{-# 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.Nat.Properties where

import MAlonzo.RTE (coe, erased, AgdaAny, addInt, subInt, mulInt,
                    quotInt, remInt, geqInt, ltInt, eqInt, add64, sub64, mul64, quot64,
                    rem64, lt64, eq64, word64FromNat, word64ToNat)
import qualified MAlonzo.RTE
import qualified Data.Text
import qualified MAlonzo.Code.Agda.Builtin.Bool
import qualified MAlonzo.Code.Agda.Builtin.Equality
import qualified MAlonzo.Code.Agda.Builtin.Nat
import qualified MAlonzo.Code.Agda.Builtin.Sigma
import qualified MAlonzo.Code.Agda.Builtin.Unit
import qualified MAlonzo.Code.Agda.Primitive
import qualified MAlonzo.Code.Algebra.Bundles
import qualified MAlonzo.Code.Algebra.Construct.NaturalChoice.Base
import qualified MAlonzo.Code.Algebra.Construct.NaturalChoice.MinMaxOp
import qualified MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp
import qualified MAlonzo.Code.Algebra.Definitions.RawMagma
import qualified MAlonzo.Code.Algebra.Lattice.Bundles
import qualified MAlonzo.Code.Algebra.Lattice.Construct.NaturalChoice.MinMaxOp
import qualified MAlonzo.Code.Algebra.Lattice.Construct.NaturalChoice.MinOp
import qualified MAlonzo.Code.Algebra.Lattice.Structures
import qualified MAlonzo.Code.Algebra.Morphism
import qualified MAlonzo.Code.Algebra.Structures
import qualified MAlonzo.Code.Data.Irrelevant
import qualified MAlonzo.Code.Data.Nat.Base
import qualified MAlonzo.Code.Data.Sum.Base
import qualified MAlonzo.Code.Function.Base
import qualified MAlonzo.Code.Function.Bundles
import qualified MAlonzo.Code.Function.Metric.Nat.Bundles
import qualified MAlonzo.Code.Function.Metric.Structures
import qualified MAlonzo.Code.Relation.Binary.Bundles
import qualified MAlonzo.Code.Relation.Binary.Consequences
import qualified MAlonzo.Code.Relation.Binary.Construct.Flip.EqAndOrd
import qualified MAlonzo.Code.Relation.Binary.Definitions
import qualified MAlonzo.Code.Relation.Binary.PropositionalEquality.Algebra
import qualified MAlonzo.Code.Relation.Binary.PropositionalEquality.Core
import qualified MAlonzo.Code.Relation.Binary.PropositionalEquality.Properties
import qualified MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple
import qualified MAlonzo.Code.Relation.Binary.Reasoning.Syntax
import qualified MAlonzo.Code.Relation.Binary.Structures
import qualified MAlonzo.Code.Relation.Binary.Structures.Biased
import qualified MAlonzo.Code.Relation.Nullary.Decidable
import qualified MAlonzo.Code.Relation.Nullary.Decidable.Core
import qualified MAlonzo.Code.Relation.Nullary.Negation.Core
import qualified MAlonzo.Code.Relation.Nullary.Reflects

-- Data.Nat.Properties._._DistributesOver_
d__DistributesOver__10 ::
  (Integer -> Integer -> Integer) ->
  (Integer -> Integer -> Integer) -> ()
d__DistributesOver__10 :: (Integer -> Integer -> Integer)
-> (Integer -> Integer -> Integer) -> ()
d__DistributesOver__10 = (Integer -> Integer -> Integer)
-> (Integer -> Integer -> Integer) -> ()
forall a. a
erased
-- Data.Nat.Properties._._DistributesOverʳ_
d__DistributesOver'691'__12 ::
  (Integer -> Integer -> Integer) ->
  (Integer -> Integer -> Integer) -> ()
d__DistributesOver'691'__12 :: (Integer -> Integer -> Integer)
-> (Integer -> Integer -> Integer) -> ()
d__DistributesOver'691'__12 = (Integer -> Integer -> Integer)
-> (Integer -> Integer -> Integer) -> ()
forall a. a
erased
-- Data.Nat.Properties._._DistributesOverˡ_
d__DistributesOver'737'__14 ::
  (Integer -> Integer -> Integer) ->
  (Integer -> Integer -> Integer) -> ()
d__DistributesOver'737'__14 :: (Integer -> Integer -> Integer)
-> (Integer -> Integer -> Integer) -> ()
d__DistributesOver'737'__14 = (Integer -> Integer -> Integer)
-> (Integer -> Integer -> Integer) -> ()
forall a. a
erased
-- Data.Nat.Properties._.Associative
d_Associative_30 :: (Integer -> Integer -> Integer) -> ()
d_Associative_30 :: (Integer -> Integer -> Integer) -> ()
d_Associative_30 = (Integer -> Integer -> Integer) -> ()
forall a. a
erased
-- Data.Nat.Properties._.Commutative
d_Commutative_32 :: (Integer -> Integer -> Integer) -> ()
d_Commutative_32 :: (Integer -> Integer -> Integer) -> ()
d_Commutative_32 = (Integer -> Integer -> Integer) -> ()
forall a. a
erased
-- Data.Nat.Properties._.Identity
d_Identity_48 :: Integer -> (Integer -> Integer -> Integer) -> ()
d_Identity_48 :: Integer -> (Integer -> Integer -> Integer) -> ()
d_Identity_48 = Integer -> (Integer -> Integer -> Integer) -> ()
forall a. a
erased
-- Data.Nat.Properties._.LeftIdentity
d_LeftIdentity_72 ::
  Integer -> (Integer -> Integer -> Integer) -> ()
d_LeftIdentity_72 :: Integer -> (Integer -> Integer -> Integer) -> ()
d_LeftIdentity_72 = Integer -> (Integer -> Integer -> Integer) -> ()
forall a. a
erased
-- Data.Nat.Properties._.LeftZero
d_LeftZero_80 :: Integer -> (Integer -> Integer -> Integer) -> ()
d_LeftZero_80 :: Integer -> (Integer -> Integer -> Integer) -> ()
d_LeftZero_80 = Integer -> (Integer -> Integer -> Integer) -> ()
forall a. a
erased
-- Data.Nat.Properties._.RightIdentity
d_RightIdentity_100 ::
  Integer -> (Integer -> Integer -> Integer) -> ()
d_RightIdentity_100 :: Integer -> (Integer -> Integer -> Integer) -> ()
d_RightIdentity_100 = Integer -> (Integer -> Integer -> Integer) -> ()
forall a. a
erased
-- Data.Nat.Properties._.RightZero
d_RightZero_108 :: Integer -> (Integer -> Integer -> Integer) -> ()
d_RightZero_108 :: Integer -> (Integer -> Integer -> Integer) -> ()
d_RightZero_108 = Integer -> (Integer -> Integer -> Integer) -> ()
forall a. a
erased
-- Data.Nat.Properties._.Zero
d_Zero_128 :: Integer -> (Integer -> Integer -> Integer) -> ()
d_Zero_128 :: Integer -> (Integer -> Integer -> Integer) -> ()
d_Zero_128 = Integer -> (Integer -> Integer -> Integer) -> ()
forall a. a
erased
-- Data.Nat.Properties._.IsCommutativeMonoid
d_IsCommutativeMonoid_144 :: p -> p -> ()
d_IsCommutativeMonoid_144 p
a0 p
a1 = ()
-- Data.Nat.Properties._.IsCommutativeSemigroup
d_IsCommutativeSemigroup_148 :: p -> ()
d_IsCommutativeSemigroup_148 p
a0 = ()
-- Data.Nat.Properties._.IsCommutativeSemiring
d_IsCommutativeSemiring_150 :: p -> p -> p -> p -> ()
d_IsCommutativeSemiring_150 p
a0 p
a1 p
a2 p
a3 = ()
-- Data.Nat.Properties._.IsCommutativeSemiringWithoutOne
d_IsCommutativeSemiringWithoutOne_152 :: p -> p -> p -> ()
d_IsCommutativeSemiringWithoutOne_152 p
a0 p
a1 p
a2 = ()
-- Data.Nat.Properties._.IsMagma
d_IsMagma_176 :: p -> ()
d_IsMagma_176 p
a0 = ()
-- Data.Nat.Properties._.IsMonoid
d_IsMonoid_182 :: p -> p -> ()
d_IsMonoid_182 p
a0 p
a1 = ()
-- Data.Nat.Properties._.IsSemigroup
d_IsSemigroup_204 :: p -> ()
d_IsSemigroup_204 p
a0 = ()
-- Data.Nat.Properties._.IsSemiring
d_IsSemiring_208 :: p -> p -> p -> p -> ()
d_IsSemiring_208 p
a0 p
a1 p
a2 p
a3 = ()
-- Data.Nat.Properties._.IsSemiringWithoutOne
d_IsSemiringWithoutOne_212 :: p -> p -> p -> ()
d_IsSemiringWithoutOne_212 p
a0 p
a1 p
a2 = ()
-- Data.Nat.Properties._.IsCommutativeMonoid.comm
d_comm_514 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMonoid_736 ->
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_comm_514 :: T_IsCommutativeMonoid_736 -> Integer -> Integer -> T__'8801'__12
d_comm_514 = T_IsCommutativeMonoid_736 -> Integer -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Nat.Properties._.IsCommutativeMonoid.isMonoid
d_isMonoid_530 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMonoid_736 ->
  MAlonzo.Code.Algebra.Structures.T_IsMonoid_686
d_isMonoid_530 :: T_IsCommutativeMonoid_736 -> T_IsMonoid_686
d_isMonoid_530 T_IsCommutativeMonoid_736
v0
  = (T_IsCommutativeMonoid_736 -> T_IsMonoid_686)
-> Any -> T_IsMonoid_686
forall a b. a -> b
coe T_IsCommutativeMonoid_736 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.d_isMonoid_746 (T_IsCommutativeMonoid_736 -> Any
forall a b. a -> b
coe T_IsCommutativeMonoid_736
v0)
-- Data.Nat.Properties._.IsCommutativeSemigroup.comm
d_comm_682 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_548 ->
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_comm_682 :: T_IsCommutativeSemigroup_548 -> Integer -> Integer -> T__'8801'__12
d_comm_682 = T_IsCommutativeSemigroup_548 -> Integer -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Nat.Properties._.IsCommutativeSemigroup.isSemigroup
d_isSemigroup_692 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_548 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_472
d_isSemigroup_692 :: T_IsCommutativeSemigroup_548 -> T_IsSemigroup_472
d_isSemigroup_692 T_IsCommutativeSemigroup_548
v0
  = (T_IsCommutativeSemigroup_548 -> T_IsSemigroup_472)
-> Any -> T_IsSemigroup_472
forall a b. a -> b
coe T_IsCommutativeSemigroup_548 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_556 (T_IsCommutativeSemigroup_548 -> Any
forall a b. a -> b
coe T_IsCommutativeSemigroup_548
v0)
-- Data.Nat.Properties._.IsCommutativeSemiring.*-comm
d_'42''45'comm_714 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiring_1678 ->
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'42''45'comm_714 :: T_IsCommutativeSemiring_1678 -> Integer -> Integer -> T__'8801'__12
d_'42''45'comm_714 = T_IsCommutativeSemiring_1678 -> Integer -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Nat.Properties._.IsCommutativeSemiring.isSemiring
d_isSemiring_784 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiring_1678 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemiring_1570
d_isSemiring_784 :: T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570
d_isSemiring_784 T_IsCommutativeSemiring_1678
v0
  = (T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570)
-> Any -> T_IsSemiring_1570
forall a b. a -> b
coe T_IsCommutativeSemiring_1678 -> T_IsSemiring_1570
MAlonzo.Code.Algebra.Structures.d_isSemiring_1692 (T_IsCommutativeSemiring_1678 -> Any
forall a b. a -> b
coe T_IsCommutativeSemiring_1678
v0)
-- Data.Nat.Properties._.IsCommutativeSemiringWithoutOne.*-comm
d_'42''45'comm_814 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiringWithoutOne_1382 ->
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'42''45'comm_814 :: T_IsCommutativeSemiringWithoutOne_1382
-> Integer -> Integer -> T__'8801'__12
d_'42''45'comm_814 = T_IsCommutativeSemiringWithoutOne_1382
-> Integer -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Nat.Properties._.IsCommutativeSemiringWithoutOne.isSemiringWithoutOne
d_isSemiringWithoutOne_850 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiringWithoutOne_1382 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutOne_1298
d_isSemiringWithoutOne_850 :: T_IsCommutativeSemiringWithoutOne_1382
-> T_IsSemiringWithoutOne_1298
d_isSemiringWithoutOne_850 T_IsCommutativeSemiringWithoutOne_1382
v0
  = (T_IsCommutativeSemiringWithoutOne_1382
 -> T_IsSemiringWithoutOne_1298)
-> Any -> T_IsSemiringWithoutOne_1298
forall a b. a -> b
coe
      T_IsCommutativeSemiringWithoutOne_1382
-> T_IsSemiringWithoutOne_1298
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutOne_1394
      (T_IsCommutativeSemiringWithoutOne_1382 -> Any
forall a b. a -> b
coe T_IsCommutativeSemiringWithoutOne_1382
v0)
-- Data.Nat.Properties._.IsMagma.isEquivalence
d_isEquivalence_1476 ::
  MAlonzo.Code.Algebra.Structures.T_IsMagma_176 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_1476 :: T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_1476 T_IsMagma_176
v0
  = (T_IsMagma_176 -> T_IsEquivalence_26) -> Any -> T_IsEquivalence_26
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184 (T_IsMagma_176 -> Any
forall a b. a -> b
coe T_IsMagma_176
v0)
-- Data.Nat.Properties._.IsMagma.∙-cong
d_'8729''45'cong_1490 ::
  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_1490 :: T_IsMagma_176
-> Integer
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
d_'8729''45'cong_1490 = T_IsMagma_176
-> Integer
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Nat.Properties._.IsMonoid.identity
d_identity_1586 ::
  MAlonzo.Code.Algebra.Structures.T_IsMonoid_686 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_identity_1586 :: T_IsMonoid_686 -> T_Σ_14
d_identity_1586 T_IsMonoid_686
v0
  = (T_IsMonoid_686 -> T_Σ_14) -> Any -> T_Σ_14
forall a b. a -> b
coe T_IsMonoid_686 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_identity_698 (T_IsMonoid_686 -> Any
forall a b. a -> b
coe T_IsMonoid_686
v0)
-- Data.Nat.Properties._.IsMonoid.isSemigroup
d_isSemigroup_1598 ::
  MAlonzo.Code.Algebra.Structures.T_IsMonoid_686 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_472
d_isSemigroup_1598 :: T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_1598 T_IsMonoid_686
v0
  = (T_IsMonoid_686 -> T_IsSemigroup_472) -> Any -> T_IsSemigroup_472
forall a b. a -> b
coe T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (T_IsMonoid_686 -> Any
forall a b. a -> b
coe T_IsMonoid_686
v0)
-- Data.Nat.Properties._.IsSemigroup.assoc
d_assoc_2330 ::
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_472 ->
  Integer ->
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_assoc_2330 :: T_IsSemigroup_472 -> Integer -> Integer -> Integer -> T__'8801'__12
d_assoc_2330 = T_IsSemigroup_472 -> Integer -> Integer -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Nat.Properties._.IsSemigroup.isMagma
d_isMagma_2334 ::
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_472 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_176
d_isMagma_2334 :: T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_2334 T_IsSemigroup_472
v0
  = (T_IsSemigroup_472 -> T_IsMagma_176) -> Any -> T_IsMagma_176
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (T_IsSemigroup_472 -> Any
forall a b. a -> b
coe T_IsSemigroup_472
v0)
-- Data.Nat.Properties._.IsSemiring.isSemiringWithoutAnnihilatingZero
d_isSemiringWithoutAnnihilatingZero_2448 ::
  MAlonzo.Code.Algebra.Structures.T_IsSemiring_1570 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_2448 :: T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
d_isSemiringWithoutAnnihilatingZero_2448 T_IsSemiring_1570
v0
  = (T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> Any -> T_IsSemiringWithoutAnnihilatingZero_1468
forall a b. a -> b
coe
      T_IsSemiring_1570 -> T_IsSemiringWithoutAnnihilatingZero_1468
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1584
      (T_IsSemiring_1570 -> Any
forall a b. a -> b
coe T_IsSemiring_1570
v0)
-- Data.Nat.Properties._.IsSemiring.zero
d_zero_2462 ::
  MAlonzo.Code.Algebra.Structures.T_IsSemiring_1570 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_zero_2462 :: T_IsSemiring_1570 -> T_Σ_14
d_zero_2462 T_IsSemiring_1570
v0
  = (T_IsSemiring_1570 -> T_Σ_14) -> Any -> T_Σ_14
forall a b. a -> b
coe T_IsSemiring_1570 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_zero_1586 (T_IsSemiring_1570 -> Any
forall a b. a -> b
coe T_IsSemiring_1570
v0)
-- Data.Nat.Properties._.IsSemiringWithoutOne.*-assoc
d_'42''45'assoc_2546 ::
  MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutOne_1298 ->
  Integer ->
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'42''45'assoc_2546 :: T_IsSemiringWithoutOne_1298
-> Integer -> Integer -> Integer -> T__'8801'__12
d_'42''45'assoc_2546 = T_IsSemiringWithoutOne_1298
-> Integer -> Integer -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Nat.Properties._.IsSemiringWithoutOne.*-cong
d_'42''45'cong_2548 ::
  MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutOne_1298 ->
  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_2548 :: T_IsSemiringWithoutOne_1298
-> Integer
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
d_'42''45'cong_2548 = T_IsSemiringWithoutOne_1298
-> Integer
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Nat.Properties._.IsSemiringWithoutOne.+-isCommutativeMonoid
d_'43''45'isCommutativeMonoid_2562 ::
  MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutOne_1298 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_2562 :: T_IsSemiringWithoutOne_1298 -> T_IsCommutativeMonoid_736
d_'43''45'isCommutativeMonoid_2562 T_IsSemiringWithoutOne_1298
v0
  = (T_IsSemiringWithoutOne_1298 -> T_IsCommutativeMonoid_736)
-> Any -> T_IsCommutativeMonoid_736
forall a b. a -> b
coe
      T_IsSemiringWithoutOne_1298 -> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.d_'43''45'isCommutativeMonoid_1316
      (T_IsSemiringWithoutOne_1298 -> Any
forall a b. a -> b
coe T_IsSemiringWithoutOne_1298
v0)
-- Data.Nat.Properties._.IsSemiringWithoutOne.distrib
d_distrib_2570 ::
  MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutOne_1298 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_distrib_2570 :: T_IsSemiringWithoutOne_1298 -> T_Σ_14
d_distrib_2570 T_IsSemiringWithoutOne_1298
v0
  = (T_IsSemiringWithoutOne_1298 -> T_Σ_14) -> Any -> T_Σ_14
forall a b. a -> b
coe T_IsSemiringWithoutOne_1298 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_distrib_1322 (T_IsSemiringWithoutOne_1298 -> Any
forall a b. a -> b
coe T_IsSemiringWithoutOne_1298
v0)
-- Data.Nat.Properties._.IsSemiringWithoutOne.zero
d_zero_2590 ::
  MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutOne_1298 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_zero_2590 :: T_IsSemiringWithoutOne_1298 -> T_Σ_14
d_zero_2590 T_IsSemiringWithoutOne_1298
v0
  = (T_IsSemiringWithoutOne_1298 -> T_Σ_14) -> Any -> T_Σ_14
forall a b. a -> b
coe T_IsSemiringWithoutOne_1298 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_zero_1324 (T_IsSemiringWithoutOne_1298 -> Any
forall a b. a -> b
coe T_IsSemiringWithoutOne_1298
v0)
-- Data.Nat.Properties.nonZero?
d_nonZero'63'_2652 ::
  Integer -> MAlonzo.Code.Relation.Nullary.Decidable.Core.T_Dec_20
d_nonZero'63'_2652 :: Integer -> T_Dec_20
d_nonZero'63'_2652 Integer
v0
  = case Integer -> Integer
forall a b. a -> b
coe Integer
v0 of
      Integer
0 -> (Bool -> T_Reflects_16 -> T_Dec_20) -> Any -> Any -> T_Dec_20
forall a b. a -> b
coe
             Bool -> T_Reflects_16 -> T_Dec_20
MAlonzo.Code.Relation.Nullary.Decidable.Core.C__because__32
             (Bool -> Any
forall a b. a -> b
coe Bool
MAlonzo.Code.Agda.Builtin.Bool.C_false_8)
             (T_Reflects_16 -> Any
forall a b. a -> b
coe T_Reflects_16
MAlonzo.Code.Relation.Nullary.Reflects.C_of'8319'_26)
      Integer
_ -> (Bool -> T_Reflects_16 -> T_Dec_20) -> Any -> Any -> T_Dec_20
forall a b. a -> b
coe
             Bool -> T_Reflects_16 -> T_Dec_20
MAlonzo.Code.Relation.Nullary.Decidable.Core.C__because__32
             (Bool -> Any
forall a b. a -> b
coe Bool
MAlonzo.Code.Agda.Builtin.Bool.C_true_10)
             ((Any -> T_Reflects_16) -> Any -> Any
forall a b. a -> b
coe
                Any -> T_Reflects_16
MAlonzo.Code.Relation.Nullary.Reflects.C_of'696'_22
                ((Any -> T_NonZero_112) -> Any -> Any
forall a b. a -> b
coe
                   Any -> T_NonZero_112
MAlonzo.Code.Data.Nat.Base.C_NonZero'46'constructor_3575
                   (() -> Any
forall a b. a -> b
coe ()
MAlonzo.Code.Agda.Builtin.Unit.C_tt_8)))
-- Data.Nat.Properties.nonTrivial?
d_nonTrivial'63'_2656 ::
  Integer -> MAlonzo.Code.Relation.Nullary.Decidable.Core.T_Dec_20
d_nonTrivial'63'_2656 :: Integer -> T_Dec_20
d_nonTrivial'63'_2656 Integer
v0
  = case Integer -> Integer
forall a b. a -> b
coe Integer
v0 of
      Integer
0 -> (Bool -> T_Reflects_16 -> T_Dec_20) -> Any -> Any -> T_Dec_20
forall a b. a -> b
coe
             Bool -> T_Reflects_16 -> T_Dec_20
MAlonzo.Code.Relation.Nullary.Decidable.Core.C__because__32
             (Bool -> Any
forall a b. a -> b
coe Bool
MAlonzo.Code.Agda.Builtin.Bool.C_false_8)
             (T_Reflects_16 -> Any
forall a b. a -> b
coe T_Reflects_16
MAlonzo.Code.Relation.Nullary.Reflects.C_of'8319'_26)
      Integer
1 -> (Bool -> T_Reflects_16 -> T_Dec_20) -> Any -> Any -> T_Dec_20
forall a b. a -> b
coe
             Bool -> T_Reflects_16 -> T_Dec_20
MAlonzo.Code.Relation.Nullary.Decidable.Core.C__because__32
             (Bool -> Any
forall a b. a -> b
coe Bool
MAlonzo.Code.Agda.Builtin.Bool.C_false_8)
             (T_Reflects_16 -> Any
forall a b. a -> b
coe T_Reflects_16
MAlonzo.Code.Relation.Nullary.Reflects.C_of'8319'_26)
      Integer
_ -> (Bool -> T_Reflects_16 -> T_Dec_20) -> Any -> Any -> T_Dec_20
forall a b. a -> b
coe
             Bool -> T_Reflects_16 -> T_Dec_20
MAlonzo.Code.Relation.Nullary.Decidable.Core.C__because__32
             (Bool -> Any
forall a b. a -> b
coe Bool
MAlonzo.Code.Agda.Builtin.Bool.C_true_10)
             ((Any -> T_Reflects_16) -> Any -> Any
forall a b. a -> b
coe
                Any -> T_Reflects_16
MAlonzo.Code.Relation.Nullary.Reflects.C_of'696'_22
                ((Any -> T_NonTrivial_152) -> Any -> Any
forall a b. a -> b
coe
                   Any -> T_NonTrivial_152
MAlonzo.Code.Data.Nat.Base.C_NonTrivial'46'constructor_5661
                   (() -> Any
forall a b. a -> b
coe ()
MAlonzo.Code.Agda.Builtin.Unit.C_tt_8)))
-- Data.Nat.Properties.suc-injective
d_suc'45'injective_2660 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_suc'45'injective_2660 :: Integer -> Integer -> T__'8801'__12 -> T__'8801'__12
d_suc'45'injective_2660 = Integer -> Integer -> T__'8801'__12 -> T__'8801'__12
forall a. a
erased
-- Data.Nat.Properties.≡ᵇ⇒≡
d_'8801''7495''8658''8801'_2666 ::
  Integer ->
  Integer ->
  AgdaAny -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8801''7495''8658''8801'_2666 :: Integer -> Integer -> Any -> T__'8801'__12
d_'8801''7495''8658''8801'_2666 = Integer -> Integer -> Any -> T__'8801'__12
forall a. a
erased
-- Data.Nat.Properties.≡⇒≡ᵇ
d_'8801''8658''8801''7495'_2678 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_'8801''8658''8801''7495'_2678 :: Integer -> Integer -> T__'8801'__12 -> Any
d_'8801''8658''8801''7495'_2678 Integer
v0 ~Integer
v1 ~T__'8801'__12
v2
  = Integer -> Any
du_'8801''8658''8801''7495'_2678 Integer
v0
du_'8801''8658''8801''7495'_2678 :: Integer -> AgdaAny
du_'8801''8658''8801''7495'_2678 :: Integer -> Any
du_'8801''8658''8801''7495'_2678 Integer
v0
  = case Integer -> Integer
forall a b. a -> b
coe Integer
v0 of
      Integer
0 -> () -> Any
forall a b. a -> b
coe ()
MAlonzo.Code.Agda.Builtin.Unit.C_tt_8
      Integer
_ -> let v1 :: Integer
v1 = Integer -> Integer -> Integer
subInt (Integer -> Integer
forall a b. a -> b
coe Integer
v0) (Integer -> Integer
forall a b. a -> b
coe (Integer
1 :: Integer)) in
           Any -> Any
forall a b. a -> b
coe ((Integer -> Any) -> Any -> Any
forall a b. a -> b
coe Integer -> Any
du_'8801''8658''8801''7495'_2678 (Integer -> Any
forall a b. a -> b
coe Integer
v1))
-- Data.Nat.Properties._≟_
d__'8799'__2688 ::
  Integer ->
  Integer -> MAlonzo.Code.Relation.Nullary.Decidable.Core.T_Dec_20
d__'8799'__2688 :: Integer -> Integer -> T_Dec_20
d__'8799'__2688 Integer
v0 Integer
v1
  = ((Any -> Any) -> (Any -> Any) -> T_Dec_20 -> T_Dec_20)
-> Any -> (Any -> Any) -> Any -> T_Dec_20
forall a b. a -> b
coe
      (Any -> Any) -> (Any -> Any) -> T_Dec_20 -> T_Dec_20
MAlonzo.Code.Relation.Nullary.Decidable.Core.du_map'8242'_168
      Any
forall a. a
erased (\ Any
v2 -> (Integer -> Any) -> Any -> Any
forall a b. a -> b
coe Integer -> Any
du_'8801''8658''8801''7495'_2678 (Integer -> Any
forall a b. a -> b
coe Integer
v0))
      ((Bool -> T_Dec_20) -> Any -> Any
forall a b. a -> b
coe
         Bool -> T_Dec_20
MAlonzo.Code.Relation.Nullary.Decidable.Core.d_T'63'_66
         ((Integer -> Integer -> Bool) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> Bool
eqInt (Integer -> Any
forall a b. a -> b
coe Integer
v0) (Integer -> Any
forall a b. a -> b
coe Integer
v1)))
-- Data.Nat.Properties.≡-irrelevant
d_'8801''45'irrelevant_2694 ::
  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_'8801''45'irrelevant_2694 :: Integer
-> Integer -> T__'8801'__12 -> T__'8801'__12 -> T__'8801'__12
d_'8801''45'irrelevant_2694 = Integer
-> Integer -> T__'8801'__12 -> T__'8801'__12 -> T__'8801'__12
forall a. a
erased
-- Data.Nat.Properties.≟-diag
d_'8799''45'diag_2698 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8799''45'diag_2698 :: Integer -> Integer -> T__'8801'__12 -> T__'8801'__12
d_'8799''45'diag_2698 = Integer -> Integer -> T__'8801'__12 -> T__'8801'__12
forall a. a
erased
-- Data.Nat.Properties.≡-isDecEquivalence
d_'8801''45'isDecEquivalence_2700 ::
  MAlonzo.Code.Relation.Binary.Structures.T_IsDecEquivalence_44
d_'8801''45'isDecEquivalence_2700 :: T_IsDecEquivalence_44
d_'8801''45'isDecEquivalence_2700
  = (T_IsEquivalence_26
 -> (Any -> Any -> T_Dec_20) -> T_IsDecEquivalence_44)
-> Any -> Any -> T_IsDecEquivalence_44
forall a b. a -> b
coe
      T_IsEquivalence_26
-> (Any -> Any -> T_Dec_20) -> T_IsDecEquivalence_44
MAlonzo.Code.Relation.Binary.Structures.C_IsDecEquivalence'46'constructor_3083
      (T_IsEquivalence_26 -> Any
forall a b. a -> b
coe
         T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.PropositionalEquality.Properties.du_isEquivalence_396)
      ((Integer -> Integer -> T_Dec_20) -> Any
forall a b. a -> b
coe Integer -> Integer -> T_Dec_20
d__'8799'__2688)
-- Data.Nat.Properties.≡-decSetoid
d_'8801''45'decSetoid_2702 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_DecSetoid_84
d_'8801''45'decSetoid_2702 :: T_DecSetoid_84
d_'8801''45'decSetoid_2702
  = (T_IsDecEquivalence_44 -> T_DecSetoid_84)
-> T_IsDecEquivalence_44 -> T_DecSetoid_84
forall a b. a -> b
coe
      T_IsDecEquivalence_44 -> T_DecSetoid_84
MAlonzo.Code.Relation.Binary.Bundles.C_DecSetoid'46'constructor_1389
      T_IsDecEquivalence_44
d_'8801''45'isDecEquivalence_2700
-- Data.Nat.Properties.0≢1+n
d_0'8802'1'43'n_2704 ::
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Data.Irrelevant.T_Irrelevant_20
d_0'8802'1'43'n_2704 :: Integer -> T__'8801'__12 -> T_Irrelevant_20
d_0'8802'1'43'n_2704 = Integer -> T__'8801'__12 -> T_Irrelevant_20
forall a. a
erased
-- Data.Nat.Properties.1+n≢0
d_1'43'n'8802'0_2706 ::
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Data.Irrelevant.T_Irrelevant_20
d_1'43'n'8802'0_2706 :: Integer -> T__'8801'__12 -> T_Irrelevant_20
d_1'43'n'8802'0_2706 = Integer -> T__'8801'__12 -> T_Irrelevant_20
forall a. a
erased
-- Data.Nat.Properties.1+n≢n
d_1'43'n'8802'n_2708 ::
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Data.Irrelevant.T_Irrelevant_20
d_1'43'n'8802'n_2708 :: Integer -> T__'8801'__12 -> T_Irrelevant_20
d_1'43'n'8802'n_2708 = Integer -> T__'8801'__12 -> T_Irrelevant_20
forall a. a
erased
-- Data.Nat.Properties.<ᵇ⇒<
d_'60''7495''8658''60'_2716 ::
  Integer ->
  Integer -> AgdaAny -> MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_'60''7495''8658''60'_2716 :: Integer -> Integer -> Any -> T__'8804'__22
d_'60''7495''8658''60'_2716 Integer
v0 ~Integer
v1 ~Any
v2
  = Integer -> T__'8804'__22
du_'60''7495''8658''60'_2716 Integer
v0
du_'60''7495''8658''60'_2716 ::
  Integer -> MAlonzo.Code.Data.Nat.Base.T__'8804'__22
du_'60''7495''8658''60'_2716 :: Integer -> T__'8804'__22
du_'60''7495''8658''60'_2716 Integer
v0
  = case Integer -> Integer
forall a b. a -> b
coe Integer
v0 of
      Integer
0 -> (T__'8804'__22 -> T__'8804'__22) -> Any -> T__'8804'__22
forall a b. a -> b
coe
             T__'8804'__22 -> T__'8804'__22
MAlonzo.Code.Data.Nat.Base.C_s'8804's_34
             (T__'8804'__22 -> Any
forall a b. a -> b
coe T__'8804'__22
MAlonzo.Code.Data.Nat.Base.C_z'8804'n_26)
      Integer
_ -> let v1 :: Integer
v1 = Integer -> Integer -> Integer
subInt (Integer -> Integer
forall a b. a -> b
coe Integer
v0) (Integer -> Integer
forall a b. a -> b
coe (Integer
1 :: Integer)) in
           Any -> T__'8804'__22
forall a b. a -> b
coe
             ((T__'8804'__22 -> T__'8804'__22) -> Any -> Any
forall a b. a -> b
coe
                T__'8804'__22 -> T__'8804'__22
MAlonzo.Code.Data.Nat.Base.C_s'8804's_34
                ((Integer -> T__'8804'__22) -> Any -> Any
forall a b. a -> b
coe Integer -> T__'8804'__22
du_'60''7495''8658''60'_2716 (Integer -> Any
forall a b. a -> b
coe Integer
v1)))
-- Data.Nat.Properties.<⇒<ᵇ
d_'60''8658''60''7495'_2728 ::
  Integer ->
  Integer -> MAlonzo.Code.Data.Nat.Base.T__'8804'__22 -> AgdaAny
d_'60''8658''60''7495'_2728 :: Integer -> Integer -> T__'8804'__22 -> Any
d_'60''8658''60''7495'_2728 ~Integer
v0 ~Integer
v1 T__'8804'__22
v2
  = T__'8804'__22 -> Any
du_'60''8658''60''7495'_2728 T__'8804'__22
v2
du_'60''8658''60''7495'_2728 ::
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 -> AgdaAny
du_'60''8658''60''7495'_2728 :: T__'8804'__22 -> Any
du_'60''8658''60''7495'_2728 T__'8804'__22
v0
  = case T__'8804'__22 -> T__'8804'__22
forall a b. a -> b
coe T__'8804'__22
v0 of
      MAlonzo.Code.Data.Nat.Base.C_s'8804's_34 T__'8804'__22
v3
        -> case T__'8804'__22 -> T__'8804'__22
forall a b. a -> b
coe T__'8804'__22
v3 of
             T__'8804'__22
MAlonzo.Code.Data.Nat.Base.C_z'8804'n_26
               -> () -> Any
forall a b. a -> b
coe ()
MAlonzo.Code.Agda.Builtin.Unit.C_tt_8
             MAlonzo.Code.Data.Nat.Base.C_s'8804's_34 T__'8804'__22
v6
               -> (T__'8804'__22 -> Any) -> Any -> Any
forall a b. a -> b
coe
                    T__'8804'__22 -> Any
du_'60''8658''60''7495'_2728
                    ((T__'8804'__22 -> T__'8804'__22) -> T__'8804'__22 -> Any
forall a b. a -> b
coe T__'8804'__22 -> T__'8804'__22
MAlonzo.Code.Data.Nat.Base.C_s'8804's_34 T__'8804'__22
v6)
             T__'8804'__22
_ -> Any
forall a. a
MAlonzo.RTE.mazUnreachableError
      T__'8804'__22
_ -> Any
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Data.Nat.Properties.<ᵇ-reflects-<
d_'60''7495''45'reflects'45''60'_2736 ::
  Integer ->
  Integer -> MAlonzo.Code.Relation.Nullary.Reflects.T_Reflects_16
d_'60''7495''45'reflects'45''60'_2736 :: Integer -> Integer -> T_Reflects_16
d_'60''7495''45'reflects'45''60'_2736 Integer
v0 Integer
v1
  = (Bool -> (Any -> Any) -> (Any -> Any) -> T_Reflects_16)
-> Any -> (Any -> Any) -> Any -> T_Reflects_16
forall a b. a -> b
coe
      Bool -> (Any -> Any) -> (Any -> Any) -> T_Reflects_16
MAlonzo.Code.Relation.Nullary.Reflects.du_fromEquivalence_132
      ((Integer -> Integer -> Bool) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> Bool
ltInt (Integer -> Any
forall a b. a -> b
coe Integer
v0) (Integer -> Any
forall a b. a -> b
coe Integer
v1))
      (\ Any
v2 -> (Integer -> T__'8804'__22) -> Any -> Any
forall a b. a -> b
coe Integer -> T__'8804'__22
du_'60''7495''8658''60'_2716 (Integer -> Any
forall a b. a -> b
coe Integer
v0))
      ((T__'8804'__22 -> Any) -> Any
forall a b. a -> b
coe T__'8804'__22 -> Any
du_'60''8658''60''7495'_2728)
-- Data.Nat.Properties.≤ᵇ⇒≤
d_'8804''7495''8658''8804'_2746 ::
  Integer ->
  Integer -> AgdaAny -> MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_'8804''7495''8658''8804'_2746 :: Integer -> Integer -> Any -> T__'8804'__22
d_'8804''7495''8658''8804'_2746 Integer
v0 ~Integer
v1 ~Any
v2
  = Integer -> T__'8804'__22
du_'8804''7495''8658''8804'_2746 Integer
v0
du_'8804''7495''8658''8804'_2746 ::
  Integer -> MAlonzo.Code.Data.Nat.Base.T__'8804'__22
du_'8804''7495''8658''8804'_2746 :: Integer -> T__'8804'__22
du_'8804''7495''8658''8804'_2746 Integer
v0
  = case Integer -> Integer
forall a b. a -> b
coe Integer
v0 of
      Integer
0 -> T__'8804'__22 -> T__'8804'__22
forall a b. a -> b
coe T__'8804'__22
MAlonzo.Code.Data.Nat.Base.C_z'8804'n_26
      Integer
_ -> let v1 :: Integer
v1 = Integer -> Integer -> Integer
subInt (Integer -> Integer
forall a b. a -> b
coe Integer
v0) (Integer -> Integer
forall a b. a -> b
coe (Integer
1 :: Integer)) in
           Any -> T__'8804'__22
forall a b. a -> b
coe ((Integer -> T__'8804'__22) -> Any -> Any
forall a b. a -> b
coe Integer -> T__'8804'__22
du_'60''7495''8658''60'_2716 (Integer -> Any
forall a b. a -> b
coe Integer
v1))
-- Data.Nat.Properties.≤⇒≤ᵇ
d_'8804''8658''8804''7495'_2758 ::
  Integer ->
  Integer -> MAlonzo.Code.Data.Nat.Base.T__'8804'__22 -> AgdaAny
d_'8804''8658''8804''7495'_2758 :: Integer -> Integer -> T__'8804'__22 -> Any
d_'8804''8658''8804''7495'_2758 ~Integer
v0 ~Integer
v1 T__'8804'__22
v2
  = T__'8804'__22 -> Any
du_'8804''8658''8804''7495'_2758 T__'8804'__22
v2
du_'8804''8658''8804''7495'_2758 ::
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 -> AgdaAny
du_'8804''8658''8804''7495'_2758 :: T__'8804'__22 -> Any
du_'8804''8658''8804''7495'_2758 T__'8804'__22
v0
  = case T__'8804'__22 -> T__'8804'__22
forall a b. a -> b
coe T__'8804'__22
v0 of
      T__'8804'__22
MAlonzo.Code.Data.Nat.Base.C_z'8804'n_26
        -> () -> Any
forall a b. a -> b
coe ()
MAlonzo.Code.Agda.Builtin.Unit.C_tt_8
      MAlonzo.Code.Data.Nat.Base.C_s'8804's_34 T__'8804'__22
v3
        -> (T__'8804'__22 -> Any) -> Any -> Any
forall a b. a -> b
coe
             T__'8804'__22 -> Any
du_'60''8658''60''7495'_2728
             ((T__'8804'__22 -> T__'8804'__22) -> T__'8804'__22 -> Any
forall a b. a -> b
coe T__'8804'__22 -> T__'8804'__22
MAlonzo.Code.Data.Nat.Base.C_s'8804's_34 T__'8804'__22
v3)
      T__'8804'__22
_ -> Any
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Data.Nat.Properties.≤ᵇ-reflects-≤
d_'8804''7495''45'reflects'45''8804'_2766 ::
  Integer ->
  Integer -> MAlonzo.Code.Relation.Nullary.Reflects.T_Reflects_16
d_'8804''7495''45'reflects'45''8804'_2766 :: Integer -> Integer -> T_Reflects_16
d_'8804''7495''45'reflects'45''8804'_2766 Integer
v0 Integer
v1
  = (Bool -> (Any -> Any) -> (Any -> Any) -> T_Reflects_16)
-> Any -> (Any -> Any) -> Any -> T_Reflects_16
forall a b. a -> b
coe
      Bool -> (Any -> Any) -> (Any -> Any) -> T_Reflects_16
MAlonzo.Code.Relation.Nullary.Reflects.du_fromEquivalence_132
      ((Integer -> Integer -> Bool) -> Any -> Any -> Any
forall a b. a -> b
coe
         Integer -> Integer -> Bool
MAlonzo.Code.Data.Nat.Base.d__'8804''7495'__14 (Integer -> Any
forall a b. a -> b
coe Integer
v0) (Integer -> Any
forall a b. a -> b
coe Integer
v1))
      (\ Any
v2 -> (Integer -> T__'8804'__22) -> Any -> Any
forall a b. a -> b
coe Integer -> T__'8804'__22
du_'8804''7495''8658''8804'_2746 (Integer -> Any
forall a b. a -> b
coe Integer
v0))
      ((T__'8804'__22 -> Any) -> Any
forall a b. a -> b
coe T__'8804'__22 -> Any
du_'8804''8658''8804''7495'_2758)
-- Data.Nat.Properties.≤-reflexive
d_'8804''45'reflexive_2772 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_'8804''45'reflexive_2772 :: Integer -> Integer -> T__'8801'__12 -> T__'8804'__22
d_'8804''45'reflexive_2772 Integer
v0 ~Integer
v1 ~T__'8801'__12
v2
  = Integer -> T__'8804'__22
du_'8804''45'reflexive_2772 Integer
v0
du_'8804''45'reflexive_2772 ::
  Integer -> MAlonzo.Code.Data.Nat.Base.T__'8804'__22
du_'8804''45'reflexive_2772 :: Integer -> T__'8804'__22
du_'8804''45'reflexive_2772 Integer
v0
  = case Integer -> Integer
forall a b. a -> b
coe Integer
v0 of
      Integer
0 -> T__'8804'__22 -> T__'8804'__22
forall a b. a -> b
coe T__'8804'__22
MAlonzo.Code.Data.Nat.Base.C_z'8804'n_26
      Integer
_ -> let v1 :: Integer
v1 = Integer -> Integer -> Integer
subInt (Integer -> Integer
forall a b. a -> b
coe Integer
v0) (Integer -> Integer
forall a b. a -> b
coe (Integer
1 :: Integer)) in
           Any -> T__'8804'__22
forall a b. a -> b
coe
             ((T__'8804'__22 -> T__'8804'__22) -> Any -> Any
forall a b. a -> b
coe
                T__'8804'__22 -> T__'8804'__22
MAlonzo.Code.Data.Nat.Base.C_s'8804's_34
                ((Integer -> T__'8804'__22) -> Any -> Any
forall a b. a -> b
coe Integer -> T__'8804'__22
du_'8804''45'reflexive_2772 (Integer -> Any
forall a b. a -> b
coe Integer
v1)))
-- Data.Nat.Properties.≤-refl
d_'8804''45'refl_2776 ::
  Integer -> MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_'8804''45'refl_2776 :: Integer -> T__'8804'__22
d_'8804''45'refl_2776 Integer
v0 = (Integer -> T__'8804'__22) -> Any -> T__'8804'__22
forall a b. a -> b
coe Integer -> T__'8804'__22
du_'8804''45'reflexive_2772 (Integer -> Any
forall a b. a -> b
coe Integer
v0)
-- Data.Nat.Properties.≤-antisym
d_'8804''45'antisym_2778 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8804''45'antisym_2778 :: Integer
-> Integer -> T__'8804'__22 -> T__'8804'__22 -> T__'8801'__12
d_'8804''45'antisym_2778 = Integer
-> Integer -> T__'8804'__22 -> T__'8804'__22 -> T__'8801'__12
forall a. a
erased
-- Data.Nat.Properties.≤-trans
d_'8804''45'trans_2784 ::
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_'8804''45'trans_2784 :: Integer
-> Integer
-> Integer
-> T__'8804'__22
-> T__'8804'__22
-> T__'8804'__22
d_'8804''45'trans_2784 ~Integer
v0 ~Integer
v1 ~Integer
v2 T__'8804'__22
v3 T__'8804'__22
v4
  = T__'8804'__22 -> T__'8804'__22 -> T__'8804'__22
du_'8804''45'trans_2784 T__'8804'__22
v3 T__'8804'__22
v4
du_'8804''45'trans_2784 ::
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
du_'8804''45'trans_2784 :: T__'8804'__22 -> T__'8804'__22 -> T__'8804'__22
du_'8804''45'trans_2784 T__'8804'__22
v0 T__'8804'__22
v1
  = case T__'8804'__22 -> T__'8804'__22
forall a b. a -> b
coe T__'8804'__22
v0 of
      T__'8804'__22
MAlonzo.Code.Data.Nat.Base.C_z'8804'n_26
        -> T__'8804'__22 -> T__'8804'__22
forall a b. a -> b
coe T__'8804'__22
MAlonzo.Code.Data.Nat.Base.C_z'8804'n_26
      MAlonzo.Code.Data.Nat.Base.C_s'8804's_34 T__'8804'__22
v4
        -> case T__'8804'__22 -> T__'8804'__22
forall a b. a -> b
coe T__'8804'__22
v1 of
             MAlonzo.Code.Data.Nat.Base.C_s'8804's_34 T__'8804'__22
v7
               -> (T__'8804'__22 -> T__'8804'__22) -> Any -> T__'8804'__22
forall a b. a -> b
coe
                    T__'8804'__22 -> T__'8804'__22
MAlonzo.Code.Data.Nat.Base.C_s'8804's_34
                    ((T__'8804'__22 -> T__'8804'__22 -> T__'8804'__22)
-> Any -> Any -> Any
forall a b. a -> b
coe T__'8804'__22 -> T__'8804'__22 -> T__'8804'__22
du_'8804''45'trans_2784 (T__'8804'__22 -> Any
forall a b. a -> b
coe T__'8804'__22
v4) (T__'8804'__22 -> Any
forall a b. a -> b
coe T__'8804'__22
v7))
             T__'8804'__22
_ -> T__'8804'__22
forall a. a
MAlonzo.RTE.mazUnreachableError
      T__'8804'__22
_ -> T__'8804'__22
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Data.Nat.Properties.≤-total
d_'8804''45'total_2790 ::
  Integer -> Integer -> MAlonzo.Code.Data.Sum.Base.T__'8846'__30
d_'8804''45'total_2790 :: Integer -> Integer -> T__'8846'__30
d_'8804''45'total_2790 Integer
v0 Integer
v1
  = case Integer -> Integer
forall a b. a -> b
coe Integer
v0 of
      Integer
0 -> (Any -> T__'8846'__30) -> Any -> T__'8846'__30
forall a b. a -> b
coe
             Any -> T__'8846'__30
MAlonzo.Code.Data.Sum.Base.C_inj'8321'_38
             (T__'8804'__22 -> Any
forall a b. a -> b
coe T__'8804'__22
MAlonzo.Code.Data.Nat.Base.C_z'8804'n_26)
      Integer
_ -> let v2 :: Integer
v2 = Integer -> Integer -> Integer
subInt (Integer -> Integer
forall a b. a -> b
coe Integer
v0) (Integer -> Integer
forall a b. a -> b
coe (Integer
1 :: Integer)) in
           Any -> T__'8846'__30
forall a b. a -> b
coe
             (case Integer -> Integer
forall a b. a -> b
coe Integer
v1 of
                Integer
0 -> (Any -> T__'8846'__30) -> Any -> Any
forall a b. a -> b
coe
                       Any -> T__'8846'__30
MAlonzo.Code.Data.Sum.Base.C_inj'8322'_42
                       (T__'8804'__22 -> Any
forall a b. a -> b
coe T__'8804'__22
MAlonzo.Code.Data.Nat.Base.C_z'8804'n_26)
                Integer
_ -> let v3 :: Integer
v3 = Integer -> Integer -> Integer
subInt (Integer -> Integer
forall a b. a -> b
coe Integer
v1) (Integer -> Integer
forall a b. a -> b
coe (Integer
1 :: Integer)) in
                     Any -> Any
forall a b. a -> b
coe
                       (((Any -> Any) -> (Any -> Any) -> T__'8846'__30 -> T__'8846'__30)
-> Any -> Any -> T__'8846'__30 -> Any
forall a b. a -> b
coe
                          (Any -> Any) -> (Any -> Any) -> T__'8846'__30 -> T__'8846'__30
MAlonzo.Code.Data.Sum.Base.du_map_84
                          ((T__'8804'__22 -> T__'8804'__22) -> Any
forall a b. a -> b
coe T__'8804'__22 -> T__'8804'__22
MAlonzo.Code.Data.Nat.Base.C_s'8804's_34)
                          ((T__'8804'__22 -> T__'8804'__22) -> Any
forall a b. a -> b
coe T__'8804'__22 -> T__'8804'__22
MAlonzo.Code.Data.Nat.Base.C_s'8804's_34)
                          (Integer -> Integer -> T__'8846'__30
d_'8804''45'total_2790 (Integer -> Integer
forall a b. a -> b
coe Integer
v2) (Integer -> Integer
forall a b. a -> b
coe Integer
v3))))
-- Data.Nat.Properties.≤-irrelevant
d_'8804''45'irrelevant_2796 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8804''45'irrelevant_2796 :: Integer
-> Integer -> T__'8804'__22 -> T__'8804'__22 -> T__'8801'__12
d_'8804''45'irrelevant_2796 = Integer
-> Integer -> T__'8804'__22 -> T__'8804'__22 -> T__'8801'__12
forall a. a
erased
-- Data.Nat.Properties._≤?_
d__'8804''63'__2802 ::
  Integer ->
  Integer -> MAlonzo.Code.Relation.Nullary.Decidable.Core.T_Dec_20
d__'8804''63'__2802 :: Integer -> Integer -> T_Dec_20
d__'8804''63'__2802 Integer
v0 Integer
v1
  = ((Any -> Any) -> (Any -> Any) -> T_Dec_20 -> T_Dec_20)
-> (Any -> Any) -> Any -> Any -> T_Dec_20
forall a b. a -> b
coe
      (Any -> Any) -> (Any -> Any) -> T_Dec_20 -> T_Dec_20
MAlonzo.Code.Relation.Nullary.Decidable.Core.du_map'8242'_168
      (\ Any
v2 -> (Integer -> T__'8804'__22) -> Any -> Any
forall a b. a -> b
coe Integer -> T__'8804'__22
du_'8804''7495''8658''8804'_2746 (Integer -> Any
forall a b. a -> b
coe Integer
v0))
      ((T__'8804'__22 -> Any) -> Any
forall a b. a -> b
coe T__'8804'__22 -> Any
du_'8804''8658''8804''7495'_2758)
      ((Bool -> T_Dec_20) -> Any -> Any
forall a b. a -> b
coe
         Bool -> T_Dec_20
MAlonzo.Code.Relation.Nullary.Decidable.Core.d_T'63'_66
         ((Integer -> Integer -> Bool) -> Any -> Any -> Any
forall a b. a -> b
coe
            Integer -> Integer -> Bool
MAlonzo.Code.Data.Nat.Base.d__'8804''7495'__14 (Integer -> Any
forall a b. a -> b
coe Integer
v0) (Integer -> Any
forall a b. a -> b
coe Integer
v1)))
-- Data.Nat.Properties._≥?_
d__'8805''63'__2808 ::
  Integer ->
  Integer -> MAlonzo.Code.Relation.Nullary.Decidable.Core.T_Dec_20
d__'8805''63'__2808 :: Integer -> Integer -> T_Dec_20
d__'8805''63'__2808 Integer
v0 Integer
v1
  = (Integer -> Integer -> T_Dec_20) -> Any -> Any -> T_Dec_20
forall a b. a -> b
coe Integer -> Integer -> T_Dec_20
d__'8804''63'__2802 (Integer -> Any
forall a b. a -> b
coe Integer
v1) (Integer -> Any
forall a b. a -> b
coe Integer
v0)
-- Data.Nat.Properties.≤-isPreorder
d_'8804''45'isPreorder_2810 ::
  MAlonzo.Code.Relation.Binary.Structures.T_IsPreorder_70
d_'8804''45'isPreorder_2810 :: T_IsPreorder_70
d_'8804''45'isPreorder_2810
  = (T_IsEquivalence_26
 -> (Any -> Any -> Any -> Any)
 -> (Any -> Any -> Any -> Any -> Any -> Any)
 -> T_IsPreorder_70)
-> Any
-> (Any -> Any -> Any -> Any)
-> (Any -> Any -> Any -> Any -> Any -> Any)
-> T_IsPreorder_70
forall a b. a -> b
coe
      T_IsEquivalence_26
-> (Any -> Any -> Any -> Any)
-> (Any -> Any -> Any -> Any -> Any -> Any)
-> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.C_IsPreorder'46'constructor_4003
      (T_IsEquivalence_26 -> Any
forall a b. a -> b
coe
         T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.PropositionalEquality.Properties.du_isEquivalence_396)
      (\ Any
v0 Any
v1 Any
v2 -> (Integer -> T__'8804'__22) -> Any -> Any
forall a b. a -> b
coe Integer -> T__'8804'__22
du_'8804''45'reflexive_2772 Any
v0)
      (\ Any
v0 Any
v1 Any
v2 Any
v3 Any
v4 -> (T__'8804'__22 -> T__'8804'__22 -> T__'8804'__22)
-> Any -> Any -> Any
forall a b. a -> b
coe T__'8804'__22 -> T__'8804'__22 -> T__'8804'__22
du_'8804''45'trans_2784 Any
v3 Any
v4)
-- Data.Nat.Properties.≤-isTotalPreorder
d_'8804''45'isTotalPreorder_2812 ::
  MAlonzo.Code.Relation.Binary.Structures.T_IsTotalPreorder_124
d_'8804''45'isTotalPreorder_2812 :: T_IsTotalPreorder_124
d_'8804''45'isTotalPreorder_2812
  = (T_IsPreorder_70
 -> (Any -> Any -> T__'8846'__30) -> T_IsTotalPreorder_124)
-> Any -> Any -> T_IsTotalPreorder_124
forall a b. a -> b
coe
      T_IsPreorder_70
-> (Any -> Any -> T__'8846'__30) -> T_IsTotalPreorder_124
MAlonzo.Code.Relation.Binary.Structures.C_IsTotalPreorder'46'constructor_8325
      (T_IsPreorder_70 -> Any
forall a b. a -> b
coe T_IsPreorder_70
d_'8804''45'isPreorder_2810) ((Integer -> Integer -> T__'8846'__30) -> Any
forall a b. a -> b
coe Integer -> Integer -> T__'8846'__30
d_'8804''45'total_2790)
-- Data.Nat.Properties.≤-isPartialOrder
d_'8804''45'isPartialOrder_2814 ::
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialOrder_174
d_'8804''45'isPartialOrder_2814 :: T_IsPartialOrder_174
d_'8804''45'isPartialOrder_2814
  = (T_IsPreorder_70
 -> (Any -> Any -> Any -> Any -> Any) -> T_IsPartialOrder_174)
-> Any -> Any -> T_IsPartialOrder_174
forall a b. a -> b
coe
      T_IsPreorder_70
-> (Any -> Any -> Any -> Any -> Any) -> T_IsPartialOrder_174
MAlonzo.Code.Relation.Binary.Structures.C_IsPartialOrder'46'constructor_9853
      (T_IsPreorder_70 -> Any
forall a b. a -> b
coe T_IsPreorder_70
d_'8804''45'isPreorder_2810) Any
forall a. a
erased
-- Data.Nat.Properties.≤-isTotalOrder
d_'8804''45'isTotalOrder_2816 ::
  MAlonzo.Code.Relation.Binary.Structures.T_IsTotalOrder_404
d_'8804''45'isTotalOrder_2816 :: T_IsTotalOrder_404
d_'8804''45'isTotalOrder_2816
  = (T_IsPartialOrder_174
 -> (Any -> Any -> T__'8846'__30) -> T_IsTotalOrder_404)
-> Any -> Any -> T_IsTotalOrder_404
forall a b. a -> b
coe
      T_IsPartialOrder_174
-> (Any -> Any -> T__'8846'__30) -> T_IsTotalOrder_404
MAlonzo.Code.Relation.Binary.Structures.C_IsTotalOrder'46'constructor_20555
      (T_IsPartialOrder_174 -> Any
forall a b. a -> b
coe T_IsPartialOrder_174
d_'8804''45'isPartialOrder_2814) ((Integer -> Integer -> T__'8846'__30) -> Any
forall a b. a -> b
coe Integer -> Integer -> T__'8846'__30
d_'8804''45'total_2790)
-- Data.Nat.Properties.≤-isDecTotalOrder
d_'8804''45'isDecTotalOrder_2818 ::
  MAlonzo.Code.Relation.Binary.Structures.T_IsDecTotalOrder_460
d_'8804''45'isDecTotalOrder_2818 :: T_IsDecTotalOrder_460
d_'8804''45'isDecTotalOrder_2818
  = (T_IsTotalOrder_404
 -> (Any -> Any -> T_Dec_20)
 -> (Any -> Any -> T_Dec_20)
 -> T_IsDecTotalOrder_460)
-> Any -> Any -> Any -> T_IsDecTotalOrder_460
forall a b. a -> b
coe
      T_IsTotalOrder_404
-> (Any -> Any -> T_Dec_20)
-> (Any -> Any -> T_Dec_20)
-> T_IsDecTotalOrder_460
MAlonzo.Code.Relation.Binary.Structures.C_IsDecTotalOrder'46'constructor_22695
      (T_IsTotalOrder_404 -> Any
forall a b. a -> b
coe T_IsTotalOrder_404
d_'8804''45'isTotalOrder_2816) ((Integer -> Integer -> T_Dec_20) -> Any
forall a b. a -> b
coe Integer -> Integer -> T_Dec_20
d__'8799'__2688)
      ((Integer -> Integer -> T_Dec_20) -> Any
forall a b. a -> b
coe Integer -> Integer -> T_Dec_20
d__'8804''63'__2802)
-- Data.Nat.Properties.≤-preorder
d_'8804''45'preorder_2820 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Preorder_132
d_'8804''45'preorder_2820 :: T_Preorder_132
d_'8804''45'preorder_2820
  = (T_IsPreorder_70 -> T_Preorder_132)
-> T_IsPreorder_70 -> T_Preorder_132
forall a b. a -> b
coe
      T_IsPreorder_70 -> T_Preorder_132
MAlonzo.Code.Relation.Binary.Bundles.C_Preorder'46'constructor_2267
      T_IsPreorder_70
d_'8804''45'isPreorder_2810
-- Data.Nat.Properties.≤-totalPreorder
d_'8804''45'totalPreorder_2822 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_222
d_'8804''45'totalPreorder_2822 :: T_TotalPreorder_222
d_'8804''45'totalPreorder_2822
  = (T_IsTotalPreorder_124 -> T_TotalPreorder_222)
-> T_IsTotalPreorder_124 -> T_TotalPreorder_222
forall a b. a -> b
coe
      T_IsTotalPreorder_124 -> T_TotalPreorder_222
MAlonzo.Code.Relation.Binary.Bundles.C_TotalPreorder'46'constructor_4573
      T_IsTotalPreorder_124
d_'8804''45'isTotalPreorder_2812
-- Data.Nat.Properties.≤-poset
d_'8804''45'poset_2824 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Poset_314
d_'8804''45'poset_2824 :: T_Poset_314
d_'8804''45'poset_2824
  = (T_IsPartialOrder_174 -> T_Poset_314)
-> T_IsPartialOrder_174 -> T_Poset_314
forall a b. a -> b
coe
      T_IsPartialOrder_174 -> T_Poset_314
MAlonzo.Code.Relation.Binary.Bundles.C_Poset'46'constructor_6389
      T_IsPartialOrder_174
d_'8804''45'isPartialOrder_2814
-- Data.Nat.Properties.≤-totalOrder
d_'8804''45'totalOrder_2826 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_TotalOrder_764
d_'8804''45'totalOrder_2826 :: T_TotalOrder_764
d_'8804''45'totalOrder_2826
  = (T_IsTotalOrder_404 -> T_TotalOrder_764)
-> T_IsTotalOrder_404 -> T_TotalOrder_764
forall a b. a -> b
coe
      T_IsTotalOrder_404 -> T_TotalOrder_764
MAlonzo.Code.Relation.Binary.Bundles.C_TotalOrder'46'constructor_15747
      T_IsTotalOrder_404
d_'8804''45'isTotalOrder_2816
-- Data.Nat.Properties.≤-decTotalOrder
d_'8804''45'decTotalOrder_2828 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_DecTotalOrder_866
d_'8804''45'decTotalOrder_2828 :: T_DecTotalOrder_866
d_'8804''45'decTotalOrder_2828
  = (T_IsDecTotalOrder_460 -> T_DecTotalOrder_866)
-> T_IsDecTotalOrder_460 -> T_DecTotalOrder_866
forall a b. a -> b
coe
      T_IsDecTotalOrder_460 -> T_DecTotalOrder_866
MAlonzo.Code.Relation.Binary.Bundles.C_DecTotalOrder'46'constructor_17849
      T_IsDecTotalOrder_460
d_'8804''45'isDecTotalOrder_2818
-- Data.Nat.Properties.s≤s-injective
d_s'8804's'45'injective_2834 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_s'8804's'45'injective_2834 :: Integer
-> Integer
-> T__'8804'__22
-> T__'8804'__22
-> T__'8801'__12
-> T__'8801'__12
d_s'8804's'45'injective_2834 = Integer
-> Integer
-> T__'8804'__22
-> T__'8804'__22
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Nat.Properties.≤-pred
d_'8804''45'pred_2836 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_'8804''45'pred_2836 :: Integer -> Integer -> T__'8804'__22 -> T__'8804'__22
d_'8804''45'pred_2836 ~Integer
v0 ~Integer
v1 = T__'8804'__22 -> T__'8804'__22
du_'8804''45'pred_2836
du_'8804''45'pred_2836 ::
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
du_'8804''45'pred_2836 :: T__'8804'__22 -> T__'8804'__22
du_'8804''45'pred_2836
  = (T__'8804'__22 -> T__'8804'__22) -> T__'8804'__22 -> T__'8804'__22
forall a b. a -> b
coe T__'8804'__22 -> T__'8804'__22
MAlonzo.Code.Data.Nat.Base.du_s'8804's'8315''185'_62
-- Data.Nat.Properties.m≤n⇒m≤1+n
d_m'8804'n'8658'm'8804'1'43'n_2838 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_m'8804'n'8658'm'8804'1'43'n_2838 :: Integer -> Integer -> T__'8804'__22 -> T__'8804'__22
d_m'8804'n'8658'm'8804'1'43'n_2838 ~Integer
v0 ~Integer
v1 T__'8804'__22
v2
  = T__'8804'__22 -> T__'8804'__22
du_m'8804'n'8658'm'8804'1'43'n_2838 T__'8804'__22
v2
du_m'8804'n'8658'm'8804'1'43'n_2838 ::
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
du_m'8804'n'8658'm'8804'1'43'n_2838 :: T__'8804'__22 -> T__'8804'__22
du_m'8804'n'8658'm'8804'1'43'n_2838 T__'8804'__22
v0 = T__'8804'__22 -> T__'8804'__22
forall a b. a -> b
coe T__'8804'__22
v0
-- Data.Nat.Properties.n≤1+n
d_n'8804'1'43'n_2844 ::
  Integer -> MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_n'8804'1'43'n_2844 :: Integer -> T__'8804'__22
d_n'8804'1'43'n_2844 Integer
v0 = (Integer -> T__'8804'__22) -> Any -> T__'8804'__22
forall a b. a -> b
coe Integer -> T__'8804'__22
d_'8804''45'refl_2776 (Integer -> Any
forall a b. a -> b
coe Integer
v0)
-- Data.Nat.Properties.1+n≰n
d_1'43'n'8816'n_2846 ::
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Irrelevant.T_Irrelevant_20
d_1'43'n'8816'n_2846 :: Integer -> T__'8804'__22 -> T_Irrelevant_20
d_1'43'n'8816'n_2846 = Integer -> T__'8804'__22 -> T_Irrelevant_20
forall a. a
erased
-- Data.Nat.Properties.n≤0⇒n≡0
d_n'8804'0'8658'n'8801'0_2850 ::
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_n'8804'0'8658'n'8801'0_2850 :: Integer -> T__'8804'__22 -> T__'8801'__12
d_n'8804'0'8658'n'8801'0_2850 = Integer -> T__'8804'__22 -> T__'8801'__12
forall a. a
erased
-- Data.Nat.Properties.n≤1⇒n≡0∨n≡1
d_n'8804'1'8658'n'8801'0'8744'n'8801'1_2852 ::
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Sum.Base.T__'8846'__30
d_n'8804'1'8658'n'8801'0'8744'n'8801'1_2852 :: Integer -> T__'8804'__22 -> T__'8846'__30
d_n'8804'1'8658'n'8801'0'8744'n'8801'1_2852 ~Integer
v0 T__'8804'__22
v1
  = T__'8804'__22 -> T__'8846'__30
du_n'8804'1'8658'n'8801'0'8744'n'8801'1_2852 T__'8804'__22
v1
du_n'8804'1'8658'n'8801'0'8744'n'8801'1_2852 ::
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Sum.Base.T__'8846'__30
du_n'8804'1'8658'n'8801'0'8744'n'8801'1_2852 :: T__'8804'__22 -> T__'8846'__30
du_n'8804'1'8658'n'8801'0'8744'n'8801'1_2852 T__'8804'__22
v0
  = case T__'8804'__22 -> T__'8804'__22
forall a b. a -> b
coe T__'8804'__22
v0 of
      T__'8804'__22
MAlonzo.Code.Data.Nat.Base.C_z'8804'n_26
        -> (Any -> T__'8846'__30) -> Any -> T__'8846'__30
forall a b. a -> b
coe Any -> T__'8846'__30
MAlonzo.Code.Data.Sum.Base.C_inj'8321'_38 Any
forall a. a
erased
      MAlonzo.Code.Data.Nat.Base.C_s'8804's_34 T__'8804'__22
v3
        -> (Any -> Any -> Any) -> Any -> Any -> T__'8846'__30
forall a b. a -> b
coe
             Any -> Any -> Any
forall a b. a -> b -> b
seq (T__'8804'__22 -> Any
forall a b. a -> b
coe T__'8804'__22
v3) ((Any -> T__'8846'__30) -> Any -> Any
forall a b. a -> b
coe Any -> T__'8846'__30
MAlonzo.Code.Data.Sum.Base.C_inj'8322'_42 Any
forall a. a
erased)
      T__'8804'__22
_ -> T__'8846'__30
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Data.Nat.Properties.<⇒≤
d_'60''8658''8804'_2854 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_'60''8658''8804'_2854 :: Integer -> Integer -> T__'8804'__22 -> T__'8804'__22
d_'60''8658''8804'_2854 ~Integer
v0 ~Integer
v1 T__'8804'__22
v2 = T__'8804'__22 -> T__'8804'__22
du_'60''8658''8804'_2854 T__'8804'__22
v2
du_'60''8658''8804'_2854 ::
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
du_'60''8658''8804'_2854 :: T__'8804'__22 -> T__'8804'__22
du_'60''8658''8804'_2854 T__'8804'__22
v0
  = case T__'8804'__22 -> T__'8804'__22
forall a b. a -> b
coe T__'8804'__22
v0 of
      MAlonzo.Code.Data.Nat.Base.C_s'8804's_34 T__'8804'__22
v3
        -> case T__'8804'__22 -> T__'8804'__22
forall a b. a -> b
coe T__'8804'__22
v3 of
             T__'8804'__22
MAlonzo.Code.Data.Nat.Base.C_z'8804'n_26
               -> T__'8804'__22 -> T__'8804'__22
forall a b. a -> b
coe T__'8804'__22
MAlonzo.Code.Data.Nat.Base.C_z'8804'n_26
             MAlonzo.Code.Data.Nat.Base.C_s'8804's_34 T__'8804'__22
v6
               -> (T__'8804'__22 -> T__'8804'__22) -> Any -> T__'8804'__22
forall a b. a -> b
coe
                    T__'8804'__22 -> T__'8804'__22
MAlonzo.Code.Data.Nat.Base.C_s'8804's_34
                    ((T__'8804'__22 -> T__'8804'__22) -> Any -> Any
forall a b. a -> b
coe
                       T__'8804'__22 -> T__'8804'__22
du_'60''8658''8804'_2854
                       ((T__'8804'__22 -> T__'8804'__22) -> T__'8804'__22 -> Any
forall a b. a -> b
coe T__'8804'__22 -> T__'8804'__22
MAlonzo.Code.Data.Nat.Base.C_s'8804's_34 T__'8804'__22
v6))
             T__'8804'__22
_ -> T__'8804'__22
forall a. a
MAlonzo.RTE.mazUnreachableError
      T__'8804'__22
_ -> T__'8804'__22
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Data.Nat.Properties.<⇒≢
d_'60''8658''8802'_2858 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Data.Irrelevant.T_Irrelevant_20
d_'60''8658''8802'_2858 :: Integer
-> Integer -> T__'8804'__22 -> T__'8801'__12 -> T_Irrelevant_20
d_'60''8658''8802'_2858 = Integer
-> Integer -> T__'8804'__22 -> T__'8801'__12 -> T_Irrelevant_20
forall a. a
erased
-- Data.Nat.Properties.>⇒≢
d_'62''8658''8802'_2862 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Data.Irrelevant.T_Irrelevant_20
d_'62''8658''8802'_2862 :: Integer
-> Integer -> T__'8804'__22 -> T__'8801'__12 -> T_Irrelevant_20
d_'62''8658''8802'_2862 = Integer
-> Integer -> T__'8804'__22 -> T__'8801'__12 -> T_Irrelevant_20
forall a. a
erased
-- Data.Nat.Properties.≤⇒≯
d_'8804''8658''8815'_2864 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Irrelevant.T_Irrelevant_20
d_'8804''8658''8815'_2864 :: Integer
-> Integer -> T__'8804'__22 -> T__'8804'__22 -> T_Irrelevant_20
d_'8804''8658''8815'_2864 = Integer
-> Integer -> T__'8804'__22 -> T__'8804'__22 -> T_Irrelevant_20
forall a. a
erased
-- Data.Nat.Properties.<⇒≱
d_'60''8658''8817'_2870 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Irrelevant.T_Irrelevant_20
d_'60''8658''8817'_2870 :: Integer
-> Integer -> T__'8804'__22 -> T__'8804'__22 -> T_Irrelevant_20
d_'60''8658''8817'_2870 = Integer
-> Integer -> T__'8804'__22 -> T__'8804'__22 -> T_Irrelevant_20
forall a. a
erased
-- Data.Nat.Properties.<⇒≯
d_'60''8658''8815'_2876 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Irrelevant.T_Irrelevant_20
d_'60''8658''8815'_2876 :: Integer
-> Integer -> T__'8804'__22 -> T__'8804'__22 -> T_Irrelevant_20
d_'60''8658''8815'_2876 = Integer
-> Integer -> T__'8804'__22 -> T__'8804'__22 -> T_Irrelevant_20
forall a. a
erased
-- Data.Nat.Properties.≰⇒≮
d_'8816''8658''8814'_2882 ::
  Integer ->
  Integer ->
  (MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
   MAlonzo.Code.Data.Irrelevant.T_Irrelevant_20) ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Irrelevant.T_Irrelevant_20
d_'8816''8658''8814'_2882 :: Integer
-> Integer
-> (T__'8804'__22 -> T_Irrelevant_20)
-> T__'8804'__22
-> T_Irrelevant_20
d_'8816''8658''8814'_2882 = Integer
-> Integer
-> (T__'8804'__22 -> T_Irrelevant_20)
-> T__'8804'__22
-> T_Irrelevant_20
forall a. a
erased
-- Data.Nat.Properties.≰⇒>
d_'8816''8658''62'_2888 ::
  Integer ->
  Integer ->
  (MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
   MAlonzo.Code.Data.Irrelevant.T_Irrelevant_20) ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_'8816''8658''62'_2888 :: Integer
-> Integer -> (T__'8804'__22 -> T_Irrelevant_20) -> T__'8804'__22
d_'8816''8658''62'_2888 Integer
v0 Integer
v1 ~T__'8804'__22 -> T_Irrelevant_20
v2 = Integer -> Integer -> T__'8804'__22
du_'8816''8658''62'_2888 Integer
v0 Integer
v1
du_'8816''8658''62'_2888 ::
  Integer -> Integer -> MAlonzo.Code.Data.Nat.Base.T__'8804'__22
du_'8816''8658''62'_2888 :: Integer -> Integer -> T__'8804'__22
du_'8816''8658''62'_2888 Integer
v0 Integer
v1
  = case Integer -> Integer
forall a b. a -> b
coe Integer
v0 of
      Integer
0 -> ((Any -> T_Irrelevant_20) -> Any) -> Any -> T__'8804'__22
forall a b. a -> b
coe
             (Any -> T_Irrelevant_20) -> Any
MAlonzo.Code.Relation.Nullary.Negation.Core.du_contradiction_44
             Any
forall a. a
erased
      Integer
_ -> let v2 :: Integer
v2 = Integer -> Integer -> Integer
subInt (Integer -> Integer
forall a b. a -> b
coe Integer
v0) (Integer -> Integer
forall a b. a -> b
coe (Integer
1 :: Integer)) in
           Any -> T__'8804'__22
forall a b. a -> b
coe
             (case Integer -> Integer
forall a b. a -> b
coe Integer
v1 of
                Integer
0 -> (T__'8804'__22 -> T__'8804'__22) -> Any -> Any
forall a b. a -> b
coe
                       T__'8804'__22 -> T__'8804'__22
MAlonzo.Code.Data.Nat.Base.C_s'8804's_34
                       (T__'8804'__22 -> Any
forall a b. a -> b
coe T__'8804'__22
MAlonzo.Code.Data.Nat.Base.C_z'8804'n_26)
                Integer
_ -> let v3 :: Integer
v3 = Integer -> Integer -> Integer
subInt (Integer -> Integer
forall a b. a -> b
coe Integer
v1) (Integer -> Integer
forall a b. a -> b
coe (Integer
1 :: Integer)) in
                     Any -> Any
forall a b. a -> b
coe
                       ((T__'8804'__22 -> T__'8804'__22) -> Any -> Any
forall a b. a -> b
coe
                          T__'8804'__22 -> T__'8804'__22
MAlonzo.Code.Data.Nat.Base.C_s'8804's_34
                          ((Integer -> Integer -> T__'8804'__22) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> T__'8804'__22
du_'8816''8658''62'_2888 (Integer -> Any
forall a b. a -> b
coe Integer
v2) (Integer -> Any
forall a b. a -> b
coe Integer
v3))))
-- Data.Nat.Properties.≰⇒≥
d_'8816''8658''8805'_2900 ::
  Integer ->
  Integer ->
  (MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
   MAlonzo.Code.Data.Irrelevant.T_Irrelevant_20) ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_'8816''8658''8805'_2900 :: Integer
-> Integer -> (T__'8804'__22 -> T_Irrelevant_20) -> T__'8804'__22
d_'8816''8658''8805'_2900 Integer
v0 Integer
v1 ~T__'8804'__22 -> T_Irrelevant_20
v2
  = Integer -> Integer -> T__'8804'__22
du_'8816''8658''8805'_2900 Integer
v0 Integer
v1
du_'8816''8658''8805'_2900 ::
  Integer -> Integer -> MAlonzo.Code.Data.Nat.Base.T__'8804'__22
du_'8816''8658''8805'_2900 :: Integer -> Integer -> T__'8804'__22
du_'8816''8658''8805'_2900 Integer
v0 Integer
v1
  = (T__'8804'__22 -> T__'8804'__22) -> Any -> T__'8804'__22
forall a b. a -> b
coe
      T__'8804'__22 -> T__'8804'__22
du_'60''8658''8804'_2854
      ((Integer -> Integer -> T__'8804'__22) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> T__'8804'__22
du_'8816''8658''62'_2888 (Integer -> Any
forall a b. a -> b
coe Integer
v0) (Integer -> Any
forall a b. a -> b
coe Integer
v1))
-- Data.Nat.Properties.≮⇒≥
d_'8814''8658''8805'_2902 ::
  Integer ->
  Integer ->
  (MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
   MAlonzo.Code.Data.Irrelevant.T_Irrelevant_20) ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_'8814''8658''8805'_2902 :: Integer
-> Integer -> (T__'8804'__22 -> T_Irrelevant_20) -> T__'8804'__22
d_'8814''8658''8805'_2902 Integer
v0 Integer
v1 ~T__'8804'__22 -> T_Irrelevant_20
v2
  = Integer -> Integer -> T__'8804'__22
du_'8814''8658''8805'_2902 Integer
v0 Integer
v1
du_'8814''8658''8805'_2902 ::
  Integer -> Integer -> MAlonzo.Code.Data.Nat.Base.T__'8804'__22
du_'8814''8658''8805'_2902 :: Integer -> Integer -> T__'8804'__22
du_'8814''8658''8805'_2902 Integer
v0 Integer
v1
  = case Integer -> Integer
forall a b. a -> b
coe Integer
v1 of
      Integer
0 -> T__'8804'__22 -> T__'8804'__22
forall a b. a -> b
coe T__'8804'__22
MAlonzo.Code.Data.Nat.Base.C_z'8804'n_26
      Integer
_ -> let v2 :: Integer
v2 = Integer -> Integer -> Integer
subInt (Integer -> Integer
forall a b. a -> b
coe Integer
v1) (Integer -> Integer
forall a b. a -> b
coe (Integer
1 :: Integer)) in
           Any -> T__'8804'__22
forall a b. a -> b
coe
             (case Integer -> Integer
forall a b. a -> b
coe Integer
v0 of
                Integer
0 -> ((Any -> T_Irrelevant_20) -> Any) -> Any -> Any
forall a b. a -> b
coe
                       (Any -> T_Irrelevant_20) -> Any
MAlonzo.Code.Relation.Nullary.Negation.Core.du_contradiction_44
                       Any
forall a. a
erased
                Integer
_ -> let v3 :: Integer
v3 = Integer -> Integer -> Integer
subInt (Integer -> Integer
forall a b. a -> b
coe Integer
v0) (Integer -> Integer
forall a b. a -> b
coe (Integer
1 :: Integer)) in
                     Any -> Any
forall a b. a -> b
coe
                       ((T__'8804'__22 -> T__'8804'__22) -> Any -> Any
forall a b. a -> b
coe
                          T__'8804'__22 -> T__'8804'__22
MAlonzo.Code.Data.Nat.Base.C_s'8804's_34
                          ((Integer -> Integer -> T__'8804'__22) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> T__'8804'__22
du_'8814''8658''8805'_2902 (Integer -> Any
forall a b. a -> b
coe Integer
v3) (Integer -> Any
forall a b. a -> b
coe Integer
v2))))
-- Data.Nat.Properties.≤∧≢⇒<
d_'8804''8743''8802''8658''60'_2918 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  (MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
   MAlonzo.Code.Data.Irrelevant.T_Irrelevant_20) ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_'8804''8743''8802''8658''60'_2918 :: Integer
-> Integer
-> T__'8804'__22
-> (T__'8801'__12 -> T_Irrelevant_20)
-> T__'8804'__22
d_'8804''8743''8802''8658''60'_2918 ~Integer
v0 Integer
v1 T__'8804'__22
v2 ~T__'8801'__12 -> T_Irrelevant_20
v3
  = Integer -> T__'8804'__22 -> T__'8804'__22
du_'8804''8743''8802''8658''60'_2918 Integer
v1 T__'8804'__22
v2
du_'8804''8743''8802''8658''60'_2918 ::
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
du_'8804''8743''8802''8658''60'_2918 :: Integer -> T__'8804'__22 -> T__'8804'__22
du_'8804''8743''8802''8658''60'_2918 Integer
v0 T__'8804'__22
v1
  = case Integer -> Integer
forall a b. a -> b
coe Integer
v0 of
      Integer
0 -> (Any -> Any -> Any) -> Any -> Any -> T__'8804'__22
forall a b. a -> b
coe
             Any -> Any -> Any
forall a b. a -> b -> b
seq (T__'8804'__22 -> Any
forall a b. a -> b
coe T__'8804'__22
v1)
             (((Any -> T_Irrelevant_20) -> Any) -> Any -> Any
forall a b. a -> b
coe
                (Any -> T_Irrelevant_20) -> Any
MAlonzo.Code.Relation.Nullary.Negation.Core.du_contradiction_44
                Any
forall a. a
erased)
      Integer
_ -> let v2 :: Integer
v2 = Integer -> Integer -> Integer
subInt (Integer -> Integer
forall a b. a -> b
coe Integer
v0) (Integer -> Integer
forall a b. a -> b
coe (Integer
1 :: Integer)) in
           Any -> T__'8804'__22
forall a b. a -> b
coe
             (case T__'8804'__22 -> T__'8804'__22
forall a b. a -> b
coe T__'8804'__22
v1 of
                T__'8804'__22
MAlonzo.Code.Data.Nat.Base.C_z'8804'n_26
                  -> (T__'8804'__22 -> T__'8804'__22) -> Any -> Any
forall a b. a -> b
coe
                       T__'8804'__22 -> T__'8804'__22
MAlonzo.Code.Data.Nat.Base.C_s'8804's_34
                       (T__'8804'__22 -> Any
forall a b. a -> b
coe T__'8804'__22
MAlonzo.Code.Data.Nat.Base.C_z'8804'n_26)
                MAlonzo.Code.Data.Nat.Base.C_s'8804's_34 T__'8804'__22
v5
                  -> (T__'8804'__22 -> T__'8804'__22) -> Any -> Any
forall a b. a -> b
coe
                       T__'8804'__22 -> T__'8804'__22
MAlonzo.Code.Data.Nat.Base.C_s'8804's_34
                       ((Integer -> T__'8804'__22 -> T__'8804'__22) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> T__'8804'__22 -> T__'8804'__22
du_'8804''8743''8802''8658''60'_2918 (Integer -> Any
forall a b. a -> b
coe Integer
v2) (T__'8804'__22 -> Any
forall a b. a -> b
coe T__'8804'__22
v5))
                T__'8804'__22
_ -> Any
forall a. a
MAlonzo.RTE.mazUnreachableError)
-- Data.Nat.Properties.≤∧≮⇒≡
d_'8804''8743''8814''8658''8801'_2936 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  (MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
   MAlonzo.Code.Data.Irrelevant.T_Irrelevant_20) ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8804''8743''8814''8658''8801'_2936 :: Integer
-> Integer
-> T__'8804'__22
-> (T__'8804'__22 -> T_Irrelevant_20)
-> T__'8801'__12
d_'8804''8743''8814''8658''8801'_2936 = Integer
-> Integer
-> T__'8804'__22
-> (T__'8804'__22 -> T_Irrelevant_20)
-> T__'8801'__12
forall a. a
erased
-- Data.Nat.Properties.≤-<-connex
d_'8804''45''60''45'connex_2942 ::
  Integer -> Integer -> MAlonzo.Code.Data.Sum.Base.T__'8846'__30
d_'8804''45''60''45'connex_2942 :: Integer -> Integer -> T__'8846'__30
d_'8804''45''60''45'connex_2942 Integer
v0 Integer
v1
  = let v2 :: t
v2
          = ((Any -> Any) -> (Any -> Any) -> T_Dec_20 -> T_Dec_20)
-> (Any -> Any) -> Any -> Any -> t
forall a b. a -> b
coe
              (Any -> Any) -> (Any -> Any) -> T_Dec_20 -> T_Dec_20
MAlonzo.Code.Relation.Nullary.Decidable.Core.du_map'8242'_168
              (\ Any
v2 -> (Integer -> T__'8804'__22) -> Any -> Any
forall a b. a -> b
coe Integer -> T__'8804'__22
du_'8804''7495''8658''8804'_2746 (Integer -> Any
forall a b. a -> b
coe Integer
v0))
              ((T__'8804'__22 -> Any) -> Any
forall a b. a -> b
coe T__'8804'__22 -> Any
du_'8804''8658''8804''7495'_2758)
              ((Bool -> T_Dec_20) -> Any -> Any
forall a b. a -> b
coe
                 Bool -> T_Dec_20
MAlonzo.Code.Relation.Nullary.Decidable.Core.d_T'63'_66
                 ((Integer -> Integer -> Bool) -> Any -> Any -> Any
forall a b. a -> b
coe
                    Integer -> Integer -> Bool
MAlonzo.Code.Data.Nat.Base.d__'8804''7495'__14 (Integer -> Any
forall a b. a -> b
coe Integer
v0)
                    (Integer -> Any
forall a b. a -> b
coe Integer
v1))) in
    Any -> T__'8846'__30
forall a b. a -> b
coe
      (case Any -> T_Dec_20
forall a b. a -> b
coe Any
forall a. a
v2 of
         MAlonzo.Code.Relation.Nullary.Decidable.Core.C__because__32 Bool
v3 T_Reflects_16
v4
           -> if Bool -> Bool
forall a b. a -> b
coe Bool
v3
                then case T_Reflects_16 -> T_Reflects_16
forall a b. a -> b
coe T_Reflects_16
v4 of
                       MAlonzo.Code.Relation.Nullary.Reflects.C_of'696'_22 Any
v5
                         -> (Any -> T__'8846'__30) -> Any -> Any
forall a b. a -> b
coe Any -> T__'8846'__30
MAlonzo.Code.Data.Sum.Base.C_inj'8321'_38 (Any -> Any
forall a b. a -> b
coe Any
v5)
                       T_Reflects_16
_ -> Any
forall a. a
MAlonzo.RTE.mazUnreachableError
                else (Any -> Any -> Any) -> Any -> Any -> Any
forall a b. a -> b
coe
                       Any -> Any -> Any
forall a b. a -> b -> b
seq (T_Reflects_16 -> Any
forall a b. a -> b
coe T_Reflects_16
v4)
                       ((Any -> T__'8846'__30) -> Any -> Any
forall a b. a -> b
coe
                          Any -> T__'8846'__30
MAlonzo.Code.Data.Sum.Base.C_inj'8322'_42
                          ((Integer -> Integer -> T__'8804'__22) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> T__'8804'__22
du_'8816''8658''62'_2888 (Integer -> Any
forall a b. a -> b
coe Integer
v0) (Integer -> Any
forall a b. a -> b
coe Integer
v1)))
         T_Dec_20
_ -> Any
forall a. a
MAlonzo.RTE.mazUnreachableError)
-- Data.Nat.Properties.≥->-connex
d_'8805''45''62''45'connex_2964 ::
  Integer -> Integer -> MAlonzo.Code.Data.Sum.Base.T__'8846'__30
d_'8805''45''62''45'connex_2964 :: Integer -> Integer -> T__'8846'__30
d_'8805''45''62''45'connex_2964 Integer
v0 Integer
v1
  = (Integer -> Integer -> T__'8846'__30)
-> Any -> Any -> T__'8846'__30
forall a b. a -> b
coe Integer -> Integer -> T__'8846'__30
d_'8804''45''60''45'connex_2942 (Integer -> Any
forall a b. a -> b
coe Integer
v1) (Integer -> Any
forall a b. a -> b
coe Integer
v0)
-- Data.Nat.Properties.<-≤-connex
d_'60''45''8804''45'connex_2966 ::
  Integer -> Integer -> MAlonzo.Code.Data.Sum.Base.T__'8846'__30
d_'60''45''8804''45'connex_2966 :: Integer -> Integer -> T__'8846'__30
d_'60''45''8804''45'connex_2966
  = ((Any -> Any -> T__'8846'__30) -> Any -> Any -> T__'8846'__30)
-> Any -> Integer -> Integer -> T__'8846'__30
forall a b. a -> b
coe
      (Any -> Any -> T__'8846'__30) -> Any -> Any -> T__'8846'__30
MAlonzo.Code.Relation.Binary.Consequences.du_flip'45'Connex_854
      ((Integer -> Integer -> T__'8846'__30) -> Any
forall a b. a -> b
coe Integer -> Integer -> T__'8846'__30
d_'8804''45''60''45'connex_2942)
-- Data.Nat.Properties.>-≥-connex
d_'62''45''8805''45'connex_2968 ::
  Integer -> Integer -> MAlonzo.Code.Data.Sum.Base.T__'8846'__30
d_'62''45''8805''45'connex_2968 :: Integer -> Integer -> T__'8846'__30
d_'62''45''8805''45'connex_2968
  = ((Any -> Any -> T__'8846'__30) -> Any -> Any -> T__'8846'__30)
-> Any -> Integer -> Integer -> T__'8846'__30
forall a b. a -> b
coe
      (Any -> Any -> T__'8846'__30) -> Any -> Any -> T__'8846'__30
MAlonzo.Code.Relation.Binary.Consequences.du_flip'45'Connex_854
      ((Integer -> Integer -> T__'8846'__30) -> Any
forall a b. a -> b
coe Integer -> Integer -> T__'8846'__30
d_'8805''45''62''45'connex_2964)
-- Data.Nat.Properties.<-irrefl
d_'60''45'irrefl_2970 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Irrelevant.T_Irrelevant_20
d_'60''45'irrefl_2970 :: Integer
-> Integer -> T__'8801'__12 -> T__'8804'__22 -> T_Irrelevant_20
d_'60''45'irrefl_2970 = Integer
-> Integer -> T__'8801'__12 -> T__'8804'__22 -> T_Irrelevant_20
forall a. a
erased
-- Data.Nat.Properties.<-asym
d_'60''45'asym_2974 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Irrelevant.T_Irrelevant_20
d_'60''45'asym_2974 :: Integer
-> Integer -> T__'8804'__22 -> T__'8804'__22 -> T_Irrelevant_20
d_'60''45'asym_2974 = Integer
-> Integer -> T__'8804'__22 -> T__'8804'__22 -> T_Irrelevant_20
forall a. a
erased
-- Data.Nat.Properties.<-trans
d_'60''45'trans_2980 ::
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_'60''45'trans_2980 :: Integer
-> Integer
-> Integer
-> T__'8804'__22
-> T__'8804'__22
-> T__'8804'__22
d_'60''45'trans_2980 ~Integer
v0 Integer
v1 ~Integer
v2 T__'8804'__22
v3 T__'8804'__22
v4
  = Integer -> T__'8804'__22 -> T__'8804'__22 -> T__'8804'__22
du_'60''45'trans_2980 Integer
v1 T__'8804'__22
v3 T__'8804'__22
v4
du_'60''45'trans_2980 ::
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
du_'60''45'trans_2980 :: Integer -> T__'8804'__22 -> T__'8804'__22 -> T__'8804'__22
du_'60''45'trans_2980 Integer
v0 T__'8804'__22
v1 T__'8804'__22
v2
  = case T__'8804'__22 -> T__'8804'__22
forall a b. a -> b
coe T__'8804'__22
v1 of
      MAlonzo.Code.Data.Nat.Base.C_s'8804's_34 T__'8804'__22
v5
        -> let v6 :: Integer
v6 = Integer -> Integer -> Integer
subInt (Integer -> Integer
forall a b. a -> b
coe Integer
v0) (Integer -> Integer
forall a b. a -> b
coe (Integer
1 :: Integer)) in
           Any -> T__'8804'__22
forall a b. a -> b
coe
             (case T__'8804'__22 -> T__'8804'__22
forall a b. a -> b
coe T__'8804'__22
v2 of
                MAlonzo.Code.Data.Nat.Base.C_s'8804's_34 T__'8804'__22
v9
                  -> (T__'8804'__22 -> T__'8804'__22) -> Any -> Any
forall a b. a -> b
coe
                       T__'8804'__22 -> T__'8804'__22
MAlonzo.Code.Data.Nat.Base.C_s'8804's_34
                       ((T__'8804'__22 -> T__'8804'__22 -> T__'8804'__22)
-> Any -> Any -> Any
forall a b. a -> b
coe
                          T__'8804'__22 -> T__'8804'__22 -> T__'8804'__22
du_'8804''45'trans_2784 (T__'8804'__22 -> Any
forall a b. a -> b
coe T__'8804'__22
v5)
                          ((T__'8804'__22 -> T__'8804'__22 -> T__'8804'__22)
-> Any -> Any -> Any
forall a b. a -> b
coe
                             T__'8804'__22 -> T__'8804'__22 -> T__'8804'__22
du_'8804''45'trans_2784 ((Integer -> T__'8804'__22) -> Any -> Any
forall a b. a -> b
coe Integer -> T__'8804'__22
d_n'8804'1'43'n_2844 (Integer -> Any
forall a b. a -> b
coe Integer
v6))
                             (T__'8804'__22 -> Any
forall a b. a -> b
coe T__'8804'__22
v9)))
                T__'8804'__22
_ -> Any
forall a. a
MAlonzo.RTE.mazUnreachableError)
      T__'8804'__22
_ -> T__'8804'__22
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Data.Nat.Properties.≤-<-trans
d_'8804''45''60''45'trans_2986 ::
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_'8804''45''60''45'trans_2986 :: Integer
-> Integer
-> Integer
-> T__'8804'__22
-> T__'8804'__22
-> T__'8804'__22
d_'8804''45''60''45'trans_2986 ~Integer
v0 ~Integer
v1 ~Integer
v2 T__'8804'__22
v3 T__'8804'__22
v4
  = T__'8804'__22 -> T__'8804'__22 -> T__'8804'__22
du_'8804''45''60''45'trans_2986 T__'8804'__22
v3 T__'8804'__22
v4
du_'8804''45''60''45'trans_2986 ::
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
du_'8804''45''60''45'trans_2986 :: T__'8804'__22 -> T__'8804'__22 -> T__'8804'__22
du_'8804''45''60''45'trans_2986 T__'8804'__22
v0 T__'8804'__22
v1
  = case T__'8804'__22 -> T__'8804'__22
forall a b. a -> b
coe T__'8804'__22
v1 of
      MAlonzo.Code.Data.Nat.Base.C_s'8804's_34 T__'8804'__22
v4
        -> (T__'8804'__22 -> T__'8804'__22) -> Any -> T__'8804'__22
forall a b. a -> b
coe
             T__'8804'__22 -> T__'8804'__22
MAlonzo.Code.Data.Nat.Base.C_s'8804's_34
             ((T__'8804'__22 -> T__'8804'__22 -> T__'8804'__22)
-> Any -> Any -> Any
forall a b. a -> b
coe T__'8804'__22 -> T__'8804'__22 -> T__'8804'__22
du_'8804''45'trans_2784 (T__'8804'__22 -> Any
forall a b. a -> b
coe T__'8804'__22
v0) (T__'8804'__22 -> Any
forall a b. a -> b
coe T__'8804'__22
v4))
      T__'8804'__22
_ -> T__'8804'__22
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Data.Nat.Properties.<-≤-trans
d_'60''45''8804''45'trans_2992 ::
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_'60''45''8804''45'trans_2992 :: Integer
-> Integer
-> Integer
-> T__'8804'__22
-> T__'8804'__22
-> T__'8804'__22
d_'60''45''8804''45'trans_2992 ~Integer
v0 ~Integer
v1 ~Integer
v2 T__'8804'__22
v3 T__'8804'__22
v4
  = T__'8804'__22 -> T__'8804'__22 -> T__'8804'__22
du_'60''45''8804''45'trans_2992 T__'8804'__22
v3 T__'8804'__22
v4
du_'60''45''8804''45'trans_2992 ::
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
du_'60''45''8804''45'trans_2992 :: T__'8804'__22 -> T__'8804'__22 -> T__'8804'__22
du_'60''45''8804''45'trans_2992 T__'8804'__22
v0 T__'8804'__22
v1
  = case T__'8804'__22 -> T__'8804'__22
forall a b. a -> b
coe T__'8804'__22
v0 of
      MAlonzo.Code.Data.Nat.Base.C_s'8804's_34 T__'8804'__22
v4
        -> case T__'8804'__22 -> T__'8804'__22
forall a b. a -> b
coe T__'8804'__22
v1 of
             MAlonzo.Code.Data.Nat.Base.C_s'8804's_34 T__'8804'__22
