v1) (coe (1 :: Integer)))
                                                  (coe v12)
                                                  (coe MAlonzo.Code.Data.Nat.Base.C_s'8804's_34 v11)))
                                            erased)))
                            _ -> MAlonzo.RTE.mazUnreachableError
                     _ -> 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 v0 v1 v2 v3
    = case coe v0 of
        0 -> coe MAlonzo.Code.Data.Integer.Base.C_'43''60''43'_72 v3
        _ -> let v4 = subInt (coe v0) (coe (1 :: Integer)) in
             coe
               (let v5 = subInt (coe v2) (coe (1 :: Integer)) in
                coe
                  (case coe v3 of
                     MAlonzo.Code.Data.Nat.Base.C_s'8804's_34 v8
                       -> case coe v8 of
                            MAlonzo.Code.Data.Nat.Base.C_z'8804'n_26
                              -> let v10
                                       = coe
                                           MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_strictRelation_202 in
                                 coe
                                   (coe
                                      MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_begin__126
                                      (coe v10) (coe subInt (coe (0 :: Integer)) (coe v0))
                                      (coe
                                         MAlonzo.Code.Data.Integer.Base.d__'8854'__258 (coe v2)
                                         (coe v0))
                                      (coe
                                         MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''60'_312
                                         (coe
                                            MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_'60''45'go_152
                                            (\ v11 v12 v13 v14 v15 ->
                                               coe du_'60''45'trans_2986 v14 v15)
                                            (coe
                                               MAlonzo.Code.Relation.Binary.PropositionalEquality.Core.du_resp'8322'_160)
                                            (\ v11 v12 v13 v14 v15 ->
                                               coe du_'60''45''8804''45'trans_2972 v14 v15))
                                         (subInt (coe (0 :: Integer)) (coe v0))
                                         (MAlonzo.Code.Data.Integer.Base.d__'8854'__258
                                            (coe v5) (coe v4))
                                         (MAlonzo.Code.Data.Integer.Base.d__'8854'__258
                                            (coe v2) (coe v0))
                                         (coe
                                            MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8801''45''10216'_448
                                            (\ v11 v12 v13 v14 v15 -> v15)
                                            (MAlonzo.Code.Data.Integer.Base.d__'8854'__258
                                               (coe v5) (coe v4))
                                            (MAlonzo.Code.Data.Integer.Base.d__'8854'__258
                                               (coe v2) (coe v0))
                                            (MAlonzo.Code.Data.Integer.Base.d__'8854'__258
                                               (coe v2) (coe v0))
                                            (coe
                                               MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du__'8718'_492
                                               (coe
                                                  MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_stop_166
                                                  (coe d_'8804''45'isPreorder_2800))
                                               (coe
                                                  MAlonzo.Code.Data.Integer.Base.d__'8854'__258
                                                  (coe v2) (coe v0)))
                                            erased)
                                         (d_'45'1'43'm'60'n'8854'm_3958 (coe v4) (coe v5))))
                            MAlonzo.Code.Data.Nat.Base.C_s'8804's_34 v11
                              -> let v12 = subInt (coe v1) (coe (1 :: Integer)) in
                                 coe
                                   (let v13
                                          = coe
                                              MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_strictRelation_202 in
                                    coe
                                      (coe
                                         MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_begin__126
                                         (coe v13)
                                         (coe
                                            MAlonzo.Code.Data.Integer.Base.d__'8854'__258 (coe v1)
                                            (coe v0))
                                         (coe
                                            MAlonzo.Code.Data.Integer.Base.d__'8854'__258 (coe v2)
                                            (coe v0))
                                         (coe
                                            MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8801''45''10217'_436
                                            (\ v14 v15 v16 v17 v18 -> v18)
                                            (MAlonzo.Code.Data.Integer.Base.d__'8854'__258
                                               (coe v1) (coe v0))
                                            (MAlonzo.Code.Data.Integer.Base.d__'8854'__258
                                               (coe v12) (coe v4))
                                            (MAlonzo.Code.Data.Integer.Base.d__'8854'__258
                                               (coe v2) (coe v0))
                                            (coe
                                               MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''60'_312
                                               (coe
                                                  MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_'60''45'go_152
                                                  (\ v14 v15 v16 v17 v18 ->
                                                     coe du_'60''45'trans_2986 v17 v18)
                                                  (coe
                                                     MAlonzo.Code.Relation.Binary.PropositionalEquality.Core.du_resp'8322'_160)
                                                  (\ v14 v15 v16 v17 v18 ->
                                                     coe du_'60''45''8804''45'trans_2972 v17 v18))
                                               (MAlonzo.Code.Data.Integer.Base.d__'8854'__258
                                                  (coe v12) (coe v4))
                                               (MAlonzo.Code.Data.Integer.Base.d__'8854'__258
                                                  (coe subInt (coe v2) (coe (1 :: Integer))) (coe v4))
                                               (MAlonzo.Code.Data.Integer.Base.d__'8854'__258
                                                  (coe v2) (coe v0))
                                               (coe
                                                  MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8801''45''10216'_448
                                                  (\ v14 v15 v16 v17 v18 -> v18)
                                                  (MAlonzo.Code.Data.Integer.Base.d__'8854'__258
                                                     (coe subInt (coe v2) (coe (1 :: Integer)))
                                                     (coe v4))
                                                  (MAlonzo.Code.Data.Integer.Base.d__'8854'__258
                                                     (coe v2) (coe v0))
                                                  (MAlonzo.Code.Data.Integer.Base.d__'8854'__258
                                                     (coe v2) (coe v0))
                                                  (coe
                                                     MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du__'8718'_492
                                                     (coe
                                                        MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_stop_166
                                                        (coe d_'8804''45'isPreorder_2800))
                                                     (coe
                                                        MAlonzo.Code.Data.Integer.Base.d__'8854'__258
                                                        (coe v2) (coe v0)))
                                                  erased)
                                               (d_'8854''45'mono'737''45''60'_4114
                                                  (coe v4) (coe v12)
                                                  (coe subInt (coe v2) (coe (1 :: Integer)))
                                                  (coe MAlonzo.Code.Data.Nat.Base.C_s'8804's_34 v11)))
                                            erased)))
                            _ -> MAlonzo.RTE.mazUnreachableError
                     _ -> 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 = 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 = 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 = erased
  -- Data.Integer.Properties.+-identity
  d_'43''45'identity_4152 :: MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  d_'43''45'identity_4152
    = coe MAlonzo.Code.Agda.Builtin.Sigma.C__'44'__32 erased 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 = 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 = 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 = 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 = 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 = 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 = 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 = erased
  -- Data.Integer.Properties.+-inverse
  d_'43''45'inverse_4422 :: MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  d_'43''45'inverse_4422
    = coe MAlonzo.Code.Agda.Builtin.Sigma.C__'44'__32 erased erased
  -- Data.Integer.Properties.+-isMagma
  d_'43''45'isMagma_4424 ::
    MAlonzo.Code.Algebra.Structures.T_IsMagma_176
  d_'43''45'isMagma_4424
    = coe
        MAlonzo.Code.Algebra.Structures.C_IsMagma'46'constructor_1867
        (coe
           MAlonzo.Code.Relation.Binary.PropositionalEquality.Properties.du_isEquivalence_396)
        erased
  -- Data.Integer.Properties.+-isSemigroup
  d_'43''45'isSemigroup_4426 ::
    MAlonzo.Code.Algebra.Structures.T_IsSemigroup_472
  d_'43''45'isSemigroup_4426
    = coe
        MAlonzo.Code.Algebra.Structures.C_IsSemigroup'46'constructor_10417
        (coe d_'43''45'isMagma_4424) erased
  -- Data.Integer.Properties.+-isCommutativeSemigroup
  d_'43''45'isCommutativeSemigroup_4428 ::
    MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_548
  d_'43''45'isCommutativeSemigroup_4428
    = coe
        MAlonzo.Code.Algebra.Structures.C_IsCommutativeSemigroup'46'constructor_12093
        (coe d_'43''45'isSemigroup_4426) 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
    = coe
        MAlonzo.Code.Algebra.Structures.C_IsMonoid'46'constructor_15873
        (coe d_'43''45'isSemigroup_4426) (coe 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
    = coe
        MAlonzo.Code.Algebra.Structures.C_IsCommutativeMonoid'46'constructor_17695
        (coe d_'43''45'0'45'isMonoid_4430) 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
    = coe
        MAlonzo.Code.Algebra.Structures.C_IsGroup'46'constructor_26963
        (coe d_'43''45'0'45'isMonoid_4430) (coe d_'43''45'inverse_4422)
        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
    = coe
        MAlonzo.Code.Algebra.Structures.C_IsAbelianGroup'46'constructor_32441
        (coe d_'43''45'0'45'isGroup_4434) erased
  -- Data.Integer.Properties.+-magma
  d_'43''45'magma_4438 :: MAlonzo.Code.Algebra.Bundles.T_Magma_68
  d_'43''45'magma_4438
    = coe
        MAlonzo.Code.Algebra.Bundles.C_Magma'46'constructor_1279
        MAlonzo.Code.Data.Integer.Base.d__'43'__276 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
    = coe
        MAlonzo.Code.Algebra.Bundles.C_Semigroup'46'constructor_9793
        MAlonzo.Code.Data.Integer.Base.d__'43'__276
        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
    = coe
        MAlonzo.Code.Algebra.Bundles.C_CommutativeSemigroup'46'constructor_12035
        MAlonzo.Code.Data.Integer.Base.d__'43'__276
        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
    = coe
        MAlonzo.Code.Algebra.Bundles.C_Monoid'46'constructor_16157
        MAlonzo.Code.Data.Integer.Base.d__'43'__276 (0 :: Integer)
        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
    = coe
        MAlonzo.Code.Algebra.Bundles.C_CommutativeMonoid'46'constructor_17931
        MAlonzo.Code.Data.Integer.Base.d__'43'__276 (0 :: Integer)
        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
    = coe
        MAlonzo.Code.Algebra.Bundles.C_AbelianGroup'46'constructor_29855
        MAlonzo.Code.Data.Integer.Base.d__'43'__276 (0 :: Integer)
        MAlonzo.Code.Data.Integer.Base.d_'45'__252
        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 = 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 = 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 = 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 v0 v1 v2 v3
    = case coe v0 of
        _ | coe geqInt (coe v0) (coe (0 :: Integer)) ->
            case coe v3 of
              MAlonzo.Code.Data.Integer.Base.C_'45''8804''45'_34 v6
                -> coe
                     d_'8854''45'mono'691''45''8805''45''8804'_4024 (coe v0)
                     (coe subInt (coe (0 :: Integer)) (coe v1))
                     (coe subInt (coe (0 :: Integer)) (coe v2))
                     (coe MAlonzo.Code.Data.Nat.Base.C_s'8804's_34 v6)
              MAlonzo.Code.Data.Integer.Base.C_'45''8804''43'_40
                -> coe
                     du_'8804''45'trans_2730
                     (coe
                        d_m'8854'n'8804'm_3912 (coe v0)
                        (coe subInt (coe (0 :: Integer)) (coe v1)))
                     (coe
                        MAlonzo.Code.Data.Integer.Base.C_'43''8804''43'_48
                        (coe
                           MAlonzo.Code.Data.Nat.Properties.du_m'8804'm'43'n_3482 (coe v0)))
              MAlonzo.Code.Data.Integer.Base.C_'43''8804''43'_48 v6
                -> coe
                     MAlonzo.Code.Data.Integer.Base.C_'43''8804''43'_48
                     (coe
                        MAlonzo.Code.Data.Nat.Properties.du_'43''45'mono'691''45''8804'_3554
                        (coe v0) (coe v2) (coe v6))
              _ -> MAlonzo.RTE.mazUnreachableError
        _ -> case coe v3 of
               MAlonzo.Code.Data.Integer.Base.C_'45''8804''45'_34 v6
                 -> let v7 = subInt (coe (-1 :: Integer)) (coe v1) in
                    coe
                      (coe
                         MAlonzo.Code.Data.Integer.Base.C_'45''8804''45'_34
                         (coe
                            MAlonzo.Code.Data.Nat.Properties.du_'43''45'mono'691''45''8804'_3554
                            (coe subInt (coe (0 :: Integer)) (coe v0)) (coe v7) (coe v6)))
               MAlonzo.Code.Data.Integer.Base.C_'45''8804''43'_40
                 -> coe
                      du_'8804''45'trans_2730
                      (coe
                         MAlonzo.Code.Data.Integer.Base.C_'45''8804''45'_34
                         (coe
                            MAlonzo.Code.Data.Nat.Properties.du_m'8804'm'43'n_3482
                            (coe subInt (coe (0 :: Integer)) (coe v0))))
                      (coe
                         d_'45'1'43'm'8804'n'8854'm_3992
                         (coe subInt (coe (0 :: Integer)) (coe v0)) (coe v2))
               MAlonzo.Code.Data.Integer.Base.C_'43''8804''43'_48 v6
                 -> coe
                      d_'8854''45'mono'737''45''8804'_4056
                      (coe subInt (coe (0 :: Integer)) (coe v0)) (coe v1) (coe v2)
                      (coe v6)
               _ -> 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 v0 v1 v2
    = coe d_'43''45'mono'691''45''8804'_4510 (coe v0) (coe v1) (coe 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 v0 v1 v2 v3 v4 v5
    = coe
        MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_begin__46
        (coe
           MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_start_96
           (coe d_'8804''45'isPreorder_2800)
           (\ v6 v7 v8 -> coe du_'60''8658''8804'_2846 v8))
        (MAlonzo.Code.Data.Integer.Base.d__'43'__276 (coe v0) (coe v2))
        (MAlonzo.Code.Data.Integer.Base.d__'43'__276 (coe v1) (coe v3))
        (coe
           MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8804'_308
           (coe
              MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_'8804''45'go_138
              (coe d_'8804''45'isPreorder_2800)
              (\ v6 v7 v8 v9 v10 -> coe du_'8804''45''60''45'trans_2958 v9 v10))
           (MAlonzo.Code.Data.Integer.Base.d__'43'__276 (coe v0) (coe v2))