v7
               -> (T__'8804'__22 -> T__'8804'__22) -> Any -> T__'8804'__22
forall a b. a -> b
coe
                    T__'8804'__22 -> T__'8804'__22
MAlonzo.Code.Data.Nat.Base.C_s'8804's_34
                    ((T__'8804'__22 -> T__'8804'__22 -> T__'8804'__22)
-> Any -> Any -> Any
forall a b. a -> b
coe T__'8804'__22 -> T__'8804'__22 -> T__'8804'__22
du_'8804''45'trans_2784 (T__'8804'__22 -> Any
forall a b. a -> b
coe T__'8804'__22
v4) (T__'8804'__22 -> Any
forall a b. a -> b
coe T__'8804'__22
v7))
             T__'8804'__22
_ -> T__'8804'__22
forall a. a
MAlonzo.RTE.mazUnreachableError
      T__'8804'__22
_ -> T__'8804'__22
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Data.Nat.Properties.<-cmp
d_'60''45'cmp_2998 ::
  Integer ->
  Integer -> MAlonzo.Code.Relation.Binary.Definitions.T_Tri_158
d_'60''45'cmp_2998 :: Integer -> Integer -> T_Tri_158
d_'60''45'cmp_2998 Integer
v0 Integer
v1
  = let v2 :: t
v2
          = ((Any -> Any) -> (Any -> Any) -> T_Dec_20 -> T_Dec_20)
-> Any -> (Any -> Any) -> Any -> t
forall a b. a -> b
coe
              (Any -> Any) -> (Any -> Any) -> T_Dec_20 -> T_Dec_20
MAlonzo.Code.Relation.Nullary.Decidable.Core.du_map'8242'_168
              Any
forall a. a
erased (\ Any
v2 -> (Integer -> Any) -> Any -> Any
forall a b. a -> b
coe Integer -> Any
du_'8801''8658''8801''7495'_2678 (Integer -> Any
forall a b. a -> b
coe Integer
v0))
              ((Bool -> T_Dec_20) -> Any -> Any
forall a b. a -> b
coe
                 Bool -> T_Dec_20
MAlonzo.Code.Relation.Nullary.Decidable.Core.d_T'63'_66
                 ((Integer -> Integer -> Bool) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> Bool
eqInt (Integer -> Any
forall a b. a -> b
coe Integer
v0) (Integer -> Any
forall a b. a -> b
coe Integer
v1))) in
    Any -> T_Tri_158
forall a b. a -> b
coe
      (case Any -> T_Dec_20
forall a b. a -> b
coe Any
forall a. a
v2 of
         MAlonzo.Code.Relation.Nullary.Decidable.Core.C__because__32 Bool
v3 T_Reflects_16
v4
           -> if Bool -> Bool
forall a b. a -> b
coe Bool
v3
                then case T_Reflects_16 -> T_Reflects_16
forall a b. a -> b
coe T_Reflects_16
v4 of
                       MAlonzo.Code.Relation.Nullary.Reflects.C_of'696'_22 Any
v5
                         -> (Any -> T_Tri_158) -> Any -> Any
forall a b. a -> b
coe Any -> T_Tri_158
MAlonzo.Code.Relation.Binary.Definitions.C_tri'8776'_180 Any
v5
                       T_Reflects_16
_ -> Any
forall a. a
MAlonzo.RTE.mazUnreachableError
                else (Any -> Any -> Any) -> Any -> Any -> Any
forall a b. a -> b
coe
                       Any -> Any -> Any
forall a b. a -> b -> b
seq (T_Reflects_16 -> Any
forall a b. a -> b
coe T_Reflects_16
v4)
                       (let v5 :: Bool
v5 = Integer -> Integer -> Bool
ltInt (Integer -> Integer
forall a b. a -> b
coe Integer
v0) (Integer -> Integer
forall a b. a -> b
coe Integer
v1) in
                        Any -> Any
forall a b. a -> b
coe
                          (if Bool -> Bool
forall a b. a -> b
coe Bool
v5
                             then (Any -> Any -> Any) -> Any -> Any -> Any
forall a b. a -> b
coe
                                    Any -> Any -> Any
forall a b. a -> b -> b
seq
                                    ((Bool -> T_Reflects_16) -> Any -> Any
forall a b. a -> b
coe
                                       Bool -> T_Reflects_16
MAlonzo.Code.Relation.Nullary.Reflects.d_T'45'reflects_66
                                       (Bool -> Any
forall a b. a -> b
coe Bool
v5))
                                    ((Any -> T_Tri_158) -> Any -> Any
forall a b. a -> b
coe
                                       Any -> T_Tri_158
MAlonzo.Code.Relation.Binary.Definitions.C_tri'60'_172
                                       ((Integer -> T__'8804'__22) -> Any -> Any
forall a b. a -> b
coe Integer -> T__'8804'__22
du_'60''7495''8658''60'_2716 (Integer -> Any
forall a b. a -> b
coe Integer
v0)))
                             else (Any -> Any -> Any) -> Any -> Any -> Any
forall a b. a -> b
coe
                                    Any -> Any -> Any
forall a b. a -> b -> b
seq
                                    ((Bool -> T_Reflects_16) -> Any -> Any
forall a b. a -> b
coe
                                       Bool -> T_Reflects_16
MAlonzo.Code.Relation.Nullary.Reflects.d_T'45'reflects_66
                                       (Bool -> Any
forall a b. a -> b
coe Bool
v5))
                                    ((Any -> T_Tri_158) -> Any -> Any
forall a b. a -> b
coe
                                       Any -> T_Tri_158
MAlonzo.Code.Relation.Binary.Definitions.C_tri'62'_188
                                       ((Integer -> T__'8804'__22 -> T__'8804'__22) -> Any -> Any -> Any
forall a b. a -> b
coe
                                          Integer -> T__'8804'__22 -> T__'8804'__22
du_'8804''8743''8802''8658''60'_2918 (Integer -> Any
forall a b. a -> b
coe Integer
v0)
                                          ((Integer -> Integer -> T__'8804'__22) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> T__'8804'__22
du_'8814''8658''8805'_2902 (Integer -> Any
forall a b. a -> b
coe Integer
v0) (Integer -> Any
forall a b. a -> b
coe Integer
v1))))))
         T_Dec_20
_ -> Any
forall a. a
MAlonzo.RTE.mazUnreachableError)
-- Data.Nat.Properties._<?_
d__'60''63'__3030 ::
  Integer ->
  Integer -> MAlonzo.Code.Relation.Nullary.Decidable.Core.T_Dec_20
d__'60''63'__3030 :: Integer -> Integer -> T_Dec_20
d__'60''63'__3030 Integer
v0 Integer
v1
  = (Integer -> Integer -> T_Dec_20) -> Any -> Any -> T_Dec_20
forall a b. a -> b
coe
      Integer -> Integer -> T_Dec_20
d__'8804''63'__2802 ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> Integer
addInt (Integer -> Any
forall a b. a -> b
coe (Integer
1 :: Integer)) (Integer -> Any
forall a b. a -> b
coe Integer
v0))
      (Integer -> Any
forall a b. a -> b
coe Integer
v1)
-- Data.Nat.Properties._>?_
d__'62''63'__3036 ::
  Integer ->
  Integer -> MAlonzo.Code.Relation.Nullary.Decidable.Core.T_Dec_20
d__'62''63'__3036 :: Integer -> Integer -> T_Dec_20
d__'62''63'__3036 Integer
v0 Integer
v1 = (Integer -> Integer -> T_Dec_20) -> Any -> Any -> T_Dec_20
forall a b. a -> b
coe Integer -> Integer -> T_Dec_20
d__'60''63'__3030 (Integer -> Any
forall a b. a -> b
coe Integer
v1) (Integer -> Any
forall a b. a -> b
coe Integer
v0)
-- Data.Nat.Properties.<-irrelevant
d_'60''45'irrelevant_3038 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'60''45'irrelevant_3038 :: Integer
-> Integer -> T__'8804'__22 -> T__'8804'__22 -> T__'8801'__12
d_'60''45'irrelevant_3038 = Integer
-> Integer -> T__'8804'__22 -> T__'8804'__22 -> T__'8801'__12
forall a. a
erased
-- Data.Nat.Properties.<-resp₂-≡
d_'60''45'resp'8322''45''8801'_3040 ::
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'60''45'resp'8322''45''8801'_3040 :: T_Σ_14
d_'60''45'resp'8322''45''8801'_3040
  = (Any -> Any -> T_Σ_14) -> Any -> Any -> T_Σ_14
forall a b. a -> b
coe
      Any -> Any -> T_Σ_14
MAlonzo.Code.Agda.Builtin.Sigma.C__'44'__32
      ((Any -> Any -> Any -> Any -> Any -> Any) -> Any
forall a b. a -> b
coe (\ Any
v0 Any
v1 Any
v2 Any
v3 Any
v4 -> Any
v4)) ((Any -> Any -> Any -> Any -> Any -> Any) -> Any
forall a b. a -> b
coe (\ Any
v0 Any
v1 Any
v2 Any
v3 Any
v4 -> Any
v4))
-- Data.Nat.Properties.<-isStrictPartialOrder
d_'60''45'isStrictPartialOrder_3046 ::
  MAlonzo.Code.Relation.Binary.Structures.T_IsStrictPartialOrder_290
d_'60''45'isStrictPartialOrder_3046 :: T_IsStrictPartialOrder_290
d_'60''45'isStrictPartialOrder_3046
  = (T_IsEquivalence_26
 -> (Any -> Any -> Any -> Any -> Any -> Any)
 -> T_Σ_14
 -> T_IsStrictPartialOrder_290)
-> Any
-> (Any -> Any -> Any -> Any -> Any -> Any)
-> T_Σ_14
-> T_IsStrictPartialOrder_290
forall a b. a -> b
coe
      T_IsEquivalence_26
-> (Any -> Any -> Any -> Any -> Any -> Any)
-> T_Σ_14
-> T_IsStrictPartialOrder_290
MAlonzo.Code.Relation.Binary.Structures.C_IsStrictPartialOrder'46'constructor_14045
      (T_IsEquivalence_26 -> Any
forall a b. a -> b
coe
         T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.PropositionalEquality.Properties.du_isEquivalence_396)
      (\ Any
v0 Any
v1 Any
v2 Any
v3 Any
v4 -> (Integer -> T__'8804'__22 -> T__'8804'__22 -> T__'8804'__22)
-> Any -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> T__'8804'__22 -> T__'8804'__22 -> T__'8804'__22
du_'60''45'trans_2980 Any
v1 Any
v3 Any
v4)
      T_Σ_14
d_'60''45'resp'8322''45''8801'_3040
-- Data.Nat.Properties.<-isStrictTotalOrder
d_'60''45'isStrictTotalOrder_3048 ::
  MAlonzo.Code.Relation.Binary.Structures.T_IsStrictTotalOrder_534
d_'60''45'isStrictTotalOrder_3048 :: T_IsStrictTotalOrder_534
d_'60''45'isStrictTotalOrder_3048
  = (T_IsStrictTotalOrder'7580'_522 -> T_IsStrictTotalOrder_534)
-> Any -> T_IsStrictTotalOrder_534
forall a b. a -> b
coe
      T_IsStrictTotalOrder'7580'_522 -> T_IsStrictTotalOrder_534
MAlonzo.Code.Relation.Binary.Structures.Biased.du_isStrictTotalOrder'7580'_538
      ((T_IsEquivalence_26
 -> (Any -> Any -> Any -> Any -> Any -> Any)
 -> (Any -> Any -> T_Tri_158)
 -> T_IsStrictTotalOrder'7580'_522)
-> Any -> (Any -> Any -> Any -> Any -> Any -> Any) -> Any -> Any
forall a b. a -> b
coe
         T_IsEquivalence_26
-> (Any -> Any -> Any -> Any -> Any -> Any)
-> (Any -> Any -> T_Tri_158)
-> T_IsStrictTotalOrder'7580'_522
MAlonzo.Code.Relation.Binary.Structures.Biased.C_IsStrictTotalOrder'7580''46'constructor_6029
         (T_IsEquivalence_26 -> Any
forall a b. a -> b
coe
            T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.PropositionalEquality.Properties.du_isEquivalence_396)
         (\ Any
v0 Any
v1 Any
v2 Any
v3 Any
v4 -> (Integer -> T__'8804'__22 -> T__'8804'__22 -> T__'8804'__22)
-> Any -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> T__'8804'__22 -> T__'8804'__22 -> T__'8804'__22
du_'60''45'trans_2980 Any
v1 Any
v3 Any
v4)
         ((Integer -> Integer -> T_Tri_158) -> Any
forall a b. a -> b
coe Integer -> Integer -> T_Tri_158
d_'60''45'cmp_2998))
-- Data.Nat.Properties.<-strictPartialOrder
d_'60''45'strictPartialOrder_3050 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_StrictPartialOrder_556
d_'60''45'strictPartialOrder_3050 :: T_StrictPartialOrder_556
d_'60''45'strictPartialOrder_3050
  = (T_IsStrictPartialOrder_290 -> T_StrictPartialOrder_556)
-> T_IsStrictPartialOrder_290 -> T_StrictPartialOrder_556
forall a b. a -> b
coe
      T_IsStrictPartialOrder_290 -> T_StrictPartialOrder_556
MAlonzo.Code.Relation.Binary.Bundles.C_StrictPartialOrder'46'constructor_11097
      T_IsStrictPartialOrder_290
d_'60''45'isStrictPartialOrder_3046
-- Data.Nat.Properties.<-strictTotalOrder
d_'60''45'strictTotalOrder_3052 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_StrictTotalOrder_1036
d_'60''45'strictTotalOrder_3052 :: T_StrictTotalOrder_1036
d_'60''45'strictTotalOrder_3052
  = (T_IsStrictTotalOrder_534 -> T_StrictTotalOrder_1036)
-> T_IsStrictTotalOrder_534 -> T_StrictTotalOrder_1036
forall a b. a -> b
coe
      T_IsStrictTotalOrder_534 -> T_StrictTotalOrder_1036
MAlonzo.Code.Relation.Binary.Bundles.C_StrictTotalOrder'46'constructor_21059
      T_IsStrictTotalOrder_534
d_'60''45'isStrictTotalOrder_3048
-- Data.Nat.Properties.s<s-injective
d_s'60's'45'injective_3058 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_s'60's'45'injective_3058 :: Integer
-> Integer
-> T__'8804'__22
-> T__'8804'__22
-> T__'8801'__12
-> T__'8801'__12
d_s'60's'45'injective_3058 = Integer
-> Integer
-> T__'8804'__22
-> T__'8804'__22
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Nat.Properties.<-pred
d_'60''45'pred_3060 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_'60''45'pred_3060 :: Integer -> Integer -> T__'8804'__22 -> T__'8804'__22
d_'60''45'pred_3060 ~Integer
v0 ~Integer
v1 = T__'8804'__22 -> T__'8804'__22
du_'60''45'pred_3060
du_'60''45'pred_3060 ::
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
du_'60''45'pred_3060 :: T__'8804'__22 -> T__'8804'__22
du_'60''45'pred_3060
  = (T__'8804'__22 -> T__'8804'__22) -> T__'8804'__22 -> T__'8804'__22
forall a b. a -> b
coe T__'8804'__22 -> T__'8804'__22
MAlonzo.Code.Data.Nat.Base.du_s'60's'8315''185'_70
-- Data.Nat.Properties.m<n⇒m<1+n
d_m'60'n'8658'm'60'1'43'n_3062 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_m'60'n'8658'm'60'1'43'n_3062 :: Integer -> Integer -> T__'8804'__22 -> T__'8804'__22
d_m'60'n'8658'm'60'1'43'n_3062 ~Integer
v0 ~Integer
v1 T__'8804'__22
v2
  = T__'8804'__22 -> T__'8804'__22
du_m'60'n'8658'm'60'1'43'n_3062 T__'8804'__22
v2
du_m'60'n'8658'm'60'1'43'n_3062 ::
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
du_m'60'n'8658'm'60'1'43'n_3062 :: T__'8804'__22 -> T__'8804'__22
du_m'60'n'8658'm'60'1'43'n_3062 T__'8804'__22
v0
  = case T__'8804'__22 -> T__'8804'__22
forall a b. a -> b
coe T__'8804'__22
v0 of
      MAlonzo.Code.Data.Nat.Base.C_s'8804's_34 T__'8804'__22
v3
        -> case T__'8804'__22 -> T__'8804'__22
forall a b. a -> b
coe T__'8804'__22
v3 of
             T__'8804'__22
MAlonzo.Code.Data.Nat.Base.C_z'8804'n_26
               -> (T__'8804'__22 -> T__'8804'__22) -> Any -> T__'8804'__22
forall a b. a -> b
coe
                    T__'8804'__22 -> T__'8804'__22
MAlonzo.Code.Data.Nat.Base.C_s'8804's_34
                    (T__'8804'__22 -> Any
forall a b. a -> b
coe T__'8804'__22
MAlonzo.Code.Data.Nat.Base.C_z'8804'n_26)
             MAlonzo.Code.Data.Nat.Base.C_s'8804's_34 T__'8804'__22
v6
               -> (T__'8804'__22 -> T__'8804'__22) -> Any -> T__'8804'__22
forall a b. a -> b
coe
                    T__'8804'__22 -> T__'8804'__22
MAlonzo.Code.Data.Nat.Base.C_s'8804's_34
                    ((T__'8804'__22 -> T__'8804'__22) -> Any -> Any
forall a b. a -> b
coe
                       T__'8804'__22 -> T__'8804'__22
du_m'60'n'8658'm'60'1'43'n_3062
                       ((T__'8804'__22 -> T__'8804'__22) -> T__'8804'__22 -> Any
forall a b. a -> b
coe T__'8804'__22 -> T__'8804'__22
MAlonzo.Code.Data.Nat.Base.C_s'8804's_34 T__'8804'__22
v6))
             T__'8804'__22
_ -> T__'8804'__22
forall a. a
MAlonzo.RTE.mazUnreachableError
      T__'8804'__22
_ -> T__'8804'__22
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Data.Nat.Properties.n≮0
d_n'8814'0_3066 ::
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Irrelevant.T_Irrelevant_20
d_n'8814'0_3066 :: Integer -> T__'8804'__22 -> T_Irrelevant_20
d_n'8814'0_3066 = Integer -> T__'8804'__22 -> T_Irrelevant_20
forall a. a
erased
-- Data.Nat.Properties.n≮n
d_n'8814'n_3070 ::
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Irrelevant.T_Irrelevant_20
d_n'8814'n_3070 :: Integer -> T__'8804'__22 -> T_Irrelevant_20
d_n'8814'n_3070 = Integer -> T__'8804'__22 -> T_Irrelevant_20
forall a. a
erased
-- Data.Nat.Properties.0<1+n
d_0'60'1'43'n_3074 ::
  Integer -> MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_0'60'1'43'n_3074 :: Integer -> T__'8804'__22
d_0'60'1'43'n_3074 ~Integer
v0 = T__'8804'__22
du_0'60'1'43'n_3074
du_0'60'1'43'n_3074 :: MAlonzo.Code.Data.Nat.Base.T__'8804'__22
du_0'60'1'43'n_3074 :: T__'8804'__22
du_0'60'1'43'n_3074
  = (T__'8804'__22 -> T__'8804'__22) -> Any -> T__'8804'__22
forall a b. a -> b
coe
      T__'8804'__22 -> T__'8804'__22
MAlonzo.Code.Data.Nat.Base.C_s'8804's_34
      (T__'8804'__22 -> Any
forall a b. a -> b
coe T__'8804'__22
MAlonzo.Code.Data.Nat.Base.C_z'8804'n_26)
-- Data.Nat.Properties.n<1+n
d_n'60'1'43'n_3078 ::
  Integer -> MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_n'60'1'43'n_3078 :: Integer -> T__'8804'__22
d_n'60'1'43'n_3078 Integer
v0
  = (Integer -> T__'8804'__22) -> Any -> T__'8804'__22
forall a b. a -> b
coe
      Integer -> T__'8804'__22
d_'8804''45'refl_2776 ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> Integer
addInt (Integer -> Any
forall a b. a -> b
coe (Integer
1 :: Integer)) (Integer -> Any
forall a b. a -> b
coe Integer
v0))
-- Data.Nat.Properties.n<1⇒n≡0
d_n'60'1'8658'n'8801'0_3082 ::
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_n'60'1'8658'n'8801'0_3082 :: Integer -> T__'8804'__22 -> T__'8801'__12
d_n'60'1'8658'n'8801'0_3082 = Integer -> T__'8804'__22 -> T__'8801'__12
forall a. a
erased
-- Data.Nat.Properties.n>0⇒n≢0
d_n'62'0'8658'n'8802'0_3086 ::
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Data.Irrelevant.T_Irrelevant_20
d_n'62'0'8658'n'8802'0_3086 :: Integer -> T__'8804'__22 -> T__'8801'__12 -> T_Irrelevant_20
d_n'62'0'8658'n'8802'0_3086 = Integer -> T__'8804'__22 -> T__'8801'__12 -> T_Irrelevant_20
forall a. a
erased
-- Data.Nat.Properties.n≢0⇒n>0
d_n'8802'0'8658'n'62'0_3090 ::
  Integer ->
  (MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
   MAlonzo.Code.Data.Irrelevant.T_Irrelevant_20) ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_n'8802'0'8658'n'62'0_3090 :: Integer -> (T__'8801'__12 -> T_Irrelevant_20) -> T__'8804'__22
d_n'8802'0'8658'n'62'0_3090 Integer
v0 ~T__'8801'__12 -> T_Irrelevant_20
v1
  = Integer -> T__'8804'__22
du_n'8802'0'8658'n'62'0_3090 Integer
v0
du_n'8802'0'8658'n'62'0_3090 ::
  Integer -> MAlonzo.Code.Data.Nat.Base.T__'8804'__22
du_n'8802'0'8658'n'62'0_3090 :: Integer -> T__'8804'__22
du_n'8802'0'8658'n'62'0_3090 Integer
v0
  = case Integer -> Integer
forall a b. a -> b
coe Integer
v0 of
      Integer
0 -> ((Any -> T_Irrelevant_20) -> Any) -> Any -> T__'8804'__22
forall a b. a -> b
coe
             (Any -> T_Irrelevant_20) -> Any
MAlonzo.Code.Relation.Nullary.Negation.Core.du_contradiction_44
             Any
forall a. a
erased
      Integer
_ -> T__'8804'__22 -> T__'8804'__22
forall a b. a -> b
coe T__'8804'__22
du_0'60'1'43'n_3074
-- Data.Nat.Properties.m<n⇒0<n
d_m'60'n'8658'0'60'n_3096 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_m'60'n'8658'0'60'n_3096 :: Integer -> Integer -> T__'8804'__22 -> T__'8804'__22
d_m'60'n'8658'0'60'n_3096 ~Integer
v0 ~Integer
v1 = T__'8804'__22 -> T__'8804'__22
du_m'60'n'8658'0'60'n_3096
du_m'60'n'8658'0'60'n_3096 ::
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
du_m'60'n'8658'0'60'n_3096 :: T__'8804'__22 -> T__'8804'__22
du_m'60'n'8658'0'60'n_3096
  = (T__'8804'__22 -> T__'8804'__22 -> T__'8804'__22)
-> Any -> T__'8804'__22 -> T__'8804'__22
forall a b. a -> b
coe T__'8804'__22 -> T__'8804'__22 -> T__'8804'__22
du_'8804''45'trans_2784 (T__'8804'__22 -> Any
forall a b. a -> b
coe T__'8804'__22
du_0'60'1'43'n_3074)
-- Data.Nat.Properties.m<n⇒n≢0
d_m'60'n'8658'n'8802'0_3098 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Data.Irrelevant.T_Irrelevant_20
d_m'60'n'8658'n'8802'0_3098 :: Integer
-> Integer -> T__'8804'__22 -> T__'8801'__12 -> T_Irrelevant_20
d_m'60'n'8658'n'8802'0_3098 = Integer
-> Integer -> T__'8804'__22 -> T__'8801'__12 -> T_Irrelevant_20
forall a. a
erased
-- Data.Nat.Properties.m<n⇒m≤1+n
d_m'60'n'8658'm'8804'1'43'n_3102 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_m'60'n'8658'm'8804'1'43'n_3102 :: Integer -> Integer -> T__'8804'__22 -> T__'8804'__22
d_m'60'n'8658'm'8804'1'43'n_3102 ~Integer
v0 ~Integer
v1 T__'8804'__22
v2
  = T__'8804'__22 -> T__'8804'__22
du_m'60'n'8658'm'8804'1'43'n_3102 T__'8804'__22
v2
du_m'60'n'8658'm'8804'1'43'n_3102 ::
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
du_m'60'n'8658'm'8804'1'43'n_3102 :: T__'8804'__22 -> T__'8804'__22
du_m'60'n'8658'm'8804'1'43'n_3102 T__'8804'__22
v0
  = (T__'8804'__22 -> T__'8804'__22) -> Any -> T__'8804'__22
forall a b. a -> b
coe T__'8804'__22 -> T__'8804'__22
du_'60''8658''8804'_2854 (T__'8804'__22 -> Any
forall a b. a -> b
coe T__'8804'__22
v0)
-- Data.Nat.Properties.m<1+n⇒m<n∨m≡n
d_m'60'1'43'n'8658'm'60'n'8744'm'8801'n_3108 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Sum.Base.T__'8846'__30
d_m'60'1'43'n'8658'm'60'n'8744'm'8801'n_3108 :: Integer -> Integer -> T__'8804'__22 -> T__'8846'__30
d_m'60'1'43'n'8658'm'60'n'8744'm'8801'n_3108 Integer
v0 Integer
v1 T__'8804'__22
v2
  = case Integer -> Integer
forall a b. a -> b
coe Integer
v0 of
      Integer
0 -> case Integer -> Integer
forall a b. a -> b
coe Integer
v1 of
             Integer
0 -> (Any -> T__'8846'__30) -> Any -> T__'8846'__30
forall a b. a -> b
coe Any -> T__'8846'__30
MAlonzo.Code.Data.Sum.Base.C_inj'8322'_42 Any
forall a. a
erased
             Integer
_ -> (Any -> T__'8846'__30) -> Any -> T__'8846'__30
forall a b. a -> b
coe
                    Any -> T__'8846'__30
MAlonzo.Code.Data.Sum.Base.C_inj'8321'_38 (T__'8804'__22 -> Any
forall a b. a -> b
coe T__'8804'__22
du_0'60'1'43'n_3074)
      Integer
_ -> let v3 :: Integer
v3 = Integer -> Integer -> Integer
subInt (Integer -> Integer
forall a b. a -> b
coe Integer
v0) (Integer -> Integer
forall a b. a -> b
coe (Integer
1 :: Integer)) in
           Any -> T__'8846'__30
forall a b. a -> b
coe
             (case T__'8804'__22 -> T__'8804'__22
forall a b. a -> b
coe T__'8804'__22
v2 of
                MAlonzo.Code.Data.Nat.Base.C_s'8804's_34 T__'8804'__22
v6
                  -> let v7 :: Integer
v7 = Integer -> Integer -> Integer
subInt (Integer -> Integer
forall a b. a -> b
coe Integer
v1) (Integer -> Integer
forall a b. a -> b
coe (Integer
1 :: Integer)) in
                     Any -> Any
forall a b. a -> b
coe
                       (((Any -> Any) -> (Any -> Any) -> T__'8846'__30 -> T__'8846'__30)
-> Any -> Any -> T__'8846'__30 -> Any
forall a b. a -> b
coe
                          (Any -> Any) -> (Any -> Any) -> T__'8846'__30 -> T__'8846'__30
MAlonzo.Code.Data.Sum.Base.du_map_84
                          ((T__'8804'__22 -> T__'8804'__22) -> Any
forall a b. a -> b
coe T__'8804'__22 -> T__'8804'__22
MAlonzo.Code.Data.Nat.Base.C_s'8804's_34) Any
forall a. a
erased
                          (Integer -> Integer -> T__'8804'__22 -> T__'8846'__30
d_m'60'1'43'n'8658'm'60'n'8744'm'8801'n_3108
                             (Integer -> Integer
forall a b. a -> b
coe Integer
v3) (Integer -> Integer
forall a b. a -> b
coe Integer
v7) (T__'8804'__22 -> T__'8804'__22
forall a b. a -> b
coe T__'8804'__22
v6)))
                T__'8804'__22
_ -> Any
forall a. a
MAlonzo.RTE.mazUnreachableError)
-- Data.Nat.Properties.m≤n⇒m<n∨m≡n
d_m'8804'n'8658'm'60'n'8744'm'8801'n_3118 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Sum.Base.T__'8846'__30
d_m'8804'n'8658'm'60'n'8744'm'8801'n_3118 :: Integer -> Integer -> T__'8804'__22 -> T__'8846'__30
d_m'8804'n'8658'm'60'n'8744'm'8801'n_3118 Integer
v0 Integer
v1 T__'8804'__22
v2
  = (Integer -> Integer -> T__'8804'__22 -> T__'8846'__30)
-> Any -> Any -> Any -> T__'8846'__30
forall a b. a -> b
coe
      Integer -> Integer -> T__'8804'__22 -> T__'8846'__30
d_m'60'1'43'n'8658'm'60'n'8744'm'8801'n_3108 (Integer -> Any
forall a b. a -> b
coe Integer
v0) (Integer -> Any
forall a b. a -> b
coe Integer
v1)
      ((T__'8804'__22 -> T__'8804'__22) -> T__'8804'__22 -> Any
forall a b. a -> b
coe T__'8804'__22 -> T__'8804'__22
MAlonzo.Code.Data.Nat.Base.C_s'8804's_34 T__'8804'__22
v2)
-- Data.Nat.Properties.m<1+n⇒m≤n
d_m'60'1'43'n'8658'm'8804'n_3122 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_m'60'1'43'n'8658'm'8804'n_3122 :: Integer -> Integer -> T__'8804'__22 -> T__'8804'__22
d_m'60'1'43'n'8658'm'8804'n_3122 ~Integer
v0 ~Integer
v1 T__'8804'__22
v2
  = T__'8804'__22 -> T__'8804'__22
du_m'60'1'43'n'8658'm'8804'n_3122 T__'8804'__22
v2
du_m'60'1'43'n'8658'm'8804'n_3122 ::
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
du_m'60'1'43'n'8658'm'8804'n_3122 :: T__'8804'__22 -> T__'8804'__22
du_m'60'1'43'n'8658'm'8804'n_3122 T__'8804'__22
v0
  = case T__'8804'__22 -> T__'8804'__22
forall a b. a -> b
coe T__'8804'__22
v0 of
      MAlonzo.Code.Data.Nat.Base.C_s'8804's_34 T__'8804'__22
v3 -> T__'8804'__22 -> T__'8804'__22
forall a b. a -> b
coe T__'8804'__22
v3
      T__'8804'__22
_ -> T__'8804'__22
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Data.Nat.Properties.∀[m≤n⇒m≢o]⇒n<o
d_'8704''91'm'8804'n'8658'm'8802'o'93''8658'n'60'o_3132 ::
  Integer ->
  Integer ->
  (Integer ->
   MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
   MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
   MAlonzo.Code.Data.Irrelevant.T_Irrelevant_20) ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_'8704''91'm'8804'n'8658'm'8802'o'93''8658'n'60'o_3132 :: Integer
-> Integer
-> (Integer -> T__'8804'__22 -> T__'8801'__12 -> T_Irrelevant_20)
-> T__'8804'__22
d_'8704''91'm'8804'n'8658'm'8802'o'93''8658'n'60'o_3132 Integer
v0 Integer
v1 ~Integer -> T__'8804'__22 -> T__'8801'__12 -> T_Irrelevant_20
v2
  = Integer -> Integer -> T__'8804'__22
du_'8704''91'm'8804'n'8658'm'8802'o'93''8658'n'60'o_3132 Integer
v0 Integer
v1
du_'8704''91'm'8804'n'8658'm'8802'o'93''8658'n'60'o_3132 ::
  Integer -> Integer -> MAlonzo.Code.Data.Nat.Base.T__'8804'__22
du_'8704''91'm'8804'n'8658'm'8802'o'93''8658'n'60'o_3132 :: Integer -> Integer -> T__'8804'__22
du_'8704''91'm'8804'n'8658'm'8802'o'93''8658'n'60'o_3132 Integer
v0 Integer
v1
  = case Integer -> Integer
forall a b. a -> b
coe Integer
v1 of
      Integer
0 -> ((Any -> T_Irrelevant_20) -> Any) -> Any -> T__'8804'__22
forall a b. a -> b
coe
             (Any -> T_Irrelevant_20) -> Any
MAlonzo.Code.Relation.Nullary.Negation.Core.du_contradiction_44
             Any
forall a. a
erased
      Integer
_ -> let v2 :: Integer
v2 = Integer -> Integer -> Integer
subInt (Integer -> Integer
forall a b. a -> b
coe Integer
v1) (Integer -> Integer
forall a b. a -> b
coe (Integer
1 :: Integer)) in
           Any -> T__'8804'__22
forall a b. a -> b
coe
             (case Integer -> Integer
forall a b. a -> b
coe Integer
v0 of
                Integer
0 -> T__'8804'__22 -> Any
forall a b. a -> b
coe T__'8804'__22
du_0'60'1'43'n_3074
                Integer
_ -> let v3 :: Integer
v3 = Integer -> Integer -> Integer
subInt (Integer -> Integer
forall a b. a -> b
coe Integer
v0) (Integer -> Integer
forall a b. a -> b
coe (Integer
1 :: Integer)) in
                     Any -> Any
forall a b. a -> b
coe
                       ((T__'8804'__22 -> T__'8804'__22) -> Any -> Any
forall a b. a -> b
coe
                          T__'8804'__22 -> T__'8804'__22
MAlonzo.Code.Data.Nat.Base.C_s'8804's_34
                          ((Integer -> Integer -> T__'8804'__22) -> Any -> Any -> Any
forall a b. a -> b
coe
                             Integer -> Integer -> T__'8804'__22
du_'8704''91'm'8804'n'8658'm'8802'o'93''8658'n'60'o_3132 (Integer -> Any
forall a b. a -> b
coe Integer
v3)
                             (Integer -> Any
forall a b. a -> b
coe Integer
v2))))
-- Data.Nat.Properties._.rec
d_rec_3150 ::
  Integer ->
  Integer ->
  (Integer ->
   MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
   MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
   MAlonzo.Code.Data.Irrelevant.T_Irrelevant_20) ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Data.Irrelevant.T_Irrelevant_20
d_rec_3150 :: Integer
-> Integer
-> (Integer -> T__'8804'__22 -> T__'8801'__12 -> T_Irrelevant_20)
-> Integer
-> T__'8804'__22
-> T__'8801'__12
-> T_Irrelevant_20
d_rec_3150 = Integer
-> Integer
-> (Integer -> T__'8804'__22 -> T__'8801'__12 -> T_Irrelevant_20)
-> Integer
-> T__'8804'__22
-> T__'8801'__12
-> T_Irrelevant_20
forall a. a
erased
-- Data.Nat.Properties.∀[m<n⇒m≢o]⇒n≤o
d_'8704''91'm'60'n'8658'm'8802'o'93''8658'n'8804'o_3160 ::
  Integer ->
  Integer ->
  (Integer ->
   MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
   MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
   MAlonzo.Code.Data.Irrelevant.T_Irrelevant_20) ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_'8704''91'm'60'n'8658'm'8802'o'93''8658'n'8804'o_3160 :: Integer
-> Integer
-> (Integer -> T__'8804'__22 -> T__'8801'__12 -> T_Irrelevant_20)
-> T__'8804'__22
d_'8704''91'm'60'n'8658'm'8802'o'93''8658'n'8804'o_3160 Integer
v0 Integer
v1 ~Integer -> T__'8804'__22 -> T__'8801'__12 -> T_Irrelevant_20
v2
  = Integer -> Integer -> T__'8804'__22
du_'8704''91'm'60'n'8658'm'8802'o'93''8658'n'8804'o_3160 Integer
v0 Integer
v1
du_'8704''91'm'60'n'8658'm'8802'o'93''8658'n'8804'o_3160 ::
  Integer -> Integer -> MAlonzo.Code.Data.Nat.Base.T__'8804'__22
du_'8704''91'm'60'n'8658'm'8802'o'93''8658'n'8804'o_3160 :: Integer -> Integer -> T__'8804'__22
du_'8704''91'm'60'n'8658'm'8802'o'93''8658'n'8804'o_3160 Integer
v0 Integer
v1
  = case Integer -> Integer
forall a b. a -> b
coe Integer
v0 of
      Integer
0 -> T__'8804'__22 -> T__'8804'__22
forall a b. a -> b
coe T__'8804'__22
MAlonzo.Code.Data.Nat.Base.C_z'8804'n_26
      Integer
_ -> let v2 :: Integer
v2 = Integer -> Integer -> Integer
subInt (Integer -> Integer
forall a b. a -> b
coe Integer
v0) (Integer -> Integer
forall a b. a -> b
coe (Integer
1 :: Integer)) in
           Any -> T__'8804'__22
forall a b. a -> b
coe
             (case Integer -> Integer
forall a b. a -> b
coe Integer
v1 of
                Integer
0 -> ((Any -> T_Irrelevant_20) -> Any) -> Any -> Any
forall a b. a -> b
coe
                       (Any -> T_Irrelevant_20) -> Any
MAlonzo.Code.Relation.Nullary.Negation.Core.du_contradiction_44
                       Any
forall a. a
erased
                Integer
_ -> let v3 :: Integer
v3 = Integer -> Integer -> Integer
subInt (Integer -> Integer
forall a b. a -> b
coe Integer
v1) (Integer -> Integer
forall a b. a -> b
coe (Integer
1 :: Integer)) in
                     Any -> Any
forall a b. a -> b
coe
                       ((T__'8804'__22 -> T__'8804'__22) -> Any -> Any
forall a b. a -> b
coe
                          T__'8804'__22 -> T__'8804'__22
MAlonzo.Code.Data.Nat.Base.C_s'8804's_34
                          ((Integer -> Integer -> T__'8804'__22) -> Any -> Any -> Any
forall a b. a -> b
coe
                             Integer -> Integer -> T__'8804'__22
du_'8704''91'm'60'n'8658'm'8802'o'93''8658'n'8804'o_3160 (Integer -> Any
forall a b. a -> b
coe Integer
v2)
                             (Integer -> Any
forall a b. a -> b
coe Integer
v3))))
-- Data.Nat.Properties._.rec
d_rec_3180 ::
  Integer ->
  Integer ->
  (Integer ->
   MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
   MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
   MAlonzo.Code.Data.Irrelevant.T_Irrelevant_20) ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Data.Irrelevant.T_Irrelevant_20
d_rec_3180 :: Integer
-> Integer
-> (Integer -> T__'8804'__22 -> T__'8801'__12 -> T_Irrelevant_20)
-> Integer
-> T__'8804'__22
-> T__'8801'__12
-> T_Irrelevant_20
d_rec_3180 = Integer
-> Integer
-> (Integer -> T__'8804'__22 -> T__'8801'__12 -> T_Irrelevant_20)
-> Integer
-> T__'8804'__22
-> T__'8801'__12
-> T_Irrelevant_20
forall a. a
erased
-- Data.Nat.Properties.≤-Reasoning._._IsRelatedTo_
d__IsRelatedTo__3188 :: p -> p -> ()
d__IsRelatedTo__3188 p
a0 p
a1 = ()
-- Data.Nat.Properties.≤-Reasoning._._∎
d__'8718'_3190 ::
  Integer ->
  MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.T__IsRelatedTo__78
d__'8718'_3190 :: Integer -> T__IsRelatedTo__78
d__'8718'_3190
  = let v0 :: T_IsPreorder_70
v0 = T_IsPreorder_70
d_'8804''45'isPreorder_2810 in
    Any -> Integer -> T__IsRelatedTo__78
forall a b. a -> b
coe
      (((Any -> Any) -> Any -> Any) -> Any -> Any
forall a b. a -> b
coe
         (Any -> Any) -> Any -> Any
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du__'8718'_492
         ((T_IsPreorder_70 -> Any -> T__IsRelatedTo__78) -> Any -> Any
forall a b. a -> b
coe
            T_IsPreorder_70 -> Any -> T__IsRelatedTo__78
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_stop_166
            (T_IsPreorder_70 -> Any
forall a b. a -> b
coe T_IsPreorder_70
v0)))
-- Data.Nat.Properties.≤-Reasoning._.<-go
d_'60''45'go_3192 ::
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.T__IsRelatedTo__78 ->
  MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.T__IsRelatedTo__78
d_'60''45'go_3192 :: Integer
-> Integer
-> Integer
-> T__'8804'__22
-> T__IsRelatedTo__78
-> T__IsRelatedTo__78
d_'60''45'go_3192
  = ((Any -> Any -> Any -> Any -> Any -> Any)
 -> T_Σ_14
 -> (Any -> Any -> Any -> Any -> Any -> Any)
 -> Any
 -> Any
 -> Any
 -> Any
 -> T__IsRelatedTo__78
 -> T__IsRelatedTo__78)
-> (Any -> Any -> Any -> Any -> Any -> Any)
-> Any
-> (Any -> Any -> Any -> Any -> Any -> Any)
-> Integer
-> Integer
-> Integer
-> T__'8804'__22
-> T__IsRelatedTo__78
-> T__IsRelatedTo__78
forall a b. a -> b
coe
      (Any -> Any -> Any -> Any -> Any -> Any)
-> T_Σ_14
-> (Any -> Any -> Any -> Any -> Any -> Any)
-> Any
-> Any
-> Any
-> Any
-> T__IsRelatedTo__78
-> T__IsRelatedTo__78
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_'60''45'go_152
      (\ Any
v0 Any
v1 Any
v2 Any
v3 Any
v4 -> (Integer -> T__'8804'__22 -> T__'8804'__22 -> T__'8804'__22)
-> Any -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> T__'8804'__22 -> T__'8804'__22 -> T__'8804'__22
du_'60''45'trans_2980 Any
v1 Any
v3 Any
v4)
      (T_Σ_14 -> Any
forall a b. a -> b
coe
         T_Σ_14
MAlonzo.Code.Relation.Binary.PropositionalEquality.Core.du_resp'8322'_160)
      (\ Any
v0 Any
v1 Any
v2 Any
v3 Any
v4 -> (T__'8804'__22 -> T__'8804'__22 -> T__'8804'__22)
-> Any -> Any -> Any
forall a b. a -> b
coe T__'8804'__22 -> T__'8804'__22 -> T__'8804'__22
du_'60''45''8804''45'trans_2992 Any
v3 Any
v4)
-- Data.Nat.Properties.≤-Reasoning._.IsEquality
d_IsEquality_3194 :: p -> p -> p -> ()
d_IsEquality_3194 p
a0 p
a1 p
a2 = ()
-- Data.Nat.Properties.≤-Reasoning._.IsEquality?
d_IsEquality'63'_3196 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.T__IsRelatedTo__78 ->
  MAlonzo.Code.Relation.Nullary.Decidable.Core.T_Dec_20
d_IsEquality'63'_3196 :: Integer -> Integer -> T__IsRelatedTo__78 -> T_Dec_20
d_IsEquality'63'_3196 Integer
v0 Integer
v1 T__IsRelatedTo__78
v2
  = (T__IsRelatedTo__78 -> T_Dec_20) -> T__IsRelatedTo__78 -> T_Dec_20
forall a b. a -> b
coe
      T__IsRelatedTo__78 -> T_Dec_20
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_IsEquality'63'_224
      T__IsRelatedTo__78
v2
-- Data.Nat.Properties.≤-Reasoning._.IsStrict
d_IsStrict_3198 :: p -> p -> p -> ()
d_IsStrict_3198 p
a0 p
a1 p
a2 = ()
-- Data.Nat.Properties.≤-Reasoning._.IsStrict?
d_IsStrict'63'_3200 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.T__IsRelatedTo__78 ->
  MAlonzo.Code.Relation.Nullary.Decidable.Core.T_Dec_20
d_IsStrict'63'_3200 :: Integer -> Integer -> T__IsRelatedTo__78 -> T_Dec_20
d_IsStrict'63'_3200 Integer
v0 Integer
v1 T__IsRelatedTo__78
v2
  = (T__IsRelatedTo__78 -> T_Dec_20) -> T__IsRelatedTo__78 -> T_Dec_20
forall a b. a -> b
coe
      T__IsRelatedTo__78 -> T_Dec_20
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_IsStrict'63'_188
      T__IsRelatedTo__78
v2
-- Data.Nat.Properties.≤-Reasoning._.begin_
d_begin__3202 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.T__IsRelatedTo__78 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_begin__3202 :: Integer -> Integer -> T__IsRelatedTo__78 -> T__'8804'__22
d_begin__3202
  = let v0 :: T_IsPreorder_70
v0 = T_IsPreorder_70
d_'8804''45'isPreorder_2810 in
    Any -> Integer -> Integer -> T__IsRelatedTo__78 -> T__'8804'__22
forall a b. a -> b
coe
      (let v1 :: p -> p -> t -> t
v1 = \ p
v1 p
v2 t
v3 -> (T__'8804'__22 -> T__'8804'__22) -> t -> t
forall a b. a -> b
coe T__'8804'__22 -> T__'8804'__22
du_'60''8658''8804'_2854 t
v3 in
       Any -> Any
forall a b. a -> b
coe
         (((Any -> Any -> Any -> Any) -> Any -> Any -> Any -> Any)
-> Any -> Any
forall a b. a -> b
coe
            (Any -> Any -> Any -> Any) -> Any -> Any -> Any -> Any
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_begin__46
            ((T_IsPreorder_70
 -> (Any -> Any -> Any -> Any)
 -> Any
 -> Any
 -> T__IsRelatedTo__78
 -> Any)
-> Any -> Any -> Any
forall a b. a -> b
coe
               T_IsPreorder_70
-> (Any -> Any -> Any -> Any)
-> Any
-> Any
-> T__IsRelatedTo__78
-> Any
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_start_96
               (T_IsPreorder_70 -> Any
forall a b. a -> b
coe T_IsPreorder_70
v0) ((Any -> Any -> Any -> Any) -> Any
forall a b. a -> b
coe Any -> Any -> Any -> Any
forall {p} {p} {t} {t}. p -> p -> t -> t
v1))))
-- Data.Nat.Properties.≤-Reasoning._.begin-contradiction_
d_begin'45'contradiction__3204 ::
  Integer ->
  MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.T__IsRelatedTo__78 ->
  AgdaAny -> MAlonzo.Code.Agda.Primitive.T_Level_18 -> () -> AgdaAny
d_begin'45'contradiction__3204 :: Integer -> T__IsRelatedTo__78 -> Any -> () -> () -> Any
d_begin'45'contradiction__3204 Integer
v0 T__IsRelatedTo__78
v1 Any
v2 ()
v3 ()
v4
  = Any -> Any
forall a b. a -> b
coe
      Any
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_begin'45'contradiction__246
-- Data.Nat.Properties.≤-Reasoning._.begin_
d_begin__3206 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.T__IsRelatedTo__78 ->
  AgdaAny -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_begin__3206 :: Integer -> Integer -> T__IsRelatedTo__78 -> Any -> T__'8801'__12
d_begin__3206 = Integer -> Integer -> T__IsRelatedTo__78 -> Any -> T__'8801'__12
forall a. a
erased
-- Data.Nat.Properties.≤-Reasoning._.begin_
d_begin__3208 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.T__IsRelatedTo__78 ->
  AgdaAny -> MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_begin__3208 :: Integer -> Integer -> T__IsRelatedTo__78 -> Any -> T__'8804'__22
d_begin__3208
  = let v0 :: b
v0
          = T_SubRelation_60 -> b
forall a b. a -> b
coe
              T_SubRelation_60
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_strictRelation_202 in
    (Any -> Any -> Any -> Any -> Any)
-> Integer -> Integer -> T__IsRelatedTo__78 -> Any -> T__'8804'__22
forall a b. a -> b
coe
      (\ Any
v1 Any
v2 Any
v3 Any
v4 ->
         (T_SubRelation_60 -> Any -> Any -> Any -> Any)
-> Any -> Any -> Any -> Any -> Any
forall a b. a -> b
coe
           T_SubRelation_60 -> Any -> Any -> Any -> Any
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_begin__126
           (Any -> Any
forall a b. a -> b
coe Any
forall a. a
v0) Any
v1 Any
v2 Any
v3)
-- Data.Nat.Properties.≤-Reasoning._.eqRelation
d_eqRelation_3210 ::
  MAlonzo.Code.Relation.Binary.Reasoning.Syntax.T_SubRelation_60
d_eqRelation_3210 :: T_SubRelation_60
d_eqRelation_3210
  = T_SubRelation_60 -> T_SubRelation_60
forall a b. a -> b
coe
      T_SubRelation_60
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_eqRelation_238
-- Data.Nat.Properties.≤-Reasoning._.extractEquality
d_extractEquality_3214 ::
  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_3214 :: Integer
-> Integer
-> T__IsRelatedTo__78
-> T_IsEquality_208
-> T__'8801'__12
d_extractEquality_3214 = Integer
-> Integer
-> T__IsRelatedTo__78
-> T_IsEquality_208
-> T__'8801'__12
forall a. a
erased
-- Data.Nat.Properties.≤-Reasoning._.extractStrict
d_extractStrict_3216 ::
  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.Nat.Base.T__'8804'__22
d_extractStrict_3216 :: Integer
-> Integer -> T__IsRelatedTo__78 -> T_IsStrict_172 -> T__'8804'__22
d_extractStrict_3216 Integer
v0 Integer
v1 T__IsRelatedTo__78
v2 T_IsStrict_172
v3
  = (T__IsRelatedTo__78 -> T_IsStrict_172 -> Any)
-> T__IsRelatedTo__78 -> T_IsStrict_172 -> T__'8804'__22
forall a b. a -> b
coe
      T__IsRelatedTo__78 -> T_IsStrict_172 -> Any
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_extractStrict_198
      T__IsRelatedTo__78
v2 T_IsStrict_172
v3
-- Data.Nat.Properties.≤-Reasoning._.start
d_start_3224 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.T__IsRelatedTo__78 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_start_3224 :: Integer -> Integer -> T__IsRelatedTo__78 -> T__'8804'__22
d_start_3224
  = (T_IsPreorder_70
 -> (Any -> Any -> Any -> Any)
 -> Any
 -> Any
 -> T__IsRelatedTo__78
 -> Any)
-> Any
-> (Any -> Any -> Any -> Any)
-> Integer
-> Integer
-> T__IsRelatedTo__78
-> T__'8804'__22
forall a b. a -> b
coe
      T_IsPreorder_70
-> (Any -> Any -> Any -> Any)
-> Any
-> Any
-> T__IsRelatedTo__78
-> Any
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_start_96
      (T_IsPreorder_70 -> Any
forall a b. a -> b
coe T_IsPreorder_70
d_'8804''45'isPreorder_2810)
      (\ Any
v0 Any
v1 Any
v2 -> (T__'8804'__22 -> T__'8804'__22) -> Any -> Any
forall a b. a -> b
coe T__'8804'__22 -> T__'8804'__22
du_'60''8658''8804'_2854 Any
v2)
-- Data.Nat.Properties.≤-Reasoning._.step-<
d_step'45''60'_3226 ::
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.T__IsRelatedTo__78 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.T__IsRelatedTo__78
d_step'45''60'_3226 :: Integer
-> Integer
-> Integer
-> T__IsRelatedTo__78
-> T__'8804'__22
-> T__IsRelatedTo__78
d_step'45''60'_3226
  = let v0 :: p -> t -> p -> t -> t -> t
v0
          = \ p
v0 t
v1 p
v2 t
v3 t
v4 -> (Integer -> T__'8804'__22 -> T__'8804'__22 -> T__'8804'__22)
-> t -> t -> t -> t
forall a b. a -> b
coe Integer -> T__'8804'__22 -> T__'8804'__22 -> T__'8804'__22
du_'60''45'trans_2980 t
v1 t
v3 t
v4 in
    Any
-> Integer
-> Integer
-> Integer
-> T__IsRelatedTo__78
-> T__'8804'__22
-> T__IsRelatedTo__78
forall a b. a -> b
coe
      (let v1 :: b
v1
             = T_Σ_14 -> b
forall a b. a -> b
coe
                 T_Σ_14
MAlonzo.Code.Relation.Binary.PropositionalEquality.Core.du_resp'8322'_160 in
       Any -> Any
forall a b. a -> b
coe
         (let v2 :: p -> p -> p -> t -> t -> t
v2
                = \ p
v2 p
v3 p
v4 t
v5 t
v6 -> (T__'8804'__22 -> T__'8804'__22 -> T__'8804'__22) -> t -> t -> t
forall a b. a -> b
coe T__'8804'__22 -> T__'8804'__22 -> T__'8804'__22
du_'60''45''8804''45'trans_2992 t
v5 t
v6 in
          Any -> Any
forall a b. a -> b
coe
            (((Any -> Any -> Any -> Any -> Any -> Any)
 -> Any -> Any -> Any -> Any -> Any -> Any)
-> Any -> Any
forall a b. a -> b
coe
               (Any -> Any -> Any -> Any -> Any -> Any)
-> Any -> Any -> Any -> Any -> Any -> Any
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''60'_312
               (((Any -> Any -> Any -> Any -> Any -> Any)
 -> T_Σ_14
 -> (Any -> Any -> Any -> Any -> Any -> Any)
 -> Any
 -> Any
 -> Any
 -> Any
 -> T__IsRelatedTo__78
 -> T__IsRelatedTo__78)
-> Any -> Any -> Any -> Any
forall a b. a -> b
coe
                  (Any -> Any -> Any -> Any -> Any -> Any)
-> T_Σ_14
-> (Any -> Any -> Any -> Any -> Any -> Any)
-> Any
-> Any
-> Any
-> Any
-> T__IsRelatedTo__78
-> T__IsRelatedTo__78
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_'60''45'go_152
                  ((Any -> Any -> Any -> Any -> Any -> Any) -> Any
forall a b. a -> b
coe Any -> Any -> Any -> Any -> Any -> Any
forall {p} {t} {p} {t} {t} {t}. p -> t -> p -> t -> t -> t
v0) (Any -> Any
forall a b. a -> b
coe Any
forall a. a
v1) ((Any -> Any -> Any -> Any -> Any -> Any) -> Any
forall a b. a -> b
coe Any -> Any -> Any -> Any -> Any -> Any
forall {p} {t} {p} {t} {t} {t}. p -> t -> p -> t -> t -> t
v2)))))
-- Data.Nat.Properties.≤-Reasoning._.step-≡
d_step'45''8801'_3228 ::
  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'_3228 :: Integer
-> Integer
-> Integer
-> T__IsRelatedTo__78
-> T__'8801'__12
-> T__IsRelatedTo__78
d_step'45''8801'_3228
  = ((Any -> Any -> Any -> T__'8801'__12 -> Any -> Any)
 -> Any -> Any -> Any -> Any -> T__'8801'__12 -> Any)
-> Any
-> Integer
-> Integer
-> Integer
-> T__IsRelatedTo__78
-> T__'8801'__12
-> T__IsRelatedTo__78
forall a b. a -> b
coe
      (Any -> Any -> Any -> T__'8801'__12 -> Any -> Any)
-> Any -> Any -> Any -> Any -> T__'8801'__12 -> Any
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8801'_450
      ((Any -> Any -> Any -> Any -> Any -> Any) -> Any
forall a b. a -> b
coe (\ Any
v0 Any
v1 Any
v2 Any
v3 Any
v4 -> Any
v4))
-- Data.Nat.Properties.≤-Reasoning._.step-≡-∣
d_step'45''8801''45''8739'_3230 ::
  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'_3230 :: Integer -> Integer -> T__IsRelatedTo__78 -> T__IsRelatedTo__78
d_step'45''8801''45''8739'_3230 ~Integer
v0 ~Integer
v1 T__IsRelatedTo__78
v2
  = T__IsRelatedTo__78 -> T__IsRelatedTo__78
du_step'45''8801''45''8739'_3230 T__IsRelatedTo__78
v2
du_step'45''8801''45''8739'_3230 ::
  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'_3230 :: T__IsRelatedTo__78 -> T__IsRelatedTo__78
du_step'45''8801''45''8739'_3230 T__IsRelatedTo__78
v0 = T__IsRelatedTo__78 -> T__IsRelatedTo__78
forall a b. a -> b
coe T__IsRelatedTo__78
v0
-- Data.Nat.Properties.≤-Reasoning._.step-≡-⟨
d_step'45''8801''45''10216'_3232 ::
  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'_3232 :: Integer
-> Integer
-> Integer
-> T__IsRelatedTo__78
-> T__'8801'__12
-> T__IsRelatedTo__78
d_step'45''8801''45''10216'_3232
  = ((Any -> Any -> Any -> T__'8801'__12 -> Any -> Any)
 -> Any -> Any -> Any -> Any -> T__'8801'__12 -> Any)
-> Any
-> Integer
-> Integer
-> Integer
-> T__IsRelatedTo__78
-> T__'8801'__12
-> T__IsRelatedTo__78
forall a b. a -> b
coe
      (Any -> Any -> Any -> T__'8801'__12 -> Any -> Any)
-> Any -> Any -> Any -> Any -> T__'8801'__12 -> Any
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8801''45''10216'_448
      ((Any -> Any -> Any -> Any -> Any -> Any) -> Any
forall a b. a -> b
coe (\ Any
v0 Any
v1 Any
v2 Any
v3 Any
v4 -> Any
v4))
-- Data.Nat.Properties.≤-Reasoning._.step-≡-⟩
d_step'45''8801''45''10217'_3234 ::
  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'_3234 :: Integer
-> Integer
-> Integer
-> T__IsRelatedTo__78
-> T__'8801'__12
-> T__IsRelatedTo__78
d_step'45''8801''45''10217'_3234
  = ((Any -> Any -> Any -> T__'8801'__12 -> Any -> Any)
 -> Any -> Any -> Any -> Any -> T__'8801'__12 -> Any)
-> Any
-> Integer
-> Integer
-> Integer
-> T__IsRelatedTo__78
-> T__'8801'__12
-> T__IsRelatedTo__78
forall a b. a -> b
coe
      (Any -> Any -> Any -> T__'8801'__12 -> Any -> Any)
-> Any -> Any -> Any -> Any -> T__'8801'__12 -> Any
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8801''45''10217'_436
      ((Any -> Any -> Any -> Any -> Any -> Any) -> Any
forall a b. a -> b
coe (\ Any
v0 Any
v1 Any
v2 Any
v3 Any
v4 -> Any
v4))
-- Data.Nat.Properties.≤-Reasoning._.step-≡˘
d_step'45''8801''728'_3236 ::
  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'_3236 :: Integer
-> Integer
-> Integer
-> T__IsRelatedTo__78
-> T__'8801'__12
-> T__IsRelatedTo__78
d_step'45''8801''728'_3236
  = ((Any -> Any -> Any -> T__'8801'__12 -> Any -> Any)
 -> Any -> Any -> Any -> Any -> T__'8801'__12 -> Any)
-> Any
-> Integer
-> Integer
-> Integer
-> T__IsRelatedTo__78
-> T__'8801'__12
-> T__IsRelatedTo__78
forall a b. a -> b
coe
      (Any -> Any -> Any -> T__'8801'__12 -> Any -> Any)
-> Any -> Any -> Any -> Any -> T__'8801'__12 -> Any
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8801''728'_452
      ((Any -> Any -> Any -> Any -> Any -> Any) -> Any
forall a b. a -> b
coe (\ Any
v0 Any
v1 Any
v2 Any
v3 Any
v4 -> Any
v4))
-- Data.Nat.Properties.≤-Reasoning._.step-≤
d_step'45''8804'_3238 ::
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.T__IsRelatedTo__78 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.T__IsRelatedTo__78
d_step'45''8804'_3238 :: Integer
-> Integer
-> Integer
-> T__IsRelatedTo__78
-> T__'8804'__22
-> T__IsRelatedTo__78
d_step'45''8804'_3238
  = let v0 :: T_IsPreorder_70
v0 = T_IsPreorder_70
d_'8804''45'isPreorder_2810 in
    Any
-> Integer
-> Integer
-> Integer
-> T__IsRelatedTo__78
-> T__'8804'__22
-> T__IsRelatedTo__78
forall a b. a -> b
coe
      (let v1 :: p -> p -> p -> t -> t -> t
v1
             = \ p
v1 p
v2 p
v3 t
v4 t
v5 -> (T__'8804'__22 -> T__'8804'__22 -> T__'8804'__22) -> t -> t -> t
forall a b. a -> b
coe T__'8804'__22 -> T__'8804'__22 -> T__'8804'__22
du_'8804''45''60''45'trans_2986 t
v4 t
v5 in
       Any -> Any
forall a b. a -> b
coe
         (((Any -> Any -> Any -> Any -> Any -> Any)
 -> Any -> Any -> Any -> Any -> Any -> Any)
-> Any -> Any
forall a b. a -> b
coe
            (Any -> Any -> Any -> Any -> Any -> Any)
-> Any -> Any -> Any -> Any -> Any -> Any
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8804'_308
            ((T_IsPreorder_70
 -> (Any -> Any -> Any -> Any -> Any -> Any)
 -> Any
 -> Any
 -> Any
 -> Any
 -> T__IsRelatedTo__78
 -> T__IsRelatedTo__78)
-> Any -> Any -> Any
forall a b. a -> b
coe
               T_IsPreorder_70
-> (Any -> Any -> Any -> Any -> Any -> Any)
-> Any
-> Any
-> Any
-> Any
-> T__IsRelatedTo__78
-> T__IsRelatedTo__78
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_'8804''45'go_138
               (T_IsPreorder_70 -> Any
forall a b. a -> b
coe T_IsPreorder_70
v0) ((Any -> Any -> Any -> Any -> Any -> Any) -> Any
forall a b. a -> b
coe Any -> Any -> Any -> Any -> Any -> Any
forall {p} {t} {p} {t} {t} {t}. p -> t -> p -> t -> t -> t
v1))))
-- Data.Nat.Properties.≤-Reasoning._.stop
d_stop_3240 ::
  Integer ->
  MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.T__IsRelatedTo__78
d_stop_3240 :: Integer -> T__IsRelatedTo__78
d_stop_3240
  = (T_IsPreorder_70 -> Any -> T__IsRelatedTo__78)
-> Any -> Integer -> T__IsRelatedTo__78
forall a b. a -> b
coe
      T_IsPreorder_70 -> Any -> T__IsRelatedTo__78
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_stop_166
      (T_IsPreorder_70 -> Any
forall a b. a -> b
coe T_IsPreorder_70
d_'8804''45'isPreorder_2810)
-- Data.Nat.Properties.≤-Reasoning._.strictRelation
d_strictRelation_3244 ::
  MAlonzo.Code.Relation.Binary.Reasoning.Syntax.T_SubRelation_60
d_strictRelation_3244 :: T_SubRelation_60
d_strictRelation_3244
  = T_SubRelation_60 -> T_SubRelation_60
forall a b. a -> b
coe
      T_SubRelation_60
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_strictRelation_202
-- Data.Nat.Properties.≤-Reasoning._.≈-go
d_'8776''45'go_3246 ::
  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_3246 :: Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__IsRelatedTo__78
-> T__IsRelatedTo__78
d_'8776''45'go_3246
  = (T_IsPreorder_70
 -> T_Σ_14
 -> Any
 -> Any
 -> Any
 -> Any
 -> T__IsRelatedTo__78
 -> T__IsRelatedTo__78)
-> Any
-> Any
-> Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__IsRelatedTo__78
-> T__IsRelatedTo__78
forall a b. a -> b
coe
      T_IsPreorder_70
-> T_Σ_14
-> Any
-> Any
-> Any
-> Any
-> T__IsRelatedTo__78
-> T__IsRelatedTo__78
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_'8776''45'go_124
      (T_IsPreorder_70 -> Any
forall a b. a -> b
coe T_IsPreorder_70
d_'8804''45'isPreorder_2810)
      (T_Σ_14 -> Any
forall a b. a -> b
coe
         T_Σ_14
MAlonzo.Code.Relation.Binary.PropositionalEquality.Core.du_resp'8322'_160)
-- Data.Nat.Properties.≤-Reasoning._.≡-go
d_'8801''45'go_3248 ::
  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_3248 :: Integer
-> Integer
-> Integer
-> T__'8801'__12
-> T__IsRelatedTo__78
-> T__IsRelatedTo__78
d_'8801''45'go_3248 ~Integer
v0 ~Integer
v1 ~Integer
v2 ~T__'8801'__12
v3 T__IsRelatedTo__78
v4 = T__IsRelatedTo__78 -> T__IsRelatedTo__78
du_'8801''45'go_3248 T__IsRelatedTo__78
v4
du_'8801''45'go_3248 ::
  MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.T__IsRelatedTo__78 ->
  MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.T__IsRelatedTo__78
du_'8801''45'go_3248 :: T__IsRelatedTo__78 -> T__IsRelatedTo__78
du_'8801''45'go_3248 T__IsRelatedTo__78
v0 = T__IsRelatedTo__78 -> T__IsRelatedTo__78
forall a b. a -> b
coe T__IsRelatedTo__78
v0
-- Data.Nat.Properties.≤-Reasoning._.≤-go
d_'8804''45'go_3250 ::
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.T__IsRelatedTo__78 ->
  MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.T__IsRelatedTo__78
d_'8804''45'go_3250 :: Integer
-> Integer
-> Integer
-> T__'8804'__22
-> T__IsRelatedTo__78
-> T__IsRelatedTo__78
d_'8804''45'go_3250
  = (T_IsPreorder_70
 -> (Any -> Any -> Any -> Any -> Any -> Any)
 -> Any
 -> Any
 -> Any
 -> Any
 -> T__IsRelatedTo__78
 -> T__IsRelatedTo__78)
-> Any
-> (Any -> Any -> Any -> Any -> Any -> Any)
-> Integer
-> Integer
-> Integer
-> T__'8804'__22
-> T__IsRelatedTo__78
-> T__IsRelatedTo__78
forall a b. a -> b
coe
      T_IsPreorder_70
-> (Any -> Any -> Any -> Any -> Any -> Any)
-> Any
-> Any
-> Any
-> Any
-> T__IsRelatedTo__78
-> T__IsRelatedTo__78
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_'8804''45'go_138
      (T_IsPreorder_70 -> Any
forall a b. a -> b
coe T_IsPreorder_70
d_'8804''45'isPreorder_2810)
      (\ Any
v0 Any
v1 Any
v2 Any
v3 Any
v4 -> (T__'8804'__22 -> T__'8804'__22 -> T__'8804'__22)
-> Any -> Any -> Any
forall a b. a -> b
coe T__'8804'__22 -> T__'8804'__22 -> T__'8804'__22
du_'8804''45''60''45'trans_2986 Any
v3 Any
v4)
-- Data.Nat.Properties.+-suc
d_'43''45'suc_3272 ::
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'43''45'suc_3272 :: Integer -> Integer -> T__'8801'__12
d_'43''45'suc_3272 = Integer -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Nat.Properties.+-assoc
d_'43''45'assoc_3280 ::
  Integer ->
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'43''45'assoc_3280 :: Integer -> Integer -> Integer -> T__'8801'__12
d_'43''45'assoc_3280 = Integer -> Integer -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Nat.Properties.+-identityˡ
d_'43''45'identity'737'_3288 ::
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'43''45'identity'737'_3288 :: Integer -> T__'8801'__12
d_'43''45'identity'737'_3288 = Integer -> T__'8801'__12
forall a. a
erased
-- Data.Nat.Properties.+-identityʳ
d_'43''45'identity'691'_3290 ::
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'43''45'identity'691'_3290 :: Integer -> T__'8801'__12
d_'43''45'identity'691'_3290 = Integer -> T__'8801'__12
forall a. a
erased
-- Data.Nat.Properties.+-identity
d_'43''45'identity_3294 :: MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'43''45'identity_3294 :: T_Σ_14
d_'43''45'identity_3294
  = (Any -> Any -> T_Σ_14) -> Any -> Any -> T_Σ_14
forall a b. a -> b
coe Any -> Any -> T_Σ_14
MAlonzo.Code.Agda.Builtin.Sigma.C__'44'__32 Any
forall a. a
erased Any
forall a. a
erased
-- Data.Nat.Properties.+-comm
d_'43''45'comm_3296 ::
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'43''45'comm_3296 :: Integer -> Integer -> T__'8801'__12
d_'43''45'comm_3296 = Integer -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Nat.Properties.+-cancelˡ-≡
d_'43''45'cancel'737''45''8801'_3304 ::
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'43''45'cancel'737''45''8801'_3304 :: Integer -> Integer -> Integer -> T__'8801'__12 -> T__'8801'__12
d_'43''45'cancel'737''45''8801'_3304 = Integer -> Integer -> Integer -> T__'8801'__12 -> T__'8801'__12
forall a. a
erased
-- Data.Nat.Properties.+-cancelʳ-≡
d_'43''45'cancel'691''45''8801'_3312 ::
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'43''45'cancel'691''45''8801'_3312 :: Integer -> Integer -> Integer -> T__'8801'__12 -> T__'8801'__12
d_'43''45'cancel'691''45''8801'_3312 = Integer -> Integer -> Integer -> T__'8801'__12 -> T__'8801'__12
forall a. a
erased
-- Data.Nat.Properties.+-cancel-≡
d_'43''45'cancel'45''8801'_3314 ::
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'43''45'cancel'45''8801'_3314 :: T_Σ_14
d_'43''45'cancel'45''8801'_3314
  = (Any -> Any -> T_Σ_14) -> Any -> Any -> T_Σ_14
forall a b. a -> b
coe Any -> Any -> T_Σ_14
MAlonzo.Code.Agda.Builtin.Sigma.C__'44'__32 Any
forall a. a
erased Any
forall a. a
erased
-- Data.Nat.Properties.+-isMagma
d_'43''45'isMagma_3316 ::
  MAlonzo.Code.Algebra.Structures.T_IsMagma_176
d_'43''45'isMagma_3316 :: T_IsMagma_176
d_'43''45'isMagma_3316
  = (T_IsEquivalence_26
 -> (Any -> Any -> Any -> Any -> Any -> Any -> Any)
 -> T_IsMagma_176)
-> Any -> Any -> T_IsMagma_176
forall a b. a -> b
coe
      T_IsEquivalence_26
-> (Any -> Any -> Any -> Any -> Any -> Any -> Any) -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.C_IsMagma'46'constructor_1867
      (T_IsEquivalence_26 -> Any
forall a b. a -> b
coe
         T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.PropositionalEquality.Properties.du_isEquivalence_396)
      Any
forall a. a
erased
-- Data.Nat.Properties.+-isSemigroup
d_'43''45'isSemigroup_3318 ::
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_472
d_'43''45'isSemigroup_3318 :: T_IsSemigroup_472
d_'43''45'isSemigroup_3318
  = (T_IsMagma_176 -> (Any -> Any -> Any -> Any) -> T_IsSemigroup_472)
-> Any -> Any -> T_IsSemigroup_472
forall a b. a -> b
coe
      T_IsMagma_176 -> (Any -> Any -> Any -> Any) -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.C_IsSemigroup'46'constructor_10417
      (T_IsMagma_176 -> Any
forall a b. a -> b
coe T_IsMagma_176
d_'43''45'isMagma_3316) Any
forall a. a
erased
-- Data.Nat.Properties.+-isCommutativeSemigroup
d_'43''45'isCommutativeSemigroup_3320 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_548
d_'43''45'isCommutativeSemigroup_3320 :: T_IsCommutativeSemigroup_548
d_'43''45'isCommutativeSemigroup_3320
  = (T_IsSemigroup_472
 -> (Any -> Any -> Any) -> T_IsCommutativeSemigroup_548)
-> Any -> Any -> T_IsCommutativeSemigroup_548
forall a b. a -> b
coe
      T_IsSemigroup_472
-> (Any -> Any -> Any) -> T_IsCommutativeSemigroup_548
MAlonzo.Code.Algebra.Structures.C_IsCommutativeSemigroup'46'constructor_12093
      (T_IsSemigroup_472 -> Any
forall a b. a -> b
coe T_IsSemigroup_472
d_'43''45'isSemigroup_3318) Any
forall a. a
erased
-- Data.Nat.Properties.+-0-isMonoid
d_'43''45'0'45'isMonoid_3322 ::
  MAlonzo.Code.Algebra.Structures.T_IsMonoid_686
d_'43''45'0'45'isMonoid_3322 :: T_IsMonoid_686
d_'43''45'0'45'isMonoid_3322
  = (T_IsSemigroup_472 -> T_Σ_14 -> T_IsMonoid_686)
-> Any -> Any -> T_IsMonoid_686
forall a b. a -> b
coe
      T_IsSemigroup_472 -> T_Σ_14 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.C_IsMonoid'46'constructor_15873
      (T_IsSemigroup_472 -> Any
forall a b. a -> b
coe T_IsSemigroup_472
d_'43''45'isSemigroup_3318) (T_Σ_14 -> Any
forall a b. a -> b
coe T_Σ_14
d_'43''45'identity_3294)
-- Data.Nat.Properties.+-0-isCommutativeMonoid
d_'43''45'0'45'isCommutativeMonoid_3324 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMonoid_736
d_'43''45'0'45'isCommutativeMonoid_3324 :: T_IsCommutativeMonoid_736
d_'43''45'0'45'isCommutativeMonoid_3324
  = (T_IsMonoid_686
 -> (Any -> Any -> Any) -> T_IsCommutativeMonoid_736)
-> Any -> Any -> T_IsCommutativeMonoid_736
forall a b. a -> b
coe
      T_IsMonoid_686 -> (Any -> Any -> Any) -> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.C_IsCommutativeMonoid'46'constructor_17695
      (T_IsMonoid_686 -> Any
forall a b. a -> b
coe T_IsMonoid_686
d_'43''45'0'45'isMonoid_3322) Any
forall a. a
erased
-- Data.Nat.Properties.+-magma
d_'43''45'magma_3326 :: MAlonzo.Code.Algebra.Bundles.T_Magma_68
d_'43''45'magma_3326 :: T_Magma_68
d_'43''45'magma_3326
  = ((Any -> Any -> Any) -> T_IsMagma_176 -> T_Magma_68)
-> (Integer -> Integer -> Integer) -> T_IsMagma_176 -> T_Magma_68
forall a b. a -> b
coe
      (Any -> Any -> Any) -> T_IsMagma_176 -> T_Magma_68
MAlonzo.Code.Algebra.Bundles.C_Magma'46'constructor_1279 Integer -> Integer -> Integer
addInt
      T_IsMagma_176
d_'43''45'isMagma_3316
-- Data.Nat.Properties.+-semigroup
d_'43''45'semigroup_3328 ::
  MAlonzo.Code.Algebra.Bundles.T_Semigroup_536
d_'43''45'semigroup_3328 :: T_Semigroup_536
d_'43''45'semigroup_3328
  = ((Any -> Any -> Any) -> T_IsSemigroup_472 -> T_Semigroup_536)
-> (Integer -> Integer -> Integer)
-> T_IsSemigroup_472
-> T_Semigroup_536
forall a b. a -> b
coe
      (Any -> Any -> Any) -> T_IsSemigroup_472 -> T_Semigroup_536
MAlonzo.Code.Algebra.Bundles.C_Semigroup'46'constructor_9793 Integer -> Integer -> Integer
addInt
      T_IsSemigroup_472
d_'43''45'isSemigroup_3318
-- Data.Nat.Properties.+-commutativeSemigroup
d_'43''45'commutativeSemigroup_3330 ::
  MAlonzo.Code.Algebra.Bundles.T_CommutativeSemigroup_662
d_'43''45'commutativeSemigroup_3330 :: T_CommutativeSemigroup_662
d_'43''45'commutativeSemigroup_3330
  = ((Any -> Any -> Any)
 -> T_IsCommutativeSemigroup_548 -> T_CommutativeSemigroup_662)
-> (Integer -> Integer -> Integer)
-> T_IsCommutativeSemigroup_548
-> T_CommutativeSemigroup_662
forall a b. a -> b
coe
      (Any -> Any -> Any)
-> T_IsCommutativeSemigroup_548 -> T_CommutativeSemigroup_662
MAlonzo.Code.Algebra.Bundles.C_CommutativeSemigroup'46'constructor_12035
      Integer -> Integer -> Integer
addInt T_IsCommutativeSemigroup_548
d_'43''45'isCommutativeSemigroup_3320
-- Data.Nat.Properties.+-0-monoid
d_'43''45'0'45'monoid_3332 ::
  MAlonzo.Code.Algebra.Bundles.T_Monoid_882
d_'43''45'0'45'monoid_3332 :: T_Monoid_882
d_'43''45'0'45'monoid_3332
  = ((Any -> Any -> Any) -> Any -> T_IsMonoid_686 -> T_Monoid_882)
-> (Integer -> Integer -> Integer)
-> Integer
-> T_IsMonoid_686
-> T_Monoid_882
forall a b. a -> b
coe
      (Any -> Any -> Any) -> Any -> T_IsMonoid_686 -> T_Monoid_882
MAlonzo.Code.Algebra.Bundles.C_Monoid'46'constructor_16157 Integer -> Integer -> Integer
addInt
      (Integer
0 :: Integer) T_IsMonoid_686
d_'43''45'0'45'isMonoid_3322
-- Data.Nat.Properties.+-0-commutativeMonoid
d_'43''45'0'45'commutativeMonoid_3334 ::
  MAlonzo.Code.Algebra.Bundles.T_CommutativeMonoid_962
d_'43''45'0'45'commutativeMonoid_3334 :: T_CommutativeMonoid_962
d_'43''45'0'45'commutativeMonoid_3334
  = ((Any -> Any -> Any)
 -> Any -> T_IsCommutativeMonoid_736 -> T_CommutativeMonoid_962)
-> (Integer -> Integer -> Integer)
-> Integer
-> T_IsCommutativeMonoid_736
-> T_CommutativeMonoid_962
forall a b. a -> b
coe
      (Any -> Any -> Any)
-> Any -> T_IsCommutativeMonoid_736 -> T_CommutativeMonoid_962
MAlonzo.Code.Algebra.Bundles.C_CommutativeMonoid'46'constructor_17931
      Integer -> Integer -> Integer
addInt (Integer
0 :: Integer) T_IsCommutativeMonoid_736
d_'43''45'0'45'isCommutativeMonoid_3324
-- Data.Nat.Properties.∸-magma
d_'8760''45'magma_3336 :: MAlonzo.Code.Algebra.Bundles.T_Magma_68
d_'8760''45'magma_3336 :: T_Magma_68
d_'8760''45'magma_3336
  = ((Any -> Any -> Any) -> T_Magma_68) -> Any -> T_Magma_68
forall a b. a -> b
coe
      (Any -> Any -> Any) -> T_Magma_68
MAlonzo.Code.Relation.Binary.PropositionalEquality.Algebra.du_magma_20
      ((Integer -> Integer -> Integer) -> Any
forall a b. a -> b
coe Integer -> Integer -> Integer
MAlonzo.Code.Agda.Builtin.Nat.d__'45'__22)
-- Data.Nat.Properties.m≢1+m+n
d_m'8802'1'43'm'43'n_3342 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Data.Irrelevant.T_Irrelevant_20
d_m'8802'1'43'm'43'n_3342 :: Integer -> Integer -> T__'8801'__12 -> T_Irrelevant_20
d_m'8802'1'43'm'43'n_3342 = Integer -> Integer -> T__'8801'__12 -> T_Irrelevant_20
forall a. a
erased
-- Data.Nat.Properties.m≢1+n+m
d_m'8802'1'43'n'43'm_3352 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Data.Irrelevant.T_Irrelevant_20
d_m'8802'1'43'n'43'm_3352 :: Integer -> Integer -> T__'8801'__12 -> T_Irrelevant_20
d_m'8802'1'43'n'43'm_3352 = Integer -> Integer -> T__'8801'__12 -> T_Irrelevant_20
forall a. a
erased
-- Data.Nat.Properties.m+1+n≢m
d_m'43'1'43'n'8802'm_3362 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Data.Irrelevant.T_Irrelevant_20
d_m'43'1'43'n'8802'm_3362 :: Integer -> Integer -> T__'8801'__12 -> T_Irrelevant_20
d_m'43'1'43'n'8802'm_3362 = Integer -> Integer -> T__'8801'__12 -> T_Irrelevant_20
forall a. a
erased
-- Data.Nat.Properties.m+1+n≢n
d_m'43'1'43'n'8802'n_3370 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Data.Irrelevant.T_Irrelevant_20
d_m'43'1'43'n'8802'n_3370 :: Integer -> Integer -> T__'8801'__12 -> T_Irrelevant_20
d_m'43'1'43'n'8802'n_3370 = Integer -> Integer -> T__'8801'__12 -> T_Irrelevant_20
forall a. a
erased
-- Data.Nat.Properties.m+1+n≢0
d_m'43'1'43'n'8802'0_3384 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Data.Irrelevant.T_Irrelevant_20
d_m'43'1'43'n'8802'0_3384 :: Integer -> Integer -> T__'8801'__12 -> T_Irrelevant_20
d_m'43'1'43'n'8802'0_3384 = Integer -> Integer -> T__'8801'__12 -> T_Irrelevant_20
forall a. a
erased
-- Data.Nat.Properties.m+n≡0⇒m≡0
d_m'43'n'8801'0'8658'm'8801'0_3398 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_m'43'n'8801'0'8658'm'8801'0_3398 :: Integer -> Integer -> T__'8801'__12 -> T__'8801'__12
d_m'43'n'8801'0'8658'm'8801'0_3398 = Integer -> Integer -> T__'8801'__12 -> T__'8801'__12
forall a. a
erased
-- Data.Nat.Properties.m+n≡0⇒n≡0
d_m'43'n'8801'0'8658'n'8801'0_3406 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_m'43'n'8801'0'8658'n'8801'0_3406 :: Integer -> Integer -> T__'8801'__12 -> T__'8801'__12
d_m'43'n'8801'0'8658'n'8801'0_3406 = Integer -> Integer -> T__'8801'__12 -> T__'8801'__12
forall a. a
erased
-- Data.Nat.Properties.+-cancelˡ-≤
d_'43''45'cancel'737''45''8804'_3414 ::
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_'43''45'cancel'737''45''8804'_3414 :: Integer -> Integer -> Integer -> T__'8804'__22 -> T__'8804'__22
d_'43''45'cancel'737''45''8804'_3414 Integer
v0 ~Integer
v1 ~Integer
v2 T__'8804'__22
v3
  = Integer -> T__'8804'__22 -> T__'8804'__22
du_'43''45'cancel'737''45''8804'_3414 Integer
v0 T__'8804'__22
v3
du_'43''45'cancel'737''45''8804'_3414 ::
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
du_'43''45'cancel'737''45''8804'_3414 :: Integer -> T__'8804'__22 -> T__'8804'__22
du_'43''45'cancel'737''45''8804'_3414 Integer
v0 T__'8804'__22
v1
  = case Integer -> Integer
forall a b. a -> b
coe Integer
v0 of
      Integer
0 -> T__'8804'__22 -> T__'8804'__22
forall a b. a -> b
coe T__'8804'__22
v1
      Integer
_ -> let v2 :: Integer
v2 = Integer -> Integer -> Integer
subInt (Integer -> Integer
forall a b. a -> b
coe Integer
v0) (Integer -> Integer
forall a b. a -> b
coe (Integer
1 :: Integer)) in
           Any -> T__'8804'__22
forall a b. a -> b
coe
             (case T__'8804'__22 -> T__'8804'__22
forall a b. a -> b
coe T__'8804'__22
v1 of
                MAlonzo.Code.Data.Nat.Base.C_s'8804's_34 T__'8804'__22
v5
                  -> (Integer -> T__'8804'__22 -> T__'8804'__22) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> T__'8804'__22 -> T__'8804'__22
du_'43''45'cancel'737''45''8804'_3414 (Integer -> Any
forall a b. a -> b
coe Integer
v2) (T__'8804'__22 -> Any
forall a b. a -> b
coe T__'8804'__22
v5)
                T__'8804'__22
_ -> Any
forall a. a
MAlonzo.RTE.mazUnreachableError)
-- Data.Nat.Properties.+-cancelʳ-≤
d_'43''45'cancel'691''45''8804'_3422 ::
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_'43''45'cancel'691''45''8804'_3422 :: Integer -> Integer -> Integer -> T__'8804'__22 -> T__'8804'__22
d_'43''45'cancel'691''45''8804'_3422 Integer
v0 ~Integer
v1 ~Integer
v2 T__'8804'__22
v3
  = Integer -> T__'8804'__22 -> T__'8804'__22
du_'43''45'cancel'691''45''8804'_3422 Integer
v0 T__'8804'__22
v3
du_'43''45'cancel'691''45''8804'_3422 ::
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
du_'43''45'cancel'691''45''8804'_3422 :: Integer -> T__'8804'__22 -> T__'8804'__22
du_'43''45'cancel'691''45''8804'_3422 Integer
v0 T__'8804'__22
v1
  = (Integer -> T__'8804'__22 -> T__'8804'__22)
-> Any -> Any -> T__'8804'__22
forall a b. a -> b
coe Integer -> T__'8804'__22 -> T__'8804'__22
du_'43''45'cancel'737''45''8804'_3414 (Integer -> Any
forall a b. a -> b
coe Integer
v0) (T__'8804'__22 -> Any
forall a b. a -> b
coe T__'8804'__22
v1)
-- Data.Nat.Properties.+-cancel-≤
d_'43''45'cancel'45''8804'_3432 ::
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'43''45'cancel'45''8804'_3432 :: T_Σ_14
d_'43''45'cancel'45''8804'_3432
  = (Any -> Any -> T_Σ_14)
-> (Any -> Any -> Any -> Any -> Any)
-> (Any -> Any -> Any -> Any -> Any)
-> T_Σ_14
forall a b. a -> b
coe
      Any -> Any -> T_Σ_14
MAlonzo.Code.Agda.Builtin.Sigma.C__'44'__32
      (\ Any
v0 Any
v1 Any
v2 Any
v3 -> (Integer -> T__'8804'__22 -> T__'8804'__22) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> T__'8804'__22 -> T__'8804'__22
du_'43''45'cancel'737''45''8804'_3414 Any
v0 Any
v3)
      (\ Any
v0 Any
v1 Any
v2 Any
v3 -> (Integer -> T__'8804'__22 -> T__'8804'__22) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> T__'8804'__22 -> T__'8804'__22
du_'43''45'cancel'691''45''8804'_3422 Any
v0 Any
v3)
-- Data.Nat.Properties.+-cancelˡ-<
d_'43''45'cancel'737''45''60'_3434 ::
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_'43''45'cancel'737''45''60'_3434 :: Integer -> Integer -> Integer -> T__'8804'__22 -> T__'8804'__22
d_'43''45'cancel'737''45''60'_3434 Integer
v0 ~Integer
v1 ~Integer
v2 T__'8804'__22
v3
  = Integer -> T__'8804'__22 -> T__'8804'__22
du_'43''45'cancel'737''45''60'_3434 Integer
v0 T__'8804'__22
v3
du_'43''45'cancel'737''45''60'_3434 ::
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
du_'43''45'cancel'737''45''60'_3434 :: Integer -> T__'8804'__22 -> T__'8804'__22
du_'43''45'cancel'737''45''60'_3434 Integer
v0 T__'8804'__22
v1
  = (Integer -> T__'8804'__22 -> T__'8804'__22)
-> Any -> Any -> T__'8804'__22
forall a b. a -> b
coe Integer -> T__'8804'__22 -> T__'8804'__22
du_'43''45'cancel'737''45''8804'_3414 (Integer -> Any
forall a b. a -> b
coe Integer
v0) (T__'8804'__22 -> Any
forall a b. a -> b
coe T__'8804'__22
v1)
-- Data.Nat.Properties.+-cancelʳ-<
d_'43''45'cancel'691''45''60'_3444 ::
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_'43''45'cancel'691''45''60'_3444 :: Integer -> Integer -> Integer -> T__'8804'__22 -> T__'8804'__22
d_'43''45'cancel'691''45''60'_3444 Integer
v0 ~Integer
v1 ~Integer
v2 T__'8804'__22
v3
  = Integer -> T__'8804'__22 -> T__'8804'__22
du_'43''45'cancel'691''45''60'_3444 Integer
v0 T__'8804'__22
v3
du_'43''45'cancel'691''45''60'_3444 ::
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
du_'43''45'cancel'691''45''60'_3444 :: Integer -> T__'8804'__22 -> T__'8804'__22
du_'43''45'cancel'691''45''60'_3444 Integer
v0 T__'8804'__22
v1
  = (Integer -> T__'8804'__22 -> T__'8804'__22)
-> Any -> Any -> T__'8804'__22
forall a b. a -> b
coe Integer -> T__'8804'__22 -> T__'8804'__22
du_'43''45'cancel'691''45''8804'_3422 (Integer -> Any
forall a b. a -> b
coe Integer
v0) (T__'8804'__22 -> Any
forall a b. a -> b
coe T__'8804'__22
v1)
-- Data.Nat.Properties.+-cancel-<
d_'43''45'cancel'45''60'_3454 ::
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'43''45'cancel'45''60'_3454 :: T_Σ_14
d_'43''45'cancel'45''60'_3454
  = (Any -> Any -> T_Σ_14)
-> (Any -> Any -> Any -> Any -> Any)
-> (Any -> Any -> Any -> Any -> Any)
-> T_Σ_14
forall a b. a -> b
coe
      Any -> Any -> T_Σ_14
MAlonzo.Code.Agda.Builtin.Sigma.C__'44'__32
      (\ Any
v0 Any
v1 Any
v2 Any
v3 -> (Integer -> T__'8804'__22 -> T__'8804'__22) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> T__'8804'__22 -> T__'8804'__22
du_'43''45'cancel'737''45''60'_3434 Any
v0 Any
v3)
      (\ Any
v0 Any
v1 Any
v2 Any
v3 -> (Integer -> T__'8804'__22 -> T__'8804'__22) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> T__'8804'__22 -> T__'8804'__22
du_'43''45'cancel'691''45''60'_3444 Any
v0 Any
v3)
-- Data.Nat.Properties.m≤n⇒m≤o+n
d_m'8804'n'8658'm'8804'o'43'n_3458 ::
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_m'8804'n'8658'm'8804'o'43'n_3458 :: Integer -> Integer -> Integer -> T__'8804'__22 -> T__'8804'__22
d_m'8804'n'8658'm'8804'o'43'n_3458 ~Integer
v0 ~Integer
v1 ~Integer
v2 T__'8804'__22
v3
  = T__'8804'__22 -> T__'8804'__22
du_m'8804'n'8658'm'8804'o'43'n_3458 T__'8804'__22
v3
du_m'8804'n'8658'm'8804'o'43'n_3458 ::
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
du_m'8804'n'8658'm'8804'o'43'n_3458 :: T__'8804'__22 -> T__'8804'__22
du_m'8804'n'8658'm'8804'o'43'n_3458 T__'8804'__22
v0 = T__'8804'__22 -> T__'8804'__22
forall a b. a -> b
coe T__'8804'__22
v0
-- Data.Nat.Properties.m≤n⇒m≤n+o
d_m'8804'n'8658'm'8804'n'43'o_3468 ::
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_m'8804'n'8658'm'8804'n'43'o_3468 :: Integer -> Integer -> Integer -> T__'8804'__22 -> T__'8804'__22
d_m'8804'n'8658'm'8804'n'43'o_3468 ~Integer
v0 ~Integer
v1 ~Integer
v2 T__'8804'__22
v3
  = T__'8804'__22 -> T__'8804'__22
du_m'8804'n'8658'm'8804'n'43'o_3468 T__'8804'__22
v3
du_m'8804'n'8658'm'8804'n'43'o_3468 ::
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
du_m'8804'n'8658'm'8804'n'43'o_3468 :: T__'8804'__22 -> T__'8804'__22
du_m'8804'n'8658'm'8804'n'43'o_3468 T__'8804'__22
v0 = T__'8804'__22 -> T__'8804'__22
forall a b. a -> b
coe T__'8804'__22
v0
-- Data.Nat.Properties.m≤m+n
d_m'8804'm'43'n_3482 ::
  Integer -> Integer -> MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_m'8804'm'43'n_3482 :: Integer -> Integer -> T__'8804'__22
d_m'8804'm'43'n_3482 Integer
v0 ~Integer
v1 = Integer -> T__'8804'__22
du_m'8804'm'43'n_3482 Integer
v0
du_m'8804'm'43'n_3482 ::
  Integer -> MAlonzo.Code.Data.Nat.Base.T__'8804'__22
du_m'8804'm'43'n_3482 :: Integer -> T__'8804'__22
du_m'8804'm'43'n_3482 Integer
v0
  = case Integer -> Integer
forall a b. a -> b
coe Integer
v0 of
      Integer
0 -> T__'8804'__22 -> T__'8804'__22
forall a b. a -> b
coe T__'8804'__22
MAlonzo.Code.Data.Nat.Base.C_z'8804'n_26
      Integer
_ -> let v1 :: Integer
v1 = Integer -> Integer -> Integer
subInt (Integer -> Integer
forall a b. a -> b
coe Integer
v0) (Integer -> Integer
forall a b. a -> b
coe (Integer
1 :: Integer)) in
           Any -> T__'8804'__22
forall a b. a -> b
coe
             ((T__'8804'__22 -> T__'8804'__22) -> Any -> Any
forall a b. a -> b
coe
                T__'8804'__22 -> T__'8804'__22
MAlonzo.Code.Data.Nat.Base.C_s'8804's_34
                ((Integer -> T__'8804'__22) -> Any -> Any
forall a b. a -> b
coe Integer -> T__'8804'__22
du_m'8804'm'43'n_3482 (Integer -> Any
forall a b. a -> b
coe Integer
v1)))
-- Data.Nat.Properties.m≤n+m
d_m'8804'n'43'm_3494 ::
  Integer -> Integer -> MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_m'8804'n'43'm_3494 :: Integer -> Integer -> T__'8804'__22
d_m'8804'n'43'm_3494 Integer
v0 ~Integer
v1 = Integer -> T__'8804'__22
du_m'8804'n'43'm_3494 Integer
v0
du_m'8804'n'43'm_3494 ::
  Integer -> MAlonzo.Code.Data.Nat.Base.T__'8804'__22
du_m'8804'n'43'm_3494 :: Integer -> T__'8804'__22
du_m'8804'n'43'm_3494 Integer
v0 = (Integer -> T__'8804'__22) -> Any -> T__'8804'__22
forall a b. a -> b
coe Integer -> T__'8804'__22
du_m'8804'm'43'n_3482 (Integer -> Any
forall a b. a -> b
coe Integer
v0)
-- Data.Nat.Properties.m+n≤o⇒m≤o
d_m'43'n'8804'o'8658'm'8804'o_3508 ::
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_m'43'n'8804'o'8658'm'8804'o_3508 :: Integer -> Integer -> Integer -> T__'8804'__22 -> T__'8804'__22
d_m'43'n'8804'o'8658'm'8804'o_3508 Integer
v0 ~Integer
v1 ~Integer
v2 T__'8804'__22
v3
  = Integer -> T__'8804'__22 -> T__'8804'__22
du_m'43'n'8804'o'8658'm'8804'o_3508 Integer
v0 T__'8804'__22
v3
du_m'43'n'8804'o'8658'm'8804'o_3508 ::
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
du_m'43'n'8804'o'8658'm'8804'o_3508 :: Integer -> T__'8804'__22 -> T__'8804'__22
du_m'43'n'8804'o'8658'm'8804'o_3508 Integer
v0 T__'8804'__22
v1
  = case Integer -> Integer
forall a b. a -> b
coe Integer
v0 of
      Integer
0 -> T__'8804'__22 -> T__'8804'__22
forall a b. a -> b
coe T__'8804'__22
MAlonzo.Code.Data.Nat.Base.C_z'8804'n_26
      Integer
_ -> let v2 :: Integer
v2 = Integer -> Integer -> Integer
subInt (Integer -> Integer
forall a b. a -> b
coe Integer
v0) (Integer -> Integer
forall a b. a -> b
coe (Integer
1 :: Integer)) in
           Any -> T__'8804'__22
forall a b. a -> b
coe
             (case T__'8804'__22 -> T__'8804'__22
forall a b. a -> b
coe T__'8804'__22
v1 of
                MAlonzo.Code.Data.Nat.Base.C_s'8804's_34 T__'8804'__22
v5
                  -> (T__'8804'__22 -> T__'8804'__22) -> Any -> Any
forall a b. a -> b
coe
                       T__'8804'__22 -> T__'8804'__22
MAlonzo.Code.Data.Nat.Base.C_s'8804's_34
                       ((Integer -> T__'8804'__22 -> T__'8804'__22) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> T__'8804'__22 -> T__'8804'__22
du_m'43'n'8804'o'8658'm'8804'o_3508 (Integer -> Any
forall a b. a -> b
coe Integer
v2) (T__'8804'__22 -> Any
forall a b. a -> b
coe T__'8804'__22
v5))
                T__'8804'__22
_ -> Any
forall a. a
MAlonzo.RTE.mazUnreachableError)
-- Data.Nat.Properties.m+n≤o⇒n≤o
d_m'43'n'8804'o'8658'n'8804'o_3522 ::
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_m'43'n'8804'o'8658'n'8804'o_3522 :: Integer -> Integer -> Integer -> T__'8804'__22 -> T__'8804'__22
d_m'43'n'8804'o'8658'n'8804'o_3522 Integer
v0 ~Integer
v1 ~Integer
v2 T__'8804'__22
v3
  = Integer -> T__'8804'__22 -> T__'8804'__22
du_m'43'n'8804'o'8658'n'8804'o_3522 Integer
v0 T__'8804'__22
v3
du_m'43'n'8804'o'8658'n'8804'o_3522 ::
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
du_m'43'n'8804'o'8658'n'8804'o_3522 :: Integer -> T__'8804'__22 -> T__'8804'__22
du_m'43'n'8804'o'8658'n'8804'o_3522 Integer
v0 T__'8804'__22
v1
  = case Integer -> Integer
forall a b. a -> b
coe Integer
v0 of
      Integer
0 -> T__'8804'__22 -> T__'8804'__22
forall a b. a -> b
coe T__'8804'__22
v1
      Integer
_ -> let v2 :: Integer
v2 = Integer -> Integer -> Integer
subInt (Integer -> Integer
forall a b. a -> b
coe Integer
v0) (Integer -> Integer
forall a b. a -> b
coe (Integer
1 :: Integer)) in
           Any -> T__'8804'__22
forall a b. a -> b
coe
             ((Integer -> T__'8804'__22 -> T__'8804'__22) -> Any -> Any -> Any
forall a b. a -> b
coe
                Integer -> T__'8804'__22 -> T__'8804'__22
du_m'43'n'8804'o'8658'n'8804'o_3522 (Integer -> Any
forall a b. a -> b
coe Integer
v2)
                ((T__'8804'__22 -> T__'8804'__22) -> Any -> Any
forall a b. a -> b
coe T__'8804'__22 -> T__'8804'__22
du_'60''8658''8804'_2854 (T__'8804'__22 -> Any
forall a b. a -> b
coe T__'8804'__22
v1)))
-- Data.Nat.Properties.+-mono-≤
d_'43''45'mono'45''8804'_3530 ::
  Integer ->
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_'43''45'mono'45''8804'_3530 :: Integer
-> Integer
-> Integer
-> Integer
-> T__'8804'__22
-> T__'8804'__22
-> T__'8804'__22
d_'43''45'mono'45''8804'_3530 ~Integer
v0 ~Integer
v1 ~Integer
v2 Integer
v3 T__'8804'__22
v4 T__'8804'__22
v5
  = Integer -> T__'8804'__22 -> T__'8804'__22 -> T__'8804'__22
du_'43''45'mono'45''8804'_3530 Integer
v3 T__'8804'__22
v4 T__'8804'__22
v5
du_'43''45'mono'45''8804'_3530 ::
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
du_'43''45'mono'45''8804'_3530 :: Integer -> T__'8804'__22 -> T__'8804'__22 -> T__'8804'__22
du_'43''45'mono'45''8804'_3530 Integer
v0 T__'8804'__22
v1 T__'8804'__22
v2
  = case T__'8804'__22 -> T__'8804'__22
forall a b. a -> b
coe T__'8804'__22
v1 of
      T__'8804'__22
MAlonzo.Code.Data.Nat.Base.C_z'8804'n_26
        -> (T__'8804'__22 -> T__'8804'__22 -> T__'8804'__22)
-> Any -> Any -> T__'8804'__22
forall a b. a -> b
coe
             T__'8804'__22 -> T__'8804'__22 -> T__'8804'__22
du_'8804''45'trans_2784 (T__'8804'__22 -> Any
forall a b. a -> b
coe T__'8804'__22
v2)
             ((Integer -> T__'8804'__22) -> Any -> Any
forall a b. a -> b
coe Integer -> T__'8804'__22
du_m'8804'n'43'm_3494 (Integer -> Any
forall a b. a -> b
coe Integer
v0))
      MAlonzo.Code.Data.Nat.Base.C_s'8804's_34 T__'8804'__22
v5
        -> (T__'8804'__22 -> T__'8804'__22) -> Any -> T__'8804'__22
forall a b. a -> b
coe
             T__'8804'__22 -> T__'8804'__22
MAlonzo.Code.Data.Nat.Base.C_s'8804's_34
             ((Integer -> T__'8804'__22 -> T__'8804'__22 -> T__'8804'__22)
-> Any -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> T__'8804'__22 -> T__'8804'__22 -> T__'8804'__22
du_'43''45'mono'45''8804'_3530 (Integer -> Any
forall a b. a -> b
coe Integer
v0) (T__'8804'__22 -> Any
forall a b. a -> b
coe T__'8804'__22
v5) (T__'8804'__22 -> Any
forall a b. a -> b
coe T__'8804'__22
v2))
      T__'8804'__22
_ -> T__'8804'__22
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Data.Nat.Properties.+-monoˡ-≤
d_'43''45'mono'737''45''8804'_3544 ::
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_'43''45'mono'737''45''8804'_3544 :: Integer -> Integer -> Integer -> T__'8804'__22 -> T__'8804'__22
d_'43''45'mono'737''45''8804'_3544 Integer
v0 ~Integer
v1 ~Integer
v2 T__'8804'__22
v3
  = Integer -> T__'8804'__22 -> T__'8804'__22
du_'43''45'mono'737''45''8804'_3544 Integer
v0 T__'8804'__22
v3
du_'43''45'mono'737''45''8804'_3544 ::
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
du_'43''45'mono'737''45''8804'_3544 :: Integer -> T__'8804'__22 -> T__'8804'__22
du_'43''45'mono'737''45''8804'_3544 Integer
v0 T__'8804'__22
v1
  = (Integer -> T__'8804'__22 -> T__'8804'__22 -> T__'8804'__22)
-> Any -> Any -> Any -> T__'8804'__22
forall a b. a -> b
coe
      Integer -> T__'8804'__22 -> T__'8804'__22 -> T__'8804'__22
du_'43''45'mono'45''8804'_3530 (Integer -> Any
forall a b. a -> b
coe Integer
v0) (T__'8804'__22 -> Any
forall a b. a -> b
coe T__'8804'__22
v1)
      ((Integer -> T__'8804'__22) -> Any -> Any
forall a b. a -> b
coe Integer -> T__'8804'__22
d_'8804''45'refl_2776 (Integer -> Any
forall a b. a -> b
coe Integer
v0))
-- Data.Nat.Properties.+-monoʳ-≤
d_'43''45'mono'691''45''8804'_3554 ::
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_'43''45'mono'691''45''8804'_3554 :: Integer -> Integer -> Integer -> T__'8804'__22 -> T__'8804'__22
d_'43''45'mono'691''45''8804'_3554 Integer
v0 ~Integer
v1 Integer
v2 T__'8804'__22
v3
  = Integer -> Integer -> T__'8804'__22 -> T__'8804'__22
du_'43''45'mono'691''45''8804'_3554 Integer
v0 Integer
v2 T__'8804'__22
v3
du_'43''45'mono'691''45''8804'_3554 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
du_'43''45'mono'691''45''8804'_3554 :: Integer -> Integer -> T__'8804'__22 -> T__'8804'__22
du_'43''45'mono'691''45''8804'_3554 Integer
v0 Integer
v1 T__'8804'__22
v2
  = (Integer -> T__'8804'__22 -> T__'8804'__22 -> T__'8804'__22)
-> Any -> Any -> Any -> T__'8804'__22
forall a b. a -> b
coe
      Integer -> T__'8804'__22 -> T__'8804'__22 -> T__'8804'__22
du_'43''45'mono'45''8804'_3530 (Integer -> Any
forall a b. a -> b
coe Integer
v1)
      ((Integer -> T__'8804'__22) -> Any -> Any
forall a b. a -> b
coe Integer -> T__'8804'__22
d_'8804''45'refl_2776 (Integer -> Any
forall a b. a -> b
coe Integer
v0)) (T__'8804'__22 -> Any
forall a b. a -> b
coe T__'8804'__22
v2)
-- Data.Nat.Properties.+-mono-<-≤
d_'43''45'mono'45''60''45''8804'_3560 ::
  Integer ->
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_'43''45'mono'45''60''45''8804'_3560 :: Integer
-> Integer
-> Integer
-> Integer
-> T__'8804'__22
-> T__'8804'__22
-> T__'8804'__22
d_'43''45'mono'45''60''45''8804'_3560 ~Integer
v0 ~Integer
v1 ~Integer
v2 ~Integer
v3 T__'8804'__22
v4 T__'8804'__22
v5
  = T__'8804'__22 -> T__'8804'__22 -> T__'8804'__22
du_'43''45'mono'45''60''45''8804'_3560 T__'8804'__22
v4 T__'8804'__22
v5
du_'43''45'mono'45''60''45''8804'_3560 ::
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
du_'43''45'mono'45''60''45''8804'_3560 :: T__'8804'__22 -> T__'8804'__22 -> T__'8804'__22
du_'43''45'mono'45''60''45''8804'_3560 T__'8804'__22
v0 T__'8804'__22
v1
  = case T__'8804'__22 -> T__'8804'__22
forall a b. a -> b
coe T__'8804'__22
v0 of
      MAlonzo.Code.Data.Nat.Base.C_s'8804's_34 T__'8804'__22
v4
        -> case T__'8804'__22 -> T__'8804'__22
forall a b. a -> b
coe T__'8804'__22
v4 of
             T__'8804'__22
MAlonzo.Code.Data.Nat.Base.C_z'8804'n_26
               -> (T__'8804'__22 -> T__'8804'__22) -> T__'8804'__22 -> T__'8804'__22
forall a b. a -> b
coe T__'8804'__22 -> T__'8804'__22
MAlonzo.Code.Data.Nat.Base.C_s'8804's_34 T__'8804'__22
v1
             MAlonzo.Code.Data.Nat.Base.C_s'8804's_34 T__'8804'__22
v7
               -> (T__'8804'__22 -> T__'8804'__22) -> Any -> T__'8804'__22
forall a b. a -> b
coe
                    T__'8804'__22 -> T__'8804'__22
MAlonzo.Code.Data.Nat.Base.C_s'8804's_34
                    ((T__'8804'__22 -> T__'8804'__22 -> T__'8804'__22)
-> Any -> Any -> Any
forall a b. a -> b
coe
                       T__'8804'__22 -> T__'8804'__22 -> T__'8804'__22
du_'43''45'mono'45''60''45''8804'_3560
                       ((T__'8804'__22 -> T__'8804'__22) -> T__'8804'__22 -> Any
forall a b. a -> b
coe T__'8804'__22 -> T__'8804'__22
MAlonzo.Code.Data.Nat.Base.C_s'8804's_34 T__'8804'__22
v7) (T__'8804'__22 -> Any
forall a b. a -> b
coe T__'8804'__22
v1))
             T__'8804'__22
_ -> T__'8804'__22
forall a. a
MAlonzo.RTE.mazUnreachableError
      T__'8804'__22
_ -> T__'8804'__22
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Data.Nat.Properties.+-mono-≤-<
d_'43''45'mono'45''8804''45''60'_3570 ::
  Integer ->
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_'43''45'mono'45''8804''45''60'_3570 :: Integer
-> Integer
-> Integer
-> Integer
-> T__'8804'__22
-> T__'8804'__22
-> T__'8804'__22
d_'43''45'mono'45''8804''45''60'_3570 ~Integer
v0 ~Integer
v1 ~Integer
v2 Integer
v3 T__'8804'__22
v4 T__'8804'__22
v5
  = Integer -> T__'8804'__22 -> T__'8804'__22 -> T__'8804'__22
du_'43''45'mono'45''8804''45''60'_3570 Integer
v3 T__'8804'__22
v4 T__'8804'__22
v5
du_'43''45'mono'45''8804''45''60'_3570 ::
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
du_'43''45'mono'45''8804''45''60'_3570 :: Integer -> T__'8804'__22 -> T__'8804'__22 -> T__'8804'__22
du_'43''45'mono'45''8804''45''60'_3570 Integer
v0 T__'8804'__22
v1 T__'8804'__22
v2
  = case T__'8804'__22 -> T__'8804'__22
forall a b. a -> b
coe T__'8804'__22
v1 of
      T__'8804'__22
MAlonzo.Code.Data.Nat.Base.C_z'8804'n_26
        -> (T__'8804'__22 -> T__'8804'__22 -> T__'8804'__22)
-> Any -> Any -> T__'8804'__22
forall a b. a -> b
coe
             T__'8804'__22 -> T__'8804'__22 -> T__'8804'__22
du_'8804''45'trans_2784 (T__'8804'__22 -> Any
forall a b. a -> b
coe T__'8804'__22
v2)
             ((Integer -> T__'8804'__22) -> Any -> Any
forall a b. a -> b
coe Integer -> T__'8804'__22
du_m'8804'n'43'm_3494 (Integer -> Any
forall a b. a -> b
coe Integer
v0))
      MAlonzo.Code.Data.Nat.Base.C_s'8804's_34 T__'8804'__22
v5
        -> (T__'8804'__22 -> T__'8804'__22) -> Any -> T__'8804'__22
forall a b. a -> b
coe
             T__'8804'__22 -> T__'8804'__22
MAlonzo.Code.Data.Nat.Base.C_s'8804's_34
             ((Integer -> T__'8804'__22 -> T__'8804'__22 -> T__'8804'__22)
-> Any -> Any -> Any -> Any
forall a b. a -> b
coe
                Integer -> T__'8804'__22 -> T__'8804'__22 -> T__'8804'__22
du_'43''45'mono'45''8804''45''60'_3570 (Integer -> Any
forall a b. a -> b
coe Integer
v0) (T__'8804'__22 -> Any
forall a b. a -> b
coe T__'8804'__22
v5) (T__'8804'__22 -> Any
forall a b. a -> b
coe T__'8804'__22
v2))
      T__'8804'__22
_ -> T__'8804'__22
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Data.Nat.Properties.+-mono-<
d_'43''45'mono'45''60'_3580 ::
  Integer ->
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_'43''45'mono'45''60'_3580 :: Integer
-> Integer
-> Integer
-> Integer
-> T__'8804'__22
-> T__'8804'__22
-> T__'8804'__22
d_'43''45'mono'45''60'_3580 ~Integer
v0 ~Integer
v1 ~Integer
v2 Integer
v3 T__'8804'__22
v4
  = Integer -> T__'8804'__22 -> T__'8804'__22 -> T__'8804'__22
du_'43''45'mono'45''60'_3580 Integer
v3 T__'8804'__22
v4
du_'43''45'mono'45''60'_3580 ::
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
du_'43''45'mono'45''60'_3580 :: Integer -> T__'8804'__22 -> T__'8804'__22 -> T__'8804'__22
du_'43''45'mono'45''60'_3580 Integer
v0 T__'8804'__22
v1
  = (Integer -> T__'8804'__22 -> T__'8804'__22 -> T__'8804'__22)
-> Any -> Any -> T__'8804'__22 -> T__'8804'__22
forall a b. a -> b
coe
      Integer -> T__'8804'__22 -> T__'8804'__22 -> T__'8804'__22
du_'43''45'mono'45''8804''45''60'_3570 (Integer -> Any
forall a b. a -> b
coe Integer
v0)
      ((T__'8804'__22 -> T__'8804'__22) -> Any -> Any
forall a b. a -> b
coe T__'8804'__22 -> T__'8804'__22
du_'60''8658''8804'_2854 (T__'8804'__22 -> Any
forall a b. a -> b
coe T__'8804'__22
v1))
-- Data.Nat.Properties.+-monoˡ-<
d_'43''45'mono'737''45''60'_3588 ::
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_'43''45'mono'737''45''60'_3588 :: Integer -> Integer -> Integer -> T__'8804'__22 -> T__'8804'__22
d_'43''45'mono'737''45''60'_3588 Integer
v0 ~Integer
v1 ~Integer
v2
  = Integer -> T__'8804'__22 -> T__'8804'__22
du_'43''45'mono'737''45''60'_3588 Integer
v0
du_'43''45'mono'737''45''60'_3588 ::
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
du_'43''45'mono'737''45''60'_3588 :: Integer -> T__'8804'__22 -> T__'8804'__22
du_'43''45'mono'737''45''60'_3588 Integer
v0
  = (Integer -> T__'8804'__22 -> T__'8804'__22)
-> Any -> T__'8804'__22 -> T__'8804'__22
forall a b. a -> b
coe Integer -> T__'8804'__22 -> T__'8804'__22
du_'43''45'mono'737''45''8804'_3544 (Integer -> Any
forall a b. a -> b
coe Integer
v0)
-- Data.Nat.Properties.+-monoʳ-<
d_'43''45'mono'691''45''60'_3596 ::
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_'43''45'mono'691''45''60'_3596 :: Integer -> Integer -> Integer -> T__'8804'__22 -> T__'8804'__22
d_'43''45'mono'691''45''60'_3596 Integer
v0 ~Integer
v1 ~Integer
v2 T__'8804'__22
v3
  = Integer -> T__'8804'__22 -> T__'8804'__22
du_'43''45'mono'691''45''60'_3596 Integer
v0 T__'8804'__22
v3
du_'43''45'mono'691''45''60'_3596 ::
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
du_'43''45'mono'691''45''60'_3596 :: Integer -> T__'8804'__22 -> T__'8804'__22
du_'43''45'mono'691''45''60'_3596 Integer
v0 T__'8804'__22
v1
  = case Integer -> Integer
forall a b. a -> b
coe Integer
v0 of
      Integer
0 -> T__'8804'__22 -> T__'8804'__22
forall a b. a -> b
coe T__'8804'__22
v1
      Integer
_ -> let v2 :: Integer
v2 = Integer -> Integer -> Integer
subInt (Integer -> Integer
forall a b. a -> b
coe Integer
v0) (Integer -> Integer
forall a b. a -> b
coe (Integer
1 :: Integer)) in
           Any -> T__'8804'__22
forall a b. a -> b
coe
             ((T__'8804'__22 -> T__'8804'__22) -> Any -> Any
forall a b. a -> b
coe
                T__'8804'__22 -> T__'8804'__22
MAlonzo.Code.Data.Nat.Base.C_s'8804's_34
                ((Integer -> T__'8804'__22 -> T__'8804'__22) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> T__'8804'__22 -> T__'8804'__22
du_'43''45'mono'691''45''60'_3596 (Integer -> Any
forall a b. a -> b
coe Integer
v2) (T__'8804'__22 -> Any
forall a b. a -> b
coe T__'8804'__22
v1)))
-- Data.Nat.Properties.m+1+n≰m
d_m'43'1'43'n'8816'm_3608 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Irrelevant.T_Irrelevant_20
d_m'43'1'43'n'8816'm_3608 :: Integer -> Integer -> T__'8804'__22 -> T_Irrelevant_20
d_m'43'1'43'n'8816'm_3608 = Integer -> Integer -> T__'8804'__22 -> T_Irrelevant_20
forall a. a
erased
-- Data.Nat.Properties.m<m+n
d_m'60'm'43'n_3618 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_m'60'm'43'n_3618 :: Integer -> Integer -> T__'8804'__22 -> T__'8804'__22
d_m'60'm'43'n_3618 Integer
v0 ~Integer
v1 T__'8804'__22
v2 = Integer -> T__'8804'__22 -> T__'8804'__22
du_m'60'm'43'n_3618 Integer
v0 T__'8804'__22
v2
du_m'60'm'43'n_3618 ::
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
du_m'60'm'43'n_3618 :: Integer -> T__'8804'__22 -> T__'8804'__22
du_m'60'm'43'n_3618 Integer
v0 T__'8804'__22
v1
  = case Integer -> Integer
forall a b. a -> b
coe Integer
v0 of
      Integer
0 -> T__'8804'__22 -> T__'8804'__22
forall a b. a -> b
coe T__'8804'__22
v1
      Integer
_ -> let v2 :: Integer
v2 = Integer -> Integer -> Integer
subInt (Integer -> Integer
forall a b. a -> b
coe Integer
v0) (Integer -> Integer
forall a b. a -> b
coe (Integer
1 :: Integer)) in
           Any -> T__'8804'__22
forall a b. a -> b
coe
             ((T__'8804'__22 -> T__'8804'__22) -> Any -> Any
forall a b. a -> b
coe
                T__'8804'__22 -> T__'8804'__22
MAlonzo.Code.Data.Nat.Base.C_s'8804's_34
                ((Integer -> T__'8804'__22 -> T__'8804'__22) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> T__'8804'__22 -> T__'8804'__22
du_m'60'm'43'n_3618 (Integer -> Any
forall a b. a -> b
coe Integer
v2) (T__'8804'__22 -> Any
forall a b. a -> b
coe T__'8804'__22
v1)))
-- Data.Nat.Properties.m<n+m
d_m'60'n'43'm_3630 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_m'60'n'43'm_3630 :: Integer -> Integer -> T__'8804'__22 -> T__'8804'__22
d_m'60'n'43'm_3630 Integer
v0 ~Integer
v1 T__'8804'__22
v2 = Integer -> T__'8804'__22 -> T__'8804'__22
du_m'60'n'43'm_3630 Integer
v0 T__'8804'__22
v2
du_m'60'n'43'm_3630 ::
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
du_m'60'n'43'm_3630 :: Integer -> T__'8804'__22 -> T__'8804'__22
du_m'60'n'43'm_3630 Integer
v0 T__'8804'__22
v1
  = (Integer -> T__'8804'__22 -> T__'8804'__22)
-> Any -> Any -> T__'8804'__22
forall a b. a -> b
coe Integer -> T__'8804'__22 -> T__'8804'__22
du_m'60'm'43'n_3618 (Integer -> Any
forall a b. a -> b
coe Integer
v0) (T__'8804'__22 -> Any
forall a b. a -> b
coe T__'8804'__22
v1)
-- Data.Nat.Properties.m+n≮n
d_m'43'n'8814'n_3646 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Irrelevant.T_Irrelevant_20
d_m'43'n'8814'n_3646 :: Integer -> Integer -> T__'8804'__22 -> T_Irrelevant_20
d_m'43'n'8814'n_3646 = Integer -> Integer -> T__'8804'__22 -> T_Irrelevant_20
forall a. a
erased
-- Data.Nat.Properties.m+n≮m
d_m'43'n'8814'm_3660 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Irrelevant.T_Irrelevant_20
d_m'43'n'8814'm_3660 :: Integer -> Integer -> T__'8804'__22 -> T_Irrelevant_20
d_m'43'n'8814'm_3660 = Integer -> Integer -> T__'8804'__22 -> T_Irrelevant_20
forall a. a
erased
-- Data.Nat.Properties.*-suc
d_'42''45'suc_3672 ::
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'42''45'suc_3672 :: Integer -> Integer -> T__'8801'__12
d_'42''45'suc_3672 = Integer -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Nat.Properties.*-identityˡ
d_'42''45'identity'737'_3684 ::
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'42''45'identity'737'_3684 :: Integer -> T__'8801'__12
d_'42''45'identity'737'_3684 = Integer -> T__'8801'__12
forall a. a
erased
-- Data.Nat.Properties.*-identityʳ
d_'42''45'identity'691'_3688 ::
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'42''45'identity'691'_3688 :: Integer -> T__'8801'__12
d_'42''45'identity'691'_3688 = Integer -> T__'8801'__12
forall a. a
erased
-- Data.Nat.Properties.*-identity
d_'42''45'identity_3692 :: MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'42''45'identity_3692 :: T_Σ_14
d_'42''45'identity_3692
  = (Any -> Any -> T_Σ_14) -> Any -> Any -> T_Σ_14
forall a b. a -> b
coe Any -> Any -> T_Σ_14
MAlonzo.Code.Agda.Builtin.Sigma.C__'44'__32 Any
forall a. a
erased Any
forall a. a
erased
-- Data.Nat.Properties.*-zeroˡ
d_'42''45'zero'737'_3694 ::
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'42''45'zero'737'_3694 :: Integer -> T__'8801'__12
d_'42''45'zero'737'_3694 = Integer -> T__'8801'__12
forall a. a
erased
-- Data.Nat.Properties.*-zeroʳ
d_'42''45'zero'691'_3696 ::
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'42''45'zero'691'_3696 :: Integer -> T__'8801'__12
d_'42''45'zero'691'_3696 = Integer -> T__'8801'__12
forall a. a
erased
-- Data.Nat.Properties.*-zero
d_'42''45'zero_3700 :: MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'42''45'zero_3700 :: T_Σ_14
d_'42''45'zero_3700
  = (Any -> Any -> T_Σ_14) -> Any -> Any -> T_Σ_14
forall a b. a -> b
coe Any -> Any -> T_Σ_14
MAlonzo.Code.Agda.Builtin.Sigma.C__'44'__32 Any
forall a. a
erased Any
forall a. a
erased
-- Data.Nat.Properties.*-comm
d_'42''45'comm_3702 ::
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'42''45'comm_3702 :: Integer -> Integer -> T__'8801'__12
d_'42''45'comm_3702 = Integer -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Nat.Properties.*-distribʳ-+
d_'42''45'distrib'691''45''43'_3712 ::
  Integer ->
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'42''45'distrib'691''45''43'_3712 :: Integer -> Integer -> Integer -> T__'8801'__12
d_'42''45'distrib'691''45''43'_3712 = Integer -> Integer -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Nat.Properties.*-distribˡ-+
d_'42''45'distrib'737''45''43'_3726 ::
  Integer ->
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'42''45'distrib'737''45''43'_3726 :: Integer -> Integer -> Integer -> T__'8801'__12
d_'42''45'distrib'737''45''43'_3726 = Integer -> Integer -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Nat.Properties.*-distrib-+
d_'42''45'distrib'45''43'_3728 ::
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'42''45'distrib'45''43'_3728 :: T_Σ_14
d_'42''45'distrib'45''43'_3728
  = (Any -> Any -> T_Σ_14) -> Any -> Any -> T_Σ_14
forall a b. a -> b
coe Any -> Any -> T_Σ_14
MAlonzo.Code.Agda.Builtin.Sigma.C__'44'__32 Any
forall a. a
erased Any
forall a. a
erased
-- Data.Nat.Properties.*-assoc
d_'42''45'assoc_3730 ::
  Integer ->
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'42''45'assoc_3730 :: Integer -> Integer -> Integer -> T__'8801'__12
d_'42''45'assoc_3730 = Integer -> Integer -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Nat.Properties.*-isMagma
d_'42''45'isMagma_3744 ::
  MAlonzo.Code.Algebra.Structures.T_IsMagma_176
d_'42''45'isMagma_3744 :: T_IsMagma_176
d_'42''45'isMagma_3744
  = (T_IsEquivalence_26
 -> (Any -> Any -> Any -> Any -> Any -> Any -> Any)
 -> T_IsMagma_176)
-> Any -> Any -> T_IsMagma_176
forall a b. a -> b
coe
      T_IsEquivalence_26
-> (Any -> Any -> Any -> Any -> Any -> Any -> Any) -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.C_IsMagma'46'constructor_1867
      (T_IsEquivalence_26 -> Any
forall a b. a -> b
coe
         T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.PropositionalEquality.Properties.du_isEquivalence_396)
      Any
forall a. a
erased
-- Data.Nat.Properties.*-isSemigroup
d_'42''45'isSemigroup_3746 ::
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_472
d_'42''45'isSemigroup_3746 :: T_IsSemigroup_472
d_'42''45'isSemigroup_3746
  = (T_IsMagma_176 -> (Any -> Any -> Any -> Any) -> T_IsSemigroup_472)
-> Any -> Any -> T_IsSemigroup_472
forall a b. a -> b
coe
      T_IsMagma_176 -> (Any -> Any -> Any -> Any) -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.C_IsSemigroup'46'constructor_10417
      (T_IsMagma_176 -> Any
forall a b. a -> b
coe T_IsMagma_176
d_'42''45'isMagma_3744) Any
forall a. a
erased
-- Data.Nat.Properties.*-isCommutativeSemigroup
d_'42''45'isCommutativeSemigroup_3748 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_548
d_'42''45'isCommutativeSemigroup_3748 :: T_IsCommutativeSemigroup_548
d_'42''45'isCommutativeSemigroup_3748
  = (T_IsSemigroup_472
 -> (Any -> Any -> Any) -> T_IsCommutativeSemigroup_548)
-> Any -> Any -> T_IsCommutativeSemigroup_548
forall a b. a -> b
coe
      T_IsSemigroup_472
-> (Any -> Any -> Any) -> T_IsCommutativeSemigroup_548
MAlonzo.Code.Algebra.Structures.C_IsCommutativeSemigroup'46'constructor_12093
      (T_IsSemigroup_472 -> Any
forall a b. a -> b
coe T_IsSemigroup_472
d_'42''45'isSemigroup_3746) Any
forall a. a
erased
-- Data.Nat.Properties.*-1-isMonoid
d_'42''45'1'45'isMonoid_3750 ::
  MAlonzo.Code.Algebra.Structures.T_IsMonoid_686
d_'42''45'1'45'isMonoid_3750 :: T_IsMonoid_686
d_'42''45'1'45'isMonoid_3750
  = (T_IsSemigroup_472 -> T_Σ_14 -> T_IsMonoid_686)
-> Any -> Any -> T_IsMonoid_686
forall a b. a -> b
coe
      T_IsSemigroup_472 -> T_Σ_14 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.C_IsMonoid'46'constructor_15873
      (T_IsSemigroup_472 -> Any
forall a b. a -> b
coe T_IsSemigroup_472
d_'42''45'isSemigroup_3746) (T_Σ_14 -> Any
forall a b. a -> b
coe T_Σ_14
d_'42''45'identity_3692)
-- Data.Nat.Properties.*-1-isCommutativeMonoid
d_'42''45'1'45'isCommutativeMonoid_3752 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMonoid_736
d_'42''45'1'45'isCommutativeMonoid_3752 :: T_IsCommutativeMonoid_736
d_'42''45'1'45'isCommutativeMonoid_3752
  = (T_IsMonoid_686
 -> (Any -> Any -> Any) -> T_IsCommutativeMonoid_736)
-> Any -> Any -> T_IsCommutativeMonoid_736
forall a b. a -> b
coe
      T_IsMonoid_686 -> (Any -> Any -> Any) -> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.C_IsCommutativeMonoid'46'constructor_17695
      (T_IsMonoid_686 -> Any
forall a b. a -> b
coe T_IsMonoid_686
d_'42''45'1'45'isMonoid_3750) Any
forall a. a
erased
-- Data.Nat.Properties.+-*-isSemiring
d_'43''45''42''45'isSemiring_3754 ::
  MAlonzo.Code.Algebra.Structures.T_IsSemiring_1570
d_'43''45''42''45'isSemiring_3754 :: T_IsSemiring_1570
d_'43''45''42''45'isSemiring_3754
  = (T_IsSemiringWithoutAnnihilatingZero_1468
 -> T_Σ_14 -> T_IsSemiring_1570)
-> Any -> Any -> T_IsSemiring_1570
forall a b. a -> b
coe
      T_IsSemiringWithoutAnnihilatingZero_1468
-> T_Σ_14 -> T_IsSemiring_1570
MAlonzo.Code.Algebra.Structures.C_IsSemiring'46'constructor_48071
      ((T_IsCommutativeMonoid_736
 -> (Any -> Any -> Any -> Any -> Any -> Any -> Any)
 -> (Any -> Any -> Any -> Any)
 -> T_Σ_14
 -> T_Σ_14
 -> T_IsSemiringWithoutAnnihilatingZero_1468)
-> Any -> Any -> Any -> Any -> Any -> Any
forall a b. a -> b
coe
         T_IsCommutativeMonoid_736
-> (Any -> Any -> Any -> Any -> Any -> Any -> Any)
-> (Any -> Any -> Any -> Any)
-> T_Σ_14
-> T_Σ_14
-> T_IsSemiringWithoutAnnihilatingZero_1468
MAlonzo.Code.Algebra.Structures.C_IsSemiringWithoutAnnihilatingZero'46'constructor_43811
         (T_IsCommutativeMonoid_736 -> Any
forall a b. a -> b
coe T_IsCommutativeMonoid_736
d_'43''45'0'45'isCommutativeMonoid_3324) Any
forall a. a
erased Any
forall a. a
erased
         (T_Σ_14 -> Any
forall a b. a -> b
coe T_Σ_14
d_'42''45'identity_3692) (T_Σ_14 -> Any
forall a b. a -> b
coe T_Σ_14
d_'42''45'distrib'45''43'_3728))
      (T_Σ_14 -> Any
forall a b. a -> b
coe T_Σ_14
d_'42''45'zero_3700)
-- Data.Nat.Properties.+-*-isCommutativeSemiring
d_'43''45''42''45'isCommutativeSemiring_3756 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiring_1678
d_'43''45''42''45'isCommutativeSemiring_3756 :: T_IsCommutativeSemiring_1678
d_'43''45''42''45'isCommutativeSemiring_3756
  = (T_IsSemiring_1570
 -> (Any -> Any -> Any) -> T_IsCommutativeSemiring_1678)
-> Any -> Any -> T_IsCommutativeSemiring_1678
forall a b. a -> b
coe
      T_IsSemiring_1570
-> (Any -> Any -> Any) -> T_IsCommutativeSemiring_1678
MAlonzo.Code.Algebra.Structures.C_IsCommutativeSemiring'46'constructor_51895
      (T_IsSemiring_1570 -> Any
forall a b. a -> b
coe T_IsSemiring_1570
d_'43''45''42''45'isSemiring_3754) Any
forall a. a
erased
-- Data.Nat.Properties.*-magma
d_'42''45'magma_3758 :: MAlonzo.Code.Algebra.Bundles.T_Magma_68
d_'42''45'magma_3758 :: T_Magma_68
d_'42''45'magma_3758
  = ((Any -> Any -> Any) -> T_IsMagma_176 -> T_Magma_68)
-> (Integer -> Integer -> Integer) -> T_IsMagma_176 -> T_Magma_68
forall a b. a -> b
coe
      (Any -> Any -> Any) -> T_IsMagma_176 -> T_Magma_68
MAlonzo.Code.Algebra.Bundles.C_Magma'46'constructor_1279 Integer -> Integer -> Integer
mulInt
      T_IsMagma_176
d_'42''45'isMagma_3744
-- Data.Nat.Properties.*-semigroup
d_'42''45'semigroup_3760 ::
  MAlonzo.Code.Algebra.Bundles.T_Semigroup_536
d_'42''45'semigroup_3760 :: T_Semigroup_536
d_'42''45'semigroup_3760
  = ((Any -> Any -> Any) -> T_IsSemigroup_472 -> T_Semigroup_536)
-> (Integer -> Integer -> Integer)
-> T_IsSemigroup_472
-> T_Semigroup_536
forall a b. a -> b
coe
      (Any -> Any -> Any) -> T_IsSemigroup_472 -> T_Semigroup_536
MAlonzo.Code.Algebra.Bundles.C_Semigroup'46'constructor_9793 Integer -> Integer -> Integer
mulInt
      T_IsSemigroup_472
d_'42''45'isSemigroup_3746
-- Data.Nat.Properties.*-commutativeSemigroup
d_'42''45'commutativeSemigroup_3762 ::
  MAlonzo.Code.Algebra.Bundles.T_CommutativeSemigroup_662
d_'42''45'commutativeSemigroup_3762 :: T_CommutativeSemigroup_662
d_'42''45'commutativeSemigroup_3762
  = ((Any -> Any -> Any)
 -> T_IsCommutativeSemigroup_548 -> T_CommutativeSemigroup_662)
-> (Integer -> Integer -> Integer)
-> T_IsCommutativeSemigroup_548
-> T_CommutativeSemigroup_662
forall a b. a -> b
coe
      (Any -> Any -> Any)
-> T_IsCommutativeSemigroup_548 -> T_CommutativeSemigroup_662
MAlonzo.Code.Algebra.Bundles.C_CommutativeSemigroup'46'constructor_12035
      Integer -> Integer -> Integer
mulInt T_IsCommutativeSemigroup_548
d_'42''45'isCommutativeSemigroup_3748
-- Data.Nat.Properties.*-1-monoid
d_'42''45'1'45'monoid_3764 ::
  MAlonzo.Code.Algebra.Bundles.T_Monoid_882
d_'42''45'1'45'monoid_3764 :: T_Monoid_882
d_'42''45'1'45'monoid_3764
  = ((Any -> Any -> Any) -> Any -> T_IsMonoid_686 -> T_Monoid_882)
-> (Integer -> Integer -> Integer)
-> Integer
-> T_IsMonoid_686
-> T_Monoid_882
forall a b. a -> b
coe
      (Any -> Any -> Any) -> Any -> T_IsMonoid_686 -> T_Monoid_882
MAlonzo.Code.Algebra.Bundles.C_Monoid'46'constructor_16157 Integer -> Integer -> Integer
mulInt
      (Integer
1 :: Integer) T_IsMonoid_686
d_'42''45'1'45'isMonoid_3750
-- Data.Nat.Properties.*-1-commutativeMonoid
d_'42''45'1'45'commutativeMonoid_3766 ::
  MAlonzo.Code.Algebra.Bundles.T_CommutativeMonoid_962
d_'42''45'1'45'commutativeMonoid_3766 :: T_CommutativeMonoid_962
d_'42''45'1'45'commutativeMonoid_3766
  = ((Any -> Any -> Any)
 -> Any -> T_IsCommutativeMonoid_736 -> T_CommutativeMonoid_962)
-> (Integer -> Integer -> Integer)
-> Integer
-> T_IsCommutativeMonoid_736
-> T_CommutativeMonoid_962
forall a b. a -> b
coe
      (Any -> Any -> Any)
-> Any -> T_IsCommutativeMonoid_736 -> T_CommutativeMonoid_962
MAlonzo.Code.Algebra.Bundles.C_CommutativeMonoid'46'constructor_17931
      Integer -> Integer -> Integer
mulInt (Integer
1 :: Integer) T_IsCommutativeMonoid_736
d_'42''45'1'45'isCommutativeMonoid_3752
-- Data.Nat.Properties.+-*-semiring
d_'43''45''42''45'semiring_3768 ::
  MAlonzo.Code.Algebra.Bundles.T_Semiring_2280
d_'43''45''42''45'semiring_3768 :: T_Semiring_2280
d_'43''45''42''45'semiring_3768
  = ((Any -> Any -> Any)
 -> (Any -> Any -> Any)
 -> Any
 -> Any
 -> T_IsSemiring_1570
 -> T_Semiring_2280)
-> (Integer -> Integer -> Integer)
-> (Integer -> Integer -> Integer)
-> Integer
-> Integer
-> T_IsSemiring_1570
-> T_Semiring_2280
forall a b. a -> b
coe
      (Any -> Any -> Any)
-> (Any -> Any -> Any)
-> Any
-> Any
-> T_IsSemiring_1570
-> T_Semiring_2280
MAlonzo.Code.Algebra.Bundles.C_Semiring'46'constructor_41765 Integer -> Integer -> Integer
addInt
      Integer -> Integer -> Integer
mulInt (Integer
0 :: Integer) (Integer
1 :: Integer)
      T_IsSemiring_1570
d_'43''45''42''45'isSemiring_3754
-- Data.Nat.Properties.+-*-commutativeSemiring
d_'43''45''42''45'commutativeSemiring_3770 ::
  MAlonzo.Code.Algebra.Bundles.T_CommutativeSemiring_2446
d_'43''45''42''45'commutativeSemiring_3770 :: T_CommutativeSemiring_2446
d_'43''45''42''45'commutativeSemiring_3770
  = ((Any -> Any -> Any)
 -> (Any -> Any -> Any)
 -> Any
 -> Any
 -> T_IsCommutativeSemiring_1678
 -> T_CommutativeSemiring_2446)
-> (Integer -> Integer -> Integer)
-> (Integer -> Integer -> Integer)
-> Integer
-> Integer
-> T_IsCommutativeSemiring_1678
-> T_CommutativeSemiring_2446
forall a b. a -> b
coe
      (Any -> Any -> Any)
-> (Any -> Any -> Any)
-> Any
-> Any
-> T_IsCommutativeSemiring_1678
-> T_CommutativeSemiring_2446
MAlonzo.Code.Algebra.Bundles.C_CommutativeSemiring'46'constructor_44731
      Integer -> Integer -> Integer
addInt Integer -> Integer -> Integer
mulInt (Integer
0 :: Integer) (Integer
1 :: Integer)
      T_IsCommutativeSemiring_1678
d_'43''45''42''45'isCommutativeSemiring_3756
-- Data.Nat.Properties.*-cancelʳ-≡
d_'42''45'cancel'691''45''8801'_3780 ::
  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'_3780 :: Integer
-> Integer
-> Integer
-> T_NonZero_112
-> T__'8801'__12
-> T__'8801'__12
d_'42''45'cancel'691''45''8801'_3780 = Integer
-> Integer
-> Integer
-> T_NonZero_112
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Nat.Properties.*-cancelˡ-≡
d_'42''45'cancel'737''45''8801'_3802 ::
  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'_3802 :: Integer
-> Integer
-> Integer
-> T_NonZero_112
-> T__'8801'__12
-> T__'8801'__12
d_'42''45'cancel'737''45''8801'_3802 = Integer
-> Integer
-> Integer
-> T_NonZero_112
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Nat.Properties.m*n≡0⇒m≡0∨n≡0
d_m'42'n'8801'0'8658'm'8801'0'8744'n'8801'0_3822 ::
  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_3822 :: Integer -> Integer -> T__'8801'__12 -> T__'8846'__30
d_m'42'n'8801'0'8658'm'8801'0'8744'n'8801'0_3822 Integer
v0 ~Integer
v1 ~T__'8801'__12
v2
  = Integer -> T__'8846'__30
du_m'42'n'8801'0'8658'm'8801'0'8744'n'8801'0_3822 Integer
v0
du_m'42'n'8801'0'8658'm'8801'0'8744'n'8801'0_3822 ::
  Integer -> MAlonzo.Code.Data.Sum.Base.T__'8846'__30
du_m'42'n'8801'0'8658'm'8801'0'8744'n'8801'0_3822 :: Integer -> T__'8846'__30
du_m'42'n'8801'0'8658'm'8801'0'8744'n'8801'0_3822 Integer
v0
  = case Integer -> Integer
forall a b. a -> b
coe Integer
v0 of
      Integer
0 -> (Any -> T__'8846'__30) -> Any -> T__'8846'__30
forall a b. a -> b
coe Any -> T__'8846'__30
MAlonzo.Code.Data.Sum.Base.C_inj'8321'_38 Any
forall a. a
erased
      Integer
_ -> (Any -> T__'8846'__30) -> Any -> T__'8846'__30
forall a b. a -> b
coe Any -> T__'8846'__30
MAlonzo.Code.Data.Sum.Base.C_inj'8322'_42 Any
forall a. a
erased
-- Data.Nat.Properties.m*n≢0
d_m'42'n'8802'0_3840 ::
  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_m'42'n'8802'0_3840 :: Integer
-> Integer -> T_NonZero_112 -> T_NonZero_112 -> T_NonZero_112
d_m'42'n'8802'0_3840 ~Integer
v0 ~Integer
v1 ~T_NonZero_112
v2 ~T_NonZero_112
v3 = T_NonZero_112
du_m'42'n'8802'0_3840
du_m'42'n'8802'0_3840 :: MAlonzo.Code.Data.Nat.Base.T_NonZero_112
du_m'42'n'8802'0_3840 :: T_NonZero_112
du_m'42'n'8802'0_3840
  = (Any -> T_NonZero_112) -> Any -> T_NonZero_112
forall a b. a -> b
coe
      Any -> T_NonZero_112
MAlonzo.Code.Data.Nat.Base.C_NonZero'46'constructor_3575
      (() -> Any
forall a b. a -> b
coe ()
MAlonzo.Code.Agda.Builtin.Unit.C_tt_8)
-- Data.Nat.Properties.m*n≢0⇒m≢0
d_m'42'n'8802'0'8658'm'8802'0_3850 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T_NonZero_112 ->
  MAlonzo.Code.Data.Nat.Base.T_NonZero_112
d_m'42'n'8802'0'8658'm'8802'0_3850 :: Integer -> Integer -> T_NonZero_112 -> T_NonZero_112
d_m'42'n'8802'0'8658'm'8802'0_3850 ~Integer
v0 ~Integer
v1 ~T_NonZero_112
v2
  = T_NonZero_112
du_m'42'n'8802'0'8658'm'8802'0_3850
du_m'42'n'8802'0'8658'm'8802'0_3850 ::
  MAlonzo.Code.Data.Nat.Base.T_NonZero_112
du_m'42'n'8802'0'8658'm'8802'0_3850 :: T_NonZero_112
du_m'42'n'8802'0'8658'm'8802'0_3850
  = (Any -> T_NonZero_112) -> Any -> T_NonZero_112
forall a b. a -> b
coe
      Any -> T_NonZero_112
MAlonzo.Code.Data.Nat.Base.C_NonZero'46'constructor_3575
      (() -> Any
forall a b. a -> b
coe ()
MAlonzo.Code.Agda.Builtin.Unit.C_tt_8)
-- Data.Nat.Properties.m*n≢0⇒n≢0
d_m'42'n'8802'0'8658'n'8802'0_3856 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T_NonZero_112 ->
  MAlonzo.Code.Data.Nat.Base.T_NonZero_112
d_m'42'n'8802'0'8658'n'8802'0_3856 :: Integer -> Integer -> T_NonZero_112 -> T_NonZero_112
d_m'42'n'8802'0'8658'n'8802'0_3856 ~Integer
v0 ~Integer
v1 ~T_NonZero_112
v2
  = T_NonZero_112
du_m'42'n'8802'0'8658'n'8802'0_3856
du_m'42'n'8802'0'8658'n'8802'0_3856 ::
  MAlonzo.Code.Data.Nat.Base.T_NonZero_112
du_m'42'n'8802'0'8658'n'8802'0_3856 :: T_NonZero_112
du_m'42'n'8802'0'8658'n'8802'0_3856
  = T_NonZero_112 -> T_NonZero_112
forall a b. a -> b
coe T_NonZero_112
du_m'42'n'8802'0'8658'm'8802'0_3850
-- Data.Nat.Properties.m*n≡0⇒m≡0
d_m'42'n'8801'0'8658'm'8801'0_3872 ::
  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_m'42'n'8801'0'8658'm'8801'0_3872 :: Integer
-> Integer -> T_NonZero_112 -> T__'8801'__12 -> T__'8801'__12
d_m'42'n'8801'0'8658'm'8801'0_3872 = Integer
-> Integer -> T_NonZero_112 -> T__'8801'__12 -> T__'8801'__12
forall a. a
erased
-- Data.Nat.Properties.m*n≡1⇒m≡1
d_m'42'n'8801'1'8658'm'8801'1_3880 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_m'42'n'8801'1'8658'm'8801'1_3880 :: Integer -> Integer -> T__'8801'__12 -> T__'8801'__12
d_m'42'n'8801'1'8658'm'8801'1_3880 = Integer -> Integer -> T__'8801'__12 -> T__'8801'__12
forall a. a
erased
-- Data.Nat.Properties.m*n≡1⇒n≡1
d_m'42'n'8801'1'8658'n'8801'1_3894 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_m'42'n'8801'1'8658'n'8801'1_3894 :: Integer -> Integer -> T__'8801'__12 -> T__'8801'__12
d_m'42'n'8801'1'8658'n'8801'1_3894 = Integer -> Integer -> T__'8801'__12 -> T__'8801'__12
forall a. a
erased
-- Data.Nat.Properties.[m*n]*[o*p]≡[m*o]*[n*p]
d_'91'm'42'n'93''42''91'o'42'p'93''8801''91'm'42'o'93''42''91'n'42'p'93'_3910 ::
  Integer ->
  Integer ->
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'91'm'42'n'93''42''91'o'42'p'93''8801''91'm'42'o'93''42''91'n'42'p'93'_3910 :: Integer -> Integer -> Integer -> Integer -> T__'8801'__12
d_'91'm'42'n'93''42''91'o'42'p'93''8801''91'm'42'o'93''42''91'n'42'p'93'_3910
  = Integer -> Integer -> Integer -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Nat.Properties.m≢0∧n>1⇒m*n>1
d_m'8802'0'8743'n'62'1'8658'm'42'n'62'1_3998 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T_NonZero_112 ->
  MAlonzo.Code.Data.Nat.Base.T_NonTrivial_152 ->
  MAlonzo.Code.Data.Nat.Base.T_NonTrivial_152
d_m'8802'0'8743'n'62'1'8658'm'42'n'62'1_3998 :: Integer
-> Integer -> T_NonZero_112 -> T_NonTrivial_152 -> T_NonTrivial_152
d_m'8802'0'8743'n'62'1'8658'm'42'n'62'1_3998 ~Integer
v0 ~Integer
v1 ~T_NonZero_112
v2 ~T_NonTrivial_152
v3
  = T_NonTrivial_152
du_m'8802'0'8743'n'62'1'8658'm'42'n'62'1_3998
du_m'8802'0'8743'n'62'1'8658'm'42'n'62'1_3998 ::
  MAlonzo.Code.Data.Nat.Base.T_NonTrivial_152
du_m'8802'0'8743'n'62'1'8658'm'42'n'62'1_3998 :: T_NonTrivial_152
du_m'8802'0'8743'n'62'1'8658'm'42'n'62'1_3998
  = (Any -> T_NonTrivial_152) -> Any -> T_NonTrivial_152
forall a b. a -> b
coe
      Any -> T_NonTrivial_152
MAlonzo.Code.Data.Nat.Base.C_NonTrivial'46'constructor_5661
      (() -> Any
forall a b. a -> b
coe ()
MAlonzo.Code.Agda.Builtin.Unit.C_tt_8)
-- Data.Nat.Properties.n≢0∧m>1⇒m*n>1
d_n'8802'0'8743'm'62'1'8658'm'42'n'62'1_4012 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T_NonZero_112 ->
  MAlonzo.Code.Data.Nat.Base.T_NonTrivial_152 ->
  MAlonzo.Code.Data.Nat.Base.T_NonTrivial_152
d_n'8802'0'8743'm'62'1'8658'm'42'n'62'1_4012 :: Integer
-> Integer -> T_NonZero_112 -> T_NonTrivial_152 -> T_NonTrivial_152
d_n'8802'0'8743'm'62'1'8658'm'42'n'62'1_4012 ~Integer
v0 ~Integer
v1 ~T_NonZero_112
v2 ~T_NonTrivial_152
v3
  = T_NonTrivial_152
du_n'8802'0'8743'm'62'1'8658'm'42'n'62'1_4012
du_n'8802'0'8743'm'62'1'8658'm'42'n'62'1_4012 ::
  MAlonzo.Code.Data.Nat.Base.T_NonTrivial_152
du_n'8802'0'8743'm'62'1'8658'm'42'n'62'1_4012 :: T_NonTrivial_152
du_n'8802'0'8743'm'62'1'8658'm'42'n'62'1_4012
  = T_NonTrivial_152 -> T_NonTrivial_152
forall a b. a -> b
coe T_NonTrivial_152
du_m'8802'0'8743'n'62'1'8658'm'42'n'62'1_3998
-- Data.Nat.Properties.*-cancelʳ-≤
d_'42''45'cancel'691''45''8804'_4030 ::
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T_NonZero_112 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_'42''45'cancel'691''45''8804'_4030 :: Integer
-> Integer
-> Integer
-> T_NonZero_112
-> T__'8804'__22
-> T__'8804'__22
d_'42''45'cancel'691''45''8804'_4030 Integer
v0 ~Integer
v1 ~Integer
v2 ~T_NonZero_112
v3 ~T__'8804'__22
v4
  = Integer -> T__'8804'__22
du_'42''45'cancel'691''45''8804'_4030 Integer
v0
du_'42''45'cancel'691''45''8804'_4030 ::
  Integer -> MAlonzo.Code.Data.Nat.Base.T__'8804'__22
du_'42''45'cancel'691''45''8804'_4030 :: Integer -> T__'8804'__22
du_'42''45'cancel'691''45''8804'_4030 Integer
v0
  = case Integer -> Integer
forall a b. a -> b
coe Integer
v0 of
      Integer
0 -> T__'8804'__22 -> T__'8804'__22
forall a b. a -> b
coe T__'8804'__22
MAlonzo.Code.Data.Nat.Base.C_z'8804'n_26
      Integer
_ -> let v1 :: Integer
v1 = Integer -> Integer -> Integer
subInt (Integer -> Integer
forall a b. a -> b
coe Integer
v0) (Integer -> Integer
forall a b. a -> b
coe (Integer
1 :: Integer)) in
           Any -> T__'8804'__22
forall a b. a -> b
coe
             ((T__'8804'__22 -> T__'8804'__22) -> Any -> Any
forall a b. a -> b
coe
                T__'8804'__22 -> T__'8804'__22
MAlonzo.Code.Data.Nat.Base.C_s'8804's_34
                ((Integer -> T__'8804'__22) -> Any -> Any
forall a b. a -> b
coe Integer -> T__'8804'__22
du_'42''45'cancel'691''45''8804'_4030 (Integer -> Any
forall a b. a -> b
coe Integer
v1)))
-- Data.Nat.Properties.*-cancelˡ-≤
d_'42''45'cancel'737''45''8804'_4044 ::
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T_NonZero_112 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_'42''45'cancel'737''45''8804'_4044 :: Integer
-> Integer
-> Integer
-> T_NonZero_112
-> T__'8804'__22
-> T__'8804'__22
d_'42''45'cancel'737''45''8804'_4044 Integer
v0 ~Integer
v1 ~Integer
v2 ~T_NonZero_112
v3
  = Integer -> T__'8804'__22 -> T__'8804'__22
du_'42''45'cancel'737''45''8804'_4044 Integer
v0
du_'42''45'cancel'737''45''8804'_4044 ::
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
du_'42''45'cancel'737''45''8804'_4044 :: Integer -> T__'8804'__22 -> T__'8804'__22
du_'42''45'cancel'737''45''8804'_4044 Integer
v0 T__'8804'__22
v1
  = (Integer -> T__'8804'__22) -> Any -> T__'8804'__22
forall a b. a -> b
coe Integer -> T__'8804'__22
du_'42''45'cancel'691''45''8804'_4030 (Integer -> Any
forall a b. a -> b
coe Integer
v0)
-- Data.Nat.Properties.*-mono-≤
d_'42''45'mono'45''8804'_4060 ::
  Integer ->
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_'42''45'mono'45''8804'_4060 :: Integer
-> Integer
-> Integer
-> Integer
-> T__'8804'__22
-> T__'8804'__22
-> T__'8804'__22
d_'42''45'mono'45''8804'_4060 ~Integer
v0 Integer
v1 ~Integer
v2 Integer
v3 T__'8804'__22
v4 T__'8804'__22
v5
  = Integer
-> Integer -> T__'8804'__22 -> T__'8804'__22 -> T__'8804'__22
du_'42''45'mono'45''8804'_4060 Integer
v1 Integer
v3 T__'8804'__22
v4 T__'8804'__22
v5
du_'42''45'mono'45''8804'_4060 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
du_'42''45'mono'45''8804'_4060 :: Integer
-> Integer -> T__'8804'__22 -> T__'8804'__22 -> T__'8804'__22
du_'42''45'mono'45''8804'_4060 Integer
v0 Integer
v1 T__'8804'__22
v2 T__'8804'__22
v3
  = case T__'8804'__22 -> T__'8804'__22
forall a b. a -> b
coe T__'8804'__22
v2 of
      T__'8804'__22
MAlonzo.Code.Data.Nat.Base.C_z'8804'n_26
        -> T__'8804'__22 -> T__'8804'__22
forall a b. a -> b
coe T__'8804'__22
MAlonzo.Code.Data.Nat.Base.C_z'8804'n_26
      MAlonzo.Code.Data.Nat.Base.C_s'8804's_34 T__'8804'__22
v6
        -> let v7 :: Integer
v7 = Integer -> Integer -> Integer
subInt (Integer -> Integer
forall a b. a -> b
coe Integer
v0) (Integer -> Integer
forall a b. a -> b
coe (Integer
1 :: Integer)) in
           Any -> T__'8804'__22
forall a b. a -> b
coe
             ((Integer -> T__'8804'__22 -> T__'8804'__22 -> T__'8804'__22)
-> Any -> Any -> Any -> Any
forall a b. a -> b
coe
                Integer -> T__'8804'__22 -> T__'8804'__22 -> T__'8804'__22
du_'43''45'mono'45''8804'_3530 ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> Integer
mulInt (Integer -> Any
forall a b. a -> b
coe Integer
v7) (Integer -> Any
forall a b. a -> b
coe Integer
v1))
                (T__'8804'__22 -> Any
forall a b. a -> b
coe T__'8804'__22
v3)
                ((Integer
 -> Integer -> T__'8804'__22 -> T__'8804'__22 -> T__'8804'__22)
-> Any -> Any -> Any -> Any -> Any
forall a b. a -> b
coe
                   Integer
-> Integer -> T__'8804'__22 -> T__'8804'__22 -> T__'8804'__22
du_'42''45'mono'45''8804'_4060 (Integer -> Any
forall a b. a -> b
coe Integer
v7) (Integer -> Any
forall a b. a -> b
coe Integer
v1) (T__'8804'__22 -> Any
forall a b. a -> b
coe T__'8804'__22
v6)
                   (T__'8804'__22 -> Any
forall a b. a -> b
coe T__'8804'__22
v3)))
      T__'8804'__22
_ -> T__'8804'__22
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Data.Nat.Properties.*-monoˡ-≤
d_'42''45'mono'737''45''8804'_4070 ::
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_'42''45'mono'737''45''8804'_4070 :: Integer -> Integer -> Integer -> T__'8804'__22 -> T__'8804'__22
d_'42''45'mono'737''45''8804'_4070 Integer
v0 ~Integer
v1 Integer
v2 T__'8804'__22
v3
  = Integer -> Integer -> T__'8804'__22 -> T__'8804'__22
du_'42''45'mono'737''45''8804'_4070 Integer
v0 Integer
v2 T__'8804'__22
v3
du_'42''45'mono'737''45''8804'_4070 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
du_'42''45'mono'737''45''8804'_4070 :: Integer -> Integer -> T__'8804'__22 -> T__'8804'__22
du_'42''45'mono'737''45''8804'_4070 Integer
v0 Integer
v1 T__'8804'__22
v2
  = (Integer
 -> Integer -> T__'8804'__22 -> T__'8804'__22 -> T__'8804'__22)
-> Any -> Any -> Any -> Any -> T__'8804'__22
forall a b. a -> b
coe
      Integer
-> Integer -> T__'8804'__22 -> T__'8804'__22 -> T__'8804'__22
du_'42''45'mono'45''8804'_4060 (Integer -> Any
forall a b. a -> b
coe Integer
v1) (Integer -> Any
forall a b. a -> b
coe Integer
v0) (T__'8804'__22 -> Any
forall a b. a -> b
coe T__'8804'__22
v2)
      ((Integer -> T__'8804'__22) -> Any -> Any
forall a b. a -> b
coe Integer -> T__'8804'__22
d_'8804''45'refl_2776 (Integer -> Any
forall a b. a -> b
coe Integer
v0))
-- Data.Nat.Properties.*-monoʳ-≤
d_'42''45'mono'691''45''8804'_4080 ::
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_'42''45'mono'691''45''8804'_4080 :: Integer -> Integer -> Integer -> T__'8804'__22 -> T__'8804'__22
d_'42''45'mono'691''45''8804'_4080 Integer
v0 ~Integer
v1 Integer
v2 T__'8804'__22
v3
  = Integer -> Integer -> T__'8804'__22 -> T__'8804'__22
du_'42''45'mono'691''45''8804'_4080 Integer
v0 Integer
v2 T__'8804'__22
v3
du_'42''45'mono'691''45''8804'_4080 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
du_'42''45'mono'691''45''8804'_4080 :: Integer -> Integer -> T__'8804'__22 -> T__'8804'__22
du_'42''45'mono'691''45''8804'_4080 Integer
v0 Integer
v1 T__'8804'__22
v2
  = (Integer
 -> Integer -> T__'8804'__22 -> T__'8804'__22 -> T__'8804'__22)
-> Any -> Any -> Any -> Any -> T__'8804'__22
forall a b. a -> b
coe
      Integer
-> Integer -> T__'8804'__22 -> T__'8804'__22 -> T__'8804'__22
du_'42''45'mono'45''8804'_4060 (Integer -> Any
forall a b. a -> b
coe Integer
v0) (Integer -> Any
forall a b. a -> b
coe Integer
v1)
      ((Integer -> T__'8804'__22) -> Any -> Any
forall a b. a -> b
coe Integer -> T__'8804'__22
d_'8804''45'refl_2776 (Integer -> Any
forall a b. a -> b
coe Integer
v0)) (T__'8804'__22 -> Any
forall a b. a -> b
coe T__'8804'__22
v2)
-- Data.Nat.Properties.*-mono-<
d_'42''45'mono'45''60'_4086 ::
  Integer ->
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_'42''45'mono'45''60'_4086 :: Integer
-> Integer
-> Integer
-> Integer
-> T__'8804'__22
-> T__'8804'__22
-> T__'8804'__22
d_'42''45'mono'45''60'_4086 ~Integer
v0 Integer
v1 ~Integer
v2 Integer
v3 T__'8804'__22
v4 T__'8804'__22
v5
  = Integer
-> Integer -> T__'8804'__22 -> T__'8804'__22 -> T__'8804'__22
du_'42''45'mono'45''60'_4086 Integer
v1 Integer
v3 T__'8804'__22
v4 T__'8804'__22
v5
du_'42''45'mono'45''60'_4086 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
du_'42''45'mono'45''60'_4086 :: Integer
-> Integer -> T__'8804'__22 -> T__'8804'__22 -> T__'8804'__22
du_'42''45'mono'45''60'_4086 Integer
v0 Integer
v1 T__'8804'__22
v2 T__'8804'__22
v3
  = case T__'8804'__22 -> T__'8804'__22
forall a b. a -> b
coe T__'8804'__22
v2 of
      MAlonzo.Code.Data.Nat.Base.C_s'8804's_34 T__'8804'__22
v6
        -> case T__'8804'__22 -> T__'8804'__22
forall a b. a -> b
coe T__'8804'__22
v6 of
             T__'8804'__22
MAlonzo.Code.Data.Nat.Base.C_z'8804'n_26
               -> (Any -> Any -> Any) -> Any -> Any -> T__'8804'__22
forall a b. a -> b
coe Any -> Any -> Any
forall a b. a -> b -> b
seq (T__'8804'__22 -> Any
forall a b. a -> b
coe T__'8804'__22
v3) (T__'8804'__22 -> Any
forall a b. a -> b
coe T__'8804'__22
du_0'60'1'43'n_3074)
             MAlonzo.Code.Data.Nat.Base.C_s'8804's_34 T__'8804'__22
v9
               -> case T__'8804'__22 -> T__'8804'__22
forall a b. a -> b
coe T__'8804'__22
v3 of
                    MAlonzo.Code.Data.Nat.Base.C_s'8804's_34 T__'8804'__22
v12
                      -> (Integer -> T__'8804'__22 -> T__'8804'__22 -> T__'8804'__22)
-> Integer -> Any -> Any -> T__'8804'__22
forall a b. a -> b
coe
                           Integer -> T__'8804'__22 -> T__'8804'__22 -> T__'8804'__22
du_'43''45'mono'45''60'_3580
                           (Integer -> Integer -> Integer
mulInt ((Integer -> Integer -> Integer) -> Any -> Any -> Integer
forall a b. a -> b
coe Integer -> Integer -> Integer
subInt (Integer -> Any
forall a b. a -> b
coe Integer
v0) (Integer -> Any
forall a b. a -> b
coe (Integer
1 :: Integer))) (Integer -> Integer
forall a b. a -> b
coe Integer
v1))
                           ((T__'8804'__22 -> T__'8804'__22) -> T__'8804'__22 -> Any
forall a b. a -> b
coe T__'8804'__22 -> T__'8804'__22
MAlonzo.Code.Data.Nat.Base.C_s'8804's_34 T__'8804'__22
v12)
                           ((Integer
 -> Integer -> T__'8804'__22 -> T__'8804'__22 -> T__'8804'__22)
-> Any -> Any -> Any -> Any -> Any
forall a b. a -> b
coe
                              Integer
-> Integer -> T__'8804'__22 -> T__'8804'__22 -> T__'8804'__22
du_'42''45'mono'45''60'_4086
                              ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> Integer
subInt (Integer -> Any
forall a b. a -> b
coe Integer
v0) (Integer -> Any
forall a b. a -> b
coe (Integer
1 :: Integer))) (Integer -> Any
forall a b. a -> b
coe Integer
v1)
                              ((T__'8804'__22 -> T__'8804'__22) -> T__'8804'__22 -> Any
forall a b. a -> b
coe T__'8804'__22 -> T__'8804'__22
MAlonzo.Code.Data.Nat.Base.C_s'8804's_34 T__'8804'__22
v9)
                              ((T__'8804'__22 -> T__'8804'__22) -> T__'8804'__22 -> Any
forall a b. a -> b
coe T__'8804'__22 -> T__'8804'__22
MAlonzo.Code.Data.Nat.Base.C_s'8804's_34 T__'8804'__22
v12))
                    T__'8804'__22
_ -> T__'8804'__22
forall a. a
MAlonzo.RTE.mazUnreachableError
             T__'8804'__22
_ -> T__'8804'__22
forall a. a
MAlonzo.RTE.mazUnreachableError
      T__'8804'__22
_ -> T__'8804'__22
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Data.Nat.Properties.*-monoˡ-<
d_'42''45'mono'737''45''60'_4100 ::
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T_NonZero_112 ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_'42''45'mono'737''45''60'_4100 :: Integer
-> T_NonZero_112
-> Integer
-> Integer
-> T__'8804'__22
-> T__'8804'__22
d_'42''45'mono'737''45''60'_4100 Integer
v0 ~T_NonZero_112
v1 Integer
v2 Integer
v3 T__'8804'__22
v4
  = Integer -> Integer -> Integer -> T__'8804'__22 -> T__'8804'__22
du_'42''45'mono'737''45''60'_4100 Integer
v0 Integer
v2 Integer
v3 T__'8804'__22
v4
du_'42''45'mono'737''45''60'_4100 ::
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
du_'42''45'mono'737''45''60'_4100 :: Integer -> Integer -> Integer -> T__'8804'__22 -> T__'8804'__22
du_'42''45'mono'737''45''60'_4100 Integer
v0 Integer
v1 Integer
v2 T__'8804'__22
v3
  = case T__'8804'__22 -> T__'8804'__22
forall a b. a -> b
coe T__'8804'__22
v3 of
      MAlonzo.Code.Data.Nat.Base.C_s'8804's_34 T__'8804'__22
v6
        -> case T__'8804'__22 -> T__'8804'__22
forall a b. a -> b
coe T__'8804'__22
v6 of
             T__'8804'__22
MAlonzo.Code.Data.Nat.Base.C_z'8804'n_26 -> T__'8804'__22 -> T__'8804'__22
forall a b. a -> b
coe T__'8804'__22
du_0'60'1'43'n_3074
             MAlonzo.Code.Data.Nat.Base.C_s'8804's_34 T__'8804'__22
v9
               -> let v10 :: Integer
v10 = Integer -> Integer -> Integer
subInt (Integer -> Integer
forall a b. a -> b
coe Integer
v1) (Integer -> Integer
forall a b. a -> b
coe (Integer
1 :: Integer)) in
                  Any -> T__'8804'__22
forall a b. a -> b
coe
                    ((Integer -> T__'8804'__22 -> T__'8804'__22 -> T__'8804'__22)
-> Any -> Any -> Any -> Any
forall a b. a -> b
coe
                       Integer -> T__'8804'__22 -> T__'8804'__22 -> T__'8804'__22
du_'43''45'mono'45''8804''45''60'_3570
                       (((Any -> Any -> Any) -> (Any -> Any) -> Any -> Any -> Any)
-> (Any -> Any -> Any)
-> (Any -> Integer)
-> Integer
-> Integer
-> Any
forall a b. a -> b
coe
                          (Any -> Any -> Any) -> (Any -> Any) -> Any -> Any -> Any
MAlonzo.Code.Function.Base.du_'8739'_'10217''45'__298
                          (\ Any
v11 Any
v12 -> Any
v12) (\ Any
v11 -> Integer -> Integer -> Integer
mulInt (Any -> Integer
forall a b. a -> b
coe Any
v11) (Integer -> Integer
forall a b. a -> b
coe Integer
v0)) Integer
v10
                          (Integer -> Integer -> Integer
subInt (Integer -> Integer
forall a b. a -> b
coe Integer
v2) (Integer -> Integer
forall a b. a -> b
coe (Integer
1 :: Integer))))
                       ((Integer -> T__'8804'__22) -> Any -> Any
forall a b. a -> b
coe Integer -> T__'8804'__22
d_'8804''45'refl_2776 (Integer -> Any
forall a b. a -> b
coe Integer
v0))
                       ((Integer -> Integer -> Integer -> T__'8804'__22 -> T__'8804'__22)
-> Any -> Any -> Any -> Any -> Any
forall a b. a -> b
coe
                          Integer -> Integer -> Integer -> T__'8804'__22 -> T__'8804'__22
du_'42''45'mono'737''45''60'_4100 (Integer -> Any
forall a b. a -> b
coe Integer
v0) (Integer -> Any
forall a b. a -> b
coe Integer
v10)
                          ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> Integer
subInt (Integer -> Any
forall a b. a -> b
coe Integer
v2) (Integer -> Any
forall a b. a -> b
coe (Integer
1 :: Integer)))
                          ((T__'8804'__22 -> T__'8804'__22) -> T__'8804'__22 -> Any
forall a b. a -> b
coe T__'8804'__22 -> T__'8804'__22
MAlonzo.Code.Data.Nat.Base.C_s'8804's_34 T__'8804'__22
v9)))
             T__'8804'__22
_ -> T__'8804'__22
forall a. a
MAlonzo.RTE.mazUnreachableError
      T__'8804'__22
_ -> T__'8804'__22
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Data.Nat.Properties.*-monoʳ-<
d_'42''45'mono'691''45''60'_4114 ::
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T_NonZero_112 ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_'42''45'mono'691''45''60'_4114 :: Integer
-> T_NonZero_112
-> Integer
-> Integer
-> T__'8804'__22
-> T__'8804'__22
d_'42''45'mono'691''45''60'_4114 Integer
v0 ~T_NonZero_112
v1 ~Integer
v2 Integer
v3 T__'8804'__22
v4
  = Integer -> Integer -> T__'8804'__22 -> T__'8804'__22
du_'42''45'mono'691''45''60'_4114 Integer
v0 Integer
v3 T__'8804'__22
v4
du_'42''45'mono'691''45''60'_4114 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
du_'42''45'mono'691''45''60'_4114 :: Integer -> Integer -> T__'8804'__22 -> T__'8804'__22
du_'42''45'mono'691''45''60'_4114 Integer
v0 Integer
v1 T__'8804'__22
v2
  = case Integer -> Integer
forall a b. a -> b
coe Integer
v0 of
      Integer
1 -> case T__'8804'__22 -> T__'8804'__22
forall a b. a -> b
coe T__'8804'__22
v2 of
             MAlonzo.Code.Data.Nat.Base.C_s'8804's_34 T__'8804'__22
v5
               -> (Integer -> T__'8804'__22 -> T__'8804'__22 -> T__'8804'__22)
-> Any -> Any -> Any -> T__'8804'__22
forall a b. a -> b
coe
                    Integer -> T__'8804'__22 -> T__'8804'__22 -> T__'8804'__22
du_'43''45'mono'45''8804'_3530 (Integer -> Any
forall a b. a -> b
coe (Integer
0 :: Integer))
                    ((T__'8804'__22 -> T__'8804'__22) -> T__'8804'__22 -> Any
forall a b. a -> b
coe T__'8804'__22 -> T__'8804'__22
MAlonzo.Code.Data.Nat.Base.C_s'8804's_34 T__'8804'__22
v5)
                    (T__'8804'__22 -> Any
forall a b. a -> b
coe T__'8804'__22
MAlonzo.Code.Data.Nat.Base.C_z'8804'n_26)
             T__'8804'__22
_ -> T__'8804'__22
forall a. a
MAlonzo.RTE.mazUnreachableError
      Integer
_ -> case T__'8804'__22 -> T__'8804'__22
forall a b. a -> b
coe T__'8804'__22
v2 of
             MAlonzo.Code.Data.Nat.Base.C_s'8804's_34 T__'8804'__22
v5
               -> (Integer -> T__'8804'__22 -> T__'8804'__22 -> T__'8804'__22)
-> Any -> Any -> Any -> T__'8804'__22
forall a b. a -> b
coe
                    Integer -> T__'8804'__22 -> T__'8804'__22 -> T__'8804'__22
du_'43''45'mono'45''8804'_3530
                    ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> Integer
mulInt ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> Integer
subInt (Integer -> Any
forall a b. a -> b
coe Integer
v0) (Integer -> Any
forall a b. a -> b
coe (Integer
1 :: Integer))) (Integer -> Any
forall a b. a -> b
coe Integer
v1))
                    ((T__'8804'__22 -> T__'8804'__22) -> T__'8804'__22 -> Any
forall a b. a -> b
coe T__'8804'__22 -> T__'8804'__22
MAlonzo.Code.Data.Nat.Base.C_s'8804's_34 T__'8804'__22
v5)
                    ((T__'8804'__22 -> T__'8804'__22) -> Any -> Any
forall a b. a -> b
coe
                       T__'8804'__22 -> T__'8804'__22
du_'60''8658''8804'_2854
                       ((Integer -> Integer -> T__'8804'__22 -> T__'8804'__22)
-> Any -> Any -> Any -> Any
forall a b. a -> b
coe
                          Integer -> Integer -> T__'8804'__22 -> T__'8804'__22
du_'42''45'mono'691''45''60'_4114
                          ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> Integer
subInt (Integer -> Any
forall a b. a -> b
coe Integer
v0) (Integer -> Any
forall a b. a -> b
coe (Integer
1 :: Integer))) (Integer -> Any
forall a b. a -> b
coe Integer
v1)
                          ((T__'8804'__22 -> T__'8804'__22) -> T__'8804'__22 -> Any
forall a b. a -> b
coe T__'8804'__22 -> T__'8804'__22
MAlonzo.Code.Data.Nat.Base.C_s'8804's_34 T__'8804'__22
v5)))
             T__'8804'__22
_ -> T__'8804'__22
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Data.Nat.Properties.m≤m*n
d_m'8804'm'42'n_4128 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T_NonZero_112 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_m'8804'm'42'n_4128 :: Integer -> Integer -> T_NonZero_112 -> T__'8804'__22
d_m'8804'm'42'n_4128 Integer
v0 Integer
v1 ~T_NonZero_112
v2 = Integer -> Integer -> T__'8804'__22
du_m'8804'm'42'n_4128 Integer
v0 Integer
v1
du_m'8804'm'42'n_4128 ::
  Integer -> Integer -> MAlonzo.Code.Data.Nat.Base.T__'8804'__22
du_m'8804'm'42'n_4128 :: Integer -> Integer -> T__'8804'__22
du_m'8804'm'42'n_4128 Integer
v0 Integer
v1
  = ((Any -> Any -> Any -> Any) -> Any -> Any -> Any -> Any)
-> Any -> Integer -> Integer -> Any -> T__'8804'__22
forall a b. a -> b
coe
      (Any -> Any -> Any -> Any) -> Any -> Any -> Any -> Any
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_begin__46
      ((T_IsPreorder_70
 -> (Any -> Any -> Any -> Any)
 -> Any
 -> Any
 -> T__IsRelatedTo__78
 -> Any)
-> Any -> (Any -> Any -> Any -> Any) -> Any
forall a b. a -> b
coe
         T_IsPreorder_70
-> (Any -> Any -> Any -> Any)
-> Any
-> Any
-> T__IsRelatedTo__78
-> Any
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_start_96
         (T_IsPreorder_70 -> Any
forall a b. a -> b
coe T_IsPreorder_70
d_'8804''45'isPreorder_2810)
         (\ Any
v2 Any
v3 Any
v4 -> (T__'8804'__22 -> T__'8804'__22) -> Any -> Any
forall a b. a -> b
coe T__'8804'__22 -> T__'8804'__22
du_'60''8658''8804'_2854 Any
v4))
      Integer
v0 (Integer -> Integer -> Integer
mulInt (Integer -> Integer
forall a b. a -> b
coe Integer
v0) (Integer -> Integer
forall a b. a -> b
coe Integer
v1))
      (((Any -> Any -> Any -> T__'8801'__12 -> Any -> Any)
 -> Any -> Any -> Any -> Any -> T__'8801'__12 -> Any)
-> (Any -> Any -> Any -> Any -> Any -> Any)
-> Integer
-> Integer
-> Integer
-> Any
-> Any
-> Any
forall a b. a -> b
coe
         (Any -> Any -> Any -> T__'8801'__12 -> Any -> Any)
-> Any -> Any -> Any -> Any -> T__'8801'__12 -> Any
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8801''45''10217'_436
         (\ Any
v2 Any
v3 Any
v4 Any
v5 Any
v6 -> Any
v6) Integer
v0 (Integer -> Integer -> Integer
mulInt (Integer -> Integer
forall a b. a -> b
coe Integer
v0) (Integer -> Integer
forall a b. a -> b
coe (Integer
1 :: Integer)))
         (Integer -> Integer -> Integer
mulInt (Integer -> Integer
forall a b. a -> b
coe Integer
v0) (Integer -> Integer
forall a b. a -> b
coe Integer
v1))
         (((Any -> Any -> Any -> Any -> Any -> Any)
 -> Any -> Any -> Any -> Any -> Any -> Any)
-> Any -> Integer -> Integer -> Integer -> Any -> Any -> Any
forall a b. a -> b
coe
            (Any -> Any -> Any -> Any -> Any -> Any)
-> Any -> Any -> Any -> Any -> Any -> Any
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8804'_308
            ((T_IsPreorder_70
 -> (Any -> Any -> Any -> Any -> Any -> Any)
 -> Any
 -> Any
 -> Any
 -> Any
 -> T__IsRelatedTo__78
 -> T__IsRelatedTo__78)
-> Any -> (Any -> Any -> Any -> Any -> Any -> Any) -> Any
forall a b. a -> b
coe
               T_IsPreorder_70
-> (Any -> Any -> Any -> Any -> Any -> Any)
-> Any
-> Any
-> Any
-> Any
-> T__IsRelatedTo__78
-> T__IsRelatedTo__78
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_'8804''45'go_138
               (T_IsPreorder_70 -> Any
forall a b. a -> b
coe T_IsPreorder_70
d_'8804''45'isPreorder_2810)
               (\ Any
v2 Any
v3 Any
v4 Any
v5 Any
v6 -> (T__'8804'__22 -> T__'8804'__22 -> T__'8804'__22)
-> Any -> Any -> Any
forall a b. a -> b
coe T__'8804'__22 -> T__'8804'__22 -> T__'8804'__22
du_'8804''45''60''45'trans_2986 Any
v5 Any
v6))
            (Integer -> Integer -> Integer
mulInt (Integer -> Integer
forall a b. a -> b
coe Integer
v0) (Integer -> Integer
forall a b. a -> b
coe (Integer
1 :: Integer))) (Integer -> Integer -> Integer
mulInt (Integer -> Integer
forall a b. a -> b
coe Integer
v0) (Integer -> Integer
forall a b. a -> b
coe Integer
v1))
            (Integer -> Integer -> Integer
mulInt (Integer -> Integer
forall a b. a -> b
coe Integer
v0) (Integer -> Integer
forall a b. a -> b
coe Integer
v1))
            (((Any -> Any) -> Any -> Any) -> Any -> Any -> Any
forall a b. a -> b
coe
               (Any -> Any) -> Any -> Any
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du__'8718'_492
               ((T_IsPreorder_70 -> Any -> T__IsRelatedTo__78) -> Any -> Any
forall a b. a -> b
coe
                  T_IsPreorder_70 -> Any -> T__IsRelatedTo__78
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_stop_166
                  (T_IsPreorder_70 -> Any
forall a b. a -> b
coe T_IsPreorder_70
d_'8804''45'isPreorder_2810))
               ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> Integer
mulInt (Integer -> Any
forall a b. a -> b
coe Integer
v0) (Integer -> Any
forall a b. a -> b
coe Integer
v1)))
            ((Integer -> Integer -> T__'8804'__22 -> T__'8804'__22)
-> Any -> Any -> Any -> Any
forall a b. a -> b
coe
               Integer -> Integer -> T__'8804'__22 -> T__'8804'__22
du_'42''45'mono'691''45''8804'_4080 (Integer -> Any
forall a b. a -> b
coe Integer
v0) (Integer -> Any
forall a b. a -> b
coe Integer
v1)
               (T__'8804'__22 -> Any
forall a b. a -> b
coe T__'8804'__22
du_0'60'1'43'n_3074)))
         Any
forall a. a
erased)
-- Data.Nat.Properties.m≤n*m
d_m'8804'n'42'm_4140 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T_NonZero_112 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_m'8804'n'42'm_4140 :: Integer -> Integer -> T_NonZero_112 -> T__'8804'__22
d_m'8804'n'42'm_4140 Integer
v0 Integer
v1 ~T_NonZero_112
v2 = Integer -> Integer -> T__'8804'__22
du_m'8804'n'42'm_4140 Integer
v0 Integer
v1
du_m'8804'n'42'm_4140 ::
  Integer -> Integer -> MAlonzo.Code.Data.Nat.Base.T__'8804'__22
du_m'8804'n'42'm_4140 :: Integer -> Integer -> T__'8804'__22
du_m'8804'n'42'm_4140 Integer
v0 Integer
v1
  = ((Any -> Any -> Any -> Any) -> Any -> Any -> Any -> Any)
-> Any -> Integer -> Integer -> Any -> T__'8804'__22
forall a b. a -> b
coe
      (Any -> Any -> Any -> Any) -> Any -> Any -> Any -> Any
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_begin__46
      ((T_IsPreorder_70
 -> (Any -> Any -> Any -> Any)
 -> Any
 -> Any
 -> T__IsRelatedTo__78
 -> Any)
-> Any -> (Any -> Any -> Any -> Any) -> Any
forall a b. a -> b
coe
         T_IsPreorder_70
-> (Any -> Any -> Any -> Any)
-> Any
-> Any
-> T__IsRelatedTo__78
-> Any
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_start_96
         (T_IsPreorder_70 -> Any
forall a b. a -> b
coe T_IsPreorder_70
d_'8804''45'isPreorder_2810)
         (\ Any
v2 Any
v3 Any
v4 -> (T__'8804'__22 -> T__'8804'__22) -> Any -> Any
forall a b. a -> b
coe T__'8804'__22 -> T__'8804'__22
du_'60''8658''8804'_2854 Any
v4))
      Integer
v0 (Integer -> Integer -> Integer
mulInt (Integer -> Integer
forall a b. a -> b
coe Integer
v1) (Integer -> Integer
forall a b. a -> b
coe Integer
v0))
      (((Any -> Any -> Any -> Any -> Any -> Any)
 -> Any -> Any -> Any -> Any -> Any -> Any)
-> Any -> Integer -> Integer -> Integer -> Any -> Any -> Any
forall a b. a -> b
coe
         (Any -> Any -> Any -> Any -> Any -> Any)
-> Any -> Any -> Any -> Any -> Any -> Any
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8804'_308
         ((T_IsPreorder_70
 -> (Any -> Any -> Any -> Any -> Any -> Any)
 -> Any
 -> Any
 -> Any
 -> Any
 -> T__IsRelatedTo__78
 -> T__IsRelatedTo__78)
-> Any -> (Any -> Any -> Any -> Any -> Any -> Any) -> Any
forall a b. a -> b
coe
            T_IsPreorder_70
-> (Any -> Any -> Any -> Any -> Any -> Any)
-> Any
-> Any
-> Any
-> Any
-> T__IsRelatedTo__78
-> T__IsRelatedTo__78
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_'8804''45'go_138
            (T_IsPreorder_70 -> Any
forall a b. a -> b
coe T_IsPreorder_70
d_'8804''45'isPreorder_2810)
            (\ Any
v2 Any
v3 Any
v4 Any
v5 Any
v6 -> (T__'8804'__22 -> T__'8804'__22 -> T__'8804'__22)
-> Any -> Any -> Any
forall a b. a -> b
coe T__'8804'__22 -> T__'8804'__22 -> T__'8804'__22
du_'8804''45''60''45'trans_2986 Any
v5 Any
v6))
         Integer
v0 (Integer -> Integer -> Integer
mulInt (Integer -> Integer
forall a b. a -> b
coe Integer
v0) (Integer -> Integer
forall a b. a -> b
coe Integer
v1)) (Integer -> Integer -> Integer
mulInt (Integer -> Integer
forall a b. a -> b
coe Integer
v1) (Integer -> Integer
forall a b. a -> b
coe Integer
v0))
         (((Any -> Any -> Any -> T__'8801'__12 -> Any -> Any)
 -> Any -> Any -> Any -> Any -> T__'8801'__12 -> Any)
-> (Any -> Any -> Any -> Any -> Any -> Any)
-> Integer
-> Integer
-> Integer
-> Any
-> Any
-> Any
forall a b. a -> b
coe
            (Any -> Any -> Any -> T__'8801'__12 -> Any -> Any)
-> Any -> Any -> Any -> Any -> T__'8801'__12 -> Any
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8801''45''10217'_436
            (\ Any
v2 Any
v3 Any
v4 Any
v5 Any
v6 -> Any
v6) (Integer -> Integer -> Integer
mulInt (Integer -> Integer
forall a b. a -> b
coe Integer
v0) (Integer -> Integer
forall a b. a -> b
coe Integer
v1))
            (Integer -> Integer -> Integer
mulInt (Integer -> Integer
forall a b. a -> b
coe Integer
v1) (Integer -> Integer
forall a b. a -> b
coe Integer
v0)) (Integer -> Integer -> Integer
mulInt (Integer -> Integer
forall a b. a -> b
coe Integer
v1) (Integer -> Integer
forall a b. a -> b
coe Integer
v0))
            (((Any -> Any) -> Any -> Any) -> Any -> Any -> Any
forall a b. a -> b
coe
               (Any -> Any) -> Any -> Any
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du__'8718'_492
               ((T_IsPreorder_70 -> Any -> T__IsRelatedTo__78) -> Any -> Any
forall a b. a -> b
coe
                  T_IsPreorder_70 -> Any -> T__IsRelatedTo__78
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_stop_166
                  (T_IsPreorder_70 -> Any
forall a b. a -> b
coe T_IsPreorder_70
d_'8804''45'isPreorder_2810))
               ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> Integer
mulInt (Integer -> Any
forall a b. a -> b
coe Integer
v1) (Integer -> Any
forall a b. a -> b
coe Integer
v0)))
            Any
forall a. a
erased)
         ((Integer -> Integer -> T__'8804'__22) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> T__'8804'__22
du_m'8804'm'42'n_4128 (Integer -> Any
forall a b. a -> b
coe Integer
v0) (Integer -> Any
forall a b. a -> b
coe Integer
v1)))
-- Data.Nat.Properties.m<m*n
d_m'60'm'42'n_4152 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T_NonZero_112 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_m'60'm'42'n_4152 :: Integer
-> Integer -> T_NonZero_112 -> T__'8804'__22 -> T__'8804'__22
d_m'60'm'42'n_4152 Integer
v0 Integer
v1 ~T_NonZero_112
v2 T__'8804'__22
v3 = Integer -> Integer -> T__'8804'__22 -> T__'8804'__22
du_m'60'm'42'n_4152 Integer
v0 Integer
v1 T__'8804'__22
v3
du_m'60'm'42'n_4152 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
du_m'60'm'42'n_4152 :: Integer -> Integer -> T__'8804'__22 -> T__'8804'__22
du_m'60'm'42'n_4152 Integer
v0 Integer
v1 T__'8804'__22
v2
  = let v3 :: Integer
v3 = Integer -> Integer -> Integer
subInt (Integer -> Integer
forall a b. a -> b
coe Integer
v0) (Integer -> Integer
forall a b. a -> b
coe (Integer
1 :: Integer)) in
    Any -> T__'8804'__22
forall a b. a -> b
coe
      (case T__'8804'__22 -> T__'8804'__22
forall a b. a -> b
coe T__'8804'__22
v2 of
         MAlonzo.Code.Data.Nat.Base.C_s'8804's_34 T__'8804'__22
v6
           -> (Any -> Any -> Any) -> Any -> Any -> Any
forall a b. a -> b
coe
                Any -> Any -> Any
forall a b. a -> b -> b
seq (T__'8804'__22 -> Any
forall a b. a -> b
coe T__'8804'__22
v6)
                ((T_SubRelation_60 -> Any -> Any -> Any -> Any)
-> Any -> Any -> Any -> Any -> Any
forall a b. a -> b
coe
                   T_SubRelation_60 -> Any -> Any -> Any -> Any
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_begin__126
                   (T_SubRelation_60 -> Any
forall a b. a -> b
coe
                      T_SubRelation_60
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_strictRelation_202)
                   (Integer -> Any
forall a b. a -> b
coe Integer
v0) ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> Integer
mulInt (Integer -> Any
forall a b. a -> b
coe Integer
v0) (Integer -> Any
forall a b. a -> b
coe Integer
v1))
                   (((Any -> Any -> Any -> Any -> Any -> Any)
 -> Any -> Any -> Any -> Any -> Any -> Any)
-> Any -> Integer -> Integer -> Integer -> Any -> Any -> Any
forall a b. a -> b
coe
                      (Any -> Any -> Any -> Any -> Any -> Any)
-> Any -> Any -> Any -> Any -> Any -> Any
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''60'_312
                      (((Any -> Any -> Any -> Any -> Any -> Any)
 -> T_Σ_14
 -> (Any -> Any -> Any -> Any -> Any -> Any)
 -> Any
 -> Any
 -> Any
 -> Any
 -> T__IsRelatedTo__78
 -> T__IsRelatedTo__78)
-> (Any -> Any -> Any -> Any -> Any -> Any)
-> Any
-> (Any -> Any -> Any -> Any -> Any -> Any)
-> Any
forall a b. a -> b
coe
                         (Any -> Any -> Any -> Any -> Any -> Any)
-> T_Σ_14
-> (Any -> Any -> Any -> Any -> Any -> Any)
-> Any
-> Any
-> Any
-> Any
-> T__IsRelatedTo__78
-> T__IsRelatedTo__78
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_'60''45'go_152
                         (\ Any
v7 Any
v8 Any
v9 Any
v10 Any
v11 -> (Integer -> T__'8804'__22 -> T__'8804'__22 -> T__'8804'__22)
-> Any -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> T__'8804'__22 -> T__'8804'__22 -> T__'8804'__22
du_'60''45'trans_2980 Any
v8 Any
v10 Any
v11)
                         (T_Σ_14 -> Any
forall a b. a -> b
coe
                            T_Σ_14
MAlonzo.Code.Relation.Binary.PropositionalEquality.Core.du_resp'8322'_160)
                         (\ Any
v7 Any
v8 Any
v9 Any
v10 Any
v11 ->
                            (T__'8804'__22 -> T__'8804'__22 -> T__'8804'__22)
-> Any -> Any -> Any
forall a b. a -> b
coe T__'8804'__22 -> T__'8804'__22 -> T__'8804'__22
du_'60''45''8804''45'trans_2992 Any
v10 Any
v11))
                      Integer
v0 (Integer -> Integer -> Integer
addInt (Integer -> Integer
forall a b. a -> b
coe Integer
v1) (Integer -> Integer
forall a b. a -> b
coe Integer
v3)) (Integer -> Integer -> Integer
mulInt (Integer -> Integer
forall a b. a -> b
coe Integer
v0) (Integer -> Integer
forall a b. a -> b
coe Integer
v1))
                      (((Any -> Any -> Any -> Any -> Any -> Any)
 -> Any -> Any -> Any -> Any -> Any -> Any)
-> Any -> Integer -> Integer -> Integer -> Any -> Any -> Any
forall a b. a -> b
coe
                         (Any -> Any -> Any -> Any -> Any -> Any)
-> Any -> Any -> Any -> Any -> Any -> Any
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8804'_308
                         ((T_IsPreorder_70
 -> (Any -> Any -> Any -> Any -> Any -> Any)
 -> Any
 -> Any
 -> Any
 -> Any
 -> T__IsRelatedTo__78
 -> T__IsRelatedTo__78)
-> Any -> (Any -> Any -> Any -> Any -> Any -> Any) -> Any
forall a b. a -> b
coe
                            T_IsPreorder_70
-> (Any -> Any -> Any -> Any -> Any -> Any)
-> Any
-> Any
-> Any
-> Any
-> T__IsRelatedTo__78
-> T__IsRelatedTo__78
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_'8804''45'go_138
                            (T_IsPreorder_70 -> Any
forall a b. a -> b
coe T_IsPreorder_70
d_'8804''45'isPreorder_2810)
                            (\ Any
v7 Any
v8 Any
v9 Any
v10 Any
v11 ->
                               (T__'8804'__22 -> T__'8804'__22 -> T__'8804'__22)
-> Any -> Any -> Any
forall a b. a -> b
coe T__'8804'__22 -> T__'8804'__22 -> T__'8804'__22
du_'8804''45''60''45'trans_2986 Any
v10 Any
v11))
                         (Integer -> Integer -> Integer
addInt (Integer -> Integer
forall a b. a -> b
coe Integer
v1) (Integer -> Integer
forall a b. a -> b
coe Integer
v3))
                         (Integer -> Integer -> Integer
addInt (Integer -> Integer
forall a b. a -> b
coe Integer
v1) ((Integer -> Integer -> Integer) -> Any -> Any -> Integer
forall a b. a -> b
coe Integer -> Integer -> Integer
mulInt (Integer -> Any
forall a b. a -> b
coe Integer
v3) (Integer -> Any
forall a b. a -> b
coe Integer
v1)))
                         (Integer -> Integer -> Integer
mulInt (Integer -> Integer
forall a b. a -> b
coe Integer
v0) (Integer -> Integer
forall a b. a -> b
coe Integer
v1))
                         (((Any -> Any) -> Any -> Any) -> Any -> Any -> Any
forall a b. a -> b
coe
                            (Any -> Any) -> Any -> Any
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du__'8718'_492
                            ((T_IsPreorder_70 -> Any -> T__IsRelatedTo__78) -> Any -> Any
forall a b. a -> b
coe
                               T_IsPreorder_70 -> Any -> T__IsRelatedTo__78
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_stop_166
                               (T_IsPreorder_70 -> Any
forall a b. a -> b
coe T_IsPreorder_70
d_'8804''45'isPreorder_2810))
                            ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> Integer
mulInt (Integer -> Any
forall a b. a -> b
coe Integer
v0) (Integer -> Any
forall a b. a -> b
coe Integer
v1)))
                         ((Integer -> Integer -> T__'8804'__22 -> T__'8804'__22)
-> Any -> Any -> Any -> Any
forall a b. a -> b
coe
                            Integer -> Integer -> T__'8804'__22 -> T__'8804'__22
du_'43''45'mono'691''45''8804'_3554 (Integer -> Any
forall a b. a -> b
coe Integer
v1)
                            ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> Integer
mulInt (Integer -> Any
forall a b. a -> b
coe Integer
v3) (Integer -> Any
forall a b. a -> b
coe Integer
v1))
                            ((Integer -> Integer -> T__'8804'__22) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> T__'8804'__22
du_m'8804'm'42'n_4128 (Integer -> Any
forall a b. a -> b
coe Integer
v3) (Integer -> Any
forall a b. a -> b
coe Integer
v1))))
                      ((T__'8804'__22 -> T__'8804'__22) -> Any -> Any
forall a b. a -> b
coe
                         T__'8804'__22 -> T__'8804'__22
MAlonzo.Code.Data.Nat.Base.C_s'8804's_34
                         ((T__'8804'__22 -> T__'8804'__22) -> Any -> Any
forall a b. a -> b
coe
                            T__'8804'__22 -> T__'8804'__22
MAlonzo.Code.Data.Nat.Base.C_s'8804's_34
                            ((Integer -> T__'8804'__22) -> Any -> Any
forall a b. a -> b
coe Integer -> T__'8804'__22
du_m'8804'n'43'm_3494 (Integer -> Any
forall a b. a -> b
coe Integer
v3))))))
         T__'8804'__22
_ -> Any
forall a. a
MAlonzo.RTE.mazUnreachableError)
-- Data.Nat.Properties.m<n⇒m<n*o
d_m'60'n'8658'm'60'n'42'o_4166 ::
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T_NonZero_112 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_m'60'n'8658'm'60'n'42'o_4166 :: Integer
-> Integer
-> Integer
-> T_NonZero_112
-> T__'8804'__22
-> T__'8804'__22
d_m'60'n'8658'm'60'n'42'o_4166 ~Integer
v0 Integer
v1 Integer
v2 ~T_NonZero_112
v3 T__'8804'__22
v4
  = Integer -> Integer -> T__'8804'__22 -> T__'8804'__22
du_m'60'n'8658'm'60'n'42'o_4166 Integer
v1 Integer
v2 T__'8804'__22
v4
du_m'60'n'8658'm'60'n'42'o_4166 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
du_m'60'n'8658'm'60'n'42'o_4166 :: Integer -> Integer -> T__'8804'__22 -> T__'8804'__22
du_m'60'n'8658'm'60'n'42'o_4166 Integer
v0 Integer
v1 T__'8804'__22
v2
  = (T__'8804'__22 -> T__'8804'__22 -> T__'8804'__22)
-> Any -> Any -> T__'8804'__22
forall a b. a -> b
coe
      T__'8804'__22 -> T__'8804'__22 -> T__'8804'__22
du_'60''45''8804''45'trans_2992 (T__'8804'__22 -> Any
forall a b. a -> b
coe T__'8804'__22
v2)
      ((Integer -> Integer -> T__'8804'__22) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> T__'8804'__22
du_m'8804'm'42'n_4128 (Integer -> Any
forall a b. a -> b
coe Integer
v0) (Integer -> Any
forall a b. a -> b
coe Integer
v1))
-- Data.Nat.Properties.m<n⇒m<o*n
d_m'60'n'8658'm'60'o'42'n_4182 ::
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T_NonZero_112 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_m'60'n'8658'm'60'o'42'n_4182 :: Integer
-> Integer
-> Integer
-> T_NonZero_112
-> T__'8804'__22
-> T__'8804'__22
d_m'60'n'8658'm'60'o'42'n_4182 Integer
v0 Integer
v1 Integer
v2 ~T_NonZero_112
v3 T__'8804'__22
v4
  = Integer -> Integer -> Integer -> T__'8804'__22 -> T__'8804'__22
du_m'60'n'8658'm'60'o'42'n_4182 Integer
v0 Integer
v1 Integer
v2 T__'8804'__22
v4
du_m'60'n'8658'm'60'o'42'n_4182 ::
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
du_m'60'n'8658'm'60'o'42'n_4182 :: Integer -> Integer -> Integer -> T__'8804'__22 -> T__'8804'__22