           (MAlonzo.Code.Data.Integer.Base.d__'43'__276 (coe v1) (coe v2))
           (MAlonzo.Code.Data.Integer.Base.d__'43'__276 (coe v1) (coe v3))
           (coe
              MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8804'_308
              (coe
                 MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_'8804''45'go_138
                 (coe d_'8804''45'isPreorder_2800)
                 (\ v6 v7 v8 v9 v10 -> coe du_'8804''45''60''45'trans_2958 v9 v10))
              (MAlonzo.Code.Data.Integer.Base.d__'43'__276 (coe v1) (coe v2))
              (MAlonzo.Code.Data.Integer.Base.d__'43'__276 (coe v1) (coe v3))
              (MAlonzo.Code.Data.Integer.Base.d__'43'__276 (coe v1) (coe v3))
              (coe
                 MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du__'8718'_492
                 (coe
                    MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_stop_166
                    (coe d_'8804''45'isPreorder_2800))
                 (coe
                    MAlonzo.Code.Data.Integer.Base.d__'43'__276 (coe v1) (coe v3)))
              (d_'43''45'mono'691''45''8804'_4510
                 (coe v1) (coe v2) (coe v3) (coe v5)))
           (coe d_'43''45'mono'737''45''8804'_4540 v2 v0 v1 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 v0 v1 v2 ~v3 v4
    = du_i'8804'j'8658'i'8804'k'43'j_4578 v0 v1 v2 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 v0 v1 v2 v3
    = coe
        d_'43''45'mono'45''8804'_4556 (coe (0 :: Integer)) (coe v2)
        (coe v0) (coe v1)
        (coe
           MAlonzo.Code.Data.Integer.Base.C_'43''8804''43'_48
           (coe MAlonzo.Code.Data.Nat.Base.C_z'8804'n_26))
        (coe 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 v0 v1 ~v2 = du_i'8804'j'43'i_4592 v0 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 v0 v1
    = coe
        du_i'8804'j'8658'i'8804'k'43'j_4578 (coe v0) (coe v0) (coe v1)
        (coe d_'8804''45'refl_2728 (coe 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 v0 v1 ~v2 = du_i'8804'i'43'j_4604 v0 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 v0 v1
    = coe du_i'8804'j'43'i_4592 (coe v0) (coe 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 v0 v1 v2 v3
    = case coe v0 of
        _ | coe geqInt (coe v0) (coe (0 :: Integer)) ->
            case coe v3 of
              MAlonzo.Code.Data.Integer.Base.C_'45''60''45'_58 v6
                -> coe
                     d_'8854''45'mono'691''45''62''45''60'_4086 (coe v0)
                     (coe subInt (coe (0 :: Integer)) (coe v1))
                     (coe subInt (coe (0 :: Integer)) (coe v2))
                     (coe MAlonzo.Code.Data.Nat.Base.C_s'8804's_34 v6)
              MAlonzo.Code.Data.Integer.Base.C_'45''60''43'_64
                -> coe
                     du_'60''45''8804''45'trans_2972
                     (coe
                        du_m'8854'1'43'n'60'm_3942 (coe v0)
                        (coe subInt (coe (0 :: Integer)) (coe v1)))
                     (coe
                        MAlonzo.Code.Data.Integer.Base.C_'43''8804''43'_48
                        (coe
                           MAlonzo.Code.Data.Nat.Properties.du_m'8804'm'43'n_3482 (coe v0)))
              MAlonzo.Code.Data.Integer.Base.C_'43''60''43'_72 v6
                -> coe
                     MAlonzo.Code.Data.Integer.Base.C_'43''60''43'_72
                     (coe
                        MAlonzo.Code.Data.Nat.Properties.du_'43''45'mono'691''45''60'_3596
                        (coe v0) (coe v6))
              _ -> MAlonzo.RTE.mazUnreachableError
        _ -> let v4 = subInt (coe (-1 :: Integer)) (coe v0) in
             coe
               (case coe v3 of
                  MAlonzo.Code.Data.Integer.Base.C_'45''60''45'_58 v7
                    -> coe
                         MAlonzo.Code.Data.Integer.Base.C_'45''60''45'_58
                         (coe
                            MAlonzo.Code.Data.Nat.Properties.du_'43''45'mono'691''45''60'_3596
                            (coe subInt (coe (0 :: Integer)) (coe v0)) (coe v7))
                  MAlonzo.Code.Data.Integer.Base.C_'45''60''43'_64
                    -> coe
                         du_'60''45''8804''45'trans_2972
                         (coe
                            MAlonzo.Code.Data.Integer.Base.C_'45''60''45'_58
                            (coe
                               MAlonzo.Code.Data.Nat.Properties.du_m'8804'm'43'n_3482
                               (coe subInt (coe (0 :: Integer)) (coe v0))))
                         (coe
                            d_'45''91'1'43'm'93''8804'n'8854'm'43'1_3976 (coe v4) (coe v2))
                  MAlonzo.Code.Data.Integer.Base.C_'43''60''43'_72 v7
                    -> coe
                         d_'8854''45'mono'737''45''60'_4114
                         (coe subInt (coe (0 :: Integer)) (coe v0)) (coe v1) (coe v2)
                         (coe v7)
                  _ -> 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 v0 v1 v2
    = coe d_'43''45'mono'691''45''60'_4616 (coe v0) (coe v1) (coe 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 v0 v1 v2 v3 v4 v5
    = let v6
            = coe
                MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_strictRelation_202 in
      coe
        (coe
           MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_begin__126
           (coe v6)
           (coe MAlonzo.Code.Data.Integer.Base.d__'43'__276 (coe v0) (coe v2))
           (coe MAlonzo.Code.Data.Integer.Base.d__'43'__276 (coe v1) (coe v3))
           (coe
              MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''60'_312
              (coe
                 MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_'60''45'go_152
                 (\ v7 v8 v9 v10 v11 -> coe du_'60''45'trans_2986 v10 v11)
                 (coe
                    MAlonzo.Code.Relation.Binary.PropositionalEquality.Core.du_resp'8322'_160)
                 (\ v7 v8 v9 v10 v11 ->
                    coe du_'60''45''8804''45'trans_2972 v10 v11))
              (MAlonzo.Code.Data.Integer.Base.d__'43'__276 (coe v0) (coe v2))
              (MAlonzo.Code.Data.Integer.Base.d__'43'__276 (coe v1) (coe v2))
              (MAlonzo.Code.Data.Integer.Base.d__'43'__276 (coe v1) (coe v3))
              (coe
                 MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''60'_312
                 (coe
                    MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_'60''45'go_152
                    (\ v7 v8 v9 v10 v11 -> coe du_'60''45'trans_2986 v10 v11)
                    (coe
                       MAlonzo.Code.Relation.Binary.PropositionalEquality.Core.du_resp'8322'_160)
                    (\ v7 v8 v9 v10 v11 ->
                       coe du_'60''45''8804''45'trans_2972 v10 v11))
                 (MAlonzo.Code.Data.Integer.Base.d__'43'__276 (coe v1) (coe v2))
                 (MAlonzo.Code.Data.Integer.Base.d__'43'__276 (coe v1) (coe v3))
                 (MAlonzo.Code.Data.Integer.Base.d__'43'__276 (coe v1) (coe v3))
                 (coe
                    MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du__'8718'_492
                    (coe
                       MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_stop_166
                       (coe d_'8804''45'isPreorder_2800))
                    (coe
                       MAlonzo.Code.Data.Integer.Base.d__'43'__276 (coe v1) (coe v3)))
                 (d_'43''45'mono'691''45''60'_4616
                    (coe v1) (coe v2) (coe v3) (coe v5)))
              (coe d_'43''45'mono'737''45''60'_4644 v2 v0 v1 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 v0 v1 v2 v3 v4 v5
    = coe
        du_'8804''45''60''45'trans_2958
        (coe d_'43''45'mono'737''45''8804'_4540 v2 v0 v1 v4)
        (coe
           d_'43''45'mono'691''45''60'_4616 (coe v1) (coe v2) (coe v3)
           (coe 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 v0 v1 v2 v3 v4 v5
    = coe
        du_'60''45''8804''45'trans_2972
        (coe d_'43''45'mono'737''45''60'_4644 v2 v0 v1 v4)
        (coe
           d_'43''45'mono'691''45''8804'_4510 (coe v1) (coe v2) (coe v3)
           (coe 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 = 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 = 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 = 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 = 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 = 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 = 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 = 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 v0 ~v1 v2 ~v3 v4
    = du_i'8804'j'8658'i'45'k'8804'j_4852 v0 v2 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 v0 v1 v2
    = case coe v1 of
        0 -> coe v2
        _ -> let v3 = subInt (coe v1) (coe (1 :: Integer)) in
             coe
               (case coe v0 of
                  _ | coe geqInt (coe v0) (coe (0 :: Integer)) ->
                      coe
                        du_'8804''45'trans_2730
                        (coe d_m'8854'n'8804'm_3912 (coe v0) (coe v1)) (coe v2)
                  _ -> let v4 = subInt (coe (-1 :: Integer)) (coe v0) in
                       coe
                         (coe
                            du_'8804''45'trans_2730
                            (coe
                               MAlonzo.Code.Data.Integer.Base.C_'45''8804''45'_34
                               (coe
                                  MAlonzo.Code.Data.Nat.Properties.du_'8804''45'trans_2784
                                  (coe
                                     MAlonzo.Code.Data.Nat.Properties.du_m'8804'm'43'n_3482 (coe v4))
                                  (coe
                                     MAlonzo.Code.Data.Nat.Properties.d_n'8804'1'43'n_2844
                                     (coe addInt (coe v4) (coe v3)))))
                            (coe 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 v0 v1 ~v2 = du_i'45'j'8804'i_4880 v0 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 v0 v1
    = coe
        du_i'8804'j'8658'i'45'k'8804'j_4852 (coe v0) (coe v1)
        (coe d_'8804''45'refl_2728 (coe 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 v0 v1 v2
    = case coe v2 of
        MAlonzo.Code.Data.Integer.Base.C_'45''8804''45'_34 v5
          -> let v6 = subInt (coe (-1 :: Integer)) (coe v0) in
             coe
               (let v7 = subInt (coe (-1 :: Integer)) (coe v1) in
                coe
                  (coe
                     MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_begin__46
                     (coe
                        MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_start_96
                        (coe d_'8804''45'isPreorder_2800)
                        (\ v8 v9 v10 -> coe du_'60''8658''8804'_2846 v10))
                     (MAlonzo.Code.Data.Integer.Base.d__'45'__294 (coe v0) (coe v1))
                     MAlonzo.Code.Data.Integer.Base.d_0ℤ_12
                     (coe
                        MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8801''45''10217'_436
                        (\ v8 v9 v10 v11 v12 -> v12)
                        (MAlonzo.Code.Data.Integer.Base.d__'8854'__258
                           (coe subInt (coe (0 :: Integer)) (coe v1))
                           (coe subInt (coe (0 :: Integer)) (coe v0)))
                        (MAlonzo.Code.Data.Integer.Base.d__'8854'__258 (coe v7) (coe v6))
                        MAlonzo.Code.Data.Integer.Base.d_0ℤ_12
                        (coe
                           MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8804'_308
                           (coe
                              MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_'8804''45'go_138
                              (coe d_'8804''45'isPreorder_2800)
                              (\ v8 v9 v10 v11 v12 ->
                                 coe du_'8804''45''60''45'trans_2958 v11 v12))
                           (MAlonzo.Code.Data.Integer.Base.d__'8854'__258 (coe v7) (coe v6))
                           (MAlonzo.Code.Data.Integer.Base.d__'8854'__258 (coe v7) (coe v7))
                           MAlonzo.Code.Data.Integer.Base.d_0ℤ_12
                           (coe
                              MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8801''45''10217'_436
                              (\ v8 v9 v10 v11 v12 -> v12)
                              (MAlonzo.Code.Data.Integer.Base.d__'8854'__258 (coe v7) (coe v7))
                              MAlonzo.Code.Data.Integer.Base.d_0ℤ_12
                              MAlonzo.Code.Data.Integer.Base.d_0ℤ_12
                              (coe
                                 MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du__'8718'_492
                                 (coe
                                    MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_stop_166
                                    (coe d_'8804''45'isPreorder_2800))
                                 (coe MAlonzo.Code.Data.Integer.Base.d_0ℤ_12))
                              erased)
                           (d_'8854''45'mono'691''45''8805''45''8804'_4024
                              (coe v7) (coe v6) (coe v7) (coe v5)))
                        erased)))
        MAlonzo.Code.Data.Integer.Base.C_'45''8804''43'_40
          -> coe
               du_i'8804'j'8658'i'45'k'8804'j_4852 (coe v0) (coe v1)
               (coe MAlonzo.Code.Data.Integer.Base.C_'45''8804''43'_40)
        MAlonzo.Code.Data.Integer.Base.C_'43''8804''43'_48 v5
          -> case coe v1 of
               0 -> coe
                      seq (coe v5)
                      (coe
                         MAlonzo.Code.Data.Integer.Base.C_'43''8804''43'_48
                         (coe MAlonzo.Code.Data.Nat.Base.C_z'8804'n_26))
               _ -> let v6 = subInt (coe v1) (coe (1 :: Integer)) in
                    coe
                      (case coe v5 of
                         MAlonzo.Code.Data.Nat.Base.C_z'8804'n_26
                           -> coe MAlonzo.Code.Data.Integer.Base.C_'45''8804''43'_40
                         MAlonzo.Code.Data.Nat.Base.C_s'8804's_34 v9
                           -> let v10 = subInt (coe v0) (coe (1 :: Integer)) in
                              coe
                                (coe
                                   MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_begin__46
                                   (coe
                                      MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_start_96
                                      (coe d_'8804''45'isPreorder_2800)
                                      (\ v11 v12 v13 -> coe du_'60''8658''8804'_2846 v13))
                                   (MAlonzo.Code.Data.Integer.Base.d__'45'__294 (coe v0) (coe v1))
                                   MAlonzo.Code.Data.Integer.Base.d_0ℤ_12
                                   (coe
                                      MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8801''45''10217'_436
                                      (\ v11 v12 v13 v14 v15 -> v15)
                                      (MAlonzo.Code.Data.Integer.Base.d__'8854'__258
                                         (coe v0) (coe v1))
                                      (MAlonzo.Code.Data.Integer.Base.d__'8854'__258
                                         (coe v10) (coe v6))
                                      MAlonzo.Code.Data.Integer.Base.d_0ℤ_12
                                      (coe
                                         MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8804'_308
                                         (coe
                                            MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_'8804''45'go_138
                                            (coe d_'8804''45'isPreorder_2800)
                                            (\ v11 v12 v13 v14 v15 ->
                                               coe du_'8804''45''60''45'trans_2958 v14 v15))
                                         (MAlonzo.Code.Data.Integer.Base.d__'8854'__258
                                            (coe v10) (coe v6))
                                         (MAlonzo.Code.Data.Integer.Base.d__'8854'__258
                                            (coe v10) (coe v10))
                                         MAlonzo.Code.Data.Integer.Base.d_0ℤ_12
                                         (coe
                                            MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8801''45''10217'_436
                                            (\ v11 v12 v13 v14 v15 -> v15)
                                            (MAlonzo.Code.Data.Integer.Base.d__'8854'__258
                                               (coe v10) (coe v10))
                                            MAlonzo.Code.Data.Integer.Base.d_0ℤ_12
                                            MAlonzo.Code.Data.Integer.Base.d_0ℤ_12
                                            (coe
                                               MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du__'8718'_492
                                               (coe
                                                  MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_stop_166
                                                  (coe d_'8804''45'isPreorder_2800))
                                               (coe MAlonzo.Code.Data.Integer.Base.d_0ℤ_12))
                                            erased)
                                         (d_'8854''45'mono'691''45''8805''45''8804'_4024
                                            (coe v10) (coe v6) (coe v10) (coe v9)))
                                      erased))
                         _ -> MAlonzo.RTE.mazUnreachableError)
        _ -> 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 v0 v1 v2
    = coe
        MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_begin__46
        (coe
           MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_start_96
           (coe d_'8804''45'isPreorder_2800)
           (\ v3 v4 v5 -> coe du_'60''8658''8804'_2846 v5))
        v0 v1
        (coe
           MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8801''45''10216'_448
           (\ v3 v4 v5 v6 v7 -> v7) v0
           (MAlonzo.Code.Data.Integer.Base.d__'43'__276
              (coe v0) (coe MAlonzo.Code.Data.Integer.Base.d_0ℤ_12))
           v1
           (coe
              MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8801''45''10216'_448
              (\ v3 v4 v5 v6 v7 -> v7)
              (MAlonzo.Code.Data.Integer.Base.d__'43'__276
                 (coe v0) (coe MAlonzo.Code.Data.Integer.Base.d_0ℤ_12))
              (MAlonzo.Code.Data.Integer.Base.d__'43'__276
                 (coe v0)
                 (coe
                    MAlonzo.Code.Data.Integer.Base.d__'43'__276
                    (coe MAlonzo.Code.Data.Integer.Base.d_'45'__252 (coe v1))
                    (coe v1)))
              v1
              (coe
                 MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8801''45''10216'_448
                 (\ v3 v4 v5 v6 v7 -> v7)
                 (MAlonzo.Code.Data.Integer.Base.d__'43'__276
                    (coe v0)
                    (coe
                       MAlonzo.Code.Data.Integer.Base.d__'43'__276
                       (coe MAlonzo.Code.Data.Integer.Base.d_'45'__252 (coe v1))
                       (coe v1)))
                 (MAlonzo.Code.Data.Integer.Base.d__'43'__276
                    (coe MAlonzo.Code.Data.Integer.Base.d__'45'__294 (coe v0) (coe v1))
                    (coe v1))
                 v1
                 (coe
                    MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8804'_308
                    (coe
                       MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_'8804''45'go_138
                       (coe d_'8804''45'isPreorder_2800)
                       (\ v3 v4 v5 v6 v7 -> coe du_'8804''45''60''45'trans_2958 v6 v7))
                    (MAlonzo.Code.Data.Integer.Base.d__'43'__276
                       (coe MAlonzo.Code.Data.Integer.Base.d__'45'__294 (coe v0) (coe v1))
                       (coe v1))
                    (MAlonzo.Code.Data.Integer.Base.d__'43'__276
                       (coe MAlonzo.Code.Data.Integer.Base.d_0ℤ_12) (coe v1))
                    v1
                    (coe
                       MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8801''45''10217'_436
                       (\ v3 v4 v5 v6 v7 -> v7)
                       (MAlonzo.Code.Data.Integer.Base.d__'43'__276
                          (coe MAlonzo.Code.Data.Integer.Base.d_0ℤ_12) (coe v1))
                       v1 v1
                       (coe
                          MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du__'8718'_492
                          (coe
                             MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_stop_166
                             (coe d_'8804''45'isPreorder_2800))
                          (coe v1))
                       erased)
                    (coe
                       d_'43''45'mono'737''45''8804'_4540 v1
                       (MAlonzo.Code.Data.Integer.Base.d__'45'__294 (coe v0) (coe v1))
                       MAlonzo.Code.Data.Integer.Base.d_0ℤ_12 v2))
                 erased)
              erased)
           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 v0 v1 v2
    = coe
        MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_begin__46
        (coe
           MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_start_96
           (coe d_'8804''45'isPreorder_2800)
           (\ v3 v4 v5 -> coe du_'60''8658''8804'_2846 v5))
        MAlonzo.Code.Data.Integer.Base.d_0ℤ_12
        (MAlonzo.Code.Data.Integer.Base.d__'45'__294 (coe v1) (coe v0))
        (coe
           MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8801''45''10216'_448
           (\ v3 v4 v5 v6 v7 -> v7) MAlonzo.Code.Data.Integer.Base.d_0ℤ_12
           (MAlonzo.Code.Data.Integer.Base.d__'45'__294 (coe v0) (coe v0))
           (MAlonzo.Code.Data.Integer.Base.d__'45'__294 (coe v1) (coe v0))
           (coe
              MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8804'_308
              (coe
                 MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_'8804''45'go_138
                 (coe d_'8804''45'isPreorder_2800)
                 (\ v3 v4 v5 v6 v7 -> coe du_'8804''45''60''45'trans_2958 v6 v7))
              (MAlonzo.Code.Data.Integer.Base.d__'45'__294 (coe v0) (coe v0))
              (MAlonzo.Code.Data.Integer.Base.d__'45'__294 (coe v1) (coe v0))
              (MAlonzo.Code.Data.Integer.Base.d__'45'__294 (coe v1) (coe v0))
              (coe
                 MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du__'8718'_492
                 (coe
                    MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_stop_166
                    (coe d_'8804''45'isPreorder_2800))
                 (coe
                    MAlonzo.Code.Data.Integer.Base.d__'45'__294 (coe v1) (coe v0)))
              (coe
                 d_'43''45'mono'737''45''8804'_4540
                 (MAlonzo.Code.Data.Integer.Base.d_'45'__252 (coe v0)) v0 v1 v2))
           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 v0 v1 v2
    = coe
        MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_begin__46
        (coe
           MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_start_96
           (coe d_'8804''45'isPreorder_2800)
           (\ v3 v4 v5 -> coe du_'60''8658''8804'_2846 v5))
        v1 v0
        (coe
           MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8801''45''10216'_448
           (\ v3 v4 v5 v6 v7 -> v7) v1
           (MAlonzo.Code.Data.Integer.Base.d__'43'__276
              (coe MAlonzo.Code.Data.Integer.Base.d_0ℤ_12) (coe v1))
           v0
           (coe
              MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8804'_308
              (coe
                 MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_'8804''45'go_138
                 (coe d_'8804''45'isPreorder_2800)
                 (\ v3 v4 v5 v6 v7 -> coe du_'8804''45''60''45'trans_2958 v6 v7))
              (MAlonzo.Code.Data.Integer.Base.d__'43'__276
                 (coe MAlonzo.Code.Data.Integer.Base.d_0ℤ_12) (coe v1))
              (MAlonzo.Code.Data.Integer.Base.d__'43'__276
                 (coe MAlonzo.Code.Data.Integer.Base.d__'45'__294 (coe v0) (coe v1))
                 (coe v1))
              v0
              (coe
                 MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8801''45''10217'_436
                 (\ v3 v4 v5 v6 v7 -> v7)
                 (MAlonzo.Code.Data.Integer.Base.d__'43'__276
                    (coe MAlonzo.Code.Data.Integer.Base.d__'45'__294 (coe v0) (coe v1))
                    (coe v1))
                 (MAlonzo.Code.Data.Integer.Base.d__'43'__276
                    (coe v0)
                    (coe
                       MAlonzo.Code.Data.Integer.Base.d__'43'__276
                       (coe MAlonzo.Code.Data.Integer.Base.d_'45'__252 (coe v1))
                       (coe v1)))
                 v0
                 (coe
                    MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8801''45''10217'_436
                    (\ v3 v4 v5 v6 v7 -> v7)
                    (MAlonzo.Code.Data.Integer.Base.d__'43'__276
                       (coe v0)
                       (coe
                          MAlonzo.Code.Data.Integer.Base.d__'43'__276
                          (coe MAlonzo.Code.Data.Integer.Base.d_'45'__252 (coe v1))
                          (coe v1)))
                    (MAlonzo.Code.Data.Integer.Base.d__'43'__276
                       (coe v0) (coe MAlonzo.Code.Data.Integer.Base.d_0ℤ_12))
                    v0
                    (coe
                       MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8801''45''10217'_436
                       (\ v3 v4 v5 v6 v7 -> v7)
                       (MAlonzo.Code.Data.Integer.Base.d__'43'__276
                          (coe v0) (coe MAlonzo.Code.Data.Integer.Base.d_0ℤ_12))
                       v0 v0
                       (coe
                          MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du__'8718'_492
                          (coe
                             MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_stop_166
                             (coe d_'8804''45'isPreorder_2800))
                          (coe v0))
                       erased)
                    erased)
                 erased)
              (coe
                 d_'43''45'mono'737''45''8804'_4540 v1
                 MAlonzo.Code.Data.Integer.Base.d_0ℤ_12
                 (MAlonzo.Code.Data.Integer.Base.d__'45'__294 (coe v0) (coe v1))
                 v2))
           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 v0 v1
    = coe
        du_i'8804'j'8658'i'8804'k'43'j_4578 (coe v0) (coe v1)
        (coe (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 v0
    = coe du_i'8804'j'43'i_4592 (coe v0) (coe (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 = 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 = 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 = 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 v0 v1 v2
    = case coe v2 of
        MAlonzo.Code.Data.Integer.Base.C_'45''8804''45'_34 v5
          -> coe
               d_'8854''45'mono'691''45''8805''45''8804'_4024 (coe (1 :: Integer))
               (coe subInt (coe (0 :: Integer)) (coe v0))
               (coe subInt (coe (0 :: Integer)) (coe v1))
               (coe MAlonzo.Code.Data.Nat.Base.C_s'8804's_34 v5)
        MAlonzo.Code.Data.Integer.Base.C_'45''8804''43'_40
          -> let v5 = subInt (coe (-1 :: Integer)) (coe v0) in
             coe
               (coe
                  MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_begin__46
                  (coe
                     MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_start_96
                     (coe d_'8804''45'isPreorder_2800)
                     (\ v6 v7 v8 -> coe du_'60''8658''8804'_2846 v8))
                  (coe
                     MAlonzo.Code.Function.Base.du__'45''10216'_'8739'_292
                     MAlonzo.Code.Data.Integer.Base.d_suc_300 (\ v6 v7 -> v6) v0 v1)
                  (coe
                     MAlonzo.Code.Function.Base.du_'8739'_'10217''45'__298
                     (\ v6 v7 -> v7) MAlonzo.Code.Data.Integer.Base.d_suc_300 v0 v1)
                  (coe
                     MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8801''45''10217'_436
                     (\ v6 v7 v8 v9 v10 -> v10)
                     (MAlonzo.Code.Data.Integer.Base.d__'8854'__258
                        (coe (1 :: Integer)) (coe subInt (coe (0 :: Integer)) (coe v0)))
                     (MAlonzo.Code.Data.Integer.Base.d__'8854'__258
                        (coe (0 :: Integer)) (coe v5))
                     (coe
                        MAlonzo.Code.Function.Base.du_'8739'_'10217''45'__298
                        (\ v6 v7 -> v7) MAlonzo.Code.Data.Integer.Base.d_suc_300 v0 v1)
                     (coe
                        MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8804'_308
                        (coe
                           MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_'8804''45'go_138
                           (coe d_'8804''45'isPreorder_2800)
                           (\ v6 v7 v8 v9 v10 -> coe du_'8804''45''60''45'trans_2958 v9 v10))
                        (MAlonzo.Code.Data.Integer.Base.d__'8854'__258
                           (coe (0 :: Integer)) (coe v5))
                        (MAlonzo.Code.Data.Integer.Base.d_suc_300 (coe v1))
                        (coe
                           MAlonzo.Code.Function.Base.du_'8739'_'10217''45'__298
                           (\ v6 v7 -> v7) MAlonzo.Code.Data.Integer.Base.d_suc_300 v0 v1)
                        (coe
                           MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du__'8718'_492
                           (coe
                              MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_stop_166
                              (coe d_'8804''45'isPreorder_2800))
                           (coe MAlonzo.Code.Data.Integer.Base.d_suc_300 (coe v1)))
                        (coe du_0'8854'm'8804''43'_4002 (coe v5)))
                     erased))
        MAlonzo.Code.Data.Integer.Base.C_'43''8804''43'_48 v5
          -> coe
               MAlonzo.Code.Data.Integer.Base.C_'43''8804''43'_48
               (coe MAlonzo.Code.Data.Nat.Base.C_s'8804's_34 v5)
        _ -> 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 v0 v1 v2
    = case coe v0 of
        _ | coe geqInt (coe v0) (coe (0 :: Integer)) ->
            case coe v2 of
              MAlonzo.Code.Data.Integer.Base.C_'43''8804''43'_48 v5
                -> coe MAlonzo.Code.Data.Integer.Base.C_'43''60''43'_72 v5
              _ -> MAlonzo.RTE.mazUnreachableError
        -1 -> coe MAlonzo.Code.Data.Integer.Base.C_'45''60''43'_64
        _ -> case coe v1 of
               _ | coe geqInt (coe v1) (coe (0 :: Integer)) ->
                   coe
                     seq (coe v2) (coe MAlonzo.Code.Data.Integer.Base.C_'45''60''43'_64)
               _ -> case coe v2 of
                      MAlonzo.Code.Data.Integer.Base.C_'45''8804''45'_34 v5
                        -> coe
                             MAlonzo.Code.Data.Integer.Base.C_'45''60''45'_58
                             (coe MAlonzo.Code.Data.Nat.Base.C_s'8804's_34 v5)
                      _ -> 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 v0 v1 v2
    = case coe v0 of
        _ | coe geqInt (coe v0) (coe (0 :: Integer)) ->
            case coe v2 of
              MAlonzo.Code.Data.Integer.Base.C_'43''60''43'_72 v5
                -> coe MAlonzo.Code.Data.Integer.Base.C_'43''8804''43'_48 v5
              _ -> MAlonzo.RTE.mazUnreachableError
        -1
          -> coe
               seq (coe v2)
               (coe
                  MAlonzo.Code.Data.Integer.Base.C_'43''8804''43'_48
                  (coe MAlonzo.Code.Data.Nat.Base.C_z'8804'n_26))
        _ -> case coe v1 of
               _ | coe geqInt (coe v1) (coe (0 :: Integer)) ->
                   coe
                     seq (coe v2)
                     (coe MAlonzo.Code.Data.Integer.Base.C_'45''8804''43'_40)
               _ -> case coe v2 of
                      MAlonzo.Code.Data.Integer.Base.C_'45''60''45'_58 v5
                        -> coe
                             MAlonzo.Code.Data.Integer.Base.C_'45''8804''45'_34
                             (coe MAlonzo.Code.Data.Nat.Base.du_s'8804's'8315''185'_62 (coe v5))
                      _ -> 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 = 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 = 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 = 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 = 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 = 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 = 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 ~v0 v1 v2
    = du_i'8804'pred'91'j'93''8658'i'60'j_5094 v1 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 v0 v1
    = case coe v0 of
        _ | coe geqInt (coe v0) (coe (0 :: Integer)) ->
            coe
              du_'8804''45''60''45'trans_2958 (coe v1)
              (coe du_m'8854'1'43'n'60'm_3942 (coe v0) (coe (1 :: Integer)))
        _ -> coe
               du_'8804''45''60''45'trans_2958 (coe v1)
               (coe
                  MAlonzo.Code.Data.Integer.Base.C_'45''60''45'_58
                  (MAlonzo.Code.Data.Nat.Properties.d_'8804''45'refl_2776
                     (coe subInt (coe (0 :: Integer)) (coe 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 ~v0 v1 v2
    = du_i'60'j'8658'i'8804'pred'91'j'93'_5104 v1 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 v0 v1
    = case coe v0 of
        0 -> coe
               seq (coe v1)
               (coe
                  MAlonzo.Code.Data.Integer.Base.C_'45''8804''45'_34
                  (coe MAlonzo.Code.Data.Nat.Base.C_z'8804'n_26))
        _ | coe geqInt (coe v0) (coe (1 :: Integer)) ->
            case coe v1 of
              MAlonzo.Code.Data.Integer.Base.C_'45''60''43'_64
                -> coe MAlonzo.Code.Data.Integer.Base.C_'45''8804''43'_40
              MAlonzo.Code.Data.Integer.Base.C_'43''60''43'_72 v4
                -> coe
                     MAlonzo.Code.Data.Integer.Base.C_'43''8804''43'_48
                     (coe MAlonzo.Code.Data.Nat.Base.du_s'8804's'8315''185'_62 (coe v4))
              _ -> MAlonzo.RTE.mazUnreachableError
        _ -> case coe v1 of
               MAlonzo.Code.Data.Integer.Base.C_'45''60''45'_58 v4
                 -> coe MAlonzo.Code.Data.Integer.Base.C_'45''8804''45'_34 v4
               _ -> 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 ~v0 ~v1 v2