du_m'60'n'8658'm'60'o'42'n_4182 Integer
v0 Integer
v1 Integer
v2 T__'8804'__22
v3
  = let v4 :: b
v4
          = T_SubRelation_60 -> b
forall a b. a -> b
coe
              T_SubRelation_60
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_strictRelation_202 in
    Any -> T__'8804'__22
forall a b. a -> b
coe
      ((T_SubRelation_60 -> Any -> Any -> Any -> Any)
-> Any -> Any -> Any -> Any -> Any
forall a b. a -> b
coe
         T_SubRelation_60 -> Any -> Any -> Any -> Any
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_begin__126
         (Any -> Any
forall a b. a -> b
coe Any
forall a. a
v4) (Integer -> Any
forall a b. a -> b
coe Integer
v0) ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> Integer
mulInt (Integer -> Any
forall a b. a -> b
coe Integer
v2) (Integer -> Any
forall a b. a -> b
coe Integer
v1))
         (((Any -> Any -> Any -> Any -> Any -> Any)
 -> Any -> Any -> Any -> Any -> Any -> Any)
-> Any -> Integer -> Integer -> Integer -> Any -> Any -> Any
forall a b. a -> b
coe
            (Any -> Any -> Any -> Any -> Any -> Any)
-> Any -> Any -> Any -> Any -> Any -> Any
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''60'_312
            (((Any -> Any -> Any -> Any -> Any -> Any)
 -> T_Σ_14
 -> (Any -> Any -> Any -> Any -> Any -> Any)
 -> Any
 -> Any
 -> Any
 -> Any
 -> T__IsRelatedTo__78
 -> T__IsRelatedTo__78)
-> (Any -> Any -> Any -> Any -> Any -> Any)
-> Any
-> (Any -> Any -> Any -> Any -> Any -> Any)
-> Any
forall a b. a -> b
coe
               (Any -> Any -> Any -> Any -> Any -> Any)
-> T_Σ_14
-> (Any -> Any -> Any -> Any -> Any -> Any)
-> Any
-> Any
-> Any
-> Any
-> T__IsRelatedTo__78
-> T__IsRelatedTo__78
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_'60''45'go_152
               (\ Any
v5 Any
v6 Any
v7 Any
v8 Any
v9 -> (Integer -> T__'8804'__22 -> T__'8804'__22 -> T__'8804'__22)
-> Any -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> T__'8804'__22 -> T__'8804'__22 -> T__'8804'__22
du_'60''45'trans_2980 Any
v6 Any
v8 Any
v9)
               (T_Σ_14 -> Any
forall a b. a -> b
coe
                  T_Σ_14
MAlonzo.Code.Relation.Binary.PropositionalEquality.Core.du_resp'8322'_160)
               (\ Any
v5 Any
v6 Any
v7 Any
v8 Any
v9 -> (T__'8804'__22 -> T__'8804'__22 -> T__'8804'__22)
-> Any -> Any -> Any
forall a b. a -> b
coe T__'8804'__22 -> T__'8804'__22 -> T__'8804'__22
du_'60''45''8804''45'trans_2992 Any
v8 Any
v9))
            Integer
v0 (Integer -> Integer -> Integer
mulInt (Integer -> Integer
forall a b. a -> b
coe Integer
v1) (Integer -> Integer
forall a b. a -> b
coe Integer
v2)) (Integer -> Integer -> Integer
mulInt (Integer -> Integer
forall a b. a -> b
coe Integer
v2) (Integer -> Integer
forall a b. a -> b
coe Integer
v1))
            (((Any -> Any -> Any -> T__'8801'__12 -> Any -> Any)
 -> Any -> Any -> Any -> Any -> T__'8801'__12 -> Any)
-> (Any -> Any -> Any -> Any -> Any -> Any)
-> Integer
-> Integer
-> Integer
-> Any
-> Any
-> Any
forall a b. a -> b
coe
               (Any -> Any -> Any -> T__'8801'__12 -> Any -> Any)
-> Any -> Any -> Any -> Any -> T__'8801'__12 -> Any
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8801''45''10217'_436
               (\ Any
v5 Any
v6 Any
v7 Any
v8 Any
v9 -> Any
v9) (Integer -> Integer -> Integer
mulInt (Integer -> Integer
forall a b. a -> b
coe Integer
v1) (Integer -> Integer
forall a b. a -> b
coe Integer
v2))
               (Integer -> Integer -> Integer
mulInt (Integer -> Integer
forall a b. a -> b
coe Integer
v2) (Integer -> Integer
forall a b. a -> b
coe Integer
v1)) (Integer -> Integer -> Integer
mulInt (Integer -> Integer
forall a b. a -> b
coe Integer
v2) (Integer -> Integer
forall a b. a -> b
coe Integer
v1))
               (((Any -> Any) -> Any -> Any) -> Any -> Any -> Any
forall a b. a -> b
coe
                  (Any -> Any) -> Any -> Any
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du__'8718'_492
                  ((T_IsPreorder_70 -> Any -> T__IsRelatedTo__78) -> Any -> Any
forall a b. a -> b
coe
                     T_IsPreorder_70 -> Any -> T__IsRelatedTo__78
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_stop_166
                     (T_IsPreorder_70 -> Any
forall a b. a -> b
coe T_IsPreorder_70
d_'8804''45'isPreorder_2810))
                  ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> Integer
mulInt (Integer -> Any
forall a b. a -> b
coe Integer
v2) (Integer -> Any
forall a b. a -> b
coe Integer
v1)))
               Any
forall a. a
erased)
            ((Integer -> Integer -> T__'8804'__22 -> T__'8804'__22)
-> Any -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> T__'8804'__22 -> T__'8804'__22
du_m'60'n'8658'm'60'n'42'o_4166 (Integer -> Any
forall a b. a -> b
coe Integer
v1) (Integer -> Any
forall a b. a -> b
coe Integer
v2) (T__'8804'__22 -> Any
forall a b. a -> b
coe T__'8804'__22
v3))))
-- Data.Nat.Properties.*-cancelʳ-<
d_'42''45'cancel'691''45''60'_4192 ::
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_'42''45'cancel'691''45''60'_4192 :: Integer -> Integer -> Integer -> T__'8804'__22 -> T__'8804'__22
d_'42''45'cancel'691''45''60'_4192 Integer
v0 Integer
v1 Integer
v2 ~T__'8804'__22
v3
  = Integer -> Integer -> Integer -> T__'8804'__22
du_'42''45'cancel'691''45''60'_4192 Integer
v0 Integer
v1 Integer
v2
du_'42''45'cancel'691''45''60'_4192 ::
  Integer ->
  Integer -> Integer -> MAlonzo.Code.Data.Nat.Base.T__'8804'__22
du_'42''45'cancel'691''45''60'_4192 :: Integer -> Integer -> Integer -> T__'8804'__22
du_'42''45'cancel'691''45''60'_4192 Integer
v0 Integer
v1 Integer
v2
  = let v3 :: b
v3
          = let v3 :: Integer
v3 = Integer -> Integer -> Integer
subInt (Integer -> Integer
forall a b. a -> b
coe Integer
v1) (Integer -> Integer
forall a b. a -> b
coe (Integer
1 :: Integer)) in
            Any -> b
forall a b. a -> b
coe
              (let v4 :: Integer
v4 = Integer -> Integer -> Integer
subInt (Integer -> Integer
forall a b. a -> b
coe Integer
v2) (Integer -> Integer
forall a b. a -> b
coe (Integer
1 :: Integer)) in
               Any -> Any
forall a b. a -> b
coe
                 ((T__'8804'__22 -> T__'8804'__22) -> Any -> Any
forall a b. a -> b
coe
                    T__'8804'__22 -> T__'8804'__22
MAlonzo.Code.Data.Nat.Base.C_s'8804's_34
                    ((Integer -> Integer -> Integer -> T__'8804'__22)
-> Any -> Any -> Any -> Any
forall a b. a -> b
coe
                       Integer -> Integer -> Integer -> T__'8804'__22
du_'42''45'cancel'691''45''60'_4192 (Integer -> Any
forall a b. a -> b
coe Integer
v0) (Integer -> Any
forall a b. a -> b
coe Integer
v3)
                       (Integer -> Any
forall a b. a -> b
coe Integer
v4)))) in
    Any -> T__'8804'__22
forall a b. a -> b
coe
      ((Any -> Any -> Any) -> Any -> Any -> Any
forall a b. a -> b
coe
         Any -> Any -> Any
forall a b. a -> b -> b
seq (Integer -> Any
forall a b. a -> b
coe Integer
v0)
         (case Integer -> Integer
forall a b. a -> b
coe Integer
v1 of
            Integer
0 -> case Integer -> Any
forall a b. a -> b
coe Integer
v2 of
                   Any
_ | (Integer -> Integer -> Bool) -> Any -> Any -> Bool
forall a b. a -> b
coe Integer -> Integer -> Bool
geqInt (Integer -> Any
forall a b. a -> b
coe Integer
v2) (Integer -> Any
forall a b. a -> b
coe (Integer
1 :: Integer)) ->
                       T__'8804'__22 -> Any
forall a b. a -> b
coe T__'8804'__22
du_0'60'1'43'n_3074
                   Any
_ -> Any -> Any
forall a b. a -> b
coe Any
forall a. a
v3
            Integer
_ -> let v4 :: Integer
v4 = Integer -> Integer -> Integer
subInt (Integer -> Integer
forall a b. a -> b
coe Integer
v1) (Integer -> Integer
forall a b. a -> b
coe (Integer
1 :: Integer)) in
                 Any -> Any
forall a b. a -> b
coe
                   (case Integer -> Any
forall a b. a -> b
coe Integer
v2 of
                      Any
_ | (Integer -> Integer -> Bool) -> Any -> Any -> Bool
forall a b. a -> b
coe Integer -> Integer -> Bool
geqInt (Integer -> Any
forall a b. a -> b
coe Integer
v2) (Integer -> Any
forall a b. a -> b
coe (Integer
1 :: Integer)) ->
                          let v5 :: Integer
v5 = Integer -> Integer -> Integer
subInt (Integer -> Integer
forall a b. a -> b
coe Integer
v2) (Integer -> Integer
forall a b. a -> b
coe (Integer
1 :: Integer)) in
                          Any -> Any
forall a b. a -> b
coe
                            ((T__'8804'__22 -> T__'8804'__22) -> Any -> Any
forall a b. a -> b
coe
                               T__'8804'__22 -> T__'8804'__22
MAlonzo.Code.Data.Nat.Base.C_s'8804's_34
                               ((Integer -> Integer -> Integer -> T__'8804'__22)
-> Any -> Any -> Any -> Any
forall a b. a -> b
coe
                                  Integer -> Integer -> Integer -> T__'8804'__22
du_'42''45'cancel'691''45''60'_4192 (Integer -> Any
forall a b. a -> b
coe Integer
v0) (Integer -> Any
forall a b. a -> b
coe Integer
v4) (Integer -> Any
forall a b. a -> b
coe Integer
v5)))
                      Any
_ -> Any -> Any
forall a b. a -> b
coe Any
forall a. a
v3)))
-- Data.Nat.Properties.*-cancelˡ-<
d_'42''45'cancel'737''45''60'_4208 ::
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_'42''45'cancel'737''45''60'_4208 :: Integer -> Integer -> Integer -> T__'8804'__22 -> T__'8804'__22
d_'42''45'cancel'737''45''60'_4208 Integer
v0 Integer
v1 Integer
v2 T__'8804'__22
v3
  = (Integer -> Integer -> Integer -> T__'8804'__22)
-> Any -> Any -> Any -> T__'8804'__22
forall a b. a -> b
coe
      Integer -> Integer -> Integer -> T__'8804'__22
du_'42''45'cancel'691''45''60'_4192 (Integer -> Any
forall a b. a -> b
coe Integer
v0) (Integer -> Any
forall a b. a -> b
coe Integer
v1) (Integer -> Any
forall a b. a -> b
coe Integer
v2)
-- Data.Nat.Properties.*-cancel-<
d_'42''45'cancel'45''60'_4224 ::
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'42''45'cancel'45''60'_4224 :: T_Σ_14
d_'42''45'cancel'45''60'_4224
  = (Any -> Any -> T_Σ_14)
-> Any -> (Any -> Any -> Any -> Any -> Any) -> T_Σ_14
forall a b. a -> b
coe
      Any -> Any -> T_Σ_14
MAlonzo.Code.Agda.Builtin.Sigma.C__'44'__32
      ((Integer -> Integer -> Integer -> T__'8804'__22 -> T__'8804'__22)
-> Any
forall a b. a -> b
coe Integer -> Integer -> Integer -> T__'8804'__22 -> T__'8804'__22
d_'42''45'cancel'737''45''60'_4208)
      (\ Any
v0 Any
v1 Any
v2 Any
v3 -> (Integer -> Integer -> Integer -> T__'8804'__22)
-> Any -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> Integer -> T__'8804'__22
du_'42''45'cancel'691''45''60'_4192 Any
v0 Any
v1 Any
v2)
-- Data.Nat.Properties.^-identityʳ
d_'94''45'identity'691'_4226 ::
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'94''45'identity'691'_4226 :: Integer -> T__'8801'__12
d_'94''45'identity'691'_4226 = Integer -> T__'8801'__12
forall a. a
erased
-- Data.Nat.Properties.^-zeroˡ
d_'94''45'zero'737'_4230 ::
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'94''45'zero'737'_4230 :: Integer -> T__'8801'__12
d_'94''45'zero'737'_4230 = Integer -> T__'8801'__12
forall a. a
erased
-- Data.Nat.Properties.^-distribˡ-+-*
d_'94''45'distrib'737''45''43''45''42'_4240 ::
  Integer ->
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'94''45'distrib'737''45''43''45''42'_4240 :: Integer -> Integer -> Integer -> T__'8801'__12
d_'94''45'distrib'737''45''43''45''42'_4240 = Integer -> Integer -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Nat.Properties.^-semigroup-morphism
d_'94''45'semigroup'45'morphism_4258 ::
  Integer -> MAlonzo.Code.Algebra.Morphism.T_IsSemigroupMorphism_148
d_'94''45'semigroup'45'morphism_4258 :: Integer -> T_IsSemigroupMorphism_148
d_'94''45'semigroup'45'morphism_4258 ~Integer
v0
  = T_IsSemigroupMorphism_148
du_'94''45'semigroup'45'morphism_4258
du_'94''45'semigroup'45'morphism_4258 ::
  MAlonzo.Code.Algebra.Morphism.T_IsSemigroupMorphism_148
du_'94''45'semigroup'45'morphism_4258 :: T_IsSemigroupMorphism_148
du_'94''45'semigroup'45'morphism_4258
  = ((Any -> Any -> Any -> Any)
 -> (Any -> Any -> Any) -> T_IsSemigroupMorphism_148)
-> Any -> Any -> T_IsSemigroupMorphism_148
forall a b. a -> b
coe
      (Any -> Any -> Any -> Any)
-> (Any -> Any -> Any) -> T_IsSemigroupMorphism_148
MAlonzo.Code.Algebra.Morphism.C_IsSemigroupMorphism'46'constructor_1081
      Any
forall a. a
erased Any
forall a. a
erased
-- Data.Nat.Properties.^-monoid-morphism
d_'94''45'monoid'45'morphism_4266 ::
  Integer -> MAlonzo.Code.Algebra.Morphism.T_IsMonoidMorphism_306
d_'94''45'monoid'45'morphism_4266 :: Integer -> T_IsMonoidMorphism_306
d_'94''45'monoid'45'morphism_4266 ~Integer
v0
  = T_IsMonoidMorphism_306
du_'94''45'monoid'45'morphism_4266
du_'94''45'monoid'45'morphism_4266 ::
  MAlonzo.Code.Algebra.Morphism.T_IsMonoidMorphism_306
du_'94''45'monoid'45'morphism_4266 :: T_IsMonoidMorphism_306
du_'94''45'monoid'45'morphism_4266
  = (T_IsSemigroupMorphism_148 -> Any -> T_IsMonoidMorphism_306)
-> Any -> Any -> T_IsMonoidMorphism_306
forall a b. a -> b
coe
      T_IsSemigroupMorphism_148 -> Any -> T_IsMonoidMorphism_306
MAlonzo.Code.Algebra.Morphism.C_IsMonoidMorphism'46'constructor_2139
      (T_IsSemigroupMorphism_148 -> Any
forall a b. a -> b
coe T_IsSemigroupMorphism_148
du_'94''45'semigroup'45'morphism_4258) Any
forall a. a
erased
-- Data.Nat.Properties.^-*-assoc
d_'94''45''42''45'assoc_4274 ::
  Integer ->
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'94''45''42''45'assoc_4274 :: Integer -> Integer -> Integer -> T__'8801'__12
d_'94''45''42''45'assoc_4274 = Integer -> Integer -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Nat.Properties.m^n≡0⇒m≡0
d_m'94'n'8801'0'8658'm'8801'0_4296 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_m'94'n'8801'0'8658'm'8801'0_4296 :: Integer -> Integer -> T__'8801'__12 -> T__'8801'__12
d_m'94'n'8801'0'8658'm'8801'0_4296 = Integer -> Integer -> T__'8801'__12 -> T__'8801'__12
forall a. a
erased
-- Data.Nat.Properties.m^n≡1⇒n≡0∨m≡1
d_m'94'n'8801'1'8658'n'8801'0'8744'm'8801'1_4308 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Data.Sum.Base.T__'8846'__30
d_m'94'n'8801'1'8658'n'8801'0'8744'm'8801'1_4308 :: Integer -> Integer -> T__'8801'__12 -> T__'8846'__30
d_m'94'n'8801'1'8658'n'8801'0'8744'm'8801'1_4308 ~Integer
v0 Integer
v1 ~T__'8801'__12
v2
  = Integer -> T__'8846'__30
du_m'94'n'8801'1'8658'n'8801'0'8744'm'8801'1_4308 Integer
v1
du_m'94'n'8801'1'8658'n'8801'0'8744'm'8801'1_4308 ::
  Integer -> MAlonzo.Code.Data.Sum.Base.T__'8846'__30
du_m'94'n'8801'1'8658'n'8801'0'8744'm'8801'1_4308 :: Integer -> T__'8846'__30
du_m'94'n'8801'1'8658'n'8801'0'8744'm'8801'1_4308 Integer
v0
  = case Integer -> Integer
forall a b. a -> b
coe Integer
v0 of
      Integer
0 -> (Any -> T__'8846'__30) -> Any -> T__'8846'__30
forall a b. a -> b
coe Any -> T__'8846'__30
MAlonzo.Code.Data.Sum.Base.C_inj'8321'_38 Any
forall a. a
erased
      Integer
_ -> (Any -> T__'8846'__30) -> Any -> T__'8846'__30
forall a b. a -> b
coe Any -> T__'8846'__30
MAlonzo.Code.Data.Sum.Base.C_inj'8322'_42 Any
forall a. a
erased
-- Data.Nat.Properties.m^n≢0
d_m'94'n'8802'0_4324 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T_NonZero_112 ->
  MAlonzo.Code.Data.Nat.Base.T_NonZero_112
d_m'94'n'8802'0_4324 :: Integer -> Integer -> T_NonZero_112 -> T_NonZero_112
d_m'94'n'8802'0_4324 Integer
v0 Integer
v1 ~T_NonZero_112
v2 = Integer -> Integer -> T_NonZero_112
du_m'94'n'8802'0_4324 Integer
v0 Integer
v1
du_m'94'n'8802'0_4324 ::
  Integer -> Integer -> MAlonzo.Code.Data.Nat.Base.T_NonZero_112
du_m'94'n'8802'0_4324 :: Integer -> Integer -> T_NonZero_112
du_m'94'n'8802'0_4324 Integer
v0 Integer
v1
  = (Integer -> T_NonZero_112) -> Any -> T_NonZero_112
forall a b. a -> b
coe
      Integer -> T_NonZero_112
MAlonzo.Code.Data.Nat.Base.du_'8802''45'nonZero_126
      ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> Integer
MAlonzo.Code.Data.Nat.Base.d__'94'__272 (Integer -> Any
forall a b. a -> b
coe Integer
v0) (Integer -> Any
forall a b. a -> b
coe Integer
v1))
-- Data.Nat.Properties.m^n>0
d_m'94'n'62'0_4336 ::
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T_NonZero_112 ->
  Integer -> MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_m'94'n'62'0_4336 :: Integer -> T_NonZero_112 -> Integer -> T__'8804'__22
d_m'94'n'62'0_4336 ~Integer
v0 ~T_NonZero_112
v1 ~Integer
v2 = T__'8804'__22
du_m'94'n'62'0_4336
du_m'94'n'62'0_4336 :: MAlonzo.Code.Data.Nat.Base.T__'8804'__22
du_m'94'n'62'0_4336 :: T__'8804'__22
du_m'94'n'62'0_4336
  = T__'8804'__22 -> T__'8804'__22
forall a b. a -> b
coe T__'8804'__22
MAlonzo.Code.Data.Nat.Base.du_'62''45'nonZero'8315''185'_146
-- Data.Nat.Properties.^-monoˡ-≤
d_'94''45'mono'737''45''8804'_4346 ::
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_'94''45'mono'737''45''8804'_4346 :: Integer -> Integer -> Integer -> T__'8804'__22 -> T__'8804'__22
d_'94''45'mono'737''45''8804'_4346 Integer
v0 ~Integer
v1 Integer
v2 T__'8804'__22
v3
  = Integer -> Integer -> T__'8804'__22 -> T__'8804'__22
du_'94''45'mono'737''45''8804'_4346 Integer
v0 Integer
v2 T__'8804'__22
v3
du_'94''45'mono'737''45''8804'_4346 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
du_'94''45'mono'737''45''8804'_4346 :: Integer -> Integer -> T__'8804'__22 -> T__'8804'__22
du_'94''45'mono'737''45''8804'_4346 Integer
v0 Integer
v1 T__'8804'__22
v2
  = case Integer -> Integer
forall a b. a -> b
coe Integer
v0 of
      Integer
0 -> (T__'8804'__22 -> T__'8804'__22) -> Any -> T__'8804'__22
forall a b. a -> b
coe
             T__'8804'__22 -> T__'8804'__22
MAlonzo.Code.Data.Nat.Base.C_s'8804's_34
             (T__'8804'__22 -> Any
forall a b. a -> b
coe T__'8804'__22
MAlonzo.Code.Data.Nat.Base.C_z'8804'n_26)
      Integer
_ -> let v3 :: Integer
v3 = Integer -> Integer -> Integer
subInt (Integer -> Integer
forall a b. a -> b
coe Integer
v0) (Integer -> Integer
forall a b. a -> b
coe (Integer
1 :: Integer)) in
           Any -> T__'8804'__22
forall a b. a -> b
coe
             ((Integer
 -> Integer -> T__'8804'__22 -> T__'8804'__22 -> T__'8804'__22)
-> Any -> Any -> Any -> Any -> Any
forall a b. a -> b
coe
                Integer
-> Integer -> T__'8804'__22 -> T__'8804'__22 -> T__'8804'__22
du_'42''45'mono'45''8804'_4060 (Integer -> Any
forall a b. a -> b
coe Integer
v1)
                ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> Integer
MAlonzo.Code.Data.Nat.Base.d__'94'__272 (Integer -> Any
forall a b. a -> b
coe Integer
v1) (Integer -> Any
forall a b. a -> b
coe Integer
v3))
                (T__'8804'__22 -> Any
forall a b. a -> b
coe T__'8804'__22
v2)
                ((Integer -> Integer -> T__'8804'__22 -> T__'8804'__22)
-> Any -> Any -> Any -> Any
forall a b. a -> b
coe
                   Integer -> Integer -> T__'8804'__22 -> T__'8804'__22
du_'94''45'mono'737''45''8804'_4346 (Integer -> Any
forall a b. a -> b
coe Integer
v3) (Integer -> Any
forall a b. a -> b
coe Integer
v1) (T__'8804'__22 -> Any
forall a b. a -> b
coe T__'8804'__22
v2)))
-- Data.Nat.Properties.^-monoʳ-≤
d_'94''45'mono'691''45''8804'_4360 ::
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T_NonZero_112 ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_'94''45'mono'691''45''8804'_4360 :: Integer
-> T_NonZero_112
-> Integer
-> Integer
-> T__'8804'__22
-> T__'8804'__22
d_'94''45'mono'691''45''8804'_4360 Integer
v0 ~T_NonZero_112
v1 Integer
v2 Integer
v3 T__'8804'__22
v4
  = Integer -> Integer -> Integer -> T__'8804'__22 -> T__'8804'__22
du_'94''45'mono'691''45''8804'_4360 Integer
v0 Integer
v2 Integer
v3 T__'8804'__22
v4
du_'94''45'mono'691''45''8804'_4360 ::
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
du_'94''45'mono'691''45''8804'_4360 :: Integer -> Integer -> Integer -> T__'8804'__22 -> T__'8804'__22
du_'94''45'mono'691''45''8804'_4360 Integer
v0 Integer
v1 Integer
v2 T__'8804'__22
v3
  = case T__'8804'__22 -> T__'8804'__22
forall a b. a -> b
coe T__'8804'__22
v3 of
      T__'8804'__22
MAlonzo.Code.Data.Nat.Base.C_z'8804'n_26
        -> (Integer -> T__'8804'__22) -> Any -> T__'8804'__22
forall a b. a -> b
coe
             Integer -> T__'8804'__22
du_n'8802'0'8658'n'62'0_3090
             ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> Integer
MAlonzo.Code.Data.Nat.Base.d__'94'__272 (Integer -> Any
forall a b. a -> b
coe Integer
v0) (Integer -> Any
forall a b. a -> b
coe Integer
v2))
      MAlonzo.Code.Data.Nat.Base.C_s'8804's_34 T__'8804'__22
v6
        -> let v7 :: Integer
v7 = Integer -> Integer -> Integer
subInt (Integer -> Integer
forall a b. a -> b
coe Integer
v1) (Integer -> Integer
forall a b. a -> b
coe (Integer
1 :: Integer)) in
           Any -> T__'8804'__22
forall a b. a -> b
coe
             (let v8 :: Integer
v8 = Integer -> Integer -> Integer
subInt (Integer -> Integer
forall a b. a -> b
coe Integer
v2) (Integer -> Integer
forall a b. a -> b
coe (Integer
1 :: Integer)) in
              Any -> Any
forall a b. a -> b
coe
                ((Integer -> Integer -> T__'8804'__22 -> T__'8804'__22)
-> Any -> Any -> Any -> Any
forall a b. a -> b
coe
                   Integer -> Integer -> T__'8804'__22 -> T__'8804'__22
du_'42''45'mono'691''45''8804'_4080 (Integer -> Any
forall a b. a -> b
coe Integer
v0)
                   (((Any -> Any -> Any) -> (Any -> Any) -> Any -> Any -> Any)
-> (Any -> Any -> Any)
-> (Integer -> Integer)
-> Integer
-> Integer
-> Any
forall a b. a -> b
coe
                      (Any -> Any -> Any) -> (Any -> Any) -> Any -> Any -> Any
MAlonzo.Code.Function.Base.du_'8739'_'10217''45'__298
                      (\ Any
v9 Any
v10 -> Any
v10)
                      (Integer -> Integer -> Integer
MAlonzo.Code.Data.Nat.Base.d__'94'__272 (Integer -> Integer
forall a b. a -> b
coe Integer
v0)) Integer
v7 Integer
v8)
                   ((Integer -> Integer -> Integer -> T__'8804'__22 -> T__'8804'__22)
-> Any -> Any -> Any -> Any -> Any
forall a b. a -> b
coe
                      Integer -> Integer -> Integer -> T__'8804'__22 -> T__'8804'__22
du_'94''45'mono'691''45''8804'_4360 (Integer -> Any
forall a b. a -> b
coe Integer
v0) (Integer -> Any
forall a b. a -> b
coe Integer
v7) (Integer -> Any
forall a b. a -> b
coe Integer
v8)
                      (T__'8804'__22 -> Any
forall a b. a -> b
coe T__'8804'__22
v6))))
      T__'8804'__22
_ -> T__'8804'__22
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Data.Nat.Properties.^-monoˡ-<
d_'94''45'mono'737''45''60'_4376 ::
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T_NonZero_112 ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_'94''45'mono'737''45''60'_4376 :: Integer
-> T_NonZero_112
-> Integer
-> Integer
-> T__'8804'__22
-> T__'8804'__22
d_'94''45'mono'737''45''60'_4376 Integer
v0 ~T_NonZero_112
v1 Integer
v2 Integer
v3 T__'8804'__22
v4
  = Integer -> Integer -> Integer -> T__'8804'__22 -> T__'8804'__22
du_'94''45'mono'737''45''60'_4376 Integer
v0 Integer
v2 Integer
v3 T__'8804'__22
v4
du_'94''45'mono'737''45''60'_4376 ::
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
du_'94''45'mono'737''45''60'_4376 :: Integer -> Integer -> Integer -> T__'8804'__22 -> T__'8804'__22
du_'94''45'mono'737''45''60'_4376 Integer
v0 Integer
v1 Integer
v2 T__'8804'__22
v3
  = case Integer -> Integer
forall a b. a -> b
coe Integer
v0 of
      Integer
1 -> (Integer -> Integer -> Integer -> T__'8804'__22 -> T__'8804'__22)
-> Any -> Any -> Any -> Any -> T__'8804'__22
forall a b. a -> b
coe
             Integer -> Integer -> Integer -> T__'8804'__22 -> T__'8804'__22
du_'42''45'mono'737''45''60'_4100 (Integer -> Any
forall a b. a -> b
coe (Integer
1 :: Integer)) (Integer -> Any
forall a b. a -> b
coe Integer
v1)
             (Integer -> Any
forall a b. a -> b
coe Integer
v2) (T__'8804'__22 -> Any
forall a b. a -> b
coe T__'8804'__22
v3)
      Integer
_ -> (Integer
 -> Integer -> T__'8804'__22 -> T__'8804'__22 -> T__'8804'__22)
-> Any -> Any -> Any -> Any -> T__'8804'__22
forall a b. a -> b
coe
             Integer
-> Integer -> T__'8804'__22 -> T__'8804'__22 -> T__'8804'__22
du_'42''45'mono'45''60'_4086 (Integer -> Any
forall a b. a -> b
coe Integer
v2)
             (((Any -> Any -> Any) -> (Any -> Any) -> Any -> Any -> Any)
-> (Any -> Any -> Any)
-> (Any -> Integer)
-> Integer
-> Integer
-> Any
forall a b. a -> b
coe
                (Any -> Any -> Any) -> (Any -> Any) -> Any -> Any -> Any
MAlonzo.Code.Function.Base.du_'8739'_'10217''45'__298
                (\ Any
v4 Any
v5 -> Any
v5)
                (\ Any
v4 ->
                   Integer -> Integer -> Integer
MAlonzo.Code.Data.Nat.Base.d__'94'__272
                     (Any -> Integer
forall a b. a -> b
coe Any
v4) ((Integer -> Integer -> Integer) -> Any -> Any -> Integer
forall a b. a -> b
coe Integer -> Integer -> Integer
subInt (Integer -> Any
forall a b. a -> b
coe Integer
v0) (Integer -> Any
forall a b. a -> b
coe (Integer
1 :: Integer))))
                Integer
v1 Integer
v2)
             (T__'8804'__22 -> Any
forall a b. a -> b
coe T__'8804'__22
v3)
             ((Integer -> Integer -> Integer -> T__'8804'__22 -> T__'8804'__22)
-> Any -> Any -> Any -> Any -> Any
forall a b. a -> b
coe
                Integer -> Integer -> Integer -> T__'8804'__22 -> T__'8804'__22
du_'94''45'mono'737''45''60'_4376
                ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> Integer
subInt (Integer -> Any
forall a b. a -> b
coe Integer
v0) (Integer -> Any
forall a b. a -> b
coe (Integer
1 :: Integer))) (Integer -> Any
forall a b. a -> b
coe Integer
v1) (Integer -> Any
forall a b. a -> b
coe Integer
v2)
                (T__'8804'__22 -> Any
forall a b. a -> b
coe T__'8804'__22
v3))
-- Data.Nat.Properties.^-monoʳ-<
d_'94''45'mono'691''45''60'_4388 ::
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_'94''45'mono'691''45''60'_4388 :: Integer
-> T__'8804'__22
-> Integer
-> Integer
-> T__'8804'__22
-> T__'8804'__22
d_'94''45'mono'691''45''60'_4388 Integer
v0 T__'8804'__22
v1 Integer
v2 Integer
v3 T__'8804'__22
v4
  = case Integer -> Integer
forall a b. a -> b
coe Integer
v2 of
      Integer
0 -> let v5 :: Integer
v5 = Integer -> Integer -> Integer
subInt (Integer -> Integer
forall a b. a -> b
coe Integer
v3) (Integer -> Integer
forall a b. a -> b
coe (Integer
1 :: Integer)) in
           Any -> T__'8804'__22
forall a b. a -> b
coe
             (case T__'8804'__22 -> T__'8804'__22
forall a b. a -> b
coe T__'8804'__22
v4 of
                MAlonzo.Code.Data.Nat.Base.C_s'8804's_34 T__'8804'__22
v8
                  -> (Any -> Any -> Any) -> Any -> Any -> Any
forall a b. a -> b
coe
                       Any -> Any -> Any
forall a b. a -> b -> b
seq (T__'8804'__22 -> Any
forall a b. a -> b
coe T__'8804'__22
v8)
                       ((Integer
 -> Integer -> T__'8804'__22 -> T__'8804'__22 -> T__'8804'__22)
-> Any -> Any -> Any -> Any -> Any
forall a b. a -> b
coe
                          Integer
-> Integer -> T__'8804'__22 -> T__'8804'__22 -> T__'8804'__22
du_'42''45'mono'45''8804'_4060 (Integer -> Any
forall a b. a -> b
coe Integer
v0)
                          ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> Integer
MAlonzo.Code.Data.Nat.Base.d__'94'__272 (Integer -> Any
forall a b. a -> b
coe Integer
v0) (Integer -> Any
forall a b. a -> b
coe Integer
v5))
                          (T__'8804'__22 -> Any
forall a b. a -> b
coe T__'8804'__22
v1) (T__'8804'__22 -> Any
forall a b. a -> b
coe T__'8804'__22
du_m'94'n'62'0_4336))
                T__'8804'__22
_ -> Any
forall a. a
MAlonzo.RTE.mazUnreachableError)
      Integer
_ -> let v5 :: Integer
v5 = Integer -> Integer -> Integer
subInt (Integer -> Integer
forall a b. a -> b
coe Integer
v2) (Integer -> Integer
forall a b. a -> b
coe (Integer
1 :: Integer)) in
           Any -> T__'8804'__22
forall a b. a -> b
coe
             (let v6 :: Integer
v6 = Integer -> Integer -> Integer
subInt (Integer -> Integer
forall a b. a -> b
coe Integer
v3) (Integer -> Integer
forall a b. a -> b
coe (Integer
1 :: Integer)) in
              Any -> Any
forall a b. a -> b
coe
                (case T__'8804'__22 -> T__'8804'__22
forall a b. a -> b
coe T__'8804'__22
v4 of
                   MAlonzo.Code.Data.Nat.Base.C_s'8804's_34 T__'8804'__22
v9
                     -> (Integer -> Integer -> T__'8804'__22 -> T__'8804'__22)
-> Any -> Any -> Any -> Any
forall a b. a -> b
coe
                          Integer -> Integer -> T__'8804'__22 -> T__'8804'__22
du_'42''45'mono'691''45''60'_4114 (Integer -> Any
forall a b. a -> b
coe Integer
v0)
                          (((Any -> Any -> Any) -> (Any -> Any) -> Any -> Any -> Any)
-> (Any -> Any -> Any)
-> (Integer -> Integer)
-> Integer
-> Integer
-> Any
forall a b. a -> b
coe
                             (Any -> Any -> Any) -> (Any -> Any) -> Any -> Any -> Any
MAlonzo.Code.Function.Base.du_'8739'_'10217''45'__298
                             (\ Any
v10 Any
v11 -> Any
v11)
                             (Integer -> Integer -> Integer
MAlonzo.Code.Data.Nat.Base.d__'94'__272 (Integer -> Integer
forall a b. a -> b
coe Integer
v0)) Integer
v5 Integer
v6)
                          ((Integer
 -> T__'8804'__22
 -> Integer
 -> Integer
 -> T__'8804'__22
 -> T__'8804'__22)
-> Any -> Any -> Any -> Any -> Any -> Any
forall a b. a -> b
coe
                             Integer
-> T__'8804'__22
-> Integer
-> Integer
-> T__'8804'__22
-> T__'8804'__22
d_'94''45'mono'691''45''60'_4388 (Integer -> Any
forall a b. a -> b
coe Integer
v0) (T__'8804'__22 -> Any
forall a b. a -> b
coe T__'8804'__22
v1) (Integer -> Any
forall a b. a -> b
coe Integer
v5)
                             (Integer -> Any
forall a b. a -> b
coe Integer
v6) (T__'8804'__22 -> Any
forall a b. a -> b
coe T__'8804'__22
v9))
                   T__'8804'__22
_ -> Any
forall a. a
MAlonzo.RTE.mazUnreachableError))
-- Data.Nat.Properties.m≤n⇒m⊔n≡n
d_m'8804'n'8658'm'8852'n'8801'n_4406 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_m'8804'n'8658'm'8852'n'8801'n_4406 :: Integer -> Integer -> T__'8804'__22 -> T__'8801'__12
d_m'8804'n'8658'm'8852'n'8801'n_4406 = Integer -> Integer -> T__'8804'__22 -> T__'8801'__12
forall a. a
erased
-- Data.Nat.Properties.m≥n⇒m⊔n≡m
d_m'8805'n'8658'm'8852'n'8801'm_4412 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_m'8805'n'8658'm'8852'n'8801'm_4412 :: Integer -> Integer -> T__'8804'__22 -> T__'8801'__12
d_m'8805'n'8658'm'8852'n'8801'm_4412 = Integer -> Integer -> T__'8804'__22 -> T__'8801'__12
forall a. a
erased
-- Data.Nat.Properties.m≤n⇒m⊓n≡m
d_m'8804'n'8658'm'8851'n'8801'm_4422 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_m'8804'n'8658'm'8851'n'8801'm_4422 :: Integer -> Integer -> T__'8804'__22 -> T__'8801'__12
d_m'8804'n'8658'm'8851'n'8801'm_4422 = Integer -> Integer -> T__'8804'__22 -> T__'8801'__12
forall a. a
erased
-- Data.Nat.Properties.m≥n⇒m⊓n≡n
d_m'8805'n'8658'm'8851'n'8801'n_4428 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_m'8805'n'8658'm'8851'n'8801'n_4428 :: Integer -> Integer -> T__'8804'__22 -> T__'8801'__12
d_m'8805'n'8658'm'8851'n'8801'n_4428 = Integer -> Integer -> T__'8804'__22 -> T__'8801'__12
forall a. a
erased
-- Data.Nat.Properties.⊓-operator
d_'8851''45'operator_4438 ::
  MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98
d_'8851''45'operator_4438 :: T_MinOperator_98
d_'8851''45'operator_4438
  = ((Any -> Any -> Any)
 -> (Any -> Any -> Any -> Any)
 -> (Any -> Any -> Any -> Any)
 -> T_MinOperator_98)
-> Any -> Any -> Any -> T_MinOperator_98
forall a b. a -> b
coe
      (Any -> Any -> Any)
-> (Any -> Any -> Any -> Any)
-> (Any -> Any -> Any -> Any)
-> T_MinOperator_98
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.C_MinOperator'46'constructor_1121
      ((Integer -> Integer -> Integer) -> Any
forall a b. a -> b
coe Integer -> Integer -> Integer
MAlonzo.Code.Data.Nat.Base.d__'8851'__232) Any
forall a. a
erased Any
forall a. a
erased
-- Data.Nat.Properties.⊔-operator
d_'8852''45'operator_4440 ::
  MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MaxOperator_128
d_'8852''45'operator_4440 :: T_MaxOperator_128
d_'8852''45'operator_4440
  = ((Any -> Any -> Any)
 -> (Any -> Any -> Any -> Any)
 -> (Any -> Any -> Any -> Any)
 -> T_MaxOperator_128)
-> Any -> Any -> Any -> T_MaxOperator_128
forall a b. a -> b
coe
      (Any -> Any -> Any)
-> (Any -> Any -> Any -> Any)
-> (Any -> Any -> Any -> Any)
-> T_MaxOperator_128
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.C_MaxOperator'46'constructor_1665
      ((Integer -> Integer -> Integer) -> Any
forall a b. a -> b
coe Integer -> Integer -> Integer
MAlonzo.Code.Data.Nat.Base.d__'8852'__204) Any
forall a. a
erased Any
forall a. a
erased
-- Data.Nat.Properties.⊔≡⊔′
d_'8852''8801''8852''8242'_4446 ::
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8852''8801''8852''8242'_4446 :: Integer -> Integer -> T__'8801'__12
d_'8852''8801''8852''8242'_4446 = Integer -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Nat.Properties.⊓≡⊓′
d_'8851''8801''8851''8242'_4472 ::
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8851''8801''8851''8242'_4472 :: Integer -> Integer -> T__'8801'__12
d_'8851''8801''8851''8242'_4472 = Integer -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Nat.Properties.⊓-⊔-properties.x⊓y≤x
d_x'8851'y'8804'x_4504 ::
  Integer -> Integer -> MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_x'8851'y'8804'x_4504 :: Integer -> Integer -> T__'8804'__22
d_x'8851'y'8804'x_4504
  = let v0 :: T_TotalPreorder_222
v0 = T_TotalPreorder_222
d_'8804''45'totalPreorder_2822 in
    Any -> Integer -> Integer -> T__'8804'__22
forall a b. a -> b
coe
      (let v1 :: T_MaxOperator_128
v1 = T_MaxOperator_128
d_'8852''45'operator_4440 in
       Any -> Any
forall a b. a -> b
coe
         ((T_TotalPreorder_222 -> T_MinOperator_98 -> Any -> Any -> Any)
-> Any -> Any -> Any
forall a b. a -> b
coe
            T_TotalPreorder_222 -> T_MinOperator_98 -> Any -> Any -> Any
MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_x'8851'y'8804'x_2808
            ((T_TotalPreorder_222 -> T_TotalPreorder_222) -> Any -> Any
forall a b. a -> b
coe
               T_TotalPreorder_222 -> T_TotalPreorder_222
MAlonzo.Code.Relation.Binary.Construct.Flip.EqAndOrd.du_totalPreorder_746
               (T_TotalPreorder_222 -> Any
forall a b. a -> b
coe T_TotalPreorder_222
v0))
            ((T_MaxOperator_128 -> T_MinOperator_98) -> Any -> Any
forall a b. a -> b
coe
               T_MaxOperator_128 -> T_MinOperator_98
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.du_MaxOp'8658'MinOp_174
               (T_MaxOperator_128 -> Any
forall a b. a -> b
coe T_MaxOperator_128
v1))))
-- Data.Nat.Properties.⊓-⊔-properties.x≤y⇒x⊓z≤y
d_x'8804'y'8658'x'8851'z'8804'y_4506 ::
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_x'8804'y'8658'x'8851'z'8804'y_4506 :: Integer -> Integer -> Integer -> T__'8804'__22 -> T__'8804'__22
d_x'8804'y'8658'x'8851'z'8804'y_4506
  = let v0 :: T_TotalPreorder_222
v0 = T_TotalPreorder_222
d_'8804''45'totalPreorder_2822 in
    Any
-> Integer -> Integer -> Integer -> T__'8804'__22 -> T__'8804'__22
forall a b. a -> b
coe
      (let v1 :: T_MaxOperator_128
v1 = T_MaxOperator_128
d_'8852''45'operator_4440 in
       Any -> Any
forall a b. a -> b
coe
         ((T_TotalPreorder_222
 -> T_MinOperator_98 -> Any -> Any -> Any -> Any -> Any)
-> Any -> Any -> Any
forall a b. a -> b
coe
            T_TotalPreorder_222
-> T_MinOperator_98 -> Any -> Any -> Any -> Any -> Any
MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_x'8804'y'8658'x'8851'z'8804'y_3160
            ((T_TotalPreorder_222 -> T_TotalPreorder_222) -> Any -> Any
forall a b. a -> b
coe
               T_TotalPreorder_222 -> T_TotalPreorder_222
MAlonzo.Code.Relation.Binary.Construct.Flip.EqAndOrd.du_totalPreorder_746
               (T_TotalPreorder_222 -> Any
forall a b. a -> b
coe T_TotalPreorder_222
v0))
            ((T_MaxOperator_128 -> T_MinOperator_98) -> Any -> Any
forall a b. a -> b
coe
               T_MaxOperator_128 -> T_MinOperator_98
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.du_MaxOp'8658'MinOp_174
               (T_MaxOperator_128 -> Any
forall a b. a -> b
coe T_MaxOperator_128
v1))))
-- Data.Nat.Properties.⊓-⊔-properties.x≤y⇒z⊓x≤y
d_x'8804'y'8658'z'8851'x'8804'y_4508 ::
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_x'8804'y'8658'z'8851'x'8804'y_4508 :: Integer -> Integer -> Integer -> T__'8804'__22 -> T__'8804'__22
d_x'8804'y'8658'z'8851'x'8804'y_4508
  = let v0 :: T_TotalPreorder_222
v0 = T_TotalPreorder_222
d_'8804''45'totalPreorder_2822 in
    Any
-> Integer -> Integer -> Integer -> T__'8804'__22 -> T__'8804'__22
forall a b. a -> b
coe
      (let v1 :: T_MaxOperator_128
v1 = T_MaxOperator_128
d_'8852''45'operator_4440 in
       Any -> Any
forall a b. a -> b
coe
         ((T_TotalPreorder_222
 -> T_MinOperator_98 -> Any -> Any -> Any -> Any -> Any)
-> Any -> Any -> Any
forall a b. a -> b
coe
            T_TotalPreorder_222
-> T_MinOperator_98 -> Any -> Any -> Any -> Any -> Any
MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_x'8804'y'8658'z'8851'x'8804'y_3172
            ((T_TotalPreorder_222 -> T_TotalPreorder_222) -> Any -> Any
forall a b. a -> b
coe
               T_TotalPreorder_222 -> T_TotalPreorder_222
MAlonzo.Code.Relation.Binary.Construct.Flip.EqAndOrd.du_totalPreorder_746
               (T_TotalPreorder_222 -> Any
forall a b. a -> b
coe T_TotalPreorder_222
v0))
            ((T_MaxOperator_128 -> T_MinOperator_98) -> Any -> Any
forall a b. a -> b
coe
               T_MaxOperator_128 -> T_MinOperator_98
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.du_MaxOp'8658'MinOp_174
               (T_MaxOperator_128 -> Any
forall a b. a -> b
coe T_MaxOperator_128
v1))))
-- Data.Nat.Properties.⊓-⊔-properties.x≤y⇒x⊓z≤y
d_x'8804'y'8658'x'8851'z'8804'y_4510 ::
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_x'8804'y'8658'x'8851'z'8804'y_4510 :: Integer -> Integer -> Integer -> T__'8804'__22 -> T__'8804'__22
d_x'8804'y'8658'x'8851'z'8804'y_4510
  = let v0 :: T_TotalPreorder_222
v0 = T_TotalPreorder_222
d_'8804''45'totalPreorder_2822 in
    Any
-> Integer -> Integer -> Integer -> T__'8804'__22 -> T__'8804'__22
forall a b. a -> b
coe
      (let v1 :: T_MinOperator_98
v1 = T_MinOperator_98
d_'8851''45'operator_4438 in
       Any -> Any
forall a b. a -> b
coe
         ((T_TotalPreorder_222
 -> T_MinOperator_98 -> Any -> Any -> Any -> Any -> Any)
-> Any -> Any -> Any
forall a b. a -> b
coe
            T_TotalPreorder_222
-> T_MinOperator_98 -> Any -> Any -> Any -> Any -> Any
MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_x'8804'y'8658'x'8851'z'8804'y_3160
            (T_TotalPreorder_222 -> Any
forall a b. a -> b
coe T_TotalPreorder_222
v0) (T_MinOperator_98 -> Any
forall a b. a -> b
coe T_MinOperator_98
v1)))
-- Data.Nat.Properties.⊓-⊔-properties.x≤y⇒z⊓x≤y
d_x'8804'y'8658'z'8851'x'8804'y_4512 ::
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_x'8804'y'8658'z'8851'x'8804'y_4512 :: Integer -> Integer -> Integer -> T__'8804'__22 -> T__'8804'__22
d_x'8804'y'8658'z'8851'x'8804'y_4512
  = let v0 :: T_TotalPreorder_222
v0 = T_TotalPreorder_222
d_'8804''45'totalPreorder_2822 in
    Any
-> Integer -> Integer -> Integer -> T__'8804'__22 -> T__'8804'__22
forall a b. a -> b
coe
      (let v1 :: T_MinOperator_98
v1 = T_MinOperator_98
d_'8851''45'operator_4438 in
       Any -> Any
forall a b. a -> b
coe
         ((T_TotalPreorder_222
 -> T_MinOperator_98 -> Any -> Any -> Any -> Any -> Any)
-> Any -> Any -> Any
forall a b. a -> b
coe
            T_TotalPreorder_222
-> T_MinOperator_98 -> Any -> Any -> Any -> Any -> Any
MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_x'8804'y'8658'z'8851'x'8804'y_3172
            (T_TotalPreorder_222 -> Any
forall a b. a -> b
coe T_TotalPreorder_222
v0) (T_MinOperator_98 -> Any
forall a b. a -> b
coe T_MinOperator_98
v1)))
-- Data.Nat.Properties.⊓-⊔-properties.x≤y⊓z⇒x≤y
d_x'8804'y'8851'z'8658'x'8804'y_4514 ::
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_x'8804'y'8851'z'8658'x'8804'y_4514 :: Integer -> Integer -> Integer -> T__'8804'__22 -> T__'8804'__22
d_x'8804'y'8851'z'8658'x'8804'y_4514
  = let v0 :: T_TotalPreorder_222
v0 = T_TotalPreorder_222
d_'8804''45'totalPreorder_2822 in
    Any
-> Integer -> Integer -> Integer -> T__'8804'__22 -> T__'8804'__22
forall a b. a -> b
coe
      (let v1 :: T_MinOperator_98
v1 = T_MinOperator_98
d_'8851''45'operator_4438 in
       Any -> Any
forall a b. a -> b
coe
         ((T_TotalPreorder_222
 -> T_MinOperator_98 -> Any -> Any -> Any -> Any -> Any)
-> Any -> Any -> Any
forall a b. a -> b
coe
            T_TotalPreorder_222
-> T_MinOperator_98 -> Any -> Any -> Any -> Any -> Any
MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_x'8804'y'8851'z'8658'x'8804'y_3184
            (T_TotalPreorder_222 -> Any
forall a b. a -> b
coe T_TotalPreorder_222
v0) (T_MinOperator_98 -> Any
forall a b. a -> b
coe T_MinOperator_98
v1)))
-- Data.Nat.Properties.⊓-⊔-properties.x≤y⊓z⇒x≤z
d_x'8804'y'8851'z'8658'x'8804'z_4516 ::
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_x'8804'y'8851'z'8658'x'8804'z_4516 :: Integer -> Integer -> Integer -> T__'8804'__22 -> T__'8804'__22
d_x'8804'y'8851'z'8658'x'8804'z_4516
  = let v0 :: T_TotalPreorder_222
v0 = T_TotalPreorder_222
d_'8804''45'totalPreorder_2822 in
    Any
-> Integer -> Integer -> Integer -> T__'8804'__22 -> T__'8804'__22
forall a b. a -> b
coe
      (let v1 :: T_MinOperator_98
v1 = T_MinOperator_98
d_'8851''45'operator_4438 in
       Any -> Any
forall a b. a -> b
coe
         ((T_TotalPreorder_222
 -> T_MinOperator_98 -> Any -> Any -> Any -> Any -> Any)
-> Any -> Any -> Any
forall a b. a -> b
coe
            T_TotalPreorder_222
-> T_MinOperator_98 -> Any -> Any -> Any -> Any -> Any
MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_x'8804'y'8851'z'8658'x'8804'z_3198
            (T_TotalPreorder_222 -> Any
forall a b. a -> b
coe T_TotalPreorder_222
v0) (T_MinOperator_98 -> Any
forall a b. a -> b
coe T_MinOperator_98
v1)))
-- Data.Nat.Properties.⊓-⊔-properties.x⊓y≤y
d_x'8851'y'8804'y_4518 ::
  Integer -> Integer -> MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_x'8851'y'8804'y_4518 :: Integer -> Integer -> T__'8804'__22
d_x'8851'y'8804'y_4518
  = let v0 :: T_TotalPreorder_222
v0 = T_TotalPreorder_222
d_'8804''45'totalPreorder_2822 in
    Any -> Integer -> Integer -> T__'8804'__22
forall a b. a -> b
coe
      (let v1 :: T_MaxOperator_128
v1 = T_MaxOperator_128
d_'8852''45'operator_4440 in
       Any -> Any
forall a b. a -> b
coe
         ((T_TotalPreorder_222 -> T_MinOperator_98 -> Any -> Any -> Any)
-> Any -> Any -> Any
forall a b. a -> b
coe
            T_TotalPreorder_222 -> T_MinOperator_98 -> Any -> Any -> Any
MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_x'8851'y'8804'y_2834
            ((T_TotalPreorder_222 -> T_TotalPreorder_222) -> Any -> Any
forall a b. a -> b
coe
               T_TotalPreorder_222 -> T_TotalPreorder_222
MAlonzo.Code.Relation.Binary.Construct.Flip.EqAndOrd.du_totalPreorder_746
               (T_TotalPreorder_222 -> Any
forall a b. a -> b
coe T_TotalPreorder_222
v0))
            ((T_MaxOperator_128 -> T_MinOperator_98) -> Any -> Any
forall a b. a -> b
coe
               T_MaxOperator_128 -> T_MinOperator_98
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.du_MaxOp'8658'MinOp_174
               (T_MaxOperator_128 -> Any
forall a b. a -> b
coe T_MaxOperator_128
v1))))
-- Data.Nat.Properties.⊓-⊔-properties.x⊓y≈x⇒x≤y
d_x'8851'y'8776'x'8658'x'8804'y_4520 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_x'8851'y'8776'x'8658'x'8804'y_4520 :: Integer -> Integer -> T__'8801'__12 -> T__'8804'__22
d_x'8851'y'8776'x'8658'x'8804'y_4520
  = let v0 :: T_TotalPreorder_222
v0 = T_TotalPreorder_222
d_'8804''45'totalPreorder_2822 in
    Any -> Integer -> Integer -> T__'8801'__12 -> T__'8804'__22
forall a b. a -> b
coe
      (let v1 :: T_MinOperator_98
v1 = T_MinOperator_98
d_'8851''45'operator_4438 in
       Any -> Any
forall a b. a -> b
coe
         ((T_TotalPreorder_222
 -> T_MinOperator_98 -> Any -> Any -> Any -> Any)
-> Any -> Any -> Any
forall a b. a -> b
coe
            T_TotalPreorder_222 -> T_MinOperator_98 -> Any -> Any -> Any -> Any
MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_x'8851'y'8776'x'8658'x'8804'y_3068
            (T_TotalPreorder_222 -> Any
forall a b. a -> b
coe T_TotalPreorder_222
v0) (T_MinOperator_98 -> Any
forall a b. a -> b
coe T_MinOperator_98
v1)))
-- Data.Nat.Properties.⊓-⊔-properties.x⊓y≈y⇒y≤x
d_x'8851'y'8776'y'8658'y'8804'x_4522 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_x'8851'y'8776'y'8658'y'8804'x_4522 :: Integer -> Integer -> T__'8801'__12 -> T__'8804'__22
d_x'8851'y'8776'y'8658'y'8804'x_4522
  = let v0 :: T_TotalPreorder_222
v0 = T_TotalPreorder_222
d_'8804''45'totalPreorder_2822 in
    Any -> Integer -> Integer -> T__'8801'__12 -> T__'8804'__22
forall a b. a -> b
coe
      (let v1 :: T_MinOperator_98
v1 = T_MinOperator_98
d_'8851''45'operator_4438 in
       Any -> Any
forall a b. a -> b
coe
         ((T_TotalPreorder_222
 -> T_MinOperator_98 -> Any -> Any -> Any -> Any)
-> Any -> Any -> Any
forall a b. a -> b
coe
            T_TotalPreorder_222 -> T_MinOperator_98 -> Any -> Any -> Any -> Any
MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_x'8851'y'8776'y'8658'y'8804'x_3100
            (T_TotalPreorder_222 -> Any
forall a b. a -> b
coe T_TotalPreorder_222
v0) (T_MinOperator_98 -> Any
forall a b. a -> b
coe T_MinOperator_98
v1)))
-- Data.Nat.Properties.⊓-⊔-properties.x⊓y≤x
d_x'8851'y'8804'x_4524 ::
  Integer -> Integer -> MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_x'8851'y'8804'x_4524 :: Integer -> Integer -> T__'8804'__22
d_x'8851'y'8804'x_4524
  = let v0 :: T_TotalPreorder_222
v0 = T_TotalPreorder_222
d_'8804''45'totalPreorder_2822 in
    Any -> Integer -> Integer -> T__'8804'__22
forall a b. a -> b
coe
      (let v1 :: T_MinOperator_98
v1 = T_MinOperator_98
d_'8851''45'operator_4438 in
       Any -> Any
forall a b. a -> b
coe
         ((T_TotalPreorder_222 -> T_MinOperator_98 -> Any -> Any -> Any)
-> Any -> Any -> Any
forall a b. a -> b
coe
            T_TotalPreorder_222 -> T_MinOperator_98 -> Any -> Any -> Any
MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_x'8851'y'8804'x_2808
            (T_TotalPreorder_222 -> Any
forall a b. a -> b
coe T_TotalPreorder_222
v0) (T_MinOperator_98 -> Any
forall a b. a -> b
coe T_MinOperator_98
v1)))
-- Data.Nat.Properties.⊓-⊔-properties.x⊓y≤x⊔y
d_x'8851'y'8804'x'8852'y_4526 ::
  Integer -> Integer -> MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_x'8851'y'8804'x'8852'y_4526 :: Integer -> Integer -> T__'8804'__22
d_x'8851'y'8804'x'8852'y_4526
  = (T_TotalPreorder_222
 -> T_MinOperator_98 -> T_MaxOperator_128 -> Any -> Any -> Any)
-> Any -> Any -> Any -> Integer -> Integer -> T__'8804'__22
forall a b. a -> b
coe
      T_TotalPreorder_222
-> T_MinOperator_98 -> T_MaxOperator_128 -> Any -> Any -> Any
MAlonzo.Code.Algebra.Construct.NaturalChoice.MinMaxOp.du_x'8851'y'8804'x'8852'y_3318
      (T_TotalPreorder_222 -> Any
forall a b. a -> b
coe T_TotalPreorder_222
d_'8804''45'totalPreorder_2822)
      (T_MinOperator_98 -> Any
forall a b. a -> b
coe T_MinOperator_98
d_'8851''45'operator_4438) (T_MaxOperator_128 -> Any
forall a b. a -> b
coe T_MaxOperator_128
d_'8852''45'operator_4440)
-- Data.Nat.Properties.⊓-⊔-properties.x⊓y≤y
d_x'8851'y'8804'y_4528 ::
  Integer -> Integer -> MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_x'8851'y'8804'y_4528 :: Integer -> Integer -> T__'8804'__22
d_x'8851'y'8804'y_4528
  = let v0 :: T_TotalPreorder_222
v0 = T_TotalPreorder_222
d_'8804''45'totalPreorder_2822 in
    Any -> Integer -> Integer -> T__'8804'__22
forall a b. a -> b
coe
      (let v1 :: T_MinOperator_98
v1 = T_MinOperator_98
d_'8851''45'operator_4438 in
       Any -> Any
forall a b. a -> b
coe
         ((T_TotalPreorder_222 -> T_MinOperator_98 -> Any -> Any -> Any)
-> Any -> Any -> Any
forall a b. a -> b
coe
            T_TotalPreorder_222 -> T_MinOperator_98 -> Any -> Any -> Any
MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_x'8851'y'8804'y_2834
            (T_TotalPreorder_222 -> Any
forall a b. a -> b
coe T_TotalPreorder_222
v0) (T_MinOperator_98 -> Any
forall a b. a -> b
coe T_MinOperator_98
v1)))
-- Data.Nat.Properties.⊓-⊔-properties.x⊓y≈x⇒x≤y
d_x'8851'y'8776'x'8658'x'8804'y_4530 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_x'8851'y'8776'x'8658'x'8804'y_4530 :: Integer -> Integer -> T__'8801'__12 -> T__'8804'__22
d_x'8851'y'8776'x'8658'x'8804'y_4530
  = let v0 :: T_TotalPreorder_222
v0 = T_TotalPreorder_222
d_'8804''45'totalPreorder_2822 in
    Any -> Integer -> Integer -> T__'8801'__12 -> T__'8804'__22
forall a b. a -> b
coe
      (let v1 :: T_MaxOperator_128
v1 = T_MaxOperator_128
d_'8852''45'operator_4440 in
       Any -> Any
forall a b. a -> b
coe
         ((T_TotalPreorder_222
 -> T_MinOperator_98 -> Any -> Any -> Any -> Any)
-> Any -> Any -> Any
forall a b. a -> b
coe
            T_TotalPreorder_222 -> T_MinOperator_98 -> Any -> Any -> Any -> Any
MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_x'8851'y'8776'x'8658'x'8804'y_3068
            ((T_TotalPreorder_222 -> T_TotalPreorder_222) -> Any -> Any
forall a b. a -> b
coe
               T_TotalPreorder_222 -> T_TotalPreorder_222
MAlonzo.Code.Relation.Binary.Construct.Flip.EqAndOrd.du_totalPreorder_746
               (T_TotalPreorder_222 -> Any
forall a b. a -> b
coe T_TotalPreorder_222
v0))
            ((T_MaxOperator_128 -> T_MinOperator_98) -> Any -> Any
forall a b. a -> b
coe
               T_MaxOperator_128 -> T_MinOperator_98
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.du_MaxOp'8658'MinOp_174
               (T_MaxOperator_128 -> Any
forall a b. a -> b
coe T_MaxOperator_128
v1))))
-- Data.Nat.Properties.⊓-⊔-properties.x⊓y≈y⇒y≤x
d_x'8851'y'8776'y'8658'y'8804'x_4532 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_x'8851'y'8776'y'8658'y'8804'x_4532 :: Integer -> Integer -> T__'8801'__12 -> T__'8804'__22
d_x'8851'y'8776'y'8658'y'8804'x_4532
  = let v0 :: T_TotalPreorder_222
v0 = T_TotalPreorder_222
d_'8804''45'totalPreorder_2822 in
    Any -> Integer -> Integer -> T__'8801'__12 -> T__'8804'__22
forall a b. a -> b
coe
      (let v1 :: T_MaxOperator_128
v1 = T_MaxOperator_128
d_'8852''45'operator_4440 in
       Any -> Any
forall a b. a -> b
coe
         ((T_TotalPreorder_222
 -> T_MinOperator_98 -> Any -> Any -> Any -> Any)
-> Any -> Any -> Any
forall a b. a -> b
coe
            T_TotalPreorder_222 -> T_MinOperator_98 -> Any -> Any -> Any -> Any
MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_x'8851'y'8776'y'8658'y'8804'x_3100
            ((T_TotalPreorder_222 -> T_TotalPreorder_222) -> Any -> Any
forall a b. a -> b
coe
               T_TotalPreorder_222 -> T_TotalPreorder_222
MAlonzo.Code.Relation.Binary.Construct.Flip.EqAndOrd.du_totalPreorder_746
               (T_TotalPreorder_222 -> Any
forall a b. a -> b
coe T_TotalPreorder_222
v0))
            ((T_MaxOperator_128 -> T_MinOperator_98) -> Any -> Any
forall a b. a -> b
coe
               T_MaxOperator_128 -> T_MinOperator_98
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.du_MaxOp'8658'MinOp_174
               (T_MaxOperator_128 -> Any
forall a b. a -> b
coe T_MaxOperator_128
v1))))
-- Data.Nat.Properties.⊓-⊔-properties.x≤y⊓z⇒x≤y
d_x'8804'y'8851'z'8658'x'8804'y_4534 ::
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_x'8804'y'8851'z'8658'x'8804'y_4534 :: Integer -> Integer -> Integer -> T__'8804'__22 -> T__'8804'__22
d_x'8804'y'8851'z'8658'x'8804'y_4534
  = let v0 :: T_TotalPreorder_222
v0 = T_TotalPreorder_222
d_'8804''45'totalPreorder_2822 in
    Any
-> Integer -> Integer -> Integer -> T__'8804'__22 -> T__'8804'__22
forall a b. a -> b
coe
      (let v1 :: T_MaxOperator_128
v1 = T_MaxOperator_128
d_'8852''45'operator_4440 in
       Any -> Any
forall a b. a -> b
coe
         ((T_TotalPreorder_222
 -> T_MinOperator_98 -> Any -> Any -> Any -> Any -> Any)
-> Any -> Any -> Any
forall a b. a -> b
coe
            T_TotalPreorder_222
-> T_MinOperator_98 -> Any -> Any -> Any -> Any -> Any
MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_x'8804'y'8851'z'8658'x'8804'y_3184
            ((T_TotalPreorder_222 -> T_TotalPreorder_222) -> Any -> Any
forall a b. a -> b
coe
               T_TotalPreorder_222 -> T_TotalPreorder_222
MAlonzo.Code.Relation.Binary.Construct.Flip.EqAndOrd.du_totalPreorder_746
               (T_TotalPreorder_222 -> Any
forall a b. a -> b
coe T_TotalPreorder_222
v0))
            ((T_MaxOperator_128 -> T_MinOperator_98) -> Any -> Any
forall a b. a -> b
coe
               T_MaxOperator_128 -> T_MinOperator_98
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.du_MaxOp'8658'MinOp_174
               (T_MaxOperator_128 -> Any
forall a b. a -> b
coe T_MaxOperator_128
v1))))
-- Data.Nat.Properties.⊓-⊔-properties.x≤y⊓z⇒x≤z
d_x'8804'y'8851'z'8658'x'8804'z_4536 ::
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_x'8804'y'8851'z'8658'x'8804'z_4536 :: Integer -> Integer -> Integer -> T__'8804'__22 -> T__'8804'__22
d_x'8804'y'8851'z'8658'x'8804'z_4536
  = let v0 :: T_TotalPreorder_222
v0 = T_TotalPreorder_222
d_'8804''45'totalPreorder_2822 in
    Any
-> Integer -> Integer -> Integer -> T__'8804'__22 -> T__'8804'__22
forall a b. a -> b
coe
      (let v1 :: T_MaxOperator_128
v1 = T_MaxOperator_128
d_'8852''45'operator_4440 in
       Any -> Any
forall a b. a -> b
coe
         ((T_TotalPreorder_222
 -> T_MinOperator_98 -> Any -> Any -> Any -> Any -> Any)
-> Any -> Any -> Any
forall a b. a -> b
coe
            T_TotalPreorder_222
-> T_MinOperator_98 -> Any -> Any -> Any -> Any -> Any
MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_x'8804'y'8851'z'8658'x'8804'z_3198
            ((T_TotalPreorder_222 -> T_TotalPreorder_222) -> Any -> Any
forall a b. a -> b
coe
               T_TotalPreorder_222 -> T_TotalPreorder_222
MAlonzo.Code.Relation.Binary.Construct.Flip.EqAndOrd.du_totalPreorder_746
               (T_TotalPreorder_222 -> Any
forall a b. a -> b
coe T_TotalPreorder_222
v0))
            ((T_MaxOperator_128 -> T_MinOperator_98) -> Any -> Any
forall a b. a -> b
coe
               T_MaxOperator_128 -> T_MinOperator_98
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.du_MaxOp'8658'MinOp_174
               (T_MaxOperator_128 -> Any
forall a b. a -> b
coe T_MaxOperator_128
v1))))
-- Data.Nat.Properties.⊓-⊔-properties.⊓-absorbs-⊔
d_'8851''45'absorbs'45''8852'_4538 ::
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8851''45'absorbs'45''8852'_4538 :: Integer -> Integer -> T__'8801'__12
d_'8851''45'absorbs'45''8852'_4538 = Integer -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Nat.Properties.⊓-⊔-properties.⊓-assoc
d_'8851''45'assoc_4540 ::
  Integer ->
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8851''45'assoc_4540 :: Integer -> Integer -> Integer -> T__'8801'__12
d_'8851''45'assoc_4540 = Integer -> Integer -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Nat.Properties.⊓-⊔-properties.⊓-band
d_'8851''45'band_4542 :: MAlonzo.Code.Algebra.Bundles.T_Band_596
d_'8851''45'band_4542 :: T_Band_596
d_'8851''45'band_4542
  = let v0 :: T_TotalPreorder_222
v0 = T_TotalPreorder_222
d_'8804''45'totalPreorder_2822 in
    Any -> T_Band_596
forall a b. a -> b
coe
      (let v1 :: T_MinOperator_98
v1 = T_MinOperator_98
d_'8851''45'operator_4438 in
       Any -> Any
forall a b. a -> b
coe
         ((T_TotalPreorder_222 -> T_MinOperator_98 -> T_Band_596)
-> Any -> Any -> Any
forall a b. a -> b
coe
            T_TotalPreorder_222 -> T_MinOperator_98 -> T_Band_596
MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_'8851''45'band_3052
            (T_TotalPreorder_222 -> Any
forall a b. a -> b
coe T_TotalPreorder_222
v0) (T_MinOperator_98 -> Any
forall a b. a -> b
coe T_MinOperator_98
v1)))
-- Data.Nat.Properties.⊓-⊔-properties.⊓-comm
d_'8851''45'comm_4544 ::
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8851''45'comm_4544 :: Integer -> Integer -> T__'8801'__12
d_'8851''45'comm_4544 = Integer -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Nat.Properties.⊓-⊔-properties.⊓-commutativeSemigroup
d_'8851''45'commutativeSemigroup_4546 ::
  MAlonzo.Code.Algebra.Bundles.T_CommutativeSemigroup_662
d_'8851''45'commutativeSemigroup_4546 :: T_CommutativeSemigroup_662
d_'8851''45'commutativeSemigroup_4546
  = let v0 :: T_TotalPreorder_222
v0 = T_TotalPreorder_222
d_'8804''45'totalPreorder_2822 in
    Any -> T_CommutativeSemigroup_662
forall a b. a -> b
coe
      (let v1 :: T_MinOperator_98
v1 = T_MinOperator_98
d_'8851''45'operator_4438 in
       Any -> Any
forall a b. a -> b
coe
         ((T_TotalPreorder_222
 -> T_MinOperator_98 -> T_CommutativeSemigroup_662)
-> Any -> Any -> Any
forall a b. a -> b
coe
            T_TotalPreorder_222
-> T_MinOperator_98 -> T_CommutativeSemigroup_662
MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_'8851''45'commutativeSemigroup_3054
            (T_TotalPreorder_222 -> Any
forall a b. a -> b
coe T_TotalPreorder_222
v0) (T_MinOperator_98 -> Any
forall a b. a -> b
coe T_MinOperator_98
v1)))
-- Data.Nat.Properties.⊓-⊔-properties.⊓-distrib-⊔
d_'8851''45'distrib'45''8852'_4554 ::
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'8851''45'distrib'45''8852'_4554 :: T_Σ_14
d_'8851''45'distrib'45''8852'_4554
  = (T_TotalPreorder_222
 -> T_MinOperator_98 -> T_MaxOperator_128 -> T_Σ_14)
-> Any -> Any -> Any -> T_Σ_14
forall a b. a -> b
coe
      T_TotalPreorder_222
-> T_MinOperator_98 -> T_MaxOperator_128 -> T_Σ_14
MAlonzo.Code.Algebra.Construct.NaturalChoice.MinMaxOp.du_'8851''45'distrib'45''8852'_3138
      (T_TotalPreorder_222 -> Any
forall a b. a -> b
coe T_TotalPreorder_222
d_'8804''45'totalPreorder_2822)
      (T_MinOperator_98 -> Any
forall a b. a -> b
coe T_MinOperator_98
d_'8851''45'operator_4438) (T_MaxOperator_128 -> Any
forall a b. a -> b
coe T_MaxOperator_128
d_'8852''45'operator_4440)
-- Data.Nat.Properties.⊓-⊔-properties.⊓-distribʳ-⊔
d_'8851''45'distrib'691''45''8852'_4556 ::
  Integer ->
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8851''45'distrib'691''45''8852'_4556 :: Integer -> Integer -> Integer -> T__'8801'__12
d_'8851''45'distrib'691''45''8852'_4556 = Integer -> Integer -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Nat.Properties.⊓-⊔-properties.⊓-distribˡ-⊔
d_'8851''45'distrib'737''45''8852'_4558 ::
  Integer ->
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8851''45'distrib'737''45''8852'_4558 :: Integer -> Integer -> Integer -> T__'8801'__12
d_'8851''45'distrib'737''45''8852'_4558 = Integer -> Integer -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Nat.Properties.⊓-⊔-properties.⊓-glb
d_'8851''45'glb_4560 ::
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_'8851''45'glb_4560 :: Integer
-> Integer
-> Integer
-> T__'8804'__22
-> T__'8804'__22
-> T__'8804'__22
d_'8851''45'glb_4560
  = let v0 :: T_TotalPreorder_222
v0 = T_TotalPreorder_222
d_'8804''45'totalPreorder_2822 in
    Any
-> Integer
-> Integer
-> Integer
-> T__'8804'__22
-> T__'8804'__22
-> T__'8804'__22
forall a b. a -> b
coe
      (let v1 :: T_MinOperator_98
v1 = T_MinOperator_98
d_'8851''45'operator_4438 in
       Any -> Any
forall a b. a -> b
coe
         ((T_TotalPreorder_222
 -> T_MinOperator_98 -> Any -> Any -> Any -> Any -> Any -> Any)
-> Any -> Any -> Any
forall a b. a -> b
coe
            T_TotalPreorder_222
-> T_MinOperator_98 -> Any -> Any -> Any -> Any -> Any -> Any
MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_'8851''45'glb_3278
            (T_TotalPreorder_222 -> Any
forall a b. a -> b
coe T_TotalPreorder_222
v0) (T_MinOperator_98 -> Any
forall a b. a -> b
coe T_MinOperator_98
v1)))
-- Data.Nat.Properties.⊓-⊔-properties.⊓-idem
d_'8851''45'idem_4562 ::
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8851''45'idem_4562 :: Integer -> T__'8801'__12
d_'8851''45'idem_4562 = Integer -> T__'8801'__12
forall a. a
erased
-- Data.Nat.Properties.⊓-⊔-properties.⊓-isBand
d_'8851''45'isBand_4570 ::
  MAlonzo.Code.Algebra.Structures.T_IsBand_508
d_'8851''45'isBand_4570 :: T_IsBand_508
d_'8851''45'isBand_4570
  = let v0 :: T_TotalPreorder_222
v0 = T_TotalPreorder_222
d_'8804''45'totalPreorder_2822 in
    Any -> T_IsBand_508
forall a b. a -> b
coe
      (let v1 :: T_MinOperator_98
v1 = T_MinOperator_98
d_'8851''45'operator_4438 in
       Any -> Any
forall a b. a -> b
coe
         ((T_TotalPreorder_222 -> T_MinOperator_98 -> T_IsBand_508)
-> Any -> Any -> Any
forall a b. a -> b
coe
            T_TotalPreorder_222 -> T_MinOperator_98 -> T_IsBand_508
MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_'8851''45'isBand_3034
            (T_TotalPreorder_222 -> Any
forall a b. a -> b
coe T_TotalPreorder_222
v0) (T_MinOperator_98 -> Any
forall a b. a -> b
coe T_MinOperator_98
v1)))
-- Data.Nat.Properties.⊓-⊔-properties.⊓-isCommutativeSemigroup
d_'8851''45'isCommutativeSemigroup_4572 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_548
d_'8851''45'isCommutativeSemigroup_4572 :: T_IsCommutativeSemigroup_548
d_'8851''45'isCommutativeSemigroup_4572
  = let v0 :: T_TotalPreorder_222
v0 = T_TotalPreorder_222
d_'8804''45'totalPreorder_2822 in
    Any -> T_IsCommutativeSemigroup_548
forall a b. a -> b
coe
      (let v1 :: T_MinOperator_98
v1 = T_MinOperator_98
d_'8851''45'operator_4438 in
       Any -> Any
forall a b. a -> b
coe
         ((T_TotalPreorder_222
 -> T_MinOperator_98 -> T_IsCommutativeSemigroup_548)
-> Any -> Any -> Any
forall a b. a -> b
coe
            T_TotalPreorder_222
-> T_MinOperator_98 -> T_IsCommutativeSemigroup_548
MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_'8851''45'isCommutativeSemigroup_3036
            (T_TotalPreorder_222 -> Any
forall a b. a -> b
coe T_TotalPreorder_222
v0) (T_MinOperator_98 -> Any
forall a b. a -> b
coe T_MinOperator_98
v1)))
-- Data.Nat.Properties.⊓-⊔-properties.⊓-isMagma
d_'8851''45'isMagma_4574 ::
  MAlonzo.Code.Algebra.Structures.T_IsMagma_176
d_'8851''45'isMagma_4574 :: T_IsMagma_176
d_'8851''45'isMagma_4574
  = let v0 :: T_TotalPreorder_222
v0 = T_TotalPreorder_222
d_'8804''45'totalPreorder_2822 in
    Any -> T_IsMagma_176
forall a b. a -> b
coe
      (let v1 :: T_MinOperator_98
v1 = T_MinOperator_98
d_'8851''45'operator_4438 in
       Any -> Any
forall a b. a -> b
coe
         ((T_TotalPreorder_222 -> T_MinOperator_98 -> T_IsMagma_176)
-> Any -> Any -> Any
forall a b. a -> b
coe
            T_TotalPreorder_222 -> T_MinOperator_98 -> T_IsMagma_176
MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_'8851''45'isMagma_3030
            (T_TotalPreorder_222 -> Any
forall a b. a -> b
coe T_TotalPreorder_222
v0) (T_MinOperator_98 -> Any
forall a b. a -> b
coe T_MinOperator_98
v1)))
-- Data.Nat.Properties.⊓-⊔-properties.⊓-isSelectiveMagma
d_'8851''45'isSelectiveMagma_4578 ::
  MAlonzo.Code.Algebra.Structures.T_IsSelectiveMagma_436
d_'8851''45'isSelectiveMagma_4578 :: T_IsSelectiveMagma_436
d_'8851''45'isSelectiveMagma_4578
  = let v0 :: T_TotalPreorder_222
v0 = T_TotalPreorder_222
d_'8804''45'totalPreorder_2822 in
    Any -> T_IsSelectiveMagma_436
forall a b. a -> b
coe
      (let v1 :: T_MinOperator_98
v1 = T_MinOperator_98
d_'8851''45'operator_4438 in
       Any -> Any
forall a b. a -> b
coe
         ((T_TotalPreorder_222 -> T_MinOperator_98 -> T_IsSelectiveMagma_436)
-> Any -> Any -> Any
forall a b. a -> b
coe
            T_TotalPreorder_222 -> T_MinOperator_98 -> T_IsSelectiveMagma_436
MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_'8851''45'isSelectiveMagma_3038
            (T_TotalPreorder_222 -> Any
forall a b. a -> b
coe T_TotalPreorder_222
v0) (T_MinOperator_98 -> Any
forall a b. a -> b
coe T_MinOperator_98
v1)))
-- Data.Nat.Properties.⊓-⊔-properties.⊓-isSemigroup
d_'8851''45'isSemigroup_4580 ::
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_472
d_'8851''45'isSemigroup_4580 :: T_IsSemigroup_472
d_'8851''45'isSemigroup_4580
  = let v0 :: T_TotalPreorder_222
v0 = T_TotalPreorder_222
d_'8804''45'totalPreorder_2822 in
    Any -> T_IsSemigroup_472
forall a b. a -> b
coe
      (let v1 :: T_MinOperator_98
v1 = T_MinOperator_98
d_'8851''45'operator_4438 in
       Any -> Any
forall a b. a -> b
coe
         ((T_TotalPreorder_222 -> T_MinOperator_98 -> T_IsSemigroup_472)
-> Any -> Any -> Any
forall a b. a -> b
coe
            T_TotalPreorder_222 -> T_MinOperator_98 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_'8851''45'isSemigroup_3032
            (T_TotalPreorder_222 -> Any
forall a b. a -> b
coe T_TotalPreorder_222
v0) (T_MinOperator_98 -> Any
forall a b. a -> b
coe T_MinOperator_98
v1)))
-- Data.Nat.Properties.⊓-⊔-properties.⊓-magma
d_'8851''45'magma_4582 :: MAlonzo.Code.Algebra.Bundles.T_Magma_68
d_'8851''45'magma_4582 :: T_Magma_68
d_'8851''45'magma_4582
  = let v0 :: T_TotalPreorder_222
v0 = T_TotalPreorder_222
d_'8804''45'totalPreorder_2822 in
    Any -> T_Magma_68
forall a b. a -> b
coe
      (let v1 :: T_MinOperator_98
v1 = T_MinOperator_98
d_'8851''45'operator_4438 in
       Any -> Any
forall a b. a -> b
coe
         ((T_TotalPreorder_222 -> T_MinOperator_98 -> T_Magma_68)
-> Any -> Any -> Any
forall a b. a -> b
coe
            T_TotalPreorder_222 -> T_MinOperator_98 -> T_Magma_68
MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_'8851''45'magma_3048
            (T_TotalPreorder_222 -> Any
forall a b. a -> b
coe T_TotalPreorder_222
v0) (T_MinOperator_98 -> Any
forall a b. a -> b
coe T_MinOperator_98
v1)))
-- Data.Nat.Properties.⊓-⊔-properties.⊓-mono-≤
d_'8851''45'mono'45''8804'_4584 ::
  Integer ->
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_'8851''45'mono'45''8804'_4584 :: Integer
-> Integer
-> Integer
-> Integer
-> T__'8804'__22
-> T__'8804'__22
-> T__'8804'__22
d_'8851''45'mono'45''8804'_4584
  = let v0 :: T_TotalPreorder_222
v0 = T_TotalPreorder_222
d_'8804''45'totalPreorder_2822 in
    Any
-> Integer
-> Integer
-> Integer
-> Integer
-> T__'8804'__22
-> T__'8804'__22
-> T__'8804'__22
forall a b. a -> b
coe
      (let v1 :: T_MinOperator_98
v1 = T_MinOperator_98
d_'8851''45'operator_4438 in
       Any -> Any
forall a b. a -> b
coe
         ((T_TotalPreorder_222
 -> T_MinOperator_98
 -> Any
 -> Any
 -> Any
 -> Any
 -> Any
 -> Any
 -> Any)
-> Any -> Any -> Any
forall a b. a -> b
coe
            T_TotalPreorder_222
-> T_MinOperator_98
-> Any
-> Any
-> Any
-> Any
-> Any
-> Any
-> Any
MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_'8851''45'mono'45''8804'_3206
            (T_TotalPreorder_222 -> Any
forall a b. a -> b
coe T_TotalPreorder_222
v0) (T_MinOperator_98 -> Any
forall a b. a -> b
coe T_MinOperator_98
v1)))
-- Data.Nat.Properties.⊓-⊔-properties.⊓-monoʳ-≤
d_'8851''45'mono'691''45''8804'_4588 ::
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_'8851''45'mono'691''45''8804'_4588 :: Integer -> Integer -> Integer -> T__'8804'__22 -> T__'8804'__22
d_'8851''45'mono'691''45''8804'_4588
  = let v0 :: T_TotalPreorder_222
v0 = T_TotalPreorder_222
d_'8804''45'totalPreorder_2822 in
    Any
-> Integer -> Integer -> Integer -> T__'8804'__22 -> T__'8804'__22
forall a b. a -> b
coe
      (let v1 :: T_MinOperator_98
v1 = T_MinOperator_98
d_'8851''45'operator_4438 in
       Any -> Any
forall a b. a -> b
coe
         ((T_TotalPreorder_222
 -> T_MinOperator_98 -> Any -> Any -> Any -> Any -> Any)
-> Any -> Any -> Any
forall a b. a -> b
coe
            T_TotalPreorder_222
-> T_MinOperator_98 -> Any -> Any -> Any -> Any -> Any
MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_'8851''45'mono'691''45''8804'_3266
            (T_TotalPreorder_222 -> Any
forall a b. a -> b
coe T_TotalPreorder_222
v0) (T_MinOperator_98 -> Any
forall a b. a -> b
coe T_MinOperator_98
v1)))
-- Data.Nat.Properties.⊓-⊔-properties.⊓-monoˡ-≤
d_'8851''45'mono'737''45''8804'_4590 ::
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_'8851''45'mono'737''45''8804'_4590 :: Integer -> Integer -> Integer -> T__'8804'__22 -> T__'8804'__22
d_'8851''45'mono'737''45''8804'_4590
  = let v0 :: T_TotalPreorder_222
v0 = T_TotalPreorder_222
d_'8804''45'totalPreorder_2822 in
    Any
-> Integer -> Integer -> Integer -> T__'8804'__22 -> T__'8804'__22
forall a b. a -> b
coe
      (let v1 :: T_MinOperator_98
v1 = T_MinOperator_98
d_'8851''45'operator_4438 in
       Any -> Any
forall a b. a -> b
coe
         ((T_TotalPreorder_222
 -> T_MinOperator_98 -> Any -> Any -> Any -> Any -> Any)
-> Any -> Any -> Any
forall a b. a -> b
coe
            T_TotalPreorder_222
-> T_MinOperator_98 -> Any -> Any -> Any -> Any -> Any
MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_'8851''45'mono'737''45''8804'_3256
            (T_TotalPreorder_222 -> Any
forall a b. a -> b
coe T_TotalPreorder_222
v0) (T_MinOperator_98 -> Any
forall a b. a -> b
coe T_MinOperator_98
v1)))
-- Data.Nat.Properties.⊓-⊔-properties.⊓-sel
d_'8851''45'sel_4594 ::
  Integer -> Integer -> MAlonzo.Code.Data.Sum.Base.T__'8846'__30
d_'8851''45'sel_4594 :: Integer -> Integer -> T__'8846'__30
d_'8851''45'sel_4594
  = let v0 :: T_TotalPreorder_222
v0 = T_TotalPreorder_222
d_'8804''45'totalPreorder_2822 in
    Any -> Integer -> Integer -> T__'8846'__30
forall a b. a -> b
coe
      (let v1 :: T_MinOperator_98
v1 = T_MinOperator_98
d_'8851''45'operator_4438 in
       Any -> Any
forall a b. a -> b
coe
         ((T_TotalPreorder_222
 -> T_MinOperator_98 -> Any -> Any -> T__'8846'__30)
-> Any -> Any -> Any
forall a b. a -> b
coe
            T_TotalPreorder_222
-> T_MinOperator_98 -> Any -> Any -> T__'8846'__30
MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_'8851''45'sel_2988
            (T_TotalPreorder_222 -> Any
forall a b. a -> b
coe T_TotalPreorder_222
v0) (T_MinOperator_98 -> Any
forall a b. a -> b
coe T_MinOperator_98
v1)))
-- Data.Nat.Properties.⊓-⊔-properties.⊓-selectiveMagma
d_'8851''45'selectiveMagma_4596 ::
  MAlonzo.Code.Algebra.Bundles.T_SelectiveMagma_122
d_'8851''45'selectiveMagma_4596 :: T_SelectiveMagma_122
d_'8851''45'selectiveMagma_4596
  = let v0 :: T_TotalPreorder_222
v0 = T_TotalPreorder_222
d_'8804''45'totalPreorder_2822 in
    Any -> T_SelectiveMagma_122
forall a b. a -> b
coe
      (let v1 :: T_MinOperator_98
v1 = T_MinOperator_98
d_'8851''45'operator_4438 in
       Any -> Any
forall a b. a -> b
coe
         ((T_TotalPreorder_222 -> T_MinOperator_98 -> T_SelectiveMagma_122)
-> Any -> Any -> Any
forall a b. a -> b
coe
            T_TotalPreorder_222 -> T_MinOperator_98 -> T_SelectiveMagma_122
MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_'8851''45'selectiveMagma_3056
            (T_TotalPreorder_222 -> Any
forall a b. a -> b
coe T_TotalPreorder_222
v0) (T_MinOperator_98 -> Any
forall a b. a -> b
coe T_MinOperator_98
v1)))
-- Data.Nat.Properties.⊓-⊔-properties.⊓-semigroup
d_'8851''45'semigroup_4598 ::
  MAlonzo.Code.Algebra.Bundles.T_Semigroup_536
d_'8851''45'semigroup_4598 :: T_Semigroup_536
d_'8851''45'semigroup_4598
  = let v0 :: T_TotalPreorder_222
v0 = T_TotalPreorder_222
d_'8804''45'totalPreorder_2822 in
    Any -> T_Semigroup_536
forall a b. a -> b
coe
      (let v1 :: T_MinOperator_98
v1 = T_MinOperator_98
d_'8851''45'operator_4438 in
       Any -> Any
forall a b. a -> b
coe
         ((T_TotalPreorder_222 -> T_MinOperator_98 -> T_Semigroup_536)
-> Any -> Any -> Any
forall a b. a -> b
coe
            T_TotalPreorder_222 -> T_MinOperator_98 -> T_Semigroup_536
MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_'8851''45'semigroup_3050
            (T_TotalPreorder_222 -> Any
forall a b. a -> b
coe T_TotalPreorder_222
v0) (T_MinOperator_98 -> Any
forall a b. a -> b
coe T_MinOperator_98
v1)))
-- Data.Nat.Properties.⊓-⊔-properties.⊓-triangulate
d_'8851''45'triangulate_4600 ::
  Integer ->
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8851''45'triangulate_4600 :: Integer -> Integer -> Integer -> T__'8801'__12
d_'8851''45'triangulate_4600 = Integer -> Integer -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Nat.Properties.⊓-⊔-properties.⊓-⊔-absorptive
d_'8851''45''8852''45'absorptive_4608 ::
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'8851''45''8852''45'absorptive_4608 :: T_Σ_14
d_'8851''45''8852''45'absorptive_4608
  = (T_TotalPreorder_222
 -> T_MinOperator_98 -> T_MaxOperator_128 -> T_Σ_14)
-> Any -> Any -> Any -> T_Σ_14
forall a b. a -> b
coe
      T_TotalPreorder_222
-> T_MinOperator_98 -> T_MaxOperator_128 -> T_Σ_14
MAlonzo.Code.Algebra.Construct.NaturalChoice.MinMaxOp.du_'8851''45''8852''45'absorptive_3218
      (T_TotalPreorder_222 -> Any
forall a b. a -> b
coe T_TotalPreorder_222
d_'8804''45'totalPreorder_2822)
      (T_MinOperator_98 -> Any
forall a b. a -> b
coe T_MinOperator_98
d_'8851''45'operator_4438) (T_MaxOperator_128 -> Any
forall a b. a -> b
coe T_MaxOperator_128
d_'8852''45'operator_4440)
-- Data.Nat.Properties.⊓-⊔-properties.⊔-absorbs-⊓
d_'8852''45'absorbs'45''8851'_4610 ::
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8852''45'absorbs'45''8851'_4610 :: Integer -> Integer -> T__'8801'__12
d_'8852''45'absorbs'45''8851'_4610 = Integer -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Nat.Properties.⊓-⊔-properties.⊓-assoc
d_'8851''45'assoc_4612 ::
  Integer ->
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8851''45'assoc_4612 :: Integer -> Integer -> Integer -> T__'8801'__12
d_'8851''45'assoc_4612 = Integer -> Integer -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Nat.Properties.⊓-⊔-properties.⊓-band
d_'8851''45'band_4614 :: MAlonzo.Code.Algebra.Bundles.T_Band_596
d_'8851''45'band_4614 :: T_Band_596
d_'8851''45'band_4614
  = let v0 :: T_TotalPreorder_222
v0 = T_TotalPreorder_222
d_'8804''45'totalPreorder_2822 in
    Any -> T_Band_596
forall a b. a -> b
coe
      (let v1 :: T_MaxOperator_128
v1 = T_MaxOperator_128
d_'8852''45'operator_4440 in
       Any -> Any
forall a b. a -> b
coe
         ((T_TotalPreorder_222 -> T_MinOperator_98 -> T_Band_596)
-> Any -> Any -> Any
forall a b. a -> b
coe
            T_TotalPreorder_222 -> T_MinOperator_98 -> T_Band_596
MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_'8851''45'band_3052
            ((T_TotalPreorder_222 -> T_TotalPreorder_222) -> Any -> Any
forall a b. a -> b
coe
               T_TotalPreorder_222 -> T_TotalPreorder_222
MAlonzo.Code.Relation.Binary.Construct.Flip.EqAndOrd.du_totalPreorder_746
               (T_TotalPreorder_222 -> Any
forall a b. a -> b
coe T_TotalPreorder_222
v0))
            ((T_MaxOperator_128 -> T_MinOperator_98) -> Any -> Any
forall a b. a -> b
coe
               T_MaxOperator_128 -> T_MinOperator_98
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.du_MaxOp'8658'MinOp_174
               (T_MaxOperator_128 -> Any
forall a b. a -> b
coe T_MaxOperator_128
v1))))
-- Data.Nat.Properties.⊓-⊔-properties.⊓-comm
d_'8851''45'comm_4616 ::
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8851''45'comm_4616 :: Integer -> Integer -> T__'8801'__12
d_'8851''45'comm_4616 = Integer -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Nat.Properties.⊓-⊔-properties.⊓-commutativeSemigroup
d_'8851''45'commutativeSemigroup_4618 ::
  MAlonzo.Code.Algebra.Bundles.T_CommutativeSemigroup_662
d_'8851''45'commutativeSemigroup_4618 :: T_CommutativeSemigroup_662
d_'8851''45'commutativeSemigroup_4618
  = let v0 :: T_TotalPreorder_222
v0 = T_TotalPreorder_222
d_'8804''45'totalPreorder_2822 in
    Any -> T_CommutativeSemigroup_662
forall a b. a -> b
coe
      (let v1 :: T_MaxOperator_128
v1 = T_MaxOperator_128
d_'8852''45'operator_4440 in
       Any -> Any
forall a b. a -> b
coe
         ((T_TotalPreorder_222
 -> T_MinOperator_98 -> T_CommutativeSemigroup_662)
-> Any -> Any -> Any
forall a b. a -> b
coe
            T_TotalPreorder_222
-> T_MinOperator_98 -> T_CommutativeSemigroup_662
MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_'8851''45'commutativeSemigroup_3054
            ((T_TotalPreorder_222 -> T_TotalPreorder_222) -> Any -> Any
forall a b. a -> b
coe
               T_TotalPreorder_222 -> T_TotalPreorder_222
MAlonzo.Code.Relation.Binary.Construct.Flip.EqAndOrd.du_totalPreorder_746
               (T_TotalPreorder_222 -> Any
forall a b. a -> b
coe T_TotalPreorder_222
v0))
            ((T_MaxOperator_128 -> T_MinOperator_98) -> Any -> Any
forall a b. a -> b
coe
               T_MaxOperator_128 -> T_MinOperator_98
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.du_MaxOp'8658'MinOp_174
               (T_MaxOperator_128 -> Any
forall a b. a -> b
coe T_MaxOperator_128
v1))))
-- Data.Nat.Properties.⊓-⊔-properties.⊔-distrib-⊓
d_'8852''45'distrib'45''8851'_4626 ::