    = du_i'8804'j'8658'pred'91'i'93''8804'j_5116 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 v0
    = case coe v0 of
        MAlonzo.Code.Data.Integer.Base.C_'45''8804''45'_34 v3
          -> coe MAlonzo.Code.Data.Integer.Base.C_'45''8804''45'_34 v3
        MAlonzo.Code.Data.Integer.Base.C_'45''8804''43'_40
          -> coe MAlonzo.Code.Data.Integer.Base.C_'45''8804''43'_40
        MAlonzo.Code.Data.Integer.Base.C_'43''8804''43'_48 v3
          -> case coe v3 of
               MAlonzo.Code.Data.Nat.Base.C_z'8804'n_26
                 -> coe MAlonzo.Code.Data.Integer.Base.C_'45''8804''43'_40
               MAlonzo.Code.Data.Nat.Base.C_s'8804's_34 v6
                 -> coe MAlonzo.Code.Data.Integer.Base.C_'43''8804''43'_48 v6
               _ -> MAlonzo.RTE.mazUnreachableError
        _ -> 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 v0 v1 v2
    = case coe v2 of
        MAlonzo.Code.Data.Integer.Base.C_'45''8804''45'_34 v5
          -> coe
               MAlonzo.Code.Data.Integer.Base.C_'45''8804''45'_34
               (coe MAlonzo.Code.Data.Nat.Base.C_s'8804's_34 v5)
        MAlonzo.Code.Data.Integer.Base.C_'45''8804''43'_40
          -> case coe v1 of
               0 -> coe
                      MAlonzo.Code.Data.Integer.Base.C_'45''8804''45'_34
                      (coe MAlonzo.Code.Data.Nat.Base.C_z'8804'n_26)
               _ -> coe MAlonzo.Code.Data.Integer.Base.C_'45''8804''43'_40
        MAlonzo.Code.Data.Integer.Base.C_'43''8804''43'_48 v5
          -> coe
               d_'8854''45'mono'737''45''8804'_4056 (coe (1 :: Integer)) (coe v0)
               (coe v1) (coe v5)
        _ -> 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 = 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 = 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 = erased
  -- Data.Integer.Properties.*-identity
  d_'42''45'identity_5180 :: MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  d_'42''45'identity_5180
    = coe MAlonzo.Code.Agda.Builtin.Sigma.C__'44'__32 erased 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 = 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 = erased
  -- Data.Integer.Properties.*-zero
  d_'42''45'zero_5186 :: MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  d_'42''45'zero_5186
    = coe MAlonzo.Code.Agda.Builtin.Sigma.C__'44'__32 erased 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 = 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 = 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 = 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 = 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
    = coe MAlonzo.Code.Agda.Builtin.Sigma.C__'44'__32 erased erased
  -- Data.Integer.Properties.*-isMagma
  d_'42''45'isMagma_5612 ::
    MAlonzo.Code.Algebra.Structures.T_IsMagma_176
  d_'42''45'isMagma_5612
    = coe
        MAlonzo.Code.Algebra.Structures.C_IsMagma'46'constructor_1867
        (coe
           MAlonzo.Code.Relation.Binary.PropositionalEquality.Properties.du_isEquivalence_396)
        erased
  -- Data.Integer.Properties.*-isSemigroup
  d_'42''45'isSemigroup_5614 ::
    MAlonzo.Code.Algebra.Structures.T_IsSemigroup_472
  d_'42''45'isSemigroup_5614
    = coe
        MAlonzo.Code.Algebra.Structures.C_IsSemigroup'46'constructor_10417
        (coe d_'42''45'isMagma_5612) erased
  -- Data.Integer.Properties.*-isCommutativeSemigroup
  d_'42''45'isCommutativeSemigroup_5616 ::
    MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_548
  d_'42''45'isCommutativeSemigroup_5616
    = coe
        MAlonzo.Code.Algebra.Structures.C_IsCommutativeSemigroup'46'constructor_12093
        (coe d_'42''45'isSemigroup_5614) 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
    = coe
        MAlonzo.Code.Algebra.Structures.C_IsMonoid'46'constructor_15873
        (coe d_'42''45'isSemigroup_5614) (coe 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
    = coe
        MAlonzo.Code.Algebra.Structures.C_IsCommutativeMonoid'46'constructor_17695
        (coe d_'42''45'1'45'isMonoid_5618) 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
    = coe
        MAlonzo.Code.Algebra.Structures.C_IsSemiring'46'constructor_48071
        (coe
           MAlonzo.Code.Algebra.Structures.C_IsSemiringWithoutAnnihilatingZero'46'constructor_43811
           (coe d_'43''45'0'45'isCommutativeMonoid_4432) erased erased
           (coe d_'42''45'identity_5180) (coe d_'42''45'distrib'45''43'_5610))
        (coe 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
    = coe
        MAlonzo.Code.Algebra.Structures.C_IsCommutativeSemiring'46'constructor_51895
        (coe d_'43''45''42''45'isSemiring_5622) 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
    = coe
        MAlonzo.Code.Algebra.Structures.C_IsRing'46'constructor_95033
        (coe d_'43''45'0'45'isAbelianGroup_4436) erased erased
        (coe d_'42''45'identity_5180) (coe 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
    = coe
        MAlonzo.Code.Algebra.Structures.C_IsCommutativeRing'46'constructor_100945
        (coe d_'43''45''42''45'isRing_5626) erased
  -- Data.Integer.Properties.*-magma
  d_'42''45'magma_5630 :: MAlonzo.Code.Algebra.Bundles.T_Magma_68
  d_'42''45'magma_5630
    = coe
        MAlonzo.Code.Algebra.Bundles.C_Magma'46'constructor_1279
        MAlonzo.Code.Data.Integer.Base.d__'42'__308 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
    = coe
        MAlonzo.Code.Algebra.Bundles.C_Semigroup'46'constructor_9793
        MAlonzo.Code.Data.Integer.Base.d__'42'__308
        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
    = coe
        MAlonzo.Code.Algebra.Bundles.C_CommutativeSemigroup'46'constructor_12035
        MAlonzo.Code.Data.Integer.Base.d__'42'__308
        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
    = coe
        MAlonzo.Code.Algebra.Bundles.C_Monoid'46'constructor_16157
        MAlonzo.Code.Data.Integer.Base.d__'42'__308
        MAlonzo.Code.Data.Integer.Base.d_1ℤ_16 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
    = coe
        MAlonzo.Code.Algebra.Bundles.C_CommutativeMonoid'46'constructor_17931
        MAlonzo.Code.Data.Integer.Base.d__'42'__308
        MAlonzo.Code.Data.Integer.Base.d_1ℤ_16
        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
    = coe
        MAlonzo.Code.Algebra.Bundles.C_Semiring'46'constructor_41765
        MAlonzo.Code.Data.Integer.Base.d__'43'__276
        MAlonzo.Code.Data.Integer.Base.d__'42'__308
        MAlonzo.Code.Data.Integer.Base.d_0ℤ_12
        MAlonzo.Code.Data.Integer.Base.d_1ℤ_16
        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
    = coe
        MAlonzo.Code.Algebra.Bundles.C_CommutativeSemiring'46'constructor_44731
        MAlonzo.Code.Data.Integer.Base.d__'43'__276
        MAlonzo.Code.Data.Integer.Base.d__'42'__308
        MAlonzo.Code.Data.Integer.Base.d_0ℤ_12
        MAlonzo.Code.Data.Integer.Base.d_1ℤ_16
        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
    = coe
        MAlonzo.Code.Algebra.Bundles.C_Ring'46'constructor_68489
        MAlonzo.Code.Data.Integer.Base.d__'43'__276
        MAlonzo.Code.Data.Integer.Base.d__'42'__308
        MAlonzo.Code.Data.Integer.Base.d_'45'__252
        MAlonzo.Code.Data.Integer.Base.d_0ℤ_12
        MAlonzo.Code.Data.Integer.Base.d_1ℤ_16
        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
    = coe
        MAlonzo.Code.Algebra.Bundles.C_CommutativeRing'46'constructor_72553
        MAlonzo.Code.Data.Integer.Base.d__'43'__276
        MAlonzo.Code.Data.Integer.Base.d__'42'__308
        MAlonzo.Code.Data.Integer.Base.d_'45'__252
        MAlonzo.Code.Data.Integer.Base.d_0ℤ_12
        MAlonzo.Code.Data.Integer.Base.d_1ℤ_16
        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 = 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 = 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 = 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 = 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 = 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 = 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 = 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 v0 ~v1 ~v2
    = du_i'42'j'8801'0'8658'i'8801'0'8744'j'8801'0_5780 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 v0
    = coe
        MAlonzo.Code.Data.Nat.Properties.du_m'42'n'8801'0'8658'm'8801'0'8744'n'8801'0_3822
        (coe MAlonzo.Code.Data.Integer.Base.d_'8739'_'8739'_18 (coe 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 ~v0 ~v1 ~v2 ~v3 = 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
    = coe 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 = 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 = 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 = erased
  -- Data.Integer.Properties.^-isMagmaHomomorphism
  d_'94''45'isMagmaHomomorphism_5862 ::
    Integer ->
    MAlonzo.Code.Algebra.Morphism.Structures.T_IsMagmaHomomorphism_176
  d_'94''45'isMagmaHomomorphism_5862 ~v0
    = du_'94''45'isMagmaHomomorphism_5862
  du_'94''45'isMagmaHomomorphism_5862 ::
    MAlonzo.Code.Algebra.Morphism.Structures.T_IsMagmaHomomorphism_176
  du_'94''45'isMagmaHomomorphism_5862
    = coe
        MAlonzo.Code.Algebra.Morphism.Structures.C_IsMagmaHomomorphism'46'constructor_4629
        (coe
           MAlonzo.Code.Relation.Binary.Morphism.Structures.C_IsRelHomomorphism'46'constructor_587
           erased)
        erased
  -- Data.Integer.Properties.^-isMonoidHomomorphism
  d_'94''45'isMonoidHomomorphism_5872 ::
    Integer ->
    MAlonzo.Code.Algebra.Morphism.Structures.T_IsMonoidHomomorphism_350
  d_'94''45'isMonoidHomomorphism_5872 ~v0
    = du_'94''45'isMonoidHomomorphism_5872
  du_'94''45'isMonoidHomomorphism_5872 ::
    MAlonzo.Code.Algebra.Morphism.Structures.T_IsMonoidHomomorphism_350
  du_'94''45'isMonoidHomomorphism_5872
    = coe
        MAlonzo.Code.Algebra.Morphism.Structures.C_IsMonoidHomomorphism'46'constructor_9411
        (coe du_'94''45'isMagmaHomomorphism_5862) 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 = 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 = 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 = 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 = 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 = 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 = 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 v0 v1 ~v2 ~v3 v4
    = du_'42''45'cancel'691''45''8804''45'pos_5998 v0 v1 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 v0 v1 v2
    = case coe v0 of
        0 -> coe
               seq (coe v1)
               (coe
                  MAlonzo.Code.Data.Integer.Base.C_'43''8804''43'_48
                  (coe MAlonzo.Code.Data.Nat.Base.C_z'8804'n_26))
        _ | coe geqInt (coe v0) (coe (1 :: Integer)) ->
            coe
              seq (coe v2)
              (coe
                 MAlonzo.Code.Data.Integer.Base.C_'43''8804''43'_48
                 (coe
                    MAlonzo.Code.Data.Nat.Properties.du_'42''45'cancel'691''45''8804'_4030
                    (coe v0)))
        _ -> case coe v1 of
               _ | coe geqInt (coe v1) (coe (0 :: Integer)) ->
                   coe MAlonzo.Code.Data.Integer.Base.C_'45''8804''43'_40
               _ -> coe
                      seq (coe v2)
                      (coe
                         MAlonzo.Code.Data.Integer.Base.C_'45''8804''45'_34
                         (coe
                            MAlonzo.Code.Data.Nat.Base.du_s'8804's'8315''185'_62
                            (coe
                               MAlonzo.Code.Data.Nat.Properties.du_'42''45'cancel'691''45''8804'_4030
                               (coe subInt (coe (0 :: Integer)) (coe 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 v0 v1 ~v2 ~v3
    = du_'42''45'cancel'737''45''8804''45'pos_6032 v0 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 v0 v1
    = coe
        du_'42''45'cancel'691''45''8804''45'pos_5998 (coe v0) (coe 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 v0 ~v1 v2 v3 v4
    = du_'42''45'mono'691''45''8804''45'nonNeg_6054 v0 v2 v3 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 v0 v1 v2 v3
    = case coe v0 of
        0 -> coe
               MAlonzo.Code.Data.Integer.Base.C_'43''8804''43'_48
               (coe MAlonzo.Code.Data.Nat.Base.C_z'8804'n_26)
        _ -> case coe v3 of
               MAlonzo.Code.Data.Integer.Base.C_'45''8804''45'_34 v6
                 -> coe
                      MAlonzo.Code.Data.Integer.Base.C_'45''8804''45'_34
                      (coe
                         MAlonzo.Code.Data.Nat.Base.du_s'8804's'8315''185'_62
                         (coe
                            MAlonzo.Code.Data.Nat.Properties.du_'42''45'mono'45''8804'_4060
                            (coe subInt (coe (0 :: Integer)) (coe v1)) (coe v0)
                            (coe MAlonzo.Code.Data.Nat.Base.C_s'8804's_34 v6)
                            (coe
                               MAlonzo.Code.Data.Nat.Properties.d_'8804''45'refl_2776 (coe v0))))
               MAlonzo.Code.Data.Integer.Base.C_'45''8804''43'_40
                 -> coe MAlonzo.Code.Data.Integer.Base.C_'45''8804''43'_40
               MAlonzo.Code.Data.Integer.Base.C_'43''8804''43'_48 v6
                 -> case coe v1 of
                      0 -> case coe v2 of
                             0 -> coe MAlonzo.Code.Data.Integer.Base.C_'43''8804''43'_48 v6
                             _ -> coe
                                    MAlonzo.Code.Data.Integer.Base.C_'43''8804''43'_48
                                    (coe MAlonzo.Code.Data.Nat.Base.C_z'8804'n_26)
                      _ -> coe
                             MAlonzo.Code.Data.Integer.Base.C_'43''8804''43'_48
                             (coe
                                MAlonzo.Code.Data.Nat.Properties.du_'42''45'mono'737''45''8804'_4070
                                (coe v0) (coe v2) (coe v6))
               _ -> 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 v0 ~v1 v2 v3
    = du_'42''45'mono'737''45''8804''45'nonNeg_6096 v0 v2 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 v0 v1 v2
    = coe
        du_'42''45'mono'691''45''8804''45'nonNeg_6054 (coe v0) (coe v1)
        (coe 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 v0 v1 v2 ~v3 v4
    = du_'42''45'cancel'737''45''8804''45'neg_6120 v0 v1 v2 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 v0 v1 v2 v3
    = coe
        d_neg'45'cancel'45''8804'_3278 (coe v1) (coe v2)
        (coe
           du_'42''45'cancel'737''45''8804''45'pos_6032
           (MAlonzo.Code.Data.Integer.Base.d_'45'__252 (coe v1))
           (MAlonzo.Code.Data.Integer.Base.d_'45'__252 (coe v2))
           (coe
              MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_begin__46
              (coe
                 MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_start_96
                 (coe d_'8804''45'isPreorder_2800)
                 (\ v4 v5 v6 -> coe du_'60''8658''8804'_2846 v6))
              (MAlonzo.Code.Data.Integer.Base.d__'42'__308
                 (coe MAlonzo.Code.Data.Integer.Base.d_'45'__252 (coe v0))
                 (coe MAlonzo.Code.Data.Integer.Base.d_'45'__252 (coe v1)))
              (MAlonzo.Code.Data.Integer.Base.d__'42'__308
                 (coe MAlonzo.Code.Data.Integer.Base.d_'45'__252 (coe v0))
                 (coe MAlonzo.Code.Data.Integer.Base.d_'45'__252 (coe v2)))
              (coe
                 MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8801''45''10216'_448
                 (\ v4 v5 v6 v7 v8 -> v8)
                 (MAlonzo.Code.Data.Integer.Base.d__'42'__308
                    (coe MAlonzo.Code.Data.Integer.Base.d_'45'__252 (coe v0))
                    (coe MAlonzo.Code.Data.Integer.Base.d_'45'__252 (coe v1)))
                 (MAlonzo.Code.Data.Integer.Base.d_'45'__252
                    (coe
                       MAlonzo.Code.Data.Integer.Base.d__'42'__308
                       (coe MAlonzo.Code.Data.Integer.Base.d_'45'__252 (coe v0))
                       (coe v1)))
                 (MAlonzo.Code.Data.Integer.Base.d__'42'__308
                    (coe MAlonzo.Code.Data.Integer.Base.d_'45'__252 (coe v0))
                    (coe MAlonzo.Code.Data.Integer.Base.d_'45'__252 (coe v2)))
                 (coe
                    MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8801''45''10217'_436
                    (\ v4 v5 v6 v7 v8 -> v8)
                    (MAlonzo.Code.Data.Integer.Base.d_'45'__252
                       (coe
                          MAlonzo.Code.Data.Integer.Base.d__'42'__308
                          (coe MAlonzo.Code.Data.Integer.Base.d_'45'__252 (coe v0))
                          (coe v1)))
                    (MAlonzo.Code.Data.Integer.Base.d__'42'__308 (coe v0) (coe v1))
                    (MAlonzo.Code.Data.Integer.Base.d__'42'__308
                       (coe MAlonzo.Code.Data.Integer.Base.d_'45'__252 (coe v0))
                       (coe MAlonzo.Code.Data.Integer.Base.d_'45'__252 (coe v2)))
                    (coe
                       MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8804'_308
                       (coe
                          MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_'8804''45'go_138
                          (coe d_'8804''45'isPreorder_2800)
                          (\ v4 v5 v6 v7 v8 -> coe du_'8804''45''60''45'trans_2958 v7 v8))
                       (MAlonzo.Code.Data.Integer.Base.d__'42'__308 (coe v0) (coe v1))
                       (MAlonzo.Code.Data.Integer.Base.d__'42'__308 (coe v0) (coe v2))
                       (MAlonzo.Code.Data.Integer.Base.d__'42'__308
                          (coe MAlonzo.Code.Data.Integer.Base.d_'45'__252 (coe v0))
                          (coe MAlonzo.Code.Data.Integer.Base.d_'45'__252 (coe v2)))
                       (coe
                          MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8801''45''10216'_448
                          (\ v4 v5 v6 v7 v8 -> v8)
                          (MAlonzo.Code.Data.Integer.Base.d__'42'__308 (coe v0) (coe v2))
                          (MAlonzo.Code.Data.Integer.Base.d_'45'__252
                             (coe
                                MAlonzo.Code.Data.Integer.Base.d__'42'__308
                                (coe MAlonzo.Code.Data.Integer.Base.d_'45'__252 (coe v0))
                                (coe v2)))
                          (MAlonzo.Code.Data.Integer.Base.d__'42'__308
                             (coe MAlonzo.Code.Data.Integer.Base.d_'45'__252 (coe v0))
                             (coe MAlonzo.Code.Data.Integer.Base.d_'45'__252 (coe v2)))
                          (coe
                             MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8801''45''10217'_436
                             (\ v4 v5 v6 v7 v8 -> v8)
                             (MAlonzo.Code.Data.Integer.Base.d_'45'__252
                                (coe
                                   MAlonzo.Code.Data.Integer.Base.d__'42'__308
                                   (coe MAlonzo.Code.Data.Integer.Base.d_'45'__252 (coe v0))
                                   (coe v2)))
                             (MAlonzo.Code.Data.Integer.Base.d__'42'__308
                                (coe MAlonzo.Code.Data.Integer.Base.d_'45'__252 (coe v0))
                                (coe MAlonzo.Code.Data.Integer.Base.d_'45'__252 (coe v2)))
                             (MAlonzo.Code.Data.Integer.Base.d__'42'__308
                                (coe MAlonzo.Code.Data.Integer.Base.d_'45'__252 (coe v0))
                                (coe MAlonzo.Code.Data.Integer.Base.d_'45'__252 (coe v2)))
                             (coe
                                MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du__'8718'_492
                                (coe
                                   MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_stop_166
                                   (coe d_'8804''45'isPreorder_2800))
                                (coe
                                   MAlonzo.Code.Data.Integer.Base.d__'42'__308
                                   (coe MAlonzo.Code.Data.Integer.Base.d_'45'__252 (coe v0))
                                   (coe MAlonzo.Code.Data.Integer.Base.d_'45'__252 (coe v2))))
                             erased)
                          erased)
                       v3)
                    erased)
                 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 v0 v1 v2 ~v3
    = du_'42''45'cancel'691''45''8804''45'neg_6142 v0 v1 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 v0 v1 v2
    = coe
        du_'42''45'cancel'737''45''8804''45'neg_6120 (coe v2) (coe v0)
        (coe 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 v0 ~v1 v2 v3 v4
    = du_'42''45'mono'737''45''8804''45'nonPos_6164 v0 v2 v3 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 v0 v1 v2 v3
    = case coe v0 of
        0 -> coe
               MAlonzo.Code.Data.Integer.Base.C_'43''8804''43'_48
               (coe MAlonzo.Code.Data.Nat.Base.C_z'8804'n_26)
        _ -> coe
               MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_begin__46
               (coe
                  MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_start_96
                  (coe d_'8804''45'isPreorder_2800)
                  (\ v4 v5 v6 -> coe du_'60''8658''8804'_2846 v6))
               (coe
                  MAlonzo.Code.Function.Base.du_'8739'_'10217''45'__298
                  (\ v4 v5 -> v5)
                  (MAlonzo.Code.Data.Integer.Base.d__'42'__308 (coe v0)) v1 v2)
               (coe
                  MAlonzo.Code.Function.Base.du__'45''10216'_'8739'_292
                  (MAlonzo.Code.Data.Integer.Base.d__'42'__308 (coe v0))
                  (\ v4 v5 -> v4) v1 v2)
               (coe
                  MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8801''45''10216'_448
                  (\ v4 v5 v6 v7 v8 -> v8)
                  (MAlonzo.Code.Data.Integer.Base.d__'42'__308 (coe v0) (coe v2))
                  (MAlonzo.Code.Data.Integer.Base.d_'45'__252
                     (coe
                        MAlonzo.Code.Data.Integer.Base.d__'42'__308
                        (coe MAlonzo.Code.Data.Integer.Base.d_'45'__252 (coe v0))
                        (coe v2)))
                  (coe
                     MAlonzo.Code.Function.Base.du__'45''10216'_'8739'_292
                     (MAlonzo.Code.Data.Integer.Base.d__'42'__308 (coe v0))
                     (\ v4 v5 -> v4) v1 v2)
                  (coe
                     MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8801''45''10217'_436
                     (\ v4 v5 v6 v7 v8 -> v8)
                     (MAlonzo.Code.Data.Integer.Base.d_'45'__252
                        (coe
                           MAlonzo.Code.Data.Integer.Base.d__'42'__308
                           (coe MAlonzo.Code.Data.Integer.Base.d_'45'__252 (coe v0))
                           (coe v2)))
                     (MAlonzo.Code.Data.Integer.Base.d__'42'__308
                        (coe MAlonzo.Code.Data.Integer.Base.d_'45'__252 (coe v0))
                        (coe MAlonzo.Code.Data.Integer.Base.d_'45'__252 (coe v2)))
                     (coe
                        MAlonzo.Code.Function.Base.du__'45''10216'_'8739'_292
                        (MAlonzo.Code.Data.Integer.Base.d__'42'__308 (coe v0))
                        (\ v4 v5 -> v4) v1 v2)
                     (coe
                        MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8804'_308
                        (coe
                           MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_'8804''45'go_138
                           (coe d_'8804''45'isPreorder_2800)
                           (\ v4 v5 v6 v7 v8 -> coe du_'8804''45''60''45'trans_2958 v7 v8))
                        (MAlonzo.Code.Data.Integer.Base.d__'42'__308
                           (coe MAlonzo.Code.Data.Integer.Base.d_'45'__252 (coe v0))
                           (coe MAlonzo.Code.Data.Integer.Base.d_'45'__252 (coe v2)))
                        (MAlonzo.Code.Data.Integer.Base.d__'42'__308
                           (coe MAlonzo.Code.Data.Integer.Base.d_'45'__252 (coe v0))
                           (coe MAlonzo.Code.Data.Integer.Base.d_'45'__252 (coe v1)))
                        (coe
                           MAlonzo.Code.Function.Base.du__'45''10216'_'8739'_292
                           (MAlonzo.Code.Data.Integer.Base.d__'42'__308 (coe v0))
                           (\ v4 v5 -> v4) v1 v2)
                        (coe
                           MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8801''45''10216'_448
                           (\ v4 v5 v6 v7 v8 -> v8)
                           (MAlonzo.Code.Data.Integer.Base.d__'42'__308
                              (coe MAlonzo.Code.Data.Integer.Base.d_'45'__252 (coe v0))
                              (coe MAlonzo.Code.Data.Integer.Base.d_'45'__252 (coe v1)))
                           (MAlonzo.Code.Data.Integer.Base.d_'45'__252
                              (coe
                                 MAlonzo.Code.Data.Integer.Base.d__'42'__308
                                 (coe MAlonzo.Code.Data.Integer.Base.d_'45'__252 (coe v0))
                                 (coe v1)))
                           (coe
                              MAlonzo.Code.Function.Base.du__'45''10216'_'8739'_292
                              (MAlonzo.Code.Data.Integer.Base.d__'42'__308 (coe v0))
                              (\ v4 v5 -> v4) v1 v2)
                           (coe
                              MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8801''45''10217'_436
                              (\ v4 v5 v6 v7 v8 -> v8)
                              (MAlonzo.Code.Data.Integer.Base.d_'45'__252
                                 (coe
                                    MAlonzo.Code.Data.Integer.Base.d__'42'__308
                                    (coe MAlonzo.Code.Data.Integer.Base.d_'45'__252 (coe v0))
                                    (coe v1)))
                              (MAlonzo.Code.Data.Integer.Base.d__'42'__308 (coe v0) (coe v1))
                              (coe
                                 MAlonzo.Code.Function.Base.du__'45''10216'_'8739'_292
                                 (MAlonzo.Code.Data.Integer.Base.d__'42'__308 (coe v0))
                                 (\ v4 v5 -> v4) v1 v2)
                              (coe
                                 MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du__'8718'_492
                                 (coe
                                    MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_stop_166
                                    (coe d_'8804''45'isPreorder_2800))
                                 (coe
                                    MAlonzo.Code.Data.Integer.Base.d__'42'__308 (coe v0) (coe v1)))
                              erased)
                           erased)
                        (coe
                           du_'42''45'mono'737''45''8804''45'nonNeg_6096
                           (MAlonzo.Code.Data.Integer.Base.d_'45'__252 (coe v0))
                           (coe
                              MAlonzo.Code.Function.Base.du_'8739'_'10217''45'__298
                              (\ v4 v5 -> v5) MAlonzo.Code.Data.Integer.Base.d_'45'__252 v1 v2)
                           (coe
                              MAlonzo.Code.Function.Base.du__'45''10216'_'8739'_292
                              MAlonzo.Code.Data.Integer.Base.d_'45'__252 (\ v4 v5 -> v4) v1 v2)
                           (coe du_neg'45'mono'45''8804'_3272 (coe v2) (coe v3))))
                     erased)
                  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 v0 ~v1 v2 v3
    = du_'42''45'mono'691''45''8804''45'nonPos_6192 v0 v2 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 v0 v1 v2
    = coe
        du_'42''45'mono'737''45''8804''45'nonPos_6164 (coe v0) (coe v1)
        (coe 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 v0 ~v1 v2 v3 v4
    = du_'42''45'mono'737''45''60''45'pos_6214 v0 v2 v3 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 v0 v1 v2 v3
    = let v4 = subInt (coe v0) (coe (1 :: Integer)) in
      coe
        (case coe v1 of
           _ | coe geqInt (coe v1) (coe (0 :: Integer)) ->
               case coe v3 of
                 MAlonzo.Code.Data.Integer.Base.C_'43''60''43'_72 v7
                   -> coe
                        du_'43''9667''45'mono'45''60'_3600
                        (coe addInt (coe v1) (coe mulInt (coe v4) (coe v1)))
                        (coe
                           MAlonzo.Code.Data.Nat.Properties.du_'43''45'mono'45''60''45''8804'_3560
                           (coe v7)
                           (coe
                              MAlonzo.Code.Data.Nat.Properties.du_'42''45'mono'691''45''8804'_4080
                              (coe v4) (coe v2)
                              (coe
                                 MAlonzo.Code.Data.Nat.Properties.du_'60''8658''8804'_2854
                                 (coe v7))))
                 _ -> MAlonzo.RTE.mazUnreachableError
           _ -> case coe v2 of
                  _ | coe geqInt (coe v2) (coe (0 :: Integer)) ->
                      coe du_'45''9667''60''43''9667'_3642 (coe mulInt (coe v0) (coe v2))
                  _ -> case coe v3 of
                         MAlonzo.Code.Data.Integer.Base.C_'45''60''45'_58 v7
                           -> coe
                                MAlonzo.Code.Data.Integer.Base.C_'45''60''45'_58
                                (coe
                                   MAlonzo.Code.Data.Nat.Properties.du_'43''45'mono'45''60''45''8804'_3560
                                   (coe v7)
                                   (coe
                                      MAlonzo.Code.Data.Nat.Properties.du_'42''45'mono'691''45''8804'_4080
                                      (coe v4) (coe subInt (coe (0 :: Integer)) (coe v1))
                                      (coe
                                         MAlonzo.Code.Data.Nat.Properties.du_'60''8658''8804'_2854
                                         (coe MAlonzo.Code.Data.Nat.Base.C_s'8804's_34 v7))))
                         _ -> 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 v0 ~v1 v2 v3
    = du_'42''45'mono'691''45''60''45'pos_6246 v0 v2 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 v0 v1 v2
    = coe
        du_'42''45'mono'737''45''60''45'pos_6214 (coe v0) (coe v1) (coe 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 v0 v1 v2 ~v3 v4
    = du_'42''45'cancel'737''45''60''45'nonNeg_6266 v0 v1 v2 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 v0 v1 v2 v3
    = case coe v0 of
        _ | coe geqInt (coe v0) (coe (0 :: Integer)) ->
            case coe v1 of
              _ | coe geqInt (coe v1) (coe (0 :: Integer)) ->
                  coe
                    MAlonzo.Code.Data.Integer.Base.C_'43''60''43'_72
                    (coe
                       MAlonzo.Code.Data.Nat.Properties.d_'42''45'cancel'737''45''60'_4208
                       v2 (MAlonzo.Code.Data.Integer.Base.d_'8739'_'8739'_18 (coe v0))
                       (MAlonzo.Code.Data.Integer.Base.d_'8739'_'8739'_18 (coe v1))
                       (coe
                          du_'43''9667''45'cancel'45''60'_3612
                          (coe
                             mulInt (coe v2)
                             (coe MAlonzo.Code.Data.Integer.Base.d_'8739'_'8739'_18 (coe v0)))
                          (coe v3)))
              _ -> coe
                     MAlonzo.Code.Relation.Nullary.Negation.Core.du_contradiction_44
                     erased
        _ -> case coe v1 of
               _ | coe geqInt (coe v1) (coe (0 :: Integer)) ->
                   coe MAlonzo.Code.Data.Integer.Base.C_'45''60''43'_64
               _ -> coe
                      MAlonzo.Code.Data.Integer.Base.C_'45''60''45'_58
                      (coe
                         MAlonzo.Code.Data.Nat.Base.du_s'60's'8315''185'_70
                         (coe
                            MAlonzo.Code.Data.Nat.Properties.d_'42''45'cancel'737''45''60'_4208
                            v2 (MAlonzo.Code.Data.Integer.Base.d_'8739'_'8739'_18 (coe v1))
                            (MAlonzo.Code.Data.Integer.Base.d_'8739'_'8739'_18 (coe v0))
                            (coe
                               du_neg'9667''45'cancel'45''60'_3626
                               (coe
                                  mulInt (coe v2)
                                  (coe MAlonzo.Code.Data.Integer.Base.d_'8739'_'8739'_18 (coe v1)))
                               (coe 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 v0 v1 v2 ~v3
    = du_'42''45'cancel'691''45''60''45'nonNeg_6304 v0 v1 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 v0 v1 v2
    = coe
        du_'42''45'cancel'737''45''60''45'nonNeg_6266 (coe v0) (coe v1)
        (coe 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 v0 ~v1 v2 v3 v4
    = du_'42''45'mono'737''45''60''45'neg_6326 v0 v2 v3 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 v0 v1 v2 v3
    = let v4
            = coe
                MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_strictRelation_202 in
      coe
        (coe
           MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_begin__126
           (coe v4)
           (coe MAlonzo.Code.Data.Integer.Base.d__'42'__308 (coe v0) (coe v2))
           (coe MAlonzo.Code.Data.Integer.Base.d__'42'__308 (coe v0) (coe v1))
           (coe
              MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8801''45''10216'_448
              (\ v5 v6 v7 v8 v9 -> v9)
              (MAlonzo.Code.Data.Integer.Base.d__'42'__308 (coe v0) (coe v2))
              (MAlonzo.Code.Data.Integer.Base.d_'45'__252
                 (coe
                    MAlonzo.Code.Data.Integer.Base.d__'42'__308
                    (coe MAlonzo.Code.Data.Integer.Base.d_'45'__252 (coe v0))
                    (coe v2)))
              (MAlonzo.Code.Data.Integer.Base.d__'42'__308 (coe v0) (coe v1))
              (coe
                 MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8801''45''10217'_436
                 (\ v5 v6 v7 v8 v9 -> v9)
                 (MAlonzo.Code.Data.Integer.Base.d_'45'__252
                    (coe
                       MAlonzo.Code.Data.Integer.Base.d__'42'__308
                       (coe MAlonzo.Code.Data.Integer.Base.d_'45'__252 (coe v0))
                       (coe v2)))
                 (MAlonzo.Code.Data.Integer.Base.d__'42'__308
                    (coe MAlonzo.Code.Data.Integer.Base.d_'45'__252 (coe v0))
                    (coe MAlonzo.Code.Data.Integer.Base.d_'45'__252 (coe v2)))
                 (MAlonzo.Code.Data.Integer.Base.d__'42'__308 (coe v0) (coe v1))
                 (coe
                    MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''60'_312
                    (coe