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'8852''45'distrib'45''8851'_4626 :: T_Σ_14
d_'8852''45'distrib'45''8851'_4626
  = (T_TotalPreorder_222
 -> T_MinOperator_98 -> T_MaxOperator_128 -> T_Σ_14)
-> Any -> Any -> Any -> T_Σ_14
forall a b. a -> b
coe
      T_TotalPreorder_222
-> T_MinOperator_98 -> T_MaxOperator_128 -> T_Σ_14
MAlonzo.Code.Algebra.Construct.NaturalChoice.MinMaxOp.du_'8852''45'distrib'45''8851'_3170
      (T_TotalPreorder_222 -> Any
forall a b. a -> b
coe T_TotalPreorder_222
d_'8804''45'totalPreorder_2822)
      (T_MinOperator_98 -> Any
forall a b. a -> b
coe T_MinOperator_98
d_'8851''45'operator_4438) (T_MaxOperator_128 -> Any
forall a b. a -> b
coe T_MaxOperator_128
d_'8852''45'operator_4440)
-- Data.Nat.Properties.⊓-⊔-properties.⊔-distribʳ-⊓
d_'8852''45'distrib'691''45''8851'_4628 ::
  Integer ->
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8852''45'distrib'691''45''8851'_4628 :: Integer -> Integer -> Integer -> T__'8801'__12
d_'8852''45'distrib'691''45''8851'_4628 = Integer -> Integer -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Nat.Properties.⊓-⊔-properties.⊔-distribˡ-⊓
d_'8852''45'distrib'737''45''8851'_4630 ::
  Integer ->
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8852''45'distrib'737''45''8851'_4630 :: Integer -> Integer -> Integer -> T__'8801'__12
d_'8852''45'distrib'737''45''8851'_4630 = Integer -> Integer -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Nat.Properties.⊓-⊔-properties.⊓-idem
d_'8851''45'idem_4632 ::
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8851''45'idem_4632 :: Integer -> T__'8801'__12
d_'8851''45'idem_4632 = Integer -> T__'8801'__12
forall a. a
erased
-- Data.Nat.Properties.⊓-⊔-properties.⊓-isBand
d_'8851''45'isBand_4640 ::
  MAlonzo.Code.Algebra.Structures.T_IsBand_508
d_'8851''45'isBand_4640 :: T_IsBand_508
d_'8851''45'isBand_4640
  = let v0 :: T_TotalPreorder_222
v0 = T_TotalPreorder_222
d_'8804''45'totalPreorder_2822 in
    Any -> T_IsBand_508
forall a b. a -> b
coe
      (let v1 :: T_MaxOperator_128
v1 = T_MaxOperator_128
d_'8852''45'operator_4440 in
       Any -> Any
forall a b. a -> b
coe
         ((T_TotalPreorder_222 -> T_MinOperator_98 -> T_IsBand_508)
-> Any -> Any -> Any
forall a b. a -> b
coe
            T_TotalPreorder_222 -> T_MinOperator_98 -> T_IsBand_508
MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_'8851''45'isBand_3034
            ((T_TotalPreorder_222 -> T_TotalPreorder_222) -> Any -> Any
forall a b. a -> b
coe
               T_TotalPreorder_222 -> T_TotalPreorder_222
MAlonzo.Code.Relation.Binary.Construct.Flip.EqAndOrd.du_totalPreorder_746
               (T_TotalPreorder_222 -> Any
forall a b. a -> b
coe T_TotalPreorder_222
v0))
            ((T_MaxOperator_128 -> T_MinOperator_98) -> Any -> Any
forall a b. a -> b
coe
               T_MaxOperator_128 -> T_MinOperator_98
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.du_MaxOp'8658'MinOp_174
               (T_MaxOperator_128 -> Any
forall a b. a -> b
coe T_MaxOperator_128
v1))))
-- Data.Nat.Properties.⊓-⊔-properties.⊓-isCommutativeSemigroup
d_'8851''45'isCommutativeSemigroup_4642 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_548
d_'8851''45'isCommutativeSemigroup_4642 :: T_IsCommutativeSemigroup_548
d_'8851''45'isCommutativeSemigroup_4642
  = let v0 :: T_TotalPreorder_222
v0 = T_TotalPreorder_222
d_'8804''45'totalPreorder_2822 in
    Any -> T_IsCommutativeSemigroup_548
forall a b. a -> b
coe
      (let v1 :: T_MaxOperator_128
v1 = T_MaxOperator_128
d_'8852''45'operator_4440 in
       Any -> Any
forall a b. a -> b
coe
         ((T_TotalPreorder_222
 -> T_MinOperator_98 -> T_IsCommutativeSemigroup_548)
-> Any -> Any -> Any
forall a b. a -> b
coe
            T_TotalPreorder_222
-> T_MinOperator_98 -> T_IsCommutativeSemigroup_548
MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_'8851''45'isCommutativeSemigroup_3036
            ((T_TotalPreorder_222 -> T_TotalPreorder_222) -> Any -> Any
forall a b. a -> b
coe
               T_TotalPreorder_222 -> T_TotalPreorder_222
MAlonzo.Code.Relation.Binary.Construct.Flip.EqAndOrd.du_totalPreorder_746
               (T_TotalPreorder_222 -> Any
forall a b. a -> b
coe T_TotalPreorder_222
v0))
            ((T_MaxOperator_128 -> T_MinOperator_98) -> Any -> Any
forall a b. a -> b
coe
               T_MaxOperator_128 -> T_MinOperator_98
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.du_MaxOp'8658'MinOp_174
               (T_MaxOperator_128 -> Any
forall a b. a -> b
coe T_MaxOperator_128
v1))))
-- Data.Nat.Properties.⊓-⊔-properties.⊓-isMagma
d_'8851''45'isMagma_4644 ::
  MAlonzo.Code.Algebra.Structures.T_IsMagma_176
d_'8851''45'isMagma_4644 :: T_IsMagma_176
d_'8851''45'isMagma_4644
  = let v0 :: T_TotalPreorder_222
v0 = T_TotalPreorder_222
d_'8804''45'totalPreorder_2822 in
    Any -> T_IsMagma_176
forall a b. a -> b
coe
      (let v1 :: T_MaxOperator_128
v1 = T_MaxOperator_128
d_'8852''45'operator_4440 in
       Any -> Any
forall a b. a -> b
coe
         ((T_TotalPreorder_222 -> T_MinOperator_98 -> T_IsMagma_176)
-> Any -> Any -> Any
forall a b. a -> b
coe
            T_TotalPreorder_222 -> T_MinOperator_98 -> T_IsMagma_176
MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_'8851''45'isMagma_3030
            ((T_TotalPreorder_222 -> T_TotalPreorder_222) -> Any -> Any
forall a b. a -> b
coe
               T_TotalPreorder_222 -> T_TotalPreorder_222
MAlonzo.Code.Relation.Binary.Construct.Flip.EqAndOrd.du_totalPreorder_746
               (T_TotalPreorder_222 -> Any
forall a b. a -> b
coe T_TotalPreorder_222
v0))
            ((T_MaxOperator_128 -> T_MinOperator_98) -> Any -> Any
forall a b. a -> b
coe
               T_MaxOperator_128 -> T_MinOperator_98
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.du_MaxOp'8658'MinOp_174
               (T_MaxOperator_128 -> Any
forall a b. a -> b
coe T_MaxOperator_128
v1))))
-- Data.Nat.Properties.⊓-⊔-properties.⊓-isSelectiveMagma
d_'8851''45'isSelectiveMagma_4648 ::
  MAlonzo.Code.Algebra.Structures.T_IsSelectiveMagma_436
d_'8851''45'isSelectiveMagma_4648 :: T_IsSelectiveMagma_436
d_'8851''45'isSelectiveMagma_4648
  = let v0 :: T_TotalPreorder_222
v0 = T_TotalPreorder_222
d_'8804''45'totalPreorder_2822 in
    Any -> T_IsSelectiveMagma_436
forall a b. a -> b
coe
      (let v1 :: T_MaxOperator_128
v1 = T_MaxOperator_128
d_'8852''45'operator_4440 in
       Any -> Any
forall a b. a -> b
coe
         ((T_TotalPreorder_222 -> T_MinOperator_98 -> T_IsSelectiveMagma_436)
-> Any -> Any -> Any
forall a b. a -> b
coe
            T_TotalPreorder_222 -> T_MinOperator_98 -> T_IsSelectiveMagma_436
MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_'8851''45'isSelectiveMagma_3038
            ((T_TotalPreorder_222 -> T_TotalPreorder_222) -> Any -> Any
forall a b. a -> b
coe
               T_TotalPreorder_222 -> T_TotalPreorder_222
MAlonzo.Code.Relation.Binary.Construct.Flip.EqAndOrd.du_totalPreorder_746
               (T_TotalPreorder_222 -> Any
forall a b. a -> b
coe T_TotalPreorder_222
v0))
            ((T_MaxOperator_128 -> T_MinOperator_98) -> Any -> Any
forall a b. a -> b
coe
               T_MaxOperator_128 -> T_MinOperator_98
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.du_MaxOp'8658'MinOp_174
               (T_MaxOperator_128 -> Any
forall a b. a -> b
coe T_MaxOperator_128
v1))))
-- Data.Nat.Properties.⊓-⊔-properties.⊓-isSemigroup
d_'8851''45'isSemigroup_4650 ::
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_472
d_'8851''45'isSemigroup_4650 :: T_IsSemigroup_472
d_'8851''45'isSemigroup_4650
  = let v0 :: T_TotalPreorder_222
v0 = T_TotalPreorder_222
d_'8804''45'totalPreorder_2822 in
    Any -> T_IsSemigroup_472
forall a b. a -> b
coe
      (let v1 :: T_MaxOperator_128
v1 = T_MaxOperator_128
d_'8852''45'operator_4440 in
       Any -> Any
forall a b. a -> b
coe
         ((T_TotalPreorder_222 -> T_MinOperator_98 -> T_IsSemigroup_472)
-> Any -> Any -> Any
forall a b. a -> b
coe
            T_TotalPreorder_222 -> T_MinOperator_98 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_'8851''45'isSemigroup_3032
            ((T_TotalPreorder_222 -> T_TotalPreorder_222) -> Any -> Any
forall a b. a -> b
coe
               T_TotalPreorder_222 -> T_TotalPreorder_222
MAlonzo.Code.Relation.Binary.Construct.Flip.EqAndOrd.du_totalPreorder_746
               (T_TotalPreorder_222 -> Any
forall a b. a -> b
coe T_TotalPreorder_222
v0))
            ((T_MaxOperator_128 -> T_MinOperator_98) -> Any -> Any
forall a b. a -> b
coe
               T_MaxOperator_128 -> T_MinOperator_98
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.du_MaxOp'8658'MinOp_174
               (T_MaxOperator_128 -> Any
forall a b. a -> b
coe T_MaxOperator_128
v1))))
-- Data.Nat.Properties.⊓-⊔-properties.⊓-glb
d_'8851''45'glb_4652 ::
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_'8851''45'glb_4652 :: Integer
-> Integer
-> Integer
-> T__'8804'__22
-> T__'8804'__22
-> T__'8804'__22
d_'8851''45'glb_4652
  = let v0 :: T_TotalPreorder_222
v0 = T_TotalPreorder_222
d_'8804''45'totalPreorder_2822 in
    Any
-> Integer
-> Integer
-> Integer
-> T__'8804'__22
-> T__'8804'__22
-> T__'8804'__22
forall a b. a -> b
coe
      (let v1 :: T_MaxOperator_128
v1 = T_MaxOperator_128
d_'8852''45'operator_4440 in
       Any -> Any
forall a b. a -> b
coe
         ((T_TotalPreorder_222
 -> T_MinOperator_98 -> Any -> Any -> Any -> Any -> Any -> Any)
-> Any -> Any -> Any
forall a b. a -> b
coe
            T_TotalPreorder_222
-> T_MinOperator_98 -> Any -> Any -> Any -> Any -> Any -> Any
MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_'8851''45'glb_3278
            ((T_TotalPreorder_222 -> T_TotalPreorder_222) -> Any -> Any
forall a b. a -> b
coe
               T_TotalPreorder_222 -> T_TotalPreorder_222
MAlonzo.Code.Relation.Binary.Construct.Flip.EqAndOrd.du_totalPreorder_746
               (T_TotalPreorder_222 -> Any
forall a b. a -> b
coe T_TotalPreorder_222
v0))
            ((T_MaxOperator_128 -> T_MinOperator_98) -> Any -> Any
forall a b. a -> b
coe
               T_MaxOperator_128 -> T_MinOperator_98
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.du_MaxOp'8658'MinOp_174
               (T_MaxOperator_128 -> Any
forall a b. a -> b
coe T_MaxOperator_128
v1))))
-- Data.Nat.Properties.⊓-⊔-properties.⊓-magma
d_'8851''45'magma_4654 :: MAlonzo.Code.Algebra.Bundles.T_Magma_68
d_'8851''45'magma_4654 :: T_Magma_68
d_'8851''45'magma_4654
  = let v0 :: T_TotalPreorder_222
v0 = T_TotalPreorder_222
d_'8804''45'totalPreorder_2822 in
    Any -> T_Magma_68
forall a b. a -> b
coe
      (let v1 :: T_MaxOperator_128
v1 = T_MaxOperator_128
d_'8852''45'operator_4440 in
       Any -> Any
forall a b. a -> b
coe
         ((T_TotalPreorder_222 -> T_MinOperator_98 -> T_Magma_68)
-> Any -> Any -> Any
forall a b. a -> b
coe
            T_TotalPreorder_222 -> T_MinOperator_98 -> T_Magma_68
MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_'8851''45'magma_3048
            ((T_TotalPreorder_222 -> T_TotalPreorder_222) -> Any -> Any
forall a b. a -> b
coe
               T_TotalPreorder_222 -> T_TotalPreorder_222
MAlonzo.Code.Relation.Binary.Construct.Flip.EqAndOrd.du_totalPreorder_746
               (T_TotalPreorder_222 -> Any
forall a b. a -> b
coe T_TotalPreorder_222
v0))
            ((T_MaxOperator_128 -> T_MinOperator_98) -> Any -> Any
forall a b. a -> b
coe
               T_MaxOperator_128 -> T_MinOperator_98
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.du_MaxOp'8658'MinOp_174
               (T_MaxOperator_128 -> Any
forall a b. a -> b
coe T_MaxOperator_128
v1))))
-- Data.Nat.Properties.⊓-⊔-properties.⊓-mono-≤
d_'8851''45'mono'45''8804'_4656 ::
  Integer ->
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_'8851''45'mono'45''8804'_4656 :: Integer
-> Integer
-> Integer
-> Integer
-> T__'8804'__22
-> T__'8804'__22
-> T__'8804'__22
d_'8851''45'mono'45''8804'_4656
  = let v0 :: T_TotalPreorder_222
v0 = T_TotalPreorder_222
d_'8804''45'totalPreorder_2822 in
    Any
-> Integer
-> Integer
-> Integer
-> Integer
-> T__'8804'__22
-> T__'8804'__22
-> T__'8804'__22
forall a b. a -> b
coe
      (let v1 :: T_MaxOperator_128
v1 = T_MaxOperator_128
d_'8852''45'operator_4440 in
       Any -> Any
forall a b. a -> b
coe
         ((T_TotalPreorder_222
 -> T_MinOperator_98
 -> Any
 -> Any
 -> Any
 -> Any
 -> Any
 -> Any
 -> Any)
-> Any -> Any -> Any
forall a b. a -> b
coe
            T_TotalPreorder_222
-> T_MinOperator_98
-> Any
-> Any
-> Any
-> Any
-> Any
-> Any
-> Any
MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_'8851''45'mono'45''8804'_3206
            ((T_TotalPreorder_222 -> T_TotalPreorder_222) -> Any -> Any
forall a b. a -> b
coe
               T_TotalPreorder_222 -> T_TotalPreorder_222
MAlonzo.Code.Relation.Binary.Construct.Flip.EqAndOrd.du_totalPreorder_746
               (T_TotalPreorder_222 -> Any
forall a b. a -> b
coe T_TotalPreorder_222
v0))
            ((T_MaxOperator_128 -> T_MinOperator_98) -> Any -> Any
forall a b. a -> b
coe
               T_MaxOperator_128 -> T_MinOperator_98
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.du_MaxOp'8658'MinOp_174
               (T_MaxOperator_128 -> Any
forall a b. a -> b
coe T_MaxOperator_128
v1))))
-- Data.Nat.Properties.⊓-⊔-properties.⊓-monoʳ-≤
d_'8851''45'mono'691''45''8804'_4660 ::
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_'8851''45'mono'691''45''8804'_4660 :: Integer -> Integer -> Integer -> T__'8804'__22 -> T__'8804'__22
d_'8851''45'mono'691''45''8804'_4660
  = let v0 :: T_TotalPreorder_222
v0 = T_TotalPreorder_222
d_'8804''45'totalPreorder_2822 in
    Any
-> Integer -> Integer -> Integer -> T__'8804'__22 -> T__'8804'__22
forall a b. a -> b
coe
      (let v1 :: T_MaxOperator_128
v1 = T_MaxOperator_128
d_'8852''45'operator_4440 in
       Any -> Any
forall a b. a -> b
coe
         ((T_TotalPreorder_222
 -> T_MinOperator_98 -> Any -> Any -> Any -> Any -> Any)
-> Any -> Any -> Any
forall a b. a -> b
coe
            T_TotalPreorder_222
-> T_MinOperator_98 -> Any -> Any -> Any -> Any -> Any
MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_'8851''45'mono'691''45''8804'_3266
            ((T_TotalPreorder_222 -> T_TotalPreorder_222) -> Any -> Any
forall a b. a -> b
coe
               T_TotalPreorder_222 -> T_TotalPreorder_222
MAlonzo.Code.Relation.Binary.Construct.Flip.EqAndOrd.du_totalPreorder_746
               (T_TotalPreorder_222 -> Any
forall a b. a -> b
coe T_TotalPreorder_222
v0))
            ((T_MaxOperator_128 -> T_MinOperator_98) -> Any -> Any
forall a b. a -> b
coe
               T_MaxOperator_128 -> T_MinOperator_98
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.du_MaxOp'8658'MinOp_174
               (T_MaxOperator_128 -> Any
forall a b. a -> b
coe T_MaxOperator_128
v1))))
-- Data.Nat.Properties.⊓-⊔-properties.⊓-monoˡ-≤
d_'8851''45'mono'737''45''8804'_4662 ::
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_'8851''45'mono'737''45''8804'_4662 :: Integer -> Integer -> Integer -> T__'8804'__22 -> T__'8804'__22
d_'8851''45'mono'737''45''8804'_4662
  = let v0 :: T_TotalPreorder_222
v0 = T_TotalPreorder_222
d_'8804''45'totalPreorder_2822 in
    Any
-> Integer -> Integer -> Integer -> T__'8804'__22 -> T__'8804'__22
forall a b. a -> b
coe
      (let v1 :: T_MaxOperator_128
v1 = T_MaxOperator_128
d_'8852''45'operator_4440 in
       Any -> Any
forall a b. a -> b
coe
         ((T_TotalPreorder_222
 -> T_MinOperator_98 -> Any -> Any -> Any -> Any -> Any)
-> Any -> Any -> Any
forall a b. a -> b
coe
            T_TotalPreorder_222
-> T_MinOperator_98 -> Any -> Any -> Any -> Any -> Any
MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_'8851''45'mono'737''45''8804'_3256
            ((T_TotalPreorder_222 -> T_TotalPreorder_222) -> Any -> Any
forall a b. a -> b
coe
               T_TotalPreorder_222 -> T_TotalPreorder_222
MAlonzo.Code.Relation.Binary.Construct.Flip.EqAndOrd.du_totalPreorder_746
               (T_TotalPreorder_222 -> Any
forall a b. a -> b
coe T_TotalPreorder_222
v0))
            ((T_MaxOperator_128 -> T_MinOperator_98) -> Any -> Any
forall a b. a -> b
coe
               T_MaxOperator_128 -> T_MinOperator_98
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.du_MaxOp'8658'MinOp_174
               (T_MaxOperator_128 -> Any
forall a b. a -> b
coe T_MaxOperator_128
v1))))
-- Data.Nat.Properties.⊓-⊔-properties.⊓-sel
d_'8851''45'sel_4664 ::
  Integer -> Integer -> MAlonzo.Code.Data.Sum.Base.T__'8846'__30
d_'8851''45'sel_4664 :: Integer -> Integer -> T__'8846'__30
d_'8851''45'sel_4664
  = let v0 :: T_TotalPreorder_222
v0 = T_TotalPreorder_222
d_'8804''45'totalPreorder_2822 in
    Any -> Integer -> Integer -> T__'8846'__30
forall a b. a -> b
coe
      (let v1 :: T_MaxOperator_128
v1 = T_MaxOperator_128
d_'8852''45'operator_4440 in
       Any -> Any
forall a b. a -> b
coe
         ((T_TotalPreorder_222
 -> T_MinOperator_98 -> Any -> Any -> T__'8846'__30)
-> Any -> Any -> Any
forall a b. a -> b
coe
            T_TotalPreorder_222
-> T_MinOperator_98 -> Any -> Any -> T__'8846'__30
MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_'8851''45'sel_2988
            ((T_TotalPreorder_222 -> T_TotalPreorder_222) -> Any -> Any
forall a b. a -> b
coe
               T_TotalPreorder_222 -> T_TotalPreorder_222
MAlonzo.Code.Relation.Binary.Construct.Flip.EqAndOrd.du_totalPreorder_746
               (T_TotalPreorder_222 -> Any
forall a b. a -> b
coe T_TotalPreorder_222
v0))
            ((T_MaxOperator_128 -> T_MinOperator_98) -> Any -> Any
forall a b. a -> b
coe
               T_MaxOperator_128 -> T_MinOperator_98
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.du_MaxOp'8658'MinOp_174
               (T_MaxOperator_128 -> Any
forall a b. a -> b
coe T_MaxOperator_128
v1))))
-- Data.Nat.Properties.⊓-⊔-properties.⊓-selectiveMagma
d_'8851''45'selectiveMagma_4666 ::
  MAlonzo.Code.Algebra.Bundles.T_SelectiveMagma_122
d_'8851''45'selectiveMagma_4666 :: T_SelectiveMagma_122
d_'8851''45'selectiveMagma_4666
  = let v0 :: T_TotalPreorder_222
v0 = T_TotalPreorder_222
d_'8804''45'totalPreorder_2822 in
    Any -> T_SelectiveMagma_122
forall a b. a -> b
coe
      (let v1 :: T_MaxOperator_128
v1 = T_MaxOperator_128
d_'8852''45'operator_4440 in
       Any -> Any
forall a b. a -> b
coe
         ((T_TotalPreorder_222 -> T_MinOperator_98 -> T_SelectiveMagma_122)
-> Any -> Any -> Any
forall a b. a -> b
coe
            T_TotalPreorder_222 -> T_MinOperator_98 -> T_SelectiveMagma_122
MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_'8851''45'selectiveMagma_3056
            ((T_TotalPreorder_222 -> T_TotalPreorder_222) -> Any -> Any
forall a b. a -> b
coe
               T_TotalPreorder_222 -> T_TotalPreorder_222
MAlonzo.Code.Relation.Binary.Construct.Flip.EqAndOrd.du_totalPreorder_746
               (T_TotalPreorder_222 -> Any
forall a b. a -> b
coe T_TotalPreorder_222
v0))
            ((T_MaxOperator_128 -> T_MinOperator_98) -> Any -> Any
forall a b. a -> b
coe
               T_MaxOperator_128 -> T_MinOperator_98
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.du_MaxOp'8658'MinOp_174
               (T_MaxOperator_128 -> Any
forall a b. a -> b
coe T_MaxOperator_128
v1))))
-- Data.Nat.Properties.⊓-⊔-properties.⊓-semigroup
d_'8851''45'semigroup_4668 ::
  MAlonzo.Code.Algebra.Bundles.T_Semigroup_536
d_'8851''45'semigroup_4668 :: T_Semigroup_536
d_'8851''45'semigroup_4668
  = let v0 :: T_TotalPreorder_222
v0 = T_TotalPreorder_222
d_'8804''45'totalPreorder_2822 in
    Any -> T_Semigroup_536
forall a b. a -> b
coe
      (let v1 :: T_MaxOperator_128
v1 = T_MaxOperator_128
d_'8852''45'operator_4440 in
       Any -> Any
forall a b. a -> b
coe
         ((T_TotalPreorder_222 -> T_MinOperator_98 -> T_Semigroup_536)
-> Any -> Any -> Any
forall a b. a -> b
coe
            T_TotalPreorder_222 -> T_MinOperator_98 -> T_Semigroup_536
MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_'8851''45'semigroup_3050
            ((T_TotalPreorder_222 -> T_TotalPreorder_222) -> Any -> Any
forall a b. a -> b
coe
               T_TotalPreorder_222 -> T_TotalPreorder_222
MAlonzo.Code.Relation.Binary.Construct.Flip.EqAndOrd.du_totalPreorder_746
               (T_TotalPreorder_222 -> Any
forall a b. a -> b
coe T_TotalPreorder_222
v0))
            ((T_MaxOperator_128 -> T_MinOperator_98) -> Any -> Any
forall a b. a -> b
coe
               T_MaxOperator_128 -> T_MinOperator_98
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.du_MaxOp'8658'MinOp_174
               (T_MaxOperator_128 -> Any
forall a b. a -> b
coe T_MaxOperator_128
v1))))
-- Data.Nat.Properties.⊓-⊔-properties.⊓-triangulate
d_'8851''45'triangulate_4670 ::
  Integer ->
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8851''45'triangulate_4670 :: Integer -> Integer -> Integer -> T__'8801'__12
d_'8851''45'triangulate_4670 = Integer -> Integer -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Nat.Properties.⊓-⊔-properties.⊔-⊓-absorptive
d_'8852''45''8851''45'absorptive_4678 ::
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'8852''45''8851''45'absorptive_4678 :: T_Σ_14
d_'8852''45''8851''45'absorptive_4678
  = (T_TotalPreorder_222
 -> T_MinOperator_98 -> T_MaxOperator_128 -> T_Σ_14)
-> Any -> Any -> Any -> T_Σ_14
forall a b. a -> b
coe
      T_TotalPreorder_222
-> T_MinOperator_98 -> T_MaxOperator_128 -> T_Σ_14
MAlonzo.Code.Algebra.Construct.NaturalChoice.MinMaxOp.du_'8852''45''8851''45'absorptive_3216
      (T_TotalPreorder_222 -> Any
forall a b. a -> b
coe T_TotalPreorder_222
d_'8804''45'totalPreorder_2822)
      (T_MinOperator_98 -> Any
forall a b. a -> b
coe T_MinOperator_98
d_'8851''45'operator_4438) (T_MaxOperator_128 -> Any
forall a b. a -> b
coe T_MaxOperator_128
d_'8852''45'operator_4440)
-- Data.Nat.Properties.⊓-⊔-latticeProperties.⊓-isSemilattice
d_'8851''45'isSemilattice_4682 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_590
d_'8851''45'isSemilattice_4682 :: T_IsCommutativeBand_590
d_'8851''45'isSemilattice_4682
  = let v0 :: T_TotalPreorder_222
v0 = T_TotalPreorder_222
d_'8804''45'totalPreorder_2822 in
    Any -> T_IsCommutativeBand_590
forall a b. a -> b
coe
      (let v1 :: T_MinOperator_98
v1 = T_MinOperator_98
d_'8851''45'operator_4438 in
       Any -> Any
forall a b. a -> b
coe
         ((T_TotalPreorder_222
 -> T_MinOperator_98 -> T_IsCommutativeBand_590)
-> Any -> Any -> Any
forall a b. a -> b
coe
            T_TotalPreorder_222 -> T_MinOperator_98 -> T_IsCommutativeBand_590
MAlonzo.Code.Algebra.Lattice.Construct.NaturalChoice.MinOp.du_'8851''45'isSemilattice_602
            (T_TotalPreorder_222 -> Any
forall a b. a -> b
coe T_TotalPreorder_222
v0) (T_MinOperator_98 -> Any
forall a b. a -> b
coe T_MinOperator_98
v1)))
-- Data.Nat.Properties.⊓-⊔-latticeProperties.⊓-semilattice
d_'8851''45'semilattice_4684 ::
  MAlonzo.Code.Algebra.Lattice.Bundles.T_Semilattice_10
d_'8851''45'semilattice_4684 :: T_Semilattice_10
d_'8851''45'semilattice_4684
  = let v0 :: T_TotalPreorder_222
v0 = T_TotalPreorder_222
d_'8804''45'totalPreorder_2822 in
    Any -> T_Semilattice_10
forall a b. a -> b
coe
      (let v1 :: T_MinOperator_98
v1 = T_MinOperator_98
d_'8851''45'operator_4438 in
       Any -> Any
forall a b. a -> b
coe
         ((T_TotalPreorder_222 -> T_MinOperator_98 -> T_Semilattice_10)
-> Any -> Any -> Any
forall a b. a -> b
coe
            T_TotalPreorder_222 -> T_MinOperator_98 -> T_Semilattice_10
MAlonzo.Code.Algebra.Lattice.Construct.NaturalChoice.MinOp.du_'8851''45'semilattice_604
            (T_TotalPreorder_222 -> Any
forall a b. a -> b
coe T_TotalPreorder_222
v0) (T_MinOperator_98 -> Any
forall a b. a -> b
coe T_MinOperator_98
v1)))
-- Data.Nat.Properties.⊓-⊔-latticeProperties.⊓-⊔-distributiveLattice
d_'8851''45''8852''45'distributiveLattice_4686 ::
  MAlonzo.Code.Algebra.Lattice.Bundles.T_DistributiveLattice_584
d_'8851''45''8852''45'distributiveLattice_4686 :: T_DistributiveLattice_584
d_'8851''45''8852''45'distributiveLattice_4686
  = (T_TotalPreorder_222
 -> T_MinOperator_98
 -> T_MaxOperator_128
 -> T_DistributiveLattice_584)
-> Any -> Any -> Any -> T_DistributiveLattice_584
forall a b. a -> b
coe
      T_TotalPreorder_222
-> T_MinOperator_98
-> T_MaxOperator_128
-> T_DistributiveLattice_584
MAlonzo.Code.Algebra.Lattice.Construct.NaturalChoice.MinMaxOp.du_'8851''45''8852''45'distributiveLattice_808
      (T_TotalPreorder_222 -> Any
forall a b. a -> b
coe T_TotalPreorder_222
d_'8804''45'totalPreorder_2822)
      (T_MinOperator_98 -> Any
forall a b. a -> b
coe T_MinOperator_98
d_'8851''45'operator_4438) (T_MaxOperator_128 -> Any
forall a b. a -> b
coe T_MaxOperator_128
d_'8852''45'operator_4440)
-- Data.Nat.Properties.⊓-⊔-latticeProperties.⊓-⊔-isDistributiveLattice
d_'8851''45''8852''45'isDistributiveLattice_4688 ::
  MAlonzo.Code.Algebra.Lattice.Structures.T_IsDistributiveLattice_3036
d_'8851''45''8852''45'isDistributiveLattice_4688 :: T_IsDistributiveLattice_3036
d_'8851''45''8852''45'isDistributiveLattice_4688
  = (T_TotalPreorder_222
 -> T_MinOperator_98
 -> T_MaxOperator_128
 -> T_IsDistributiveLattice_3036)
-> Any -> Any -> Any -> T_IsDistributiveLattice_3036
forall a b. a -> b
coe
      T_TotalPreorder_222
-> T_MinOperator_98
-> T_MaxOperator_128
-> T_IsDistributiveLattice_3036
MAlonzo.Code.Algebra.Lattice.Construct.NaturalChoice.MinMaxOp.du_'8851''45''8852''45'isDistributiveLattice_798
      (T_TotalPreorder_222 -> Any
forall a b. a -> b
coe T_TotalPreorder_222
d_'8804''45'totalPreorder_2822)
      (T_MinOperator_98 -> Any
forall a b. a -> b
coe T_MinOperator_98
d_'8851''45'operator_4438) (T_MaxOperator_128 -> Any
forall a b. a -> b
coe T_MaxOperator_128
d_'8852''45'operator_4440)
-- Data.Nat.Properties.⊓-⊔-latticeProperties.⊓-⊔-isLattice
d_'8851''45''8852''45'isLattice_4690 ::
  MAlonzo.Code.Algebra.Lattice.Structures.T_IsLattice_2962
d_'8851''45''8852''45'isLattice_4690 :: T_IsLattice_2962
d_'8851''45''8852''45'isLattice_4690
  = (T_TotalPreorder_222
 -> T_MinOperator_98 -> T_MaxOperator_128 -> T_IsLattice_2962)
-> Any -> Any -> Any -> T_IsLattice_2962
forall a b. a -> b
coe
      T_TotalPreorder_222
-> T_MinOperator_98 -> T_MaxOperator_128 -> T_IsLattice_2962
MAlonzo.Code.Algebra.Lattice.Construct.NaturalChoice.MinMaxOp.du_'8851''45''8852''45'isLattice_796
      (T_TotalPreorder_222 -> Any
forall a b. a -> b
coe T_TotalPreorder_222
d_'8804''45'totalPreorder_2822)
      (T_MinOperator_98 -> Any
forall a b. a -> b
coe T_MinOperator_98
d_'8851''45'operator_4438) (T_MaxOperator_128 -> Any
forall a b. a -> b
coe T_MaxOperator_128
d_'8852''45'operator_4440)
-- Data.Nat.Properties.⊓-⊔-latticeProperties.⊓-⊔-lattice
d_'8851''45''8852''45'lattice_4692 ::
  MAlonzo.Code.Algebra.Lattice.Bundles.T_Lattice_500
d_'8851''45''8852''45'lattice_4692 :: T_Lattice_500
d_'8851''45''8852''45'lattice_4692
  = (T_TotalPreorder_222
 -> T_MinOperator_98 -> T_MaxOperator_128 -> T_Lattice_500)
-> Any -> Any -> Any -> T_Lattice_500
forall a b. a -> b
coe
      T_TotalPreorder_222
-> T_MinOperator_98 -> T_MaxOperator_128 -> T_Lattice_500
MAlonzo.Code.Algebra.Lattice.Construct.NaturalChoice.MinMaxOp.du_'8851''45''8852''45'lattice_804
      (T_TotalPreorder_222 -> Any
forall a b. a -> b
coe T_TotalPreorder_222
d_'8804''45'totalPreorder_2822)
      (T_MinOperator_98 -> Any
forall a b. a -> b
coe T_MinOperator_98
d_'8851''45'operator_4438) (T_MaxOperator_128 -> Any
forall a b. a -> b
coe T_MaxOperator_128
d_'8852''45'operator_4440)
-- Data.Nat.Properties.⊓-⊔-latticeProperties.⊓-isSemilattice
d_'8851''45'isSemilattice_4694 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_590
d_'8851''45'isSemilattice_4694 :: T_IsCommutativeBand_590
d_'8851''45'isSemilattice_4694
  = let v0 :: T_TotalPreorder_222
v0 = T_TotalPreorder_222
d_'8804''45'totalPreorder_2822 in
    Any -> T_IsCommutativeBand_590
forall a b. a -> b
coe
      (let v1 :: T_MaxOperator_128
v1 = T_MaxOperator_128
d_'8852''45'operator_4440 in
       Any -> Any
forall a b. a -> b
coe
         ((T_TotalPreorder_222
 -> T_MinOperator_98 -> T_IsCommutativeBand_590)
-> Any -> Any -> Any
forall a b. a -> b
coe
            T_TotalPreorder_222 -> T_MinOperator_98 -> T_IsCommutativeBand_590
MAlonzo.Code.Algebra.Lattice.Construct.NaturalChoice.MinOp.du_'8851''45'isSemilattice_602
            ((T_TotalPreorder_222 -> T_TotalPreorder_222) -> Any -> Any
forall a b. a -> b
coe
               T_TotalPreorder_222 -> T_TotalPreorder_222
MAlonzo.Code.Relation.Binary.Construct.Flip.EqAndOrd.du_totalPreorder_746
               (T_TotalPreorder_222 -> Any
forall a b. a -> b
coe T_TotalPreorder_222
v0))
            ((T_MaxOperator_128 -> T_MinOperator_98) -> Any -> Any
forall a b. a -> b
coe
               T_MaxOperator_128 -> T_MinOperator_98
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.du_MaxOp'8658'MinOp_174
               (T_MaxOperator_128 -> Any
forall a b. a -> b
coe T_MaxOperator_128
v1))))
-- Data.Nat.Properties.⊓-⊔-latticeProperties.⊓-semilattice
d_'8851''45'semilattice_4696 ::
  MAlonzo.Code.Algebra.Lattice.Bundles.T_Semilattice_10
d_'8851''45'semilattice_4696 :: T_Semilattice_10
d_'8851''45'semilattice_4696
  = let v0 :: T_TotalPreorder_222
v0 = T_TotalPreorder_222
d_'8804''45'totalPreorder_2822 in
    Any -> T_Semilattice_10
forall a b. a -> b
coe
      (let v1 :: T_MaxOperator_128
v1 = T_MaxOperator_128
d_'8852''45'operator_4440 in
       Any -> Any
forall a b. a -> b
coe
         ((T_TotalPreorder_222 -> T_MinOperator_98 -> T_Semilattice_10)
-> Any -> Any -> Any
forall a b. a -> b
coe
            T_TotalPreorder_222 -> T_MinOperator_98 -> T_Semilattice_10
MAlonzo.Code.Algebra.Lattice.Construct.NaturalChoice.MinOp.du_'8851''45'semilattice_604
            ((T_TotalPreorder_222 -> T_TotalPreorder_222) -> Any -> Any
forall a b. a -> b
coe
               T_TotalPreorder_222 -> T_TotalPreorder_222
MAlonzo.Code.Relation.Binary.Construct.Flip.EqAndOrd.du_totalPreorder_746
               (T_TotalPreorder_222 -> Any
forall a b. a -> b
coe T_TotalPreorder_222
v0))
            ((T_MaxOperator_128 -> T_MinOperator_98) -> Any -> Any
forall a b. a -> b
coe
               T_MaxOperator_128 -> T_MinOperator_98
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.du_MaxOp'8658'MinOp_174
               (T_MaxOperator_128 -> Any
forall a b. a -> b
coe T_MaxOperator_128
v1))))
-- Data.Nat.Properties.⊓-⊔-latticeProperties.⊔-⊓-distributiveLattice
d_'8852''45''8851''45'distributiveLattice_4698 ::
  MAlonzo.Code.Algebra.Lattice.Bundles.T_DistributiveLattice_584
d_'8852''45''8851''45'distributiveLattice_4698 :: T_DistributiveLattice_584
d_'8852''45''8851''45'distributiveLattice_4698
  = (T_TotalPreorder_222
 -> T_MinOperator_98
 -> T_MaxOperator_128
 -> T_DistributiveLattice_584)
-> Any -> Any -> Any -> T_DistributiveLattice_584
forall a b. a -> b
coe
      T_TotalPreorder_222
-> T_MinOperator_98
-> T_MaxOperator_128
-> T_DistributiveLattice_584
MAlonzo.Code.Algebra.Lattice.Construct.NaturalChoice.MinMaxOp.du_'8852''45''8851''45'distributiveLattice_806
      (T_TotalPreorder_222 -> Any
forall a b. a -> b
coe T_TotalPreorder_222
d_'8804''45'totalPreorder_2822)
      (T_MinOperator_98 -> Any
forall a b. a -> b
coe T_MinOperator_98
d_'8851''45'operator_4438) (T_MaxOperator_128 -> Any
forall a b. a -> b
coe T_MaxOperator_128
d_'8852''45'operator_4440)
-- Data.Nat.Properties.⊓-⊔-latticeProperties.⊔-⊓-isDistributiveLattice
d_'8852''45''8851''45'isDistributiveLattice_4700 ::
  MAlonzo.Code.Algebra.Lattice.Structures.T_IsDistributiveLattice_3036
d_'8852''45''8851''45'isDistributiveLattice_4700 :: T_IsDistributiveLattice_3036
d_'8852''45''8851''45'isDistributiveLattice_4700
  = (T_TotalPreorder_222
 -> T_MinOperator_98
 -> T_MaxOperator_128
 -> T_IsDistributiveLattice_3036)
-> Any -> Any -> Any -> T_IsDistributiveLattice_3036
forall a b. a -> b
coe
      T_TotalPreorder_222
-> T_MinOperator_98
-> T_MaxOperator_128
-> T_IsDistributiveLattice_3036
MAlonzo.Code.Algebra.Lattice.Construct.NaturalChoice.MinMaxOp.du_'8852''45''8851''45'isDistributiveLattice_800
      (T_TotalPreorder_222 -> Any
forall a b. a -> b
coe T_TotalPreorder_222
d_'8804''45'totalPreorder_2822)
      (T_MinOperator_98 -> Any
forall a b. a -> b
coe T_MinOperator_98
d_'8851''45'operator_4438) (T_MaxOperator_128 -> Any
forall a b. a -> b
coe T_MaxOperator_128
d_'8852''45'operator_4440)
-- Data.Nat.Properties.⊓-⊔-latticeProperties.⊔-⊓-isLattice
d_'8852''45''8851''45'isLattice_4702 ::
  MAlonzo.Code.Algebra.Lattice.Structures.T_IsLattice_2962
d_'8852''45''8851''45'isLattice_4702 :: T_IsLattice_2962
d_'8852''45''8851''45'isLattice_4702
  = (T_TotalPreorder_222
 -> T_MinOperator_98 -> T_MaxOperator_128 -> T_IsLattice_2962)
-> Any -> Any -> Any -> T_IsLattice_2962
forall a b. a -> b
coe
      T_TotalPreorder_222
-> T_MinOperator_98 -> T_MaxOperator_128 -> T_IsLattice_2962
MAlonzo.Code.Algebra.Lattice.Construct.NaturalChoice.MinMaxOp.du_'8852''45''8851''45'isLattice_794
      (T_TotalPreorder_222 -> Any
forall a b. a -> b
coe T_TotalPreorder_222
d_'8804''45'totalPreorder_2822)
      (T_MinOperator_98 -> Any
forall a b. a -> b
coe T_MinOperator_98
d_'8851''45'operator_4438) (T_MaxOperator_128 -> Any
forall a b. a -> b
coe T_MaxOperator_128
d_'8852''45'operator_4440)
-- Data.Nat.Properties.⊓-⊔-latticeProperties.⊔-⊓-lattice
d_'8852''45''8851''45'lattice_4704 ::
  MAlonzo.Code.Algebra.Lattice.Bundles.T_Lattice_500
d_'8852''45''8851''45'lattice_4704 :: T_Lattice_500
d_'8852''45''8851''45'lattice_4704
  = (T_TotalPreorder_222
 -> T_MinOperator_98 -> T_MaxOperator_128 -> T_Lattice_500)
-> Any -> Any -> Any -> T_Lattice_500
forall a b. a -> b
coe
      T_TotalPreorder_222
-> T_MinOperator_98 -> T_MaxOperator_128 -> T_Lattice_500
MAlonzo.Code.Algebra.Lattice.Construct.NaturalChoice.MinMaxOp.du_'8852''45''8851''45'lattice_802
      (T_TotalPreorder_222 -> Any
forall a b. a -> b
coe T_TotalPreorder_222
d_'8804''45'totalPreorder_2822)
      (T_MinOperator_98 -> Any
forall a b. a -> b
coe T_MinOperator_98
d_'8851''45'operator_4438) (T_MaxOperator_128 -> Any
forall a b. a -> b
coe T_MaxOperator_128
d_'8852''45'operator_4440)
-- Data.Nat.Properties.⊔-identityˡ
d_'8852''45'identity'737'_4706 ::
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8852''45'identity'737'_4706 :: Integer -> T__'8801'__12
d_'8852''45'identity'737'_4706 = Integer -> T__'8801'__12
forall a. a
erased
-- Data.Nat.Properties.⊔-identityʳ
d_'8852''45'identity'691'_4708 ::
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8852''45'identity'691'_4708 :: Integer -> T__'8801'__12
d_'8852''45'identity'691'_4708 = Integer -> T__'8801'__12
forall a. a
erased
-- Data.Nat.Properties.⊔-identity
d_'8852''45'identity_4712 :: MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'8852''45'identity_4712 :: T_Σ_14
d_'8852''45'identity_4712
  = (Any -> Any -> T_Σ_14) -> Any -> Any -> T_Σ_14
forall a b. a -> b
coe Any -> Any -> T_Σ_14
MAlonzo.Code.Agda.Builtin.Sigma.C__'44'__32 Any
forall a. a
erased Any
forall a. a
erased
-- Data.Nat.Properties.⊔-0-isMonoid
d_'8852''45'0'45'isMonoid_4714 ::
  MAlonzo.Code.Algebra.Structures.T_IsMonoid_686
d_'8852''45'0'45'isMonoid_4714 :: T_IsMonoid_686
d_'8852''45'0'45'isMonoid_4714
  = (T_IsSemigroup_472 -> T_Σ_14 -> T_IsMonoid_686)
-> Any -> Any -> T_IsMonoid_686
forall a b. a -> b
coe
      T_IsSemigroup_472 -> T_Σ_14 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.C_IsMonoid'46'constructor_15873
      (let v0 :: T_TotalPreorder_222
v0 = T_TotalPreorder_222
d_'8804''45'totalPreorder_2822 in
       Any -> Any
forall a b. a -> b
coe
         (let v1 :: T_MaxOperator_128
v1 = T_MaxOperator_128
d_'8852''45'operator_4440 in
          Any -> Any
forall a b. a -> b
coe
            ((T_TotalPreorder_222 -> T_MinOperator_98 -> T_IsSemigroup_472)
-> Any -> Any -> Any
forall a b. a -> b
coe
               T_TotalPreorder_222 -> T_MinOperator_98 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_'8851''45'isSemigroup_3032
               ((T_TotalPreorder_222 -> T_TotalPreorder_222) -> Any -> Any
forall a b. a -> b
coe
                  T_TotalPreorder_222 -> T_TotalPreorder_222
MAlonzo.Code.Relation.Binary.Construct.Flip.EqAndOrd.du_totalPreorder_746
                  (T_TotalPreorder_222 -> Any
forall a b. a -> b
coe T_TotalPreorder_222
v0))
               ((T_MaxOperator_128 -> T_MinOperator_98) -> Any -> Any
forall a b. a -> b
coe
                  T_MaxOperator_128 -> T_MinOperator_98
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.du_MaxOp'8658'MinOp_174
                  (T_MaxOperator_128 -> Any
forall a b. a -> b
coe T_MaxOperator_128
v1)))))
      (T_Σ_14 -> Any
forall a b. a -> b
coe T_Σ_14
d_'8852''45'identity_4712)
-- Data.Nat.Properties.⊔-0-isCommutativeMonoid
d_'8852''45'0'45'isCommutativeMonoid_4716 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMonoid_736
d_'8852''45'0'45'isCommutativeMonoid_4716 :: T_IsCommutativeMonoid_736
d_'8852''45'0'45'isCommutativeMonoid_4716
  = (T_IsMonoid_686
 -> (Any -> Any -> Any) -> T_IsCommutativeMonoid_736)
-> Any -> Any -> T_IsCommutativeMonoid_736
forall a b. a -> b
coe
      T_IsMonoid_686 -> (Any -> Any -> Any) -> T_IsCommutativeMonoid_736
MAlonzo.Code.Algebra.Structures.C_IsCommutativeMonoid'46'constructor_17695
      (T_IsMonoid_686 -> Any
forall a b. a -> b
coe T_IsMonoid_686
d_'8852''45'0'45'isMonoid_4714)
      (let v0 :: T_TotalPreorder_222
v0 = T_TotalPreorder_222
d_'8804''45'totalPreorder_2822 in
       Any -> Any
forall a b. a -> b
coe
         (let v1 :: T_MaxOperator_128
v1 = T_MaxOperator_128
d_'8852''45'operator_4440 in
          Any -> Any
forall a b. a -> b
coe
            ((T_TotalPreorder_222 -> T_MinOperator_98 -> Any -> Any -> Any)
-> Any -> Any -> Any
forall a b. a -> b
coe
               T_TotalPreorder_222 -> T_MinOperator_98 -> Any -> Any -> Any
MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_'8851''45'comm_2856
               ((T_TotalPreorder_222 -> T_TotalPreorder_222) -> Any -> Any
forall a b. a -> b
coe
                  T_TotalPreorder_222 -> T_TotalPreorder_222
MAlonzo.Code.Relation.Binary.Construct.Flip.EqAndOrd.du_totalPreorder_746
                  (T_TotalPreorder_222 -> Any
forall a b. a -> b
coe T_TotalPreorder_222
v0))
               ((T_MaxOperator_128 -> T_MinOperator_98) -> Any -> Any
forall a b. a -> b
coe
                  T_MaxOperator_128 -> T_MinOperator_98
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.du_MaxOp'8658'MinOp_174
                  (T_MaxOperator_128 -> Any
forall a b. a -> b
coe T_MaxOperator_128
v1)))))
-- Data.Nat.Properties.⊔-0-monoid
d_'8852''45'0'45'monoid_4718 ::
  MAlonzo.Code.Algebra.Bundles.T_Monoid_882
d_'8852''45'0'45'monoid_4718 :: T_Monoid_882
d_'8852''45'0'45'monoid_4718
  = ((Any -> Any -> Any) -> Any -> T_IsMonoid_686 -> T_Monoid_882)
-> (Integer -> Integer -> Integer)
-> Integer
-> T_IsMonoid_686
-> T_Monoid_882
forall a b. a -> b
coe
      (Any -> Any -> Any) -> Any -> T_IsMonoid_686 -> T_Monoid_882
MAlonzo.Code.Algebra.Bundles.C_Monoid'46'constructor_16157
      Integer -> Integer -> Integer
MAlonzo.Code.Data.Nat.Base.d__'8852'__204 (Integer
0 :: Integer)
      T_IsMonoid_686
d_'8852''45'0'45'isMonoid_4714
-- Data.Nat.Properties.⊔-0-commutativeMonoid
d_'8852''45'0'45'commutativeMonoid_4720 ::
  MAlonzo.Code.Algebra.Bundles.T_CommutativeMonoid_962
d_'8852''45'0'45'commutativeMonoid_4720 :: T_CommutativeMonoid_962
d_'8852''45'0'45'commutativeMonoid_4720
  = ((Any -> Any -> Any)
 -> Any -> T_IsCommutativeMonoid_736 -> T_CommutativeMonoid_962)
-> (Integer -> Integer -> Integer)
-> Integer
-> T_IsCommutativeMonoid_736
-> T_CommutativeMonoid_962
forall a b. a -> b
coe
      (Any -> Any -> Any)
-> Any -> T_IsCommutativeMonoid_736 -> T_CommutativeMonoid_962
MAlonzo.Code.Algebra.Bundles.C_CommutativeMonoid'46'constructor_17931
      Integer -> Integer -> Integer
MAlonzo.Code.Data.Nat.Base.d__'8852'__204 (Integer
0 :: Integer)
      T_IsCommutativeMonoid_736
d_'8852''45'0'45'isCommutativeMonoid_4716
-- Data.Nat.Properties.mono-≤-distrib-⊔
d_mono'45''8804''45'distrib'45''8852'_4728 ::
  (Integer -> Integer) ->
  (Integer ->
   Integer ->
   MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
   MAlonzo.Code.Data.Nat.Base.T__'8804'__22) ->
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_mono'45''8804''45'distrib'45''8852'_4728 :: (Integer -> Integer)
-> (Integer -> Integer -> T__'8804'__22 -> T__'8804'__22)
-> Integer
-> Integer
-> T__'8801'__12
d_mono'45''8804''45'distrib'45''8852'_4728 = (Integer -> Integer)
-> (Integer -> Integer -> T__'8804'__22 -> T__'8804'__22)
-> Integer
-> Integer
-> T__'8801'__12
forall a. a
erased
-- Data.Nat.Properties.mono-≤-distrib-⊓
d_mono'45''8804''45'distrib'45''8851'_4738 ::
  (Integer -> Integer) ->
  (Integer ->
   Integer ->
   MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
   MAlonzo.Code.Data.Nat.Base.T__'8804'__22) ->
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_mono'45''8804''45'distrib'45''8851'_4738 :: (Integer -> Integer)
-> (Integer -> Integer -> T__'8804'__22 -> T__'8804'__22)
-> Integer
-> Integer
-> T__'8801'__12
d_mono'45''8804''45'distrib'45''8851'_4738 = (Integer -> Integer)
-> (Integer -> Integer -> T__'8804'__22 -> T__'8804'__22)
-> Integer
-> Integer
-> T__'8801'__12
forall a. a
erased
-- Data.Nat.Properties.antimono-≤-distrib-⊓
d_antimono'45''8804''45'distrib'45''8851'_4748 ::
  (Integer -> Integer) ->
  (Integer ->
   Integer ->
   MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
   MAlonzo.Code.Data.Nat.Base.T__'8804'__22) ->
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_antimono'45''8804''45'distrib'45''8851'_4748 :: (Integer -> Integer)
-> (Integer -> Integer -> T__'8804'__22 -> T__'8804'__22)
-> Integer
-> Integer
-> T__'8801'__12
d_antimono'45''8804''45'distrib'45''8851'_4748 = (Integer -> Integer)
-> (Integer -> Integer -> T__'8804'__22 -> T__'8804'__22)
-> Integer
-> Integer
-> T__'8801'__12
forall a. a
erased
-- Data.Nat.Properties.antimono-≤-distrib-⊔
d_antimono'45''8804''45'distrib'45''8852'_4758 ::
  (Integer -> Integer) ->
  (Integer ->
   Integer ->
   MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
   MAlonzo.Code.Data.Nat.Base.T__'8804'__22) ->
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_antimono'45''8804''45'distrib'45''8852'_4758 :: (Integer -> Integer)
-> (Integer -> Integer -> T__'8804'__22 -> T__'8804'__22)
-> Integer
-> Integer
-> T__'8801'__12
d_antimono'45''8804''45'distrib'45''8852'_4758 = (Integer -> Integer)
-> (Integer -> Integer -> T__'8804'__22 -> T__'8804'__22)
-> Integer
-> Integer
-> T__'8801'__12
forall a. a
erased
-- Data.Nat.Properties.m<n⇒m<n⊔o
d_m'60'n'8658'm'60'n'8852'o_4764 ::
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_m'60'n'8658'm'60'n'8852'o_4764 :: Integer -> Integer -> Integer -> T__'8804'__22 -> T__'8804'__22
d_m'60'n'8658'm'60'n'8852'o_4764 Integer
v0 Integer
v1
  = let v2 :: T_TotalPreorder_222
v2 = T_TotalPreorder_222
d_'8804''45'totalPreorder_2822 in
    Any -> Integer -> T__'8804'__22 -> T__'8804'__22
forall a b. a -> b
coe
      (let v3 :: T_MaxOperator_128
v3 = T_MaxOperator_128
d_'8852''45'operator_4440 in
       Any -> Any
forall a b. a -> b
coe
         ((T_TotalPreorder_222
 -> T_MinOperator_98 -> Any -> Any -> Any -> Any -> Any)
-> Any -> Any -> Any -> Any -> Any
forall a b. a -> b
coe
            T_TotalPreorder_222
-> T_MinOperator_98 -> Any -> Any -> Any -> Any -> Any
MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_x'8804'y'8658'x'8851'z'8804'y_3160
            ((T_TotalPreorder_222 -> T_TotalPreorder_222) -> Any -> Any
forall a b. a -> b
coe
               T_TotalPreorder_222 -> T_TotalPreorder_222
MAlonzo.Code.Relation.Binary.Construct.Flip.EqAndOrd.du_totalPreorder_746
               (T_TotalPreorder_222 -> Any
forall a b. a -> b
coe T_TotalPreorder_222
v2))
            ((T_MaxOperator_128 -> T_MinOperator_98) -> Any -> Any
forall a b. a -> b
coe
               T_MaxOperator_128 -> T_MinOperator_98
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.du_MaxOp'8658'MinOp_174
               (T_MaxOperator_128 -> Any
forall a b. a -> b
coe T_MaxOperator_128
v3))
            (Integer -> Any
forall a b. a -> b
coe Integer
v1) ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> Integer
addInt (Integer -> Any
forall a b. a -> b
coe (Integer
1 :: Integer)) (Integer -> Any
forall a b. a -> b
coe Integer
v0))))
-- Data.Nat.Properties.m<n⇒m<o⊔n
d_m'60'n'8658'm'60'o'8852'n_4768 ::
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_m'60'n'8658'm'60'o'8852'n_4768 :: Integer -> Integer -> Integer -> T__'8804'__22 -> T__'8804'__22
d_m'60'n'8658'm'60'o'8852'n_4768 Integer
v0 Integer
v1
  = let v2 :: T_TotalPreorder_222
v2 = T_TotalPreorder_222
d_'8804''45'totalPreorder_2822 in
    Any -> Integer -> T__'8804'__22 -> T__'8804'__22
forall a b. a -> b
coe
      (let v3 :: T_MaxOperator_128
v3 = T_MaxOperator_128
d_'8852''45'operator_4440 in
       Any -> Any
forall a b. a -> b
coe
         ((T_TotalPreorder_222
 -> T_MinOperator_98 -> Any -> Any -> Any -> Any -> Any)
-> Any -> Any -> Any -> Any -> Any
forall a b. a -> b
coe
            T_TotalPreorder_222
-> T_MinOperator_98 -> Any -> Any -> Any -> Any -> Any
MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_x'8804'y'8658'z'8851'x'8804'y_3172
            ((T_TotalPreorder_222 -> T_TotalPreorder_222) -> Any -> Any
forall a b. a -> b
coe
               T_TotalPreorder_222 -> T_TotalPreorder_222
MAlonzo.Code.Relation.Binary.Construct.Flip.EqAndOrd.du_totalPreorder_746
               (T_TotalPreorder_222 -> Any
forall a b. a -> b
coe T_TotalPreorder_222
v2))
            ((T_MaxOperator_128 -> T_MinOperator_98) -> Any -> Any
forall a b. a -> b
coe
               T_MaxOperator_128 -> T_MinOperator_98
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.du_MaxOp'8658'MinOp_174
               (T_MaxOperator_128 -> Any
forall a b. a -> b
coe T_MaxOperator_128
v3))
            (Integer -> Any
forall a b. a -> b
coe Integer
v1) ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> Integer
addInt (Integer -> Any
forall a b. a -> b
coe (Integer
1 :: Integer)) (Integer -> Any
forall a b. a -> b
coe Integer
v0))))
-- Data.Nat.Properties.m⊔n<o⇒m<o
d_m'8852'n'60'o'8658'm'60'o_4776 ::
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_m'8852'n'60'o'8658'm'60'o_4776 :: Integer -> Integer -> Integer -> T__'8804'__22 -> T__'8804'__22
d_m'8852'n'60'o'8658'm'60'o_4776 Integer
v0 Integer
v1 ~Integer
v2 T__'8804'__22
v3
  = Integer -> Integer -> T__'8804'__22 -> T__'8804'__22
du_m'8852'n'60'o'8658'm'60'o_4776 Integer
v0 Integer
v1 T__'8804'__22
v3
du_m'8852'n'60'o'8658'm'60'o_4776 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
du_m'8852'n'60'o'8658'm'60'o_4776 :: Integer -> Integer -> T__'8804'__22 -> T__'8804'__22
du_m'8852'n'60'o'8658'm'60'o_4776 Integer
v0 Integer
v1 T__'8804'__22
v2
  = (T__'8804'__22 -> T__'8804'__22 -> T__'8804'__22)
-> Any -> Any -> T__'8804'__22
forall a b. a -> b
coe
      T__'8804'__22 -> T__'8804'__22 -> T__'8804'__22
du_'8804''45''60''45'trans_2986
      (let v3 :: T_TotalPreorder_222
v3 = T_TotalPreorder_222
d_'8804''45'totalPreorder_2822 in
       Any -> Any
forall a b. a -> b
coe
         (let v4 :: T_MaxOperator_128
v4 = T_MaxOperator_128
d_'8852''45'operator_4440 in
          Any -> Any
forall a b. a -> b
coe
            ((T_TotalPreorder_222 -> T_MinOperator_98 -> Any -> Any -> Any)
-> Any -> Any -> Any -> Any -> Any
forall a b. a -> b
coe
               T_TotalPreorder_222 -> T_MinOperator_98 -> Any -> Any -> Any
MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_x'8851'y'8804'x_2808
               ((T_TotalPreorder_222 -> T_TotalPreorder_222) -> Any -> Any
forall a b. a -> b
coe
                  T_TotalPreorder_222 -> T_TotalPreorder_222
MAlonzo.Code.Relation.Binary.Construct.Flip.EqAndOrd.du_totalPreorder_746
                  (T_TotalPreorder_222 -> Any
forall a b. a -> b
coe T_TotalPreorder_222
v3))
               ((T_MaxOperator_128 -> T_MinOperator_98) -> Any -> Any
forall a b. a -> b
coe
                  T_MaxOperator_128 -> T_MinOperator_98
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.du_MaxOp'8658'MinOp_174
                  (T_MaxOperator_128 -> Any
forall a b. a -> b
coe T_MaxOperator_128
v4))
               (Integer -> Any
forall a b. a -> b
coe Integer
v0) (Integer -> Any
forall a b. a -> b
coe Integer
v1))))
      (T__'8804'__22 -> Any
forall a b. a -> b
coe T__'8804'__22
v2)
-- Data.Nat.Properties.m⊔n<o⇒n<o
d_m'8852'n'60'o'8658'n'60'o_4790 ::
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_m'8852'n'60'o'8658'n'60'o_4790 :: Integer -> Integer -> Integer -> T__'8804'__22 -> T__'8804'__22
d_m'8852'n'60'o'8658'n'60'o_4790 Integer
v0 Integer
v1 ~Integer
v2 T__'8804'__22
v3
  = Integer -> Integer -> T__'8804'__22 -> T__'8804'__22
du_m'8852'n'60'o'8658'n'60'o_4790 Integer
v0 Integer
v1 T__'8804'__22
v3
du_m'8852'n'60'o'8658'n'60'o_4790 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
du_m'8852'n'60'o'8658'n'60'o_4790 :: Integer -> Integer -> T__'8804'__22 -> T__'8804'__22
du_m'8852'n'60'o'8658'n'60'o_4790 Integer
v0 Integer
v1 T__'8804'__22
v2
  = (T__'8804'__22 -> T__'8804'__22 -> T__'8804'__22)
-> Any -> Any -> T__'8804'__22
forall a b. a -> b
coe
      T__'8804'__22 -> T__'8804'__22 -> T__'8804'__22
du_'8804''45''60''45'trans_2986
      (let v3 :: T_TotalPreorder_222
v3 = T_TotalPreorder_222
d_'8804''45'totalPreorder_2822 in
       Any -> Any
forall a b. a -> b
coe
         (let v4 :: T_MaxOperator_128
v4 = T_MaxOperator_128
d_'8852''45'operator_4440 in
          Any -> Any
forall a b. a -> b
coe
            ((T_TotalPreorder_222 -> T_MinOperator_98 -> Any -> Any -> Any)
-> Any -> Any -> Any -> Any -> Any
forall a b. a -> b
coe
               T_TotalPreorder_222 -> T_MinOperator_98 -> Any -> Any -> Any
MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_x'8851'y'8804'y_2834
               ((T_TotalPreorder_222 -> T_TotalPreorder_222) -> Any -> Any
forall a b. a -> b
coe
                  T_TotalPreorder_222 -> T_TotalPreorder_222
MAlonzo.Code.Relation.Binary.Construct.Flip.EqAndOrd.du_totalPreorder_746
                  (T_TotalPreorder_222 -> Any
forall a b. a -> b
coe T_TotalPreorder_222
v3))
               ((T_MaxOperator_128 -> T_MinOperator_98) -> Any -> Any
forall a b. a -> b
coe
                  T_MaxOperator_128 -> T_MinOperator_98
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.du_MaxOp'8658'MinOp_174
                  (T_MaxOperator_128 -> Any
forall a b. a -> b
coe T_MaxOperator_128
v4))
               (Integer -> Any
forall a b. a -> b
coe Integer
v0) (Integer -> Any
forall a b. a -> b
coe Integer
v1))))
      (T__'8804'__22 -> Any
forall a b. a -> b
coe T__'8804'__22
v2)
-- Data.Nat.Properties.⊔-mono-<
d_'8852''45'mono'45''60'_4798 ::
  Integer ->
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_'8852''45'mono'45''60'_4798 :: Integer
-> Integer
-> Integer
-> Integer
-> T__'8804'__22
-> T__'8804'__22
-> T__'8804'__22
d_'8852''45'mono'45''60'_4798 Integer
v0 Integer
v1 Integer
v2 Integer
v3
  = let v4 :: T_TotalPreorder_222
v4 = T_TotalPreorder_222
d_'8804''45'totalPreorder_2822 in
    Any -> T__'8804'__22 -> T__'8804'__22 -> T__'8804'__22
forall a b. a -> b
coe
      (let v5 :: T_MaxOperator_128
v5 = T_MaxOperator_128
d_'8852''45'operator_4440 in
       Any -> Any
forall a b. a -> b
coe
         ((T_TotalPreorder_222
 -> T_MinOperator_98
 -> Any
 -> Any
 -> Any
 -> Any
 -> Any
 -> Any
 -> Any)
-> Any -> Any -> Any -> Any -> Any -> Any -> Any
forall a b. a -> b
coe
            T_TotalPreorder_222
-> T_MinOperator_98
-> Any
-> Any
-> Any
-> Any
-> Any
-> Any
-> Any
MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_'8851''45'mono'45''8804'_3206
            ((T_TotalPreorder_222 -> T_TotalPreorder_222) -> Any -> Any
forall a b. a -> b
coe
               T_TotalPreorder_222 -> T_TotalPreorder_222
MAlonzo.Code.Relation.Binary.Construct.Flip.EqAndOrd.du_totalPreorder_746
               (T_TotalPreorder_222 -> Any
forall a b. a -> b
coe T_TotalPreorder_222
v4))
            ((T_MaxOperator_128 -> T_MinOperator_98) -> Any -> Any
forall a b. a -> b
coe
               T_MaxOperator_128 -> T_MinOperator_98
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.du_MaxOp'8658'MinOp_174
               (T_MaxOperator_128 -> Any
forall a b. a -> b
coe T_MaxOperator_128
v5))
            (Integer -> Any
forall a b. a -> b
coe Integer
v1) ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> Integer
addInt (Integer -> Any
forall a b. a -> b
coe (Integer
1 :: Integer)) (Integer -> Any
forall a b. a -> b
coe Integer
v0)) (Integer -> Any
forall a b. a -> b
coe Integer
v3)
            ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> Integer
addInt (Integer -> Any
forall a b. a -> b
coe (Integer
1 :: Integer)) (Integer -> Any
forall a b. a -> b
coe Integer
v2))))
-- Data.Nat.Properties.⊔-pres-<m
d_'8852''45'pres'45''60'm_4800 ::
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_'8852''45'pres'45''60'm_4800 :: Integer
-> Integer
-> Integer
-> T__'8804'__22
-> T__'8804'__22
-> T__'8804'__22
d_'8852''45'pres'45''60'm_4800 Integer
v0 Integer
v1 Integer
v2 T__'8804'__22
v3 T__'8804'__22
v4
  = (Integer
 -> Integer
 -> Integer
 -> Integer
 -> T__'8804'__22
 -> T__'8804'__22
 -> T__'8804'__22)
-> Integer
-> Integer
-> Integer
-> Integer
-> T__'8804'__22
-> T__'8804'__22
-> T__'8804'__22
forall a b. a -> b
coe Integer
-> Integer
-> Integer
-> Integer
-> T__'8804'__22
-> T__'8804'__22
-> T__'8804'__22
d_'8852''45'mono'45''60'_4798 Integer
v0 Integer
v1 Integer
v2 Integer
v1 T__'8804'__22
v3 T__'8804'__22
v4
-- Data.Nat.Properties.+-distribˡ-⊔
d_'43''45'distrib'737''45''8852'_4810 ::
  Integer ->
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'43''45'distrib'737''45''8852'_4810 :: Integer -> Integer -> Integer -> T__'8801'__12
d_'43''45'distrib'737''45''8852'_4810 = Integer -> Integer -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Nat.Properties.+-distribʳ-⊔
d_'43''45'distrib'691''45''8852'_4822 ::
  Integer ->
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'43''45'distrib'691''45''8852'_4822 :: Integer -> Integer -> Integer -> T__'8801'__12
d_'43''45'distrib'691''45''8852'_4822 = Integer -> Integer -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Nat.Properties.+-distrib-⊔
d_'43''45'distrib'45''8852'_4824 ::
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'43''45'distrib'45''8852'_4824 :: T_Σ_14
d_'43''45'distrib'45''8852'_4824
  = (Any -> Any -> T_Σ_14) -> Any -> Any -> T_Σ_14
forall a b. a -> b
coe Any -> Any -> T_Σ_14
MAlonzo.Code.Agda.Builtin.Sigma.C__'44'__32 Any
forall a. a
erased Any
forall a. a
erased
-- Data.Nat.Properties.m⊔n≤m+n
d_m'8852'n'8804'm'43'n_4830 ::
  Integer -> Integer -> MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_m'8852'n'8804'm'43'n_4830 :: Integer -> Integer -> T__'8804'__22
d_m'8852'n'8804'm'43'n_4830 Integer
v0 Integer
v1
  = let v2 :: t
v2
          = ((Any -> Any) -> (Any -> Any) -> T__'8846'__30 -> Any)
-> Any -> Any -> Any -> t
forall a b. a -> b
coe
              (Any -> Any) -> (Any -> Any) -> T__'8846'__30 -> Any
MAlonzo.Code.Data.Sum.Base.du_'91'_'44'_'93'_52
              ((Any -> Any) -> Any
forall a b. a -> b
coe
                 (\ Any
v2 -> (Any -> T__'8846'__30) -> Any -> Any
forall a b. a -> b
coe Any -> T__'8846'__30
MAlonzo.Code.Data.Sum.Base.C_inj'8321'_38 Any
forall a. a
erased))
              ((Any -> Any) -> Any
forall a b. a -> b
coe
                 (\ Any
v2 -> (Any -> T__'8846'__30) -> Any -> Any
forall a b. a -> b
coe Any -> T__'8846'__30
MAlonzo.Code.Data.Sum.Base.C_inj'8322'_42 Any
forall a. a
erased))
              ((Integer -> Integer -> T__'8846'__30) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> T__'8846'__30
d_'8804''45'total_2790 (Integer -> Any
forall a b. a -> b
coe Integer
v1) (Integer -> Any
forall a b. a -> b
coe Integer
v0)) in
    Any -> T__'8804'__22
forall a b. a -> b
coe
      (case Any -> T__'8846'__30
forall a b. a -> b
coe Any
forall a. a
v2 of
         MAlonzo.Code.Data.Sum.Base.C_inj'8321'_38 Any
v3
           -> (Integer -> T__'8804'__22) -> Any -> Any
forall a b. a -> b
coe Integer -> T__'8804'__22
du_m'8804'm'43'n_3482 (Integer -> Any
forall a b. a -> b
coe Integer
v0)
         MAlonzo.Code.Data.Sum.Base.C_inj'8322'_42 Any
v3
           -> (Integer -> T__'8804'__22) -> Any -> Any
forall a b. a -> b
coe Integer -> T__'8804'__22
du_m'8804'n'43'm_3494 (Integer -> Any
forall a b. a -> b
coe Integer
v1)
         T__'8846'__30
_ -> Any
forall a. a
MAlonzo.RTE.mazUnreachableError)
-- Data.Nat.Properties.*-distribˡ-⊔
d_'42''45'distrib'737''45''8852'_4860 ::
  Integer ->
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'42''45'distrib'737''45''8852'_4860 :: Integer -> Integer -> Integer -> T__'8801'__12
d_'42''45'distrib'737''45''8852'_4860 = Integer -> Integer -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Nat.Properties.*-distribʳ-⊔
d_'42''45'distrib'691''45''8852'_4882 ::
  Integer ->
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'42''45'distrib'691''45''8852'_4882 :: Integer -> Integer -> Integer -> T__'8801'__12
d_'42''45'distrib'691''45''8852'_4882 = Integer -> Integer -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Nat.Properties.*-distrib-⊔
d_'42''45'distrib'45''8852'_4884 ::
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'42''45'distrib'45''8852'_4884 :: T_Σ_14
d_'42''45'distrib'45''8852'_4884
  = (Any -> Any -> T_Σ_14) -> Any -> Any -> T_Σ_14
forall a b. a -> b
coe Any -> Any -> T_Σ_14
MAlonzo.Code.Agda.Builtin.Sigma.C__'44'__32 Any
forall a. a
erased Any
forall a. a
erased
-- Data.Nat.Properties.⊓-zeroˡ
d_'8851''45'zero'737'_4886 ::
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8851''45'zero'737'_4886 :: Integer -> T__'8801'__12
d_'8851''45'zero'737'_4886 = Integer -> T__'8801'__12
forall a. a
erased
-- Data.Nat.Properties.⊓-zeroʳ
d_'8851''45'zero'691'_4888 ::
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8851''45'zero'691'_4888 :: Integer -> T__'8801'__12
d_'8851''45'zero'691'_4888 = Integer -> T__'8801'__12
forall a. a
erased
-- Data.Nat.Properties.⊓-zero
d_'8851''45'zero_4892 :: MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'8851''45'zero_4892 :: T_Σ_14
d_'8851''45'zero_4892
  = (Any -> Any -> T_Σ_14) -> Any -> Any -> T_Σ_14
forall a b. a -> b
coe Any -> Any -> T_Σ_14
MAlonzo.Code.Agda.Builtin.Sigma.C__'44'__32 Any
forall a. a
erased Any
forall a. a
erased
-- Data.Nat.Properties.⊔-⊓-isSemiringWithoutOne
d_'8852''45''8851''45'isSemiringWithoutOne_4894 ::
  MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutOne_1298
d_'8852''45''8851''45'isSemiringWithoutOne_4894 :: T_IsSemiringWithoutOne_1298
d_'8852''45''8851''45'isSemiringWithoutOne_4894
  = (T_IsCommutativeMonoid_736
 -> (Any -> Any -> Any -> Any -> Any -> Any -> Any)
 -> (Any -> Any -> Any -> Any)
 -> T_Σ_14
 -> T_Σ_14
 -> T_IsSemiringWithoutOne_1298)
-> Any -> Any -> Any -> Any -> Any -> T_IsSemiringWithoutOne_1298
forall a b. a -> b
coe
      T_IsCommutativeMonoid_736
-> (Any -> Any -> Any -> Any -> Any -> Any -> Any)
-> (Any -> Any -> Any -> Any)
-> T_Σ_14
-> T_Σ_14
-> T_IsSemiringWithoutOne_1298
MAlonzo.Code.Algebra.Structures.C_IsSemiringWithoutOne'46'constructor_37629
      (T_IsCommutativeMonoid_736 -> Any
forall a b. a -> b
coe T_IsCommutativeMonoid_736
d_'8852''45'0'45'isCommutativeMonoid_4716) Any
forall a. a
erased
      ((T_TotalPreorder_222
 -> T_MinOperator_98 -> Any -> Any -> Any -> Any)
-> Any -> Any -> Any
forall a b. a -> b
coe
         T_TotalPreorder_222 -> T_MinOperator_98 -> Any -> Any -> Any -> Any
MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_'8851''45'assoc_2944
         (T_TotalPreorder_222 -> Any
forall a b. a -> b
coe T_TotalPreorder_222
d_'8804''45'totalPreorder_2822)
         (T_MinOperator_98 -> Any
forall a b. a -> b
coe T_MinOperator_98
d_'8851''45'operator_4438))
      ((T_TotalPreorder_222
 -> T_MinOperator_98 -> T_MaxOperator_128 -> T_Σ_14)
-> Any -> Any -> Any -> Any
forall a b. a -> b
coe
         T_TotalPreorder_222
-> T_MinOperator_98 -> T_MaxOperator_128 -> T_Σ_14
MAlonzo.Code.Algebra.Construct.NaturalChoice.MinMaxOp.du_'8851''45'distrib'45''8852'_3138
         (T_TotalPreorder_222 -> Any
forall a b. a -> b
coe T_TotalPreorder_222
d_'8804''45'totalPreorder_2822)
         (T_MinOperator_98 -> Any
forall a b. a -> b
coe T_MinOperator_98
d_'8851''45'operator_4438) (T_MaxOperator_128 -> Any
forall a b. a -> b
coe T_MaxOperator_128
d_'8852''45'operator_4440))
      (T_Σ_14 -> Any
forall a b. a -> b
coe T_Σ_14
d_'8851''45'zero_4892)
-- Data.Nat.Properties.⊔-⊓-isCommutativeSemiringWithoutOne
d_'8852''45''8851''45'isCommutativeSemiringWithoutOne_4896 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiringWithoutOne_1382
d_'8852''45''8851''45'isCommutativeSemiringWithoutOne_4896 :: T_IsCommutativeSemiringWithoutOne_1382
d_'8852''45''8851''45'isCommutativeSemiringWithoutOne_4896
  = (T_IsSemiringWithoutOne_1298
 -> (Any -> Any -> Any) -> T_IsCommutativeSemiringWithoutOne_1382)
-> Any -> Any -> T_IsCommutativeSemiringWithoutOne_1382
forall a b. a -> b
coe
      T_IsSemiringWithoutOne_1298
-> (Any -> Any -> Any) -> T_IsCommutativeSemiringWithoutOne_1382
MAlonzo.Code.Algebra.Structures.C_IsCommutativeSemiringWithoutOne'46'constructor_41457
      (T_IsSemiringWithoutOne_1298 -> Any
forall a b. a -> b
coe T_IsSemiringWithoutOne_1298
d_'8852''45''8851''45'isSemiringWithoutOne_4894)
      ((T_TotalPreorder_222 -> T_MinOperator_98 -> Any -> Any -> Any)
-> Any -> Any -> Any
forall a b. a -> b
coe
         T_TotalPreorder_222 -> T_MinOperator_98 -> Any -> Any -> Any
MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_'8851''45'comm_2856
         (T_TotalPreorder_222 -> Any
forall a b. a -> b
coe T_TotalPreorder_222
d_'8804''45'totalPreorder_2822)
         (T_MinOperator_98 -> Any
forall a b. a -> b
coe T_MinOperator_98
d_'8851''45'operator_4438))
-- Data.Nat.Properties.⊔-⊓-commutativeSemiringWithoutOne
d_'8852''45''8851''45'commutativeSemiringWithoutOne_4898 ::
  MAlonzo.Code.Algebra.Bundles.T_CommutativeSemiringWithoutOne_2002
d_'8852''45''8851''45'commutativeSemiringWithoutOne_4898 :: T_CommutativeSemiringWithoutOne_2002
d_'8852''45''8851''45'commutativeSemiringWithoutOne_4898
  = ((Any -> Any -> Any)
 -> (Any -> Any -> Any)
 -> Any
 -> T_IsCommutativeSemiringWithoutOne_1382
 -> T_CommutativeSemiringWithoutOne_2002)
-> (Integer -> Integer -> Integer)
-> (Integer -> Integer -> Integer)
-> Integer
-> T_IsCommutativeSemiringWithoutOne_1382
-> T_CommutativeSemiringWithoutOne_2002
forall a b. a -> b
coe
      (Any -> Any -> Any)
-> (Any -> Any -> Any)
-> Any
-> T_IsCommutativeSemiringWithoutOne_1382
-> T_CommutativeSemiringWithoutOne_2002
MAlonzo.Code.Algebra.Bundles.C_CommutativeSemiringWithoutOne'46'constructor_36869
      Integer -> Integer -> Integer
MAlonzo.Code.Data.Nat.Base.d__'8852'__204
      Integer -> Integer -> Integer
MAlonzo.Code.Data.Nat.Base.d__'8851'__232 (Integer
0 :: Integer)
      T_IsCommutativeSemiringWithoutOne_1382
d_'8852''45''8851''45'isCommutativeSemiringWithoutOne_4896
-- Data.Nat.Properties.m<n⇒m⊓o<n
d_m'60'n'8658'm'8851'o'60'n_4902 ::
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_m'60'n'8658'm'8851'o'60'n_4902 :: Integer -> Integer -> Integer -> T__'8804'__22 -> T__'8804'__22
d_m'60'n'8658'm'8851'o'60'n_4902 Integer
v0 ~Integer
v1 Integer
v2 T__'8804'__22
v3
  = Integer -> Integer -> T__'8804'__22 -> T__'8804'__22
du_m'60'n'8658'm'8851'o'60'n_4902 Integer
v0 Integer
v2 T__'8804'__22
v3
du_m'60'n'8658'm'8851'o'60'n_4902 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
du_m'60'n'8658'm'8851'o'60'n_4902 :: Integer -> Integer -> T__'8804'__22 -> T__'8804'__22
du_m'60'n'8658'm'8851'o'60'n_4902 Integer
v0 Integer
v1 T__'8804'__22
v2
  = (T__'8804'__22 -> T__'8804'__22 -> T__'8804'__22)
-> Any -> Any -> T__'8804'__22
forall a b. a -> b
coe
      T__'8804'__22 -> T__'8804'__22 -> T__'8804'__22
du_'8804''45''60''45'trans_2986
      ((T_TotalPreorder_222 -> T_MinOperator_98 -> Any -> Any -> Any)
-> Any -> Any -> Any -> Any -> Any
forall a b. a -> b
coe
         T_TotalPreorder_222 -> T_MinOperator_98 -> Any -> Any -> Any
MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_x'8851'y'8804'x_2808
         (T_TotalPreorder_222 -> Any
forall a b. a -> b
coe T_TotalPreorder_222
d_'8804''45'totalPreorder_2822)
         (T_MinOperator_98 -> Any
forall a b. a -> b
coe T_MinOperator_98
d_'8851''45'operator_4438) (Integer -> Any
forall a b. a -> b
coe Integer
v0) (Integer -> Any
forall a b. a -> b
coe Integer
v1))
      (T__'8804'__22 -> Any
forall a b. a -> b
coe T__'8804'__22
v2)
-- Data.Nat.Properties.m<n⇒o⊓m<n
d_m'60'n'8658'o'8851'm'60'n_4910 ::
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_m'60'n'8658'o'8851'm'60'n_4910 :: Integer -> Integer -> Integer -> T__'8804'__22 -> T__'8804'__22
d_m'60'n'8658'o'8851'm'60'n_4910 Integer
v0 ~Integer
v1 Integer
v2 T__'8804'__22
v3
  = Integer -> Integer -> T__'8804'__22 -> T__'8804'__22
du_m'60'n'8658'o'8851'm'60'n_4910 Integer
v0 Integer
v2 T__'8804'__22
v3
du_m'60'n'8658'o'8851'm'60'n_4910 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
du_m'60'n'8658'o'8851'm'60'n_4910 :: Integer -> Integer -> T__'8804'__22 -> T__'8804'__22
du_m'60'n'8658'o'8851'm'60'n_4910 Integer
v0 Integer
v1 T__'8804'__22
v2
  = (T__'8804'__22 -> T__'8804'__22 -> T__'8804'__22)
-> Any -> Any -> T__'8804'__22
forall a b. a -> b
coe
      T__'8804'__22 -> T__'8804'__22 -> T__'8804'__22
du_'8804''45''60''45'trans_2986
      ((T_TotalPreorder_222 -> T_MinOperator_98 -> Any -> Any -> Any)
-> Any -> Any -> Any -> Any -> Any
forall a b. a -> b
coe
         T_TotalPreorder_222 -> T_MinOperator_98 -> Any -> Any -> Any
MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_x'8851'y'8804'y_2834
         (T_TotalPreorder_222 -> Any
forall a b. a -> b
coe T_TotalPreorder_222
d_'8804''45'totalPreorder_2822)
         (T_MinOperator_98 -> Any
forall a b. a -> b
coe T_MinOperator_98
d_'8851''45'operator_4438) (Integer -> Any
forall a b. a -> b
coe Integer
v1) (Integer -> Any
forall a b. a -> b
coe Integer
v0))
      (T__'8804'__22 -> Any
forall a b. a -> b
coe T__'8804'__22
v2)
-- Data.Nat.Properties.m<n⊓o⇒m<n
d_m'60'n'8851'o'8658'm'60'n_4920 ::
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_m'60'n'8851'o'8658'm'60'n_4920 :: Integer -> Integer -> Integer -> T__'8804'__22 -> T__'8804'__22
d_m'60'n'8851'o'8658'm'60'n_4920 Integer
v0
  = (T_TotalPreorder_222
 -> T_MinOperator_98 -> Any -> Any -> Any -> Any -> Any)
-> Any
-> Any
-> Any
-> Integer
-> Integer
-> T__'8804'__22
-> T__'8804'__22
forall a b. a -> b
coe
      T_TotalPreorder_222
-> T_MinOperator_98 -> Any -> Any -> Any -> Any -> Any
MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_x'8804'y'8851'z'8658'x'8804'y_3184
      (T_TotalPreorder_222 -> Any
forall a b. a -> b
coe T_TotalPreorder_222
d_'8804''45'totalPreorder_2822)
      (T_MinOperator_98 -> Any
forall a b. a -> b
coe T_MinOperator_98
d_'8851''45'operator_4438)
      ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> Integer
addInt (Integer -> Any
forall a b. a -> b
coe (Integer
1 :: Integer)) (Integer -> Any
forall a b. a -> b
coe Integer
v0))
-- Data.Nat.Properties.m<n⊓o⇒m<o
d_m'60'n'8851'o'8658'm'60'o_4926 ::
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_m'60'n'8851'o'8658'm'60'o_4926 :: Integer -> Integer -> Integer -> T__'8804'__22 -> T__'8804'__22
d_m'60'n'8851'o'8658'm'60'o_4926 Integer
v0
  = (T_TotalPreorder_222
 -> T_MinOperator_98 -> Any -> Any -> Any -> Any -> Any)
-> Any
-> Any
-> Any
-> Integer
-> Integer
-> T__'8804'__22
-> T__'8804'__22
forall a b. a -> b
coe
      T_TotalPreorder_222
-> T_MinOperator_98 -> Any -> Any -> Any -> Any -> Any
MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_x'8804'y'8851'z'8658'x'8804'z_3198
      (T_TotalPreorder_222 -> Any
forall a b. a -> b
coe T_TotalPreorder_222
d_'8804''45'totalPreorder_2822)
      (T_MinOperator_98 -> Any
forall a b. a -> b
coe T_MinOperator_98
d_'8851''45'operator_4438)
      ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> Integer
addInt (Integer -> Any
forall a b. a -> b
coe (Integer
1 :: Integer)) (Integer -> Any
forall a b. a -> b
coe Integer
v0))
-- Data.Nat.Properties.⊓-mono-<
d_'8851''45'mono'45''60'_4928 ::
  Integer ->
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_'8851''45'mono'45''60'_4928 :: Integer
-> Integer
-> Integer
-> Integer
-> T__'8804'__22
-> T__'8804'__22
-> T__'8804'__22
d_'8851''45'mono'45''60'_4928 Integer
v0 Integer
v1 Integer
v2 Integer
v3
  = (T_TotalPreorder_222
 -> T_MinOperator_98
 -> Any
 -> Any
 -> Any
 -> Any
 -> Any
 -> Any
 -> Any)
-> Any
-> Any
-> Any
-> Any
-> Any
-> Any
-> T__'8804'__22
-> T__'8804'__22
-> T__'8804'__22
forall a b. a -> b
coe
      T_TotalPreorder_222
-> T_MinOperator_98
-> Any
-> Any
-> Any
-> Any
-> Any
-> Any
-> Any
MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_'8851''45'mono'45''8804'_3206
      (T_TotalPreorder_222 -> Any
forall a b. a -> b
coe T_TotalPreorder_222
d_'8804''45'totalPreorder_2822)
      (T_MinOperator_98 -> Any
forall a b. a -> b
coe T_MinOperator_98
d_'8851''45'operator_4438)
      ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> Integer
addInt (Integer -> Any
forall a b. a -> b
coe (Integer
1 :: Integer)) (Integer -> Any
forall a b. a -> b
coe Integer
v0)) (Integer -> Any
forall a b. a -> b
coe Integer
v1)
      ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> Integer
addInt (Integer -> Any
forall a b. a -> b
coe (Integer
1 :: Integer)) (Integer -> Any
forall a b. a -> b
coe Integer
v2)) (Integer -> Any
forall a b. a -> b
coe Integer
v3)
-- Data.Nat.Properties.⊓-pres-m<
d_'8851''45'pres'45'm'60'_4930 ::
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_'8851''45'pres'45'm'60'_4930 :: Integer
-> Integer
-> Integer
-> T__'8804'__22
-> T__'8804'__22
-> T__'8804'__22
d_'8851''45'pres'45'm'60'_4930 Integer
v0 Integer
v1 Integer
v2 T__'8804'__22
v3 T__'8804'__22
v4
  = (Integer
 -> Integer
 -> Integer
 -> Integer
 -> T__'8804'__22
 -> T__'8804'__22
 -> T__'8804'__22)
-> Integer
-> Integer
-> Integer
-> Integer
-> T__'8804'__22
-> T__'8804'__22
-> T__'8804'__22
forall a b. a -> b
coe Integer
-> Integer
-> Integer
-> Integer
-> T__'8804'__22
-> T__'8804'__22
-> T__'8804'__22
d_'8851''45'mono'45''60'_4928 Integer
v0 Integer
v1 Integer
v0 Integer
v2 T__'8804'__22
v3 T__'8804'__22
v4
-- Data.Nat.Properties.+-distribˡ-⊓
d_'43''45'distrib'737''45''8851'_4940 ::
  Integer ->
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'43''45'distrib'737''45''8851'_4940 :: Integer -> Integer -> Integer -> T__'8801'__12
d_'43''45'distrib'737''45''8851'_4940 = Integer -> Integer -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Nat.Properties.+-distribʳ-⊓
d_'43''45'distrib'691''45''8851'_4952 ::
  Integer ->
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'43''45'distrib'691''45''8851'_4952 :: Integer -> Integer -> Integer -> T__'8801'__12
d_'43''45'distrib'691''45''8851'_4952 = Integer -> Integer -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Nat.Properties.+-distrib-⊓
d_'43''45'distrib'45''8851'_4954 ::
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'43''45'distrib'45''8851'_4954 :: T_Σ_14
d_'43''45'distrib'45''8851'_4954
  = (Any -> Any -> T_Σ_14) -> Any -> Any -> T_Σ_14
forall a b. a -> b
coe Any -> Any -> T_Σ_14
MAlonzo.Code.Agda.Builtin.Sigma.C__'44'__32 Any
forall a. a
erased Any
forall a. a
erased
-- Data.Nat.Properties.m⊓n≤m+n
d_m'8851'n'8804'm'43'n_4960 ::
  Integer -> Integer -> MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_m'8851'n'8804'm'43'n_4960 :: Integer -> Integer -> T__'8804'__22
d_m'8851'n'8804'm'43'n_4960 Integer
v0 Integer
v1
  = let v2 :: t
v2
          = ((Any -> Any) -> (Any -> Any) -> T__'8846'__30 -> Any)
-> Any -> Any -> Any -> t
forall a b. a -> b
coe
              (Any -> Any) -> (Any -> Any) -> T__'8846'__30 -> Any
MAlonzo.Code.Data.Sum.Base.du_'91'_'44'_'93'_52
              ((Any -> Any) -> Any
forall a b. a -> b
coe
                 (\ Any
v2 -> (Any -> T__'8846'__30) -> Any -> Any
forall a b. a -> b
coe Any -> T__'8846'__30
MAlonzo.Code.Data.Sum.Base.C_inj'8321'_38 Any
forall a. a
erased))
              ((Any -> Any) -> Any
forall a b. a -> b
coe
                 (\ Any
v2 -> (Any -> T__'8846'__30) -> Any -> Any
forall a b. a -> b
coe Any -> T__'8846'__30
MAlonzo.Code.Data.Sum.Base.C_inj'8322'_42 Any
forall a. a
erased))
              ((Integer -> Integer -> T__'8846'__30) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> T__'8846'__30
d_'8804''45'total_2790 (Integer -> Any
forall a b. a -> b
coe Integer
v0) (Integer -> Any
forall a b. a -> b
coe Integer
v1)) in
    Any -> T__'8804'__22
forall a b. a -> b
coe
      (case Any -> T__'8846'__30
forall a b. a -> b
coe Any
forall a. a
v2 of
         MAlonzo.Code.Data.Sum.Base.C_inj'8321'_38 Any
v3
           -> (Integer -> T__'8804'__22) -> Any -> Any
forall a b. a -> b
coe Integer -> T__'8804'__22
du_m'8804'm'43'n_3482 (Integer -> Any
forall a b. a -> b
coe Integer
v0)
         MAlonzo.Code.Data.Sum.Base.C_inj'8322'_42 Any
v3
           -> (Integer -> T__'8804'__22) -> Any -> Any
forall a b. a -> b
coe Integer -> T__'8804'__22
du_m'8804'n'43'm_3494 (Integer -> Any
forall a b. a -> b
coe Integer
v1)
         T__'8846'__30
_ -> Any
forall a. a
MAlonzo.RTE.mazUnreachableError)
-- Data.Nat.Properties.*-distribˡ-⊓
d_'42''45'distrib'737''45''8851'_4990 ::
  Integer ->
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'42''45'distrib'737''45''8851'_4990 :: Integer -> Integer -> Integer -> T__'8801'__12
d_'42''45'distrib'737''45''8851'_4990 = Integer -> Integer -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Nat.Properties.*-distribʳ-⊓
d_'42''45'distrib'691''45''8851'_5012 ::
  Integer ->
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'42''45'distrib'691''45''8851'_5012 :: Integer -> Integer -> Integer -> T__'8801'__12
d_'42''45'distrib'691''45''8851'_5012 = Integer -> Integer -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Nat.Properties.*-distrib-⊓
d_'42''45'distrib'45''8851'_5014 ::
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'42''45'distrib'45''8851'_5014 :: T_Σ_14
d_'42''45'distrib'45''8851'_5014
  = (Any -> Any -> T_Σ_14) -> Any -> Any -> T_Σ_14
forall a b. a -> b
coe Any -> Any -> T_Σ_14
MAlonzo.Code.Agda.Builtin.Sigma.C__'44'__32 Any
forall a. a
erased Any
forall a. a
erased
-- Data.Nat.Properties.0∸n≡0
d_0'8760'n'8801'0_5016 ::
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_0'8760'n'8801'0_5016 :: Integer -> T__'8801'__12
d_0'8760'n'8801'0_5016 = Integer -> T__'8801'__12
forall a. a
erased
-- Data.Nat.Properties.n∸n≡0
d_n'8760'n'8801'0_5020 ::
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_n'8760'n'8801'0_5020 :: Integer -> T__'8801'__12
d_n'8760'n'8801'0_5020 = Integer -> T__'8801'__12
forall a. a
erased
-- Data.Nat.Properties.pred[m∸n]≡m∸[1+n]
d_pred'91'm'8760'n'93''8801'm'8760''91'1'43'n'93'_5028 ::
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_pred'91'm'8760'n'93''8801'm'8760''91'1'43'n'93'_5028 :: Integer -> Integer -> T__'8801'__12
d_pred'91'm'8760'n'93''8801'm'8760''91'1'43'n'93'_5028 = Integer -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Nat.Properties.m∸n≤m
d_m'8760'n'8804'm_5042 ::
  Integer -> Integer -> MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_m'8760'n'8804'm_5042 :: Integer -> Integer -> T__'8804'__22
d_m'8760'n'8804'm_5042 Integer
v0 Integer
v1
  = case Integer -> Integer
forall a b. a -> b
coe Integer
v1 of
      Integer
0 -> (Integer -> T__'8804'__22) -> Any -> T__'8804'__22
forall a b. a -> b
coe
             Integer -> T__'8804'__22
d_'8804''45'refl_2776
             ((Integer -> Integer -> Integer) -> Integer -> Integer -> Any
forall a b. a -> b
coe Integer -> Integer -> Integer
MAlonzo.Code.Agda.Builtin.Nat.d__'45'__22 Integer
v0 (Integer
0 :: Integer))
      Integer
_ -> let v2 :: Integer
v2 = Integer -> Integer -> Integer
subInt (Integer -> Integer
forall a b. a -> b
coe Integer
v1) (Integer -> Integer
forall a b. a -> b
coe (Integer
1 :: Integer)) in
           Any -> T__'8804'__22
forall a b. a -> b
coe
             (case Integer -> Integer
forall a b. a -> b
coe Integer
v0 of
                Integer
0 -> (Integer -> T__'8804'__22) -> Any -> Any
forall a b. a -> b
coe
                       Integer -> T__'8804'__22
d_'8804''45'refl_2776
                       ((Integer -> Integer -> Integer) -> Integer -> Integer -> Any
forall a b. a -> b
coe Integer -> Integer -> Integer
MAlonzo.Code.Agda.Builtin.Nat.d__'45'__22 (Integer
0 :: Integer) Integer
v1)
                Integer
_ -> let v3 :: Integer
v3 = Integer -> Integer -> Integer
subInt (Integer -> Integer
forall a b. a -> b
coe Integer
v0) (Integer -> Integer
forall a b. a -> b
coe (Integer
1 :: Integer)) in
                     Any -> Any
forall a b. a -> b
coe
                       ((T__'8804'__22 -> T__'8804'__22 -> T__'8804'__22)
-> Any -> Any -> Any
forall a b. a -> b
coe
                          T__'8804'__22 -> T__'8804'__22 -> T__'8804'__22
du_'8804''45'trans_2784
                          ((Integer -> Integer -> T__'8804'__22) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> T__'8804'__22
d_m'8760'n'8804'm_5042 (Integer -> Any
forall a b. a -> b
coe Integer
v3) (Integer -> Any
forall a b. a -> b
coe Integer
v2))
                          ((Integer -> T__'8804'__22) -> Any -> Any
forall a b. a -> b
coe Integer -> T__'8804'__22
d_n'8804'1'43'n_2844 (Integer -> Any
forall a b. a -> b
coe Integer
v3))))
-- Data.Nat.Properties.m≮m∸n
d_m'8814'm'8760'n_5056 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Irrelevant.T_Irrelevant_20
d_m'8814'm'8760'n_5056 :: Integer -> Integer -> T__'8804'__22 -> T_Irrelevant_20
d_m'8814'm'8760'n_5056 = Integer -> Integer -> T__'8804'__22 -> T_Irrelevant_20
forall a. a
erased
-- Data.Nat.Properties.1+m≢m∸n
d_1'43'm'8802'm'8760'n_5068 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Data.Irrelevant.T_Irrelevant_20
d_1'43'm'8802'm'8760'n_5068 :: Integer -> Integer -> T__'8801'__12 -> T_Irrelevant_20
d_1'43'm'8802'm'8760'n_5068 = Integer -> Integer -> T__'8801'__12 -> T_Irrelevant_20
forall a. a
erased
-- Data.Nat.Properties.∸-mono
d_'8760''45'mono_5076 ::
  Integer ->
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_'8760''45'mono_5076 :: Integer
-> Integer
-> Integer
-> Integer
-> T__'8804'__22
-> T__'8804'__22
-> T__'8804'__22
d_'8760''45'mono_5076 Integer
v0 Integer
v1 Integer
v2 Integer
v3 T__'8804'__22
v4 T__'8804'__22
v5
  = let v6 :: b
v6
          = Any -> b -> b
forall a b. a -> b -> b
seq
              (T__'8804'__22 -> Any
forall a b. a -> b
coe T__'8804'__22
v5)
              ((T__'8804'__22 -> T__'8804'__22 -> T__'8804'__22)
-> Any -> Any -> b
forall a b. a -> b
coe
                 T__'8804'__22 -> T__'8804'__22 -> T__'8804'__22
du_'8804''45'trans_2784
                 ((Integer -> Integer -> T__'8804'__22) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> T__'8804'__22
d_m'8760'n'8804'm_5042 (Integer -> Any
forall a b. a -> b
coe Integer
v0) (Integer -> Any
forall a b. a -> b
coe Integer
v2)) (T__'8804'__22 -> Any
forall a b. a -> b
coe T__'8804'__22
v4)) in
    Any -> T__'8804'__22
forall a b. a -> b
coe
      (case T__'8804'__22 -> T__'8804'__22
forall a b. a -> b
coe T__'8804'__22
v4 of
         T__'8804'__22
MAlonzo.Code.Data.Nat.Base.C_z'8804'n_26
           -> case T__'8804'__22 -> T__'8804'__22
forall a b. a -> b
coe T__'8804'__22
v5 of
                T__'8804'__22
MAlonzo.Code.Data.Nat.Base.C_z'8804'n_26
                  -> (T__'8804'__22 -> T__'8804'__22 -> T__'8804'__22)
-> Any -> Any -> Any
forall a b. a -> b
coe
                       T__'8804'__22 -> T__'8804'__22 -> T__'8804'__22
du_'8804''45'trans_2784
                       ((Integer -> Integer -> T__'8804'__22) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> T__'8804'__22
d_m'8760'n'8804'm_5042 (Integer -> Any
forall a b. a -> b
coe Integer
v0) (Integer -> Any
forall a b. a -> b
coe Integer
v2))
                       (T__'8804'__22 -> Any
forall a b. a -> b
coe T__'8804'__22
MAlonzo.Code.Data.Nat.Base.C_z'8804'n_26)
                MAlonzo.Code.Data.Nat.Base.C_s'8804's_34 T__'8804'__22
v10
                  -> case Integer -> Any
forall a b. a -> b
coe Integer
v2 of
                       Any
_ | (Integer -> Integer -> Bool) -> Any -> Any -> Bool
forall a b. a -> b
coe Integer -> Integer -> Bool
geqInt (Integer -> Any
forall a b. a -> b
coe Integer
v2) (Integer -> Any
forall a b. a -> b
coe (Integer
1 :: Integer)) ->
                           case Integer -> Any
forall a b. a -> b
coe Integer
v3 of
                             Any
_ | (Integer -> Integer -> Bool) -> Any -> Any -> Bool
forall a b. a -> b
coe Integer -> Integer -> Bool
geqInt (Integer -> Any
forall a b. a -> b
coe Integer
v3) (Integer -> Any
forall a b. a -> b
coe (Integer
1 :: Integer)) ->
                                 T__'8804'__22 -> Any
forall a b. a -> b
coe T__'8804'__22
MAlonzo.Code.Data.Nat.Base.C_z'8804'n_26
                             Any
_ -> Any -> Any
forall a b. a -> b
coe Any
forall a. a
v6
                       Any
_ -> Any -> Any
forall a b. a -> b
coe Any
forall a. a
v6
                T__'8804'__22
_ -> Any
forall a. a
MAlonzo.RTE.mazUnreachableError
         MAlonzo.Code.Data.Nat.Base.C_s'8804's_34 T__'8804'__22
v9
           -> let v10 :: b
v10
                    = Any -> b -> b
forall a b. a -> b -> b
seq
                        (T__'8804'__22 -> Any
forall a b. a -> b
coe T__'8804'__22
v5)
                        ((T__'8804'__22 -> T__'8804'__22 -> T__'8804'__22)
-> Any -> Any -> b
forall a b. a -> b
coe
                           T__'8804'__22 -> T__'8804'__22 -> T__'8804'__22
du_'8804''45'trans_2784
                           ((Integer -> Integer -> T__'8804'__22) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> T__'8804'__22
d_m'8760'n'8804'm_5042 (Integer -> Any
forall a b. a -> b
coe Integer
v0) (Integer -> Any
forall a b. a -> b
coe Integer
v2))
                           ((T__'8804'__22 -> T__'8804'__22) -> T__'8804'__22 -> Any
forall a b. a -> b
coe T__'8804'__22 -> T__'8804'__22
MAlonzo.Code.Data.Nat.Base.C_s'8804's_34 T__'8804'__22
v9)) in
              Any -> Any
forall a b. a -> b
coe
                (case Integer -> Any
forall a b. a -> b
coe Integer
v0 of
                   Any
_ | (Integer -> Integer -> Bool) -> Any -> Any -> Bool
forall a b. a -> b
coe Integer -> Integer -> Bool
geqInt (Integer -> Any
forall a b. a -> b
coe Integer
v0) (Integer -> Any
forall a b. a -> b
coe (Integer
1 :: Integer)) ->
                       let v11 :: Integer
v11 = Integer -> Integer -> Integer
subInt (Integer -> Integer
forall a b. a -> b
coe Integer
v0) (Integer -> Integer
forall a b. a -> b
coe (Integer
1 :: Integer)) in
                       Any -> Any
forall a b. a -> b
coe
                         (let v12 :: b
v12
                                = Any -> b -> b
forall a b. a -> b -> b
seq
                                    (T__'8804'__22 -> Any
forall a b. a -> b
coe T__'8804'__22
v5)
                                    ((T__'8804'__22 -> T__'8804'__22 -> T__'8804'__22)
-> Any -> Any -> b
forall a b. a -> b
coe
                                       T__'8804'__22 -> T__'8804'__22 -> T__'8804'__22
du_'8804''45'trans_2784
                                       ((Integer -> Integer -> T__'8804'__22) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> T__'8804'__22
d_m'8760'n'8804'm_5042 (Integer -> Any
forall a b. a -> b
coe Integer
v0) (Integer -> Any
forall a b. a -> b
coe Integer
v2))
                                       ((T__'8804'__22 -> T__'8804'__22) -> T__'8804'__22 -> Any
forall a b. a -> b
coe T__'8804'__22 -> T__'8804'__22
MAlonzo.Code.Data.Nat.Base.C_s'8804's_34 T__'8804'__22
v9)) in
                          Any -> Any
forall a b. a -> b
coe
                            (case Integer -> Any
forall a b. a -> b
coe Integer
v1 of
                               Any
_ | (Integer -> Integer -> Bool) -> Any -> Any -> Bool
forall a b. a -> b
coe Integer -> Integer -> Bool
geqInt (Integer -> Any
forall a b. a -> b
coe Integer
v1) (Integer -> Any
forall a b. a -> b
coe (Integer
1 :: Integer)) ->
                                   let v13 :: Integer
v13 = Integer -> Integer -> Integer
subInt (Integer -> Integer
forall a b. a -> b
coe Integer
v1) (Integer -> Integer
forall a b. a -> b
coe (Integer
1 :: Integer)) in
                                   Any -> Any
forall a b. a -> b
coe
                                     (case T__'8804'__22 -> T__'8804'__22
forall a b. a -> b
coe T__'8804'__22
v5 of
                                        T__'8804'__22
MAlonzo.Code.Data.Nat.Base.C_z'8804'n_26
                                          -> (T__'8804'__22 -> T__'8804'__22 -> T__'8804'__22)
-> Any -> Any -> Any
forall a b. a -> b
coe
                                               T__'8804'__22 -> T__'8804'__22 -> T__'8804'__22
du_'8804''45'trans_2784
                                               ((Integer -> Integer -> T__'8804'__22) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> T__'8804'__22
d_m'8760'n'8804'm_5042 (Integer -> Any
forall a b. a -> b
coe Integer
v0) (Integer -> Any
forall a b. a -> b
coe Integer
v2))
                                               ((T__'8804'__22 -> T__'8804'__22) -> T__'8804'__22 -> Any
forall a b. a -> b
coe T__'8804'__22 -> T__'8804'__22
MAlonzo.Code.Data.Nat.Base.C_s'8804's_34 T__'8804'__22
v9)
                                        MAlonzo.Code.Data.Nat.Base.C_s'8804's_34 T__'8804'__22
v16
                                          -> case Integer -> Any
forall a b. a -> b
coe Integer
v2 of
                                               Any
_ | (Integer -> Integer -> Bool) -> Any -> Any -> Bool
forall a b. a -> b
coe Integer -> Integer -> Bool
geqInt (Integer -> Any
forall a b. a -> b
coe Integer
v2) (Integer -> Any
forall a b. a -> b
coe (Integer
1 :: Integer)) ->
                                                   let v17 :: Integer
v17 = Integer -> Integer -> Integer
subInt (Integer -> Integer
forall a b. a -> b
coe Integer
v2) (Integer -> Integer
forall a b. a -> b
coe (Integer
1 :: Integer)) in
                                                   Any -> Any
forall a b. a -> b
coe
                                                     (case Integer -> Any
forall a b. a -> b
coe Integer
v3 of
                                                        Any
_ | (Integer -> Integer -> Bool) -> Any -> Any -> Bool
forall a b. a -> b
coe
                                                              Integer -> Integer -> Bool
geqInt (Integer -> Any
forall a b. a -> b
coe Integer
v3)
                                                              (Integer -> Any
forall a b. a -> b
coe (Integer
1 :: Integer)) ->
                                                            let v18 :: Integer
v18
                                                                  = Integer -> Integer -> Integer
subInt
                                                                      (Integer -> Integer
forall a b. a -> b
coe Integer
v3)
                                                                      (Integer -> Integer
forall a b. a -> b
coe (Integer
1 :: Integer)) in
                                                            Any -> Any
forall a b. a -> b
coe
                                                              ((Integer
 -> Integer
 -> Integer
 -> Integer
 -> T__'8804'__22
 -> T__'8804'__22
 -> T__'8804'__22)
-> Any -> Any -> Any -> Any -> Any -> Any -> Any
forall a b. a -> b
coe
                                                                 Integer
-> Integer
-> Integer
-> Integer
-> T__'8804'__22
-> T__'8804'__22
-> T__'8804'__22
d_'8760''45'mono_5076 (Integer -> Any
forall a b. a -> b
coe Integer
v11)
                                                                 (Integer -> Any
forall a b. a -> b
coe Integer
v13) (Integer -> Any
forall a b. a -> b
coe Integer
v17) (Integer -> Any
forall a b. a -> b
coe Integer
v18)
                                                                 (T__'8804'__22 -> Any
forall a b. a -> b
coe T__'8804'__22
v9) (T__'8804'__22 -> Any
forall a b. a -> b
coe T__'8804'__22
v16))
                                                        Any
_ -> Any -> Any
forall a b. a -> b
coe Any
forall a. a
v12)
                                               Any
_ -> Any -> Any
forall a b. a -> b
coe Any
forall a. a
v12
                                        T__'8804'__22
_ -> Any
forall a. a
MAlonzo.RTE.mazUnreachableError)
                               Any
_ -> Any -> Any
forall a b. a -> b
coe Any
forall a. a
v12))
                   Any
_ -> Any -> Any
forall a b. a -> b
coe Any
forall a. a
v10)
         T__'8804'__22
_ -> Any
forall a. a
MAlonzo.RTE.mazUnreachableError)
-- Data.Nat.Properties.∸-monoˡ-≤
d_'8760''45'mono'737''45''8804'_5090 ::
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_'8760''45'mono'737''45''8804'_5090 :: Integer -> Integer -> Integer -> T__'8804'__22 -> T__'8804'__22
d_'8760''45'mono'737''45''8804'_5090 Integer
v0 Integer
v1 Integer
v2 T__'8804'__22
v3
  = (Integer
 -> Integer
 -> Integer
 -> Integer
 -> T__'8804'__22
 -> T__'8804'__22
 -> T__'8804'__22)
-> Any -> Any -> Any -> Any -> Any -> Any -> T__'8804'__22
forall a b. a -> b
coe
      Integer
-> Integer
-> Integer
-> Integer
-> T__'8804'__22
-> T__'8804'__22
-> T__'8804'__22
d_'8760''45'mono_5076 (Integer -> Any
forall a b. a -> b
coe Integer
v0) (Integer -> Any
forall a b. a -> b
coe Integer
v1) (Integer -> Any
forall a b. a -> b
coe Integer
v2) (Integer -> Any
forall a b. a -> b
coe Integer
v2) (T__'8804'__22 -> Any
forall a b. a -> b
coe T__'8804'__22
v3)
      ((Integer -> T__'8804'__22) -> Any -> Any
forall a b. a -> b
coe Integer -> T__'8804'__22
d_'8804''45'refl_2776 (Integer -> Any
forall a b. a -> b
coe Integer
v2))
-- Data.Nat.Properties.∸-monoʳ-≤
d_'8760''45'mono'691''45''8804'_5098 ::
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_'8760''45'mono'691''45''8804'_5098 :: Integer -> Integer -> Integer -> T__'8804'__22 -> T__'8804'__22
d_'8760''45'mono'691''45''8804'_5098 Integer
v0 Integer
v1 Integer
v2 T__'8804'__22
v3
  = (Integer
 -> Integer
 -> Integer
 -> Integer
 -> T__'8804'__22
 -> T__'8804'__22
 -> T__'8804'__22)
-> Any -> Any -> Any -> Any -> Any -> Any -> T__'8804'__22
forall a b. a -> b
coe
      Integer
-> Integer
-> Integer
-> Integer
-> T__'8804'__22
-> T__'8804'__22
-> T__'8804'__22
d_'8760''45'mono_5076 (Integer -> Any
forall a b. a -> b
coe Integer
v2) (Integer -> Any
forall a b. a -> b
coe Integer
v2) (Integer -> Any
forall a b. a -> b
coe Integer
v1) (Integer -> Any
forall a b. a -> b
coe Integer
v0)
      ((Integer -> T__'8804'__22) -> Any -> Any
forall a b. a -> b
coe Integer -> T__'8804'__22
d_'8804''45'refl_2776 (Integer -> Any
forall a b. a -> b
coe Integer
v2)) (T__'8804'__22 -> Any
forall a b. a -> b
coe T__'8804'__22
v3)
-- Data.Nat.Properties.∸-monoˡ-<
d_'8760''45'mono'737''45''60'_5108 ::
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_'8760''45'mono'737''45''60'_5108 :: Integer
-> Integer
-> Integer
-> T__'8804'__22
-> T__'8804'__22
-> T__'8804'__22
d_'8760''45'mono'737''45''60'_5108 ~Integer
v0 Integer
v1 ~Integer
v2 T__'8804'__22
v3 T__'8804'__22
v4
  = Integer -> T__'8804'__22 -> T__'8804'__22 -> T__'8804'__22
du_'8760''45'mono'737''45''60'_5108 Integer
v1 T__'8804'__22
v3 T__'8804'__22
v4
du_'8760''45'mono'737''45''60'_5108 ::
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
du_'8760''45'mono'737''45''60'_5108 :: Integer -> T__'8804'__22 -> T__'8804'__22 -> T__'8804'__22
du_'8760''45'mono'737''45''60'_5108 Integer
v0 T__'8804'__22
v1 T__'8804'__22
v2
  = case Integer -> Integer
forall a b. a -> b
coe Integer
v0 of
      Integer
0 -> T__'8804'__22 -> T__'8804'__22
forall a b. a -> b
coe T__'8804'__22
v1
      Integer
_ -> let v3 :: Integer
v3 = Integer -> Integer -> Integer
subInt (Integer -> Integer
forall a b. a -> b
coe Integer
v0) (Integer -> Integer
forall a b. a -> b
coe (Integer
1 :: Integer)) in
           Any -> T__'8804'__22
forall a b. a -> b
coe
             (case T__'8804'__22 -> T__'8804'__22
forall a b. a -> b
coe T__'8804'__22
v1 of
                MAlonzo.Code.Data.Nat.Base.C_s'8804's_34 T__'8804'__22
v6
                  -> case T__'8804'__22 -> T__'8804'__22
forall a b. a -> b
coe T__'8804'__22
v2 of
                       MAlonzo.Code.Data.Nat.Base.C_s'8804's_34 T__'8804'__22
v9
                         -> (Integer -> T__'8804'__22 -> T__'8804'__22 -> T__'8804'__22)
-> Any -> Any -> Any -> Any
forall a b. a -> b
coe
                              Integer -> T__'8804'__22 -> T__'8804'__22 -> T__'8804'__22
du_'8760''45'mono'737''45''60'_5108 (Integer -> Any
forall a b. a -> b
coe Integer
v3) (T__'8804'__22 -> Any
forall a b. a -> b
coe T__'8804'__22
v6) (T__'8804'__22 -> Any
forall a b. a -> b
coe T__'8804'__22
v9)
                       T__'8804'__22
_ -> Any
forall a. a
MAlonzo.RTE.mazUnreachableError
                T__'8804'__22
_ -> Any
forall a. a
MAlonzo.RTE.mazUnreachableError)
-- Data.Nat.Properties.∸-monoʳ-<
d_'8760''45'mono'691''45''60'_5134 ::
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_'8760''45'mono'691''45''60'_5134 :: Integer
-> Integer
-> Integer
-> T__'8804'__22
-> T__'8804'__22
-> T__'8804'__22
d_'8760''45'mono'691''45''60'_5134 Integer
v0 Integer
v1 Integer
v2 T__'8804'__22
v3 T__'8804'__22
v4
  = let v5 :: Integer
v5 = Integer -> Integer -> Integer
subInt (Integer -> Integer
forall a b. a -> b
coe Integer
v1) (Integer -> Integer
forall a b. a -> b
coe (Integer
1 :: Integer)) in
    Any -> T__'8804'__22
forall a b. a -> b
coe
      (case Integer -> Integer
forall a b. a -> b
coe Integer
v2 of
         Integer
0 -> (Any -> Any -> Any) -> Any -> Any -> Any
forall a b. a -> b
coe
                Any -> Any -> Any
forall a b. a -> b -> b
seq (T__'8804'__22 -> Any
forall a b. a -> b
coe T__'8804'__22
v3)
                ((Any -> Any -> Any) -> Any -> Any -> Any
forall a b. a -> b
coe
                   Any -> Any -> Any
forall a b. a -> b -> b
seq (T__'8804'__22 -> Any
forall a b. a -> b
coe T__'8804'__22
v4)
                   ((T__'8804'__22 -> T__'8804'__22) -> T__'8804'__22 -> Any
forall a b. a -> b
coe
                      T__'8804'__22 -> T__'8804'__22
MAlonzo.Code.Data.Nat.Base.C_s'8804's_34
                      (Integer -> Integer -> T__'8804'__22
d_m'8760'n'8804'm_5042
                         ((Integer -> Integer -> Integer) -> Any -> Any -> Integer
forall a b. a -> b
coe Integer -> Integer -> Integer
subInt (Integer -> Any
forall a b. a -> b
coe Integer
v0) (Integer -> Any
forall a b. a -> b
coe (Integer
1 :: Integer))) (Integer -> Integer
forall a b. a -> b
coe Integer
v5))))
         Integer
_ -> let v6 :: Integer
v6 = Integer -> Integer -> Integer
subInt (Integer -> Integer
forall a b. a -> b
coe Integer
v2) (Integer -> Integer
forall a b. a -> b
coe (Integer
1 :: Integer)) in
              Any -> Any
forall a b. a -> b
coe
                (case T__'8804'__22 -> T__'8804'__22
forall a b. a -> b
coe T__'8804'__22
v3 of
                   MAlonzo.Code.Data.Nat.Base.C_s'8804's_34 T__'8804'__22
v9
                     -> case T__'8804'__22 -> T__'8804'__22
forall a b. a -> b
coe T__'8804'__22
v4 of
                          MAlonzo.Code.Data.Nat.Base.C_s'8804's_34 T__'8804'__22
v12
                            -> let v13 :: Integer
v13 = Integer -> Integer -> Integer
subInt (Integer -> Integer
forall a b. a -> b
coe Integer
v0) (Integer -> Integer
forall a b. a -> b
coe (Integer
1 :: Integer)) in
                               Any -> Any
forall a b. a -> b
coe
                                 ((Integer
 -> Integer
 -> Integer
 -> T__'8804'__22
 -> T__'8804'__22
 -> T__'8804'__22)
-> Any -> Any -> Any -> Any -> Any -> Any
forall a b. a -> b
coe
                                    Integer
-> Integer
-> Integer
-> T__'8804'__22
-> T__'8804'__22
-> T__'8804'__22
d_'8760''45'mono'691''45''60'_5134 (Integer -> Any
forall a b. a -> b
coe Integer
v13) (Integer -> Any
forall a b. a -> b
coe Integer
v5) (Integer -> Any
forall a b. a -> b
coe Integer
v6)
                                    (T__'8804'__22 -> Any
forall a b. a -> b
coe T__'8804'__22
v9) (T__'8804'__22 -> Any
forall a b. a -> b
coe T__'8804'__22
v12))
                          T__'8804'__22
_ -> Any
forall a. a
MAlonzo.RTE.mazUnreachableError
                   T__'8804'__22
_ -> Any
forall a. a
MAlonzo.RTE.mazUnreachableError))
-- Data.Nat.Properties.∸-cancelʳ-≤
d_'8760''45'cancel'691''45''8804'_5156 ::
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_'8760''45'cancel'691''45''8804'_5156 :: Integer
-> Integer
-> Integer
-> T__'8804'__22
-> T__'8804'__22
-> T__'8804'__22
d_'8760''45'cancel'691''45''8804'_5156 ~Integer
v0 Integer
v1 ~Integer
v2 T__'8804'__22
v3 ~T__'8804'__22
v4
  = Integer -> T__'8804'__22 -> T__'8804'__22
du_'8760''45'cancel'691''45''8804'_5156 Integer
v1 T__'8804'__22
v3
du_'8760''45'cancel'691''45''8804'_5156 ::
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
du_'8760''45'cancel'691''45''8804'_5156 :: Integer -> T__'8804'__22 -> T__'8804'__22
du_'8760''45'cancel'691''45''8804'_5156 Integer
v0 T__'8804'__22
v1
  = case T__'8804'__22 -> T__'8804'__22
forall a b. a -> b
coe T__'8804'__22
v1 of
      T__'8804'__22
MAlonzo.Code.Data.Nat.Base.C_z'8804'n_26
        -> T__'8804'__22 -> T__'8804'__22
forall a b. a -> b
coe T__'8804'__22
MAlonzo.Code.Data.Nat.Base.C_z'8804'n_26
      MAlonzo.Code.Data.Nat.Base.C_s'8804's_34 T__'8804'__22
v4
        -> case Integer -> Integer
forall a b. a -> b
coe Integer
v0 of
             Integer
0 -> ((Any -> T_Irrelevant_20) -> Any) -> Any -> T__'8804'__22
forall a b. a -> b
coe
                    (Any -> T_Irrelevant_20) -> Any
MAlonzo.Code.Relation.Nullary.Negation.Core.du_contradiction_44
                    Any
forall a. a
erased
             Integer
_ -> let v5 :: Integer
v5 = Integer -> Integer -> Integer
subInt (Integer -> Integer
forall a b. a -> b
coe Integer
v0) (Integer -> Integer
forall a b. a -> b
coe (Integer
1 :: Integer)) in
                  Any -> T__'8804'__22
forall a b. a -> b
coe
                    ((T__'8804'__22 -> T__'8804'__22) -> Any -> Any
forall a b. a -> b
coe
                       T__'8804'__22 -> T__'8804'__22
MAlonzo.Code.Data.Nat.Base.C_s'8804's_34
                       ((Integer -> T__'8804'__22 -> T__'8804'__22) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> T__'8804'__22 -> T__'8804'__22
du_'8760''45'cancel'691''45''8804'_5156 (Integer -> Any
forall a b. a -> b
coe Integer
v5) (T__'8804'__22 -> Any
forall a b. a -> b
coe T__'8804'__22
v4)))
      T__'8804'__22
_ -> T__'8804'__22
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Data.Nat.Properties.∸-cancelʳ-<
d_'8760''45'cancel'691''45''60'_5176 ::
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_'8760''45'cancel'691''45''60'_5176 :: Integer -> Integer -> Integer -> T__'8804'__22 -> T__'8804'__22
d_'8760''45'cancel'691''45''60'_5176 Integer
v0 Integer
v1 ~Integer
v2 ~T__'8804'__22
v3
  = Integer -> Integer -> T__'8804'__22
du_'8760''45'cancel'691''45''60'_5176 Integer
v0 Integer
v1
du_'8760''45'cancel'691''45''60'_5176 ::
  Integer -> Integer -> MAlonzo.Code.Data.Nat.Base.T__'8804'__22
du_'8760''45'cancel'691''45''60'_5176 :: Integer -> Integer -> T__'8804'__22
du_'8760''45'cancel'691''45''60'_5176 Integer
v0 Integer
v1
  = case Integer -> Integer
forall a b. a -> b
coe Integer
v0 of
      Integer
0 -> ((Any -> T_Irrelevant_20) -> Any) -> Any -> T__'8804'__22
forall a b. a -> b
coe
             (Any -> T_Irrelevant_20) -> Any
MAlonzo.Code.Relation.Nullary.Negation.Core.du_contradiction_44
             Any
forall a. a
erased
      Integer
_ -> let v2 :: Integer
v2 = Integer -> Integer -> Integer
subInt (Integer -> Integer
forall a b. a -> b
coe Integer
v0) (Integer -> Integer
forall a b. a -> b
coe (Integer
1 :: Integer)) in
           Any -> T__'8804'__22
forall a b. a -> b
coe
             (case Integer -> Integer
forall a b. a -> b
coe Integer
v1 of
                Integer
0 -> T__'8804'__22 -> Any
forall a b. a -> b
coe T__'8804'__22
du_0'60'1'43'n_3074
                Integer
_ -> let v3 :: Integer
v3 = Integer -> Integer -> Integer
subInt (Integer -> Integer
forall a b. a -> b
coe Integer
v1) (Integer -> Integer
forall a b. a -> b
coe (Integer
1 :: Integer)) in
                     Any -> Any
forall a b. a -> b
coe
                       ((T__'8804'__22 -> T__'8804'__22) -> Any -> Any
forall a b. a -> b
coe
                          T__'8804'__22 -> T__'8804'__22
MAlonzo.Code.Data.Nat.Base.C_s'8804's_34
                          ((Integer -> Integer -> T__'8804'__22) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> T__'8804'__22
du_'8760''45'cancel'691''45''60'_5176 (Integer -> Any
forall a b. a -> b
coe Integer
v2) (Integer -> Any
forall a b. a -> b
coe Integer
v3))))
-- Data.Nat.Properties.∸-cancelˡ-≡
d_'8760''45'cancel'737''45''8801'_5196 ::
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8760''45'cancel'737''45''8801'_5196 :: Integer
-> Integer
-> Integer
-> T__'8804'__22
-> T__'8804'__22
-> T__'8801'__12
-> T__'8801'__12
d_'8760''45'cancel'737''45''8801'_5196 = Integer
-> Integer
-> Integer
-> T__'8804'__22
-> T__'8804'__22
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Nat.Properties.∸-cancelʳ-≡
d_'8760''45'cancel'691''45''8801'_5212 ::
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8760''45'cancel'691''45''8801'_5212 :: Integer
-> Integer
-> Integer
-> T__'8804'__22
-> T__'8804'__22
-> T__'8801'__12
-> T__'8801'__12
d_'8760''45'cancel'691''45''8801'_5212 = Integer
-> Integer
-> Integer
-> T__'8804'__22
-> T__'8804'__22
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Nat.Properties.m∸n≡0⇒m≤n
d_m'8760'n'8801'0'8658'm'8804'n_5222 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_m'8760'n'8801'0'8658'm'8804'n_5222 :: Integer -> Integer -> T__'8801'__12 -> T__'8804'__22
d_m'8760'n'8801'0'8658'm'8804'n_5222 Integer
v0 ~Integer
v1 ~T__'8801'__12
v2
  = Integer -> T__'8804'__22
du_m'8760'n'8801'0'8658'm'8804'n_5222 Integer
v0
du_m'8760'n'8801'0'8658'm'8804'n_5222 ::
  Integer -> MAlonzo.Code.Data.Nat.Base.T__'8804'__22
du_m'8760'n'8801'0'8658'm'8804'n_5222 :: Integer -> T__'8804'__22
du_m'8760'n'8801'0'8658'm'8804'n_5222 Integer
v0
  = case Integer -> Integer
forall a b. a -> b
coe Integer
v0 of
      Integer
0 -> T__'8804'__22 -> T__'8804'__22
forall a b. a -> b
coe T__'8804'__22
MAlonzo.Code.Data.Nat.Base.C_z'8804'n_26
      Integer
_ -> let v1 :: Integer
v1 = Integer -> Integer -> Integer
subInt (Integer -> Integer
forall a b. a -> b
coe Integer
v0) (Integer -> Integer
forall a b. a -> b
coe (Integer
1 :: Integer)) in
           Any -> T__'8804'__22
forall a b. a -> b
coe
             ((T__'8804'__22 -> T__'8804'__22) -> Any -> Any
forall a b. a -> b
coe
                T__'8804'__22 -> T__'8804'__22
MAlonzo.Code.Data.Nat.Base.C_s'8804's_34
                ((Integer -> T__'8804'__22) -> Any -> Any
forall a b. a -> b
coe Integer -> T__'8804'__22
du_m'8760'n'8801'0'8658'm'8804'n_5222 (Integer -> Any
forall a b. a -> b
coe Integer
v1)))
-- Data.Nat.Properties.m≤n⇒m∸n≡0
d_m'8804'n'8658'm'8760'n'8801'0_5230 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_m'8804'n'8658'm'8760'n'8801'0_5230 :: Integer -> Integer -> T__'8804'__22 -> T__'8801'__12
d_m'8804'n'8658'm'8760'n'8801'0_5230 = Integer -> Integer -> T__'8804'__22 -> T__'8801'__12
forall a. a
erased
-- Data.Nat.Properties.m<n⇒0<n∸m
d_m'60'n'8658'0'60'n'8760'm_5236 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_m'60'n'8658'0'60'n'8760'm_5236 :: Integer -> Integer -> T__'8804'__22 -> T__'8804'__22
d_m'60'n'8658'0'60'n'8760'm_5236 Integer
v0 ~Integer
v1 T__'8804'__22
v2
  = Integer -> T__'8804'__22 -> T__'8804'__22
du_m'60'n'8658'0'60'n'8760'm_5236 Integer
v0 T__'8804'__22
v2
du_m'60'n'8658'0'60'n'8760'm_5236 ::
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
du_m'60'n'8658'0'60'n'8760'm_5236 :: Integer -> T__'8804'__22 -> T__'8804'__22
du_m'60'n'8658'0'60'n'8760'm_5236 Integer
v0 T__'8804'__22
v1
  = case Integer -> Integer
forall a b. a -> b
coe Integer
v0 of
      Integer
0 -> T__'8804'__22 -> T__'8804'__22
forall a b. a -> b
coe T__'8804'__22
du_0'60'1'43'n_3074
      Integer
_ -> let v2 :: Integer
v2 = Integer -> Integer -> Integer
subInt (Integer -> Integer
forall a b. a -> b
coe Integer
v0) (Integer -> Integer
forall a b. a -> b
coe (Integer
1 :: Integer)) in
           Any -> T__'8804'__22
forall a b. a -> b
coe
             (case T__'8804'__22 -> T__'8804'__22
forall a b. a -> b
coe T__'8804'__22
v1 of
                MAlonzo.Code.Data.Nat.Base.C_s'8804's_34 T__'8804'__22
v5
                  -> (Integer -> T__'8804'__22 -> T__'8804'__22) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> T__'8804'__22 -> T__'8804'__22
du_m'60'n'8658'0'60'n'8760'm_5236 (Integer -> Any
forall a b. a -> b
coe Integer
v2) (T__'8804'__22 -> Any
forall a b. a -> b
coe T__'8804'__22
v5)
                T__'8804'__22
_ -> Any
forall a. a
MAlonzo.RTE.mazUnreachableError)
-- Data.Nat.Properties.m∸n≢0⇒n<m
d_m'8760'n'8802'0'8658'n'60'm_5246 ::
  Integer ->
  Integer ->
  (MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
   MAlonzo.Code.Data.Irrelevant.T_Irrelevant_20) ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_m'8760'n'8802'0'8658'n'60'm_5246 :: Integer
-> Integer -> (T__'8801'__12 -> T_Irrelevant_20) -> T__'8804'__22
d_m'8760'n'8802'0'8658'n'60'm_5246 Integer
v0 Integer
v1 ~T__'8801'__12 -> T_Irrelevant_20
v2
  = Integer -> Integer -> T__'8804'__22
du_m'8760'n'8802'0'8658'n'60'm_5246 Integer
v0 Integer
v1
du_m'8760'n'8802'0'8658'n'60'm_5246 ::
  Integer -> Integer -> MAlonzo.Code.Data.Nat.Base.T__'8804'__22
du_m'8760'n'8802'0'8658'n'60'm_5246 :: Integer -> Integer -> T__'8804'__22
du_m'8760'n'8802'0'8658'n'60'm_5246 Integer
v0 Integer
v1
  = let v2 :: t
v2
          = ((Any -> Any) -> (Any -> Any) -> T_Dec_20 -> T_Dec_20)
-> (Any -> Any) -> Any -> Any -> t
forall a b. a -> b
coe
              (Any -> Any) -> (Any -> Any) -> T_Dec_20 -> T_Dec_20
MAlonzo.Code.Relation.Nullary.Decidable.Core.du_map'8242'_168
              (\ Any
v2 ->
                 (Integer -> T__'8804'__22) -> Any -> Any
forall a b. a -> b
coe
                   Integer -> T__'8804'__22
du_'8804''7495''8658''8804'_2746
                   ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> Integer
addInt (Integer -> Any
forall a b. a -> b
coe (Integer
1 :: Integer)) (Integer -> Any
forall a b. a -> b
coe Integer
v1)))
              ((T__'8804'__22 -> Any) -> Any
forall a b. a -> b
coe T__'8804'__22 -> Any
du_'8804''8658''8804''7495'_2758)
              ((Bool -> T_Dec_20) -> Any -> Any
forall a b. a -> b
coe
                 Bool -> T_Dec_20
MAlonzo.Code.Relation.Nullary.Decidable.Core.d_T'63'_66
                 ((Integer -> Integer -> Bool) -> Any -> Any -> Any
forall a b. a -> b
coe
                    Integer -> Integer -> Bool
MAlonzo.Code.Data.Nat.Base.d__'8804''7495'__14
                    ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> Integer
addInt (Integer -> Any
forall a b. a -> b
coe (Integer
1 :: Integer)) (Integer -> Any
forall a b. a -> b
coe Integer
v1)) (Integer -> Any
forall a b. a -> b
coe Integer
v0))) in
    Any -> T__'8804'__22
forall a b. a -> b
coe
      (case Any -> T_Dec_20
forall a b. a -> b
coe Any
forall a. a
v2 of
         MAlonzo.Code.Relation.Nullary.Decidable.Core.C__because__32 Bool
v3 T_Reflects_16
v4
           -> if Bool -> Bool
forall a b. a -> b
coe Bool
v3
                then case T_Reflects_16 -> T_Reflects_16
forall a b. a -> b
coe T_Reflects_16
v4 of
                       MAlonzo.Code.Relation.Nullary.Reflects.C_of'696'_22 Any
v5 -> Any -> Any
forall a b. a -> b
coe Any
v5
                       T_Reflects_16
_ -> Any
forall a. a
MAlonzo.RTE.mazUnreachableError
                else (Any -> Any -> Any) -> Any -> Any -> Any
forall a b. a -> b
coe
                       Any -> Any -> Any
forall a b. a -> b -> b
seq (T_Reflects_16 -> Any
forall a b. a -> b
coe T_Reflects_16
v4)
                       (((Any -> T_Irrelevant_20) -> Any) -> Any -> Any
forall a b. a -> b
coe
                          (Any -> T_Irrelevant_20) -> Any
MAlonzo.Code.Relation.Nullary.Negation.Core.du_contradiction_44
                          Any
forall a. a
erased)
         T_Dec_20
_ -> Any
forall a. a
MAlonzo.RTE.mazUnreachableError)
-- Data.Nat.Properties.m>n⇒m∸n≢0
d_m'62'n'8658'm'8760'n'8802'0_5274 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Data.Irrelevant.T_Irrelevant_20
d_m'62'n'8658'm'8760'n'8802'0_5274 :: Integer
-> Integer -> T__'8804'__22 -> T__'8801'__12 -> T_Irrelevant_20
d_m'62'n'8658'm'8760'n'8802'0_5274 = Integer
-> Integer -> T__'8804'__22 -> T__'8801'__12 -> T_Irrelevant_20
forall a. a
erased
-- Data.Nat.Properties.m≤n⇒n∸m≤n
d_m'8804'n'8658'n'8760'm'8804'n_5280 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_m'8804'n'8658'n'8760'm'8804'n_5280 :: Integer -> Integer -> T__'8804'__22 -> T__'8804'__22
d_m'8804'n'8658'n'8760'm'8804'n_5280 ~Integer
v0 Integer
v1 T__'8804'__22
v2
  = Integer -> T__'8804'__22 -> T__'8804'__22
du_m'8804'n'8658'n'8760'm'8804'n_5280 Integer
v1 T__'8804'__22
v2
du_m'8804'n'8658'n'8760'm'8804'n_5280 ::
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
du_m'8804'n'8658'n'8760'm'8804'n_5280 :: Integer -> T__'8804'__22 -> T__'8804'__22
du_m'8804'n'8658'n'8760'm'8804'n_5280 Integer
v0 T__'8804'__22
v1
  = case T__'8804'__22 -> T__'8804'__22
forall a b. a -> b
coe T__'8804'__22
v1 of
      T__'8804'__22
MAlonzo.Code.Data.Nat.Base.C_z'8804'n_26
        -> (Integer -> T__'8804'__22) -> Any -> T__'8804'__22
forall a b. a -> b
coe
             Integer -> T__'8804'__22
d_'8804''45'refl_2776
             ((Integer -> Integer -> Integer) -> Integer -> Integer -> Any
forall a b. a -> b
coe Integer -> Integer -> Integer
MAlonzo.Code.Agda.Builtin.Nat.d__'45'__22 Integer
v0 (Integer
0 :: Integer))
      MAlonzo.Code.Data.Nat.Base.C_s'8804's_34 T__'8804'__22
v4
        -> let v5 :: Integer
v5 = Integer -> Integer -> Integer
subInt (Integer -> Integer
forall a b. a -> b
coe Integer
v0) (Integer -> Integer
forall a b. a -> b
coe (Integer
1 :: Integer)) in
           Any -> T__'8804'__22
forall a b. a -> b
coe ((Integer -> T__'8804'__22 -> T__'8804'__22) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> T__'8804'__22 -> T__'8804'__22
du_m'8804'n'8658'n'8760'm'8804'n_5280 (Integer -> Any
forall a b. a -> b
coe Integer
v5) (T__'8804'__22 -> Any
forall a b. a -> b
coe T__'8804'__22
v4))
      T__'8804'__22
_ -> T__'8804'__22
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Data.Nat.Properties.+-∸-comm
d_'43''45''8760''45'comm_5290 ::
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'43''45''8760''45'comm_5290 :: Integer -> Integer -> Integer -> T__'8804'__22 -> T__'8801'__12
d_'43''45''8760''45'comm_5290 = Integer -> Integer -> Integer -> T__'8804'__22 -> T__'8801'__12
forall a. a
erased
-- Data.Nat.Properties.∸-+-assoc
d_'8760''45''43''45'assoc_5308 ::
  Integer ->
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8760''45''43''45'assoc_5308 :: Integer -> Integer -> Integer -> T__'8801'__12
d_'8760''45''43''45'assoc_5308 = Integer -> Integer -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Nat.Properties.+-∸-assoc
d_'43''45''8760''45'assoc_5332 ::
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'43''45''8760''45'assoc_5332 :: Integer -> Integer -> Integer -> T__'8804'__22 -> T__'8801'__12
d_'43''45''8760''45'assoc_5332 = Integer -> Integer -> Integer -> T__'8804'__22 -> T__'8801'__12
forall a. a
erased
-- Data.Nat.Properties.m≤n+o⇒m∸n≤o
d_m'8804'n'43'o'8658'm'8760'n'8804'o_5354 ::
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_m'8804'n'43'o'8658'm'8760'n'8804'o_5354 :: Integer -> Integer -> Integer -> T__'8804'__22 -> T__'8804'__22
d_m'8804'n'43'o'8658'm'8760'n'8804'o_5354 Integer
v0 Integer
v1 ~Integer
v2 T__'8804'__22
v3
  = Integer -> Integer -> T__'8804'__22 -> T__'8804'__22
du_m'8804'n'43'o'8658'm'8760'n'8804'o_5354 Integer
v0 Integer
v1 T__'8804'__22
v3
du_m'8804'n'43'o'8658'm'8760'n'8804'o_5354 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
du_m'8804'n'43'o'8658'm'8760'n'8804'o_5354 :: Integer -> Integer -> T__'8804'__22 -> T__'8804'__22
du_m'8804'n'43'o'8658'm'8760'n'8804'o_5354 Integer
v0 Integer
v1 T__'8804'__22
v2
  = case Integer -> Integer
forall a b. a -> b
coe Integer
v1 of
      Integer
0 -> T__'8804'__22 -> T__'8804'__22
forall a b. a -> b
coe T__'8804'__22
v2
      Integer
_ -> let v3 :: Integer
v3 = Integer -> Integer -> Integer
subInt (Integer -> Integer
forall a b. a -> b
coe Integer
v1) (Integer -> Integer
forall a b. a -> b
coe (Integer
1 :: Integer)) in
           Any -> T__'8804'__22
forall a b. a -> b
coe
             (case Integer -> Integer
forall a b. a -> b
coe Integer
v0 of
                Integer
0 -> T__'8804'__22 -> Any
forall a b. a -> b
coe T__'8804'__22
MAlonzo.Code.Data.Nat.Base.C_z'8804'n_26
                Integer
_ -> let v4 :: Integer
v4 = Integer -> Integer -> Integer
subInt (Integer -> Integer
forall a b. a -> b
coe Integer
v0) (Integer -> Integer
forall a b. a -> b
coe (Integer
1 :: Integer)) in
                     Any -> Any
forall a b. a -> b
coe
                       ((Integer -> Integer -> T__'8804'__22 -> T__'8804'__22)
-> Any -> Any -> Any -> Any
forall a b. a -> b
coe
                          Integer -> Integer -> T__'8804'__22 -> T__'8804'__22
du_m'8804'n'43'o'8658'm'8760'n'8804'o_5354 (Integer -> Any
forall a b. a -> b
coe Integer
v4) (Integer -> Any
forall a b. a -> b
coe Integer
v3)
                          ((T__'8804'__22 -> T__'8804'__22) -> Any -> Any
forall a b. a -> b
coe
                             T__'8804'__22 -> T__'8804'__22
MAlonzo.Code.Data.Nat.Base.du_s'8804's'8315''185'_62 (T__'8804'__22 -> Any
forall a b. a -> b
coe T__'8804'__22
v2))))
-- Data.Nat.Properties.m<n+o⇒m∸n<o
d_m'60'n'43'o'8658'm'8760'n'60'o_5374 ::
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T_NonZero_112 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_m'60'n'43'o'8658'm'8760'n'60'o_5374 :: Integer
-> Integer
-> Integer
-> T_NonZero_112
-> T__'8804'__22
-> T__'8804'__22
d_m'60'n'43'o'8658'm'8760'n'60'o_5374 Integer
v0 Integer
v1 ~Integer
v2 ~T_NonZero_112
v3 T__'8804'__22
v4
  = Integer -> Integer -> T__'8804'__22 -> T__'8804'__22
du_m'60'n'43'o'8658'm'8760'n'60'o_5374 Integer
v0 Integer
v1 T__'8804'__22
v4
du_m'60'n'43'o'8658'm'8760'n'60'o_5374 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
du_m'60'n'43'o'8658'm'8760'n'60'o_5374 :: Integer -> Integer -> T__'8804'__22 -> T__'8804'__22
du_m'60'n'43'o'8658'm'8760'n'60'o_5374 Integer
v0 Integer
v1 T__'8804'__22
v2
  = case Integer -> Integer
forall a b. a -> b
coe Integer
v1 of
      Integer
0 -> T__'8804'__22 -> T__'8804'__22
forall a b. a -> b
coe T__'8804'__22
v2
      Integer
_ -> let v3 :: Integer
v3 = Integer -> Integer -> Integer
subInt (Integer -> Integer
forall a b. a -> b
coe Integer
v1) (Integer -> Integer
forall a b. a -> b
coe (Integer
1 :: Integer)) in
           Any -> T__'8804'__22
forall a b. a -> b
coe
             (case Integer -> Integer
forall a b. a -> b
coe Integer
v0 of
                Integer
0 -> (T__'8804'__22 -> T__'8804'__22) -> Any -> Any
forall a b. a -> b
coe
                       T__'8804'__22 -> T__'8804'__22
MAlonzo.Code.Data.Nat.Base.C_s'8804's_34
                       (T__'8804'__22 -> Any
forall a b. a -> b
coe T__'8804'__22
MAlonzo.Code.Data.Nat.Base.C_z'8804'n_26)
                Integer
_ -> let v4 :: Integer
v4 = Integer -> Integer -> Integer
subInt (Integer -> Integer
forall a b. a -> b
coe Integer
v0) (Integer -> Integer
forall a b. a -> b
coe (Integer
1 :: Integer)) in
                     Any -> Any
forall a b. a -> b
coe
                       ((Integer -> Integer -> T__'8804'__22 -> T__'8804'__22)
-> Any -> Any -> Any -> Any
forall a b. a -> b
coe
                          Integer -> Integer -> T__'8804'__22 -> T__'8804'__22
du_m'60'n'43'o'8658'm'8760'n'60'o_5374 (Integer -> Any
forall a b. a -> b
coe Integer
v4) (Integer -> Any
forall a b. a -> b
coe Integer
v3)
                          ((T__'8804'__22 -> T__'8804'__22) -> Any -> Any
forall a b. a -> b
coe T__'8804'__22 -> T__'8804'__22
MAlonzo.Code.Data.Nat.Base.du_s'60's'8315''185'_70 (T__'8804'__22 -> Any
forall a b. a -> b
coe T__'8804'__22
v2))))
-- Data.Nat.Properties.m+n≤o⇒m≤o∸n
d_m'43'n'8804'o'8658'm'8804'o'8760'n_5398 ::
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_m'43'n'8804'o'8658'm'8804'o'8760'n_5398 :: Integer -> Integer -> Integer -> T__'8804'__22 -> T__'8804'__22
d_m'43'n'8804'o'8658'm'8804'o'8760'n_5398 Integer
v0 ~Integer
v1 ~Integer
v2 T__'8804'__22
v3
  = Integer -> T__'8804'__22 -> T__'8804'__22
du_m'43'n'8804'o'8658'm'8804'o'8760'n_5398 Integer
v0 T__'8804'__22
v3
du_m'43'n'8804'o'8658'm'8804'o'8760'n_5398 ::
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
du_m'43'n'8804'o'8658'm'8804'o'8760'n_5398 :: Integer -> T__'8804'__22 -> T__'8804'__22
du_m'43'n'8804'o'8658'm'8804'o'8760'n_5398 Integer
v0 T__'8804'__22
v1
  = case Integer -> Integer
forall a b. a -> b
coe Integer
v0 of
      Integer
0 -> T__'8804'__22 -> T__'8804'__22
forall a b. a -> b
coe T__'8804'__22
MAlonzo.Code.Data.Nat.Base.C_z'8804'n_26
      Integer
_ -> let v2 :: Integer
v2 = Integer -> Integer -> Integer
subInt (Integer -> Integer
forall a b. a -> b
coe Integer
v0) (Integer -> Integer
forall a b. a -> b
coe (Integer
1 :: Integer)) in
           Any -> T__'8804'__22
forall a b. a -> b
coe
             (case T__'8804'__22 -> T__'8804'__22
forall a b. a -> b
coe T__'8804'__22
v1 of
                MAlonzo.Code.Data.Nat.Base.C_s'8804's_34 T__'8804'__22
v5
                  -> (T__'8804'__22 -> T__'8804'__22) -> Any -> Any
forall a b. a -> b
coe
                       T__'8804'__22 -> T__'8804'__22
MAlonzo.Code.Data.Nat.Base.C_s'8804's_34
                       ((Integer -> T__'8804'__22 -> T__'8804'__22) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> T__'8804'__22 -> T__'8804'__22
du_m'43'n'8804'o'8658'm'8804'o'8760'n_5398 (Integer -> Any
forall a b. a -> b
coe Integer
v2) (T__'8804'__22 -> Any
forall a b. a -> b
coe T__'8804'__22
v5))
                T__'8804'__22
_ -> Any
forall a. a
MAlonzo.RTE.mazUnreachableError)
-- Data.Nat.Properties.m≤o∸n⇒m+n≤o
d_m'8804'o'8760'n'8658'm'43'n'8804'o_5418 ::
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_m'8804'o'8760'n'8658'm'43'n'8804'o_5418 :: Integer
-> Integer
-> Integer
-> T__'8804'__22
-> T__'8804'__22
-> T__'8804'__22
d_m'8804'o'8760'n'8658'm'43'n'8804'o_5418 ~Integer
v0 ~Integer
v1 ~Integer
v2 T__'8804'__22
v3 T__'8804'__22
v4
  = T__'8804'__22 -> T__'8804'__22 -> T__'8804'__22
du_m'8804'o'8760'n'8658'm'43'n'8804'o_5418 T__'8804'__22
v3 T__'8804'__22
v4
du_m'8804'o'8760'n'8658'm'43'n'8804'o_5418 ::
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
du_m'8804'o'8760'n'8658'm'43'n'8804'o_5418 :: T__'8804'__22 -> T__'8804'__22 -> T__'8804'__22
du_m'8804'o'8760'n'8658'm'43'n'8804'o_5418 T__'8804'__22
v0 T__'8804'__22
v1
  = case T__'8804'__22 -> T__'8804'__22
forall a b. a -> b
coe T__'8804'__22
v0 of
      T__'8804'__22
MAlonzo.Code.Data.Nat.Base.C_z'8804'n_26 -> T__'8804'__22 -> T__'8804'__22
forall a b. a -> b
coe T__'8804'__22
v1
      MAlonzo.Code.Data.Nat.Base.C_s'8804's_34 T__'8804'__22
v4
        -> (T__'8804'__22 -> T__'8804'__22) -> Any -> T__'8804'__22
forall a b. a -> b
coe
             T__'8804'__22 -> T__'8804'__22
MAlonzo.Code.Data.Nat.Base.C_s'8804's_34
             ((T__'8804'__22 -> T__'8804'__22 -> T__'8804'__22)
-> Any -> Any -> Any
forall a b. a -> b
coe T__'8804'__22 -> T__'8804'__22 -> T__'8804'__22
du_m'8804'o'8760'n'8658'm'43'n'8804'o_5418 (T__'8804'__22 -> Any
forall a b. a -> b
coe T__'8804'__22
v4) (T__'8804'__22 -> Any
forall a b. a -> b
coe T__'8804'__22
v1))
      T__'8804'__22
_ -> T__'8804'__22
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Data.Nat.Properties.m≤n+m∸n
d_m'8804'n'43'm'8760'n_5444 ::
  Integer -> Integer -> MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_m'8804'n'43'm'8760'n_5444 :: Integer -> Integer -> T__'8804'__22
d_m'8804'n'43'm'8760'n_5444 Integer
v0 Integer
v1
  = case Integer -> Integer
forall a b. a -> b
coe Integer
v0 of
      Integer
0 -> T__'8804'__22 -> T__'8804'__22
forall a b. a -> b
coe T__'8804'__22
MAlonzo.Code.Data.Nat.Base.C_z'8804'n_26
      Integer
_ -> let v2 :: Integer
v2 = Integer -> Integer -> Integer
subInt (Integer -> Integer
forall a b. a -> b
coe Integer
v0) (Integer -> Integer
forall a b. a -> b
coe (Integer
1 :: Integer)) in
           Any -> T__'8804'__22
forall a b. a -> b
coe
             (case Integer -> Integer
forall a b. a -> b
coe Integer
v1 of
                Integer
0 -> (Integer -> T__'8804'__22) -> Any -> Any
forall a b. a -> b
coe Integer -> T__'8804'__22
d_'8804''45'refl_2776 (Integer -> Any
forall a b. a -> b
coe Integer
v0)
                Integer
_ -> let v3 :: Integer
v3 = Integer -> Integer -> Integer
subInt (Integer -> Integer
forall a b. a -> b
coe Integer
v1) (Integer -> Integer
forall a b. a -> b
coe (Integer
1 :: Integer)) in
                     Any -> Any
forall a b. a -> b
coe
                       ((T__'8804'__22 -> T__'8804'__22) -> T__'8804'__22 -> Any
forall a b. a -> b
coe
                          T__'8804'__22 -> T__'8804'__22
MAlonzo.Code.Data.Nat.Base.C_s'8804's_34
                          (Integer -> Integer -> T__'8804'__22
d_m'8804'n'43'm'8760'n_5444 (Integer -> Integer
forall a b. a -> b
coe Integer
v2) (Integer -> Integer
forall a b. a -> b
coe Integer
v3))))
-- Data.Nat.Properties.m+n∸n≡m
d_m'43'n'8760'n'8801'm_5458 ::
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_m'43'n'8760'n'8801'm_5458 :: Integer -> Integer -> T__'8801'__12
d_m'43'n'8760'n'8801'm_5458 = Integer -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Nat.Properties.m+n∸m≡n
d_m'43'n'8760'm'8801'n_5470 ::
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_m'43'n'8760'm'8801'n_5470 :: Integer -> Integer -> T__'8801'__12
d_m'43'n'8760'm'8801'n_5470 = Integer -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Nat.Properties.m+[n∸m]≡n
d_m'43''91'n'8760'm'93''8801'n_5478 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_m'43''91'n'8760'm'93''8801'n_5478 :: Integer -> Integer -> T__'8804'__22 -> T__'8801'__12
d_m'43''91'n'8760'm'93''8801'n_5478 = Integer -> Integer -> T__'8804'__22 -> T__'8801'__12
forall a. a
erased
-- Data.Nat.Properties.m∸n+n≡m
d_m'8760'n'43'n'8801'm_5492 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_m'8760'n'43'n'8801'm_5492 :: Integer -> Integer -> T__'8804'__22 -> T__'8801'__12
d_m'8760'n'43'n'8801'm_5492 = Integer -> Integer -> T__'8804'__22 -> T__'8801'__12
forall a. a
erased
-- Data.Nat.Properties.m∸[m∸n]≡n
d_m'8760''91'm'8760'n'93''8801'n_5504 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_m'8760''91'm'8760'n'93''8801'n_5504 :: Integer -> Integer -> T__'8804'__22 -> T__'8801'__12
d_m'8760''91'm'8760'n'93''8801'n_5504 = Integer -> Integer -> T__'8804'__22 -> T__'8801'__12
forall a. a
erased
-- Data.Nat.Properties.[m+n]∸[m+o]≡n∸o
d_'91'm'43'n'93''8760''91'm'43'o'93''8801'n'8760'o_5520 ::
  Integer ->
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'91'm'43'n'93''8760''91'm'43'o'93''8801'n'8760'o_5520 :: Integer -> Integer -> Integer -> T__'8801'__12
d_'91'm'43'n'93''8760''91'm'43'o'93''8801'n'8760'o_5520 = Integer -> Integer -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Nat.Properties.*-distribʳ-∸
d_'42''45'distrib'691''45''8760'_5532 ::
  Integer ->
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'42''45'distrib'691''45''8760'_5532 :: Integer -> Integer -> Integer -> T__'8801'__12
d_'42''45'distrib'691''45''8760'_5532 = Integer -> Integer -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Nat.Properties.*-distribˡ-∸
d_'42''45'distrib'737''45''8760'_5552 ::
  Integer ->
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'42''45'distrib'737''45''8760'_5552 :: Integer -> Integer -> Integer -> T__'8801'__12
d_'42''45'distrib'737''45''8760'_5552 = Integer -> Integer -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Nat.Properties.*-distrib-∸
d_'42''45'distrib'45''8760'_5554 ::
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'42''45'distrib'45''8760'_5554 :: T_Σ_14
d_'42''45'distrib'45''8760'_5554
  = (Any -> Any -> T_Σ_14) -> Any -> Any -> T_Σ_14
forall a b. a -> b
coe Any -> Any -> T_Σ_14
MAlonzo.Code.Agda.Builtin.Sigma.C__'44'__32 Any
forall a. a
erased Any
forall a. a
erased
-- Data.Nat.Properties.even≢odd
d_even'8802'odd_5560 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Data.Irrelevant.T_Irrelevant_20
d_even'8802'odd_5560 :: Integer -> Integer -> T__'8801'__12 -> T_Irrelevant_20
d_even'8802'odd_5560 = Integer -> Integer -> T__'8801'__12 -> T_Irrelevant_20
forall a. a
erased
-- Data.Nat.Properties.m⊓n+n∸m≡n
d_m'8851'n'43'n'8760'm'8801'n_5576 ::
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_m'8851'n'43'n'8760'm'8801'n_5576 :: Integer -> Integer -> T__'8801'__12
d_m'8851'n'43'n'8760'm'8801'n_5576 = Integer -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Nat.Properties.[m∸n]⊓[n∸m]≡0
d_'91'm'8760'n'93''8851''91'n'8760'm'93''8801'0_5590 ::
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'91'm'8760'n'93''8851''91'n'8760'm'93''8801'0_5590 :: Integer -> Integer -> T__'8801'__12
d_'91'm'8760'n'93''8851''91'n'8760'm'93''8801'0_5590 = Integer -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Nat.Properties.∸-distribˡ-⊓-⊔
d_'8760''45'distrib'737''45''8851''45''8852'_5606 ::
  Integer ->
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8760''45'distrib'737''45''8851''45''8852'_5606 :: Integer -> Integer -> Integer -> T__'8801'__12
d_'8760''45'distrib'737''45''8851''45''8852'_5606 = Integer -> Integer -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Nat.Properties.∸-distribʳ-⊓
d_'8760''45'distrib'691''45''8851'_5614 ::
  Integer ->
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8760''45'distrib'691''45''8851'_5614 :: Integer -> Integer -> Integer -> T__'8801'__12
d_'8760''45'distrib'691''45''8851'_5614 = Integer -> Integer -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Nat.Properties.∸-distribˡ-⊔-⊓
d_'8760''45'distrib'737''45''8852''45''8851'_5628 ::
  Integer ->
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8760''45'distrib'737''45''8852''45''8851'_5628 :: Integer -> Integer -> Integer -> T__'8801'__12
d_'8760''45'distrib'737''45''8852''45''8851'_5628 = Integer -> Integer -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Nat.Properties.∸-distribʳ-⊔
d_'8760''45'distrib'691''45''8852'_5636 ::
  Integer ->
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8760''45'distrib'691''45''8852'_5636 :: Integer -> Integer -> Integer -> T__'8801'__12
d_'8760''45'distrib'691''45''8852'_5636 = Integer -> Integer -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Nat.Properties.pred[n]≤n
d_pred'91'n'93''8804'n_5644 ::
  Integer -> MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_pred'91'n'93''8804'n_5644 :: Integer -> T__'8804'__22
d_pred'91'n'93''8804'n_5644 Integer
v0
  = case Integer -> Integer
forall a b. a -> b
coe Integer
v0 of
      Integer
0 -> T__'8804'__22 -> T__'8804'__22
forall a b. a -> b
coe T__'8804'__22
MAlonzo.Code.Data.Nat.Base.C_z'8804'n_26
      Integer
_ -> let v1 :: Integer
v1 = Integer -> Integer -> Integer
subInt (Integer -> Integer
forall a b. a -> b
coe Integer
v0) (Integer -> Integer
forall a b. a -> b
coe (Integer
1 :: Integer)) in
           Any -> T__'8804'__22
forall a b. a -> b
coe ((Integer -> T__'8804'__22) -> Any -> Any
forall a b. a -> b
coe Integer -> T__'8804'__22
d_n'8804'1'43'n_2844 (Integer -> Any
forall a b. a -> b
coe Integer
v1))
-- Data.Nat.Properties.≤pred⇒≤
d_'8804'pred'8658''8804'_5648 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_'8804'pred'8658''8804'_5648 :: Integer -> Integer -> T__'8804'__22 -> T__'8804'__22
d_'8804'pred'8658''8804'_5648 ~Integer
v0 Integer
v1 T__'8804'__22
v2
  = Integer -> T__'8804'__22 -> T__'8804'__22
du_'8804'pred'8658''8804'_5648 Integer
v1 T__'8804'__22
v2
du_'8804'pred'8658''8804'_5648 ::
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
du_'8804'pred'8658''8804'_5648 :: Integer -> T__'8804'__22 -> T__'8804'__22
du_'8804'pred'8658''8804'_5648 Integer
v0 T__'8804'__22
v1 = (Any -> Any -> Any) -> Any -> Any -> T__'8804'__22
forall a b. a -> b
coe Any -> Any -> Any
forall a b. a -> b -> b
seq (Integer -> Any
forall a b. a -> b
coe Integer
v0) (T__'8804'__22 -> Any
forall a b. a -> b
coe T__'8804'__22
v1)
-- Data.Nat.Properties.≤⇒pred≤
d_'8804''8658'pred'8804'_5656 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_'8804''8658'pred'8804'_5656 :: Integer -> Integer -> T__'8804'__22 -> T__'8804'__22
d_'8804''8658'pred'8804'_5656 Integer
v0 ~Integer
v1 T__'8804'__22
v2
  = Integer -> T__'8804'__22 -> T__'8804'__22
du_'8804''8658'pred'8804'_5656 Integer
v0 T__'8804'__22
v2
du_'8804''8658'pred'8804'_5656 ::
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
du_'8804''8658'pred'8804'_5656 :: Integer -> T__'8804'__22 -> T__'8804'__22
du_'8804''8658'pred'8804'_5656 Integer
v0 T__'8804'__22
v1
  = case Integer -> Integer
forall a b. a -> b
coe Integer
v0 of
      Integer
0 -> T__'8804'__22 -> T__'8804'__22
forall a b. a -> b
coe T__'8804'__22
v1
      Integer
_ -> let v2 :: Integer
v2 = Integer -> Integer -> Integer
subInt (Integer -> Integer
forall a b. a -> b
coe Integer
v0) (Integer -> Integer
forall a b. a -> b
coe (Integer
1 :: Integer)) in
           Any -> T__'8804'__22
forall a b. a -> b
coe
             ((T__'8804'__22 -> T__'8804'__22 -> T__'8804'__22)
-> Any -> Any -> Any
forall a b. a -> b
coe
                T__'8804'__22 -> T__'8804'__22 -> T__'8804'__22
du_'8804''45'trans_2784 ((Integer -> T__'8804'__22) -> Any -> Any
forall a b. a -> b
coe Integer -> T__'8804'__22
d_n'8804'1'43'n_2844 (Integer -> Any
forall a b. a -> b
coe Integer
v2))
                (T__'8804'__22 -> Any
forall a b. a -> b
coe T__'8804'__22
v1))
-- Data.Nat.Properties.<⇒≤pred
d_'60''8658''8804'pred_5664 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_'60''8658''8804'pred_5664 :: Integer -> Integer -> T__'8804'__22 -> T__'8804'__22
d_'60''8658''8804'pred_5664 ~Integer
v0 ~Integer
v1 T__'8804'__22
v2
  = T__'8804'__22 -> T__'8804'__22
du_'60''8658''8804'pred_5664 T__'8804'__22
v2
du_'60''8658''8804'pred_5664 ::
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
du_'60''8658''8804'pred_5664 :: T__'8804'__22 -> T__'8804'__22
du_'60''8658''8804'pred_5664 T__'8804'__22
v0
  = case T__'8804'__22 -> T__'8804'__22
forall a b. a -> b
coe T__'8804'__22
v0 of
      MAlonzo.Code.Data.Nat.Base.C_s'8804's_34 T__'8804'__22
v3 -> T__'8804'__22 -> T__'8804'__22
forall a b. a -> b
coe T__'8804'__22
v3
      T__'8804'__22
_ -> T__'8804'__22
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Data.Nat.Properties.suc-pred
d_suc'45'pred_5672 ::
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T_NonZero_112 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_suc'45'pred_5672 :: Integer -> T_NonZero_112 -> T__'8801'__12
d_suc'45'pred_5672 = Integer -> T_NonZero_112 -> T__'8801'__12
forall a. a
erased
-- Data.Nat.Properties.pred-mono-≤
d_pred'45'mono'45''8804'_5676 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_pred'45'mono'45''8804'_5676 :: Integer -> Integer -> T__'8804'__22 -> T__'8804'__22
d_pred'45'mono'45''8804'_5676 Integer
v0 ~Integer
v1 T__'8804'__22
v2
  = Integer -> T__'8804'__22 -> T__'8804'__22
du_pred'45'mono'45''8804'_5676 Integer
v0 T__'8804'__22
v2
du_pred'45'mono'45''8804'_5676 ::
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
du_pred'45'mono'45''8804'_5676 :: Integer -> T__'8804'__22 -> T__'8804'__22
du_pred'45'mono'45''8804'_5676 Integer
v0 T__'8804'__22
v1
  = case Integer -> Integer
forall a b. a -> b
coe Integer
v0 of
      Integer
0 -> T__'8804'__22 -> T__'8804'__22
forall a b. a -> b
coe T__'8804'__22
MAlonzo.Code.Data.Nat.Base.C_z'8804'n_26
      Integer
_ -> (T__'8804'__22 -> T__'8804'__22) -> Any -> T__'8804'__22
forall a b. a -> b
coe
             T__'8804'__22 -> T__'8804'__22
MAlonzo.Code.Data.Nat.Base.du_s'8804's'8315''185'_62 (T__'8804'__22 -> Any
forall a b. a -> b
coe T__'8804'__22
v1)
-- Data.Nat.Properties.pred-mono-<
d_pred'45'mono'45''60'_5680 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T_NonZero_112 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_pred'45'mono'45''60'_5680 :: Integer
-> Integer -> T_NonZero_112 -> T__'8804'__22 -> T__'8804'__22
d_pred'45'mono'45''60'_5680 Integer
v0 Integer
v1 ~T_NonZero_112
v2
  = Integer -> Integer -> T__'8804'__22 -> T__'8804'__22
du_pred'45'mono'45''60'_5680 Integer
v0 Integer
v1
du_pred'45'mono'45''60'_5680 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
du_pred'45'mono'45''60'_5680 :: Integer -> Integer -> T__'8804'__22 -> T__'8804'__22
du_pred'45'mono'45''60'_5680 Integer
v0 Integer
v1
  = case Integer -> Integer
forall a b. a -> b
coe Integer
v0 of
      Integer
0 -> (Any -> Any) -> T__'8804'__22 -> T__'8804'__22
forall a b. a -> b
coe (\ Any
v2 -> Any
forall a. a
MAlonzo.RTE.mazUnreachableError)
      Integer
_ -> case Integer -> Integer
forall a b. a -> b
coe Integer
v1 of
             Integer
0 -> (Any -> Any) -> T__'8804'__22 -> T__'8804'__22
forall a b. a -> b
coe (\ Any
v2 -> Any
forall a. a
MAlonzo.RTE.mazUnreachableError)
             Integer
_ -> (T__'8804'__22 -> T__'8804'__22) -> T__'8804'__22 -> T__'8804'__22
forall a b. a -> b
coe T__'8804'__22 -> T__'8804'__22
MAlonzo.Code.Data.Nat.Base.du_s'60's'8315''185'_70
-- Data.Nat.Properties.pred-cancel-≤
d_pred'45'cancel'45''8804'_5682 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Sum.Base.T__'8846'__30
d_pred'45'cancel'45''8804'_5682 :: Integer -> Integer -> T__'8804'__22 -> T__'8846'__30
d_pred'45'cancel'45''8804'_5682 Integer
v0 Integer
v1 T__'8804'__22
v2
  = case Integer -> Integer
forall a b. a -> b
coe Integer
v0 of
      Integer
0 -> (Any -> Any -> Any) -> Any -> Any -> T__'8846'__30
forall a b. a -> b
coe
             Any -> Any -> Any
forall a b. a -> b -> b
seq (Integer -> Any
forall a b. a -> b
coe Integer
v1)
             ((Any -> T__'8846'__30) -> Any -> Any
forall a b. a -> b
coe
                Any -> T__'8846'__30
MAlonzo.Code.Data.Sum.Base.C_inj'8322'_42
                (T__'8804'__22 -> Any
forall a b. a -> b
coe T__'8804'__22
MAlonzo.Code.Data.Nat.Base.C_z'8804'n_26))
      Integer
_ -> case Integer -> Integer
forall a b. a -> b
coe Integer
v1 of
             Integer
0 -> (Any -> Any -> Any) -> Any -> Any -> T__'8846'__30
forall a b. a -> b
coe
                    Any -> Any -> Any
forall a b. a -> b -> b
seq (T__'8804'__22 -> Any
forall a b. a -> b
coe T__'8804'__22
v2)
                    ((Any -> T__'8846'__30) -> Any -> Any
forall a b. a -> b
coe
                       Any -> T__'8846'__30
MAlonzo.Code.Data.Sum.Base.C_inj'8321'_38
                       ((Any -> Any -> T_Σ_14) -> Any -> Any -> Any
forall a b. a -> b
coe Any -> Any -> T_Σ_14
MAlonzo.Code.Agda.Builtin.Sigma.C__'44'__32 Any
forall a. a
erased Any
forall a. a
erased))
             Integer
_ -> (Any -> T__'8846'__30) -> Any -> T__'8846'__30
forall a b. a -> b
coe
                    Any -> T__'8846'__30
MAlonzo.Code.Data.Sum.Base.C_inj'8322'_42
                    ((T__'8804'__22 -> T__'8804'__22) -> T__'8804'__22 -> Any
forall a b. a -> b
coe T__'8804'__22 -> T__'8804'__22
MAlonzo.Code.Data.Nat.Base.C_s'8804's_34 T__'8804'__22
v2)
-- Data.Nat.Properties.pred-cancel-<
d_pred'45'cancel'45''60'_5686 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_pred'45'cancel'45''60'_5686 :: Integer -> Integer -> T__'8804'__22 -> T__'8804'__22
d_pred'45'cancel'45''60'_5686 Integer
v0 Integer
v1
  = case Integer -> Integer
forall a b. a -> b
coe Integer
v0 of
      Integer
0 -> case Integer -> Integer
forall a b. a -> b
coe Integer
v1 of
             Integer
0 -> (Any -> Any) -> T__'8804'__22 -> T__'8804'__22
forall a b. a -> b
coe (\ Any
v2 -> Any
forall a. a
MAlonzo.RTE.mazUnreachableError)
             Integer
_ -> (Any -> Any) -> T__'8804'__22 -> T__'8804'__22
forall a b. a -> b
coe
                    (\ Any
v2 ->
                       (T__'8804'__22 -> T__'8804'__22) -> Any -> Any
forall a b. a -> b
coe
                         T__'8804'__22 -> T__'8804'__22
MAlonzo.Code.Data.Nat.Base.C_s'8804's_34
                         (T__'8804'__22 -> Any
forall a b. a -> b
coe T__'8804'__22
MAlonzo.Code.Data.Nat.Base.C_z'8804'n_26))
      Integer
_ -> case Integer -> Integer
forall a b. a -> b
coe Integer
v1 of
             Integer
0 -> (Any -> Any) -> T__'8804'__22 -> T__'8804'__22
forall a b. a -> b
coe (\ Any
v2 -> Any
forall a. a
MAlonzo.RTE.mazUnreachableError)
             Integer
_ -> (T__'8804'__22 -> T__'8804'__22) -> T__'8804'__22 -> T__'8804'__22
forall a b. a -> b
coe T__'8804'__22 -> T__'8804'__22
MAlonzo.Code.Data.Nat.Base.C_s'8804's_34
-- Data.Nat.Properties.pred-injective
d_pred'45'injective_5688 ::
  Integer ->
  Integer ->
  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_pred'45'injective_5688 :: Integer
-> Integer
-> T_NonZero_112
-> T_NonZero_112
-> T__'8801'__12
-> T__'8801'__12
d_pred'45'injective_5688 = Integer
-> Integer
-> T_NonZero_112
-> T_NonZero_112
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Nat.Properties.pred-cancel-≡
d_pred'45'cancel'45''8801'_5694 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Data.Sum.Base.T__'8846'__30
d_pred'45'cancel'45''8801'_5694 :: Integer -> Integer -> T__'8801'__12 -> T__'8846'__30
d_pred'45'cancel'45''8801'_5694 Integer
v0 Integer
v1
  = case Integer -> Integer
forall a b. a -> b
coe Integer
v0 of
      Integer
0 -> case Integer -> Integer
forall a b. a -> b
coe Integer
v1 of
             Integer
0 -> (Any -> Any) -> T__'8801'__12 -> T__'8846'__30
forall a b. a -> b
coe
                    (\ Any
v2 -> (Any -> T__'8846'__30) -> Any -> Any
forall a b. a -> b
coe Any -> T__'8846'__30
MAlonzo.Code.Data.Sum.Base.C_inj'8322'_42 Any
forall a. a
erased)
             Integer
_ -> (Any -> Any) -> T__'8801'__12 -> T__'8846'__30
forall a b. a -> b
coe
                    (\ Any
v2 ->
                       (Any -> T__'8846'__30) -> Any -> Any
forall a b. a -> b
coe
                         Any -> T__'8846'__30
MAlonzo.Code.Data.Sum.Base.C_inj'8321'_38
                         ((Any -> T__'8846'__30) -> Any -> Any
forall a b. a -> b
coe
                            Any -> T__'8846'__30
MAlonzo.Code.Data.Sum.Base.C_inj'8321'_38
                            ((Any -> Any -> T_Σ_14) -> Any -> Any -> Any
forall a b. a -> b
coe Any -> Any -> T_Σ_14
MAlonzo.Code.Agda.Builtin.Sigma.C__'44'__32 Any
forall a. a
erased Any
forall a. a
erased)))
      Integer
_ -> case Integer -> Integer
forall a b. a -> b
coe Integer
v1 of
             Integer
0 -> (Any -> Any) -> T__'8801'__12 -> T__'8846'__30
forall a b. a -> b
coe
                    (\ Any
v2 ->
                       (Any -> T__'8846'__30) -> Any -> Any
forall a b. a -> b
coe
                         Any -> T__'8846'__30
MAlonzo.Code.Data.Sum.Base.C_inj'8321'_38
                         ((Any -> T__'8846'__30) -> Any -> Any
forall a b. a -> b
coe
                            Any -> T__'8846'__30
MAlonzo.Code.Data.Sum.Base.C_inj'8322'_42
                            ((Any -> Any -> T_Σ_14) -> Any -> Any -> Any
forall a b. a -> b
coe Any -> Any -> T_Σ_14
MAlonzo.Code.Agda.Builtin.Sigma.C__'44'__32 Any
forall a. a
erased Any
forall a. a
erased)))
             Integer
_ -> (Any -> Any) -> T__'8801'__12 -> T__'8846'__30
forall a b. a -> b
coe
                    (\ Any
v2 -> (Any -> T__'8846'__30) -> Any -> Any
forall a b. a -> b
coe Any -> T__'8846'__30
MAlonzo.Code.Data.Sum.Base.C_inj'8322'_42 Any
forall a. a
erased)
-- Data.Nat.Properties.m≡n⇒∣m-n∣≡0
d_m'8801'n'8658''8739'm'45'n'8739''8801'0_5696 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_m'8801'n'8658''8739'm'45'n'8739''8801'0_5696 :: Integer -> Integer -> T__'8801'__12 -> T__'8801'__12
d_m'8801'n'8658''8739'm'45'n'8739''8801'0_5696 = Integer -> Integer -> T__'8801'__12 -> T__'8801'__12
forall a. a
erased
-- Data.Nat.Properties.∣m-n∣≡0⇒m≡n
d_'8739'm'45'n'8739''8801'0'8658'm'8801'n_5700 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8739'm'45'n'8739''8801'0'8658'm'8801'n_5700 :: Integer -> Integer -> T__'8801'__12 -> T__'8801'__12
d_'8739'm'45'n'8739''8801'0'8658'm'8801'n_5700 = Integer -> Integer -> T__'8801'__12 -> T__'8801'__12
forall a. a
erased
-- Data.Nat.Properties.m≤n⇒∣n-m∣≡n∸m
d_m'8804'n'8658''8739'n'45'm'8739''8801'n'8760'm_5710 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_m'8804'n'8658''8739'n'45'm'8739''8801'n'8760'm_5710 :: Integer -> Integer -> T__'8804'__22 -> T__'8801'__12
d_m'8804'n'8658''8739'n'45'm'8739''8801'n'8760'm_5710 = Integer -> Integer -> T__'8804'__22 -> T__'8801'__12
forall a. a
erased
-- Data.Nat.Properties.m≤n⇒∣m-n∣≡n∸m
d_m'8804'n'8658''8739'm'45'n'8739''8801'n'8760'm_5716 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_m'8804'n'8658''8739'm'45'n'8739''8801'n'8760'm_5716 :: Integer -> Integer -> T__'8804'__22 -> T__'8801'__12
d_m'8804'n'8658''8739'm'45'n'8739''8801'n'8760'm_5716 = Integer -> Integer -> T__'8804'__22 -> T__'8801'__12
forall a. a
erased
-- Data.Nat.Properties.∣m-n∣≡m∸n⇒n≤m
d_'8739'm'45'n'8739''8801'm'8760'n'8658'n'8804'm_5722 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_'8739'm'45'n'8739''8801'm'8760'n'8658'n'8804'm_5722 :: Integer -> Integer -> T__'8801'__12 -> T__'8804'__22
d_'8739'm'45'n'8739''8801'm'8760'n'8658'n'8804'm_5722 Integer
v0 Integer
v1 ~T__'8801'__12
v2
  = Integer -> Integer -> T__'8804'__22
du_'8739'm'45'n'8739''8801'm'8760'n'8658'n'8804'm_5722 Integer
v0 Integer
v1
du_'8739'm'45'n'8739''8801'm'8760'n'8658'n'8804'm_5722 ::
  Integer -> Integer -> MAlonzo.Code.Data.Nat.Base.T__'8804'__22
du_'8739'm'45'n'8739''8801'm'8760'n'8658'n'8804'm_5722 :: Integer -> Integer -> T__'8804'__22
du_'8739'm'45'n'8739''8801'm'8760'n'8658'n'8804'm_5722 Integer
v0 Integer
v1
  = case Integer -> Integer
forall a b. a -> b
coe Integer
v0 of
      Integer
0 -> T__'8804'__22 -> T__'8804'__22
forall a b. a -> b
coe T__'8804'__22
MAlonzo.Code.Data.Nat.Base.C_z'8804'n_26
      Integer
_ -> let v2 :: Integer
v2 = Integer -> Integer -> Integer
subInt (Integer -> Integer
forall a b. a -> b
coe Integer
v0) (Integer -> Integer
forall a b. a -> b
coe (Integer
1 :: Integer)) in
           Any -> T__'8804'__22
forall a b. a -> b
coe
             (case Integer -> Integer
forall a b. a -> b
coe Integer
v1 of
                Integer
0 -> T__'8804'__22 -> Any
forall a b. a -> b
coe T__'8804'__22
MAlonzo.Code.Data.Nat.Base.C_z'8804'n_26
                Integer
_ -> let v3 :: Integer
v3 = Integer -> Integer -> Integer
subInt (Integer -> Integer
forall a b. a -> b
coe Integer
v1) (Integer -> Integer
forall a b. a -> b
coe (Integer
1 :: Integer)) in
                     Any -> Any
forall a b. a -> b
coe
                       ((T__'8804'__22 -> T__'8804'__22) -> Any -> Any
forall a b. a -> b
coe
                          T__'8804'__22 -> T__'8804'__22
MAlonzo.Code.Data.Nat.Base.C_s'8804's_34
                          ((Integer -> Integer -> T__'8804'__22) -> Any -> Any -> Any
forall a b. a -> b
coe
                             Integer -> Integer -> T__'8804'__22
du_'8739'm'45'n'8739''8801'm'8760'n'8658'n'8804'm_5722 (Integer -> Any
forall a b. a -> b
coe Integer
v2)
                             (Integer -> Any
forall a b. a -> b
coe Integer
v3))))
-- Data.Nat.Properties.∣n-n∣≡0
d_'8739'n'45'n'8739''8801'0_5738 ::
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8739'n'45'n'8739''8801'0_5738 :: Integer -> T__'8801'__12
d_'8739'n'45'n'8739''8801'0_5738 = Integer -> T__'8801'__12
forall a. a
erased
-- Data.Nat.Properties.∣m-m+n∣≡n
d_'8739'm'45'm'43'n'8739''8801'n_5746 ::
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8739'm'45'm'43'n'8739''8801'n_5746 :: Integer -> Integer -> T__'8801'__12
d_'8739'm'45'm'43'n'8739''8801'n_5746 = Integer -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Nat.Properties.∣m+n-m+o∣≡∣n-o∣
d_'8739'm'43'n'45'm'43'o'8739''8801''8739'n'45'o'8739'_5760 ::
  Integer ->
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8739'm'43'n'45'm'43'o'8739''8801''8739'n'45'o'8739'_5760 :: Integer -> Integer -> Integer -> T__'8801'__12
d_'8739'm'43'n'45'm'43'o'8739''8801''8739'n'45'o'8739'_5760
  = Integer -> Integer -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Nat.Properties.m∸n≤∣m-n∣
d_m'8760'n'8804''8739'm'45'n'8739'_5776 ::
  Integer -> Integer -> MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_m'8760'n'8804''8739'm'45'n'8739'_5776 :: Integer -> Integer -> T__'8804'__22
d_m'8760'n'8804''8739'm'45'n'8739'_5776 Integer
v0 Integer
v1
  = let v2 :: T__'8846'__30
v2 = Integer -> Integer -> T__'8846'__30
d_'8804''45'total_2790 (Integer -> Integer
forall a b. a -> b
coe Integer
v0) (Integer -> Integer
forall a b. a -> b
coe Integer
v1) in
    Any -> T__'8804'__22
forall a b. a -> b
coe
      (case T__'8846'__30 -> T__'8846'__30
forall a b. a -> b
coe T__'8846'__30
v2 of
         MAlonzo.Code.Data.Sum.Base.C_inj'8321'_38 Any
v3
           -> T__'8804'__22 -> Any
forall a b. a -> b
coe T__'8804'__22
MAlonzo.Code.Data.Nat.Base.C_z'8804'n_26
         MAlonzo.Code.Data.Sum.Base.C_inj'8322'_42 Any
v3
           -> (Integer -> T__'8804'__22) -> Any -> Any
forall a b. a -> b
coe
                Integer -> T__'8804'__22
d_'8804''45'refl_2776
                ((Integer -> Integer -> Integer) -> Integer -> Integer -> Any
forall a b. a -> b
coe Integer -> Integer -> Integer
MAlonzo.Code.Agda.Builtin.Nat.d__'45'__22 Integer
v0 Integer
v1)
         T__'8846'__30
_ -> Any
forall a. a
MAlonzo.RTE.mazUnreachableError)
-- Data.Nat.Properties.∣m-n∣≤m⊔n
d_'8739'm'45'n'8739''8804'm'8852'n_5806 ::
  Integer -> Integer -> MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_'8739'm'45'n'8739''8804'm'8852'n_5806 :: Integer -> Integer -> T__'8804'__22
d_'8739'm'45'n'8739''8804'm'8852'n_5806 Integer
v0 Integer
v1
  = case Integer -> Integer
forall a b. a -> b
coe Integer
v0 of
      Integer
0 -> (Integer -> T__'8804'__22) -> Any -> T__'8804'__22
forall a b. a -> b
coe
             Integer -> T__'8804'__22
d_'8804''45'refl_2776
             ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe
                Integer -> Integer -> Integer
MAlonzo.Code.Data.Nat.Base.d_'8739'_'45'_'8739'_280
                (Integer -> Any
forall a b. a -> b
coe (Integer
0 :: Integer)) (Integer -> Any
forall a b. a -> b
coe Integer
v1))
      Integer
_ -> let v2 :: Integer
v2 = Integer -> Integer -> Integer
subInt (Integer -> Integer
forall a b. a -> b
coe Integer
v0) (Integer -> Integer
forall a b. a -> b
coe (Integer
1 :: Integer)) in
           Any -> T__'8804'__22
forall a b. a -> b
coe
             (case Integer -> Integer
forall a b. a -> b
coe Integer
v1 of
                Integer
0 -> (Integer -> T__'8804'__22) -> Any -> Any
forall a b. a -> b
coe
                       Integer -> T__'8804'__22
d_'8804''45'refl_2776
                       ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe
                          Integer -> Integer -> Integer
MAlonzo.Code.Data.Nat.Base.d_'8739'_'45'_'8739'_280 (Integer -> Any
forall a b. a -> b
coe Integer
v0)
                          (Integer -> Any
forall a b. a -> b
coe (Integer
0 :: Integer)))
                Integer
_ -> let v3 :: Integer
v3 = Integer -> Integer -> Integer
subInt (Integer -> Integer
forall a b. a -> b
coe Integer
v1) (Integer -> Integer
forall a b. a -> b
coe (Integer
1 :: Integer)) in
                     Any -> Any
forall a b. a -> b
coe
                       ((Integer -> Integer -> T__'8804'__22) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> T__'8804'__22
d_'8739'm'45'n'8739''8804'm'8852'n_5806 (Integer -> Any
forall a b. a -> b
coe Integer
v2) (Integer -> Any
forall a b. a -> b
coe Integer
v3)))
-- Data.Nat.Properties.∣-∣-identityˡ
d_'8739''45''8739''45'identity'737'_5816 ::
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8739''45''8739''45'identity'737'_5816 :: Integer -> T__'8801'__12
d_'8739''45''8739''45'identity'737'_5816 = Integer -> T__'8801'__12
forall a. a
erased
-- Data.Nat.Properties.∣-∣-identityʳ
d_'8739''45''8739''45'identity'691'_5820 ::
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8739''45''8739''45'identity'691'_5820 :: Integer -> T__'8801'__12
d_'8739''45''8739''45'identity'691'_5820 = Integer -> T__'8801'__12
forall a. a
erased
-- Data.Nat.Properties.∣-∣-identity
d_'8739''45''8739''45'identity_5824 ::
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'8739''45''8739''45'identity_5824 :: T_Σ_14
d_'8739''45''8739''45'identity_5824
  = (Any -> Any -> T_Σ_14) -> Any -> Any -> T_Σ_14
forall a b. a -> b
coe Any -> Any -> T_Σ_14
MAlonzo.Code.Agda.Builtin.Sigma.C__'44'__32 Any
forall a. a
erased Any
forall a. a
erased
-- Data.Nat.Properties.∣-∣-comm
d_'8739''45''8739''45'comm_5826 ::
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8739''45''8739''45'comm_5826 :: Integer -> Integer -> T__'8801'__12
d_'8739''45''8739''45'comm_5826 = Integer -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Nat.Properties.∣m-n∣≡[m∸n]∨[n∸m]
d_'8739'm'45'n'8739''8801''91'm'8760'n'93''8744''91'n'8760'm'93'_5840 ::
  Integer -> Integer -> MAlonzo.Code.Data.Sum.Base.T__'8846'__30
d_'8739'm'45'n'8739''8801''91'm'8760'n'93''8744''91'n'8760'm'93'_5840 :: Integer -> Integer -> T__'8846'__30
d_'8739'm'45'n'8739''8801''91'm'8760'n'93''8744''91'n'8760'm'93'_5840 Integer
v0
                                                                      Integer
v1
  = let v2 :: T__'8846'__30
v2 = Integer -> Integer -> T__'8846'__30
d_'8804''45'total_2790 (Integer -> Integer
forall a b. a -> b
coe Integer
v0) (Integer -> Integer
forall a b. a -> b
coe Integer
v1) in
    Any -> T__'8846'__30
forall a b. a -> b
coe
      (case T__'8846'__30 -> T__'8846'__30
forall a b. a -> b
coe T__'8846'__30
v2 of
         MAlonzo.Code.Data.Sum.Base.C_inj'8321'_38 Any
v3
           -> (Any -> T__'8846'__30) -> Any -> Any
forall a b. a -> b
coe
                Any -> T__'8846'__30
MAlonzo.Code.Data.Sum.Base.C_inj'8322'_42
                (let v4 :: b
v4
                       = T_SubRelation_60 -> b
forall a b. a -> b
coe
                           T_SubRelation_60
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_eqRelation_238 in
                 Any -> Any
forall a b. a -> b
coe
                   ((T_SubRelation_60 -> Any -> Any -> Any -> Any)
-> Any -> Any -> Any -> Any -> Any
forall a b. a -> b
coe
                      T_SubRelation_60 -> Any -> Any -> Any -> Any
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_begin__126
                      (Any -> Any
forall a b. a -> b
coe Any
forall a. a
v4)
                      ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe
                         Integer -> Integer -> Integer
MAlonzo.Code.Data.Nat.Base.d_'8739'_'45'_'8739'_280 (Integer -> Any
forall a b. a -> b
coe Integer
v0)
                         (Integer -> Any
forall a b. a -> b
coe Integer
v1))
                      ((Integer -> Integer -> Integer) -> Integer -> Integer -> Any
forall a b. a -> b
coe Integer -> Integer -> Integer
MAlonzo.Code.Agda.Builtin.Nat.d__'45'__22 Integer
v1 Integer
v0)
                      (((Any -> Any -> Any -> T__'8801'__12 -> Any -> Any)
 -> Any -> Any -> Any -> Any -> T__'8801'__12 -> Any)
-> (Any -> Any -> Any -> Any -> Any -> Any)
-> Integer
-> Integer
-> Any
-> Any
-> Any
-> Any
forall a b. a -> b
coe
                         (Any -> Any -> Any -> T__'8801'__12 -> Any -> Any)
-> Any -> Any -> Any -> Any -> T__'8801'__12 -> Any
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8801''45''10217'_436
                         (\ Any
v5 Any
v6 Any
v7 Any
v8 Any
v9 -> Any
v9)
                         (Integer -> Integer -> Integer
MAlonzo.Code.Data.Nat.Base.d_'8739'_'45'_'8739'_280
                            (Integer -> Integer
forall a b. a -> b
coe Integer
v0) (Integer -> Integer
forall a b. a -> b
coe Integer
v1))
                         (Integer -> Integer -> Integer
MAlonzo.Code.Data.Nat.Base.d_'8739'_'45'_'8739'_280
                            (Integer -> Integer
forall a b. a -> b
coe Integer
v1) (Integer -> Integer
forall a b. a -> b
coe Integer
v0))
                         ((Integer -> Integer -> Integer) -> Integer -> Integer -> Any
forall a b. a -> b
coe Integer -> Integer -> Integer
MAlonzo.Code.Agda.Builtin.Nat.d__'45'__22 Integer
v1 Integer
v0)