                       MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_'60''45'go_152
                       (\ v5 v6 v7 v8 v9 -> coe du_'60''45'trans_2986 v8 v9)
                       (coe
                          MAlonzo.Code.Relation.Binary.PropositionalEquality.Core.du_resp'8322'_160)
                       (\ v5 v6 v7 v8 v9 -> coe du_'60''45''8804''45'trans_2972 v8 v9))
                    (MAlonzo.Code.Data.Integer.Base.d__'42'__308
                       (coe MAlonzo.Code.Data.Integer.Base.d_'45'__252 (coe v0))
                       (coe MAlonzo.Code.Data.Integer.Base.d_'45'__252 (coe v2)))
                    (MAlonzo.Code.Data.Integer.Base.d__'42'__308
                       (coe MAlonzo.Code.Data.Integer.Base.d_'45'__252 (coe v0))
                       (coe MAlonzo.Code.Data.Integer.Base.d_'45'__252 (coe v1)))
                    (MAlonzo.Code.Data.Integer.Base.d__'42'__308 (coe v0) (coe v1))
                    (coe
                       MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8801''45''10216'_448
                       (\ v5 v6 v7 v8 v9 -> v9)
                       (MAlonzo.Code.Data.Integer.Base.d__'42'__308
                          (coe MAlonzo.Code.Data.Integer.Base.d_'45'__252 (coe v0))
                          (coe MAlonzo.Code.Data.Integer.Base.d_'45'__252 (coe v1)))
                       (MAlonzo.Code.Data.Integer.Base.d_'45'__252
                          (coe
                             MAlonzo.Code.Data.Integer.Base.d__'42'__308
                             (coe MAlonzo.Code.Data.Integer.Base.d_'45'__252 (coe v0))
                             (coe v1)))
                       (MAlonzo.Code.Data.Integer.Base.d__'42'__308 (coe v0) (coe v1))
                       (coe
                          MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8801''45''10217'_436
                          (\ v5 v6 v7 v8 v9 -> v9)
                          (MAlonzo.Code.Data.Integer.Base.d_'45'__252
                             (coe
                                MAlonzo.Code.Data.Integer.Base.d__'42'__308
                                (coe MAlonzo.Code.Data.Integer.Base.d_'45'__252 (coe v0))
                                (coe v1)))
                          (MAlonzo.Code.Data.Integer.Base.d__'42'__308 (coe v0) (coe v1))
                          (MAlonzo.Code.Data.Integer.Base.d__'42'__308 (coe v0) (coe v1))
                          (coe
                             MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du__'8718'_492
                             (coe
                                MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_stop_166
                                (coe d_'8804''45'isPreorder_2800))
                             (coe
                                MAlonzo.Code.Data.Integer.Base.d__'42'__308 (coe v0) (coe v1)))
                          erased)
                       erased)
                    (coe
                       du_'42''45'mono'737''45''60''45'pos_6214
                       (coe MAlonzo.Code.Data.Integer.Base.d_'45'__252 (coe v0))
                       (coe
                          MAlonzo.Code.Function.Base.du_'8739'_'10217''45'__298
                          (\ v5 v6 -> v6) MAlonzo.Code.Data.Integer.Base.d_'45'__252 v1 v2)
                       (coe
                          MAlonzo.Code.Function.Base.du__'45''10216'_'8739'_292
                          MAlonzo.Code.Data.Integer.Base.d_'45'__252 (\ v5 v6 -> v5) v1 v2)
                       (coe d_neg'45'mono'45''60'_3302 (coe v1) (coe v2) (coe v3))))
                 erased)
              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 v0 ~v1 v2 v3
    = du_'42''45'mono'691''45''60''45'neg_6346 v0 v2 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 v0 v1 v2
    = coe
        du_'42''45'mono'737''45''60''45'neg_6326 (coe v0) (coe v1) (coe 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 v0 v1 v2 ~v3 v4
    = du_'42''45'cancel'737''45''60''45'nonPos_6366 v0 v1 v2 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 v0 v1 v2 v3
    = coe
        d_neg'45'cancel'45''60'_3316 (coe v0) (coe v1)
        (coe
           du_'42''45'cancel'737''45''60''45'nonNeg_6266
           (coe MAlonzo.Code.Data.Integer.Base.d_'45'__252 (coe v0))
           (coe MAlonzo.Code.Data.Integer.Base.d_'45'__252 (coe v1))
           (coe MAlonzo.Code.Data.Integer.Base.d_'45'__252 (coe v2))
           (let v4
                  = coe
                      MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_strictRelation_202 in
            coe
              (coe
                 MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_begin__126
                 (coe v4)
                 (coe
                    MAlonzo.Code.Data.Integer.Base.d__'42'__308
                    (coe MAlonzo.Code.Data.Integer.Base.d_'45'__252 (coe v2))
                    (coe MAlonzo.Code.Data.Integer.Base.d_'45'__252 (coe v0)))
                 (coe
                    MAlonzo.Code.Data.Integer.Base.d__'42'__308
                    (coe MAlonzo.Code.Data.Integer.Base.d_'45'__252 (coe v2))
                    (coe MAlonzo.Code.Data.Integer.Base.d_'45'__252 (coe v1)))
                 (coe
                    MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8801''45''10216'_448
                    (\ v5 v6 v7 v8 v9 -> v9)
                    (MAlonzo.Code.Data.Integer.Base.d__'42'__308
                       (coe MAlonzo.Code.Data.Integer.Base.d_'45'__252 (coe v2))
                       (coe MAlonzo.Code.Data.Integer.Base.d_'45'__252 (coe v0)))
                    (MAlonzo.Code.Data.Integer.Base.d_'45'__252
                       (coe
                          MAlonzo.Code.Data.Integer.Base.d__'42'__308
                          (coe MAlonzo.Code.Data.Integer.Base.d_'45'__252 (coe v2))
                          (coe v0)))
                    (MAlonzo.Code.Data.Integer.Base.d__'42'__308
                       (coe MAlonzo.Code.Data.Integer.Base.d_'45'__252 (coe v2))
                       (coe MAlonzo.Code.Data.Integer.Base.d_'45'__252 (coe v1)))
                    (coe
                       MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8801''45''10217'_436
                       (\ v5 v6 v7 v8 v9 -> v9)
                       (MAlonzo.Code.Data.Integer.Base.d_'45'__252
                          (coe
                             MAlonzo.Code.Data.Integer.Base.d__'42'__308
                             (coe MAlonzo.Code.Data.Integer.Base.d_'45'__252 (coe v2))
                             (coe v0)))
                       (MAlonzo.Code.Data.Integer.Base.d__'42'__308 (coe v2) (coe v0))
                       (MAlonzo.Code.Data.Integer.Base.d__'42'__308
                          (coe MAlonzo.Code.Data.Integer.Base.d_'45'__252 (coe v2))
                          (coe MAlonzo.Code.Data.Integer.Base.d_'45'__252 (coe v1)))
                       (coe
                          MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''60'_312
                          (coe
                             MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_'60''45'go_152
                             (\ v5 v6 v7 v8 v9 -> coe du_'60''45'trans_2986 v8 v9)
                             (coe
                                MAlonzo.Code.Relation.Binary.PropositionalEquality.Core.du_resp'8322'_160)
                             (\ v5 v6 v7 v8 v9 -> coe du_'60''45''8804''45'trans_2972 v8 v9))
                          (MAlonzo.Code.Data.Integer.Base.d__'42'__308 (coe v2) (coe v0))
                          (MAlonzo.Code.Data.Integer.Base.d__'42'__308 (coe v2) (coe v1))
                          (MAlonzo.Code.Data.Integer.Base.d__'42'__308
                             (coe MAlonzo.Code.Data.Integer.Base.d_'45'__252 (coe v2))
                             (coe MAlonzo.Code.Data.Integer.Base.d_'45'__252 (coe v1)))
                          (coe
                             MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8801''45''10216'_448
                             (\ v5 v6 v7 v8 v9 -> v9)
                             (MAlonzo.Code.Data.Integer.Base.d__'42'__308 (coe v2) (coe v1))
                             (MAlonzo.Code.Data.Integer.Base.d_'45'__252
                                (coe
                                   MAlonzo.Code.Data.Integer.Base.d__'42'__308
                                   (coe MAlonzo.Code.Data.Integer.Base.d_'45'__252 (coe v2))
                                   (coe v1)))
                             (MAlonzo.Code.Data.Integer.Base.d__'42'__308
                                (coe MAlonzo.Code.Data.Integer.Base.d_'45'__252 (coe v2))
                                (coe MAlonzo.Code.Data.Integer.Base.d_'45'__252 (coe v1)))
                             (coe
                                MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8801''45''10217'_436
                                (\ v5 v6 v7 v8 v9 -> v9)
                                (MAlonzo.Code.Data.Integer.Base.d_'45'__252
                                   (coe
                                      MAlonzo.Code.Data.Integer.Base.d__'42'__308
                                      (coe MAlonzo.Code.Data.Integer.Base.d_'45'__252 (coe v2))
                                      (coe v1)))
                                (MAlonzo.Code.Data.Integer.Base.d__'42'__308
                                   (coe MAlonzo.Code.Data.Integer.Base.d_'45'__252 (coe v2))
                                   (coe MAlonzo.Code.Data.Integer.Base.d_'45'__252 (coe v1)))
                                (MAlonzo.Code.Data.Integer.Base.d__'42'__308
                                   (coe MAlonzo.Code.Data.Integer.Base.d_'45'__252 (coe v2))
                                   (coe MAlonzo.Code.Data.Integer.Base.d_'45'__252 (coe v1)))
                                (coe
                                   MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du__'8718'_492
                                   (coe
                                      MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_stop_166
                                      (coe d_'8804''45'isPreorder_2800))
                                   (coe
                                      MAlonzo.Code.Data.Integer.Base.d__'42'__308
                                      (coe MAlonzo.Code.Data.Integer.Base.d_'45'__252 (coe v2))
                                      (coe MAlonzo.Code.Data.Integer.Base.d_'45'__252 (coe v1))))
                                erased)
                             erased)
                          v3)
                       erased)
                    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 v0 v1 v2 ~v3
    = du_'42''45'cancel'691''45''60''45'nonPos_6388 v0 v1 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 v0 v1 v2
    = coe
        du_'42''45'cancel'737''45''60''45'nonPos_6366 (coe v0) (coe v1)
        (coe 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 v0 v1 v2
    = coe
        du_'42''45'cancel'737''45''60''45'nonPos_6366 (coe v0) (coe v1)
        (coe subInt (coe (-1 :: Integer)) (coe 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 v0 v1 v2
    = coe
        du_'42''45'cancel'691''45''60''45'nonPos_6388 (coe v0) (coe v1)
        (coe subInt (coe (-1 :: Integer)) (coe 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
    = 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 = 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 = 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 = 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 = erased
  -- Data.Integer.Properties.⊓-operator
  d_'8851''45'operator_6454 ::
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98
  d_'8851''45'operator_6454
    = coe
        MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.C_MinOperator'46'constructor_1121
        (coe MAlonzo.Code.Data.Integer.Base.d__'8851'__340) erased erased
  -- Data.Integer.Properties.⊔-operator
  d_'8852''45'operator_6456 ::
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MaxOperator_128
  d_'8852''45'operator_6456
    = coe
        MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.C_MaxOperator'46'constructor_1665
        (coe MAlonzo.Code.Data.Integer.Base.d__'8852'__322) erased 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
    = let v0 = d_'8804''45'totalPreorder_2812 in
      coe
        (let v1 = d_'8852''45'operator_6456 in
         coe
           (coe
              MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_x'8851'y'8804'x_2808
              (coe
                 MAlonzo.Code.Relation.Binary.Construct.Flip.EqAndOrd.du_totalPreorder_746
                 (coe v0))
              (coe
                 MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.du_MaxOp'8658'MinOp_174
                 (coe 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
    = let v0 = d_'8804''45'totalPreorder_2812 in
      coe
        (let v1 = d_'8852''45'operator_6456 in
         coe
           (coe
              MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_x'8804'y'8658'x'8851'z'8804'y_3160
              (coe
                 MAlonzo.Code.Relation.Binary.Construct.Flip.EqAndOrd.du_totalPreorder_746
                 (coe v0))
              (coe
                 MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.du_MaxOp'8658'MinOp_174
                 (coe 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
    = let v0 = d_'8804''45'totalPreorder_2812 in
      coe
        (let v1 = d_'8852''45'operator_6456 in
         coe
           (coe
              MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_x'8804'y'8658'z'8851'x'8804'y_3172
              (coe
                 MAlonzo.Code.Relation.Binary.Construct.Flip.EqAndOrd.du_totalPreorder_746
                 (coe v0))
              (coe
                 MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.du_MaxOp'8658'MinOp_174
                 (coe 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
    = let v0 = d_'8804''45'totalPreorder_2812 in
      coe
        (let v1 = d_'8851''45'operator_6454 in
         coe
           (coe
              MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_x'8804'y'8658'x'8851'z'8804'y_3160
              (coe v0) (coe 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
    = let v0 = d_'8804''45'totalPreorder_2812 in
      coe
        (let v1 = d_'8851''45'operator_6454 in
         coe
           (coe
              MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_x'8804'y'8658'z'8851'x'8804'y_3172
              (coe v0) (coe 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
    = let v0 = d_'8804''45'totalPreorder_2812 in
      coe
        (let v1 = d_'8851''45'operator_6454 in
         coe
           (coe
              MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_x'8804'y'8851'z'8658'x'8804'y_3184
              (coe v0) (coe 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
    = let v0 = d_'8804''45'totalPreorder_2812 in
      coe
        (let v1 = d_'8851''45'operator_6454 in
         coe
           (coe
              MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_x'8804'y'8851'z'8658'x'8804'z_3198
              (coe v0) (coe 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
    = let v0 = d_'8804''45'totalPreorder_2812 in
      coe
        (let v1 = d_'8852''45'operator_6456 in
         coe
           (coe
              MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_x'8851'y'8804'y_2834
              (coe
                 MAlonzo.Code.Relation.Binary.Construct.Flip.EqAndOrd.du_totalPreorder_746
                 (coe v0))
              (coe
                 MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.du_MaxOp'8658'MinOp_174
                 (coe 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
    = let v0 = d_'8804''45'totalPreorder_2812 in
      coe
        (let v1 = d_'8851''45'operator_6454 in
         coe
           (coe
              MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_x'8851'y'8776'x'8658'x'8804'y_3068
              (coe v0) (coe 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
    = let v0 = d_'8804''45'totalPreorder_2812 in
      coe
        (let v1 = d_'8851''45'operator_6454 in
         coe
           (coe
              MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_x'8851'y'8776'y'8658'y'8804'x_3100
              (coe v0) (coe 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
    = let v0 = d_'8804''45'totalPreorder_2812 in
      coe
        (let v1 = d_'8851''45'operator_6454 in
         coe
           (coe
              MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_x'8851'y'8804'x_2808
              (coe v0) (coe 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
    = coe
        MAlonzo.Code.Algebra.Construct.NaturalChoice.MinMaxOp.du_x'8851'y'8804'x'8852'y_3318
        (coe d_'8804''45'totalPreorder_2812)
        (coe d_'8851''45'operator_6454) (coe 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
    = let v0 = d_'8804''45'totalPreorder_2812 in
      coe
        (let v1 = d_'8851''45'operator_6454 in
         coe
           (coe
              MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_x'8851'y'8804'y_2834
              (coe v0) (coe 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
    = let v0 = d_'8804''45'totalPreorder_2812 in
      coe
        (let v1 = d_'8852''45'operator_6456 in
         coe
           (coe
              MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_x'8851'y'8776'x'8658'x'8804'y_3068
              (coe
                 MAlonzo.Code.Relation.Binary.Construct.Flip.EqAndOrd.du_totalPreorder_746
                 (coe v0))
              (coe
                 MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.du_MaxOp'8658'MinOp_174
                 (coe 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
    = let v0 = d_'8804''45'totalPreorder_2812 in
      coe
        (let v1 = d_'8852''45'operator_6456 in
         coe
           (coe
              MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_x'8851'y'8776'y'8658'y'8804'x_3100
              (coe
                 MAlonzo.Code.Relation.Binary.Construct.Flip.EqAndOrd.du_totalPreorder_746
                 (coe v0))
              (coe
                 MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.du_MaxOp'8658'MinOp_174
                 (coe 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
    = let v0 = d_'8804''45'totalPreorder_2812 in
      coe
        (let v1 = d_'8852''45'operator_6456 in
         coe
           (coe
              MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_x'8804'y'8851'z'8658'x'8804'y_3184
              (coe
                 MAlonzo.Code.Relation.Binary.Construct.Flip.EqAndOrd.du_totalPreorder_746
                 (coe v0))
              (coe
                 MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.du_MaxOp'8658'MinOp_174
                 (coe 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
    = let v0 = d_'8804''45'totalPreorder_2812 in
      coe
        (let v1 = d_'8852''45'operator_6456 in
         coe
           (coe
              MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_x'8804'y'8851'z'8658'x'8804'z_3198
              (coe
                 MAlonzo.Code.Relation.Binary.Construct.Flip.EqAndOrd.du_totalPreorder_746
                 (coe v0))
              (coe
                 MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.du_MaxOp'8658'MinOp_174
                 (coe 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 = 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 = erased
  -- Data.Integer.Properties.⊓-⊔-properties.⊓-band
  d_'8851''45'band_6506 :: MAlonzo.Code.Algebra.Bundles.T_Band_596
  d_'8851''45'band_6506
    = let v0 = d_'8804''45'totalPreorder_2812 in
      coe
        (let v1 = d_'8851''45'operator_6454 in
         coe
           (coe
              MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_'8851''45'band_3052
              (coe v0) (coe 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 = erased
  -- Data.Integer.Properties.⊓-⊔-properties.⊓-commutativeSemigroup
  d_'8851''45'commutativeSemigroup_6510 ::
    MAlonzo.Code.Algebra.Bundles.T_CommutativeSemigroup_662
  d_'8851''45'commutativeSemigroup_6510
    = let v0 = d_'8804''45'totalPreorder_2812 in
      coe
        (let v1 = d_'8851''45'operator_6454 in
         coe
           (coe
              MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_'8851''45'commutativeSemigroup_3054
              (coe v0) (coe 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
    = coe
        MAlonzo.Code.Algebra.Construct.NaturalChoice.MinMaxOp.du_'8851''45'distrib'45''8852'_3138
        (coe d_'8804''45'totalPreorder_2812)
        (coe d_'8851''45'operator_6454) (coe 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 = 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 = 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
    = let v0 = d_'8804''45'totalPreorder_2812 in
      coe
        (let v1 = d_'8851''45'operator_6454 in
         coe
           (coe
              MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_'8851''45'glb_3278
              (coe v0) (coe 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 = erased
  -- Data.Integer.Properties.⊓-⊔-properties.⊓-isBand
  d_'8851''45'isBand_6534 ::
    MAlonzo.Code.Algebra.Structures.T_IsBand_508
  d_'8851''45'isBand_6534
    = let v0 = d_'8804''45'totalPreorder_2812 in
      coe
        (let v1 = d_'8851''45'operator_6454 in
         coe
           (coe
              MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_'8851''45'isBand_3034
              (coe v0) (coe v1)))
  -- Data.Integer.Properties.⊓-⊔-properties.⊓-isCommutativeSemigroup
  d_'8851''45'isCommutativeSemigroup_6536 ::
    MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_548
  d_'8851''45'isCommutativeSemigroup_6536
    = let v0 = d_'8804''45'totalPreorder_2812 in
      coe
        (let v1 = d_'8851''45'operator_6454 in
         coe
           (coe
              MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_'8851''45'isCommutativeSemigroup_3036
              (coe v0) (coe v1)))
  -- Data.Integer.Properties.⊓-⊔-properties.⊓-isMagma
  d_'8851''45'isMagma_6538 ::
    MAlonzo.Code.Algebra.Structures.T_IsMagma_176
  d_'8851''45'isMagma_6538
    = let v0 = d_'8804''45'totalPreorder_2812 in
      coe
        (let v1 = d_'8851''45'operator_6454 in
         coe
           (coe
              MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_'8851''45'isMagma_3030
              (coe v0) (coe v1)))
  -- Data.Integer.Properties.⊓-⊔-properties.⊓-isSelectiveMagma
  d_'8851''45'isSelectiveMagma_6542 ::
    MAlonzo.Code.Algebra.Structures.T_IsSelectiveMagma_436
  d_'8851''45'isSelectiveMagma_6542
    = let v0 = d_'8804''45'totalPreorder_2812 in
      coe
        (let v1 = d_'8851''45'operator_6454 in
         coe
           (coe
              MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_'8851''45'isSelectiveMagma_3038
              (coe v0) (coe v1)))
  -- Data.Integer.Properties.⊓-⊔-properties.⊓-isSemigroup
  d_'8851''45'isSemigroup_6544 ::
    MAlonzo.Code.Algebra.Structures.T_IsSemigroup_472
  d_'8851''45'isSemigroup_6544
    = let v0 = d_'8804''45'totalPreorder_2812 in
      coe
        (let v1 = d_'8851''45'operator_6454 in
         coe
           (coe
              MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_'8851''45'isSemigroup_3032
              (coe v0) (coe v1)))
  -- Data.Integer.Properties.⊓-⊔-properties.⊓-magma
  d_'8851''45'magma_6546 :: MAlonzo.Code.Algebra.Bundles.T_Magma_68
  d_'8851''45'magma_6546
    = let v0 = d_'8804''45'totalPreorder_2812 in
      coe
        (let v1 = d_'8851''45'operator_6454 in
         coe
           (coe
              MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_'8851''45'magma_3048
              (coe v0) (coe 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
    = let v0 = d_'8804''45'totalPreorder_2812 in
      coe
        (let v1 = d_'8851''45'operator_6454 in
         coe
           (coe
              MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_'8851''45'mono'45''8804'_3206
              (coe v0) (coe 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
    = let v0 = d_'8804''45'totalPreorder_2812 in
      coe
        (let v1 = d_'8851''45'operator_6454 in
         coe
           (coe
              MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_'8851''45'mono'691''45''8804'_3266
              (coe v0) (coe 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
    = let v0 = d_'8804''45'totalPreorder_2812 in
      coe
        (let v1 = d_'8851''45'operator_6454 in
         coe
           (coe
              MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_'8851''45'mono'737''45''8804'_3256
              (coe v0) (coe 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
    = let v0 = d_'8804''45'totalPreorder_2812 in
      coe
        (let v1 = d_'8851''45'operator_6454 in
         coe
           (coe
              MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_'8851''45'sel_2988
              (coe v0) (coe v1)))
  -- Data.Integer.Properties.⊓-⊔-properties.⊓-selectiveMagma
  d_'8851''45'selectiveMagma_6560 ::
    MAlonzo.Code.Algebra.Bundles.T_SelectiveMagma_122
  d_'8851''45'selectiveMagma_6560
    = let v0 = d_'8804''45'totalPreorder_2812 in
      coe
        (let v1 = d_'8851''45'operator_6454 in
         coe
           (coe
              MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_'8851''45'selectiveMagma_3056
              (coe v0) (coe v1)))
  -- Data.Integer.Properties.⊓-⊔-properties.⊓-semigroup
  d_'8851''45'semigroup_6562 ::
    MAlonzo.Code.Algebra.Bundles.T_Semigroup_536
  d_'8851''45'semigroup_6562
    = let v0 = d_'8804''45'totalPreorder_2812 in
      coe
        (let v1 = d_'8851''45'operator_6454 in
         coe
           (coe
              MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_'8851''45'semigroup_3050
              (coe v0) (coe 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 = 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
    = coe
        MAlonzo.Code.Algebra.Construct.NaturalChoice.MinMaxOp.du_'8851''45''8852''45'absorptive_3218
        (coe d_'8804''45'totalPreorder_2812)
        (coe d_'8851''45'operator_6454) (coe 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 = 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 = erased
  -- Data.Integer.Properties.⊓-⊔-properties.⊓-band
  d_'8851''45'band_6578 :: MAlonzo.Code.Algebra.Bundles.T_Band_596
  d_'8851''45'band_6578
    = let v0 = d_'8804''45'totalPreorder_2812 in
      coe
        (let v1 = d_'8852''45'operator_6456 in
         coe
           (coe
              MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_'8851''45'band_3052
              (coe
                 MAlonzo.Code.Relation.Binary.Construct.Flip.EqAndOrd.du_totalPreorder_746
                 (coe v0))
              (coe
                 MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.du_MaxOp'8658'MinOp_174
                 (coe 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 = erased
  -- Data.Integer.Properties.⊓-⊔-properties.⊓-commutativeSemigroup
  d_'8851''45'commutativeSemigroup_6582 ::
    MAlonzo.Code.Algebra.Bundles.T_CommutativeSemigroup_662
  d_'8851''45'commutativeSemigroup_6582
    = let v0 = d_'8804''45'totalPreorder_2812 in
      coe
        (let v1 = d_'8852''45'operator_6456 in
         coe
           (coe
              MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_'8851''45'commutativeSemigroup_3054
              (coe
                 MAlonzo.Code.Relation.Binary.Construct.Flip.EqAndOrd.du_totalPreorder_746
                 (coe v0))
              (coe
                 MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.du_MaxOp'8658'MinOp_174
                 (coe 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
    = coe
        MAlonzo.Code.Algebra.Construct.NaturalChoice.MinMaxOp.du_'8852''45'distrib'45''8851'_3170
        (coe d_'8804''45'totalPreorder_2812)
        (coe d_'8851''45'operator_6454) (coe 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 = 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 = 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 = erased
  -- Data.Integer.Properties.⊓-⊔-properties.⊓-isBand
  d_'8851''45'isBand_6604 ::
    MAlonzo.Code.Algebra.Structures.T_IsBand_508
  d_'8851''45'isBand_6604
    = let v0 = d_'8804''45'totalPreorder_2812 in
      coe
        (let v1 = d_'8852''45'operator_6456 in
         coe
           (coe
              MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_'8851''45'isBand_3034
              (coe
                 MAlonzo.Code.Relation.Binary.Construct.Flip.EqAndOrd.du_totalPreorder_746
                 (coe v0))
              (coe
                 MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.du_MaxOp'8658'MinOp_174
                 (coe v1))))
  -- Data.Integer.Properties.⊓-⊔-properties.⊓-isCommutativeSemigroup
  d_'8851''45'isCommutativeSemigroup_6606 ::
    MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_548
  d_'8851''45'isCommutativeSemigroup_6606
    = let v0 = d_'8804''45'totalPreorder_2812 in
      coe
        (let v1 = d_'8852''45'operator_6456 in
         coe
           (coe
              MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_'8851''45'isCommutativeSemigroup_3036
              (coe
                 MAlonzo.Code.Relation.Binary.Construct.Flip.EqAndOrd.du_totalPreorder_746
                 (coe v0))
              (coe
                 MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.du_MaxOp'8658'MinOp_174
                 (coe v1))))
  -- Data.Integer.Properties.⊓-⊔-properties.⊓-isMagma
  d_'8851''45'isMagma_6608 ::
    MAlonzo.Code.Algebra.Structures.T_IsMagma_176
  d_'8851''45'isMagma_6608
    = let v0 = d_'8804''45'totalPreorder_2812 in
      coe
        (let v1 = d_'8852''45'operator_6456 in
         coe
           (coe
              MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_'8851''45'isMagma_3030
              (coe
                 MAlonzo.Code.Relation.Binary.Construct.Flip.EqAndOrd.du_totalPreorder_746
                 (coe v0))
              (coe
                 MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.du_MaxOp'8658'MinOp_174
                 (coe v1))))
  -- Data.Integer.Properties.⊓-⊔-properties.⊓-isSelectiveMagma
  d_'8851''45'isSelectiveMagma_6612 ::
    MAlonzo.Code.Algebra.Structures.T_IsSelectiveMagma_436
  d_'8851''45'isSelectiveMagma_6612
    = let v0 = d_'8804''45'totalPreorder_2812 in
      coe
        (let v1 = d_'8852''45'operator_6456 in
         coe
           (coe
              MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_'8851''45'isSelectiveMagma_3038
              (coe
                 MAlonzo.Code.Relation.Binary.Construct.Flip.EqAndOrd.du_totalPreorder_746
                 (coe v0))
              (coe
                 MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.du_MaxOp'8658'MinOp_174
                 (coe v1))))
  -- Data.Integer.Properties.⊓-⊔-properties.⊓-isSemigroup
  d_'8851''45'isSemigroup_6614 ::
    MAlonzo.Code.Algebra.Structures.T_IsSemigroup_472
  d_'8851''45'isSemigroup_6614
    = let v0 = d_'8804''45'totalPreorder_2812 in
      coe
        (let v1 = d_'8852''45'operator_6456 in
         coe
           (coe
              MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_'8851''45'isSemigroup_3032
              (coe
                 MAlonzo.Code.Relation.Binary.Construct.Flip.EqAndOrd.du_totalPreorder_746
                 (coe v0))
              (coe
                 MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.du_MaxOp'8658'MinOp_174
                 (coe 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
    = let v0 = d_'8804''45'totalPreorder_2812 in
      coe
        (let v1 = d_'8852''45'operator_6456 in
         coe
           (coe
              MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_'8851''45'glb_3278
              (coe
                 MAlonzo.Code.Relation.Binary.Construct.Flip.EqAndOrd.du_totalPreorder_746
                 (coe v0))
              (coe
                 MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.du_MaxOp'8658'MinOp_174
                 (coe v1))))
  -- Data.Integer.Properties.⊓-⊔-properties.⊓-magma
  d_'8851''45'magma_6618 :: MAlonzo.Code.Algebra.Bundles.T_Magma_68
  d_'8851''45'magma_6618
    = let v0 = d_'8804''45'totalPreorder_2812 in
      coe
        (let v1 = d_'8852''45'operator_6456 in
         coe
           (coe
              MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_'8851''45'magma_3048
              (coe
                 MAlonzo.Code.Relation.Binary.Construct.Flip.EqAndOrd.du_totalPreorder_746
                 (coe v0))
              (coe
                 MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.du_MaxOp'8658'MinOp_174
                 (coe 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
    = let v0 = d_'8804''45'totalPreorder_2812 in
      coe
        (let v1 = d_'8852''45'operator_6456 in
         coe
           (coe
              MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_'8851''45'mono'45''8804'_3206
              (coe
                 MAlonzo.Code.Relation.Binary.Construct.Flip.EqAndOrd.du_totalPreorder_746
                 (coe v0))
              (coe
                 MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.du_MaxOp'8658'MinOp_174
                 (coe 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
    = let v0 = d_'8804''45'totalPreorder_2812 in
      coe
        (let v1 = d_'8852''45'operator_6456 in
         coe
           (coe
              MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_'8851''45'mono'691''45''8804'_3266
              (coe
                 MAlonzo.Code.Relation.Binary.Construct.Flip.EqAndOrd.du_totalPreorder_746
                 (coe v0))
              (coe
                 MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.du_MaxOp'8658'MinOp_174
                 (coe 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
    = let v0 = d_'8804''45'totalPreorder_2812 in
      coe
        (let v1 = d_'8852''45'operator_6456 in
         coe
           (coe
              MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_'8851''45'mono'737''45''8804'_3256
              (coe
                 MAlonzo.Code.Relation.Binary.Construct.Flip.EqAndOrd.du_totalPreorder_746
                 (coe v0))
              (coe
                 MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.du_MaxOp'8658'MinOp_174
                 (coe 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
    = let v0 = d_'8804''45'totalPreorder_2812 in
      coe
        (let v1 = d_'8852''45'operator_6456 in
         coe
           (coe
              MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_'8851''45'sel_2988