                         (((Any -> Any -> Any -> T__'8801'__12 -> Any -> Any)
 -> Any -> Any -> Any -> Any -> T__'8801'__12 -> Any)
-> (Any -> Any -> Any -> Any -> Any -> Any)
-> Integer
-> Any
-> Any
-> Any
-> Any
-> Any
forall a b. a -> b
coe
                            (Any -> Any -> Any -> T__'8801'__12 -> Any -> Any)
-> Any -> Any -> Any -> Any -> T__'8801'__12 -> Any
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8801''45''10217'_436
                            (\ Any
v5 Any
v6 Any
v7 Any
v8 Any
v9 -> Any
v9)
                            (Integer -> Integer -> Integer
MAlonzo.Code.Data.Nat.Base.d_'8739'_'45'_'8739'_280
                               (Integer -> Integer
forall a b. a -> b
coe Integer
v1) (Integer -> Integer
forall a b. a -> b
coe Integer
v0))
                            ((Integer -> Integer -> Integer) -> Integer -> Integer -> Any
forall a b. a -> b
coe Integer -> Integer -> Integer
MAlonzo.Code.Agda.Builtin.Nat.d__'45'__22 Integer
v1 Integer
v0)
                            ((Integer -> Integer -> Integer) -> Integer -> Integer -> Any
forall a b. a -> b
coe Integer -> Integer -> Integer
MAlonzo.Code.Agda.Builtin.Nat.d__'45'__22 Integer
v1 Integer
v0)
                            (((Any -> Any) -> Any -> Any) -> Any -> Any -> Any
forall a b. a -> b
coe
                               (Any -> Any) -> Any -> Any
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du__'8718'_492
                               ((T_IsPreorder_70 -> Any -> T__IsRelatedTo__78) -> Any -> Any
forall a b. a -> b
coe
                                  T_IsPreorder_70 -> Any -> T__IsRelatedTo__78
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_stop_166
                                  (T_IsPreorder_70 -> Any
forall a b. a -> b
coe T_IsPreorder_70
d_'8804''45'isPreorder_2810))
                               ((Integer -> Integer -> Integer) -> Integer -> Integer -> Any
forall a b. a -> b
coe Integer -> Integer -> Integer
MAlonzo.Code.Agda.Builtin.Nat.d__'45'__22 Integer
v1 Integer
v0))
                            Any
forall a. a
erased)
                         Any
forall a. a
erased)))
         MAlonzo.Code.Data.Sum.Base.C_inj'8322'_42 Any
v3
           -> (Any -> T__'8846'__30) -> Any -> Any
forall a b. a -> b
coe Any -> T__'8846'__30
MAlonzo.Code.Data.Sum.Base.C_inj'8321'_38 Any
forall a. a
erased
         T__'8846'__30
_ -> Any
forall a. a
MAlonzo.RTE.mazUnreachableError)
-- Data.Nat.Properties.*-distribˡ-∣-∣-aux
d_'42''45'distrib'737''45''8739''45''8739''45'aux_5868 ::
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'42''45'distrib'737''45''8739''45''8739''45'aux_5868 :: Integer -> Integer -> Integer -> T__'8804'__22 -> T__'8801'__12
d_'42''45'distrib'737''45''8739''45''8739''45'aux_5868 = Integer -> Integer -> Integer -> T__'8804'__22 -> T__'8801'__12
forall a. a
erased
-- Data.Nat.Properties.*-distribˡ-∣-∣
d_'42''45'distrib'737''45''8739''45''8739'_5880 ::
  Integer ->
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'42''45'distrib'737''45''8739''45''8739'_5880 :: Integer -> Integer -> Integer -> T__'8801'__12
d_'42''45'distrib'737''45''8739''45''8739'_5880 = Integer -> Integer -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Nat.Properties.*-distribʳ-∣-∣
d_'42''45'distrib'691''45''8739''45''8739'_5910 ::
  Integer ->
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'42''45'distrib'691''45''8739''45''8739'_5910 :: Integer -> Integer -> Integer -> T__'8801'__12
d_'42''45'distrib'691''45''8739''45''8739'_5910 = Integer -> Integer -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Nat.Properties.*-distrib-∣-∣
d_'42''45'distrib'45''8739''45''8739'_5912 ::
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'42''45'distrib'45''8739''45''8739'_5912 :: T_Σ_14
d_'42''45'distrib'45''8739''45''8739'_5912
  = (Any -> Any -> T_Σ_14) -> Any -> Any -> T_Σ_14
forall a b. a -> b
coe Any -> Any -> T_Σ_14
MAlonzo.Code.Agda.Builtin.Sigma.C__'44'__32 Any
forall a. a
erased Any
forall a. a
erased
-- Data.Nat.Properties.m≤n+∣n-m∣
d_m'8804'n'43''8739'n'45'm'8739'_5918 ::
  Integer -> Integer -> MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_m'8804'n'43''8739'n'45'm'8739'_5918 :: Integer -> Integer -> T__'8804'__22
d_m'8804'n'43''8739'n'45'm'8739'_5918 Integer
v0 Integer
v1
  = case Integer -> Integer
forall a b. a -> b
coe Integer
v0 of
      Integer
0 -> T__'8804'__22 -> T__'8804'__22
forall a b. a -> b
coe T__'8804'__22
MAlonzo.Code.Data.Nat.Base.C_z'8804'n_26
      Integer
_ -> let v2 :: Integer
v2 = Integer -> Integer -> Integer
subInt (Integer -> Integer
forall a b. a -> b
coe Integer
v0) (Integer -> Integer
forall a b. a -> b
coe (Integer
1 :: Integer)) in
           Any -> T__'8804'__22
forall a b. a -> b
coe
             (case Integer -> Integer
forall a b. a -> b
coe Integer
v1 of
                Integer
0 -> (Integer -> T__'8804'__22) -> Any -> Any
forall a b. a -> b
coe Integer -> T__'8804'__22
d_'8804''45'refl_2776 (Integer -> Any
forall a b. a -> b
coe Integer
v0)
                Integer
_ -> let v3 :: Integer
v3 = Integer -> Integer -> Integer
subInt (Integer -> Integer
forall a b. a -> b
coe Integer
v1) (Integer -> Integer
forall a b. a -> b
coe (Integer
1 :: Integer)) in
                     Any -> Any
forall a b. a -> b
coe
                       ((T__'8804'__22 -> T__'8804'__22) -> T__'8804'__22 -> Any
forall a b. a -> b
coe
                          T__'8804'__22 -> T__'8804'__22
MAlonzo.Code.Data.Nat.Base.C_s'8804's_34
                          (Integer -> Integer -> T__'8804'__22
d_m'8804'n'43''8739'n'45'm'8739'_5918 (Integer -> Integer
forall a b. a -> b
coe Integer
v2) (Integer -> Integer
forall a b. a -> b
coe Integer
v3))))
-- Data.Nat.Properties.m≤n+∣m-n∣
d_m'8804'n'43''8739'm'45'n'8739'_5932 ::
  Integer -> Integer -> MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_m'8804'n'43''8739'm'45'n'8739'_5932 :: Integer -> Integer -> T__'8804'__22
d_m'8804'n'43''8739'm'45'n'8739'_5932 Integer
v0 Integer
v1
  = (Integer -> Integer -> T__'8804'__22)
-> Any -> Any -> T__'8804'__22
forall a b. a -> b
coe Integer -> Integer -> T__'8804'__22
d_m'8804'n'43''8739'n'45'm'8739'_5918 (Integer -> Any
forall a b. a -> b
coe Integer
v0) (Integer -> Any
forall a b. a -> b
coe Integer
v1)
-- Data.Nat.Properties.m≤∣m-n∣+n
d_m'8804''8739'm'45'n'8739''43'n_5946 ::
  Integer -> Integer -> MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_m'8804''8739'm'45'n'8739''43'n_5946 :: Integer -> Integer -> T__'8804'__22
d_m'8804''8739'm'45'n'8739''43'n_5946 Integer
v0 Integer
v1
  = (Integer -> Integer -> T__'8804'__22)
-> Any -> Any -> T__'8804'__22
forall a b. a -> b
coe Integer -> Integer -> T__'8804'__22
d_m'8804'n'43''8739'm'45'n'8739'_5932 (Integer -> Any
forall a b. a -> b
coe Integer
v0) (Integer -> Any
forall a b. a -> b
coe Integer
v1)
-- Data.Nat.Properties.∣-∣-triangle
d_'8739''45''8739''45'triangle_5954 ::
  Integer ->
  Integer -> Integer -> MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_'8739''45''8739''45'triangle_5954 :: Integer -> Integer -> Integer -> T__'8804'__22
d_'8739''45''8739''45'triangle_5954 Integer
v0 Integer
v1 Integer
v2
  = case Integer -> Integer
forall a b. a -> b
coe Integer
v0 of
      Integer
0 -> (Integer -> Integer -> T__'8804'__22)
-> Any -> Any -> T__'8804'__22
forall a b. a -> b
coe Integer -> Integer -> T__'8804'__22
d_m'8804'n'43''8739'n'45'm'8739'_5918 (Integer -> Any
forall a b. a -> b
coe Integer
v2) (Integer -> Any
forall a b. a -> b
coe Integer
v1)
      Integer
_ -> let v3 :: Integer
v3 = Integer -> Integer -> Integer
subInt (Integer -> Integer
forall a b. a -> b
coe Integer
v0) (Integer -> Integer
forall a b. a -> b
coe (Integer
1 :: Integer)) in
           Any -> T__'8804'__22
forall a b. a -> b
coe
             (case Integer -> Integer
forall a b. a -> b
coe Integer
v1 of
                Integer
0 -> ((Any -> Any -> Any -> Any) -> Any -> Any -> Any -> Any)
-> Any -> Integer -> Integer -> Any -> Any
forall a b. a -> b
coe
                       (Any -> Any -> Any -> Any) -> Any -> Any -> Any -> Any
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_begin__46
                       ((T_IsPreorder_70
 -> (Any -> Any -> Any -> Any)
 -> Any
 -> Any
 -> T__IsRelatedTo__78
 -> Any)
-> Any -> (Any -> Any -> Any -> Any) -> Any
forall a b. a -> b
coe
                          T_IsPreorder_70
-> (Any -> Any -> Any -> Any)
-> Any
-> Any
-> T__IsRelatedTo__78
-> Any
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_start_96
                          (T_IsPreorder_70 -> Any
forall a b. a -> b
coe T_IsPreorder_70
d_'8804''45'isPreorder_2810)
                          (\ Any
v4 Any
v5 Any
v6 -> (T__'8804'__22 -> T__'8804'__22) -> Any -> Any
forall a b. a -> b
coe T__'8804'__22 -> T__'8804'__22
du_'60''8658''8804'_2854 Any
v6))
                       (Integer -> Integer -> Integer
MAlonzo.Code.Data.Nat.Base.d_'8739'_'45'_'8739'_280
                          (Integer -> Integer
forall a b. a -> b
coe Integer
v0) (Integer -> Integer
forall a b. a -> b
coe Integer
v2))
                       (Integer -> Integer -> Integer
addInt
                          ((Integer -> Integer -> Integer) -> Any -> Any -> Integer
forall a b. a -> b
coe
                             Integer -> Integer -> Integer
MAlonzo.Code.Data.Nat.Base.d_'8739'_'45'_'8739'_280
                             (Integer -> Any
forall a b. a -> b
coe (Integer
0 :: Integer)) (Integer -> Any
forall a b. a -> b
coe Integer
v2))
                          ((Integer -> Integer -> Integer) -> Any -> Any -> Integer
forall a b. a -> b
coe
                             Integer -> Integer -> Integer
MAlonzo.Code.Data.Nat.Base.d_'8739'_'45'_'8739'_280 (Integer -> Any
forall a b. a -> b
coe Integer
v0)
                             (Integer -> Any
forall a b. a -> b
coe (Integer
0 :: Integer))))
                       (((Any -> Any -> Any -> Any -> Any -> Any)
 -> Any -> Any -> Any -> Any -> Any -> Any)
-> Any
-> Integer
-> Integer
-> Integer
-> Any
-> T__'8804'__22
-> Any
forall a b. a -> b
coe
                          (Any -> Any -> Any -> Any -> Any -> Any)
-> Any -> Any -> Any -> Any -> Any -> Any
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8804'_308
                          ((T_IsPreorder_70
 -> (Any -> Any -> Any -> Any -> Any -> Any)
 -> Any
 -> Any
 -> Any
 -> Any
 -> T__IsRelatedTo__78
 -> T__IsRelatedTo__78)
-> Any -> (Any -> Any -> Any -> Any -> Any -> Any) -> Any
forall a b. a -> b
coe
                             T_IsPreorder_70
-> (Any -> Any -> Any -> Any -> Any -> Any)
-> Any
-> Any
-> Any
-> Any
-> T__IsRelatedTo__78
-> T__IsRelatedTo__78
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_'8804''45'go_138
                             (T_IsPreorder_70 -> Any
forall a b. a -> b
coe T_IsPreorder_70
d_'8804''45'isPreorder_2810)
                             (\ Any
v4 Any
v5 Any
v6 Any
v7 Any
v8 -> (T__'8804'__22 -> T__'8804'__22 -> T__'8804'__22)
-> Any -> Any -> Any
forall a b. a -> b
coe T__'8804'__22 -> T__'8804'__22 -> T__'8804'__22
du_'8804''45''60''45'trans_2986 Any
v7 Any
v8))
                          (Integer -> Integer -> Integer
MAlonzo.Code.Data.Nat.Base.d_'8739'_'45'_'8739'_280
                             (Integer -> Integer
forall a b. a -> b
coe Integer
v0) (Integer -> Integer
forall a b. a -> b
coe Integer
v2))
                          (Integer -> Integer -> Integer
MAlonzo.Code.Data.Nat.Base.d__'8852'__204 (Integer -> Integer
forall a b. a -> b
coe Integer
v0) (Integer -> Integer
forall a b. a -> b
coe Integer
v2))
                          (Integer -> Integer -> Integer
addInt
                             ((Integer -> Integer -> Integer) -> Any -> Any -> Integer
forall a b. a -> b
coe
                                Integer -> Integer -> Integer
MAlonzo.Code.Data.Nat.Base.d_'8739'_'45'_'8739'_280
                                (Integer -> Any
forall a b. a -> b
coe (Integer
0 :: Integer)) (Integer -> Any
forall a b. a -> b
coe Integer
v2))
                             ((Integer -> Integer -> Integer) -> Any -> Any -> Integer
forall a b. a -> b
coe
                                Integer -> Integer -> Integer
MAlonzo.Code.Data.Nat.Base.d_'8739'_'45'_'8739'_280 (Integer -> Any
forall a b. a -> b
coe Integer
v0)
                                (Integer -> Any
forall a b. a -> b
coe (Integer
0 :: Integer))))
                          (((Any -> Any -> Any -> Any -> Any -> Any)
 -> Any -> Any -> Any -> Any -> Any -> Any)
-> Any
-> Integer
-> Integer
-> Integer
-> Any
-> T__'8804'__22
-> Any
forall a b. a -> b
coe
                             (Any -> Any -> Any -> Any -> Any -> Any)
-> Any -> Any -> Any -> Any -> Any -> Any
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8804'_308
                             ((T_IsPreorder_70
 -> (Any -> Any -> Any -> Any -> Any -> Any)
 -> Any
 -> Any
 -> Any
 -> Any
 -> T__IsRelatedTo__78
 -> T__IsRelatedTo__78)
-> Any -> (Any -> Any -> Any -> Any -> Any -> Any) -> Any
forall a b. a -> b
coe
                                T_IsPreorder_70
-> (Any -> Any -> Any -> Any -> Any -> Any)
-> Any
-> Any
-> Any
-> Any
-> T__IsRelatedTo__78
-> T__IsRelatedTo__78
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_'8804''45'go_138
                                (T_IsPreorder_70 -> Any
forall a b. a -> b
coe T_IsPreorder_70
d_'8804''45'isPreorder_2810)
                                (\ Any
v4 Any
v5 Any
v6 Any
v7 Any
v8 -> (T__'8804'__22 -> T__'8804'__22 -> T__'8804'__22)
-> Any -> Any -> Any
forall a b. a -> b
coe T__'8804'__22 -> T__'8804'__22 -> T__'8804'__22
du_'8804''45''60''45'trans_2986 Any
v7 Any
v8))
                             (Integer -> Integer -> Integer
MAlonzo.Code.Data.Nat.Base.d__'8852'__204 (Integer -> Integer
forall a b. a -> b
coe Integer
v0) (Integer -> Integer
forall a b. a -> b
coe Integer
v2))
                             (Integer -> Integer -> Integer
addInt (Integer -> Integer
forall a b. a -> b
coe Integer
v0) (Integer -> Integer
forall a b. a -> b
coe Integer
v2))
                             (Integer -> Integer -> Integer
addInt
                                ((Integer -> Integer -> Integer) -> Any -> Any -> Integer
forall a b. a -> b
coe
                                   Integer -> Integer -> Integer
MAlonzo.Code.Data.Nat.Base.d_'8739'_'45'_'8739'_280
                                   (Integer -> Any
forall a b. a -> b
coe (Integer
0 :: Integer)) (Integer -> Any
forall a b. a -> b
coe Integer
v2))
                                ((Integer -> Integer -> Integer) -> Any -> Any -> Integer
forall a b. a -> b
coe
                                   Integer -> Integer -> Integer
MAlonzo.Code.Data.Nat.Base.d_'8739'_'45'_'8739'_280 (Integer -> Any
forall a b. a -> b
coe Integer
v0)
                                   (Integer -> Any
forall a b. a -> b
coe (Integer
0 :: Integer))))
                             (((Any -> Any -> Any -> T__'8801'__12 -> Any -> Any)
 -> Any -> Any -> Any -> Any -> T__'8801'__12 -> Any)
-> (Any -> Any -> Any -> Any -> Any -> Any)
-> Integer
-> Integer
-> Integer
-> Any
-> Any
-> Any
forall a b. a -> b
coe
                                (Any -> Any -> Any -> T__'8801'__12 -> Any -> Any)
-> Any -> Any -> Any -> Any -> T__'8801'__12 -> Any
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8801''45''10217'_436
                                (\ Any
v4 Any
v5 Any
v6 Any
v7 Any
v8 -> Any
v8) (Integer -> Integer -> Integer
addInt (Integer -> Integer
forall a b. a -> b
coe Integer
v0) (Integer -> Integer
forall a b. a -> b
coe Integer
v2))
                                (Integer -> Integer -> Integer
addInt
                                   ((Integer -> Integer -> Integer) -> Any -> Any -> Integer
forall a b. a -> b
coe
                                      Integer -> Integer -> Integer
MAlonzo.Code.Data.Nat.Base.d_'8739'_'45'_'8739'_280 (Integer -> Any
forall a b. a -> b
coe Integer
v0)
                                      (Integer -> Any
forall a b. a -> b
coe (Integer
0 :: Integer)))
                                   (Integer -> Integer
forall a b. a -> b
coe Integer
v2))
                                (Integer -> Integer -> Integer
addInt
                                   ((Integer -> Integer -> Integer) -> Any -> Any -> Integer
forall a b. a -> b
coe
                                      Integer -> Integer -> Integer
MAlonzo.Code.Data.Nat.Base.d_'8739'_'45'_'8739'_280
                                      (Integer -> Any
forall a b. a -> b
coe (Integer
0 :: Integer)) (Integer -> Any
forall a b. a -> b
coe Integer
v2))
                                   ((Integer -> Integer -> Integer) -> Any -> Any -> Integer
forall a b. a -> b
coe
                                      Integer -> Integer -> Integer
MAlonzo.Code.Data.Nat.Base.d_'8739'_'45'_'8739'_280 (Integer -> Any
forall a b. a -> b
coe Integer
v0)
                                      (Integer -> Any
forall a b. a -> b
coe (Integer
0 :: Integer))))
                                (((Any -> Any) -> Any -> Any) -> Any -> Any -> Any
forall a b. a -> b
coe
                                   (Any -> Any) -> Any -> Any
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du__'8718'_492
                                   ((T_IsPreorder_70 -> Any -> T__IsRelatedTo__78) -> Any -> Any
forall a b. a -> b
coe
                                      T_IsPreorder_70 -> Any -> T__IsRelatedTo__78
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_stop_166
                                      (T_IsPreorder_70 -> Any
forall a b. a -> b
coe T_IsPreorder_70
d_'8804''45'isPreorder_2810))
                                   ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe
                                      Integer -> Integer -> Integer
addInt
                                      ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe
                                         Integer -> Integer -> Integer
MAlonzo.Code.Data.Nat.Base.d_'8739'_'45'_'8739'_280
                                         (Integer -> Any
forall a b. a -> b
coe Integer
v0) (Integer -> Any
forall a b. a -> b
coe (Integer
0 :: Integer)))
                                      (Integer -> Any
forall a b. a -> b
coe Integer
v2)))
                                Any
forall a. a
erased)
                             (Integer -> Integer -> T__'8804'__22
d_m'8852'n'8804'm'43'n_4830 (Integer -> Integer
forall a b. a -> b
coe Integer
v0) (Integer -> Integer
forall a b. a -> b
coe Integer
v2)))
                          (Integer -> Integer -> T__'8804'__22
d_'8739'm'45'n'8739''8804'm'8852'n_5806 (Integer -> Integer
forall a b. a -> b
coe Integer
v0) (Integer -> Integer
forall a b. a -> b
coe Integer
v2)))
                Integer
_ -> let v4 :: Integer
v4 = Integer -> Integer -> Integer
subInt (Integer -> Integer
forall a b. a -> b
coe Integer
v1) (Integer -> Integer
forall a b. a -> b
coe (Integer
1 :: Integer)) in
                     Any -> Any
forall a b. a -> b
coe
                       (case Integer -> Integer
forall a b. a -> b
coe Integer
v2 of
                          Integer
0 -> ((Any -> Any -> Any -> Any) -> Any -> Any -> Any -> Any)
-> Any -> Integer -> Integer -> Any -> Any
forall a b. a -> b
coe
                                 (Any -> Any -> Any -> Any) -> Any -> Any -> Any -> Any
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_begin__46
                                 ((T_IsPreorder_70
 -> (Any -> Any -> Any -> Any)
 -> Any
 -> Any
 -> T__IsRelatedTo__78
 -> Any)
-> Any -> (Any -> Any -> Any -> Any) -> Any
forall a b. a -> b
coe
                                    T_IsPreorder_70
-> (Any -> Any -> Any -> Any)
-> Any
-> Any
-> T__IsRelatedTo__78
-> Any
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_start_96
                                    (T_IsPreorder_70 -> Any
forall a b. a -> b
coe T_IsPreorder_70
d_'8804''45'isPreorder_2810)
                                    (\ Any
v5 Any
v6 Any
v7 -> (T__'8804'__22 -> T__'8804'__22) -> Any -> Any
forall a b. a -> b
coe T__'8804'__22 -> T__'8804'__22
du_'60''8658''8804'_2854 Any
v7))
                                 (Integer -> Integer -> Integer
MAlonzo.Code.Data.Nat.Base.d_'8739'_'45'_'8739'_280
                                    (Integer -> Integer
forall a b. a -> b
coe Integer
v0) (Integer -> Integer
forall a b. a -> b
coe (Integer
0 :: Integer)))
                                 (Integer -> Integer -> Integer
addInt
                                    ((Integer -> Integer -> Integer) -> Any -> Any -> Integer
forall a b. a -> b
coe
                                       Integer -> Integer -> Integer
MAlonzo.Code.Data.Nat.Base.d_'8739'_'45'_'8739'_280 (Integer -> Any
forall a b. a -> b
coe Integer
v0)
                                       (Integer -> Any
forall a b. a -> b
coe Integer
v1))
                                    ((Integer -> Integer -> Integer) -> Any -> Any -> Integer
forall a b. a -> b
coe
                                       Integer -> Integer -> Integer
MAlonzo.Code.Data.Nat.Base.d_'8739'_'45'_'8739'_280 (Integer -> Any
forall a b. a -> b
coe Integer
v1)
                                       (Integer -> Any
forall a b. a -> b
coe (Integer
0 :: Integer))))
                                 (((Any -> Any -> Any -> T__'8801'__12 -> Any -> Any)
 -> Any -> Any -> Any -> Any -> T__'8801'__12 -> Any)
-> (Any -> Any -> Any -> Any -> Any -> Any)
-> Integer
-> Integer
-> Integer
-> Any
-> Any
-> Any
forall a b. a -> b
coe
                                    (Any -> Any -> Any -> T__'8801'__12 -> Any -> Any)
-> Any -> Any -> Any -> Any -> T__'8801'__12 -> Any
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8801''45''10217'_436
                                    (\ Any
v5 Any
v6 Any
v7 Any
v8 Any
v9 -> Any
v9)
                                    (Integer -> Integer -> Integer
MAlonzo.Code.Data.Nat.Base.d_'8739'_'45'_'8739'_280
                                       (Integer -> Integer
forall a b. a -> b
coe Integer
v0) (Integer -> Integer
forall a b. a -> b
coe (Integer
0 :: Integer)))
                                    Integer
v0
                                    (Integer -> Integer -> Integer
addInt
                                       ((Integer -> Integer -> Integer) -> Any -> Any -> Integer
forall a b. a -> b
coe
                                          Integer -> Integer -> Integer
MAlonzo.Code.Data.Nat.Base.d_'8739'_'45'_'8739'_280
                                          (Integer -> Any
forall a b. a -> b
coe Integer
v0) (Integer -> Any
forall a b. a -> b
coe Integer
v1))
                                       ((Integer -> Integer -> Integer) -> Any -> Any -> Integer
forall a b. a -> b
coe
                                          Integer -> Integer -> Integer
MAlonzo.Code.Data.Nat.Base.d_'8739'_'45'_'8739'_280
                                          (Integer -> Any
forall a b. a -> b
coe Integer
v1) (Integer -> Any
forall a b. a -> b
coe (Integer
0 :: Integer))))
                                    (((Any -> Any -> Any -> Any -> Any -> Any)
 -> Any -> Any -> Any -> Any -> Any -> Any)
-> Any
-> Integer
-> Integer
-> Integer
-> Any
-> T__'8804'__22
-> Any
forall a b. a -> b
coe
                                       (Any -> Any -> Any -> Any -> Any -> Any)
-> Any -> Any -> Any -> Any -> Any -> Any
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8804'_308
                                       ((T_IsPreorder_70
 -> (Any -> Any -> Any -> Any -> Any -> Any)
 -> Any
 -> Any
 -> Any
 -> Any
 -> T__IsRelatedTo__78
 -> T__IsRelatedTo__78)
-> Any -> (Any -> Any -> Any -> Any -> Any -> Any) -> Any
forall a b. a -> b
coe
                                          T_IsPreorder_70
-> (Any -> Any -> Any -> Any -> Any -> Any)
-> Any
-> Any
-> Any
-> Any
-> T__IsRelatedTo__78
-> T__IsRelatedTo__78
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_'8804''45'go_138
                                          (T_IsPreorder_70 -> Any
forall a b. a -> b
coe T_IsPreorder_70
d_'8804''45'isPreorder_2810)
                                          (\ Any
v5 Any
v6 Any
v7 Any
v8 Any
v9 ->
                                             (T__'8804'__22 -> T__'8804'__22 -> T__'8804'__22)
-> Any -> Any -> Any
forall a b. a -> b
coe T__'8804'__22 -> T__'8804'__22 -> T__'8804'__22
du_'8804''45''60''45'trans_2986 Any
v8 Any
v9))
                                       Integer
v0
                                       (Integer -> Integer -> Integer
addInt
                                          ((Integer -> Integer -> Integer) -> Any -> Any -> Integer
forall a b. a -> b
coe
                                             Integer -> Integer -> Integer
MAlonzo.Code.Data.Nat.Base.d_'8739'_'45'_'8739'_280
                                             (Integer -> Any
forall a b. a -> b
coe Integer
v0) (Integer -> Any
forall a b. a -> b
coe Integer
v1))
                                          (Integer -> Integer
forall a b. a -> b
coe Integer
v1))
                                       (Integer -> Integer -> Integer
addInt
                                          ((Integer -> Integer -> Integer) -> Any -> Any -> Integer
forall a b. a -> b
coe
                                             Integer -> Integer -> Integer
MAlonzo.Code.Data.Nat.Base.d_'8739'_'45'_'8739'_280
                                             (Integer -> Any
forall a b. a -> b
coe Integer
v0) (Integer -> Any
forall a b. a -> b
coe Integer
v1))
                                          ((Integer -> Integer -> Integer) -> Any -> Any -> Integer
forall a b. a -> b
coe
                                             Integer -> Integer -> Integer
MAlonzo.Code.Data.Nat.Base.d_'8739'_'45'_'8739'_280
                                             (Integer -> Any
forall a b. a -> b
coe Integer
v1) (Integer -> Any
forall a b. a -> b
coe (Integer
0 :: Integer))))
                                       (((Any -> Any -> Any -> T__'8801'__12 -> Any -> Any)
 -> Any -> Any -> Any -> Any -> T__'8801'__12 -> Any)
-> (Any -> Any -> Any -> Any -> Any -> Any)
-> Integer
-> Integer
-> Integer
-> Any
-> Any
-> Any
forall a b. a -> b
coe
                                          (Any -> Any -> Any -> T__'8801'__12 -> Any -> Any)
-> Any -> Any -> Any -> Any -> T__'8801'__12 -> Any
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8801''45''10217'_436
                                          (\ Any
v5 Any
v6 Any
v7 Any
v8 Any
v9 -> Any
v9)
                                          (Integer -> Integer -> Integer
addInt
                                             ((Integer -> Integer -> Integer) -> Any -> Any -> Integer
forall a b. a -> b
coe
                                                Integer -> Integer -> Integer
MAlonzo.Code.Data.Nat.Base.d_'8739'_'45'_'8739'_280
                                                (Integer -> Any
forall a b. a -> b
coe Integer
v0) (Integer -> Any
forall a b. a -> b
coe Integer
v1))
                                             (Integer -> Integer
forall a b. a -> b
coe Integer
v1))
                                          (Integer -> Integer -> Integer
addInt
                                             ((Integer -> Integer -> Integer) -> Any -> Any -> Integer
forall a b. a -> b
coe
                                                Integer -> Integer -> Integer
MAlonzo.Code.Data.Nat.Base.d_'8739'_'45'_'8739'_280
                                                (Integer -> Any
forall a b. a -> b
coe Integer
v0) (Integer -> Any
forall a b. a -> b
coe Integer
v1))
                                             ((Integer -> Integer -> Integer) -> Any -> Any -> Integer
forall a b. a -> b
coe
                                                Integer -> Integer -> Integer
MAlonzo.Code.Data.Nat.Base.d_'8739'_'45'_'8739'_280
                                                (Integer -> Any
forall a b. a -> b
coe Integer
v1) (Integer -> Any
forall a b. a -> b
coe (Integer
0 :: Integer))))
                                          (Integer -> Integer -> Integer
addInt
                                             ((Integer -> Integer -> Integer) -> Any -> Any -> Integer
forall a b. a -> b
coe
                                                Integer -> Integer -> Integer
MAlonzo.Code.Data.Nat.Base.d_'8739'_'45'_'8739'_280
                                                (Integer -> Any
forall a b. a -> b
coe Integer
v0) (Integer -> Any
forall a b. a -> b
coe Integer
v1))
                                             ((Integer -> Integer -> Integer) -> Any -> Any -> Integer
forall a b. a -> b
coe
                                                Integer -> Integer -> Integer
MAlonzo.Code.Data.Nat.Base.d_'8739'_'45'_'8739'_280
                                                (Integer -> Any
forall a b. a -> b
coe Integer
v1) (Integer -> Any
forall a b. a -> b
coe (Integer
0 :: Integer))))
                                          (((Any -> Any) -> Any -> Any) -> Any -> Any -> Any
forall a b. a -> b
coe
                                             (Any -> Any) -> Any -> Any
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du__'8718'_492
                                             ((T_IsPreorder_70 -> Any -> T__IsRelatedTo__78) -> Any -> Any
forall a b. a -> b
coe
                                                T_IsPreorder_70 -> Any -> T__IsRelatedTo__78
MAlonzo.Code.Relation.Binary.Reasoning.Base.Triple.du_stop_166
                                                (T_IsPreorder_70 -> Any
forall a b. a -> b
coe T_IsPreorder_70
d_'8804''45'isPreorder_2810))
                                             ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe
                                                Integer -> Integer -> Integer
addInt
                                                ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe
                                                   Integer -> Integer -> Integer
MAlonzo.Code.Data.Nat.Base.d_'8739'_'45'_'8739'_280
                                                   (Integer -> Any
forall a b. a -> b
coe Integer
v0) (Integer -> Any
forall a b. a -> b
coe Integer
v1))
                                                ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe
                                                   Integer -> Integer -> Integer
MAlonzo.Code.Data.Nat.Base.d_'8739'_'45'_'8739'_280
                                                   (Integer -> Any
forall a b. a -> b
coe Integer
v1) (Integer -> Any
forall a b. a -> b
coe (Integer
0 :: Integer)))))
                                          Any
forall a. a
erased)
                                       (Integer -> Integer -> T__'8804'__22
d_m'8804''8739'm'45'n'8739''43'n_5946 (Integer -> Integer
forall a b. a -> b
coe Integer
v0) (Integer -> Integer
forall a b. a -> b
coe Integer
v1)))
                                    Any
forall a. a
erased)
                          Integer
_ -> let v5 :: Integer
v5 = Integer -> Integer -> Integer
subInt (Integer -> Integer
forall a b. a -> b
coe Integer
v2) (Integer -> Integer
forall a b. a -> b
coe (Integer
1 :: Integer)) in
                               Any -> Any
forall a b. a -> b
coe
                                 ((Integer -> Integer -> Integer -> T__'8804'__22)
-> Any -> Any -> Any -> Any
forall a b. a -> b
coe
                                    Integer -> Integer -> Integer -> T__'8804'__22
d_'8739''45''8739''45'triangle_5954 (Integer -> Any
forall a b. a -> b
coe Integer
v3) (Integer -> Any
forall a b. a -> b
coe Integer
v4)
                                    (Integer -> Any
forall a b. a -> b
coe Integer
v5))))
-- Data.Nat.Properties.∣-∣≡∣-∣′
d_'8739''45''8739''8801''8739''45''8739''8242'_5986 ::
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8739''45''8739''8801''8739''45''8739''8242'_5986 :: Integer -> Integer -> T__'8801'__12
d_'8739''45''8739''8801''8739''45''8739''8242'_5986 = Integer -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Nat.Properties.∣-∣-isProtoMetric
d_'8739''45''8739''45'isProtoMetric_6008 ::
  MAlonzo.Code.Function.Metric.Structures.T_IsProtoMetric_30
d_'8739''45''8739''45'isProtoMetric_6008 :: T_IsProtoMetric_30
d_'8739''45''8739''45'isProtoMetric_6008
  = (T_IsPartialOrder_174
 -> T_IsEquivalence_26
 -> (Any -> Any -> Any -> Any -> Any -> Any -> Any)
 -> (Any -> Any -> Any)
 -> T_IsProtoMetric_30)
-> Any -> Any -> Any -> Any -> T_IsProtoMetric_30
forall a b. a -> b
coe
      T_IsPartialOrder_174
-> T_IsEquivalence_26
-> (Any -> Any -> Any -> Any -> Any -> Any -> Any)
-> (Any -> Any -> Any)
-> T_IsProtoMetric_30
MAlonzo.Code.Function.Metric.Structures.C_IsProtoMetric'46'constructor_2109
      (T_IsPartialOrder_174 -> Any
forall a b. a -> b
coe T_IsPartialOrder_174
d_'8804''45'isPartialOrder_2814)
      (T_IsEquivalence_26 -> Any
forall a b. a -> b
coe
         T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.PropositionalEquality.Properties.du_isEquivalence_396)
      Any
forall a. a
erased
      ((Any -> Any -> Any) -> Any
forall a b. a -> b
coe (\ Any
v0 Any
v1 -> T__'8804'__22 -> Any
forall a b. a -> b
coe T__'8804'__22
MAlonzo.Code.Data.Nat.Base.C_z'8804'n_26))
-- Data.Nat.Properties.∣-∣-isPreMetric
d_'8739''45''8739''45'isPreMetric_6010 ::
  MAlonzo.Code.Function.Metric.Structures.T_IsPreMetric_102
d_'8739''45''8739''45'isPreMetric_6010 :: T_IsPreMetric_102
d_'8739''45''8739''45'isPreMetric_6010
  = (T_IsProtoMetric_30
 -> (Any -> Any -> Any -> Any) -> T_IsPreMetric_102)
-> Any -> Any -> T_IsPreMetric_102
forall a b. a -> b
coe
      T_IsProtoMetric_30
-> (Any -> Any -> Any -> Any) -> T_IsPreMetric_102
MAlonzo.Code.Function.Metric.Structures.C_IsPreMetric'46'constructor_6347
      (T_IsProtoMetric_30 -> Any
forall a b. a -> b
coe T_IsProtoMetric_30
d_'8739''45''8739''45'isProtoMetric_6008) Any
forall a. a
erased
-- Data.Nat.Properties.∣-∣-isQuasiSemiMetric
d_'8739''45''8739''45'isQuasiSemiMetric_6012 ::
  MAlonzo.Code.Function.Metric.Structures.T_IsQuasiSemiMetric_174
d_'8739''45''8739''45'isQuasiSemiMetric_6012 :: T_IsQuasiSemiMetric_174
d_'8739''45''8739''45'isQuasiSemiMetric_6012
  = (T_IsPreMetric_102
 -> (Any -> Any -> Any -> Any) -> T_IsQuasiSemiMetric_174)
-> Any -> Any -> T_IsQuasiSemiMetric_174
forall a b. a -> b
coe
      T_IsPreMetric_102
-> (Any -> Any -> Any -> Any) -> T_IsQuasiSemiMetric_174
MAlonzo.Code.Function.Metric.Structures.C_IsQuasiSemiMetric'46'constructor_10111
      (T_IsPreMetric_102 -> Any
forall a b. a -> b
coe T_IsPreMetric_102
d_'8739''45''8739''45'isPreMetric_6010) Any
forall a. a
erased
-- Data.Nat.Properties.∣-∣-isSemiMetric
d_'8739''45''8739''45'isSemiMetric_6014 ::
  MAlonzo.Code.Function.Metric.Structures.T_IsSemiMetric_250
d_'8739''45''8739''45'isSemiMetric_6014 :: T_IsSemiMetric_250
d_'8739''45''8739''45'isSemiMetric_6014
  = (T_IsQuasiSemiMetric_174
 -> (Any -> Any -> Any) -> T_IsSemiMetric_250)
-> Any -> Any -> T_IsSemiMetric_250
forall a b. a -> b
coe
      T_IsQuasiSemiMetric_174
-> (Any -> Any -> Any) -> T_IsSemiMetric_250
MAlonzo.Code.Function.Metric.Structures.C_IsSemiMetric'46'constructor_14005
      (T_IsQuasiSemiMetric_174 -> Any
forall a b. a -> b
coe T_IsQuasiSemiMetric_174
d_'8739''45''8739''45'isQuasiSemiMetric_6012) Any
forall a. a
erased
-- Data.Nat.Properties.∣-∣-isMetric
d_'8739''45''8739''45'isMetric_6016 ::
  MAlonzo.Code.Function.Metric.Structures.T_IsGeneralMetric_332
d_'8739''45''8739''45'isMetric_6016 :: T_IsGeneralMetric_332
d_'8739''45''8739''45'isMetric_6016
  = (T_IsSemiMetric_250
 -> (Any -> Any -> Any -> Any) -> T_IsGeneralMetric_332)
-> Any -> Any -> T_IsGeneralMetric_332
forall a b. a -> b
coe
      T_IsSemiMetric_250
-> (Any -> Any -> Any -> Any) -> T_IsGeneralMetric_332
MAlonzo.Code.Function.Metric.Structures.C_IsGeneralMetric'46'constructor_18255
      (T_IsSemiMetric_250 -> Any
forall a b. a -> b
coe T_IsSemiMetric_250
d_'8739''45''8739''45'isSemiMetric_6014)
      ((Integer -> Integer -> Integer -> T__'8804'__22) -> Any
forall a b. a -> b
coe Integer -> Integer -> Integer -> T__'8804'__22
d_'8739''45''8739''45'triangle_5954)
-- Data.Nat.Properties.∣-∣-quasiSemiMetric
d_'8739''45''8739''45'quasiSemiMetric_6018 ::
  MAlonzo.Code.Function.Metric.Nat.Bundles.T_QuasiSemiMetric_186
d_'8739''45''8739''45'quasiSemiMetric_6018 :: T_QuasiSemiMetric_186
d_'8739''45''8739''45'quasiSemiMetric_6018
  = ((Any -> Any -> Integer)
 -> T_IsQuasiSemiMetric_174 -> T_QuasiSemiMetric_186)
-> (Integer -> Integer -> Integer)
-> T_IsQuasiSemiMetric_174
-> T_QuasiSemiMetric_186
forall a b. a -> b
coe
      (Any -> Any -> Integer)
-> T_IsQuasiSemiMetric_174 -> T_QuasiSemiMetric_186
MAlonzo.Code.Function.Metric.Nat.Bundles.C_QuasiSemiMetric'46'constructor_3255
      Integer -> Integer -> Integer
MAlonzo.Code.Data.Nat.Base.d_'8739'_'45'_'8739'_280
      T_IsQuasiSemiMetric_174
d_'8739''45''8739''45'isQuasiSemiMetric_6012
-- Data.Nat.Properties.∣-∣-semiMetric
d_'8739''45''8739''45'semiMetric_6020 ::
  MAlonzo.Code.Function.Metric.Nat.Bundles.T_SemiMetric_284
d_'8739''45''8739''45'semiMetric_6020 :: T_SemiMetric_284
d_'8739''45''8739''45'semiMetric_6020
  = ((Any -> Any -> Integer) -> T_IsSemiMetric_250 -> T_SemiMetric_284)
-> (Integer -> Integer -> Integer)
-> T_IsSemiMetric_250
-> T_SemiMetric_284
forall a b. a -> b
coe
      (Any -> Any -> Integer) -> T_IsSemiMetric_250 -> T_SemiMetric_284
MAlonzo.Code.Function.Metric.Nat.Bundles.C_SemiMetric'46'constructor_4991
      Integer -> Integer -> Integer
MAlonzo.Code.Data.Nat.Base.d_'8739'_'45'_'8739'_280
      T_IsSemiMetric_250
d_'8739''45''8739''45'isSemiMetric_6014
-- Data.Nat.Properties.∣-∣-preMetric
d_'8739''45''8739''45'preMetric_6022 ::
  MAlonzo.Code.Function.Metric.Nat.Bundles.T_PreMetric_96
d_'8739''45''8739''45'preMetric_6022 :: T_PreMetric_96
d_'8739''45''8739''45'preMetric_6022
  = ((Any -> Any -> Integer) -> T_IsPreMetric_102 -> T_PreMetric_96)
-> (Integer -> Integer -> Integer)
-> T_IsPreMetric_102
-> T_PreMetric_96
forall a b. a -> b
coe
      (Any -> Any -> Integer) -> T_IsPreMetric_102 -> T_PreMetric_96
MAlonzo.Code.Function.Metric.Nat.Bundles.C_PreMetric'46'constructor_1629
      Integer -> Integer -> Integer
MAlonzo.Code.Data.Nat.Base.d_'8739'_'45'_'8739'_280
      T_IsPreMetric_102
d_'8739''45''8739''45'isPreMetric_6010
-- Data.Nat.Properties.∣-∣-metric
d_'8739''45''8739''45'metric_6024 ::
  MAlonzo.Code.Function.Metric.Nat.Bundles.T_Metric_388
d_'8739''45''8739''45'metric_6024 :: T_Metric_388
d_'8739''45''8739''45'metric_6024
  = ((Any -> Any -> Integer) -> T_IsGeneralMetric_332 -> T_Metric_388)
-> (Integer -> Integer -> Integer)
-> T_IsGeneralMetric_332
-> T_Metric_388
forall a b. a -> b
coe
      (Any -> Any -> Integer) -> T_IsGeneralMetric_332 -> T_Metric_388
MAlonzo.Code.Function.Metric.Nat.Bundles.C_Metric'46'constructor_6797
      Integer -> Integer -> Integer
MAlonzo.Code.Data.Nat.Base.d_'8739'_'45'_'8739'_280
      T_IsGeneralMetric_332
d_'8739''45''8739''45'isMetric_6016
-- Data.Nat.Properties.⌊n/2⌋-mono
d_'8970'n'47'2'8971''45'mono_6026 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_'8970'n'47'2'8971''45'mono_6026 :: Integer -> Integer -> T__'8804'__22 -> T__'8804'__22
d_'8970'n'47'2'8971''45'mono_6026 ~Integer
v0 ~Integer
v1 T__'8804'__22
v2
  = T__'8804'__22 -> T__'8804'__22
du_'8970'n'47'2'8971''45'mono_6026 T__'8804'__22
v2
du_'8970'n'47'2'8971''45'mono_6026 ::
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
du_'8970'n'47'2'8971''45'mono_6026 :: T__'8804'__22 -> T__'8804'__22
du_'8970'n'47'2'8971''45'mono_6026 T__'8804'__22
v0
  = case T__'8804'__22 -> T__'8804'__22
forall a b. a -> b
coe T__'8804'__22
v0 of
      T__'8804'__22
MAlonzo.Code.Data.Nat.Base.C_z'8804'n_26
        -> T__'8804'__22 -> T__'8804'__22
forall a b. a -> b
coe T__'8804'__22
MAlonzo.Code.Data.Nat.Base.C_z'8804'n_26
      MAlonzo.Code.Data.Nat.Base.C_s'8804's_34 T__'8804'__22
v3
        -> case T__'8804'__22 -> T__'8804'__22
forall a b. a -> b
coe T__'8804'__22
v3 of
             T__'8804'__22
MAlonzo.Code.Data.Nat.Base.C_z'8804'n_26
               -> T__'8804'__22 -> T__'8804'__22
forall a b. a -> b
coe T__'8804'__22
MAlonzo.Code.Data.Nat.Base.C_z'8804'n_26
             MAlonzo.Code.Data.Nat.Base.C_s'8804's_34 T__'8804'__22
v6
               -> (T__'8804'__22 -> T__'8804'__22) -> Any -> T__'8804'__22
forall a b. a -> b
coe
                    T__'8804'__22 -> T__'8804'__22
MAlonzo.Code.Data.Nat.Base.C_s'8804's_34
                    ((T__'8804'__22 -> T__'8804'__22) -> Any -> Any
forall a b. a -> b
coe T__'8804'__22 -> T__'8804'__22
du_'8970'n'47'2'8971''45'mono_6026 (T__'8804'__22 -> Any
forall a b. a -> b
coe T__'8804'__22
v6))
             T__'8804'__22
_ -> T__'8804'__22
forall a. a
MAlonzo.RTE.mazUnreachableError
      T__'8804'__22
_ -> T__'8804'__22
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Data.Nat.Properties.⌈n/2⌉-mono
d_'8968'n'47'2'8969''45'mono_6030 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_'8968'n'47'2'8969''45'mono_6030 :: Integer -> Integer -> T__'8804'__22 -> T__'8804'__22
d_'8968'n'47'2'8969''45'mono_6030 ~Integer
v0 ~Integer
v1 T__'8804'__22
v2
  = T__'8804'__22 -> T__'8804'__22
du_'8968'n'47'2'8969''45'mono_6030 T__'8804'__22
v2
du_'8968'n'47'2'8969''45'mono_6030 ::
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
du_'8968'n'47'2'8969''45'mono_6030 :: T__'8804'__22 -> T__'8804'__22
du_'8968'n'47'2'8969''45'mono_6030 T__'8804'__22
v0
  = (T__'8804'__22 -> T__'8804'__22) -> Any -> T__'8804'__22
forall a b. a -> b
coe
      T__'8804'__22 -> T__'8804'__22
du_'8970'n'47'2'8971''45'mono_6026
      ((T__'8804'__22 -> T__'8804'__22) -> T__'8804'__22 -> Any
forall a b. a -> b
coe T__'8804'__22 -> T__'8804'__22
MAlonzo.Code.Data.Nat.Base.C_s'8804's_34 T__'8804'__22
v0)
-- Data.Nat.Properties.⌊n/2⌋≤⌈n/2⌉
d_'8970'n'47'2'8971''8804''8968'n'47'2'8969'_6036 ::
  Integer -> MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_'8970'n'47'2'8971''8804''8968'n'47'2'8969'_6036 :: Integer -> T__'8804'__22
d_'8970'n'47'2'8971''8804''8968'n'47'2'8969'_6036 Integer
v0
  = case Integer -> Integer
forall a b. a -> b
coe Integer
v0 of
      Integer
0 -> T__'8804'__22 -> T__'8804'__22
forall a b. a -> b
coe T__'8804'__22
MAlonzo.Code.Data.Nat.Base.C_z'8804'n_26
      Integer
1 -> T__'8804'__22 -> T__'8804'__22
forall a b. a -> b
coe T__'8804'__22
MAlonzo.Code.Data.Nat.Base.C_z'8804'n_26
      Integer
_ -> let v1 :: Integer
v1 = Integer -> Integer -> Integer
subInt (Integer -> Integer
forall a b. a -> b
coe Integer
v0) (Integer -> Integer
forall a b. a -> b
coe (Integer
2 :: Integer)) in
           Any -> T__'8804'__22
forall a b. a -> b
coe
             ((T__'8804'__22 -> T__'8804'__22) -> T__'8804'__22 -> Any
forall a b. a -> b
coe
                T__'8804'__22 -> T__'8804'__22
MAlonzo.Code.Data.Nat.Base.C_s'8804's_34
                (Integer -> T__'8804'__22
d_'8970'n'47'2'8971''8804''8968'n'47'2'8969'_6036 (Integer -> Integer
forall a b. a -> b
coe Integer
v1)))
-- Data.Nat.Properties.⌊n/2⌋+⌈n/2⌉≡n
d_'8970'n'47'2'8971''43''8968'n'47'2'8969''8801'n_6042 ::
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8970'n'47'2'8971''43''8968'n'47'2'8969''8801'n_6042 :: Integer -> T__'8801'__12
d_'8970'n'47'2'8971''43''8968'n'47'2'8969''8801'n_6042 = Integer -> T__'8801'__12
forall a. a
erased
-- Data.Nat.Properties.⌊n/2⌋≤n
d_'8970'n'47'2'8971''8804'n_6048 ::
  Integer -> MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_'8970'n'47'2'8971''8804'n_6048 :: Integer -> T__'8804'__22
d_'8970'n'47'2'8971''8804'n_6048 Integer
v0
  = case Integer -> Integer
forall a b. a -> b
coe Integer
v0 of
      Integer
0 -> T__'8804'__22 -> T__'8804'__22
forall a b. a -> b
coe T__'8804'__22
MAlonzo.Code.Data.Nat.Base.C_z'8804'n_26
      Integer
1 -> T__'8804'__22 -> T__'8804'__22
forall a b. a -> b
coe T__'8804'__22
MAlonzo.Code.Data.Nat.Base.C_z'8804'n_26
      Integer
_ -> let v1 :: Integer
v1 = Integer -> Integer -> Integer
subInt (Integer -> Integer
forall a b. a -> b
coe Integer
v0) (Integer -> Integer
forall a b. a -> b
coe (Integer
2 :: Integer)) in
           Any -> T__'8804'__22
forall a b. a -> b
coe
             ((T__'8804'__22 -> T__'8804'__22) -> T__'8804'__22 -> Any
forall a b. a -> b
coe
                T__'8804'__22 -> T__'8804'__22
MAlonzo.Code.Data.Nat.Base.C_s'8804's_34
                (Integer -> T__'8804'__22
d_'8970'n'47'2'8971''8804'n_6048 (Integer -> Integer
forall a b. a -> b
coe Integer
v1)))
-- Data.Nat.Properties.⌊n/2⌋<n
d_'8970'n'47'2'8971''60'n_6054 ::
  Integer -> MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_'8970'n'47'2'8971''60'n_6054 :: Integer -> T__'8804'__22
d_'8970'n'47'2'8971''60'n_6054 Integer
v0
  = case Integer -> Integer
forall a b. a -> b
coe Integer
v0 of
      Integer
0 -> (T__'8804'__22 -> T__'8804'__22) -> Any -> T__'8804'__22
forall a b. a -> b
coe
             T__'8804'__22 -> T__'8804'__22
MAlonzo.Code.Data.Nat.Base.C_s'8804's_34
             (T__'8804'__22 -> Any
forall a b. a -> b
coe T__'8804'__22
MAlonzo.Code.Data.Nat.Base.C_z'8804'n_26)
      Integer
_ -> let v1 :: Integer
v1 = Integer -> Integer -> Integer
subInt (Integer -> Integer
forall a b. a -> b
coe Integer
v0) (Integer -> Integer
forall a b. a -> b
coe (Integer
1 :: Integer)) in
           Any -> T__'8804'__22
forall a b. a -> b
coe
             ((T__'8804'__22 -> T__'8804'__22) -> Any -> Any
forall a b. a -> b
coe
                T__'8804'__22 -> T__'8804'__22
MAlonzo.Code.Data.Nat.Base.C_s'8804's_34
                ((T__'8804'__22 -> T__'8804'__22) -> T__'8804'__22 -> Any
forall a b. a -> b
coe
                   T__'8804'__22 -> T__'8804'__22
MAlonzo.Code.Data.Nat.Base.C_s'8804's_34
                   (Integer -> T__'8804'__22
d_'8970'n'47'2'8971''8804'n_6048 (Integer -> Integer
forall a b. a -> b
coe Integer
v1))))
-- Data.Nat.Properties.n≡⌊n+n/2⌋
d_n'8801''8970'n'43'n'47'2'8971'_6060 ::
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_n'8801''8970'n'43'n'47'2'8971'_6060 :: Integer -> T__'8801'__12
d_n'8801''8970'n'43'n'47'2'8971'_6060 = Integer -> T__'8801'__12
forall a. a
erased
-- Data.Nat.Properties.⌈n/2⌉≤n
d_'8968'n'47'2'8969''8804'n_6068 ::
  Integer -> MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_'8968'n'47'2'8969''8804'n_6068 :: Integer -> T__'8804'__22
d_'8968'n'47'2'8969''8804'n_6068 Integer
v0
  = case Integer -> Integer
forall a b. a -> b
coe Integer
v0 of
      Integer
0 -> T__'8804'__22 -> T__'8804'__22
forall a b. a -> b
coe T__'8804'__22
MAlonzo.Code.Data.Nat.Base.C_z'8804'n_26
      Integer
_ -> let v1 :: Integer
v1 = Integer -> Integer -> Integer
subInt (Integer -> Integer
forall a b. a -> b
coe Integer
v0) (Integer -> Integer
forall a b. a -> b
coe (Integer
1 :: Integer)) in
           Any -> T__'8804'__22
forall a b. a -> b
coe
             ((T__'8804'__22 -> T__'8804'__22) -> T__'8804'__22 -> Any
forall a b. a -> b
coe
                T__'8804'__22 -> T__'8804'__22
MAlonzo.Code.Data.Nat.Base.C_s'8804's_34
                (Integer -> T__'8804'__22
d_'8970'n'47'2'8971''8804'n_6048 (Integer -> Integer
forall a b. a -> b
coe Integer
v1)))
-- Data.Nat.Properties.⌈n/2⌉<n
d_'8968'n'47'2'8969''60'n_6074 ::
  Integer -> MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_'8968'n'47'2'8969''60'n_6074 :: Integer -> T__'8804'__22
d_'8968'n'47'2'8969''60'n_6074 Integer
v0
  = (T__'8804'__22 -> T__'8804'__22) -> T__'8804'__22 -> T__'8804'__22
forall a b. a -> b
coe
      T__'8804'__22 -> T__'8804'__22
MAlonzo.Code.Data.Nat.Base.C_s'8804's_34
      (Integer -> T__'8804'__22
d_'8970'n'47'2'8971''60'n_6054 (Integer -> Integer
forall a b. a -> b
coe Integer
v0))
-- Data.Nat.Properties.n≡⌈n+n/2⌉
d_n'8801''8968'n'43'n'47'2'8969'_6080 ::
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_n'8801''8968'n'43'n'47'2'8969'_6080 :: Integer -> T__'8801'__12
d_n'8801''8968'n'43'n'47'2'8969'_6080 = Integer -> T__'8801'__12
forall a. a
erased
-- Data.Nat.Properties.1≤n!
d_1'8804'n'33'_6088 ::
  Integer -> MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_1'8804'n'33'_6088 :: Integer -> T__'8804'__22
d_1'8804'n'33'_6088 Integer
v0
  = case Integer -> Integer
forall a b. a -> b
coe Integer
v0 of
      Integer
0 -> (Integer -> T__'8804'__22) -> Any -> T__'8804'__22
forall a b. a -> b
coe Integer -> T__'8804'__22
d_'8804''45'refl_2776 (Integer -> Any
forall a b. a -> b
coe (Integer
1 :: Integer))
      Integer
_ -> let v1 :: Integer
v1 = Integer -> Integer -> Integer
subInt (Integer -> Integer
forall a b. a -> b
coe Integer
v0) (Integer -> Integer
forall a b. a -> b
coe (Integer
1 :: Integer)) in
           Any -> T__'8804'__22
forall a b. a -> b
coe
             ((Integer
 -> Integer -> T__'8804'__22 -> T__'8804'__22 -> T__'8804'__22)
-> Any -> Any -> Any -> Any -> Any
forall a b. a -> b
coe
                Integer
-> Integer -> T__'8804'__22 -> T__'8804'__22 -> T__'8804'__22
du_'42''45'mono'45''8804'_4060 (Integer -> Any
forall a b. a -> b
coe Integer
v0)
                ((Integer -> Integer) -> Any -> Any
forall a b. a -> b
coe Integer -> Integer
MAlonzo.Code.Data.Nat.Base.d__'33'_332 (Integer -> Any
forall a b. a -> b
coe Integer
v1))
                ((Integer -> T__'8804'__22) -> Any -> Any
forall a b. a -> b
coe Integer -> T__'8804'__22
du_m'8804'm'43'n_3482 (Integer -> Any
forall a b. a -> b
coe (Integer
1 :: Integer)))
                ((Integer -> T__'8804'__22) -> Any -> Any
forall a b. a -> b
coe Integer -> T__'8804'__22
d_1'8804'n'33'_6088 (Integer -> Any
forall a b. a -> b
coe Integer
v1)))
-- Data.Nat.Properties._!≢0
d__'33''8802'0_6094 ::
  Integer -> MAlonzo.Code.Data.Nat.Base.T_NonZero_112
d__'33''8802'0_6094 :: Integer -> T_NonZero_112
d__'33''8802'0_6094 Integer
v0
  = (T__'8804'__22 -> T_NonZero_112) -> Any -> T_NonZero_112
forall a b. a -> b
coe
      T__'8804'__22 -> T_NonZero_112
MAlonzo.Code.Data.Nat.Base.du_'62''45'nonZero_136
      ((Integer -> T__'8804'__22) -> Any -> Any
forall a b. a -> b
coe Integer -> T__'8804'__22
d_1'8804'n'33'_6088 (Integer -> Any
forall a b. a -> b
coe Integer
v0))
-- Data.Nat.Properties._!*_!≢0
d__'33''42'_'33''8802'0_6102 ::
  Integer -> Integer -> MAlonzo.Code.Data.Nat.Base.T_NonZero_112
d__'33''42'_'33''8802'0_6102 :: Integer -> Integer -> T_NonZero_112
d__'33''42'_'33''8802'0_6102 ~Integer
v0 ~Integer
v1
  = T_NonZero_112
du__'33''42'_'33''8802'0_6102
du__'33''42'_'33''8802'0_6102 ::
  MAlonzo.Code.Data.Nat.Base.T_NonZero_112
du__'33''42'_'33''8802'0_6102 :: T_NonZero_112
du__'33''42'_'33''8802'0_6102 = T_NonZero_112 -> T_NonZero_112
forall a b. a -> b
coe T_NonZero_112
du_m'42'n'8802'0_3840
-- Data.Nat.Properties.≤′-trans
d_'8804''8242''45'trans_6108 ::
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804''8242'__338 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804''8242'__338 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804''8242'__338
d_'8804''8242''45'trans_6108 :: Integer
-> Integer
-> Integer
-> T__'8804''8242'__338
-> T__'8804''8242'__338
-> T__'8804''8242'__338
d_'8804''8242''45'trans_6108 ~Integer
v0 ~Integer
v1 ~Integer
v2 T__'8804''8242'__338
v3 T__'8804''8242'__338
v4
  = T__'8804''8242'__338
-> T__'8804''8242'__338 -> T__'8804''8242'__338
du_'8804''8242''45'trans_6108 T__'8804''8242'__338
v3 T__'8804''8242'__338
v4
du_'8804''8242''45'trans_6108 ::
  MAlonzo.Code.Data.Nat.Base.T__'8804''8242'__338 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804''8242'__338 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804''8242'__338
du_'8804''8242''45'trans_6108 :: T__'8804''8242'__338
-> T__'8804''8242'__338 -> T__'8804''8242'__338
du_'8804''8242''45'trans_6108 T__'8804''8242'__338
v0 T__'8804''8242'__338
v1
  = case T__'8804''8242'__338 -> T__'8804''8242'__338
forall a b. a -> b
coe T__'8804''8242'__338
v1 of
      T__'8804''8242'__338
MAlonzo.Code.Data.Nat.Base.C_'8804''8242''45'refl_342 -> T__'8804''8242'__338 -> T__'8804''8242'__338
forall a b. a -> b
coe T__'8804''8242'__338
v0
      MAlonzo.Code.Data.Nat.Base.C_'8804''8242''45'step_348 T__'8804''8242'__338
v3
        -> (T__'8804''8242'__338 -> T__'8804''8242'__338)
-> Any -> T__'8804''8242'__338
forall a b. a -> b
coe
             T__'8804''8242'__338 -> T__'8804''8242'__338
MAlonzo.Code.Data.Nat.Base.C_'8804''8242''45'step_348
             ((T__'8804''8242'__338
 -> T__'8804''8242'__338 -> T__'8804''8242'__338)
-> Any -> Any -> Any
forall a b. a -> b
coe T__'8804''8242'__338
-> T__'8804''8242'__338 -> T__'8804''8242'__338
du_'8804''8242''45'trans_6108 (T__'8804''8242'__338 -> Any
forall a b. a -> b
coe T__'8804''8242'__338
v0) (T__'8804''8242'__338 -> Any
forall a b. a -> b
coe T__'8804''8242'__338
v3))
      T__'8804''8242'__338
_ -> T__'8804''8242'__338
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Data.Nat.Properties.z≤′n
d_z'8804''8242'n_6116 ::
  Integer -> MAlonzo.Code.Data.Nat.Base.T__'8804''8242'__338
d_z'8804''8242'n_6116 :: Integer -> T__'8804''8242'__338
d_z'8804''8242'n_6116 Integer
v0
  = case Integer -> Integer
forall a b. a -> b
coe Integer
v0 of
      Integer
0 -> T__'8804''8242'__338 -> T__'8804''8242'__338
forall a b. a -> b
coe T__'8804''8242'__338
MAlonzo.Code.Data.Nat.Base.C_'8804''8242''45'refl_342
      Integer
_ -> let v1 :: Integer
v1 = Integer -> Integer -> Integer
subInt (Integer -> Integer
forall a b. a -> b
coe Integer
v0) (Integer -> Integer
forall a b. a -> b
coe (Integer
1 :: Integer)) in
           Any -> T__'8804''8242'__338
forall a b. a -> b
coe
             ((T__'8804''8242'__338 -> T__'8804''8242'__338)
-> T__'8804''8242'__338 -> Any
forall a b. a -> b
coe
                T__'8804''8242'__338 -> T__'8804''8242'__338
MAlonzo.Code.Data.Nat.Base.C_'8804''8242''45'step_348
                (Integer -> T__'8804''8242'__338
d_z'8804''8242'n_6116 (Integer -> Integer
forall a b. a -> b
coe Integer
v1)))
-- Data.Nat.Properties.s≤′s
d_s'8804''8242's_6120 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804''8242'__338 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804''8242'__338
d_s'8804''8242's_6120 :: Integer -> Integer -> T__'8804''8242'__338 -> T__'8804''8242'__338
d_s'8804''8242's_6120 ~Integer
v0 ~Integer
v1 T__'8804''8242'__338
v2 = T__'8804''8242'__338 -> T__'8804''8242'__338
du_s'8804''8242's_6120 T__'8804''8242'__338
v2
du_s'8804''8242's_6120 ::
  MAlonzo.Code.Data.Nat.Base.T__'8804''8242'__338 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804''8242'__338
du_s'8804''8242's_6120 :: T__'8804''8242'__338 -> T__'8804''8242'__338
du_s'8804''8242's_6120 T__'8804''8242'__338
v0 = T__'8804''8242'__338 -> T__'8804''8242'__338
forall a b. a -> b
coe T__'8804''8242'__338
v0
-- Data.Nat.Properties.≤′⇒≤
d_'8804''8242''8658''8804'_6124 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804''8242'__338 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_'8804''8242''8658''8804'_6124 :: Integer -> Integer -> T__'8804''8242'__338 -> T__'8804'__22
d_'8804''8242''8658''8804'_6124 Integer
v0 ~Integer
v1 T__'8804''8242'__338
v2
  = Integer -> T__'8804''8242'__338 -> T__'8804'__22
du_'8804''8242''8658''8804'_6124 Integer
v0 T__'8804''8242'__338
v2
du_'8804''8242''8658''8804'_6124 ::
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804''8242'__338 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
du_'8804''8242''8658''8804'_6124 :: Integer -> T__'8804''8242'__338 -> T__'8804'__22
du_'8804''8242''8658''8804'_6124 Integer
v0 T__'8804''8242'__338
v1
  = case T__'8804''8242'__338 -> T__'8804''8242'__338
forall a b. a -> b
coe T__'8804''8242'__338
v1 of
      T__'8804''8242'__338
MAlonzo.Code.Data.Nat.Base.C_'8804''8242''45'refl_342
        -> (Integer -> T__'8804'__22) -> Any -> T__'8804'__22
forall a b. a -> b
coe Integer -> T__'8804'__22
d_'8804''45'refl_2776 (Integer -> Any
forall a b. a -> b
coe Integer
v0)
      MAlonzo.Code.Data.Nat.Base.C_'8804''8242''45'step_348 T__'8804''8242'__338
v3
        -> (Integer -> T__'8804''8242'__338 -> T__'8804'__22)
-> Any -> Any -> T__'8804'__22
forall a b. a -> b
coe Integer -> T__'8804''8242'__338 -> T__'8804'__22
du_'8804''8242''8658''8804'_6124 (Integer -> Any
forall a b. a -> b
coe Integer
v0) (T__'8804''8242'__338 -> Any
forall a b. a -> b
coe T__'8804''8242'__338
v3)
      T__'8804''8242'__338
_ -> T__'8804'__22
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Data.Nat.Properties.≤⇒≤′
d_'8804''8658''8804''8242'_6128 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804''8242'__338
d_'8804''8658''8804''8242'_6128 :: Integer -> Integer -> T__'8804'__22 -> T__'8804''8242'__338
d_'8804''8658''8804''8242'_6128 ~Integer
v0 Integer
v1 T__'8804'__22
v2
  = Integer -> T__'8804'__22 -> T__'8804''8242'__338
du_'8804''8658''8804''8242'_6128 Integer
v1 T__'8804'__22
v2
du_'8804''8658''8804''8242'_6128 ::
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804''8242'__338
du_'8804''8658''8804''8242'_6128 :: Integer -> T__'8804'__22 -> T__'8804''8242'__338
du_'8804''8658''8804''8242'_6128 Integer
v0 T__'8804'__22
v1
  = case T__'8804'__22 -> T__'8804'__22
forall a b. a -> b
coe T__'8804'__22
v1 of
      T__'8804'__22
MAlonzo.Code.Data.Nat.Base.C_z'8804'n_26
        -> (Integer -> T__'8804''8242'__338) -> Any -> T__'8804''8242'__338
forall a b. a -> b
coe Integer -> T__'8804''8242'__338
d_z'8804''8242'n_6116 (Integer -> Any
forall a b. a -> b
coe Integer
v0)
      MAlonzo.Code.Data.Nat.Base.C_s'8804's_34 T__'8804'__22
v4
        -> let v5 :: Integer
v5 = Integer -> Integer -> Integer
subInt (Integer -> Integer
forall a b. a -> b
coe Integer
v0) (Integer -> Integer
forall a b. a -> b
coe (Integer
1 :: Integer)) in
           Any -> T__'8804''8242'__338
forall a b. a -> b
coe ((Integer -> T__'8804'__22 -> T__'8804''8242'__338)
-> Any -> Any -> Any
forall a b. a -> b
coe Integer -> T__'8804'__22 -> T__'8804''8242'__338
du_'8804''8658''8804''8242'_6128 (Integer -> Any
forall a b. a -> b
coe Integer
v5) (T__'8804'__22 -> Any
forall a b. a -> b
coe T__'8804'__22
v4))
      T__'8804'__22
_ -> T__'8804''8242'__338
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Data.Nat.Properties.≤′-step-injective
d_'8804''8242''45'step'45'injective_6136 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804''8242'__338 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804''8242'__338 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8804''8242''45'step'45'injective_6136 :: Integer
-> Integer
-> T__'8804''8242'__338
-> T__'8804''8242'__338
-> T__'8801'__12
-> T__'8801'__12
d_'8804''8242''45'step'45'injective_6136 = Integer
-> Integer
-> T__'8804''8242'__338
-> T__'8804''8242'__338
-> T__'8801'__12
-> T__'8801'__12
forall a. a
erased
-- Data.Nat.Properties.z<′s
d_z'60''8242's_6138 ::
  Integer -> MAlonzo.Code.Data.Nat.Base.T__'8804''8242'__338
d_z'60''8242's_6138 :: Integer -> T__'8804''8242'__338
d_z'60''8242's_6138 Integer
v0
  = case Integer -> Integer
forall a b. a -> b
coe Integer
v0 of
      Integer
0 -> T__'8804''8242'__338 -> T__'8804''8242'__338
forall a b. a -> b
coe T__'8804''8242'__338
MAlonzo.Code.Data.Nat.Base.C_'8804''8242''45'refl_342
      Integer
_ -> let v1 :: Integer
v1 = Integer -> Integer -> Integer
subInt (Integer -> Integer
forall a b. a -> b
coe Integer
v0) (Integer -> Integer
forall a b. a -> b
coe (Integer
1 :: Integer)) in
           Any -> T__'8804''8242'__338
forall a b. a -> b
coe
             ((T__'8804''8242'__338 -> T__'8804''8242'__338)
-> T__'8804''8242'__338 -> Any
forall a b. a -> b
coe
                T__'8804''8242'__338 -> T__'8804''8242'__338
MAlonzo.Code.Data.Nat.Base.C_'8804''8242''45'step_348
                (Integer -> T__'8804''8242'__338
d_z'60''8242's_6138 (Integer -> Integer
forall a b. a -> b
coe Integer
v1)))
-- Data.Nat.Properties.s<′s
d_s'60''8242's_6142 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804''8242'__338 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804''8242'__338
d_s'60''8242's_6142 :: Integer -> Integer -> T__'8804''8242'__338 -> T__'8804''8242'__338
d_s'60''8242's_6142 ~Integer
v0 ~Integer
v1 T__'8804''8242'__338
v2 = T__'8804''8242'__338 -> T__'8804''8242'__338
du_s'60''8242's_6142 T__'8804''8242'__338
v2
du_s'60''8242's_6142 ::
  MAlonzo.Code.Data.Nat.Base.T__'8804''8242'__338 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804''8242'__338
du_s'60''8242's_6142 :: T__'8804''8242'__338 -> T__'8804''8242'__338
du_s'60''8242's_6142 T__'8804''8242'__338
v0 = T__'8804''8242'__338 -> T__'8804''8242'__338
forall a b. a -> b
coe T__'8804''8242'__338
v0
-- Data.Nat.Properties.<⇒<′
d_'60''8658''60''8242'_6146 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804''8242'__338
d_'60''8658''60''8242'_6146 :: Integer -> Integer -> T__'8804'__22 -> T__'8804''8242'__338
d_'60''8658''60''8242'_6146 ~Integer
v0 Integer
v1 T__'8804'__22
v2
  = Integer -> T__'8804'__22 -> T__'8804''8242'__338
du_'60''8658''60''8242'_6146 Integer
v1 T__'8804'__22
v2
du_'60''8658''60''8242'_6146 ::
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804''8242'__338
du_'60''8658''60''8242'_6146 :: Integer -> T__'8804'__22 -> T__'8804''8242'__338
du_'60''8658''60''8242'_6146 Integer
v0 T__'8804'__22
v1
  = case T__'8804'__22 -> T__'8804'__22
forall a b. a -> b
coe T__'8804'__22
v1 of
      MAlonzo.Code.Data.Nat.Base.C_s'8804's_34 T__'8804'__22
v4
        -> let v5 :: Integer
v5 = Integer -> Integer -> Integer
subInt (Integer -> Integer
forall a b. a -> b
coe Integer
v0) (Integer -> Integer
forall a b. a -> b
coe (Integer
1 :: Integer)) in
           Any -> T__'8804''8242'__338
forall a b. a -> b
coe
             (case T__'8804'__22 -> T__'8804'__22
forall a b. a -> b
coe T__'8804'__22
v4 of
                T__'8804'__22
MAlonzo.Code.Data.Nat.Base.C_z'8804'n_26
                  -> (Integer -> T__'8804''8242'__338) -> Any -> Any
forall a b. a -> b
coe Integer -> T__'8804''8242'__338
d_z'60''8242's_6138 (Integer -> Any
forall a b. a -> b
coe Integer
v5)
                MAlonzo.Code.Data.Nat.Base.C_s'8804's_34 T__'8804'__22
v8
                  -> (Integer -> T__'8804'__22 -> T__'8804''8242'__338)
-> Any -> Any -> Any
forall a b. a -> b
coe
                       Integer -> T__'8804'__22 -> T__'8804''8242'__338
du_'60''8658''60''8242'_6146
                       ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> Integer
subInt (Integer -> Any
forall a b. a -> b
coe Integer
v0) (Integer -> Any
forall a b. a -> b
coe (Integer
1 :: Integer)))
                       ((T__'8804'__22 -> T__'8804'__22) -> T__'8804'__22 -> Any
forall a b. a -> b
coe T__'8804'__22 -> T__'8804'__22
MAlonzo.Code.Data.Nat.Base.C_s'8804's_34 T__'8804'__22
v8)
                T__'8804'__22
_ -> Any
forall a. a
MAlonzo.RTE.mazUnreachableError)
      T__'8804'__22
_ -> T__'8804''8242'__338
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Data.Nat.Properties.<′⇒<
d_'60''8242''8658''60'_6150 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804''8242'__338 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_'60''8242''8658''60'_6150 :: Integer -> Integer -> T__'8804''8242'__338 -> T__'8804'__22
d_'60''8242''8658''60'_6150 Integer
v0 ~Integer
v1 T__'8804''8242'__338
v2
  = Integer -> T__'8804''8242'__338 -> T__'8804'__22
du_'60''8242''8658''60'_6150 Integer
v0 T__'8804''8242'__338
v2
du_'60''8242''8658''60'_6150 ::
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804''8242'__338 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
du_'60''8242''8658''60'_6150 :: Integer -> T__'8804''8242'__338 -> T__'8804'__22
du_'60''8242''8658''60'_6150 Integer
v0 T__'8804''8242'__338
v1
  = case T__'8804''8242'__338 -> T__'8804''8242'__338
forall a b. a -> b
coe T__'8804''8242'__338
v1 of
      T__'8804''8242'__338
MAlonzo.Code.Data.Nat.Base.C_'8804''8242''45'refl_342
        -> (Integer -> T__'8804'__22) -> Any -> T__'8804'__22
forall a b. a -> b
coe Integer -> T__'8804'__22
d_n'60'1'43'n_3078 (Integer -> Any
forall a b. a -> b
coe Integer
v0)
      MAlonzo.Code.Data.Nat.Base.C_'8804''8242''45'step_348 T__'8804''8242'__338
v3
        -> (T__'8804'__22 -> T__'8804'__22) -> Any -> T__'8804'__22
forall a b. a -> b
coe
             T__'8804'__22 -> T__'8804'__22
du_m'60'n'8658'm'60'1'43'n_3062
             ((Integer -> T__'8804''8242'__338 -> T__'8804'__22)
-> Any -> Any -> Any
forall a b. a -> b
coe Integer -> T__'8804''8242'__338 -> T__'8804'__22
du_'60''8242''8658''60'_6150 (Integer -> Any
forall a b. a -> b
coe Integer
v0) (T__'8804''8242'__338 -> Any
forall a b. a -> b
coe T__'8804''8242'__338
v3))
      T__'8804''8242'__338
_ -> T__'8804'__22
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Data.Nat.Properties.m<1+n⇒m<n∨m≡n′
d_m'60'1'43'n'8658'm'60'n'8744'm'8801'n'8242'_6154 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Sum.Base.T__'8846'__30
d_m'60'1'43'n'8658'm'60'n'8744'm'8801'n'8242'_6154 :: Integer -> Integer -> T__'8804'__22 -> T__'8846'__30
d_m'60'1'43'n'8658'm'60'n'8744'm'8801'n'8242'_6154 Integer
v0 Integer
v1 T__'8804'__22
v2
  = let v3 :: t
v3
          = (Integer -> T__'8804'__22 -> T__'8804''8242'__338)
-> Any -> Any -> t
forall a b. a -> b
coe
              Integer -> T__'8804'__22 -> T__'8804''8242'__338
du_'60''8658''60''8242'_6146
              ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> Integer
addInt (Integer -> Any
forall a b. a -> b
coe (Integer
1 :: Integer)) (Integer -> Any
forall a b. a -> b
coe Integer
v1)) (T__'8804'__22 -> Any
forall a b. a -> b
coe T__'8804'__22
v2) in
    Any -> T__'8846'__30
forall a b. a -> b
coe
      (case Any -> T__'8804''8242'__338
forall a b. a -> b
coe Any
forall a. a
v3 of
         T__'8804''8242'__338
MAlonzo.Code.Data.Nat.Base.C_'8804''8242''45'refl_342
           -> (Any -> T__'8846'__30) -> Any -> Any
forall a b. a -> b
coe Any -> T__'8846'__30
MAlonzo.Code.Data.Sum.Base.C_inj'8322'_42 Any
forall a. a
erased
         MAlonzo.Code.Data.Nat.Base.C_'8804''8242''45'step_348 T__'8804''8242'__338
v5
           -> (Any -> T__'8846'__30) -> Any -> Any
forall a b. a -> b
coe
                Any -> T__'8846'__30
MAlonzo.Code.Data.Sum.Base.C_inj'8321'_38
                ((Integer -> T__'8804''8242'__338 -> T__'8804'__22)
-> Any -> Any -> Any
forall a b. a -> b
coe Integer -> T__'8804''8242'__338 -> T__'8804'__22
du_'60''8242''8658''60'_6150 (Integer -> Any
forall a b. a -> b
coe Integer
v0) (T__'8804''8242'__338 -> Any
forall a b. a -> b
coe T__'8804''8242'__338
v5))
         T__'8804''8242'__338
_ -> Any
forall a. a
MAlonzo.RTE.mazUnreachableError)
-- Data.Nat.Properties._≤′?_
d__'8804''8242''63'__6168 ::
  Integer ->
  Integer -> MAlonzo.Code.Relation.Nullary.Decidable.Core.T_Dec_20
d__'8804''8242''63'__6168 :: Integer -> Integer -> T_Dec_20
d__'8804''8242''63'__6168 Integer
v0 Integer
v1
  = ((Any -> Any) -> (Any -> Any) -> T_Dec_20 -> T_Dec_20)
-> Any -> Any -> Any -> T_Dec_20
forall a b. a -> b
coe
      (Any -> Any) -> (Any -> Any) -> T_Dec_20 -> T_Dec_20
MAlonzo.Code.Relation.Nullary.Decidable.Core.du_map'8242'_168
      ((Integer -> T__'8804'__22 -> T__'8804''8242'__338) -> Any -> Any
forall a b. a -> b
coe Integer -> T__'8804'__22 -> T__'8804''8242'__338
du_'8804''8658''8804''8242'_6128 (Integer -> Any
forall a b. a -> b
coe Integer
v1))
      ((Integer -> T__'8804''8242'__338 -> T__'8804'__22) -> Any -> Any
forall a b. a -> b
coe Integer -> T__'8804''8242'__338 -> T__'8804'__22
du_'8804''8242''8658''8804'_6124 (Integer -> Any
forall a b. a -> b
coe Integer
v0))
      ((Integer -> Integer -> T_Dec_20) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> T_Dec_20
d__'8804''63'__2802 (Integer -> Any
forall a b. a -> b
coe Integer
v0) (Integer -> Any
forall a b. a -> b
coe Integer
v1))
-- Data.Nat.Properties._<′?_
d__'60''8242''63'__6174 ::
  Integer ->
  Integer -> MAlonzo.Code.Relation.Nullary.Decidable.Core.T_Dec_20
d__'60''8242''63'__6174 :: Integer -> Integer -> T_Dec_20
d__'60''8242''63'__6174 Integer
v0 Integer
v1
  = (Integer -> Integer -> T_Dec_20) -> Any -> Any -> T_Dec_20
forall a b. a -> b
coe
      Integer -> Integer -> T_Dec_20
d__'8804''8242''63'__6168
      ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> Integer
addInt (Integer -> Any
forall a b. a -> b
coe (Integer
1 :: Integer)) (Integer -> Any
forall a b. a -> b
coe Integer
v0)) (Integer -> Any
forall a b. a -> b
coe Integer
v1)
-- Data.Nat.Properties._≥′?_
d__'8805''8242''63'__6180 ::
  Integer ->
  Integer -> MAlonzo.Code.Relation.Nullary.Decidable.Core.T_Dec_20
d__'8805''8242''63'__6180 :: Integer -> Integer -> T_Dec_20
d__'8805''8242''63'__6180 Integer
v0 Integer
v1
  = (Integer -> Integer -> T_Dec_20) -> Any -> Any -> T_Dec_20
forall a b. a -> b
coe Integer -> Integer -> T_Dec_20
d__'8804''8242''63'__6168 (Integer -> Any
forall a b. a -> b
coe Integer
v1) (Integer -> Any
forall a b. a -> b
coe Integer
v0)
-- Data.Nat.Properties._>′?_
d__'62''8242''63'__6182 ::
  Integer ->
  Integer -> MAlonzo.Code.Relation.Nullary.Decidable.Core.T_Dec_20
d__'62''8242''63'__6182 :: Integer -> Integer -> T_Dec_20
d__'62''8242''63'__6182 Integer
v0 Integer
v1
  = (Integer -> Integer -> T_Dec_20) -> Any -> Any -> T_Dec_20
forall a b. a -> b
coe Integer -> Integer -> T_Dec_20
d__'60''8242''63'__6174 (Integer -> Any
forall a b. a -> b
coe Integer
v1) (Integer -> Any
forall a b. a -> b
coe Integer
v0)
-- Data.Nat.Properties.m≤′m+n
d_m'8804''8242'm'43'n_6188 ::
  Integer ->
  Integer -> MAlonzo.Code.Data.Nat.Base.T__'8804''8242'__338
d_m'8804''8242'm'43'n_6188 :: Integer -> Integer -> T__'8804''8242'__338
d_m'8804''8242'm'43'n_6188 Integer
v0 Integer
v1
  = (Integer -> T__'8804'__22 -> T__'8804''8242'__338)
-> Any -> Any -> T__'8804''8242'__338
forall a b. a -> b
coe
      Integer -> T__'8804'__22 -> T__'8804''8242'__338
du_'8804''8658''8804''8242'_6128 ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> Integer
addInt (Integer -> Any
forall a b. a -> b
coe Integer
v0) (Integer -> Any
forall a b. a -> b
coe Integer
v1))
      ((Integer -> T__'8804'__22) -> Any -> Any
forall a b. a -> b
coe Integer -> T__'8804'__22
du_m'8804'm'43'n_3482 (Integer -> Any
forall a b. a -> b
coe Integer
v0))
-- Data.Nat.Properties.n≤′m+n
d_n'8804''8242'm'43'n_6198 ::
  Integer ->
  Integer -> MAlonzo.Code.Data.Nat.Base.T__'8804''8242'__338
d_n'8804''8242'm'43'n_6198 :: Integer -> Integer -> T__'8804''8242'__338
d_n'8804''8242'm'43'n_6198 Integer
v0 ~Integer
v1 = Integer -> T__'8804''8242'__338
du_n'8804''8242'm'43'n_6198 Integer
v0
du_n'8804''8242'm'43'n_6198 ::
  Integer -> MAlonzo.Code.Data.Nat.Base.T__'8804''8242'__338
du_n'8804''8242'm'43'n_6198 :: Integer -> T__'8804''8242'__338
du_n'8804''8242'm'43'n_6198 Integer
v0
  = case Integer -> Integer
forall a b. a -> b
coe Integer
v0 of
      Integer
0 -> T__'8804''8242'__338 -> T__'8804''8242'__338
forall a b. a -> b
coe T__'8804''8242'__338
MAlonzo.Code.Data.Nat.Base.C_'8804''8242''45'refl_342
      Integer
_ -> let v1 :: Integer
v1 = Integer -> Integer -> Integer
subInt (Integer -> Integer
forall a b. a -> b
coe Integer
v0) (Integer -> Integer
forall a b. a -> b
coe (Integer
1 :: Integer)) in
           Any -> T__'8804''8242'__338
forall a b. a -> b
coe
             ((T__'8804''8242'__338 -> T__'8804''8242'__338) -> Any -> Any
forall a b. a -> b
coe
                T__'8804''8242'__338 -> T__'8804''8242'__338
MAlonzo.Code.Data.Nat.Base.C_'8804''8242''45'step_348
                ((Integer -> T__'8804''8242'__338) -> Any -> Any
forall a b. a -> b
coe Integer -> T__'8804''8242'__338
du_n'8804''8242'm'43'n_6198 (Integer -> Any
forall a b. a -> b
coe Integer
v1)))
-- Data.Nat.Properties.⌈n/2⌉≤′n
d_'8968'n'47'2'8969''8804''8242'n_6208 ::
  Integer -> MAlonzo.Code.Data.Nat.Base.T__'8804''8242'__338
d_'8968'n'47'2'8969''8804''8242'n_6208 :: Integer -> T__'8804''8242'__338
d_'8968'n'47'2'8969''8804''8242'n_6208 Integer
v0
  = case Integer -> Integer
forall a b. a -> b
coe Integer
v0 of
      Integer
0 -> T__'8804''8242'__338 -> T__'8804''8242'__338
forall a b. a -> b
coe T__'8804''8242'__338
MAlonzo.Code.Data.Nat.Base.C_'8804''8242''45'refl_342
      Integer
1 -> T__'8804''8242'__338 -> T__'8804''8242'__338
forall a b. a -> b
coe T__'8804''8242'__338
MAlonzo.Code.Data.Nat.Base.C_'8804''8242''45'refl_342
      Integer
_ -> let v1 :: Integer
v1 = Integer -> Integer -> Integer
subInt (Integer -> Integer
forall a b. a -> b
coe Integer
v0) (Integer -> Integer
forall a b. a -> b
coe (Integer
2 :: Integer)) in
           Any -> T__'8804''8242'__338
forall a b. a -> b
coe
             ((T__'8804''8242'__338 -> T__'8804''8242'__338)
-> T__'8804''8242'__338 -> Any
forall a b. a -> b
coe
                T__'8804''8242'__338 -> T__'8804''8242'__338
MAlonzo.Code.Data.Nat.Base.C_'8804''8242''45'step_348
                (Integer -> T__'8804''8242'__338
d_'8968'n'47'2'8969''8804''8242'n_6208 (Integer -> Integer
forall a b. a -> b
coe Integer
v1)))
-- Data.Nat.Properties.⌊n/2⌋≤′n
d_'8970'n'47'2'8971''8804''8242'n_6214 ::
  Integer -> MAlonzo.Code.Data.Nat.Base.T__'8804''8242'__338
d_'8970'n'47'2'8971''8804''8242'n_6214 :: Integer -> T__'8804''8242'__338
d_'8970'n'47'2'8971''8804''8242'n_6214 Integer
v0
  = case Integer -> Integer
forall a b. a -> b
coe Integer
v0 of
      Integer
0 -> T__'8804''8242'__338 -> T__'8804''8242'__338
forall a b. a -> b
coe T__'8804''8242'__338
MAlonzo.Code.Data.Nat.Base.C_'8804''8242''45'refl_342
      Integer
_ -> let v1 :: Integer
v1 = Integer -> Integer -> Integer
subInt (Integer -> Integer
forall a b. a -> b
coe Integer
v0) (Integer -> Integer
forall a b. a -> b
coe (Integer
1 :: Integer)) in
           Any -> T__'8804''8242'__338
forall a b. a -> b
coe
             ((T__'8804''8242'__338 -> T__'8804''8242'__338)
-> T__'8804''8242'__338 -> Any
forall a b. a -> b
coe
                T__'8804''8242'__338 -> T__'8804''8242'__338
MAlonzo.Code.Data.Nat.Base.C_'8804''8242''45'step_348
                (Integer -> T__'8804''8242'__338
d_'8968'n'47'2'8969''8804''8242'n_6208 (Integer -> Integer
forall a b. a -> b
coe Integer
v1)))
-- Data.Nat.Properties.≤⇒≤″
d_'8804''8658''8804''8243'_6218 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Algebra.Definitions.RawMagma.T__'8739''737'__26
d_'8804''8658''8804''8243'_6218 :: Integer -> Integer -> T__'8804'__22 -> T__'8739''737'__26
d_'8804''8658''8804''8243'_6218 Integer
v0 Integer
v1 ~T__'8804'__22
v2
  = Integer -> Integer -> T__'8739''737'__26
du_'8804''8658''8804''8243'_6218 Integer
v0 Integer
v1
du_'8804''8658''8804''8243'_6218 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Algebra.Definitions.RawMagma.T__'8739''737'__26
du_'8804''8658''8804''8243'_6218 :: Integer -> Integer -> T__'8739''737'__26
du_'8804''8658''8804''8243'_6218 Integer
v0 Integer
v1
  = (Any -> Any -> T__'8739''737'__26)
-> Any -> Any -> T__'8739''737'__26
forall a b. a -> b
coe
      Any -> Any -> T__'8739''737'__26
MAlonzo.Code.Algebra.Definitions.RawMagma.C__'44'__40
      ((Integer -> Integer -> Integer) -> Integer -> Integer -> Any
forall a b. a -> b
coe Integer -> Integer -> Integer
MAlonzo.Code.Agda.Builtin.Nat.d__'45'__22 Integer
v1 Integer
v0) Any
forall a. a
erased
-- Data.Nat.Properties.<⇒<″
d_'60''8658''60''8243'_6222 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Algebra.Definitions.RawMagma.T__'8739''737'__26
d_'60''8658''60''8243'_6222 :: Integer -> Integer -> T__'8804'__22 -> T__'8739''737'__26
d_'60''8658''60''8243'_6222 Integer
v0 Integer
v1 T__'8804'__22
v2
  = (Integer -> Integer -> T__'8739''737'__26)
-> Any -> Any -> T__'8739''737'__26
forall a b. a -> b
coe
      Integer -> Integer -> T__'8739''737'__26
du_'8804''8658''8804''8243'_6218
      ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> Integer
addInt (Integer -> Any
forall a b. a -> b
coe (Integer
1 :: Integer)) (Integer -> Any
forall a b. a -> b
coe Integer
v0)) (Integer -> Any
forall a b. a -> b
coe Integer
v1)
-- Data.Nat.Properties.≤″⇒≤
d_'8804''8243''8658''8804'_6224 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Algebra.Definitions.RawMagma.T__'8739''737'__26 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_'8804''8243''8658''8804'_6224 :: Integer -> Integer -> T__'8739''737'__26 -> T__'8804'__22
d_'8804''8243''8658''8804'_6224 Integer
v0 ~Integer
v1 T__'8739''737'__26
v2
  = Integer -> T__'8739''737'__26 -> T__'8804'__22
du_'8804''8243''8658''8804'_6224 Integer
v0 T__'8739''737'__26
v2
du_'8804''8243''8658''8804'_6224 ::
  Integer ->
  MAlonzo.Code.Algebra.Definitions.RawMagma.T__'8739''737'__26 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
du_'8804''8243''8658''8804'_6224 :: Integer -> T__'8739''737'__26 -> T__'8804'__22