              (coe
                 MAlonzo.Code.Relation.Binary.Construct.Flip.EqAndOrd.du_totalPreorder_746
                 (coe v0))
              (coe
                 MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.du_MaxOp'8658'MinOp_174
                 (coe v1))))
  -- Data.Integer.Properties.⊓-⊔-properties.⊓-selectiveMagma
  d_'8851''45'selectiveMagma_6630 ::
    MAlonzo.Code.Algebra.Bundles.T_SelectiveMagma_122
  d_'8851''45'selectiveMagma_6630
    = let v0 = d_'8804''45'totalPreorder_2812 in
      coe
        (let v1 = d_'8852''45'operator_6456 in
         coe
           (coe
              MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_'8851''45'selectiveMagma_3056
              (coe
                 MAlonzo.Code.Relation.Binary.Construct.Flip.EqAndOrd.du_totalPreorder_746
                 (coe v0))
              (coe
                 MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.du_MaxOp'8658'MinOp_174
                 (coe v1))))
  -- Data.Integer.Properties.⊓-⊔-properties.⊓-semigroup
  d_'8851''45'semigroup_6632 ::
    MAlonzo.Code.Algebra.Bundles.T_Semigroup_536
  d_'8851''45'semigroup_6632
    = let v0 = d_'8804''45'totalPreorder_2812 in
      coe
        (let v1 = d_'8852''45'operator_6456 in
         coe
           (coe
              MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_'8851''45'semigroup_3050
              (coe
                 MAlonzo.Code.Relation.Binary.Construct.Flip.EqAndOrd.du_totalPreorder_746
                 (coe v0))
              (coe
                 MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.du_MaxOp'8658'MinOp_174
                 (coe 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 = 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
    = coe
        MAlonzo.Code.Algebra.Construct.NaturalChoice.MinMaxOp.du_'8852''45''8851''45'absorptive_3216
        (coe d_'8804''45'totalPreorder_2812)
        (coe d_'8851''45'operator_6454) (coe 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
    = let v0 = d_'8804''45'totalPreorder_2812 in
      coe
        (let v1 = d_'8851''45'operator_6454 in
         coe
           (coe
              MAlonzo.Code.Algebra.Lattice.Construct.NaturalChoice.MinOp.du_'8851''45'isSemilattice_602
              (coe v0) (coe v1)))
  -- Data.Integer.Properties.⊓-⊔-latticeProperties.⊓-semilattice
  d_'8851''45'semilattice_6648 ::
    MAlonzo.Code.Algebra.Lattice.Bundles.T_Semilattice_10
  d_'8851''45'semilattice_6648
    = let v0 = d_'8804''45'totalPreorder_2812 in
      coe
        (let v1 = d_'8851''45'operator_6454 in
         coe
           (coe
              MAlonzo.Code.Algebra.Lattice.Construct.NaturalChoice.MinOp.du_'8851''45'semilattice_604
              (coe v0) (coe 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
    = coe
        MAlonzo.Code.Algebra.Lattice.Construct.NaturalChoice.MinMaxOp.du_'8851''45''8852''45'distributiveLattice_808
        (coe d_'8804''45'totalPreorder_2812)
        (coe d_'8851''45'operator_6454) (coe 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
    = coe
        MAlonzo.Code.Algebra.Lattice.Construct.NaturalChoice.MinMaxOp.du_'8851''45''8852''45'isDistributiveLattice_798
        (coe d_'8804''45'totalPreorder_2812)
        (coe d_'8851''45'operator_6454) (coe 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
    = coe
        MAlonzo.Code.Algebra.Lattice.Construct.NaturalChoice.MinMaxOp.du_'8851''45''8852''45'isLattice_796
        (coe d_'8804''45'totalPreorder_2812)
        (coe d_'8851''45'operator_6454) (coe 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
    = coe
        MAlonzo.Code.Algebra.Lattice.Construct.NaturalChoice.MinMaxOp.du_'8851''45''8852''45'lattice_804
        (coe d_'8804''45'totalPreorder_2812)
        (coe d_'8851''45'operator_6454) (coe 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
    = let v0 = d_'8804''45'totalPreorder_2812 in
      coe
        (let v1 = d_'8852''45'operator_6456 in
         coe
           (coe
              MAlonzo.Code.Algebra.Lattice.Construct.NaturalChoice.MinOp.du_'8851''45'isSemilattice_602
              (coe
                 MAlonzo.Code.Relation.Binary.Construct.Flip.EqAndOrd.du_totalPreorder_746
                 (coe v0))
              (coe
                 MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.du_MaxOp'8658'MinOp_174
                 (coe v1))))
  -- Data.Integer.Properties.⊓-⊔-latticeProperties.⊓-semilattice
  d_'8851''45'semilattice_6660 ::
    MAlonzo.Code.Algebra.Lattice.Bundles.T_Semilattice_10
  d_'8851''45'semilattice_6660
    = let v0 = d_'8804''45'totalPreorder_2812 in
      coe
        (let v1 = d_'8852''45'operator_6456 in
         coe
           (coe
              MAlonzo.Code.Algebra.Lattice.Construct.NaturalChoice.MinOp.du_'8851''45'semilattice_604
              (coe
                 MAlonzo.Code.Relation.Binary.Construct.Flip.EqAndOrd.du_totalPreorder_746
                 (coe v0))
              (coe
                 MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.du_MaxOp'8658'MinOp_174
                 (coe 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
    = coe
        MAlonzo.Code.Algebra.Lattice.Construct.NaturalChoice.MinMaxOp.du_'8852''45''8851''45'distributiveLattice_806
        (coe d_'8804''45'totalPreorder_2812)
        (coe d_'8851''45'operator_6454) (coe 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
    = coe
        MAlonzo.Code.Algebra.Lattice.Construct.NaturalChoice.MinMaxOp.du_'8852''45''8851''45'isDistributiveLattice_800
        (coe d_'8804''45'totalPreorder_2812)
        (coe d_'8851''45'operator_6454) (coe 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
    = coe
        MAlonzo.Code.Algebra.Lattice.Construct.NaturalChoice.MinMaxOp.du_'8852''45''8851''45'isLattice_794
        (coe d_'8804''45'totalPreorder_2812)
        (coe d_'8851''45'operator_6454) (coe 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
    = coe
        MAlonzo.Code.Algebra.Lattice.Construct.NaturalChoice.MinMaxOp.du_'8852''45''8851''45'lattice_802
        (coe d_'8804''45'totalPreorder_2812)
        (coe d_'8851''45'operator_6454) (coe 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 = 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 = 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 = 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 = 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 = 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 = 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 = 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 = 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 = 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 = 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 = 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 = 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 = 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 = 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 = 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 = 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 = 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 = 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 = coe 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 v0 v1 v2
    = coe du_neg'45'mono'45''8804'_3272 v1 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 v0 v1 v2 v3 v4
    = coe du_'42''45'mono'691''45''8804''45'nonNeg_6054 v0 v2 v3 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 v0 v1 v2 v3
    = coe du_'42''45'mono'737''45''8804''45'nonNeg_6096 v0 v2 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 v0 v1 v2 v3 v4
    = coe du_'42''45'cancel'737''45''60''45'nonNeg_6266 v0 v1 v2 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 v0 v1 v2 v3
    = coe du_'42''45'cancel'691''45''60''45'nonNeg_6304 v0 v1 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 = 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
    = let v0 = d_'8804''45'totalPreorder_2812 in
      coe
        (let v1 = d_'8851''45'operator_6454 in
         coe
           (coe
              MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_x'8851'y'8776'x'8658'x'8804'y_3068
              (coe v0) (coe 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 = 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
    = let v0 = d_'8804''45'totalPreorder_2812 in
      coe
        (let v1 = d_'8851''45'operator_6454 in
         coe
           (coe
              MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_x'8851'y'8776'y'8658'y'8804'x_3100
              (coe v0) (coe 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
    = let v0 = d_'8804''45'totalPreorder_2812 in
      coe
        (let v1 = d_'8851''45'operator_6454 in
         coe
           (coe
              MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_x'8851'y'8804'y_2834
              (coe v0) (coe 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
    = let v0 = d_'8804''45'totalPreorder_2812 in
      coe
        (let v1 = d_'8851''45'operator_6454 in
         coe
           (coe
              MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_x'8851'y'8804'x_2808
              (coe v0) (coe 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 = 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
    = let v0 = d_'8804''45'totalPreorder_2812 in
      coe
        (let v1 = d_'8852''45'operator_6456 in
         coe
           (coe
              MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_x'8851'y'8776'y'8658'y'8804'x_3100
              (coe
                 MAlonzo.Code.Relation.Binary.Construct.Flip.EqAndOrd.du_totalPreorder_746
                 (coe v0))
              (coe
                 MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.du_MaxOp'8658'MinOp_174
                 (coe 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 = 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
    = let v0 = d_'8804''45'totalPreorder_2812 in
      coe
        (let v1 = d_'8852''45'operator_6456 in
         coe
           (coe
              MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_x'8851'y'8776'x'8658'x'8804'y_3068
              (coe
                 MAlonzo.Code.Relation.Binary.Construct.Flip.EqAndOrd.du_totalPreorder_746
                 (coe v0))
              (coe
                 MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.du_MaxOp'8658'MinOp_174
                 (coe 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
    = let v0 = d_'8804''45'totalPreorder_2812 in
      coe
        (let v1 = d_'8852''45'operator_6456 in
         coe
           (coe
              MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_x'8851'y'8804'x_2808
              (coe
                 MAlonzo.Code.Relation.Binary.Construct.Flip.EqAndOrd.du_totalPreorder_746
                 (coe v0))
              (coe
                 MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.du_MaxOp'8658'MinOp_174
                 (coe 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
    = let v0 = d_'8804''45'totalPreorder_2812 in
      coe
        (let v1 = d_'8852''45'operator_6456 in
         coe
           (coe
              MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_x'8851'y'8804'y_2834
              (coe
                 MAlonzo.Code.Relation.Binary.Construct.Flip.EqAndOrd.du_totalPreorder_746
                 (coe v0))
              (coe
                 MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.du_MaxOp'8658'MinOp_174
                 (coe 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 v0 v1 v2 v3
    = case coe v3 of
        MAlonzo.Code.Data.Integer.Base.C_'45''8804''45'_34 v6
          -> coe
               d_'8854''45'mono'691''45''8805''45''8804'_4024 (coe v0)
               (coe subInt (coe (0 :: Integer)) (coe v1))
               (coe subInt (coe (0 :: Integer)) (coe v2))
               (coe MAlonzo.Code.Data.Nat.Base.C_s'8804's_34 v6)
        MAlonzo.Code.Data.Integer.Base.C_'45''8804''43'_40
          -> coe
               du_'8804''45'trans_2730
               (coe
                  d_m'8854'n'8804'm_3912 (coe v0)
                  (coe subInt (coe (0 :: Integer)) (coe v1)))
               (coe
                  MAlonzo.Code.Data.Integer.Base.C_'43''8804''43'_48
                  (coe
                     MAlonzo.Code.Data.Nat.Properties.du_m'8804'm'43'n_3482 (coe v0)))
        MAlonzo.Code.Data.Integer.Base.C_'43''8804''43'_48 v6
          -> coe
               MAlonzo.Code.Data.Integer.Base.C_'43''8804''43'_48
               (coe
                  MAlonzo.Code.Data.Nat.Properties.du_'43''45'mono'691''45''8804'_3554
                  (coe v0) (coe v2) (coe v6))
        _ -> 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 v0 v1 v2 v3
    = case coe v3 of
        MAlonzo.Code.Data.Integer.Base.C_'45''8804''45'_34 v6
          -> let v7 = subInt (coe (-1 :: Integer)) (coe v1) in
             coe
               (coe
                  MAlonzo.Code.Data.Integer.Base.C_'45''8804''45'_34
                  (coe
                     MAlonzo.Code.Data.Nat.Properties.du_'43''45'mono'691''45''8804'_3554
                     (coe addInt (coe (1 :: Integer)) (coe v0)) (coe v7) (coe v6)))
        MAlonzo.Code.Data.Integer.Base.C_'45''8804''43'_40
          -> coe
               du_'8804''45'trans_2730
               (coe
                  MAlonzo.Code.Data.Integer.Base.C_'45''8804''45'_34
                  (coe
                     MAlonzo.Code.Data.Nat.Properties.du_m'8804'm'43'n_3482
                     (coe addInt (coe (1 :: Integer)) (coe v0))))
               (coe
                  d_'45'1'43'm'8804'n'8854'm_3992
                  (coe addInt (coe (1 :: Integer)) (coe v0)) (coe v2))
        MAlonzo.Code.Data.Integer.Base.C_'43''8804''43'_48 v6
          -> coe
               d_'8854''45'mono'737''45''8804'_4056
               (coe addInt (coe (1 :: Integer)) (coe v0)) (coe v1) (coe v2)
               (coe v6)
        _ -> 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 = 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 = 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 = 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 = 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 v0 v1
    = coe 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
    = coe
        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
    = coe 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
    = coe 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 = 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 = 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 = 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 = 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 = 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 v0 v1 v2 v3 v4
    = coe du_i'8804'j'8658'i'8804'k'43'j_4578 v0 v1 v2 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 v0 v1 v2 v3 v4
    = coe du_i'8804'j'8658'i'45'k'8804'j_4852 v0 v2 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 = coe 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 v0 v1 v2
    = coe du_i'8804'j'8658'pred'91'i'93''8804'j_5116 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
    = coe 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
    = coe 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
    = coe 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
    = coe 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 = coe 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 = 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 v0 v1 v2
    = coe du_i'8804'pred'91'j'93''8658'i'60'j_5094 v1 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 v0 v1 v2
    = coe du_i'60'j'8658'i'8804'pred'91'j'93'_5104 v1 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 = 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 v0 v1 v2
    = coe du_i'42'j'8801'0'8658'i'8801'0'8744'j'8801'0_5780 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
    = 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 v0 v1
    = coe du_i'8804'j'43'i_4592 (coe v0) (coe 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 v0 v1
    = coe du_i'8804'i'43'j_4604 (coe v0) (coe 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 v0 v1
    = coe du_i'45'j'8804'i_4880 (coe v0) (coe 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 v0 v1 v2
    = coe
        du_'42''45'mono'691''45''8804''45'nonNeg_6054
        (coe addInt (coe (1 :: Integer)) (coe v0)) (coe v1) (coe 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 v0 v1 v2
    = coe
        du_'42''45'mono'737''45''8804''45'nonNeg_6096
        (coe addInt (coe (1 :: Integer)) (coe v0)) (coe v1) (coe 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 v0 v1 v2
    = coe
        du_'42''45'mono'737''45''8804''45'nonPos_6164
        (coe subInt (coe (-1 :: Integer)) (coe v0)) (coe v1) (coe 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 v0 v1 v2
    = coe
        du_'42''45'mono'691''45''8804''45'nonPos_6192
        (coe subInt (coe (-1 :: Integer)) (coe v0)) (coe v1) (coe 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 = 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 = 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 = erased
  -- Data.Integer.Properties.+-isAbelianGroup
  d_'43''45'isAbelianGroup_7238 ::
    MAlonzo.Code.Algebra.Structures.T_IsAbelianGroup_1132
  d_'43''45'isAbelianGroup_7238
    = coe d_'43''45'0'45'isAbelianGroup_4436
  