du_'8804''8243''8658''8804'_6224 Integer
v0 T__'8739''737'__26
v1
  = (Any -> Any -> Any) -> Any -> Any -> T__'8804'__22
forall a b. a -> b
coe Any -> Any -> Any
forall a b. a -> b -> b
seq (T__'8739''737'__26 -> Any
forall a b. a -> b
coe T__'8739''737'__26
v1) ((Integer -> T__'8804'__22) -> Any -> Any
forall a b. a -> b
coe Integer -> T__'8804'__22
du_m'8804'm'43'n_3482 (Integer -> Any
forall a b. a -> b
coe Integer
v0))
-- Data.Nat.Properties.≤″-proof
d_'8804''8243''45'proof_6232 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Algebra.Definitions.RawMagma.T__'8739''737'__26 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8804''8243''45'proof_6232 :: Integer -> Integer -> T__'8739''737'__26 -> T__'8801'__12
d_'8804''8243''45'proof_6232 = Integer -> Integer -> T__'8739''737'__26 -> T__'8801'__12
forall a. a
erased
-- Data.Nat.Properties.m≤n⇒∃[o]m+o≡n
d_m'8804'n'8658''8707''91'o'93'm'43'o'8801'n_6238 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_m'8804'n'8658''8707''91'o'93'm'43'o'8801'n_6238 :: Integer -> Integer -> T__'8804'__22 -> T_Σ_14
d_m'8804'n'8658''8707''91'o'93'm'43'o'8801'n_6238 Integer
v0 Integer
v1 ~T__'8804'__22
v2
  = Integer -> Integer -> T_Σ_14
du_m'8804'n'8658''8707''91'o'93'm'43'o'8801'n_6238 Integer
v0 Integer
v1
du_m'8804'n'8658''8707''91'o'93'm'43'o'8801'n_6238 ::
  Integer -> Integer -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
du_m'8804'n'8658''8707''91'o'93'm'43'o'8801'n_6238 :: Integer -> Integer -> T_Σ_14
du_m'8804'n'8658''8707''91'o'93'm'43'o'8801'n_6238 Integer
v0 Integer
v1
  = (Any -> Any -> T_Σ_14) -> Any -> Any -> T_Σ_14
forall a b. a -> b
coe
      Any -> Any -> T_Σ_14
MAlonzo.Code.Agda.Builtin.Sigma.C__'44'__32
      ((Integer -> Integer -> Integer) -> Integer -> Integer -> Any
forall a b. a -> b
coe Integer -> Integer -> Integer
MAlonzo.Code.Agda.Builtin.Nat.d__'45'__22 Integer
v1 Integer
v0) Any
forall a. a
erased
-- Data.Nat.Properties.guarded-∸≗∸
d_guarded'45''8760''8791''8760'_6250 ::
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_guarded'45''8760''8791''8760'_6250 :: T__'8804'__22 -> T__'8801'__12
d_guarded'45''8760''8791''8760'_6250 = T__'8804'__22 -> T__'8801'__12
forall a. a
erased
-- Data.Nat.Properties.m<ᵇn⇒1+m+[n-1+m]≡n
d_m'60''7495'n'8658'1'43'm'43''91'n'45'1'43'm'93''8801'n_6258 ::
  Integer ->
  Integer ->
  AgdaAny -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_m'60''7495'n'8658'1'43'm'43''91'n'45'1'43'm'93''8801'n_6258 :: Integer -> Integer -> Any -> T__'8801'__12
d_m'60''7495'n'8658'1'43'm'43''91'n'45'1'43'm'93''8801'n_6258
  = Integer -> Integer -> Any -> T__'8801'__12
forall a. a
erased
-- Data.Nat.Properties.m<ᵇ1+m+n
d_m'60''7495'1'43'm'43'n_6270 :: Integer -> Integer -> AgdaAny
d_m'60''7495'1'43'm'43'n_6270 :: Integer -> Integer -> Any
d_m'60''7495'1'43'm'43'n_6270 Integer
v0 ~Integer
v1
  = Integer -> Any
du_m'60''7495'1'43'm'43'n_6270 Integer
v0
du_m'60''7495'1'43'm'43'n_6270 :: Integer -> AgdaAny
du_m'60''7495'1'43'm'43'n_6270 :: Integer -> Any
du_m'60''7495'1'43'm'43'n_6270 Integer
v0
  = (T__'8804'__22 -> Any) -> Any -> Any
forall a b. a -> b
coe
      T__'8804'__22 -> Any
du_'60''8658''60''7495'_2728
      ((Integer -> T__'8804'__22) -> Any -> Any
forall a b. a -> b
coe
         Integer -> T__'8804'__22
du_m'8804'm'43'n_3482 ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> Integer
addInt (Integer -> Any
forall a b. a -> b
coe (Integer
1 :: Integer)) (Integer -> Any
forall a b. a -> b
coe Integer
v0)))
-- Data.Nat.Properties.<ᵇ⇒<″
d_'60''7495''8658''60''8243'_6274 ::
  Integer ->
  Integer ->
  AgdaAny ->
  MAlonzo.Code.Algebra.Definitions.RawMagma.T__'8739''737'__26
d_'60''7495''8658''60''8243'_6274 :: Integer -> Integer -> Any -> T__'8739''737'__26
d_'60''7495''8658''60''8243'_6274 Integer
v0 Integer
v1 ~Any
v2
  = Integer -> Integer -> T__'8739''737'__26
du_'60''7495''8658''60''8243'_6274 Integer
v0 Integer
v1
du_'60''7495''8658''60''8243'_6274 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Algebra.Definitions.RawMagma.T__'8739''737'__26
du_'60''7495''8658''60''8243'_6274 :: Integer -> Integer -> T__'8739''737'__26
du_'60''7495''8658''60''8243'_6274 Integer
v0 Integer
v1
  = (Integer -> Integer -> T__'8804'__22 -> T__'8739''737'__26)
-> Integer -> Integer -> Any -> T__'8739''737'__26
forall a b. a -> b
coe
      Integer -> Integer -> T__'8804'__22 -> T__'8739''737'__26
d_'60''8658''60''8243'_6222 Integer
v0 Integer
v1
      ((Integer -> T__'8804'__22) -> Any -> Any
forall a b. a -> b
coe Integer -> T__'8804'__22
du_'60''7495''8658''60'_2716 (Integer -> Any
forall a b. a -> b
coe Integer
v0))
-- Data.Nat.Properties.<″⇒<ᵇ
d_'60''8243''8658''60''7495'_6284 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Algebra.Definitions.RawMagma.T__'8739''737'__26 ->
  AgdaAny
d_'60''8243''8658''60''7495'_6284 :: Integer -> Integer -> T__'8739''737'__26 -> Any
d_'60''8243''8658''60''7495'_6284 Integer
v0 ~Integer
v1 T__'8739''737'__26
v2
  = Integer -> T__'8739''737'__26 -> Any
du_'60''8243''8658''60''7495'_6284 Integer
v0 T__'8739''737'__26
v2
du_'60''8243''8658''60''7495'_6284 ::
  Integer ->
  MAlonzo.Code.Algebra.Definitions.RawMagma.T__'8739''737'__26 ->
  AgdaAny
du_'60''8243''8658''60''7495'_6284 :: Integer -> T__'8739''737'__26 -> Any
du_'60''8243''8658''60''7495'_6284 Integer
v0 T__'8739''737'__26
v1
  = (Any -> Any -> Any) -> Any -> Any -> Any
forall a b. a -> b
coe
      Any -> Any -> Any
forall a b. a -> b -> b
seq (T__'8739''737'__26 -> Any
forall a b. a -> b
coe T__'8739''737'__26
v1)
      ((T__'8804'__22 -> Any) -> Any -> Any
forall a b. a -> b
coe
         T__'8804'__22 -> Any
du_'60''8658''60''7495'_2728
         ((Integer -> T__'8804'__22) -> Any -> Any
forall a b. a -> b
coe
            Integer -> T__'8804'__22
du_m'8804'm'43'n_3482 ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> Integer
addInt (Integer -> Any
forall a b. a -> b
coe (Integer
1 :: Integer)) (Integer -> Any
forall a b. a -> b
coe Integer
v0))))
-- Data.Nat.Properties._<″?_
d__'60''8243''63'__6290 ::
  Integer ->
  Integer -> MAlonzo.Code.Relation.Nullary.Decidable.Core.T_Dec_20
d__'60''8243''63'__6290 :: Integer -> Integer -> T_Dec_20
d__'60''8243''63'__6290 Integer
v0 Integer
v1
  = ((Any -> Any) -> (Any -> Any) -> T_Dec_20 -> T_Dec_20)
-> (Any -> Any) -> Any -> Any -> T_Dec_20
forall a b. a -> b
coe
      (Any -> Any) -> (Any -> Any) -> T_Dec_20 -> T_Dec_20
MAlonzo.Code.Relation.Nullary.Decidable.Core.du_map'8242'_168
      (\ Any
v2 -> (Integer -> Integer -> T__'8739''737'__26) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> T__'8739''737'__26
du_'60''7495''8658''60''8243'_6274 (Integer -> Any
forall a b. a -> b
coe Integer
v0) (Integer -> Any
forall a b. a -> b
coe Integer
v1))
      ((Integer -> T__'8739''737'__26 -> Any) -> Any -> Any
forall a b. a -> b
coe Integer -> T__'8739''737'__26 -> Any
du_'60''8243''8658''60''7495'_6284 (Integer -> Any
forall a b. a -> b
coe Integer
v0))
      ((Bool -> T_Dec_20) -> Any -> Any
forall a b. a -> b
coe
         Bool -> T_Dec_20
MAlonzo.Code.Relation.Nullary.Decidable.Core.d_T'63'_66
         ((Integer -> Integer -> Bool) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> Bool
ltInt (Integer -> Any
forall a b. a -> b
coe Integer
v0) (Integer -> Any
forall a b. a -> b
coe Integer
v1)))
-- Data.Nat.Properties._≤″?_
d__'8804''8243''63'__6296 ::
  Integer ->
  Integer -> MAlonzo.Code.Relation.Nullary.Decidable.Core.T_Dec_20
d__'8804''8243''63'__6296 :: Integer -> Integer -> T_Dec_20
d__'8804''8243''63'__6296 Integer
v0 Integer
v1
  = case Integer -> Integer
forall a b. a -> b
coe Integer
v0 of
      Integer
0 -> (Bool -> T_Reflects_16 -> T_Dec_20) -> Any -> Any -> T_Dec_20
forall a b. a -> b
coe
             Bool -> T_Reflects_16 -> T_Dec_20
MAlonzo.Code.Relation.Nullary.Decidable.Core.C__because__32
             (Bool -> Any
forall a b. a -> b
coe Bool
MAlonzo.Code.Agda.Builtin.Bool.C_true_10)
             ((Any -> T_Reflects_16) -> Any -> Any
forall a b. a -> b
coe
                Any -> T_Reflects_16
MAlonzo.Code.Relation.Nullary.Reflects.C_of'696'_22
                ((Any -> Any -> T__'8739''737'__26) -> Any -> Any -> Any
forall a b. a -> b
coe
                   Any -> Any -> T__'8739''737'__26
MAlonzo.Code.Algebra.Definitions.RawMagma.C__'44'__40 (Integer -> Any
forall a b. a -> b
coe Integer
v1)
                   Any
forall a. a
erased))
      Integer
_ -> let v2 :: Integer
v2 = Integer -> Integer -> Integer
subInt (Integer -> Integer
forall a b. a -> b
coe Integer
v0) (Integer -> Integer
forall a b. a -> b
coe (Integer
1 :: Integer)) in
           Any -> T_Dec_20
forall a b. a -> b
coe ((Integer -> Integer -> T_Dec_20) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> T_Dec_20
d__'60''8243''63'__6290 (Integer -> Any
forall a b. a -> b
coe Integer
v2) (Integer -> Any
forall a b. a -> b
coe Integer
v1))
-- Data.Nat.Properties._≥″?_
d__'8805''8243''63'__6304 ::
  Integer ->
  Integer -> MAlonzo.Code.Relation.Nullary.Decidable.Core.T_Dec_20
d__'8805''8243''63'__6304 :: Integer -> Integer -> T_Dec_20
d__'8805''8243''63'__6304 Integer
v0 Integer
v1
  = (Integer -> Integer -> T_Dec_20) -> Any -> Any -> T_Dec_20
forall a b. a -> b
coe Integer -> Integer -> T_Dec_20
d__'8804''8243''63'__6296 (Integer -> Any
forall a b. a -> b
coe Integer
v1) (Integer -> Any
forall a b. a -> b
coe Integer
v0)
-- Data.Nat.Properties._>″?_
d__'62''8243''63'__6306 ::
  Integer ->
  Integer -> MAlonzo.Code.Relation.Nullary.Decidable.Core.T_Dec_20
d__'62''8243''63'__6306 :: Integer -> Integer -> T_Dec_20
d__'62''8243''63'__6306 Integer
v0 Integer
v1
  = (Integer -> Integer -> T_Dec_20) -> Any -> Any -> T_Dec_20
forall a b. a -> b
coe Integer -> Integer -> T_Dec_20
d__'60''8243''63'__6290 (Integer -> Any
forall a b. a -> b
coe Integer
v1) (Integer -> Any
forall a b. a -> b
coe Integer
v0)
-- Data.Nat.Properties.≤″-irrelevant
d_'8804''8243''45'irrelevant_6308 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Algebra.Definitions.RawMagma.T__'8739''737'__26 ->
  MAlonzo.Code.Algebra.Definitions.RawMagma.T__'8739''737'__26 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8804''8243''45'irrelevant_6308 :: Integer
-> Integer
-> T__'8739''737'__26
-> T__'8739''737'__26
-> T__'8801'__12
d_'8804''8243''45'irrelevant_6308 = Integer
-> Integer
-> T__'8739''737'__26
-> T__'8739''737'__26
-> T__'8801'__12
forall a. a
erased
-- Data.Nat.Properties.<″-irrelevant
d_'60''8243''45'irrelevant_6322 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Algebra.Definitions.RawMagma.T__'8739''737'__26 ->
  MAlonzo.Code.Algebra.Definitions.RawMagma.T__'8739''737'__26 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'60''8243''45'irrelevant_6322 :: Integer
-> Integer
-> T__'8739''737'__26
-> T__'8739''737'__26
-> T__'8801'__12
d_'60''8243''45'irrelevant_6322 = Integer
-> Integer
-> T__'8739''737'__26
-> T__'8739''737'__26
-> T__'8801'__12
forall a. a
erased
-- Data.Nat.Properties.>″-irrelevant
d_'62''8243''45'irrelevant_6324 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Algebra.Definitions.RawMagma.T__'8739''737'__26 ->
  MAlonzo.Code.Algebra.Definitions.RawMagma.T__'8739''737'__26 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'62''8243''45'irrelevant_6324 :: Integer
-> Integer
-> T__'8739''737'__26
-> T__'8739''737'__26
-> T__'8801'__12
d_'62''8243''45'irrelevant_6324 = Integer
-> Integer
-> T__'8739''737'__26
-> T__'8739''737'__26
-> T__'8801'__12
forall a. a
erased
-- Data.Nat.Properties.≥″-irrelevant
d_'8805''8243''45'irrelevant_6326 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Algebra.Definitions.RawMagma.T__'8739''737'__26 ->
  MAlonzo.Code.Algebra.Definitions.RawMagma.T__'8739''737'__26 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8805''8243''45'irrelevant_6326 :: Integer
-> Integer
-> T__'8739''737'__26
-> T__'8739''737'__26
-> T__'8801'__12
d_'8805''8243''45'irrelevant_6326 = Integer
-> Integer
-> T__'8739''737'__26
-> T__'8739''737'__26
-> T__'8801'__12
forall a. a
erased
-- Data.Nat.Properties.≤‴⇒≤″
d_'8804''8244''8658''8804''8243'_6332 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804''8244'__408 ->
  MAlonzo.Code.Algebra.Definitions.RawMagma.T__'8739''737'__26
d_'8804''8244''8658''8804''8243'_6332 :: Integer -> Integer -> T__'8804''8244'__408 -> T__'8739''737'__26
d_'8804''8244''8658''8804''8243'_6332 ~Integer
v0 ~Integer
v1 T__'8804''8244'__408
v2
  = T__'8804''8244'__408 -> T__'8739''737'__26
du_'8804''8244''8658''8804''8243'_6332 T__'8804''8244'__408
v2
du_'8804''8244''8658''8804''8243'_6332 ::
  MAlonzo.Code.Data.Nat.Base.T__'8804''8244'__408 ->
  MAlonzo.Code.Algebra.Definitions.RawMagma.T__'8739''737'__26
du_'8804''8244''8658''8804''8243'_6332 :: T__'8804''8244'__408 -> T__'8739''737'__26
du_'8804''8244''8658''8804''8243'_6332 T__'8804''8244'__408
v0
  = case T__'8804''8244'__408 -> T__'8804''8244'__408
forall a b. a -> b
coe T__'8804''8244'__408
v0 of
      T__'8804''8244'__408
MAlonzo.Code.Data.Nat.Base.C_'8804''8244''45'refl_412
        -> (Any -> Any -> T__'8739''737'__26)
-> Any -> Any -> T__'8739''737'__26
forall a b. a -> b
coe
             Any -> Any -> T__'8739''737'__26
MAlonzo.Code.Algebra.Definitions.RawMagma.C__'44'__40
             (Integer -> Any
forall a b. a -> b
coe (Integer
0 :: Integer)) Any
forall a. a
erased
      MAlonzo.Code.Data.Nat.Base.C_'8804''8244''45'step_418 T__'8804''8244'__408
v3
        -> (Any -> Any -> T__'8739''737'__26)
-> Any -> Any -> T__'8739''737'__26
forall a b. a -> b
coe
             Any -> Any -> T__'8739''737'__26
MAlonzo.Code.Algebra.Definitions.RawMagma.C__'44'__40
             ((Integer -> Integer -> Integer) -> Any -> Any -> Any
forall a b. a -> b
coe
                Integer -> Integer -> Integer
addInt (Integer -> Any
forall a b. a -> b
coe (Integer
1 :: Integer))
                ((T__'8739''737'__26 -> Any) -> Any -> Any
forall a b. a -> b
coe
                   T__'8739''737'__26 -> Any
MAlonzo.Code.Algebra.Definitions.RawMagma.d_quotient_36
                   ((T__'8804''8244'__408 -> T__'8739''737'__26) -> Any -> Any
forall a b. a -> b
coe T__'8804''8244'__408 -> T__'8739''737'__26
du_'8804''8244''8658''8804''8243'_6332 (T__'8804''8244'__408 -> Any
forall a b. a -> b
coe T__'8804''8244'__408
v3))))
             Any
forall a. a
erased
      T__'8804''8244'__408
_ -> T__'8739''737'__26
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Data.Nat.Properties.m≤‴m+k
d_m'8804''8244'm'43'k_6346 ::
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804''8244'__408
d_m'8804''8244'm'43'k_6346 :: Integer
-> Integer -> Integer -> T__'8801'__12 -> T__'8804''8244'__408
d_m'8804''8244'm'43'k_6346 ~Integer
v0 ~Integer
v1 Integer
v2 ~T__'8801'__12
v3
  = Integer -> T__'8804''8244'__408
du_m'8804''8244'm'43'k_6346 Integer
v2
du_m'8804''8244'm'43'k_6346 ::
  Integer -> MAlonzo.Code.Data.Nat.Base.T__'8804''8244'__408
du_m'8804''8244'm'43'k_6346 :: Integer -> T__'8804''8244'__408
du_m'8804''8244'm'43'k_6346 Integer
v0
  = case Integer -> Integer
forall a b. a -> b
coe Integer
v0 of
      Integer
0 -> T__'8804''8244'__408 -> T__'8804''8244'__408
forall a b. a -> b
coe T__'8804''8244'__408
MAlonzo.Code.Data.Nat.Base.C_'8804''8244''45'refl_412
      Integer
_ -> let v1 :: Integer
v1 = Integer -> Integer -> Integer
subInt (Integer -> Integer
forall a b. a -> b
coe Integer
v0) (Integer -> Integer
forall a b. a -> b
coe (Integer
1 :: Integer)) in
           Any -> T__'8804''8244'__408
forall a b. a -> b
coe
             ((T__'8804''8244'__408 -> T__'8804''8244'__408) -> Any -> Any
forall a b. a -> b
coe
                T__'8804''8244'__408 -> T__'8804''8244'__408
MAlonzo.Code.Data.Nat.Base.C_'8804''8244''45'step_418
                ((Integer -> T__'8804''8244'__408) -> Any -> Any
forall a b. a -> b
coe Integer -> T__'8804''8244'__408
du_m'8804''8244'm'43'k_6346 (Integer -> Any
forall a b. a -> b
coe Integer
v1)))
-- Data.Nat.Properties.≤″⇒≤‴
d_'8804''8243''8658''8804''8244'_6362 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Algebra.Definitions.RawMagma.T__'8739''737'__26 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804''8244'__408
d_'8804''8243''8658''8804''8244'_6362 :: Integer -> Integer -> T__'8739''737'__26 -> T__'8804''8244'__408
d_'8804''8243''8658''8804''8244'_6362 ~Integer
v0 ~Integer
v1 T__'8739''737'__26
v2
  = T__'8739''737'__26 -> T__'8804''8244'__408
du_'8804''8243''8658''8804''8244'_6362 T__'8739''737'__26
v2
du_'8804''8243''8658''8804''8244'_6362 ::
  MAlonzo.Code.Algebra.Definitions.RawMagma.T__'8739''737'__26 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804''8244'__408
du_'8804''8243''8658''8804''8244'_6362 :: T__'8739''737'__26 -> T__'8804''8244'__408
du_'8804''8243''8658''8804''8244'_6362 T__'8739''737'__26
v0
  = (Integer -> T__'8804''8244'__408) -> Any -> T__'8804''8244'__408
forall a b. a -> b
coe
      Integer -> T__'8804''8244'__408
du_m'8804''8244'm'43'k_6346
      ((T__'8739''737'__26 -> Any) -> Any -> Any
forall a b. a -> b
coe
         T__'8739''737'__26 -> Any
MAlonzo.Code.Algebra.Definitions.RawMagma.d_quotient_36 (T__'8739''737'__26 -> Any
forall a b. a -> b
coe T__'8739''737'__26
v0))
-- Data.Nat.Properties.0≤‴n
d_0'8804''8244'n_6366 ::
  Integer -> MAlonzo.Code.Data.Nat.Base.T__'8804''8244'__408
d_0'8804''8244'n_6366 :: Integer -> T__'8804''8244'__408
d_0'8804''8244'n_6366 Integer
v0 = (Integer -> T__'8804''8244'__408) -> Any -> T__'8804''8244'__408
forall a b. a -> b
coe Integer -> T__'8804''8244'__408
du_m'8804''8244'm'43'k_6346 (Integer -> Any
forall a b. a -> b
coe Integer
v0)
-- Data.Nat.Properties.<ᵇ⇒<‴
d_'60''7495''8658''60''8244'_6368 ::
  Integer ->
  Integer ->
  AgdaAny -> MAlonzo.Code.Data.Nat.Base.T__'8804''8244'__408
d_'60''7495''8658''60''8244'_6368 :: Integer -> Integer -> Any -> T__'8804''8244'__408
d_'60''7495''8658''60''8244'_6368 Integer
v0 Integer
v1 ~Any
v2
  = Integer -> Integer -> T__'8804''8244'__408
du_'60''7495''8658''60''8244'_6368 Integer
v0 Integer
v1
du_'60''7495''8658''60''8244'_6368 ::
  Integer ->
  Integer -> MAlonzo.Code.Data.Nat.Base.T__'8804''8244'__408
du_'60''7495''8658''60''8244'_6368 :: Integer -> Integer -> T__'8804''8244'__408
du_'60''7495''8658''60''8244'_6368 Integer
v0 Integer
v1
  = (T__'8739''737'__26 -> T__'8804''8244'__408)
-> Any -> T__'8804''8244'__408
forall a b. a -> b
coe
      T__'8739''737'__26 -> T__'8804''8244'__408
du_'8804''8243''8658''8804''8244'_6362
      ((Integer -> Integer -> T__'8739''737'__26) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> T__'8739''737'__26
du_'60''7495''8658''60''8243'_6274 (Integer -> Any
forall a b. a -> b
coe Integer
v0) (Integer -> Any
forall a b. a -> b
coe Integer
v1))
-- Data.Nat.Properties.<‴⇒<ᵇ
d_'60''8244''8658''60''7495'_6376 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804''8244'__408 -> AgdaAny
d_'60''8244''8658''60''7495'_6376 :: Integer -> Integer -> T__'8804''8244'__408 -> Any
d_'60''8244''8658''60''7495'_6376 Integer
v0 ~Integer
v1 T__'8804''8244'__408
v2
  = Integer -> T__'8804''8244'__408 -> Any
du_'60''8244''8658''60''7495'_6376 Integer
v0 T__'8804''8244'__408
v2
du_'60''8244''8658''60''7495'_6376 ::
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804''8244'__408 -> AgdaAny
du_'60''8244''8658''60''7495'_6376 :: Integer -> T__'8804''8244'__408 -> Any
du_'60''8244''8658''60''7495'_6376 Integer
v0 T__'8804''8244'__408
v1
  = (Integer -> T__'8739''737'__26 -> Any) -> Any -> Any -> Any
forall a b. a -> b
coe
      Integer -> T__'8739''737'__26 -> Any
du_'60''8243''8658''60''7495'_6284 (Integer -> Any
forall a b. a -> b
coe Integer
v0)
      ((T__'8804''8244'__408 -> T__'8739''737'__26) -> Any -> Any
forall a b. a -> b
coe T__'8804''8244'__408 -> T__'8739''737'__26
du_'8804''8244''8658''8804''8243'_6332 (T__'8804''8244'__408 -> Any
forall a b. a -> b
coe T__'8804''8244'__408
v1))
-- Data.Nat.Properties._<‴?_
d__'60''8244''63'__6380 ::
  Integer ->
  Integer -> MAlonzo.Code.Relation.Nullary.Decidable.Core.T_Dec_20
d__'60''8244''63'__6380 :: Integer -> Integer -> T_Dec_20
d__'60''8244''63'__6380 Integer
v0 Integer
v1
  = ((Any -> Any) -> (Any -> Any) -> T_Dec_20 -> T_Dec_20)
-> (Any -> Any) -> Any -> Any -> T_Dec_20
forall a b. a -> b
coe
      (Any -> Any) -> (Any -> Any) -> T_Dec_20 -> T_Dec_20
MAlonzo.Code.Relation.Nullary.Decidable.Core.du_map'8242'_168
      (\ Any
v2 -> (Integer -> Integer -> T__'8804''8244'__408) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> T__'8804''8244'__408
du_'60''7495''8658''60''8244'_6368 (Integer -> Any
forall a b. a -> b
coe Integer
v0) (Integer -> Any
forall a b. a -> b
coe Integer
v1))
      ((Integer -> T__'8804''8244'__408 -> Any) -> Any -> Any
forall a b. a -> b
coe Integer -> T__'8804''8244'__408 -> Any
du_'60''8244''8658''60''7495'_6376 (Integer -> Any
forall a b. a -> b
coe Integer
v0))
      ((Bool -> T_Dec_20) -> Any -> Any
forall a b. a -> b
coe
         Bool -> T_Dec_20
MAlonzo.Code.Relation.Nullary.Decidable.Core.d_T'63'_66
         ((Integer -> Integer -> Bool) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> Bool
ltInt (Integer -> Any
forall a b. a -> b
coe Integer
v0) (Integer -> Any
forall a b. a -> b
coe Integer
v1)))
-- Data.Nat.Properties._≤‴?_
d__'8804''8244''63'__6386 ::
  Integer ->
  Integer -> MAlonzo.Code.Relation.Nullary.Decidable.Core.T_Dec_20
d__'8804''8244''63'__6386 :: Integer -> Integer -> T_Dec_20
d__'8804''8244''63'__6386 Integer
v0 Integer
v1
  = case Integer -> Integer
forall a b. a -> b
coe Integer
v0 of
      Integer
0 -> (Bool -> T_Reflects_16 -> T_Dec_20) -> Any -> Any -> T_Dec_20
forall a b. a -> b
coe
             Bool -> T_Reflects_16 -> T_Dec_20
MAlonzo.Code.Relation.Nullary.Decidable.Core.C__because__32
             (Bool -> Any
forall a b. a -> b
coe Bool
MAlonzo.Code.Agda.Builtin.Bool.C_true_10)
             ((Any -> T_Reflects_16) -> Any -> Any
forall a b. a -> b
coe
                Any -> T_Reflects_16
MAlonzo.Code.Relation.Nullary.Reflects.C_of'696'_22
                ((Integer -> T__'8804''8244'__408) -> Any -> Any
forall a b. a -> b
coe Integer -> T__'8804''8244'__408
d_0'8804''8244'n_6366 (Integer -> Any
forall a b. a -> b
coe Integer
v1)))
      Integer
_ -> let v2 :: Integer
v2 = Integer -> Integer -> Integer
subInt (Integer -> Integer
forall a b. a -> b
coe Integer
v0) (Integer -> Integer
forall a b. a -> b
coe (Integer
1 :: Integer)) in
           Any -> T_Dec_20
forall a b. a -> b
coe ((Integer -> Integer -> T_Dec_20) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> T_Dec_20
d__'60''8244''63'__6380 (Integer -> Any
forall a b. a -> b
coe Integer
v2) (Integer -> Any
forall a b. a -> b
coe Integer
v1))
-- Data.Nat.Properties._≥‴?_
d__'8805''8244''63'__6394 ::
  Integer ->
  Integer -> MAlonzo.Code.Relation.Nullary.Decidable.Core.T_Dec_20
d__'8805''8244''63'__6394 :: Integer -> Integer -> T_Dec_20
d__'8805''8244''63'__6394 Integer
v0 Integer
v1
  = (Integer -> Integer -> T_Dec_20) -> Any -> Any -> T_Dec_20
forall a b. a -> b
coe Integer -> Integer -> T_Dec_20
d__'8804''8244''63'__6386 (Integer -> Any
forall a b. a -> b
coe Integer
v1) (Integer -> Any
forall a b. a -> b
coe Integer
v0)
-- Data.Nat.Properties._>‴?_
d__'62''8244''63'__6396 ::
  Integer ->
  Integer -> MAlonzo.Code.Relation.Nullary.Decidable.Core.T_Dec_20
d__'62''8244''63'__6396 :: Integer -> Integer -> T_Dec_20
d__'62''8244''63'__6396 Integer
v0 Integer
v1
  = (Integer -> Integer -> T_Dec_20) -> Any -> Any -> T_Dec_20
forall a b. a -> b
coe Integer -> Integer -> T_Dec_20
d__'60''8244''63'__6380 (Integer -> Any
forall a b. a -> b
coe Integer
v1) (Integer -> Any
forall a b. a -> b
coe Integer
v0)
-- Data.Nat.Properties.≤⇒≤‴
d_'8804''8658''8804''8244'_6398 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804''8244'__408
d_'8804''8658''8804''8244'_6398 :: Integer -> Integer -> T__'8804'__22 -> T__'8804''8244'__408
d_'8804''8658''8804''8244'_6398 Integer
v0 Integer
v1 ~T__'8804'__22
v2
  = Integer -> Integer -> T__'8804''8244'__408
du_'8804''8658''8804''8244'_6398 Integer
v0 Integer
v1
du_'8804''8658''8804''8244'_6398 ::
  Integer ->
  Integer -> MAlonzo.Code.Data.Nat.Base.T__'8804''8244'__408
du_'8804''8658''8804''8244'_6398 :: Integer -> Integer -> T__'8804''8244'__408
du_'8804''8658''8804''8244'_6398 Integer
v0 Integer
v1
  = (T__'8739''737'__26 -> T__'8804''8244'__408)
-> Any -> T__'8804''8244'__408
forall a b. a -> b
coe
      T__'8739''737'__26 -> T__'8804''8244'__408
du_'8804''8243''8658''8804''8244'_6362
      ((Integer -> Integer -> T__'8739''737'__26) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> T__'8739''737'__26
du_'8804''8658''8804''8243'_6218 (Integer -> Any
forall a b. a -> b
coe Integer
v0) (Integer -> Any
forall a b. a -> b
coe Integer
v1))
-- Data.Nat.Properties.≤‴⇒≤
d_'8804''8244''8658''8804'_6400 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804''8244'__408 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_'8804''8244''8658''8804'_6400 :: Integer -> Integer -> T__'8804''8244'__408 -> T__'8804'__22
d_'8804''8244''8658''8804'_6400 Integer
v0 ~Integer
v1 T__'8804''8244'__408
v2
  = Integer -> T__'8804''8244'__408 -> T__'8804'__22
du_'8804''8244''8658''8804'_6400 Integer
v0 T__'8804''8244'__408
v2
du_'8804''8244''8658''8804'_6400 ::
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804''8244'__408 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
du_'8804''8244''8658''8804'_6400 :: Integer -> T__'8804''8244'__408 -> T__'8804'__22
du_'8804''8244''8658''8804'_6400 Integer
v0 T__'8804''8244'__408
v1
  = (Integer -> T__'8739''737'__26 -> T__'8804'__22)
-> Any -> Any -> T__'8804'__22
forall a b. a -> b
coe
      Integer -> T__'8739''737'__26 -> T__'8804'__22
du_'8804''8243''8658''8804'_6224 (Integer -> Any
forall a b. a -> b
coe Integer
v0)
      ((T__'8804''8244'__408 -> T__'8739''737'__26) -> Any -> Any
forall a b. a -> b
coe T__'8804''8244'__408 -> T__'8739''737'__26
du_'8804''8244''8658''8804''8243'_6332 (T__'8804''8244'__408 -> Any
forall a b. a -> b
coe T__'8804''8244'__408
v1))
-- Data.Nat.Properties.eq?
d_eq'63'_6406 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  MAlonzo.Code.Function.Bundles.T_Injection_776 ->
  AgdaAny ->
  AgdaAny -> MAlonzo.Code.Relation.Nullary.Decidable.Core.T_Dec_20
d_eq'63'_6406 :: () -> () -> T_Injection_776 -> Any -> Any -> T_Dec_20
d_eq'63'_6406 ~()
v0 ~()
v1 T_Injection_776
v2 = T_Injection_776 -> Any -> Any -> T_Dec_20
du_eq'63'_6406 T_Injection_776
v2
du_eq'63'_6406 ::
  MAlonzo.Code.Function.Bundles.T_Injection_776 ->
  AgdaAny ->
  AgdaAny -> MAlonzo.Code.Relation.Nullary.Decidable.Core.T_Dec_20
du_eq'63'_6406 :: T_Injection_776 -> Any -> Any -> T_Dec_20
du_eq'63'_6406 T_Injection_776
v0
  = (T_Injection_776
 -> (Any -> Any -> T_Dec_20) -> Any -> Any -> T_Dec_20)
-> Any -> Any -> Any -> Any -> T_Dec_20
forall a b. a -> b
coe
      T_Injection_776
-> (Any -> Any -> T_Dec_20) -> Any -> Any -> T_Dec_20
MAlonzo.Code.Relation.Nullary.Decidable.du_via'45'injection_160
      (T_Injection_776 -> Any
forall a b. a -> b
coe T_Injection_776
v0) ((Integer -> Integer -> T_Dec_20) -> Any
forall a b. a -> b
coe Integer -> Integer -> T_Dec_20
d__'8799'__2688)
-- Data.Nat.Properties._.anyUpTo?
d_anyUpTo'63'_6424 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  (Integer -> ()) ->
  (Integer ->
   MAlonzo.Code.Relation.Nullary.Decidable.Core.T_Dec_20) ->
  Integer -> MAlonzo.Code.Relation.Nullary.Decidable.Core.T_Dec_20
d_anyUpTo'63'_6424 :: ()
-> (Integer -> ()) -> (Integer -> T_Dec_20) -> Integer -> T_Dec_20
d_anyUpTo'63'_6424 ~()
v0 ~Integer -> ()
v1 Integer -> T_Dec_20
v2 Integer
v3 = (Integer -> T_Dec_20) -> Integer -> T_Dec_20
du_anyUpTo'63'_6424 Integer -> T_Dec_20
v2 Integer
v3
du_anyUpTo'63'_6424 ::
  (Integer ->
   MAlonzo.Code.Relation.Nullary.Decidable.Core.T_Dec_20) ->
  Integer -> MAlonzo.Code.Relation.Nullary.Decidable.Core.T_Dec_20
du_anyUpTo'63'_6424 :: (Integer -> T_Dec_20) -> Integer -> T_Dec_20
du_anyUpTo'63'_6424 Integer -> T_Dec_20
v0 Integer
v1
  = case Integer -> Integer
forall a b. a -> b
coe Integer
v1 of
      Integer
0 -> (Bool -> T_Reflects_16 -> T_Dec_20) -> Any -> Any -> T_Dec_20
forall a b. a -> b
coe
             Bool -> T_Reflects_16 -> T_Dec_20
MAlonzo.Code.Relation.Nullary.Decidable.Core.C__because__32
             (Bool -> Any
forall a b. a -> b
coe Bool
MAlonzo.Code.Agda.Builtin.Bool.C_false_8)
             (T_Reflects_16 -> Any
forall a b. a -> b
coe T_Reflects_16
MAlonzo.Code.Relation.Nullary.Reflects.C_of'8319'_26)
      Integer
_ -> let v2 :: Integer
v2 = Integer -> Integer -> Integer
subInt (Integer -> Integer
forall a b. a -> b
coe Integer
v1) (Integer -> Integer
forall a b. a -> b
coe (Integer
1 :: Integer)) in
           Any -> T_Dec_20
forall a b. a -> b
coe
             (let v3 :: t
v3 = (Integer -> T_Dec_20) -> Integer -> t
forall a b. a -> b
coe Integer -> T_Dec_20
v0 Integer
v2 in
              Any -> Any
forall a b. a -> b
coe
                (let v4 :: t
v4 = ((Integer -> T_Dec_20) -> Integer -> T_Dec_20) -> Any -> Any -> t
forall a b. a -> b
coe (Integer -> T_Dec_20) -> Integer -> T_Dec_20
du_anyUpTo'63'_6424 ((Integer -> T_Dec_20) -> Any
forall a b. a -> b
coe Integer -> T_Dec_20
v0) (Integer -> Any
forall a b. a -> b
coe Integer
v2) in
                 Any -> Any
forall a b. a -> b
coe
                   (let v5 :: t
v5
                          = case Any -> T_Dec_20
forall a b. a -> b
coe Any
forall a. a
v4 of
                              MAlonzo.Code.Relation.Nullary.Decidable.Core.C__because__32 Bool
v5 T_Reflects_16
v6
                                -> (Any -> Any -> Any) -> Any -> Any -> t
forall a b. a -> b
coe
                                     Any -> Any -> Any
forall a b. a -> b -> b
seq (Bool -> Any
forall a b. a -> b
coe Bool
v5)
                                     (case T_Reflects_16 -> T_Reflects_16
forall a b. a -> b
coe T_Reflects_16
v6 of
                                        MAlonzo.Code.Relation.Nullary.Reflects.C_of'696'_22 Any
v7
                                          -> case Any -> T_Σ_14
forall a b. a -> b
coe Any
v7 of
                                               MAlonzo.Code.Agda.Builtin.Sigma.C__'44'__32 Any
v8 Any
v9
                                                 -> (Any -> Any -> Any) -> Any -> Any -> Any
forall a b. a -> b
coe
                                                      Any -> Any -> Any
forall a b. a -> b -> b
seq (Any -> Any
forall a b. a -> b
coe Any
v9)
                                                      ((Bool -> T_Reflects_16 -> T_Dec_20) -> Any -> Any -> Any
forall a b. a -> b
coe
                                                         Bool -> T_Reflects_16 -> T_Dec_20
MAlonzo.Code.Relation.Nullary.Decidable.Core.C__because__32
                                                         (Bool -> Any
forall a b. a -> b
coe
                                                            Bool
MAlonzo.Code.Agda.Builtin.Bool.C_true_10)
                                                         (T_Reflects_16 -> Any
forall a b. a -> b
coe T_Reflects_16
v6))
                                               T_Σ_14
_ -> Any
forall a. a
MAlonzo.RTE.mazUnreachableError
                                        T_Reflects_16
_ -> Any
forall a. a
MAlonzo.RTE.mazUnreachableError)
                              T_Dec_20
_ -> t
forall a. a
MAlonzo.RTE.mazUnreachableError in
                    Any -> Any
forall a b. a -> b
coe
                      (case Any -> T_Dec_20
forall a b. a -> b
coe Any
forall a. a
v3 of
                         MAlonzo.Code.Relation.Nullary.Decidable.Core.C__because__32 Bool
v6 T_Reflects_16
v7
                           -> let v8 :: t
v8
                                    = case Any -> T_Dec_20
forall a b. a -> b
coe Any
forall a. a
v4 of
                                        MAlonzo.Code.Relation.Nullary.Decidable.Core.C__because__32 Bool
v8 T_Reflects_16
v9
                                          -> case Bool -> Bool
forall a b. a -> b
coe Bool
v8 of
                                               Bool
MAlonzo.Code.Agda.Builtin.Bool.C_true_10
                                                 -> case T_Reflects_16 -> T_Reflects_16
forall a b. a -> b
coe T_Reflects_16
v9 of
                                                      MAlonzo.Code.Relation.Nullary.Reflects.C_of'696'_22 Any
v10
                                                        -> case Any -> T_Σ_14
forall a b. a -> b
coe Any
v10 of
                                                             MAlonzo.Code.Agda.Builtin.Sigma.C__'44'__32 Any
v11 Any
v12
                                                               -> (Any -> Any -> Any) -> Any -> Any -> t
forall a b. a -> b
coe Any -> Any -> Any
forall a b. a -> b -> b
seq (Any -> Any
forall a b. a -> b
coe Any
v12) (Any -> Any
forall a b. a -> b
coe Any
forall a. a
v4)
                                                             T_Σ_14
_ -> t
forall a. a
MAlonzo.RTE.mazUnreachableError
                                                      T_Reflects_16
_ -> Any -> t
forall a b. a -> b
coe Any
forall a. a
v5
                                               Bool
_ -> Any -> t
forall a b. a -> b
coe Any
forall a. a
v5
                                        T_Dec_20
_ -> t
forall a. a
MAlonzo.RTE.mazUnreachableError in
                              Any -> Any
forall a b. a -> b
coe
                                (if Bool -> Bool
forall a b. a -> b
coe Bool
v6
                                   then let v9 :: t
v9
                                              = case Any -> T_Dec_20
forall a b. a -> b
coe Any
forall a. a
v4 of
                                                  MAlonzo.Code.Relation.Nullary.Decidable.Core.C__because__32 Bool
v9 T_Reflects_16
v10
                                                    -> case Bool -> Bool
forall a b. a -> b
coe Bool
v9 of
                                                         Bool
MAlonzo.Code.Agda.Builtin.Bool.C_true_10
                                                           -> case T_Reflects_16 -> T_Reflects_16
forall a b. a -> b
coe T_Reflects_16
v10 of
                                                                MAlonzo.Code.Relation.Nullary.Reflects.C_of'696'_22 Any
v11
                                                                  -> case Any -> T_Σ_14
forall a b. a -> b
coe Any
v11 of
                                                                       MAlonzo.Code.Agda.Builtin.Sigma.C__'44'__32 Any
v12 Any
v13
                                                                         -> (Any -> Any -> Any) -> Any -> Any -> t
forall a b. a -> b
coe
                                                                              Any -> Any -> Any
forall a b. a -> b -> b
seq (Any -> Any
forall a b. a -> b
coe Any
v13) (Any -> Any
forall a b. a -> b
coe Any
forall a. a
v4)
                                                                       T_Σ_14
_ -> t
forall a. a
MAlonzo.RTE.mazUnreachableError
                                                                T_Reflects_16
_ -> Any -> t
forall a b. a -> b
coe Any
forall a. a
v8
                                                         Bool
_ -> Any -> t
forall a b. a -> b
coe Any
forall a. a
v8
                                                  T_Dec_20
_ -> t
forall a. a
MAlonzo.RTE.mazUnreachableError in
                                        Any -> Any
forall a b. a -> b
coe
                                          (case T_Reflects_16 -> T_Reflects_16
forall a b. a -> b
coe T_Reflects_16
v7 of
                                             MAlonzo.Code.Relation.Nullary.Reflects.C_of'696'_22 Any
v10
                                               -> (Bool -> T_Reflects_16 -> T_Dec_20) -> Any -> Any -> Any
forall a b. a -> b
coe
                                                    Bool -> T_Reflects_16 -> T_Dec_20
MAlonzo.Code.Relation.Nullary.Decidable.Core.C__because__32
                                                    (Bool -> Any
forall a b. a -> b
coe Bool
v6)
                                                    ((Any -> T_Reflects_16) -> Any -> Any
forall a b. a -> b
coe
                                                       Any -> T_Reflects_16
MAlonzo.Code.Relation.Nullary.Reflects.C_of'696'_22
                                                       ((Any -> Any -> T_Σ_14) -> Any -> Any -> Any
forall a b. a -> b
coe
                                                          Any -> Any -> T_Σ_14
MAlonzo.Code.Agda.Builtin.Sigma.C__'44'__32
                                                          (Integer -> Any
forall a b. a -> b
coe Integer
v2)
                                                          ((Any -> Any -> T_Σ_14) -> Any -> Any -> Any
forall a b. a -> b
coe
                                                             Any -> Any -> T_Σ_14
MAlonzo.Code.Agda.Builtin.Sigma.C__'44'__32
                                                             ((Integer -> T__'8804'__22) -> Any -> Any
forall a b. a -> b
coe Integer -> T__'8804'__22
d_'8804''45'refl_2776 (Integer -> Any
forall a b. a -> b
coe Integer
v1))
                                                             (Any -> Any
forall a b. a -> b
coe Any
v10))))
                                             T_Reflects_16
_ -> Any -> Any
forall a b. a -> b
coe Any
forall a. a
v9)
                                   else (case Any -> T_Dec_20
forall a b. a -> b
coe Any
forall a. a
v4 of
                                           MAlonzo.Code.Relation.Nullary.Decidable.Core.C__because__32 Bool
v9 T_Reflects_16
v10
                                             -> if Bool -> Bool
forall a b. a -> b
coe Bool
v9
                                                  then case T_Reflects_16 -> T_Reflects_16
forall a b. a -> b
coe T_Reflects_16
v10 of
                                                         MAlonzo.Code.Relation.Nullary.Reflects.C_of'696'_22 Any
v11
                                                           -> case Any -> T_Σ_14
forall a b. a -> b
coe Any
v11 of
                                                                MAlonzo.Code.Agda.Builtin.Sigma.C__'44'__32 Any
v12 Any
v13
                                                                  -> (Any -> Any -> Any) -> Any -> Any -> Any
forall a b. a -> b
coe Any -> Any -> Any
forall a b. a -> b -> b
seq (Any -> Any
forall a b. a -> b
coe Any
v13) (Any -> Any
forall a b. a -> b
coe Any
forall a. a
v4)
                                                                T_Σ_14
_ -> Any
forall a. a
MAlonzo.RTE.mazUnreachableError
                                                         T_Reflects_16
_ -> Any -> Any
forall a b. a -> b
coe Any
forall a. a
v8
                                                  else (case T_Reflects_16 -> T_Reflects_16
forall a b. a -> b
coe T_Reflects_16
v7 of
                                                          T_Reflects_16
MAlonzo.Code.Relation.Nullary.Reflects.C_of'8319'_26
                                                            -> case T_Reflects_16 -> T_Reflects_16
forall a b. a -> b
coe T_Reflects_16
v10 of
                                                                 T_Reflects_16
MAlonzo.Code.Relation.Nullary.Reflects.C_of'8319'_26
                                                                   -> (Bool -> T_Reflects_16 -> T_Dec_20) -> Any -> Any -> Any
forall a b. a -> b
coe
                                                                        Bool -> T_Reflects_16 -> T_Dec_20
MAlonzo.Code.Relation.Nullary.Decidable.Core.C__because__32
                                                                        (Bool -> Any
forall a b. a -> b
coe Bool
v9)
                                                                        (T_Reflects_16 -> Any
forall a b. a -> b
coe
                                                                           T_Reflects_16
MAlonzo.Code.Relation.Nullary.Reflects.C_of'8319'_26)
                                                                 T_Reflects_16
_ -> Any -> Any
forall a b. a -> b
coe Any
forall a. a
v8
                                                          T_Reflects_16
_ -> Any -> Any
forall a b. a -> b
coe Any
forall a. a
v8)
                                           T_Dec_20
_ -> Any
forall a. a
MAlonzo.RTE.mazUnreachableError))
                         T_Dec_20
_ -> Any
forall a. a
MAlonzo.RTE.mazUnreachableError))))
-- Data.Nat.Properties._._.¬Pn<1+v
d_'172'Pn'60'1'43'v_6458 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  (Integer -> ()) ->
  (Integer ->
   MAlonzo.Code.Relation.Nullary.Decidable.Core.T_Dec_20) ->
  Integer ->
  (AgdaAny -> MAlonzo.Code.Data.Irrelevant.T_Irrelevant_20) ->
  (MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14 ->
   MAlonzo.Code.Data.Irrelevant.T_Irrelevant_20) ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14 ->
  MAlonzo.Code.Data.Irrelevant.T_Irrelevant_20
d_'172'Pn'60'1'43'v_6458 :: ()
-> (Integer -> ())
-> (Integer -> T_Dec_20)
-> Integer
-> (Any -> T_Irrelevant_20)
-> (T_Σ_14 -> T_Irrelevant_20)
-> T_Σ_14
-> T_Irrelevant_20
d_'172'Pn'60'1'43'v_6458 = ()
-> (Integer -> ())
-> (Integer -> T_Dec_20)
-> Integer
-> (Any -> T_Irrelevant_20)
-> (T_Σ_14 -> T_Irrelevant_20)
-> T_Σ_14
-> T_Irrelevant_20
forall a. a
erased
-- Data.Nat.Properties._.allUpTo?
d_allUpTo'63'_6488 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  (Integer -> ()) ->
  (Integer ->
   MAlonzo.Code.Relation.Nullary.Decidable.Core.T_Dec_20) ->
  Integer -> MAlonzo.Code.Relation.Nullary.Decidable.Core.T_Dec_20
d_allUpTo'63'_6488 :: ()
-> (Integer -> ()) -> (Integer -> T_Dec_20) -> Integer -> T_Dec_20
d_allUpTo'63'_6488 ~()
v0 ~Integer -> ()
v1 Integer -> T_Dec_20
v2 Integer
v3 = (Integer -> T_Dec_20) -> Integer -> T_Dec_20
du_allUpTo'63'_6488 Integer -> T_Dec_20
v2 Integer
v3
du_allUpTo'63'_6488 ::
  (Integer ->
   MAlonzo.Code.Relation.Nullary.Decidable.Core.T_Dec_20) ->
  Integer -> MAlonzo.Code.Relation.Nullary.Decidable.Core.T_Dec_20
du_allUpTo'63'_6488 :: (Integer -> T_Dec_20) -> Integer -> T_Dec_20
du_allUpTo'63'_6488 Integer -> T_Dec_20
v0 Integer
v1
  = case Integer -> Integer
forall a b. a -> b
coe Integer
v1 of
      Integer
0 -> (Bool -> T_Reflects_16 -> T_Dec_20) -> Any -> Any -> T_Dec_20
forall a b. a -> b
coe
             Bool -> T_Reflects_16 -> T_Dec_20
MAlonzo.Code.Relation.Nullary.Decidable.Core.C__because__32
             (Bool -> Any
forall a b. a -> b
coe Bool
MAlonzo.Code.Agda.Builtin.Bool.C_true_10)
             ((Any -> T_Reflects_16) -> Any -> Any
forall a b. a -> b
coe Any -> T_Reflects_16
MAlonzo.Code.Relation.Nullary.Reflects.C_of'696'_22 Any
forall a. a
erased)
      Integer
_ -> let v2 :: Integer
v2 = Integer -> Integer -> Integer
subInt (Integer -> Integer
forall a b. a -> b
coe Integer
v1) (Integer -> Integer
forall a b. a -> b
coe (Integer
1 :: Integer)) in
           Any -> T_Dec_20
forall a b. a -> b
coe
             (let v3 :: t
v3 = (Integer -> T_Dec_20) -> Integer -> t
forall a b. a -> b
coe Integer -> T_Dec_20
v0 Integer
v2 in
              Any -> Any
forall a b. a -> b
coe
                (let v4 :: t
v4 = ((Integer -> T_Dec_20) -> Integer -> T_Dec_20) -> Any -> Any -> t
forall a b. a -> b
coe (Integer -> T_Dec_20) -> Integer -> T_Dec_20
du_allUpTo'63'_6488 ((Integer -> T_Dec_20) -> Any
forall a b. a -> b
coe Integer -> T_Dec_20
v0) (Integer -> Any
forall a b. a -> b
coe Integer
v2) in
                 Any -> Any
forall a b. a -> b
coe
                   (let v5 :: t
v5
                          = case Any -> T_Dec_20
forall a b. a -> b
coe Any
forall a. a
v4 of
                              MAlonzo.Code.Relation.Nullary.Decidable.Core.C__because__32 Bool
v5 T_Reflects_16
v6
                                -> (Any -> Any -> Any) -> Any -> Any -> t
forall a b. a -> b
coe
                                     Any -> Any -> Any
forall a b. a -> b -> b
seq (Bool -> Any
forall a b. a -> b
coe Bool
v5)
                                     ((Any -> Any -> Any) -> Any -> Any -> Any
forall a b. a -> b
coe
                                        Any -> Any -> Any
forall a b. a -> b -> b
seq (T_Reflects_16 -> Any
forall a b. a -> b
coe T_Reflects_16
v6)
                                        ((Bool -> T_Reflects_16 -> T_Dec_20) -> Any -> Any -> Any
forall a b. a -> b
coe
                                           Bool -> T_Reflects_16 -> T_Dec_20
MAlonzo.Code.Relation.Nullary.Decidable.Core.C__because__32
                                           (Bool -> Any
forall a b. a -> b
coe Bool
MAlonzo.Code.Agda.Builtin.Bool.C_false_8)
                                           (T_Reflects_16 -> Any
forall a b. a -> b
coe
                                              T_Reflects_16
MAlonzo.Code.Relation.Nullary.Reflects.C_of'8319'_26)))
                              T_Dec_20
_ -> t
forall a. a
MAlonzo.RTE.mazUnreachableError in
                    Any -> Any
forall a b. a -> b
coe
                      (case Any -> T_Dec_20
forall a b. a -> b
coe Any
forall a. a
v3 of
                         MAlonzo.Code.Relation.Nullary.Decidable.Core.C__because__32 Bool
v6 T_Reflects_16
v7
                           -> let v8 :: t
v8
                                    = case Any -> T_Dec_20
forall a b. a -> b
coe Any
forall a. a
v4 of
                                        MAlonzo.Code.Relation.Nullary.Decidable.Core.C__because__32 Bool
v8 T_Reflects_16
v9
                                          -> case Bool -> Bool
forall a b. a -> b
coe Bool
v8 of
                                               Bool
MAlonzo.Code.Agda.Builtin.Bool.C_false_8
                                                 -> case T_Reflects_16 -> T_Reflects_16
forall a b. a -> b
coe T_Reflects_16
v9 of
                                                      T_Reflects_16
MAlonzo.Code.Relation.Nullary.Reflects.C_of'8319'_26
                                                        -> (Bool -> T_Reflects_16 -> T_Dec_20) -> Any -> Any -> t
forall a b. a -> b
coe
                                                             Bool -> T_Reflects_16 -> T_Dec_20
MAlonzo.Code.Relation.Nullary.Decidable.Core.C__because__32
                                                             (Bool -> Any
forall a b. a -> b
coe Bool
v8)
                                                             (T_Reflects_16 -> Any
forall a b. a -> b
coe
                                                                T_Reflects_16
MAlonzo.Code.Relation.Nullary.Reflects.C_of'8319'_26)
                                                      T_Reflects_16
_ -> Any -> t
forall a b. a -> b
coe Any
forall a. a
v5
                                               Bool
_ -> Any -> t
forall a b. a -> b
coe Any
forall a. a
v5
                                        T_Dec_20
_ -> t
forall a. a
MAlonzo.RTE.mazUnreachableError in
                              Any -> Any
forall a b. a -> b
coe
                                (if Bool -> Bool
forall a b. a -> b
coe Bool
v6
                                   then case Any -> T_Dec_20
forall a b. a -> b
coe Any
forall a. a
v4 of
                                          MAlonzo.Code.Relation.Nullary.Decidable.Core.C__because__32 Bool
v9 T_Reflects_16
v10
                                            -> if Bool -> Bool
forall a b. a -> b
coe Bool
v9
                                                 then case T_Reflects_16 -> T_Reflects_16
forall a b. a -> b
coe T_Reflects_16
v7 of
                                                        MAlonzo.Code.Relation.Nullary.Reflects.C_of'696'_22 Any
v11
                                                          -> case T_Reflects_16 -> T_Reflects_16
forall a b. a -> b
coe T_Reflects_16
v10 of
                                                               MAlonzo.Code.Relation.Nullary.Reflects.C_of'696'_22 Any
v12
                                                                 -> (Bool -> T_Reflects_16 -> T_Dec_20) -> Any -> Any -> Any
forall a b. a -> b
coe
                                                                      Bool -> T_Reflects_16 -> T_Dec_20
MAlonzo.Code.Relation.Nullary.Decidable.Core.C__because__32
                                                                      (Bool -> Any
forall a b. a -> b
coe Bool
v9)
                                                                      ((Any -> T_Reflects_16) -> Any -> Any
forall a b. a -> b
coe
                                                                         Any -> T_Reflects_16
MAlonzo.Code.Relation.Nullary.Reflects.C_of'696'_22
                                                                         ((Integer
 -> Any
 -> (Integer -> T__'8804'__22 -> Any)
 -> Integer
 -> T__'8804'__22
 -> Any)
-> Any -> Any -> Any -> Any
forall a b. a -> b
coe
                                                                            Integer
-> Any
-> (Integer -> T__'8804'__22 -> Any)
-> Integer
-> T__'8804'__22
-> Any
du_Pn'60'1'43'v_6520
                                                                            (Integer -> Any
forall a b. a -> b
coe Integer
v2) (Any -> Any
forall a b. a -> b
coe Any
v11)
                                                                            (Any -> Any
forall a b. a -> b
coe Any
v12)))
                                                               T_Reflects_16
_ -> Any -> Any
forall a b. a -> b
coe Any
forall a. a
v8
                                                        T_Reflects_16
_ -> Any -> Any
forall a b. a -> b
coe Any
forall a. a
v8
                                                 else (case T_Reflects_16 -> T_Reflects_16
forall a b. a -> b
coe T_Reflects_16
v10 of
                                                         T_Reflects_16
MAlonzo.Code.Relation.Nullary.Reflects.C_of'8319'_26
                                                           -> (Bool -> T_Reflects_16 -> T_Dec_20) -> Any -> Any -> Any
forall a b. a -> b
coe
                                                                Bool -> T_Reflects_16 -> T_Dec_20
MAlonzo.Code.Relation.Nullary.Decidable.Core.C__because__32
                                                                (Bool -> Any
forall a b. a -> b
coe Bool
v9)
                                                                (T_Reflects_16 -> Any
forall a b. a -> b
coe
                                                                   T_Reflects_16
MAlonzo.Code.Relation.Nullary.Reflects.C_of'8319'_26)
                                                         T_Reflects_16
_ -> Any -> Any
forall a b. a -> b
coe Any
forall a. a
v8)
                                          T_Dec_20
_ -> Any
forall a. a
MAlonzo.RTE.mazUnreachableError
                                   else (let v9 :: t
v9
                                               = case Any -> T_Dec_20
forall a b. a -> b
coe Any
forall a. a
v4 of
                                                   MAlonzo.Code.Relation.Nullary.Decidable.Core.C__because__32 Bool
v9 T_Reflects_16
v10
                                                     -> case Bool -> Bool
forall a b. a -> b
coe Bool
v9 of
                                                          Bool
MAlonzo.Code.Agda.Builtin.Bool.C_false_8
                                                            -> case T_Reflects_16 -> T_Reflects_16
forall a b. a -> b
coe T_Reflects_16
v10 of
                                                                 T_Reflects_16
MAlonzo.Code.Relation.Nullary.Reflects.C_of'8319'_26
                                                                   -> (Bool -> T_Reflects_16 -> T_Dec_20) -> Any -> Any -> t
forall a b. a -> b
coe
                                                                        Bool -> T_Reflects_16 -> T_Dec_20
MAlonzo.Code.Relation.Nullary.Decidable.Core.C__because__32
                                                                        (Bool -> Any
forall a b. a -> b
coe Bool
v9)
                                                                        (T_Reflects_16 -> Any
forall a b. a -> b
coe
                                                                           T_Reflects_16
MAlonzo.Code.Relation.Nullary.Reflects.C_of'8319'_26)
                                                                 T_Reflects_16
_ -> Any -> t
forall a b. a -> b
coe Any
forall a. a
v8
                                                          Bool
_ -> Any -> t
forall a b. a -> b
coe Any
forall a. a
v8
                                                   T_Dec_20
_ -> t
forall a. a
MAlonzo.RTE.mazUnreachableError in
                                         Any -> Any
forall a b. a -> b
coe
                                           (case T_Reflects_16 -> T_Reflects_16
forall a b. a -> b
coe T_Reflects_16
v7 of
                                              T_Reflects_16
MAlonzo.Code.Relation.Nullary.Reflects.C_of'8319'_26
                                                -> (Bool -> T_Reflects_16 -> T_Dec_20) -> Any -> Any -> Any
forall a b. a -> b
coe
                                                     Bool -> T_Reflects_16 -> T_Dec_20
MAlonzo.Code.Relation.Nullary.Decidable.Core.C__because__32
                                                     (Bool -> Any
forall a b. a -> b
coe Bool
v6)
                                                     (T_Reflects_16 -> Any
forall a b. a -> b
coe
                                                        T_Reflects_16
MAlonzo.Code.Relation.Nullary.Reflects.C_of'8319'_26)
                                              T_Reflects_16
_ -> Any -> Any
forall a b. a -> b
coe Any
forall a. a
v9)))
                         T_Dec_20
_ -> Any
forall a. a
MAlonzo.RTE.mazUnreachableError))))
-- Data.Nat.Properties._._.Pn<1+v
d_Pn'60'1'43'v_6520 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  (Integer -> ()) ->
  (Integer ->
   MAlonzo.Code.Relation.Nullary.Decidable.Core.T_Dec_20) ->
  Integer ->
  AgdaAny ->
  (Integer -> MAlonzo.Code.Data.Nat.Base.T__'8804'__22 -> AgdaAny) ->
  Integer -> MAlonzo.Code.Data.Nat.Base.T__'8804'__22 -> AgdaAny
d_Pn'60'1'43'v_6520 :: ()
-> (Integer -> ())
-> (Integer -> T_Dec_20)
-> Integer
-> Any
-> (Integer -> T__'8804'__22 -> Any)
-> Integer
-> T__'8804'__22
-> Any
d_Pn'60'1'43'v_6520 ~()
v0 ~Integer -> ()
v1 ~Integer -> T_Dec_20
v2 Integer
v3 Any
v4 Integer -> T__'8804'__22 -> Any
v5 Integer
v6 T__'8804'__22
v7
  = Integer
-> Any
-> (Integer -> T__'8804'__22 -> Any)
-> Integer
-> T__'8804'__22
-> Any
du_Pn'60'1'43'v_6520 Integer
v3 Any
v4 Integer -> T__'8804'__22 -> Any
v5 Integer
v6 T__'8804'__22
v7
du_Pn'60'1'43'v_6520 ::
  Integer ->
  AgdaAny ->
  (Integer -> MAlonzo.Code.Data.Nat.Base.T__'8804'__22 -> AgdaAny) ->
  Integer -> MAlonzo.Code.Data.Nat.Base.T__'8804'__22 -> AgdaAny
du_Pn'60'1'43'v_6520 :: Integer
-> Any
-> (Integer -> T__'8804'__22 -> Any)
-> Integer
-> T__'8804'__22
-> Any
du_Pn'60'1'43'v_6520 Integer
v0 Any
v1 Integer -> T__'8804'__22 -> Any
v2 Integer
v3 T__'8804'__22
v4
  = case T__'8804'__22 -> T__'8804'__22
forall a b. a -> b
coe T__'8804'__22
v4 of
      MAlonzo.Code.Data.Nat.Base.C_s'8804's_34 T__'8804'__22
v7
        -> let v8 :: t
v8
                 = ((Any -> Any) -> (Any -> Any) -> T_Dec_20 -> T_Dec_20)
-> Any -> (Any -> Any) -> Any -> t
forall a b. a -> b
coe
                     (Any -> Any) -> (Any -> Any) -> T_Dec_20 -> T_Dec_20
MAlonzo.Code.Relation.Nullary.Decidable.Core.du_map'8242'_168
                     Any
forall a. a
erased (\ Any
v8 -> (Integer -> Any) -> Any -> Any
forall a b. a -> b
coe Integer -> Any
du_'8801''8658''8801''7495'_2678 (Integer -> Any
forall a b. a -> b
coe Integer
v3))
                     ((Bool -> T_Dec_20) -> Any -> Any
forall a b. a -> b
coe
                        Bool -> T_Dec_20
MAlonzo.Code.Relation.Nullary.Decidable.Core.d_T'63'_66
                        ((Integer -> Integer -> Bool) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> Integer -> Bool
eqInt (Integer -> Any
forall a b. a -> b
coe Integer
v3) (Integer -> Any
forall a b. a -> b
coe Integer
v0))) in
           Any -> Any
forall a b. a -> b
coe
             (case Any -> T_Dec_20
forall a b. a -> b
coe Any
forall a. a
v8 of
                MAlonzo.Code.Relation.Nullary.Decidable.Core.C__because__32 Bool
v9 T_Reflects_16
v10
                  -> if Bool -> Bool
forall a b. a -> b
coe Bool
v9
                       then (Any -> Any -> Any) -> Any -> Any -> Any
forall a b. a -> b
coe Any -> Any -> Any
forall a b. a -> b -> b
seq (T_Reflects_16 -> Any
forall a b. a -> b
coe T_Reflects_16
v10) (Any -> Any
forall a b. a -> b
coe Any
v1)
                       else (Any -> Any -> Any) -> Any -> Any -> Any
forall a b. a -> b
coe
                              Any -> Any -> Any
forall a b. a -> b -> b
seq (T_Reflects_16 -> Any
forall a b. a -> b
coe T_Reflects_16
v10)
                              ((Integer -> T__'8804'__22 -> Any) -> Integer -> Any -> Any
forall a b. a -> b
coe
                                 Integer -> T__'8804'__22 -> Any
v2 Integer
v3 ((Integer -> T__'8804'__22 -> T__'8804'__22) -> Any -> Any -> Any
forall a b. a -> b
coe Integer -> T__'8804'__22 -> T__'8804'__22
du_'8804''8743''8802''8658''60'_2918 (Integer -> Any
forall a b. a -> b
coe Integer
v0) (T__'8804'__22 -> Any
forall a b. a -> b
coe T__'8804'__22
v7)))
                T_Dec_20
_ -> Any
forall a. a
MAlonzo.RTE.mazUnreachableError)
      T__'8804'__22
_ -> Any
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Data.Nat.Properties.∀[m≤n⇒m≢o]⇒o<n
d_'8704''91'm'8804'n'8658'm'8802'o'93''8658'o'60'n_6546 ::
  Integer ->
  Integer ->
  (Integer ->
   MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
   MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
   MAlonzo.Code.Data.Irrelevant.T_Irrelevant_20) ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_'8704''91'm'8804'n'8658'm'8802'o'93''8658'o'60'n_6546 :: Integer
-> Integer
-> (Integer -> T__'8804'__22 -> T__'8801'__12 -> T_Irrelevant_20)
-> T__'8804'__22
d_'8704''91'm'8804'n'8658'm'8802'o'93''8658'o'60'n_6546 Integer
v0 Integer
v1 Integer -> T__'8804'__22 -> T__'8801'__12 -> T_Irrelevant_20
v2
  = (Integer -> Integer -> T__'8804'__22)
-> Integer -> Integer -> T__'8804'__22
forall a b. a -> b
coe
      Integer -> Integer -> T__'8804'__22
du_'8704''91'm'8804'n'8658'm'8802'o'93''8658'n'60'o_3132 Integer
v0 Integer
v1
-- Data.Nat.Properties.∀[m<n⇒m≢o]⇒o≤n
d_'8704''91'm'60'n'8658'm'8802'o'93''8658'o'8804'n_6554 ::
  Integer ->
  Integer ->
  (Integer ->
   MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
   MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
   MAlonzo.Code.Data.Irrelevant.T_Irrelevant_20) ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_'8704''91'm'60'n'8658'm'8802'o'93''8658'o'8804'n_6554 :: Integer
-> Integer
-> (Integer -> T__'8804'__22 -> T__'8801'__12 -> T_Irrelevant_20)
-> T__'8804'__22
d_'8704''91'm'60'n'8658'm'8802'o'93''8658'o'8804'n_6554 Integer
v0 Integer
v1 Integer -> T__'8804'__22 -> T__'8801'__12 -> T_Irrelevant_20
v2
  = (Integer -> Integer -> T__'8804'__22)
-> Integer -> Integer -> T__'8804'__22
forall a b. a -> b
coe
      Integer -> Integer -> T__'8804'__22
du_'8704''91'm'60'n'8658'm'8802'o'93''8658'n'8804'o_3160 Integer
v0 Integer
v1
-- Data.Nat.Properties.*-+-isSemiring
d_'42''45''43''45'isSemiring_6556 ::
  MAlonzo.Code.Algebra.Structures.T_IsSemiring_1570
d_'42''45''43''45'isSemiring_6556 :: T_IsSemiring_1570
d_'42''45''43''45'isSemiring_6556
  = T_IsSemiring_1570 -> T_IsSemiring_1570
forall a b. a -> b
coe T_IsSemiring_1570
d_'43''45''42''45'isSemiring_3754
-- Data.Nat.Properties.*-+-isCommutativeSemiring
d_'42''45''43''45'isCommutativeSemiring_6558 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiring_1678
d_'42''45''43''45'isCommutativeSemiring_6558 :: T_IsCommutativeSemiring_1678
d_'42''45''43''45'isCommutativeSemiring_6558
  = T_IsCommutativeSemiring_1678 -> T_IsCommutativeSemiring_1678
forall a b. a -> b
coe T_IsCommutativeSemiring_1678
d_'43''45''42''45'isCommutativeSemiring_3756
-- Data.Nat.Properties.*-+-semiring
d_'42''45''43''45'semiring_6560 ::
  MAlonzo.Code.Algebra.Bundles.T_Semiring_2280
d_'42''45''43''45'semiring_6560 :: T_Semiring_2280
d_'42''45''43''45'semiring_6560
  = T_Semiring_2280 -> T_Semiring_2280
forall a b. a -> b
coe T_Semiring_2280
d_'43''45''42''45'semiring_3768
-- Data.Nat.Properties.*-+-commutativeSemiring
d_'42''45''43''45'commutativeSemiring_6562 ::
  MAlonzo.Code.Algebra.Bundles.T_CommutativeSemiring_2446
d_'42''45''43''45'commutativeSemiring_6562 :: T_CommutativeSemiring_2446
d_'42''45''43''45'commutativeSemiring_6562
  = T_CommutativeSemiring_2446 -> T_CommutativeSemiring_2446
forall a b. a -> b
coe T_CommutativeSemiring_2446
d_'43''45''42''45'commutativeSemiring_3770
-- Data.Nat.Properties.∣m+n-m+o∣≡∣n-o|
d_'8739'm'43'n'45'm'43'o'8739''8801''8739'n'45'o'124'_6564 ::
  Integer ->
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8739'm'43'n'45'm'43'o'8739''8801''8739'n'45'o'124'_6564 :: Integer -> Integer -> Integer -> T__'8801'__12
d_'8739'm'43'n'45'm'43'o'8739''8801''8739'n'45'o'124'_6564 = Integer -> Integer -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Nat.Properties.m≤n⇒n⊔m≡n
d_m'8804'n'8658'n'8852'm'8801'n_6566 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_m'8804'n'8658'n'8852'm'8801'n_6566 :: Integer -> Integer -> T__'8804'__22 -> T__'8801'__12
d_m'8804'n'8658'n'8852'm'8801'n_6566 = Integer -> Integer -> T__'8804'__22 -> T__'8801'__12
forall a. a
erased
-- Data.Nat.Properties.m≤n⇒n⊓m≡m
d_m'8804'n'8658'n'8851'm'8801'm_6568 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_m'8804'n'8658'n'8851'm'8801'm_6568 :: Integer -> Integer -> T__'8804'__22 -> T__'8801'__12
d_m'8804'n'8658'n'8851'm'8801'm_6568 = Integer -> Integer -> T__'8804'__22 -> T__'8801'__12
forall a. a
erased
-- Data.Nat.Properties.n⊔m≡m⇒n≤m
d_n'8852'm'8801'm'8658'n'8804'm_6570 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_n'8852'm'8801'm'8658'n'8804'm_6570 :: Integer -> Integer -> T__'8801'__12 -> T__'8804'__22
d_n'8852'm'8801'm'8658'n'8804'm_6570
  = let v0 :: T_TotalPreorder_222
v0 = T_TotalPreorder_222
d_'8804''45'totalPreorder_2822 in
    Any -> Integer -> Integer -> T__'8801'__12 -> T__'8804'__22
forall a b. a -> b
coe
      (let v1 :: T_MaxOperator_128
v1 = T_MaxOperator_128
d_'8852''45'operator_4440 in
       Any -> Any
forall a b. a -> b
coe
         ((T_TotalPreorder_222
 -> T_MinOperator_98 -> Any -> Any -> Any -> Any)
-> Any -> Any -> Any
forall a b. a -> b
coe
            T_TotalPreorder_222 -> T_MinOperator_98 -> Any -> Any -> Any -> Any
MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_x'8851'y'8776'y'8658'y'8804'x_3100
            ((T_TotalPreorder_222 -> T_TotalPreorder_222) -> Any -> Any
forall a b. a -> b
coe
               T_TotalPreorder_222 -> T_TotalPreorder_222
MAlonzo.Code.Relation.Binary.Construct.Flip.EqAndOrd.du_totalPreorder_746
               (T_TotalPreorder_222 -> Any
forall a b. a -> b
coe T_TotalPreorder_222
v0))
            ((T_MaxOperator_128 -> T_MinOperator_98) -> Any -> Any
forall a b. a -> b
coe
               T_MaxOperator_128 -> T_MinOperator_98
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.du_MaxOp'8658'MinOp_174
               (T_MaxOperator_128 -> Any
forall a b. a -> b
coe T_MaxOperator_128
v1))))
-- Data.Nat.Properties.n⊔m≡n⇒m≤n
d_n'8852'm'8801'n'8658'm'8804'n_6572 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_n'8852'm'8801'n'8658'm'8804'n_6572 :: Integer -> Integer -> T__'8801'__12 -> T__'8804'__22
d_n'8852'm'8801'n'8658'm'8804'n_6572
  = let v0 :: T_TotalPreorder_222
v0 = T_TotalPreorder_222
d_'8804''45'totalPreorder_2822 in
    Any -> Integer -> Integer -> T__'8801'__12 -> T__'8804'__22
forall a b. a -> b
coe
      (let v1 :: T_MaxOperator_128
v1 = T_MaxOperator_128
d_'8852''45'operator_4440 in
       Any -> Any
forall a b. a -> b
coe
         ((T_TotalPreorder_222
 -> T_MinOperator_98 -> Any -> Any -> Any -> Any)
-> Any -> Any -> Any
forall a b. a -> b
coe
            T_TotalPreorder_222 -> T_MinOperator_98 -> Any -> Any -> Any -> Any
MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_x'8851'y'8776'x'8658'x'8804'y_3068
            ((T_TotalPreorder_222 -> T_TotalPreorder_222) -> Any -> Any
forall a b. a -> b
coe
               T_TotalPreorder_222 -> T_TotalPreorder_222
MAlonzo.Code.Relation.Binary.Construct.Flip.EqAndOrd.du_totalPreorder_746
               (T_TotalPreorder_222 -> Any
forall a b. a -> b
coe T_TotalPreorder_222
v0))
            ((T_MaxOperator_128 -> T_MinOperator_98) -> Any -> Any
forall a b. a -> b
coe
               T_MaxOperator_128 -> T_MinOperator_98
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.du_MaxOp'8658'MinOp_174
               (T_MaxOperator_128 -> Any
forall a b. a -> b
coe T_MaxOperator_128
v1))))
-- Data.Nat.Properties.n≤m⊔n
d_n'8804'm'8852'n_6574 ::
  Integer -> Integer -> MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_n'8804'm'8852'n_6574 :: Integer -> Integer -> T__'8804'__22
d_n'8804'm'8852'n_6574
  = let v0 :: T_TotalPreorder_222
v0 = T_TotalPreorder_222
d_'8804''45'totalPreorder_2822 in
    Any -> Integer -> Integer -> T__'8804'__22
forall a b. a -> b
coe
      (let v1 :: T_MaxOperator_128
v1 = T_MaxOperator_128
d_'8852''45'operator_4440 in
       Any -> Any
forall a b. a -> b
coe
         ((T_TotalPreorder_222 -> T_MinOperator_98 -> Any -> Any -> Any)
-> Any -> Any -> Any
forall a b. a -> b
coe
            T_TotalPreorder_222 -> T_MinOperator_98 -> Any -> Any -> Any
MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_x'8851'y'8804'y_2834
            ((T_TotalPreorder_222 -> T_TotalPreorder_222) -> Any -> Any
forall a b. a -> b
coe
               T_TotalPreorder_222 -> T_TotalPreorder_222
MAlonzo.Code.Relation.Binary.Construct.Flip.EqAndOrd.du_totalPreorder_746
               (T_TotalPreorder_222 -> Any
forall a b. a -> b
coe T_TotalPreorder_222
v0))
            ((T_MaxOperator_128 -> T_MinOperator_98) -> Any -> Any
forall a b. a -> b
coe
               T_MaxOperator_128 -> T_MinOperator_98
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.du_MaxOp'8658'MinOp_174
               (T_MaxOperator_128 -> Any
forall a b. a -> b
coe T_MaxOperator_128
v1))))
-- Data.Nat.Properties.⊔-least
d_'8852''45'least_6576 ::
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_'8852''45'least_6576 :: Integer
-> Integer
-> Integer
-> T__'8804'__22
-> T__'8804'__22
-> T__'8804'__22
d_'8852''45'least_6576
  = let v0 :: T_TotalPreorder_222
v0 = T_TotalPreorder_222
d_'8804''45'totalPreorder_2822 in
    Any
-> Integer
-> Integer
-> Integer
-> T__'8804'__22
-> T__'8804'__22
-> T__'8804'__22
forall a b. a -> b
coe
      (let v1 :: T_MaxOperator_128
v1 = T_MaxOperator_128
d_'8852''45'operator_4440 in
       Any -> Any
forall a b. a -> b
coe
         ((T_TotalPreorder_222
 -> T_MinOperator_98 -> Any -> Any -> Any -> Any -> Any -> Any)
-> Any -> Any -> Any
forall a b. a -> b
coe
            T_TotalPreorder_222
-> T_MinOperator_98 -> Any -> Any -> Any -> Any -> Any -> Any
MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_'8851''45'glb_3278
            ((T_TotalPreorder_222 -> T_TotalPreorder_222) -> Any -> Any
forall a b. a -> b
coe
               T_TotalPreorder_222 -> T_TotalPreorder_222
MAlonzo.Code.Relation.Binary.Construct.Flip.EqAndOrd.du_totalPreorder_746
               (T_TotalPreorder_222 -> Any
forall a b. a -> b
coe T_TotalPreorder_222
v0))
            ((T_MaxOperator_128 -> T_MinOperator_98) -> Any -> Any
forall a b. a -> b
coe
               T_MaxOperator_128 -> T_MinOperator_98
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.du_MaxOp'8658'MinOp_174
               (T_MaxOperator_128 -> Any
forall a b. a -> b
coe T_MaxOperator_128
v1))))
-- Data.Nat.Properties.⊓-greatest
d_'8851''45'greatest_6578 ::
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_'8851''45'greatest_6578 :: Integer
-> Integer
-> Integer
-> T__'8804'__22
-> T__'8804'__22
-> T__'8804'__22
d_'8851''45'greatest_6578
  = let v0 :: T_TotalPreorder_222
v0 = T_TotalPreorder_222
d_'8804''45'totalPreorder_2822 in
    Any
-> Integer
-> Integer
-> Integer
-> T__'8804'__22
-> T__'8804'__22
-> T__'8804'__22
forall a b. a -> b
coe
      (let v1 :: T_MinOperator_98
v1 = T_MinOperator_98
d_'8851''45'operator_4438 in
       Any -> Any
forall a b. a -> b
coe
         ((T_TotalPreorder_222
 -> T_MinOperator_98 -> Any -> Any -> Any -> Any -> Any -> Any)
-> Any -> Any -> Any
forall a b. a -> b
coe
            T_TotalPreorder_222
-> T_MinOperator_98 -> Any -> Any -> Any -> Any -> Any -> Any
MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_'8851''45'glb_3278
            (T_TotalPreorder_222 -> Any
forall a b. a -> b
coe T_TotalPreorder_222
v0) (T_MinOperator_98 -> Any
forall a b. a -> b
coe T_MinOperator_98
v1)))
-- Data.Nat.Properties.⊔-pres-≤m
d_'8852''45'pres'45''8804'm_6580 ::
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_'8852''45'pres'45''8804'm_6580 :: Integer
-> Integer
-> Integer
-> T__'8804'__22
-> T__'8804'__22
-> T__'8804'__22
d_'8852''45'pres'45''8804'm_6580
  = let v0 :: T_TotalPreorder_222
v0 = T_TotalPreorder_222
d_'8804''45'totalPreorder_2822 in
    Any
-> Integer
-> Integer
-> Integer
-> T__'8804'__22
-> T__'8804'__22
-> T__'8804'__22
forall a b. a -> b
coe
      (let v1 :: T_MaxOperator_128
v1 = T_MaxOperator_128
d_'8852''45'operator_4440 in
       Any -> Any
forall a b. a -> b
coe
         ((T_TotalPreorder_222
 -> T_MinOperator_98 -> Any -> Any -> Any -> Any -> Any -> Any)
-> Any -> Any -> Any
forall a b. a -> b
coe
            T_TotalPreorder_222
-> T_MinOperator_98 -> Any -> Any -> Any -> Any -> Any -> Any
MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_'8851''45'glb_3278
            ((T_TotalPreorder_222 -> T_TotalPreorder_222) -> Any -> Any
forall a b. a -> b
coe
               T_TotalPreorder_222 -> T_TotalPreorder_222
MAlonzo.Code.Relation.Binary.Construct.Flip.EqAndOrd.du_totalPreorder_746
               (T_TotalPreorder_222 -> Any
forall a b. a -> b
coe T_TotalPreorder_222
v0))
            ((T_MaxOperator_128 -> T_MinOperator_98) -> Any -> Any
forall a b. a -> b
coe
               T_MaxOperator_128 -> T_MinOperator_98
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.du_MaxOp'8658'MinOp_174
               (T_MaxOperator_128 -> Any
forall a b. a -> b
coe T_MaxOperator_128
v1))))
-- Data.Nat.Properties.⊓-pres-m≤
d_'8851''45'pres'45'm'8804'_6582 ::
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_'8851''45'pres'45'm'8804'_6582 :: Integer
-> Integer
-> Integer
-> T__'8804'__22
-> T__'8804'__22
-> T__'8804'__22
d_'8851''45'pres'45'm'8804'_6582
  = let v0 :: T_TotalPreorder_222
v0 = T_TotalPreorder_222
d_'8804''45'totalPreorder_2822 in
    Any
-> Integer
-> Integer
-> Integer
-> T__'8804'__22
-> T__'8804'__22
-> T__'8804'__22
forall a b. a -> b
coe
      (let v1 :: T_MinOperator_98
v1 = T_MinOperator_98
d_'8851''45'operator_4438 in
       Any -> Any
forall a b. a -> b
coe
         ((T_TotalPreorder_222
 -> T_MinOperator_98 -> Any -> Any -> Any -> Any -> Any -> Any)
-> Any -> Any -> Any
forall a b. a -> b
coe
            T_TotalPreorder_222
-> T_MinOperator_98 -> Any -> Any -> Any -> Any -> Any -> Any
MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_'8851''45'glb_3278
            (T_TotalPreorder_222 -> Any
forall a b. a -> b
coe T_TotalPreorder_222
v0) (T_MinOperator_98 -> Any
forall a b. a -> b
coe T_MinOperator_98
v1)))
-- Data.Nat.Properties.⊔-abs-⊓
d_'8852''45'abs'45''8851'_6584 ::
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8852''45'abs'45''8851'_6584 :: Integer -> Integer -> T__'8801'__12
d_'8852''45'abs'45''8851'_6584 = Integer -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Nat.Properties.⊓-abs-⊔
d_'8851''45'abs'45''8852'_6586 ::
  Integer ->
  Integer -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_'8851''45'abs'45''8852'_6586 :: Integer -> Integer -> T__'8801'__12
d_'8851''45'abs'45''8852'_6586 = Integer -> Integer -> T__'8801'__12
forall a. a
erased
-- Data.Nat.Properties.suc[pred[n]]≡n
d_suc'91'pred'91'n'93''93''8801'n_6588 ::
  Integer ->
  (MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
   MAlonzo.Code.Data.Irrelevant.T_Irrelevant_20) ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_suc'91'pred'91'n'93''93''8801'n_6588 :: Integer -> (T__'8801'__12 -> T_Irrelevant_20) -> T__'8801'__12
d_suc'91'pred'91'n'93''93''8801'n_6588 = Integer -> (T__'8801'__12 -> T_Irrelevant_20) -> T__'8801'__12
forall a. a
erased
-- Data.Nat.Properties.≤-step
d_'8804''45'step_6594 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_'8804''45'step_6594 :: Integer -> Integer -> T__'8804'__22 -> T__'8804'__22
d_'8804''45'step_6594 ~Integer
v0 ~Integer
v1 T__'8804'__22
v2 = T__'8804'__22 -> T__'8804'__22
du_'8804''45'step_6594 T__'8804'__22
v2
du_'8804''45'step_6594 ::
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
du_'8804''45'step_6594 :: T__'8804'__22 -> T__'8804'__22
du_'8804''45'step_6594 T__'8804'__22
v0 = T__'8804'__22 -> T__'8804'__22
forall a b. a -> b
coe T__'8804'__22
v0
-- Data.Nat.Properties.≤-stepsˡ
d_'8804''45'steps'737'_6596 ::
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_'8804''45'steps'737'_6596 :: Integer -> Integer -> Integer -> T__'8804'__22 -> T__'8804'__22
d_'8804''45'steps'737'_6596 ~Integer
v0 ~Integer
v1 ~Integer
v2 T__'8804'__22
v3
  = T__'8804'__22 -> T__'8804'__22
du_'8804''45'steps'737'_6596 T__'8804'__22
v3
du_'8804''45'steps'737'_6596 ::
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
du_'8804''45'steps'737'_6596 :: T__'8804'__22 -> T__'8804'__22
du_'8804''45'steps'737'_6596 T__'8804'__22
v0 = T__'8804'__22 -> T__'8804'__22
forall a b. a -> b
coe T__'8804'__22
v0
-- Data.Nat.Properties.≤-stepsʳ
d_'8804''45'steps'691'_6598 ::
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_'8804''45'steps'691'_6598 :: Integer -> Integer -> Integer -> T__'8804'__22 -> T__'8804'__22
d_'8804''45'steps'691'_6598 ~Integer
v0 ~Integer
v1 ~Integer
v2 T__'8804'__22
v3
  = T__'8804'__22 -> T__'8804'__22
du_'8804''45'steps'691'_6598 T__'8804'__22
v3
du_'8804''45'steps'691'_6598 ::
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
du_'8804''45'steps'691'_6598 :: T__'8804'__22 -> T__'8804'__22
du_'8804''45'steps'691'_6598 T__'8804'__22
v0 = T__'8804'__22 -> T__'8804'__22
forall a b. a -> b
coe T__'8804'__22
v0
-- Data.Nat.Properties.<-step
d_'60''45'step_6600 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_'60''45'step_6600 :: Integer -> Integer -> T__'8804'__22 -> T__'8804'__22
d_'60''45'step_6600 Integer
v0 Integer
v1 T__'8804'__22
v2
  = (T__'8804'__22 -> T__'8804'__22) -> T__'8804'__22 -> T__'8804'__22
forall a b. a -> b
coe T__'8804'__22 -> T__'8804'__22
du_m'60'n'8658'm'60'1'43'n_3062 T__'8804'__22
v2
-- Data.Nat.Properties.pred-mono
d_pred'45'mono_6602 ::
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_pred'45'mono_6602 :: Integer -> Integer -> T__'8804'__22 -> T__'8804'__22
d_pred'45'mono_6602 Integer
v0 Integer
v1 T__'8804'__22
v2
  = (Integer -> T__'8804'__22 -> T__'8804'__22)
-> Integer -> T__'8804'__22 -> T__'8804'__22
forall a b. a -> b
coe Integer -> T__'8804'__22 -> T__'8804'__22
du_pred'45'mono'45''8804'_5676 Integer
v0 T__'8804'__22
v2
-- Data.Nat.Properties.<-transʳ
d_'60''45'trans'691'_6604 ::
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_'60''45'trans'691'_6604 :: Integer
-> Integer
-> Integer
-> T__'8804'__22
-> T__'8804'__22
-> T__'8804'__22
d_'60''45'trans'691'_6604 Integer
v0 Integer
v1 Integer
v2 T__'8804'__22
v3 T__'8804'__22
v4
  = (T__'8804'__22 -> T__'8804'__22 -> T__'8804'__22)
-> T__'8804'__22 -> T__'8804'__22 -> T__'8804'__22
forall a b. a -> b
coe T__'8804'__22 -> T__'8804'__22 -> T__'8804'__22
du_'8804''45''60''45'trans_2986 T__'8804'__22
v3 T__'8804'__22
v4
-- Data.Nat.Properties.<-transˡ
d_'60''45'trans'737'_6606 ::
  Integer ->
  Integer ->
  Integer ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22 ->
  MAlonzo.Code.Data.Nat.Base.T__'8804'__22
d_'60''45'trans'737'_6606 :: Integer
-> Integer
-> Integer
-> T__'8804'__22
-> T__'8804'__22
-> T__'8804'__22
d_'60''45'trans'737'_6606 Integer
v0 Integer
v1 Integer
v2 T__'8804'__22
v3 T__'8804'__22
v4
  = (T__'8804'__22 -> T__'8804'__22 -> T__'8804'__22)
-> T__'8804'__22 -> T__'8804'__22 -> T__'8804'__22
forall a b. a -> b
coe T__'8804'__22 -> T__'8804'__22 -> T__'8804'__22
du_'60''45''8804''45'trans_2992 T__'8804'__22
v3 T__'8804'__22
v4